%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU587^1 : 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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:26 AM UTC 2026
% Result : Theorem 22.59s 4.66s
% Output : Refutation 22.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 20 unt; 0 typ; 9 def)
% Number of atoms : 2075 ( 523 equ; 0 cnn)
% Maximal formula atoms : 104 ( 22 avg)
% Number of connectives : 1374 ( 69 ~; 84 |; 309 &; 409 @)
% ( 11 <=>; 449 =>; 0 <=; 0 <~>)
% Maximal formula depth : 110 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 661 ( 657 usr; 118 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 126 ( 51 ^; 69 !; 6 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_143,type,
sK6: $i > $o ).
thf(func_def_152,type,
sK15: $i > ( $i > $i > $o ) > $i ).
thf(func_def_153,type,
sK16: $i > ( $i > $i > $o ) > $i ).
thf(func_def_155,type,
sK18: $i > $i > $o ).
thf(func_def_156,type,
sK19: $i > $i ).
thf(func_def_157,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK21: $i > $o ).
thf(func_def_162,type,
sK25: $i > $o ).
thf(func_def_169,type,
sK32: $i > $o ).
thf(func_def_170,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK34: $i > $o ).
thf(func_def_172,type,
sK35: $i > $i ).
thf(func_def_173,type,
sK36: $i > $i > $i ).
thf(func_def_178,type,
sK41: $i > $o ).
thf(func_def_186,type,
sK49: $i > $i ).
thf(func_def_188,type,
sK51: $i > $i ).
thf(func_def_191,type,
sK54: $i > $i ).
thf(func_def_192,type,
sK55: $i > $i > $i ).
thf(func_def_205,type,
sK68: $i > $i ).
thf(func_def_207,type,
sK70: $i > $o ).
thf(func_def_212,type,
sK75: $i > $o ).
thf(func_def_224,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_225,type,
sK88: $i > $o ).
thf(func_def_226,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK90: $i > $o ).
thf(func_def_233,type,
sK96: $i > $i ).
thf(func_def_239,type,
sK102: ( $i > $o ) > $i > $i ).
thf(func_def_240,type,
sK103: $i > $o ).
thf(func_def_249,type,
sK112: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK113: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK114: $i > $o ).
thf(func_def_252,type,
sK115: $i > $o ).
thf(func_def_255,type,
sK118: ( $i > $o ) > $i > $i ).
thf(func_def_256,type,
sK119: $i > $o ).
thf(func_def_263,type,
sK126: $i > $i ).
thf(func_def_264,type,
sK127: $i > $i > $i > $i ).
thf(func_def_265,type,
sK128: $i > $i > $i ).
thf(func_def_266,type,
sK129: $i > $i > $i ).
thf(func_def_267,type,
sK130: $i > $i > $i ).
thf(func_def_268,type,
sK131: $i > $i > $i ).
thf(func_def_269,type,
sK132: $i > $i > $i ).
thf(func_def_270,type,
sK133: $i > $i > $i ).
thf(func_def_272,type,
sK135: $i > $i ).
thf(func_def_273,type,
sK136: $i > $i ).
thf(func_def_274,type,
sK137: $i > $i ).
thf(func_def_275,type,
sK138: $i > $i ).
thf(func_def_276,type,
sK139: $i > $i ).
thf(func_def_277,type,
sK140: $i > $i ).
thf(func_def_278,type,
sK141: $i > $i ).
thf(func_def_279,type,
sK142: $i > $i ).
thf(func_def_280,type,
sK143: $i > $i ).
thf(func_def_281,type,
sK144: $i > $i ).
thf(func_def_282,type,
sK145: $i > $i ).
thf(func_def_283,type,
sK146: $i > $i ).
thf(func_def_284,type,
sK147: $i > $i ).
thf(func_def_285,type,
sK148: $i > $i ).
thf(func_def_286,type,
sK149: $i > $i ).
thf(func_def_287,type,
sK150: $i > $i ).
thf(func_def_288,type,
sK151: $i > $i ).
thf(func_def_289,type,
sK152: $i > $i ).
thf(func_def_290,type,
sK153: $i > $i ).
thf(func_def_291,type,
sK154: $i > $i ).
thf(func_def_292,type,
sK155: $i > $i ).
thf(func_def_293,type,
sK156: $i > $i ).
thf(func_def_294,type,
sK157: $i > $i ).
thf(func_def_295,type,
sK158: $i > $i ).
thf(func_def_296,type,
sK159: $i > $i ).
thf(func_def_297,type,
sK160: $i > $i > $i > $i ).
thf(func_def_298,type,
sK161: $i > $i > $i ).
thf(func_def_299,type,
sK162: $i > $i > $i > $i ).
thf(func_def_300,type,
sK163: $i > $i > $i > $i ).
thf(func_def_301,type,
sK164: $i > $i > $i > $i ).
thf(func_def_302,type,
sK165: $i > $i > $i ).
thf(func_def_303,type,
sK166: $i > $i > $i > $i ).
thf(func_def_304,type,
sK167: $i > $i > $i ).
thf(func_def_305,type,
sK168: $i > $i > $i ).
thf(func_def_306,type,
sK169: $i > $i > $i ).
thf(func_def_307,type,
sK170: $i > $i ).
thf(func_def_308,type,
sK171: $i > $i > $i > $i ).
thf(func_def_309,type,
sK172: $i > $i > $i ).
thf(func_def_310,type,
sK173: $i > $i > $i ).
thf(func_def_311,type,
sK174: $i > $i > $i ).
thf(func_def_312,type,
sK175: $i > $i > $i > $i ).
thf(func_def_313,type,
sK176: $i > $i > $i > $i ).
thf(func_def_314,type,
sK177: $i > $i > $i ).
thf(func_def_315,type,
sK178: $i > $i > $i ).
thf(func_def_316,type,
sK179: $i > $i > $i > $i ).
thf(func_def_317,type,
sK180: $i > $i > $i > $i ).
thf(func_def_318,type,
sK181: $i > $i ).
thf(func_def_319,type,
sK182: $i > $i > $i ).
thf(func_def_320,type,
sK183: $i > $i > $i > $i ).
thf(func_def_321,type,
sK184: $i > $i > $i > $i ).
thf(func_def_322,type,
sK185: $i > $i > $i > $i ).
thf(func_def_323,type,
sK186: $i > $i > $i > $i ).
thf(func_def_324,type,
sK187: $i > $i > $i ).
thf(func_def_325,type,
sK188: $i > $i > $i > $i ).
thf(func_def_326,type,
sK189: $i > $i > $i > $i ).
thf(func_def_327,type,
sK190: $i > $i ).
thf(func_def_328,type,
sK191: $i > $i ).
thf(func_def_329,type,
sK192: $i > $i > $i > $i ).
thf(func_def_330,type,
sK193: $i > $i > $i ).
thf(func_def_331,type,
sK194: $i > $i > $i > $i ).
thf(func_def_332,type,
sK195: $i > $i > $i > $i ).
thf(func_def_333,type,
sK196: $i > $i > $i ).
thf(func_def_334,type,
sK197: $i > $i > $i ).
thf(func_def_335,type,
sK198: $i > $i > $i > $i ).
thf(func_def_336,type,
sK199: $i > $i > $i > $i ).
thf(func_def_337,type,
sK200: $i > $i ).
thf(func_def_338,type,
sK201: $i > $i > $i ).
thf(func_def_339,type,
sK202: $i > $i > $i > $i ).
thf(func_def_340,type,
sK203: $i > $i > $i > $i ).
thf(func_def_341,type,
sK204: $i > $i > $i > $i ).
thf(func_def_342,type,
sK205: $i > $i > $i ).
thf(func_def_343,type,
sK206: $i > $i > $i > $i ).
thf(func_def_344,type,
sK207: $i > $i > $i > $i ).
thf(func_def_345,type,
sK208: $i > $i > $i > $i ).
thf(func_def_346,type,
sK209: $i > $i > $i > $i ).
thf(func_def_347,type,
sK210: $i > $i > $i ).
thf(func_def_348,type,
sK211: $i > $i ).
thf(func_def_349,type,
sK212: $i > $i > $i > $i ).
thf(func_def_350,type,
sK213: $i > $i > $i > $i ).
thf(func_def_351,type,
sK214: $i > $i > $i > $i ).
thf(func_def_352,type,
sK215: $i > $i > $i > $i ).
thf(func_def_353,type,
sK216: $i > $i > $i ).
thf(func_def_354,type,
sK217: $i > $i > $i > $i ).
thf(func_def_355,type,
sK218: $i > $i > $i > $i ).
thf(func_def_356,type,
sK219: $i > $i > $i > $i ).
thf(func_def_357,type,
sK220: $i > $i > $i ).
thf(func_def_358,type,
sK221: $i > $i > $i > $i ).
thf(func_def_359,type,
sK222: $i > $i > $i ).
thf(func_def_360,type,
sK223: $i > $i > $i ).
thf(func_def_361,type,
sK224: $i > $i > $i ).
thf(func_def_362,type,
sK225: $i > $i ).
thf(func_def_363,type,
sK226: $i > $i > $i > $i ).
thf(func_def_364,type,
sK227: $i > $i > $i ).
thf(func_def_365,type,
sK228: $i > $i > $i ).
thf(func_def_366,type,
sK229: $i > $i > $i ).
thf(func_def_367,type,
sK230: $i > $i > $i > $i ).
thf(func_def_368,type,
sK231: $i > $i > $i > $i ).
thf(func_def_369,type,
sK232: $i > $i > $i ).
thf(func_def_370,type,
sK233: $i > $i > $i > $i ).
thf(func_def_371,type,
sK234: $i > $i > $i > $i ).
thf(func_def_372,type,
sK235: $i > $i ).
thf(func_def_373,type,
sK236: $i > $i > $i ).
thf(func_def_374,type,
sK237: $i > $i > $i > $i ).
thf(func_def_375,type,
sK238: $i > $i > $i > $i ).
thf(func_def_376,type,
sK239: $i > $i > $i > $i ).
thf(func_def_377,type,
sK240: $i > $i > $i > $i ).
thf(func_def_378,type,
sK241: $i > $i > $i > $i ).
thf(func_def_379,type,
sK242: $i > $i > $i > $i ).
thf(func_def_380,type,
sK243: $i > $i ).
thf(func_def_381,type,
sK244: $i > $i ).
thf(func_def_382,type,
sK245: $i > $i ).
thf(func_def_383,type,
sK246: $i > $i ).
thf(func_def_384,type,
sK247: $i > $i ).
thf(func_def_385,type,
sK248: $i > $i ).
thf(func_def_386,type,
sK249: $i > $i ).
thf(func_def_387,type,
sK250: $i > $i ).
thf(func_def_388,type,
sK251: $i > $i ).
thf(func_def_389,type,
sK252: $i > $i ).
thf(func_def_390,type,
sK253: $i > $i ).
thf(func_def_391,type,
sK254: $i > $i ).
thf(func_def_392,type,
sK255: $i > $i ).
thf(func_def_393,type,
sK256: $i > $i ).
thf(func_def_394,type,
sK257: $i > $i ).
thf(func_def_395,type,
sK258: $i > $i ).
thf(func_def_396,type,
sK259: $i > $i ).
thf(func_def_397,type,
sK260: $i > $i ).
thf(func_def_398,type,
sK261: $i > $i ).
thf(func_def_399,type,
sK262: $i > $i ).
thf(func_def_400,type,
sK263: $i > $i ).
thf(func_def_401,type,
sK264: $i > $i ).
thf(func_def_402,type,
sK265: $i > $i ).
thf(func_def_403,type,
sK266: $i > $i ).
thf(func_def_404,type,
sK267: $i > $i ).
thf(func_def_405,type,
sK268: $i > $i ).
thf(func_def_406,type,
sK269: $i > $i > $i ).
thf(func_def_407,type,
sK270: $i > $i > $i > $i ).
thf(func_def_408,type,
sK271: $i > $i > $i > $i ).
thf(func_def_409,type,
sK272: $i > $i > $i > $i ).
thf(func_def_410,type,
sK273: $i > $i > $i ).
thf(func_def_411,type,
sK274: $i > $i > $i > $i ).
thf(func_def_412,type,
sK275: $i > $i > $i > $i ).
thf(func_def_413,type,
sK276: $i > $i > $i > $i ).
thf(func_def_414,type,
sK277: $i > $i > $i > $i ).
thf(func_def_415,type,
sK278: $i > $i > $i > $i ).
thf(func_def_416,type,
sK279: $i > $i ).
thf(func_def_417,type,
sK280: $i > $i > $i ).
thf(func_def_418,type,
sK281: $i > $i > $i > $i ).
thf(func_def_419,type,
sK282: $i > $i > $i > $i ).
thf(func_def_420,type,
sK283: $i > $i > $i ).
thf(func_def_421,type,
sK284: $i > $i > $i ).
thf(func_def_422,type,
sK285: $i > $i > $i > $i ).
thf(func_def_423,type,
sK286: $i > $i > $i > $i ).
thf(func_def_424,type,
sK287: $i > $i ).
thf(func_def_425,type,
sK288: $i > $i > $i > $i ).
thf(func_def_426,type,
sK289: $i > $i > $i ).
thf(func_def_427,type,
sK290: $i > $i > $i ).
thf(func_def_428,type,
sK291: $i > $i > $i > $i ).
thf(func_def_429,type,
sK292: $i > $i > $i ).
thf(func_def_430,type,
sK293: $i > $i > $i ).
thf(func_def_431,type,
sK294: $i > $i > $i > $i ).
thf(func_def_432,type,
sK295: $i > $i > $i > $i ).
thf(func_def_433,type,
sK296: $i > $i > $i > $i ).
thf(func_def_434,type,
sK297: $i > $i > $i > $i ).
thf(func_def_435,type,
sK298: $i > $i ).
thf(func_def_436,type,
sK299: $i > $i ).
thf(func_def_437,type,
sK300: $i > $i ).
thf(func_def_438,type,
sK301: $i > $i > $i > $i ).
thf(func_def_439,type,
sK302: $i > $i > $i ).
thf(func_def_440,type,
sK303: $i > $i > $i ).
thf(func_def_441,type,
sK304: $i > $i > $i ).
thf(func_def_442,type,
sK305: $i > $i ).
thf(func_def_443,type,
sK306: $i > $i > $i ).
thf(func_def_444,type,
sK307: $i > $i > $i ).
thf(func_def_445,type,
sK308: $i > $i > $i ).
thf(func_def_446,type,
sK309: $i > $i ).
thf(func_def_447,type,
sK310: $i > $i ).
thf(func_def_448,type,
sK311: $i > $i > $i ).
thf(func_def_449,type,
sK312: $i > $i > $i ).
thf(func_def_450,type,
sK313: $i > $i ).
thf(func_def_451,type,
sK314: $i > $i ).
thf(func_def_452,type,
sK315: $i > $i > $i ).
thf(func_def_453,type,
sK316: $i > $i > $i > $i ).
thf(func_def_454,type,
sK317: $i > $i > $i > $i ).
thf(func_def_455,type,
sK318: $i > $i > $i > $i ).
thf(func_def_456,type,
sK319: $i > $i ).
thf(func_def_457,type,
sK320: $i > $i > $i > $i ).
thf(func_def_458,type,
sK321: $i > $i > $i > $i ).
thf(func_def_459,type,
sK322: $i > $i > $i > $i ).
thf(func_def_460,type,
sK323: $i > $i > $i > $i ).
thf(func_def_461,type,
sK324: $i > $i ).
thf(func_def_462,type,
sK325: $i > $i ).
thf(func_def_463,type,
sK326: $i > $i ).
thf(func_def_464,type,
sK327: $i > $i ).
thf(func_def_465,type,
sK328: $i > $i ).
thf(func_def_466,type,
sK329: $i > $i > $i > $i ).
thf(func_def_467,type,
sK330: $i > $i > $i ).
thf(func_def_468,type,
sK331: $i > $i > $i ).
thf(func_def_469,type,
sK332: $i > $i > $i ).
thf(func_def_470,type,
sK333: $i > $i > $i ).
thf(func_def_471,type,
sK334: $i > $i > $i > $i ).
thf(func_def_472,type,
sK335: $i > $i > $i > $i ).
thf(func_def_473,type,
sK336: $i > $i > $i > $i ).
thf(func_def_474,type,
sK337: $i > $i ).
thf(func_def_475,type,
sK338: $i > $i > $i ).
thf(func_def_476,type,
sK339: $i > $i > $i ).
thf(func_def_477,type,
sK340: $i > $i > $i ).
thf(func_def_478,type,
sK341: $i > $i ).
thf(func_def_479,type,
sK342: $i > $i ).
thf(func_def_480,type,
sK343: $i > $i > $i ).
thf(func_def_481,type,
sK344: $i > $i > $i ).
thf(func_def_482,type,
sK345: $i > $i > $i ).
thf(func_def_483,type,
sK346: $i > $i ).
thf(func_def_484,type,
sK347: $i > $i > $i ).
thf(func_def_485,type,
sK348: $i > $i ).
thf(func_def_486,type,
sK349: $i > $i > $i ).
thf(func_def_487,type,
sK350: $i > $i ).
thf(func_def_488,type,
sK351: $i > $i ).
thf(func_def_489,type,
sK352: $i > $i ).
thf(func_def_490,type,
sK353: $i > $i ).
thf(func_def_491,type,
sK354: $i > $i ).
thf(func_def_492,type,
sK355: $i > $i ).
thf(func_def_493,type,
sK356: $i > $i ).
thf(func_def_494,type,
sK357: $i > $i ).
thf(func_def_495,type,
sK358: $i > $i ).
thf(func_def_496,type,
sK359: $i > $i ).
thf(func_def_497,type,
sK360: $i > $i ).
thf(func_def_498,type,
sK361: $i > $i ).
thf(func_def_499,type,
sK362: $i > $i ).
thf(func_def_500,type,
sK363: $i > $i ).
thf(func_def_501,type,
sK364: $i > $i ).
thf(func_def_502,type,
sK365: $i > $i ).
thf(func_def_503,type,
sK366: $i > $i ).
thf(func_def_504,type,
sK367: $i > $i ).
thf(func_def_505,type,
sK368: $i > $i ).
thf(func_def_506,type,
sK369: $i > $i ).
thf(func_def_507,type,
sK370: $i > $i ).
thf(func_def_508,type,
sK371: $i > $i ).
thf(func_def_509,type,
sK372: $i > $i ).
thf(func_def_510,type,
sK373: $i > $i ).
thf(func_def_511,type,
sK374: $i > $i ).
thf(func_def_512,type,
sK375: $i > $i ).
thf(func_def_513,type,
sK376: $i > $i ).
thf(func_def_514,type,
sK377: $i > $i ).
thf(func_def_515,type,
sK378: $i > $i ).
thf(func_def_516,type,
sK379: $i > $i > $i > $i ).
thf(func_def_517,type,
sK380: $i > $i > $i ).
thf(func_def_518,type,
sK381: $i > $i ).
thf(func_def_519,type,
sK382: $i > $i ).
thf(func_def_520,type,
sK383: $i > $i ).
thf(func_def_521,type,
sK384: $i > $i ).
thf(func_def_522,type,
sK385: $i > $i ).
thf(func_def_523,type,
sK386: $i > $i ).
thf(func_def_524,type,
sK387: $i > $i > $i > $i ).
thf(func_def_525,type,
sK388: $i > $i ).
thf(func_def_526,type,
sK389: $i > $i ).
thf(func_def_527,type,
sK390: $i > $i ).
thf(func_def_528,type,
sK391: $i > $i ).
thf(func_def_529,type,
sK392: $i > $i ).
thf(func_def_530,type,
sK393: $i > $i ).
thf(func_def_531,type,
sK394: $i > $i ).
thf(func_def_532,type,
sK395: $i > $i ).
thf(func_def_533,type,
sK396: $i > $i ).
thf(func_def_534,type,
sK397: $i > $i > $i > $i ).
thf(func_def_535,type,
sK398: $i > $i ).
thf(func_def_536,type,
sK399: $i > $i ).
thf(func_def_537,type,
sK400: $i > $i ).
thf(func_def_538,type,
sK401: $i > $i ).
thf(func_def_539,type,
sK402: $i > $i ).
thf(func_def_540,type,
sK403: $i > $i ).
thf(func_def_541,type,
sK404: $i > $i ).
thf(func_def_542,type,
sK405: $i > $i ).
thf(func_def_543,type,
sK406: $i > $i ).
thf(func_def_544,type,
sK407: $i > $i ).
thf(func_def_545,type,
sK408: $i > $i > $i > $i ).
thf(func_def_546,type,
sK409: $i > $i > $i ).
thf(func_def_547,type,
sK410: $i > $i > $i ).
thf(func_def_548,type,
sK411: $i > $i > $i > $i ).
thf(func_def_549,type,
sK412: $i > $i > $i > $i ).
thf(func_def_550,type,
sK413: $i > $i > $i ).
thf(func_def_551,type,
sK414: $i > $i > $i > $i ).
thf(func_def_552,type,
sK415: $i > $i > $i ).
thf(func_def_553,type,
sK416: $i > $i > $i ).
thf(func_def_554,type,
sK417: $i > $i > $i ).
thf(func_def_555,type,
sK418: $i > $i > $i > $i ).
thf(func_def_556,type,
sK419: $i > $i > $i ).
thf(func_def_557,type,
sK420: $i > $i > $i ).
thf(func_def_558,type,
sK421: $i > $i > $i > $i ).
thf(func_def_559,type,
sK422: $i > $i > $i > $i ).
thf(func_def_560,type,
sK423: $i > $i > $i ).
thf(func_def_561,type,
sK424: $i > $i > $i > $i ).
thf(func_def_562,type,
sK425: $i > $i > $i ).
thf(func_def_563,type,
sK426: $i > $i > $i ).
thf(func_def_564,type,
sK427: $i > $i > $i ).
thf(func_def_565,type,
sK428: $i > $i > $i > $i ).
thf(func_def_566,type,
sK429: $i > $i ).
thf(func_def_567,type,
sK430: $i > $i > $i ).
thf(func_def_568,type,
sK431: $i > $i > $i ).
thf(func_def_569,type,
sK432: $i > $i > $i > $i ).
thf(func_def_570,type,
sK433: $i > $i > $i > $i ).
thf(func_def_571,type,
sK434: $i > $i > $i ).
thf(func_def_572,type,
sK435: $i > $i > $i ).
thf(func_def_573,type,
sK436: $i > $i > $i > $i ).
thf(func_def_574,type,
sK437: $i > $i > $i ).
thf(func_def_575,type,
sK438: $i > $i ).
thf(func_def_576,type,
sK439: $i > $i > $i > $i ).
thf(func_def_577,type,
sK440: $i > $i > $i ).
thf(func_def_578,type,
sK441: $i > $i > $i ).
thf(func_def_579,type,
sK442: $i > $i > $i ).
thf(func_def_580,type,
sK443: $i > $i > $i > $i ).
thf(func_def_581,type,
sK444: $i > $i > $i > $i ).
thf(func_def_582,type,
sK445: $i > $i > $i ).
thf(func_def_583,type,
sK446: $i > $i > $i > $i ).
thf(func_def_584,type,
sK447: $i > $i > $i > $i ).
thf(func_def_585,type,
sK448: $i > $i ).
thf(func_def_586,type,
sK449: $i > $i > $i > $i ).
thf(func_def_587,type,
sK450: $i > $i > $i ).
thf(func_def_588,type,
sK451: $i > $i > $i > $i ).
thf(func_def_589,type,
sK452: $i > $i > $i ).
thf(func_def_590,type,
sK453: $i > $i > $i ).
thf(func_def_591,type,
sK454: $i > $i > $i ).
thf(func_def_592,type,
sK455: $i > $i > $i > $i ).
thf(func_def_593,type,
sK456: $i > $i > $i > $i ).
thf(func_def_594,type,
sK457: $i > $i > $i > $i ).
thf(func_def_595,type,
sK458: $i > $i > $i ).
thf(func_def_596,type,
sK459: $i > $i > $i ).
thf(func_def_597,type,
sK460: $i > $i > $i > $i ).
thf(func_def_598,type,
sK461: $i > $i > $i > $i ).
thf(func_def_599,type,
sK462: $i > $i > $i ).
thf(func_def_600,type,
sK463: $i > $i > $i > $i ).
thf(func_def_601,type,
sK464: $i > $i > $i > $i ).
thf(func_def_602,type,
sK465: $i > $i ).
thf(func_def_603,type,
sK466: $i > $i ).
thf(func_def_604,type,
sK467: $i > $i ).
thf(func_def_605,type,
sK468: $i > $i ).
thf(func_def_606,type,
sK469: $i > $i ).
thf(func_def_607,type,
sK470: $i > $i ).
thf(func_def_608,type,
sK471: $i > $i ).
thf(func_def_609,type,
sK472: $i > $i ).
thf(func_def_610,type,
sK473: $i > $i ).
thf(func_def_611,type,
sK474: $i > $i ).
thf(func_def_612,type,
sK475: $i > $i ).
thf(func_def_613,type,
sK476: $i > $i ).
thf(func_def_614,type,
sK477: $i > $i ).
thf(func_def_615,type,
sK478: $i > $i ).
thf(func_def_616,type,
sK479: $i > $i ).
thf(func_def_617,type,
sK480: $i > $i ).
thf(func_def_618,type,
sK481: $i > $i ).
thf(func_def_619,type,
sK482: $i > $i ).
thf(func_def_620,type,
sK483: $i > $i ).
thf(func_def_621,type,
sK484: $i > $i ).
thf(func_def_622,type,
sK485: $i > $i ).
thf(func_def_623,type,
sK486: $i > $i ).
thf(func_def_624,type,
sK487: $i > $i ).
thf(func_def_625,type,
sK488: $i > $i ).
thf(func_def_626,type,
sK489: $i > $i ).
thf(func_def_627,type,
sK490: $i > $i ).
thf(func_def_628,type,
sK491: $i > $i ).
thf(func_def_629,type,
sK492: $i > $i ).
thf(func_def_630,type,
sK493: $i > $i ).
thf(func_def_631,type,
sK494: $i > $i > $i > $i ).
thf(func_def_632,type,
sK495: $i > $i > $i ).
thf(func_def_633,type,
sK496: $i > $i > $i > $i ).
thf(func_def_634,type,
sK497: $i > $i > $i ).
thf(func_def_635,type,
sK498: $i > $i > $i ).
thf(func_def_636,type,
sK499: $i > $i > $i ).
thf(func_def_637,type,
sK500: $i > $i > $i ).
thf(func_def_638,type,
sK501: $i > $i > $i ).
thf(func_def_639,type,
sK502: $i > $i > $i > $i ).
thf(func_def_640,type,
sK503: $i > $i > $i ).
thf(func_def_641,type,
sK504: $i > $i ).
thf(func_def_642,type,
sK505: $i > $i > $i ).
thf(func_def_643,type,
sK506: $i > $i > $i ).
thf(func_def_644,type,
sK507: $i > $i > $i ).
thf(func_def_645,type,
sK508: $i > $i > $i > $i ).
thf(func_def_646,type,
sK509: $i > $i ).
thf(func_def_647,type,
sK510: $i > $i ).
thf(func_def_648,type,
sK511: $i > $i ).
thf(func_def_649,type,
sK512: $i > $i ).
thf(func_def_650,type,
sK513: $i > $i > $i ).
thf(func_def_651,type,
sK514: $i > $i > $i > $i ).
thf(func_def_652,type,
sK515: $i > $i > $i > $i ).
thf(func_def_653,type,
sK516: $i > $i > $i ).
thf(func_def_654,type,
sK517: $i > $i > $i ).
thf(func_def_655,type,
sK518: $i > $i > $i > $i ).
thf(func_def_656,type,
sK519: $i > $i > $i > $i ).
thf(func_def_657,type,
sK520: $i > $i > $i ).
thf(func_def_658,type,
sK521: $i > $i > $i > $i ).
thf(func_def_659,type,
sK522: $i > $i ).
thf(func_def_660,type,
sK523: $i > $i > $i ).
thf(func_def_661,type,
sK524: $i > $i > $i ).
thf(func_def_662,type,
sK525: $i > $i > $i ).
thf(func_def_663,type,
sK526: $i > $i > $i > $i ).
thf(func_def_664,type,
sK527: $i > $i > $i > $i ).
thf(func_def_665,type,
sK528: $i > $i > $i ).
thf(func_def_666,type,
sK529: $i > $i > $i > $i ).
thf(func_def_667,type,
sK530: $i > $i > $i > $i ).
thf(func_def_668,type,
sK531: $i > $i > $i ).
thf(func_def_669,type,
sK532: $i > $i > $i ).
thf(func_def_670,type,
sK533: $i > $i > $i ).
thf(func_def_671,type,
sK534: $i > $i > $i > $i ).
thf(func_def_672,type,
sK535: $i > $i > $i > $i ).
thf(func_def_673,type,
sK536: $i > $i ).
thf(func_def_674,type,
sK537: $i > $i > $i ).
thf(func_def_675,type,
sK538: $i > $i > $i ).
thf(func_def_676,type,
sK539: $i > $i ).
thf(func_def_677,type,
sK540: $i > $i > $i ).
thf(func_def_678,type,
sK541: $i > $i > $i ).
thf(func_def_679,type,
sK542: $i > $i > $i ).
thf(func_def_680,type,
sK543: $i > $i > $i > $i ).
thf(func_def_681,type,
sK544: $i > $i ).
thf(func_def_682,type,
sK545: $i > $i ).
thf(func_def_683,type,
sK546: $i > $i > $i > $i ).
thf(func_def_684,type,
sK547: $i > $i > $i > $i ).
thf(func_def_685,type,
sK548: $i > $i ).
thf(func_def_686,type,
sK549: $i > $i ).
thf(func_def_687,type,
sK550: $i > $i ).
thf(func_def_688,type,
sK551: $i > $i > $i > $i ).
thf(func_def_689,type,
sK552: $i > $i > $i > $i ).
thf(func_def_690,type,
sK553: $i > $i ).
thf(func_def_691,type,
sK554: $i > $i > $i > $i ).
thf(func_def_692,type,
sK555: $i > $i > $i > $i ).
thf(func_def_693,type,
sK556: $i > $i > $i ).
thf(func_def_694,type,
sK557: $i > $i ).
thf(func_def_695,type,
sK558: $i > $i ).
thf(func_def_696,type,
sK559: $i > $i > $i ).
thf(func_def_697,type,
sK560: $i > $i > $i > $i ).
thf(func_def_698,type,
sK561: $i > $i ).
thf(func_def_699,type,
sK562: $i > $i ).
thf(func_def_700,type,
sK563: $i > $i ).
thf(func_def_701,type,
sK564: $i > $i ).
thf(func_def_702,type,
sK565: $i > $i > $i ).
thf(func_def_703,type,
sK566: $i > $i > $i ).
thf(func_def_704,type,
sK567: $i > $i > $i > $i ).
thf(func_def_705,type,
sK568: $i > $i > $i ).
thf(func_def_706,type,
sK569: $i > $i ).
thf(func_def_707,type,
sK570: $i > $i ).
thf(func_def_708,type,
sK571: $i > $i > $i ).
thf(func_def_710,type,
sK573: $i > $o ).
thf(func_def_713,type,
sK576: $i > $o ).
thf(func_def_714,type,
sK577: $i > $i ).
thf(func_def_719,type,
sK582: ( $i > $o ) > $i > $i ).
thf(func_def_720,type,
sK583: $i > $o ).
thf(func_def_723,type,
sK586: $i > $i ).
thf(func_def_742,type,
sK605: $i > $o ).
thf(func_def_746,type,
sK609: $i > $o ).
thf(func_def_753,type,
sK616: $i > $i > $i ).
thf(func_def_759,type,
sK622: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_760,type,
sK623: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_763,type,
sK626: $i > $o ).
thf(func_def_764,type,
sK627: $i > $o ).
thf(func_def_768,type,
sK631: $i > $i > $i ).
thf(func_def_769,type,
sK632: $i > $i > $i ).
thf(func_def_770,type,
sK633: $i > $i > $i ).
thf(func_def_773,type,
sK636: ( $i > $o ) > $i > $i ).
thf(func_def_774,type,
sK637: $i > $o ).
thf(func_def_777,type,
sK640: $i > $o ).
thf(func_def_779,type,
sK642: ( $i > $o ) > $i ).
thf(func_def_780,type,
sK643: $i > $o ).
thf(func_def_781,type,
sK644: $i > $i ).
thf(func_def_789,type,
sK652: ( $i > $o ) > $i > $i ).
thf(func_def_790,type,
sK653: $i > $o ).
thf(func_def_796,type,
sK659: ( $i > $o ) > $i ).
thf(func_def_797,type,
sK660: ( $i > $o ) > $i ).
thf(func_def_798,type,
sK661: $i > $o ).
thf(func_def_806,type,
sK669: $i > $o > $i > $i ).
thf(func_def_824,type,
sK687: $i > ( $i > $o ) > $i ).
thf(func_def_826,type,
sK689: $i > $o ).
thf(func_def_831,type,
sK694: $i > $i > $i ).
thf(func_def_835,type,
sK698: $i > $o ).
thf(func_def_836,type,
sK699: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_837,type,
sK700: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_838,type,
sK701: $i > $o ).
thf(func_def_839,type,
sK702: $i > $o ).
thf(func_def_842,type,
ph705:
!>[X0: $tType] : X0 ).
thf(func_def_843,type,
sK706: ( $i > $o ) > $i > $i ).
thf(func_def_844,type,
sK707: ( $i > $o ) > $i ).
thf(func_def_845,type,
sK708: $i > $i > $i ).
thf(func_def_846,type,
sK709: $i > $i > $i ).
thf(func_def_847,type,
sK710: $i > $i > $i ).
thf(func_def_848,type,
sK711: $i > $i > $i ).
thf(func_def_850,type,
sK713: $i > $i > $i ).
thf(func_def_851,type,
sK714: $i > $i > $i ).
thf(func_def_852,type,
sK715: $i > $i > $i ).
thf(func_def_853,type,
sK716: $i > $i ).
thf(func_def_854,type,
sK717: $i > $i ).
thf(func_def_855,type,
sK718: $i > $i > $i ).
thf(f12864,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f9323,f9632,f9768,f10350,f10439,f10453,f10527,f11185,f12669,f12863]) ).
thf(f12863,plain,
( ~ spl2_1260
| ~ spl2_1264 ),
inference(avatar_contradiction_clause,[status(thm)],[f12862]) ).
thf(f12862,plain,
( $false
| ~ spl2_1260
| ~ spl2_1264 ),
inference(trivial_inequality_removal,[status(thm)],[f12861]) ).
thf(f12861,plain,
( ( $false = $true )
| ~ spl2_1260
| ~ spl2_1264 ),
inference(forward_demodulation,[status(thm)],[f10332,f10349]) ).
thf(f10349,plain,
( ( binunionIL = $false )
| ~ spl2_1264 ),
inference(avatar_component_clause,[status(thm)],[f10347]) ).
thf(f10347,definition,
( spl2_1264
<=> ( binunionIL = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1264])],[avatar_definition]) ).
thf(f10332,plain,
( ( binunionIL = $true )
| ~ spl2_1260 ),
inference(avatar_component_clause,[status(thm)],[f10330]) ).
thf(f10330,definition,
( spl2_1260
<=> ( binunionIL = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1260])],[avatar_definition]) ).
thf(f12669,plain,
( ~ spl2_1039
| ~ spl2_1108
| ~ spl2_1263 ),
inference(avatar_contradiction_clause,[status(thm)],[f12668]) ).
thf(f12668,plain,
( $false
| ~ spl2_1039
| ~ spl2_1108
| ~ spl2_1263 ),
inference(trivial_inequality_removal,[status(thm)],[f12635]) ).
thf(f12635,plain,
( ( $false = $true )
| ~ spl2_1039
| ~ spl2_1108
| ~ spl2_1263 ),
inference(superposition,[status(thm)],[f12452,f12420]) ).
thf(f12420,plain,
( ( ( in @ sK712 @ ( binunion @ sK1 @ sK0 ) )
= $false )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(binary_proxy_clausification,[status(thm)],[f12419]) ).
thf(f12419,plain,
( ( $false
= ( ( in @ sK712 @ sK1 )
=> ( in @ sK712 @ ( binunion @ sK1 @ sK0 ) ) ) )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(beta_eta_normalization,[status(thm)],[f12418]) ).
thf(f12418,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( binunion @ sK1 @ sK0 ) ) )
@ sK712 ) )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(sigma_clausification,[status(thm)],[f12417]) ).
thf(f12417,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( binunion @ sK1 @ sK0 ) ) ) ) )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(not_proxy_clausification,[status(thm)],[f12416]) ).
thf(f12416,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( binunion @ sK1 @ sK0 ) ) ) ) )
= $true )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(boolean_simplification,[status(thm)],[f12367]) ).
thf(f12367,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( binunion @ sK1 @ sK0 ) ) ) )
= $false )
= $true )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(superposition,[status(thm)],[f9322,f11198]) ).
thf(f11198,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) )
| ~ spl2_1108 ),
inference(trivial_inequality_removal,[status(thm)],[f11194]) ).
thf(f11194,plain,
( ( $true != $true )
| ( $false
= ( in @ sK1 @ ( powerset @ ( binunion @ sK1 @ sK0 ) ) ) )
| ~ spl2_1108 ),
inference(superposition,[status(thm)],[f518,f9631]) ).
thf(f9631,plain,
( ! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl2_1108 ),
inference(avatar_component_clause,[status(thm)],[f9630]) ).
thf(f9630,definition,
( spl2_1108
<=> ! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1108])],[avatar_definition]) ).
thf(f518,plain,
( ( subset @ sK1 @ ( binunion @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f318]) ).
thf(f318,plain,
( ( powersetI1 = $true )
& ( sepSubset = $true )
& ( ( subset @ sK1 @ ( binunion @ sK1 @ sK0 ) )
!= $true )
& ( emptyE1 = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( exuI1 = $true )
& ( quantDeMorgan2 = $true )
& ( binunionIR = $true )
& ( emptyI = $true )
& ( eqinunit = $true )
& ( vacuousDall = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( setadjoinSub = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( setunionE = $true )
& ( singletonsswitch = $true )
& ( omega0Ax = $true )
& ( notinsingleton = $true )
& ( powersetsubset = $true )
& ( setunionAx = $true )
& ( notequalI2 = $true )
& ( exu__Cong = $true )
& ( setextsub = $true )
& ( nonemptyImpWitness = $true )
& ( exuI3 = $true )
& ( subset2powerset = $true )
& ( nonemptyI1 = $true )
& ( foundationAx = $true )
& ( inPowerset = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( upairsetE = $true )
& ( subsetemptysetimpeq = $true )
& ( emptysetAx = $true )
& ( upairset2IR = $true )
& ( setadjoinOr = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE1 = $true )
& ( omegaIndAx = $true )
& ( notequalI1 = $true )
& ( powersetE = $true )
& ( notdexE = $true )
& ( binunionE = $true )
& ( inCongP = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( subPowSU = $true )
& ( exuE1 = $true )
& ( omega__Cong = $true )
& ( emptyinPowerset = $true )
& ( subsetI1 = $true )
& ( emptysetimpfalse = $true )
& ( uniqinunit = $true )
& ( prop2setE = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( replAx = $true )
& ( binunionEcases = $true )
& ( exuI2 = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( emptyset__Cong = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( subsetTrans = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan4 = $true )
& ( in__Cong = $true )
& ( dsetconstrER = $true )
& ( exuE3u = $true )
& ( emptysetE = $true )
& ( binunionIL = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrI = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( subsetE = $true )
& ( notdallE = $true )
& ( setadjoinIR = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( powersetI = $true )
& ( setext = $true )
& ( setunionI = $true )
& ( wellorderingAx = $true )
& ( prop2setI = $true )
& ( setadjoinAx = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( upairsetIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f316,f317]) ).
thf(f317,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
!= $true )
=> ( ( subset @ sK1 @ ( binunion @ sK1 @ sK0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f316,plain,
( ( powersetI1 = $true )
& ( sepSubset = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( emptyE1 = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( exuI1 = $true )
& ( quantDeMorgan2 = $true )
& ( binunionIR = $true )
& ( emptyI = $true )
& ( eqinunit = $true )
& ( vacuousDall = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( setadjoinSub = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( setunionE = $true )
& ( singletonsswitch = $true )
& ( omega0Ax = $true )
& ( notinsingleton = $true )
& ( powersetsubset = $true )
& ( setunionAx = $true )
& ( notequalI2 = $true )
& ( exu__Cong = $true )
& ( setextsub = $true )
& ( nonemptyImpWitness = $true )
& ( exuI3 = $true )
& ( subset2powerset = $true )
& ( nonemptyI1 = $true )
& ( foundationAx = $true )
& ( inPowerset = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( upairsetE = $true )
& ( subsetemptysetimpeq = $true )
& ( emptysetAx = $true )
& ( upairset2IR = $true )
& ( setadjoinOr = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE1 = $true )
& ( omegaIndAx = $true )
& ( notequalI1 = $true )
& ( powersetE = $true )
& ( notdexE = $true )
& ( binunionE = $true )
& ( inCongP = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( subPowSU = $true )
& ( exuE1 = $true )
& ( omega__Cong = $true )
& ( emptyinPowerset = $true )
& ( subsetI1 = $true )
& ( emptysetimpfalse = $true )
& ( uniqinunit = $true )
& ( prop2setE = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( replAx = $true )
& ( binunionEcases = $true )
& ( exuI2 = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( emptyset__Cong = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( subsetTrans = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan4 = $true )
& ( in__Cong = $true )
& ( dsetconstrER = $true )
& ( exuE3u = $true )
& ( emptysetE = $true )
& ( binunionIL = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrI = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( subsetE = $true )
& ( notdallE = $true )
& ( setadjoinIR = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( powersetI = $true )
& ( setext = $true )
& ( setunionI = $true )
& ( wellorderingAx = $true )
& ( prop2setI = $true )
& ( setadjoinAx = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( upairsetIR = $true ) ),
inference(flattening,[status(thm)],[f315]) ).
thf(f315,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
!= $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)],[f128]) ).
thf(f128,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 )
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f127]) ).
thf(f127,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
=> ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f107]) ).
thf(f107,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
=> ! [X4: $i,X3: $i] : ( subset @ X3 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
thf(f106,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
=> ! [X4: $i,X3: $i] : ( subset @ X3 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',binunionLsub) ).
thf(f9322,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true )
| ~ spl2_1039 ),
inference(avatar_component_clause,[status(thm)],[f9321]) ).
thf(f9321,definition,
( spl2_1039
<=> ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1039])],[avatar_definition]) ).
thf(f12452,plain,
( ! [X0: $i] :
( ( in @ sK712 @ ( binunion @ sK1 @ X0 ) )
= $true )
| ~ spl2_1039
| ~ spl2_1108
| ~ spl2_1263 ),
inference(trivial_inequality_removal,[status(thm)],[f12444]) ).
thf(f12444,plain,
( ! [X0: $i] :
( ( ( in @ sK712 @ ( binunion @ sK1 @ X0 ) )
= $true )
| ( $false = $true ) )
| ~ spl2_1039
| ~ spl2_1108
| ~ spl2_1263 ),
inference(superposition,[status(thm)],[f12421,f10345]) ).
thf(f10345,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ ( binunion @ X1 @ X3 ) )
= $true ) )
| ~ spl2_1263 ),
inference(avatar_component_clause,[status(thm)],[f10344]) ).
thf(f10344,definition,
( spl2_1263
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ ( binunion @ X1 @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1263])],[avatar_definition]) ).
thf(f12421,plain,
( ( $true
= ( in @ sK712 @ sK1 ) )
| ~ spl2_1039
| ~ spl2_1108 ),
inference(binary_proxy_clausification,[status(thm)],[f12419]) ).
thf(f11185,plain,
( ~ spl2_1104
| ~ spl2_1107 ),
inference(avatar_contradiction_clause,[status(thm)],[f11184]) ).
thf(f11184,plain,
( $false
| ~ spl2_1104
| ~ spl2_1107 ),
inference(trivial_inequality_removal,[status(thm)],[f11183]) ).
thf(f11183,plain,
( ( $false = $true )
| ~ spl2_1104
| ~ spl2_1107 ),
inference(forward_demodulation,[status(thm)],[f9614,f9628]) ).
thf(f9628,plain,
( ( powersetE1 = $false )
| ~ spl2_1107 ),
inference(avatar_component_clause,[status(thm)],[f9626]) ).
thf(f9626,definition,
( spl2_1107
<=> ( powersetE1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1107])],[avatar_definition]) ).
thf(f9614,plain,
( ( powersetE1 = $true )
| ~ spl2_1104 ),
inference(avatar_component_clause,[status(thm)],[f9612]) ).
thf(f9612,definition,
( spl2_1104
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1104])],[avatar_definition]) ).
thf(f10527,plain,
( ~ spl2_1036
| ~ spl2_1038 ),
inference(avatar_contradiction_clause,[status(thm)],[f10526]) ).
thf(f10526,plain,
( $false
| ~ spl2_1036
| ~ spl2_1038 ),
inference(trivial_inequality_removal,[status(thm)],[f10525]) ).
thf(f10525,plain,
( ( $false = $true )
| ~ spl2_1036
| ~ spl2_1038 ),
inference(backward_demodulation,[status(thm)],[f9310,f9319]) ).
thf(f9319,plain,
( ( powersetAx = $false )
| ~ spl2_1038 ),
inference(avatar_component_clause,[status(thm)],[f9317]) ).
thf(f9317,definition,
( spl2_1038
<=> ( powersetAx = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1038])],[avatar_definition]) ).
thf(f9310,plain,
( ( powersetAx = $true )
| ~ spl2_1036 ),
inference(avatar_component_clause,[status(thm)],[f9308]) ).
thf(f9308,definition,
( spl2_1036
<=> ( powersetAx = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1036])],[avatar_definition]) ).
thf(f10453,plain,
spl2_1104,
inference(avatar_split_clause,[status(thm)],[f475,f9612]) ).
thf(f475,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f318]) ).
thf(f10439,plain,
spl2_1260,
inference(avatar_split_clause,[status(thm)],[f440,f10330]) ).
thf(f440,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f318]) ).
thf(f10350,plain,
( spl2_1263
| spl2_1264 ),
inference(avatar_split_clause,[status(thm)],[f594,f10347,f10344]) ).
thf(f594,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( binunionIL = $false )
| ( ( in @ X2 @ ( binunion @ X1 @ X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f593]) ).
thf(f593,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( binunionIL = $false )
| ( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f592]) ).
thf(f592,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) )
@ X3 )
= $true )
| ( binunionIL = $false ) ),
inference(pi_clausification,[status(thm)],[f591]) ).
thf(f591,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) ) ) )
| ( binunionIL = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f590]) ).
thf(f590,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( binunionIL = $false ) ),
inference(pi_clausification,[status(thm)],[f589]) ).
thf(f589,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) ) )
= $true )
| ( binunionIL = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f588]) ).
thf(f588,plain,
! [X1: $i] :
( ( binunionIL = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f587]) ).
thf(f587,plain,
( ( binunionIL = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
thf(f269,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f268]) ).
thf(f268,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( binunionIL
= ( ! [X4: $i,X1: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',binunionIL) ).
thf(f9768,plain,
spl2_1036,
inference(avatar_split_clause,[status(thm)],[f418,f9308]) ).
thf(f418,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f318]) ).
thf(f9632,plain,
( spl2_1107
| spl2_1108 ),
inference(avatar_split_clause,[status(thm)],[f1128,f9630,f9626]) ).
thf(f1128,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1127]) ).
thf(f1127,plain,
! [X2: $i,X1: $i] :
( ( powersetE1 = $false )
| ( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1126]) ).
thf(f1126,plain,
! [X2: $i,X1: $i] :
( ( powersetE1 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1125]) ).
thf(f1125,plain,
! [X1: $i] :
( ( powersetE1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1124]) ).
thf(f1124,plain,
! [X1: $i] :
( ( powersetE1 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1123]) ).
thf(f1123,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f527]) ).
thf(f527,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
thf(f267,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f266]) ).
thf(f266,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
( powersetE1
= ( ! [X4: $i,X3: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',powersetE1) ).
thf(f9323,plain,
( spl2_1038
| spl2_1039 ),
inference(avatar_split_clause,[status(thm)],[f1366,f9321,f9317]) ).
thf(f1366,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1365]) ).
thf(f1365,plain,
! [X2: $i,X1: $i] :
( ( powersetAx = $false )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1364]) ).
thf(f1364,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1363]) ).
thf(f1363,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true )
| ( powersetAx = $false ) ),
inference(pi_clausification,[status(thm)],[f1362]) ).
thf(f1362,plain,
( ( powersetAx = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
thf(f144,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f143]) ).
thf(f143,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
<=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( powersetAx
= ( ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',powersetAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU587^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n022.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:27:36 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU587^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (! A:i.! B:i.subset A (binunion A B))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC089g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 225 ( 105 unt; 119 typ; 105 def)
% 0.16/0.39 % Number of atoms : 565 ( 154 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 104 ( 5 avg)
% 0.16/0.39 % Number of connectives : 890 ( 29 ~; 6 |; 27 &; 559 @)
% 0.16/0.39 % ( 14 <=>; 255 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 109 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 122 ( 119 usr; 107 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 311 ( 30 ^; 253 !; 28 ?; 311 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=163
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext_type,type,
% 0.16/0.39 setext: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setext,definition,
% 0.16/0.39 ( setext
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI_type,type,
% 0.16/0.39 emptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI,definition,
% 0.16/0.39 ( emptyI
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty_type,type,
% 0.16/0.39 noeltsimpempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty,definition,
% 0.16/0.39 ( noeltsimpempty
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta_type,type,
% 0.16/0.39 setbeta: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta,definition,
% 0.16/0.39 ( setbeta
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty_type,type,
% 0.16/0.39 nonempty: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty,definition,
% 0.16/0.39 ( nonempty
% 0.16/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1_type,type,
% 0.16/0.39 nonemptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1,definition,
% 0.16/0.39 ( nonemptyE1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI_type,type,
% 0.16/0.39 nonemptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI,definition,
% 0.16/0.39 ( nonemptyI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( nonempty
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1_type,type,
% 0.16/0.39 nonemptyI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1,definition,
% 0.16/0.39 ( nonemptyI1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL_type,type,
% 0.16/0.39 setadjoinIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL,definition,
% 0.16/0.39 ( setadjoinIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty_type,type,
% 0.16/0.39 emptyinunitempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty,definition,
% 0.16/0.39 ( emptyinunitempty
% 0.16/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR_type,type,
% 0.16/0.39 setadjoinIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR,definition,
% 0.16/0.39 ( setadjoinIR
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE_type,type,
% 0.16/0.39 setadjoinE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE,definition,
% 0.16/0.39 ( setadjoinE
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( Xy = Xx )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xy @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr_type,type,
% 0.16/0.39 setadjoinOr: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr,definition,
% 0.16/0.39 ( setadjoinOr
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq_type,type,
% 0.16/0.39 setoftrueEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq,definition,
% 0.16/0.39 ( setoftrueEq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : $true )
% 0.16/0.39 = A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI_type,type,
% 0.16/0.39 powersetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI,definition,
% 0.16/0.39 ( powersetI
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset_type,type,
% 0.16/0.39 emptyinPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset,definition,
% 0.16/0.39 ( emptyinPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset_type,type,
% 0.16/0.39 emptyInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset,definition,
% 0.16/0.39 ( emptyInPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE_type,type,
% 0.16/0.39 powersetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE,definition,
% 0.16/0.39 ( powersetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI_type,type,
% 0.16/0.39 setunionI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI,definition,
% 0.16/0.39 ( setunionI
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE_type,type,
% 0.16/0.39 setunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE,definition,
% 0.16/0.39 ( setunionE
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ! [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU_type,type,
% 0.16/0.39 subPowSU: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU,definition,
% 0.16/0.39 ( subPowSU
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2_type,type,
% 0.16/0.39 exuE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2,definition,
% 0.16/0.39 ( exuE2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness_type,type,
% 0.16/0.39 nonemptyImpWitness: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness,definition,
% 0.16/0.39 ( nonemptyImpWitness
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton_type,type,
% 0.16/0.39 notinsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton,definition,
% 0.16/0.39 ( notinsingleton
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx != Xy )
% 0.16/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit_type,type,
% 0.16/0.39 eqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit,definition,
% 0.16/0.39 ( eqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch_type,type,
% 0.16/0.39 singletonsswitch: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch,definition,
% 0.16/0.39 ( singletonsswitch
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE_type,type,
% 0.16/0.39 upairsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE,definition,
% 0.16/0.39 ( upairsetE
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL_type,type,
% 0.16/0.39 upairsetIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL,definition,
% 0.16/0.39 ( upairsetIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR_type,type,
% 0.16/0.39 upairsetIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR,definition,
% 0.16/0.39 ( upairsetIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1_type,type,
% 0.16/0.39 emptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1,definition,
% 0.16/0.39 ( emptyE1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => $false ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall_type,type,
% 0.16/0.39 vacuousDall: $o ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall,definition,
% 0.16/0.39 ( vacuousDall
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1_type,type,
% 0.16/0.39 quantDeMorgan1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1,definition,
% 0.16/0.39 ( quantDeMorgan1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2_type,type,
% 0.16/0.39 quantDeMorgan2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2,definition,
% 0.16/0.39 ( quantDeMorgan2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3_type,type,
% 0.16/0.39 quantDeMorgan3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3,definition,
% 0.16/0.39 ( quantDeMorgan3
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4_type,type,
% 0.16/0.39 quantDeMorgan4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4,definition,
% 0.16/0.39 ( quantDeMorgan4
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI_type,type,
% 0.16/0.39 prop2setI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI,definition,
% 0.16/0.39 ( prop2setI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(set2prop_type,type,
% 0.16/0.39 set2prop: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI_type,type,
% 0.16/0.39 prop2set2propI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI,definition,
% 0.16/0.39 ( prop2set2propI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE_type,type,
% 0.16/0.39 notdexE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE,definition,
% 0.16/0.39 ( notdexE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE_type,type,
% 0.16/0.39 notdallE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE,definition,
% 0.16/0.39 ( notdallE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1_type,type,
% 0.16/0.39 exuI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1,definition,
% 0.16/0.39 ( exuI1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3_type,type,
% 0.16/0.39 exuI3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3,definition,
% 0.16/0.39 ( exuI3
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2_type,type,
% 0.16/0.39 exuI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2,definition,
% 0.16/0.39 ( exuI2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP_type,type,
% 0.16/0.39 inCongP: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP,definition,
% 0.16/0.39 ( inCongP
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong_type,type,
% 0.16/0.39 in__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong,definition,
% 0.16/0.39 ( in__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u_type,type,
% 0.16/0.39 exuE3u: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u,definition,
% 0.16/0.39 ( exuE3u
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong_type,type,
% 0.16/0.39 exu__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong,definition,
% 0.16/0.39 ( exu__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 <=> ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong_type,type,
% 0.16/0.39 emptyset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong,definition,
% 0.16/0.39 ( emptyset__Cong
% 0.16/0.39 = ( emptyset = emptyset ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong_type,type,
% 0.16/0.39 setadjoin__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong,definition,
% 0.16/0.39 ( setadjoin__Cong
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ! [Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( Xz = Xu )
% 0.16/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong_type,type,
% 0.16/0.39 powerset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong,definition,
% 0.16/0.39 ( powerset__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( powerset @ A )
% 0.16/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong_type,type,
% 0.16/0.39 setunion__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong,definition,
% 0.16/0.39 ( setunion__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( setunion @ A )
% 0.16/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong_type,type,
% 0.16/0.39 omega__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong,definition,
% 0.16/0.39 ( omega__Cong
% 0.16/0.39 = ( omega = omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu_type,type,
% 0.16/0.39 exuEu: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu,definition,
% 0.16/0.39 ( exuEu
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong_type,type,
% 0.16/0.39 descr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong,definition,
% 0.16/0.39 ( descr__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.39 => ( ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong_type,type,
% 0.16/0.39 dsetconstr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong,definition,
% 0.16/0.39 ( dsetconstr__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjoint_type,type,
% 0.16/0.39 disjoint: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setsmeet_type,type,
% 0.16/0.39 setsmeet: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2_type,type,
% 0.16/0.39 eqimpsubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2,definition,
% 0.16/0.39 ( eqimpsubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1_type,type,
% 0.16/0.39 eqimpsubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1,definition,
% 0.16/0.39 ( eqimpsubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2_type,type,
% 0.16/0.39 subsetI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2,definition,
% 0.16/0.39 ( subsetI2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset_type,type,
% 0.16/0.39 emptysetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset,definition,
% 0.16/0.39 ( emptysetsubset
% 0.16/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE_type,type,
% 0.16/0.39 subsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE,definition,
% 0.16/0.39 ( subsetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2_type,type,
% 0.16/0.39 subsetE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2,definition,
% 0.16/0.39 ( subsetE2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI_type,type,
% 0.16/0.39 notsubsetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI,definition,
% 0.16/0.39 ( notsubsetI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1_type,type,
% 0.16/0.39 notequalI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1,definition,
% 0.16/0.39 ( notequalI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ( subset @ A @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2_type,type,
% 0.16/0.39 notequalI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2,definition,
% 0.16/0.39 ( notequalI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl_type,type,
% 0.16/0.39 subsetRefl: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl,definition,
% 0.16/0.39 ( subsetRefl
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans_type,type,
% 0.16/0.39 subsetTrans: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans,definition,
% 0.16/0.39 ( subsetTrans
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ C )
% 0.16/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub_type,type,
% 0.16/0.39 setadjoinSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub,definition,
% 0.16/0.39 ( setadjoinSub
% 0.16/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2_type,type,
% 0.16/0.39 setadjoinSub2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2,definition,
% 0.16/0.39 ( setadjoinSub2
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset_type,type,
% 0.16/0.39 subset2powerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset,definition,
% 0.16/0.39 ( subset2powerset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub_type,type,
% 0.16/0.39 setextsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub,definition,
% 0.16/0.39 ( setextsub
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ A )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq_type,type,
% 0.16/0.39 subsetemptysetimpeq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq,definition,
% 0.16/0.39 ( subsetemptysetimpeq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( subset @ A @ emptyset )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1_type,type,
% 0.16/0.39 powersetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1,definition,
% 0.16/0.39 ( powersetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1_type,type,
% 0.16/0.39 powersetE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1,definition,
% 0.16/0.39 ( powersetE1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset_type,type,
% 0.16/0.39 inPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset,definition,
% 0.16/0.39 ( inPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset_type,type,
% 0.16/0.39 powersetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset,definition,
% 0.16/0.39 ( powersetsubset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset_type,type,
% 0.16/0.39 sepInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset,definition,
% 0.16/0.39 ( sepInPowerset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( in
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset_type,type,
% 0.16/0.39 sepSubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset,definition,
% 0.16/0.39 ( sepSubset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( subset
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunion_type,type,
% 0.16/0.39 binunion: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL_type,type,
% 0.16/0.39 binunionIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL,definition,
% 0.16/0.39 ( binunionIL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR_type,type,
% 0.16/0.39 upairset2IR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR,definition,
% 0.16/0.39 ( upairset2IR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR_type,type,
% 0.16/0.39 binunionIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR,definition,
% 0.16/0.39 ( binunionIR
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases_type,type,
% 0.16/0.39 binunionEcases: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases,definition,
% 0.16/0.39 ( binunionEcases
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( ( in @ Xx @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xx @ B )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE_type,type,
% 0.16/0.39 binunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE,definition,
% 0.16/0.39 ( binunionE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionLsub,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ( setext
% 0.16/0.39 => ( emptyI
% 0.16/0.39 => ( noeltsimpempty
% 0.16/0.39 => ( setbeta
% 0.16/0.39 => ( nonemptyE1
% 0.16/0.39 => ( nonemptyI
% 0.16/0.39 => ( nonemptyI1
% 0.16/0.39 => ( setadjoinIL
% 0.16/0.39 => ( emptyinunitempty
% 0.16/0.39 => ( setadjoinIR
% 0.16/0.39 => ( setadjoinE
% 0.16/0.39 => ( setadjoinOr
% 0.16/0.39 => ( setoftrueEq
% 0.16/0.39 => ( powersetI
% 0.16/0.39 => ( emptyinPowerset
% 0.16/0.39 => ( emptyInPowerset
% 0.16/0.39 => ( powersetE
% 0.16/0.39 => ( setunionI
% 0.16/0.39 => ( setunionE
% 0.16/0.39 => ( subPowSU
% 0.16/0.39 => ( exuE2
% 0.16/0.39 => ( nonemptyImpWitness
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ( notinsingleton
% 0.16/0.39 => ( eqinunit
% 0.16/0.39 => ( singletonsswitch
% 0.16/0.39 => ( upairsetE
% 0.16/0.39 => ( upairsetIL
% 0.16/0.39 => ( upairsetIR
% 0.16/0.39 => ( emptyE1
% 0.16/0.39 => ( vacuousDall
% 0.16/0.39 => ( quantDeMorgan1
% 0.16/0.39 => ( quantDeMorgan2
% 0.16/0.39 => ( quantDeMorgan3
% 0.16/0.39 => ( quantDeMorgan4
% 0.16/0.39 => ( prop2setI
% 0.16/0.39 => ( prop2set2propI
% 0.16/0.39 => ( notdexE
% 0.16/0.39 => ( notdallE
% 0.16/0.39 => ( exuI1
% 0.16/0.39 => ( exuI3
% 0.16/0.39 => ( exuI2
% 0.16/0.39 => ( inCongP
% 0.16/0.39 => ( in__Cong
% 0.16/0.39 => ( exuE3u
% 0.16/0.39 => ( exu__Cong
% 0.16/0.39 => ( emptyset__Cong
% 0.16/0.39 => ( setadjoin__Cong
% 0.16/0.39 => ( powerset__Cong
% 0.16/0.39 => ( setunion__Cong
% 0.16/0.39 => ( omega__Cong
% 0.16/0.39 => ( exuEu
% 0.16/0.39 => ( descr__Cong
% 0.16/0.39 => ( dsetconstr__Cong
% 0.16/0.39 => ( subsetI1
% 0.16/0.39 => ( eqimpsubset2
% 0.16/0.39 => ( eqimpsubset1
% 0.16/0.39 => ( subsetI2
% 0.16/0.39 => ( emptysetsubset
% 0.16/0.39 => ( subsetE
% 0.16/0.39 => ( subsetE2
% 0.16/0.39 => ( notsubsetI
% 0.16/0.39 => ( notequalI1
% 0.16/0.39 => ( notequalI2
% 0.16/0.39 => ( subsetRefl
% 0.16/0.39 => ( subsetTrans
% 0.16/0.39 => ( setadjoinSub
% 0.16/0.39 => ( setadjoinSub2
% 0.16/0.39 => ( subset2powerset
% 0.16/0.39 => ( setextsub
% 0.16/0.39 => ( subsetemptysetimpeq
% 0.16/0.39 => ( powersetI1
% 0.16/0.39 => ( powersetE1
% 0.16/0.39 => ( inPowerset
% 0.16/0.39 => ( powersetsubset
% 0.16/0.39 => ( sepInPowerset
% 0.16/0.39 => ( sepSubset
% 0.16/0.39 => ( binunionIL
% 0.16/0.39 => ( upairset2IR
% 0.16/0.39 => ( binunionIR
% 0.16/0.39 => ( binunionEcases
% 0.16/0.39 => ( binunionE
% 0.16/0.39 => ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.46/1.51 ---- Embedded in THF ---
% 2.46/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.51 %%% Generated on Tue Feb 24 12:27:37 EST 2026
% 2.46/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.51 %%% Logic specification used:
% 2.46/1.51 %%% thf(spec, logic, $$dhol).
% 2.46/1.51
% 2.46/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2DTF4475.p
% See solution above
% 2.46/1.52 ------------------------
% 2.46/1.54 ---- Cleaned THF ---
% 2.46/1.54 thf(in_type,type,
% 2.46/1.54 in: $i > $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(exu_type,type,
% 2.46/1.54 exu: ( $i > $o ) > $o ).
% 2.46/1.54
% 2.46/1.54 thf(exu,definition,
% 2.46/1.54 ( exu
% 2.46/1.54 = ( ^ [Xphi: $i > $o] :
% 2.46/1.54 ? [Xx: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 & ! [Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setextAx_type,type,
% 2.46/1.54 setextAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setextAx,definition,
% 2.46/1.54 ( setextAx
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 <=> ( in @ Xx @ B ) )
% 2.46/1.54 => ( A = B ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyset_type,type,
% 2.46/1.54 emptyset: $i ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetAx_type,type,
% 2.46/1.54 emptysetAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetAx,definition,
% 2.46/1.54 ( emptysetAx
% 2.46/1.54 = ( ! [Xx: $i] :
% 2.46/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoin_type,type,
% 2.46/1.54 setadjoin: $i > $i > $i ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinAx_type,type,
% 2.46/1.54 setadjoinAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinAx,definition,
% 2.46/1.54 ( setadjoinAx
% 2.46/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.54 <=> ( ( Xy = Xx )
% 2.46/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powerset_type,type,
% 2.46/1.54 powerset: $i > $i ).
% 2.46/1.54
% 2.46/1.54 thf(powersetAx_type,type,
% 2.46/1.54 powersetAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetAx,definition,
% 2.46/1.54 ( powersetAx
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.54 <=> ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setunion_type,type,
% 2.46/1.54 setunion: $i > $i ).
% 2.46/1.54
% 2.46/1.54 thf(setunionAx_type,type,
% 2.46/1.54 setunionAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setunionAx,definition,
% 2.46/1.54 ( setunionAx
% 2.46/1.54 = ( ! [A: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.46/1.54 <=> ? [B: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 & ( in @ B @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(omega_type,type,
% 2.46/1.54 omega: $i ).
% 2.46/1.54
% 2.46/1.54 thf(omega0Ax_type,type,
% 2.46/1.54 omega0Ax: $o ).
% 2.46/1.54
% 2.46/1.54 thf(omega0Ax,definition,
% 2.46/1.54 ( omega0Ax
% 2.46/1.54 = ( in @ emptyset @ omega ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(omegaSAx_type,type,
% 2.46/1.54 omegaSAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(omegaSAx,definition,
% 2.46/1.54 ( omegaSAx
% 2.46/1.54 = ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ omega )
% 2.46/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(omegaIndAx_type,type,
% 2.46/1.54 omegaIndAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(omegaIndAx,definition,
% 2.46/1.54 ( omegaIndAx
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ( ( in @ emptyset @ A )
% 2.46/1.54 & ! [Xx: $i] :
% 2.46/1.54 ( ( ( in @ Xx @ omega )
% 2.46/1.54 & ( in @ Xx @ A ) )
% 2.46/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.46/1.54 => ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ omega )
% 2.46/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(replAx_type,type,
% 2.46/1.54 replAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(replAx,definition,
% 2.46/1.54 ( replAx
% 2.46/1.54 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( exu
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.46/1.54 => ? [B: $i] :
% 2.46/1.54 ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 <=> ? [Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ A )
% 2.46/1.54 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(foundationAx_type,type,
% 2.46/1.54 foundationAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(foundationAx,definition,
% 2.46/1.54 ( foundationAx
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.46/1.54 => ? [B: $i] :
% 2.46/1.54 ( ( in @ B @ A )
% 2.46/1.54 & ~ ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(wellorderingAx_type,type,
% 2.46/1.54 wellorderingAx: $o ).
% 2.46/1.54
% 2.46/1.54 thf(wellorderingAx,definition,
% 2.46/1.54 ( wellorderingAx
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ? [B: $i] :
% 2.46/1.54 ( ! [C: $i] :
% 2.46/1.54 ( ( in @ C @ B )
% 2.46/1.54 => ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ C )
% 2.46/1.54 => ( in @ Xx @ A ) ) )
% 2.46/1.54 & ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( ( in @ Xx @ A )
% 2.46/1.54 & ( in @ Xy @ A ) )
% 2.46/1.54 => ( ! [C: $i] :
% 2.46/1.54 ( ( in @ C @ B )
% 2.46/1.54 => ( ( in @ Xx @ C )
% 2.46/1.54 <=> ( in @ Xy @ C ) ) )
% 2.46/1.54 => ( Xx = Xy ) ) )
% 2.46/1.54 & ! [C: $i,D: $i] :
% 2.46/1.54 ( ( ( in @ C @ B )
% 2.46/1.54 & ( in @ D @ B ) )
% 2.46/1.54 => ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ C )
% 2.46/1.54 => ( in @ Xx @ D ) )
% 2.46/1.54 | ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ D )
% 2.46/1.54 => ( in @ Xx @ C ) ) ) )
% 2.46/1.54 & ! [C: $i] :
% 2.46/1.54 ( ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ C )
% 2.46/1.54 => ( in @ Xx @ A ) )
% 2.46/1.54 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.46/1.54 => ? [D: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ D @ B )
% 2.46/1.54 & ( in @ Xx @ C )
% 2.46/1.54 & ~ ? [Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ D )
% 2.46/1.54 & ( in @ Xy @ C ) )
% 2.46/1.54 & ! [E: $i] :
% 2.46/1.54 ( ( in @ E @ B )
% 2.46/1.54 => ( ! [Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ E )
% 2.46/1.54 => ( in @ Xy @ D ) )
% 2.46/1.54 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(descr_type,type,
% 2.46/1.54 descr: ( $i > $o ) > $i ).
% 2.46/1.54
% 2.46/1.54 thf(descrp_type,type,
% 2.46/1.54 descrp: $o ).
% 2.46/1.54
% 2.46/1.54 thf(descrp,definition,
% 2.46/1.54 ( descrp
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ( Xphi
% 2.46/1.54 @ ( descr
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstr_type,type,
% 2.46/1.54 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrI_type,type,
% 2.46/1.54 dsetconstrI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrI,definition,
% 2.46/1.54 ( dsetconstrI
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( ( Xphi @ Xx )
% 2.46/1.54 => ( in @ Xx
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrEL_type,type,
% 2.46/1.54 dsetconstrEL: $o ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrEL,definition,
% 2.46/1.54 ( dsetconstrEL
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrER_type,type,
% 2.46/1.54 dsetconstrER: $o ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstrER,definition,
% 2.46/1.54 ( dsetconstrER
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuE1_type,type,
% 2.46/1.54 exuE1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuE1,definition,
% 2.46/1.54 ( exuE1
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ? [Xx: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 & ! [Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(prop2set_type,type,
% 2.46/1.54 prop2set: $o > $i ).
% 2.46/1.54
% 2.46/1.54 thf(prop2setE_type,type,
% 2.46/1.54 prop2setE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(prop2setE,definition,
% 2.46/1.54 ( prop2setE
% 2.46/1.54 = ( ! [Xphi: $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.46/1.54 => Xphi ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetE_type,type,
% 2.46/1.54 emptysetE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetE,definition,
% 2.46/1.54 ( emptysetE
% 2.46/1.54 = ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ emptyset )
% 2.46/1.54 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetimpfalse_type,type,
% 2.46/1.54 emptysetimpfalse: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetimpfalse,definition,
% 2.46/1.54 ( emptysetimpfalse
% 2.46/1.54 = ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ emptyset )
% 2.46/1.54 => $false ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notinemptyset_type,type,
% 2.46/1.54 notinemptyset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notinemptyset,definition,
% 2.46/1.54 ( notinemptyset
% 2.46/1.54 = ( ! [Xx: $i] :
% 2.46/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuE3e_type,type,
% 2.46/1.54 exuE3e: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuE3e,definition,
% 2.46/1.54 ( exuE3e
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setext_type,type,
% 2.46/1.54 setext: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setext,definition,
% 2.46/1.54 ( setext
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ B ) )
% 2.46/1.54 => ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( in @ Xx @ A ) )
% 2.46/1.54 => ( A = B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyI_type,type,
% 2.46/1.54 emptyI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyI,definition,
% 2.46/1.54 ( emptyI
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ~ ( in @ Xx @ A )
% 2.46/1.54 => ( A = emptyset ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(noeltsimpempty_type,type,
% 2.46/1.54 noeltsimpempty: $o ).
% 2.46/1.54
% 2.46/1.54 thf(noeltsimpempty,definition,
% 2.46/1.54 ( noeltsimpempty
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ~ ( in @ Xx @ A )
% 2.46/1.54 => ( A = emptyset ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setbeta_type,type,
% 2.46/1.54 setbeta: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setbeta,definition,
% 2.46/1.54 ( setbeta
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( ( in @ Xx
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.54 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(nonempty_type,type,
% 2.46/1.54 nonempty: $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(nonempty,definition,
% 2.46/1.54 ( nonempty
% 2.46/1.54 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyE1_type,type,
% 2.46/1.54 nonemptyE1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyE1,definition,
% 2.46/1.54 ( nonemptyE1
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ( nonempty @ A )
% 2.46/1.54 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyI_type,type,
% 2.46/1.54 nonemptyI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyI,definition,
% 2.46/1.54 ( nonemptyI
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( ( Xphi @ Xx )
% 2.46/1.54 => ( nonempty
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyI1_type,type,
% 2.46/1.54 nonemptyI1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyI1,definition,
% 2.46/1.54 ( nonemptyI1
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.46/1.54 => ( nonempty @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinIL_type,type,
% 2.46/1.54 setadjoinIL: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinIL,definition,
% 2.46/1.54 ( setadjoinIL
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyinunitempty_type,type,
% 2.46/1.54 emptyinunitempty: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyinunitempty,definition,
% 2.46/1.54 ( emptyinunitempty
% 2.46/1.54 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinIR_type,type,
% 2.46/1.54 setadjoinIR: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinIR,definition,
% 2.46/1.54 ( setadjoinIR
% 2.46/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ A )
% 2.46/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinE_type,type,
% 2.46/1.54 setadjoinE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinE,definition,
% 2.46/1.54 ( setadjoinE
% 2.46/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.54 => ! [Xphi: $o] :
% 2.46/1.54 ( ( ( Xy = Xx )
% 2.46/1.54 => Xphi )
% 2.46/1.54 => ( ( ( in @ Xy @ A )
% 2.46/1.54 => Xphi )
% 2.46/1.54 => Xphi ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinOr_type,type,
% 2.46/1.54 setadjoinOr: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinOr,definition,
% 2.46/1.54 ( setadjoinOr
% 2.46/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.54 => ( ( Xy = Xx )
% 2.46/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setoftrueEq_type,type,
% 2.46/1.54 setoftrueEq: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setoftrueEq,definition,
% 2.46/1.54 ( setoftrueEq
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xx: $i] : $true )
% 2.46/1.54 = A ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powersetI_type,type,
% 2.46/1.54 powersetI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetI,definition,
% 2.46/1.54 ( powersetI
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( in @ Xx @ A ) )
% 2.46/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyinPowerset_type,type,
% 2.46/1.54 emptyinPowerset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyinPowerset,definition,
% 2.46/1.54 ( emptyinPowerset
% 2.46/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyInPowerset_type,type,
% 2.46/1.54 emptyInPowerset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyInPowerset,definition,
% 2.46/1.54 ( emptyInPowerset
% 2.46/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powersetE_type,type,
% 2.46/1.54 powersetE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetE,definition,
% 2.46/1.54 ( powersetE
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.54 => ( ( in @ Xx @ B )
% 2.46/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setunionI_type,type,
% 2.46/1.54 setunionI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setunionI,definition,
% 2.46/1.54 ( setunionI
% 2.46/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( ( in @ B @ A )
% 2.46/1.54 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setunionE_type,type,
% 2.46/1.54 setunionE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setunionE,definition,
% 2.46/1.54 ( setunionE
% 2.46/1.54 = ( ! [A: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.46/1.54 => ! [Xphi: $o] :
% 2.46/1.54 ( ! [B: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( ( in @ B @ A )
% 2.46/1.54 => Xphi ) )
% 2.46/1.54 => Xphi ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subPowSU_type,type,
% 2.46/1.54 subPowSU: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subPowSU,definition,
% 2.46/1.54 ( subPowSU
% 2.46/1.54 = ( ! [A: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuE2_type,type,
% 2.46/1.54 exuE2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuE2,definition,
% 2.46/1.54 ( exuE2
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ? [Xx: $i] :
% 2.46/1.54 ! [Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xy )
% 2.46/1.54 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyImpWitness_type,type,
% 2.46/1.54 nonemptyImpWitness: $o ).
% 2.46/1.54
% 2.46/1.54 thf(nonemptyImpWitness,definition,
% 2.46/1.54 ( nonemptyImpWitness
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ( nonempty @ A )
% 2.46/1.54 => ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & $true ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(uniqinunit_type,type,
% 2.46/1.54 uniqinunit: $o ).
% 2.46/1.54
% 2.46/1.54 thf(uniqinunit,definition,
% 2.46/1.54 ( uniqinunit
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.54 => ( Xx = Xy ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notinsingleton_type,type,
% 2.46/1.54 notinsingleton: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notinsingleton,definition,
% 2.46/1.54 ( notinsingleton
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx != Xy )
% 2.46/1.54 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(eqinunit_type,type,
% 2.46/1.54 eqinunit: $o ).
% 2.46/1.54
% 2.46/1.54 thf(eqinunit,definition,
% 2.46/1.54 ( eqinunit
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(singletonsswitch_type,type,
% 2.46/1.54 singletonsswitch: $o ).
% 2.46/1.54
% 2.46/1.54 thf(singletonsswitch,definition,
% 2.46/1.54 ( singletonsswitch
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetE_type,type,
% 2.46/1.54 upairsetE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetE,definition,
% 2.46/1.54 ( upairsetE
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.46/1.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.46/1.54 => ( ( Xz = Xx )
% 2.46/1.54 | ( Xz = Xy ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetIL_type,type,
% 2.46/1.54 upairsetIL: $o ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetIL,definition,
% 2.46/1.54 ( upairsetIL
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetIR_type,type,
% 2.46/1.54 upairsetIR: $o ).
% 2.46/1.54
% 2.46/1.54 thf(upairsetIR,definition,
% 2.46/1.54 ( upairsetIR
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyE1_type,type,
% 2.46/1.54 emptyE1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyE1,definition,
% 2.46/1.54 ( emptyE1
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ( Xphi @ Xx ) )
% 2.46/1.54 => ( ( ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 = emptyset )
% 2.46/1.54 => $false ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(vacuousDall_type,type,
% 2.46/1.54 vacuousDall: $o ).
% 2.46/1.54
% 2.46/1.54 thf(vacuousDall,definition,
% 2.46/1.54 ( vacuousDall
% 2.46/1.54 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ emptyset )
% 2.46/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan1_type,type,
% 2.46/1.54 quantDeMorgan1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan1,definition,
% 2.46/1.54 ( quantDeMorgan1
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ~ ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( Xphi @ Xx ) )
% 2.46/1.54 => ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan2_type,type,
% 2.46/1.54 quantDeMorgan2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan2,definition,
% 2.46/1.54 ( quantDeMorgan2
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ~ ( Xphi @ Xx ) )
% 2.46/1.54 => ~ ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan3_type,type,
% 2.46/1.54 quantDeMorgan3: $o ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan3,definition,
% 2.46/1.54 ( quantDeMorgan3
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ~ ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ( Xphi @ Xx ) )
% 2.46/1.54 => ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan4_type,type,
% 2.46/1.54 quantDeMorgan4: $o ).
% 2.46/1.54
% 2.46/1.54 thf(quantDeMorgan4,definition,
% 2.46/1.54 ( quantDeMorgan4
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ~ ( Xphi @ Xx ) )
% 2.46/1.54 => ~ ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(prop2setI_type,type,
% 2.46/1.54 prop2setI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(prop2setI,definition,
% 2.46/1.54 ( prop2setI
% 2.46/1.54 = ( ! [Xphi: $o] :
% 2.46/1.54 ( Xphi
% 2.46/1.54 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(set2prop_type,type,
% 2.46/1.54 set2prop: $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(prop2set2propI_type,type,
% 2.46/1.54 prop2set2propI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(prop2set2propI,definition,
% 2.46/1.54 ( prop2set2propI
% 2.46/1.54 = ( ! [Xphi: $o] :
% 2.46/1.54 ( Xphi
% 2.46/1.54 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notdexE_type,type,
% 2.46/1.54 notdexE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notdexE,definition,
% 2.46/1.54 ( notdexE
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ~ ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ( Xphi @ Xx ) )
% 2.46/1.54 => ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notdallE_type,type,
% 2.46/1.54 notdallE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notdallE,definition,
% 2.46/1.54 ( notdallE
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( ~ ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( Xphi @ Xx ) )
% 2.46/1.54 => ? [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuI1_type,type,
% 2.46/1.54 exuI1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuI1,definition,
% 2.46/1.54 ( exuI1
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ? [Xx: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 & ! [Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) )
% 2.46/1.54 => ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuI3_type,type,
% 2.46/1.54 exuI3: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuI3,definition,
% 2.46/1.54 ( exuI3
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.46/1.54 => ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 => ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) )
% 2.46/1.54 => ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuI2_type,type,
% 2.46/1.54 exuI2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuI2,definition,
% 2.46/1.54 ( exuI2
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ? [Xx: $i] :
% 2.46/1.54 ! [Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xy )
% 2.46/1.54 <=> ( Xy = Xx ) )
% 2.46/1.54 => ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(inCongP_type,type,
% 2.46/1.54 inCongP: $o ).
% 2.46/1.54
% 2.46/1.54 thf(inCongP,definition,
% 2.46/1.54 ( inCongP
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(in__Cong_type,type,
% 2.46/1.54 in__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(in__Cong,definition,
% 2.46/1.54 ( in__Cong
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ( ( in @ Xx @ A )
% 2.46/1.54 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuE3u_type,type,
% 2.46/1.54 exuE3u: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuE3u,definition,
% 2.46/1.54 ( exuE3u
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 => ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exu__Cong_type,type,
% 2.46/1.54 exu__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exu__Cong,definition,
% 2.46/1.54 ( exu__Cong
% 2.46/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.54 ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ( ( Xphi @ Xx )
% 2.46/1.54 <=> ( Xpsi @ Xy ) ) )
% 2.46/1.54 => ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 <=> ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptyset__Cong_type,type,
% 2.46/1.54 emptyset__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptyset__Cong,definition,
% 2.46/1.54 ( emptyset__Cong
% 2.46/1.54 = ( emptyset = emptyset ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoin__Cong_type,type,
% 2.46/1.54 setadjoin__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoin__Cong,definition,
% 2.46/1.54 ( setadjoin__Cong
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ! [Xz: $i,Xu: $i] :
% 2.46/1.54 ( ( Xz = Xu )
% 2.46/1.54 => ( ( setadjoin @ Xx @ Xz )
% 2.46/1.54 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powerset__Cong_type,type,
% 2.46/1.54 powerset__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powerset__Cong,definition,
% 2.46/1.54 ( powerset__Cong
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ( ( powerset @ A )
% 2.46/1.54 = ( powerset @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setunion__Cong_type,type,
% 2.46/1.54 setunion__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setunion__Cong,definition,
% 2.46/1.54 ( setunion__Cong
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ( ( setunion @ A )
% 2.46/1.54 = ( setunion @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(omega__Cong_type,type,
% 2.46/1.54 omega__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(omega__Cong,definition,
% 2.46/1.54 ( omega__Cong
% 2.46/1.54 = ( omega = omega ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(exuEu_type,type,
% 2.46/1.54 exuEu: $o ).
% 2.46/1.54
% 2.46/1.54 thf(exuEu,definition,
% 2.46/1.54 ( exuEu
% 2.46/1.54 = ( ! [Xphi: $i > $o] :
% 2.46/1.54 ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xphi @ Xx )
% 2.46/1.54 => ( ( Xphi @ Xy )
% 2.46/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(descr__Cong_type,type,
% 2.46/1.54 descr__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(descr__Cong,definition,
% 2.46/1.54 ( descr__Cong
% 2.46/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.54 ( ! [Xx: $i,Xy: $i] :
% 2.46/1.54 ( ( Xx = Xy )
% 2.46/1.54 => ( ( Xphi @ Xx )
% 2.46/1.54 <=> ( Xpsi @ Xy ) ) )
% 2.46/1.54 => ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 => ( ( exu
% 2.46/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.46/1.54 => ( ( descr
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 = ( descr
% 2.46/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstr__Cong_type,type,
% 2.46/1.54 dsetconstr__Cong: $o ).
% 2.46/1.54
% 2.46/1.54 thf(dsetconstr__Cong,definition,
% 2.46/1.54 ( dsetconstr__Cong
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ! [Xy: $i] :
% 2.46/1.54 ( ( in @ Xy @ B )
% 2.46/1.54 => ( ( Xx = Xy )
% 2.46/1.54 => ( ( Xphi @ Xx )
% 2.46/1.54 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.46/1.54 => ( ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 = ( dsetconstr @ B
% 2.46/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subset_type,type,
% 2.46/1.54 subset: $i > $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(disjoint_type,type,
% 2.46/1.54 disjoint: $i > $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(setsmeet_type,type,
% 2.46/1.54 setsmeet: $i > $i > $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetI1_type,type,
% 2.46/1.54 subsetI1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetI1,definition,
% 2.46/1.54 ( subsetI1
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ B ) )
% 2.46/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(eqimpsubset2_type,type,
% 2.46/1.54 eqimpsubset2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(eqimpsubset2,definition,
% 2.46/1.54 ( eqimpsubset2
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(eqimpsubset1_type,type,
% 2.46/1.54 eqimpsubset1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(eqimpsubset1,definition,
% 2.46/1.54 ( eqimpsubset1
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( A = B )
% 2.46/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetI2_type,type,
% 2.46/1.54 subsetI2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetI2,definition,
% 2.46/1.54 ( subsetI2
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ! [Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ B ) )
% 2.46/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetsubset_type,type,
% 2.46/1.54 emptysetsubset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(emptysetsubset,definition,
% 2.46/1.54 ( emptysetsubset
% 2.46/1.54 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetE_type,type,
% 2.46/1.54 subsetE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetE,definition,
% 2.46/1.54 ( subsetE
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetE2_type,type,
% 2.46/1.54 subsetE2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetE2,definition,
% 2.46/1.54 ( subsetE2
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( ~ ( in @ Xx @ B )
% 2.46/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notsubsetI_type,type,
% 2.46/1.54 notsubsetI: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notsubsetI,definition,
% 2.46/1.54 ( notsubsetI
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( ~ ( in @ Xx @ B )
% 2.46/1.54 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notequalI1_type,type,
% 2.46/1.54 notequalI1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notequalI1,definition,
% 2.46/1.54 ( notequalI1
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ~ ( subset @ A @ B )
% 2.46/1.54 => ( A != B ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(notequalI2_type,type,
% 2.46/1.54 notequalI2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(notequalI2,definition,
% 2.46/1.54 ( notequalI2
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( ~ ( in @ Xx @ B )
% 2.46/1.54 => ( A != B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetRefl_type,type,
% 2.46/1.54 subsetRefl: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetRefl,definition,
% 2.46/1.54 ( subsetRefl
% 2.46/1.54 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetTrans_type,type,
% 2.46/1.54 subsetTrans: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetTrans,definition,
% 2.46/1.54 ( subsetTrans
% 2.46/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( ( subset @ B @ C )
% 2.46/1.54 => ( subset @ A @ C ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinSub_type,type,
% 2.46/1.54 setadjoinSub: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinSub,definition,
% 2.46/1.54 ( setadjoinSub
% 2.46/1.54 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinSub2_type,type,
% 2.46/1.54 setadjoinSub2: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setadjoinSub2,definition,
% 2.46/1.54 ( setadjoinSub2
% 2.46/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subset2powerset_type,type,
% 2.46/1.54 subset2powerset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subset2powerset,definition,
% 2.46/1.54 ( subset2powerset
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(setextsub_type,type,
% 2.46/1.54 setextsub: $o ).
% 2.46/1.54
% 2.46/1.54 thf(setextsub,definition,
% 2.46/1.54 ( setextsub
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( ( subset @ B @ A )
% 2.46/1.54 => ( A = B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(subsetemptysetimpeq_type,type,
% 2.46/1.54 subsetemptysetimpeq: $o ).
% 2.46/1.54
% 2.46/1.54 thf(subsetemptysetimpeq,definition,
% 2.46/1.54 ( subsetemptysetimpeq
% 2.46/1.54 = ( ! [A: $i] :
% 2.46/1.54 ( ( subset @ A @ emptyset )
% 2.46/1.54 => ( A = emptyset ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powersetI1_type,type,
% 2.46/1.54 powersetI1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetI1,definition,
% 2.46/1.54 ( powersetI1
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( subset @ B @ A )
% 2.46/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powersetE1_type,type,
% 2.46/1.54 powersetE1: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetE1,definition,
% 2.46/1.54 ( powersetE1
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(inPowerset_type,type,
% 2.46/1.54 inPowerset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(inPowerset,definition,
% 2.46/1.54 ( inPowerset
% 2.46/1.54 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(powersetsubset_type,type,
% 2.46/1.54 powersetsubset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(powersetsubset,definition,
% 2.46/1.54 ( powersetsubset
% 2.46/1.54 = ( ! [A: $i,B: $i] :
% 2.46/1.54 ( ( subset @ A @ B )
% 2.46/1.54 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(sepInPowerset_type,type,
% 2.46/1.54 sepInPowerset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(sepInPowerset,definition,
% 2.46/1.54 ( sepInPowerset
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( in
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 @ ( powerset @ A ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(sepSubset_type,type,
% 2.46/1.54 sepSubset: $o ).
% 2.46/1.54
% 2.46/1.54 thf(sepSubset,definition,
% 2.46/1.54 ( sepSubset
% 2.46/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.54 ( subset
% 2.46/1.54 @ ( dsetconstr @ A
% 2.46/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.54 @ A ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(binunion_type,type,
% 2.46/1.54 binunion: $i > $i > $i ).
% 2.46/1.54
% 2.46/1.54 thf(binunionIL_type,type,
% 2.46/1.54 binunionIL: $o ).
% 2.46/1.54
% 2.46/1.54 thf(binunionIL,definition,
% 2.46/1.54 ( binunionIL
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ A )
% 2.46/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(upairset2IR_type,type,
% 2.46/1.54 upairset2IR: $o ).
% 2.46/1.54
% 2.46/1.54 thf(upairset2IR,definition,
% 2.46/1.54 ( upairset2IR
% 2.46/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(binunionIR_type,type,
% 2.46/1.54 binunionIR: $o ).
% 2.46/1.54
% 2.46/1.54 thf(binunionIR,definition,
% 2.46/1.54 ( binunionIR
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ B )
% 2.46/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(binunionEcases_type,type,
% 2.46/1.54 binunionEcases: $o ).
% 2.46/1.54
% 2.46/1.54 thf(binunionEcases,definition,
% 2.46/1.54 ( binunionEcases
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.46/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.46/1.54 => ( ( ( in @ Xx @ A )
% 2.46/1.54 => Xphi )
% 2.46/1.54 => ( ( ( in @ Xx @ B )
% 2.46/1.54 => Xphi )
% 2.46/1.54 => Xphi ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(binunionE_type,type,
% 2.46/1.54 binunionE: $o ).
% 2.46/1.54
% 2.46/1.54 thf(binunionE,definition,
% 2.46/1.54 ( binunionE
% 2.46/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.46/1.54 => ( ( in @ Xx @ A )
% 2.46/1.54 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.46/1.54
% 2.46/1.54 thf(binunionLsub,conjecture,
% 2.46/1.54 ( setextAx
% 2.46/1.54 => ( emptysetAx
% 2.46/1.54 => ( setadjoinAx
% 2.46/1.54 => ( powersetAx
% 2.46/1.54 => ( setunionAx
% 2.46/1.54 => ( omega0Ax
% 2.46/1.54 => ( omegaSAx
% 2.46/1.54 => ( omegaIndAx
% 2.46/1.54 => ( replAx
% 2.46/1.54 => ( foundationAx
% 2.46/1.54 => ( wellorderingAx
% 2.46/1.54 => ( descrp
% 2.46/1.54 => ( dsetconstrI
% 2.46/1.54 => ( dsetconstrEL
% 2.46/1.54 => ( dsetconstrER
% 2.46/1.54 => ( exuE1
% 2.46/1.54 => ( prop2setE
% 2.46/1.54 => ( emptysetE
% 2.46/1.54 => ( emptysetimpfalse
% 2.46/1.54 => ( notinemptyset
% 2.46/1.54 => ( exuE3e
% 2.46/1.54 => ( setext
% 2.46/1.54 => ( emptyI
% 2.46/1.54 => ( noeltsimpempty
% 2.46/1.54 => ( setbeta
% 2.46/1.54 => ( nonemptyE1
% 2.46/1.54 => ( nonemptyI
% 2.46/1.54 => ( nonemptyI1
% 2.46/1.54 => ( setadjoinIL
% 2.46/1.54 => ( emptyinunitempty
% 2.46/1.54 => ( setadjoinIR
% 2.46/1.54 => ( setadjoinE
% 2.46/1.54 => ( setadjoinOr
% 2.46/1.54 => ( setoftrueEq
% 2.46/1.54 => ( powersetI
% 2.46/1.54 => ( emptyinPowerset
% 2.46/1.54 => ( emptyInPowerset
% 2.46/1.54 => ( powersetE
% 2.46/1.54 => ( setunionI
% 2.46/1.54 => ( setunionE
% 2.46/1.54 => ( subPowSU
% 2.46/1.54 => ( exuE2
% 2.46/1.54 => ( nonemptyImpWitness
% 2.46/1.54 => ( uniqinunit
% 2.46/1.54 => ( notinsingleton
% 2.46/1.54 => ( eqinunit
% 2.46/1.54 => ( singletonsswitch
% 2.46/1.54 => ( upairsetE
% 2.46/1.54 => ( upairsetIL
% 2.46/1.54 => ( upairsetIR
% 2.46/1.54 => ( emptyE1
% 2.46/1.54 => ( vacuousDall
% 2.46/1.54 => ( quantDeMorgan1
% 2.46/1.54 => ( quantDeMorgan2
% 2.46/1.54 => ( quantDeMorgan3
% 2.46/1.54 => ( quantDeMorgan4
% 2.46/1.54 => ( prop2setI
% 2.46/1.54 => ( prop2set2propI
% 2.46/1.54 => ( notdexE
% 2.46/1.54 => ( notdallE
% 2.46/1.54 => ( exuI1
% 2.46/1.54 => ( exuI3
% 2.46/1.54 => ( exuI2
% 2.46/1.54 => ( inCongP
% 2.46/1.54 => ( in__Cong
% 2.46/1.54 => ( exuE3u
% 2.46/1.54 => ( exu__Cong
% 2.46/1.54 => ( emptyset__Cong
% 2.46/1.54 => ( setadjoin__Cong
% 2.46/1.54 => ( powerset__Cong
% 2.46/1.54 => ( setunion__Cong
% 2.46/1.54 => ( omega__Cong
% 2.46/1.54 => ( exuEu
% 2.46/1.54 => ( descr__Cong
% 2.46/1.54 => ( dsetconstr__Cong
% 2.46/1.54 => ( subsetI1
% 2.46/1.54 => ( eqimpsubset2
% 2.46/1.54 => ( eqimpsubset1
% 2.46/1.54 => ( subsetI2
% 2.46/1.54 => ( emptysetsubset
% 2.46/1.54 => ( subsetE
% 2.46/1.54 => ( subsetE2
% 2.46/1.54 => ( notsubsetI
% 2.46/1.54 => ( notequalI1
% 2.46/1.54 => ( notequalI2
% 2.46/1.54 => ( subsetRefl
% 2.46/1.54 => ( subsetTrans
% 2.46/1.54 => ( setadjoinSub
% 2.46/1.54 => ( setadjoinSub2
% 2.46/1.54 => ( subset2powerset
% 2.46/1.54 => ( setextsub
% 2.46/1.54 => ( subsetemptysetimpeq
% 2.46/1.54 => ( powersetI1
% 2.46/1.54 => ( powersetE1
% 2.46/1.54 => ( inPowerset
% 2.46/1.54 => ( powersetsubset
% 2.46/1.54 => ( sepInPowerset
% 2.46/1.54 => ( sepSubset
% 2.46/1.54 => ( binunionIL
% 2.46/1.54 => ( upairset2IR
% 2.46/1.54 => ( binunionIR
% 2.46/1.54 => ( binunionEcases
% 2.46/1.54 => ( binunionE
% 2.46/1.54 => ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.54 ------------------------
% 2.46/1.57 % (4574)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/183Mi)
% 2.46/1.57 % (4577)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/2Mi)
% 2.46/1.57 % (4575)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_4475 for (2999ds/4Mi)
% 2.46/1.57 % (4578)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_4475 for (2999ds/2Mi)
% 2.46/1.57 % (4576)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_4475 for (2999ds/27Mi)
% 2.46/1.57 % (4579)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_4475 for (2999ds/275Mi)
% 2.46/1.57 % (4580)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/18Mi)
% 2.46/1.57 % (4577)Instruction limit reached!
% 2.46/1.57 % (4577)------------------------------
% 2.46/1.57 % (4577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (4577)Termination reason: Unknown
% 2.46/1.57 % (4577)Termination phase: shuffling
% 2.46/1.57 % (4578)Instruction limit reached!
% 2.46/1.57 % (4578)------------------------------
% 2.46/1.57 % (4578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (4578)Termination reason: Unknown
% 2.46/1.57 % (4578)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (4578)Memory used [KB]: 1151
% 2.46/1.57 % (4578)Time elapsed: 0.003 s
% 2.46/1.57 % (4578)Instructions burned: 2 (million)
% 2.46/1.57 % (4578)------------------------------
% 2.46/1.57 % (4578)------------------------------
% 2.46/1.57
% 2.46/1.57 % (4577)Memory used [KB]: 1151
% 2.46/1.57 % (4577)Time elapsed: 0.003 s
% 2.46/1.57 % (4577)Instructions burned: 2 (million)
% 2.46/1.57 % (4577)------------------------------
% 2.46/1.57 % (4577)------------------------------
% 2.46/1.57 % (4575)Instruction limit reached!
% 2.46/1.57 % (4575)------------------------------
% 2.46/1.57 % (4575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (4575)Termination reason: Unknown
% 2.46/1.57 % (4575)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (4575)Memory used [KB]: 1151
% 2.46/1.57 % (4575)Time elapsed: 0.004 s
% 2.46/1.57 % (4575)Instructions burned: 4 (million)
% 2.46/1.57 % (4575)------------------------------
% 2.46/1.57 % (4575)------------------------------
% 2.46/1.57 % (4580)Instruction limit reached!
% 2.46/1.57 % (4580)------------------------------
% 2.46/1.57 % (4580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (4580)Termination reason: Unknown
% 2.46/1.57 % (4580)Termination phase: Preprocessing 3
% 2.46/1.57
% 2.46/1.57 % (4580)Memory used [KB]: 1535
% 2.46/1.57 % (4580)Time elapsed: 0.011 s
% 2.46/1.57 % (4580)Instructions burned: 19 (million)
% 2.46/1.57 % (4580)------------------------------
% 2.46/1.57 % (4580)------------------------------
% 2.46/1.58 % (4576)Instruction limit reached!
% 2.46/1.58 % (4576)------------------------------
% 2.46/1.58 % (4576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.58 % (4576)Termination reason: Unknown
% 2.46/1.58 % (4576)Termination phase: Property scanning
% 2.46/1.58
% 2.46/1.58 % (4576)Memory used [KB]: 1535
% 2.46/1.58 % (4576)Time elapsed: 0.015 s
% 2.46/1.58 % (4576)Instructions burned: 29 (million)
% 2.46/1.58 % (4576)------------------------------
% 2.46/1.58 % (4576)------------------------------
% 2.46/1.58 % (4582)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_4475 for (2999ds/37Mi)
% 2.46/1.58 % (4581)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/3Mi)
% 2.46/1.58 % (4583)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_4475 for (2999ds/15Mi)
% 2.46/1.58 % (4581)Instruction limit reached!
% 2.46/1.58 % (4581)------------------------------
% 2.46/1.58 % (4581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.58 % (4581)Termination reason: Unknown
% 2.46/1.58 % (4581)Termination phase: shuffling
% 2.46/1.58
% 2.46/1.58 % (4581)Memory used [KB]: 1151
% 2.46/1.58 % (4581)Time elapsed: 0.003 s
% 2.46/1.58 % (4581)Instructions burned: 3 (million)
% 2.46/1.58 % (4581)------------------------------
% 2.46/1.58 % (4581)------------------------------
% 2.46/1.59 % (4583)Instruction limit reached!
% 2.46/1.59 % (4583)------------------------------
% 2.46/1.59 % (4583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (4583)Termination reason: Unknown
% 2.46/1.59 % (4583)Termination phase: Naming
% 2.46/1.59
% 2.46/1.59 % (4583)Memory used [KB]: 1535
% 2.46/1.59 % (4583)Time elapsed: 0.009 s
% 2.46/1.59 % (4584)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_4475 for (2999ds/3Mi)
% 2.46/1.59 % (4583)Instructions burned: 15 (million)
% 2.46/1.59 % (4583)------------------------------
% 2.46/1.59 % (4583)------------------------------
% 2.46/1.59 % (4584)Instruction limit reached!
% 2.46/1.59 % (4584)------------------------------
% 2.46/1.59 % (4584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (4584)Termination reason: Unknown
% 2.46/1.59 % (4584)Termination phase: shuffling
% 2.46/1.59
% 2.46/1.59 % (4584)Memory used [KB]: 1151
% 2.46/1.59 % (4584)Time elapsed: 0.003 s
% 2.46/1.59 % (4584)Instructions burned: 3 (million)
% 2.46/1.59 % (4584)------------------------------
% 2.46/1.59 % (4584)------------------------------
% 2.46/1.59 % (4585)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_4475 for (2999ds/1041Mi)
% 2.52/1.60 % (4582)Instruction limit reached!
% 2.52/1.60 % (4582)------------------------------
% 2.52/1.60 % (4582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (4582)Termination reason: Unknown
% 2.52/1.60 % (4582)Termination phase: Function definition elimination
% 2.52/1.60
% 2.52/1.60 % (4582)Memory used [KB]: 1535
% 2.52/1.60 % (4582)Time elapsed: 0.018 s
% 2.52/1.60 % (4582)Instructions burned: 38 (million)
% 2.52/1.60 % (4582)------------------------------
% 2.52/1.60 % (4582)------------------------------
% 2.52/1.60 % (4586)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/7Mi)
% 2.52/1.60 % (4586)Instruction limit reached!
% 2.52/1.60 % (4586)------------------------------
% 2.52/1.60 % (4586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (4586)Termination reason: Unknown
% 2.52/1.60 % (4586)Termination phase: shuffling
% 2.52/1.60
% 2.52/1.60 % (4586)Memory used [KB]: 1279
% 2.52/1.60 % (4586)Time elapsed: 0.005 s
% 2.52/1.60 % (4586)Instructions burned: 8 (million)
% 2.52/1.60 % (4586)------------------------------
% 2.52/1.60 % (4586)------------------------------
% 2.52/1.61 % (4587)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/16Mi)
% 2.52/1.61 % (4588)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_4475 for (2999ds/3Mi)
% 2.52/1.61 % (4588)Instruction limit reached!
% 2.52/1.61 % (4588)------------------------------
% 2.52/1.61 % (4588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.61 % (4588)Termination reason: Unknown
% 2.52/1.61 % (4588)Termination phase: shuffling
% 2.52/1.61
% 2.52/1.61 % (4588)Memory used [KB]: 1151
% 2.52/1.61 % (4588)Time elapsed: 0.003 s
% 2.52/1.61 % (4588)Instructions burned: 3 (million)
% 2.52/1.61 % (4588)------------------------------
% 2.52/1.61 % (4588)------------------------------
% 2.52/1.61 % (4587)Instruction limit reached!
% 2.52/1.61 % (4587)------------------------------
% 2.52/1.61 % (4587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.61 % (4587)Termination reason: Unknown
% 2.52/1.61 % (4587)Termination phase: Property scanning
% 2.52/1.61
% 2.52/1.61 % (4587)Memory used [KB]: 1407
% 2.52/1.61 % (4587)Time elapsed: 0.010 s
% 2.52/1.61 % (4587)Instructions burned: 18 (million)
% 2.52/1.61 % (4587)------------------------------
% 2.52/1.61 % (4587)------------------------------
% 2.52/1.62 % (4589)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_4475 for (2999ds/3Mi)
% 2.52/1.62 % (4589)Instruction limit reached!
% 2.52/1.62 % (4589)------------------------------
% 2.52/1.62 % (4589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (4589)Termination reason: Unknown
% 2.52/1.62 % (4589)Termination phase: shuffling
% 2.52/1.62
% 2.52/1.62 % (4589)Memory used [KB]: 1151
% 2.52/1.62 % (4589)Time elapsed: 0.003 s
% 2.52/1.62 % (4589)Instructions burned: 3 (million)
% 2.52/1.62 % (4589)------------------------------
% 2.52/1.62 % (4589)------------------------------
% 2.52/1.62 % (4590)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/7Mi)
% 2.52/1.62 % (4590)Instruction limit reached!
% 2.52/1.62 % (4590)------------------------------
% 2.52/1.62 % (4590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (4590)Termination reason: Unknown
% 2.52/1.62 % (4590)Termination phase: shuffling
% 2.52/1.62
% 2.52/1.62 % (4590)Memory used [KB]: 1279
% 2.52/1.62 % (4590)Time elapsed: 0.005 s
% 2.52/1.62 % (4590)Instructions burned: 8 (million)
% 2.52/1.62 % (4590)------------------------------
% 2.52/1.62 % (4590)------------------------------
% 2.52/1.63 % (4591)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/3Mi)
% 2.52/1.63 % (4591)Instruction limit reached!
% 2.52/1.63 % (4591)------------------------------
% 2.52/1.63 % (4591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.63 % (4591)Termination reason: Unknown
% 2.52/1.63 % (4591)Termination phase: shuffling
% 2.52/1.63
% 2.52/1.63 % (4591)Memory used [KB]: 1151
% 2.52/1.63 % (4591)Time elapsed: 0.003 s
% 2.52/1.63 % (4591)Instructions burned: 4 (million)
% 2.52/1.63 % (4591)------------------------------
% 2.52/1.63 % (4591)------------------------------
% 2.52/1.63 % (4592)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/4Mi)
% 2.52/1.63 % (4593)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/18Mi)
% 2.52/1.63 % (4592)Instruction limit reached!
% 2.52/1.63 % (4592)------------------------------
% 2.52/1.63 % (4592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.63 % (4592)Termination reason: Unknown
% 2.52/1.63 % (4592)Termination phase: shuffling
% 2.52/1.63
% 2.52/1.63 % (4592)Memory used [KB]: 1279
% 2.52/1.63 % (4592)Time elapsed: 0.004 s
% 2.52/1.63 % (4592)Instructions burned: 5 (million)
% 2.52/1.63 % (4592)------------------------------
% 2.52/1.63 % (4592)------------------------------
% 2.52/1.64 % (4594)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/710Mi)
% 2.52/1.64 % (4593)Instruction limit reached!
% 2.52/1.64 % (4593)------------------------------
% 2.52/1.64 % (4593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.64 % (4593)Termination reason: Unknown
% 2.52/1.64 % (4593)Termination phase: Property scanning
% 2.52/1.64
% 2.52/1.64 % (4593)Memory used [KB]: 1407
% 2.52/1.64 % (4593)Time elapsed: 0.010 s
% 2.52/1.64 % (4593)Instructions burned: 19 (million)
% 2.52/1.64 % (4593)------------------------------
% 2.52/1.64 % (4593)------------------------------
% 2.52/1.64 % (4595)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/6Mi)
% 2.52/1.65 % (4595)Instruction limit reached!
% 2.52/1.65 % (4595)------------------------------
% 2.52/1.65 % (4595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.65 % (4595)Termination reason: Unknown
% 2.52/1.65 % (4595)Termination phase: shuffling
% 2.52/1.65
% 2.52/1.65 % (4595)Memory used [KB]: 1279
% 2.52/1.65 % (4595)Time elapsed: 0.004 s
% 2.52/1.65 % (4595)Instructions burned: 6 (million)
% 2.52/1.65 % (4595)------------------------------
% 2.52/1.65 % (4595)------------------------------
% 2.52/1.65 % (4596)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_4475 for (2999ds/902Mi)
% 2.52/1.65 % (4574)Instruction limit reached!
% 2.52/1.65 % (4574)------------------------------
% 2.52/1.65 % (4574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.65 % (4574)Termination reason: Unknown
% 2.52/1.65 % (4574)Termination phase: Saturation
% 2.52/1.65
% 2.52/1.65 % (4574)Memory used [KB]: 6908
% 2.52/1.65 % (4574)Time elapsed: 0.090 s
% 2.52/1.65 % (4574)Instructions burned: 184 (million)
% 2.52/1.65 % (4574)------------------------------
% 2.52/1.65 % (4574)------------------------------
% 2.52/1.66 % (4597)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_4475 for (2999ds/21Mi)
% 2.52/1.66 % (4598)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4475 for (2999ds/5Mi)
% 2.52/1.66 % (4598)Instruction limit reached!
% 2.52/1.66 % (4598)------------------------------
% 2.52/1.66 % (4598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.66 % (4598)Termination reason: Unknown
% 2.52/1.66 % (4598)Termination phase: shuffling
% 2.52/1.66
% 2.52/1.66 % (4598)Memory used [KB]: 1279
% 2.52/1.66 % (4598)Time elapsed: 0.004 s
% 2.52/1.66 % (4598)Instructions burned: 6 (million)
% 2.52/1.66 % (4598)------------------------------
% 2.52/1.66 % (4598)------------------------------
% 2.52/1.67 % (4597)Instruction limit reached!
% 2.52/1.67 % (4597)------------------------------
% 2.52/1.67 % (4597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.67 % (4597)Termination reason: Unknown
% 2.52/1.67 % (4597)Termination phase: Property scanning
% 2.52/1.67
% 2.52/1.67 % (4597)Memory used [KB]: 1407
% 2.52/1.67 % (4597)Time elapsed: 0.011 s
% 2.52/1.67 % (4597)Instructions burned: 21 (million)
% 2.52/1.67 % (4597)------------------------------
% 2.52/1.67 % (4597)------------------------------
% 2.52/1.67 % (4600)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_4475 for (2998ds/6Mi)
% 2.52/1.67 % (4600)Instruction limit reached!
% 2.52/1.67 % (4600)------------------------------
% 2.52/1.67 % (4600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.67 % (4600)Termination reason: Unknown
% 2.52/1.67 % (4600)Termination phase: shuffling
% 2.52/1.67
% 2.52/1.67 % (4600)Memory used [KB]: 1279
% 2.52/1.67 % (4600)Time elapsed: 0.005 s
% 2.52/1.67 % (4600)Instructions burned: 8 (million)
% 2.52/1.67 % (4600)------------------------------
% 2.52/1.67 % (4600)------------------------------
% 2.52/1.68 % (4601)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4475 for (2998ds/377Mi)
% 2.52/1.68 % (4602)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_4475 for (2998ds/779Mi)
% 2.52/1.69 % (4603)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_4475 for (2998ds/19Mi)
% 2.52/1.70 % (4603)Instruction limit reached!
% 2.52/1.70 % (4603)------------------------------
% 2.52/1.70 % (4603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.70 % (4603)Termination reason: Unknown
% 2.52/1.70 % (4603)Termination phase: Property scanning
% 2.52/1.70
% 2.52/1.70 % (4603)Memory used [KB]: 1407
% 2.52/1.70 % (4603)Time elapsed: 0.010 s
% 2.52/1.70 % (4603)Instructions burned: 19 (million)
% 2.52/1.70 % (4603)------------------------------
% 2.52/1.70 % (4603)------------------------------
% 2.52/1.70 % (4579)Instruction limit reached!
% 2.52/1.70 % (4579)------------------------------
% 2.52/1.70 % (4579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.70 % (4579)Termination reason: Unknown
% 2.52/1.70 % (4579)Termination phase: Saturation
% 2.52/1.70
% 2.52/1.70 % (4579)Memory used [KB]: 7675
% 2.52/1.70 % (4579)Time elapsed: 0.140 s
% 2.52/1.70 % (4579)Instructions burned: 275 (million)
% 2.52/1.70 % (4579)------------------------------
% 2.52/1.70 % (4579)------------------------------
% 2.52/1.71 % (4604)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4475 for (2998ds/879Mi)
% 2.52/1.72 % (4605)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4475 for (2998ds/17Mi)
% 2.52/1.73 % (4605)Instruction limit reached!
% 2.52/1.73 % (4605)------------------------------
% 2.52/1.73 % (4605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.73 % (4605)Termination reason: Unknown
% 2.52/1.73 % (4605)Termination phase: Property scanning
% 2.52/1.73
% 2.52/1.73 % (4605)Memory used [KB]: 1407
% 2.52/1.73 % (4605)Time elapsed: 0.010 s
% 2.52/1.73 % (4605)Instructions burned: 18 (million)
% 2.52/1.73 % (4605)------------------------------
% 2.52/1.73 % (4605)------------------------------
% 2.52/1.74 % (4606)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4475 for (2998ds/3Mi)
% 2.52/1.75 % (4606)Instruction limit reached!
% 2.52/1.75 % (4606)------------------------------
% 2.52/1.75 % (4606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.75 % (4606)Termination reason: Unknown
% 2.52/1.75 % (4606)Termination phase: shuffling
% 2.52/1.75
% 2.52/1.75 % (4606)Memory used [KB]: 1151
% 2.52/1.75 % (4606)Time elapsed: 0.003 s
% 2.52/1.75 % (4606)Instructions burned: 3 (million)
% 2.52/1.75 % (4606)------------------------------
% 2.52/1.75 % (4606)------------------------------
% 2.52/1.76 % (4607)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4475 for (2998ds/30Mi)
% 2.52/1.77 % (4607)Instruction limit reached!
% 2.52/1.77 % (4607)------------------------------
% 2.52/1.77 % (4607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.77 % (4607)Termination reason: Unknown
% 2.52/1.77 % (4607)Termination phase: Property scanning
% 2.52/1.77
% 2.52/1.77 % (4607)Memory used [KB]: 1535
% 2.52/1.77 % (4607)Time elapsed: 0.015 s
% 2.52/1.77 % (4607)Instructions burned: 30 (million)
% 2.52/1.77 % (4607)------------------------------
% 2.52/1.77 % (4607)------------------------------
% 2.52/1.79 % (4608)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4475 for (2997ds/127Mi)
% 2.52/1.85 % (4608)Instruction limit reached!
% 2.52/1.85 % (4608)------------------------------
% 2.52/1.85 % (4608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.85 % (4608)Termination reason: Unknown
% 2.52/1.85 % (4608)Termination phase: Saturation
% 2.52/1.85
% 2.52/1.85 % (4608)Memory used [KB]: 6780
% 2.52/1.85 % (4608)Time elapsed: 0.061 s
% 2.52/1.85 % (4608)Instructions burned: 127 (million)
% 2.52/1.85 % (4608)------------------------------
% 2.52/1.85 % (4608)------------------------------
% 2.52/1.86 % (4601)Instruction limit reached!
% 2.52/1.86 % (4601)------------------------------
% 2.52/1.86 % (4601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.86 % (4601)Termination reason: Unknown
% 2.52/1.86 % (4601)Termination phase: Saturation
% 2.52/1.86
% 2.52/1.86 % (4601)Memory used [KB]: 7164
% 2.52/1.86 % (4601)Time elapsed: 0.182 s
% 2.52/1.86 % (4601)Instructions burned: 378 (million)
% 2.52/1.86 % (4601)------------------------------
% 2.52/1.86 % (4601)------------------------------
% 2.52/1.87 % (4609)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4475 for (2996ds/100Mi)
% 2.52/1.88 % (4610)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_4475 for (2996ds/3Mi)
% 2.52/1.88 % (4610)Instruction limit reached!
% 2.52/1.88 % (4610)------------------------------
% 2.52/1.88 % (4610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.88 % (4610)Termination reason: Unknown
% 2.52/1.88 % (4610)Termination phase: shuffling
% 2.52/1.88
% 2.52/1.88 % (4610)Memory used [KB]: 1151
% 2.52/1.88 % (4610)Time elapsed: 0.003 s
% 2.52/1.88 % (4610)Instructions burned: 3 (million)
% 2.52/1.88 % (4610)------------------------------
% 2.52/1.88 % (4610)------------------------------
% 2.52/1.89 % (4611)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_4475 for (2996ds/20Mi)
% 2.52/1.90 % (4611)Instruction limit reached!
% 2.52/1.90 % (4611)------------------------------
% 2.52/1.90 % (4611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.90 % (4611)Termination reason: Unknown
% 2.52/1.90 % (4611)Termination phase: Preprocessing 2
% 2.52/1.90
% 2.52/1.90 % (4611)Memory used [KB]: 1407
% 2.52/1.90 % (4611)Time elapsed: 0.011 s
% 2.52/1.90 % (4611)Instructions burned: 20 (million)
% 2.52/1.90 % (4611)------------------------------
% 2.52/1.90 % (4611)------------------------------
% 2.52/1.91 % (4609)Instruction limit reached!
% 2.52/1.91 % (4609)------------------------------
% 2.52/1.91 % (4609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (4609)Termination reason: Unknown
% 2.52/1.91 % (4609)Termination phase: Saturation
% 2.52/1.91
% 2.52/1.91 % (4609)Memory used [KB]: 6396
% 2.52/1.91 % (4609)Time elapsed: 0.049 s
% 2.52/1.91 % (4609)Instructions burned: 100 (million)
% 2.52/1.91 % (4609)------------------------------
% 2.52/1.91 % (4609)------------------------------
% 2.52/1.92 % (4612)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_4475 for (2996ds/86Mi)
% 2.52/1.93 % (4613)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_4475 for (2996ds/107Mi)
% 2.52/1.96 % (4612)Instruction limit reached!
% 2.52/1.96 % (4612)------------------------------
% 2.52/1.96 % (4612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.96 % (4612)Termination reason: Unknown
% 2.52/1.96 % (4612)Termination phase: Saturation
% 2.52/1.96
% 2.52/1.96 % (4612)Memory used [KB]: 6396
% 2.52/1.96 % (4612)Time elapsed: 0.041 s
% 2.52/1.96 % (4612)Instructions burned: 87 (million)
% 2.52/1.96 % (4612)------------------------------
% 2.52/1.96 % (4612)------------------------------
% 2.52/1.97 % (4602)Instruction limit reached!
% 2.52/1.97 % (4602)------------------------------
% 2.52/1.97 % (4602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.97 % (4602)Termination reason: Unknown
% 2.52/1.97 % (4602)Termination phase: Saturation
% 2.52/1.97
% 2.52/1.97 % (4602)Memory used [KB]: 6652
% 2.52/1.97 % (4602)Time elapsed: 0.294 s
% 2.52/1.97 % (4602)Instructions burned: 779 (million)
% 2.52/1.97 % (4602)------------------------------
% 2.52/1.97 % (4602)------------------------------
% 2.52/1.98 % (4614)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_4475 for (2995ds/39Mi)
% 2.52/1.98 % (4613)Instruction limit reached!
% 2.52/1.98 % (4613)------------------------------
% 2.52/1.98 % (4613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.98 % (4613)Termination reason: Unknown
% 2.52/1.98 % (4613)Termination phase: Saturation
% 2.52/1.98
% 2.52/1.98 % (4613)Memory used [KB]: 6524
% 2.52/1.98 % (4613)Time elapsed: 0.050 s
% 2.52/1.98 % (4613)Instructions burned: 107 (million)
% 2.52/1.98 % (4613)------------------------------
% 2.52/1.98 % (4613)------------------------------
% 2.52/1.98 % (4585)Instruction limit reached!
% 2.52/1.98 % (4585)------------------------------
% 2.52/1.98 % (4585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.98 % (4585)Termination reason: Unknown
% 2.52/1.98 % (4585)Termination phase: Saturation
% 2.52/1.98
% 2.52/1.98 % (4585)Memory used [KB]: 7931
% 2.52/1.98 % (4585)Time elapsed: 0.392 s
% 2.52/1.98 % (4585)Instructions burned: 1041 (million)
% 2.52/1.98 % (4585)------------------------------
% 2.52/1.98 % (4585)------------------------------
% 2.52/1.99 % (4615)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_4475 for (2995ds/448Mi)
% 2.52/1.99 % (4614)Instruction limit reached!
% 2.52/1.99 % (4614)------------------------------
% 2.52/1.99 % (4614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.99 % (4614)Termination reason: Unknown
% 2.52/1.99 % (4614)Termination phase: Function definition elimination
% 2.52/1.99
% 2.52/1.99 % (4614)Memory used [KB]: 1535
% 2.52/1.99 % (4614)Time elapsed: 0.019 s
% 2.52/1.99 % (4614)Instructions burned: 39 (million)
% 2.52/1.99 % (4614)------------------------------
% 2.52/1.99 % (4614)------------------------------
% 2.52/2.00 % (4616)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_4475 for (2995ds/46Mi)
% 2.52/2.00 % (4594)Instruction limit reached!
% 2.52/2.00 % (4594)------------------------------
% 2.52/2.00 % (4594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/2.00 % (4594)Termination reason: Unknown
% 2.52/2.00 % (4594)Termination phase: Saturation
% 2.52/2.00
% 2.52/2.00 % (4594)Memory used [KB]: 8955
% 2.52/2.00 % (4594)Time elapsed: 0.362 s
% 2.52/2.00 % (4594)Instructions burned: 712 (million)
% 2.52/2.00 % (4594)------------------------------
% 2.52/2.00 % (4594)------------------------------
% 2.52/2.00 % (4617)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_4475 for (2995ds/98Mi)
% 2.52/2.01 % (4618)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_4475 for (2995ds/507Mi)
% 2.52/2.02 % (4616)Instruction limit reached!
% 2.52/2.02 % (4616)------------------------------
% 2.52/2.02 % (4616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/2.02 % (4616)Termination reason: Unknown
% 2.52/2.02 % (4616)Termination phase: Twee Goal Transformation
% 2.52/2.02
% 2.52/2.02 % (4616)Memory used [KB]: 1535
% 2.52/2.02 % (4616)Time elapsed: 0.022 s
% 2.52/2.02 % (4616)Instructions burned: 47 (million)
% 2.52/2.02 % (4616)------------------------------
% 2.52/2.02 % (4616)------------------------------
% 2.52/2.02 % (4619)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_4475 for (2995ds/149Mi)
% 5.74/2.03 % (4620)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_4475 for (2995ds/39Mi)
% 5.74/2.04 % (4617)Instruction limit reached!
% 5.74/2.04 % (4617)------------------------------
% 5.74/2.04 % (4617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.04 % (4617)Termination reason: Unknown
% 5.74/2.04 % (4617)Termination phase: Saturation
% 5.74/2.04
% 5.74/2.04 % (4617)Memory used [KB]: 1663
% 5.74/2.04 % (4617)Time elapsed: 0.043 s
% 5.74/2.04 % (4617)Instructions burned: 99 (million)
% 5.74/2.04 % (4617)------------------------------
% 5.74/2.04 % (4617)------------------------------
% 5.74/2.05 % (4620)Instruction limit reached!
% 5.74/2.05 % (4620)------------------------------
% 5.74/2.05 % (4620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.05 % (4620)Termination reason: Unknown
% 5.74/2.05 % (4620)Termination phase: Property scanning
% 5.74/2.05
% 5.74/2.05 % (4620)Memory used [KB]: 1535
% 5.74/2.05 % (4620)Time elapsed: 0.020 s
% 5.74/2.05 % (4620)Instructions burned: 40 (million)
% 5.74/2.05 % (4620)------------------------------
% 5.74/2.05 % (4620)------------------------------
% 5.74/2.06 % (4621)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_4475 for (2995ds/6Mi)
% 5.74/2.06 % (4621)Instruction limit reached!
% 5.74/2.06 % (4621)------------------------------
% 5.74/2.06 % (4621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.06 % (4621)Termination reason: Unknown
% 5.74/2.06 % (4621)Termination phase: shuffling
% 5.74/2.06
% 5.74/2.06 % (4621)Memory used [KB]: 1279
% 5.74/2.06 % (4621)Time elapsed: 0.005 s
% 5.74/2.06 % (4621)Instructions burned: 7 (million)
% 5.74/2.06 % (4621)------------------------------
% 5.74/2.06 % (4621)------------------------------
% 5.74/2.07 % (4622)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_4475 for (2994ds/1087Mi)
% 5.74/2.08 % (4623)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_4475 for (2994ds/47Mi)
% 5.74/2.09 % (4619)Instruction limit reached!
% 5.74/2.09 % (4619)------------------------------
% 5.74/2.09 % (4619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.09 % (4619)Termination reason: Unknown
% 5.74/2.09 % (4619)Termination phase: Saturation
% 5.74/2.09
% 5.74/2.09 % (4619)Memory used [KB]: 6652
% 5.74/2.09 % (4619)Time elapsed: 0.075 s
% 5.74/2.09 % (4619)Instructions burned: 150 (million)
% 5.74/2.09 % (4619)------------------------------
% 5.74/2.09 % (4619)------------------------------
% 5.74/2.10 % (4623)Instruction limit reached!
% 5.74/2.10 % (4623)------------------------------
% 5.74/2.10 % (4623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.10 % (4623)Termination reason: Unknown
% 5.74/2.10 % (4623)Termination phase: Property scanning
% 5.74/2.10
% 5.74/2.10 % (4623)Memory used [KB]: 1535
% 5.74/2.10 % (4623)Time elapsed: 0.022 s
% 5.74/2.10 % (4623)Instructions burned: 47 (million)
% 5.74/2.10 % (4623)------------------------------
% 5.74/2.10 % (4623)------------------------------
% 5.74/2.10 % (4596)Instruction limit reached!
% 5.74/2.10 % (4596)------------------------------
% 5.74/2.10 % (4596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.10 % (4596)Termination reason: Unknown
% 5.74/2.10 % (4596)Termination phase: Saturation
% 5.74/2.10
% 5.74/2.10 % (4596)Memory used [KB]: 9338
% 5.74/2.10 % (4596)Time elapsed: 0.454 s
% 5.74/2.10 % (4596)Instructions burned: 903 (million)
% 5.74/2.10 % (4596)------------------------------
% 5.74/2.10 % (4596)------------------------------
% 5.74/2.11 % (4624)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_4475 for (2994ds/44Mi)
% 5.74/2.11 % (4625)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_4475 for (2994ds/432Mi)
% 5.74/2.12 % (4626)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_4475 for (2994ds/62Mi)
% 5.74/2.12 % (4624)Instruction limit reached!
% 5.74/2.12 % (4624)------------------------------
% 5.74/2.12 % (4624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.12 % (4624)Termination reason: Unknown
% 5.74/2.12 % (4624)Termination phase: Function definition elimination
% 5.74/2.12
% 5.74/2.12 % (4624)Memory used [KB]: 1535
% 5.74/2.12 % (4624)Time elapsed: 0.021 s
% 5.74/2.12 % (4624)Instructions burned: 45 (million)
% 5.74/2.12 % (4624)------------------------------
% 5.74/2.12 % (4624)------------------------------
% 6.39/2.14 % (4627)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_4475 for (2994ds/31Mi)
% 6.39/2.15 % (4626)Instruction limit reached!
% 6.39/2.15 % (4626)------------------------------
% 6.39/2.15 % (4626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.15 % (4626)Termination reason: Unknown
% 6.39/2.15 % (4626)Termination phase: Saturation
% 6.39/2.15
% 6.39/2.15 % (4626)Memory used [KB]: 6140
% 6.39/2.15 % (4626)Time elapsed: 0.029 s
% 6.39/2.15 % (4626)Instructions burned: 64 (million)
% 6.39/2.15 % (4626)------------------------------
% 6.39/2.15 % (4626)------------------------------
% 6.39/2.15 % (4604)Instruction limit reached!
% 6.39/2.15 % (4604)------------------------------
% 6.39/2.15 % (4604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.15 % (4604)Termination reason: Unknown
% 6.39/2.15 % (4604)Termination phase: Saturation
% 6.39/2.15
% 6.39/2.15 % (4604)Memory used [KB]: 7931
% 6.39/2.15 % (4604)Time elapsed: 0.461 s
% 6.39/2.15 % (4604)Instructions burned: 879 (million)
% 6.39/2.15 % (4604)------------------------------
% 6.39/2.15 % (4604)------------------------------
% 6.39/2.16 % (4627)Instruction limit reached!
% 6.39/2.16 % (4627)------------------------------
% 6.39/2.16 % (4627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.16 % (4627)Termination reason: Unknown
% 6.39/2.16 % (4627)Termination phase: Property scanning
% 6.39/2.16
% 6.39/2.16 % (4627)Memory used [KB]: 1535
% 6.39/2.16 % (4627)Time elapsed: 0.016 s
% 6.39/2.16 % (4627)Instructions burned: 32 (million)
% 6.39/2.16 % (4627)------------------------------
% 6.39/2.16 % (4627)------------------------------
% 6.39/2.16 % (4615)Instruction limit reached!
% 6.39/2.16 % (4615)------------------------------
% 6.39/2.16 % (4615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.16 % (4615)Termination reason: Unknown
% 6.39/2.16 % (4615)Termination phase: Saturation
% 6.39/2.16
% 6.39/2.16 % (4615)Memory used [KB]: 6396
% 6.39/2.16 % (4615)Time elapsed: 0.167 s
% 6.39/2.16 % (4615)Instructions burned: 450 (million)
% 6.39/2.16 % (4615)------------------------------
% 6.39/2.16 % (4615)------------------------------
% 6.39/2.16 % (4628)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_4475 for (2994ds/96Mi)
% 6.39/2.17 % (4629)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_4475 for (2993ds/453Mi)
% 6.39/2.17 % (4630)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_4475 for (2993ds/71Mi)
% 6.39/2.17 % (4631)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_4475 for (2993ds/83Mi)
% 6.61/2.20 % (4630)Instruction limit reached!
% 6.61/2.20 % (4630)------------------------------
% 6.61/2.20 % (4630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.20 % (4630)Termination reason: Unknown
% 6.61/2.20 % (4630)Termination phase: Saturation
% 6.61/2.20
% 6.61/2.20 % (4630)Memory used [KB]: 6268
% 6.61/2.20 % (4630)Time elapsed: 0.034 s
% 6.61/2.20 % (4630)Instructions burned: 72 (million)
% 6.61/2.20 % (4630)------------------------------
% 6.61/2.20 % (4630)------------------------------
% 6.61/2.21 % (4628)Instruction limit reached!
% 6.61/2.21 % (4628)------------------------------
% 6.61/2.21 % (4628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.21 % (4628)Termination reason: Unknown
% 6.61/2.21 % (4628)Termination phase: Saturation
% 6.61/2.21
% 6.61/2.21 % (4628)Memory used [KB]: 6524
% 6.61/2.21 % (4628)Time elapsed: 0.046 s
% 6.61/2.21 % (4628)Instructions burned: 97 (million)
% 6.61/2.21 % (4628)------------------------------
% 6.61/2.21 % (4628)------------------------------
% 6.61/2.21 % (4631)Instruction limit reached!
% 6.61/2.21 % (4631)------------------------------
% 6.61/2.21 % (4631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.21 % (4631)Termination reason: Unknown
% 6.61/2.21 % (4631)Termination phase: Saturation
% 6.61/2.21
% 6.61/2.21 % (4631)Memory used [KB]: 6268
% 6.61/2.21 % (4631)Time elapsed: 0.039 s
% 6.61/2.21 % (4631)Instructions burned: 84 (million)
% 6.61/2.21 % (4631)------------------------------
% 6.61/2.21 % (4631)------------------------------
% 6.61/2.22 % (4632)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_4475 for (2993ds/11Mi)
% 6.61/2.22 % (4633)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_4475 for (2993ds/41Mi)
% 6.61/2.23 % (4632)Instruction limit reached!
% 6.61/2.23 % (4632)------------------------------
% 6.61/2.23 % (4632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.23 % (4632)Termination reason: Unknown
% 6.61/2.23 % (4632)Termination phase: shuffling
% 6.61/2.23
% 6.61/2.23 % (4632)Memory used [KB]: 1407
% 6.61/2.23 % (4632)Time elapsed: 0.007 s
% 6.61/2.23 % (4632)Instructions burned: 11 (million)
% 6.61/2.23 % (4632)------------------------------
% 6.61/2.23 % (4632)------------------------------
% 6.61/2.23 % (4634)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4475 for (2993ds/6Mi)
% 6.61/2.23 % (4634)Instruction limit reached!
% 6.61/2.23 % (4634)------------------------------
% 6.61/2.23 % (4634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.23 % (4634)Termination reason: Unknown
% 6.61/2.23 % (4634)Termination phase: shuffling
% 6.61/2.23
% 6.61/2.23 % (4634)Memory used [KB]: 1279
% 6.61/2.23 % (4634)Time elapsed: 0.005 s
% 6.61/2.23 % (4634)Instructions burned: 7 (million)
% 6.61/2.23 % (4634)------------------------------
% 6.61/2.23 % (4634)------------------------------
% 6.61/2.24 % (4635)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_4475 for (2993ds/150Mi)
% 6.61/2.24 % (4633)Instruction limit reached!
% 6.61/2.24 % (4633)------------------------------
% 6.61/2.24 % (4633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.24 % (4633)Termination reason: Unknown
% 6.61/2.24 % (4633)Termination phase: Property scanning
% 6.61/2.24
% 6.61/2.24 % (4633)Memory used [KB]: 1535
% 6.61/2.24 % (4633)Time elapsed: 0.020 s
% 6.61/2.24 % (4633)Instructions burned: 42 (million)
% 6.61/2.24 % (4633)------------------------------
% 6.61/2.24 % (4633)------------------------------
% 6.61/2.25 % (4636)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_4475 for (2993ds/343Mi)
% 6.61/2.26 % (4618)Instruction limit reached!
% 6.61/2.26 % (4618)------------------------------
% 6.61/2.26 % (4618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.26 % (4618)Termination reason: Unknown
% 6.61/2.26 % (4618)Termination phase: Saturation
% 6.61/2.26
% 6.61/2.26 % (4618)Memory used [KB]: 7036
% 6.61/2.26 % (4618)Time elapsed: 0.249 s
% 6.61/2.26 % (4618)Instructions burned: 509 (million)
% 6.61/2.26 % (4618)------------------------------
% 6.61/2.26 % (4618)------------------------------
% 6.61/2.26 % (4637)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_4475 for (2993ds/109Mi)
% 6.61/2.27 % (4638)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_4475 for (2992ds/253Mi)
% 6.61/2.29 % (4625)Instruction limit reached!
% 6.61/2.29 % (4625)------------------------------
% 6.61/2.29 % (4625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.29 % (4625)Termination reason: Unknown
% 6.61/2.29 % (4625)Termination phase: Saturation
% 6.61/2.29
% 6.61/2.29 % (4625)Memory used [KB]: 2430
% 6.61/2.29 % (4625)Time elapsed: 0.173 s
% 6.61/2.29 % (4625)Instructions burned: 433 (million)
% 6.61/2.29 % (4625)------------------------------
% 6.61/2.29 % (4625)------------------------------
% 7.11/2.30 % (4639)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_4475 for (2992ds/140Mi)
% 7.11/2.31 % (4637)Instruction limit reached!
% 7.11/2.31 % (4637)------------------------------
% 7.11/2.31 % (4637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.31 % (4637)Termination reason: Unknown
% 7.11/2.31 % (4637)Termination phase: Saturation
% 7.11/2.31
% 7.11/2.31 % (4637)Memory used [KB]: 6652
% 7.11/2.31 % (4637)Time elapsed: 0.051 s
% 7.11/2.31 % (4637)Instructions burned: 110 (million)
% 7.11/2.31 % (4637)------------------------------
% 7.11/2.31 % (4637)------------------------------
% 7.11/2.32 % (4635)Instruction limit reached!
% 7.11/2.32 % (4635)------------------------------
% 7.11/2.32 % (4635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.32 % (4635)Termination reason: Unknown
% 7.11/2.32 % (4635)Termination phase: Saturation
% 7.11/2.32
% 7.11/2.32 % (4635)Memory used [KB]: 7291
% 7.11/2.32 % (4635)Time elapsed: 0.076 s
% 7.11/2.32 % (4635)Instructions burned: 151 (million)
% 7.11/2.32 % (4635)------------------------------
% 7.11/2.32 % (4635)------------------------------
% 7.11/2.32 % (4640)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_4475 for (2992ds/614Mi)
% 7.11/2.33 % (4641)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_4475 for (2992ds/202Mi)
% 7.11/2.34 % (4629)Instruction limit reached!
% 7.11/2.34 % (4629)------------------------------
% 7.11/2.34 % (4629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.34 % (4629)Termination reason: Unknown
% 7.11/2.34 % (4629)Termination phase: Saturation
% 7.11/2.34
% 7.11/2.34 % (4629)Memory used [KB]: 6268
% 7.11/2.34 % (4629)Time elapsed: 0.173 s
% 7.11/2.34 % (4629)Instructions burned: 453 (million)
% 7.11/2.34 % (4629)------------------------------
% 7.11/2.34 % (4629)------------------------------
% 7.11/2.36 % (4642)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_4475 for (2992ds/339Mi)
% 7.11/2.36 % (4639)Refutation not found, incomplete strategy
% 7.11/2.36 % (4639)------------------------------
% 7.11/2.36 % (4639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.36 % (4639)Termination reason: Refutation not found, incomplete strategy
% 7.11/2.36
% 7.11/2.36
% 7.11/2.36 % (4639)Memory used [KB]: 6140
% 7.11/2.36 % (4639)Time elapsed: 0.077 s
% 7.11/2.36 % (4639)Instructions burned: 121 (million)
% 7.11/2.36 % (4639)------------------------------
% 7.11/2.36 % (4639)------------------------------
% 7.11/2.37 % (4643)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_4475 for (2991ds/283Mi)
% 7.53/2.40 % (4638)Instruction limit reached!
% 7.53/2.40 % (4638)------------------------------
% 7.53/2.40 % (4638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.53/2.40 % (4638)Termination reason: Unknown
% 7.53/2.40 % (4638)Termination phase: Saturation
% 7.53/2.40
% 7.53/2.40 % (4638)Memory used [KB]: 7803
% 7.53/2.40 % (4638)Time elapsed: 0.126 s
% 7.53/2.40 % (4638)Instructions burned: 253 (million)
% 7.53/2.40 % (4638)------------------------------
% 7.53/2.40 % (4638)------------------------------
% 7.53/2.41 % (4636)Instruction limit reached!
% 7.53/2.41 % (4636)------------------------------
% 7.53/2.41 % (4636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.53/2.41 % (4636)Termination reason: Unknown
% 7.53/2.41 % (4636)Termination phase: Saturation
% 7.53/2.41
% 7.53/2.41 % (4636)Memory used [KB]: 7164
% 7.53/2.41 % (4636)Time elapsed: 0.168 s
% 7.53/2.41 % (4636)Instructions burned: 343 (million)
% 7.53/2.41 % (4636)------------------------------
% 7.53/2.41 % (4636)------------------------------
% 7.53/2.41 % (4644)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_4475 for (2991ds/134Mi)
% 7.53/2.43 % (4645)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_4475 for (2991ds/298Mi)
% 7.53/2.44 % (4641)Instruction limit reached!
% 7.53/2.44 % (4641)------------------------------
% 7.53/2.44 % (4641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.53/2.44 % (4641)Termination reason: Unknown
% 7.53/2.44 % (4641)Termination phase: Saturation
% 7.53/2.44
% 7.53/2.44 % (4641)Memory used [KB]: 7547
% 7.53/2.44 % (4641)Time elapsed: 0.127 s
% 7.53/2.44 % (4641)Instructions burned: 202 (million)
% 7.53/2.44 % (4641)------------------------------
% 7.53/2.44 % (4641)------------------------------
% 7.53/2.45 % (4646)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_4475 for (2991ds/192Mi)
% 7.53/2.48 % (4644)Instruction limit reached!
% 7.53/2.48 % (4644)------------------------------
% 7.53/2.48 % (4644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.53/2.48 % (4644)Termination reason: Unknown
% 7.53/2.48 % (4644)Termination phase: Saturation
% 7.53/2.48
% 7.53/2.48 % (4644)Memory used [KB]: 6780
% 7.53/2.48 % (4644)Time elapsed: 0.088 s
% 7.53/2.48 % (4644)Instructions burned: 135 (million)
% 7.53/2.48 % (4644)------------------------------
% 7.53/2.48 % (4644)------------------------------
% 7.53/2.49 % (4643)Instruction limit reached!
% 7.53/2.49 % (4643)------------------------------
% 7.53/2.49 % (4643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.53/2.49 % (4643)Termination reason: Unknown
% 7.53/2.49 % (4643)Termination phase: Saturation
% 7.53/2.49
% 7.53/2.49 % (4643)Memory used [KB]: 8059
% 7.53/2.49 % (4643)Time elapsed: 0.114 s
% 7.53/2.49 % (4643)Instructions burned: 284 (million)
% 7.53/2.49 % (4643)------------------------------
% 7.53/2.49 % (4643)------------------------------
% 7.53/2.49 % (4647)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_4475 for (2990ds/258Mi)
% 8.18/2.50 % (4648)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_4475 for (2990ds/90Mi)
% 8.18/2.52 % (4642)Instruction limit reached!
% 8.18/2.52 % (4642)------------------------------
% 8.18/2.52 % (4642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.52 % (4642)Termination reason: Unknown
% 8.18/2.52 % (4642)Termination phase: Saturation
% 8.18/2.52
% 8.18/2.52 % (4642)Memory used [KB]: 7675
% 8.18/2.52 % (4642)Time elapsed: 0.164 s
% 8.18/2.52 % (4642)Instructions burned: 339 (million)
% 8.18/2.52 % (4642)------------------------------
% 8.18/2.52 % (4642)------------------------------
% 8.18/2.54 % (4649)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_4475 for (2990ds/231Mi)
% 8.18/2.54 % (4646)Instruction limit reached!
% 8.18/2.54 % (4646)------------------------------
% 8.18/2.54 % (4646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.54 % (4646)Termination reason: Unknown
% 8.18/2.54 % (4646)Termination phase: Saturation
% 8.18/2.54
% 8.18/2.54 % (4646)Memory used [KB]: 7036
% 8.18/2.54 % (4646)Time elapsed: 0.094 s
% 8.18/2.54 % (4646)Instructions burned: 193 (million)
% 8.18/2.54 % (4646)------------------------------
% 8.18/2.54 % (4646)------------------------------
% 8.18/2.55 % (4648)Instruction limit reached!
% 8.18/2.55 % (4648)------------------------------
% 8.18/2.55 % (4648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.55 % (4648)Termination reason: Unknown
% 8.18/2.55 % (4648)Termination phase: Saturation
% 8.18/2.55
% 8.18/2.55 % (4648)Memory used [KB]: 6524
% 8.18/2.55 % (4648)Time elapsed: 0.044 s
% 8.18/2.55 % (4648)Instructions burned: 91 (million)
% 8.18/2.55 % (4648)------------------------------
% 8.18/2.55 % (4648)------------------------------
% 8.18/2.55 % (4645)Instruction limit reached!
% 8.18/2.55 % (4645)------------------------------
% 8.18/2.55 % (4645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.55 % (4645)Termination reason: Unknown
% 8.18/2.55 % (4645)Termination phase: Saturation
% 8.18/2.55
% 8.18/2.55 % (4645)Memory used [KB]: 6396
% 8.18/2.55 % (4645)Time elapsed: 0.127 s
% 8.18/2.55 % (4645)Instructions burned: 299 (million)
% 8.18/2.55 % (4645)------------------------------
% 8.18/2.55 % (4645)------------------------------
% 8.18/2.56 % (4650)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_4475 for (2989ds/458Mi)
% 8.18/2.56 % (4651)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_4475 for (2989ds/31Mi)
% 8.18/2.57 % (4652)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_4475 for (2989ds/297Mi)
% 8.18/2.58 % (4651)Instruction limit reached!
% 8.18/2.58 % (4651)------------------------------
% 8.18/2.58 % (4651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.58 % (4651)Termination reason: Unknown
% 8.18/2.58 % (4651)Termination phase: Property scanning
% 8.18/2.58
% 8.18/2.58 % (4651)Memory used [KB]: 1535
% 8.18/2.58 % (4651)Time elapsed: 0.016 s
% 8.18/2.58 % (4651)Instructions burned: 32 (million)
% 8.18/2.58 % (4651)------------------------------
% 8.18/2.58 % (4651)------------------------------
% 8.18/2.59 % (4653)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_4475 for (2989ds/987Mi)
% 8.70/2.62 % (4647)Instruction limit reached!
% 8.70/2.62 % (4647)------------------------------
% 8.70/2.62 % (4647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.62 % (4647)Termination reason: Unknown
% 8.70/2.62 % (4647)Termination phase: Saturation
% 8.70/2.62
% 8.70/2.62 % (4647)Memory used [KB]: 6908
% 8.70/2.62 % (4647)Time elapsed: 0.127 s
% 8.70/2.62 % (4647)Instructions burned: 259 (million)
% 8.70/2.62 % (4647)------------------------------
% 8.70/2.62 % (4647)------------------------------
% 8.70/2.62 % (4622)Instruction limit reached!
% 8.70/2.62 % (4622)------------------------------
% 8.70/2.62 % (4622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.62 % (4622)Termination reason: Unknown
% 8.70/2.62 % (4622)Termination phase: Saturation
% 8.70/2.62
% 8.70/2.62 % (4622)Memory used [KB]: 10106
% 8.70/2.62 % (4622)Time elapsed: 0.555 s
% 8.70/2.62 % (4622)Instructions burned: 1088 (million)
% 8.70/2.62 % (4622)------------------------------
% 8.70/2.62 % (4622)------------------------------
% 8.70/2.63 % (4640)Instruction limit reached!
% 8.70/2.63 % (4640)------------------------------
% 8.70/2.63 % (4640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.63 % (4640)Termination reason: Unknown
% 8.70/2.63 % (4640)Termination phase: Saturation
% 8.70/2.63
% 8.70/2.63 % (4640)Memory used [KB]: 7931
% 8.70/2.63 % (4640)Time elapsed: 0.328 s
% 8.70/2.63 % (4640)Instructions burned: 615 (million)
% 8.70/2.63 % (4640)------------------------------
% 8.70/2.63 % (4640)------------------------------
% 8.70/2.64 % (4654)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_4475 for (2989ds/182Mi)
% 8.70/2.64 % (4655)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_4475 for (2989ds/182Mi)
% 8.70/2.65 % (4656)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_4475 for (2989ds/154Mi)
% 8.70/2.65 % (4649)Instruction limit reached!
% 8.70/2.65 % (4649)------------------------------
% 8.70/2.65 % (4649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.65 % (4649)Termination reason: Unknown
% 8.70/2.65 % (4649)Termination phase: Saturation
% 8.70/2.65
% 8.70/2.65 % (4649)Memory used [KB]: 9466
% 8.70/2.65 % (4649)Time elapsed: 0.115 s
% 8.70/2.65 % (4649)Instructions burned: 231 (million)
% 8.70/2.65 % (4649)------------------------------
% 8.70/2.65 % (4649)------------------------------
% 8.70/2.67 % (4657)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_4475 for (2988ds/79Mi)
% 8.70/2.69 % (4652)Instruction limit reached!
% 8.70/2.69 % (4652)------------------------------
% 8.70/2.69 % (4652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.69 % (4652)Termination reason: Unknown
% 8.70/2.69 % (4652)Termination phase: Saturation
% 8.70/2.69
% 8.70/2.69 % (4652)Memory used [KB]: 7291
% 8.70/2.69 % (4652)Time elapsed: 0.118 s
% 8.70/2.69 % (4652)Instructions burned: 298 (million)
% 8.70/2.69 % (4652)------------------------------
% 8.70/2.69 % (4652)------------------------------
% 10.00/2.70 % (4657)Instruction limit reached!
% 10.00/2.70 % (4657)------------------------------
% 10.00/2.70 % (4657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.70 % (4657)Termination reason: Unknown
% 10.00/2.70 % (4657)Termination phase: Saturation
% 10.00/2.70
% 10.00/2.70 % (4657)Memory used [KB]: 6396
% 10.00/2.70 % (4657)Time elapsed: 0.039 s
% 10.00/2.70 % (4657)Instructions burned: 80 (million)
% 10.00/2.70 % (4657)------------------------------
% 10.00/2.70 % (4657)------------------------------
% 10.00/2.70 % (4658)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_4475 for (2988ds/216Mi)
% 10.00/2.71 % (4656)Instruction limit reached!
% 10.00/2.71 % (4656)------------------------------
% 10.00/2.71 % (4656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.71 % (4656)Termination reason: Unknown
% 10.00/2.71 % (4656)Termination phase: Saturation
% 10.00/2.71
% 10.00/2.71 % (4656)Memory used [KB]: 6140
% 10.00/2.71 % (4656)Time elapsed: 0.063 s
% 10.00/2.71 % (4656)Instructions burned: 156 (million)
% 10.00/2.71 % (4656)------------------------------
% 10.00/2.71 % (4656)------------------------------
% 10.00/2.72 % (4659)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_4475 for (2988ds/114Mi)
% 10.00/2.72 % (4660)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_4475 for (2988ds/922Mi)
% 10.00/2.72 % (4654)Instruction limit reached!
% 10.00/2.72 % (4654)------------------------------
% 10.00/2.72 % (4654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.72 % (4654)Termination reason: Unknown
% 10.00/2.72 % (4654)Termination phase: Saturation
% 10.00/2.72
% 10.00/2.72 % (4654)Memory used [KB]: 6908
% 10.00/2.72 % (4654)Time elapsed: 0.089 s
% 10.00/2.72 % (4654)Instructions burned: 182 (million)
% 10.00/2.72 % (4654)------------------------------
% 10.00/2.72 % (4654)------------------------------
% 10.00/2.73 % (4655)Instruction limit reached!
% 10.00/2.73 % (4655)------------------------------
% 10.00/2.73 % (4655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.73 % (4655)Termination reason: Unknown
% 10.00/2.73 % (4655)Termination phase: Saturation
% 10.00/2.73
% 10.00/2.73 % (4655)Memory used [KB]: 8827
% 10.00/2.73 % (4655)Time elapsed: 0.095 s
% 10.00/2.73 % (4655)Instructions burned: 182 (million)
% 10.00/2.73 % (4655)------------------------------
% 10.00/2.73 % (4655)------------------------------
% 10.00/2.74 % (4661)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_4475 for (2988ds/182Mi)
% 10.00/2.75 % (4662)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_4475 for (2988ds/164Mi)
% 10.00/2.77 % (4659)Instruction limit reached!
% 10.00/2.77 % (4659)------------------------------
% 10.00/2.77 % (4659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.77 % (4659)Termination reason: Unknown
% 10.00/2.77 % (4659)Termination phase: Saturation
% 10.00/2.77
% 10.00/2.77 % (4659)Memory used [KB]: 6780
% 10.00/2.77 % (4659)Time elapsed: 0.054 s
% 10.00/2.77 % (4659)Instructions burned: 114 (million)
% 10.00/2.77 % (4659)------------------------------
% 10.00/2.77 % (4659)------------------------------
% 10.00/2.79 % (4663)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_4475 for (2987ds/50Mi)
% 10.00/2.79 % (4658)Instruction limit reached!
% 10.00/2.79 % (4658)------------------------------
% 10.00/2.79 % (4658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.79 % (4658)Termination reason: Unknown
% 10.00/2.79 % (4658)Termination phase: Saturation
% 10.00/2.79
% 10.00/2.79 % (4658)Memory used [KB]: 7036
% 10.00/2.79 % (4658)Time elapsed: 0.087 s
% 10.00/2.79 % (4658)Instructions burned: 216 (million)
% 10.00/2.79 % (4658)------------------------------
% 10.00/2.79 % (4658)------------------------------
% 10.00/2.79 % (4650)Instruction limit reached!
% 10.00/2.79 % (4650)------------------------------
% 10.00/2.79 % (4650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.79 % (4650)Termination reason: Unknown
% 10.00/2.79 % (4650)Termination phase: Saturation
% 10.00/2.79
% 10.00/2.79 % (4650)Memory used [KB]: 7419
% 10.00/2.79 % (4650)Time elapsed: 0.230 s
% 10.00/2.79 % (4650)Instructions burned: 459 (million)
% 10.00/2.79 % (4650)------------------------------
% 10.00/2.79 % (4650)------------------------------
% 10.75/2.81 % (4664)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_4475 for (2987ds/368Mi)
% 10.75/2.81 % (4665)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_4475 for (2987ds/1021Mi)
% 10.75/2.81 % (4663)Instruction limit reached!
% 10.75/2.81 % (4663)------------------------------
% 10.75/2.81 % (4663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.75/2.81 % (4663)Termination reason: Unknown
% 10.75/2.81 % (4663)Termination phase: Saturation
% 10.75/2.81
% 10.75/2.81 % (4663)Memory used [KB]: 10618
% 10.75/2.81 % (4663)Time elapsed: 0.024 s
% 10.75/2.81 % (4663)Instructions burned: 50 (million)
% 10.75/2.81 % (4663)------------------------------
% 10.75/2.81 % (4663)------------------------------
% 10.75/2.81 % (4661)Instruction limit reached!
% 10.75/2.81 % (4661)------------------------------
% 10.75/2.81 % (4661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.75/2.81 % (4661)Termination reason: Unknown
% 10.75/2.81 % (4661)Termination phase: Saturation
% 10.75/2.81
% 10.75/2.81 % (4661)Memory used [KB]: 6268
% 10.75/2.81 % (4661)Time elapsed: 0.074 s
% 10.75/2.81 % (4661)Instructions burned: 182 (million)
% 10.75/2.81 % (4661)------------------------------
% 10.75/2.81 % (4661)------------------------------
% 10.75/2.82 % (4662)Instruction limit reached!
% 10.75/2.82 % (4662)------------------------------
% 10.75/2.82 % (4662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.75/2.82 % (4662)Termination reason: Unknown
% 10.75/2.82 % (4662)Termination phase: Saturation
% 10.75/2.82
% 10.75/2.82 % (4662)Memory used [KB]: 2046
% 10.75/2.82 % (4662)Time elapsed: 0.078 s
% 10.75/2.82 % (4662)Instructions burned: 164 (million)
% 10.75/2.82 % (4662)------------------------------
% 10.75/2.82 % (4662)------------------------------
% 10.75/2.83 % (4666)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_4475 for (2987ds/267Mi)
% 10.75/2.83 % (4667)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_4475 for (2987ds/204Mi)
% 10.75/2.84 % (4668)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_4475 for (2987ds/26Mi)
% 10.75/2.85 % (4668)Instruction limit reached!
% 10.75/2.85 % (4668)------------------------------
% 10.75/2.85 % (4668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.75/2.85 % (4668)Termination reason: Unknown
% 10.75/2.85 % (4668)Termination phase: Property scanning
% 10.75/2.85
% 10.75/2.85 % (4668)Memory used [KB]: 1535
% 10.75/2.85 % (4668)Time elapsed: 0.014 s
% 10.75/2.85 % (4668)Instructions burned: 27 (million)
% 10.75/2.85 % (4668)------------------------------
% 10.75/2.85 % (4668)------------------------------
% 10.75/2.87 % (4669)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_4475 for (2986ds/53Mi)
% 10.75/2.89 % (4669)Instruction limit reached!
% 10.75/2.89 % (4669)------------------------------
% 10.75/2.89 % (4669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.75/2.89 % (4669)Termination reason: Unknown
% 10.75/2.89 % (4669)Termination phase: Saturation
% 10.75/2.89
% 10.75/2.89 % (4669)Memory used [KB]: 6140
% 10.75/2.89 % (4669)Time elapsed: 0.025 s
% 10.75/2.89 % (4669)Instructions burned: 53 (million)
% 10.75/2.89 % (4669)------------------------------
% 10.75/2.89 % (4669)------------------------------
% 11.04/2.91 % (4670)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_4475 for (2986ds/4436Mi)
% 11.04/2.93 % (4667)Instruction limit reached!
% 11.04/2.93 % (4667)------------------------------
% 11.04/2.93 % (4667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.93 % (4667)Termination reason: Unknown
% 11.04/2.93 % (4667)Termination phase: Saturation
% 11.04/2.93
% 11.04/2.93 % (4667)Memory used [KB]: 6908
% 11.04/2.93 % (4667)Time elapsed: 0.099 s
% 11.04/2.93 % (4667)Instructions burned: 205 (million)
% 11.04/2.93 % (4667)------------------------------
% 11.04/2.93 % (4667)------------------------------
% 11.04/2.93 % (4666)Instruction limit reached!
% 11.04/2.93 % (4666)------------------------------
% 11.04/2.93 % (4666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.93 % (4666)Termination reason: Unknown
% 11.04/2.93 % (4666)Termination phase: Saturation
% 11.04/2.93
% 11.04/2.93 % (4666)Memory used [KB]: 8059
% 11.04/2.93 % (4666)Time elapsed: 0.108 s
% 11.04/2.93 % (4666)Instructions burned: 267 (million)
% 11.04/2.93 % (4666)------------------------------
% 11.04/2.93 % (4666)------------------------------
% 11.04/2.94 % (4671)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_4475 for (2986ds/1539Mi)
% 11.04/2.95 % (4672)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_4475 for (2986ds/408Mi)
% 11.04/2.96 % (4653)Instruction limit reached!
% 11.04/2.96 % (4653)------------------------------
% 11.04/2.96 % (4653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.96 % (4653)Termination reason: Unknown
% 11.04/2.96 % (4653)Termination phase: Saturation
% 11.04/2.96
% 11.04/2.96 % (4653)Memory used [KB]: 7803
% 11.04/2.96 % (4653)Time elapsed: 0.371 s
% 11.04/2.96 % (4653)Instructions burned: 988 (million)
% 11.04/2.96 % (4653)------------------------------
% 11.04/2.96 % (4653)------------------------------
% 11.04/2.98 % (4673)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_4475 for (2985ds/5205Mi)
% 11.04/2.99 % (4664)Instruction limit reached!
% 11.04/2.99 % (4664)------------------------------
% 11.04/2.99 % (4664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.99 % (4664)Termination reason: Unknown
% 11.04/2.99 % (4664)Termination phase: Saturation
% 11.04/2.99
% 11.04/2.99 % (4664)Memory used [KB]: 7291
% 11.04/2.99 % (4664)Time elapsed: 0.184 s
% 11.04/2.99 % (4664)Instructions burned: 368 (million)
% 11.04/2.99 % (4664)------------------------------
% 11.04/2.99 % (4664)------------------------------
% 11.04/3.00 % (4674)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_4475 for (2985ds/1913Mi)
% 13.48/3.16 % (4672)Instruction limit reached!
% 13.48/3.16 % (4672)------------------------------
% 13.48/3.16 % (4672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.16 % (4672)Termination reason: Unknown
% 13.48/3.16 % (4672)Termination phase: Saturation
% 13.48/3.16
% 13.48/3.16 % (4672)Memory used [KB]: 8955
% 13.48/3.16 % (4672)Time elapsed: 0.213 s
% 13.48/3.16 % (4672)Instructions burned: 409 (million)
% 13.48/3.16 % (4672)------------------------------
% 13.48/3.16 % (4672)------------------------------
% 13.48/3.18 % (4675)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_4475 for (2983ds/4350Mi)
% 13.48/3.19 % (4660)Instruction limit reached!
% 13.48/3.19 % (4660)------------------------------
% 13.48/3.19 % (4660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.19 % (4660)Termination reason: Unknown
% 13.48/3.19 % (4660)Termination phase: Saturation
% 13.48/3.19
% 13.48/3.19 % (4660)Memory used [KB]: 8955
% 13.48/3.19 % (4660)Time elapsed: 0.466 s
% 13.48/3.19 % (4660)Instructions burned: 923 (million)
% 13.48/3.19 % (4660)------------------------------
% 13.48/3.19 % (4660)------------------------------
% 13.95/3.20 % (4676)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_4475 for (2983ds/68Mi)
% 13.95/3.23 % (4676)Instruction limit reached!
% 13.95/3.23 % (4676)------------------------------
% 13.95/3.23 % (4676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.23 % (4676)Termination reason: Unknown
% 13.95/3.23 % (4676)Termination phase: Saturation
% 13.95/3.23
% 13.95/3.23 % (4676)Memory used [KB]: 6268
% 13.95/3.23 % (4676)Time elapsed: 0.032 s
% 13.95/3.23 % (4676)Instructions burned: 68 (million)
% 13.95/3.23 % (4676)------------------------------
% 13.95/3.23 % (4676)------------------------------
% 13.95/3.25 % (4677)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_4475 for (2983ds/358Mi)
% 14.50/3.32 % (4665)Instruction limit reached!
% 14.50/3.32 % (4665)------------------------------
% 14.50/3.32 % (4665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.32 % (4665)Termination reason: Unknown
% 14.50/3.32 % (4665)Termination phase: Saturation
% 14.50/3.32
% 14.50/3.32 % (4665)Memory used [KB]: 9466
% 14.50/3.32 % (4665)Time elapsed: 0.518 s
% 14.50/3.32 % (4665)Instructions burned: 1021 (million)
% 14.50/3.32 % (4665)------------------------------
% 14.50/3.32 % (4665)------------------------------
% 14.50/3.34 % (4678)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_4475 for (2982ds/31Mi)
% 14.50/3.35 % (4678)Instruction limit reached!
% 14.50/3.35 % (4678)------------------------------
% 14.50/3.35 % (4678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.35 % (4678)Termination reason: Unknown
% 14.50/3.35 % (4678)Termination phase: Property scanning
% 14.50/3.35
% 14.50/3.35 % (4678)Memory used [KB]: 1535
% 14.50/3.35 % (4678)Time elapsed: 0.016 s
% 14.50/3.35 % (4678)Instructions burned: 31 (million)
% 14.50/3.35 % (4678)------------------------------
% 14.50/3.35 % (4678)------------------------------
% 14.50/3.37 % (4679)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_4475 for (2981ds/279Mi)
% 14.98/3.43 % (4677)Instruction limit reached!
% 14.98/3.43 % (4677)------------------------------
% 14.98/3.43 % (4677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.43 % (4677)Termination reason: Unknown
% 14.98/3.43 % (4677)Termination phase: Saturation
% 14.98/3.43
% 14.98/3.43 % (4677)Memory used [KB]: 7036
% 14.98/3.43 % (4677)Time elapsed: 0.199 s
% 14.98/3.43 % (4677)Instructions burned: 358 (million)
% 14.98/3.43 % (4677)------------------------------
% 14.98/3.43 % (4677)------------------------------
% 14.98/3.44 % (4680)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_4475 for (2981ds/258Mi)
% 14.98/3.48 % (4679)Instruction limit reached!
% 14.98/3.48 % (4679)------------------------------
% 14.98/3.48 % (4679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.98/3.48 % (4679)Termination reason: Unknown
% 14.98/3.48 % (4679)Termination phase: Saturation
% 14.98/3.48
% 14.98/3.48 % (4679)Memory used [KB]: 6396
% 14.98/3.48 % (4679)Time elapsed: 0.109 s
% 14.98/3.48 % (4679)Instructions burned: 279 (million)
% 14.98/3.48 % (4679)------------------------------
% 14.98/3.48 % (4679)------------------------------
% 14.98/3.49 % (4681)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_4475 for (2980ds/26Mi)
% 15.69/3.51 % (4681)Instruction limit reached!
% 15.69/3.51 % (4681)------------------------------
% 15.69/3.51 % (4681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.69/3.51 % (4681)Termination reason: Unknown
% 15.69/3.51 % (4681)Termination phase: Property scanning
% 15.69/3.51
% 15.69/3.51 % (4681)Memory used [KB]: 1535
% 15.69/3.51 % (4681)Time elapsed: 0.014 s
% 15.69/3.51 % (4681)Instructions burned: 27 (million)
% 15.69/3.51 % (4681)------------------------------
% 15.69/3.51 % (4681)------------------------------
% 15.69/3.52 % (4682)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_4475 for (2980ds/995Mi)
% 15.69/3.56 % (4680)Instruction limit reached!
% 15.69/3.56 % (4680)------------------------------
% 15.69/3.56 % (4680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.69/3.56 % (4680)Termination reason: Unknown
% 15.69/3.56 % (4680)Termination phase: Saturation
% 15.69/3.56
% 15.69/3.56 % (4680)Memory used [KB]: 7547
% 15.69/3.56 % (4680)Time elapsed: 0.121 s
% 15.69/3.56 % (4680)Instructions burned: 258 (million)
% 15.69/3.56 % (4680)------------------------------
% 15.69/3.56 % (4680)------------------------------
% 15.69/3.58 % (4683)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_4475 for (2979ds/373Mi)
% 16.66/3.70 % (4671)Instruction limit reached!
% 16.66/3.70 % (4671)------------------------------
% 16.66/3.70 % (4671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.70 % (4671)Termination reason: Unknown
% 16.66/3.70 % (4671)Termination phase: Saturation
% 16.66/3.70
% 16.66/3.70 % (4671)Memory used [KB]: 8571
% 16.66/3.70 % (4671)Time elapsed: 0.760 s
% 16.66/3.70 % (4671)Instructions burned: 1539 (million)
% 16.66/3.70 % (4671)------------------------------
% 16.66/3.70 % (4671)------------------------------
% 16.66/3.72 % (4684)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_4475 for (2978ds/253Mi)
% 16.66/3.76 % (4683)Instruction limit reached!
% 16.66/3.76 % (4683)------------------------------
% 16.66/3.76 % (4683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.76 % (4683)Termination reason: Unknown
% 16.66/3.76 % (4683)Termination phase: Saturation
% 16.66/3.76
% 16.66/3.76 % (4683)Memory used [KB]: 7164
% 16.66/3.76 % (4683)Time elapsed: 0.186 s
% 16.66/3.76 % (4683)Instructions burned: 374 (million)
% 16.66/3.76 % (4683)------------------------------
% 16.66/3.76 % (4683)------------------------------
% 16.66/3.78 % (4685)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_4475 for (2977ds/832Mi)
% 17.16/3.82 % (4684)Instruction limit reached!
% 17.16/3.82 % (4684)------------------------------
% 17.16/3.82 % (4684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.82 % (4684)Termination reason: Unknown
% 17.16/3.82 % (4684)Termination phase: Saturation
% 17.16/3.82
% 17.16/3.82 % (4684)Memory used [KB]: 6268
% 17.16/3.82 % (4684)Time elapsed: 0.101 s
% 17.16/3.82 % (4684)Instructions burned: 255 (million)
% 17.16/3.82 % (4684)------------------------------
% 17.16/3.82 % (4684)------------------------------
% 17.16/3.83 % (4686)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_4475 for (2977ds/668Mi)
% 17.59/3.91 % (4674)Instruction limit reached!
% 17.59/3.91 % (4674)------------------------------
% 17.59/3.91 % (4674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.59/3.91 % (4674)Termination reason: Unknown
% 17.59/3.91 % (4674)Termination phase: Saturation
% 17.59/3.91
% 17.59/3.91 % (4674)Memory used [KB]: 3198
% 17.59/3.91 % (4674)Time elapsed: 0.905 s
% 17.59/3.91 % (4674)Instructions burned: 1914 (million)
% 17.59/3.91 % (4674)------------------------------
% 17.59/3.91 % (4674)------------------------------
% 17.59/3.92 % (4682)Instruction limit reached!
% 17.59/3.92 % (4682)------------------------------
% 17.59/3.92 % (4682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.59/3.92 % (4682)Termination reason: Unknown
% 17.59/3.92 % (4682)Termination phase: Saturation
% 17.59/3.92
% 17.59/3.92 % (4682)Memory used [KB]: 7931
% 17.59/3.92 % (4682)Time elapsed: 0.395 s
% 17.59/3.92 % (4682)Instructions burned: 996 (million)
% 17.59/3.92 % (4682)------------------------------
% 17.59/3.92 % (4682)------------------------------
% 17.59/3.92 % (4687)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_4475 for (2976ds/40Mi)
% 17.59/3.93 % (4688)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_4475 for (2976ds/294Mi)
% 17.59/3.94 % (4687)Instruction limit reached!
% 17.59/3.94 % (4687)------------------------------
% 17.59/3.94 % (4687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.59/3.94 % (4687)Termination reason: Unknown
% 17.59/3.94 % (4687)Termination phase: Property scanning
% 17.59/3.94
% 17.59/3.94 % (4687)Memory used [KB]: 1535
% 17.59/3.94 % (4687)Time elapsed: 0.020 s
% 17.59/3.94 % (4687)Instructions burned: 41 (million)
% 17.59/3.94 % (4687)------------------------------
% 17.59/3.94 % (4687)------------------------------
% 17.59/3.96 % (4689)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_4475 for (2975ds/187Mi)
% 19.75/4.05 % (4689)Instruction limit reached!
% 19.75/4.05 % (4689)------------------------------
% 19.75/4.05 % (4689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.05 % (4689)Termination reason: Unknown
% 19.75/4.05 % (4689)Termination phase: Saturation
% 19.75/4.05
% 19.75/4.05 % (4689)Memory used [KB]: 7036
% 19.75/4.05 % (4689)Time elapsed: 0.092 s
% 19.75/4.05 % (4689)Instructions burned: 187 (million)
% 19.75/4.05 % (4689)------------------------------
% 19.75/4.05 % (4689)------------------------------
% 19.75/4.07 % (4690)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_4475 for (2974ds/371Mi)
% 19.75/4.07 % (4688)Instruction limit reached!
% 19.75/4.07 % (4688)------------------------------
% 19.75/4.07 % (4688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.07 % (4688)Termination reason: Unknown
% 19.75/4.07 % (4688)Termination phase: Saturation
% 19.75/4.07
% 19.75/4.07 % (4688)Memory used [KB]: 6140
% 19.75/4.07 % (4688)Time elapsed: 0.127 s
% 19.75/4.07 % (4688)Instructions burned: 294 (million)
% 19.75/4.07 % (4688)------------------------------
% 19.75/4.07 % (4688)------------------------------
% 19.75/4.08 % (4691)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_4475 for (2974ds/1827Mi)
% 19.75/4.09 % (4686)Instruction limit reached!
% 19.75/4.09 % (4686)------------------------------
% 19.75/4.09 % (4686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.09 % (4686)Termination reason: Unknown
% 19.75/4.09 % (4686)Termination phase: Saturation
% 19.75/4.09
% 19.75/4.09 % (4686)Memory used [KB]: 12281
% 19.75/4.09 % (4686)Time elapsed: 0.259 s
% 19.75/4.09 % (4686)Instructions burned: 669 (million)
% 19.75/4.09 % (4686)------------------------------
% 19.75/4.09 % (4686)------------------------------
% 19.75/4.11 % (4692)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_4475 for (2974ds/70Mi)
% 20.32/4.14 % (4692)Instruction limit reached!
% 20.32/4.14 % (4692)------------------------------
% 20.32/4.14 % (4692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.14 % (4692)Termination reason: Unknown
% 20.32/4.14 % (4692)Termination phase: Saturation
% 20.32/4.14
% 20.32/4.14 % (4692)Memory used [KB]: 1663
% 20.32/4.14 % (4692)Time elapsed: 0.032 s
% 20.32/4.14 % (4692)Instructions burned: 71 (million)
% 20.32/4.14 % (4692)------------------------------
% 20.32/4.14 % (4692)------------------------------
% 20.32/4.15 % (4693)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_4475 for (2974ds/316Mi)
% 20.32/4.19 % (4685)Instruction limit reached!
% 20.32/4.19 % (4685)------------------------------
% 20.32/4.19 % (4685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.19 % (4685)Termination reason: Unknown
% 20.32/4.19 % (4685)Termination phase: Saturation
% 20.32/4.19
% 20.32/4.19 % (4685)Memory used [KB]: 8059
% 20.32/4.19 % (4685)Time elapsed: 0.408 s
% 20.32/4.19 % (4685)Instructions burned: 832 (million)
% 20.32/4.19 % (4685)------------------------------
% 20.32/4.19 % (4685)------------------------------
% 20.66/4.20 % (4694)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_4475 for (2973ds/932Mi)
% 20.66/4.25 % (4690)Instruction limit reached!
% 20.66/4.25 % (4690)------------------------------
% 20.66/4.25 % (4690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.66/4.25 % (4690)Termination reason: Unknown
% 20.66/4.25 % (4690)Termination phase: Saturation
% 20.66/4.25
% 20.66/4.25 % (4690)Memory used [KB]: 7164
% 20.66/4.25 % (4690)Time elapsed: 0.186 s
% 20.66/4.25 % (4690)Instructions burned: 372 (million)
% 20.66/4.25 % (4690)------------------------------
% 20.66/4.25 % (4690)------------------------------
% 20.66/4.27 % (4695)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_4475 for (2972ds/4714Mi)
% 20.66/4.28 % (4693)Instruction limit reached!
% 20.66/4.28 % (4693)------------------------------
% 20.66/4.28 % (4693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.66/4.28 % (4693)Termination reason: Unknown
% 20.66/4.28 % (4693)Termination phase: Saturation
% 20.66/4.28
% 20.66/4.28 % (4693)Memory used [KB]: 6780
% 20.66/4.28 % (4693)Time elapsed: 0.128 s
% 20.66/4.28 % (4693)Instructions burned: 317 (million)
% 20.66/4.28 % (4693)------------------------------
% 20.66/4.28 % (4693)------------------------------
% 21.30/4.30 % (4696)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_4475 for (2972ds/8250Mi)
% 21.90/4.57 % (4694)Instruction limit reached!
% 21.90/4.57 % (4694)------------------------------
% 21.90/4.57 % (4694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.90/4.57 % (4694)Termination reason: Unknown
% 21.90/4.57 % (4694)Termination phase: Saturation
% 21.90/4.57
% 21.90/4.57 % (4694)Memory used [KB]: 8187
% 21.90/4.57 % (4694)Time elapsed: 0.371 s
% 21.90/4.57 % (4694)Instructions burned: 933 (million)
% 21.90/4.57 % (4694)------------------------------
% 21.90/4.57 % (4694)------------------------------
% 21.90/4.59 % (4697)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_4475 for (2969ds/770Mi)
% 22.59/4.65 % (4691)First to succeed.
% 22.59/4.66 % (4691)Refutation found. Thanks to Tanya!
% 22.59/4.66 % SZS status Theorem for DTF2THF_4475
% 22.59/4.66 % SZS output start Proof for DTF2THF_4475
% 22.59/4.66 thf(func_def_0, type, in: $i > $i > $o).
% 22.59/4.66 thf(func_def_1, type, exu: ($i > $o) > $o).
% 22.59/4.66 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 22.59/4.66 thf(func_def_8, type, powerset: $i > $i).
% 22.59/4.66 thf(func_def_10, type, setunion: $i > $i).
% 22.59/4.66 thf(func_def_19, type, descr: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_26, type, prop2set: $o > $i).
% 22.59/4.66 thf(func_def_36, type, nonempty: $i > $o).
% 22.59/4.66 thf(func_def_69, type, set2prop: $i > $o).
% 22.59/4.66 thf(func_def_88, type, subset: $i > $i > $o).
% 22.59/4.66 thf(func_def_89, type, disjoint: $i > $i > $o).
% 22.59/4.66 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 22.59/4.66 thf(func_def_114, type, binunion: $i > $i > $i).
% 22.59/4.66 thf(func_def_143, type, sK6: $i > $o).
% 22.59/4.66 thf(func_def_152, type, sK15: $i > ($i > $i > $o) > $i).
% 22.59/4.66 thf(func_def_153, type, sK16: $i > ($i > $i > $o) > $i).
% 22.59/4.66 thf(func_def_155, type, sK18: $i > $i > $o).
% 22.59/4.66 thf(func_def_156, type, sK19: $i > $i).
% 22.59/4.66 thf(func_def_157, type, sK20: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_158, type, sK21: $i > $o).
% 22.59/4.66 thf(func_def_162, type, sK25: $i > $o).
% 22.59/4.66 thf(func_def_169, type, sK32: $i > $o).
% 22.59/4.66 thf(func_def_170, type, sK33: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_171, type, sK34: $i > $o).
% 22.59/4.66 thf(func_def_172, type, sK35: $i > $i).
% 22.59/4.66 thf(func_def_173, type, sK36: $i > $i > $i).
% 22.59/4.66 thf(func_def_178, type, sK41: $i > $o).
% 22.59/4.66 thf(func_def_186, type, sK49: $i > $i).
% 22.59/4.66 thf(func_def_188, type, sK51: $i > $i).
% 22.59/4.66 thf(func_def_191, type, sK54: $i > $i).
% 22.59/4.66 thf(func_def_192, type, sK55: $i > $i > $i).
% 22.59/4.66 thf(func_def_205, type, sK68: $i > $i).
% 22.59/4.66 thf(func_def_207, type, sK70: $i > $o).
% 22.59/4.66 thf(func_def_212, type, sK75: $i > $o).
% 22.59/4.66 thf(func_def_224, type, sK87: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_225, type, sK88: $i > $o).
% 22.59/4.66 thf(func_def_226, type, sK89: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_227, type, sK90: $i > $o).
% 22.59/4.66 thf(func_def_233, type, sK96: $i > $i).
% 22.59/4.66 thf(func_def_239, type, sK102: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_240, type, sK103: $i > $o).
% 22.59/4.66 thf(func_def_249, type, sK112: ($i > $o) > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_250, type, sK113: ($i > $o) > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_251, type, sK114: $i > $o).
% 22.59/4.66 thf(func_def_252, type, sK115: $i > $o).
% 22.59/4.66 thf(func_def_255, type, sK118: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_256, type, sK119: $i > $o).
% 22.59/4.66 thf(func_def_263, type, sK126: $i > $i).
% 22.59/4.66 thf(func_def_264, type, sK127: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_265, type, sK128: $i > $i > $i).
% 22.59/4.66 thf(func_def_266, type, sK129: $i > $i > $i).
% 22.59/4.66 thf(func_def_267, type, sK130: $i > $i > $i).
% 22.59/4.66 thf(func_def_268, type, sK131: $i > $i > $i).
% 22.59/4.66 thf(func_def_269, type, sK132: $i > $i > $i).
% 22.59/4.66 thf(func_def_270, type, sK133: $i > $i > $i).
% 22.59/4.66 thf(func_def_272, type, sK135: $i > $i).
% 22.59/4.66 thf(func_def_273, type, sK136: $i > $i).
% 22.59/4.66 thf(func_def_274, type, sK137: $i > $i).
% 22.59/4.66 thf(func_def_275, type, sK138: $i > $i).
% 22.59/4.66 thf(func_def_276, type, sK139: $i > $i).
% 22.59/4.66 thf(func_def_277, type, sK140: $i > $i).
% 22.59/4.66 thf(func_def_278, type, sK141: $i > $i).
% 22.59/4.66 thf(func_def_279, type, sK142: $i > $i).
% 22.59/4.66 thf(func_def_280, type, sK143: $i > $i).
% 22.59/4.66 thf(func_def_281, type, sK144: $i > $i).
% 22.59/4.66 thf(func_def_282, type, sK145: $i > $i).
% 22.59/4.66 thf(func_def_283, type, sK146: $i > $i).
% 22.59/4.66 thf(func_def_284, type, sK147: $i > $i).
% 22.59/4.66 thf(func_def_285, type, sK148: $i > $i).
% 22.59/4.66 thf(func_def_286, type, sK149: $i > $i).
% 22.59/4.66 thf(func_def_287, type, sK150: $i > $i).
% 22.59/4.66 thf(func_def_288, type, sK151: $i > $i).
% 22.59/4.66 thf(func_def_289, type, sK152: $i > $i).
% 22.59/4.66 thf(func_def_290, type, sK153: $i > $i).
% 22.59/4.66 thf(func_def_291, type, sK154: $i > $i).
% 22.59/4.66 thf(func_def_292, type, sK155: $i > $i).
% 22.59/4.66 thf(func_def_293, type, sK156: $i > $i).
% 22.59/4.66 thf(func_def_294, type, sK157: $i > $i).
% 22.59/4.66 thf(func_def_295, type, sK158: $i > $i).
% 22.59/4.66 thf(func_def_296, type, sK159: $i > $i).
% 22.59/4.66 thf(func_def_297, type, sK160: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_298, type, sK161: $i > $i > $i).
% 22.59/4.66 thf(func_def_299, type, sK162: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_300, type, sK163: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_301, type, sK164: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_302, type, sK165: $i > $i > $i).
% 22.59/4.66 thf(func_def_303, type, sK166: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_304, type, sK167: $i > $i > $i).
% 22.59/4.66 thf(func_def_305, type, sK168: $i > $i > $i).
% 22.59/4.66 thf(func_def_306, type, sK169: $i > $i > $i).
% 22.59/4.66 thf(func_def_307, type, sK170: $i > $i).
% 22.59/4.66 thf(func_def_308, type, sK171: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_309, type, sK172: $i > $i > $i).
% 22.59/4.66 thf(func_def_310, type, sK173: $i > $i > $i).
% 22.59/4.66 thf(func_def_311, type, sK174: $i > $i > $i).
% 22.59/4.66 thf(func_def_312, type, sK175: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_313, type, sK176: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_314, type, sK177: $i > $i > $i).
% 22.59/4.66 thf(func_def_315, type, sK178: $i > $i > $i).
% 22.59/4.66 thf(func_def_316, type, sK179: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_317, type, sK180: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_318, type, sK181: $i > $i).
% 22.59/4.66 thf(func_def_319, type, sK182: $i > $i > $i).
% 22.59/4.66 thf(func_def_320, type, sK183: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_321, type, sK184: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_322, type, sK185: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_323, type, sK186: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_324, type, sK187: $i > $i > $i).
% 22.59/4.66 thf(func_def_325, type, sK188: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_326, type, sK189: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_327, type, sK190: $i > $i).
% 22.59/4.66 thf(func_def_328, type, sK191: $i > $i).
% 22.59/4.66 thf(func_def_329, type, sK192: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_330, type, sK193: $i > $i > $i).
% 22.59/4.66 thf(func_def_331, type, sK194: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_332, type, sK195: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_333, type, sK196: $i > $i > $i).
% 22.59/4.66 thf(func_def_334, type, sK197: $i > $i > $i).
% 22.59/4.66 thf(func_def_335, type, sK198: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_336, type, sK199: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_337, type, sK200: $i > $i).
% 22.59/4.66 thf(func_def_338, type, sK201: $i > $i > $i).
% 22.59/4.66 thf(func_def_339, type, sK202: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_340, type, sK203: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_341, type, sK204: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_342, type, sK205: $i > $i > $i).
% 22.59/4.66 thf(func_def_343, type, sK206: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_344, type, sK207: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_345, type, sK208: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_346, type, sK209: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_347, type, sK210: $i > $i > $i).
% 22.59/4.66 thf(func_def_348, type, sK211: $i > $i).
% 22.59/4.66 thf(func_def_349, type, sK212: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_350, type, sK213: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_351, type, sK214: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_352, type, sK215: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_353, type, sK216: $i > $i > $i).
% 22.59/4.66 thf(func_def_354, type, sK217: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_355, type, sK218: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_356, type, sK219: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_357, type, sK220: $i > $i > $i).
% 22.59/4.66 thf(func_def_358, type, sK221: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_359, type, sK222: $i > $i > $i).
% 22.59/4.66 thf(func_def_360, type, sK223: $i > $i > $i).
% 22.59/4.66 thf(func_def_361, type, sK224: $i > $i > $i).
% 22.59/4.66 thf(func_def_362, type, sK225: $i > $i).
% 22.59/4.66 thf(func_def_363, type, sK226: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_364, type, sK227: $i > $i > $i).
% 22.59/4.66 thf(func_def_365, type, sK228: $i > $i > $i).
% 22.59/4.66 thf(func_def_366, type, sK229: $i > $i > $i).
% 22.59/4.66 thf(func_def_367, type, sK230: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_368, type, sK231: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_369, type, sK232: $i > $i > $i).
% 22.59/4.66 thf(func_def_370, type, sK233: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_371, type, sK234: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_372, type, sK235: $i > $i).
% 22.59/4.66 thf(func_def_373, type, sK236: $i > $i > $i).
% 22.59/4.66 thf(func_def_374, type, sK237: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_375, type, sK238: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_376, type, sK239: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_377, type, sK240: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_378, type, sK241: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_379, type, sK242: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_380, type, sK243: $i > $i).
% 22.59/4.66 thf(func_def_381, type, sK244: $i > $i).
% 22.59/4.66 thf(func_def_382, type, sK245: $i > $i).
% 22.59/4.66 thf(func_def_383, type, sK246: $i > $i).
% 22.59/4.66 thf(func_def_384, type, sK247: $i > $i).
% 22.59/4.66 thf(func_def_385, type, sK248: $i > $i).
% 22.59/4.66 thf(func_def_386, type, sK249: $i > $i).
% 22.59/4.66 thf(func_def_387, type, sK250: $i > $i).
% 22.59/4.66 thf(func_def_388, type, sK251: $i > $i).
% 22.59/4.66 thf(func_def_389, type, sK252: $i > $i).
% 22.59/4.66 thf(func_def_390, type, sK253: $i > $i).
% 22.59/4.66 thf(func_def_391, type, sK254: $i > $i).
% 22.59/4.66 thf(func_def_392, type, sK255: $i > $i).
% 22.59/4.66 thf(func_def_393, type, sK256: $i > $i).
% 22.59/4.66 thf(func_def_394, type, sK257: $i > $i).
% 22.59/4.66 thf(func_def_395, type, sK258: $i > $i).
% 22.59/4.66 thf(func_def_396, type, sK259: $i > $i).
% 22.59/4.66 thf(func_def_397, type, sK260: $i > $i).
% 22.59/4.66 thf(func_def_398, type, sK261: $i > $i).
% 22.59/4.66 thf(func_def_399, type, sK262: $i > $i).
% 22.59/4.66 thf(func_def_400, type, sK263: $i > $i).
% 22.59/4.66 thf(func_def_401, type, sK264: $i > $i).
% 22.59/4.66 thf(func_def_402, type, sK265: $i > $i).
% 22.59/4.66 thf(func_def_403, type, sK266: $i > $i).
% 22.59/4.66 thf(func_def_404, type, sK267: $i > $i).
% 22.59/4.66 thf(func_def_405, type, sK268: $i > $i).
% 22.59/4.66 thf(func_def_406, type, sK269: $i > $i > $i).
% 22.59/4.66 thf(func_def_407, type, sK270: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_408, type, sK271: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_409, type, sK272: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_410, type, sK273: $i > $i > $i).
% 22.59/4.66 thf(func_def_411, type, sK274: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_412, type, sK275: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_413, type, sK276: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_414, type, sK277: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_415, type, sK278: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_416, type, sK279: $i > $i).
% 22.59/4.66 thf(func_def_417, type, sK280: $i > $i > $i).
% 22.59/4.66 thf(func_def_418, type, sK281: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_419, type, sK282: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_420, type, sK283: $i > $i > $i).
% 22.59/4.66 thf(func_def_421, type, sK284: $i > $i > $i).
% 22.59/4.66 thf(func_def_422, type, sK285: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_423, type, sK286: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_424, type, sK287: $i > $i).
% 22.59/4.66 thf(func_def_425, type, sK288: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_426, type, sK289: $i > $i > $i).
% 22.59/4.66 thf(func_def_427, type, sK290: $i > $i > $i).
% 22.59/4.66 thf(func_def_428, type, sK291: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_429, type, sK292: $i > $i > $i).
% 22.59/4.66 thf(func_def_430, type, sK293: $i > $i > $i).
% 22.59/4.66 thf(func_def_431, type, sK294: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_432, type, sK295: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_433, type, sK296: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_434, type, sK297: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_435, type, sK298: $i > $i).
% 22.59/4.66 thf(func_def_436, type, sK299: $i > $i).
% 22.59/4.66 thf(func_def_437, type, sK300: $i > $i).
% 22.59/4.66 thf(func_def_438, type, sK301: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_439, type, sK302: $i > $i > $i).
% 22.59/4.66 thf(func_def_440, type, sK303: $i > $i > $i).
% 22.59/4.66 thf(func_def_441, type, sK304: $i > $i > $i).
% 22.59/4.66 thf(func_def_442, type, sK305: $i > $i).
% 22.59/4.66 thf(func_def_443, type, sK306: $i > $i > $i).
% 22.59/4.66 thf(func_def_444, type, sK307: $i > $i > $i).
% 22.59/4.66 thf(func_def_445, type, sK308: $i > $i > $i).
% 22.59/4.66 thf(func_def_446, type, sK309: $i > $i).
% 22.59/4.66 thf(func_def_447, type, sK310: $i > $i).
% 22.59/4.66 thf(func_def_448, type, sK311: $i > $i > $i).
% 22.59/4.66 thf(func_def_449, type, sK312: $i > $i > $i).
% 22.59/4.66 thf(func_def_450, type, sK313: $i > $i).
% 22.59/4.66 thf(func_def_451, type, sK314: $i > $i).
% 22.59/4.66 thf(func_def_452, type, sK315: $i > $i > $i).
% 22.59/4.66 thf(func_def_453, type, sK316: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_454, type, sK317: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_455, type, sK318: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_456, type, sK319: $i > $i).
% 22.59/4.66 thf(func_def_457, type, sK320: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_458, type, sK321: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_459, type, sK322: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_460, type, sK323: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_461, type, sK324: $i > $i).
% 22.59/4.66 thf(func_def_462, type, sK325: $i > $i).
% 22.59/4.66 thf(func_def_463, type, sK326: $i > $i).
% 22.59/4.66 thf(func_def_464, type, sK327: $i > $i).
% 22.59/4.66 thf(func_def_465, type, sK328: $i > $i).
% 22.59/4.66 thf(func_def_466, type, sK329: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_467, type, sK330: $i > $i > $i).
% 22.59/4.66 thf(func_def_468, type, sK331: $i > $i > $i).
% 22.59/4.66 thf(func_def_469, type, sK332: $i > $i > $i).
% 22.59/4.66 thf(func_def_470, type, sK333: $i > $i > $i).
% 22.59/4.66 thf(func_def_471, type, sK334: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_472, type, sK335: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_473, type, sK336: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_474, type, sK337: $i > $i).
% 22.59/4.66 thf(func_def_475, type, sK338: $i > $i > $i).
% 22.59/4.66 thf(func_def_476, type, sK339: $i > $i > $i).
% 22.59/4.66 thf(func_def_477, type, sK340: $i > $i > $i).
% 22.59/4.66 thf(func_def_478, type, sK341: $i > $i).
% 22.59/4.66 thf(func_def_479, type, sK342: $i > $i).
% 22.59/4.66 thf(func_def_480, type, sK343: $i > $i > $i).
% 22.59/4.66 thf(func_def_481, type, sK344: $i > $i > $i).
% 22.59/4.66 thf(func_def_482, type, sK345: $i > $i > $i).
% 22.59/4.66 thf(func_def_483, type, sK346: $i > $i).
% 22.59/4.66 thf(func_def_484, type, sK347: $i > $i > $i).
% 22.59/4.66 thf(func_def_485, type, sK348: $i > $i).
% 22.59/4.66 thf(func_def_486, type, sK349: $i > $i > $i).
% 22.59/4.66 thf(func_def_487, type, sK350: $i > $i).
% 22.59/4.66 thf(func_def_488, type, sK351: $i > $i).
% 22.59/4.66 thf(func_def_489, type, sK352: $i > $i).
% 22.59/4.66 thf(func_def_490, type, sK353: $i > $i).
% 22.59/4.66 thf(func_def_491, type, sK354: $i > $i).
% 22.59/4.66 thf(func_def_492, type, sK355: $i > $i).
% 22.59/4.66 thf(func_def_493, type, sK356: $i > $i).
% 22.59/4.66 thf(func_def_494, type, sK357: $i > $i).
% 22.59/4.66 thf(func_def_495, type, sK358: $i > $i).
% 22.59/4.66 thf(func_def_496, type, sK359: $i > $i).
% 22.59/4.66 thf(func_def_497, type, sK360: $i > $i).
% 22.59/4.66 thf(func_def_498, type, sK361: $i > $i).
% 22.59/4.66 thf(func_def_499, type, sK362: $i > $i).
% 22.59/4.66 thf(func_def_500, type, sK363: $i > $i).
% 22.59/4.66 thf(func_def_501, type, sK364: $i > $i).
% 22.59/4.66 thf(func_def_502, type, sK365: $i > $i).
% 22.59/4.66 thf(func_def_503, type, sK366: $i > $i).
% 22.59/4.66 thf(func_def_504, type, sK367: $i > $i).
% 22.59/4.66 thf(func_def_505, type, sK368: $i > $i).
% 22.59/4.66 thf(func_def_506, type, sK369: $i > $i).
% 22.59/4.66 thf(func_def_507, type, sK370: $i > $i).
% 22.59/4.66 thf(func_def_508, type, sK371: $i > $i).
% 22.59/4.66 thf(func_def_509, type, sK372: $i > $i).
% 22.59/4.66 thf(func_def_510, type, sK373: $i > $i).
% 22.59/4.66 thf(func_def_511, type, sK374: $i > $i).
% 22.59/4.66 thf(func_def_512, type, sK375: $i > $i).
% 22.59/4.66 thf(func_def_513, type, sK376: $i > $i).
% 22.59/4.66 thf(func_def_514, type, sK377: $i > $i).
% 22.59/4.66 thf(func_def_515, type, sK378: $i > $i).
% 22.59/4.66 thf(func_def_516, type, sK379: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_517, type, sK380: $i > $i > $i).
% 22.59/4.66 thf(func_def_518, type, sK381: $i > $i).
% 22.59/4.66 thf(func_def_519, type, sK382: $i > $i).
% 22.59/4.66 thf(func_def_520, type, sK383: $i > $i).
% 22.59/4.66 thf(func_def_521, type, sK384: $i > $i).
% 22.59/4.66 thf(func_def_522, type, sK385: $i > $i).
% 22.59/4.66 thf(func_def_523, type, sK386: $i > $i).
% 22.59/4.66 thf(func_def_524, type, sK387: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_525, type, sK388: $i > $i).
% 22.59/4.66 thf(func_def_526, type, sK389: $i > $i).
% 22.59/4.66 thf(func_def_527, type, sK390: $i > $i).
% 22.59/4.66 thf(func_def_528, type, sK391: $i > $i).
% 22.59/4.66 thf(func_def_529, type, sK392: $i > $i).
% 22.59/4.66 thf(func_def_530, type, sK393: $i > $i).
% 22.59/4.66 thf(func_def_531, type, sK394: $i > $i).
% 22.59/4.66 thf(func_def_532, type, sK395: $i > $i).
% 22.59/4.66 thf(func_def_533, type, sK396: $i > $i).
% 22.59/4.66 thf(func_def_534, type, sK397: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_535, type, sK398: $i > $i).
% 22.59/4.66 thf(func_def_536, type, sK399: $i > $i).
% 22.59/4.66 thf(func_def_537, type, sK400: $i > $i).
% 22.59/4.66 thf(func_def_538, type, sK401: $i > $i).
% 22.59/4.66 thf(func_def_539, type, sK402: $i > $i).
% 22.59/4.66 thf(func_def_540, type, sK403: $i > $i).
% 22.59/4.66 thf(func_def_541, type, sK404: $i > $i).
% 22.59/4.66 thf(func_def_542, type, sK405: $i > $i).
% 22.59/4.66 thf(func_def_543, type, sK406: $i > $i).
% 22.59/4.66 thf(func_def_544, type, sK407: $i > $i).
% 22.59/4.66 thf(func_def_545, type, sK408: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_546, type, sK409: $i > $i > $i).
% 22.59/4.66 thf(func_def_547, type, sK410: $i > $i > $i).
% 22.59/4.66 thf(func_def_548, type, sK411: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_549, type, sK412: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_550, type, sK413: $i > $i > $i).
% 22.59/4.66 thf(func_def_551, type, sK414: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_552, type, sK415: $i > $i > $i).
% 22.59/4.66 thf(func_def_553, type, sK416: $i > $i > $i).
% 22.59/4.66 thf(func_def_554, type, sK417: $i > $i > $i).
% 22.59/4.66 thf(func_def_555, type, sK418: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_556, type, sK419: $i > $i > $i).
% 22.59/4.66 thf(func_def_557, type, sK420: $i > $i > $i).
% 22.59/4.66 thf(func_def_558, type, sK421: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_559, type, sK422: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_560, type, sK423: $i > $i > $i).
% 22.59/4.66 thf(func_def_561, type, sK424: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_562, type, sK425: $i > $i > $i).
% 22.59/4.66 thf(func_def_563, type, sK426: $i > $i > $i).
% 22.59/4.66 thf(func_def_564, type, sK427: $i > $i > $i).
% 22.59/4.66 thf(func_def_565, type, sK428: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_566, type, sK429: $i > $i).
% 22.59/4.66 thf(func_def_567, type, sK430: $i > $i > $i).
% 22.59/4.66 thf(func_def_568, type, sK431: $i > $i > $i).
% 22.59/4.66 thf(func_def_569, type, sK432: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_570, type, sK433: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_571, type, sK434: $i > $i > $i).
% 22.59/4.66 thf(func_def_572, type, sK435: $i > $i > $i).
% 22.59/4.66 thf(func_def_573, type, sK436: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_574, type, sK437: $i > $i > $i).
% 22.59/4.66 thf(func_def_575, type, sK438: $i > $i).
% 22.59/4.66 thf(func_def_576, type, sK439: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_577, type, sK440: $i > $i > $i).
% 22.59/4.66 thf(func_def_578, type, sK441: $i > $i > $i).
% 22.59/4.66 thf(func_def_579, type, sK442: $i > $i > $i).
% 22.59/4.66 thf(func_def_580, type, sK443: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_581, type, sK444: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_582, type, sK445: $i > $i > $i).
% 22.59/4.66 thf(func_def_583, type, sK446: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_584, type, sK447: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_585, type, sK448: $i > $i).
% 22.59/4.66 thf(func_def_586, type, sK449: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_587, type, sK450: $i > $i > $i).
% 22.59/4.66 thf(func_def_588, type, sK451: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_589, type, sK452: $i > $i > $i).
% 22.59/4.66 thf(func_def_590, type, sK453: $i > $i > $i).
% 22.59/4.66 thf(func_def_591, type, sK454: $i > $i > $i).
% 22.59/4.66 thf(func_def_592, type, sK455: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_593, type, sK456: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_594, type, sK457: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_595, type, sK458: $i > $i > $i).
% 22.59/4.66 thf(func_def_596, type, sK459: $i > $i > $i).
% 22.59/4.66 thf(func_def_597, type, sK460: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_598, type, sK461: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_599, type, sK462: $i > $i > $i).
% 22.59/4.66 thf(func_def_600, type, sK463: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_601, type, sK464: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_602, type, sK465: $i > $i).
% 22.59/4.66 thf(func_def_603, type, sK466: $i > $i).
% 22.59/4.66 thf(func_def_604, type, sK467: $i > $i).
% 22.59/4.66 thf(func_def_605, type, sK468: $i > $i).
% 22.59/4.66 thf(func_def_606, type, sK469: $i > $i).
% 22.59/4.66 thf(func_def_607, type, sK470: $i > $i).
% 22.59/4.66 thf(func_def_608, type, sK471: $i > $i).
% 22.59/4.66 thf(func_def_609, type, sK472: $i > $i).
% 22.59/4.66 thf(func_def_610, type, sK473: $i > $i).
% 22.59/4.66 thf(func_def_611, type, sK474: $i > $i).
% 22.59/4.66 thf(func_def_612, type, sK475: $i > $i).
% 22.59/4.66 thf(func_def_613, type, sK476: $i > $i).
% 22.59/4.66 thf(func_def_614, type, sK477: $i > $i).
% 22.59/4.66 thf(func_def_615, type, sK478: $i > $i).
% 22.59/4.66 thf(func_def_616, type, sK479: $i > $i).
% 22.59/4.66 thf(func_def_617, type, sK480: $i > $i).
% 22.59/4.66 thf(func_def_618, type, sK481: $i > $i).
% 22.59/4.66 thf(func_def_619, type, sK482: $i > $i).
% 22.59/4.66 thf(func_def_620, type, sK483: $i > $i).
% 22.59/4.66 thf(func_def_621, type, sK484: $i > $i).
% 22.59/4.66 thf(func_def_622, type, sK485: $i > $i).
% 22.59/4.66 thf(func_def_623, type, sK486: $i > $i).
% 22.59/4.66 thf(func_def_624, type, sK487: $i > $i).
% 22.59/4.66 thf(func_def_625, type, sK488: $i > $i).
% 22.59/4.66 thf(func_def_626, type, sK489: $i > $i).
% 22.59/4.66 thf(func_def_627, type, sK490: $i > $i).
% 22.59/4.66 thf(func_def_628, type, sK491: $i > $i).
% 22.59/4.66 thf(func_def_629, type, sK492: $i > $i).
% 22.59/4.66 thf(func_def_630, type, sK493: $i > $i).
% 22.59/4.66 thf(func_def_631, type, sK494: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_632, type, sK495: $i > $i > $i).
% 22.59/4.66 thf(func_def_633, type, sK496: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_634, type, sK497: $i > $i > $i).
% 22.59/4.66 thf(func_def_635, type, sK498: $i > $i > $i).
% 22.59/4.66 thf(func_def_636, type, sK499: $i > $i > $i).
% 22.59/4.66 thf(func_def_637, type, sK500: $i > $i > $i).
% 22.59/4.66 thf(func_def_638, type, sK501: $i > $i > $i).
% 22.59/4.66 thf(func_def_639, type, sK502: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_640, type, sK503: $i > $i > $i).
% 22.59/4.66 thf(func_def_641, type, sK504: $i > $i).
% 22.59/4.66 thf(func_def_642, type, sK505: $i > $i > $i).
% 22.59/4.66 thf(func_def_643, type, sK506: $i > $i > $i).
% 22.59/4.66 thf(func_def_644, type, sK507: $i > $i > $i).
% 22.59/4.66 thf(func_def_645, type, sK508: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_646, type, sK509: $i > $i).
% 22.59/4.66 thf(func_def_647, type, sK510: $i > $i).
% 22.59/4.66 thf(func_def_648, type, sK511: $i > $i).
% 22.59/4.66 thf(func_def_649, type, sK512: $i > $i).
% 22.59/4.66 thf(func_def_650, type, sK513: $i > $i > $i).
% 22.59/4.66 thf(func_def_651, type, sK514: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_652, type, sK515: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_653, type, sK516: $i > $i > $i).
% 22.59/4.66 thf(func_def_654, type, sK517: $i > $i > $i).
% 22.59/4.66 thf(func_def_655, type, sK518: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_656, type, sK519: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_657, type, sK520: $i > $i > $i).
% 22.59/4.66 thf(func_def_658, type, sK521: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_659, type, sK522: $i > $i).
% 22.59/4.66 thf(func_def_660, type, sK523: $i > $i > $i).
% 22.59/4.66 thf(func_def_661, type, sK524: $i > $i > $i).
% 22.59/4.66 thf(func_def_662, type, sK525: $i > $i > $i).
% 22.59/4.66 thf(func_def_663, type, sK526: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_664, type, sK527: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_665, type, sK528: $i > $i > $i).
% 22.59/4.66 thf(func_def_666, type, sK529: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_667, type, sK530: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_668, type, sK531: $i > $i > $i).
% 22.59/4.66 thf(func_def_669, type, sK532: $i > $i > $i).
% 22.59/4.66 thf(func_def_670, type, sK533: $i > $i > $i).
% 22.59/4.66 thf(func_def_671, type, sK534: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_672, type, sK535: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_673, type, sK536: $i > $i).
% 22.59/4.66 thf(func_def_674, type, sK537: $i > $i > $i).
% 22.59/4.66 thf(func_def_675, type, sK538: $i > $i > $i).
% 22.59/4.66 thf(func_def_676, type, sK539: $i > $i).
% 22.59/4.66 thf(func_def_677, type, sK540: $i > $i > $i).
% 22.59/4.66 thf(func_def_678, type, sK541: $i > $i > $i).
% 22.59/4.66 thf(func_def_679, type, sK542: $i > $i > $i).
% 22.59/4.66 thf(func_def_680, type, sK543: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_681, type, sK544: $i > $i).
% 22.59/4.66 thf(func_def_682, type, sK545: $i > $i).
% 22.59/4.66 thf(func_def_683, type, sK546: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_684, type, sK547: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_685, type, sK548: $i > $i).
% 22.59/4.66 thf(func_def_686, type, sK549: $i > $i).
% 22.59/4.66 thf(func_def_687, type, sK550: $i > $i).
% 22.59/4.66 thf(func_def_688, type, sK551: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_689, type, sK552: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_690, type, sK553: $i > $i).
% 22.59/4.66 thf(func_def_691, type, sK554: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_692, type, sK555: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_693, type, sK556: $i > $i > $i).
% 22.59/4.66 thf(func_def_694, type, sK557: $i > $i).
% 22.59/4.66 thf(func_def_695, type, sK558: $i > $i).
% 22.59/4.66 thf(func_def_696, type, sK559: $i > $i > $i).
% 22.59/4.66 thf(func_def_697, type, sK560: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_698, type, sK561: $i > $i).
% 22.59/4.66 thf(func_def_699, type, sK562: $i > $i).
% 22.59/4.66 thf(func_def_700, type, sK563: $i > $i).
% 22.59/4.66 thf(func_def_701, type, sK564: $i > $i).
% 22.59/4.66 thf(func_def_702, type, sK565: $i > $i > $i).
% 22.59/4.66 thf(func_def_703, type, sK566: $i > $i > $i).
% 22.59/4.66 thf(func_def_704, type, sK567: $i > $i > $i > $i).
% 22.59/4.66 thf(func_def_705, type, sK568: $i > $i > $i).
% 22.59/4.66 thf(func_def_706, type, sK569: $i > $i).
% 22.59/4.66 thf(func_def_707, type, sK570: $i > $i).
% 22.59/4.66 thf(func_def_708, type, sK571: $i > $i > $i).
% 22.59/4.66 thf(func_def_710, type, sK573: $i > $o).
% 22.59/4.66 thf(func_def_713, type, sK576: $i > $o).
% 22.59/4.66 thf(func_def_714, type, sK577: $i > $i).
% 22.59/4.66 thf(func_def_719, type, sK582: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_720, type, sK583: $i > $o).
% 22.59/4.66 thf(func_def_723, type, sK586: $i > $i).
% 22.59/4.66 thf(func_def_742, type, sK605: $i > $o).
% 22.59/4.66 thf(func_def_746, type, sK609: $i > $o).
% 22.59/4.66 thf(func_def_753, type, sK616: $i > $i > $i).
% 22.59/4.66 thf(func_def_759, type, sK622: ($i > $o) > ($i > $o) > $i > $i > $i).
% 22.59/4.66 thf(func_def_760, type, sK623: $i > $i > ($i > $o) > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_763, type, sK626: $i > $o).
% 22.59/4.66 thf(func_def_764, type, sK627: $i > $o).
% 22.59/4.66 thf(func_def_768, type, sK631: $i > $i > $i).
% 22.59/4.66 thf(func_def_769, type, sK632: $i > $i > $i).
% 22.59/4.66 thf(func_def_770, type, sK633: $i > $i > $i).
% 22.59/4.66 thf(func_def_773, type, sK636: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_774, type, sK637: $i > $o).
% 22.59/4.66 thf(func_def_777, type, sK640: $i > $o).
% 22.59/4.66 thf(func_def_779, type, sK642: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_780, type, sK643: $i > $o).
% 22.59/4.66 thf(func_def_781, type, sK644: $i > $i).
% 22.59/4.66 thf(func_def_789, type, sK652: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_790, type, sK653: $i > $o).
% 22.59/4.66 thf(func_def_796, type, sK659: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_797, type, sK660: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_798, type, sK661: $i > $o).
% 22.59/4.66 thf(func_def_806, type, sK669: $i > $o > $i > $i).
% 22.59/4.66 thf(func_def_824, type, sK687: $i > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_826, type, sK689: $i > $o).
% 22.59/4.66 thf(func_def_831, type, sK694: $i > $i > $i).
% 22.59/4.66 thf(func_def_835, type, sK698: $i > $o).
% 22.59/4.66 thf(func_def_836, type, sK699: ($i > $o) > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_837, type, sK700: ($i > $o) > ($i > $o) > $i).
% 22.59/4.66 thf(func_def_838, type, sK701: $i > $o).
% 22.59/4.66 thf(func_def_839, type, sK702: $i > $o).
% 22.59/4.66 thf(func_def_842, type, ph705: !>[X0: $tType]:(X0)).
% 22.59/4.66 thf(func_def_843, type, sK706: ($i > $o) > $i > $i).
% 22.59/4.66 thf(func_def_844, type, sK707: ($i > $o) > $i).
% 22.59/4.66 thf(func_def_845, type, sK708: $i > $i > $i).
% 22.59/4.66 thf(func_def_846, type, sK709: $i > $i > $i).
% 22.59/4.66 thf(func_def_847, type, sK710: $i > $i > $i).
% 22.59/4.66 thf(func_def_848, type, sK711: $i > $i > $i).
% 22.59/4.66 thf(func_def_850, type, sK713: $i > $i > $i).
% 22.59/4.66 thf(func_def_851, type, sK714: $i > $i > $i).
% 22.59/4.66 thf(func_def_852, type, sK715: $i > $i > $i).
% 22.59/4.66 thf(func_def_853, type, sK716: $i > $i).
% 22.59/4.66 thf(func_def_854, type, sK717: $i > $i).
% 22.59/4.66 thf(func_def_855, type, sK718: $i > $i > $i).
% 22.59/4.66 thf(f12864,plain,(
% 22.59/4.66 $false),
% 22.59/4.66 inference(avatar_sat_refutation,[status(thm)],[f9323,f9632,f9768,f10350,f10439,f10453,f10527,f11185,f12669,f12863])).
% 22.59/4.66 thf(f12863,plain,(
% 22.59/4.66 ~spl2_1260 | ~spl2_1264),
% 22.59/4.66 inference(avatar_contradiction_clause,[status(thm)],[f12862])).
% 22.59/4.66 thf(f12862,plain,(
% 22.59/4.66 $false | (~spl2_1260 | ~spl2_1264)),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f12861])).
% 22.59/4.66 thf(f12861,plain,(
% 22.59/4.66 ($false = $true) | (~spl2_1260 | ~spl2_1264)),
% 22.59/4.66 inference(forward_demodulation,[status(thm)],[f10332,f10349])).
% 22.59/4.66 thf(f10349,plain,(
% 22.59/4.66 (binunionIL = $false) | ~spl2_1264),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f10347])).
% 22.59/4.66 thf(f10347,definition,(
% 22.59/4.66 spl2_1264 <=> (binunionIL = $false)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1264])],[avatar_definition])).
% 22.59/4.66 thf(f10332,plain,(
% 22.59/4.66 (binunionIL = $true) | ~spl2_1260),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f10330])).
% 22.59/4.66 thf(f10330,definition,(
% 22.59/4.66 spl2_1260 <=> (binunionIL = $true)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1260])],[avatar_definition])).
% 22.59/4.66 thf(f12669,plain,(
% 22.59/4.66 ~spl2_1039 | ~spl2_1108 | ~spl2_1263),
% 22.59/4.66 inference(avatar_contradiction_clause,[status(thm)],[f12668])).
% 22.59/4.66 thf(f12668,plain,(
% 22.59/4.66 $false | (~spl2_1039 | ~spl2_1108 | ~spl2_1263)),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f12635])).
% 22.59/4.66 thf(f12635,plain,(
% 22.59/4.66 ($false = $true) | (~spl2_1039 | ~spl2_1108 | ~spl2_1263)),
% 22.59/4.66 inference(superposition,[status(thm)],[f12452,f12420])).
% 22.59/4.66 thf(f12420,plain,(
% 22.59/4.66 ((in @ sK712 @ (binunion @ sK1 @ sK0)) = $false) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(binary_proxy_clausification,[status(thm)],[f12419])).
% 22.59/4.66 thf(f12419,plain,(
% 22.59/4.66 ($false = ((in @ sK712 @ sK1) => (in @ sK712 @ (binunion @ sK1 @ sK0)))) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(beta_eta_normalization,[status(thm)],[f12418])).
% 22.59/4.66 thf(f12418,plain,(
% 22.59/4.66 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (binunion @ sK1 @ sK0)))) @ sK712)) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(sigma_clausification,[status(thm)],[f12417])).
% 22.59/4.66 thf(f12417,plain,(
% 22.59/4.66 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (binunion @ sK1 @ sK0)))))) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(not_proxy_clausification,[status(thm)],[f12416])).
% 22.59/4.66 thf(f12416,plain,(
% 22.59/4.66 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (binunion @ sK1 @ sK0)))))) = $true) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(boolean_simplification,[status(thm)],[f12367])).
% 22.59/4.66 thf(f12367,plain,(
% 22.59/4.66 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (binunion @ sK1 @ sK0))))) = $false) = $true) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(superposition,[status(thm)],[f9322,f11198])).
% 22.59/4.66 thf(f11198,plain,(
% 22.59/4.66 ($false = (in @ sK1 @ (powerset @ (binunion @ sK1 @ sK0)))) | ~spl2_1108),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f11194])).
% 22.59/4.66 thf(f11194,plain,(
% 22.59/4.66 ($true != $true) | ($false = (in @ sK1 @ (powerset @ (binunion @ sK1 @ sK0)))) | ~spl2_1108),
% 22.59/4.66 inference(superposition,[status(thm)],[f518,f9631])).
% 22.59/4.66 thf(f9631,plain,(
% 22.59/4.66 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) = $false)) ) | ~spl2_1108),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9630])).
% 22.59/4.66 thf(f9630,definition,(
% 22.59/4.66 spl2_1108 <=> ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) = $false))),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1108])],[avatar_definition])).
% 22.59/4.66 thf(f518,plain,(
% 22.59/4.66 ((subset @ sK1 @ (binunion @ sK1 @ sK0)) != $true)),
% 22.59/4.66 inference(cnf_transformation,[status(thm)],[f318])).
% 22.59/4.66 thf(f318,plain,(
% 22.59/4.66 (powersetI1 = $true) & (sepSubset = $true) & ((subset @ sK1 @ (binunion @ sK1 @ sK0)) != $true) & (emptyE1 = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (exuI1 = $true) & (quantDeMorgan2 = $true) & (binunionIR = $true) & (emptyI = $true) & (eqinunit = $true) & (vacuousDall = $true) & (exuE2 = $true) & (setoftrueEq = $true) & (subsetE2 = $true) & (setadjoinSub = $true) & (dsetconstr__Cong = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (setunionE = $true) & (singletonsswitch = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (powersetsubset = $true) & (setunionAx = $true) & (notequalI2 = $true) & (exu__Cong = $true) & (setextsub = $true) & (nonemptyImpWitness = $true) & (exuI3 = $true) & (subset2powerset = $true) & (nonemptyI1 = $true) & (foundationAx = $true) & (inPowerset = $true) & (quantDeMorgan1 = $true) & (setadjoinIL = $true) & (upairsetE = $true) & (subsetemptysetimpeq = $true) & (emptysetAx = $true) & (upairset2IR = $true) & (setadjoinOr = $true) & (subsetI2 = $true) & (quantDeMorgan3 = $true) & (powersetE1 = $true) & (omegaIndAx = $true) & (notequalI1 = $true) & (powersetE = $true) & (notdexE = $true) & (binunionE = $true) & (inCongP = $true) & (dsetconstrEL = $true) & (descrp = $true) & (exuEu = $true) & (subPowSU = $true) & (exuE1 = $true) & (omega__Cong = $true) & (emptyinPowerset = $true) & (subsetI1 = $true) & (emptysetimpfalse = $true) & (uniqinunit = $true) & (prop2setE = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (replAx = $true) & (binunionEcases = $true) & (exuI2 = $true) & (notsubsetI = $true) & (setextAx = $true) & (emptyset__Cong = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (subsetTrans = $true) & (setadjoinSub2 = $true) & (quantDeMorgan4 = $true) & (in__Cong = $true) & (dsetconstrER = $true) & (exuE3u = $true) & (emptysetE = $true) & (binunionIL = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (upairsetIL = $true) & (setbeta = $true) & (emptysetsubset = $true) & (subsetE = $true) & (notdallE = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (nonemptyI = $true) & (prop2set2propI = $true) & (powersetI = $true) & (setext = $true) & (setunionI = $true) & (wellorderingAx = $true) & (prop2setI = $true) & (setadjoinAx = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (upairsetIR = $true)),
% 22.59/4.66 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f316,f317])).
% 22.59/4.66 thf(f317,plain,(
% 22.59/4.66 ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X1 @ X0)) != $true) => ((subset @ sK1 @ (binunion @ sK1 @ sK0)) != $true)),
% 22.59/4.66 introduced(definition,[],[choice_axiom])).
% 22.59/4.66 thf(f316,plain,(
% 22.59/4.66 (powersetI1 = $true) & (sepSubset = $true) & ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X1 @ X0)) != $true) & (emptyE1 = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (exuI1 = $true) & (quantDeMorgan2 = $true) & (binunionIR = $true) & (emptyI = $true) & (eqinunit = $true) & (vacuousDall = $true) & (exuE2 = $true) & (setoftrueEq = $true) & (subsetE2 = $true) & (setadjoinSub = $true) & (dsetconstr__Cong = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (setunionE = $true) & (singletonsswitch = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (powersetsubset = $true) & (setunionAx = $true) & (notequalI2 = $true) & (exu__Cong = $true) & (setextsub = $true) & (nonemptyImpWitness = $true) & (exuI3 = $true) & (subset2powerset = $true) & (nonemptyI1 = $true) & (foundationAx = $true) & (inPowerset = $true) & (quantDeMorgan1 = $true) & (setadjoinIL = $true) & (upairsetE = $true) & (subsetemptysetimpeq = $true) & (emptysetAx = $true) & (upairset2IR = $true) & (setadjoinOr = $true) & (subsetI2 = $true) & (quantDeMorgan3 = $true) & (powersetE1 = $true) & (omegaIndAx = $true) & (notequalI1 = $true) & (powersetE = $true) & (notdexE = $true) & (binunionE = $true) & (inCongP = $true) & (dsetconstrEL = $true) & (descrp = $true) & (exuEu = $true) & (subPowSU = $true) & (exuE1 = $true) & (omega__Cong = $true) & (emptyinPowerset = $true) & (subsetI1 = $true) & (emptysetimpfalse = $true) & (uniqinunit = $true) & (prop2setE = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (replAx = $true) & (binunionEcases = $true) & (exuI2 = $true) & (notsubsetI = $true) & (setextAx = $true) & (emptyset__Cong = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (subsetTrans = $true) & (setadjoinSub2 = $true) & (quantDeMorgan4 = $true) & (in__Cong = $true) & (dsetconstrER = $true) & (exuE3u = $true) & (emptysetE = $true) & (binunionIL = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (upairsetIL = $true) & (setbeta = $true) & (emptysetsubset = $true) & (subsetE = $true) & (notdallE = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (nonemptyI = $true) & (prop2set2propI = $true) & (powersetI = $true) & (setext = $true) & (setunionI = $true) & (wellorderingAx = $true) & (prop2setI = $true) & (setadjoinAx = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (upairsetIR = $true)),
% 22.59/4.66 inference(flattening,[status(thm)],[f315])).
% 22.59/4.66 thf(f315,plain,(
% 22.59/4.66 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X1 @ X0)) != $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)),
% 22.59/4.66 inference(ennf_transformation,[status(thm)],[f128])).
% 22.59/4.66 thf(f128,plain,(
% 22.59/4.66 ~((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) => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X1 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.59/4.66 inference(fool_elimination,[status(thm)],[f127])).
% 22.59/4.66 thf(f127,plain,(
% 22.59/4.66 ~(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 => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.59/4.66 inference(rectify,[status(thm)],[f107])).
% 22.59/4.66 thf(f107,negated_conjecture,(
% 22.59/4.66 ~(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 => ! [X4 : $i,X3 : $i] : (subset @ X3 @ (binunion @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.59/4.66 inference(negated_conjecture,[status(cth)],[f106])).
% 22.59/4.66 thf(f106,conjecture,(
% 22.59/4.66 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 => ! [X4 : $i,X3 : $i] : (subset @ X3 @ (binunion @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.59/4.66 file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',binunionLsub)).
% 22.59/4.66 thf(f9322,plain,(
% 22.59/4.66 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)) ) | ~spl2_1039),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9321])).
% 22.59/4.66 thf(f9321,definition,(
% 22.59/4.66 spl2_1039 <=> ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1039])],[avatar_definition])).
% 22.59/4.66 thf(f12452,plain,(
% 22.59/4.66 ( ! [X0 : $i] : (((in @ sK712 @ (binunion @ sK1 @ X0)) = $true)) ) | (~spl2_1039 | ~spl2_1108 | ~spl2_1263)),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f12444])).
% 22.59/4.66 thf(f12444,plain,(
% 22.59/4.66 ( ! [X0 : $i] : (((in @ sK712 @ (binunion @ sK1 @ X0)) = $true) | ($false = $true)) ) | (~spl2_1039 | ~spl2_1108 | ~spl2_1263)),
% 22.59/4.66 inference(superposition,[status(thm)],[f12421,f10345])).
% 22.59/4.66 thf(f10345,plain,(
% 22.59/4.66 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ((in @ X2 @ (binunion @ X1 @ X3)) = $true)) ) | ~spl2_1263),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f10344])).
% 22.59/4.66 thf(f10344,definition,(
% 22.59/4.66 spl2_1263 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (((in @ X2 @ X1) = $false) | ((in @ X2 @ (binunion @ X1 @ X3)) = $true))),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1263])],[avatar_definition])).
% 22.59/4.66 thf(f12421,plain,(
% 22.59/4.66 ($true = (in @ sK712 @ sK1)) | (~spl2_1039 | ~spl2_1108)),
% 22.59/4.66 inference(binary_proxy_clausification,[status(thm)],[f12419])).
% 22.59/4.66 thf(f11185,plain,(
% 22.59/4.66 ~spl2_1104 | ~spl2_1107),
% 22.59/4.66 inference(avatar_contradiction_clause,[status(thm)],[f11184])).
% 22.59/4.66 thf(f11184,plain,(
% 22.59/4.66 $false | (~spl2_1104 | ~spl2_1107)),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f11183])).
% 22.59/4.66 thf(f11183,plain,(
% 22.59/4.66 ($false = $true) | (~spl2_1104 | ~spl2_1107)),
% 22.59/4.66 inference(forward_demodulation,[status(thm)],[f9614,f9628])).
% 22.59/4.66 thf(f9628,plain,(
% 22.59/4.66 (powersetE1 = $false) | ~spl2_1107),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9626])).
% 22.59/4.66 thf(f9626,definition,(
% 22.59/4.66 spl2_1107 <=> (powersetE1 = $false)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1107])],[avatar_definition])).
% 22.59/4.66 thf(f9614,plain,(
% 22.59/4.66 (powersetE1 = $true) | ~spl2_1104),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9612])).
% 22.59/4.66 thf(f9612,definition,(
% 22.59/4.66 spl2_1104 <=> (powersetE1 = $true)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1104])],[avatar_definition])).
% 22.59/4.66 thf(f10527,plain,(
% 22.59/4.66 ~spl2_1036 | ~spl2_1038),
% 22.59/4.66 inference(avatar_contradiction_clause,[status(thm)],[f10526])).
% 22.59/4.66 thf(f10526,plain,(
% 22.59/4.66 $false | (~spl2_1036 | ~spl2_1038)),
% 22.59/4.66 inference(trivial_inequality_removal,[status(thm)],[f10525])).
% 22.59/4.66 thf(f10525,plain,(
% 22.59/4.66 ($false = $true) | (~spl2_1036 | ~spl2_1038)),
% 22.59/4.66 inference(backward_demodulation,[status(thm)],[f9310,f9319])).
% 22.59/4.66 thf(f9319,plain,(
% 22.59/4.66 (powersetAx = $false) | ~spl2_1038),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9317])).
% 22.59/4.66 thf(f9317,definition,(
% 22.59/4.66 spl2_1038 <=> (powersetAx = $false)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1038])],[avatar_definition])).
% 22.59/4.66 thf(f9310,plain,(
% 22.59/4.66 (powersetAx = $true) | ~spl2_1036),
% 22.59/4.66 inference(avatar_component_clause,[status(thm)],[f9308])).
% 22.59/4.66 thf(f9308,definition,(
% 22.59/4.66 spl2_1036 <=> (powersetAx = $true)),
% 22.59/4.66 introduced(definition,[new_symbols(naming,[spl2_1036])],[avatar_definition])).
% 22.59/4.66 thf(f10453,plain,(
% 22.59/4.66 spl2_1104),
% 22.59/4.66 inference(avatar_split_clause,[status(thm)],[f475,f9612])).
% 22.59/4.66 thf(f475,plain,(
% 22.59/4.66 (powersetE1 = $true)),
% 22.59/4.66 inference(cnf_transformation,[status(thm)],[f318])).
% 22.59/4.66 thf(f10439,plain,(
% 22.59/4.66 spl2_1260),
% 22.59/4.66 inference(avatar_split_clause,[status(thm)],[f440,f10330])).
% 22.59/4.66 thf(f440,plain,(
% 22.59/4.66 (binunionIL = $true)),
% 22.59/4.66 inference(cnf_transformation,[status(thm)],[f318])).
% 22.59/4.66 thf(f10350,plain,(
% 22.59/4.66 spl2_1263 | spl2_1264),
% 22.59/4.66 inference(avatar_split_clause,[status(thm)],[f594,f10347,f10344])).
% 22.59/4.66 thf(f594,plain,(
% 22.59/4.66 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | (binunionIL = $false) | ((in @ X2 @ (binunion @ X1 @ X3)) = $true)) )),
% 22.59/4.66 inference(binary_proxy_clausification,[status(thm)],[f593])).
% 22.59/4.66 thf(f593,plain,(
% 22.59/4.66 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((binunionIL = $false) | (((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ X3))) = $true)) )),
% 22.59/4.66 inference(beta_eta_normalization,[status(thm)],[f592])).
% 22.59/4.66 thf(f592,plain,(
% 22.59/4.66 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ Y0)))) @ X3) = $true) | (binunionIL = $false)) )),
% 22.59/4.66 inference(pi_clausification,[status(thm)],[f591])).
% 22.59/4.66 thf(f591,plain,(
% 22.59/4.66 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ Y0)))))) | (binunionIL = $false)) )),
% 22.59/4.66 inference(beta_eta_normalization,[status(thm)],[f590])).
% 22.59/4.66 thf(f590,plain,(
% 22.59/4.66 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ (binunion @ X1 @ Y1)))))) @ X2) = $true) | (binunionIL = $false)) )),
% 22.59/4.66 inference(pi_clausification,[status(thm)],[f589])).
% 22.59/4.66 thf(f589,plain,(
% 22.59/4.66 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ (binunion @ X1 @ Y1))))))) = $true) | (binunionIL = $false)) )),
% 22.59/4.66 inference(beta_eta_normalization,[status(thm)],[f588])).
% 22.59/4.66 thf(f588,plain,(
% 22.59/4.66 ( ! [X1 : $i] : ((binunionIL = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ Y2)))))))) @ X1) = $true)) )),
% 22.59/4.66 inference(pi_clausification,[status(thm)],[f587])).
% 22.59/4.66 thf(f587,plain,(
% 22.59/4.66 (binunionIL = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 22.59/4.66 inference(binary_proxy_clausification,[status(thm)],[f347])).
% 22.59/4.66 thf(f347,plain,(
% 22.59/4.66 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 22.59/4.66 inference(cnf_transformation,[status(thm)],[f269])).
% 22.59/4.66 thf(f269,plain,(
% 22.59/4.66 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 22.59/4.66 inference(fool_elimination,[status(thm)],[f268])).
% 22.59/4.66 thf(f268,plain,(
% 22.59/4.66 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 22.59/4.66 inference(rectify,[status(thm)],[f101])).
% 22.59/4.66 thf(f101,axiom,(
% 22.59/4.66 (binunionIL = ! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))))),
% 22.59/4.66 file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',binunionIL)).
% 22.59/4.66 thf(f9768,plain,(
% 22.59/4.66 spl2_1036),
% 22.59/4.66 inference(avatar_split_clause,[status(thm)],[f418,f9308])).
% 22.59/4.66 thf(f418,plain,(
% 22.59/4.67 (powersetAx = $true)),
% 22.59/4.67 inference(cnf_transformation,[status(thm)],[f318])).
% 22.59/4.67 thf(f9632,plain,(
% 22.59/4.67 spl2_1107 | spl2_1108),
% 22.59/4.67 inference(avatar_split_clause,[status(thm)],[f1128,f9630,f9626])).
% 22.59/4.67 thf(f1128,plain,(
% 22.59/4.67 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) = $false) | (powersetE1 = $false)) )),
% 22.59/4.67 inference(binary_proxy_clausification,[status(thm)],[f1127])).
% 22.59/4.67 thf(f1127,plain,(
% 22.59/4.67 ( ! [X2 : $i,X1 : $i] : ((powersetE1 = $false) | (((in @ X2 @ (powerset @ X1)) => (subset @ X2 @ X1)) = $true)) )),
% 22.59/4.67 inference(beta_eta_normalization,[status(thm)],[f1126])).
% 22.59/4.67 thf(f1126,plain,(
% 22.59/4.67 ( ! [X2 : $i,X1 : $i] : ((powersetE1 = $false) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1))) @ X2) = $true)) )),
% 22.59/4.67 inference(pi_clausification,[status(thm)],[f1125])).
% 22.59/4.67 thf(f1125,plain,(
% 22.59/4.67 ( ! [X1 : $i] : ((powersetE1 = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1)))) = $true)) )),
% 22.59/4.67 inference(beta_eta_normalization,[status(thm)],[f1124])).
% 22.59/4.67 thf(f1124,plain,(
% 22.59/4.67 ( ! [X1 : $i] : ((powersetE1 = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))) @ X1) = $true)) )),
% 22.59/4.67 inference(pi_clausification,[status(thm)],[f1123])).
% 22.59/4.67 thf(f1123,plain,(
% 22.59/4.67 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))))) | (powersetE1 = $false)),
% 22.59/4.67 inference(binary_proxy_clausification,[status(thm)],[f527])).
% 22.59/4.67 thf(f527,plain,(
% 22.59/4.67 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 22.59/4.67 inference(cnf_transformation,[status(thm)],[f267])).
% 22.59/4.67 thf(f267,plain,(
% 22.59/4.67 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 22.59/4.67 inference(fool_elimination,[status(thm)],[f266])).
% 22.59/4.67 thf(f266,plain,(
% 22.59/4.67 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))),
% 22.59/4.67 inference(rectify,[status(thm)],[f96])).
% 22.59/4.67 thf(f96,axiom,(
% 22.59/4.67 (powersetE1 = ! [X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))),
% 22.59/4.67 file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',powersetE1)).
% 22.59/4.67 thf(f9323,plain,(
% 22.59/4.67 spl2_1038 | spl2_1039),
% 22.59/4.67 inference(avatar_split_clause,[status(thm)],[f1366,f9321,f9317])).
% 22.59/4.67 thf(f1366,plain,(
% 22.59/4.67 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true) | (powersetAx = $false)) )),
% 22.59/4.67 inference(beta_eta_normalization,[status(thm)],[f1365])).
% 22.59/4.67 thf(f1365,plain,(
% 22.59/4.67 ( ! [X2 : $i,X1 : $i] : ((powersetAx = $false) | (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1)))) @ X2) = $true)) )),
% 22.59/4.67 inference(pi_clausification,[status(thm)],[f1364])).
% 22.59/4.67 thf(f1364,plain,(
% 22.59/4.67 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1))))) = $true) | (powersetAx = $false)) )),
% 22.59/4.67 inference(beta_eta_normalization,[status(thm)],[f1363])).
% 22.59/4.67 thf(f1363,plain,(
% 22.59/4.67 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true) | (powersetAx = $false)) )),
% 22.59/4.67 inference(pi_clausification,[status(thm)],[f1362])).
% 22.59/4.67 thf(f1362,plain,(
% 22.59/4.67 (powersetAx = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) = $true)),
% 22.59/4.67 inference(binary_proxy_clausification,[status(thm)],[f320])).
% 22.59/4.67 thf(f320,plain,(
% 22.59/4.67 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 22.59/4.67 inference(cnf_transformation,[status(thm)],[f144])).
% 22.59/4.67 thf(f144,plain,(
% 22.59/4.67 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 22.59/4.67 inference(fool_elimination,[status(thm)],[f143])).
% 22.59/4.67 thf(f143,plain,(
% 22.59/4.67 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))))),
% 22.59/4.67 inference(rectify,[status(thm)],[f5])).
% 22.59/4.67 thf(f5,axiom,(
% 22.59/4.67 (powersetAx = ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))))),
% 22.59/4.67 file('/export/starexec/sandbox2/tmp/tmp.I84MLx2MBE/DTF2THF_4475.p',powersetAx)).
% 22.59/4.67 % SZS output end Proof for DTF2THF_4475
% 22.59/4.67 % (4691)------------------------------
% 22.59/4.67 % (4691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.59/4.67 % (4691)Termination reason: Refutation
% 22.59/4.67
% 22.59/4.67 % (4691)Memory used [KB]: 13560
% 22.59/4.67 % (4691)Time elapsed: 0.577 s
% 22.59/4.67 % (4691)Instructions burned: 1173 (million)
% 22.59/4.67 % (4691)------------------------------
% 22.59/4.67 % (4691)------------------------------
% 22.59/4.67 % (4573)Success in time 3.116 s
%------------------------------------------------------------------------------