%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU609^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 09:35:35 AM UTC 2026
% Result : Theorem 15.19s 3.32s
% Output : Refutation 15.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 93 ( 20 unt; 0 typ; 9 def)
% Number of atoms : 2423 ( 617 equ; 0 cnn)
% Maximal formula atoms : 126 ( 26 avg)
% Number of connectives : 1569 ( 94 ~; 88 |; 375 &; 421 @)
% ( 11 <=>; 537 =>; 0 <=; 0 <~>)
% Maximal formula depth : 133 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 696 ( 692 usr; 140 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 132 ( 51 ^; 75 !; 6 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_170,type,
sK9: $i > $o ).
thf(func_def_196,type,
sK35: $i > $i ).
thf(func_def_199,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_200,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_201,type,
sK40: $i > $o ).
thf(func_def_207,type,
sK46: $i > $i ).
thf(func_def_210,type,
sK49: $i > $i ).
thf(func_def_214,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK54: $i > $o ).
thf(func_def_216,type,
sK55: $i > $i ).
thf(func_def_223,type,
sK62: $i > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK64: $i > $o ).
thf(func_def_233,type,
sK72: $i > $o ).
thf(func_def_241,type,
sK80: $i > $o ).
thf(func_def_257,type,
sK96: $i > ( $i > $o ) > $i ).
thf(func_def_259,type,
sK98: $i > $o ).
thf(func_def_273,type,
sK112: $i > $o ).
thf(func_def_283,type,
sK122: $i > $o ).
thf(func_def_286,type,
sK125: $i > $i ).
thf(func_def_287,type,
sK126: $i > $i > $i > $i ).
thf(func_def_288,type,
sK127: $i > $i > $i ).
thf(func_def_289,type,
sK128: $i > $i > $i ).
thf(func_def_290,type,
sK129: $i > $i > $i ).
thf(func_def_292,type,
sK131: $i > $i ).
thf(func_def_293,type,
sK132: $i > $i ).
thf(func_def_294,type,
sK133: $i > $i ).
thf(func_def_295,type,
sK134: $i > $i ).
thf(func_def_296,type,
sK135: $i > $i ).
thf(func_def_297,type,
sK136: $i > $i ).
thf(func_def_298,type,
sK137: $i > $i ).
thf(func_def_299,type,
sK138: $i > $i ).
thf(func_def_300,type,
sK139: $i > $i ).
thf(func_def_301,type,
sK140: $i > $i ).
thf(func_def_302,type,
sK141: $i > $i ).
thf(func_def_303,type,
sK142: $i > $i ).
thf(func_def_304,type,
sK143: $i > $i ).
thf(func_def_305,type,
sK144: $i > $i ).
thf(func_def_306,type,
sK145: $i > $i ).
thf(func_def_307,type,
sK146: $i > $i ).
thf(func_def_308,type,
sK147: $i > $i ).
thf(func_def_309,type,
sK148: $i > $i ).
thf(func_def_310,type,
sK149: $i > $i ).
thf(func_def_311,type,
sK150: $i > $i ).
thf(func_def_312,type,
sK151: $i > $i ).
thf(func_def_313,type,
sK152: $i > $i ).
thf(func_def_314,type,
sK153: $i > $i ).
thf(func_def_315,type,
sK154: $i > $i ).
thf(func_def_316,type,
sK155: $i > $i ).
thf(func_def_317,type,
sK156: $i > $i ).
thf(func_def_318,type,
sK157: $i > $i ).
thf(func_def_319,type,
sK158: $i > $i ).
thf(func_def_320,type,
sK159: $i > $i ).
thf(func_def_321,type,
sK160: $i > $i ).
thf(func_def_322,type,
sK161: $i > $i ).
thf(func_def_323,type,
sK162: $i > $i ).
thf(func_def_324,type,
sK163: $i > $i ).
thf(func_def_325,type,
sK164: $i > $i > $i > $i ).
thf(func_def_326,type,
sK165: $i > $i > $i ).
thf(func_def_327,type,
sK166: $i > $i > $i ).
thf(func_def_328,type,
sK167: $i > $i > $i > $i ).
thf(func_def_329,type,
sK168: $i > $i > $i ).
thf(func_def_330,type,
sK169: $i > $i > $i > $i ).
thf(func_def_331,type,
sK170: $i > $i > $i ).
thf(func_def_332,type,
sK171: $i > $i > $i ).
thf(func_def_333,type,
sK172: $i > $i > $i > $i ).
thf(func_def_334,type,
sK173: $i > $i > $i ).
thf(func_def_335,type,
sK174: $i > $i > $i ).
thf(func_def_336,type,
sK175: $i > $i > $i > $i ).
thf(func_def_337,type,
sK176: $i > $i > $i ).
thf(func_def_338,type,
sK177: $i > $i > $i ).
thf(func_def_339,type,
sK178: $i > $i > $i > $i ).
thf(func_def_340,type,
sK179: $i > $i > $i ).
thf(func_def_341,type,
sK180: $i > $i > $i ).
thf(func_def_342,type,
sK181: $i > $i > $i > $i ).
thf(func_def_343,type,
sK182: $i > $i > $i ).
thf(func_def_344,type,
sK183: $i > $i > $i ).
thf(func_def_345,type,
sK184: $i > $i > $i > $i ).
thf(func_def_346,type,
sK185: $i > $i ).
thf(func_def_347,type,
sK186: $i > $i > $i ).
thf(func_def_348,type,
sK187: $i > $i > $i > $i ).
thf(func_def_349,type,
sK188: $i > $i > $i > $i ).
thf(func_def_350,type,
sK189: $i > $i > $i > $i ).
thf(func_def_351,type,
sK190: $i > $i > $i > $i ).
thf(func_def_352,type,
sK191: $i > $i > $i ).
thf(func_def_353,type,
sK192: $i > $i > $i > $i ).
thf(func_def_354,type,
sK193: $i > $i > $i > $i ).
thf(func_def_355,type,
sK194: $i > $i > $i > $i ).
thf(func_def_356,type,
sK195: $i > $i > $i > $i ).
thf(func_def_357,type,
sK196: $i > $i > $i > $i ).
thf(func_def_358,type,
sK197: $i > $i > $i ).
thf(func_def_359,type,
sK198: $i > $i > $i ).
thf(func_def_360,type,
sK199: $i > $i > $i > $i ).
thf(func_def_361,type,
sK200: $i > $i > $i > $i ).
thf(func_def_362,type,
sK201: $i > $i > $i > $i ).
thf(func_def_363,type,
sK202: $i > $i > $i ).
thf(func_def_364,type,
sK203: $i > $i > $i ).
thf(func_def_365,type,
sK204: $i > $i > $i ).
thf(func_def_366,type,
sK205: $i > $i > $i > $i ).
thf(func_def_367,type,
sK206: $i > $i ).
thf(func_def_368,type,
sK207: $i > $i > $i > $i ).
thf(func_def_369,type,
sK208: $i > $i > $i ).
thf(func_def_370,type,
sK209: $i > $i > $i ).
thf(func_def_371,type,
sK210: $i > $i > $i ).
thf(func_def_372,type,
sK211: $i > $i > $i > $i ).
thf(func_def_373,type,
sK212: $i > $i > $i ).
thf(func_def_374,type,
sK213: $i > $i > $i > $i ).
thf(func_def_375,type,
sK214: $i > $i > $i ).
thf(func_def_376,type,
sK215: $i > $i > $i > $i ).
thf(func_def_377,type,
sK216: $i > $i > $i ).
thf(func_def_378,type,
sK217: $i > $i > $i ).
thf(func_def_379,type,
sK218: $i > $i > $i > $i ).
thf(func_def_380,type,
sK219: $i > $i > $i ).
thf(func_def_381,type,
sK220: $i > $i > $i > $i ).
thf(func_def_382,type,
sK221: $i > $i > $i > $i ).
thf(func_def_383,type,
sK222: $i > $i > $i > $i ).
thf(func_def_384,type,
sK223: $i > $i ).
thf(func_def_385,type,
sK224: $i > $i > $i > $i ).
thf(func_def_386,type,
sK225: $i > $i > $i ).
thf(func_def_387,type,
sK226: $i > $i > $i ).
thf(func_def_388,type,
sK227: $i > $i > $i ).
thf(func_def_389,type,
sK228: $i > $i > $i > $i ).
thf(func_def_390,type,
sK229: $i > $i > $i ).
thf(func_def_391,type,
sK230: $i > $i > $i > $i ).
thf(func_def_392,type,
sK231: $i > $i > $i > $i ).
thf(func_def_393,type,
sK232: $i > $i > $i ).
thf(func_def_394,type,
sK233: $i > $i > $i > $i ).
thf(func_def_395,type,
sK234: $i > $i > $i > $i ).
thf(func_def_396,type,
sK235: $i > $i > $i ).
thf(func_def_397,type,
sK236: $i > $i > $i ).
thf(func_def_398,type,
sK237: $i > $i > $i ).
thf(func_def_399,type,
sK238: $i > $i > $i > $i ).
thf(func_def_400,type,
sK239: $i > $i > $i > $i ).
thf(func_def_401,type,
sK240: $i > $i > $i ).
thf(func_def_402,type,
sK241: $i > $i > $i > $i ).
thf(func_def_403,type,
sK242: $i > $i ).
thf(func_def_404,type,
sK243: $i > $i ).
thf(func_def_405,type,
sK244: $i > $i > $i > $i ).
thf(func_def_406,type,
sK245: $i > $i ).
thf(func_def_407,type,
sK246: $i > $i ).
thf(func_def_408,type,
sK247: $i > $i ).
thf(func_def_409,type,
sK248: $i > $i > $i > $i ).
thf(func_def_410,type,
sK249: $i > $i ).
thf(func_def_411,type,
sK250: $i > $i ).
thf(func_def_412,type,
sK251: $i > $i ).
thf(func_def_413,type,
sK252: $i > $i > $i > $i ).
thf(func_def_414,type,
sK253: $i > $i ).
thf(func_def_415,type,
sK254: $i > $i ).
thf(func_def_416,type,
sK255: $i > $i > $i > $i ).
thf(func_def_417,type,
sK256: $i > $i > $i > $i ).
thf(func_def_418,type,
sK257: $i > $i ).
thf(func_def_419,type,
sK258: $i > $i ).
thf(func_def_420,type,
sK259: $i > $i ).
thf(func_def_421,type,
sK260: $i > $i ).
thf(func_def_422,type,
sK261: $i > $i > $i > $i ).
thf(func_def_423,type,
sK262: $i > $i ).
thf(func_def_424,type,
sK263: $i > $i ).
thf(func_def_425,type,
sK264: $i > $i ).
thf(func_def_426,type,
sK265: $i > $i ).
thf(func_def_427,type,
sK266: $i > $i ).
thf(func_def_428,type,
sK267: $i > $i > $i > $i ).
thf(func_def_429,type,
sK268: $i > $i > $i > $i ).
thf(func_def_430,type,
sK269: $i > $i ).
thf(func_def_431,type,
sK270: $i > $i ).
thf(func_def_432,type,
sK271: $i > $i > $i > $i ).
thf(func_def_433,type,
sK272: $i > $i ).
thf(func_def_434,type,
sK273: $i > $i ).
thf(func_def_435,type,
sK274: $i > $i ).
thf(func_def_436,type,
sK275: $i > $i ).
thf(func_def_437,type,
sK276: $i > $i ).
thf(func_def_438,type,
sK277: $i > $i ).
thf(func_def_439,type,
sK278: $i > $i ).
thf(func_def_440,type,
sK279: $i > $i ).
thf(func_def_441,type,
sK280: $i > $i ).
thf(func_def_442,type,
sK281: $i > $i ).
thf(func_def_443,type,
sK282: $i > $i ).
thf(func_def_444,type,
sK283: $i > $i > $i > $i ).
thf(func_def_445,type,
sK284: $i > $i > $i ).
thf(func_def_446,type,
sK285: $i > $i > $i ).
thf(func_def_447,type,
sK286: $i > $i > $i > $i ).
thf(func_def_448,type,
sK287: $i > $i > $i > $i ).
thf(func_def_449,type,
sK288: $i > $i > $i > $i ).
thf(func_def_450,type,
sK289: $i > $i > $i ).
thf(func_def_451,type,
sK290: $i > $i > $i ).
thf(func_def_452,type,
sK291: $i > $i > $i > $i ).
thf(func_def_453,type,
sK292: $i > $i > $i ).
thf(func_def_454,type,
sK293: $i > $i > $i > $i ).
thf(func_def_455,type,
sK294: $i > $i > $i > $i ).
thf(func_def_456,type,
sK295: $i > $i > $i > $i ).
thf(func_def_457,type,
sK296: $i > $i > $i > $i ).
thf(func_def_458,type,
sK297: $i > $i ).
thf(func_def_459,type,
sK298: $i > $i ).
thf(func_def_460,type,
sK299: $i > $i ).
thf(func_def_461,type,
sK300: $i > $i ).
thf(func_def_462,type,
sK301: $i > $i > $i > $i ).
thf(func_def_463,type,
sK302: $i > $i > $i ).
thf(func_def_464,type,
sK303: $i > $i > $i ).
thf(func_def_465,type,
sK304: $i > $i > $i > $i ).
thf(func_def_466,type,
sK305: $i > $i > $i ).
thf(func_def_467,type,
sK306: $i > $i > $i ).
thf(func_def_468,type,
sK307: $i > $i > $i > $i ).
thf(func_def_469,type,
sK308: $i > $i > $i > $i ).
thf(func_def_470,type,
sK309: $i > $i > $i > $i ).
thf(func_def_471,type,
sK310: $i > $i > $i ).
thf(func_def_472,type,
sK311: $i > $i > $i > $i ).
thf(func_def_473,type,
sK312: $i > $i > $i > $i ).
thf(func_def_474,type,
sK313: $i > $i > $i > $i ).
thf(func_def_475,type,
sK314: $i > $i > $i > $i ).
thf(func_def_476,type,
sK315: $i > $i > $i > $i ).
thf(func_def_477,type,
sK316: $i > $i > $i ).
thf(func_def_478,type,
sK317: $i > $i > $i > $i ).
thf(func_def_479,type,
sK318: $i > $i > $i > $i ).
thf(func_def_480,type,
sK319: $i > $i ).
thf(func_def_481,type,
sK320: $i > $i ).
thf(func_def_482,type,
sK321: $i > $i ).
thf(func_def_483,type,
sK322: $i > $i > $i ).
thf(func_def_484,type,
sK323: $i > $i > $i > $i ).
thf(func_def_485,type,
sK324: $i > $i > $i > $i ).
thf(func_def_486,type,
sK325: $i > $i > $i > $i ).
thf(func_def_487,type,
sK326: $i > $i > $i > $i ).
thf(func_def_488,type,
sK327: $i > $i > $i ).
thf(func_def_489,type,
sK328: $i > $i > $i ).
thf(func_def_490,type,
sK329: $i > $i > $i > $i ).
thf(func_def_491,type,
sK330: $i > $i > $i ).
thf(func_def_492,type,
sK331: $i > $i > $i ).
thf(func_def_493,type,
sK332: $i > $i ).
thf(func_def_494,type,
sK333: $i > $i > $i > $i ).
thf(func_def_495,type,
sK334: $i > $i > $i ).
thf(func_def_496,type,
sK335: $i > $i > $i ).
thf(func_def_497,type,
sK336: $i > $i > $i > $i ).
thf(func_def_498,type,
sK337: $i > $i > $i ).
thf(func_def_499,type,
sK338: $i > $i > $i ).
thf(func_def_500,type,
sK339: $i > $i ).
thf(func_def_501,type,
sK340: $i > $i > $i ).
thf(func_def_502,type,
sK341: $i > $i > $i > $i ).
thf(func_def_503,type,
sK342: $i > $i > $i > $i ).
thf(func_def_504,type,
sK343: $i > $i ).
thf(func_def_505,type,
sK344: $i > $i > $i > $i ).
thf(func_def_506,type,
sK345: $i > $i > $i ).
thf(func_def_507,type,
sK346: $i > $i > $i ).
thf(func_def_508,type,
sK347: $i > $i > $i > $i ).
thf(func_def_509,type,
sK348: $i > $i > $i > $i ).
thf(func_def_510,type,
sK349: $i > $i ).
thf(func_def_511,type,
sK350: $i > $i > $i > $i ).
thf(func_def_512,type,
sK351: $i > $i > $i ).
thf(func_def_513,type,
sK352: $i > $i > $i ).
thf(func_def_514,type,
sK353: $i > $i > $i > $i ).
thf(func_def_515,type,
sK354: $i > $i > $i ).
thf(func_def_516,type,
sK355: $i > $i > $i ).
thf(func_def_517,type,
sK356: $i > $i ).
thf(func_def_518,type,
sK357: $i > $i ).
thf(func_def_519,type,
sK358: $i > $i > $i ).
thf(func_def_520,type,
sK359: $i > $i > $i > $i ).
thf(func_def_521,type,
sK360: $i > $i > $i > $i ).
thf(func_def_522,type,
sK361: $i > $i > $i > $i ).
thf(func_def_523,type,
sK362: $i > $i > $i > $i ).
thf(func_def_524,type,
sK363: $i > $i > $i > $i ).
thf(func_def_525,type,
sK364: $i > $i > $i ).
thf(func_def_526,type,
sK365: $i > $i > $i ).
thf(func_def_527,type,
sK366: $i > $i > $i > $i ).
thf(func_def_528,type,
sK367: $i > $i > $i ).
thf(func_def_529,type,
sK368: $i > $i > $i ).
thf(func_def_530,type,
sK369: $i > $i ).
thf(func_def_531,type,
sK370: $i > $i ).
thf(func_def_532,type,
sK371: $i > $i ).
thf(func_def_533,type,
sK372: $i > $i ).
thf(func_def_534,type,
sK373: $i > $i ).
thf(func_def_535,type,
sK374: $i > $i ).
thf(func_def_536,type,
sK375: $i > $i ).
thf(func_def_537,type,
sK376: $i > $i ).
thf(func_def_538,type,
sK377: $i > $i > $i ).
thf(func_def_539,type,
sK378: $i > $i > $i > $i ).
thf(func_def_540,type,
sK379: $i > $i > $i > $i ).
thf(func_def_541,type,
sK380: $i > $i > $i > $i ).
thf(func_def_542,type,
sK381: $i > $i > $i > $i ).
thf(func_def_543,type,
sK382: $i > $i > $i > $i ).
thf(func_def_544,type,
sK383: $i > $i > $i ).
thf(func_def_545,type,
sK384: $i > $i > $i ).
thf(func_def_546,type,
sK385: $i > $i > $i > $i ).
thf(func_def_547,type,
sK386: $i > $i > $i ).
thf(func_def_548,type,
sK387: $i > $i > $i ).
thf(func_def_549,type,
sK388: $i > $i > $i > $i ).
thf(func_def_550,type,
sK389: $i > $i > $i ).
thf(func_def_551,type,
sK390: $i > $i > $i > $i ).
thf(func_def_552,type,
sK391: $i > $i > $i > $i ).
thf(func_def_553,type,
sK392: $i > $i > $i ).
thf(func_def_554,type,
sK393: $i > $i > $i > $i ).
thf(func_def_555,type,
sK394: $i > $i > $i > $i ).
thf(func_def_556,type,
sK395: $i > $i > $i > $i ).
thf(func_def_557,type,
sK396: $i > $i > $i > $i ).
thf(func_def_558,type,
sK397: $i > $i ).
thf(func_def_559,type,
sK398: $i > $i ).
thf(func_def_560,type,
sK399: $i > $i ).
thf(func_def_561,type,
sK400: $i > $i > $i ).
thf(func_def_562,type,
sK401: $i > $i > $i > $i ).
thf(func_def_563,type,
sK402: $i > $i > $i > $i ).
thf(func_def_564,type,
sK403: $i > $i > $i > $i ).
thf(func_def_565,type,
sK404: $i > $i > $i > $i ).
thf(func_def_566,type,
sK405: $i > $i > $i ).
thf(func_def_567,type,
sK406: $i > $i > $i > $i ).
thf(func_def_568,type,
sK407: $i > $i > $i > $i ).
thf(func_def_569,type,
sK408: $i > $i > $i > $i ).
thf(func_def_570,type,
sK409: $i > $i ).
thf(func_def_571,type,
sK410: $i > $i ).
thf(func_def_572,type,
sK411: $i > $i > $i ).
thf(func_def_573,type,
sK412: $i > $i > $i > $i ).
thf(func_def_574,type,
sK413: $i > $i > $i > $i ).
thf(func_def_575,type,
sK414: $i > $i > $i > $i ).
thf(func_def_576,type,
sK415: $i > $i > $i > $i ).
thf(func_def_577,type,
sK416: $i > $i > $i ).
thf(func_def_578,type,
sK417: $i > $i > $i > $i ).
thf(func_def_579,type,
sK418: $i > $i > $i > $i ).
thf(func_def_580,type,
sK419: $i > $i > $i > $i ).
thf(func_def_581,type,
sK420: $i > $i > $i > $i ).
thf(func_def_582,type,
sK421: $i > $i ).
thf(func_def_583,type,
sK422: $i > $i ).
thf(func_def_584,type,
sK423: $i > $i ).
thf(func_def_585,type,
sK424: $i > $i ).
thf(func_def_586,type,
sK425: $i > $i ).
thf(func_def_587,type,
sK426: $i > $i ).
thf(func_def_588,type,
sK427: $i > $i ).
thf(func_def_589,type,
sK428: $i > $i ).
thf(func_def_590,type,
sK429: $i > $i ).
thf(func_def_591,type,
sK430: $i > $i ).
thf(func_def_592,type,
sK431: $i > $i ).
thf(func_def_593,type,
sK432: $i > $i ).
thf(func_def_594,type,
sK433: $i > $i ).
thf(func_def_595,type,
sK434: $i > $i ).
thf(func_def_596,type,
sK435: $i > $i ).
thf(func_def_597,type,
sK436: $i > $i ).
thf(func_def_598,type,
sK437: $i > $i ).
thf(func_def_599,type,
sK438: $i > $i ).
thf(func_def_600,type,
sK439: $i > $i ).
thf(func_def_601,type,
sK440: $i > $i ).
thf(func_def_602,type,
sK441: $i > $i ).
thf(func_def_603,type,
sK442: $i > $i ).
thf(func_def_604,type,
sK443: $i > $i ).
thf(func_def_605,type,
sK444: $i > $i ).
thf(func_def_606,type,
sK445: $i > $i ).
thf(func_def_607,type,
sK446: $i > $i ).
thf(func_def_608,type,
sK447: $i > $i ).
thf(func_def_609,type,
sK448: $i > $i > $i > $i ).
thf(func_def_610,type,
sK449: $i > $i > $i ).
thf(func_def_611,type,
sK450: $i > $i > $i > $i ).
thf(func_def_612,type,
sK451: $i > $i > $i > $i ).
thf(func_def_613,type,
sK452: $i > $i > $i ).
thf(func_def_614,type,
sK453: $i > $i > $i > $i ).
thf(func_def_615,type,
sK454: $i > $i > $i > $i ).
thf(func_def_616,type,
sK455: $i > $i ).
thf(func_def_617,type,
sK456: $i > $i > $i > $i ).
thf(func_def_618,type,
sK457: $i > $i > $i ).
thf(func_def_619,type,
sK458: $i > $i > $i ).
thf(func_def_620,type,
sK459: $i > $i > $i > $i ).
thf(func_def_621,type,
sK460: $i > $i > $i ).
thf(func_def_622,type,
sK461: $i > $i > $i ).
thf(func_def_623,type,
sK462: $i > $i > $i > $i ).
thf(func_def_624,type,
sK463: $i > $i > $i ).
thf(func_def_625,type,
sK464: $i > $i > $i > $i ).
thf(func_def_626,type,
sK465: $i > $i ).
thf(func_def_627,type,
sK466: $i > $i > $i > $i ).
thf(func_def_628,type,
sK467: $i > $i > $i > $i ).
thf(func_def_629,type,
sK468: $i > $i > $i > $i ).
thf(func_def_630,type,
sK469: $i > $i > $i > $i ).
thf(func_def_631,type,
sK470: $i > $i ).
thf(func_def_632,type,
sK471: $i > $i > $i > $i ).
thf(func_def_633,type,
sK472: $i > $i > $i ).
thf(func_def_634,type,
sK473: $i > $i > $i ).
thf(func_def_635,type,
sK474: $i > $i > $i ).
thf(func_def_636,type,
sK475: $i > $i > $i > $i ).
thf(func_def_637,type,
sK476: $i > $i > $i > $i ).
thf(func_def_638,type,
sK477: $i > $i > $i ).
thf(func_def_639,type,
sK478: $i > $i > $i > $i ).
thf(func_def_640,type,
sK479: $i > $i > $i > $i ).
thf(func_def_641,type,
sK480: $i > $i > $i > $i ).
thf(func_def_642,type,
sK481: $i > $i > $i > $i ).
thf(func_def_643,type,
sK482: $i > $i ).
thf(func_def_644,type,
sK483: $i > $i > $i ).
thf(func_def_645,type,
sK484: $i > $i > $i > $i ).
thf(func_def_646,type,
sK485: $i > $i > $i > $i ).
thf(func_def_647,type,
sK486: $i > $i > $i > $i ).
thf(func_def_648,type,
sK487: $i > $i > $i > $i ).
thf(func_def_649,type,
sK488: $i > $i > $i > $i ).
thf(func_def_650,type,
sK489: $i > $i > $i > $i ).
thf(func_def_651,type,
sK490: $i > $i > $i > $i ).
thf(func_def_652,type,
sK491: $i > $i > $i > $i ).
thf(func_def_653,type,
sK492: $i > $i > $i ).
thf(func_def_654,type,
sK493: $i > $i > $i > $i ).
thf(func_def_655,type,
sK494: $i > $i ).
thf(func_def_656,type,
sK495: $i > $i > $i > $i ).
thf(func_def_657,type,
sK496: $i > $i > $i > $i ).
thf(func_def_658,type,
sK497: $i > $i ).
thf(func_def_659,type,
sK498: $i > $i > $i > $i ).
thf(func_def_660,type,
sK499: $i > $i > $i > $i ).
thf(func_def_661,type,
sK500: $i > $i > $i > $i ).
thf(func_def_662,type,
sK501: $i > $i > $i > $i ).
thf(func_def_663,type,
sK502: $i > $i ).
thf(func_def_664,type,
sK503: $i > $i > $i > $i ).
thf(func_def_665,type,
sK504: $i > $i > $i ).
thf(func_def_666,type,
sK505: $i > $i > $i ).
thf(func_def_667,type,
sK506: $i > $i > $i > $i ).
thf(func_def_668,type,
sK507: $i > $i > $i ).
thf(func_def_669,type,
sK508: $i > $i > $i > $i ).
thf(func_def_670,type,
sK509: $i > $i ).
thf(func_def_671,type,
sK510: $i > $i > $i ).
thf(func_def_672,type,
sK511: $i > $i > $i > $i ).
thf(func_def_673,type,
sK512: $i > $i > $i > $i ).
thf(func_def_674,type,
sK513: $i > $i > $i > $i ).
thf(func_def_675,type,
sK514: $i > $i > $i > $i ).
thf(func_def_676,type,
sK515: $i > $i > $i > $i ).
thf(func_def_677,type,
sK516: $i > $i > $i ).
thf(func_def_678,type,
sK517: $i > $i > $i ).
thf(func_def_679,type,
sK518: $i > $i > $i > $i ).
thf(func_def_680,type,
sK519: $i > $i > $i ).
thf(func_def_681,type,
sK520: $i > $i > $i ).
thf(func_def_682,type,
sK521: $i > $i ).
thf(func_def_683,type,
sK522: $i > $i > $i > $i ).
thf(func_def_684,type,
sK523: $i > $i > $i ).
thf(func_def_685,type,
sK524: $i > $i > $i ).
thf(func_def_686,type,
sK525: $i > $i > $i > $i ).
thf(func_def_687,type,
sK526: $i > $i > $i > $i ).
thf(func_def_688,type,
sK527: $i > $i > $i ).
thf(func_def_689,type,
sK528: $i > $i > $i > $i ).
thf(func_def_690,type,
sK529: $i > $i > $i > $i ).
thf(func_def_691,type,
sK530: $i > $i > $i > $i ).
thf(func_def_692,type,
sK531: $i > $i > $i > $i ).
thf(func_def_693,type,
sK532: $i > $i ).
thf(func_def_694,type,
sK533: $i > $i > $i > $i ).
thf(func_def_695,type,
sK534: $i > $i > $i ).
thf(func_def_696,type,
sK535: $i > $i > $i > $i ).
thf(func_def_697,type,
sK536: $i > $i > $i > $i ).
thf(func_def_698,type,
sK537: $i > $i > $i ).
thf(func_def_699,type,
sK538: $i > $i > $i > $i ).
thf(func_def_700,type,
sK539: $i > $i > $i > $i ).
thf(func_def_701,type,
sK540: $i > $i > $i > $i ).
thf(func_def_702,type,
sK541: $i > $i ).
thf(func_def_703,type,
sK542: $i > $i > $i > $i ).
thf(func_def_704,type,
sK543: $i > $i > $i ).
thf(func_def_705,type,
sK544: $i > $i > $i ).
thf(func_def_706,type,
sK545: $i > $i > $i > $i ).
thf(func_def_707,type,
sK546: $i > $i > $i ).
thf(func_def_708,type,
sK547: $i > $i > $i ).
thf(func_def_709,type,
sK548: $i > $i > $i > $i ).
thf(func_def_710,type,
sK549: $i > $i > $i ).
thf(func_def_711,type,
sK550: $i > $i > $i ).
thf(func_def_712,type,
sK551: $i > $i > $i ).
thf(func_def_713,type,
sK552: $i > $i > $i > $i ).
thf(func_def_714,type,
sK553: $i > $i > $i > $i ).
thf(func_def_715,type,
sK554: $i > $i ).
thf(func_def_716,type,
sK555: $i > $i > $i ).
thf(func_def_717,type,
sK556: $i > $i > $i > $i ).
thf(func_def_718,type,
sK557: $i > $i > $i > $i ).
thf(func_def_719,type,
sK558: $i > $i > $i > $i ).
thf(func_def_720,type,
sK559: $i > $i > $i > $i ).
thf(func_def_721,type,
sK560: $i > $i > $i ).
thf(func_def_722,type,
sK561: $i > $i > $i > $i ).
thf(func_def_723,type,
sK562: $i > $i > $i > $i ).
thf(func_def_724,type,
sK563: $i > $i > $i > $i ).
thf(func_def_728,type,
sK567: $i > $i > $i ).
thf(func_def_738,type,
sK577: $i > $o ).
thf(func_def_740,type,
sK579: $i > $o ).
thf(func_def_745,type,
sK584: $i > $i ).
thf(func_def_749,type,
sK588: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_750,type,
sK589: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_751,type,
sK590: $i > $o ).
thf(func_def_752,type,
sK591: $i > $o ).
thf(func_def_757,type,
sK596: ( $i > $o ) > $i > $i ).
thf(func_def_758,type,
sK597: $i > $o ).
thf(func_def_763,type,
sK602: ( $i > $o ) > $i > $i ).
thf(func_def_764,type,
sK603: $i > $o ).
thf(func_def_770,type,
sK609: $i > $i > $i ).
thf(func_def_771,type,
sK610: $i > $i > $i ).
thf(func_def_772,type,
sK611: $i > $i > $i ).
thf(func_def_777,type,
sK616: $i > $o ).
thf(func_def_784,type,
sK623: $i > ( $i > $i > $o ) > $i ).
thf(func_def_785,type,
sK624: $i > ( $i > $i > $o ) > $i ).
thf(func_def_786,type,
sK625: $i > ( $i > $i > $o ) > $i ).
thf(func_def_788,type,
sK627: $i > $i > $o ).
thf(func_def_789,type,
sK628: $i > $i ).
thf(func_def_796,type,
sK635: $i > $o ).
thf(func_def_798,type,
sK637: $i > $o ).
thf(func_def_801,type,
sK640: $i > $i > $i ).
thf(func_def_805,type,
sK644: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_806,type,
sK645: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_809,type,
sK648: $i > $o ).
thf(func_def_810,type,
sK649: $i > $o ).
thf(func_def_815,type,
sK654: ( $i > $o ) > $i > $i ).
thf(func_def_816,type,
sK655: $i > $o ).
thf(func_def_819,type,
sK658: ( $i > $o ) > $i > $i ).
thf(func_def_820,type,
sK659: $i > $o ).
thf(func_def_822,type,
sK661: $i > $i ).
thf(func_def_824,type,
sK663: $i > $i ).
thf(func_def_826,type,
sK665: ( $i > $o ) > $i > $i ).
thf(func_def_827,type,
sK666: $i > $o ).
thf(func_def_833,type,
sK672: $i > $i > $i ).
thf(func_def_836,type,
sK675: $i > $i > $o > $i ).
thf(func_def_840,type,
sK679: $i > $i > $i ).
thf(func_def_869,type,
sK708: $i > $i ).
thf(func_def_878,type,
sK717: $i > $i > $i ).
thf(func_def_886,type,
sK725: $i > $o ).
thf(func_def_887,type,
sK726: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_888,type,
sK727: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_889,type,
sK728: $i > $o ).
thf(func_def_890,type,
sK729: $i > $o ).
thf(func_def_891,type,
sK730: ( $i > $o ) > $i ).
thf(func_def_892,type,
sK731: $i > $o ).
thf(func_def_893,type,
sK732: $i > $i ).
thf(func_def_898,type,
sK737: $i > $o ).
thf(func_def_906,type,
sK745: ( $i > $o ) > $i > $i ).
thf(func_def_907,type,
sK746: $i > $o ).
thf(func_def_915,type,
sK754: ( $i > $o ) > $i ).
thf(func_def_916,type,
sK755: $i > $o ).
thf(func_def_917,type,
ph756:
!>[X0: $tType] : X0 ).
thf(func_def_918,type,
sK757: ( $i > $o ) > $i ).
thf(func_def_919,type,
sK758: ( $i > $o ) > $i > $i ).
thf(func_def_920,type,
sK759: $i > $i > $i ).
thf(func_def_921,type,
sK760: $i > $i > $i ).
thf(func_def_922,type,
sK761: $i > $i > $i ).
thf(func_def_923,type,
sK762: $i > $i > $i ).
thf(func_def_924,type,
sK763: $i > $i > $i ).
thf(func_def_925,type,
sK764: $i > $i > $i ).
thf(func_def_927,type,
sK766: $i > $i > $i ).
thf(func_def_928,type,
sK767: $i > $i > $i ).
thf(func_def_929,type,
sK768: $i > $i > $i ).
thf(func_def_930,type,
sK769: $i > $i > $i ).
thf(func_def_931,type,
sK770: $i > $i > $i ).
thf(func_def_933,type,
sK772: $i > $i > $i ).
thf(func_def_934,type,
sK773: $i > $i > $i ).
thf(func_def_935,type,
sK774: $i > $i ).
thf(func_def_936,type,
sK775: $i > $i > $i ).
thf(func_def_937,type,
sK776: $i > $i > $i ).
thf(func_def_938,type,
sK777: $i > $i > $i ).
thf(func_def_939,type,
sK778: $i > $i ).
thf(func_def_940,type,
sK779: $i > $i ).
thf(func_def_941,type,
sK780: $i > $i > $i ).
thf(func_def_942,type,
sK781: $i > $i > $i ).
thf(func_def_943,type,
sK782: $i > $i > $i ).
thf(func_def_944,type,
sK783: $i > $i > $i ).
thf(func_def_945,type,
sK784: $i > $i > $i ).
thf(func_def_946,type,
sK785: $i > $i ).
thf(f14655,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f7005,f10685,f10707,f10993,f11692,f11726,f12116,f13894,f14645,f14654]) ).
thf(f14654,plain,
( ~ spl2_1176
| ~ spl2_1178 ),
inference(avatar_contradiction_clause,[status(thm)],[f14653]) ).
thf(f14653,plain,
( $false
| ~ spl2_1176
| ~ spl2_1178 ),
inference(trivial_inequality_removal,[status(thm)],[f14652]) ).
thf(f14652,plain,
( ( $true = $false )
| ~ spl2_1176
| ~ spl2_1178 ),
inference(backward_demodulation,[status(thm)],[f10693,f10703]) ).
thf(f10703,plain,
( ( setminusILneg = $false )
| ~ spl2_1178 ),
inference(avatar_component_clause,[status(thm)],[f10701]) ).
thf(f10701,definition,
( spl2_1178
<=> ( setminusILneg = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1178])],[avatar_definition]) ).
thf(f10693,plain,
( ( setminusILneg = $true )
| ~ spl2_1176 ),
inference(avatar_component_clause,[status(thm)],[f10691]) ).
thf(f10691,definition,
( spl2_1176
<=> ( setminusILneg = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1176])],[avatar_definition]) ).
thf(f14645,plain,
( ~ spl2_274
| ~ spl2_1173
| ~ spl2_1179 ),
inference(avatar_contradiction_clause,[status(thm)],[f14644]) ).
thf(f14644,plain,
( $false
| ~ spl2_274
| ~ spl2_1173
| ~ spl2_1179 ),
inference(trivial_inequality_removal,[status(thm)],[f14619]) ).
thf(f14619,plain,
( ( $true = $false )
| ~ spl2_274
| ~ spl2_1173
| ~ spl2_1179 ),
inference(backward_demodulation,[status(thm)],[f14315,f14374]) ).
thf(f14374,plain,
( ! [X0: $i] :
( ( in @ sK771 @ ( setminus @ sK1 @ X0 ) )
= $false )
| ~ spl2_274
| ~ spl2_1173
| ~ spl2_1179 ),
inference(trivial_inequality_removal,[status(thm)],[f14355]) ).
thf(f14355,plain,
( ! [X0: $i] :
( ( ( in @ sK771 @ ( setminus @ sK1 @ X0 ) )
= $false )
| ( $true = $false ) )
| ~ spl2_274
| ~ spl2_1173
| ~ spl2_1179 ),
inference(superposition,[status(thm)],[f14314,f10706]) ).
thf(f10706,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
| ~ spl2_1179 ),
inference(avatar_component_clause,[status(thm)],[f10705]) ).
thf(f10705,definition,
( spl2_1179
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1179])],[avatar_definition]) ).
thf(f14314,plain,
( ( ( in @ sK771 @ sK1 )
= $false )
| ~ spl2_274
| ~ spl2_1173 ),
inference(binary_proxy_clausification,[status(thm)],[f14313]) ).
thf(f14313,plain,
( ( ( ( in @ sK771 @ ( setminus @ sK1 @ sK0 ) )
=> ( in @ sK771 @ sK1 ) )
= $false )
| ~ spl2_274
| ~ spl2_1173 ),
inference(beta_eta_normalization,[status(thm)],[f14312]) ).
thf(f14312,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ sK1 @ sK0 ) )
=> ( in @ Y0 @ sK1 ) )
@ sK771 )
= $false )
| ~ spl2_274
| ~ spl2_1173 ),
inference(sigma_clausification,[status(thm)],[f14311]) ).
thf(f14311,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ sK1 @ sK0 ) )
=> ( in @ Y0 @ sK1 ) ) ) )
| ~ spl2_274
| ~ spl2_1173 ),
inference(not_proxy_clausification,[status(thm)],[f14310]) ).
thf(f14310,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ sK1 @ sK0 ) )
=> ( in @ Y0 @ sK1 ) ) ) )
= $true )
| ~ spl2_274
| ~ spl2_1173 ),
inference(boolean_simplification,[status(thm)],[f14237]) ).
thf(f14237,plain,
( ( $true
= ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ sK1 @ sK0 ) )
=> ( in @ Y0 @ sK1 ) ) ) ) )
| ~ spl2_274
| ~ spl2_1173 ),
inference(superposition,[status(thm)],[f10680,f12124]) ).
thf(f12124,plain,
( ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ~ spl2_274 ),
inference(trivial_inequality_removal,[status(thm)],[f12119]) ).
thf(f12119,plain,
( ( $true != $true )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ~ spl2_274 ),
inference(superposition,[status(thm)],[f523,f7004]) ).
thf(f7004,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) )
| ~ spl2_274 ),
inference(avatar_component_clause,[status(thm)],[f7003]) ).
thf(f7003,definition,
( spl2_274
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_274])],[avatar_definition]) ).
thf(f523,plain,
( $true
!= ( subset @ ( setminus @ sK1 @ sK0 ) @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
thf(f384,plain,
( ( setminusIRneg = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset3 = $true )
& ( setminusEL = $true )
& ( dsetconstr__Cong = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( subsetI1 = $true )
& ( exuEu = $true )
& ( binintersectSubset2 = $true )
& ( setunion__Cong = $true )
& ( inCongP = $true )
& ( setadjoinIL = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( quantDeMorgan4 = $true )
& ( wellorderingAx = $true )
& ( binintersectEL = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( setminusERneg = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( bs114d = $true )
& ( setminusER = $true )
& ( eqinunit = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( dsetconstrEL = $true )
& ( omega0Ax = $true )
& ( setoftrueEq = $true )
& ( disjointsetsI1 = $true )
& ( setminusSubset2 = $true )
& ( binintersectRsub = $true )
& ( emptyset__Cong = $true )
& ( sepSubset = $true )
& ( subsetE2 = $true )
& ( $true
!= ( subset @ ( setminus @ sK1 @ sK0 ) @ sK1 ) )
& ( notdexE = $true )
& ( notinemptyset = $true )
& ( notequalI1 = $true )
& ( setminusILneg = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( notinsingleton = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( prop2setI = $true )
& ( setadjoinIR = $true )
& ( prop2set2propI = $true )
& ( foundationAx = $true )
& ( notequalI2 = $true )
& ( powerset__Cong = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinOr = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( uniqinunit = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( binunionE = $true )
& ( inPowerset = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( subset2powerset = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetE = $true )
& ( upairset2IR = $true )
& ( setunionI = $true )
& ( emptyI = $true )
& ( subsetE = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset5 = $true )
& ( singletonsswitch = $true )
& ( setunionAx = $true )
& ( setadjoinE = $true )
& ( setminusELneg = $true )
& ( binunionIR = $true )
& ( binunionRsub = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( notsubsetI = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( nonemptyE1 = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( descr__Cong = $true )
& ( vacuousDall = $true )
& ( subsetRefl = $true )
& ( exuI3 = $true )
& ( binintersectSubset1 = $true )
& ( omegaSAx = $true )
& ( setadjoinAx = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( upairsetE = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f382,f383]) ).
thf(f383,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X0 ) @ X1 )
!= $true )
=> ( $true
!= ( subset @ ( setminus @ sK1 @ sK0 ) @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f382,plain,
( ( setminusIRneg = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset3 = $true )
& ( setminusEL = $true )
& ( dsetconstr__Cong = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( subsetI1 = $true )
& ( exuEu = $true )
& ( binintersectSubset2 = $true )
& ( setunion__Cong = $true )
& ( inCongP = $true )
& ( setadjoinIL = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( quantDeMorgan4 = $true )
& ( wellorderingAx = $true )
& ( binintersectEL = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( setminusERneg = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( bs114d = $true )
& ( setminusER = $true )
& ( eqinunit = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( dsetconstrEL = $true )
& ( omega0Ax = $true )
& ( setoftrueEq = $true )
& ( disjointsetsI1 = $true )
& ( setminusSubset2 = $true )
& ( binintersectRsub = $true )
& ( emptyset__Cong = $true )
& ( sepSubset = $true )
& ( subsetE2 = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X0 ) @ X1 )
!= $true )
& ( notdexE = $true )
& ( notinemptyset = $true )
& ( notequalI1 = $true )
& ( setminusILneg = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( notinsingleton = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( prop2setI = $true )
& ( setadjoinIR = $true )
& ( prop2set2propI = $true )
& ( foundationAx = $true )
& ( notequalI2 = $true )
& ( powerset__Cong = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinOr = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( uniqinunit = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( binunionE = $true )
& ( inPowerset = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( subset2powerset = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetE = $true )
& ( upairset2IR = $true )
& ( setunionI = $true )
& ( emptyI = $true )
& ( subsetE = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset5 = $true )
& ( singletonsswitch = $true )
& ( setunionAx = $true )
& ( setadjoinE = $true )
& ( setminusELneg = $true )
& ( binunionIR = $true )
& ( binunionRsub = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( notsubsetI = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( nonemptyE1 = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( descr__Cong = $true )
& ( vacuousDall = $true )
& ( subsetRefl = $true )
& ( exuI3 = $true )
& ( binintersectSubset1 = $true )
& ( omegaSAx = $true )
& ( setadjoinAx = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( upairsetE = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true ) ),
inference(flattening,[status(thm)],[f381]) ).
thf(f381,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X0 ) @ X1 )
!= $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f308]) ).
thf(f308,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ! [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X0 ) @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f307]) ).
thf(f307,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ! [X0: $i,X1: $i] : ( subset @ ( setminus @ X1 @ X0 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f129]) ).
thf(f129,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ! [X4: $i,X3: $i] : ( subset @ ( setminus @ X3 @ X4 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f128]) ).
thf(f128,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ! [X4: $i,X3: $i] : ( subset @ ( setminus @ X3 @ X4 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',setminusLsub) ).
thf(f10680,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ spl2_1173 ),
inference(avatar_component_clause,[status(thm)],[f10679]) ).
thf(f10679,definition,
( spl2_1173
<=> ! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1173])],[avatar_definition]) ).
thf(f14315,plain,
( ( $true
= ( in @ sK771 @ ( setminus @ sK1 @ sK0 ) ) )
| ~ spl2_274
| ~ spl2_1173 ),
inference(binary_proxy_clausification,[status(thm)],[f14313]) ).
thf(f13894,plain,
( ~ spl2_1171
| ~ spl2_1174 ),
inference(avatar_contradiction_clause,[status(thm)],[f13893]) ).
thf(f13893,plain,
( $false
| ~ spl2_1171
| ~ spl2_1174 ),
inference(trivial_inequality_removal,[status(thm)],[f13892]) ).
thf(f13892,plain,
( ( $true = $false )
| ~ spl2_1171
| ~ spl2_1174 ),
inference(backward_demodulation,[status(thm)],[f10672,f10684]) ).
thf(f10684,plain,
( ( powersetAx = $false )
| ~ spl2_1174 ),
inference(avatar_component_clause,[status(thm)],[f10682]) ).
thf(f10682,definition,
( spl2_1174
<=> ( powersetAx = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1174])],[avatar_definition]) ).
thf(f10672,plain,
( ( powersetAx = $true )
| ~ spl2_1171 ),
inference(avatar_component_clause,[status(thm)],[f10670]) ).
thf(f10670,definition,
( spl2_1171
<=> ( powersetAx = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1171])],[avatar_definition]) ).
thf(f12116,plain,
( ~ spl2_270
| ~ spl2_273 ),
inference(avatar_contradiction_clause,[status(thm)],[f12115]) ).
thf(f12115,plain,
( $false
| ~ spl2_270
| ~ spl2_273 ),
inference(trivial_inequality_removal,[status(thm)],[f12114]) ).
thf(f12114,plain,
( ( $true = $false )
| ~ spl2_270
| ~ spl2_273 ),
inference(forward_demodulation,[status(thm)],[f6987,f7001]) ).
thf(f7001,plain,
( ( powersetE1 = $false )
| ~ spl2_273 ),
inference(avatar_component_clause,[status(thm)],[f6999]) ).
thf(f6999,definition,
( spl2_273
<=> ( powersetE1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_273])],[avatar_definition]) ).
thf(f6987,plain,
( ( powersetE1 = $true )
| ~ spl2_270 ),
inference(avatar_component_clause,[status(thm)],[f6985]) ).
thf(f6985,definition,
( spl2_270
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_270])],[avatar_definition]) ).
thf(f11726,plain,
spl2_1171,
inference(avatar_split_clause,[status(thm)],[f572,f10670]) ).
thf(f572,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f384]) ).
thf(f11692,plain,
spl2_270,
inference(avatar_split_clause,[status(thm)],[f498,f6985]) ).
thf(f498,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f384]) ).
thf(f10993,plain,
spl2_1176,
inference(avatar_split_clause,[status(thm)],[f519,f10691]) ).
thf(f519,plain,
setminusILneg = $true,
inference(cnf_transformation,[status(thm)],[f384]) ).
thf(f10707,plain,
( spl2_1178
| spl2_1179 ),
inference(avatar_split_clause,[status(thm)],[f1330,f10705,f10701]) ).
thf(f1330,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( setminusILneg = $false )
| ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1329]) ).
thf(f1329,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( setminusILneg = $false )
| ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( ( ~ ( in @ X3 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1328]) ).
thf(f1328,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
| ( setminusILneg = $false )
| ( ( ~ ( in @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1327]) ).
thf(f1327,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( setminusILneg = $false )
| ( $true
= ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1326]) ).
thf(f1326,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( setminusILneg = $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f1325]) ).
thf(f1325,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) ) ) )
| ( setminusILneg = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1324]) ).
thf(f1324,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( setminus @ X1 @ Y0 ) ) ) )
@ X2 ) )
| ( setminusILneg = $false ) ),
inference(pi_clausification,[status(thm)],[f1323]) ).
thf(f1323,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( setminus @ X1 @ Y0 ) ) ) ) ) )
| ( setminusILneg = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1322]) ).
thf(f1322,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
=> ~ ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true )
| ( setminusILneg = $false ) ),
inference(pi_clausification,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
=> ~ ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) )
| ( setminusILneg = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f387]) ).
thf(f387,plain,
( setminusILneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
=> ~ ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
thf(f203,plain,
( setminusILneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
=> ~ ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f202]) ).
thf(f202,plain,
( setminusILneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f126]) ).
thf(f126,axiom,
( setminusILneg
= ( ! [X1: $i,X4: $i,X3: $i] :
( ~ ( in @ X1 @ X3 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',setminusILneg) ).
thf(f10685,plain,
( spl2_1173
| spl2_1174 ),
inference(avatar_split_clause,[status(thm)],[f1346,f10682,f10679]) ).
thf(f1346,plain,
! [X2: $i,X1: $i] :
( ( powersetAx = $false )
| ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1345]) ).
thf(f1345,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) )
| ( powersetAx = $false ) ),
inference(pi_clausification,[status(thm)],[f1344]) ).
thf(f1344,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1343]) ).
thf(f1343,plain,
! [X1: $i] :
( ( powersetAx = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f1342]) ).
thf(f1342,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
| ( powersetAx = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
thf(f366,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f365]) ).
thf(f365,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( powersetAx
= ( ! [X3: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
<=> ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',powersetAx) ).
thf(f7005,plain,
( spl2_273
| spl2_274 ),
inference(avatar_split_clause,[status(thm)],[f4842,f7003,f6999]) ).
thf(f4842,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f4841]) ).
thf(f4841,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ X2 ) ) )
| ( powersetE1 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f4840]) ).
thf(f4840,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) )
| ( powersetE1 = $false ) ),
inference(pi_clausification,[status(thm)],[f4839]) ).
thf(f4839,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) ) ) )
| ( powersetE1 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f4838]) ).
thf(f4838,plain,
! [X1: $i] :
( ( powersetE1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f4837]) ).
thf(f4837,plain,
( ( powersetE1 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
thf(f150,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f149]) ).
thf(f149,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
( powersetE1
= ( ! [X3: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',powersetE1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU609^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Feb 24 12:28:10 EST 2026
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEU609^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.44 % Domain : Set Theory
% 0.16/0.44 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English : (! A:i.! B:i.subset (setminus A B) A)
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.44 % Source : [Bro08]
% 0.16/0.44 % Names : ZFC111g [Bro08]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 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, 0.80 v5.2.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.16/0.44 % Syntax : Number of formulae : 272 ( 127 unt; 144 typ; 127 def)
% 0.16/0.44 % Number of atoms : 676 ( 183 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 126 ( 5 avg)
% 0.16/0.44 % Number of connectives : 1073 ( 39 ~; 6 |; 28 &; 687 @)
% 0.16/0.44 % ( 14 <=>; 299 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 132 ( 2 avg)
% 0.16/0.44 % Number of types : 2 ( 0 usr)
% 0.16/0.44 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 147 ( 144 usr; 129 con; 0-2 aty)
% 0.16/0.44 % Number of variables : 368 ( 30 ^; 309 !; 29 ?; 368 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : http://mathgate.info/detsetitem.php?id=464
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(in_type,type,
% 0.16/0.44 in: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(exu_type,type,
% 0.16/0.44 exu: ( $i > $o ) > $o ).
% 0.16/0.44
% 0.16/0.44 thf(exu,definition,
% 0.16/0.44 ( exu
% 0.16/0.44 = ( ^ [Xphi: $i > $o] :
% 0.16/0.44 ? [Xx: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 & ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setextAx_type,type,
% 0.16/0.44 setextAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setextAx,definition,
% 0.16/0.44 ( setextAx
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 <=> ( in @ Xx @ B ) )
% 0.16/0.44 => ( A = B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyset_type,type,
% 0.16/0.44 emptyset: $i ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetAx_type,type,
% 0.16/0.44 emptysetAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetAx,definition,
% 0.16/0.44 ( emptysetAx
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoin_type,type,
% 0.16/0.44 setadjoin: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinAx_type,type,
% 0.16/0.44 setadjoinAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinAx,definition,
% 0.16/0.44 ( setadjoinAx
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 <=> ( ( Xy = Xx )
% 0.16/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powerset_type,type,
% 0.16/0.44 powerset: $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(powersetAx_type,type,
% 0.16/0.44 powersetAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetAx,definition,
% 0.16/0.44 ( powersetAx
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.44 <=> ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunion_type,type,
% 0.16/0.44 setunion: $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setunionAx_type,type,
% 0.16/0.44 setunionAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionAx,definition,
% 0.16/0.44 ( setunionAx
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.44 <=> ? [B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omega_type,type,
% 0.16/0.44 omega: $i ).
% 0.16/0.44
% 0.16/0.44 thf(omega0Ax_type,type,
% 0.16/0.44 omega0Ax: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omega0Ax,definition,
% 0.16/0.44 ( omega0Ax
% 0.16/0.44 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omegaSAx_type,type,
% 0.16/0.44 omegaSAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omegaSAx,definition,
% 0.16/0.44 ( omegaSAx
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ omega )
% 0.16/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omegaIndAx_type,type,
% 0.16/0.44 omegaIndAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omegaIndAx,definition,
% 0.16/0.44 ( omegaIndAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( ( in @ emptyset @ A )
% 0.16/0.44 & ! [Xx: $i] :
% 0.16/0.44 ( ( ( in @ Xx @ omega )
% 0.16/0.44 & ( in @ Xx @ A ) )
% 0.16/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ omega )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(replAx_type,type,
% 0.16/0.44 replAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(replAx,definition,
% 0.16/0.44 ( replAx
% 0.16/0.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( exu
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.44 => ? [B: $i] :
% 0.16/0.44 ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 <=> ? [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ A )
% 0.16/0.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(foundationAx_type,type,
% 0.16/0.44 foundationAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(foundationAx,definition,
% 0.16/0.44 ( foundationAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.44 => ? [B: $i] :
% 0.16/0.44 ( ( in @ B @ A )
% 0.16/0.44 & ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(wellorderingAx_type,type,
% 0.16/0.44 wellorderingAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(wellorderingAx,definition,
% 0.16/0.44 ( wellorderingAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ? [B: $i] :
% 0.16/0.44 ( ! [C: $i] :
% 0.16/0.44 ( ( in @ C @ B )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ A ) ) )
% 0.16/0.44 & ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( ( in @ Xx @ A )
% 0.16/0.44 & ( in @ Xy @ A ) )
% 0.16/0.44 => ( ! [C: $i] :
% 0.16/0.44 ( ( in @ C @ B )
% 0.16/0.44 => ( ( in @ Xx @ C )
% 0.16/0.44 <=> ( in @ Xy @ C ) ) )
% 0.16/0.44 => ( Xx = Xy ) ) )
% 0.16/0.44 & ! [C: $i,D: $i] :
% 0.16/0.44 ( ( ( in @ C @ B )
% 0.16/0.44 & ( in @ D @ B ) )
% 0.16/0.44 => ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ D ) )
% 0.16/0.44 | ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ D )
% 0.16/0.44 => ( in @ Xx @ C ) ) ) )
% 0.16/0.44 & ! [C: $i] :
% 0.16/0.44 ( ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.44 => ? [D: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ D @ B )
% 0.16/0.44 & ( in @ Xx @ C )
% 0.16/0.44 & ~ ? [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ D )
% 0.16/0.44 & ( in @ Xy @ C ) )
% 0.16/0.44 & ! [E: $i] :
% 0.16/0.44 ( ( in @ E @ B )
% 0.16/0.44 => ( ! [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ E )
% 0.16/0.44 => ( in @ Xy @ D ) )
% 0.16/0.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(descr_type,type,
% 0.16/0.44 descr: ( $i > $o ) > $i ).
% 0.16/0.44
% 0.16/0.44 thf(descrp_type,type,
% 0.16/0.44 descrp: $o ).
% 0.16/0.44
% 0.16/0.44 thf(descrp,definition,
% 0.16/0.44 ( descrp
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ( Xphi
% 0.16/0.44 @ ( descr
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstr_type,type,
% 0.16/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrI_type,type,
% 0.16/0.44 dsetconstrI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrI,definition,
% 0.16/0.44 ( dsetconstrI
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 => ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrEL_type,type,
% 0.16/0.44 dsetconstrEL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrEL,definition,
% 0.16/0.44 ( dsetconstrEL
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrER_type,type,
% 0.16/0.44 dsetconstrER: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrER,definition,
% 0.16/0.44 ( dsetconstrER
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE1_type,type,
% 0.16/0.44 exuE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE1,definition,
% 0.16/0.44 ( exuE1
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 & ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(prop2set_type,type,
% 0.16/0.44 prop2set: $o > $i ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setE_type,type,
% 0.16/0.44 prop2setE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setE,definition,
% 0.16/0.44 ( prop2setE
% 0.16/0.44 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.44 => Xphi ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetE_type,type,
% 0.16/0.44 emptysetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetE,definition,
% 0.16/0.44 ( emptysetE
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetimpfalse_type,type,
% 0.16/0.44 emptysetimpfalse: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetimpfalse,definition,
% 0.16/0.44 ( emptysetimpfalse
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => $false ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notinemptyset_type,type,
% 0.16/0.44 notinemptyset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notinemptyset,definition,
% 0.16/0.44 ( notinemptyset
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3e_type,type,
% 0.16/0.44 exuE3e: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3e,definition,
% 0.16/0.44 ( exuE3e
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setext_type,type,
% 0.16/0.44 setext: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setext,definition,
% 0.16/0.44 ( setext
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) )
% 0.16/0.44 => ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 => ( A = B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyI_type,type,
% 0.16/0.44 emptyI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyI,definition,
% 0.16/0.44 ( emptyI
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ A )
% 0.16/0.44 => ( A = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(noeltsimpempty_type,type,
% 0.16/0.44 noeltsimpempty: $o ).
% 0.16/0.44
% 0.16/0.44 thf(noeltsimpempty,definition,
% 0.16/0.44 ( noeltsimpempty
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ A )
% 0.16/0.44 => ( A = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setbeta_type,type,
% 0.16/0.44 setbeta: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setbeta,definition,
% 0.16/0.44 ( setbeta
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonempty_type,type,
% 0.16/0.44 nonempty: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonempty,definition,
% 0.16/0.44 ( nonempty
% 0.16/0.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyE1_type,type,
% 0.16/0.44 nonemptyE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyE1,definition,
% 0.16/0.44 ( nonemptyE1
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( nonempty @ A )
% 0.16/0.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI_type,type,
% 0.16/0.44 nonemptyI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI,definition,
% 0.16/0.44 ( nonemptyI
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 => ( nonempty
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI1_type,type,
% 0.16/0.44 nonemptyI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI1,definition,
% 0.16/0.44 ( nonemptyI1
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.44 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIL_type,type,
% 0.16/0.44 setadjoinIL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIL,definition,
% 0.16/0.44 ( setadjoinIL
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinunitempty_type,type,
% 0.16/0.44 emptyinunitempty: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinunitempty,definition,
% 0.16/0.44 ( emptyinunitempty
% 0.16/0.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIR_type,type,
% 0.16/0.44 setadjoinIR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIR,definition,
% 0.16/0.44 ( setadjoinIR
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ A )
% 0.16/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinE_type,type,
% 0.16/0.44 setadjoinE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinE,definition,
% 0.16/0.44 ( setadjoinE
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 => ! [Xphi: $o] :
% 0.16/0.44 ( ( ( Xy = Xx )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => ( ( ( in @ Xy @ A )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => Xphi ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinOr_type,type,
% 0.16/0.44 setadjoinOr: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinOr,definition,
% 0.16/0.44 ( setadjoinOr
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 => ( ( Xy = Xx )
% 0.16/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setoftrueEq_type,type,
% 0.16/0.44 setoftrueEq: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setoftrueEq,definition,
% 0.16/0.44 ( setoftrueEq
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : $true )
% 0.16/0.44 = A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI_type,type,
% 0.16/0.44 powersetI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI,definition,
% 0.16/0.44 ( powersetI
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinPowerset_type,type,
% 0.16/0.44 emptyinPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinPowerset,definition,
% 0.16/0.44 ( emptyinPowerset
% 0.16/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyInPowerset_type,type,
% 0.16/0.44 emptyInPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyInPowerset,definition,
% 0.16/0.44 ( emptyInPowerset
% 0.16/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE_type,type,
% 0.16/0.44 powersetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE,definition,
% 0.16/0.44 ( powersetE
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.44 => ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunionI_type,type,
% 0.16/0.44 setunionI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionI,definition,
% 0.16/0.44 ( setunionI
% 0.16/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( ( in @ B @ A )
% 0.16/0.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunionE_type,type,
% 0.16/0.44 setunionE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionE,definition,
% 0.16/0.44 ( setunionE
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.44 => ! [Xphi: $o] :
% 0.16/0.44 ( ! [B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( ( in @ B @ A )
% 0.16/0.44 => Xphi ) )
% 0.16/0.44 => Xphi ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subPowSU_type,type,
% 0.16/0.44 subPowSU: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subPowSU,definition,
% 0.16/0.44 ( subPowSU
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE2_type,type,
% 0.16/0.44 exuE2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE2,definition,
% 0.16/0.44 ( exuE2
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyImpWitness_type,type,
% 0.16/0.44 nonemptyImpWitness: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyImpWitness,definition,
% 0.16/0.44 ( nonemptyImpWitness
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( nonempty @ A )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & $true ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(uniqinunit_type,type,
% 0.16/0.44 uniqinunit: $o ).
% 0.16/0.44
% 0.16/0.44 thf(uniqinunit,definition,
% 0.16/0.44 ( uniqinunit
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notinsingleton_type,type,
% 0.16/0.44 notinsingleton: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notinsingleton,definition,
% 0.16/0.44 ( notinsingleton
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx != Xy )
% 0.16/0.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(eqinunit_type,type,
% 0.16/0.44 eqinunit: $o ).
% 0.16/0.44
% 0.16/0.44 thf(eqinunit,definition,
% 0.16/0.44 ( eqinunit
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(singletonsswitch_type,type,
% 0.16/0.44 singletonsswitch: $o ).
% 0.16/0.44
% 0.16/0.44 thf(singletonsswitch,definition,
% 0.16/0.44 ( singletonsswitch
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetE_type,type,
% 0.16/0.44 upairsetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetE,definition,
% 0.16/0.44 ( upairsetE
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.44 => ( ( Xz = Xx )
% 0.16/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIL_type,type,
% 0.16/0.44 upairsetIL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIL,definition,
% 0.16/0.44 ( upairsetIL
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIR_type,type,
% 0.16/0.44 upairsetIR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIR,definition,
% 0.16/0.44 ( upairsetIR
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyE1_type,type,
% 0.16/0.44 emptyE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyE1,definition,
% 0.16/0.44 ( emptyE1
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) )
% 0.16/0.44 => ( ( ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 = emptyset )
% 0.16/0.44 => $false ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(vacuousDall_type,type,
% 0.16/0.44 vacuousDall: $o ).
% 0.16/0.44
% 0.16/0.44 thf(vacuousDall,definition,
% 0.16/0.44 ( vacuousDall
% 0.16/0.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan1_type,type,
% 0.16/0.44 quantDeMorgan1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan1,definition,
% 0.16/0.44 ( quantDeMorgan1
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan2_type,type,
% 0.16/0.44 quantDeMorgan2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan2,definition,
% 0.16/0.44 ( quantDeMorgan2
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ~ ( Xphi @ Xx ) )
% 0.16/0.44 => ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan3_type,type,
% 0.16/0.44 quantDeMorgan3: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan3,definition,
% 0.16/0.44 ( quantDeMorgan3
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan4_type,type,
% 0.16/0.44 quantDeMorgan4: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan4,definition,
% 0.16/0.44 ( quantDeMorgan4
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ~ ( Xphi @ Xx ) )
% 0.16/0.44 => ~ ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setI_type,type,
% 0.16/0.44 prop2setI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setI,definition,
% 0.16/0.44 ( prop2setI
% 0.16/0.44 = ( ! [Xphi: $o] :
% 0.16/0.44 ( Xphi
% 0.16/0.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(set2prop_type,type,
% 0.16/0.44 set2prop: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(prop2set2propI_type,type,
% 0.16/0.44 prop2set2propI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(prop2set2propI,definition,
% 0.16/0.44 ( prop2set2propI
% 0.16/0.44 = ( ! [Xphi: $o] :
% 0.16/0.44 ( Xphi
% 0.16/0.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notdexE_type,type,
% 0.16/0.44 notdexE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notdexE,definition,
% 0.16/0.44 ( notdexE
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notdallE_type,type,
% 0.16/0.44 notdallE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notdallE,definition,
% 0.16/0.44 ( notdallE
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuI1_type,type,
% 0.16/0.44 exuI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuI1,definition,
% 0.16/0.44 ( exuI1
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 & ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) )
% 0.16/0.44 => ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuI3_type,type,
% 0.16/0.44 exuI3: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuI3,definition,
% 0.16/0.44 ( exuI3
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.44 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 => ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) )
% 0.16/0.44 => ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuI2_type,type,
% 0.16/0.44 exuI2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuI2,definition,
% 0.16/0.44 ( exuI2
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 <=> ( Xy = Xx ) )
% 0.16/0.44 => ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(inCongP_type,type,
% 0.16/0.44 inCongP: $o ).
% 0.16/0.44
% 0.16/0.44 thf(inCongP,definition,
% 0.16/0.44 ( inCongP
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(in__Cong_type,type,
% 0.16/0.44 in__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(in__Cong,definition,
% 0.16/0.44 ( in__Cong
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( ( in @ Xx @ A )
% 0.16/0.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3u_type,type,
% 0.16/0.44 exuE3u: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3u,definition,
% 0.16/0.44 ( exuE3u
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 => ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exu__Cong_type,type,
% 0.16/0.44 exu__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exu__Cong,definition,
% 0.16/0.44 ( exu__Cong
% 0.16/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.44 => ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 <=> ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyset__Cong_type,type,
% 0.16/0.44 emptyset__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyset__Cong,definition,
% 0.16/0.44 ( emptyset__Cong
% 0.16/0.44 = ( emptyset = emptyset ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoin__Cong_type,type,
% 0.16/0.44 setadjoin__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoin__Cong,definition,
% 0.16/0.44 ( setadjoin__Cong
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ! [Xz: $i,Xu: $i] :
% 0.16/0.44 ( ( Xz = Xu )
% 0.16/0.44 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.44 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powerset__Cong_type,type,
% 0.16/0.44 powerset__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powerset__Cong,definition,
% 0.16/0.44 ( powerset__Cong
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ( ( powerset @ A )
% 0.16/0.44 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunion__Cong_type,type,
% 0.16/0.44 setunion__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunion__Cong,definition,
% 0.16/0.44 ( setunion__Cong
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ( ( setunion @ A )
% 0.16/0.44 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omega__Cong_type,type,
% 0.16/0.44 omega__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omega__Cong,definition,
% 0.16/0.44 ( omega__Cong
% 0.16/0.44 = ( omega = omega ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuEu_type,type,
% 0.16/0.44 exuEu: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuEu,definition,
% 0.16/0.44 ( exuEu
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 => ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(descr__Cong_type,type,
% 0.16/0.44 descr__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(descr__Cong,definition,
% 0.16/0.44 ( descr__Cong
% 0.16/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.44 => ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.44 => ( ( descr
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 = ( descr
% 0.16/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstr__Cong_type,type,
% 0.16/0.44 dsetconstr__Cong: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstr__Cong,definition,
% 0.16/0.44 ( dsetconstr__Cong
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ! [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ B )
% 0.16/0.44 => ( ( Xx = Xy )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.44 => ( ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 = ( dsetconstr @ B
% 0.16/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subset_type,type,
% 0.16/0.44 subset: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(disjoint_type,type,
% 0.16/0.44 disjoint: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(setsmeet_type,type,
% 0.16/0.44 setsmeet: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetI1_type,type,
% 0.16/0.44 subsetI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetI1,definition,
% 0.16/0.44 ( subsetI1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) )
% 0.16/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(eqimpsubset2_type,type,
% 0.16/0.44 eqimpsubset2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(eqimpsubset2,definition,
% 0.16/0.44 ( eqimpsubset2
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(eqimpsubset1_type,type,
% 0.16/0.44 eqimpsubset1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(eqimpsubset1,definition,
% 0.16/0.44 ( eqimpsubset1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( A = B )
% 0.16/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetI2_type,type,
% 0.16/0.44 subsetI2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetI2,definition,
% 0.16/0.44 ( subsetI2
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) )
% 0.16/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetsubset_type,type,
% 0.16/0.44 emptysetsubset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetsubset,definition,
% 0.16/0.44 ( emptysetsubset
% 0.16/0.44 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetE_type,type,
% 0.16/0.44 subsetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetE,definition,
% 0.16/0.44 ( subsetE
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetE2_type,type,
% 0.16/0.44 subsetE2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetE2,definition,
% 0.16/0.44 ( subsetE2
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notsubsetI_type,type,
% 0.16/0.44 notsubsetI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notsubsetI,definition,
% 0.16/0.44 ( notsubsetI
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notequalI1_type,type,
% 0.16/0.44 notequalI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notequalI1,definition,
% 0.16/0.44 ( notequalI1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ~ ( subset @ A @ B )
% 0.16/0.44 => ( A != B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notequalI2_type,type,
% 0.16/0.44 notequalI2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notequalI2,definition,
% 0.16/0.44 ( notequalI2
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ( A != B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetRefl_type,type,
% 0.16/0.44 subsetRefl: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetRefl,definition,
% 0.16/0.44 ( subsetRefl
% 0.16/0.44 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetTrans_type,type,
% 0.16/0.44 subsetTrans: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetTrans,definition,
% 0.16/0.44 ( subsetTrans
% 0.16/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ( subset @ B @ C )
% 0.16/0.44 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinSub_type,type,
% 0.16/0.44 setadjoinSub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinSub,definition,
% 0.16/0.44 ( setadjoinSub
% 0.16/0.44 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinSub2_type,type,
% 0.16/0.44 setadjoinSub2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinSub2,definition,
% 0.16/0.44 ( setadjoinSub2
% 0.16/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subset2powerset_type,type,
% 0.16/0.44 subset2powerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subset2powerset,definition,
% 0.16/0.44 ( subset2powerset
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setextsub_type,type,
% 0.16/0.44 setextsub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setextsub,definition,
% 0.16/0.44 ( setextsub
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ( subset @ B @ A )
% 0.16/0.44 => ( A = B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subsetemptysetimpeq_type,type,
% 0.16/0.44 subsetemptysetimpeq: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subsetemptysetimpeq,definition,
% 0.16/0.44 ( subsetemptysetimpeq
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( subset @ A @ emptyset )
% 0.16/0.44 => ( A = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI1_type,type,
% 0.16/0.44 powersetI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI1,definition,
% 0.16/0.44 ( powersetI1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ B @ A )
% 0.16/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE1_type,type,
% 0.16/0.44 powersetE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE1,definition,
% 0.16/0.44 ( powersetE1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(inPowerset_type,type,
% 0.16/0.44 inPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(inPowerset,definition,
% 0.16/0.44 ( inPowerset
% 0.16/0.44 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetsubset_type,type,
% 0.16/0.44 powersetsubset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetsubset,definition,
% 0.16/0.44 ( powersetsubset
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sepInPowerset_type,type,
% 0.16/0.44 sepInPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(sepInPowerset,definition,
% 0.16/0.44 ( sepInPowerset
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( in
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sepSubset_type,type,
% 0.16/0.44 sepSubset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(sepSubset,definition,
% 0.16/0.44 ( sepSubset
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( subset
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunion_type,type,
% 0.16/0.44 binunion: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(binunionIL_type,type,
% 0.16/0.44 binunionIL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionIL,definition,
% 0.16/0.44 ( binunionIL
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairset2IR_type,type,
% 0.16/0.44 upairset2IR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairset2IR,definition,
% 0.16/0.44 ( upairset2IR
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunionIR_type,type,
% 0.16/0.44 binunionIR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionIR,definition,
% 0.16/0.44 ( binunionIR
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunionEcases_type,type,
% 0.16/0.44 binunionEcases: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionEcases,definition,
% 0.16/0.44 ( binunionEcases
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.16/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.44 => ( ( ( in @ Xx @ A )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => ( ( ( in @ Xx @ B )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => Xphi ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunionE_type,type,
% 0.16/0.44 binunionE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionE,definition,
% 0.16/0.44 ( binunionE
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.44 => ( ( in @ Xx @ A )
% 0.16/0.44 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunionLsub_type,type,
% 0.16/0.44 binunionLsub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionLsub,definition,
% 0.16/0.44 ( binunionLsub
% 0.16/0.44 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binunionRsub_type,type,
% 0.16/0.44 binunionRsub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binunionRsub,definition,
% 0.16/0.44 ( binunionRsub
% 0.16/0.44 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersect_type,type,
% 0.16/0.44 binintersect: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectI_type,type,
% 0.16/0.44 binintersectI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectI,definition,
% 0.16/0.44 ( binintersectI
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset5_type,type,
% 0.16/0.44 binintersectSubset5: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset5,definition,
% 0.16/0.44 ( binintersectSubset5
% 0.16/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.44 ( ( subset @ C @ A )
% 0.16/0.44 => ( ( subset @ C @ B )
% 0.16/0.44 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectEL_type,type,
% 0.16/0.44 binintersectEL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectEL,definition,
% 0.16/0.44 ( binintersectEL
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectLsub_type,type,
% 0.16/0.44 binintersectLsub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectLsub,definition,
% 0.16/0.44 ( binintersectLsub
% 0.16/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset2_type,type,
% 0.16/0.44 binintersectSubset2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset2,definition,
% 0.16/0.44 ( binintersectSubset2
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ( binintersect @ A @ B )
% 0.16/0.44 = A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset3_type,type,
% 0.16/0.44 binintersectSubset3: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset3,definition,
% 0.16/0.44 ( binintersectSubset3
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( ( binintersect @ A @ B )
% 0.16/0.44 = B )
% 0.16/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectER_type,type,
% 0.16/0.44 binintersectER: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectER,definition,
% 0.16/0.44 ( binintersectER
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.44 => ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(disjointsetsI1_type,type,
% 0.16/0.44 disjointsetsI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(disjointsetsI1,definition,
% 0.16/0.44 ( disjointsetsI1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( in @ Xx @ B ) )
% 0.16/0.44 => ( ( binintersect @ A @ B )
% 0.16/0.44 = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectRsub_type,type,
% 0.16/0.44 binintersectRsub: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectRsub,definition,
% 0.16/0.44 ( binintersectRsub
% 0.16/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset4_type,type,
% 0.16/0.44 binintersectSubset4: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset4,definition,
% 0.16/0.44 ( binintersectSubset4
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ B @ A )
% 0.16/0.44 => ( ( binintersect @ A @ B )
% 0.16/0.44 = B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset1_type,type,
% 0.16/0.44 binintersectSubset1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(binintersectSubset1,definition,
% 0.16/0.44 ( binintersectSubset1
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( ( binintersect @ A @ B )
% 0.16/0.44 = A )
% 0.16/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(bs114d_type,type,
% 0.16/0.44 bs114d: $o ).
% 0.16/0.44
% 0.16/0.44 thf(bs114d,definition,
% 0.16/0.44 ( bs114d
% 0.16/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.44 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.16/0.44 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(regular_type,type,
% 0.16/0.44 regular: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminus_type,type,
% 0.16/0.44 setminus: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setminusI_type,type,
% 0.16/0.44 setminusI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusI,definition,
% 0.16/0.44 ( setminusI
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusEL_type,type,
% 0.16/0.44 setminusEL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusEL,definition,
% 0.16/0.44 ( setminusEL
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusER_type,type,
% 0.16/0.44 setminusER: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusER,definition,
% 0.16/0.44 ( setminusER
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.44 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusSubset2_type,type,
% 0.16/0.44 setminusSubset2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusSubset2,definition,
% 0.16/0.44 ( setminusSubset2
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( subset @ A @ B )
% 0.16/0.44 => ( ( setminus @ A @ B )
% 0.16/0.44 = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusERneg_type,type,
% 0.16/0.44 setminusERneg: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusERneg,definition,
% 0.16/0.44 ( setminusERneg
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.44 => ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusELneg_type,type,
% 0.16/0.44 setminusELneg: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusELneg,definition,
% 0.16/0.44 ( setminusELneg
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusILneg_type,type,
% 0.16/0.44 setminusILneg: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusILneg,definition,
% 0.16/0.44 ( setminusILneg
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ~ ( in @ Xx @ A )
% 0.16/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusIRneg_type,type,
% 0.16/0.44 setminusIRneg: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusIRneg,definition,
% 0.16/0.44 ( setminusIRneg
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusLsub,conjecture,
% 0.16/0.44 ( setextAx
% 0.16/0.44 => ( emptysetAx
% 0.16/0.44 => ( setadjoinAx
% 0.16/0.44 => ( powersetAx
% 0.16/0.44 => ( setunionAx
% 0.16/0.44 => ( omega0Ax
% 0.16/0.44 => ( omegaSAx
% 0.16/0.44 => ( omegaIndAx
% 0.16/0.44 => ( replAx
% 0.16/0.44 => ( foundationAx
% 0.16/0.44 => ( wellorderingAx
% 0.16/0.44 => ( descrp
% 0.16/0.44 => ( dsetconstrI
% 0.16/0.44 => ( dsetconstrEL
% 0.16/0.44 => ( dsetconstrER
% 0.16/0.44 => ( exuE1
% 0.16/0.44 => ( prop2setE
% 0.16/0.44 => ( emptysetE
% 0.16/0.44 => ( emptysetimpfalse
% 0.16/0.44 => ( notinemptyset
% 0.16/0.44 => ( exuE3e
% 0.16/0.44 => ( setext
% 0.16/0.44 => ( emptyI
% 0.16/0.44 => ( noeltsimpempty
% 0.16/0.44 => ( setbeta
% 0.16/0.44 => ( nonemptyE1
% 0.16/0.44 => ( nonemptyI
% 0.16/0.44 => ( nonemptyI1
% 0.16/0.44 => ( setadjoinIL
% 0.16/0.44 => ( emptyinunitempty
% 0.16/0.44 => ( setadjoinIR
% 0.16/0.44 => ( setadjoinE
% 0.16/0.44 => ( setadjoinOr
% 0.16/0.44 => ( setoftrueEq
% 0.16/0.44 => ( powersetI
% 0.16/0.44 => ( emptyinPowerset
% 0.16/0.44 => ( emptyInPowerset
% 0.16/0.44 => ( powersetE
% 0.16/0.44 => ( setunionI
% 0.16/0.44 => ( setunionE
% 0.16/0.44 => ( subPowSU
% 0.16/0.44 => ( exuE2
% 0.16/0.44 => ( nonemptyImpWitness
% 0.16/0.44 => ( uniqinunit
% 0.16/0.44 => ( notinsingleton
% 0.16/0.44 => ( eqinunit
% 0.16/0.44 => ( singletonsswitch
% 0.16/0.44 => ( upairsetE
% 0.16/0.44 => ( upairsetIL
% 0.16/0.44 => ( upairsetIR
% 0.16/0.44 => ( emptyE1
% 0.16/0.44 => ( vacuousDall
% 0.16/0.44 => ( quantDeMorgan1
% 0.16/0.44 => ( quantDeMorgan2
% 0.16/0.44 => ( quantDeMorgan3
% 0.16/0.44 => ( quantDeMorgan4
% 0.16/0.44 => ( prop2setI
% 0.16/0.44 => ( prop2set2propI
% 0.16/0.44 => ( notdexE
% 0.16/0.44 => ( notdallE
% 0.16/0.44 => ( exuI1
% 0.16/0.44 => ( exuI3
% 0.16/0.44 => ( exuI2
% 0.16/0.44 => ( inCongP
% 0.16/0.44 => ( in__Cong
% 0.16/0.44 => ( exuE3u
% 0.16/0.44 => ( exu__Cong
% 0.16/0.44 => ( emptyset__Cong
% 0.16/0.44 => ( setadjoin__Cong
% 0.16/0.44 => ( powerset__Cong
% 0.16/0.44 => ( setunion__Cong
% 0.16/0.44 => ( omega__Cong
% 0.16/0.44 => ( exuEu
% 0.16/0.44 => ( descr__Cong
% 0.16/0.44 => ( dsetconstr__Cong
% 0.16/0.44 => ( subsetI1
% 0.16/0.44 => ( eqimpsubset2
% 0.16/0.44 => ( eqimpsubset1
% 0.16/0.44 => ( subsetI2
% 0.16/0.44 => ( emptysetsubset
% 0.16/0.44 => ( subsetE
% 0.16/0.44 => ( subsetE2
% 0.16/0.44 => ( notsubsetI
% 0.16/0.44 => ( notequalI1
% 0.16/0.44 => ( notequalI2
% 0.16/0.44 => ( subsetRefl
% 0.16/0.44 => ( subsetTrans
% 0.16/0.44 => ( setadjoinSub
% 0.16/0.44 => ( setadjoinSub2
% 0.16/0.44 => ( subset2powerset
% 0.16/0.44 => ( setextsub
% 0.16/0.44 => ( subsetemptysetimpeq
% 0.16/0.44 => ( powersetI1
% 0.16/0.44 => ( powersetE1
% 0.16/0.44 => ( inPowerset
% 0.16/0.44 => ( powersetsubset
% 0.16/0.44 => ( sepInPowerset
% 0.16/0.44 => ( sepSubset
% 0.16/0.44 => ( binunionIL
% 0.16/0.44 => ( upairset2IR
% 0.16/0.44 => ( binunionIR
% 0.16/0.44 => ( binunionEcases
% 0.16/0.44 => ( binunionE
% 0.16/0.44 => ( binunionLsub
% 0.16/0.44 => ( binunionRsub
% 0.16/0.44 => ( binintersectI
% 0.16/0.44 => ( binintersectSubset5
% 0.16/0.44 => ( binintersectEL
% 0.16/0.44 => ( binintersectLsub
% 0.16/0.44 => ( binintersectSubset2
% 0.16/0.44 => ( binintersectSubset3
% 0.16/0.44 => ( binintersectER
% 0.16/0.44 => ( disjointsetsI1
% 0.16/0.44 => ( binintersectRsub
% 0.16/0.44 => ( binintersectSubset4
% 0.16/0.44 => ( binintersectSubset1
% 0.16/0.44 => ( bs114d
% 0.16/0.44 => ( setminusI
% 0.16/0.44 => ( setminusEL
% 0.16/0.44 => ( setminusER
% 0.16/0.44 => ( setminusSubset2
% 0.16/0.44 => ( setminusERneg
% 0.16/0.44 => ( setminusELneg
% 0.16/0.44 => ( setminusILneg
% 0.16/0.44 => ( setminusIRneg
% 0.16/0.44 => ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 2.09/1.32 ---- Embedded in THF ---
% 2.09/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.09/1.32 %%% Generated on Tue Feb 24 12:28:11 EST 2026
% 2.09/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 2.09/1.32 %%% Logic specification used:
% 2.09/1.32 %%% thf(spec, logic, $$dhol).
% 2.09/1.32
% 2.09/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2DTF14910.p
% See solution above
% 2.09/1.32 ------------------------
% 2.09/1.33 ---- Cleaned THF ---
% 2.09/1.33 thf(in_type,type,
% 2.09/1.33 in: $i > $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(exu_type,type,
% 2.09/1.33 exu: ( $i > $o ) > $o ).
% 2.09/1.33
% 2.09/1.33 thf(exu,definition,
% 2.09/1.33 ( exu
% 2.09/1.33 = ( ^ [Xphi: $i > $o] :
% 2.09/1.33 ? [Xx: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 & ! [Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setextAx_type,type,
% 2.09/1.33 setextAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setextAx,definition,
% 2.09/1.33 ( setextAx
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 <=> ( in @ Xx @ B ) )
% 2.09/1.33 => ( A = B ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyset_type,type,
% 2.09/1.33 emptyset: $i ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetAx_type,type,
% 2.09/1.33 emptysetAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetAx,definition,
% 2.09/1.33 ( emptysetAx
% 2.09/1.33 = ( ! [Xx: $i] :
% 2.09/1.33 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoin_type,type,
% 2.09/1.33 setadjoin: $i > $i > $i ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinAx_type,type,
% 2.09/1.33 setadjoinAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinAx,definition,
% 2.09/1.33 ( setadjoinAx
% 2.09/1.33 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.33 <=> ( ( Xy = Xx )
% 2.09/1.33 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(powerset_type,type,
% 2.09/1.33 powerset: $i > $i ).
% 2.09/1.33
% 2.09/1.33 thf(powersetAx_type,type,
% 2.09/1.33 powersetAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(powersetAx,definition,
% 2.09/1.33 ( powersetAx
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.33 <=> ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setunion_type,type,
% 2.09/1.33 setunion: $i > $i ).
% 2.09/1.33
% 2.09/1.33 thf(setunionAx_type,type,
% 2.09/1.33 setunionAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setunionAx,definition,
% 2.09/1.33 ( setunionAx
% 2.09/1.33 = ( ! [A: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ ( setunion @ A ) )
% 2.09/1.33 <=> ? [B: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 & ( in @ B @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(omega_type,type,
% 2.09/1.33 omega: $i ).
% 2.09/1.33
% 2.09/1.33 thf(omega0Ax_type,type,
% 2.09/1.33 omega0Ax: $o ).
% 2.09/1.33
% 2.09/1.33 thf(omega0Ax,definition,
% 2.09/1.33 ( omega0Ax
% 2.09/1.33 = ( in @ emptyset @ omega ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(omegaSAx_type,type,
% 2.09/1.33 omegaSAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(omegaSAx,definition,
% 2.09/1.33 ( omegaSAx
% 2.09/1.33 = ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ omega )
% 2.09/1.33 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(omegaIndAx_type,type,
% 2.09/1.33 omegaIndAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(omegaIndAx,definition,
% 2.09/1.33 ( omegaIndAx
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ( ( in @ emptyset @ A )
% 2.09/1.33 & ! [Xx: $i] :
% 2.09/1.33 ( ( ( in @ Xx @ omega )
% 2.09/1.33 & ( in @ Xx @ A ) )
% 2.09/1.33 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.09/1.33 => ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ omega )
% 2.09/1.33 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(replAx_type,type,
% 2.09/1.33 replAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(replAx,definition,
% 2.09/1.33 ( replAx
% 2.09/1.33 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( exu
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.09/1.33 => ? [B: $i] :
% 2.09/1.33 ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 <=> ? [Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ A )
% 2.09/1.33 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(foundationAx_type,type,
% 2.09/1.33 foundationAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(foundationAx,definition,
% 2.09/1.33 ( foundationAx
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.09/1.33 => ? [B: $i] :
% 2.09/1.33 ( ( in @ B @ A )
% 2.09/1.33 & ~ ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(wellorderingAx_type,type,
% 2.09/1.33 wellorderingAx: $o ).
% 2.09/1.33
% 2.09/1.33 thf(wellorderingAx,definition,
% 2.09/1.33 ( wellorderingAx
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ? [B: $i] :
% 2.09/1.33 ( ! [C: $i] :
% 2.09/1.33 ( ( in @ C @ B )
% 2.09/1.33 => ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ C )
% 2.09/1.33 => ( in @ Xx @ A ) ) )
% 2.09/1.33 & ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( ( in @ Xx @ A )
% 2.09/1.33 & ( in @ Xy @ A ) )
% 2.09/1.33 => ( ! [C: $i] :
% 2.09/1.33 ( ( in @ C @ B )
% 2.09/1.33 => ( ( in @ Xx @ C )
% 2.09/1.33 <=> ( in @ Xy @ C ) ) )
% 2.09/1.33 => ( Xx = Xy ) ) )
% 2.09/1.33 & ! [C: $i,D: $i] :
% 2.09/1.33 ( ( ( in @ C @ B )
% 2.09/1.33 & ( in @ D @ B ) )
% 2.09/1.33 => ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ C )
% 2.09/1.33 => ( in @ Xx @ D ) )
% 2.09/1.33 | ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ D )
% 2.09/1.33 => ( in @ Xx @ C ) ) ) )
% 2.09/1.33 & ! [C: $i] :
% 2.09/1.33 ( ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ C )
% 2.09/1.33 => ( in @ Xx @ A ) )
% 2.09/1.33 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.09/1.33 => ? [D: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ D @ B )
% 2.09/1.33 & ( in @ Xx @ C )
% 2.09/1.33 & ~ ? [Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ D )
% 2.09/1.33 & ( in @ Xy @ C ) )
% 2.09/1.33 & ! [E: $i] :
% 2.09/1.33 ( ( in @ E @ B )
% 2.09/1.33 => ( ! [Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ E )
% 2.09/1.33 => ( in @ Xy @ D ) )
% 2.09/1.33 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(descr_type,type,
% 2.09/1.33 descr: ( $i > $o ) > $i ).
% 2.09/1.33
% 2.09/1.33 thf(descrp_type,type,
% 2.09/1.33 descrp: $o ).
% 2.09/1.33
% 2.09/1.33 thf(descrp,definition,
% 2.09/1.33 ( descrp
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ( Xphi
% 2.09/1.33 @ ( descr
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstr_type,type,
% 2.09/1.33 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrI_type,type,
% 2.09/1.33 dsetconstrI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrI,definition,
% 2.09/1.33 ( dsetconstrI
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( ( Xphi @ Xx )
% 2.09/1.33 => ( in @ Xx
% 2.09/1.33 @ ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrEL_type,type,
% 2.09/1.33 dsetconstrEL: $o ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrEL,definition,
% 2.09/1.33 ( dsetconstrEL
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx
% 2.09/1.33 @ ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.33 => ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrER_type,type,
% 2.09/1.33 dsetconstrER: $o ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstrER,definition,
% 2.09/1.33 ( dsetconstrER
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx
% 2.09/1.33 @ ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.33 => ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuE1_type,type,
% 2.09/1.33 exuE1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuE1,definition,
% 2.09/1.33 ( exuE1
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ? [Xx: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 & ! [Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(prop2set_type,type,
% 2.09/1.33 prop2set: $o > $i ).
% 2.09/1.33
% 2.09/1.33 thf(prop2setE_type,type,
% 2.09/1.33 prop2setE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(prop2setE,definition,
% 2.09/1.33 ( prop2setE
% 2.09/1.33 = ( ! [Xphi: $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.09/1.33 => Xphi ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetE_type,type,
% 2.09/1.33 emptysetE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetE,definition,
% 2.09/1.33 ( emptysetE
% 2.09/1.33 = ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ emptyset )
% 2.09/1.33 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetimpfalse_type,type,
% 2.09/1.33 emptysetimpfalse: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetimpfalse,definition,
% 2.09/1.33 ( emptysetimpfalse
% 2.09/1.33 = ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ emptyset )
% 2.09/1.33 => $false ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notinemptyset_type,type,
% 2.09/1.33 notinemptyset: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notinemptyset,definition,
% 2.09/1.33 ( notinemptyset
% 2.09/1.33 = ( ! [Xx: $i] :
% 2.09/1.33 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuE3e_type,type,
% 2.09/1.33 exuE3e: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuE3e,definition,
% 2.09/1.33 ( exuE3e
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setext_type,type,
% 2.09/1.33 setext: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setext,definition,
% 2.09/1.33 ( setext
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xx @ B ) )
% 2.09/1.33 => ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 => ( in @ Xx @ A ) )
% 2.09/1.33 => ( A = B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyI_type,type,
% 2.09/1.33 emptyI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyI,definition,
% 2.09/1.33 ( emptyI
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ~ ( in @ Xx @ A )
% 2.09/1.33 => ( A = emptyset ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(noeltsimpempty_type,type,
% 2.09/1.33 noeltsimpempty: $o ).
% 2.09/1.33
% 2.09/1.33 thf(noeltsimpempty,definition,
% 2.09/1.33 ( noeltsimpempty
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ~ ( in @ Xx @ A )
% 2.09/1.33 => ( A = emptyset ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setbeta_type,type,
% 2.09/1.33 setbeta: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setbeta,definition,
% 2.09/1.33 ( setbeta
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( ( in @ Xx
% 2.09/1.33 @ ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.33 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(nonempty_type,type,
% 2.09/1.33 nonempty: $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(nonempty,definition,
% 2.09/1.33 ( nonempty
% 2.09/1.33 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyE1_type,type,
% 2.09/1.33 nonemptyE1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyE1,definition,
% 2.09/1.33 ( nonemptyE1
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ( nonempty @ A )
% 2.09/1.33 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyI_type,type,
% 2.09/1.33 nonemptyI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyI,definition,
% 2.09/1.33 ( nonemptyI
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( ( Xphi @ Xx )
% 2.09/1.33 => ( nonempty
% 2.09/1.33 @ ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyI1_type,type,
% 2.09/1.33 nonemptyI1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyI1,definition,
% 2.09/1.33 ( nonemptyI1
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.09/1.33 => ( nonempty @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinIL_type,type,
% 2.09/1.33 setadjoinIL: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinIL,definition,
% 2.09/1.33 ( setadjoinIL
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyinunitempty_type,type,
% 2.09/1.33 emptyinunitempty: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyinunitempty,definition,
% 2.09/1.33 ( emptyinunitempty
% 2.09/1.33 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinIR_type,type,
% 2.09/1.33 setadjoinIR: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinIR,definition,
% 2.09/1.33 ( setadjoinIR
% 2.09/1.33 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ A )
% 2.09/1.33 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinE_type,type,
% 2.09/1.33 setadjoinE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinE,definition,
% 2.09/1.33 ( setadjoinE
% 2.09/1.33 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.33 => ! [Xphi: $o] :
% 2.09/1.33 ( ( ( Xy = Xx )
% 2.09/1.33 => Xphi )
% 2.09/1.33 => ( ( ( in @ Xy @ A )
% 2.09/1.33 => Xphi )
% 2.09/1.33 => Xphi ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinOr_type,type,
% 2.09/1.33 setadjoinOr: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoinOr,definition,
% 2.09/1.33 ( setadjoinOr
% 2.09/1.33 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.33 => ( ( Xy = Xx )
% 2.09/1.33 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setoftrueEq_type,type,
% 2.09/1.33 setoftrueEq: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setoftrueEq,definition,
% 2.09/1.33 ( setoftrueEq
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xx: $i] : $true )
% 2.09/1.33 = A ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(powersetI_type,type,
% 2.09/1.33 powersetI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(powersetI,definition,
% 2.09/1.33 ( powersetI
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 => ( in @ Xx @ A ) )
% 2.09/1.33 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyinPowerset_type,type,
% 2.09/1.33 emptyinPowerset: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyinPowerset,definition,
% 2.09/1.33 ( emptyinPowerset
% 2.09/1.33 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyInPowerset_type,type,
% 2.09/1.33 emptyInPowerset: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyInPowerset,definition,
% 2.09/1.33 ( emptyInPowerset
% 2.09/1.33 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(powersetE_type,type,
% 2.09/1.33 powersetE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(powersetE,definition,
% 2.09/1.33 ( powersetE
% 2.09/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.33 => ( ( in @ Xx @ B )
% 2.09/1.33 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setunionI_type,type,
% 2.09/1.33 setunionI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setunionI,definition,
% 2.09/1.33 ( setunionI
% 2.09/1.33 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 => ( ( in @ B @ A )
% 2.09/1.33 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setunionE_type,type,
% 2.09/1.33 setunionE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setunionE,definition,
% 2.09/1.33 ( setunionE
% 2.09/1.33 = ( ! [A: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ ( setunion @ A ) )
% 2.09/1.33 => ! [Xphi: $o] :
% 2.09/1.33 ( ! [B: $i] :
% 2.09/1.33 ( ( in @ Xx @ B )
% 2.09/1.33 => ( ( in @ B @ A )
% 2.09/1.33 => Xphi ) )
% 2.09/1.33 => Xphi ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subPowSU_type,type,
% 2.09/1.33 subPowSU: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subPowSU,definition,
% 2.09/1.33 ( subPowSU
% 2.09/1.33 = ( ! [A: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuE2_type,type,
% 2.09/1.33 exuE2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuE2,definition,
% 2.09/1.33 ( exuE2
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ? [Xx: $i] :
% 2.09/1.33 ! [Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xy )
% 2.09/1.33 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyImpWitness_type,type,
% 2.09/1.33 nonemptyImpWitness: $o ).
% 2.09/1.33
% 2.09/1.33 thf(nonemptyImpWitness,definition,
% 2.09/1.33 ( nonemptyImpWitness
% 2.09/1.33 = ( ! [A: $i] :
% 2.09/1.33 ( ( nonempty @ A )
% 2.09/1.33 => ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & $true ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(uniqinunit_type,type,
% 2.09/1.33 uniqinunit: $o ).
% 2.09/1.33
% 2.09/1.33 thf(uniqinunit,definition,
% 2.09/1.33 ( uniqinunit
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.09/1.33 => ( Xx = Xy ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notinsingleton_type,type,
% 2.09/1.33 notinsingleton: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notinsingleton,definition,
% 2.09/1.33 ( notinsingleton
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx != Xy )
% 2.09/1.33 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(eqinunit_type,type,
% 2.09/1.33 eqinunit: $o ).
% 2.09/1.33
% 2.09/1.33 thf(eqinunit,definition,
% 2.09/1.33 ( eqinunit
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(singletonsswitch_type,type,
% 2.09/1.33 singletonsswitch: $o ).
% 2.09/1.33
% 2.09/1.33 thf(singletonsswitch,definition,
% 2.09/1.33 ( singletonsswitch
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.09/1.33 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetE_type,type,
% 2.09/1.33 upairsetE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetE,definition,
% 2.09/1.33 ( upairsetE
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.09/1.33 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.09/1.33 => ( ( Xz = Xx )
% 2.09/1.33 | ( Xz = Xy ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetIL_type,type,
% 2.09/1.33 upairsetIL: $o ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetIL,definition,
% 2.09/1.33 ( upairsetIL
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetIR_type,type,
% 2.09/1.33 upairsetIR: $o ).
% 2.09/1.33
% 2.09/1.33 thf(upairsetIR,definition,
% 2.09/1.33 ( upairsetIR
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyE1_type,type,
% 2.09/1.33 emptyE1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyE1,definition,
% 2.09/1.33 ( emptyE1
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ( Xphi @ Xx ) )
% 2.09/1.33 => ( ( ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 = emptyset )
% 2.09/1.33 => $false ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(vacuousDall_type,type,
% 2.09/1.33 vacuousDall: $o ).
% 2.09/1.33
% 2.09/1.33 thf(vacuousDall,definition,
% 2.09/1.33 ( vacuousDall
% 2.09/1.33 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ emptyset )
% 2.09/1.33 => ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan1_type,type,
% 2.09/1.33 quantDeMorgan1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan1,definition,
% 2.09/1.33 ( quantDeMorgan1
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ~ ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( Xphi @ Xx ) )
% 2.09/1.33 => ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan2_type,type,
% 2.09/1.33 quantDeMorgan2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan2,definition,
% 2.09/1.33 ( quantDeMorgan2
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ~ ( Xphi @ Xx ) )
% 2.09/1.33 => ~ ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan3_type,type,
% 2.09/1.33 quantDeMorgan3: $o ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan3,definition,
% 2.09/1.33 ( quantDeMorgan3
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ~ ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ( Xphi @ Xx ) )
% 2.09/1.33 => ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan4_type,type,
% 2.09/1.33 quantDeMorgan4: $o ).
% 2.09/1.33
% 2.09/1.33 thf(quantDeMorgan4,definition,
% 2.09/1.33 ( quantDeMorgan4
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ~ ( Xphi @ Xx ) )
% 2.09/1.33 => ~ ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(prop2setI_type,type,
% 2.09/1.33 prop2setI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(prop2setI,definition,
% 2.09/1.33 ( prop2setI
% 2.09/1.33 = ( ! [Xphi: $o] :
% 2.09/1.33 ( Xphi
% 2.09/1.33 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(set2prop_type,type,
% 2.09/1.33 set2prop: $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(prop2set2propI_type,type,
% 2.09/1.33 prop2set2propI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(prop2set2propI,definition,
% 2.09/1.33 ( prop2set2propI
% 2.09/1.33 = ( ! [Xphi: $o] :
% 2.09/1.33 ( Xphi
% 2.09/1.33 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notdexE_type,type,
% 2.09/1.33 notdexE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notdexE,definition,
% 2.09/1.33 ( notdexE
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ~ ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ( Xphi @ Xx ) )
% 2.09/1.33 => ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notdallE_type,type,
% 2.09/1.33 notdallE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notdallE,definition,
% 2.09/1.33 ( notdallE
% 2.09/1.33 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.33 ( ~ ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( Xphi @ Xx ) )
% 2.09/1.33 => ? [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuI1_type,type,
% 2.09/1.33 exuI1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuI1,definition,
% 2.09/1.33 ( exuI1
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ? [Xx: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 & ! [Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) )
% 2.09/1.33 => ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuI3_type,type,
% 2.09/1.33 exuI3: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuI3,definition,
% 2.09/1.33 ( exuI3
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.09/1.33 => ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 => ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) )
% 2.09/1.33 => ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuI2_type,type,
% 2.09/1.33 exuI2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuI2,definition,
% 2.09/1.33 ( exuI2
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ? [Xx: $i] :
% 2.09/1.33 ! [Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xy )
% 2.09/1.33 <=> ( Xy = Xx ) )
% 2.09/1.33 => ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(inCongP_type,type,
% 2.09/1.33 inCongP: $o ).
% 2.09/1.33
% 2.09/1.33 thf(inCongP,definition,
% 2.09/1.33 ( inCongP
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(in__Cong_type,type,
% 2.09/1.33 in__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(in__Cong,definition,
% 2.09/1.33 ( in__Cong
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ( ( in @ Xx @ A )
% 2.09/1.33 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuE3u_type,type,
% 2.09/1.33 exuE3u: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuE3u,definition,
% 2.09/1.33 ( exuE3u
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 => ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exu__Cong_type,type,
% 2.09/1.33 exu__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exu__Cong,definition,
% 2.09/1.33 ( exu__Cong
% 2.09/1.33 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.33 ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ( ( Xphi @ Xx )
% 2.09/1.33 <=> ( Xpsi @ Xy ) ) )
% 2.09/1.33 => ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 <=> ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptyset__Cong_type,type,
% 2.09/1.33 emptyset__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptyset__Cong,definition,
% 2.09/1.33 ( emptyset__Cong
% 2.09/1.33 = ( emptyset = emptyset ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoin__Cong_type,type,
% 2.09/1.33 setadjoin__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setadjoin__Cong,definition,
% 2.09/1.33 ( setadjoin__Cong
% 2.09/1.33 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ! [Xz: $i,Xu: $i] :
% 2.09/1.33 ( ( Xz = Xu )
% 2.09/1.33 => ( ( setadjoin @ Xx @ Xz )
% 2.09/1.33 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(powerset__Cong_type,type,
% 2.09/1.33 powerset__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(powerset__Cong,definition,
% 2.09/1.33 ( powerset__Cong
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ( ( powerset @ A )
% 2.09/1.33 = ( powerset @ B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(setunion__Cong_type,type,
% 2.09/1.33 setunion__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(setunion__Cong,definition,
% 2.09/1.33 ( setunion__Cong
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ( ( setunion @ A )
% 2.09/1.33 = ( setunion @ B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(omega__Cong_type,type,
% 2.09/1.33 omega__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(omega__Cong,definition,
% 2.09/1.33 ( omega__Cong
% 2.09/1.33 = ( omega = omega ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(exuEu_type,type,
% 2.09/1.33 exuEu: $o ).
% 2.09/1.33
% 2.09/1.33 thf(exuEu,definition,
% 2.09/1.33 ( exuEu
% 2.09/1.33 = ( ! [Xphi: $i > $o] :
% 2.09/1.33 ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xphi @ Xx )
% 2.09/1.33 => ( ( Xphi @ Xy )
% 2.09/1.33 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(descr__Cong_type,type,
% 2.09/1.33 descr__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(descr__Cong,definition,
% 2.09/1.33 ( descr__Cong
% 2.09/1.33 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.33 ( ! [Xx: $i,Xy: $i] :
% 2.09/1.33 ( ( Xx = Xy )
% 2.09/1.33 => ( ( Xphi @ Xx )
% 2.09/1.33 <=> ( Xpsi @ Xy ) ) )
% 2.09/1.33 => ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 => ( ( exu
% 2.09/1.33 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.09/1.33 => ( ( descr
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 = ( descr
% 2.09/1.33 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstr__Cong_type,type,
% 2.09/1.33 dsetconstr__Cong: $o ).
% 2.09/1.33
% 2.09/1.33 thf(dsetconstr__Cong,definition,
% 2.09/1.33 ( dsetconstr__Cong
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ! [Xy: $i] :
% 2.09/1.33 ( ( in @ Xy @ B )
% 2.09/1.33 => ( ( Xx = Xy )
% 2.09/1.33 => ( ( Xphi @ Xx )
% 2.09/1.33 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.09/1.33 => ( ( dsetconstr @ A
% 2.09/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.33 = ( dsetconstr @ B
% 2.09/1.33 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subset_type,type,
% 2.09/1.33 subset: $i > $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(disjoint_type,type,
% 2.09/1.33 disjoint: $i > $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(setsmeet_type,type,
% 2.09/1.33 setsmeet: $i > $i > $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetI1_type,type,
% 2.09/1.33 subsetI1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetI1,definition,
% 2.09/1.33 ( subsetI1
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xx @ B ) )
% 2.09/1.33 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(eqimpsubset2_type,type,
% 2.09/1.33 eqimpsubset2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(eqimpsubset2,definition,
% 2.09/1.33 ( eqimpsubset2
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ( subset @ B @ A ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(eqimpsubset1_type,type,
% 2.09/1.33 eqimpsubset1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(eqimpsubset1,definition,
% 2.09/1.33 ( eqimpsubset1
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ( A = B )
% 2.09/1.33 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subsetI2_type,type,
% 2.09/1.33 subsetI2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetI2,definition,
% 2.09/1.33 ( subsetI2
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ! [Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xx @ B ) )
% 2.09/1.33 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetsubset_type,type,
% 2.09/1.33 emptysetsubset: $o ).
% 2.09/1.33
% 2.09/1.33 thf(emptysetsubset,definition,
% 2.09/1.33 ( emptysetsubset
% 2.09/1.33 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subsetE_type,type,
% 2.09/1.33 subsetE: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetE,definition,
% 2.09/1.33 ( subsetE
% 2.09/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.33 ( ( subset @ A @ B )
% 2.09/1.33 => ( ( in @ Xx @ A )
% 2.09/1.33 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subsetE2_type,type,
% 2.09/1.33 subsetE2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetE2,definition,
% 2.09/1.33 ( subsetE2
% 2.09/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.33 ( ( subset @ A @ B )
% 2.09/1.33 => ( ~ ( in @ Xx @ B )
% 2.09/1.33 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notsubsetI_type,type,
% 2.09/1.33 notsubsetI: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notsubsetI,definition,
% 2.09/1.33 ( notsubsetI
% 2.09/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( ~ ( in @ Xx @ B )
% 2.09/1.33 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notequalI1_type,type,
% 2.09/1.33 notequalI1: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notequalI1,definition,
% 2.09/1.33 ( notequalI1
% 2.09/1.33 = ( ! [A: $i,B: $i] :
% 2.09/1.33 ( ~ ( subset @ A @ B )
% 2.09/1.33 => ( A != B ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(notequalI2_type,type,
% 2.09/1.33 notequalI2: $o ).
% 2.09/1.33
% 2.09/1.33 thf(notequalI2,definition,
% 2.09/1.33 ( notequalI2
% 2.09/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.33 ( ( in @ Xx @ A )
% 2.09/1.33 => ( ~ ( in @ Xx @ B )
% 2.09/1.33 => ( A != B ) ) ) ) ) ).
% 2.09/1.33
% 2.09/1.33 thf(subsetRefl_type,type,
% 2.09/1.33 subsetRefl: $o ).
% 2.09/1.33
% 2.09/1.33 thf(subsetRefl,definition,
% 2.09/1.33 ( subsetRefl
% 2.09/1.33 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(subsetTrans_type,type,
% 2.09/1.34 subsetTrans: $o ).
% 2.09/1.34
% 2.09/1.34 thf(subsetTrans,definition,
% 2.09/1.34 ( subsetTrans
% 2.09/1.34 = ( ! [A: $i,B: $i,C: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( ( subset @ B @ C )
% 2.09/1.34 => ( subset @ A @ C ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setadjoinSub_type,type,
% 2.09/1.34 setadjoinSub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setadjoinSub,definition,
% 2.09/1.34 ( setadjoinSub
% 2.09/1.34 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setadjoinSub2_type,type,
% 2.09/1.34 setadjoinSub2: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setadjoinSub2,definition,
% 2.09/1.34 ( setadjoinSub2
% 2.09/1.34 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(subset2powerset_type,type,
% 2.09/1.34 subset2powerset: $o ).
% 2.09/1.34
% 2.09/1.34 thf(subset2powerset,definition,
% 2.09/1.34 ( subset2powerset
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setextsub_type,type,
% 2.09/1.34 setextsub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setextsub,definition,
% 2.09/1.34 ( setextsub
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( ( subset @ B @ A )
% 2.09/1.34 => ( A = B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(subsetemptysetimpeq_type,type,
% 2.09/1.34 subsetemptysetimpeq: $o ).
% 2.09/1.34
% 2.09/1.34 thf(subsetemptysetimpeq,definition,
% 2.09/1.34 ( subsetemptysetimpeq
% 2.09/1.34 = ( ! [A: $i] :
% 2.09/1.34 ( ( subset @ A @ emptyset )
% 2.09/1.34 => ( A = emptyset ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(powersetI1_type,type,
% 2.09/1.34 powersetI1: $o ).
% 2.09/1.34
% 2.09/1.34 thf(powersetI1,definition,
% 2.09/1.34 ( powersetI1
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ B @ A )
% 2.09/1.34 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(powersetE1_type,type,
% 2.09/1.34 powersetE1: $o ).
% 2.09/1.34
% 2.09/1.34 thf(powersetE1,definition,
% 2.09/1.34 ( powersetE1
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.34 => ( subset @ B @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(inPowerset_type,type,
% 2.09/1.34 inPowerset: $o ).
% 2.09/1.34
% 2.09/1.34 thf(inPowerset,definition,
% 2.09/1.34 ( inPowerset
% 2.09/1.34 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(powersetsubset_type,type,
% 2.09/1.34 powersetsubset: $o ).
% 2.09/1.34
% 2.09/1.34 thf(powersetsubset,definition,
% 2.09/1.34 ( powersetsubset
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(sepInPowerset_type,type,
% 2.09/1.34 sepInPowerset: $o ).
% 2.09/1.34
% 2.09/1.34 thf(sepInPowerset,definition,
% 2.09/1.34 ( sepInPowerset
% 2.09/1.34 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.34 ( in
% 2.09/1.34 @ ( dsetconstr @ A
% 2.09/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.34 @ ( powerset @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(sepSubset_type,type,
% 2.09/1.34 sepSubset: $o ).
% 2.09/1.34
% 2.09/1.34 thf(sepSubset,definition,
% 2.09/1.34 ( sepSubset
% 2.09/1.34 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.34 ( subset
% 2.09/1.34 @ ( dsetconstr @ A
% 2.09/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.34 @ A ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunion_type,type,
% 2.09/1.34 binunion: $i > $i > $i ).
% 2.09/1.34
% 2.09/1.34 thf(binunionIL_type,type,
% 2.09/1.34 binunionIL: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionIL,definition,
% 2.09/1.34 ( binunionIL
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ A )
% 2.09/1.34 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(upairset2IR_type,type,
% 2.09/1.34 upairset2IR: $o ).
% 2.09/1.34
% 2.09/1.34 thf(upairset2IR,definition,
% 2.09/1.34 ( upairset2IR
% 2.09/1.34 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunionIR_type,type,
% 2.09/1.34 binunionIR: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionIR,definition,
% 2.09/1.34 ( binunionIR
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ B )
% 2.09/1.34 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunionEcases_type,type,
% 2.09/1.34 binunionEcases: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionEcases,definition,
% 2.09/1.34 ( binunionEcases
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.09/1.34 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.09/1.34 => ( ( ( in @ Xx @ A )
% 2.09/1.34 => Xphi )
% 2.09/1.34 => ( ( ( in @ Xx @ B )
% 2.09/1.34 => Xphi )
% 2.09/1.34 => Xphi ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunionE_type,type,
% 2.09/1.34 binunionE: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionE,definition,
% 2.09/1.34 ( binunionE
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.09/1.34 => ( ( in @ Xx @ A )
% 2.09/1.34 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunionLsub_type,type,
% 2.09/1.34 binunionLsub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionLsub,definition,
% 2.09/1.34 ( binunionLsub
% 2.09/1.34 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binunionRsub_type,type,
% 2.09/1.34 binunionRsub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binunionRsub,definition,
% 2.09/1.34 ( binunionRsub
% 2.09/1.34 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersect_type,type,
% 2.09/1.34 binintersect: $i > $i > $i ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectI_type,type,
% 2.09/1.34 binintersectI: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectI,definition,
% 2.09/1.34 ( binintersectI
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ A )
% 2.09/1.34 => ( ( in @ Xx @ B )
% 2.09/1.34 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset5_type,type,
% 2.09/1.34 binintersectSubset5: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset5,definition,
% 2.09/1.34 ( binintersectSubset5
% 2.09/1.34 = ( ! [A: $i,B: $i,C: $i] :
% 2.09/1.34 ( ( subset @ C @ A )
% 2.09/1.34 => ( ( subset @ C @ B )
% 2.09/1.34 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectEL_type,type,
% 2.09/1.34 binintersectEL: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectEL,definition,
% 2.09/1.34 ( binintersectEL
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.09/1.34 => ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectLsub_type,type,
% 2.09/1.34 binintersectLsub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectLsub,definition,
% 2.09/1.34 ( binintersectLsub
% 2.09/1.34 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset2_type,type,
% 2.09/1.34 binintersectSubset2: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset2,definition,
% 2.09/1.34 ( binintersectSubset2
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( ( binintersect @ A @ B )
% 2.09/1.34 = A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset3_type,type,
% 2.09/1.34 binintersectSubset3: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset3,definition,
% 2.09/1.34 ( binintersectSubset3
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( ( binintersect @ A @ B )
% 2.09/1.34 = B )
% 2.09/1.34 => ( subset @ B @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectER_type,type,
% 2.09/1.34 binintersectER: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectER,definition,
% 2.09/1.34 ( binintersectER
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.09/1.34 => ( in @ Xx @ B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(disjointsetsI1_type,type,
% 2.09/1.34 disjointsetsI1: $o ).
% 2.09/1.34
% 2.09/1.34 thf(disjointsetsI1,definition,
% 2.09/1.34 ( disjointsetsI1
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ~ ? [Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ A )
% 2.09/1.34 & ( in @ Xx @ B ) )
% 2.09/1.34 => ( ( binintersect @ A @ B )
% 2.09/1.34 = emptyset ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectRsub_type,type,
% 2.09/1.34 binintersectRsub: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectRsub,definition,
% 2.09/1.34 ( binintersectRsub
% 2.09/1.34 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset4_type,type,
% 2.09/1.34 binintersectSubset4: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset4,definition,
% 2.09/1.34 ( binintersectSubset4
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ B @ A )
% 2.09/1.34 => ( ( binintersect @ A @ B )
% 2.09/1.34 = B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset1_type,type,
% 2.09/1.34 binintersectSubset1: $o ).
% 2.09/1.34
% 2.09/1.34 thf(binintersectSubset1,definition,
% 2.09/1.34 ( binintersectSubset1
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( ( binintersect @ A @ B )
% 2.09/1.34 = A )
% 2.09/1.34 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(bs114d_type,type,
% 2.09/1.34 bs114d: $o ).
% 2.09/1.34
% 2.09/1.34 thf(bs114d,definition,
% 2.09/1.34 ( bs114d
% 2.09/1.34 = ( ! [A: $i,B: $i,C: $i] :
% 2.09/1.34 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.09/1.34 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(regular_type,type,
% 2.09/1.34 regular: $i > $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminus_type,type,
% 2.09/1.34 setminus: $i > $i > $i ).
% 2.09/1.34
% 2.09/1.34 thf(setminusI_type,type,
% 2.09/1.34 setminusI: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusI,definition,
% 2.09/1.34 ( setminusI
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ A )
% 2.09/1.34 => ( ~ ( in @ Xx @ B )
% 2.09/1.34 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusEL_type,type,
% 2.09/1.34 setminusEL: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusEL,definition,
% 2.09/1.34 ( setminusEL
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.09/1.34 => ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusER_type,type,
% 2.09/1.34 setminusER: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusER,definition,
% 2.09/1.34 ( setminusER
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.09/1.34 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusSubset2_type,type,
% 2.09/1.34 setminusSubset2: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusSubset2,definition,
% 2.09/1.34 ( setminusSubset2
% 2.09/1.34 = ( ! [A: $i,B: $i] :
% 2.09/1.34 ( ( subset @ A @ B )
% 2.09/1.34 => ( ( setminus @ A @ B )
% 2.09/1.34 = emptyset ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusERneg_type,type,
% 2.09/1.34 setminusERneg: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusERneg,definition,
% 2.09/1.34 ( setminusERneg
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.09/1.34 => ( ( in @ Xx @ A )
% 2.09/1.34 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusELneg_type,type,
% 2.09/1.34 setminusELneg: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusELneg,definition,
% 2.09/1.34 ( setminusELneg
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.09/1.34 => ( ~ ( in @ Xx @ B )
% 2.09/1.34 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusILneg_type,type,
% 2.09/1.34 setminusILneg: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusILneg,definition,
% 2.09/1.34 ( setminusILneg
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ~ ( in @ Xx @ A )
% 2.09/1.34 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusIRneg_type,type,
% 2.09/1.34 setminusIRneg: $o ).
% 2.09/1.34
% 2.09/1.34 thf(setminusIRneg,definition,
% 2.09/1.34 ( setminusIRneg
% 2.09/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.34 ( ( in @ Xx @ B )
% 2.09/1.34 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.09/1.34
% 2.09/1.34 thf(setminusLsub,conjecture,
% 2.09/1.34 ( setextAx
% 2.09/1.34 => ( emptysetAx
% 2.09/1.34 => ( setadjoinAx
% 2.09/1.34 => ( powersetAx
% 2.09/1.34 => ( setunionAx
% 2.09/1.34 => ( omega0Ax
% 2.09/1.34 => ( omegaSAx
% 2.09/1.34 => ( omegaIndAx
% 2.09/1.34 => ( replAx
% 2.09/1.34 => ( foundationAx
% 2.09/1.34 => ( wellorderingAx
% 2.09/1.34 => ( descrp
% 2.09/1.34 => ( dsetconstrI
% 2.09/1.34 => ( dsetconstrEL
% 2.09/1.34 => ( dsetconstrER
% 2.09/1.34 => ( exuE1
% 2.09/1.34 => ( prop2setE
% 2.09/1.34 => ( emptysetE
% 2.09/1.34 => ( emptysetimpfalse
% 2.09/1.34 => ( notinemptyset
% 2.09/1.34 => ( exuE3e
% 2.09/1.34 => ( setext
% 2.09/1.34 => ( emptyI
% 2.09/1.34 => ( noeltsimpempty
% 2.09/1.34 => ( setbeta
% 2.09/1.34 => ( nonemptyE1
% 2.09/1.34 => ( nonemptyI
% 2.09/1.34 => ( nonemptyI1
% 2.09/1.34 => ( setadjoinIL
% 2.09/1.34 => ( emptyinunitempty
% 2.09/1.34 => ( setadjoinIR
% 2.09/1.34 => ( setadjoinE
% 2.09/1.34 => ( setadjoinOr
% 2.09/1.34 => ( setoftrueEq
% 2.09/1.34 => ( powersetI
% 2.09/1.34 => ( emptyinPowerset
% 2.09/1.34 => ( emptyInPowerset
% 2.09/1.34 => ( powersetE
% 2.09/1.34 => ( setunionI
% 2.09/1.34 => ( setunionE
% 2.09/1.34 => ( subPowSU
% 2.09/1.34 => ( exuE2
% 2.09/1.34 => ( nonemptyImpWitness
% 2.09/1.34 => ( uniqinunit
% 2.09/1.34 => ( notinsingleton
% 2.09/1.34 => ( eqinunit
% 2.09/1.34 => ( singletonsswitch
% 2.09/1.34 => ( upairsetE
% 2.09/1.34 => ( upairsetIL
% 2.09/1.34 => ( upairsetIR
% 2.09/1.34 => ( emptyE1
% 2.09/1.34 => ( vacuousDall
% 2.09/1.34 => ( quantDeMorgan1
% 2.09/1.34 => ( quantDeMorgan2
% 2.09/1.34 => ( quantDeMorgan3
% 2.09/1.34 => ( quantDeMorgan4
% 2.09/1.34 => ( prop2setI
% 2.09/1.34 => ( prop2set2propI
% 2.09/1.34 => ( notdexE
% 2.09/1.34 => ( notdallE
% 2.09/1.34 => ( exuI1
% 2.09/1.34 => ( exuI3
% 2.09/1.34 => ( exuI2
% 2.09/1.34 => ( inCongP
% 2.09/1.34 => ( in__Cong
% 2.09/1.34 => ( exuE3u
% 2.09/1.34 => ( exu__Cong
% 2.09/1.34 => ( emptyset__Cong
% 2.09/1.34 => ( setadjoin__Cong
% 2.09/1.34 => ( powerset__Cong
% 2.09/1.34 => ( setunion__Cong
% 2.09/1.34 => ( omega__Cong
% 2.09/1.34 => ( exuEu
% 2.09/1.34 => ( descr__Cong
% 2.09/1.34 => ( dsetconstr__Cong
% 2.09/1.34 => ( subsetI1
% 2.09/1.34 => ( eqimpsubset2
% 2.09/1.34 => ( eqimpsubset1
% 2.09/1.34 => ( subsetI2
% 2.09/1.34 => ( emptysetsubset
% 2.09/1.34 => ( subsetE
% 2.09/1.34 => ( subsetE2
% 2.09/1.34 => ( notsubsetI
% 2.09/1.34 => ( notequalI1
% 2.09/1.34 => ( notequalI2
% 2.09/1.34 => ( subsetRefl
% 2.09/1.34 => ( subsetTrans
% 2.09/1.34 => ( setadjoinSub
% 2.09/1.34 => ( setadjoinSub2
% 2.09/1.34 => ( subset2powerset
% 2.09/1.34 => ( setextsub
% 2.09/1.34 => ( subsetemptysetimpeq
% 2.09/1.34 => ( powersetI1
% 2.09/1.34 => ( powersetE1
% 2.09/1.34 => ( inPowerset
% 2.09/1.34 => ( powersetsubset
% 2.09/1.34 => ( sepInPowerset
% 2.09/1.34 => ( sepSubset
% 2.09/1.34 => ( binunionIL
% 2.09/1.34 => ( upairset2IR
% 2.09/1.34 => ( binunionIR
% 2.09/1.34 => ( binunionEcases
% 2.09/1.34 => ( binunionE
% 2.09/1.34 => ( binunionLsub
% 2.09/1.34 => ( binunionRsub
% 2.09/1.34 => ( binintersectI
% 2.09/1.34 => ( binintersectSubset5
% 2.09/1.34 => ( binintersectEL
% 2.09/1.34 => ( binintersectLsub
% 2.09/1.34 => ( binintersectSubset2
% 2.09/1.34 => ( binintersectSubset3
% 2.09/1.34 => ( binintersectER
% 2.09/1.34 => ( disjointsetsI1
% 2.09/1.34 => ( binintersectRsub
% 2.09/1.34 => ( binintersectSubset4
% 2.09/1.34 => ( binintersectSubset1
% 2.09/1.34 => ( bs114d
% 2.09/1.34 => ( setminusI
% 2.09/1.34 => ( setminusEL
% 2.09/1.34 => ( setminusER
% 2.09/1.34 => ( setminusSubset2
% 2.09/1.34 => ( setminusERneg
% 2.09/1.34 => ( setminusELneg
% 2.09/1.34 => ( setminusILneg
% 2.09/1.34 => ( setminusIRneg
% 2.09/1.34 => ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.09/1.34 ------------------------
% 2.09/1.35 % (15085)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/18Mi)
% 2.09/1.35 % (15083)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_14910 for (2999ds/2Mi)
% 2.09/1.35 % (15082)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/2Mi)
% 2.09/1.35 % (15079)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/183Mi)
% 2.09/1.35 % (15080)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_14910 for (2999ds/4Mi)
% 2.09/1.35 % (15081)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_14910 for (2999ds/27Mi)
% 2.09/1.35 % (15082)Instruction limit reached!
% 2.09/1.35 % (15082)------------------------------
% 2.09/1.35 % (15082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.35 % (15082)Termination reason: Unknown
% 2.09/1.35 % (15082)Termination phase: shuffling
% 2.09/1.35
% 2.09/1.35 % (15082)Memory used [KB]: 1151
% 2.09/1.35 % (15082)Time elapsed: 0.002 s
% 2.09/1.35 % (15082)Instructions burned: 2 (million)
% 2.09/1.35 % (15082)------------------------------
% 2.09/1.35 % (15082)------------------------------
% 2.09/1.35 % (15083)Instruction limit reached!
% 2.09/1.35 % (15083)------------------------------
% 2.09/1.35 % (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.35 % (15083)Termination reason: Unknown
% 2.09/1.35 % (15083)Termination phase: shuffling
% 2.09/1.35
% 2.09/1.35 % (15083)Memory used [KB]: 1151
% 2.09/1.35 % (15083)Time elapsed: 0.002 s
% 2.09/1.35 % (15083)Instructions burned: 2 (million)
% 2.09/1.35 % (15083)------------------------------
% 2.09/1.35 % (15083)------------------------------
% 2.09/1.35 % (15080)Instruction limit reached!
% 2.09/1.35 % (15080)------------------------------
% 2.09/1.35 % (15080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.35 % (15080)Termination reason: Unknown
% 2.09/1.35 % (15080)Termination phase: shuffling
% 2.09/1.35
% 2.09/1.35 % (15080)Memory used [KB]: 1279
% 2.09/1.35 % (15080)Time elapsed: 0.003 s
% 2.09/1.35 % (15080)Instructions burned: 5 (million)
% 2.09/1.35 % (15080)------------------------------
% 2.09/1.35 % (15080)------------------------------
% 2.09/1.36 % (15085)Instruction limit reached!
% 2.09/1.36 % (15085)------------------------------
% 2.09/1.36 % (15085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.36 % (15085)Termination reason: Unknown
% 2.09/1.36 % (15085)Termination phase: Preprocessing 3
% 2.09/1.36
% 2.09/1.36 % (15085)Memory used [KB]: 1535
% 2.09/1.36 % (15085)Time elapsed: 0.007 s
% 2.09/1.36 % (15085)Instructions burned: 18 (million)
% 2.09/1.36 % (15085)------------------------------
% 2.09/1.36 % (15085)------------------------------
% 2.09/1.36 % (15081)Instruction limit reached!
% 2.09/1.36 % (15081)------------------------------
% 2.09/1.36 % (15081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.36 % (15081)Termination reason: Unknown
% 2.09/1.36 % (15081)Termination phase: Property scanning
% 2.09/1.36
% 2.09/1.36 % (15081)Memory used [KB]: 1535
% 2.09/1.36 % (15081)Time elapsed: 0.009 s
% 2.09/1.36 % (15081)Instructions burned: 28 (million)
% 2.09/1.36 % (15081)------------------------------
% 2.09/1.36 % (15081)------------------------------
% 2.09/1.36 % (15084)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_14910 for (2999ds/275Mi)
% 2.09/1.36 % (15088)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/3Mi)
% 2.09/1.36 % (15089)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_14910 for (2999ds/37Mi)
% 2.09/1.36 % (15088)Instruction limit reached!
% 2.09/1.36 % (15088)------------------------------
% 2.09/1.36 % (15088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.36 % (15088)Termination reason: Unknown
% 2.09/1.36 % (15090)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_14910 for (2999ds/15Mi)
% 2.09/1.36 % (15088)Termination phase: shuffling
% 2.09/1.36
% 2.09/1.36 % (15088)Memory used [KB]: 1151
% 2.09/1.36 % (15088)Time elapsed: 0.002 s
% 2.09/1.36 % (15088)Instructions burned: 3 (million)
% 2.09/1.36 % (15088)------------------------------
% 2.09/1.36 % (15088)------------------------------
% 2.09/1.36 % (15091)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_14910 for (2999ds/3Mi)
% 2.09/1.37 % (15090)Instruction limit reached!
% 2.09/1.37 % (15090)------------------------------
% 2.09/1.37 % (15090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.37 % (15090)Termination reason: Unknown
% 2.09/1.37 % (15090)Termination phase: shuffling
% 2.09/1.37
% 2.09/1.37 % (15090)Memory used [KB]: 1407
% 2.09/1.37 % (15090)Time elapsed: 0.006 s
% 2.09/1.37 % (15090)Instructions burned: 16 (million)
% 2.09/1.37 % (15090)------------------------------
% 2.09/1.37 % (15090)------------------------------
% 2.09/1.37 % (15091)Instruction limit reached!
% 2.09/1.37 % (15091)------------------------------
% 2.09/1.37 % (15091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.37 % (15091)Termination reason: Unknown
% 2.09/1.37 % (15091)Termination phase: shuffling
% 2.09/1.37
% 2.09/1.37 % (15091)Memory used [KB]: 1151
% 2.09/1.37 % (15091)Time elapsed: 0.002 s
% 2.09/1.37 % (15091)Instructions burned: 3 (million)
% 2.09/1.37 % (15091)------------------------------
% 2.09/1.37 % (15091)------------------------------
% 2.09/1.37 % (15092)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_14910 for (2999ds/1041Mi)
% 2.09/1.37 % (15089)Instruction limit reached!
% 2.09/1.37 % (15089)------------------------------
% 2.09/1.37 % (15089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.37 % (15089)Termination reason: Unknown
% 2.09/1.37 % (15089)Termination phase: Property scanning
% 2.09/1.37
% 2.09/1.37 % (15089)Memory used [KB]: 1663
% 2.09/1.37 % (15089)Time elapsed: 0.011 s
% 2.09/1.37 % (15089)Instructions burned: 39 (million)
% 2.09/1.37 % (15089)------------------------------
% 2.09/1.37 % (15089)------------------------------
% 2.09/1.37 % (15093)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/7Mi)
% 2.09/1.37 % (15093)Instruction limit reached!
% 2.09/1.37 % (15093)------------------------------
% 2.09/1.37 % (15093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.37 % (15093)Termination reason: Unknown
% 2.09/1.37 % (15093)Termination phase: shuffling
% 2.09/1.37
% 2.09/1.37 % (15093)Memory used [KB]: 1279
% 2.09/1.37 % (15093)Time elapsed: 0.003 s
% 2.09/1.37 % (15093)Instructions burned: 7 (million)
% 2.09/1.37 % (15093)------------------------------
% 2.09/1.37 % (15093)------------------------------
% 2.09/1.37 % (15099)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/16Mi)
% 2.09/1.37 % (15100)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_14910 for (2999ds/3Mi)
% 2.09/1.38 % (15100)Instruction limit reached!
% 2.09/1.38 % (15100)------------------------------
% 2.09/1.38 % (15100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.38 % (15100)Termination reason: Unknown
% 2.09/1.38 % (15100)Termination phase: shuffling
% 2.09/1.38
% 2.09/1.38 % (15100)Memory used [KB]: 1279
% 2.09/1.38 % (15100)Time elapsed: 0.002 s
% 2.09/1.38 % (15100)Instructions burned: 3 (million)
% 2.09/1.38 % (15100)------------------------------
% 2.09/1.38 % (15100)------------------------------
% 2.09/1.38 % (15106)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_14910 for (2999ds/3Mi)
% 2.09/1.38 % (15099)Instruction limit reached!
% 2.09/1.38 % (15099)------------------------------
% 2.09/1.38 % (15099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.38 % (15099)Termination reason: Unknown
% 2.09/1.38 % (15099)Termination phase: shuffling
% 2.09/1.38
% 2.09/1.38 % (15099)Memory used [KB]: 1535
% 2.09/1.38 % (15099)Time elapsed: 0.006 s
% 2.09/1.38 % (15099)Instructions burned: 18 (million)
% 2.09/1.38 % (15099)------------------------------
% 2.09/1.38 % (15099)------------------------------
% 2.09/1.38 % (15106)Instruction limit reached!
% 2.09/1.38 % (15106)------------------------------
% 2.09/1.38 % (15106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.38 % (15106)Termination reason: Unknown
% 2.09/1.38 % (15106)Termination phase: shuffling
% 2.09/1.38
% 2.09/1.38 % (15106)Memory used [KB]: 1151
% 2.09/1.38 % (15106)Time elapsed: 0.002 s
% 2.09/1.38 % (15106)Instructions burned: 4 (million)
% 2.09/1.38 % (15106)------------------------------
% 2.09/1.38 % (15106)------------------------------
% 2.09/1.38 % (15108)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/7Mi)
% 2.09/1.38 % (15108)Instruction limit reached!
% 2.09/1.38 % (15108)------------------------------
% 2.09/1.38 % (15108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.38 % (15108)Termination reason: Unknown
% 2.09/1.38 % (15108)Termination phase: shuffling
% 2.09/1.38
% 2.09/1.38 % (15108)Memory used [KB]: 1279
% 2.09/1.38 % (15108)Time elapsed: 0.003 s
% 2.09/1.38 % (15108)Instructions burned: 8 (million)
% 2.09/1.38 % (15108)------------------------------
% 2.09/1.38 % (15108)------------------------------
% 2.09/1.39 % (15110)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/3Mi)
% 2.09/1.39 % (15110)Instruction limit reached!
% 2.09/1.39 % (15110)------------------------------
% 2.09/1.39 % (15110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.39 % (15110)Termination reason: Unknown
% 2.09/1.39 % (15110)Termination phase: shuffling
% 2.09/1.39
% 2.09/1.39 % (15110)Memory used [KB]: 1151
% 2.09/1.39 % (15110)Time elapsed: 0.002 s
% 2.09/1.39 % (15110)Instructions burned: 3 (million)
% 2.09/1.39 % (15110)------------------------------
% 2.09/1.39 % (15110)------------------------------
% 2.09/1.39 % (15113)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/4Mi)
% 2.09/1.39 % (15114)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/18Mi)
% 2.09/1.39 % (15113)Instruction limit reached!
% 2.09/1.39 % (15113)------------------------------
% 2.09/1.39 % (15113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.39 % (15113)Termination reason: Unknown
% 2.09/1.39 % (15113)Termination phase: shuffling
% 2.09/1.39
% 2.09/1.39 % (15113)Memory used [KB]: 1279
% 2.09/1.39 % (15113)Time elapsed: 0.003 s
% 2.09/1.39 % (15113)Instructions burned: 7 (million)
% 2.09/1.39 % (15113)------------------------------
% 2.09/1.39 % (15113)------------------------------
% 2.09/1.39 % (15117)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/710Mi)
% 2.09/1.39 % (15114)Instruction limit reached!
% 2.09/1.39 % (15114)------------------------------
% 2.09/1.39 % (15114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.39 % (15114)Termination reason: Unknown
% 2.09/1.39 % (15114)Termination phase: shuffling
% 2.09/1.39
% 2.09/1.39 % (15114)Memory used [KB]: 1535
% 2.09/1.39 % (15114)Time elapsed: 0.006 s
% 2.09/1.39 % (15114)Instructions burned: 18 (million)
% 2.09/1.39 % (15114)------------------------------
% 2.09/1.39 % (15114)------------------------------
% 2.09/1.40 % (15120)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/6Mi)
% 2.14/1.40 % (15120)Instruction limit reached!
% 2.14/1.40 % (15120)------------------------------
% 2.14/1.40 % (15120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.40 % (15120)Termination reason: Unknown
% 2.14/1.40 % (15120)Termination phase: shuffling
% 2.14/1.40
% 2.14/1.40 % (15120)Memory used [KB]: 1279
% 2.14/1.40 % (15120)Time elapsed: 0.003 s
% 2.14/1.40 % (15120)Instructions burned: 7 (million)
% 2.14/1.40 % (15120)------------------------------
% 2.14/1.40 % (15120)------------------------------
% 2.14/1.40 % (15123)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_14910 for (2999ds/902Mi)
% 2.14/1.40 % (15079)Instruction limit reached!
% 2.14/1.40 % (15079)------------------------------
% 2.14/1.40 % (15079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.40 % (15079)Termination reason: Unknown
% 2.14/1.40 % (15079)Termination phase: Saturation
% 2.14/1.40
% 2.14/1.40 % (15079)Memory used [KB]: 7036
% 2.14/1.40 % (15079)Time elapsed: 0.053 s
% 2.14/1.40 % (15079)Instructions burned: 183 (million)
% 2.14/1.40 % (15079)------------------------------
% 2.14/1.40 % (15079)------------------------------
% 2.14/1.40 % (15124)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_14910 for (2999ds/21Mi)
% 2.14/1.41 % (15125)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/5Mi)
% 2.14/1.41 % (15125)Instruction limit reached!
% 2.14/1.41 % (15125)------------------------------
% 2.14/1.41 % (15125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.41 % (15125)Termination reason: Unknown
% 2.14/1.41 % (15125)Termination phase: shuffling
% 2.14/1.41
% 2.14/1.41 % (15125)Memory used [KB]: 1279
% 2.14/1.41 % (15125)Time elapsed: 0.003 s
% 2.14/1.41 % (15125)Instructions burned: 6 (million)
% 2.14/1.41 % (15125)------------------------------
% 2.14/1.41 % (15125)------------------------------
% 2.14/1.41 % (15124)Instruction limit reached!
% 2.14/1.41 % (15124)------------------------------
% 2.14/1.41 % (15124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.41 % (15124)Termination reason: Unknown
% 2.14/1.41 % (15124)Termination phase: Property scanning
% 2.14/1.41
% 2.14/1.41 % (15124)Memory used [KB]: 1535
% 2.14/1.41 % (15124)Time elapsed: 0.007 s
% 2.14/1.41 % (15124)Instructions burned: 21 (million)
% 2.14/1.41 % (15124)------------------------------
% 2.14/1.41 % (15124)------------------------------
% 2.14/1.41 % (15126)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_14910 for (2999ds/6Mi)
% 2.14/1.41 % (15126)Instruction limit reached!
% 2.14/1.41 % (15126)------------------------------
% 2.14/1.41 % (15126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.41 % (15126)Termination reason: Unknown
% 2.14/1.41 % (15126)Termination phase: shuffling
% 2.14/1.41
% 2.14/1.41 % (15126)Memory used [KB]: 1279
% 2.14/1.41 % (15126)Time elapsed: 0.003 s
% 2.14/1.41 % (15126)Instructions burned: 6 (million)
% 2.14/1.41 % (15126)------------------------------
% 2.14/1.41 % (15126)------------------------------
% 2.14/1.42 % (15133)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/377Mi)
% 2.14/1.42 % (15136)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_14910 for (2999ds/779Mi)
% 2.14/1.42 % (15139)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_14910 for (2999ds/19Mi)
% 2.14/1.43 % (15139)Instruction limit reached!
% 2.14/1.43 % (15139)------------------------------
% 2.14/1.43 % (15139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.43 % (15139)Termination reason: Unknown
% 2.14/1.43 % (15139)Termination phase: shuffling
% 2.14/1.43
% 2.14/1.43 % (15139)Memory used [KB]: 1535
% 2.14/1.43 % (15139)Time elapsed: 0.006 s
% 2.14/1.43 % (15139)Instructions burned: 19 (million)
% 2.14/1.43 % (15139)------------------------------
% 2.14/1.43 % (15139)------------------------------
% 2.14/1.44 % (15148)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14910 for (2999ds/879Mi)
% 2.14/1.47 % (15084)Instruction limit reached!
% 2.14/1.47 % (15084)------------------------------
% 2.14/1.47 % (15084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (15084)Termination reason: Unknown
% 2.14/1.47 % (15084)Termination phase: Saturation
% 2.14/1.47
% 2.14/1.47 % (15084)Memory used [KB]: 7803
% 2.14/1.47 % (15084)Time elapsed: 0.112 s
% 2.14/1.47 % (15084)Instructions burned: 277 (million)
% 2.14/1.47 % (15084)------------------------------
% 2.14/1.47 % (15084)------------------------------
% 2.14/1.48 % (15170)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14910 for (2998ds/17Mi)
% 2.14/1.48 % (15170)Instruction limit reached!
% 2.14/1.48 % (15170)------------------------------
% 2.14/1.48 % (15170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (15170)Termination reason: Unknown
% 2.14/1.48 % (15170)Termination phase: shuffling
% 2.14/1.48
% 2.14/1.48 % (15170)Memory used [KB]: 1535
% 2.14/1.48 % (15170)Time elapsed: 0.006 s
% 2.14/1.48 % (15170)Instructions burned: 18 (million)
% 2.14/1.48 % (15170)------------------------------
% 2.14/1.48 % (15170)------------------------------
% 2.14/1.49 % (15174)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14910 for (2998ds/3Mi)
% 2.14/1.49 % (15174)Instruction limit reached!
% 2.14/1.49 % (15174)------------------------------
% 2.14/1.49 % (15174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (15174)Termination reason: Unknown
% 2.14/1.49 % (15174)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (15174)Memory used [KB]: 1279
% 2.14/1.49 % (15174)Time elapsed: 0.002 s
% 2.14/1.49 % (15174)Instructions burned: 4 (million)
% 2.14/1.49 % (15174)------------------------------
% 2.14/1.49 % (15174)------------------------------
% 2.14/1.50 % (15181)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14910 for (2998ds/30Mi)
% 2.14/1.51 % (15181)Instruction limit reached!
% 2.14/1.51 % (15181)------------------------------
% 2.14/1.51 % (15181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.51 % (15181)Termination reason: Unknown
% 2.14/1.51 % (15181)Termination phase: Property scanning
% 2.14/1.51
% 2.14/1.51 % (15181)Memory used [KB]: 1663
% 2.14/1.51 % (15181)Time elapsed: 0.010 s
% 2.14/1.51 % (15181)Instructions burned: 31 (million)
% 2.14/1.51 % (15181)------------------------------
% 2.14/1.51 % (15181)------------------------------
% 2.14/1.52 % (15188)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14910 for (2998ds/127Mi)
% 2.14/1.53 % (15133)Instruction limit reached!
% 2.14/1.53 % (15133)------------------------------
% 2.14/1.53 % (15133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.53 % (15133)Termination reason: Unknown
% 2.14/1.53 % (15133)Termination phase: Saturation
% 2.14/1.53
% 2.14/1.53 % (15133)Memory used [KB]: 7291
% 2.14/1.53 % (15133)Time elapsed: 0.115 s
% 2.14/1.53 % (15133)Instructions burned: 379 (million)
% 2.14/1.53 % (15133)------------------------------
% 2.14/1.53 % (15133)------------------------------
% 2.14/1.54 % (15199)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14910 for (2998ds/100Mi)
% 2.14/1.55 % (15188)Instruction limit reached!
% 2.14/1.55 % (15188)------------------------------
% 2.14/1.55 % (15188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.55 % (15188)Termination reason: Unknown
% 2.14/1.55 % (15188)Termination phase: Saturation
% 2.14/1.55
% 2.14/1.55 % (15188)Memory used [KB]: 6780
% 2.14/1.55 % (15188)Time elapsed: 0.035 s
% 2.14/1.55 % (15188)Instructions burned: 127 (million)
% 2.14/1.55 % (15188)------------------------------
% 2.14/1.55 % (15188)------------------------------
% 2.14/1.56 % (15207)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_14910 for (2997ds/3Mi)
% 2.14/1.56 % (15207)Instruction limit reached!
% 2.14/1.56 % (15207)------------------------------
% 2.14/1.56 % (15207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.56 % (15207)Termination reason: Unknown
% 2.14/1.56 % (15207)Termination phase: shuffling
% 2.14/1.56
% 2.14/1.56 % (15207)Memory used [KB]: 1279
% 2.14/1.56 % (15207)Time elapsed: 0.002 s
% 2.14/1.56 % (15207)Instructions burned: 4 (million)
% 2.14/1.56 % (15207)------------------------------
% 2.14/1.56 % (15207)------------------------------
% 2.14/1.57 % (15199)Instruction limit reached!
% 2.14/1.57 % (15199)------------------------------
% 2.14/1.57 % (15199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.57 % (15199)Termination reason: Unknown
% 2.14/1.57 % (15199)Termination phase: Saturation
% 2.14/1.57
% 2.14/1.57 % (15199)Memory used [KB]: 6396
% 2.14/1.57 % (15199)Time elapsed: 0.029 s
% 2.14/1.57 % (15199)Instructions burned: 100 (million)
% 2.14/1.57 % (15199)------------------------------
% 2.14/1.57 % (15199)------------------------------
% 2.14/1.57 % (15213)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_14910 for (2997ds/20Mi)
% 2.14/1.58 % (15216)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_14910 for (2997ds/86Mi)
% 2.14/1.58 % (15213)Instruction limit reached!
% 2.14/1.58 % (15213)------------------------------
% 2.14/1.58 % (15213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.58 % (15213)Termination reason: Unknown
% 2.14/1.58 % (15213)Termination phase: SInE selection
% 2.14/1.58
% 2.14/1.58 % (15213)Memory used [KB]: 1407
% 2.14/1.58 % (15213)Time elapsed: 0.007 s
% 2.14/1.58 % (15213)Instructions burned: 21 (million)
% 2.14/1.58 % (15213)------------------------------
% 2.14/1.58 % (15213)------------------------------
% 2.14/1.59 % (15220)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_14910 for (2997ds/107Mi)
% 2.14/1.60 % (15136)Instruction limit reached!
% 2.14/1.60 % (15136)------------------------------
% 2.14/1.60 % (15136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.60 % (15136)Termination reason: Unknown
% 2.14/1.60 % (15136)Termination phase: Saturation
% 2.14/1.60
% 2.14/1.60 % (15136)Memory used [KB]: 6524
% 2.14/1.60 % (15136)Time elapsed: 0.180 s
% 2.14/1.60 % (15136)Instructions burned: 780 (million)
% 2.14/1.60 % (15136)------------------------------
% 2.14/1.60 % (15136)------------------------------
% 2.14/1.60 % (15216)Instruction limit reached!
% 2.14/1.60 % (15216)------------------------------
% 2.14/1.60 % (15216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.60 % (15216)Termination reason: Unknown
% 2.14/1.60 % (15216)Termination phase: Saturation
% 2.14/1.60
% 2.14/1.60 % (15216)Memory used [KB]: 6396
% 2.14/1.60 % (15216)Time elapsed: 0.024 s
% 2.14/1.60 % (15216)Instructions burned: 88 (million)
% 2.14/1.60 % (15216)------------------------------
% 2.14/1.60 % (15216)------------------------------
% 2.14/1.61 % (15226)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_14910 for (2997ds/39Mi)
% 2.14/1.61 % (15229)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_14910 for (2997ds/448Mi)
% 2.14/1.62 % (15092)Instruction limit reached!
% 2.14/1.62 % (15092)------------------------------
% 2.14/1.62 % (15092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (15092)Termination reason: Unknown
% 2.14/1.62 % (15092)Termination phase: Saturation
% 2.14/1.62
% 2.14/1.62 % (15092)Memory used [KB]: 8571
% 2.14/1.62 % (15092)Time elapsed: 0.250 s
% 2.14/1.62 % (15092)Instructions burned: 1041 (million)
% 2.14/1.62 % (15092)------------------------------
% 2.14/1.62 % (15092)------------------------------
% 2.14/1.62 % (15117)Instruction limit reached!
% 2.14/1.62 % (15117)------------------------------
% 2.14/1.62 % (15117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (15117)Termination reason: Unknown
% 2.14/1.62 % (15117)Termination phase: Saturation
% 2.14/1.62
% 2.14/1.62 % (15117)Memory used [KB]: 8827
% 2.14/1.62 % (15117)Time elapsed: 0.224 s
% 2.14/1.62 % (15117)Instructions burned: 712 (million)
% 2.14/1.62 % (15117)------------------------------
% 2.14/1.62 % (15117)------------------------------
% 2.14/1.62 % (15220)Instruction limit reached!
% 2.14/1.62 % (15220)------------------------------
% 2.14/1.62 % (15220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (15220)Termination reason: Unknown
% 2.14/1.62 % (15220)Termination phase: Saturation
% 2.14/1.62
% 2.14/1.62 % (15220)Memory used [KB]: 6652
% 2.14/1.62 % (15220)Time elapsed: 0.030 s
% 2.14/1.62 % (15220)Instructions burned: 109 (million)
% 2.14/1.62 % (15220)------------------------------
% 2.14/1.62 % (15220)------------------------------
% 2.14/1.62 % (15226)Instruction limit reached!
% 2.14/1.62 % (15226)------------------------------
% 2.14/1.62 % (15226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (15226)Termination reason: Unknown
% 2.14/1.62 % (15226)Termination phase: Property scanning
% 2.14/1.62
% 2.14/1.62 % (15226)Memory used [KB]: 1663
% 2.14/1.62 % (15226)Time elapsed: 0.012 s
% 2.14/1.62 % (15226)Instructions burned: 42 (million)
% 2.14/1.62 % (15226)------------------------------
% 2.14/1.62 % (15226)------------------------------
% 2.14/1.63 % (15233)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_14910 for (2997ds/46Mi)
% 2.14/1.63 % (15234)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_14910 for (2997ds/98Mi)
% 2.14/1.63 % (15236)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_14910 for (2997ds/507Mi)
% 2.14/1.63 % (15237)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_14910 for (2997ds/149Mi)
% 2.14/1.64 % (15233)Instruction limit reached!
% 2.14/1.64 % (15233)------------------------------
% 2.14/1.64 % (15233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.64 % (15233)Termination reason: Unknown
% 2.14/1.64 % (15233)Termination phase: Function definition elimination
% 2.14/1.64
% 2.14/1.64 % (15233)Memory used [KB]: 1663
% 2.14/1.64 % (15233)Time elapsed: 0.014 s
% 2.14/1.64 % (15233)Instructions burned: 48 (million)
% 2.14/1.64 % (15233)------------------------------
% 2.14/1.64 % (15233)------------------------------
% 2.14/1.65 % (15246)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14910 for (2997ds/39Mi)
% 2.14/1.65 % (15234)Instruction limit reached!
% 2.14/1.65 % (15234)------------------------------
% 2.14/1.65 % (15234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.65 % (15234)Termination reason: Unknown
% 2.14/1.65 % (15234)Termination phase: Saturation
% 2.14/1.65
% 2.14/1.65 % (15234)Memory used [KB]: 1791
% 2.14/1.65 % (15234)Time elapsed: 0.027 s
% 2.14/1.65 % (15234)Instructions burned: 100 (million)
% 2.14/1.65 % (15234)------------------------------
% 2.14/1.65 % (15234)------------------------------
% 2.14/1.66 % (15246)Instruction limit reached!
% 2.14/1.66 % (15246)------------------------------
% 2.14/1.66 % (15246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.66 % (15246)Termination reason: Unknown
% 2.14/1.66 % (15246)Termination phase: Property scanning
% 2.14/1.66
% 2.14/1.66 % (15246)Memory used [KB]: 1663
% 2.14/1.66 % (15246)Time elapsed: 0.012 s
% 2.14/1.66 % (15246)Instructions burned: 40 (million)
% 2.14/1.66 % (15246)------------------------------
% 2.14/1.66 % (15246)------------------------------
% 2.14/1.66 % (15252)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_14910 for (2996ds/6Mi)
% 2.14/1.66 % (15252)Instruction limit reached!
% 2.14/1.66 % (15252)------------------------------
% 2.14/1.66 % (15252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.66 % (15252)Termination reason: Unknown
% 2.14/1.66 % (15252)Termination phase: shuffling
% 2.14/1.66
% 2.14/1.66 % (15252)Memory used [KB]: 1279
% 2.14/1.66 % (15252)Time elapsed: 0.003 s
% 2.14/1.66 % (15252)Instructions burned: 7 (million)
% 2.14/1.66 % (15252)------------------------------
% 2.14/1.66 % (15252)------------------------------
% 2.14/1.67 % (15256)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_14910 for (2996ds/1087Mi)
% 2.14/1.67 % (15257)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14910 for (2996ds/47Mi)
% 2.14/1.67 % (15237)Instruction limit reached!
% 2.14/1.67 % (15237)------------------------------
% 2.14/1.67 % (15237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.67 % (15237)Termination reason: Unknown
% 2.14/1.67 % (15237)Termination phase: Saturation
% 2.14/1.67
% 2.14/1.67 % (15237)Memory used [KB]: 6908
% 2.14/1.67 % (15237)Time elapsed: 0.069 s
% 2.14/1.67 % (15237)Instructions burned: 150 (million)
% 2.14/1.67 % (15237)------------------------------
% 2.14/1.67 % (15237)------------------------------
% 2.14/1.68 % (15264)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_14910 for (2996ds/44Mi)
% 2.14/1.68 % (15257)Instruction limit reached!
% 2.14/1.68 % (15257)------------------------------
% 2.14/1.68 % (15257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.68 % (15257)Termination reason: Unknown
% 2.14/1.68 % (15257)Termination phase: Property scanning
% 2.14/1.68
% 2.14/1.68 % (15257)Memory used [KB]: 1791
% 2.14/1.68 % (15257)Time elapsed: 0.013 s
% 2.14/1.68 % (15257)Instructions burned: 48 (million)
% 2.14/1.68 % (15257)------------------------------
% 2.14/1.68 % (15257)------------------------------
% 2.14/1.69 % (15123)Instruction limit reached!
% 2.14/1.69 % (15123)------------------------------
% 2.14/1.69 % (15123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.69 % (15123)Termination reason: Unknown
% 2.14/1.69 % (15123)Termination phase: Saturation
% 2.14/1.69
% 2.14/1.69 % (15123)Memory used [KB]: 10746
% 2.14/1.69 % (15123)Time elapsed: 0.287 s
% 2.14/1.69 % (15123)Instructions burned: 905 (million)
% 2.14/1.69 % (15123)------------------------------
% 2.14/1.69 % (15123)------------------------------
% 2.14/1.69 % (15264)Instruction limit reached!
% 2.14/1.69 % (15264)------------------------------
% 2.14/1.69 % (15264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.69 % (15264)Termination reason: Unknown
% 2.14/1.69 % (15264)Termination phase: Property scanning
% 2.14/1.69
% 2.14/1.69 % (15264)Memory used [KB]: 1663
% 2.14/1.69 % (15264)Time elapsed: 0.012 s
% 2.14/1.69 % (15264)Instructions burned: 44 (million)
% 2.14/1.69 % (15264)------------------------------
% 2.14/1.69 % (15264)------------------------------
% 2.14/1.69 % (15272)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_14910 for (2996ds/432Mi)
% 2.14/1.70 % (15275)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14910 for (2996ds/62Mi)
% 2.14/1.70 % (15281)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_14910 for (2996ds/31Mi)
% 2.14/1.71 % (15281)Instruction limit reached!
% 2.14/1.71 % (15281)------------------------------
% 2.14/1.71 % (15281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (15281)Termination reason: Unknown
% 2.14/1.71 % (15281)Termination phase: Property scanning
% 2.14/1.71
% 2.14/1.71 % (15281)Memory used [KB]: 1663
% 2.14/1.71 % (15281)Time elapsed: 0.010 s
% 2.14/1.71 % (15281)Instructions burned: 33 (million)
% 2.14/1.71 % (15281)------------------------------
% 2.14/1.71 % (15281)------------------------------
% 2.14/1.71 % (15275)Instruction limit reached!
% 2.14/1.71 % (15275)------------------------------
% 2.14/1.71 % (15275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (15275)Termination reason: Unknown
% 2.14/1.71 % (15275)Termination phase: Saturation
% 2.14/1.71
% 2.14/1.71 % (15275)Memory used [KB]: 6140
% 2.14/1.71 % (15275)Time elapsed: 0.017 s
% 2.14/1.71 % (15275)Instructions burned: 62 (million)
% 2.14/1.71 % (15275)------------------------------
% 2.14/1.71 % (15275)------------------------------
% 2.14/1.71 % (15148)Instruction limit reached!
% 2.14/1.71 % (15148)------------------------------
% 2.14/1.71 % (15148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (15148)Termination reason: Unknown
% 2.14/1.71 % (15148)Termination phase: Saturation
% 2.14/1.71
% 2.14/1.71 % (15148)Memory used [KB]: 7931
% 2.14/1.71 % (15148)Time elapsed: 0.278 s
% 2.14/1.71 % (15148)Instructions burned: 881 (million)
% 2.14/1.71 % (15148)------------------------------
% 2.14/1.71 % (15148)------------------------------
% 2.14/1.72 % (15229)Instruction limit reached!
% 2.14/1.72 % (15229)------------------------------
% 2.14/1.72 % (15229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.72 % (15229)Termination reason: Unknown
% 2.14/1.72 % (15229)Termination phase: Saturation
% 2.14/1.72
% 2.14/1.72 % (15229)Memory used [KB]: 6524
% 2.14/1.72 % (15229)Time elapsed: 0.109 s
% 2.14/1.72 % (15229)Instructions burned: 451 (million)
% 2.14/1.72 % (15229)------------------------------
% 2.14/1.72 % (15229)------------------------------
% 2.14/1.72 % (15294)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14910 for (2996ds/96Mi)
% 2.14/1.72 % (15295)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_14910 for (2996ds/453Mi)
% 2.14/1.72 % (15297)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_14910 for (2996ds/71Mi)
% 2.14/1.73 % (15300)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14910 for (2996ds/83Mi)
% 2.14/1.74 % (15297)Instruction limit reached!
% 2.14/1.74 % (15297)------------------------------
% 2.14/1.74 % (15297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.74 % (15297)Termination reason: Unknown
% 2.14/1.74 % (15297)Termination phase: Saturation
% 2.14/1.74
% 2.14/1.74 % (15297)Memory used [KB]: 6268
% 2.14/1.74 % (15297)Time elapsed: 0.020 s
% 2.14/1.74 % (15297)Instructions burned: 72 (million)
% 2.14/1.74 % (15297)------------------------------
% 2.14/1.74 % (15297)------------------------------
% 2.14/1.75 % (15294)Instruction limit reached!
% 2.14/1.75 % (15294)------------------------------
% 2.14/1.75 % (15294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.75 % (15294)Termination reason: Unknown
% 2.14/1.75 % (15294)Termination phase: Saturation
% 2.14/1.75
% 2.14/1.75 % (15294)Memory used [KB]: 6652
% 2.14/1.75 % (15294)Time elapsed: 0.027 s
% 2.14/1.75 % (15294)Instructions burned: 99 (million)
% 2.14/1.75 % (15294)------------------------------
% 2.14/1.75 % (15294)------------------------------
% 2.14/1.75 % (15300)Instruction limit reached!
% 2.14/1.75 % (15300)------------------------------
% 2.14/1.75 % (15300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.75 % (15300)Termination reason: Unknown
% 2.14/1.75 % (15300)Termination phase: Saturation
% 2.14/1.75
% 2.14/1.75 % (15300)Memory used [KB]: 6268
% 2.14/1.75 % (15300)Time elapsed: 0.023 s
% 2.14/1.75 % (15300)Instructions burned: 86 (million)
% 2.14/1.75 % (15300)------------------------------
% 2.14/1.75 % (15300)------------------------------
% 2.14/1.75 % (15306)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14910 for (2995ds/11Mi)
% 2.14/1.75 % (15306)Instruction limit reached!
% 2.14/1.75 % (15306)------------------------------
% 2.14/1.75 % (15306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.75 % (15306)Termination reason: Unknown
% 2.14/1.75 % (15306)Termination phase: shuffling
% 2.14/1.75
% 2.14/1.75 % (15306)Memory used [KB]: 1407
% 2.14/1.75 % (15306)Time elapsed: 0.004 s
% 2.14/1.75 % (15306)Instructions burned: 12 (million)
% 2.14/1.75 % (15306)------------------------------
% 2.14/1.75 % (15306)------------------------------
% 2.14/1.76 % (15307)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_14910 for (2995ds/41Mi)
% 2.14/1.76 % (15308)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14910 for (2995ds/6Mi)
% 2.14/1.76 % (15308)Instruction limit reached!
% 2.14/1.76 % (15308)------------------------------
% 2.14/1.76 % (15308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.76 % (15308)Termination reason: Unknown
% 2.14/1.76 % (15308)Termination phase: shuffling
% 2.14/1.76
% 2.14/1.76 % (15308)Memory used [KB]: 1279
% 2.14/1.76 % (15308)Time elapsed: 0.003 s
% 2.14/1.76 % (15308)Instructions burned: 7 (million)
% 2.14/1.76 % (15308)------------------------------
% 2.14/1.76 % (15308)------------------------------
% 2.14/1.76 % (15309)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14910 for (2995ds/150Mi)
% 2.14/1.77 % (15307)Instruction limit reached!
% 2.14/1.77 % (15307)------------------------------
% 2.14/1.77 % (15307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.77 % (15307)Termination reason: Unknown
% 2.14/1.77 % (15307)Termination phase: Function definition elimination
% 2.14/1.77
% 2.14/1.77 % (15307)Memory used [KB]: 1663
% 2.14/1.77 % (15307)Time elapsed: 0.012 s
% 2.14/1.77 % (15307)Instructions burned: 43 (million)
% 2.14/1.77 % (15307)------------------------------
% 2.14/1.77 % (15307)------------------------------
% 2.14/1.77 % (15310)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14910 for (2995ds/343Mi)
% 2.14/1.78 % (15311)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_14910 for (2995ds/109Mi)
% 2.14/1.78 % (15236)Instruction limit reached!
% 2.14/1.78 % (15236)------------------------------
% 2.14/1.78 % (15236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.78 % (15236)Termination reason: Unknown
% 2.14/1.78 % (15236)Termination phase: Saturation
% 2.14/1.78
% 2.14/1.78 % (15236)Memory used [KB]: 7164
% 2.14/1.78 % (15236)Time elapsed: 0.178 s
% 2.14/1.78 % (15236)Instructions burned: 510 (million)
% 2.14/1.78 % (15236)------------------------------
% 2.14/1.78 % (15236)------------------------------
% 2.14/1.79 % (15312)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_14910 for (2995ds/253Mi)
% 2.14/1.80 % (15272)Instruction limit reached!
% 2.14/1.80 % (15272)------------------------------
% 2.14/1.80 % (15272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.80 % (15272)Termination reason: Unknown
% 2.14/1.80 % (15272)Termination phase: Saturation
% 2.14/1.80
% 2.14/1.80 % (15272)Memory used [KB]: 2814
% 2.14/1.80 % (15272)Time elapsed: 0.109 s
% 2.14/1.80 % (15272)Instructions burned: 435 (million)
% 2.14/1.80 % (15272)------------------------------
% 2.14/1.80 % (15272)------------------------------
% 2.14/1.81 % (15311)Instruction limit reached!
% 2.14/1.81 % (15311)------------------------------
% 2.14/1.81 % (15311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.81 % (15311)Termination reason: Unknown
% 2.14/1.81 % (15311)Termination phase: Saturation
% 2.14/1.81
% 2.14/1.81 % (15311)Memory used [KB]: 6652
% 2.14/1.81 % (15311)Time elapsed: 0.030 s
% 2.14/1.81 % (15311)Instructions burned: 111 (million)
% 2.14/1.81 % (15311)------------------------------
% 2.14/1.81 % (15311)------------------------------
% 2.14/1.81 % (15309)Instruction limit reached!
% 2.14/1.81 % (15309)------------------------------
% 2.14/1.81 % (15309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.81 % (15309)Termination reason: Unknown
% 2.14/1.81 % (15309)Termination phase: Saturation
% 2.14/1.81
% 2.14/1.81 % (15309)Memory used [KB]: 7419
% 2.14/1.81 % (15309)Time elapsed: 0.047 s
% 2.14/1.81 % (15309)Instructions burned: 152 (million)
% 2.14/1.81 % (15309)------------------------------
% 2.14/1.81 % (15309)------------------------------
% 2.14/1.81 % (15313)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14910 for (2995ds/140Mi)
% 2.14/1.81 % (15314)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_14910 for (2995ds/614Mi)
% 2.14/1.82 % (15315)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_14910 for (2995ds/202Mi)
% 2.14/1.83 % (15295)Instruction limit reached!
% 2.14/1.83 % (15295)------------------------------
% 2.14/1.83 % (15295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.83 % (15295)Termination reason: Unknown
% 2.14/1.83 % (15295)Termination phase: Saturation
% 2.14/1.83
% 2.14/1.83 % (15295)Memory used [KB]: 6268
% 2.14/1.83 % (15295)Time elapsed: 0.109 s
% 2.14/1.83 % (15295)Instructions burned: 454 (million)
% 2.14/1.83 % (15295)------------------------------
% 2.14/1.83 % (15295)------------------------------
% 2.14/1.84 % (15316)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_14910 for (2995ds/339Mi)
% 2.14/1.85 % (15313)Instruction limit reached!
% 2.14/1.85 % (15313)------------------------------
% 2.14/1.85 % (15313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.85 % (15313)Termination reason: Unknown
% 2.14/1.85 % (15313)Termination phase: Saturation
% 2.14/1.85
% 2.14/1.85 % (15313)Memory used [KB]: 6396
% 2.14/1.85 % (15313)Time elapsed: 0.038 s
% 2.14/1.85 % (15313)Instructions burned: 140 (million)
% 2.14/1.85 % (15313)------------------------------
% 2.14/1.85 % (15313)------------------------------
% 2.14/1.86 % (15317)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_14910 for (2994ds/283Mi)
% 2.14/1.87 % (15312)Instruction limit reached!
% 2.14/1.87 % (15312)------------------------------
% 2.14/1.87 % (15312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.87 % (15312)Termination reason: Unknown
% 2.14/1.87 % (15312)Termination phase: Saturation
% 2.14/1.87
% 2.14/1.87 % (15312)Memory used [KB]: 7803
% 2.14/1.87 % (15312)Time elapsed: 0.078 s
% 2.14/1.87 % (15312)Instructions burned: 255 (million)
% 2.14/1.87 % (15312)------------------------------
% 2.14/1.87 % (15312)------------------------------
% 2.14/1.87 % (15310)Instruction limit reached!
% 2.14/1.87 % (15310)------------------------------
% 2.14/1.87 % (15310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.87 % (15310)Termination reason: Unknown
% 2.14/1.87 % (15310)Termination phase: Saturation
% 2.14/1.87
% 2.14/1.87 % (15310)Memory used [KB]: 7291
% 2.14/1.87 % (15310)Time elapsed: 0.104 s
% 2.14/1.87 % (15310)Instructions burned: 345 (million)
% 2.14/1.87 % (15310)------------------------------
% 2.14/1.87 % (15310)------------------------------
% 2.14/1.88 % (15318)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14910 for (2994ds/134Mi)
% 2.14/1.88 % (15315)Instruction limit reached!
% 2.14/1.88 % (15315)------------------------------
% 2.14/1.88 % (15315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.88 % (15315)Termination reason: Unknown
% 2.14/1.88 % (15315)Termination phase: Saturation
% 2.14/1.88
% 2.14/1.88 % (15315)Memory used [KB]: 7803
% 2.14/1.88 % (15315)Time elapsed: 0.063 s
% 2.14/1.88 % (15315)Instructions burned: 203 (million)
% 2.14/1.88 % (15315)------------------------------
% 2.14/1.88 % (15315)------------------------------
% 2.14/1.88 % (15319)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14910 for (2994ds/298Mi)
% 2.14/1.89 % (15320)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14910 for (2994ds/192Mi)
% 2.14/1.91 % (15318)Instruction limit reached!
% 2.14/1.91 % (15318)------------------------------
% 2.14/1.91 % (15318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.91 % (15318)Termination reason: Unknown
% 2.14/1.91 % (15318)Termination phase: Saturation
% 2.14/1.91
% 2.14/1.91 % (15318)Memory used [KB]: 6780
% 2.14/1.91 % (15318)Time elapsed: 0.038 s
% 2.14/1.91 % (15318)Instructions burned: 134 (million)
% 2.14/1.91 % (15318)------------------------------
% 2.14/1.91 % (15318)------------------------------
% 2.14/1.92 % (15321)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_14910 for (2994ds/258Mi)
% 2.14/1.93 % (15317)Instruction limit reached!
% 2.14/1.93 % (15317)------------------------------
% 2.14/1.93 % (15317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.93 % (15317)Termination reason: Unknown
% 2.14/1.93 % (15317)Termination phase: Saturation
% 2.14/1.93
% 2.14/1.93 % (15317)Memory used [KB]: 8699
% 2.14/1.93 % (15317)Time elapsed: 0.073 s
% 2.14/1.93 % (15317)Instructions burned: 286 (million)
% 2.14/1.93 % (15317)------------------------------
% 2.14/1.93 % (15317)------------------------------
% 2.14/1.94 % (15316)Instruction limit reached!
% 2.14/1.94 % (15316)------------------------------
% 2.14/1.94 % (15316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.94 % (15316)Termination reason: Unknown
% 2.14/1.94 % (15316)Termination phase: Saturation
% 2.14/1.94
% 2.14/1.94 % (15316)Memory used [KB]: 7547
% 2.14/1.94 % (15316)Time elapsed: 0.100 s
% 2.14/1.94 % (15316)Instructions burned: 339 (million)
% 2.14/1.94 % (15316)------------------------------
% 2.14/1.94 % (15316)------------------------------
% 2.14/1.94 % (15322)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_14910 for (2994ds/90Mi)
% 2.14/1.95 % (15320)Instruction limit reached!
% 2.14/1.95 % (15320)------------------------------
% 2.14/1.95 % (15320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.95 % (15320)Termination reason: Unknown
% 2.14/1.95 % (15320)Termination phase: Saturation
% 2.14/1.95
% 2.14/1.95 % (15320)Memory used [KB]: 7036
% 2.14/1.95 % (15320)Time elapsed: 0.056 s
% 2.14/1.95 % (15320)Instructions burned: 192 (million)
% 2.14/1.95 % (15320)------------------------------
% 2.14/1.95 % (15320)------------------------------
% 2.14/1.95 % (15323)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_14910 for (2994ds/231Mi)
% 2.14/1.95 % (15324)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_14910 for (2994ds/458Mi)
% 2.14/1.96 % (15319)Instruction limit reached!
% 2.14/1.96 % (15319)------------------------------
% 2.14/1.96 % (15319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.96 % (15319)Termination reason: Unknown
% 2.14/1.96 % (15319)Termination phase: Saturation
% 2.14/1.96
% 2.14/1.96 % (15319)Memory used [KB]: 6524
% 2.14/1.96 % (15319)Time elapsed: 0.077 s
% 2.14/1.96 % (15319)Instructions burned: 298 (million)
% 2.14/1.96 % (15319)------------------------------
% 2.14/1.96 % (15319)------------------------------
% 2.14/1.96 % (15322)Instruction limit reached!
% 2.14/1.96 % (15322)------------------------------
% 2.14/1.96 % (15322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.96 % (15322)Termination reason: Unknown
% 2.14/1.96 % (15322)Termination phase: Saturation
% 2.14/1.96
% 2.14/1.96 % (15322)Memory used [KB]: 6652
% 2.14/1.96 % (15322)Time elapsed: 0.025 s
% 2.14/1.96 % (15322)Instructions burned: 90 (million)
% 2.14/1.96 % (15322)------------------------------
% 2.14/1.96 % (15322)------------------------------
% 2.14/1.97 % (15325)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_14910 for (2993ds/31Mi)
% 2.14/1.97 % (15326)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_14910 for (2993ds/297Mi)
% 2.14/1.98 % (15325)Instruction limit reached!
% 2.14/1.98 % (15325)------------------------------
% 2.14/1.98 % (15325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.98 % (15325)Termination reason: Unknown
% 2.14/1.98 % (15325)Termination phase: Property scanning
% 2.14/1.98
% 2.14/1.98 % (15325)Memory used [KB]: 1663
% 2.14/1.98 % (15325)Time elapsed: 0.010 s
% 2.14/1.98 % (15325)Instructions burned: 32 (million)
% 2.14/1.98 % (15325)------------------------------
% 2.14/1.98 % (15325)------------------------------
% 2.14/1.99 % (15327)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_14910 for (2993ds/987Mi)
% 2.14/2.00 % (15321)Instruction limit reached!
% 2.14/2.00 % (15321)------------------------------
% 2.14/2.00 % (15321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/2.00 % (15321)Termination reason: Unknown
% 2.14/2.00 % (15321)Termination phase: Saturation
% 2.14/2.00
% 2.14/2.00 % (15321)Memory used [KB]: 7036
% 2.14/2.00 % (15321)Time elapsed: 0.080 s
% 2.14/2.00 % (15321)Instructions burned: 259 (million)
% 2.14/2.00 % (15321)------------------------------
% 2.14/2.00 % (15321)------------------------------
% 2.14/2.00 % (15314)Instruction limit reached!
% 2.14/2.00 % (15314)------------------------------
% 2.14/2.00 % (15314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/2.00 % (15314)Termination reason: Unknown
% 2.14/2.00 % (15314)Termination phase: Saturation
% 2.14/2.00
% 2.14/2.00 % (15314)Memory used [KB]: 7931
% 2.14/2.00 % (15314)Time elapsed: 0.190 s
% 2.14/2.00 % (15314)Instructions burned: 617 (million)
% 2.14/2.00 % (15314)------------------------------
% 2.14/2.00 % (15314)------------------------------
% 6.77/2.01 % (15323)Instruction limit reached!
% 6.77/2.01 % (15323)------------------------------
% 6.77/2.01 % (15323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.01 % (15323)Termination reason: Unknown
% 6.77/2.01 % (15323)Termination phase: Saturation
% 6.77/2.01
% 6.77/2.01 % (15323)Memory used [KB]: 9850
% 6.77/2.01 % (15323)Time elapsed: 0.067 s
% 6.77/2.01 % (15323)Instructions burned: 232 (million)
% 6.77/2.01 % (15323)------------------------------
% 6.77/2.01 % (15323)------------------------------
% 6.77/2.01 % (15329)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_14910 for (2993ds/182Mi)
% 6.77/2.01 % (15256)Instruction limit reached!
% 6.77/2.01 % (15256)------------------------------
% 6.77/2.01 % (15256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.01 % (15256)Termination reason: Unknown
% 6.77/2.01 % (15256)Termination phase: Saturation
% 6.77/2.01
% 6.77/2.01 % (15256)Memory used [KB]: 10362
% 6.77/2.01 % (15256)Time elapsed: 0.348 s
% 6.77/2.01 % (15256)Instructions burned: 1088 (million)
% 6.77/2.01 % (15256)------------------------------
% 6.77/2.01 % (15256)------------------------------
% 6.77/2.02 % (15328)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_14910 for (2993ds/182Mi)
% 6.77/2.02 % (15330)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_14910 for (2993ds/154Mi)
% 6.77/2.02 % (15331)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_14910 for (2993ds/79Mi)
% 6.77/2.04 % (15326)Instruction limit reached!
% 6.77/2.04 % (15326)------------------------------
% 6.77/2.04 % (15326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.04 % (15326)Termination reason: Unknown
% 6.77/2.04 % (15326)Termination phase: Saturation
% 6.77/2.04
% 6.77/2.04 % (15326)Memory used [KB]: 7675
% 6.77/2.04 % (15326)Time elapsed: 0.073 s
% 6.77/2.04 % (15326)Instructions burned: 299 (million)
% 6.77/2.04 % (15326)------------------------------
% 6.77/2.04 % (15326)------------------------------
% 6.77/2.05 % (15331)Instruction limit reached!
% 6.77/2.05 % (15331)------------------------------
% 6.77/2.05 % (15331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.05 % (15331)Termination reason: Unknown
% 6.77/2.05 % (15331)Termination phase: Saturation
% 6.77/2.05
% 6.77/2.05 % (15331)Memory used [KB]: 6396
% 6.77/2.05 % (15331)Time elapsed: 0.022 s
% 6.77/2.05 % (15331)Instructions burned: 80 (million)
% 6.77/2.05 % (15331)------------------------------
% 6.77/2.05 % (15331)------------------------------
% 6.77/2.05 % (15332)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_14910 for (2993ds/216Mi)
% 6.77/2.05 % (15333)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14910 for (2993ds/114Mi)
% 6.77/2.06 % (15330)Instruction limit reached!
% 6.77/2.06 % (15330)------------------------------
% 6.77/2.06 % (15330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.06 % (15330)Termination reason: Unknown
% 6.77/2.06 % (15330)Termination phase: Saturation
% 6.77/2.06
% 6.77/2.06 % (15330)Memory used [KB]: 6268
% 6.77/2.06 % (15330)Time elapsed: 0.039 s
% 6.77/2.06 % (15330)Instructions burned: 155 (million)
% 6.77/2.06 % (15330)------------------------------
% 6.77/2.06 % (15330)------------------------------
% 6.77/2.07 % (15329)Instruction limit reached!
% 6.77/2.07 % (15329)------------------------------
% 6.77/2.07 % (15329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.07 % (15329)Termination reason: Unknown
% 6.77/2.07 % (15329)Termination phase: Saturation
% 6.77/2.07
% 6.77/2.07 % (15329)Memory used [KB]: 8827
% 6.77/2.07 % (15329)Time elapsed: 0.081 s
% 6.77/2.07 % (15329)Instructions burned: 184 (million)
% 6.77/2.07 % (15329)------------------------------
% 6.77/2.07 % (15329)------------------------------
% 6.77/2.07 % (15334)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_14910 for (2992ds/922Mi)
% 6.77/2.08 % (15335)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_14910 for (2992ds/182Mi)
% 6.77/2.09 % (15333)Instruction limit reached!
% 6.77/2.09 % (15333)------------------------------
% 6.77/2.09 % (15333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.09 % (15333)Termination reason: Unknown
% 6.77/2.09 % (15333)Termination phase: Saturation
% 6.77/2.09
% 6.77/2.09 % (15333)Memory used [KB]: 6780
% 6.77/2.09 % (15333)Time elapsed: 0.032 s
% 6.77/2.09 % (15333)Instructions burned: 114 (million)
% 6.77/2.09 % (15333)------------------------------
% 6.77/2.09 % (15333)------------------------------
% 6.77/2.09 % (15324)Instruction limit reached!
% 6.77/2.09 % (15324)------------------------------
% 6.77/2.09 % (15324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.09 % (15324)Termination reason: Unknown
% 6.77/2.09 % (15324)Termination phase: Saturation
% 6.77/2.09
% 6.77/2.09 % (15324)Memory used [KB]: 7419
% 6.77/2.09 % (15324)Time elapsed: 0.140 s
% 6.77/2.09 % (15324)Instructions burned: 459 (million)
% 6.77/2.09 % (15324)------------------------------
% 6.77/2.09 % (15324)------------------------------
% 6.77/2.10 % (15336)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_14910 for (2992ds/164Mi)
% 6.77/2.10 % (15337)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_14910 for (2992ds/50Mi)
% 6.77/2.11 % (15332)Instruction limit reached!
% 6.77/2.11 % (15332)------------------------------
% 6.77/2.11 % (15332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.77/2.11 % (15332)Termination reason: Unknown
% 6.77/2.11 % (15332)Termination phase: Saturation
% 6.77/2.11
% 6.77/2.11 % (15332)Memory used [KB]: 7036
% 6.77/2.11 % (15332)Time elapsed: 0.056 s
% 6.77/2.11 % (15332)Instructions burned: 218 (million)
% 6.77/2.11 % (15332)------------------------------
% 6.77/2.11 % (15332)------------------------------
% 7.28/2.11 % (15328)Instruction limit reached!
% 7.28/2.11 % (15328)------------------------------
% 7.28/2.11 % (15328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.11 % (15328)Termination reason: Unknown
% 7.28/2.11 % (15328)Termination phase: Saturation
% 7.28/2.11
% 7.28/2.11 % (15328)Memory used [KB]: 7036
% 7.28/2.11 % (15328)Time elapsed: 0.096 s
% 7.28/2.11 % (15328)Instructions burned: 182 (million)
% 7.28/2.11 % (15328)------------------------------
% 7.28/2.11 % (15328)------------------------------
% 7.28/2.12 % (15337)Instruction limit reached!
% 7.28/2.12 % (15337)------------------------------
% 7.28/2.12 % (15337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.12 % (15337)Termination reason: Unknown
% 7.28/2.12 % (15337)Termination phase: Property scanning
% 7.28/2.12
% 7.28/2.12 % (15337)Memory used [KB]: 1663
% 7.28/2.12 % (15337)Time elapsed: 0.015 s
% 7.28/2.12 % (15337)Instructions burned: 53 (million)
% 7.28/2.12 % (15337)------------------------------
% 7.28/2.12 % (15337)------------------------------
% 7.28/2.12 % (15338)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14910 for (2992ds/368Mi)
% 7.28/2.13 % (15339)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_14910 for (2992ds/1021Mi)
% 7.28/2.13 % (15340)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_14910 for (2992ds/267Mi)
% 7.28/2.13 % (15335)Instruction limit reached!
% 7.28/2.13 % (15335)------------------------------
% 7.28/2.13 % (15335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.13 % (15335)Termination reason: Unknown
% 7.28/2.13 % (15335)Termination phase: Saturation
% 7.28/2.13
% 7.28/2.13 % (15335)Memory used [KB]: 6396
% 7.28/2.13 % (15335)Time elapsed: 0.048 s
% 7.28/2.13 % (15335)Instructions burned: 185 (million)
% 7.28/2.13 % (15335)------------------------------
% 7.28/2.13 % (15335)------------------------------
% 7.28/2.14 % (15341)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_14910 for (2992ds/204Mi)
% 7.28/2.14 % (15336)Instruction limit reached!
% 7.28/2.14 % (15336)------------------------------
% 7.28/2.14 % (15336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.14 % (15336)Termination reason: Unknown
% 7.28/2.14 % (15336)Termination phase: Saturation
% 7.28/2.14
% 7.28/2.14 % (15336)Memory used [KB]: 2174
% 7.28/2.14 % (15336)Time elapsed: 0.048 s
% 7.28/2.14 % (15336)Instructions burned: 165 (million)
% 7.28/2.14 % (15336)------------------------------
% 7.28/2.14 % (15336)------------------------------
% 7.28/2.15 % (15342)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_14910 for (2991ds/26Mi)
% 7.28/2.16 % (15342)Instruction limit reached!
% 7.28/2.16 % (15342)------------------------------
% 7.28/2.16 % (15342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.16 % (15342)Termination reason: Unknown
% 7.28/2.16 % (15342)Termination phase: Property scanning
% 7.28/2.16
% 7.28/2.16 % (15342)Memory used [KB]: 1535
% 7.28/2.16 % (15342)Time elapsed: 0.008 s
% 7.28/2.16 % (15342)Instructions burned: 28 (million)
% 7.28/2.16 % (15342)------------------------------
% 7.28/2.16 % (15342)------------------------------
% 7.28/2.17 % (15343)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_14910 for (2991ds/53Mi)
% 7.28/2.18 % (15343)Instruction limit reached!
% 7.28/2.18 % (15343)------------------------------
% 7.28/2.18 % (15343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.18 % (15343)Termination reason: Unknown
% 7.28/2.18 % (15343)Termination phase: Property scanning
% 7.28/2.18
% 7.28/2.18 % (15343)Memory used [KB]: 1663
% 7.28/2.18 % (15343)Time elapsed: 0.015 s
% 7.28/2.18 % (15343)Instructions burned: 56 (million)
% 7.28/2.18 % (15343)------------------------------
% 7.28/2.18 % (15343)------------------------------
% 7.28/2.19 % (15344)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_14910 for (2991ds/4436Mi)
% 7.28/2.19 % (15340)Instruction limit reached!
% 7.28/2.19 % (15340)------------------------------
% 7.28/2.19 % (15340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.19 % (15340)Termination reason: Unknown
% 7.28/2.19 % (15340)Termination phase: Saturation
% 7.28/2.19
% 7.28/2.19 % (15340)Memory used [KB]: 8699
% 7.28/2.19 % (15340)Time elapsed: 0.067 s
% 7.28/2.19 % (15340)Instructions burned: 267 (million)
% 7.28/2.19 % (15340)------------------------------
% 7.28/2.19 % (15340)------------------------------
% 7.28/2.20 % (15341)Instruction limit reached!
% 7.28/2.20 % (15341)------------------------------
% 7.28/2.20 % (15341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.20 % (15341)Termination reason: Unknown
% 7.28/2.20 % (15341)Termination phase: Saturation
% 7.28/2.20
% 7.28/2.20 % (15341)Memory used [KB]: 7036
% 7.28/2.20 % (15341)Time elapsed: 0.060 s
% 7.28/2.20 % (15341)Instructions burned: 205 (million)
% 7.28/2.20 % (15341)------------------------------
% 7.28/2.20 % (15341)------------------------------
% 7.73/2.20 % (15345)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_14910 for (2991ds/1539Mi)
% 7.73/2.21 % (15346)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_14910 for (2991ds/408Mi)
% 7.73/2.23 % (15327)Instruction limit reached!
% 7.73/2.23 % (15327)------------------------------
% 7.73/2.23 % (15327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.23 % (15327)Termination reason: Unknown
% 7.73/2.23 % (15327)Termination phase: Saturation
% 7.73/2.23
% 7.73/2.23 % (15327)Memory used [KB]: 8571
% 7.73/2.23 % (15327)Time elapsed: 0.239 s
% 7.73/2.23 % (15327)Instructions burned: 989 (million)
% 7.73/2.23 % (15327)------------------------------
% 7.73/2.23 % (15327)------------------------------
% 7.73/2.23 % (15338)Instruction limit reached!
% 7.73/2.23 % (15338)------------------------------
% 7.73/2.23 % (15338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.23 % (15338)Termination reason: Unknown
% 7.73/2.23 % (15338)Termination phase: Saturation
% 7.73/2.23
% 7.73/2.23 % (15338)Memory used [KB]: 7419
% 7.73/2.23 % (15338)Time elapsed: 0.114 s
% 7.73/2.23 % (15338)Instructions burned: 369 (million)
% 7.73/2.23 % (15338)------------------------------
% 7.73/2.23 % (15338)------------------------------
% 7.73/2.24 % (15347)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_14910 for (2991ds/5205Mi)
% 7.73/2.24 % (15348)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_14910 for (2991ds/1913Mi)
% 7.96/2.33 % (15346)Instruction limit reached!
% 7.96/2.33 % (15346)------------------------------
% 7.96/2.33 % (15346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.33 % (15346)Termination reason: Unknown
% 7.96/2.33 % (15346)Termination phase: Saturation
% 7.96/2.33
% 7.96/2.33 % (15346)Memory used [KB]: 8827
% 7.96/2.33 % (15346)Time elapsed: 0.129 s
% 7.96/2.33 % (15346)Instructions burned: 408 (million)
% 7.96/2.33 % (15346)------------------------------
% 7.96/2.33 % (15346)------------------------------
% 7.96/2.34 % (15349)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_14910 for (2990ds/4350Mi)
% 7.96/2.36 % (15334)Instruction limit reached!
% 7.96/2.36 % (15334)------------------------------
% 7.96/2.36 % (15334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.36 % (15334)Termination reason: Unknown
% 7.96/2.36 % (15334)Termination phase: Saturation
% 7.96/2.36
% 7.96/2.36 % (15334)Memory used [KB]: 9083
% 7.96/2.36 % (15334)Time elapsed: 0.291 s
% 7.96/2.36 % (15334)Instructions burned: 922 (million)
% 7.96/2.36 % (15334)------------------------------
% 7.96/2.36 % (15334)------------------------------
% 7.96/2.37 % (15350)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_14910 for (2989ds/68Mi)
% 7.96/2.39 % (15350)Instruction limit reached!
% 7.96/2.39 % (15350)------------------------------
% 7.96/2.39 % (15350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.39 % (15350)Termination reason: Unknown
% 7.96/2.39 % (15350)Termination phase: Saturation
% 7.96/2.39
% 7.96/2.39 % (15350)Memory used [KB]: 6268
% 7.96/2.39 % (15350)Time elapsed: 0.019 s
% 7.96/2.39 % (15350)Instructions burned: 70 (million)
% 7.96/2.39 % (15350)------------------------------
% 7.96/2.39 % (15350)------------------------------
% 8.43/2.40 % (15351)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_14910 for (2989ds/358Mi)
% 8.43/2.44 % (15339)Instruction limit reached!
% 8.43/2.44 % (15339)------------------------------
% 8.43/2.44 % (15339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.44 % (15339)Termination reason: Unknown
% 8.43/2.44 % (15339)Termination phase: Saturation
% 8.43/2.44
% 8.43/2.44 % (15339)Memory used [KB]: 9594
% 8.43/2.44 % (15339)Time elapsed: 0.321 s
% 8.43/2.44 % (15339)Instructions burned: 1023 (million)
% 8.43/2.44 % (15339)------------------------------
% 8.43/2.44 % (15339)------------------------------
% 8.43/2.45 % (15352)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_14910 for (2988ds/31Mi)
% 8.43/2.46 % (15352)Instruction limit reached!
% 8.43/2.46 % (15352)------------------------------
% 8.43/2.46 % (15352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.46 % (15352)Termination reason: Unknown
% 8.43/2.46 % (15352)Termination phase: Property scanning
% 8.43/2.46
% 8.43/2.46 % (15352)Memory used [KB]: 1663
% 8.43/2.46 % (15352)Time elapsed: 0.010 s
% 8.43/2.46 % (15352)Instructions burned: 31 (million)
% 8.43/2.46 % (15352)------------------------------
% 8.43/2.46 % (15352)------------------------------
% 8.43/2.47 % (15353)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14910 for (2988ds/279Mi)
% 8.79/2.50 % (15351)Instruction limit reached!
% 8.79/2.50 % (15351)------------------------------
% 8.79/2.50 % (15351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.50 % (15351)Termination reason: Unknown
% 8.79/2.50 % (15351)Termination phase: Saturation
% 8.79/2.50
% 8.79/2.50 % (15351)Memory used [KB]: 7291
% 8.79/2.50 % (15351)Time elapsed: 0.107 s
% 8.79/2.50 % (15351)Instructions burned: 358 (million)
% 8.79/2.50 % (15351)------------------------------
% 8.79/2.50 % (15351)------------------------------
% 8.79/2.51 % (15354)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14910 for (2988ds/258Mi)
% 8.79/2.54 % (15353)Instruction limit reached!
% 8.79/2.54 % (15353)------------------------------
% 8.79/2.54 % (15353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.54 % (15353)Termination reason: Unknown
% 8.79/2.54 % (15353)Termination phase: Saturation
% 8.79/2.54
% 8.79/2.54 % (15353)Memory used [KB]: 6396
% 8.79/2.54 % (15353)Time elapsed: 0.068 s
% 8.79/2.54 % (15353)Instructions burned: 280 (million)
% 8.79/2.54 % (15353)------------------------------
% 8.79/2.54 % (15353)------------------------------
% 8.79/2.55 % (15355)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_14910 for (2988ds/26Mi)
% 8.79/2.56 % (15355)Instruction limit reached!
% 8.79/2.56 % (15355)------------------------------
% 8.79/2.56 % (15355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.56 % (15355)Termination reason: Unknown
% 8.79/2.56 % (15355)Termination phase: Property scanning
% 8.79/2.56
% 8.79/2.56 % (15355)Memory used [KB]: 1663
% 8.79/2.56 % (15355)Time elapsed: 0.008 s
% 8.79/2.56 % (15355)Instructions burned: 27 (million)
% 8.79/2.56 % (15355)------------------------------
% 8.79/2.56 % (15355)------------------------------
% 8.79/2.57 % (15356)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_14910 for (2987ds/995Mi)
% 8.79/2.58 % (15354)Instruction limit reached!
% 8.79/2.58 % (15354)------------------------------
% 8.79/2.58 % (15354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.58 % (15354)Termination reason: Unknown
% 8.79/2.58 % (15354)Termination phase: Saturation
% 8.79/2.58
% 8.79/2.58 % (15354)Memory used [KB]: 7547
% 8.79/2.58 % (15354)Time elapsed: 0.071 s
% 8.79/2.58 % (15354)Instructions burned: 258 (million)
% 8.79/2.58 % (15354)------------------------------
% 8.79/2.58 % (15354)------------------------------
% 8.79/2.59 % (15357)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_14910 for (2987ds/373Mi)
% 9.07/2.68 % (15345)Instruction limit reached!
% 9.07/2.68 % (15345)------------------------------
% 9.07/2.68 % (15345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.68 % (15345)Termination reason: Unknown
% 9.07/2.68 % (15345)Termination phase: Saturation
% 9.07/2.68
% 9.07/2.68 % (15345)Memory used [KB]: 8699
% 9.07/2.68 % (15345)Time elapsed: 0.479 s
% 9.07/2.68 % (15345)Instructions burned: 1540 (million)
% 9.07/2.68 % (15345)------------------------------
% 9.07/2.68 % (15345)------------------------------
% 9.07/2.69 % (15358)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_14910 for (2986ds/253Mi)
% 9.56/2.71 % (15357)Instruction limit reached!
% 9.56/2.71 % (15357)------------------------------
% 9.56/2.71 % (15357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.71 % (15357)Termination reason: Unknown
% 9.56/2.71 % (15357)Termination phase: Saturation
% 9.56/2.71
% 9.56/2.71 % (15357)Memory used [KB]: 7291
% 9.56/2.71 % (15357)Time elapsed: 0.115 s
% 9.56/2.71 % (15357)Instructions burned: 374 (million)
% 9.56/2.71 % (15357)------------------------------
% 9.56/2.71 % (15357)------------------------------
% 9.56/2.72 % (15359)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_14910 for (2986ds/832Mi)
% 9.56/2.75 % (15358)Instruction limit reached!
% 9.56/2.75 % (15358)------------------------------
% 9.56/2.75 % (15358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.75 % (15358)Termination reason: Unknown
% 9.56/2.75 % (15358)Termination phase: Saturation
% 9.56/2.75
% 9.56/2.75 % (15358)Memory used [KB]: 6396
% 9.56/2.75 % (15358)Time elapsed: 0.062 s
% 9.56/2.75 % (15358)Instructions burned: 253 (million)
% 9.56/2.75 % (15358)------------------------------
% 9.56/2.75 % (15358)------------------------------
% 9.56/2.76 % (15360)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_14910 for (2985ds/668Mi)
% 9.75/2.80 % (15356)Instruction limit reached!
% 9.75/2.80 % (15356)------------------------------
% 9.75/2.80 % (15356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.80 % (15356)Termination reason: Unknown
% 9.75/2.80 % (15356)Termination phase: Saturation
% 9.75/2.80
% 9.75/2.80 % (15356)Memory used [KB]: 8315
% 9.75/2.80 % (15356)Time elapsed: 0.239 s
% 9.75/2.80 % (15356)Instructions burned: 998 (million)
% 9.75/2.80 % (15356)------------------------------
% 9.75/2.80 % (15356)------------------------------
% 9.75/2.81 % (15361)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_14910 for (2985ds/40Mi)
% 9.75/2.82 % (15348)Instruction limit reached!
% 9.75/2.82 % (15348)------------------------------
% 9.75/2.82 % (15348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.82 % (15348)Termination reason: Unknown
% 9.75/2.82 % (15348)Termination phase: Saturation
% 9.75/2.82
% 9.75/2.82 % (15348)Memory used [KB]: 3709
% 9.75/2.82 % (15348)Time elapsed: 0.580 s
% 9.75/2.82 % (15348)Instructions burned: 1913 (million)
% 9.75/2.82 % (15348)------------------------------
% 9.75/2.82 % (15348)------------------------------
% 9.75/2.82 % (15361)Instruction limit reached!
% 9.75/2.82 % (15361)------------------------------
% 9.75/2.82 % (15361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.82 % (15361)Termination reason: Unknown
% 9.75/2.82 % (15361)Termination phase: Function definition elimination
% 9.75/2.82
% 9.75/2.82 % (15361)Memory used [KB]: 1663
% 9.75/2.82 % (15361)Time elapsed: 0.012 s
% 9.75/2.82 % (15361)Instructions burned: 43 (million)
% 9.75/2.82 % (15361)------------------------------
% 9.75/2.82 % (15361)------------------------------
% 9.75/2.83 % (15362)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_14910 for (2985ds/294Mi)
% 9.75/2.83 % (15363)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_14910 for (2985ds/187Mi)
% 9.75/2.89 % (15363)Instruction limit reached!
% 9.75/2.89 % (15363)------------------------------
% 9.75/2.89 % (15363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.89 % (15363)Termination reason: Unknown
% 9.75/2.89 % (15363)Termination phase: Saturation
% 9.75/2.89
% 9.75/2.89 % (15363)Memory used [KB]: 7164
% 9.75/2.89 % (15363)Time elapsed: 0.057 s
% 9.75/2.89 % (15363)Instructions burned: 190 (million)
% 9.75/2.89 % (15363)------------------------------
% 9.75/2.89 % (15363)------------------------------
% 10.69/2.90 % (15364)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14910 for (2984ds/371Mi)
% 10.69/2.90 % (15362)Instruction limit reached!
% 10.69/2.90 % (15362)------------------------------
% 10.69/2.90 % (15362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.90 % (15362)Termination reason: Unknown
% 10.69/2.90 % (15362)Termination phase: Saturation
% 10.69/2.90
% 10.69/2.90 % (15362)Memory used [KB]: 6268
% 10.69/2.90 % (15362)Time elapsed: 0.076 s
% 10.69/2.90 % (15362)Instructions burned: 294 (million)
% 10.69/2.90 % (15362)------------------------------
% 10.69/2.90 % (15362)------------------------------
% 10.69/2.91 % (15365)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14910 for (2984ds/1827Mi)
% 10.69/2.92 % (15360)Instruction limit reached!
% 10.69/2.92 % (15360)------------------------------
% 10.69/2.92 % (15360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.92 % (15360)Termination reason: Unknown
% 10.69/2.92 % (15360)Termination phase: Saturation
% 10.69/2.92
% 10.69/2.92 % (15360)Memory used [KB]: 13048
% 10.69/2.92 % (15360)Time elapsed: 0.163 s
% 10.69/2.92 % (15360)Instructions burned: 669 (million)
% 10.69/2.92 % (15360)------------------------------
% 10.69/2.92 % (15360)------------------------------
% 10.69/2.93 % (15366)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_14910 for (2984ds/70Mi)
% 10.69/2.95 % (15366)Instruction limit reached!
% 10.69/2.95 % (15366)------------------------------
% 10.69/2.95 % (15366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.95 % (15366)Termination reason: Unknown
% 10.69/2.95 % (15366)Termination phase: Saturation
% 10.69/2.95
% 10.69/2.95 % (15366)Memory used [KB]: 1791
% 10.69/2.95 % (15366)Time elapsed: 0.020 s
% 10.69/2.95 % (15366)Instructions burned: 73 (million)
% 10.69/2.95 % (15366)------------------------------
% 10.69/2.95 % (15366)------------------------------
% 10.69/2.96 % (15367)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_14910 for (2983ds/316Mi)
% 10.69/2.98 % (15359)Instruction limit reached!
% 10.69/2.98 % (15359)------------------------------
% 10.69/2.98 % (15359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/2.98 % (15359)Termination reason: Unknown
% 10.69/2.98 % (15359)Termination phase: Saturation
% 10.69/2.98
% 10.69/2.98 % (15359)Memory used [KB]: 8827
% 10.69/2.98 % (15359)Time elapsed: 0.262 s
% 10.69/2.98 % (15359)Instructions burned: 834 (million)
% 10.69/2.98 % (15359)------------------------------
% 10.69/2.98 % (15359)------------------------------
% 10.69/2.99 % (15368)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_14910 for (2983ds/932Mi)
% 10.69/3.01 % (15364)Instruction limit reached!
% 10.69/3.01 % (15364)------------------------------
% 10.69/3.01 % (15364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.69/3.01 % (15364)Termination reason: Unknown
% 10.69/3.01 % (15364)Termination phase: Saturation
% 10.69/3.01
% 10.69/3.01 % (15364)Memory used [KB]: 7291
% 10.69/3.01 % (15364)Time elapsed: 0.111 s
% 10.69/3.01 % (15364)Instructions burned: 372 (million)
% 10.69/3.01 % (15364)------------------------------
% 10.69/3.01 % (15364)------------------------------
% 10.69/3.02 % (15369)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_14910 for (2983ds/4714Mi)
% 13.87/3.04 % (15367)Instruction limit reached!
% 13.87/3.04 % (15367)------------------------------
% 13.87/3.04 % (15367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.04 % (15367)Termination reason: Unknown
% 13.87/3.04 % (15367)Termination phase: Saturation
% 13.87/3.04
% 13.87/3.04 % (15367)Memory used [KB]: 7164
% 13.87/3.04 % (15367)Time elapsed: 0.079 s
% 13.87/3.04 % (15367)Instructions burned: 318 (million)
% 13.87/3.04 % (15367)------------------------------
% 13.87/3.04 % (15367)------------------------------
% 13.87/3.05 % (15370)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_14910 for (2983ds/8250Mi)
% 14.76/3.22 % (15368)Instruction limit reached!
% 14.76/3.22 % (15368)------------------------------
% 14.76/3.22 % (15368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.76/3.22 % (15368)Termination reason: Unknown
% 14.76/3.22 % (15368)Termination phase: Saturation
% 14.76/3.22
% 14.76/3.22 % (15368)Memory used [KB]: 9210
% 14.76/3.22 % (15368)Time elapsed: 0.236 s
% 14.76/3.22 % (15368)Instructions burned: 932 (million)
% 14.76/3.22 % (15368)------------------------------
% 14.76/3.22 % (15368)------------------------------
% 14.76/3.23 % (15371)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_14910 for (2981ds/770Mi)
% 15.19/3.31 % (15365)First to succeed.
% 15.19/3.32 % (15365)Refutation found. Thanks to Tanya!
% 15.19/3.32 % SZS status Theorem for DTF2THF_14910
% 15.19/3.32 % SZS output start Proof for DTF2THF_14910
% 15.19/3.32 thf(func_def_0, type, in: $i > $i > $o).
% 15.19/3.32 thf(func_def_1, type, exu: ($i > $o) > $o).
% 15.19/3.32 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 15.19/3.32 thf(func_def_8, type, powerset: $i > $i).
% 15.19/3.32 thf(func_def_10, type, setunion: $i > $i).
% 15.19/3.32 thf(func_def_19, type, descr: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_26, type, prop2set: $o > $i).
% 15.19/3.32 thf(func_def_36, type, nonempty: $i > $o).
% 15.19/3.32 thf(func_def_69, type, set2prop: $i > $o).
% 15.19/3.32 thf(func_def_88, type, subset: $i > $i > $o).
% 15.19/3.32 thf(func_def_89, type, disjoint: $i > $i > $o).
% 15.19/3.32 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 15.19/3.32 thf(func_def_114, type, binunion: $i > $i > $i).
% 15.19/3.32 thf(func_def_122, type, binintersect: $i > $i > $i).
% 15.19/3.32 thf(func_def_135, type, regular: $i > $o).
% 15.19/3.32 thf(func_def_136, type, setminus: $i > $i > $i).
% 15.19/3.32 thf(func_def_170, type, sK9: $i > $o).
% 15.19/3.32 thf(func_def_196, type, sK35: $i > $i).
% 15.19/3.32 thf(func_def_199, type, sK38: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_200, type, sK39: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_201, type, sK40: $i > $o).
% 15.19/3.32 thf(func_def_207, type, sK46: $i > $i).
% 15.19/3.32 thf(func_def_210, type, sK49: $i > $i).
% 15.19/3.32 thf(func_def_214, type, sK53: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_215, type, sK54: $i > $o).
% 15.19/3.32 thf(func_def_216, type, sK55: $i > $i).
% 15.19/3.32 thf(func_def_223, type, sK62: $i > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_225, type, sK64: $i > $o).
% 15.19/3.32 thf(func_def_233, type, sK72: $i > $o).
% 15.19/3.32 thf(func_def_241, type, sK80: $i > $o).
% 15.19/3.32 thf(func_def_257, type, sK96: $i > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_259, type, sK98: $i > $o).
% 15.19/3.32 thf(func_def_273, type, sK112: $i > $o).
% 15.19/3.32 thf(func_def_283, type, sK122: $i > $o).
% 15.19/3.32 thf(func_def_286, type, sK125: $i > $i).
% 15.19/3.32 thf(func_def_287, type, sK126: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_288, type, sK127: $i > $i > $i).
% 15.19/3.32 thf(func_def_289, type, sK128: $i > $i > $i).
% 15.19/3.32 thf(func_def_290, type, sK129: $i > $i > $i).
% 15.19/3.32 thf(func_def_292, type, sK131: $i > $i).
% 15.19/3.32 thf(func_def_293, type, sK132: $i > $i).
% 15.19/3.32 thf(func_def_294, type, sK133: $i > $i).
% 15.19/3.32 thf(func_def_295, type, sK134: $i > $i).
% 15.19/3.32 thf(func_def_296, type, sK135: $i > $i).
% 15.19/3.32 thf(func_def_297, type, sK136: $i > $i).
% 15.19/3.32 thf(func_def_298, type, sK137: $i > $i).
% 15.19/3.32 thf(func_def_299, type, sK138: $i > $i).
% 15.19/3.32 thf(func_def_300, type, sK139: $i > $i).
% 15.19/3.32 thf(func_def_301, type, sK140: $i > $i).
% 15.19/3.32 thf(func_def_302, type, sK141: $i > $i).
% 15.19/3.32 thf(func_def_303, type, sK142: $i > $i).
% 15.19/3.32 thf(func_def_304, type, sK143: $i > $i).
% 15.19/3.32 thf(func_def_305, type, sK144: $i > $i).
% 15.19/3.32 thf(func_def_306, type, sK145: $i > $i).
% 15.19/3.32 thf(func_def_307, type, sK146: $i > $i).
% 15.19/3.32 thf(func_def_308, type, sK147: $i > $i).
% 15.19/3.32 thf(func_def_309, type, sK148: $i > $i).
% 15.19/3.32 thf(func_def_310, type, sK149: $i > $i).
% 15.19/3.32 thf(func_def_311, type, sK150: $i > $i).
% 15.19/3.32 thf(func_def_312, type, sK151: $i > $i).
% 15.19/3.32 thf(func_def_313, type, sK152: $i > $i).
% 15.19/3.32 thf(func_def_314, type, sK153: $i > $i).
% 15.19/3.32 thf(func_def_315, type, sK154: $i > $i).
% 15.19/3.32 thf(func_def_316, type, sK155: $i > $i).
% 15.19/3.32 thf(func_def_317, type, sK156: $i > $i).
% 15.19/3.32 thf(func_def_318, type, sK157: $i > $i).
% 15.19/3.32 thf(func_def_319, type, sK158: $i > $i).
% 15.19/3.32 thf(func_def_320, type, sK159: $i > $i).
% 15.19/3.32 thf(func_def_321, type, sK160: $i > $i).
% 15.19/3.32 thf(func_def_322, type, sK161: $i > $i).
% 15.19/3.32 thf(func_def_323, type, sK162: $i > $i).
% 15.19/3.32 thf(func_def_324, type, sK163: $i > $i).
% 15.19/3.32 thf(func_def_325, type, sK164: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_326, type, sK165: $i > $i > $i).
% 15.19/3.32 thf(func_def_327, type, sK166: $i > $i > $i).
% 15.19/3.32 thf(func_def_328, type, sK167: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_329, type, sK168: $i > $i > $i).
% 15.19/3.32 thf(func_def_330, type, sK169: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_331, type, sK170: $i > $i > $i).
% 15.19/3.32 thf(func_def_332, type, sK171: $i > $i > $i).
% 15.19/3.32 thf(func_def_333, type, sK172: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_334, type, sK173: $i > $i > $i).
% 15.19/3.32 thf(func_def_335, type, sK174: $i > $i > $i).
% 15.19/3.32 thf(func_def_336, type, sK175: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_337, type, sK176: $i > $i > $i).
% 15.19/3.32 thf(func_def_338, type, sK177: $i > $i > $i).
% 15.19/3.32 thf(func_def_339, type, sK178: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_340, type, sK179: $i > $i > $i).
% 15.19/3.32 thf(func_def_341, type, sK180: $i > $i > $i).
% 15.19/3.32 thf(func_def_342, type, sK181: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_343, type, sK182: $i > $i > $i).
% 15.19/3.32 thf(func_def_344, type, sK183: $i > $i > $i).
% 15.19/3.32 thf(func_def_345, type, sK184: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_346, type, sK185: $i > $i).
% 15.19/3.32 thf(func_def_347, type, sK186: $i > $i > $i).
% 15.19/3.32 thf(func_def_348, type, sK187: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_349, type, sK188: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_350, type, sK189: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_351, type, sK190: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_352, type, sK191: $i > $i > $i).
% 15.19/3.32 thf(func_def_353, type, sK192: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_354, type, sK193: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_355, type, sK194: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_356, type, sK195: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_357, type, sK196: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_358, type, sK197: $i > $i > $i).
% 15.19/3.32 thf(func_def_359, type, sK198: $i > $i > $i).
% 15.19/3.32 thf(func_def_360, type, sK199: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_361, type, sK200: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_362, type, sK201: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_363, type, sK202: $i > $i > $i).
% 15.19/3.32 thf(func_def_364, type, sK203: $i > $i > $i).
% 15.19/3.32 thf(func_def_365, type, sK204: $i > $i > $i).
% 15.19/3.32 thf(func_def_366, type, sK205: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_367, type, sK206: $i > $i).
% 15.19/3.32 thf(func_def_368, type, sK207: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_369, type, sK208: $i > $i > $i).
% 15.19/3.32 thf(func_def_370, type, sK209: $i > $i > $i).
% 15.19/3.32 thf(func_def_371, type, sK210: $i > $i > $i).
% 15.19/3.32 thf(func_def_372, type, sK211: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_373, type, sK212: $i > $i > $i).
% 15.19/3.32 thf(func_def_374, type, sK213: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_375, type, sK214: $i > $i > $i).
% 15.19/3.32 thf(func_def_376, type, sK215: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_377, type, sK216: $i > $i > $i).
% 15.19/3.32 thf(func_def_378, type, sK217: $i > $i > $i).
% 15.19/3.32 thf(func_def_379, type, sK218: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_380, type, sK219: $i > $i > $i).
% 15.19/3.32 thf(func_def_381, type, sK220: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_382, type, sK221: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_383, type, sK222: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_384, type, sK223: $i > $i).
% 15.19/3.32 thf(func_def_385, type, sK224: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_386, type, sK225: $i > $i > $i).
% 15.19/3.32 thf(func_def_387, type, sK226: $i > $i > $i).
% 15.19/3.32 thf(func_def_388, type, sK227: $i > $i > $i).
% 15.19/3.32 thf(func_def_389, type, sK228: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_390, type, sK229: $i > $i > $i).
% 15.19/3.32 thf(func_def_391, type, sK230: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_392, type, sK231: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_393, type, sK232: $i > $i > $i).
% 15.19/3.32 thf(func_def_394, type, sK233: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_395, type, sK234: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_396, type, sK235: $i > $i > $i).
% 15.19/3.32 thf(func_def_397, type, sK236: $i > $i > $i).
% 15.19/3.32 thf(func_def_398, type, sK237: $i > $i > $i).
% 15.19/3.32 thf(func_def_399, type, sK238: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_400, type, sK239: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_401, type, sK240: $i > $i > $i).
% 15.19/3.32 thf(func_def_402, type, sK241: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_403, type, sK242: $i > $i).
% 15.19/3.32 thf(func_def_404, type, sK243: $i > $i).
% 15.19/3.32 thf(func_def_405, type, sK244: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_406, type, sK245: $i > $i).
% 15.19/3.32 thf(func_def_407, type, sK246: $i > $i).
% 15.19/3.32 thf(func_def_408, type, sK247: $i > $i).
% 15.19/3.32 thf(func_def_409, type, sK248: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_410, type, sK249: $i > $i).
% 15.19/3.32 thf(func_def_411, type, sK250: $i > $i).
% 15.19/3.32 thf(func_def_412, type, sK251: $i > $i).
% 15.19/3.32 thf(func_def_413, type, sK252: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_414, type, sK253: $i > $i).
% 15.19/3.32 thf(func_def_415, type, sK254: $i > $i).
% 15.19/3.32 thf(func_def_416, type, sK255: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_417, type, sK256: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_418, type, sK257: $i > $i).
% 15.19/3.32 thf(func_def_419, type, sK258: $i > $i).
% 15.19/3.32 thf(func_def_420, type, sK259: $i > $i).
% 15.19/3.32 thf(func_def_421, type, sK260: $i > $i).
% 15.19/3.32 thf(func_def_422, type, sK261: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_423, type, sK262: $i > $i).
% 15.19/3.32 thf(func_def_424, type, sK263: $i > $i).
% 15.19/3.32 thf(func_def_425, type, sK264: $i > $i).
% 15.19/3.32 thf(func_def_426, type, sK265: $i > $i).
% 15.19/3.32 thf(func_def_427, type, sK266: $i > $i).
% 15.19/3.32 thf(func_def_428, type, sK267: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_429, type, sK268: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_430, type, sK269: $i > $i).
% 15.19/3.32 thf(func_def_431, type, sK270: $i > $i).
% 15.19/3.32 thf(func_def_432, type, sK271: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_433, type, sK272: $i > $i).
% 15.19/3.32 thf(func_def_434, type, sK273: $i > $i).
% 15.19/3.32 thf(func_def_435, type, sK274: $i > $i).
% 15.19/3.32 thf(func_def_436, type, sK275: $i > $i).
% 15.19/3.32 thf(func_def_437, type, sK276: $i > $i).
% 15.19/3.32 thf(func_def_438, type, sK277: $i > $i).
% 15.19/3.32 thf(func_def_439, type, sK278: $i > $i).
% 15.19/3.32 thf(func_def_440, type, sK279: $i > $i).
% 15.19/3.32 thf(func_def_441, type, sK280: $i > $i).
% 15.19/3.32 thf(func_def_442, type, sK281: $i > $i).
% 15.19/3.32 thf(func_def_443, type, sK282: $i > $i).
% 15.19/3.32 thf(func_def_444, type, sK283: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_445, type, sK284: $i > $i > $i).
% 15.19/3.32 thf(func_def_446, type, sK285: $i > $i > $i).
% 15.19/3.32 thf(func_def_447, type, sK286: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_448, type, sK287: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_449, type, sK288: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_450, type, sK289: $i > $i > $i).
% 15.19/3.32 thf(func_def_451, type, sK290: $i > $i > $i).
% 15.19/3.32 thf(func_def_452, type, sK291: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_453, type, sK292: $i > $i > $i).
% 15.19/3.32 thf(func_def_454, type, sK293: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_455, type, sK294: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_456, type, sK295: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_457, type, sK296: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_458, type, sK297: $i > $i).
% 15.19/3.32 thf(func_def_459, type, sK298: $i > $i).
% 15.19/3.32 thf(func_def_460, type, sK299: $i > $i).
% 15.19/3.32 thf(func_def_461, type, sK300: $i > $i).
% 15.19/3.32 thf(func_def_462, type, sK301: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_463, type, sK302: $i > $i > $i).
% 15.19/3.32 thf(func_def_464, type, sK303: $i > $i > $i).
% 15.19/3.32 thf(func_def_465, type, sK304: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_466, type, sK305: $i > $i > $i).
% 15.19/3.32 thf(func_def_467, type, sK306: $i > $i > $i).
% 15.19/3.32 thf(func_def_468, type, sK307: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_469, type, sK308: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_470, type, sK309: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_471, type, sK310: $i > $i > $i).
% 15.19/3.32 thf(func_def_472, type, sK311: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_473, type, sK312: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_474, type, sK313: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_475, type, sK314: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_476, type, sK315: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_477, type, sK316: $i > $i > $i).
% 15.19/3.32 thf(func_def_478, type, sK317: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_479, type, sK318: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_480, type, sK319: $i > $i).
% 15.19/3.32 thf(func_def_481, type, sK320: $i > $i).
% 15.19/3.32 thf(func_def_482, type, sK321: $i > $i).
% 15.19/3.32 thf(func_def_483, type, sK322: $i > $i > $i).
% 15.19/3.32 thf(func_def_484, type, sK323: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_485, type, sK324: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_486, type, sK325: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_487, type, sK326: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_488, type, sK327: $i > $i > $i).
% 15.19/3.32 thf(func_def_489, type, sK328: $i > $i > $i).
% 15.19/3.32 thf(func_def_490, type, sK329: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_491, type, sK330: $i > $i > $i).
% 15.19/3.32 thf(func_def_492, type, sK331: $i > $i > $i).
% 15.19/3.32 thf(func_def_493, type, sK332: $i > $i).
% 15.19/3.32 thf(func_def_494, type, sK333: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_495, type, sK334: $i > $i > $i).
% 15.19/3.32 thf(func_def_496, type, sK335: $i > $i > $i).
% 15.19/3.32 thf(func_def_497, type, sK336: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_498, type, sK337: $i > $i > $i).
% 15.19/3.32 thf(func_def_499, type, sK338: $i > $i > $i).
% 15.19/3.32 thf(func_def_500, type, sK339: $i > $i).
% 15.19/3.32 thf(func_def_501, type, sK340: $i > $i > $i).
% 15.19/3.32 thf(func_def_502, type, sK341: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_503, type, sK342: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_504, type, sK343: $i > $i).
% 15.19/3.32 thf(func_def_505, type, sK344: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_506, type, sK345: $i > $i > $i).
% 15.19/3.32 thf(func_def_507, type, sK346: $i > $i > $i).
% 15.19/3.32 thf(func_def_508, type, sK347: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_509, type, sK348: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_510, type, sK349: $i > $i).
% 15.19/3.32 thf(func_def_511, type, sK350: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_512, type, sK351: $i > $i > $i).
% 15.19/3.32 thf(func_def_513, type, sK352: $i > $i > $i).
% 15.19/3.32 thf(func_def_514, type, sK353: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_515, type, sK354: $i > $i > $i).
% 15.19/3.32 thf(func_def_516, type, sK355: $i > $i > $i).
% 15.19/3.32 thf(func_def_517, type, sK356: $i > $i).
% 15.19/3.32 thf(func_def_518, type, sK357: $i > $i).
% 15.19/3.32 thf(func_def_519, type, sK358: $i > $i > $i).
% 15.19/3.32 thf(func_def_520, type, sK359: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_521, type, sK360: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_522, type, sK361: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_523, type, sK362: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_524, type, sK363: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_525, type, sK364: $i > $i > $i).
% 15.19/3.32 thf(func_def_526, type, sK365: $i > $i > $i).
% 15.19/3.32 thf(func_def_527, type, sK366: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_528, type, sK367: $i > $i > $i).
% 15.19/3.32 thf(func_def_529, type, sK368: $i > $i > $i).
% 15.19/3.32 thf(func_def_530, type, sK369: $i > $i).
% 15.19/3.32 thf(func_def_531, type, sK370: $i > $i).
% 15.19/3.32 thf(func_def_532, type, sK371: $i > $i).
% 15.19/3.32 thf(func_def_533, type, sK372: $i > $i).
% 15.19/3.32 thf(func_def_534, type, sK373: $i > $i).
% 15.19/3.32 thf(func_def_535, type, sK374: $i > $i).
% 15.19/3.32 thf(func_def_536, type, sK375: $i > $i).
% 15.19/3.32 thf(func_def_537, type, sK376: $i > $i).
% 15.19/3.32 thf(func_def_538, type, sK377: $i > $i > $i).
% 15.19/3.32 thf(func_def_539, type, sK378: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_540, type, sK379: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_541, type, sK380: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_542, type, sK381: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_543, type, sK382: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_544, type, sK383: $i > $i > $i).
% 15.19/3.32 thf(func_def_545, type, sK384: $i > $i > $i).
% 15.19/3.32 thf(func_def_546, type, sK385: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_547, type, sK386: $i > $i > $i).
% 15.19/3.32 thf(func_def_548, type, sK387: $i > $i > $i).
% 15.19/3.32 thf(func_def_549, type, sK388: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_550, type, sK389: $i > $i > $i).
% 15.19/3.32 thf(func_def_551, type, sK390: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_552, type, sK391: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_553, type, sK392: $i > $i > $i).
% 15.19/3.32 thf(func_def_554, type, sK393: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_555, type, sK394: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_556, type, sK395: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_557, type, sK396: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_558, type, sK397: $i > $i).
% 15.19/3.32 thf(func_def_559, type, sK398: $i > $i).
% 15.19/3.32 thf(func_def_560, type, sK399: $i > $i).
% 15.19/3.32 thf(func_def_561, type, sK400: $i > $i > $i).
% 15.19/3.32 thf(func_def_562, type, sK401: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_563, type, sK402: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_564, type, sK403: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_565, type, sK404: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_566, type, sK405: $i > $i > $i).
% 15.19/3.32 thf(func_def_567, type, sK406: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_568, type, sK407: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_569, type, sK408: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_570, type, sK409: $i > $i).
% 15.19/3.32 thf(func_def_571, type, sK410: $i > $i).
% 15.19/3.32 thf(func_def_572, type, sK411: $i > $i > $i).
% 15.19/3.32 thf(func_def_573, type, sK412: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_574, type, sK413: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_575, type, sK414: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_576, type, sK415: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_577, type, sK416: $i > $i > $i).
% 15.19/3.32 thf(func_def_578, type, sK417: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_579, type, sK418: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_580, type, sK419: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_581, type, sK420: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_582, type, sK421: $i > $i).
% 15.19/3.32 thf(func_def_583, type, sK422: $i > $i).
% 15.19/3.32 thf(func_def_584, type, sK423: $i > $i).
% 15.19/3.32 thf(func_def_585, type, sK424: $i > $i).
% 15.19/3.32 thf(func_def_586, type, sK425: $i > $i).
% 15.19/3.32 thf(func_def_587, type, sK426: $i > $i).
% 15.19/3.32 thf(func_def_588, type, sK427: $i > $i).
% 15.19/3.32 thf(func_def_589, type, sK428: $i > $i).
% 15.19/3.32 thf(func_def_590, type, sK429: $i > $i).
% 15.19/3.32 thf(func_def_591, type, sK430: $i > $i).
% 15.19/3.32 thf(func_def_592, type, sK431: $i > $i).
% 15.19/3.32 thf(func_def_593, type, sK432: $i > $i).
% 15.19/3.32 thf(func_def_594, type, sK433: $i > $i).
% 15.19/3.32 thf(func_def_595, type, sK434: $i > $i).
% 15.19/3.32 thf(func_def_596, type, sK435: $i > $i).
% 15.19/3.32 thf(func_def_597, type, sK436: $i > $i).
% 15.19/3.32 thf(func_def_598, type, sK437: $i > $i).
% 15.19/3.32 thf(func_def_599, type, sK438: $i > $i).
% 15.19/3.32 thf(func_def_600, type, sK439: $i > $i).
% 15.19/3.32 thf(func_def_601, type, sK440: $i > $i).
% 15.19/3.32 thf(func_def_602, type, sK441: $i > $i).
% 15.19/3.32 thf(func_def_603, type, sK442: $i > $i).
% 15.19/3.32 thf(func_def_604, type, sK443: $i > $i).
% 15.19/3.32 thf(func_def_605, type, sK444: $i > $i).
% 15.19/3.32 thf(func_def_606, type, sK445: $i > $i).
% 15.19/3.32 thf(func_def_607, type, sK446: $i > $i).
% 15.19/3.32 thf(func_def_608, type, sK447: $i > $i).
% 15.19/3.32 thf(func_def_609, type, sK448: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_610, type, sK449: $i > $i > $i).
% 15.19/3.32 thf(func_def_611, type, sK450: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_612, type, sK451: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_613, type, sK452: $i > $i > $i).
% 15.19/3.32 thf(func_def_614, type, sK453: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_615, type, sK454: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_616, type, sK455: $i > $i).
% 15.19/3.32 thf(func_def_617, type, sK456: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_618, type, sK457: $i > $i > $i).
% 15.19/3.32 thf(func_def_619, type, sK458: $i > $i > $i).
% 15.19/3.32 thf(func_def_620, type, sK459: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_621, type, sK460: $i > $i > $i).
% 15.19/3.32 thf(func_def_622, type, sK461: $i > $i > $i).
% 15.19/3.32 thf(func_def_623, type, sK462: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_624, type, sK463: $i > $i > $i).
% 15.19/3.32 thf(func_def_625, type, sK464: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_626, type, sK465: $i > $i).
% 15.19/3.32 thf(func_def_627, type, sK466: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_628, type, sK467: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_629, type, sK468: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_630, type, sK469: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_631, type, sK470: $i > $i).
% 15.19/3.32 thf(func_def_632, type, sK471: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_633, type, sK472: $i > $i > $i).
% 15.19/3.32 thf(func_def_634, type, sK473: $i > $i > $i).
% 15.19/3.32 thf(func_def_635, type, sK474: $i > $i > $i).
% 15.19/3.32 thf(func_def_636, type, sK475: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_637, type, sK476: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_638, type, sK477: $i > $i > $i).
% 15.19/3.32 thf(func_def_639, type, sK478: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_640, type, sK479: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_641, type, sK480: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_642, type, sK481: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_643, type, sK482: $i > $i).
% 15.19/3.32 thf(func_def_644, type, sK483: $i > $i > $i).
% 15.19/3.32 thf(func_def_645, type, sK484: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_646, type, sK485: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_647, type, sK486: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_648, type, sK487: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_649, type, sK488: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_650, type, sK489: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_651, type, sK490: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_652, type, sK491: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_653, type, sK492: $i > $i > $i).
% 15.19/3.32 thf(func_def_654, type, sK493: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_655, type, sK494: $i > $i).
% 15.19/3.32 thf(func_def_656, type, sK495: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_657, type, sK496: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_658, type, sK497: $i > $i).
% 15.19/3.32 thf(func_def_659, type, sK498: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_660, type, sK499: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_661, type, sK500: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_662, type, sK501: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_663, type, sK502: $i > $i).
% 15.19/3.32 thf(func_def_664, type, sK503: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_665, type, sK504: $i > $i > $i).
% 15.19/3.32 thf(func_def_666, type, sK505: $i > $i > $i).
% 15.19/3.32 thf(func_def_667, type, sK506: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_668, type, sK507: $i > $i > $i).
% 15.19/3.32 thf(func_def_669, type, sK508: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_670, type, sK509: $i > $i).
% 15.19/3.32 thf(func_def_671, type, sK510: $i > $i > $i).
% 15.19/3.32 thf(func_def_672, type, sK511: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_673, type, sK512: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_674, type, sK513: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_675, type, sK514: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_676, type, sK515: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_677, type, sK516: $i > $i > $i).
% 15.19/3.32 thf(func_def_678, type, sK517: $i > $i > $i).
% 15.19/3.32 thf(func_def_679, type, sK518: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_680, type, sK519: $i > $i > $i).
% 15.19/3.32 thf(func_def_681, type, sK520: $i > $i > $i).
% 15.19/3.32 thf(func_def_682, type, sK521: $i > $i).
% 15.19/3.32 thf(func_def_683, type, sK522: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_684, type, sK523: $i > $i > $i).
% 15.19/3.32 thf(func_def_685, type, sK524: $i > $i > $i).
% 15.19/3.32 thf(func_def_686, type, sK525: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_687, type, sK526: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_688, type, sK527: $i > $i > $i).
% 15.19/3.32 thf(func_def_689, type, sK528: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_690, type, sK529: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_691, type, sK530: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_692, type, sK531: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_693, type, sK532: $i > $i).
% 15.19/3.32 thf(func_def_694, type, sK533: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_695, type, sK534: $i > $i > $i).
% 15.19/3.32 thf(func_def_696, type, sK535: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_697, type, sK536: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_698, type, sK537: $i > $i > $i).
% 15.19/3.32 thf(func_def_699, type, sK538: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_700, type, sK539: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_701, type, sK540: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_702, type, sK541: $i > $i).
% 15.19/3.32 thf(func_def_703, type, sK542: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_704, type, sK543: $i > $i > $i).
% 15.19/3.32 thf(func_def_705, type, sK544: $i > $i > $i).
% 15.19/3.32 thf(func_def_706, type, sK545: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_707, type, sK546: $i > $i > $i).
% 15.19/3.32 thf(func_def_708, type, sK547: $i > $i > $i).
% 15.19/3.32 thf(func_def_709, type, sK548: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_710, type, sK549: $i > $i > $i).
% 15.19/3.32 thf(func_def_711, type, sK550: $i > $i > $i).
% 15.19/3.32 thf(func_def_712, type, sK551: $i > $i > $i).
% 15.19/3.32 thf(func_def_713, type, sK552: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_714, type, sK553: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_715, type, sK554: $i > $i).
% 15.19/3.32 thf(func_def_716, type, sK555: $i > $i > $i).
% 15.19/3.32 thf(func_def_717, type, sK556: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_718, type, sK557: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_719, type, sK558: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_720, type, sK559: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_721, type, sK560: $i > $i > $i).
% 15.19/3.32 thf(func_def_722, type, sK561: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_723, type, sK562: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_724, type, sK563: $i > $i > $i > $i).
% 15.19/3.32 thf(func_def_728, type, sK567: $i > $i > $i).
% 15.19/3.32 thf(func_def_738, type, sK577: $i > $o).
% 15.19/3.32 thf(func_def_740, type, sK579: $i > $o).
% 15.19/3.32 thf(func_def_745, type, sK584: $i > $i).
% 15.19/3.32 thf(func_def_749, type, sK588: ($i > $o) > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_750, type, sK589: ($i > $o) > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_751, type, sK590: $i > $o).
% 15.19/3.32 thf(func_def_752, type, sK591: $i > $o).
% 15.19/3.32 thf(func_def_757, type, sK596: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_758, type, sK597: $i > $o).
% 15.19/3.32 thf(func_def_763, type, sK602: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_764, type, sK603: $i > $o).
% 15.19/3.32 thf(func_def_770, type, sK609: $i > $i > $i).
% 15.19/3.32 thf(func_def_771, type, sK610: $i > $i > $i).
% 15.19/3.32 thf(func_def_772, type, sK611: $i > $i > $i).
% 15.19/3.32 thf(func_def_777, type, sK616: $i > $o).
% 15.19/3.32 thf(func_def_784, type, sK623: $i > ($i > $i > $o) > $i).
% 15.19/3.32 thf(func_def_785, type, sK624: $i > ($i > $i > $o) > $i).
% 15.19/3.32 thf(func_def_786, type, sK625: $i > ($i > $i > $o) > $i).
% 15.19/3.32 thf(func_def_788, type, sK627: $i > $i > $o).
% 15.19/3.32 thf(func_def_789, type, sK628: $i > $i).
% 15.19/3.32 thf(func_def_796, type, sK635: $i > $o).
% 15.19/3.32 thf(func_def_798, type, sK637: $i > $o).
% 15.19/3.32 thf(func_def_801, type, sK640: $i > $i > $i).
% 15.19/3.32 thf(func_def_805, type, sK644: ($i > $o) > $i > ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_806, type, sK645: $i > $i > ($i > $o) > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_809, type, sK648: $i > $o).
% 15.19/3.32 thf(func_def_810, type, sK649: $i > $o).
% 15.19/3.32 thf(func_def_815, type, sK654: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_816, type, sK655: $i > $o).
% 15.19/3.32 thf(func_def_819, type, sK658: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_820, type, sK659: $i > $o).
% 15.19/3.32 thf(func_def_822, type, sK661: $i > $i).
% 15.19/3.32 thf(func_def_824, type, sK663: $i > $i).
% 15.19/3.32 thf(func_def_826, type, sK665: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_827, type, sK666: $i > $o).
% 15.19/3.32 thf(func_def_833, type, sK672: $i > $i > $i).
% 15.19/3.32 thf(func_def_836, type, sK675: $i > $i > $o > $i).
% 15.19/3.32 thf(func_def_840, type, sK679: $i > $i > $i).
% 15.19/3.32 thf(func_def_869, type, sK708: $i > $i).
% 15.19/3.32 thf(func_def_878, type, sK717: $i > $i > $i).
% 15.19/3.32 thf(func_def_886, type, sK725: $i > $o).
% 15.19/3.32 thf(func_def_887, type, sK726: ($i > $o) > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_888, type, sK727: ($i > $o) > ($i > $o) > $i).
% 15.19/3.32 thf(func_def_889, type, sK728: $i > $o).
% 15.19/3.32 thf(func_def_890, type, sK729: $i > $o).
% 15.19/3.32 thf(func_def_891, type, sK730: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_892, type, sK731: $i > $o).
% 15.19/3.32 thf(func_def_893, type, sK732: $i > $i).
% 15.19/3.32 thf(func_def_898, type, sK737: $i > $o).
% 15.19/3.32 thf(func_def_906, type, sK745: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_907, type, sK746: $i > $o).
% 15.19/3.32 thf(func_def_915, type, sK754: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_916, type, sK755: $i > $o).
% 15.19/3.32 thf(func_def_917, type, ph756: !>[X0: $tType]:(X0)).
% 15.19/3.32 thf(func_def_918, type, sK757: ($i > $o) > $i).
% 15.19/3.32 thf(func_def_919, type, sK758: ($i > $o) > $i > $i).
% 15.19/3.32 thf(func_def_920, type, sK759: $i > $i > $i).
% 15.19/3.32 thf(func_def_921, type, sK760: $i > $i > $i).
% 15.19/3.32 thf(func_def_922, type, sK761: $i > $i > $i).
% 15.19/3.32 thf(func_def_923, type, sK762: $i > $i > $i).
% 15.19/3.32 thf(func_def_924, type, sK763: $i > $i > $i).
% 15.19/3.32 thf(func_def_925, type, sK764: $i > $i > $i).
% 15.19/3.32 thf(func_def_927, type, sK766: $i > $i > $i).
% 15.19/3.32 thf(func_def_928, type, sK767: $i > $i > $i).
% 15.19/3.32 thf(func_def_929, type, sK768: $i > $i > $i).
% 15.19/3.32 thf(func_def_930, type, sK769: $i > $i > $i).
% 15.19/3.32 thf(func_def_931, type, sK770: $i > $i > $i).
% 15.19/3.32 thf(func_def_933, type, sK772: $i > $i > $i).
% 15.19/3.32 thf(func_def_934, type, sK773: $i > $i > $i).
% 15.19/3.32 thf(func_def_935, type, sK774: $i > $i).
% 15.19/3.32 thf(func_def_936, type, sK775: $i > $i > $i).
% 15.19/3.32 thf(func_def_937, type, sK776: $i > $i > $i).
% 15.19/3.32 thf(func_def_938, type, sK777: $i > $i > $i).
% 15.19/3.32 thf(func_def_939, type, sK778: $i > $i).
% 15.19/3.32 thf(func_def_940, type, sK779: $i > $i).
% 15.19/3.32 thf(func_def_941, type, sK780: $i > $i > $i).
% 15.19/3.32 thf(func_def_942, type, sK781: $i > $i > $i).
% 15.19/3.32 thf(func_def_943, type, sK782: $i > $i > $i).
% 15.19/3.32 thf(func_def_944, type, sK783: $i > $i > $i).
% 15.19/3.32 thf(func_def_945, type, sK784: $i > $i > $i).
% 15.19/3.32 thf(func_def_946, type, sK785: $i > $i).
% 15.19/3.32 thf(f14655,plain,(
% 15.19/3.32 $false),
% 15.19/3.32 inference(avatar_sat_refutation,[status(thm)],[f7005,f10685,f10707,f10993,f11692,f11726,f12116,f13894,f14645,f14654])).
% 15.19/3.32 thf(f14654,plain,(
% 15.19/3.32 ~spl2_1176 | ~spl2_1178),
% 15.19/3.32 inference(avatar_contradiction_clause,[status(thm)],[f14653])).
% 15.19/3.32 thf(f14653,plain,(
% 15.19/3.32 $false | (~spl2_1176 | ~spl2_1178)),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f14652])).
% 15.19/3.32 thf(f14652,plain,(
% 15.19/3.32 ($true = $false) | (~spl2_1176 | ~spl2_1178)),
% 15.19/3.32 inference(backward_demodulation,[status(thm)],[f10693,f10703])).
% 15.19/3.32 thf(f10703,plain,(
% 15.19/3.32 (setminusILneg = $false) | ~spl2_1178),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10701])).
% 15.19/3.32 thf(f10701,definition,(
% 15.19/3.32 spl2_1178 <=> (setminusILneg = $false)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1178])],[avatar_definition])).
% 15.19/3.32 thf(f10693,plain,(
% 15.19/3.32 (setminusILneg = $true) | ~spl2_1176),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10691])).
% 15.19/3.32 thf(f10691,definition,(
% 15.19/3.32 spl2_1176 <=> (setminusILneg = $true)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1176])],[avatar_definition])).
% 15.19/3.32 thf(f14645,plain,(
% 15.19/3.32 ~spl2_274 | ~spl2_1173 | ~spl2_1179),
% 15.19/3.32 inference(avatar_contradiction_clause,[status(thm)],[f14644])).
% 15.19/3.32 thf(f14644,plain,(
% 15.19/3.32 $false | (~spl2_274 | ~spl2_1173 | ~spl2_1179)),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f14619])).
% 15.19/3.32 thf(f14619,plain,(
% 15.19/3.32 ($true = $false) | (~spl2_274 | ~spl2_1173 | ~spl2_1179)),
% 15.19/3.32 inference(backward_demodulation,[status(thm)],[f14315,f14374])).
% 15.19/3.32 thf(f14374,plain,(
% 15.19/3.32 ( ! [X0 : $i] : (((in @ sK771 @ (setminus @ sK1 @ X0)) = $false)) ) | (~spl2_274 | ~spl2_1173 | ~spl2_1179)),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f14355])).
% 15.19/3.32 thf(f14355,plain,(
% 15.19/3.32 ( ! [X0 : $i] : (((in @ sK771 @ (setminus @ sK1 @ X0)) = $false) | ($true = $false)) ) | (~spl2_274 | ~spl2_1173 | ~spl2_1179)),
% 15.19/3.32 inference(superposition,[status(thm)],[f14314,f10706])).
% 15.19/3.32 thf(f10706,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X3 @ X1)) | ($false = (in @ X3 @ (setminus @ X1 @ X2)))) ) | ~spl2_1179),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10705])).
% 15.19/3.32 thf(f10705,definition,(
% 15.19/3.32 spl2_1179 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (($false = (in @ X3 @ (setminus @ X1 @ X2))) | ($true = (in @ X3 @ X1)))),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1179])],[avatar_definition])).
% 15.19/3.32 thf(f14314,plain,(
% 15.19/3.32 ((in @ sK771 @ sK1) = $false) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f14313])).
% 15.19/3.32 thf(f14313,plain,(
% 15.19/3.32 (((in @ sK771 @ (setminus @ sK1 @ sK0)) => (in @ sK771 @ sK1)) = $false) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f14312])).
% 15.19/3.32 thf(f14312,plain,(
% 15.19/3.32 (((^[Y0 : $i]: ((in @ Y0 @ (setminus @ sK1 @ sK0)) => (in @ Y0 @ sK1))) @ sK771) = $false) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(sigma_clausification,[status(thm)],[f14311])).
% 15.19/3.32 thf(f14311,plain,(
% 15.19/3.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ sK1 @ sK0)) => (in @ Y0 @ sK1))))) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(not_proxy_clausification,[status(thm)],[f14310])).
% 15.19/3.32 thf(f14310,plain,(
% 15.19/3.32 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ sK1 @ sK0)) => (in @ Y0 @ sK1))))) = $true) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(boolean_simplification,[status(thm)],[f14237])).
% 15.19/3.32 thf(f14237,plain,(
% 15.19/3.32 ($true = ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ sK1 @ sK0)) => (in @ Y0 @ sK1)))))) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(superposition,[status(thm)],[f10680,f12124])).
% 15.19/3.32 thf(f12124,plain,(
% 15.19/3.32 ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ~spl2_274),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f12119])).
% 15.19/3.32 thf(f12119,plain,(
% 15.19/3.32 ($true != $true) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ~spl2_274),
% 15.19/3.32 inference(superposition,[status(thm)],[f523,f7004])).
% 15.19/3.32 thf(f7004,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ($false = (in @ X1 @ (powerset @ X2)))) ) | ~spl2_274),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f7003])).
% 15.19/3.32 thf(f7003,definition,(
% 15.19/3.32 spl2_274 <=> ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ($false = (in @ X1 @ (powerset @ X2))))),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_274])],[avatar_definition])).
% 15.19/3.32 thf(f523,plain,(
% 15.19/3.32 ($true != (subset @ (setminus @ sK1 @ sK0) @ sK1))),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f384])).
% 15.19/3.32 thf(f384,plain,(
% 15.19/3.32 (setminusIRneg = $true) & (exuE2 = $true) & (powersetAx = $true) & (emptyInPowerset = $true) & (setadjoinSub = $true) & (sepInPowerset = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (dsetconstr__Cong = $true) & (setminusI = $true) & (binintersectI = $true) & (subsetI1 = $true) & (exuEu = $true) & (binintersectSubset2 = $true) & (setunion__Cong = $true) & (inCongP = $true) & (setadjoinIL = $true) & (emptyinunitempty = $true) & (exuE1 = $true) & (exuI2 = $true) & (quantDeMorgan4 = $true) & (wellorderingAx = $true) & (binintersectEL = $true) & (powersetsubset = $true) & (quantDeMorgan3 = $true) & (emptysetAx = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (setminusERneg = $true) & (omegaIndAx = $true) & (exuE3e = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (notdallE = $true) & (bs114d = $true) & (setminusER = $true) & (eqinunit = $true) & (upairsetIR = $true) & (prop2setE = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (omega0Ax = $true) & (setoftrueEq = $true) & (disjointsetsI1 = $true) & (setminusSubset2 = $true) & (binintersectRsub = $true) & (emptyset__Cong = $true) & (sepSubset = $true) & (subsetE2 = $true) & ($true != (subset @ (setminus @ sK1 @ sK0) @ sK1)) & (notdexE = $true) & (notinemptyset = $true) & (notequalI1 = $true) & (setminusILneg = $true) & (dsetconstrER = $true) & (setbeta = $true) & (subsetI2 = $true) & (emptyE1 = $true) & (notinsingleton = $true) & (exu__Cong = $true) & (upairsetIL = $true) & (prop2setI = $true) & (setadjoinIR = $true) & (prop2set2propI = $true) & (foundationAx = $true) & (notequalI2 = $true) & (powerset__Cong = $true) & (binintersectSubset4 = $true) & (setadjoinOr = $true) & (powersetE = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & (exuI1 = $true) & (powersetE1 = $true) & (setextsub = $true) & (binunionE = $true) & (inPowerset = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (subset2powerset = $true) & (powersetI1 = $true) & (quantDeMorgan1 = $true) & (noeltsimpempty = $true) & (emptysetE = $true) & (upairset2IR = $true) & (setunionI = $true) & (emptyI = $true) & (subsetE = $true) & (quantDeMorgan2 = $true) & (binintersectSubset5 = $true) & (singletonsswitch = $true) & (setunionAx = $true) & (setadjoinE = $true) & (setminusELneg = $true) & (binunionIR = $true) & (binunionRsub = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (binunionEcases = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (notsubsetI = $true) & (powersetI = $true) & (omega__Cong = $true) & (nonemptyE1 = $true) & (setadjoinSub2 = $true) & (subPowSU = $true) & (setunionE = $true) & (descr__Cong = $true) & (vacuousDall = $true) & (subsetRefl = $true) & (exuI3 = $true) & (binintersectSubset1 = $true) & (omegaSAx = $true) & (setadjoinAx = $true) & (in__Cong = $true) & (binunionLsub = $true) & (exuE3u = $true) & (descrp = $true) & (upairsetE = $true) & (setadjoin__Cong = $true) & (nonemptyImpWitness = $true) & (setext = $true)),
% 15.19/3.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f382,f383])).
% 15.19/3.32 thf(f383,plain,(
% 15.19/3.32 ? [X0 : $i,X1 : $i] : ((subset @ (setminus @ X1 @ X0) @ X1) != $true) => ($true != (subset @ (setminus @ sK1 @ sK0) @ sK1))),
% 15.19/3.32 introduced(definition,[],[choice_axiom])).
% 15.19/3.32 thf(f382,plain,(
% 15.19/3.32 (setminusIRneg = $true) & (exuE2 = $true) & (powersetAx = $true) & (emptyInPowerset = $true) & (setadjoinSub = $true) & (sepInPowerset = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (dsetconstr__Cong = $true) & (setminusI = $true) & (binintersectI = $true) & (subsetI1 = $true) & (exuEu = $true) & (binintersectSubset2 = $true) & (setunion__Cong = $true) & (inCongP = $true) & (setadjoinIL = $true) & (emptyinunitempty = $true) & (exuE1 = $true) & (exuI2 = $true) & (quantDeMorgan4 = $true) & (wellorderingAx = $true) & (binintersectEL = $true) & (powersetsubset = $true) & (quantDeMorgan3 = $true) & (emptysetAx = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (setminusERneg = $true) & (omegaIndAx = $true) & (exuE3e = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (notdallE = $true) & (bs114d = $true) & (setminusER = $true) & (eqinunit = $true) & (upairsetIR = $true) & (prop2setE = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (omega0Ax = $true) & (setoftrueEq = $true) & (disjointsetsI1 = $true) & (setminusSubset2 = $true) & (binintersectRsub = $true) & (emptyset__Cong = $true) & (sepSubset = $true) & (subsetE2 = $true) & ? [X0 : $i,X1 : $i] : ((subset @ (setminus @ X1 @ X0) @ X1) != $true) & (notdexE = $true) & (notinemptyset = $true) & (notequalI1 = $true) & (setminusILneg = $true) & (dsetconstrER = $true) & (setbeta = $true) & (subsetI2 = $true) & (emptyE1 = $true) & (notinsingleton = $true) & (exu__Cong = $true) & (upairsetIL = $true) & (prop2setI = $true) & (setadjoinIR = $true) & (prop2set2propI = $true) & (foundationAx = $true) & (notequalI2 = $true) & (powerset__Cong = $true) & (binintersectSubset4 = $true) & (setadjoinOr = $true) & (powersetE = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & (exuI1 = $true) & (powersetE1 = $true) & (setextsub = $true) & (binunionE = $true) & (inPowerset = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (subset2powerset = $true) & (powersetI1 = $true) & (quantDeMorgan1 = $true) & (noeltsimpempty = $true) & (emptysetE = $true) & (upairset2IR = $true) & (setunionI = $true) & (emptyI = $true) & (subsetE = $true) & (quantDeMorgan2 = $true) & (binintersectSubset5 = $true) & (singletonsswitch = $true) & (setunionAx = $true) & (setadjoinE = $true) & (setminusELneg = $true) & (binunionIR = $true) & (binunionRsub = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (binunionEcases = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (notsubsetI = $true) & (powersetI = $true) & (omega__Cong = $true) & (nonemptyE1 = $true) & (setadjoinSub2 = $true) & (subPowSU = $true) & (setunionE = $true) & (descr__Cong = $true) & (vacuousDall = $true) & (subsetRefl = $true) & (exuI3 = $true) & (binintersectSubset1 = $true) & (omegaSAx = $true) & (setadjoinAx = $true) & (in__Cong = $true) & (binunionLsub = $true) & (exuE3u = $true) & (descrp = $true) & (upairsetE = $true) & (setadjoin__Cong = $true) & (nonemptyImpWitness = $true) & (setext = $true)),
% 15.19/3.32 inference(flattening,[status(thm)],[f381])).
% 15.19/3.32 thf(f381,plain,(
% 15.19/3.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((subset @ (setminus @ X1 @ X0) @ X1) != $true) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 15.19/3.32 inference(ennf_transformation,[status(thm)],[f308])).
% 15.19/3.32 thf(f308,plain,(
% 15.19/3.32 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ! [X0 : $i,X1 : $i] : ((subset @ (setminus @ X1 @ X0) @ X1) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.19/3.32 inference(fool_elimination,[status(thm)],[f307])).
% 15.19/3.32 thf(f307,plain,(
% 15.19/3.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X1 @ X0) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.19/3.32 inference(rectify,[status(thm)],[f129])).
% 15.19/3.32 thf(f129,negated_conjecture,(
% 15.19/3.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => ! [X4 : $i,X3 : $i] : (subset @ (setminus @ X3 @ X4) @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.19/3.32 inference(negated_conjecture,[status(cth)],[f128])).
% 15.19/3.32 thf(f128,conjecture,(
% 15.19/3.32 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => ! [X4 : $i,X3 : $i] : (subset @ (setminus @ X3 @ X4) @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.19/3.32 file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',setminusLsub)).
% 15.19/3.32 thf(f10680,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (powerset @ X2)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))) ) | ~spl2_1173),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10679])).
% 15.19/3.32 thf(f10679,definition,(
% 15.19/3.32 spl2_1173 <=> ! [X2 : $i,X1 : $i] : ($true = ((in @ X1 @ (powerset @ X2)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1173])],[avatar_definition])).
% 15.19/3.32 thf(f14315,plain,(
% 15.19/3.32 ($true = (in @ sK771 @ (setminus @ sK1 @ sK0))) | (~spl2_274 | ~spl2_1173)),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f14313])).
% 15.19/3.32 thf(f13894,plain,(
% 15.19/3.32 ~spl2_1171 | ~spl2_1174),
% 15.19/3.32 inference(avatar_contradiction_clause,[status(thm)],[f13893])).
% 15.19/3.32 thf(f13893,plain,(
% 15.19/3.32 $false | (~spl2_1171 | ~spl2_1174)),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f13892])).
% 15.19/3.32 thf(f13892,plain,(
% 15.19/3.32 ($true = $false) | (~spl2_1171 | ~spl2_1174)),
% 15.19/3.32 inference(backward_demodulation,[status(thm)],[f10672,f10684])).
% 15.19/3.32 thf(f10684,plain,(
% 15.19/3.32 (powersetAx = $false) | ~spl2_1174),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10682])).
% 15.19/3.32 thf(f10682,definition,(
% 15.19/3.32 spl2_1174 <=> (powersetAx = $false)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1174])],[avatar_definition])).
% 15.19/3.32 thf(f10672,plain,(
% 15.19/3.32 (powersetAx = $true) | ~spl2_1171),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f10670])).
% 15.19/3.32 thf(f10670,definition,(
% 15.19/3.32 spl2_1171 <=> (powersetAx = $true)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_1171])],[avatar_definition])).
% 15.19/3.32 thf(f12116,plain,(
% 15.19/3.32 ~spl2_270 | ~spl2_273),
% 15.19/3.32 inference(avatar_contradiction_clause,[status(thm)],[f12115])).
% 15.19/3.32 thf(f12115,plain,(
% 15.19/3.32 $false | (~spl2_270 | ~spl2_273)),
% 15.19/3.32 inference(trivial_inequality_removal,[status(thm)],[f12114])).
% 15.19/3.32 thf(f12114,plain,(
% 15.19/3.32 ($true = $false) | (~spl2_270 | ~spl2_273)),
% 15.19/3.32 inference(forward_demodulation,[status(thm)],[f6987,f7001])).
% 15.19/3.32 thf(f7001,plain,(
% 15.19/3.32 (powersetE1 = $false) | ~spl2_273),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f6999])).
% 15.19/3.32 thf(f6999,definition,(
% 15.19/3.32 spl2_273 <=> (powersetE1 = $false)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_273])],[avatar_definition])).
% 15.19/3.32 thf(f6987,plain,(
% 15.19/3.32 (powersetE1 = $true) | ~spl2_270),
% 15.19/3.32 inference(avatar_component_clause,[status(thm)],[f6985])).
% 15.19/3.32 thf(f6985,definition,(
% 15.19/3.32 spl2_270 <=> (powersetE1 = $true)),
% 15.19/3.32 introduced(definition,[new_symbols(naming,[spl2_270])],[avatar_definition])).
% 15.19/3.32 thf(f11726,plain,(
% 15.19/3.32 spl2_1171),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f572,f10670])).
% 15.19/3.32 thf(f572,plain,(
% 15.19/3.32 (powersetAx = $true)),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f384])).
% 15.19/3.32 thf(f11692,plain,(
% 15.19/3.32 spl2_270),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f498,f6985])).
% 15.19/3.32 thf(f498,plain,(
% 15.19/3.32 (powersetE1 = $true)),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f384])).
% 15.19/3.32 thf(f10993,plain,(
% 15.19/3.32 spl2_1176),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f519,f10691])).
% 15.19/3.32 thf(f519,plain,(
% 15.19/3.32 (setminusILneg = $true)),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f384])).
% 15.19/3.32 thf(f10707,plain,(
% 15.19/3.32 spl2_1178 | spl2_1179),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f1330,f10705,f10701])).
% 15.19/3.32 thf(f1330,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((setminusILneg = $false) | ($false = (in @ X3 @ (setminus @ X1 @ X2))) | ($true = (in @ X3 @ X1))) )),
% 15.19/3.32 inference(not_proxy_clausification,[status(thm)],[f1329])).
% 15.19/3.32 thf(f1329,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((setminusILneg = $false) | ($false = (in @ X3 @ (setminus @ X1 @ X2))) | ((~ (in @ X3 @ X1)) = $false)) )),
% 15.19/3.32 inference(not_proxy_clausification,[status(thm)],[f1328])).
% 15.19/3.32 thf(f1328,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (in @ X3 @ (setminus @ X1 @ X2)))) | (setminusILneg = $false) | ((~ (in @ X3 @ X1)) = $false)) )),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f1327])).
% 15.19/3.32 thf(f1327,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((setminusILneg = $false) | ($true = ((~ (in @ X3 @ X1)) => (~ (in @ X3 @ (setminus @ X1 @ X2)))))) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f1326])).
% 15.19/3.32 thf(f1326,plain,(
% 15.19/3.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((setminusILneg = $false) | ($true = ((^[Y0 : $i]: ((~ (in @ Y0 @ X1)) => (~ (in @ Y0 @ (setminus @ X1 @ X2))))) @ X3))) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f1325])).
% 15.19/3.32 thf(f1325,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (in @ Y0 @ X1)) => (~ (in @ Y0 @ (setminus @ X1 @ X2))))))) | (setminusILneg = $false)) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f1324])).
% 15.19/3.32 thf(f1324,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (in @ Y1 @ X1)) => (~ (in @ Y1 @ (setminus @ X1 @ Y0))))))) @ X2)) | (setminusILneg = $false)) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f1323])).
% 15.19/3.32 thf(f1323,plain,(
% 15.19/3.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (in @ Y1 @ X1)) => (~ (in @ Y1 @ (setminus @ X1 @ Y0))))))))) | (setminusILneg = $false)) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f1322])).
% 15.19/3.32 thf(f1322,plain,(
% 15.19/3.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1))))))))) @ X1) = $true) | (setminusILneg = $false)) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f1321])).
% 15.19/3.32 thf(f1321,plain,(
% 15.19/3.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))) | (setminusILneg = $false)),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f387])).
% 15.19/3.32 thf(f387,plain,(
% 15.19/3.32 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f203])).
% 15.19/3.32 thf(f203,plain,(
% 15.19/3.32 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))),
% 15.19/3.32 inference(fool_elimination,[status(thm)],[f202])).
% 15.19/3.32 thf(f202,plain,(
% 15.19/3.32 (setminusILneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X2) => ~(in @ X0 @ (setminus @ X2 @ X1))))),
% 15.19/3.32 inference(rectify,[status(thm)],[f126])).
% 15.19/3.32 thf(f126,axiom,(
% 15.19/3.32 (setminusILneg = ! [X1 : $i,X4 : $i,X3 : $i] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))))),
% 15.19/3.32 file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',setminusILneg)).
% 15.19/3.32 thf(f10685,plain,(
% 15.19/3.32 spl2_1173 | spl2_1174),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f1346,f10682,f10679])).
% 15.19/3.32 thf(f1346,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : ((powersetAx = $false) | ($true = ((in @ X1 @ (powerset @ X2)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f1345])).
% 15.19/3.32 thf(f1345,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))))) @ X2)) | (powersetAx = $false)) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f1344])).
% 15.19/3.32 thf(f1344,plain,(
% 15.19/3.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))))))) | (powersetAx = $false)) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f1343])).
% 15.19/3.32 thf(f1343,plain,(
% 15.19/3.32 ( ! [X1 : $i] : ((powersetAx = $false) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))) @ X1))) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f1342])).
% 15.19/3.32 thf(f1342,plain,(
% 15.19/3.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))))) | (powersetAx = $false)),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f613])).
% 15.19/3.32 thf(f613,plain,(
% 15.19/3.32 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f366])).
% 15.19/3.32 thf(f366,plain,(
% 15.19/3.32 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 15.19/3.32 inference(fool_elimination,[status(thm)],[f365])).
% 15.19/3.32 thf(f365,plain,(
% 15.19/3.32 (powersetAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 15.19/3.32 inference(rectify,[status(thm)],[f5])).
% 15.19/3.32 thf(f5,axiom,(
% 15.19/3.32 (powersetAx = ! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) <=> ! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3))))),
% 15.19/3.32 file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',powersetAx)).
% 15.19/3.32 thf(f7005,plain,(
% 15.19/3.32 spl2_273 | spl2_274),
% 15.19/3.32 inference(avatar_split_clause,[status(thm)],[f4842,f7003,f6999])).
% 15.19/3.32 thf(f4842,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ($false = (in @ X1 @ (powerset @ X2))) | (powersetE1 = $false)) )),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f4841])).
% 15.19/3.32 thf(f4841,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (powerset @ X2)) => (subset @ X1 @ X2))) | (powersetE1 = $false)) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f4840])).
% 15.19/3.32 thf(f4840,plain,(
% 15.19/3.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0))) @ X2)) | (powersetE1 = $false)) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f4839])).
% 15.19/3.32 thf(f4839,plain,(
% 15.19/3.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0))))) | (powersetE1 = $false)) )),
% 15.19/3.32 inference(beta_eta_normalization,[status(thm)],[f4838])).
% 15.19/3.32 thf(f4838,plain,(
% 15.19/3.32 ( ! [X1 : $i] : ((powersetE1 = $false) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 15.19/3.32 inference(pi_clausification,[status(thm)],[f4837])).
% 15.19/3.32 thf(f4837,plain,(
% 15.19/3.32 (powersetE1 = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 15.19/3.32 inference(binary_proxy_clausification,[status(thm)],[f592])).
% 15.19/3.32 thf(f592,plain,(
% 15.19/3.32 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 15.19/3.32 inference(cnf_transformation,[status(thm)],[f150])).
% 15.19/3.32 thf(f150,plain,(
% 15.19/3.32 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 15.19/3.32 inference(fool_elimination,[status(thm)],[f149])).
% 15.19/3.32 thf(f149,plain,(
% 15.19/3.32 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 15.19/3.32 inference(rectify,[status(thm)],[f96])).
% 15.19/3.32 thf(f96,axiom,(
% 15.19/3.32 (powersetE1 = ! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))),
% 15.19/3.32 file('/export/starexec/sandbox2/tmp/tmp.pamaJuniPS/DTF2THF_14910.p',powersetE1)).
% 15.19/3.32 % SZS output end Proof for DTF2THF_14910
% 15.19/3.32 % (15365)------------------------------
% 15.19/3.32 % (15365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.32 % (15365)Termination reason: Refutation
% 15.19/3.32
% 15.19/3.32 % (15365)Memory used [KB]: 14200
% 15.19/3.32 % (15365)Time elapsed: 0.403 s
% 15.19/3.32 % (15365)Instructions burned: 1326 (million)
% 15.19/3.32 % (15365)------------------------------
% 15.19/3.32 % (15365)------------------------------
% 15.19/3.32 % (15074)Success in time 1.977 s
%------------------------------------------------------------------------------