%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 : Tue May 5 06:58:49 PM UTC 2026
% Result : Theorem 28.46s 5.33s
% Output : Refutation 28.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 163
% Syntax : Number of formulae : 388 ( 19 unt; 0 typ; 20 def)
% Number of atoms : 13070 (6062 equ; 0 cnn)
% Maximal formula atoms : 530 ( 33 avg)
% Number of connectives : 31975 (3332 ~;3260 |;2509 &;21598 @)
% ( 527 <=>; 497 =>; 0 <=; 0 <~>)
% Maximal formula depth : 186 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2550 (2550 >; 0 *; 0 +; 0 <<)
% Number of symbols : 757 ( 753 usr; 313 con; 0-4 aty)
% ( 252 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 6427 ( 390 ^;4604 !;1433 ?;6427 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(type_def_8,type,
d_term: $tType ).
thf(type_def_9,type,
d_subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_124,type,
d_term: $tType ).
thf(func_def_125,type,
d_subst: $tType ).
thf(func_def_126,type,
d2term: d_term > term ).
thf(func_def_127,type,
d2subst: d_subst > subst ).
thf(func_def_128,type,
d_one: d_term ).
thf(func_def_129,type,
d_id: d_subst ).
thf(func_def_142,type,
sP0: ( subst > term > subst > $o ) > $o ).
thf(func_def_145,type,
sP3: ( subst > term > subst > $o ) > $o ).
thf(func_def_146,type,
sP4: ( subst > term > subst > $o ) > $o ).
thf(func_def_150,type,
sP8: ( subst > term > subst > $o ) > $o ).
thf(func_def_152,type,
sP10: ( term > $o ) > $o ).
thf(func_def_153,type,
sP11: ( subst > term > subst > $o ) > $o ).
thf(func_def_154,type,
sP12: ( subst > term > subst > $o ) > $o ).
thf(func_def_155,type,
sP13: ( subst > term > subst > $o ) > $o ).
thf(func_def_156,type,
sP14: ( subst > term > subst > $o ) > $o ).
thf(func_def_157,type,
sP15: ( term > $o ) > $o ).
thf(func_def_162,type,
sP20: ( subst > term > subst > $o ) > $o ).
thf(func_def_163,type,
sP21: ( subst > term > subst > $o ) > $o ).
thf(func_def_165,type,
sP23: ( subst > term > subst > $o ) > $o ).
thf(func_def_166,type,
sP24: ( term > $o ) > $o ).
thf(func_def_171,type,
sP29: ( term > $o ) > $o ).
thf(func_def_172,type,
sP30: ( term > $o ) > $o ).
thf(func_def_175,type,
sP33: ( subst > term > subst > $o ) > $o ).
thf(func_def_178,type,
sP36: ( subst > term > subst > $o ) > $o ).
thf(func_def_179,type,
sP37: ( subst > term > subst > $o ) > $o ).
thf(func_def_180,type,
sP38: ( term > $o ) > $o ).
thf(func_def_184,type,
sP42: ( term > $o ) > $o ).
thf(func_def_186,type,
sP44: ( term > $o ) > $o ).
thf(func_def_189,type,
sP47: ( term > $o ) > $o ).
thf(func_def_190,type,
sP48: ( term > $o ) > $o ).
thf(func_def_193,type,
sP51: ( subst > term > subst > $o ) > $o ).
thf(func_def_196,type,
sP54: ( subst > term > subst > $o ) > $o ).
thf(func_def_201,type,
sK59: term ).
thf(func_def_202,type,
sK60: subst > term > subst > $o ).
thf(func_def_203,type,
sK61: ( subst > term > term ) > term ).
thf(func_def_204,type,
sK62: ( subst > term > term ) > subst ).
thf(func_def_205,type,
sK63: ( subst > term > term ) > subst ).
thf(func_def_206,type,
sK64: ( subst > term > term ) > term ).
thf(func_def_207,type,
sK65: term ).
thf(func_def_208,type,
sK66: ( subst > term > subst > $o ) > term > term ).
thf(func_def_209,type,
sK67: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_210,type,
sK68: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_211,type,
sK69: term > ( subst > term > subst > $o ) > term ).
thf(func_def_212,type,
sK70: subst > term > subst > $o ).
thf(func_def_213,type,
sK71: term ).
thf(func_def_214,type,
sK72: ( subst > term > term ) > term ).
thf(func_def_215,type,
sK73: ( subst > term > term ) > subst ).
thf(func_def_216,type,
sK74: ( subst > term > term ) > term ).
thf(func_def_217,type,
sK75: ( subst > term > term ) > subst ).
thf(func_def_218,type,
sK76: term ).
thf(func_def_219,type,
sK77: subst > term > subst > $o ).
thf(func_def_220,type,
sK78: term ).
thf(func_def_221,type,
sK79: ( subst > term > subst > $o ) > term > term ).
thf(func_def_222,type,
sK80: ( subst > term > subst > $o ) > term ).
thf(func_def_223,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_224,type,
sK82: ( subst > term > subst > $o ) > subst ).
thf(func_def_225,type,
sK83: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK84: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK85: ( subst > term > subst > $o ) > term ).
thf(func_def_228,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK88: ( subst > term > subst > $o ) > term > term ).
thf(func_def_231,type,
sK89: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_232,type,
sK90: term ).
thf(func_def_233,type,
sK91: subst > term > subst > $o ).
thf(func_def_234,type,
sK92: ( subst > term > term ) > term ).
thf(func_def_235,type,
sK93: ( subst > term > term ) > term ).
thf(func_def_236,type,
sK94: ( subst > term > term ) > subst ).
thf(func_def_237,type,
sK95: ( subst > term > term ) > subst ).
thf(func_def_238,type,
sK96: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_239,type,
sK97: ( subst > term > term ) > subst ).
thf(func_def_240,type,
sK98: ( subst > term > term ) > subst ).
thf(func_def_241,type,
sK99: ( subst > term > term ) > term ).
thf(func_def_242,type,
sK100: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_243,type,
sK101: subst > term > subst > $o ).
thf(func_def_244,type,
sK102: term ).
thf(func_def_245,type,
sK103: ( subst > term > term ) > term > subst ).
thf(func_def_246,type,
sK104: ( subst > term > term ) > term > term ).
thf(func_def_247,type,
sK105: ( subst > term > term ) > term > subst ).
thf(func_def_248,type,
sK106: ( subst > term > term ) > term > subst ).
thf(func_def_249,type,
sK107: ( subst > term > term ) > term > term ).
thf(func_def_250,type,
sK108: ( subst > term > term ) > term > subst ).
thf(func_def_251,type,
sK109: ( subst > term > term ) > term ).
thf(func_def_252,type,
sK110: ( subst > term > subst > $o ) > term ).
thf(func_def_253,type,
sK111: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_254,type,
sK112: term > ( subst > term > subst > $o ) > term ).
thf(func_def_255,type,
sK113: subst > term > subst > $o ).
thf(func_def_256,type,
sK114: term ).
thf(func_def_257,type,
sK115: term ).
thf(func_def_258,type,
sK116: ( subst > term > subst > $o ) > subst ).
thf(func_def_259,type,
sK117: ( subst > term > subst > $o ) > term ).
thf(func_def_260,type,
sK118: ( subst > term > subst > $o ) > subst ).
thf(func_def_261,type,
sK119: ( subst > term > subst > $o ) > subst ).
thf(func_def_262,type,
sK120: ( subst > term > subst > $o ) > subst ).
thf(func_def_263,type,
sK121: ( subst > term > subst > $o ) > subst ).
thf(func_def_264,type,
sK122: ( subst > term > subst > $o ) > subst ).
thf(func_def_265,type,
sK123: ( subst > term > subst > $o ) > term ).
thf(func_def_266,type,
sK124: ( subst > term > subst > $o ) > term ).
thf(func_def_267,type,
sK125: ( subst > term > subst > $o ) > term ).
thf(func_def_268,type,
sK126: ( term > $o ) > term ).
thf(func_def_269,type,
sK127: ( term > $o ) > term ).
thf(func_def_270,type,
sK128: subst ).
thf(func_def_271,type,
sK129: term ).
thf(func_def_272,type,
sK130: subst ).
thf(func_def_273,type,
sK131: term ).
thf(func_def_274,type,
sK132: subst ).
thf(func_def_275,type,
sK133: term ).
thf(func_def_276,type,
sK134: term > $o ).
thf(func_def_277,type,
sK135: subst ).
thf(func_def_278,type,
sK136: term ).
thf(func_def_279,type,
sK137: term > $o ).
thf(func_def_280,type,
sK138: term > term ).
thf(func_def_281,type,
sK139: ( term > $o ) > subst > term ).
thf(func_def_282,type,
sK140: ( term > $o ) > term ).
thf(func_def_283,type,
sK141: ( term > $o ) > term ).
thf(func_def_284,type,
sK142: ( term > $o ) > term ).
thf(func_def_285,type,
sK143: ( term > $o ) > term ).
thf(func_def_286,type,
sK144: ( term > $o ) > term ).
thf(func_def_287,type,
sK145: subst ).
thf(func_def_288,type,
sK146: subst > term > term ).
thf(func_def_289,type,
sK147: subst > term > term ).
thf(func_def_290,type,
sK148: term ).
thf(func_def_291,type,
sK149: subst ).
thf(func_def_292,type,
sK150: term ).
thf(func_def_293,type,
sK151: subst ).
thf(func_def_294,type,
sK152: term ).
thf(func_def_295,type,
sK153: ( subst > term > term ) > subst ).
thf(func_def_296,type,
sK154: ( subst > term > term ) > subst ).
thf(func_def_297,type,
sK155: ( subst > term > term ) > term ).
thf(func_def_298,type,
sK156: ( subst > term > term ) > term ).
thf(func_def_299,type,
sK157: ( subst > term > term ) > subst ).
thf(func_def_300,type,
sK158: ( subst > term > term ) > subst ).
thf(func_def_301,type,
sK159: term ).
thf(func_def_302,type,
sK160: term ).
thf(func_def_303,type,
sK161: subst ).
thf(func_def_304,type,
sK162: term > $o ).
thf(func_def_305,type,
sK163: term ).
thf(func_def_306,type,
sK164: term > term ).
thf(func_def_307,type,
sK165: ( term > $o ) > term ).
thf(func_def_308,type,
sK166: ( term > $o ) > subst > term ).
thf(func_def_309,type,
sK167: ( term > $o ) > term ).
thf(func_def_310,type,
sK168: ( term > $o ) > term ).
thf(func_def_311,type,
sK169: term > $o ).
thf(func_def_312,type,
sK170: term ).
thf(func_def_313,type,
sK171: term > term ).
thf(func_def_314,type,
sK172: ( term > $o ) > term ).
thf(func_def_315,type,
sK173: ( term > $o ) > term ).
thf(func_def_316,type,
sK174: ( term > $o ) > term ).
thf(func_def_317,type,
sK175: ( term > $o ) > term ).
thf(func_def_318,type,
sK176: ( term > $o ) > term ).
thf(func_def_319,type,
sK177: ( term > $o ) > term ).
thf(func_def_320,type,
sK178: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_321,type,
sK179: term > $o ).
thf(func_def_322,type,
sK180: term ).
thf(func_def_323,type,
sK181: term > term ).
thf(func_def_324,type,
sK182: term ).
thf(func_def_325,type,
sK183: subst > term > subst > $o ).
thf(func_def_326,type,
sK184: ( term > $o ) > term ).
thf(func_def_327,type,
sK185: subst > term > subst > $o ).
thf(func_def_328,type,
sK186: term ).
thf(func_def_329,type,
sK187: ( subst > term > subst > $o ) > term ).
thf(func_def_330,type,
sK188: ( subst > term > subst > $o ) > subst ).
thf(func_def_331,type,
sK189: ( subst > term > subst > $o ) > subst ).
thf(func_def_332,type,
sK190: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK191: ( subst > term > subst > $o ) > term ).
thf(func_def_334,type,
sK192: ( subst > term > subst > $o ) > subst ).
thf(func_def_335,type,
sK193: ( subst > term > subst > $o ) > term ).
thf(func_def_336,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK195: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK196: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_339,type,
sK197: term > ( term > $o ) > term ).
thf(func_def_340,type,
sK198: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_341,type,
sK199: term > $o ).
thf(func_def_342,type,
sK200: term ).
thf(func_def_343,type,
sK201: subst > term > subst > $o ).
thf(func_def_344,type,
sK202: ( subst > term > term ) > term ).
thf(func_def_345,type,
sK203: ( subst > term > term ) > subst ).
thf(func_def_346,type,
sK204: ( subst > term > term ) > term ).
thf(func_def_347,type,
sK205: ( subst > term > term ) > subst ).
thf(func_def_348,type,
sK206: ( term > $o ) > term ).
thf(func_def_349,type,
sK207: ( term > $o ) > term ).
thf(func_def_350,type,
sK208: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_351,type,
sK209: ( subst > term > term ) > term ).
thf(func_def_352,type,
sK210: ( subst > term > term ) > subst ).
thf(func_def_353,type,
sK211: ( subst > term > term ) > subst ).
thf(func_def_354,type,
sK212: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_355,type,
sK213: ( subst > term > subst > $o ) > term ).
thf(func_def_356,type,
sK214: ( subst > term > subst > $o ) > term ).
thf(func_def_357,type,
sK215: term ).
thf(func_def_358,type,
sK216: subst > term > subst > $o ).
thf(func_def_359,type,
sK217: ( subst > term > term ) > term ).
thf(func_def_360,type,
sK218: ( subst > term > term ) > subst ).
thf(func_def_361,type,
sK219: ( subst > term > term ) > subst ).
thf(func_def_362,type,
sK220: ( subst > term > term ) > term ).
thf(func_def_363,type,
sK221: ( subst > term > subst > $o ) > term > term ).
thf(func_def_364,type,
sK222: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_365,type,
sK223: term > $o ).
thf(func_def_366,type,
sK224: subst > term > subst > $o ).
thf(func_def_367,type,
sK225: term ).
thf(func_def_368,type,
sK226: term > ( term > $o ) > term ).
thf(func_def_369,type,
sK227: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_370,type,
sK228: ( subst > term > subst > $o ) > term ).
thf(func_def_371,type,
sK229: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK230: ( subst > term > subst > $o ) > subst ).
thf(func_def_373,type,
sK231: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_375,type,
sK233: ( subst > term > subst > $o ) > term ).
thf(func_def_376,type,
sK234: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK235: ( subst > term > subst > $o ) > subst ).
thf(func_def_378,type,
sK236: term ).
thf(func_def_379,type,
sK237: ( subst > term > term ) > term ).
thf(func_def_380,type,
sK238: ( subst > term > term ) > subst ).
thf(func_def_381,type,
sK239: ( subst > term > term ) > subst ).
thf(func_def_382,type,
sK240: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_383,type,
sK241: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_384,type,
sK242: ( term > $o ) > term ).
thf(func_def_385,type,
sK243: subst > ( term > $o ) > term ).
thf(func_def_386,type,
sK244: term > $o ).
thf(func_def_387,type,
sK245: term ).
thf(func_def_388,type,
sK246: subst ).
thf(func_def_389,type,
sK247: term > term ).
thf(func_def_390,type,
sK248: term ).
thf(func_def_391,type,
sK249: term ).
thf(func_def_392,type,
sK250: term > $o ).
thf(func_def_393,type,
sK251: term > term ).
thf(func_def_394,type,
sK252: ( term > $o ) > term ).
thf(func_def_395,type,
sK253: ( term > $o ) > term ).
thf(func_def_396,type,
sK254: ( term > $o ) > term ).
thf(func_def_397,type,
sK255: ( term > $o ) > term ).
thf(func_def_398,type,
sK256: ( term > $o ) > term ).
thf(func_def_399,type,
sK257: ( term > $o ) > term ).
thf(func_def_400,type,
sK258: term ).
thf(func_def_401,type,
sK259: term > $o ).
thf(func_def_402,type,
sK260: subst > term > subst > $o ).
thf(func_def_403,type,
sK261: ( subst > term > term ) > subst ).
thf(func_def_404,type,
sK262: ( subst > term > term ) > subst ).
thf(func_def_405,type,
sK263: ( subst > term > term ) > term ).
thf(func_def_406,type,
sK264: ( subst > term > term ) > term ).
thf(func_def_407,type,
sK265: term > subst > term > term ).
thf(func_def_408,type,
sK266: term ).
thf(func_def_409,type,
sK267: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_410,type,
sK268: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_411,type,
sK269: ( term > $o ) > term > term ).
thf(func_def_412,type,
sK270: term ).
thf(func_def_413,type,
sK271: ( subst > term > term ) > term ).
thf(func_def_414,type,
sK272: ( subst > term > term ) > subst ).
thf(func_def_415,type,
sK273: term ).
thf(func_def_416,type,
sK274: subst > term > subst > $o ).
thf(func_def_417,type,
sK275: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_418,type,
sK276: ( subst > term > subst > $o ) > term ).
thf(func_def_419,type,
sK277: ( subst > term > subst > $o ) > term ).
thf(func_def_420,type,
sK278: term ).
thf(func_def_421,type,
sK279: subst > term > subst > $o ).
thf(func_def_422,type,
sK280: ( term > $o ) > term ).
thf(func_def_423,type,
sK281: ( term > $o ) > term ).
thf(func_def_424,type,
sK282: ( term > $o ) > term ).
thf(func_def_425,type,
sK283: term > $o ).
thf(func_def_426,type,
sK284: term ).
thf(func_def_427,type,
sK285: term > term ).
thf(func_def_428,type,
sK286: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_429,type,
sK287: ( term > $o ) > term > term ).
thf(func_def_430,type,
sK288: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_431,type,
sK289: subst > term > subst > $o ).
thf(func_def_432,type,
sK290: term ).
thf(func_def_433,type,
sK291: term > $o ).
thf(func_def_434,type,
sK292: ( subst > term > term ) > term ).
thf(func_def_435,type,
sK293: ( subst > term > term ) > subst ).
thf(func_def_436,type,
sK294: ( subst > term > term ) > subst ).
thf(func_def_437,type,
sK295: ( subst > term > term ) > term ).
thf(func_def_438,type,
sK296: ( term > $o ) > term ).
thf(func_def_439,type,
sK297: ( term > $o ) > term ).
thf(func_def_440,type,
sK298: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_441,type,
sK299: ( subst > term > term ) > subst ).
thf(func_def_442,type,
sK300: ( subst > term > term ) > term ).
thf(func_def_443,type,
sK301: ( subst > term > term ) > subst ).
thf(func_def_444,type,
sK302: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_445,type,
sK303: term ).
thf(func_def_446,type,
sK304: term > $o ).
thf(func_def_447,type,
sK305: term ).
thf(func_def_448,type,
sK306: subst > term > subst > $o ).
thf(func_def_449,type,
sK307: ( subst > term > subst > $o ) > subst ).
thf(func_def_450,type,
sK308: ( subst > term > subst > $o ) > subst ).
thf(func_def_451,type,
sK309: ( subst > term > subst > $o ) > subst ).
thf(func_def_452,type,
sK310: ( subst > term > subst > $o ) > term ).
thf(func_def_453,type,
sK311: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_454,type,
sK312: ( subst > term > subst > $o ) > subst ).
thf(func_def_455,type,
sK313: ( subst > term > subst > $o ) > term ).
thf(func_def_456,type,
sK314: ( subst > term > subst > $o ) > subst ).
thf(func_def_457,type,
sK315: ( subst > term > subst > $o ) > subst ).
thf(func_def_458,type,
sK316: ( subst > term > subst > $o ) > term ).
thf(func_def_459,type,
sK317: ( subst > term > subst > $o ) > term ).
thf(func_def_460,type,
sK318: ( subst > term > subst > $o ) > term ).
thf(func_def_461,type,
sK319: ( subst > term > subst > $o ) > term ).
thf(func_def_462,type,
sK320: ( term > $o ) > term ).
thf(func_def_463,type,
sK321: ( term > $o ) > term ).
thf(func_def_464,type,
sK322: term > $o ).
thf(func_def_465,type,
sK323: term ).
thf(func_def_466,type,
sK324: term > term ).
thf(func_def_467,type,
sK325: ( subst > term > subst > $o ) > term ).
thf(func_def_468,type,
sK326: ( subst > term > subst > $o ) > subst ).
thf(func_def_469,type,
sK327: ( subst > term > subst > $o ) > subst ).
thf(func_def_470,type,
sK328: ( subst > term > subst > $o ) > subst ).
thf(func_def_471,type,
sK329: ( subst > term > subst > $o ) > term ).
thf(func_def_472,type,
sK330: ( subst > term > subst > $o ) > subst ).
thf(func_def_473,type,
sK331: ( subst > term > subst > $o ) > subst ).
thf(func_def_474,type,
sK332: ( subst > term > subst > $o ) > subst ).
thf(func_def_475,type,
sK333: term ).
thf(func_def_476,type,
sK334: term ).
thf(func_def_477,type,
sK335: subst > term > subst > $o ).
thf(func_def_478,type,
sK336: subst > term > subst > $o ).
thf(func_def_479,type,
sK337: term ).
thf(func_def_480,type,
sK338: ( subst > term > subst > $o ) > term ).
thf(func_def_481,type,
sK339: ( subst > term > subst > $o ) > subst ).
thf(func_def_482,type,
sK340: ( subst > term > subst > $o ) > subst ).
thf(func_def_483,type,
sK341: ( subst > term > subst > $o ) > subst ).
thf(func_def_484,type,
sK342: ( subst > term > subst > $o ) > term ).
thf(func_def_485,type,
sK343: ( subst > term > subst > $o ) > term ).
thf(func_def_486,type,
sK344: ( subst > term > subst > $o ) > subst ).
thf(func_def_487,type,
sK345: ( subst > term > subst > $o ) > subst ).
thf(func_def_488,type,
sK346: ( subst > term > subst > $o ) > subst ).
thf(func_def_489,type,
sK347: ( subst > term > subst > $o ) > subst ).
thf(func_def_490,type,
sK348: ( subst > term > subst > $o ) > term ).
thf(func_def_491,type,
sK349: ( subst > term > subst > $o ) > subst ).
thf(func_def_492,type,
sK350: ( subst > term > subst > $o ) > subst ).
thf(func_def_493,type,
sK351: ( subst > term > subst > $o ) > subst ).
thf(func_def_494,type,
sK352: ( subst > term > subst > $o ) > subst ).
thf(func_def_495,type,
sK353: ( subst > term > subst > $o ) > subst ).
thf(func_def_496,type,
sK354: ( subst > term > subst > $o ) > term ).
thf(func_def_497,type,
sK355: ( subst > term > subst > $o ) > term > term ).
thf(func_def_498,type,
sK356: term ).
thf(func_def_499,type,
sK357: subst > term > subst > $o ).
thf(func_def_500,type,
sK358: ( term > $o ) > term ).
thf(func_def_501,type,
sK359: ( term > $o ) > term ).
thf(func_def_502,type,
sK360: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_503,type,
sK361: ( subst > term > term ) > term ).
thf(func_def_504,type,
sK362: ( subst > term > term ) > subst ).
thf(func_def_505,type,
sK363: ( subst > term > term ) > subst ).
thf(func_def_506,type,
sK364: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_507,type,
sK365: ( subst > term > subst > $o ) > term ).
thf(func_def_508,type,
sK366: ( subst > term > subst > $o ) > term ).
thf(func_def_509,type,
sK367: ( subst > term > subst > $o ) > term ).
thf(func_def_510,type,
sK368: ( subst > term > subst > $o ) > term ).
thf(func_def_511,type,
sK369: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_512,type,
sK370: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_513,type,
sK371: ( subst > term > term ) > term ).
thf(func_def_514,type,
sK372: ( subst > term > term ) > subst ).
thf(func_def_515,type,
sK373: ( subst > term > term ) > subst ).
thf(func_def_516,type,
sK374: ( term > $o ) > term ).
thf(func_def_517,type,
sK375: ( term > $o ) > term ).
thf(func_def_518,type,
sK376: term ).
thf(func_def_519,type,
sK377: term > $o ).
thf(func_def_520,type,
sK378: subst > term > subst > $o ).
thf(func_def_521,type,
sK379: ( subst > term > subst > $o ) > subst ).
thf(func_def_522,type,
sK380: ( subst > term > subst > $o ) > subst ).
thf(func_def_523,type,
sK381: ( subst > term > subst > $o ) > term ).
thf(func_def_524,type,
sK382: ( subst > term > subst > $o ) > subst ).
thf(func_def_525,type,
sK383: ( subst > term > subst > $o ) > subst ).
thf(func_def_526,type,
sK384: ( subst > term > subst > $o ) > subst ).
thf(func_def_527,type,
sK385: ( subst > term > subst > $o ) > term ).
thf(func_def_528,type,
sK386: ( subst > term > subst > $o ) > subst ).
thf(func_def_529,type,
sK387: ( term > $o ) > term > term ).
thf(func_def_530,type,
sK388: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_531,type,
sK389: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_532,type,
sK390: ( subst > term > term ) > subst ).
thf(func_def_533,type,
sK391: ( subst > term > term ) > subst ).
thf(func_def_534,type,
sK392: ( subst > term > term ) > term ).
thf(func_def_535,type,
sK393: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_536,type,
sK394: term ).
thf(func_def_537,type,
sK395: subst > term > subst > $o ).
thf(func_def_538,type,
sK396: ( subst > term > term ) > subst ).
thf(func_def_539,type,
sK397: ( subst > term > term ) > subst ).
thf(func_def_540,type,
sK398: ( subst > term > term ) > term ).
thf(func_def_541,type,
sK399: ( subst > term > term ) > term ).
thf(func_def_542,type,
sK400: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_543,type,
sK401: ( subst > term > subst > $o ) > term > term ).
thf(func_def_544,type,
sK402: term ).
thf(func_def_545,type,
sK403: subst > term > subst > $o ).
thf(func_def_546,type,
sK404: ( subst > term > term ) > term ).
thf(func_def_547,type,
sK405: ( subst > term > term ) > subst ).
thf(func_def_548,type,
sK406: ( subst > term > term ) > subst ).
thf(func_def_549,type,
sK407: ( subst > term > term ) > term ).
thf(func_def_550,type,
sK408: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_551,type,
sK409: ( subst > term > subst > $o ) > term > term ).
thf(func_def_552,type,
sK410: term ).
thf(func_def_553,type,
sK411: subst > term > subst > $o ).
thf(func_def_554,type,
sK412: ( subst > term > subst > $o ) > subst ).
thf(func_def_555,type,
sK413: ( subst > term > subst > $o ) > subst ).
thf(func_def_556,type,
sK414: ( subst > term > subst > $o ) > term ).
thf(func_def_557,type,
sK415: ( subst > term > subst > $o ) > subst ).
thf(func_def_558,type,
sK416: ( subst > term > subst > $o ) > term ).
thf(func_def_559,type,
sK417: ( subst > term > subst > $o ) > term ).
thf(func_def_560,type,
sK418: ( subst > term > subst > $o ) > subst ).
thf(func_def_561,type,
sK419: ( subst > term > subst > $o ) > subst ).
thf(func_def_562,type,
sK420: ( subst > term > subst > $o ) > subst ).
thf(func_def_563,type,
sK421: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_564,type,
sK422: ( subst > term > term ) > subst ).
thf(func_def_565,type,
sK423: ( subst > term > term ) > term ).
thf(func_def_566,type,
sK424: ( subst > term > term ) > subst ).
thf(func_def_567,type,
sK425: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_568,type,
sK426: ( subst > term > subst > $o ) > term ).
thf(func_def_569,type,
sK427: ( subst > term > subst > $o ) > term ).
thf(func_def_570,type,
sK428: subst > term > subst > $o ).
thf(func_def_571,type,
sK429: term > $o ).
thf(func_def_572,type,
sK430: term ).
thf(func_def_573,type,
sK431: ( subst > term > term ) > subst ).
thf(func_def_574,type,
sK432: ( subst > term > term ) > term ).
thf(func_def_575,type,
sK433: ( subst > term > term ) > subst ).
thf(func_def_576,type,
sK434: ( subst > term > term ) > term ).
thf(func_def_577,type,
sK435: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_578,type,
sK436: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_579,type,
sK437: term > ( term > $o ) > term ).
thf(func_def_580,type,
sK438: subst > term > subst > $o ).
thf(func_def_581,type,
sK439: term ).
thf(func_def_582,type,
sK440: ( subst > term > subst > $o ) > subst ).
thf(func_def_583,type,
sK441: ( subst > term > subst > $o ) > term ).
thf(func_def_584,type,
sK442: ( subst > term > subst > $o ) > subst ).
thf(func_def_585,type,
sK443: ( subst > term > subst > $o ) > subst ).
thf(func_def_586,type,
sK444: term > ( subst > term > subst > $o ) > term ).
thf(func_def_587,type,
sK445: ( subst > term > subst > $o ) > subst ).
thf(func_def_588,type,
sK446: ( subst > term > subst > $o ) > subst ).
thf(func_def_589,type,
sK447: ( subst > term > subst > $o ) > subst ).
thf(func_def_590,type,
sK448: ( subst > term > subst > $o ) > term ).
thf(func_def_591,type,
sK449: ( subst > term > term ) > term ).
thf(func_def_592,type,
sK450: ( subst > term > term ) > subst ).
thf(func_def_593,type,
sK451: ( subst > term > term ) > subst ).
thf(func_def_594,type,
sK452: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_595,type,
sK453: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_596,type,
sK454: term ).
thf(func_def_597,type,
sK455: term ).
thf(func_def_598,type,
sK456: term ).
thf(func_def_599,type,
sK457: term ).
thf(func_def_600,type,
sK458: subst ).
thf(func_def_601,type,
sK459: term ).
thf(func_def_602,type,
sK460: term ).
thf(func_def_603,type,
sK461: term ).
thf(func_def_604,type,
sK462: subst ).
thf(func_def_605,type,
sK463: term ).
thf(func_def_606,type,
sK464: term ).
thf(func_def_607,type,
sK465: term > $o ).
thf(func_def_608,type,
sK466: subst ).
thf(func_def_609,type,
sK467: term > $o ).
thf(func_def_610,type,
sK468: term ).
thf(func_def_611,type,
sK469: subst ).
thf(func_def_612,type,
sK470: subst ).
thf(func_def_613,type,
sK471: term ).
thf(func_def_614,type,
sK472: subst ).
thf(func_def_615,type,
sK473: term ).
thf(func_def_616,type,
sK474: subst ).
thf(func_def_617,type,
sK475: term ).
thf(func_def_618,type,
sK476: subst ).
thf(func_def_619,type,
sK477: term ).
thf(func_def_620,type,
sK478: term > $o ).
thf(func_def_621,type,
sK479: term > $o ).
thf(func_def_622,type,
sK480: ( subst > term > term ) > term ).
thf(func_def_623,type,
sK481: ( subst > term > term ) > subst ).
thf(func_def_624,type,
sK482: ( subst > term > term ) > subst ).
thf(func_def_625,type,
sK483: subst > term > term ).
thf(func_def_626,type,
sK484: term ).
thf(func_def_627,type,
sK485: term ).
thf(func_def_628,type,
sK486: term ).
thf(func_def_629,type,
sK487: term ).
thf(func_def_630,type,
sK488: term ).
thf(func_def_631,type,
sK489: term ).
thf(func_def_632,type,
sK490: term ).
thf(func_def_633,type,
sK491: term ).
thf(func_def_634,type,
sK492: term ).
thf(func_def_635,type,
sK493: term ).
thf(func_def_636,type,
sK494: term ).
thf(func_def_637,type,
sK495: term ).
thf(func_def_638,type,
sK496: term > subst > term > term ).
thf(func_def_639,type,
sK497: term ).
thf(func_def_640,type,
sK498: term > subst > term > term ).
thf(func_def_641,type,
sK499: term ).
thf(func_def_642,type,
sK500: ( subst > term > term ) > term ).
thf(func_def_643,type,
sK501: ( subst > term > term ) > subst ).
thf(func_def_644,type,
sK502: subst > ( term > $o ) > ( term > $o ) > term > term ).
thf(func_def_645,type,
sK503: term ).
thf(func_def_646,type,
sK504: subst ).
thf(func_def_647,type,
sK505: term ).
thf(func_def_648,type,
sK506: term > $o ).
thf(func_def_649,type,
sK507: term > $o ).
thf(func_def_650,type,
sK508: subst ).
thf(func_def_651,type,
sK509: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_652,type,
sK510: subst > term > subst > $o ).
thf(func_def_653,type,
sK511: ( term > $o ) > term ).
thf(func_def_654,type,
sK512: term ).
thf(func_def_655,type,
sK513: term ).
thf(func_def_656,type,
sK514: term ).
thf(func_def_657,type,
sK515: term ).
thf(func_def_658,type,
sK516: term > $o ).
thf(func_def_659,type,
sK517: subst ).
thf(func_def_660,type,
sK518: term ).
thf(func_def_661,type,
sK519: ( term > $o ) > term ).
thf(func_def_662,type,
sK520: term > subst > ( term > $o ) > term > $o ).
thf(func_def_663,type,
sK521: subst ).
thf(func_def_664,type,
sK522: subst ).
thf(func_def_665,type,
sK523: subst ).
thf(func_def_666,type,
sK524: subst ).
thf(func_def_667,type,
sK525: subst ).
thf(func_def_668,type,
sK526: term > ( term > $o ) > subst > ( term > $o ) > term ).
thf(func_def_669,type,
sK527: term > $o ).
thf(func_def_670,type,
sK528: subst ).
thf(func_def_671,type,
sK529: term > $o ).
thf(func_def_672,type,
sK530: term ).
thf(func_def_673,type,
sK531: term ).
thf(func_def_674,type,
sK532: term ).
thf(func_def_675,type,
sK533: term ).
thf(func_def_676,type,
sK534: term ).
thf(func_def_677,type,
sK535: term ).
thf(func_def_678,type,
sK536: term > subst > term > term ).
thf(func_def_679,type,
sK537: term ).
thf(func_def_680,type,
sK538: ( subst > term > term ) > term ).
thf(func_def_681,type,
sK539: ( subst > term > term ) > subst ).
thf(func_def_682,type,
sK540: term > subst > term > term ).
thf(func_def_683,type,
sK541: subst ).
thf(func_def_684,type,
sK542: term ).
thf(func_def_685,type,
sK543: term ).
thf(func_def_686,type,
sK544: term ).
thf(func_def_687,type,
sK545: term ).
thf(func_def_688,type,
sK546: term ).
thf(func_def_689,type,
sK547: term ).
thf(func_def_690,type,
sK548: term ).
thf(func_def_691,type,
sK549: term ).
thf(func_def_692,type,
sK550: term ).
thf(func_def_693,type,
sK551: term ).
thf(func_def_694,type,
sK552: subst ).
thf(func_def_695,type,
sK553: term ).
thf(func_def_696,type,
sK554: term > $o ).
thf(func_def_697,type,
sK555: ( term > $o ) > term ).
thf(func_def_698,type,
sK556: ( term > $o ) > term > subst > term > $o ).
thf(func_def_699,type,
sK557: term ).
thf(func_def_700,type,
sK558: term ).
thf(func_def_701,type,
sK559: term ).
thf(func_def_702,type,
sK560: term ).
thf(func_def_703,type,
sK561: term ).
thf(func_def_704,type,
sK562: term ).
thf(func_def_705,type,
sK563: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_706,type,
sK564: subst > term > subst > $o ).
thf(func_def_707,type,
sK565: ( term > $o ) > term ).
thf(func_def_708,type,
sK566: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_709,type,
sK567: term ).
thf(func_def_710,type,
sK568: subst > term > subst > $o ).
thf(func_def_711,type,
sK569: ( subst > term > term ) > term ).
thf(func_def_712,type,
sK570: ( subst > term > term ) > subst ).
thf(func_def_713,type,
sK571: ( subst > term > term ) > subst ).
thf(func_def_714,type,
sK572: ( subst > term > term ) > term ).
thf(func_def_715,type,
sK573: subst ).
thf(func_def_716,type,
sK574: subst > d_subst ).
thf(func_def_717,type,
sK575: term ).
thf(func_def_718,type,
sK576: ( term > $o ) > term ).
thf(func_def_719,type,
sK577: ( term > $o ) > term ).
thf(func_def_720,type,
sK578: term ).
thf(func_def_721,type,
sK579: term > $o ).
thf(func_def_722,type,
sK580: term > d_term ).
thf(func_def_723,type,
sK581: subst ).
thf(func_def_724,type,
sK582: term ).
thf(func_def_725,type,
sK583: subst > term > term ).
thf(func_def_726,type,
sK584: subst > term > term ).
thf(func_def_727,type,
sK585: ( subst > term > term ) > term ).
thf(func_def_728,type,
sK586: ( subst > term > term ) > subst ).
thf(func_def_729,type,
sK587: ( subst > term > term ) > subst ).
thf(func_def_730,type,
sK588: ( subst > term > term ) > subst ).
thf(func_def_731,type,
sK589: ( subst > term > term ) > term ).
thf(func_def_732,type,
sK590: ( subst > term > term ) > subst ).
thf(func_def_734,type,
sK592: subst > term > subst > $o ).
thf(func_def_735,type,
sK593: term > $o ).
thf(func_def_736,type,
sK594: ( subst > term > term ) > subst ).
thf(func_def_737,type,
sK595: ( subst > term > term ) > term ).
thf(func_def_738,type,
sK596: ( subst > term > term ) > term ).
thf(func_def_739,type,
sK597: ( subst > term > term ) > subst ).
thf(func_def_740,type,
sK598: term ).
thf(func_def_741,type,
sK599: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_742,type,
sK600: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_743,type,
sK601: term > ( term > $o ) > term ).
thf(func_def_744,type,
sK602: term > ( term > $o ) > term ).
thf(func_def_745,type,
sK603: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_746,type,
sK604: term > ( term > $o ) > term ).
thf(func_def_747,type,
sK605: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_748,type,
sK606: term > ( term > $o ) > term ).
thf(func_def_750,type,
ph607:
!>[X0: $tType] : X0 ).
thf(f6955,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2084,f2438,f2549,f3134,f3781,f3809,f3991,f4282,f4291,f4331,f4348,f4364,f4464,f4579,f5462,f6673,f6744,f6750,f6780,f6792,f6951]) ).
thf(f6951,plain,
( ~ spl591_290
| ~ spl591_512
| ~ spl591_514
| ~ spl591_536 ),
inference(avatar_contradiction_clause,[status(thm)],[f6950]) ).
thf(f6950,plain,
( $false
| ~ spl591_290
| ~ spl591_512
| ~ spl591_514
| ~ spl591_536 ),
inference(trivial_inequality_removal,[status(thm)],[f6949]) ).
thf(f6949,plain,
( ( $false = $true )
| ~ spl591_290
| ~ spl591_512
| ~ spl591_514
| ~ spl591_536 ),
inference(forward_demodulation,[status(thm)],[f6948,f6888]) ).
thf(f6888,plain,
( ! [X1: subst > term > subst > $o,X4: term] :
( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ~ spl591_512
| ~ spl591_514 ),
inference(trivial_inequality_removal,[status(thm)],[f6842]) ).
thf(f6842,plain,
( ! [X1: subst > term > subst > $o,X4: term] :
( ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( $false = $true ) )
| ~ spl591_512
| ~ spl591_514 ),
inference(backward_demodulation,[status(thm)],[f4290,f4267]) ).
thf(f4267,plain,
( ! [X1: subst > term > subst > $o] :
( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl591_512 ),
inference(avatar_component_clause,[status(thm)],[f4266]) ).
thf(f4266,definition,
( spl591_512
<=> ! [X1: subst > term > subst > $o] :
( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_512])],[avatar_definition]) ).
thf(f4290,plain,
( ! [X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_514 ),
inference(avatar_component_clause,[status(thm)],[f4289]) ).
thf(f4289,definition,
( spl591_514
<=> ! [X4: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl591_514])],[avatar_definition]) ).
thf(f6948,plain,
( ! [X4: subst > term > term] :
( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ~ spl591_290
| ~ spl591_512
| ~ spl591_514
| ~ spl591_536 ),
inference(trivial_inequality_removal,[status(thm)],[f6947]) ).
thf(f6947,plain,
( ! [X4: subst > term > term] :
( ( $false = $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290
| ~ spl591_512
| ~ spl591_514
| ~ spl591_536 ),
inference(forward_demodulation,[status(thm)],[f6946,f6888]) ).
thf(f6946,plain,
( ! [X4: subst > term > term] :
( ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290
| ~ spl591_536 ),
inference(subsumption_resolution,[status(thm)],[f3133,f4463]) ).
thf(f4463,plain,
( ! [X218: term,X219: term] : ( X218 = X219 )
| ~ spl591_536 ),
inference(avatar_component_clause,[status(thm)],[f4462]) ).
thf(f4462,definition,
( spl591_536
<=> ! [X219: term,X218: term] : ( X218 = X219 ) ),
introduced(definition,[new_symbols(naming,[spl591_536])],[avatar_definition]) ).
thf(f3133,plain,
( ! [X4: subst > term > term] :
( ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290 ),
inference(avatar_component_clause,[status(thm)],[f3132]) ).
thf(f3132,definition,
( spl591_290
<=> ! [X4: subst > term > term] :
( ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl591_290])],[avatar_definition]) ).
thf(f6792,plain,
( ~ spl591_519
| ~ spl591_521
| ~ spl591_523 ),
inference(avatar_contradiction_clause,[status(thm)],[f6791]) ).
thf(f6791,plain,
( $false
| ~ spl591_519
| ~ spl591_521
| ~ spl591_523 ),
inference(trivial_inequality_removal,[status(thm)],[f6788]) ).
thf(f6788,plain,
( ( $false = $true )
| ~ spl591_519
| ~ spl591_521
| ~ spl591_523 ),
inference(backward_demodulation,[status(thm)],[f4359,f6783]) ).
thf(f6783,plain,
( ! [X1: term] :
( $false
= ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ~ spl591_519
| ~ spl591_521 ),
inference(trivial_inequality_removal,[status(thm)],[f6781]) ).
thf(f6781,plain,
( ! [X1: term] :
( ( $false = $true )
| ( $false
= ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_519
| ~ spl591_521 ),
inference(backward_demodulation,[status(thm)],[f4347,f4339]) ).
thf(f4339,plain,
( ! [X1: term] :
( $false
= ( sK593 @ X1 ) )
| ~ spl591_519 ),
inference(avatar_component_clause,[status(thm)],[f4338]) ).
thf(f4338,definition,
( spl591_519
<=> ! [X1: term] :
( $false
= ( sK593 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_519])],[avatar_definition]) ).
thf(f4347,plain,
( ! [X1: term] :
( ( $false
= ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK593 @ X1 ) ) )
| ~ spl591_521 ),
inference(avatar_component_clause,[status(thm)],[f4346]) ).
thf(f4346,definition,
( spl591_521
<=> ! [X1: term] :
( ( $true
= ( sK593 @ X1 ) )
| ( $false
= ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_521])],[avatar_definition]) ).
thf(f4359,plain,
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ~ spl591_523 ),
inference(avatar_component_clause,[status(thm)],[f4357]) ).
thf(f4357,definition,
( spl591_523
<=> ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_523])],[avatar_definition]) ).
thf(f6780,plain,
( spl591_519
| ~ spl591_517
| ~ spl591_536 ),
inference(avatar_split_clause,[status(thm)],[f6777,f4462,f4328,f4338]) ).
thf(f4328,definition,
( spl591_517
<=> ( $false
= ( sK593 @ ( lam @ sK598 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_517])],[avatar_definition]) ).
thf(f6777,plain,
( ! [X0: term] :
( $false
= ( sK593 @ X0 ) )
| ~ spl591_517
| ~ spl591_536 ),
inference(superposition,[status(thm)],[f4330,f4463]) ).
thf(f4330,plain,
( ( $false
= ( sK593 @ ( lam @ sK598 ) ) )
| ~ spl591_517 ),
inference(avatar_component_clause,[status(thm)],[f4328]) ).
thf(f6750,plain,
( ~ spl591_125
| ~ spl591_516 ),
inference(avatar_contradiction_clause,[status(thm)],[f6749]) ).
thf(f6749,plain,
( $false
| ~ spl591_125
| ~ spl591_516 ),
inference(trivial_inequality_removal,[status(thm)],[f6748]) ).
thf(f6748,plain,
( ( $false = $true )
| ~ spl591_125
| ~ spl591_516 ),
inference(forward_demodulation,[status(thm)],[f2437,f4326]) ).
thf(f4326,plain,
( ( hoasinduction_lem3v2a = $false )
| ~ spl591_516 ),
inference(avatar_component_clause,[status(thm)],[f4324]) ).
thf(f4324,definition,
( spl591_516
<=> ( hoasinduction_lem3v2a = $false ) ),
introduced(definition,[new_symbols(naming,[spl591_516])],[avatar_definition]) ).
thf(f2437,plain,
( ( hoasinduction_lem3v2a = $true )
| ~ spl591_125 ),
inference(avatar_component_clause,[status(thm)],[f2435]) ).
thf(f2435,definition,
( spl591_125
<=> ( hoasinduction_lem3v2a = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_125])],[avatar_definition]) ).
thf(f6744,plain,
( ~ spl591_290
| spl591_438
| ~ spl591_444
| ~ spl591_509
| ~ spl591_536 ),
inference(avatar_contradiction_clause,[status(thm)],[f6743]) ).
thf(f6743,plain,
( $false
| ~ spl591_290
| spl591_438
| ~ spl591_444
| ~ spl591_509
| ~ spl591_536 ),
inference(trivial_inequality_removal,[status(thm)],[f6742]) ).
thf(f6742,plain,
( ( $false = $true )
| ~ spl591_290
| spl591_438
| ~ spl591_444
| ~ spl591_509
| ~ spl591_536 ),
inference(backward_demodulation,[status(thm)],[f5350,f6741]) ).
thf(f6741,plain,
( ! [X3: term] :
( $false
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) )
| spl591_438
| ~ spl591_444
| ~ spl591_509
| ~ spl591_536 ),
inference(trivial_inequality_removal,[status(thm)],[f6739]) ).
thf(f6739,plain,
( ! [X3: term] :
( ( $false
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) )
| ( $false = $true ) )
| spl591_438
| ~ spl591_444
| ~ spl591_509
| ~ spl591_536 ),
inference(backward_demodulation,[status(thm)],[f3808,f6731]) ).
thf(f6731,plain,
( ! [X0: term] :
( ( sK429 @ X0 )
= $false )
| spl591_438
| ~ spl591_509
| ~ spl591_536 ),
inference(superposition,[status(thm)],[f6123,f4463]) ).
thf(f6123,plain,
( ( $false
= ( sK429 @ ( d2term @ d_one ) ) )
| spl591_438
| ~ spl591_509
| ~ spl591_536 ),
inference(trivial_inequality_removal,[status(thm)],[f6120]) ).
thf(f6120,plain,
( ( $true != $true )
| ( $false
= ( sK429 @ ( d2term @ d_one ) ) )
| spl591_438
| ~ spl591_509
| ~ spl591_536 ),
inference(superposition,[status(thm)],[f6103,f4252]) ).
thf(f4252,plain,
( ! [X2: term > $o] :
( ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) ) )
| ~ spl591_509 ),
inference(avatar_component_clause,[status(thm)],[f4251]) ).
thf(f4251,definition,
( spl591_509
<=> ! [X2: term > $o] :
( ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( $true
= ( X2 @ ( d2term @ d_one ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_509])],[avatar_definition]) ).
thf(f6103,plain,
( ! [X0: term] :
( ( sK429 @ X0 )
!= $true )
| spl591_438
| ~ spl591_536 ),
inference(superposition,[status(thm)],[f3780,f4463]) ).
thf(f3780,plain,
( ( ( sK429 @ ( lam @ sK430 ) )
!= $true )
| spl591_438 ),
inference(avatar_component_clause,[status(thm)],[f3778]) ).
thf(f3778,definition,
( spl591_438
<=> ( ( sK429 @ ( lam @ sK430 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_438])],[avatar_definition]) ).
thf(f3808,plain,
( ! [X3: term] :
( ( ( sK429 @ X3 )
= $true )
| ( $false
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_444 ),
inference(avatar_component_clause,[status(thm)],[f3807]) ).
thf(f3807,definition,
( spl591_444
<=> ! [X3: term] :
( ( ( sK429 @ X3 )
= $true )
| ( $false
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_444])],[avatar_definition]) ).
thf(f5350,plain,
( ( ( sK428 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ~ spl591_290 ),
inference(subsumption_resolution,[status(thm)],[f5349,f4219]) ).
thf(f4219,plain,
! [X2: term,X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4138,f4191]) ).
thf(f4191,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP11 @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4190,f4091]) ).
thf(f4091,plain,
! [X258: term] :
( ( d2term @ d_one )
= X258 ),
inference(backward_demodulation,[status(thm)],[f1057,f1159]) ).
thf(f1159,plain,
! [X119: d_term] : ( d_one = X119 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP58 != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( sK457 != sK456 )
& ( ( ap @ ( sub @ sK454 @ id ) @ sK457 )
= ( ap @ ( sub @ sK455 @ id ) @ sK456 ) ) ) )
& ( ! [X4: term,X5: term,X6: term,X7: term] :
( ( X6 = X7 )
| ( ( ap @ ( sub @ X4 @ id ) @ X7 )
!= ( ap @ ( sub @ X5 @ id ) @ X6 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( axscons = $true )
| ( sK458
!= ( push @ ( sub @ one @ sK458 ) @ ( comp @ sh @ sK458 ) ) ) )
& ( ! [X9: subst] :
( ( push @ ( sub @ one @ X9 ) @ ( comp @ sh @ X9 ) )
= X9 )
| ( axscons != $true ) )
& ( ! [X10: term,X11: term] :
( ( X10 = X11 )
| ( ( lam @ X10 )
!= ( lam @ X11 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ( ( sK459 != sK460 )
& ( ( lam @ sK460 )
= ( lam @ sK459 ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ( sK461
!= ( sub @ sK461 @ id ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
| ( sK462
!= ( comp @ sh @ ( push @ sK463 @ sK462 ) ) ) )
& ( ! [X18: subst,X19: term] :
( ( comp @ sh @ ( push @ X19 @ X18 ) )
= X18 )
| ( axshiftcons != $true ) )
& ! [X20: d_subst] : ( d_id = X20 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK465 @ ( sub @ sK468 @ ( push @ sK464 @ sK466 ) ) )
!= $true )
& ( ( sK467 @ sK468 )
= $true ) ) )
& ( ! [X26: term,X27: term > $o,X28: subst,X29: term > $o,X30: term] :
( ( ( X27 @ ( sub @ X30 @ ( push @ X26 @ X28 ) ) )
= $true )
| ( ( X29 @ X30 )
!= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( substmonoid = $true )
| ( ( comp @ id @ sK469 )
!= sK469 )
| ( ( comp @ sK470 @ id )
!= sK470 ) )
& ( ( ! [X33: subst] :
( ( comp @ id @ X33 )
= X33 )
& ! [X34: subst] :
( ( comp @ X34 @ id )
= X34 ) )
| ( substmonoid != $true ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( sK472
!= ( comp @ sh @ ( push @ sK471 @ sK472 ) ) )
| ( ( sub @ one @ ( push @ sK473 @ sK474 ) )
!= sK473 )
| ! [X39: term,X40: subst,X41: term,X42: term > $o,X43: term > $o] :
( ( ( X43 @ ( sub @ X41 @ ( push @ X39 @ X40 ) ) )
= $true )
| ( ( X42 @ X41 )
!= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X44: term,X45: subst] :
( ( comp @ sh @ ( push @ X44 @ X45 ) )
= X45 )
& ! [X46: term,X47: subst] :
( ( sub @ one @ ( push @ X46 @ X47 ) )
= X46 )
& ( ( sK479 @ ( sub @ sK477 @ ( push @ sK475 @ sK476 ) ) )
!= $true )
& ( ( sK478 @ sK477 )
= $true ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X53: subst > term > term,X54: term,X55: term] :
( ( ( X53 @ ( comp @ ( sK481 @ X53 ) @ ( sK482 @ X53 ) ) @ ( sub @ ( sK480 @ X53 ) @ ( sK482 @ X53 ) ) )
!= ( sub @ ( X53 @ ( sK481 @ X53 ) @ ( sK480 @ X53 ) ) @ ( sK482 @ X53 ) ) )
| ( ( lam @ ( X53 @ sh @ one ) )
!= ( ap @ ( sub @ X54 @ id ) @ X55 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ( ! [X62: term,X63: subst,X64: subst] :
( ( sK483 @ ( comp @ X63 @ X64 ) @ ( sub @ X62 @ X64 ) )
= ( sub @ ( sK483 @ X63 @ X62 ) @ X64 ) )
& ( ( ap @ ( sub @ sK484 @ id ) @ sK485 )
= ( lam @ ( sK483 @ sh @ one ) ) ) ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( sP52 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP52 != $true ) )
& ( hoasinduction_gthm = $true )
& ! [X65: d_subst,X66: d_subst] :
( ( ( d2subst @ X66 )
!= ( d2subst @ X65 ) )
| ( X65 = X66 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( induction2lem_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ( ( sK486 != sK487 )
& ( ( ap @ sK488 @ sK487 )
= ( ap @ sK489 @ sK486 ) ) )
| ! [X71: term,X72: term,X73: term,X74: term] :
( ( X71 = X73 )
| ( ( ap @ ( sub @ X72 @ id ) @ X71 )
!= ( ap @ ( sub @ X74 @ id ) @ X73 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X75: term,X76: term,X77: term,X78: term] :
( ( X75 = X76 )
| ( ( ap @ X77 @ X76 )
!= ( ap @ X78 @ X75 ) ) )
& ( sK490 != sK492 )
& ( ( ap @ ( sub @ sK493 @ id ) @ sK492 )
= ( ap @ ( sub @ sK491 @ id ) @ sK490 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
| ( ! [X83: term] :
( ( sub @ X83 @ id )
= X83 )
& ( sK494
!= ( sub @ sK494 @ id ) ) ) )
& ( ( sK495
!= ( sub @ sK495 @ id ) )
| ! [X86: term] :
( ( sub @ X86 @ id )
= X86 )
| ( termmset_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP46 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP46 ) )
& ( ! [X87: term] :
( ( sub @ X87 @ ( push @ one @ sh ) )
= ( sK496 @ X87 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X90: subst > term > term] :
( ( sub @ sK497 @ ( push @ one @ sh ) )
!= ( X90 @ sh @ one ) ) )
& ( ( induction2lem = $true )
| ( sP45 != $true ) )
& ( ( sP45 = $true )
| ( induction2lem != $true ) )
& ( ! [X91: term,X93: term,X94: subst] :
( ( sK498 @ X91 @ X94 @ X93 )
= ( sub @ X91 @ ( push @ X93 @ X94 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X96: subst > term > term] :
( ( X96 @ ( sK501 @ X96 ) @ ( sK500 @ X96 ) )
!= ( sub @ sK499 @ ( push @ ( sK500 @ X96 ) @ ( sK501 @ X96 ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X99: term,X100: term > $o,X101: term > $o,X102: subst] :
( ( ( X101 @ one )
= $true )
| ( ( X101 @ ( sK502 @ X102 @ X101 @ X100 @ X99 ) )
!= ( X100 @ ( sub @ ( sK502 @ X102 @ X101 @ X100 @ X99 ) @ ( push @ X99 @ X102 ) ) ) )
| ( ( X100 @ X99 )
!= $true ) )
| ( ( sub @ one @ ( push @ sK503 @ sK504 ) )
!= sK503 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ( $true
!= ( sK507 @ one ) )
& ! [X110: term] :
( ( sK507 @ X110 )
= ( sK506 @ ( sub @ X110 @ ( push @ sK505 @ sK508 ) ) ) )
& ( ( sK506 @ sK505 )
= $true )
& ! [X111: term,X112: subst] :
( ( sub @ one @ ( push @ X111 @ X112 ) )
= X111 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X113: subst > term > subst > $o,X115: term] :
( ( sK509 @ X113 @ X115 )
= ( X113 @ id @ X115 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X117: term > $o] :
( ( X117 @ ( sK511 @ X117 ) )
!= ( sK510 @ id @ ( sK511 @ X117 ) @ id ) ) )
& ( ( sP43 = $true )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( sP43 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP35 != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP34 != $true ) )
& ( ( sP34 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X119: d_term] : ( d_one = X119 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X120: term,X121: term,X122: term,X123: term] :
( ( X120 = X122 )
| ( ( ap @ X120 @ X121 )
!= ( ap @ X122 @ X123 ) ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ( ( sK512 != sK514 )
& ( ( ap @ sK512 @ sK513 )
= ( ap @ sK514 @ sK515 ) ) ) )
& ( ( pushprop_lem0 = $true )
| ! [X131: term > $o] :
( ( sK516 @ ( sub @ ( sK519 @ X131 ) @ ( push @ sK518 @ sK517 ) ) )
!= ( X131 @ ( sK519 @ X131 ) ) ) )
& ( ! [X133: term > $o,X134: subst,X135: term,X137: term] :
( ( sK520 @ X135 @ X134 @ X133 @ X137 )
= ( X133 @ ( sub @ X137 @ ( push @ X135 @ X134 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( axidl = $true )
| ( ( comp @ id @ sK521 )
!= sK521 ) )
& ( ! [X139: subst] :
( ( comp @ id @ X139 )
= X139 )
| ( axidl != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( ( comp @ id @ sK522 )
!= sK522 )
| ( ( comp @ sK523 @ id )
!= sK523 )
| ( ! [X142: subst] :
( ( comp @ X142 @ id )
= X142 )
& ! [X143: subst] :
( ( comp @ id @ X143 )
= X143 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X144: subst] :
( ( comp @ id @ X144 )
= X144 )
& ! [X145: subst] :
( ( comp @ X145 @ id )
= X145 )
& ( ( sK524
!= ( comp @ sK524 @ id ) )
| ( sK525
!= ( comp @ id @ sK525 ) ) ) ) )
& ( ! [X148: term > $o,X149: subst,X150: term > $o,X151: term] :
( ( ( X150 @ one )
= $true )
| ( ( X148 @ X151 )
!= $true )
| ( ( X148 @ ( sub @ ( sK526 @ X151 @ X150 @ X149 @ X148 ) @ ( push @ X151 @ X149 ) ) )
!= ( X150 @ ( sK526 @ X151 @ X150 @ X149 @ X148 ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ( $true
!= ( sK529 @ one ) )
& ( ( sK527 @ sK530 )
= $true )
& ! [X157: term] :
( ( sK529 @ X157 )
= ( sK527 @ ( sub @ X157 @ ( push @ sK530 @ sK528 ) ) ) ) ) )
& ( axapp = $true )
& ( ! [X158: term,X159: term,X160: term,X161: term] :
( ( ( ap @ ( sub @ X158 @ id ) @ X160 )
!= ( ap @ ( sub @ X161 @ id ) @ X159 ) )
| ( X158 = X161 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( ( ap @ ( sub @ sK534 @ id ) @ sK532 )
= ( ap @ ( sub @ sK531 @ id ) @ sK533 ) )
& ( sK531 != sK534 ) ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X167: subst > term > term] :
( ( X167 @ sh @ one )
!= ( sub @ sK535 @ ( push @ one @ sh ) ) ) )
& ( ! [X168: term] :
( ( sub @ X168 @ ( push @ one @ sh ) )
= ( sK536 @ X168 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X171: subst > term > term] :
( ( sub @ sK537 @ ( push @ ( sK538 @ X171 ) @ ( sK539 @ X171 ) ) )
!= ( X171 @ ( sK539 @ X171 ) @ ( sK538 @ X171 ) ) ) )
& ( ! [X174: term,X176: term,X177: subst] :
( ( sK540 @ X174 @ X177 @ X176 )
= ( sub @ X174 @ ( push @ X176 @ X177 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( induction2_lthm = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( induction2_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
| ( ( sub @ one @ ( push @ sK542 @ sK541 ) )
!= sK542 ) )
& ( ! [X180: subst,X181: term] :
( ( sub @ one @ ( push @ X181 @ X180 ) )
= X181 )
| ( axvarcons != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ( sK545 != sK544 )
& ( ( ap @ ( sub @ sK545 @ id ) @ sK546 )
= ( ap @ ( sub @ sK544 @ id ) @ sK543 ) )
& ! [X186: term,X187: term,X188: term,X189: term] :
( ( X187 = X189 )
| ( ( ap @ X189 @ X186 )
!= ( ap @ X187 @ X188 ) ) )
& ! [X190: term] :
( ( sub @ X190 @ id )
= X190 ) ) )
& ( ! [X191: term,X192: term,X193: term,X194: term] :
( ( X192 = X193 )
| ( ( ap @ ( sub @ X193 @ id ) @ X194 )
!= ( ap @ ( sub @ X192 @ id ) @ X191 ) ) )
| ( ( sK550 != sK548 )
& ( ( ap @ sK548 @ sK549 )
= ( ap @ sK550 @ sK547 ) ) )
| ( ( sub @ sK551 @ id )
!= sK551 )
| ( hoasapinj1_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X203: term > $o] :
( ( X203 @ ( sK555 @ X203 ) )
!= ( sK554 @ ( sub @ ( sK555 @ X203 ) @ ( push @ sK553 @ sK552 ) ) ) ) )
& ( ! [X205: subst,X206: term,X207: term > $o,X209: term] :
( ( sK556 @ X207 @ X206 @ X205 @ X209 )
= ( X207 @ ( sub @ X209 @ ( push @ X206 @ X205 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( sP28 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP28 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( sP27 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP27 != $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X210: term,X211: term,X212: term,X213: term] :
( ( X210 = X211 )
| ( ( ap @ X213 @ X210 )
!= ( ap @ X212 @ X211 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( sK557 != sK558 )
& ( ( ap @ sK560 @ sK557 )
= ( ap @ sK559 @ sK558 ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X218: term,X219: term] :
( ( X218 = X219 )
| ( ( sub @ X219 @ sh )
!= ( sub @ X218 @ sh ) ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ( ( sK561 != sK562 )
& ( ( sub @ sK561 @ sh )
= ( sub @ sK562 @ sh ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ! [X222: subst > term > subst > $o,X224: term] :
( ( X222 @ id @ X224 @ id )
= ( sK563 @ X222 @ X224 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ! [X226: term > $o] :
( ( sK564 @ id @ ( sK565 @ X226 ) @ id )
!= ( X226 @ ( sK565 @ X226 ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X228: term,X229: subst > term > subst > $o] :
( ( ! [X231: term,X232: subst,X233: subst] :
( ( sK566 @ X229 @ ( comp @ X233 @ X232 ) @ ( sub @ X231 @ X232 ) )
= ( sub @ ( sK566 @ X229 @ X233 @ X231 ) @ X232 ) )
& ! [X234: term] :
( ( $true
= ( X229 @ id @ ( sK566 @ X229 @ id @ X234 ) @ id ) )
| ( ( X229 @ id @ X234 @ id )
!= $true ) )
& ( $true
!= ( X229 @ id @ ( lam @ ( sK566 @ X229 @ sh @ one ) ) @ id ) ) )
| ( ( X229 @ id @ X228 @ id )
= $true )
| ( $true
= ( sP20 @ X229 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X237: subst > term > term] :
( ( ( sub @ ( X237 @ ( sK571 @ X237 ) @ ( sK569 @ X237 ) ) @ ( sK570 @ X237 ) )
!= ( X237 @ ( comp @ ( sK571 @ X237 ) @ ( sK570 @ X237 ) ) @ ( sub @ ( sK569 @ X237 ) @ ( sK570 @ X237 ) ) ) )
| ( ( ( sK568 @ id @ ( X237 @ id @ ( sK572 @ X237 ) ) @ id )
!= $true )
& ( ( sK568 @ id @ ( sK572 @ X237 ) @ id )
= $true ) )
| ( $true
= ( sK568 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id ) ) )
& ( ( sK568 @ id @ sK567 @ id )
!= $true )
& ( ( sP20 @ sK568 )
!= $true ) ) )
& ( ! [X242: subst] :
( ( comp @ X242 @ id )
= X242 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ( sK573
!= ( comp @ sK573 @ id ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X244: subst] :
( ( d2subst @ ( sK574 @ X244 ) )
= X244 )
& ( induction2_gthm = $true )
& ( ! [X246: term] :
( ( sub @ X246 @ id )
= X246 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ( ( sub @ sK575 @ id )
!= sK575 ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X248: term,X249: term > $o] :
( ( ( $true
!= ( X249 @ ( lam @ ( sK576 @ X249 ) ) ) )
& ( ( X249 @ ( sK576 @ X249 ) )
= $true ) )
| ( ( X249 @ X248 )
= $true )
| ( ( sP10 @ X249 )
= $true )
| ( ( ( X249 @ ( sK577 @ X249 ) )
!= $true )
& ( $true
= ( var @ ( sK577 @ X249 ) ) ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ( ! [X254: term] :
( ( ( sK579 @ ( lam @ X254 ) )
= $true )
| ( ( sK579 @ X254 )
!= $true ) )
& ( $true
!= ( sK579 @ sK578 ) )
& ( $true
!= ( sP10 @ sK579 ) )
& ! [X255: term] :
( ( ( sK579 @ X255 )
= $true )
| ( ( var @ X255 )
!= $true ) ) ) )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ( sP9 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP9 != $true ) )
& ! [X258: term] :
( ( d2term @ ( sK580 @ X258 ) )
= X258 )
& ( ( hoaslaminj = $true )
| ( ( ( sK584 @ sK581 @ sK582 )
!= ( sK583 @ sK581 @ sK582 ) )
& ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK584 @ sh @ one ) ) )
& ! [X264: term,X265: subst,X266: subst] :
( ( sub @ ( sK584 @ X265 @ X264 ) @ X266 )
= ( sK584 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) ) )
& ! [X267: subst,X268: term,X269: subst] :
( ( sub @ ( sK583 @ X269 @ X268 ) @ X267 )
= ( sK583 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) ) ) )
& ( ! [X270: subst,X271: term,X272: subst > term > term,X273: subst > term > term] :
( ( ( X273 @ X270 @ X271 )
= ( X272 @ X270 @ X271 ) )
| ( ( lam @ ( X272 @ sh @ one ) )
!= ( lam @ ( X273 @ sh @ one ) ) )
| ( ( X273 @ ( comp @ ( sK586 @ X273 ) @ ( sK587 @ X273 ) ) @ ( sub @ ( sK585 @ X273 ) @ ( sK587 @ X273 ) ) )
!= ( sub @ ( X273 @ ( sK586 @ X273 ) @ ( sK585 @ X273 ) ) @ ( sK587 @ X273 ) ) )
| ( ( sub @ ( X272 @ ( sK590 @ X272 ) @ ( sK589 @ X272 ) ) @ ( sK588 @ X272 ) )
!= ( X272 @ ( comp @ ( sK590 @ X272 ) @ ( sK588 @ X272 ) ) @ ( sub @ ( sK589 @ X272 ) @ ( sK588 @ X272 ) ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP7 != $true ) )
& ( ( sP7 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP6 != $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
| ( sP5 != $true ) )
& ( ( sP5 = $true )
| ( hoasinduction != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP2 != $true ) )
& ( ( sP2 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474]) ).
thf(f474,plain,
( ? [X0: term,X1: term,X2: term,X3: term] :
( ( X2 != X3 )
& ( ( ap @ ( sub @ X0 @ id ) @ X3 )
= ( ap @ ( sub @ X1 @ id ) @ X2 ) ) )
=> ( ( sK457 != sK456 )
& ( ( ap @ ( sub @ sK454 @ id ) @ sK457 )
= ( ap @ ( sub @ sK455 @ id ) @ sK456 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
( ? [X8: subst] :
( ( push @ ( sub @ one @ X8 ) @ ( comp @ sh @ X8 ) )
!= X8 )
=> ( sK458
!= ( push @ ( sub @ one @ sK458 ) @ ( comp @ sh @ sK458 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f476,plain,
( ? [X12: term,X13: term] :
( ( X12 != X13 )
& ( ( lam @ X13 )
= ( lam @ X12 ) ) )
=> ( ( sK459 != sK460 )
& ( ( lam @ sK460 )
= ( lam @ sK459 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
( ? [X15: term] :
( ( sub @ X15 @ id )
!= X15 )
=> ( sK461
!= ( sub @ sK461 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
( ? [X16: subst,X17: term] :
( ( comp @ sh @ ( push @ X17 @ X16 ) )
!= X16 )
=> ( sK462
!= ( comp @ sh @ ( push @ sK463 @ sK462 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X21: term,X22: term > $o,X23: subst,X24: term > $o,X25: term] :
( ( ( X22 @ ( sub @ X25 @ ( push @ X21 @ X23 ) ) )
!= $true )
& ( ( X24 @ X25 )
= $true ) )
=> ( ( ( sK465 @ ( sub @ sK468 @ ( push @ sK464 @ sK466 ) ) )
!= $true )
& ( ( sK467 @ sK468 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
( ? [X31: subst] :
( ( comp @ id @ X31 )
!= X31 )
=> ( ( comp @ id @ sK469 )
!= sK469 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
( ? [X32: subst] :
( ( comp @ X32 @ id )
!= X32 )
=> ( ( comp @ sK470 @ id )
!= sK470 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ? [X35: term,X36: subst] :
( ( comp @ sh @ ( push @ X35 @ X36 ) )
!= X36 )
=> ( sK472
!= ( comp @ sh @ ( push @ sK471 @ sK472 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
( ? [X37: term,X38: subst] :
( ( sub @ one @ ( push @ X37 @ X38 ) )
!= X37 )
=> ( ( sub @ one @ ( push @ sK473 @ sK474 ) )
!= sK473 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
( ? [X48: term,X49: subst,X50: term,X51: term > $o,X52: term > $o] :
( ( ( X52 @ ( sub @ X50 @ ( push @ X48 @ X49 ) ) )
!= $true )
& ( ( X51 @ X50 )
= $true ) )
=> ( ( ( sK479 @ ( sub @ sK477 @ ( push @ sK475 @ sK476 ) ) )
!= $true )
& ( ( sK478 @ sK477 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
! [X53: subst > term > term] :
( ? [X56: term,X57: subst,X58: subst] :
( ( sub @ ( X53 @ X57 @ X56 ) @ X58 )
!= ( X53 @ ( comp @ X57 @ X58 ) @ ( sub @ X56 @ X58 ) ) )
=> ( ( X53 @ ( comp @ ( sK481 @ X53 ) @ ( sK482 @ X53 ) ) @ ( sub @ ( sK480 @ X53 ) @ ( sK482 @ X53 ) ) )
!= ( sub @ ( X53 @ ( sK481 @ X53 ) @ ( sK480 @ X53 ) ) @ ( sK482 @ X53 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
( ? [X59: subst > term > term,X60: term,X61: term] :
( ! [X62: term,X63: subst,X64: subst] :
( ( sub @ ( X59 @ X63 @ X62 ) @ X64 )
= ( X59 @ ( comp @ X63 @ X64 ) @ ( sub @ X62 @ X64 ) ) )
& ( ( lam @ ( X59 @ sh @ one ) )
= ( ap @ ( sub @ X60 @ id ) @ X61 ) ) )
=> ( ! [X64: subst,X63: subst,X62: term] :
( ( sK483 @ ( comp @ X63 @ X64 ) @ ( sub @ X62 @ X64 ) )
= ( sub @ ( sK483 @ X63 @ X62 ) @ X64 ) )
& ( ( ap @ ( sub @ sK484 @ id ) @ sK485 )
= ( lam @ ( sK483 @ sh @ one ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
( ? [X67: term,X68: term,X69: term,X70: term] :
( ( X67 != X68 )
& ( ( ap @ X69 @ X68 )
= ( ap @ X70 @ X67 ) ) )
=> ( ( sK486 != sK487 )
& ( ( ap @ sK488 @ sK487 )
= ( ap @ sK489 @ sK486 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
( ? [X79: term,X80: term,X81: term,X82: term] :
( ( X79 != X81 )
& ( ( ap @ ( sub @ X82 @ id ) @ X81 )
= ( ap @ ( sub @ X80 @ id ) @ X79 ) ) )
=> ( ( sK490 != sK492 )
& ( ( ap @ ( sub @ sK493 @ id ) @ sK492 )
= ( ap @ ( sub @ sK491 @ id ) @ sK490 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
( ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 )
=> ( sK494
!= ( sub @ sK494 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
( ? [X85: term] :
( ( sub @ X85 @ id )
!= X85 )
=> ( sK495
!= ( sub @ sK495 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
! [X87: term] :
( ? [X88: subst > term > term] :
( ( sub @ X87 @ ( push @ one @ sh ) )
= ( X88 @ sh @ one ) )
=> ( ( sub @ X87 @ ( push @ one @ sh ) )
= ( sK496 @ X87 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
( ? [X89: term] :
! [X90: subst > term > term] :
( ( sub @ X89 @ ( push @ one @ sh ) )
!= ( X90 @ sh @ one ) )
=> ! [X90: subst > term > term] :
( ( sub @ sK497 @ ( push @ one @ sh ) )
!= ( X90 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
! [X91: term] :
( ? [X92: subst > term > term] :
! [X93: term,X94: subst] :
( ( X92 @ X94 @ X93 )
= ( sub @ X91 @ ( push @ X93 @ X94 ) ) )
=> ! [X94: subst,X93: term] :
( ( sK498 @ X91 @ X94 @ X93 )
= ( sub @ X91 @ ( push @ X93 @ X94 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
( ? [X95: term] :
! [X96: subst > term > term] :
? [X97: term,X98: subst] :
( ( sub @ X95 @ ( push @ X97 @ X98 ) )
!= ( X96 @ X98 @ X97 ) )
=> ! [X96: subst > term > term] :
? [X98: subst,X97: term] :
( ( sub @ sK499 @ ( push @ X97 @ X98 ) )
!= ( X96 @ X98 @ X97 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
! [X96: subst > term > term] :
( ? [X98: subst,X97: term] :
( ( sub @ sK499 @ ( push @ X97 @ X98 ) )
!= ( X96 @ X98 @ X97 ) )
=> ( ( X96 @ ( sK501 @ X96 ) @ ( sK500 @ X96 ) )
!= ( sub @ sK499 @ ( push @ ( sK500 @ X96 ) @ ( sK501 @ X96 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
! [X99: term,X100: term > $o,X101: term > $o,X102: subst] :
( ? [X103: term] :
( ( X100 @ ( sub @ X103 @ ( push @ X99 @ X102 ) ) )
!= ( X101 @ X103 ) )
=> ( ( X101 @ ( sK502 @ X102 @ X101 @ X100 @ X99 ) )
!= ( X100 @ ( sub @ ( sK502 @ X102 @ X101 @ X100 @ X99 ) @ ( push @ X99 @ X102 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
( ? [X104: term,X105: subst] :
( ( sub @ one @ ( push @ X104 @ X105 ) )
!= X104 )
=> ( ( sub @ one @ ( push @ sK503 @ sK504 ) )
!= sK503 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
( ? [X106: term,X107: term > $o,X108: term > $o,X109: subst] :
( ( ( X108 @ one )
!= $true )
& ! [X110: term] :
( ( X108 @ X110 )
= ( X107 @ ( sub @ X110 @ ( push @ X106 @ X109 ) ) ) )
& ( ( X107 @ X106 )
= $true ) )
=> ( ( $true
!= ( sK507 @ one ) )
& ! [X110: term] :
( ( sK507 @ X110 )
= ( sK506 @ ( sub @ X110 @ ( push @ sK505 @ sK508 ) ) ) )
& ( ( sK506 @ sK505 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
! [X113: subst > term > subst > $o] :
( ? [X114: term > $o] :
! [X115: term] :
( ( X114 @ X115 )
= ( X113 @ id @ X115 @ id ) )
=> ! [X115: term] :
( ( sK509 @ X113 @ X115 )
= ( X113 @ id @ X115 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
( ? [X116: subst > term > subst > $o] :
! [X117: term > $o] :
? [X118: term] :
( ( X117 @ X118 )
!= ( X116 @ id @ X118 @ id ) )
=> ! [X117: term > $o] :
? [X118: term] :
( ( sK510 @ id @ X118 @ id )
!= ( X117 @ X118 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
! [X117: term > $o] :
( ? [X118: term] :
( ( sK510 @ id @ X118 @ id )
!= ( X117 @ X118 ) )
=> ( ( X117 @ ( sK511 @ X117 ) )
!= ( sK510 @ id @ ( sK511 @ X117 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
( ? [X124: term,X125: term,X126: term,X127: term] :
( ( X124 != X126 )
& ( ( ap @ X126 @ X127 )
= ( ap @ X124 @ X125 ) ) )
=> ( ( sK512 != sK514 )
& ( ( ap @ sK512 @ sK513 )
= ( ap @ sK514 @ sK515 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
( ? [X128: term > $o,X129: subst,X130: term] :
! [X131: term > $o] :
? [X132: term] :
( ( X131 @ X132 )
!= ( X128 @ ( sub @ X132 @ ( push @ X130 @ X129 ) ) ) )
=> ! [X131: term > $o] :
? [X132: term] :
( ( X131 @ X132 )
!= ( sK516 @ ( sub @ X132 @ ( push @ sK518 @ sK517 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
! [X131: term > $o] :
( ? [X132: term] :
( ( X131 @ X132 )
!= ( sK516 @ ( sub @ X132 @ ( push @ sK518 @ sK517 ) ) ) )
=> ( ( sK516 @ ( sub @ ( sK519 @ X131 ) @ ( push @ sK518 @ sK517 ) ) )
!= ( X131 @ ( sK519 @ X131 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
! [X133: term > $o,X134: subst,X135: term] :
( ? [X136: term > $o] :
! [X137: term] :
( ( X133 @ ( sub @ X137 @ ( push @ X135 @ X134 ) ) )
= ( X136 @ X137 ) )
=> ! [X137: term] :
( ( sK520 @ X135 @ X134 @ X133 @ X137 )
= ( X133 @ ( sub @ X137 @ ( push @ X135 @ X134 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
( ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 )
=> ( ( comp @ id @ sK521 )
!= sK521 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
( ? [X140: subst] :
( ( comp @ id @ X140 )
!= X140 )
=> ( ( comp @ id @ sK522 )
!= sK522 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X141: subst] :
( ( comp @ X141 @ id )
!= X141 )
=> ( ( comp @ sK523 @ id )
!= sK523 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
( ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
=> ( sK524
!= ( comp @ sK524 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
( ? [X147: subst] :
( ( comp @ id @ X147 )
!= X147 )
=> ( sK525
!= ( comp @ id @ sK525 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
! [X148: term > $o,X149: subst,X150: term > $o,X151: term] :
( ? [X152: term] :
( ( X150 @ X152 )
!= ( X148 @ ( sub @ X152 @ ( push @ X151 @ X149 ) ) ) )
=> ( ( X148 @ ( sub @ ( sK526 @ X151 @ X150 @ X149 @ X148 ) @ ( push @ X151 @ X149 ) ) )
!= ( X150 @ ( sK526 @ X151 @ X150 @ X149 @ X148 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
( ? [X153: term > $o,X154: subst,X155: term > $o,X156: term] :
( ( ( X155 @ one )
!= $true )
& ( ( X153 @ X156 )
= $true )
& ! [X157: term] :
( ( X153 @ ( sub @ X157 @ ( push @ X156 @ X154 ) ) )
= ( X155 @ X157 ) ) )
=> ( ( $true
!= ( sK529 @ one ) )
& ( ( sK527 @ sK530 )
= $true )
& ! [X157: term] :
( ( sK529 @ X157 )
= ( sK527 @ ( sub @ X157 @ ( push @ sK530 @ sK528 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
( ? [X162: term,X163: term,X164: term,X165: term] :
( ( ( ap @ ( sub @ X165 @ id ) @ X163 )
= ( ap @ ( sub @ X162 @ id ) @ X164 ) )
& ( X162 != X165 ) )
=> ( ( ( ap @ ( sub @ sK534 @ id ) @ sK532 )
= ( ap @ ( sub @ sK531 @ id ) @ sK533 ) )
& ( sK531 != sK534 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ? [X166: term] :
! [X167: subst > term > term] :
( ( X167 @ sh @ one )
!= ( sub @ X166 @ ( push @ one @ sh ) ) )
=> ! [X167: subst > term > term] :
( ( X167 @ sh @ one )
!= ( sub @ sK535 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
! [X168: term] :
( ? [X169: subst > term > term] :
( ( sub @ X168 @ ( push @ one @ sh ) )
= ( X169 @ sh @ one ) )
=> ( ( sub @ X168 @ ( push @ one @ sh ) )
= ( sK536 @ X168 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
( ? [X170: term] :
! [X171: subst > term > term] :
? [X172: term,X173: subst] :
( ( X171 @ X173 @ X172 )
!= ( sub @ X170 @ ( push @ X172 @ X173 ) ) )
=> ! [X171: subst > term > term] :
? [X173: subst,X172: term] :
( ( X171 @ X173 @ X172 )
!= ( sub @ sK537 @ ( push @ X172 @ X173 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
! [X171: subst > term > term] :
( ? [X173: subst,X172: term] :
( ( X171 @ X173 @ X172 )
!= ( sub @ sK537 @ ( push @ X172 @ X173 ) ) )
=> ( ( sub @ sK537 @ ( push @ ( sK538 @ X171 ) @ ( sK539 @ X171 ) ) )
!= ( X171 @ ( sK539 @ X171 ) @ ( sK538 @ X171 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
! [X174: term] :
( ? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
=> ! [X177: subst,X176: term] :
( ( sK540 @ X174 @ X177 @ X176 )
= ( sub @ X174 @ ( push @ X176 @ X177 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
( ? [X178: subst,X179: term] :
( ( sub @ one @ ( push @ X179 @ X178 ) )
!= X179 )
=> ( ( sub @ one @ ( push @ sK542 @ sK541 ) )
!= sK542 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
( ? [X182: term,X183: term,X184: term,X185: term] :
( ( X183 != X184 )
& ( ( ap @ ( sub @ X184 @ id ) @ X185 )
= ( ap @ ( sub @ X183 @ id ) @ X182 ) ) )
=> ( ( sK545 != sK544 )
& ( ( ap @ ( sub @ sK545 @ id ) @ sK546 )
= ( ap @ ( sub @ sK544 @ id ) @ sK543 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X195: term,X196: term,X197: term,X198: term] :
( ( X196 != X198 )
& ( ( ap @ X196 @ X197 )
= ( ap @ X198 @ X195 ) ) )
=> ( ( sK550 != sK548 )
& ( ( ap @ sK548 @ sK549 )
= ( ap @ sK550 @ sK547 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
( ? [X199: term] :
( ( sub @ X199 @ id )
!= X199 )
=> ( ( sub @ sK551 @ id )
!= sK551 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
( ? [X200: subst,X201: term,X202: term > $o] :
! [X203: term > $o] :
? [X204: term] :
( ( X202 @ ( sub @ X204 @ ( push @ X201 @ X200 ) ) )
!= ( X203 @ X204 ) )
=> ! [X203: term > $o] :
? [X204: term] :
( ( sK554 @ ( sub @ X204 @ ( push @ sK553 @ sK552 ) ) )
!= ( X203 @ X204 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
! [X203: term > $o] :
( ? [X204: term] :
( ( sK554 @ ( sub @ X204 @ ( push @ sK553 @ sK552 ) ) )
!= ( X203 @ X204 ) )
=> ( ( X203 @ ( sK555 @ X203 ) )
!= ( sK554 @ ( sub @ ( sK555 @ X203 ) @ ( push @ sK553 @ sK552 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
! [X205: subst,X206: term,X207: term > $o] :
( ? [X208: term > $o] :
! [X209: term] :
( ( X207 @ ( sub @ X209 @ ( push @ X206 @ X205 ) ) )
= ( X208 @ X209 ) )
=> ! [X209: term] :
( ( sK556 @ X207 @ X206 @ X205 @ X209 )
= ( X207 @ ( sub @ X209 @ ( push @ X206 @ X205 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
( ? [X214: term,X215: term,X216: term,X217: term] :
( ( X214 != X215 )
& ( ( ap @ X216 @ X215 )
= ( ap @ X217 @ X214 ) ) )
=> ( ( sK557 != sK558 )
& ( ( ap @ sK560 @ sK557 )
= ( ap @ sK559 @ sK558 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
( ? [X220: term,X221: term] :
( ( X220 != X221 )
& ( ( sub @ X221 @ sh )
= ( sub @ X220 @ sh ) ) )
=> ( ( sK561 != sK562 )
& ( ( sub @ sK561 @ sh )
= ( sub @ sK562 @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
! [X222: subst > term > subst > $o] :
( ? [X223: term > $o] :
! [X224: term] :
( ( X223 @ X224 )
= ( X222 @ id @ X224 @ id ) )
=> ! [X224: term] :
( ( X222 @ id @ X224 @ id )
= ( sK563 @ X222 @ X224 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
( ? [X225: subst > term > subst > $o] :
! [X226: term > $o] :
? [X227: term] :
( ( X226 @ X227 )
!= ( X225 @ id @ X227 @ id ) )
=> ! [X226: term > $o] :
? [X227: term] :
( ( X226 @ X227 )
!= ( sK564 @ id @ X227 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
! [X226: term > $o] :
( ? [X227: term] :
( ( X226 @ X227 )
!= ( sK564 @ id @ X227 @ id ) )
=> ( ( sK564 @ id @ ( sK565 @ X226 ) @ id )
!= ( X226 @ ( sK565 @ X226 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
! [X229: subst > term > subst > $o] :
( ? [X230: subst > term > term] :
( ! [X231: term,X232: subst,X233: subst] :
( ( X230 @ ( comp @ X233 @ X232 ) @ ( sub @ X231 @ X232 ) )
= ( sub @ ( X230 @ X233 @ X231 ) @ X232 ) )
& ! [X234: term] :
( ( ( X229 @ id @ ( X230 @ id @ X234 ) @ id )
= $true )
| ( ( X229 @ id @ X234 @ id )
!= $true ) )
& ( ( X229 @ id @ ( lam @ ( X230 @ sh @ one ) ) @ id )
!= $true ) )
=> ( ! [X233: subst,X232: subst,X231: term] :
( ( sK566 @ X229 @ ( comp @ X233 @ X232 ) @ ( sub @ X231 @ X232 ) )
= ( sub @ ( sK566 @ X229 @ X233 @ X231 ) @ X232 ) )
& ! [X234: term] :
( ( $true
= ( X229 @ id @ ( sK566 @ X229 @ id @ X234 ) @ id ) )
| ( ( X229 @ id @ X234 @ id )
!= $true ) )
& ( $true
!= ( X229 @ id @ ( lam @ ( sK566 @ X229 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X235: term,X236: subst > term > subst > $o] :
( ! [X237: subst > term > term] :
( ? [X238: term,X239: subst,X240: subst] :
( ( sub @ ( X237 @ X240 @ X238 ) @ X239 )
!= ( X237 @ ( comp @ X240 @ X239 ) @ ( sub @ X238 @ X239 ) ) )
| ? [X241: term] :
( ( ( X236 @ id @ ( X237 @ id @ X241 ) @ id )
!= $true )
& ( ( X236 @ id @ X241 @ id )
= $true ) )
| ( ( X236 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X236 @ id @ X235 @ id )
!= $true )
& ( ( sP20 @ X236 )
!= $true ) )
=> ( ! [X237: subst > term > term] :
( ? [X238: term,X239: subst,X240: subst] :
( ( sub @ ( X237 @ X240 @ X238 ) @ X239 )
!= ( X237 @ ( comp @ X240 @ X239 ) @ ( sub @ X238 @ X239 ) ) )
| ? [X241: term] :
( ( $true
!= ( sK568 @ id @ ( X237 @ id @ X241 ) @ id ) )
& ( ( sK568 @ id @ X241 @ id )
= $true ) )
| ( $true
= ( sK568 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id ) ) )
& ( ( sK568 @ id @ sK567 @ id )
!= $true )
& ( ( sP20 @ sK568 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
! [X237: subst > term > term] :
( ? [X238: term,X239: subst,X240: subst] :
( ( sub @ ( X237 @ X240 @ X238 ) @ X239 )
!= ( X237 @ ( comp @ X240 @ X239 ) @ ( sub @ X238 @ X239 ) ) )
=> ( ( sub @ ( X237 @ ( sK571 @ X237 ) @ ( sK569 @ X237 ) ) @ ( sK570 @ X237 ) )
!= ( X237 @ ( comp @ ( sK571 @ X237 ) @ ( sK570 @ X237 ) ) @ ( sub @ ( sK569 @ X237 ) @ ( sK570 @ X237 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
! [X237: subst > term > term] :
( ? [X241: term] :
( ( $true
!= ( sK568 @ id @ ( X237 @ id @ X241 ) @ id ) )
& ( ( sK568 @ id @ X241 @ id )
= $true ) )
=> ( ( ( sK568 @ id @ ( X237 @ id @ ( sK572 @ X237 ) ) @ id )
!= $true )
& ( ( sK568 @ id @ ( sK572 @ X237 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
( ? [X243: subst] :
( ( comp @ X243 @ id )
!= X243 )
=> ( sK573
!= ( comp @ sK573 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
! [X244: subst] :
( ? [X245: d_subst] :
( ( d2subst @ X245 )
= X244 )
=> ( ( d2subst @ ( sK574 @ X244 ) )
= X244 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
( ? [X247: term] :
( ( sub @ X247 @ id )
!= X247 )
=> ( ( sub @ sK575 @ id )
!= sK575 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
! [X249: term > $o] :
( ? [X250: term] :
( ( ( X249 @ ( lam @ X250 ) )
!= $true )
& ( ( X249 @ X250 )
= $true ) )
=> ( ( $true
!= ( X249 @ ( lam @ ( sK576 @ X249 ) ) ) )
& ( ( X249 @ ( sK576 @ X249 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
! [X249: term > $o] :
( ? [X251: term] :
( ( ( X249 @ X251 )
!= $true )
& ( $true
= ( var @ X251 ) ) )
=> ( ( ( X249 @ ( sK577 @ X249 ) )
!= $true )
& ( $true
= ( var @ ( sK577 @ X249 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
( ? [X252: term,X253: term > $o] :
( ! [X254: term] :
( ( ( X253 @ ( lam @ X254 ) )
= $true )
| ( ( X253 @ X254 )
!= $true ) )
& ( ( X253 @ X252 )
!= $true )
& ( ( sP10 @ X253 )
!= $true )
& ! [X255: term] :
( ( $true
= ( X253 @ X255 ) )
| ( ( var @ X255 )
!= $true ) ) )
=> ( ! [X254: term] :
( ( ( sK579 @ ( lam @ X254 ) )
= $true )
| ( ( sK579 @ X254 )
!= $true ) )
& ( $true
!= ( sK579 @ sK578 ) )
& ( $true
!= ( sP10 @ sK579 ) )
& ! [X255: term] :
( ( ( sK579 @ X255 )
= $true )
| ( ( var @ X255 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
! [X258: term] :
( ? [X259: d_term] :
( ( d2term @ X259 )
= X258 )
=> ( ( d2term @ ( sK580 @ X258 ) )
= X258 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
( ? [X260: subst,X261: term,X262: subst > term > term,X263: subst > term > term] :
( ( ( X263 @ X260 @ X261 )
!= ( X262 @ X260 @ X261 ) )
& ( ( lam @ ( X262 @ sh @ one ) )
= ( lam @ ( X263 @ sh @ one ) ) )
& ! [X264: term,X265: subst,X266: subst] :
( ( X263 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) )
= ( sub @ ( X263 @ X265 @ X264 ) @ X266 ) )
& ! [X267: subst,X268: term,X269: subst] :
( ( X262 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) )
= ( sub @ ( X262 @ X269 @ X268 ) @ X267 ) ) )
=> ( ( ( sK584 @ sK581 @ sK582 )
!= ( sK583 @ sK581 @ sK582 ) )
& ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK584 @ sh @ one ) ) )
& ! [X266: subst,X265: subst,X264: term] :
( ( sub @ ( sK584 @ X265 @ X264 ) @ X266 )
= ( sK584 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) ) )
& ! [X269: subst,X268: term,X267: subst] :
( ( sub @ ( sK583 @ X269 @ X268 ) @ X267 )
= ( sK583 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
! [X273: subst > term > term] :
( ? [X274: term,X275: subst,X276: subst] :
( ( X273 @ ( comp @ X275 @ X276 ) @ ( sub @ X274 @ X276 ) )
!= ( sub @ ( X273 @ X275 @ X274 ) @ X276 ) )
=> ( ( X273 @ ( comp @ ( sK586 @ X273 ) @ ( sK587 @ X273 ) ) @ ( sub @ ( sK585 @ X273 ) @ ( sK587 @ X273 ) ) )
!= ( sub @ ( X273 @ ( sK586 @ X273 ) @ ( sK585 @ X273 ) ) @ ( sK587 @ X273 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
! [X272: subst > term > term] :
( ? [X277: subst,X278: term,X279: subst] :
( ( sub @ ( X272 @ X279 @ X278 ) @ X277 )
!= ( X272 @ ( comp @ X279 @ X277 ) @ ( sub @ X278 @ X277 ) ) )
=> ( ( sub @ ( X272 @ ( sK590 @ X272 ) @ ( sK589 @ X272 ) ) @ ( sK588 @ X272 ) )
!= ( X272 @ ( comp @ ( sK590 @ X272 ) @ ( sK588 @ X272 ) ) @ ( sub @ ( sK589 @ X272 ) @ ( sK588 @ X272 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f473,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP58 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X0: term,X1: term,X2: term,X3: term] :
( ( X2 != X3 )
& ( ( ap @ ( sub @ X0 @ id ) @ X3 )
= ( ap @ ( sub @ X1 @ id ) @ X2 ) ) ) )
& ( ! [X4: term,X5: term,X6: term,X7: term] :
( ( X6 = X7 )
| ( ( ap @ ( sub @ X4 @ id ) @ X7 )
!= ( ap @ ( sub @ X5 @ id ) @ X6 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( axscons = $true )
| ? [X8: subst] :
( ( push @ ( sub @ one @ X8 ) @ ( comp @ sh @ X8 ) )
!= X8 ) )
& ( ! [X9: subst] :
( ( push @ ( sub @ one @ X9 ) @ ( comp @ sh @ X9 ) )
= X9 )
| ( axscons != $true ) )
& ( ! [X10: term,X11: term] :
( ( X10 = X11 )
| ( ( lam @ X10 )
!= ( lam @ X11 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X12: term,X13: term] :
( ( X12 != X13 )
& ( ( lam @ X13 )
= ( lam @ X12 ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X15: term] :
( ( sub @ X15 @ id )
!= X15 ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
| ? [X16: subst,X17: term] :
( ( comp @ sh @ ( push @ X17 @ X16 ) )
!= X16 ) )
& ( ! [X18: subst,X19: term] :
( ( comp @ sh @ ( push @ X19 @ X18 ) )
= X18 )
| ( axshiftcons != $true ) )
& ! [X20: d_subst] : ( d_id = X20 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
| ? [X21: term,X22: term > $o,X23: subst,X24: term > $o,X25: term] :
( ( ( X22 @ ( sub @ X25 @ ( push @ X21 @ X23 ) ) )
!= $true )
& ( ( X24 @ X25 )
= $true ) ) )
& ( ! [X26: term,X27: term > $o,X28: subst,X29: term > $o,X30: term] :
( ( ( X27 @ ( sub @ X30 @ ( push @ X26 @ X28 ) ) )
= $true )
| ( ( X29 @ X30 )
!= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( substmonoid = $true )
| ? [X31: subst] :
( ( comp @ id @ X31 )
!= X31 )
| ? [X32: subst] :
( ( comp @ X32 @ id )
!= X32 ) )
& ( ( ! [X33: subst] :
( ( comp @ id @ X33 )
= X33 )
& ! [X34: subst] :
( ( comp @ X34 @ id )
= X34 ) )
| ( substmonoid != $true ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ? [X35: term,X36: subst] :
( ( comp @ sh @ ( push @ X35 @ X36 ) )
!= X36 )
| ? [X37: term,X38: subst] :
( ( sub @ one @ ( push @ X37 @ X38 ) )
!= X37 )
| ! [X39: term,X40: subst,X41: term,X42: term > $o,X43: term > $o] :
( ( ( X43 @ ( sub @ X41 @ ( push @ X39 @ X40 ) ) )
= $true )
| ( ( X42 @ X41 )
!= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X44: term,X45: subst] :
( ( comp @ sh @ ( push @ X44 @ X45 ) )
= X45 )
& ! [X46: term,X47: subst] :
( ( sub @ one @ ( push @ X46 @ X47 ) )
= X46 )
& ? [X48: term,X49: subst,X50: term,X51: term > $o,X52: term > $o] :
( ( ( X52 @ ( sub @ X50 @ ( push @ X48 @ X49 ) ) )
!= $true )
& ( ( X51 @ X50 )
= $true ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X53: subst > term > term,X54: term,X55: term] :
( ? [X56: term,X57: subst,X58: subst] :
( ( sub @ ( X53 @ X57 @ X56 ) @ X58 )
!= ( X53 @ ( comp @ X57 @ X58 ) @ ( sub @ X56 @ X58 ) ) )
| ( ( lam @ ( X53 @ sh @ one ) )
!= ( ap @ ( sub @ X54 @ id ) @ X55 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X59: subst > term > term,X60: term,X61: term] :
( ! [X62: term,X63: subst,X64: subst] :
( ( sub @ ( X59 @ X63 @ X62 ) @ X64 )
= ( X59 @ ( comp @ X63 @ X64 ) @ ( sub @ X62 @ X64 ) ) )
& ( ( lam @ ( X59 @ sh @ one ) )
= ( ap @ ( sub @ X60 @ id ) @ X61 ) ) ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( sP52 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP52 != $true ) )
& ( hoasinduction_gthm = $true )
& ! [X65: d_subst,X66: d_subst] :
( ( ( d2subst @ X66 )
!= ( d2subst @ X65 ) )
| ( X65 = X66 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( induction2lem_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ? [X67: term,X68: term,X69: term,X70: term] :
( ( X67 != X68 )
& ( ( ap @ X69 @ X68 )
= ( ap @ X70 @ X67 ) ) )
| ! [X71: term,X72: term,X73: term,X74: term] :
( ( X71 = X73 )
| ( ( ap @ ( sub @ X72 @ id ) @ X71 )
!= ( ap @ ( sub @ X74 @ id ) @ X73 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X75: term,X76: term,X77: term,X78: term] :
( ( X75 = X76 )
| ( ( ap @ X77 @ X76 )
!= ( ap @ X78 @ X75 ) ) )
& ? [X79: term,X80: term,X81: term,X82: term] :
( ( X79 != X81 )
& ( ( ap @ ( sub @ X82 @ id ) @ X81 )
= ( ap @ ( sub @ X80 @ id ) @ X79 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
| ( ! [X83: term] :
( ( sub @ X83 @ id )
= X83 )
& ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 ) ) )
& ( ? [X85: term] :
( ( sub @ X85 @ id )
!= X85 )
| ! [X86: term] :
( ( sub @ X86 @ id )
= X86 )
| ( termmset_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP46 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP46 ) )
& ( ! [X87: term] :
? [X88: subst > term > term] :
( ( sub @ X87 @ ( push @ one @ sh ) )
= ( X88 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X89: term] :
! [X90: subst > term > term] :
( ( sub @ X89 @ ( push @ one @ sh ) )
!= ( X90 @ sh @ one ) ) )
& ( ( induction2lem = $true )
| ( sP45 != $true ) )
& ( ( sP45 = $true )
| ( induction2lem != $true ) )
& ( ! [X91: term] :
? [X92: subst > term > term] :
! [X93: term,X94: subst] :
( ( X92 @ X94 @ X93 )
= ( sub @ X91 @ ( push @ X93 @ X94 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X95: term] :
! [X96: subst > term > term] :
? [X97: term,X98: subst] :
( ( sub @ X95 @ ( push @ X97 @ X98 ) )
!= ( X96 @ X98 @ X97 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X99: term,X100: term > $o,X101: term > $o,X102: subst] :
( ( ( X101 @ one )
= $true )
| ? [X103: term] :
( ( X100 @ ( sub @ X103 @ ( push @ X99 @ X102 ) ) )
!= ( X101 @ X103 ) )
| ( ( X100 @ X99 )
!= $true ) )
| ? [X104: term,X105: subst] :
( ( sub @ one @ ( push @ X104 @ X105 ) )
!= X104 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X106: term,X107: term > $o,X108: term > $o,X109: subst] :
( ( ( X108 @ one )
!= $true )
& ! [X110: term] :
( ( X108 @ X110 )
= ( X107 @ ( sub @ X110 @ ( push @ X106 @ X109 ) ) ) )
& ( ( X107 @ X106 )
= $true ) )
& ! [X111: term,X112: subst] :
( ( sub @ one @ ( push @ X111 @ X112 ) )
= X111 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X113: subst > term > subst > $o] :
? [X114: term > $o] :
! [X115: term] :
( ( X114 @ X115 )
= ( X113 @ id @ X115 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X116: subst > term > subst > $o] :
! [X117: term > $o] :
? [X118: term] :
( ( X117 @ X118 )
!= ( X116 @ id @ X118 @ id ) ) )
& ( ( sP43 = $true )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( sP43 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP35 != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP34 != $true ) )
& ( ( sP34 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X119: d_term] : ( d_one = X119 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X120: term,X121: term,X122: term,X123: term] :
( ( X120 = X122 )
| ( ( ap @ X120 @ X121 )
!= ( ap @ X122 @ X123 ) ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X124: term,X125: term,X126: term,X127: term] :
( ( X124 != X126 )
& ( ( ap @ X126 @ X127 )
= ( ap @ X124 @ X125 ) ) ) )
& ( ( pushprop_lem0 = $true )
| ? [X128: term > $o,X129: subst,X130: term] :
! [X131: term > $o] :
? [X132: term] :
( ( X131 @ X132 )
!= ( X128 @ ( sub @ X132 @ ( push @ X130 @ X129 ) ) ) ) )
& ( ! [X133: term > $o,X134: subst,X135: term] :
? [X136: term > $o] :
! [X137: term] :
( ( X133 @ ( sub @ X137 @ ( push @ X135 @ X134 ) ) )
= ( X136 @ X137 ) )
| ( pushprop_lem0 != $true ) )
& ( ( axidl = $true )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 ) )
& ( ! [X139: subst] :
( ( comp @ id @ X139 )
= X139 )
| ( axidl != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ? [X140: subst] :
( ( comp @ id @ X140 )
!= X140 )
| ? [X141: subst] :
( ( comp @ X141 @ id )
!= X141 )
| ( ! [X142: subst] :
( ( comp @ X142 @ id )
= X142 )
& ! [X143: subst] :
( ( comp @ id @ X143 )
= X143 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X144: subst] :
( ( comp @ id @ X144 )
= X144 )
& ! [X145: subst] :
( ( comp @ X145 @ id )
= X145 )
& ( ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ? [X147: subst] :
( ( comp @ id @ X147 )
!= X147 ) ) ) )
& ( ! [X148: term > $o,X149: subst,X150: term > $o,X151: term] :
( ( ( X150 @ one )
= $true )
| ( ( X148 @ X151 )
!= $true )
| ? [X152: term] :
( ( X150 @ X152 )
!= ( X148 @ ( sub @ X152 @ ( push @ X151 @ X149 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X153: term > $o,X154: subst,X155: term > $o,X156: term] :
( ( ( X155 @ one )
!= $true )
& ( ( X153 @ X156 )
= $true )
& ! [X157: term] :
( ( X153 @ ( sub @ X157 @ ( push @ X156 @ X154 ) ) )
= ( X155 @ X157 ) ) ) )
& ( axapp = $true )
& ( ! [X158: term,X159: term,X160: term,X161: term] :
( ( ( ap @ ( sub @ X158 @ id ) @ X160 )
!= ( ap @ ( sub @ X161 @ id ) @ X159 ) )
| ( X158 = X161 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X162: term,X163: term,X164: term,X165: term] :
( ( ( ap @ ( sub @ X165 @ id ) @ X163 )
= ( ap @ ( sub @ X162 @ id ) @ X164 ) )
& ( X162 != X165 ) ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X166: term] :
! [X167: subst > term > term] :
( ( X167 @ sh @ one )
!= ( sub @ X166 @ ( push @ one @ sh ) ) ) )
& ( ! [X168: term] :
? [X169: subst > term > term] :
( ( sub @ X168 @ ( push @ one @ sh ) )
= ( X169 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X170: term] :
! [X171: subst > term > term] :
? [X172: term,X173: subst] :
( ( X171 @ X173 @ X172 )
!= ( sub @ X170 @ ( push @ X172 @ X173 ) ) ) )
& ( ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( induction2_lthm = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( induction2_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
| ? [X178: subst,X179: term] :
( ( sub @ one @ ( push @ X179 @ X178 ) )
!= X179 ) )
& ( ! [X180: subst,X181: term] :
( ( sub @ one @ ( push @ X181 @ X180 ) )
= X181 )
| ( axvarcons != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X182: term,X183: term,X184: term,X185: term] :
( ( X183 != X184 )
& ( ( ap @ ( sub @ X184 @ id ) @ X185 )
= ( ap @ ( sub @ X183 @ id ) @ X182 ) ) )
& ! [X186: term,X187: term,X188: term,X189: term] :
( ( X187 = X189 )
| ( ( ap @ X189 @ X186 )
!= ( ap @ X187 @ X188 ) ) )
& ! [X190: term] :
( ( sub @ X190 @ id )
= X190 ) ) )
& ( ! [X191: term,X192: term,X193: term,X194: term] :
( ( X192 = X193 )
| ( ( ap @ ( sub @ X193 @ id ) @ X194 )
!= ( ap @ ( sub @ X192 @ id ) @ X191 ) ) )
| ? [X195: term,X196: term,X197: term,X198: term] :
( ( X196 != X198 )
& ( ( ap @ X196 @ X197 )
= ( ap @ X198 @ X195 ) ) )
| ? [X199: term] :
( ( sub @ X199 @ id )
!= X199 )
| ( hoasapinj1_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X200: subst,X201: term,X202: term > $o] :
! [X203: term > $o] :
? [X204: term] :
( ( X202 @ ( sub @ X204 @ ( push @ X201 @ X200 ) ) )
!= ( X203 @ X204 ) ) )
& ( ! [X205: subst,X206: term,X207: term > $o] :
? [X208: term > $o] :
! [X209: term] :
( ( X207 @ ( sub @ X209 @ ( push @ X206 @ X205 ) ) )
= ( X208 @ X209 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( sP28 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP28 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( sP27 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP27 != $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X210: term,X211: term,X212: term,X213: term] :
( ( X210 = X211 )
| ( ( ap @ X213 @ X210 )
!= ( ap @ X212 @ X211 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X214: term,X215: term,X216: term,X217: term] :
( ( X214 != X215 )
& ( ( ap @ X216 @ X215 )
= ( ap @ X217 @ X214 ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X218: term,X219: term] :
( ( X218 = X219 )
| ( ( sub @ X219 @ sh )
!= ( sub @ X218 @ sh ) ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X220: term,X221: term] :
( ( X220 != X221 )
& ( ( sub @ X221 @ sh )
= ( sub @ X220 @ sh ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ! [X222: subst > term > subst > $o] :
? [X223: term > $o] :
! [X224: term] :
( ( X223 @ X224 )
= ( X222 @ id @ X224 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X225: subst > term > subst > $o] :
! [X226: term > $o] :
? [X227: term] :
( ( X226 @ X227 )
!= ( X225 @ id @ X227 @ id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X228: term,X229: subst > term > subst > $o] :
( ? [X230: subst > term > term] :
( ! [X231: term,X232: subst,X233: subst] :
( ( X230 @ ( comp @ X233 @ X232 ) @ ( sub @ X231 @ X232 ) )
= ( sub @ ( X230 @ X233 @ X231 ) @ X232 ) )
& ! [X234: term] :
( ( ( X229 @ id @ ( X230 @ id @ X234 ) @ id )
= $true )
| ( ( X229 @ id @ X234 @ id )
!= $true ) )
& ( ( X229 @ id @ ( lam @ ( X230 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X229 @ id @ X228 @ id )
= $true )
| ( $true
= ( sP20 @ X229 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X235: term,X236: subst > term > subst > $o] :
( ! [X237: subst > term > term] :
( ? [X238: term,X239: subst,X240: subst] :
( ( sub @ ( X237 @ X240 @ X238 ) @ X239 )
!= ( X237 @ ( comp @ X240 @ X239 ) @ ( sub @ X238 @ X239 ) ) )
| ? [X241: term] :
( ( ( X236 @ id @ ( X237 @ id @ X241 ) @ id )
!= $true )
& ( ( X236 @ id @ X241 @ id )
= $true ) )
| ( ( X236 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X236 @ id @ X235 @ id )
!= $true )
& ( ( sP20 @ X236 )
!= $true ) ) )
& ( ! [X242: subst] :
( ( comp @ X242 @ id )
= X242 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X243: subst] :
( ( comp @ X243 @ id )
!= X243 ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X244: subst] :
? [X245: d_subst] :
( ( d2subst @ X245 )
= X244 )
& ( induction2_gthm = $true )
& ( ! [X246: term] :
( ( sub @ X246 @ id )
= X246 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X247: term] :
( ( sub @ X247 @ id )
!= X247 ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X248: term,X249: term > $o] :
( ? [X250: term] :
( ( ( X249 @ ( lam @ X250 ) )
!= $true )
& ( ( X249 @ X250 )
= $true ) )
| ( ( X249 @ X248 )
= $true )
| ( ( sP10 @ X249 )
= $true )
| ? [X251: term] :
( ( ( X249 @ X251 )
!= $true )
& ( $true
= ( var @ X251 ) ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X252: term,X253: term > $o] :
( ! [X254: term] :
( ( ( X253 @ ( lam @ X254 ) )
= $true )
| ( ( X253 @ X254 )
!= $true ) )
& ( ( X253 @ X252 )
!= $true )
& ( ( sP10 @ X253 )
!= $true )
& ! [X255: term] :
( ( $true
= ( X253 @ X255 ) )
| ( ( var @ X255 )
!= $true ) ) ) )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ( sP9 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP9 != $true ) )
& ! [X258: term] :
? [X259: d_term] :
( ( d2term @ X259 )
= X258 )
& ( ( hoaslaminj = $true )
| ? [X260: subst,X261: term,X262: subst > term > term,X263: subst > term > term] :
( ( ( X263 @ X260 @ X261 )
!= ( X262 @ X260 @ X261 ) )
& ( ( lam @ ( X262 @ sh @ one ) )
= ( lam @ ( X263 @ sh @ one ) ) )
& ! [X264: term,X265: subst,X266: subst] :
( ( X263 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) )
= ( sub @ ( X263 @ X265 @ X264 ) @ X266 ) )
& ! [X267: subst,X268: term,X269: subst] :
( ( X262 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) )
= ( sub @ ( X262 @ X269 @ X268 ) @ X267 ) ) ) )
& ( ! [X270: subst,X271: term,X272: subst > term > term,X273: subst > term > term] :
( ( ( X273 @ X270 @ X271 )
= ( X272 @ X270 @ X271 ) )
| ( ( lam @ ( X272 @ sh @ one ) )
!= ( lam @ ( X273 @ sh @ one ) ) )
| ? [X274: term,X275: subst,X276: subst] :
( ( X273 @ ( comp @ X275 @ X276 ) @ ( sub @ X274 @ X276 ) )
!= ( sub @ ( X273 @ X275 @ X274 ) @ X276 ) )
| ? [X277: subst,X278: term,X279: subst] :
( ( sub @ ( X272 @ X279 @ X278 ) @ X277 )
!= ( X272 @ ( comp @ X279 @ X277 ) @ ( sub @ X278 @ X277 ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP7 != $true ) )
& ( ( sP7 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP6 != $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
| ( sP5 != $true ) )
& ( ( sP5 = $true )
| ( hoasinduction != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP2 != $true ) )
& ( ( sP2 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP1 != $true ) ) ),
inference(rectify,[status(thm)],[f472]) ).
thf(f472,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP58 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X86: term,X87: term,X88: term,X89: term] :
( ( X88 != X89 )
& ( ( ap @ ( sub @ X86 @ id ) @ X89 )
= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( axscons = $true )
| ? [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
!= X24 ) )
& ( ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 )
| ( axscons != $true ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X455: term,X456: term] :
( ( X455 != X456 )
& ( ( lam @ X456 )
= ( lam @ X455 ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X178: term] :
( ( sub @ X178 @ id )
!= X178 ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
| ? [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
!= X530 ) )
& ( ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 )
| ( axshiftcons != $true ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
| ? [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
!= $true )
& ( $true
= ( X93 @ X94 ) ) ) )
& ( ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( substmonoid = $true )
| ? [X42: subst] :
( ( comp @ id @ X42 )
!= X42 )
| ? [X41: subst] :
( ( comp @ X41 @ id )
!= X41 ) )
& ( ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) )
| ( substmonoid != $true ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ? [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
!= X303 )
| ? [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
!= X300 )
| ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
= X303 )
& ! [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
= X300 )
& ? [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
!= $true )
& ( ( X307 @ X306 )
= $true ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ? [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
!= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
| ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X76: subst > term > term,X77: term,X78: term] :
( ! [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
& ( ( ap @ ( sub @ X77 @ id ) @ X78 )
= ( lam @ ( X76 @ sh @ one ) ) ) ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( sP52 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP52 != $true ) )
& ( hoasinduction_gthm = $true )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
!= ( d2subst @ X471 ) )
| ( X470 = X471 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( induction2lem_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X533 )
& ( ( ap @ X535 @ X532 )
= ( ap @ X534 @ X533 ) ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( X532 = X533 )
| ( ( ap @ X535 @ X532 )
!= ( ap @ X534 @ X533 ) ) )
& ? [X536: term,X537: term,X538: term,X539: term] :
( ( X536 != X538 )
& ( ( ap @ ( sub @ X539 @ id ) @ X538 )
= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
| ( ! [X298: term] :
( ( sub @ X298 @ id )
= X298 )
& ? [X299: term] :
( ( sub @ X299 @ id )
!= X299 ) ) )
& ( ? [X298: term] :
( ( sub @ X298 @ id )
!= X298 )
| ! [X299: term] :
( ( sub @ X299 @ id )
= X299 )
| ( termmset_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP46 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP46 ) )
& ( ! [X429: term] :
? [X430: subst > term > term] :
( ( X430 @ sh @ one )
= ( sub @ X429 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X429: term] :
! [X430: subst > term > term] :
( ( X430 @ sh @ one )
!= ( sub @ X429 @ ( push @ one @ sh ) ) ) )
& ( ( induction2lem = $true )
| ( sP45 != $true ) )
& ( ( sP45 = $true )
| ( induction2lem != $true ) )
& ( ! [X329: term] :
? [X330: subst > term > term] :
! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X329: term] :
! [X330: subst > term > term] :
? [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
!= ( X330 @ X332 @ X331 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
= ( X505 @ one ) )
| ? [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
!= ( X505 @ X507 ) )
| ( $true
!= ( X504 @ X503 ) ) )
| ? [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
!= X501 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
!= ( X505 @ one ) )
& ! [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
= ( X505 @ X507 ) )
& ( $true
= ( X504 @ X503 ) ) )
& ! [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
= X501 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X168: subst > term > subst > $o] :
? [X169: term > $o] :
! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X168: subst > term > subst > $o] :
! [X169: term > $o] :
? [X170: term] :
( ( X168 @ id @ X170 @ id )
!= ( X169 @ X170 ) ) )
& ( ( sP43 = $true )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( sP43 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP35 != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP34 != $true ) )
& ( ( sP34 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X370: term,X371: term,X372: term,X373: term] :
( ( X370 != X372 )
& ( ( ap @ X372 @ X373 )
= ( ap @ X370 @ X371 ) ) ) )
& ( ( pushprop_lem0 = $true )
| ? [X259: term > $o,X260: subst,X261: term] :
! [X262: term > $o] :
? [X263: term] :
( ( X262 @ X263 )
!= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) ) )
& ( ! [X259: term > $o,X260: subst,X261: term] :
? [X262: term > $o] :
! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( axidl = $true )
| ? [X257: subst] :
( ( comp @ id @ X257 )
!= X257 ) )
& ( ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 )
| ( axidl != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ? [X82: subst] :
( ( comp @ id @ X82 )
!= X82 )
| ? [X83: subst] :
( ( comp @ X83 @ id )
!= X83 )
| ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
& ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 )
& ( ? [X85: subst] :
( ( comp @ X85 @ id )
!= X85 )
| ? [X84: subst] :
( ( comp @ id @ X84 )
!= X84 ) ) ) )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ( ( X481 @ X484 )
!= $true )
| ? [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
!= ( X483 @ X485 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
!= $true )
& ( ( X481 @ X484 )
= $true )
& ! [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
= ( X483 @ X485 ) ) ) )
& ( axapp = $true )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
& ( X374 != X377 ) ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X327: term] :
! [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
!= ( X328 @ sh @ one ) ) )
& ( ! [X327: term] :
? [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
= ( X328 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X174: term] :
! [X175: subst > term > term] :
? [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
!= ( X175 @ X177 @ X176 ) ) )
& ( ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( induction2_lthm = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( induction2_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
| ? [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
!= X128 ) )
& ( ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 )
| ( axvarcons != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X477: term,X478: term,X479: term,X480: term] :
( ( X478 != X479 )
& ( ( ap @ ( sub @ X478 @ id ) @ X477 )
= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
& ! [X473: term,X474: term,X475: term,X476: term] :
( ( X474 = X476 )
| ( ( ap @ X476 @ X473 )
!= ( ap @ X474 @ X475 ) ) )
& ! [X472: term] :
( ( sub @ X472 @ id )
= X472 ) ) )
& ( ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
| ? [X473: term,X474: term,X475: term,X476: term] :
( ( X474 != X476 )
& ( ( ap @ X476 @ X473 )
= ( ap @ X474 @ X475 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 )
| ( hoasapinj1_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X241: subst,X242: term,X243: term > $o] :
! [X244: term > $o] :
? [X245: term] :
( ( X244 @ X245 )
!= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( ! [X241: subst,X242: term,X243: term > $o] :
? [X244: term > $o] :
! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( sP28 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP28 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( sP27 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP27 != $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X409: term,X410: term,X411: term,X412: term] :
( ( X409 != X410 )
& ( ( ap @ X411 @ X410 )
= ( ap @ X412 @ X409 ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X527: term,X528: term] :
( ( X527 != X528 )
& ( ( sub @ X528 @ sh )
= ( sub @ X527 @ sh ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ! [X171: subst > term > subst > $o] :
? [X172: term > $o] :
! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X171: subst > term > subst > $o] :
! [X172: term > $o] :
? [X173: term] :
( ( X171 @ id @ X173 @ id )
!= ( X172 @ X173 ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X0: term,X1: subst > term > subst > $o] :
( ? [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) )
& ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X1 @ id @ X0 @ id ) )
| ( ( sP20 @ X1 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X0: term,X1: subst > term > subst > $o] :
( ! [X4: subst > term > term] :
( ? [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
!= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ? [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true )
& ( ( X1 @ id @ X8 @ id )
= $true ) )
| ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) )
& ( ( sP20 @ X1 )
!= $true ) ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X258: subst] :
( ( comp @ X258 @ id )
!= X258 ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( induction2_gthm = $true )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X256: term] :
( ( sub @ X256 @ id )
!= X256 ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X439: term,X440: term > $o] :
( ? [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
!= $true )
& ( ( X440 @ X443 )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ( ( sP10 @ X440 )
= $true )
| ? [X444: term] :
( ( ( X440 @ X444 )
!= $true )
& ( $true
= ( var @ X444 ) ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X439: term,X440: term > $o] :
( ! [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
= $true )
| ( ( X440 @ X443 )
!= $true ) )
& ( ( X440 @ X439 )
!= $true )
& ( ( sP10 @ X440 )
!= $true )
& ! [X444: term] :
( ( ( X440 @ X444 )
= $true )
| ( $true
!= ( var @ X444 ) ) ) ) )
& ! [X294: d_term,X295: d_term] :
( ( X294 = X295 )
| ( ( d2term @ X294 )
!= ( d2term @ X295 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ( sP9 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP9 != $true ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( ( hoaslaminj = $true )
| ? [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
!= ( X448 @ X445 @ X446 ) )
& ( ( lam @ ( X447 @ sh @ one ) )
= ( lam @ ( X448 @ sh @ one ) ) )
& ! [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
& ! [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) ) )
& ( ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ? [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
!= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
| ? [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
!= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP7 != $true ) )
& ( ( sP7 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP6 != $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
| ( sP5 != $true ) )
& ( ( sP5 = $true )
| ( hoasinduction != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP2 != $true ) )
& ( ( sP2 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP1 != $true ) ) ),
inference(flattening,[status(thm)],[f471]) ).
thf(f471,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP58 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X86: term,X87: term,X88: term,X89: term] :
( ( X88 != X89 )
& ( ( ap @ ( sub @ X86 @ id ) @ X89 )
= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( axscons = $true )
| ? [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
!= X24 ) )
& ( ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 )
| ( axscons != $true ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X455: term,X456: term] :
( ( X455 != X456 )
& ( ( lam @ X456 )
= ( lam @ X455 ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X178: term] :
( ( sub @ X178 @ id )
!= X178 ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
| ? [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
!= X530 ) )
& ( ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 )
| ( axshiftcons != $true ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
| ? [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
!= $true )
& ( $true
= ( X93 @ X94 ) ) ) )
& ( ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( substmonoid = $true )
| ? [X42: subst] :
( ( comp @ id @ X42 )
!= X42 )
| ? [X41: subst] :
( ( comp @ X41 @ id )
!= X41 ) )
& ( ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) )
| ( substmonoid != $true ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ? [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
!= X303 )
| ? [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
!= X300 )
| ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
= X303 )
& ! [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
= X300 )
& ? [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
!= $true )
& ( ( X307 @ X306 )
= $true ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ? [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
!= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
| ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X76: subst > term > term,X77: term,X78: term] :
( ! [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
& ( ( ap @ ( sub @ X77 @ id ) @ X78 )
= ( lam @ ( X76 @ sh @ one ) ) ) ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( sP52 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP52 != $true ) )
& ( hoasinduction_gthm = $true )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
!= ( d2subst @ X471 ) )
| ( X470 = X471 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( induction2lem_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X533 )
& ( ( ap @ X535 @ X532 )
= ( ap @ X534 @ X533 ) ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( X532 = X533 )
| ( ( ap @ X535 @ X532 )
!= ( ap @ X534 @ X533 ) ) )
& ? [X536: term,X537: term,X538: term,X539: term] :
( ( X536 != X538 )
& ( ( ap @ ( sub @ X539 @ id ) @ X538 )
= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
| ( ! [X298: term] :
( ( sub @ X298 @ id )
= X298 )
& ? [X299: term] :
( ( sub @ X299 @ id )
!= X299 ) ) )
& ( ? [X298: term] :
( ( sub @ X298 @ id )
!= X298 )
| ! [X299: term] :
( ( sub @ X299 @ id )
= X299 )
| ( termmset_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP46 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP46 ) )
& ( ! [X429: term] :
? [X430: subst > term > term] :
( ( X430 @ sh @ one )
= ( sub @ X429 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X429: term] :
! [X430: subst > term > term] :
( ( X430 @ sh @ one )
!= ( sub @ X429 @ ( push @ one @ sh ) ) ) )
& ( ( induction2lem = $true )
| ( sP45 != $true ) )
& ( ( sP45 = $true )
| ( induction2lem != $true ) )
& ( ! [X329: term] :
? [X330: subst > term > term] :
! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X329: term] :
! [X330: subst > term > term] :
? [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
!= ( X330 @ X332 @ X331 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
= ( X505 @ one ) )
| ? [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
!= ( X505 @ X507 ) )
| ( $true
!= ( X504 @ X503 ) ) )
| ? [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
!= X501 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
!= ( X505 @ one ) )
& ! [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
= ( X505 @ X507 ) )
& ( $true
= ( X504 @ X503 ) ) )
& ! [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
= X501 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X168: subst > term > subst > $o] :
? [X169: term > $o] :
! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X168: subst > term > subst > $o] :
! [X169: term > $o] :
? [X170: term] :
( ( X168 @ id @ X170 @ id )
!= ( X169 @ X170 ) ) )
& ( ( sP43 = $true )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( sP43 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP35 != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP34 != $true ) )
& ( ( sP34 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X370: term,X371: term,X372: term,X373: term] :
( ( X370 != X372 )
& ( ( ap @ X372 @ X373 )
= ( ap @ X370 @ X371 ) ) ) )
& ( ( pushprop_lem0 = $true )
| ? [X259: term > $o,X260: subst,X261: term] :
! [X262: term > $o] :
? [X263: term] :
( ( X262 @ X263 )
!= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) ) )
& ( ! [X259: term > $o,X260: subst,X261: term] :
? [X262: term > $o] :
! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( axidl = $true )
| ? [X257: subst] :
( ( comp @ id @ X257 )
!= X257 ) )
& ( ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 )
| ( axidl != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ? [X82: subst] :
( ( comp @ id @ X82 )
!= X82 )
| ? [X83: subst] :
( ( comp @ X83 @ id )
!= X83 )
| ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
& ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 )
& ( ? [X85: subst] :
( ( comp @ X85 @ id )
!= X85 )
| ? [X84: subst] :
( ( comp @ id @ X84 )
!= X84 ) ) ) )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ( ( X481 @ X484 )
!= $true )
| ? [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
!= ( X483 @ X485 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
!= $true )
& ( ( X481 @ X484 )
= $true )
& ! [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
= ( X483 @ X485 ) ) ) )
& ( axapp = $true )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
& ( X374 != X377 ) ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X327: term] :
! [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
!= ( X328 @ sh @ one ) ) )
& ( ! [X327: term] :
? [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
= ( X328 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X174: term] :
! [X175: subst > term > term] :
? [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
!= ( X175 @ X177 @ X176 ) ) )
& ( ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( induction2_lthm = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( induction2_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
| ? [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
!= X128 ) )
& ( ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 )
| ( axvarcons != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X477: term,X478: term,X479: term,X480: term] :
( ( X478 != X479 )
& ( ( ap @ ( sub @ X478 @ id ) @ X477 )
= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
& ! [X473: term,X474: term,X475: term,X476: term] :
( ( X474 = X476 )
| ( ( ap @ X476 @ X473 )
!= ( ap @ X474 @ X475 ) ) )
& ! [X472: term] :
( ( sub @ X472 @ id )
= X472 ) ) )
& ( ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
| ? [X473: term,X474: term,X475: term,X476: term] :
( ( X474 != X476 )
& ( ( ap @ X476 @ X473 )
= ( ap @ X474 @ X475 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 )
| ( hoasapinj1_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X241: subst,X242: term,X243: term > $o] :
! [X244: term > $o] :
? [X245: term] :
( ( X244 @ X245 )
!= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( ! [X241: subst,X242: term,X243: term > $o] :
? [X244: term > $o] :
! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( sP28 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP28 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( sP27 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP27 != $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X409: term,X410: term,X411: term,X412: term] :
( ( X409 != X410 )
& ( ( ap @ X411 @ X410 )
= ( ap @ X412 @ X409 ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X527: term,X528: term] :
( ( X527 != X528 )
& ( ( sub @ X528 @ sh )
= ( sub @ X527 @ sh ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ! [X171: subst > term > subst > $o] :
? [X172: term > $o] :
! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X171: subst > term > subst > $o] :
! [X172: term > $o] :
? [X173: term] :
( ( X171 @ id @ X173 @ id )
!= ( X172 @ X173 ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X0: term,X1: subst > term > subst > $o] :
( ? [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) )
& ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X1 @ id @ X0 @ id ) )
| ( ( sP20 @ X1 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X0: term,X1: subst > term > subst > $o] :
( ! [X4: subst > term > term] :
( ? [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
!= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ? [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true )
& ( ( X1 @ id @ X8 @ id )
= $true ) )
| ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) )
& ( ( sP20 @ X1 )
!= $true ) ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X258: subst] :
( ( comp @ X258 @ id )
!= X258 ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( induction2_gthm = $true )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X256: term] :
( ( sub @ X256 @ id )
!= X256 ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X439: term,X440: term > $o] :
( ? [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
!= $true )
& ( ( X440 @ X443 )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ( ( sP10 @ X440 )
= $true )
| ? [X444: term] :
( ( ( X440 @ X444 )
!= $true )
& ( $true
= ( var @ X444 ) ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X439: term,X440: term > $o] :
( ! [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
= $true )
| ( ( X440 @ X443 )
!= $true ) )
& ( ( X440 @ X439 )
!= $true )
& ( ( sP10 @ X440 )
!= $true )
& ! [X444: term] :
( ( ( X440 @ X444 )
= $true )
| ( $true
!= ( var @ X444 ) ) ) ) )
& ! [X294: d_term,X295: d_term] :
( ( X294 = X295 )
| ( ( d2term @ X294 )
!= ( d2term @ X295 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ( sP9 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP9 != $true ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( ( hoaslaminj = $true )
| ? [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
!= ( X448 @ X445 @ X446 ) )
& ( ( lam @ ( X447 @ sh @ one ) )
= ( lam @ ( X448 @ sh @ one ) ) )
& ! [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
& ! [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) ) )
& ( ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ? [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
!= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
| ? [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
!= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP7 != $true ) )
& ( ( sP7 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP6 != $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
| ( sP5 != $true ) )
& ( ( sP5 = $true )
| ( hoasinduction != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP2 != $true ) )
& ( ( sP2 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( sP58 = $true )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ( axscons = $true )
<=> ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
<=> ( laminj = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
<=> ( axvarid = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) ) )
& ( ( substmonoid = $true )
<=> ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) ) )
& ( ( $true = sP56 )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( ? [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
!= X303 )
| ? [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
!= X300 )
| ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ? [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
!= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
| ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ( sP53 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( sP52 = $true )
<=> ( hoasinduction_lem2 = $true ) )
& ( hoasinduction_gthm = $true )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
!= ( d2subst @ X471 ) )
| ( X470 = X471 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
<=> ( sP50 = $true ) )
& ( hoaslamnotvar = $true )
& ( ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X533 )
& ( ( ap @ X535 @ X532 )
= ( ap @ X534 @ X533 ) ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X298: term] :
( ( sub @ X298 @ id )
!= X298 )
| ! [X299: term] :
( ( sub @ X299 @ id )
= X299 ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP46 )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X429: term] :
? [X430: subst > term > term] :
( ( X430 @ sh @ one )
= ( sub @ X429 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem = $true )
<=> ( sP45 = $true ) )
& ( ! [X329: term] :
? [X330: subst > term > term] :
! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
= ( X505 @ one ) )
| ? [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
!= ( X505 @ X507 ) )
| ( $true
!= ( X504 @ X503 ) ) )
| ? [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
!= X501 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X168: subst > term > subst > $o] :
? [X169: term > $o] :
! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( sP43 = $true )
<=> ( induction2 = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( sP41 = $true ) )
& ( ( sP35 = $true )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( sP34 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
<=> ( apinj1 = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X259: term > $o,X260: subst,X261: term] :
? [X262: term > $o] :
! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) ) )
& ( ( axidl = $true )
<=> ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( ? [X82: subst] :
( ( comp @ id @ X82 )
!= X82 )
| ? [X83: subst] :
( ( comp @ X83 @ id )
!= X83 )
| ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ( ( X481 @ X484 )
!= $true )
| ? [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
!= ( X483 @ X485 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( axapp = $true )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X327: term] :
? [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
= ( X328 @ sh @ one ) ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) ) )
& ( ( induction2_lthm = $true )
<=> ( sP32 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
<=> ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
| ? [X473: term,X474: term,X475: term,X476: term] :
( ( X474 != X476 )
& ( ( ap @ X476 @ X473 )
= ( ap @ X474 @ X475 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X241: subst,X242: term,X243: term > $o] :
? [X244: term > $o] :
! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( sP28 = $true )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( sP27 = $true )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
<=> ( shinj = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ( sP22 = $true ) )
& ( ! [X171: subst > term > subst > $o] :
? [X172: term > $o] :
! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X0: term,X1: subst > term > subst > $o] :
( ? [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) )
& ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X1 @ id @ X0 @ id ) )
| ( ( sP20 @ X1 )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
<=> ( axidr = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( sP19 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( induction2_gthm = $true )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
<=> ( termmset = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X439: term,X440: term > $o] :
( ? [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
!= $true )
& ( ( X440 @ X443 )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ( ( sP10 @ X440 )
= $true )
| ? [X444: term] :
( ( ( X440 @ X444 )
!= $true )
& ( $true
= ( var @ X444 ) ) ) )
<=> ( induction = $true ) )
& ! [X294: d_term,X295: d_term] :
( ( X294 = X295 )
| ( ( d2term @ X294 )
!= ( d2term @ X295 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ( sP9 = $true )
<=> ( hoasinduction_lem3v2 = $true ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( ( hoaslaminj = $true )
<=> ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ? [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
!= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
| ? [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
!= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ( sP7 = $true ) )
& ( ( sP6 = $true )
<=> ( hoasinduction_lem3a = $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
<=> ( sP5 = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ( sP2 = $true ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( sP1 = $true )
<=> ( hoasinduction_lem3 = $true ) ) ),
inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14]) ).
thf(f14,plain,
! [X60: subst > term > subst > $o] :
( ( ( sP0 @ X60 )
= $true )
<=> ? [X62: subst > term > term] :
( ! [X63: term,X64: subst,X65: subst] :
( ( sub @ ( X62 @ X65 @ X63 ) @ X64 )
= ( X62 @ ( comp @ X65 @ X64 ) @ ( sub @ X63 @ X64 ) ) )
& ! [X66: term] :
( ( ( X60 @ id @ X66 @ id )
!= $true )
| ( ( X60 @ id @ ( X62 @ id @ X66 ) @ id )
= $true ) )
& ( ( X60 @ id @ ( lam @ ( X62 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
( ( sP1 = $true )
<=> ! [X60: subst > term > subst > $o,X61: term] :
( ? [X67: subst,X68: term,X69: subst,X70: subst] :
( ( ( X60 @ X69 @ X68 @ ( comp @ X70 @ X67 ) )
!= $true )
& ( ( X60 @ ( comp @ X69 @ X70 ) @ ( sub @ X68 @ X70 ) @ X67 )
= $true ) )
| ( ( X60 @ id @ ( lam @ X61 ) @ id )
= $true )
| ? [X75: term] :
( ( ( X60 @ id @ ( sub @ X61 @ ( push @ X75 @ id ) ) @ id )
!= $true )
& ( ( X60 @ id @ X75 @ id )
= $true ) )
| ? [X71: subst,X72: subst,X73: subst,X74: term] :
( ( ( X60 @ ( comp @ X73 @ X71 ) @ ( sub @ X74 @ X71 ) @ X72 )
!= $true )
& ( ( X60 @ X73 @ X74 @ ( comp @ X71 @ X72 ) )
= $true ) )
| ( ( sP0 @ X60 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( sP2 = $true )
<=> ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
= $true )
| ? [X249: term] :
( ( X246 @ id @ X249 @ id )
!= ( X247 @ X249 ) )
| ? [X250: subst > term > term] :
( ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X251: term] :
( ( ( X246 @ id @ X251 @ id )
!= $true )
| ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true ) )
& ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X255: term] :
( ( ( X247 @ X255 )
= $true )
& ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
! [X310: subst > term > subst > $o] :
( ( ( sP3 @ X310 )
= $true )
<=> ? [X325: term,X326: term] :
( ( $true
= ( X310 @ id @ X326 @ id ) )
& ( ( X310 @ id @ X325 @ id )
= $true )
& ( ( X310 @ id @ ( ap @ ( sub @ X326 @ id ) @ X325 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
! [X310: subst > term > subst > $o] :
( ( ( sP4 @ X310 )
= $true )
<=> ? [X320: subst > term > term] :
( ! [X324: term] :
( ( ( X310 @ id @ X324 @ id )
!= $true )
| ( ( X310 @ id @ ( X320 @ id @ X324 ) @ id )
= $true ) )
& ! [X321: subst,X322: term,X323: subst] :
( ( sub @ ( X320 @ X321 @ X322 ) @ X323 )
= ( X320 @ ( comp @ X321 @ X323 ) @ ( sub @ X322 @ X323 ) ) )
& ( ( X310 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
( ( sP5 = $true )
<=> ! [X309: term,X310: subst > term > subst > $o] :
( ( ( sP4 @ X310 )
= $true )
| ? [X312: subst,X313: subst,X314: term,X315: subst] :
( ( $true
= ( X310 @ ( comp @ X315 @ X312 ) @ ( sub @ X314 @ X312 ) @ X313 ) )
& ( ( X310 @ X315 @ X314 @ ( comp @ X312 @ X313 ) )
!= $true ) )
| ? [X311: term] :
( ( ( var @ ( sub @ X311 @ id ) )
= $true )
& ( ( X310 @ id @ X311 @ id )
!= $true ) )
| ? [X316: term,X317: subst,X318: subst,X319: subst] :
( ( ( X310 @ X318 @ X316 @ ( comp @ X319 @ X317 ) )
= $true )
& ( ( X310 @ ( comp @ X318 @ X319 ) @ ( sub @ X316 @ X319 ) @ X317 )
!= $true ) )
| ( ( X310 @ id @ X309 @ id )
= $true )
| ( ( sP3 @ X310 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
( ( sP6 = $true )
<=> ! [X233: term,X234: subst > term > subst > $o] :
( ? [X235: subst > term > term] :
( ! [X239: term] :
( ( ( X234 @ id @ ( X235 @ id @ X239 ) @ id )
= $true )
| ( ( X234 @ id @ X239 @ id )
!= $true ) )
& ( ( X234 @ id @ ( lam @ ( X235 @ sh @ one ) ) @ id )
!= $true )
& ! [X236: subst,X237: subst,X238: term] :
( ( X235 @ ( comp @ X236 @ X237 ) @ ( sub @ X238 @ X237 ) )
= ( sub @ ( X235 @ X236 @ X238 ) @ X237 ) ) )
| ( ( X234 @ id @ ( lam @ X233 ) @ id )
= $true )
| ? [X240: term] :
( ( ( X234 @ id @ ( sub @ X233 @ ( push @ X240 @ id ) ) @ id )
!= $true )
& ( ( X234 @ id @ X240 @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
( ( sP7 = $true )
<=> ! [X431: term,X432: subst > term > subst > $o] :
( ? [X433: subst > term > term] :
( ! [X434: subst,X435: subst,X436: term] :
( ( sub @ ( X433 @ X434 @ X436 ) @ X435 )
= ( X433 @ ( comp @ X434 @ X435 ) @ ( sub @ X436 @ X435 ) ) )
& ( ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id )
!= $true )
& ! [X437: term] :
( ( ( X432 @ id @ ( X433 @ id @ X437 ) @ id )
= $true )
| ( ( X432 @ id @ X437 @ id )
!= $true ) ) )
| ( ( X432 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X438: term] :
( ( ( X432 @ id @ ( sub @ X431 @ ( push @ X438 @ id ) ) @ id )
!= $true )
& ( ( X432 @ id @ X438 @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X354: subst > term > subst > $o] :
( ( ( sP8 @ X354 )
= $true )
<=> ? [X361: subst > term > term] :
( ! [X365: term] :
( ( ( X354 @ id @ ( X361 @ id @ X365 ) @ id )
= $true )
| ( ( X354 @ id @ X365 @ id )
!= $true ) )
& ( ( X354 @ id @ ( lam @ ( X361 @ sh @ one ) ) @ id )
!= $true )
& ! [X362: subst,X363: subst,X364: term] :
( ( sub @ ( X361 @ X363 @ X364 ) @ X362 )
= ( X361 @ ( comp @ X363 @ X362 ) @ ( sub @ X364 @ X362 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
( ( sP9 = $true )
<=> ! [X352: term,X353: term > $o,X354: subst > term > subst > $o] :
( ? [X366: subst,X367: subst,X368: term,X369: subst] :
( ( ( X354 @ X366 @ X368 @ ( comp @ X369 @ X367 ) )
= $true )
& ( ( X354 @ ( comp @ X366 @ X369 ) @ ( sub @ X368 @ X369 ) @ X367 )
!= $true ) )
| ? [X357: subst,X358: subst,X359: term,X360: subst] :
( ( ( X354 @ ( comp @ X358 @ X360 ) @ ( sub @ X359 @ X360 ) @ X357 )
= $true )
& ( ( X354 @ X358 @ X359 @ ( comp @ X360 @ X357 ) )
!= $true ) )
| ? [X355: term] :
( ( ( X353 @ ( sub @ X352 @ ( push @ X355 @ id ) ) )
!= $true )
& ( ( X353 @ X355 )
= $true ) )
| ( ( sP8 @ X354 )
= $true )
| ? [X356: term] :
( ( X354 @ id @ X356 @ id )
!= ( X353 @ X356 ) )
| ( ( X353 @ ( lam @ X352 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
! [X440: term > $o] :
( ( ( sP10 @ X440 )
= $true )
<=> ? [X441: term,X442: term] :
( ( ( X440 @ X442 )
= $true )
& ( ( X440 @ X441 )
= $true )
& ( ( X440 @ ( ap @ X441 @ X442 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
! [X200: subst > term > subst > $o] :
( ( ( sP11 @ X200 )
= $true )
<=> ! [X206: subst > term > term] :
( ? [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
!= $true )
& ( ( X200 @ id @ X207 @ id )
= $true ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ? [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
!= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
! [X188: subst > term > subst > $o] :
( ( ( sP12 @ X188 )
= $true )
<=> ! [X189: term,X190: term] :
( ( ( X188 @ id @ ( ap @ ( sub @ X189 @ id ) @ X190 ) @ id )
= $true )
| ( ( X188 @ id @ X190 @ id )
!= $true )
| ( ( X188 @ id @ X189 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
! [X215: subst > term > subst > $o] :
( ( ( sP13 @ X215 )
= $true )
<=> ? [X231: term,X232: term] :
( ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
!= $true )
& ( ( X215 @ id @ X232 @ id )
= $true )
& ( ( X215 @ id @ X231 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X215: subst > term > subst > $o] :
( ( ( sP14 @ X215 )
= $true )
<=> ? [X218: subst > term > term] :
( ( ( X215 @ id @ ( lam @ ( X218 @ sh @ one ) ) @ id )
!= $true )
& ! [X222: term] :
( ( ( X215 @ id @ X222 @ id )
!= $true )
| ( ( X215 @ id @ ( X218 @ id @ X222 ) @ id )
= $true ) )
& ! [X219: term,X220: subst,X221: subst] :
( ( X218 @ ( comp @ X220 @ X221 ) @ ( sub @ X219 @ X221 ) )
= ( sub @ ( X218 @ X220 @ X219 ) @ X221 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
! [X179: term > $o] :
( ( ( sP15 @ X179 )
= $true )
<=> ! [X183: term,X184: term] :
( ( ( X179 @ X184 )
!= $true )
| ( ( X179 @ ( ap @ X184 @ X183 ) )
= $true )
| ( $true
!= ( X179 @ X183 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
( ( sP16 = $true )
<=> ? [X199: term,X200: subst > term > subst > $o] :
( ! [X211: subst,X212: term,X213: subst,X214: subst] :
( ( ( X200 @ ( comp @ X213 @ X214 ) @ ( sub @ X212 @ X214 ) @ X211 )
!= $true )
| ( ( X200 @ X213 @ X212 @ ( comp @ X214 @ X211 ) )
= $true ) )
& ! [X201: subst,X202: subst,X203: subst,X204: term] :
( ( ( X200 @ ( comp @ X201 @ X202 ) @ ( sub @ X204 @ X202 ) @ X203 )
= $true )
| ( ( X200 @ X201 @ X204 @ ( comp @ X202 @ X203 ) )
!= $true ) )
& ! [X205: term] :
( ( ( X200 @ id @ X205 @ id )
!= $true )
| ( ( X200 @ id @ ( sub @ X199 @ ( push @ X205 @ id ) ) @ id )
= $true ) )
& ( ( X200 @ id @ ( lam @ X199 ) @ id )
!= $true )
& ( ( sP11 @ X200 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
( ( sP17 = $true )
<=> ! [X215: subst > term > subst > $o,X216: term] :
( ? [X217: term] :
( ( ( var @ ( sub @ X217 @ id ) )
= $true )
& ( ( X215 @ id @ X217 @ id )
!= $true ) )
| ? [X227: subst,X228: subst,X229: subst,X230: term] :
( ( ( X215 @ X229 @ X230 @ ( comp @ X228 @ X227 ) )
= $true )
& ( ( X215 @ ( comp @ X229 @ X228 ) @ ( sub @ X230 @ X228 ) @ X227 )
!= $true ) )
| ? [X223: term,X224: subst,X225: subst,X226: subst] :
( ( ( X215 @ X225 @ X223 @ ( comp @ X226 @ X224 ) )
!= $true )
& ( ( X215 @ ( comp @ X225 @ X226 ) @ ( sub @ X223 @ X226 ) @ X224 )
= $true ) )
| ( ( sP14 @ X215 )
= $true )
| ( ( X215 @ id @ X216 @ id )
= $true )
| ( ( sP13 @ X215 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
( ( sP18 = $true )
<=> ? [X186: term,X187: term,X188: subst > term > subst > $o] :
( ! [X191: term,X192: subst,X193: subst,X194: subst] :
( ( ( X188 @ ( comp @ X194 @ X193 ) @ ( sub @ X191 @ X193 ) @ X192 )
!= $true )
| ( ( X188 @ X194 @ X191 @ ( comp @ X193 @ X192 ) )
= $true ) )
& ( ( X188 @ id @ X187 @ id )
= $true )
& ( ( sP12 @ X188 )
= $true )
& ( $true
!= ( X188 @ id @ ( ap @ X186 @ X187 ) @ id ) )
& ( ( X188 @ id @ X186 @ id )
= $true )
& ! [X195: term,X196: subst,X197: subst,X198: subst] :
( ( ( X188 @ ( comp @ X197 @ X198 ) @ ( sub @ X195 @ X198 ) @ X196 )
= $true )
| ( ( X188 @ X197 @ X195 @ ( comp @ X198 @ X196 ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
( ( sP19 = $true )
<=> ( ? [X179: term > $o,X180: term] :
( ( ( sP15 @ X179 )
= $true )
& ! [X181: term] :
( ? [X182: term] :
( ( ( X179 @ ( sub @ X181 @ ( push @ X182 @ id ) ) )
!= $true )
& ( ( X179 @ X182 )
= $true ) )
| ( ( X179 @ ( lam @ X181 ) )
= $true ) )
& ( ( X179 @ X180 )
!= $true )
& ! [X185: term] :
( ( ( X179 @ X185 )
= $true )
| ( ( var @ X185 )
!= $true ) ) )
| ( sP17 = $true )
| ( sP18 = $true )
| ( sP16 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
! [X1: subst > term > subst > $o] :
( ( ( sP20 @ X1 )
= $true )
<=> ? [X2: term,X3: term] :
( ( ( X1 @ id @ X3 @ id )
= $true )
& ( ( X1 @ id @ X2 @ id )
= $true )
& ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
! [X12: subst > term > subst > $o] :
( ( ( sP21 @ X12 )
= $true )
<=> ? [X22: term,X23: term] :
( ( $true
= ( X12 @ id @ X23 @ id ) )
& ( ( X12 @ id @ ( ap @ ( sub @ X23 @ id ) @ X22 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X22 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( sP22 = $true )
<=> ! [X9: term,X10: term > $o,X11: term,X12: subst > term > subst > $o] :
( ( ( X10 @ ( ap @ X11 @ X9 ) )
= $true )
| ? [X14: subst,X15: subst,X16: subst,X17: term] :
( ( ( X12 @ X15 @ X17 @ ( comp @ X16 @ X14 ) )
!= $true )
& ( ( X12 @ ( comp @ X15 @ X16 ) @ ( sub @ X17 @ X16 ) @ X14 )
= $true ) )
| ( ( X10 @ X9 )
!= $true )
| ? [X13: term] :
( ( X10 @ X13 )
!= ( X12 @ id @ X13 @ id ) )
| ? [X18: subst,X19: term,X20: subst,X21: subst] :
( ( ( X12 @ X20 @ X19 @ ( comp @ X18 @ X21 ) )
= $true )
& ( ( X12 @ ( comp @ X20 @ X18 ) @ ( sub @ X19 @ X18 ) @ X21 )
!= $true ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( sP21 @ X12 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
! [X286: subst > term > subst > $o] :
( ( ( sP23 @ X286 )
= $true )
<=> ? [X287: subst > term > term] :
( ( ( X286 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id )
!= $true )
& ! [X291: term] :
( ( ( X286 @ id @ X291 @ id )
!= $true )
| ( ( X286 @ id @ ( X287 @ id @ X291 ) @ id )
= $true ) )
& ! [X288: subst,X289: term,X290: subst] :
( ( sub @ ( X287 @ X288 @ X289 ) @ X290 )
= ( X287 @ ( comp @ X288 @ X290 ) @ ( sub @ X289 @ X290 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
! [X267: term > $o] :
( ( ( sP24 @ X267 )
= $true )
<=> ! [X269: term,X270: term] :
( ( $true
!= ( X267 @ X269 ) )
| ( ( X267 @ ( ap @ X270 @ X269 ) )
= $true )
| ( ( X267 @ X270 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
( ( $true = sP25 )
<=> ? [X275: subst > term > subst > $o,X276: term,X277: term > $o] :
( ! [X278: subst > term > term] :
( ( ( X275 @ id @ ( lam @ ( X278 @ sh @ one ) ) @ id )
= $true )
| ? [X280: term,X281: subst,X282: subst] :
( ( X278 @ ( comp @ X282 @ X281 ) @ ( sub @ X280 @ X281 ) )
!= ( sub @ ( X278 @ X282 @ X280 ) @ X281 ) )
| ? [X279: term] :
( ( ( X275 @ id @ ( X278 @ id @ X279 ) @ id )
!= $true )
& ( ( X275 @ id @ X279 @ id )
= $true ) ) )
& ( ( X277 @ ( lam @ X276 ) )
!= $true )
& ! [X284: term] :
( ( ( X277 @ X284 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X284 @ id ) ) )
= $true ) )
& ! [X283: term] :
( ( X277 @ X283 )
= ( X275 @ id @ X283 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
( ( $true = sP26 )
<=> ? [X267: term > $o,X268: term] :
( ! [X272: term] :
( ? [X273: term] :
( ( ( X267 @ ( sub @ X272 @ ( push @ X273 @ id ) ) )
!= $true )
& ( $true
= ( X267 @ X273 ) ) )
| ( ( X267 @ ( lam @ X272 ) )
= $true ) )
& ( ( sP24 @ X267 )
= $true )
& ( ( X267 @ X268 )
!= $true )
& ! [X271: term] :
( ( ( var @ X271 )
!= $true )
| ( $true
= ( X267 @ X271 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
( ( sP27 = $true )
<=> ( ( $true = sP26 )
| ! [X285: term,X286: subst > term > subst > $o] :
( ? [X292: term,X293: term] :
( ( $true
= ( X286 @ id @ X293 @ id ) )
& ( ( X286 @ id @ X292 @ id )
= $true )
& ( ( X286 @ id @ ( ap @ ( sub @ X292 @ id ) @ X293 ) @ id )
!= $true ) )
| ( ( X286 @ id @ X285 @ id )
= $true )
| ( ( sP23 @ X286 )
= $true ) )
| ( $true = sP25 )
| ? [X274: term] :
( ( sub @ X274 @ id )
!= X274 )
| ? [X264: subst > term > subst > $o] :
! [X265: term > $o] :
? [X266: term] :
( ( X265 @ X266 )
!= ( X264 @ id @ X266 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
( ( sP28 = $true )
<=> ( ? [X382: term] :
( ( sub @ X382 @ id )
!= X382 )
| ! [X383: term,X384: term > $o,X385: subst > term > subst > $o] :
( ? [X387: subst > term > term] :
( ! [X389: subst,X390: subst,X391: term] :
( ( X387 @ ( comp @ X390 @ X389 ) @ ( sub @ X391 @ X389 ) )
= ( sub @ ( X387 @ X390 @ X391 ) @ X389 ) )
& ( ( X385 @ id @ ( lam @ ( X387 @ sh @ one ) ) @ id )
!= $true )
& ! [X388: term] :
( ( ( X385 @ id @ X388 @ id )
!= $true )
| ( ( X385 @ id @ ( X387 @ id @ X388 ) @ id )
= $true ) ) )
| ? [X386: term] :
( ( X384 @ X386 )
!= ( X385 @ id @ X386 @ id ) )
| ? [X392: term] :
( ( ( X384 @ ( sub @ X383 @ ( push @ X392 @ id ) ) )
!= $true )
& ( ( X384 @ X392 )
= $true ) )
| ( ( X384 @ ( lam @ X383 ) )
= $true ) )
| ? [X378: term] :
! [X379: subst > term > term] :
? [X380: term,X381: subst] :
( ( X379 @ X381 @ X380 )
!= ( sub @ X378 @ ( push @ X380 @ X381 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
! [X35: term > $o] :
( ( ( sP29 @ X35 )
= $true )
<=> ? [X38: term,X39: term] :
( ( $true
= ( X35 @ X39 ) )
& ( ( X35 @ ( ap @ X39 @ X38 ) )
!= $true )
& ( ( X35 @ X38 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
! [X26: term > $o] :
( ( ( sP30 @ X26 )
= $true )
<=> ! [X29: term,X30: term] :
( ( ( X26 @ X29 )
!= $true )
| ( ( X26 @ X30 )
!= $true )
| ( ( X26 @ ( ap @ X29 @ X30 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
( ( sP31 = $true )
<=> ! [X34: term,X35: term > $o] :
( ( ( sP29 @ X35 )
= $true )
| ( $true
= ( X35 @ X34 ) )
| ? [X36: term] :
( ! [X37: term] :
( ( $true
= ( X35 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) )
| ( ( X35 @ X37 )
!= $true ) )
& ( ( X35 @ ( lam @ X36 ) )
!= $true ) )
| ? [X40: term] :
( ( ( var @ X40 )
= $true )
& ( ( X35 @ X40 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
( ( sP32 = $true )
<=> ( ? [X26: term > $o,X27: term,X28: subst] :
( ! [X31: term] :
( ? [X32: term] :
( ( ( X26 @ ( sub @ X31 @ ( push @ X32 @ id ) ) )
!= $true )
& ( ( X26 @ X32 )
= $true ) )
| ( ( X26 @ ( lam @ X31 ) )
= $true ) )
& ( ( sP30 @ X26 )
= $true )
& ( ( X26 @ ( sub @ X27 @ X28 ) )
!= $true )
& ! [X33: term] :
( ( ( var @ X33 )
!= $true )
| ( ( X26 @ ( sub @ X33 @ X28 ) )
= $true ) ) )
| ( sP31 = $true )
| ? [X25: term] :
( ( sub @ X25 @ id )
!= X25 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
! [X510: subst > term > subst > $o] :
( ( ( sP33 @ X510 )
= $true )
<=> ? [X521: subst > term > term] :
( ! [X522: term,X523: subst,X524: subst] :
( ( sub @ ( X521 @ X523 @ X522 ) @ X524 )
= ( X521 @ ( comp @ X523 @ X524 ) @ ( sub @ X522 @ X524 ) ) )
& ( ( X510 @ id @ ( lam @ ( X521 @ sh @ one ) ) @ id )
!= $true )
& ! [X525: term] :
( ( ( X510 @ id @ X525 @ id )
!= $true )
| ( ( X510 @ id @ ( X521 @ id @ X525 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
( ( sP34 = $true )
<=> ( ! [X509: term > $o,X510: subst > term > subst > $o,X511: term] :
( ? [X526: term] :
( ( $true
!= ( X509 @ ( sub @ X511 @ ( push @ X526 @ id ) ) ) )
& ( ( X509 @ X526 )
= $true ) )
| ( ( X509 @ ( lam @ X511 ) )
= $true )
| ? [X520: term] :
( ( X509 @ X520 )
!= ( X510 @ id @ X520 @ id ) )
| ? [X512: term,X513: subst,X514: subst,X515: subst] :
( ( ( X510 @ X513 @ X512 @ ( comp @ X514 @ X515 ) )
= $true )
& ( ( X510 @ ( comp @ X513 @ X514 ) @ ( sub @ X512 @ X514 ) @ X515 )
!= $true ) )
| ? [X516: subst,X517: term,X518: subst,X519: subst] :
( ( ( X510 @ X516 @ X517 @ ( comp @ X518 @ X519 ) )
!= $true )
& ( ( X510 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) @ X519 )
= $true ) )
| ( ( sP33 @ X510 )
= $true ) )
| ? [X508: term] :
( ( sub @ X508 @ id )
!= X508 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
( ( sP35 = $true )
<=> ! [X393: term,X394: subst > term > subst > $o] :
( ( ( X394 @ id @ ( lam @ ( sub @ X393 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X400: term] :
( ( ( X394 @ id @ ( sub @ X393 @ ( push @ X400 @ id ) ) @ id )
!= $true )
& ( ( X394 @ id @ X400 @ id )
= $true ) )
| ? [X395: subst > term > term] :
( ! [X397: term,X398: subst,X399: subst] :
( ( X395 @ ( comp @ X398 @ X399 ) @ ( sub @ X397 @ X399 ) )
= ( sub @ ( X395 @ X398 @ X397 ) @ X399 ) )
& ! [X396: term] :
( ( ( X394 @ id @ X396 @ id )
!= $true )
| ( ( X394 @ id @ ( X395 @ id @ X396 ) @ id )
= $true ) )
& ( ( X394 @ id @ ( lam @ ( X395 @ sh @ one ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
! [X150: subst > term > subst > $o] :
( ( ( sP36 @ X150 )
= $true )
<=> ? [X152: term,X153: term] :
( ( ( X150 @ id @ ( ap @ ( sub @ X152 @ id ) @ X153 ) @ id )
!= $true )
& ( ( X150 @ id @ X153 @ id )
= $true )
& ( ( X150 @ id @ X152 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
! [X150: subst > term > subst > $o] :
( ( ( sP37 @ X150 )
= $true )
<=> ? [X159: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X150 @ id @ X163 @ id ) )
| ( ( X150 @ id @ ( X159 @ id @ X163 ) @ id )
= $true ) )
& ! [X160: term,X161: subst,X162: subst] :
( ( sub @ ( X159 @ X162 @ X160 ) @ X161 )
= ( X159 @ ( comp @ X162 @ X161 ) @ ( sub @ X160 @ X161 ) ) )
& ( ( X150 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
! [X132: term > $o] :
( ( ( sP38 @ X132 )
= $true )
<=> ! [X135: term,X136: term] :
( ( ( X132 @ X135 )
!= $true )
| ( ( X132 @ ( ap @ X135 @ X136 ) )
= $true )
| ( ( X132 @ X136 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
( ( sP39 = $true )
<=> ? [X140: term > $o,X141: term,X142: subst > term > subst > $o] :
( ! [X143: subst > term > term] :
( ( $true
= ( X142 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ? [X144: term] :
( ( ( X142 @ id @ ( X143 @ id @ X144 ) @ id )
!= $true )
& ( ( X142 @ id @ X144 @ id )
= $true ) )
| ? [X145: subst,X146: term,X147: subst] :
( ( X143 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) )
!= ( sub @ ( X143 @ X147 @ X146 ) @ X145 ) ) )
& ( ( X140 @ ( lam @ X141 ) )
!= $true )
& ! [X149: term] :
( ( ( X140 @ ( sub @ X141 @ ( push @ X149 @ id ) ) )
= $true )
| ( ( X140 @ X149 )
!= $true ) )
& ! [X148: term] :
( ( X140 @ X148 )
= ( X142 @ id @ X148 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
( ( $true = sP40 )
<=> ! [X150: subst > term > subst > $o,X151: term] :
( ? [X154: term] :
( ( ( var @ ( sub @ X154 @ id ) )
= $true )
& ( ( X150 @ id @ X154 @ id )
!= $true ) )
| ? [X164: subst,X165: subst,X166: subst,X167: term] :
( ( ( X150 @ ( comp @ X166 @ X165 ) @ ( sub @ X167 @ X165 ) @ X164 )
!= $true )
& ( ( X150 @ X166 @ X167 @ ( comp @ X165 @ X164 ) )
= $true ) )
| ( ( sP37 @ X150 )
= $true )
| ? [X155: subst,X156: term,X157: subst,X158: subst] :
( ( ( X150 @ ( comp @ X158 @ X155 ) @ ( sub @ X156 @ X155 ) @ X157 )
= $true )
& ( ( X150 @ X158 @ X156 @ ( comp @ X155 @ X157 ) )
!= $true ) )
| ( ( sP36 @ X150 )
= $true )
| ( ( X150 @ id @ X151 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( sP41 = $true )
<=> ( ? [X132: term > $o,X133: term] :
( ( ( sP38 @ X132 )
= $true )
& ! [X137: term] :
( ( ( X132 @ ( lam @ X137 ) )
= $true )
| ? [X138: term] :
( ( ( X132 @ ( sub @ X137 @ ( push @ X138 @ id ) ) )
!= $true )
& ( ( X132 @ X138 )
= $true ) ) )
& ! [X134: term] :
( ( $true
= ( X132 @ X134 ) )
| ( ( var @ X134 )
!= $true ) )
& ( ( X132 @ X133 )
!= $true ) )
| ( $true = sP40 )
| ? [X139: term] :
( ( sub @ X139 @ id )
!= X139 )
| ( sP39 = $true )
| ? [X129: subst > term > subst > $o] :
! [X130: term > $o] :
? [X131: term] :
( ( X130 @ X131 )
!= ( X129 @ id @ X131 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
! [X120: term > $o] :
( ( ( sP42 @ X120 )
= $true )
<=> ? [X123: term,X124: term] :
( ( ( X120 @ ( ap @ X123 @ X124 ) )
!= $true )
& ( ( X120 @ X124 )
= $true )
& ( ( X120 @ X123 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
( ( sP43 = $true )
<=> ! [X120: term > $o,X121: term] :
( ? [X125: term] :
( ( ( X120 @ ( lam @ X125 ) )
!= $true )
& ! [X126: term] :
( ( ( X120 @ ( sub @ X125 @ ( push @ X126 @ id ) ) )
= $true )
| ( ( X120 @ X126 )
!= $true ) ) )
| ( ( sP42 @ X120 )
= $true )
| ( ( X120 @ X121 )
= $true )
| ? [X122: term] :
( ( ( X120 @ X122 )
!= $true )
& ( ( var @ X122 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
! [X402: term > $o] :
( ( ( sP44 @ X402 )
= $true )
<=> ? [X407: term,X408: term] :
( ( ( X402 @ X407 )
= $true )
& ( ( X402 @ X408 )
= $true )
& ( ( X402 @ ( ap @ X408 @ X407 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
( ( sP45 = $true )
<=> ! [X401: subst,X402: term > $o,X403: term] :
( ? [X404: term] :
( ( ( X402 @ ( lam @ X404 ) )
!= $true )
& ! [X405: term] :
( ( ( X402 @ X405 )
!= $true )
| ( ( X402 @ ( sub @ X404 @ ( push @ X405 @ id ) ) )
= $true ) ) )
| ( ( sP44 @ X402 )
= $true )
| ( ( X402 @ ( sub @ X403 @ X401 ) )
= $true )
| ? [X406: term] :
( ( ( X402 @ ( sub @ X406 @ X401 ) )
!= $true )
& ( ( var @ X406 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
( ( $true = sP46 )
<=> ( ? [X415: subst,X416: term] :
( ( comp @ sh @ ( push @ X416 @ X415 ) )
!= X415 )
| ? [X413: subst,X414: term] :
( ( sub @ one @ ( push @ X414 @ X413 ) )
!= X414 )
| ! [X419: subst,X420: subst > term > term,X421: subst > term > term,X422: term] :
( ? [X426: subst,X427: subst,X428: term] :
( ( X421 @ ( comp @ X426 @ X427 ) @ ( sub @ X428 @ X427 ) )
!= ( sub @ ( X421 @ X426 @ X428 ) @ X427 ) )
| ( ( lam @ ( X420 @ sh @ one ) )
!= ( lam @ ( X421 @ sh @ one ) ) )
| ? [X423: term,X424: subst,X425: subst] :
( ( X420 @ ( comp @ X425 @ X424 ) @ ( sub @ X423 @ X424 ) )
!= ( sub @ ( X420 @ X425 @ X423 ) @ X424 ) )
| ( ( X420 @ X419 @ X422 )
= ( X421 @ X419 @ X422 ) ) )
| ? [X417: term,X418: term] :
( ( ( lam @ X418 )
= ( lam @ X417 ) )
& ( X417 != X418 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
! [X346: term > $o] :
( ( ( sP47 @ X346 )
= $true )
<=> ? [X349: term,X350: term] :
( ( ( X346 @ X349 )
= $true )
& ( ( X346 @ ( ap @ X350 @ X349 ) )
!= $true )
& ( ( X346 @ X350 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
! [X339: term > $o] :
( ( ( sP48 @ X339 )
= $true )
<=> ! [X342: term,X343: term] :
( ( $true
!= ( X339 @ X342 ) )
| ( ( X339 @ ( ap @ X343 @ X342 ) )
= $true )
| ( ( X339 @ X343 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
( ( sP49 = $true )
<=> ! [X344: subst,X345: term,X346: term > $o] :
( ( ( sP47 @ X346 )
= $true )
| ? [X351: term] :
( ( ( var @ X351 )
= $true )
& ( $true
!= ( X346 @ ( sub @ X351 @ X344 ) ) ) )
| ? [X347: term] :
( ! [X348: term] :
( ( ( X346 @ ( sub @ X347 @ ( push @ X348 @ id ) ) )
= $true )
| ( ( X346 @ X348 )
!= $true ) )
& ( ( X346 @ ( lam @ X347 ) )
!= $true ) )
| ( ( X346 @ ( sub @ X345 @ X344 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
( ( sP50 = $true )
<=> ( ? [X335: subst,X336: term] :
( ( comp @ sh @ ( push @ X336 @ X335 ) )
!= X335 )
| ? [X337: subst] :
( ( comp @ X337 @ id )
!= X337 )
| ? [X333: term,X334: subst] :
( ( sub @ one @ ( push @ X333 @ X334 ) )
!= X333 )
| ? [X338: term,X339: term > $o] :
( ( ( sP48 @ X339 )
= $true )
& ( $true
!= ( X339 @ X338 ) )
& ! [X341: term] :
( ( ( X339 @ X341 )
!= $true )
| ( $true
= ( X339 @ ( lam @ X341 ) ) ) )
& ! [X340: term] :
( ( ( X339 @ X340 )
= $true )
| ( ( var @ X340 )
!= $true ) ) )
| ( sP49 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
! [X457: subst > term > subst > $o] :
( ( $true
= ( sP51 @ X457 ) )
<=> ? [X460: term,X461: term] :
( ( $true
= ( X457 @ id @ X460 @ id ) )
& ( ( X457 @ id @ X461 @ id )
= $true )
& ( ( X457 @ id @ ( ap @ ( sub @ X461 @ id ) @ X460 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( sP52 = $true )
<=> ! [X457: subst > term > subst > $o,X458: term,X459: term] :
( ( $true
= ( sP51 @ X457 ) )
| ( ( X457 @ id @ X458 @ id )
!= $true )
| ( ( X457 @ id @ X459 @ id )
!= $true )
| ? [X466: subst,X467: term,X468: subst,X469: subst] :
( ( ( X457 @ X469 @ X467 @ ( comp @ X468 @ X466 ) )
= $true )
& ( ( X457 @ ( comp @ X469 @ X468 ) @ ( sub @ X467 @ X468 ) @ X466 )
!= $true ) )
| ? [X462: subst,X463: subst,X464: subst,X465: term] :
( ( ( X457 @ ( comp @ X463 @ X462 ) @ ( sub @ X465 @ X462 ) @ X464 )
= $true )
& ( $true
!= ( X457 @ X463 @ X465 @ ( comp @ X462 @ X464 ) ) ) )
| ( ( X457 @ id @ ( ap @ X458 @ X459 ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
( ( sP53 = $true )
<=> ! [X489: subst > term > subst > $o,X490: term] :
( ? [X492: term,X493: subst > term > term] :
( ( ( X489 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X497: subst,X498: term,X499: subst] :
( ( sub @ ( X493 @ X499 @ X498 ) @ X497 )
= ( sub @ ( sub @ X492 @ ( push @ X498 @ X499 ) ) @ X497 ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( X493 @ ( comp @ X496 @ X494 ) @ ( sub @ X495 @ X494 ) )
= ( sub @ X492 @ ( push @ ( sub @ X495 @ X494 ) @ ( comp @ X496 @ X494 ) ) ) )
& ! [X500: term] :
( ( ( X489 @ id @ X500 @ id )
!= $true )
| ( ( X489 @ id @ ( X493 @ id @ X500 ) @ id )
= $true ) ) )
| ( ( X489 @ id @ ( lam @ ( sub @ X490 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X491: term] :
( ( ( X489 @ id @ X491 @ id )
= $true )
& ( ( X489 @ id @ ( sub @ X490 @ ( push @ X491 @ id ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X105: subst > term > subst > $o] :
( ( $true
= ( sP54 @ X105 ) )
<=> ? [X115: subst > term > term] :
( ! [X116: term] :
( ( ( X105 @ id @ ( X115 @ id @ X116 ) @ id )
= $true )
| ( ( X105 @ id @ X116 @ id )
!= $true ) )
& ( ( X105 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id )
!= $true )
& ! [X117: subst,X118: subst,X119: term] :
( ( X115 @ ( comp @ X117 @ X118 ) @ ( sub @ X119 @ X118 ) )
= ( sub @ ( X115 @ X117 @ X119 ) @ X118 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
( ( sP55 = $true )
<=> ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true )
| ( ( X97 @ id @ X103 @ id )
!= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id )
= $true )
| ? [X99: term,X100: subst,X101: subst] :
( ( sub @ ( X98 @ X101 @ X99 ) @ X100 )
!= ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) ) ) )
& ( ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( $true = sP56 )
<=> ( ( sP55 = $true )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 )
| ! [X104: term,X105: subst > term > subst > $o] :
( ? [X114: term] :
( ( ( X105 @ id @ X114 @ id )
= $true )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X114 @ id ) ) @ id )
!= $true ) )
| ? [X110: term,X111: subst,X112: subst,X113: subst] :
( ( ( X105 @ X112 @ X110 @ ( comp @ X113 @ X111 ) )
= $true )
& ( $true
!= ( X105 @ ( comp @ X112 @ X113 ) @ ( sub @ X110 @ X113 ) @ X111 ) ) )
| ? [X106: subst,X107: term,X108: subst,X109: subst] :
( ( ( X105 @ X109 @ X107 @ ( comp @ X108 @ X106 ) )
!= $true )
& ( ( X105 @ ( comp @ X109 @ X108 ) @ ( sub @ X107 @ X108 ) @ X106 )
= $true ) )
| ( $true
= ( sP54 @ X105 ) )
| ( ( X105 @ id @ ( lam @ X104 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
( ( sP57 = $true )
<=> ? [X44: subst > term > subst > $o,X45: term] :
( ! [X46: subst > term > term] :
( ( ( X44 @ id @ ( lam @ ( X46 @ sh @ one ) ) @ id )
= $true )
| ? [X47: term] :
( ( ( X44 @ id @ X47 @ id )
= $true )
& ( $true
!= ( X44 @ id @ ( X46 @ id @ X47 ) @ id ) ) )
| ? [X48: subst,X49: term,X50: subst] :
( ( X46 @ ( comp @ X50 @ X48 ) @ ( sub @ X49 @ X48 ) )
!= ( sub @ ( X46 @ X50 @ X49 ) @ X48 ) ) )
& ( ( X44 @ id @ ( lam @ ( sub @ X45 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X51: term] :
( ( ( X44 @ id @ X51 @ id )
!= $true )
| ( ( X44 @ id @ ( sub @ X45 @ ( push @ X51 @ id ) ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( sP58 = $true )
<=> ( ? [X43: term] :
( ( sub @ X43 @ id )
!= X43 )
| ( sP57 = $true )
| ! [X52: term,X53: subst > term > subst > $o] :
( ? [X59: term] :
( ( $true
= ( X53 @ id @ X59 @ id ) )
& ( ( X53 @ id @ ( sub @ X52 @ ( push @ X59 @ id ) ) @ id )
!= $true ) )
| ( ( X53 @ id @ ( lam @ X52 ) @ id )
= $true )
| ? [X54: subst > term > term] :
( ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( ( X53 @ id @ ( X54 @ id @ X55 ) @ id )
= $true ) )
& ! [X56: subst,X57: subst,X58: term] :
( ( X54 @ ( comp @ X57 @ X56 ) @ ( sub @ X58 @ X56 ) )
= ( sub @ ( X54 @ X57 @ X58 ) @ X56 ) )
& ( ( X53 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
!= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( ? [X43: term] :
( ( sub @ X43 @ id )
!= X43 )
| ? [X44: subst > term > subst > $o,X45: term] :
( ! [X46: subst > term > term] :
( ( ( X44 @ id @ ( lam @ ( X46 @ sh @ one ) ) @ id )
= $true )
| ? [X47: term] :
( ( ( X44 @ id @ X47 @ id )
= $true )
& ( $true
!= ( X44 @ id @ ( X46 @ id @ X47 ) @ id ) ) )
| ? [X48: subst,X49: term,X50: subst] :
( ( X46 @ ( comp @ X50 @ X48 ) @ ( sub @ X49 @ X48 ) )
!= ( sub @ ( X46 @ X50 @ X49 ) @ X48 ) ) )
& ( ( X44 @ id @ ( lam @ ( sub @ X45 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X51: term] :
( ( ( X44 @ id @ X51 @ id )
!= $true )
| ( ( X44 @ id @ ( sub @ X45 @ ( push @ X51 @ id ) ) @ id )
= $true ) ) )
| ! [X52: term,X53: subst > term > subst > $o] :
( ? [X59: term] :
( ( $true
= ( X53 @ id @ X59 @ id ) )
& ( ( X53 @ id @ ( sub @ X52 @ ( push @ X59 @ id ) ) @ id )
!= $true ) )
| ( ( X53 @ id @ ( lam @ X52 ) @ id )
= $true )
| ? [X54: subst > term > term] :
( ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( ( X53 @ id @ ( X54 @ id @ X55 ) @ id )
= $true ) )
& ! [X56: subst,X57: subst,X58: term] :
( ( X54 @ ( comp @ X57 @ X56 ) @ ( sub @ X58 @ X56 ) )
= ( sub @ ( X54 @ X57 @ X58 ) @ X56 ) )
& ( ( X53 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
!= $true ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ( axscons = $true )
<=> ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
<=> ( laminj = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
<=> ( axvarid = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) ) )
& ( ( substmonoid = $true )
<=> ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) ) )
& ( ( ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true )
| ( ( X97 @ id @ X103 @ id )
!= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id )
= $true )
| ? [X99: term,X100: subst,X101: subst] :
( ( sub @ ( X98 @ X101 @ X99 ) @ X100 )
!= ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) ) ) )
& ( ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 )
| ! [X104: term,X105: subst > term > subst > $o] :
( ? [X114: term] :
( ( ( X105 @ id @ X114 @ id )
= $true )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X114 @ id ) ) @ id )
!= $true ) )
| ? [X110: term,X111: subst,X112: subst,X113: subst] :
( ( ( X105 @ X112 @ X110 @ ( comp @ X113 @ X111 ) )
= $true )
& ( $true
!= ( X105 @ ( comp @ X112 @ X113 ) @ ( sub @ X110 @ X113 ) @ X111 ) ) )
| ? [X106: subst,X107: term,X108: subst,X109: subst] :
( ( ( X105 @ X109 @ X107 @ ( comp @ X108 @ X106 ) )
!= $true )
& ( ( X105 @ ( comp @ X109 @ X108 ) @ ( sub @ X107 @ X108 ) @ X106 )
= $true ) )
| ? [X115: subst > term > term] :
( ! [X116: term] :
( ( ( X105 @ id @ ( X115 @ id @ X116 ) @ id )
= $true )
| ( ( X105 @ id @ X116 @ id )
!= $true ) )
& ( ( X105 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id )
!= $true )
& ! [X117: subst,X118: subst,X119: term] :
( ( X115 @ ( comp @ X117 @ X118 ) @ ( sub @ X119 @ X118 ) )
= ( sub @ ( X115 @ X117 @ X119 ) @ X118 ) ) )
| ( ( X105 @ id @ ( lam @ X104 ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( ? [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
!= X303 )
| ? [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
!= X300 )
| ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ? [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
!= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
| ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( lamnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X489: subst > term > subst > $o,X490: term] :
( ? [X492: term,X493: subst > term > term] :
( ( ( X489 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X497: subst,X498: term,X499: subst] :
( ( sub @ ( X493 @ X499 @ X498 ) @ X497 )
= ( sub @ ( sub @ X492 @ ( push @ X498 @ X499 ) ) @ X497 ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( X493 @ ( comp @ X496 @ X494 ) @ ( sub @ X495 @ X494 ) )
= ( sub @ X492 @ ( push @ ( sub @ X495 @ X494 ) @ ( comp @ X496 @ X494 ) ) ) )
& ! [X500: term] :
( ( ( X489 @ id @ X500 @ id )
!= $true )
| ( ( X489 @ id @ ( X493 @ id @ X500 ) @ id )
= $true ) ) )
| ( ( X489 @ id @ ( lam @ ( sub @ X490 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X491: term] :
( ( ( X489 @ id @ X491 @ id )
= $true )
& ( ( X489 @ id @ ( sub @ X490 @ ( push @ X491 @ id ) ) @ id )
!= $true ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X457: subst > term > subst > $o,X458: term,X459: term] :
( ? [X460: term,X461: term] :
( ( $true
= ( X457 @ id @ X460 @ id ) )
& ( ( X457 @ id @ X461 @ id )
= $true )
& ( ( X457 @ id @ ( ap @ ( sub @ X461 @ id ) @ X460 ) @ id )
!= $true ) )
| ( ( X457 @ id @ X458 @ id )
!= $true )
| ( ( X457 @ id @ X459 @ id )
!= $true )
| ? [X466: subst,X467: term,X468: subst,X469: subst] :
( ( ( X457 @ X469 @ X467 @ ( comp @ X468 @ X466 ) )
= $true )
& ( ( X457 @ ( comp @ X469 @ X468 ) @ ( sub @ X467 @ X468 ) @ X466 )
!= $true ) )
| ? [X462: subst,X463: subst,X464: subst,X465: term] :
( ( ( X457 @ ( comp @ X463 @ X462 ) @ ( sub @ X465 @ X462 ) @ X464 )
= $true )
& ( $true
!= ( X457 @ X463 @ X465 @ ( comp @ X462 @ X464 ) ) ) )
| ( ( X457 @ id @ ( ap @ X458 @ X459 ) @ id )
= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( hoasinduction_gthm = $true )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
!= ( d2subst @ X471 ) )
| ( X470 = X471 ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction2lem_lthm = $true )
<=> ( ? [X335: subst,X336: term] :
( ( comp @ sh @ ( push @ X336 @ X335 ) )
!= X335 )
| ? [X337: subst] :
( ( comp @ X337 @ id )
!= X337 )
| ? [X333: term,X334: subst] :
( ( sub @ one @ ( push @ X333 @ X334 ) )
!= X333 )
| ? [X338: term,X339: term > $o] :
( ! [X342: term,X343: term] :
( ( $true
!= ( X339 @ X342 ) )
| ( ( X339 @ ( ap @ X343 @ X342 ) )
= $true )
| ( ( X339 @ X343 )
!= $true ) )
& ( $true
!= ( X339 @ X338 ) )
& ! [X341: term] :
( ( ( X339 @ X341 )
!= $true )
| ( $true
= ( X339 @ ( lam @ X341 ) ) ) )
& ! [X340: term] :
( ( ( X339 @ X340 )
= $true )
| ( ( var @ X340 )
!= $true ) ) )
| ! [X344: subst,X345: term,X346: term > $o] :
( ? [X349: term,X350: term] :
( ( ( X346 @ X349 )
= $true )
& ( ( X346 @ ( ap @ X350 @ X349 ) )
!= $true )
& ( ( X346 @ X350 )
= $true ) )
| ? [X351: term] :
( ( ( var @ X351 )
= $true )
& ( $true
!= ( X346 @ ( sub @ X351 @ X344 ) ) ) )
| ? [X347: term] :
( ! [X348: term] :
( ( ( X346 @ ( sub @ X347 @ ( push @ X348 @ id ) ) )
= $true )
| ( ( X346 @ X348 )
!= $true ) )
& ( ( X346 @ ( lam @ X347 ) )
!= $true ) )
| ( ( X346 @ ( sub @ X345 @ X344 ) )
= $true ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X533 )
& ( ( ap @ X535 @ X532 )
= ( ap @ X534 @ X533 ) ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X298: term] :
( ( sub @ X298 @ id )
!= X298 )
| ! [X299: term] :
( ( sub @ X299 @ id )
= X299 ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ? [X415: subst,X416: term] :
( ( comp @ sh @ ( push @ X416 @ X415 ) )
!= X415 )
| ? [X413: subst,X414: term] :
( ( sub @ one @ ( push @ X414 @ X413 ) )
!= X414 )
| ! [X419: subst,X420: subst > term > term,X421: subst > term > term,X422: term] :
( ? [X426: subst,X427: subst,X428: term] :
( ( X421 @ ( comp @ X426 @ X427 ) @ ( sub @ X428 @ X427 ) )
!= ( sub @ ( X421 @ X426 @ X428 ) @ X427 ) )
| ( ( lam @ ( X420 @ sh @ one ) )
!= ( lam @ ( X421 @ sh @ one ) ) )
| ? [X423: term,X424: subst,X425: subst] :
( ( X420 @ ( comp @ X425 @ X424 ) @ ( sub @ X423 @ X424 ) )
!= ( sub @ ( X420 @ X425 @ X423 ) @ X424 ) )
| ( ( X420 @ X419 @ X422 )
= ( X421 @ X419 @ X422 ) ) )
| ? [X417: term,X418: term] :
( ( ( lam @ X418 )
= ( lam @ X417 ) )
& ( X417 != X418 ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X429: term] :
? [X430: subst > term > term] :
( ( X430 @ sh @ one )
= ( sub @ X429 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem = $true )
<=> ! [X401: subst,X402: term > $o,X403: term] :
( ? [X404: term] :
( ( ( X402 @ ( lam @ X404 ) )
!= $true )
& ! [X405: term] :
( ( ( X402 @ X405 )
!= $true )
| ( ( X402 @ ( sub @ X404 @ ( push @ X405 @ id ) ) )
= $true ) ) )
| ? [X407: term,X408: term] :
( ( ( X402 @ X407 )
= $true )
& ( ( X402 @ X408 )
= $true )
& ( ( X402 @ ( ap @ X408 @ X407 ) )
!= $true ) )
| ( ( X402 @ ( sub @ X403 @ X401 ) )
= $true )
| ? [X406: term] :
( ( ( X402 @ ( sub @ X406 @ X401 ) )
!= $true )
& ( ( var @ X406 )
= $true ) ) ) )
& ( ! [X329: term] :
? [X330: subst > term > term] :
! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
= ( X505 @ one ) )
| ? [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
!= ( X505 @ X507 ) )
| ( $true
!= ( X504 @ X503 ) ) )
| ? [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
!= X501 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axmap = $true )
& ( ulamvar1 != $true )
& ( ! [X168: subst > term > subst > $o] :
? [X169: term > $o] :
! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ! [X120: term > $o,X121: term] :
( ? [X125: term] :
( ( ( X120 @ ( lam @ X125 ) )
!= $true )
& ! [X126: term] :
( ( ( X120 @ ( sub @ X125 @ ( push @ X126 @ id ) ) )
= $true )
| ( ( X120 @ X126 )
!= $true ) ) )
| ? [X123: term,X124: term] :
( ( ( X120 @ ( ap @ X123 @ X124 ) )
!= $true )
& ( ( X120 @ X124 )
= $true )
& ( ( X120 @ X123 )
= $true ) )
| ( ( X120 @ X121 )
= $true )
| ? [X122: term] :
( ( ( X120 @ X122 )
!= $true )
& ( ( var @ X122 )
= $true ) ) )
<=> ( induction2 = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ? [X132: term > $o,X133: term] :
( ! [X135: term,X136: term] :
( ( ( X132 @ X135 )
!= $true )
| ( ( X132 @ ( ap @ X135 @ X136 ) )
= $true )
| ( ( X132 @ X136 )
!= $true ) )
& ! [X137: term] :
( ( ( X132 @ ( lam @ X137 ) )
= $true )
| ? [X138: term] :
( ( ( X132 @ ( sub @ X137 @ ( push @ X138 @ id ) ) )
!= $true )
& ( ( X132 @ X138 )
= $true ) ) )
& ! [X134: term] :
( ( $true
= ( X132 @ X134 ) )
| ( ( var @ X134 )
!= $true ) )
& ( ( X132 @ X133 )
!= $true ) )
| ! [X150: subst > term > subst > $o,X151: term] :
( ? [X154: term] :
( ( ( var @ ( sub @ X154 @ id ) )
= $true )
& ( ( X150 @ id @ X154 @ id )
!= $true ) )
| ? [X164: subst,X165: subst,X166: subst,X167: term] :
( ( ( X150 @ ( comp @ X166 @ X165 ) @ ( sub @ X167 @ X165 ) @ X164 )
!= $true )
& ( ( X150 @ X166 @ X167 @ ( comp @ X165 @ X164 ) )
= $true ) )
| ? [X159: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X150 @ id @ X163 @ id ) )
| ( ( X150 @ id @ ( X159 @ id @ X163 ) @ id )
= $true ) )
& ! [X160: term,X161: subst,X162: subst] :
( ( sub @ ( X159 @ X162 @ X160 ) @ X161 )
= ( X159 @ ( comp @ X162 @ X161 ) @ ( sub @ X160 @ X161 ) ) )
& ( ( X150 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X155: subst,X156: term,X157: subst,X158: subst] :
( ( ( X150 @ ( comp @ X158 @ X155 ) @ ( sub @ X156 @ X155 ) @ X157 )
= $true )
& ( ( X150 @ X158 @ X156 @ ( comp @ X155 @ X157 ) )
!= $true ) )
| ? [X152: term,X153: term] :
( ( ( X150 @ id @ ( ap @ ( sub @ X152 @ id ) @ X153 ) @ id )
!= $true )
& ( ( X150 @ id @ X153 @ id )
= $true )
& ( ( X150 @ id @ X152 @ id )
= $true ) )
| ( ( X150 @ id @ X151 @ id )
= $true ) )
| ? [X139: term] :
( ( sub @ X139 @ id )
!= X139 )
| ? [X140: term > $o,X141: term,X142: subst > term > subst > $o] :
( ! [X143: subst > term > term] :
( ( $true
= ( X142 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ? [X144: term] :
( ( ( X142 @ id @ ( X143 @ id @ X144 ) @ id )
!= $true )
& ( ( X142 @ id @ X144 @ id )
= $true ) )
| ? [X145: subst,X146: term,X147: subst] :
( ( X143 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) )
!= ( sub @ ( X143 @ X147 @ X146 ) @ X145 ) ) )
& ( ( X140 @ ( lam @ X141 ) )
!= $true )
& ! [X149: term] :
( ( ( X140 @ ( sub @ X141 @ ( push @ X149 @ id ) ) )
= $true )
| ( ( X140 @ X149 )
!= $true ) )
& ! [X148: term] :
( ( X140 @ X148 )
= ( X142 @ id @ X148 @ id ) ) )
| ? [X129: subst > term > subst > $o] :
! [X130: term > $o] :
? [X131: term] :
( ( X130 @ X131 )
!= ( X129 @ id @ X131 @ id ) ) ) )
& ( ! [X393: term,X394: subst > term > subst > $o] :
( ( ( X394 @ id @ ( lam @ ( sub @ X393 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X400: term] :
( ( ( X394 @ id @ ( sub @ X393 @ ( push @ X400 @ id ) ) @ id )
!= $true )
& ( ( X394 @ id @ X400 @ id )
= $true ) )
| ? [X395: subst > term > term] :
( ! [X397: term,X398: subst,X399: subst] :
( ( X395 @ ( comp @ X398 @ X399 ) @ ( sub @ X397 @ X399 ) )
= ( sub @ ( X395 @ X398 @ X397 ) @ X399 ) )
& ! [X396: term] :
( ( ( X394 @ id @ X396 @ id )
!= $true )
| ( ( X394 @ id @ ( X395 @ id @ X396 ) @ id )
= $true ) )
& ( ( X394 @ id @ ( lam @ ( X395 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X509: term > $o,X510: subst > term > subst > $o,X511: term] :
( ? [X526: term] :
( ( $true
!= ( X509 @ ( sub @ X511 @ ( push @ X526 @ id ) ) ) )
& ( ( X509 @ X526 )
= $true ) )
| ( ( X509 @ ( lam @ X511 ) )
= $true )
| ? [X520: term] :
( ( X509 @ X520 )
!= ( X510 @ id @ X520 @ id ) )
| ? [X512: term,X513: subst,X514: subst,X515: subst] :
( ( ( X510 @ X513 @ X512 @ ( comp @ X514 @ X515 ) )
= $true )
& ( ( X510 @ ( comp @ X513 @ X514 ) @ ( sub @ X512 @ X514 ) @ X515 )
!= $true ) )
| ? [X516: subst,X517: term,X518: subst,X519: subst] :
( ( ( X510 @ X516 @ X517 @ ( comp @ X518 @ X519 ) )
!= $true )
& ( ( X510 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) @ X519 )
= $true ) )
| ? [X521: subst > term > term] :
( ! [X522: term,X523: subst,X524: subst] :
( ( sub @ ( X521 @ X523 @ X522 ) @ X524 )
= ( X521 @ ( comp @ X523 @ X524 ) @ ( sub @ X522 @ X524 ) ) )
& ( ( X510 @ id @ ( lam @ ( X521 @ sh @ one ) ) @ id )
!= $true )
& ! [X525: term] :
( ( ( X510 @ id @ X525 @ id )
!= $true )
| ( ( X510 @ id @ ( X521 @ id @ X525 ) @ id )
= $true ) ) ) )
| ? [X508: term] :
( ( sub @ X508 @ id )
!= X508 ) ) )
& ( hoaslaminj_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( axvarshift = $true )
& ( axassoc = $true )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
<=> ( apinj1 = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X259: term > $o,X260: subst,X261: term] :
? [X262: term > $o] :
! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) ) )
& ( ( axidl = $true )
<=> ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( ? [X82: subst] :
( ( comp @ id @ X82 )
!= X82 )
| ? [X83: subst] :
( ( comp @ X83 @ id )
!= X83 )
| ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ( ( X481 @ X484 )
!= $true )
| ? [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
!= ( X483 @ X485 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( axapp = $true )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X327: term] :
? [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
= ( X328 @ sh @ one ) ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) ) )
& ( ( induction2_lthm = $true )
<=> ( ? [X26: term > $o,X27: term,X28: subst] :
( ! [X31: term] :
( ? [X32: term] :
( ( ( X26 @ ( sub @ X31 @ ( push @ X32 @ id ) ) )
!= $true )
& ( ( X26 @ X32 )
= $true ) )
| ( ( X26 @ ( lam @ X31 ) )
= $true ) )
& ! [X29: term,X30: term] :
( ( ( X26 @ X29 )
!= $true )
| ( ( X26 @ X30 )
!= $true )
| ( ( X26 @ ( ap @ X29 @ X30 ) )
= $true ) )
& ( ( X26 @ ( sub @ X27 @ X28 ) )
!= $true )
& ! [X33: term] :
( ( ( var @ X33 )
!= $true )
| ( ( X26 @ ( sub @ X33 @ X28 ) )
= $true ) ) )
| ! [X34: term,X35: term > $o] :
( ? [X38: term,X39: term] :
( ( $true
= ( X35 @ X39 ) )
& ( ( X35 @ ( ap @ X39 @ X38 ) )
!= $true )
& ( ( X35 @ X38 )
= $true ) )
| ( $true
= ( X35 @ X34 ) )
| ? [X36: term] :
( ! [X37: term] :
( ( $true
= ( X35 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) )
| ( ( X35 @ X37 )
!= $true ) )
& ( ( X35 @ ( lam @ X36 ) )
!= $true ) )
| ? [X40: term] :
( ( ( var @ X40 )
= $true )
& ( ( X35 @ X40 )
!= $true ) ) )
| ? [X25: term] :
( ( sub @ X25 @ id )
!= X25 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( induction2lem_gthm = $true )
& ( ( axvarcons = $true )
<=> ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
| ? [X473: term,X474: term,X475: term,X476: term] :
( ( X474 != X476 )
& ( ( ap @ X476 @ X473 )
= ( ap @ X474 @ X475 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X241: subst,X242: term,X243: term > $o] :
? [X244: term > $o] :
! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( ? [X382: term] :
( ( sub @ X382 @ id )
!= X382 )
| ! [X383: term,X384: term > $o,X385: subst > term > subst > $o] :
( ? [X387: subst > term > term] :
( ! [X389: subst,X390: subst,X391: term] :
( ( X387 @ ( comp @ X390 @ X389 ) @ ( sub @ X391 @ X389 ) )
= ( sub @ ( X387 @ X390 @ X391 ) @ X389 ) )
& ( ( X385 @ id @ ( lam @ ( X387 @ sh @ one ) ) @ id )
!= $true )
& ! [X388: term] :
( ( ( X385 @ id @ X388 @ id )
!= $true )
| ( ( X385 @ id @ ( X387 @ id @ X388 ) @ id )
= $true ) ) )
| ? [X386: term] :
( ( X384 @ X386 )
!= ( X385 @ id @ X386 @ id ) )
| ? [X392: term] :
( ( ( X384 @ ( sub @ X383 @ ( push @ X392 @ id ) ) )
!= $true )
& ( ( X384 @ X392 )
= $true ) )
| ( ( X384 @ ( lam @ X383 ) )
= $true ) )
| ? [X378: term] :
! [X379: subst > term > term] :
? [X380: term,X381: subst] :
( ( X379 @ X381 @ X380 )
!= ( sub @ X378 @ ( push @ X380 @ X381 ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoasapnotvar = $true )
& ( ( ? [X267: term > $o,X268: term] :
( ! [X272: term] :
( ? [X273: term] :
( ( ( X267 @ ( sub @ X272 @ ( push @ X273 @ id ) ) )
!= $true )
& ( $true
= ( X267 @ X273 ) ) )
| ( ( X267 @ ( lam @ X272 ) )
= $true ) )
& ! [X269: term,X270: term] :
( ( $true
!= ( X267 @ X269 ) )
| ( ( X267 @ ( ap @ X270 @ X269 ) )
= $true )
| ( ( X267 @ X270 )
!= $true ) )
& ( ( X267 @ X268 )
!= $true )
& ! [X271: term] :
( ( ( var @ X271 )
!= $true )
| ( $true
= ( X267 @ X271 ) ) ) )
| ! [X285: term,X286: subst > term > subst > $o] :
( ? [X292: term,X293: term] :
( ( $true
= ( X286 @ id @ X293 @ id ) )
& ( ( X286 @ id @ X292 @ id )
= $true )
& ( ( X286 @ id @ ( ap @ ( sub @ X292 @ id ) @ X293 ) @ id )
!= $true ) )
| ( ( X286 @ id @ X285 @ id )
= $true )
| ? [X287: subst > term > term] :
( ( ( X286 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id )
!= $true )
& ! [X291: term] :
( ( ( X286 @ id @ X291 @ id )
!= $true )
| ( ( X286 @ id @ ( X287 @ id @ X291 ) @ id )
= $true ) )
& ! [X288: subst,X289: term,X290: subst] :
( ( sub @ ( X287 @ X288 @ X289 ) @ X290 )
= ( X287 @ ( comp @ X288 @ X290 ) @ ( sub @ X289 @ X290 ) ) ) ) )
| ? [X275: subst > term > subst > $o,X276: term,X277: term > $o] :
( ! [X278: subst > term > term] :
( ( ( X275 @ id @ ( lam @ ( X278 @ sh @ one ) ) @ id )
= $true )
| ? [X280: term,X281: subst,X282: subst] :
( ( X278 @ ( comp @ X282 @ X281 ) @ ( sub @ X280 @ X281 ) )
!= ( sub @ ( X278 @ X282 @ X280 ) @ X281 ) )
| ? [X279: term] :
( ( ( X275 @ id @ ( X278 @ id @ X279 ) @ id )
!= $true )
& ( ( X275 @ id @ X279 @ id )
= $true ) ) )
& ( ( X277 @ ( lam @ X276 ) )
!= $true )
& ! [X284: term] :
( ( ( X277 @ X284 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X284 @ id ) ) )
= $true ) )
& ! [X283: term] :
( ( X277 @ X283 )
= ( X275 @ id @ X283 @ id ) ) )
| ? [X274: term] :
( ( sub @ X274 @ id )
!= X274 )
| ? [X264: subst > term > subst > $o] :
! [X265: term > $o] :
? [X266: term] :
( ( X265 @ X266 )
!= ( X264 @ id @ X266 @ id ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
<=> ( shinj = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X9: term,X10: term > $o,X11: term,X12: subst > term > subst > $o] :
( ( ( X10 @ ( ap @ X11 @ X9 ) )
= $true )
| ? [X14: subst,X15: subst,X16: subst,X17: term] :
( ( ( X12 @ X15 @ X17 @ ( comp @ X16 @ X14 ) )
!= $true )
& ( ( X12 @ ( comp @ X15 @ X16 ) @ ( sub @ X17 @ X16 ) @ X14 )
= $true ) )
| ( ( X10 @ X9 )
!= $true )
| ? [X13: term] :
( ( X10 @ X13 )
!= ( X12 @ id @ X13 @ id ) )
| ? [X18: subst,X19: term,X20: subst,X21: subst] :
( ( ( X12 @ X20 @ X19 @ ( comp @ X18 @ X21 ) )
= $true )
& ( ( X12 @ ( comp @ X20 @ X18 ) @ ( sub @ X19 @ X18 ) @ X21 )
!= $true ) )
| ( ( X10 @ X11 )
!= $true )
| ? [X22: term,X23: term] :
( ( $true
= ( X12 @ id @ X23 @ id ) )
& ( ( X12 @ id @ ( ap @ ( sub @ X23 @ id ) @ X22 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X22 @ id ) ) ) ) )
& ( ! [X171: subst > term > subst > $o] :
? [X172: term > $o] :
! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X0: term,X1: subst > term > subst > $o] :
( ? [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) )
& ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X1 @ id @ X0 @ id ) )
| ? [X2: term,X3: term] :
( ( ( X1 @ id @ X3 @ id )
= $true )
& ( ( X1 @ id @ X2 @ id )
= $true )
& ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
!= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
<=> ( axidr = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axclos = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( ? [X179: term > $o,X180: term] :
( ! [X183: term,X184: term] :
( ( ( X179 @ X184 )
!= $true )
| ( ( X179 @ ( ap @ X184 @ X183 ) )
= $true )
| ( $true
!= ( X179 @ X183 ) ) )
& ! [X181: term] :
( ? [X182: term] :
( ( ( X179 @ ( sub @ X181 @ ( push @ X182 @ id ) ) )
!= $true )
& ( ( X179 @ X182 )
= $true ) )
| ( ( X179 @ ( lam @ X181 ) )
= $true ) )
& ( ( X179 @ X180 )
!= $true )
& ! [X185: term] :
( ( ( X179 @ X185 )
= $true )
| ( ( var @ X185 )
!= $true ) ) )
| ! [X215: subst > term > subst > $o,X216: term] :
( ? [X217: term] :
( ( ( var @ ( sub @ X217 @ id ) )
= $true )
& ( ( X215 @ id @ X217 @ id )
!= $true ) )
| ? [X227: subst,X228: subst,X229: subst,X230: term] :
( ( ( X215 @ X229 @ X230 @ ( comp @ X228 @ X227 ) )
= $true )
& ( ( X215 @ ( comp @ X229 @ X228 ) @ ( sub @ X230 @ X228 ) @ X227 )
!= $true ) )
| ? [X223: term,X224: subst,X225: subst,X226: subst] :
( ( ( X215 @ X225 @ X223 @ ( comp @ X226 @ X224 ) )
!= $true )
& ( ( X215 @ ( comp @ X225 @ X226 ) @ ( sub @ X223 @ X226 ) @ X224 )
= $true ) )
| ? [X218: subst > term > term] :
( ( ( X215 @ id @ ( lam @ ( X218 @ sh @ one ) ) @ id )
!= $true )
& ! [X222: term] :
( ( ( X215 @ id @ X222 @ id )
!= $true )
| ( ( X215 @ id @ ( X218 @ id @ X222 ) @ id )
= $true ) )
& ! [X219: term,X220: subst,X221: subst] :
( ( X218 @ ( comp @ X220 @ X221 ) @ ( sub @ X219 @ X221 ) )
= ( sub @ ( X218 @ X220 @ X219 ) @ X221 ) ) )
| ( ( X215 @ id @ X216 @ id )
= $true )
| ? [X231: term,X232: term] :
( ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
!= $true )
& ( ( X215 @ id @ X232 @ id )
= $true )
& ( ( X215 @ id @ X231 @ id )
= $true ) ) )
| ? [X186: term,X187: term,X188: subst > term > subst > $o] :
( ! [X191: term,X192: subst,X193: subst,X194: subst] :
( ( ( X188 @ ( comp @ X194 @ X193 ) @ ( sub @ X191 @ X193 ) @ X192 )
!= $true )
| ( ( X188 @ X194 @ X191 @ ( comp @ X193 @ X192 ) )
= $true ) )
& ( ( X188 @ id @ X187 @ id )
= $true )
& ! [X189: term,X190: term] :
( ( ( X188 @ id @ ( ap @ ( sub @ X189 @ id ) @ X190 ) @ id )
= $true )
| ( ( X188 @ id @ X190 @ id )
!= $true )
| ( ( X188 @ id @ X189 @ id )
!= $true ) )
& ( $true
!= ( X188 @ id @ ( ap @ X186 @ X187 ) @ id ) )
& ( ( X188 @ id @ X186 @ id )
= $true )
& ! [X195: term,X196: subst,X197: subst,X198: subst] :
( ( ( X188 @ ( comp @ X197 @ X198 ) @ ( sub @ X195 @ X198 ) @ X196 )
= $true )
| ( ( X188 @ X197 @ X195 @ ( comp @ X198 @ X196 ) )
!= $true ) ) )
| ? [X199: term,X200: subst > term > subst > $o] :
( ! [X211: subst,X212: term,X213: subst,X214: subst] :
( ( ( X200 @ ( comp @ X213 @ X214 ) @ ( sub @ X212 @ X214 ) @ X211 )
!= $true )
| ( ( X200 @ X213 @ X212 @ ( comp @ X214 @ X211 ) )
= $true ) )
& ! [X201: subst,X202: subst,X203: subst,X204: term] :
( ( ( X200 @ ( comp @ X201 @ X202 ) @ ( sub @ X204 @ X202 ) @ X203 )
= $true )
| ( ( X200 @ X201 @ X204 @ ( comp @ X202 @ X203 ) )
!= $true ) )
& ! [X205: term] :
( ( ( X200 @ id @ X205 @ id )
!= $true )
| ( ( X200 @ id @ ( sub @ X199 @ ( push @ X205 @ id ) ) @ id )
= $true ) )
& ( ( X200 @ id @ ( lam @ X199 ) @ id )
!= $true )
& ! [X206: subst > term > term] :
( ? [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
!= $true )
& ( ( X200 @ id @ X207 @ id )
= $true ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ? [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
!= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) ) ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( induction2_gthm = $true )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
<=> ( termmset = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ! [X439: term,X440: term > $o] :
( ? [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
!= $true )
& ( ( X440 @ X443 )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ? [X441: term,X442: term] :
( ( ( X440 @ X442 )
= $true )
& ( ( X440 @ X441 )
= $true )
& ( ( X440 @ ( ap @ X441 @ X442 ) )
!= $true ) )
| ? [X444: term] :
( ( ( X440 @ X444 )
!= $true )
& ( $true
= ( var @ X444 ) ) ) )
<=> ( induction = $true ) )
& ! [X294: d_term,X295: d_term] :
( ( X294 = X295 )
| ( ( d2term @ X294 )
!= ( d2term @ X295 ) ) )
& ( lamnotap != $true )
& ( termmset_gthm = $true )
& ( ! [X352: term,X353: term > $o,X354: subst > term > subst > $o] :
( ? [X366: subst,X367: subst,X368: term,X369: subst] :
( ( ( X354 @ X366 @ X368 @ ( comp @ X369 @ X367 ) )
= $true )
& ( ( X354 @ ( comp @ X366 @ X369 ) @ ( sub @ X368 @ X369 ) @ X367 )
!= $true ) )
| ? [X357: subst,X358: subst,X359: term,X360: subst] :
( ( ( X354 @ ( comp @ X358 @ X360 ) @ ( sub @ X359 @ X360 ) @ X357 )
= $true )
& ( ( X354 @ X358 @ X359 @ ( comp @ X360 @ X357 ) )
!= $true ) )
| ? [X355: term] :
( ( ( X353 @ ( sub @ X352 @ ( push @ X355 @ id ) ) )
!= $true )
& ( ( X353 @ X355 )
= $true ) )
| ? [X361: subst > term > term] :
( ! [X365: term] :
( ( ( X354 @ id @ ( X361 @ id @ X365 ) @ id )
= $true )
| ( ( X354 @ id @ X365 @ id )
!= $true ) )
& ( ( X354 @ id @ ( lam @ ( X361 @ sh @ one ) ) @ id )
!= $true )
& ! [X362: subst,X363: subst,X364: term] :
( ( sub @ ( X361 @ X363 @ X364 ) @ X362 )
= ( X361 @ ( comp @ X363 @ X362 ) @ ( sub @ X364 @ X362 ) ) ) )
| ? [X356: term] :
( ( X354 @ id @ X356 @ id )
!= ( X353 @ X356 ) )
| ( ( X353 @ ( lam @ X352 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( ( hoaslaminj = $true )
<=> ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ? [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
!= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
| ? [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
!= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X431: term,X432: subst > term > subst > $o] :
( ? [X433: subst > term > term] :
( ! [X434: subst,X435: subst,X436: term] :
( ( sub @ ( X433 @ X434 @ X436 ) @ X435 )
= ( X433 @ ( comp @ X434 @ X435 ) @ ( sub @ X436 @ X435 ) ) )
& ( ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id )
!= $true )
& ! [X437: term] :
( ( ( X432 @ id @ ( X433 @ id @ X437 ) @ id )
= $true )
| ( ( X432 @ id @ X437 @ id )
!= $true ) ) )
| ( ( X432 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X438: term] :
( ( ( X432 @ id @ ( sub @ X431 @ ( push @ X438 @ id ) ) @ id )
!= $true )
& ( ( X432 @ id @ X438 @ id )
= $true ) ) ) )
& ( ! [X233: term,X234: subst > term > subst > $o] :
( ? [X235: subst > term > term] :
( ! [X239: term] :
( ( ( X234 @ id @ ( X235 @ id @ X239 ) @ id )
= $true )
| ( ( X234 @ id @ X239 @ id )
!= $true ) )
& ( ( X234 @ id @ ( lam @ ( X235 @ sh @ one ) ) @ id )
!= $true )
& ! [X236: subst,X237: subst,X238: term] :
( ( X235 @ ( comp @ X236 @ X237 ) @ ( sub @ X238 @ X237 ) )
= ( sub @ ( X235 @ X236 @ X238 ) @ X237 ) ) )
| ( ( X234 @ id @ ( lam @ X233 ) @ id )
= $true )
| ? [X240: term] :
( ( ( X234 @ id @ ( sub @ X233 @ ( push @ X240 @ id ) ) @ id )
!= $true )
& ( ( X234 @ id @ X240 @ id )
= $true ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( pushprop_lthm = $true )
& ( pushprop = $true )
& ( ( hoasinduction = $true )
<=> ! [X309: term,X310: subst > term > subst > $o] :
( ? [X320: subst > term > term] :
( ! [X324: term] :
( ( ( X310 @ id @ X324 @ id )
!= $true )
| ( ( X310 @ id @ ( X320 @ id @ X324 ) @ id )
= $true ) )
& ! [X321: subst,X322: term,X323: subst] :
( ( sub @ ( X320 @ X321 @ X322 ) @ X323 )
= ( X320 @ ( comp @ X321 @ X323 ) @ ( sub @ X322 @ X323 ) ) )
& ( ( X310 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X312: subst,X313: subst,X314: term,X315: subst] :
( ( $true
= ( X310 @ ( comp @ X315 @ X312 ) @ ( sub @ X314 @ X312 ) @ X313 ) )
& ( ( X310 @ X315 @ X314 @ ( comp @ X312 @ X313 ) )
!= $true ) )
| ? [X311: term] :
( ( ( var @ ( sub @ X311 @ id ) )
= $true )
& ( ( X310 @ id @ X311 @ id )
!= $true ) )
| ? [X316: term,X317: subst,X318: subst,X319: subst] :
( ( ( X310 @ X318 @ X316 @ ( comp @ X319 @ X317 ) )
= $true )
& ( ( X310 @ ( comp @ X318 @ X319 ) @ ( sub @ X316 @ X319 ) @ X317 )
!= $true ) )
| ( ( X310 @ id @ X309 @ id )
= $true )
| ? [X325: term,X326: term] :
( ( $true
= ( X310 @ id @ X326 @ id ) )
& ( ( X310 @ id @ X325 @ id )
= $true )
& ( ( X310 @ id @ ( ap @ ( sub @ X326 @ id ) @ X325 ) @ id )
!= $true ) ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
= $true )
| ? [X249: term] :
( ( X246 @ id @ X249 @ id )
!= ( X247 @ X249 ) )
| ? [X250: subst > term > term] :
( ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X251: term] :
( ( ( X246 @ id @ X251 @ id )
!= $true )
| ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true ) )
& ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X255: term] :
( ( ( X247 @ X255 )
= $true )
& ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
!= $true ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X60: subst > term > subst > $o,X61: term] :
( ? [X67: subst,X68: term,X69: subst,X70: subst] :
( ( ( X60 @ X69 @ X68 @ ( comp @ X70 @ X67 ) )
!= $true )
& ( ( X60 @ ( comp @ X69 @ X70 ) @ ( sub @ X68 @ X70 ) @ X67 )
= $true ) )
| ( ( X60 @ id @ ( lam @ X61 ) @ id )
= $true )
| ? [X75: term] :
( ( ( X60 @ id @ ( sub @ X61 @ ( push @ X75 @ id ) ) @ id )
!= $true )
& ( ( X60 @ id @ X75 @ id )
= $true ) )
| ? [X71: subst,X72: subst,X73: subst,X74: term] :
( ( ( X60 @ ( comp @ X73 @ X71 ) @ ( sub @ X74 @ X71 ) @ X72 )
!= $true )
& ( ( X60 @ X73 @ X74 @ ( comp @ X71 @ X72 ) )
= $true ) )
| ? [X62: subst > term > term] :
( ! [X63: term,X64: subst,X65: subst] :
( ( sub @ ( X62 @ X65 @ X63 ) @ X64 )
= ( X62 @ ( comp @ X65 @ X64 ) @ ( sub @ X63 @ X64 ) ) )
& ! [X66: term] :
( ( ( X60 @ id @ X66 @ id )
!= $true )
| ( ( X60 @ id @ ( X62 @ id @ X66 ) @ id )
= $true ) )
& ( ( X60 @ id @ ( lam @ ( X62 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X294: d_term,X295: d_term] :
( ( X294 = X295 )
| ( ( d2term @ X294 )
!= ( d2term @ X295 ) ) )
& ( axabs = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) )
| ? [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
!= X303 )
| ? [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
!= X300 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ! [X233: term,X234: subst > term > subst > $o] :
( ? [X235: subst > term > term] :
( ! [X239: term] :
( ( ( X234 @ id @ ( X235 @ id @ X239 ) @ id )
= $true )
| ( ( X234 @ id @ X239 @ id )
!= $true ) )
& ( ( X234 @ id @ ( lam @ ( X235 @ sh @ one ) ) @ id )
!= $true )
& ! [X236: subst,X237: subst,X238: term] :
( ( X235 @ ( comp @ X236 @ X237 ) @ ( sub @ X238 @ X237 ) )
= ( sub @ ( X235 @ X236 @ X238 ) @ X237 ) ) )
| ( ( X234 @ id @ ( lam @ X233 ) @ id )
= $true )
| ? [X240: term] :
( ( ( X234 @ id @ ( sub @ X233 @ ( push @ X240 @ id ) ) @ id )
!= $true )
& ( ( X234 @ id @ X240 @ id )
= $true ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X431: term,X432: subst > term > subst > $o] :
( ? [X433: subst > term > term] :
( ! [X434: subst,X435: subst,X436: term] :
( ( sub @ ( X433 @ X434 @ X436 ) @ X435 )
= ( X433 @ ( comp @ X434 @ X435 ) @ ( sub @ X436 @ X435 ) ) )
& ( ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id )
!= $true )
& ! [X437: term] :
( ( ( X432 @ id @ ( X433 @ id @ X437 ) @ id )
= $true )
| ( ( X432 @ id @ X437 @ id )
!= $true ) ) )
| ( ( X432 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X438: term] :
( ( ( X432 @ id @ ( sub @ X431 @ ( push @ X438 @ id ) ) @ id )
!= $true )
& ( ( X432 @ id @ X438 @ id )
= $true ) ) ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ? [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
!= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) )
| ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
<=> ( axvarid = $true ) )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X419: subst,X420: subst > term > term,X421: subst > term > term,X422: term] :
( ? [X426: subst,X427: subst,X428: term] :
( ( X421 @ ( comp @ X426 @ X427 ) @ ( sub @ X428 @ X427 ) )
!= ( sub @ ( X421 @ X426 @ X428 ) @ X427 ) )
| ( ( lam @ ( X420 @ sh @ one ) )
!= ( lam @ ( X421 @ sh @ one ) ) )
| ? [X423: term,X424: subst,X425: subst] :
( ( X420 @ ( comp @ X425 @ X424 ) @ ( sub @ X423 @ X424 ) )
!= ( sub @ ( X420 @ X425 @ X423 ) @ X424 ) )
| ( ( X420 @ X419 @ X422 )
= ( X421 @ X419 @ X422 ) ) )
| ? [X417: term,X418: term] :
( ( ( lam @ X418 )
= ( lam @ X417 ) )
& ( X417 != X418 ) )
| ? [X415: subst,X416: term] :
( ( comp @ sh @ ( push @ X416 @ X415 ) )
!= X415 )
| ? [X413: subst,X414: term] :
( ( sub @ one @ ( push @ X414 @ X413 ) )
!= X414 ) ) )
& ( ulamvarsh = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( ! [X383: term,X384: term > $o,X385: subst > term > subst > $o] :
( ? [X387: subst > term > term] :
( ! [X389: subst,X390: subst,X391: term] :
( ( X387 @ ( comp @ X390 @ X389 ) @ ( sub @ X391 @ X389 ) )
= ( sub @ ( X387 @ X390 @ X391 ) @ X389 ) )
& ( ( X385 @ id @ ( lam @ ( X387 @ sh @ one ) ) @ id )
!= $true )
& ! [X388: term] :
( ( ( X385 @ id @ X388 @ id )
!= $true )
| ( ( X385 @ id @ ( X387 @ id @ X388 ) @ id )
= $true ) ) )
| ? [X386: term] :
( ( X384 @ X386 )
!= ( X385 @ id @ X386 @ id ) )
| ? [X392: term] :
( ( ( X384 @ ( sub @ X383 @ ( push @ X392 @ id ) ) )
!= $true )
& ( ( X384 @ X392 )
= $true ) )
| ( ( X384 @ ( lam @ X383 ) )
= $true ) )
| ? [X382: term] :
( ( sub @ X382 @ id )
!= X382 )
| ? [X378: term] :
! [X379: subst > term > term] :
? [X380: term,X381: subst] :
( ( X379 @ X381 @ X380 )
!= ( sub @ X378 @ ( push @ X380 @ X381 ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ulamvarind = $true )
& ( induction2_gthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X327: term] :
? [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
= ( X328 @ sh @ one ) ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( axidl = $true )
<=> ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 ) )
& ( termmset_gthm = $true )
& ( pushprop = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X489: subst > term > subst > $o,X490: term] :
( ? [X492: term,X493: subst > term > term] :
( ( ( X489 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X497: subst,X498: term,X499: subst] :
( ( sub @ ( X493 @ X499 @ X498 ) @ X497 )
= ( sub @ ( sub @ X492 @ ( push @ X498 @ X499 ) ) @ X497 ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( X493 @ ( comp @ X496 @ X494 ) @ ( sub @ X495 @ X494 ) )
= ( sub @ X492 @ ( push @ ( sub @ X495 @ X494 ) @ ( comp @ X496 @ X494 ) ) ) )
& ! [X500: term] :
( ( ( X489 @ id @ X500 @ id )
!= $true )
| ( ( X489 @ id @ ( X493 @ id @ X500 ) @ id )
= $true ) ) )
| ( ( X489 @ id @ ( lam @ ( sub @ X490 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X491: term] :
( ( ( X489 @ id @ X491 @ id )
= $true )
& ( ( X489 @ id @ ( sub @ X490 @ ( push @ X491 @ id ) ) @ id )
!= $true ) ) ) )
& ( ! [X171: subst > term > subst > $o] :
? [X172: term > $o] :
! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasinduction = $true )
<=> ! [X309: term,X310: subst > term > subst > $o] :
( ? [X320: subst > term > term] :
( ! [X324: term] :
( ( ( X310 @ id @ X324 @ id )
!= $true )
| ( ( X310 @ id @ ( X320 @ id @ X324 ) @ id )
= $true ) )
& ! [X321: subst,X322: term,X323: subst] :
( ( sub @ ( X320 @ X321 @ X322 ) @ X323 )
= ( X320 @ ( comp @ X321 @ X323 ) @ ( sub @ X322 @ X323 ) ) )
& ( ( X310 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X312: subst,X313: subst,X314: term,X315: subst] :
( ( $true
= ( X310 @ ( comp @ X315 @ X312 ) @ ( sub @ X314 @ X312 ) @ X313 ) )
& ( ( X310 @ X315 @ X314 @ ( comp @ X312 @ X313 ) )
!= $true ) )
| ? [X311: term] :
( ( ( var @ ( sub @ X311 @ id ) )
= $true )
& ( ( X310 @ id @ X311 @ id )
!= $true ) )
| ? [X316: term,X317: subst,X318: subst,X319: subst] :
( ( ( X310 @ X318 @ X316 @ ( comp @ X319 @ X317 ) )
= $true )
& ( ( X310 @ ( comp @ X318 @ X319 ) @ ( sub @ X316 @ X319 ) @ X317 )
!= $true ) )
| ( ( X310 @ id @ X309 @ id )
= $true )
| ? [X325: term,X326: term] :
( ( $true
= ( X310 @ id @ X326 @ id ) )
& ( ( X310 @ id @ X325 @ id )
= $true )
& ( ( X310 @ id @ ( ap @ ( sub @ X326 @ id ) @ X325 ) @ id )
!= $true ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ? [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
!= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) )
| ? [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
!= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( axmap = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ( ( X481 @ X484 )
!= $true )
| ? [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
!= ( X483 @ X485 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X9: term,X10: term > $o,X11: term,X12: subst > term > subst > $o] :
( ( ( X10 @ ( ap @ X11 @ X9 ) )
= $true )
| ? [X14: subst,X15: subst,X16: subst,X17: term] :
( ( ( X12 @ X15 @ X17 @ ( comp @ X16 @ X14 ) )
!= $true )
& ( ( X12 @ ( comp @ X15 @ X16 ) @ ( sub @ X17 @ X16 ) @ X14 )
= $true ) )
| ( ( X10 @ X9 )
!= $true )
| ? [X13: term] :
( ( X10 @ X13 )
!= ( X12 @ id @ X13 @ id ) )
| ? [X18: subst,X19: term,X20: subst,X21: subst] :
( ( ( X12 @ X20 @ X19 @ ( comp @ X18 @ X21 ) )
= $true )
& ( ( X12 @ ( comp @ X20 @ X18 ) @ ( sub @ X19 @ X18 ) @ X21 )
!= $true ) )
| ( ( X10 @ X11 )
!= $true )
| ? [X22: term,X23: term] :
( ( $true
= ( X12 @ id @ X23 @ id ) )
& ( ( X12 @ id @ ( ap @ ( sub @ X23 @ id ) @ X22 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X22 @ id ) ) ) ) )
& ( axvarshift = $true )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
= $true )
| ? [X249: term] :
( ( X246 @ id @ X249 @ id )
!= ( X247 @ X249 ) )
| ? [X250: subst > term > term] :
( ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X251: term] :
( ( ( X246 @ id @ X251 @ id )
!= $true )
| ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true ) )
& ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X255: term] :
( ( ( X247 @ X255 )
= $true )
& ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
!= $true ) ) ) )
& ( ! [X393: term,X394: subst > term > subst > $o] :
( ( ( X394 @ id @ ( lam @ ( sub @ X393 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X400: term] :
( ( ( X394 @ id @ ( sub @ X393 @ ( push @ X400 @ id ) ) @ id )
!= $true )
& ( ( X394 @ id @ X400 @ id )
= $true ) )
| ? [X395: subst > term > term] :
( ! [X397: term,X398: subst,X399: subst] :
( ( X395 @ ( comp @ X398 @ X399 ) @ ( sub @ X397 @ X399 ) )
= ( sub @ ( X395 @ X398 @ X397 ) @ X399 ) )
& ! [X396: term] :
( ( ( X394 @ id @ X396 @ id )
!= $true )
| ( ( X394 @ id @ ( X395 @ id @ X396 ) @ id )
= $true ) )
& ( ( X394 @ id @ ( lam @ ( X395 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X259: term > $o,X260: subst,X261: term] :
? [X262: term > $o] :
! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( axscons = $true )
<=> ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 ) )
& ( ! [X429: term] :
? [X430: subst > term > term] :
( ( X430 @ sh @ one )
= ( sub @ X429 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem = $true )
<=> ! [X401: subst,X402: term > $o,X403: term] :
( ? [X404: term] :
( ( ( X402 @ ( lam @ X404 ) )
!= $true )
& ! [X405: term] :
( ( ( X402 @ X405 )
!= $true )
| ( ( X402 @ ( sub @ X404 @ ( push @ X405 @ id ) ) )
= $true ) ) )
| ? [X407: term,X408: term] :
( ( ( X402 @ X407 )
= $true )
& ( ( X402 @ X408 )
= $true )
& ( ( X402 @ ( ap @ X408 @ X407 ) )
!= $true ) )
| ( ( X402 @ ( sub @ X403 @ X401 ) )
= $true )
| ? [X406: term] :
( ( ( X402 @ ( sub @ X406 @ X401 ) )
!= $true )
& ( ( var @ X406 )
= $true ) ) ) )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
<=> ( termmset = $true ) )
& ( ( ! [X104: term,X105: subst > term > subst > $o] :
( ? [X114: term] :
( ( ( X105 @ id @ X114 @ id )
= $true )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X114 @ id ) ) @ id )
!= $true ) )
| ? [X110: term,X111: subst,X112: subst,X113: subst] :
( ( ( X105 @ X112 @ X110 @ ( comp @ X113 @ X111 ) )
= $true )
& ( $true
!= ( X105 @ ( comp @ X112 @ X113 ) @ ( sub @ X110 @ X113 ) @ X111 ) ) )
| ? [X106: subst,X107: term,X108: subst,X109: subst] :
( ( ( X105 @ X109 @ X107 @ ( comp @ X108 @ X106 ) )
!= $true )
& ( ( X105 @ ( comp @ X109 @ X108 ) @ ( sub @ X107 @ X108 ) @ X106 )
= $true ) )
| ? [X115: subst > term > term] :
( ! [X116: term] :
( ( ( X105 @ id @ ( X115 @ id @ X116 ) @ id )
= $true )
| ( ( X105 @ id @ X116 @ id )
!= $true ) )
& ( ( X105 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id )
!= $true )
& ! [X117: subst,X118: subst,X119: term] :
( ( X115 @ ( comp @ X117 @ X118 ) @ ( sub @ X119 @ X118 ) )
= ( sub @ ( X115 @ X117 @ X119 ) @ X118 ) ) )
| ( ( X105 @ id @ ( lam @ X104 ) @ id )
= $true ) )
| ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true )
| ( ( X97 @ id @ X103 @ id )
!= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id )
= $true )
| ? [X99: term,X100: subst,X101: subst] :
( ( sub @ ( X98 @ X101 @ X99 ) @ X100 )
!= ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) ) ) )
& ( ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
<=> ( laminj = $true ) )
& ( hoasapinj1_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X344: subst,X345: term,X346: term > $o] :
( ? [X349: term,X350: term] :
( ( ( X346 @ X349 )
= $true )
& ( ( X346 @ ( ap @ X350 @ X349 ) )
!= $true )
& ( ( X346 @ X350 )
= $true ) )
| ? [X351: term] :
( ( ( var @ X351 )
= $true )
& ( $true
!= ( X346 @ ( sub @ X351 @ X344 ) ) ) )
| ? [X347: term] :
( ! [X348: term] :
( ( ( X346 @ ( sub @ X347 @ ( push @ X348 @ id ) ) )
= $true )
| ( ( X346 @ X348 )
!= $true ) )
& ( ( X346 @ ( lam @ X347 ) )
!= $true ) )
| ( ( X346 @ ( sub @ X345 @ X344 ) )
= $true ) )
| ? [X338: term,X339: term > $o] :
( ! [X342: term,X343: term] :
( ( $true
!= ( X339 @ X342 ) )
| ( ( X339 @ ( ap @ X343 @ X342 ) )
= $true )
| ( ( X339 @ X343 )
!= $true ) )
& ( $true
!= ( X339 @ X338 ) )
& ! [X341: term] :
( ( ( X339 @ X341 )
!= $true )
| ( $true
= ( X339 @ ( lam @ X341 ) ) ) )
& ! [X340: term] :
( ( ( X339 @ X340 )
= $true )
| ( ( var @ X340 )
!= $true ) ) )
| ? [X337: subst] :
( ( comp @ X337 @ id )
!= X337 )
| ? [X335: subst,X336: term] :
( ( comp @ sh @ ( push @ X336 @ X335 ) )
!= X335 )
| ? [X333: term,X334: subst] :
( ( sub @ one @ ( push @ X333 @ X334 ) )
!= X333 ) ) )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X533 )
& ( ( ap @ X535 @ X532 )
= ( ap @ X534 @ X533 ) ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X298: term] :
( ( sub @ X298 @ id )
!= X298 )
| ! [X299: term] :
( ( sub @ X299 @ id )
= X299 ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop_lem1v2_gthm = $true )
& ( pushprop_lthm = $true )
& ( ! [X457: subst > term > subst > $o,X458: term,X459: term] :
( ? [X460: term,X461: term] :
( ( $true
= ( X457 @ id @ X460 @ id ) )
& ( ( X457 @ id @ X461 @ id )
= $true )
& ( ( X457 @ id @ ( ap @ ( sub @ X461 @ id ) @ X460 ) @ id )
!= $true ) )
| ( ( X457 @ id @ X458 @ id )
!= $true )
| ( ( X457 @ id @ X459 @ id )
!= $true )
| ? [X466: subst,X467: term,X468: subst,X469: subst] :
( ( ( X457 @ X469 @ X467 @ ( comp @ X468 @ X466 ) )
= $true )
& ( ( X457 @ ( comp @ X469 @ X468 ) @ ( sub @ X467 @ X468 ) @ X466 )
!= $true ) )
| ? [X462: subst,X463: subst,X464: subst,X465: term] :
( ( ( X457 @ ( comp @ X463 @ X462 ) @ ( sub @ X465 @ X462 ) @ X464 )
= $true )
& ( $true
!= ( X457 @ X463 @ X465 @ ( comp @ X462 @ X464 ) ) ) )
| ( ( X457 @ id @ ( ap @ X458 @ X459 ) @ id )
= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( induction2lem_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X241: subst,X242: term,X243: term > $o] :
? [X244: term > $o] :
! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X120: term > $o,X121: term] :
( ? [X125: term] :
( ( ( X120 @ ( lam @ X125 ) )
!= $true )
& ! [X126: term] :
( ( ( X120 @ ( sub @ X125 @ ( push @ X126 @ id ) ) )
= $true )
| ( ( X120 @ X126 )
!= $true ) ) )
| ? [X123: term,X124: term] :
( ( ( X120 @ ( ap @ X123 @ X124 ) )
!= $true )
& ( ( X120 @ X124 )
= $true )
& ( ( X120 @ X123 )
= $true ) )
| ( ( X120 @ X121 )
= $true )
| ? [X122: term] :
( ( ( X120 @ X122 )
!= $true )
& ( ( var @ X122 )
= $true ) ) )
<=> ( induction2 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axvarcons = $true )
<=> ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 ) )
& ( ! [X329: term] :
? [X330: subst > term > term] :
! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( axshiftcons = $true )
<=> ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( hoasinduction_lem1_gthm = $true )
& ( axapp = $true )
& ( ! [X0: term,X1: subst > term > subst > $o] :
( ? [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) )
& ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X1 @ id @ X0 @ id ) )
| ? [X2: term,X3: term] :
( ( ( X1 @ id @ X3 @ id )
= $true )
& ( ( X1 @ id @ X2 @ id )
= $true )
& ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
!= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
<=> ( axidr = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
= ( X505 @ one ) )
| ? [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
!= ( X505 @ X507 ) )
| ( $true
!= ( X504 @ X503 ) ) )
| ? [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
!= X501 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( apnotvar = $true )
& ( hoasapnotvar_lthm = $true )
& ( lamnotvar = $true )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
<=> ( apinj2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) )
| ? [X473: term,X474: term,X475: term,X476: term] :
( ( X474 != X476 )
& ( ( ap @ X476 @ X473 )
= ( ap @ X474 @ X475 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X174: term] :
? [X175: subst > term > term] :
! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) ) )
& ( ( ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) )
| ? [X83: subst] :
( ( comp @ X83 @ id )
!= X83 )
| ? [X82: subst] :
( ( comp @ id @ X82 )
!= X82 ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X215: subst > term > subst > $o,X216: term] :
( ? [X217: term] :
( ( ( var @ ( sub @ X217 @ id ) )
= $true )
& ( ( X215 @ id @ X217 @ id )
!= $true ) )
| ? [X227: subst,X228: subst,X229: subst,X230: term] :
( ( ( X215 @ X229 @ X230 @ ( comp @ X228 @ X227 ) )
= $true )
& ( ( X215 @ ( comp @ X229 @ X228 ) @ ( sub @ X230 @ X228 ) @ X227 )
!= $true ) )
| ? [X223: term,X224: subst,X225: subst,X226: subst] :
( ( ( X215 @ X225 @ X223 @ ( comp @ X226 @ X224 ) )
!= $true )
& ( ( X215 @ ( comp @ X225 @ X226 ) @ ( sub @ X223 @ X226 ) @ X224 )
= $true ) )
| ? [X218: subst > term > term] :
( ( ( X215 @ id @ ( lam @ ( X218 @ sh @ one ) ) @ id )
!= $true )
& ! [X222: term] :
( ( ( X215 @ id @ X222 @ id )
!= $true )
| ( ( X215 @ id @ ( X218 @ id @ X222 ) @ id )
= $true ) )
& ! [X219: term,X220: subst,X221: subst] :
( ( X218 @ ( comp @ X220 @ X221 ) @ ( sub @ X219 @ X221 ) )
= ( sub @ ( X218 @ X220 @ X219 ) @ X221 ) ) )
| ( ( X215 @ id @ X216 @ id )
= $true )
| ? [X231: term,X232: term] :
( ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
!= $true )
& ( ( X215 @ id @ X232 @ id )
= $true )
& ( ( X215 @ id @ X231 @ id )
= $true ) ) )
| ? [X199: term,X200: subst > term > subst > $o] :
( ! [X211: subst,X212: term,X213: subst,X214: subst] :
( ( ( X200 @ ( comp @ X213 @ X214 ) @ ( sub @ X212 @ X214 ) @ X211 )
!= $true )
| ( ( X200 @ X213 @ X212 @ ( comp @ X214 @ X211 ) )
= $true ) )
& ! [X201: subst,X202: subst,X203: subst,X204: term] :
( ( ( X200 @ ( comp @ X201 @ X202 ) @ ( sub @ X204 @ X202 ) @ X203 )
= $true )
| ( ( X200 @ X201 @ X204 @ ( comp @ X202 @ X203 ) )
!= $true ) )
& ! [X205: term] :
( ( ( X200 @ id @ X205 @ id )
!= $true )
| ( ( X200 @ id @ ( sub @ X199 @ ( push @ X205 @ id ) ) @ id )
= $true ) )
& ( ( X200 @ id @ ( lam @ X199 ) @ id )
!= $true )
& ! [X206: subst > term > term] :
( ? [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
!= $true )
& ( ( X200 @ id @ X207 @ id )
= $true ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ? [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
!= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) ) )
| ? [X186: term,X187: term,X188: subst > term > subst > $o] :
( ! [X191: term,X192: subst,X193: subst,X194: subst] :
( ( ( X188 @ ( comp @ X194 @ X193 ) @ ( sub @ X191 @ X193 ) @ X192 )
!= $true )
| ( ( X188 @ X194 @ X191 @ ( comp @ X193 @ X192 ) )
= $true ) )
& ( ( X188 @ id @ X187 @ id )
= $true )
& ! [X189: term,X190: term] :
( ( ( X188 @ id @ ( ap @ ( sub @ X189 @ id ) @ X190 ) @ id )
= $true )
| ( ( X188 @ id @ X190 @ id )
!= $true )
| ( ( X188 @ id @ X189 @ id )
!= $true ) )
& ( $true
!= ( X188 @ id @ ( ap @ X186 @ X187 ) @ id ) )
& ( ( X188 @ id @ X186 @ id )
= $true )
& ! [X195: term,X196: subst,X197: subst,X198: subst] :
( ( ( X188 @ ( comp @ X197 @ X198 ) @ ( sub @ X195 @ X198 ) @ X196 )
= $true )
| ( ( X188 @ X197 @ X195 @ ( comp @ X198 @ X196 ) )
!= $true ) ) )
| ? [X179: term > $o,X180: term] :
( ! [X183: term,X184: term] :
( ( ( X179 @ X184 )
!= $true )
| ( ( X179 @ ( ap @ X184 @ X183 ) )
= $true )
| ( $true
!= ( X179 @ X183 ) ) )
& ! [X181: term] :
( ? [X182: term] :
( ( ( X179 @ ( sub @ X181 @ ( push @ X182 @ id ) ) )
!= $true )
& ( ( X179 @ X182 )
= $true ) )
| ( ( X179 @ ( lam @ X181 ) )
= $true ) )
& ( ( X179 @ X180 )
!= $true )
& ! [X185: term] :
( ( ( X179 @ X185 )
= $true )
| ( ( var @ X185 )
!= $true ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar = $true )
& ( axassoc = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ulamvar1 != $true )
& ( ! [X352: term,X353: term > $o,X354: subst > term > subst > $o] :
( ? [X366: subst,X367: subst,X368: term,X369: subst] :
( ( ( X354 @ X366 @ X368 @ ( comp @ X369 @ X367 ) )
= $true )
& ( ( X354 @ ( comp @ X366 @ X369 ) @ ( sub @ X368 @ X369 ) @ X367 )
!= $true ) )
| ? [X357: subst,X358: subst,X359: term,X360: subst] :
( ( ( X354 @ ( comp @ X358 @ X360 ) @ ( sub @ X359 @ X360 ) @ X357 )
= $true )
& ( ( X354 @ X358 @ X359 @ ( comp @ X360 @ X357 ) )
!= $true ) )
| ? [X355: term] :
( ( ( X353 @ ( sub @ X352 @ ( push @ X355 @ id ) ) )
!= $true )
& ( ( X353 @ X355 )
= $true ) )
| ? [X361: subst > term > term] :
( ! [X365: term] :
( ( ( X354 @ id @ ( X361 @ id @ X365 ) @ id )
= $true )
| ( ( X354 @ id @ X365 @ id )
!= $true ) )
& ( ( X354 @ id @ ( lam @ ( X361 @ sh @ one ) ) @ id )
!= $true )
& ! [X362: subst,X363: subst,X364: term] :
( ( sub @ ( X361 @ X363 @ X364 ) @ X362 )
= ( X361 @ ( comp @ X363 @ X362 ) @ ( sub @ X364 @ X362 ) ) ) )
| ? [X356: term] :
( ( X354 @ id @ X356 @ id )
!= ( X353 @ X356 ) )
| ( ( X353 @ ( lam @ X352 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X52: term,X53: subst > term > subst > $o] :
( ? [X59: term] :
( ( $true
= ( X53 @ id @ X59 @ id ) )
& ( ( X53 @ id @ ( sub @ X52 @ ( push @ X59 @ id ) ) @ id )
!= $true ) )
| ( ( X53 @ id @ ( lam @ X52 ) @ id )
= $true )
| ? [X54: subst > term > term] :
( ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( ( X53 @ id @ ( X54 @ id @ X55 ) @ id )
= $true ) )
& ! [X56: subst,X57: subst,X58: term] :
( ( X54 @ ( comp @ X57 @ X56 ) @ ( sub @ X58 @ X56 ) )
= ( sub @ ( X54 @ X57 @ X58 ) @ X56 ) )
& ( ( X53 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X44: subst > term > subst > $o,X45: term] :
( ! [X46: subst > term > term] :
( ( ( X44 @ id @ ( lam @ ( X46 @ sh @ one ) ) @ id )
= $true )
| ? [X47: term] :
( ( ( X44 @ id @ X47 @ id )
= $true )
& ( $true
!= ( X44 @ id @ ( X46 @ id @ X47 ) @ id ) ) )
| ? [X48: subst,X49: term,X50: subst] :
( ( X46 @ ( comp @ X50 @ X48 ) @ ( sub @ X49 @ X48 ) )
!= ( sub @ ( X46 @ X50 @ X49 ) @ X48 ) ) )
& ( ( X44 @ id @ ( lam @ ( sub @ X45 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X51: term] :
( ( ( X44 @ id @ X51 @ id )
!= $true )
| ( ( X44 @ id @ ( sub @ X45 @ ( push @ X51 @ id ) ) @ id )
= $true ) ) )
| ? [X43: term] :
( ( sub @ X43 @ id )
!= X43 ) ) )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoaslaminj_gthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) ) )
& ( pushprop_lem1_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
<=> ( shinj = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( axclos = $true )
& ( pushprop_lthm_orig = $true )
& ( hoasapinj2_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X509: term > $o,X510: subst > term > subst > $o,X511: term] :
( ? [X526: term] :
( ( $true
!= ( X509 @ ( sub @ X511 @ ( push @ X526 @ id ) ) ) )
& ( ( X509 @ X526 )
= $true ) )
| ( ( X509 @ ( lam @ X511 ) )
= $true )
| ? [X520: term] :
( ( X509 @ X520 )
!= ( X510 @ id @ X520 @ id ) )
| ? [X512: term,X513: subst,X514: subst,X515: subst] :
( ( ( X510 @ X513 @ X512 @ ( comp @ X514 @ X515 ) )
= $true )
& ( ( X510 @ ( comp @ X513 @ X514 ) @ ( sub @ X512 @ X514 ) @ X515 )
!= $true ) )
| ? [X516: subst,X517: term,X518: subst,X519: subst] :
( ( ( X510 @ X516 @ X517 @ ( comp @ X518 @ X519 ) )
!= $true )
& ( ( X510 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) @ X519 )
= $true ) )
| ? [X521: subst > term > term] :
( ! [X522: term,X523: subst,X524: subst] :
( ( sub @ ( X521 @ X523 @ X522 ) @ X524 )
= ( X521 @ ( comp @ X523 @ X524 ) @ ( sub @ X522 @ X524 ) ) )
& ( ( X510 @ id @ ( lam @ ( X521 @ sh @ one ) ) @ id )
!= $true )
& ! [X525: term] :
( ( ( X510 @ id @ X525 @ id )
!= $true )
| ( ( X510 @ id @ ( X521 @ id @ X525 ) @ id )
= $true ) ) ) )
| ? [X508: term] :
( ( sub @ X508 @ id )
!= X508 ) ) )
& ( ! [X439: term,X440: term > $o] :
( ? [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
!= $true )
& ( ( X440 @ X443 )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ? [X441: term,X442: term] :
( ( ( X440 @ X442 )
= $true )
& ( ( X440 @ X441 )
= $true )
& ( ( X440 @ ( ap @ X441 @ X442 ) )
!= $true ) )
| ? [X444: term] :
( ( ( X440 @ X444 )
!= $true )
& ( $true
= ( var @ X444 ) ) ) )
<=> ( induction = $true ) )
& ( ! [X168: subst > term > subst > $o] :
? [X169: term > $o] :
! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X34: term,X35: term > $o] :
( ? [X38: term,X39: term] :
( ( $true
= ( X35 @ X39 ) )
& ( ( X35 @ ( ap @ X39 @ X38 ) )
!= $true )
& ( ( X35 @ X38 )
= $true ) )
| ( $true
= ( X35 @ X34 ) )
| ? [X36: term] :
( ! [X37: term] :
( ( $true
= ( X35 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) )
| ( ( X35 @ X37 )
!= $true ) )
& ( ( X35 @ ( lam @ X36 ) )
!= $true ) )
| ? [X40: term] :
( ( ( var @ X40 )
= $true )
& ( ( X35 @ X40 )
!= $true ) ) )
| ? [X26: term > $o,X27: term,X28: subst] :
( ! [X31: term] :
( ? [X32: term] :
( ( ( X26 @ ( sub @ X31 @ ( push @ X32 @ id ) ) )
!= $true )
& ( ( X26 @ X32 )
= $true ) )
| ( ( X26 @ ( lam @ X31 ) )
= $true ) )
& ! [X29: term,X30: term] :
( ( ( X26 @ X29 )
!= $true )
| ( ( X26 @ X30 )
!= $true )
| ( ( X26 @ ( ap @ X29 @ X30 ) )
= $true ) )
& ( ( X26 @ ( sub @ X27 @ X28 ) )
!= $true )
& ! [X33: term] :
( ( ( var @ X33 )
!= $true )
| ( ( X26 @ ( sub @ X33 @ X28 ) )
= $true ) ) )
| ? [X25: term] :
( ( sub @ X25 @ id )
!= X25 ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
<=> ( apinj1 = $true ) )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
!= ( d2subst @ X471 ) )
| ( X470 = X471 ) )
& ( ! [X60: subst > term > subst > $o,X61: term] :
( ? [X67: subst,X68: term,X69: subst,X70: subst] :
( ( ( X60 @ X69 @ X68 @ ( comp @ X70 @ X67 ) )
!= $true )
& ( ( X60 @ ( comp @ X69 @ X70 ) @ ( sub @ X68 @ X70 ) @ X67 )
= $true ) )
| ( ( X60 @ id @ ( lam @ X61 ) @ id )
= $true )
| ? [X75: term] :
( ( ( X60 @ id @ ( sub @ X61 @ ( push @ X75 @ id ) ) @ id )
!= $true )
& ( ( X60 @ id @ X75 @ id )
= $true ) )
| ? [X71: subst,X72: subst,X73: subst,X74: term] :
( ( ( X60 @ ( comp @ X73 @ X71 ) @ ( sub @ X74 @ X71 ) @ X72 )
!= $true )
& ( ( X60 @ X73 @ X74 @ ( comp @ X71 @ X72 ) )
= $true ) )
| ? [X62: subst > term > term] :
( ! [X63: term,X64: subst,X65: subst] :
( ( sub @ ( X62 @ X65 @ X63 ) @ X64 )
= ( X62 @ ( comp @ X65 @ X64 ) @ ( sub @ X63 @ X64 ) ) )
& ! [X66: term] :
( ( ( X60 @ id @ X66 @ id )
!= $true )
| ( ( X60 @ id @ ( X62 @ id @ X66 ) @ id )
= $true ) )
& ( ( X60 @ id @ ( lam @ ( X62 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( ! [X285: term,X286: subst > term > subst > $o] :
( ? [X292: term,X293: term] :
( ( $true
= ( X286 @ id @ X293 @ id ) )
& ( ( X286 @ id @ X292 @ id )
= $true )
& ( ( X286 @ id @ ( ap @ ( sub @ X292 @ id ) @ X293 ) @ id )
!= $true ) )
| ( ( X286 @ id @ X285 @ id )
= $true )
| ? [X287: subst > term > term] :
( ( ( X286 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id )
!= $true )
& ! [X291: term] :
( ( ( X286 @ id @ X291 @ id )
!= $true )
| ( ( X286 @ id @ ( X287 @ id @ X291 ) @ id )
= $true ) )
& ! [X288: subst,X289: term,X290: subst] :
( ( sub @ ( X287 @ X288 @ X289 ) @ X290 )
= ( X287 @ ( comp @ X288 @ X290 ) @ ( sub @ X289 @ X290 ) ) ) ) )
| ? [X275: subst > term > subst > $o,X276: term,X277: term > $o] :
( ! [X278: subst > term > term] :
( ( ( X275 @ id @ ( lam @ ( X278 @ sh @ one ) ) @ id )
= $true )
| ? [X280: term,X281: subst,X282: subst] :
( ( X278 @ ( comp @ X282 @ X281 ) @ ( sub @ X280 @ X281 ) )
!= ( sub @ ( X278 @ X282 @ X280 ) @ X281 ) )
| ? [X279: term] :
( ( ( X275 @ id @ ( X278 @ id @ X279 ) @ id )
!= $true )
& ( ( X275 @ id @ X279 @ id )
= $true ) ) )
& ( ( X277 @ ( lam @ X276 ) )
!= $true )
& ! [X284: term] :
( ( ( X277 @ X284 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X284 @ id ) ) )
= $true ) )
& ! [X283: term] :
( ( X277 @ X283 )
= ( X275 @ id @ X283 @ id ) ) )
| ? [X274: term] :
( ( sub @ X274 @ id )
!= X274 )
| ? [X267: term > $o,X268: term] :
( ! [X272: term] :
( ? [X273: term] :
( ( ( X267 @ ( sub @ X272 @ ( push @ X273 @ id ) ) )
!= $true )
& ( $true
= ( X267 @ X273 ) ) )
| ( ( X267 @ ( lam @ X272 ) )
= $true ) )
& ! [X269: term,X270: term] :
( ( $true
!= ( X267 @ X269 ) )
| ( ( X267 @ ( ap @ X270 @ X269 ) )
= $true )
| ( ( X267 @ X270 )
!= $true ) )
& ( ( X267 @ X268 )
!= $true )
& ! [X271: term] :
( ( ( var @ X271 )
!= $true )
| ( $true
= ( X267 @ X271 ) ) ) )
| ? [X264: subst > term > subst > $o] :
! [X265: term > $o] :
? [X266: term] :
( ( X265 @ X266 )
!= ( X264 @ id @ X266 @ id ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( ! [X150: subst > term > subst > $o,X151: term] :
( ? [X154: term] :
( ( ( var @ ( sub @ X154 @ id ) )
= $true )
& ( ( X150 @ id @ X154 @ id )
!= $true ) )
| ? [X164: subst,X165: subst,X166: subst,X167: term] :
( ( ( X150 @ ( comp @ X166 @ X165 ) @ ( sub @ X167 @ X165 ) @ X164 )
!= $true )
& ( ( X150 @ X166 @ X167 @ ( comp @ X165 @ X164 ) )
= $true ) )
| ? [X159: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X150 @ id @ X163 @ id ) )
| ( ( X150 @ id @ ( X159 @ id @ X163 ) @ id )
= $true ) )
& ! [X160: term,X161: subst,X162: subst] :
( ( sub @ ( X159 @ X162 @ X160 ) @ X161 )
= ( X159 @ ( comp @ X162 @ X161 ) @ ( sub @ X160 @ X161 ) ) )
& ( ( X150 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X155: subst,X156: term,X157: subst,X158: subst] :
( ( ( X150 @ ( comp @ X158 @ X155 ) @ ( sub @ X156 @ X155 ) @ X157 )
= $true )
& ( ( X150 @ X158 @ X156 @ ( comp @ X155 @ X157 ) )
!= $true ) )
| ? [X152: term,X153: term] :
( ( ( X150 @ id @ ( ap @ ( sub @ X152 @ id ) @ X153 ) @ id )
!= $true )
& ( ( X150 @ id @ X153 @ id )
= $true )
& ( ( X150 @ id @ X152 @ id )
= $true ) )
| ( ( X150 @ id @ X151 @ id )
= $true ) )
| ? [X140: term > $o,X141: term,X142: subst > term > subst > $o] :
( ! [X143: subst > term > term] :
( ( $true
= ( X142 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ? [X144: term] :
( ( ( X142 @ id @ ( X143 @ id @ X144 ) @ id )
!= $true )
& ( ( X142 @ id @ X144 @ id )
= $true ) )
| ? [X145: subst,X146: term,X147: subst] :
( ( X143 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) )
!= ( sub @ ( X143 @ X147 @ X146 ) @ X145 ) ) )
& ( ( X140 @ ( lam @ X141 ) )
!= $true )
& ! [X149: term] :
( ( ( X140 @ ( sub @ X141 @ ( push @ X149 @ id ) ) )
= $true )
| ( ( X140 @ X149 )
!= $true ) )
& ! [X148: term] :
( ( X140 @ X148 )
= ( X142 @ id @ X148 @ id ) ) )
| ? [X139: term] :
( ( sub @ X139 @ id )
!= X139 )
| ? [X132: term > $o,X133: term] :
( ! [X135: term,X136: term] :
( ( ( X132 @ X135 )
!= $true )
| ( ( X132 @ ( ap @ X135 @ X136 ) )
= $true )
| ( ( X132 @ X136 )
!= $true ) )
& ! [X137: term] :
( ( ( X132 @ ( lam @ X137 ) )
= $true )
| ? [X138: term] :
( ( ( X132 @ ( sub @ X137 @ ( push @ X138 @ id ) ) )
!= $true )
& ( ( X132 @ X138 )
= $true ) ) )
& ! [X134: term] :
( ( $true
= ( X132 @ X134 ) )
| ( ( var @ X134 )
!= $true ) )
& ( ( X132 @ X133 )
!= $true ) )
| ? [X129: subst > term > subst > $o] :
! [X130: term > $o] :
? [X131: term] :
( ( X130 @ X131 )
!= ( X129 @ id @ X131 @ id ) ) )
<=> ( hoasinduction_lthm_3 = $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X294: d_term,X295: d_term] :
( ( ( d2term @ X294 )
= ( d2term @ X295 ) )
=> ( X294 = X295 ) )
& ( axabs = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
= X300 )
=> ( ! [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
= X303 )
=> ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ! [X233: term,X234: subst > term > subst > $o] :
( ~ ! [X240: term] :
( ( ( X234 @ id @ ( sub @ X233 @ ( push @ X240 @ id ) ) @ id )
= $true )
| ( ( X234 @ id @ X240 @ id )
!= $true ) )
| ~ ! [X235: subst > term > term] :
( ~ ! [X239: term] :
( ( ( X234 @ id @ ( X235 @ id @ X239 ) @ id )
= $true )
| ( ( X234 @ id @ X239 @ id )
!= $true ) )
| ~ ! [X236: subst,X237: subst,X238: term] :
( ( X235 @ ( comp @ X236 @ X237 ) @ ( sub @ X238 @ X237 ) )
= ( sub @ ( X235 @ X236 @ X238 ) @ X237 ) )
| ( ( X234 @ id @ ( lam @ ( X235 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X234 @ id @ ( lam @ X233 ) @ id )
= $true ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ! [X431: term,X432: subst > term > subst > $o] :
( ~ ! [X438: term] :
( ( ( X432 @ id @ ( sub @ X431 @ ( push @ X438 @ id ) ) @ id )
= $true )
| ( ( X432 @ id @ X438 @ id )
!= $true ) )
| ~ ! [X433: subst > term > term] :
( ~ ! [X434: subst,X435: subst,X436: term] :
( ( sub @ ( X433 @ X434 @ X436 ) @ X435 )
= ( X433 @ ( comp @ X434 @ X435 ) @ ( sub @ X436 @ X435 ) ) )
| ( ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X437: term] :
( ( ( X432 @ id @ ( X433 @ id @ X437 ) @ id )
= $true )
| ( ( X432 @ id @ X437 @ id )
!= $true ) ) )
| ( ( X432 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) )
| ~ ! [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
<=> ( axvarid = $true ) )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X413: subst,X414: term] :
( ( sub @ one @ ( push @ X414 @ X413 ) )
= X414 )
=> ( ! [X415: subst,X416: term] :
( ( comp @ sh @ ( push @ X416 @ X415 ) )
= X415 )
=> ( ! [X417: term,X418: term] :
( ( ( lam @ X418 )
!= ( lam @ X417 ) )
| ( X417 = X418 ) )
=> ! [X419: subst,X420: subst > term > term,X421: subst > term > term,X422: term] :
( ( ( lam @ ( X420 @ sh @ one ) )
!= ( lam @ ( X421 @ sh @ one ) ) )
| ~ ! [X426: subst,X427: subst,X428: term] :
( ( X421 @ ( comp @ X426 @ X427 ) @ ( sub @ X428 @ X427 ) )
= ( sub @ ( X421 @ X426 @ X428 ) @ X427 ) )
| ( ( X420 @ X419 @ X422 )
= ( X421 @ X419 @ X422 ) )
| ~ ! [X423: term,X424: subst,X425: subst] :
( ( X420 @ ( comp @ X425 @ X424 ) @ ( sub @ X423 @ X424 ) )
= ( sub @ ( X420 @ X425 @ X423 ) @ X424 ) ) ) ) ) ) )
& ( ulamvarsh = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( ! [X378: term] :
~ ! [X379: subst > term > term] :
~ ! [X380: term,X381: subst] :
( ( X379 @ X381 @ X380 )
= ( sub @ X378 @ ( push @ X380 @ X381 ) ) )
=> ( ! [X382: term] :
( ( sub @ X382 @ id )
= X382 )
=> ! [X383: term,X384: term > $o,X385: subst > term > subst > $o] :
( ~ ! [X392: term] :
( ( ( X384 @ X392 )
!= $true )
| ( ( X384 @ ( sub @ X383 @ ( push @ X392 @ id ) ) )
= $true ) )
| ~ ! [X386: term] :
( ( X384 @ X386 )
= ( X385 @ id @ X386 @ id ) )
| ( ( X384 @ ( lam @ X383 ) )
= $true )
| ~ ! [X387: subst > term > term] :
( ( ( X385 @ id @ ( lam @ ( X387 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X388: term] :
( ( ( X385 @ id @ X388 @ id )
!= $true )
| ( ( X385 @ id @ ( X387 @ id @ X388 ) @ id )
= $true ) )
| ~ ! [X389: subst,X390: subst,X391: term] :
( ( X387 @ ( comp @ X390 @ X389 ) @ ( sub @ X391 @ X389 ) )
= ( sub @ ( X387 @ X390 @ X391 ) @ X389 ) ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ulamvarind = $true )
& ( induction2_gthm = $true )
& ( ! [X327: term] :
~ ! [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
!= ( X328 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( axidl = $true )
<=> ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 ) )
& ( termmset_gthm = $true )
& ( pushprop = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true )
| ( $true
!= ( X93 @ X94 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ! [X489: subst > term > subst > $o,X490: term] :
( ~ ! [X491: term] :
( ( ( X489 @ id @ X491 @ id )
!= $true )
| ( ( X489 @ id @ ( sub @ X490 @ ( push @ X491 @ id ) ) @ id )
= $true ) )
| ~ ! [X492: term,X493: subst > term > term] :
( ~ ! [X500: term] :
( ( ( X489 @ id @ X500 @ id )
!= $true )
| ( ( X489 @ id @ ( X493 @ id @ X500 ) @ id )
= $true ) )
| ( ( X489 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X497: subst,X498: term,X499: subst] :
( ( sub @ ( X493 @ X499 @ X498 ) @ X497 )
= ( sub @ ( sub @ X492 @ ( push @ X498 @ X499 ) ) @ X497 ) )
| ~ ! [X494: subst,X495: term,X496: subst] :
( ( X493 @ ( comp @ X496 @ X494 ) @ ( sub @ X495 @ X494 ) )
= ( sub @ X492 @ ( push @ ( sub @ X495 @ X494 ) @ ( comp @ X496 @ X494 ) ) ) ) )
| ( ( X489 @ id @ ( lam @ ( sub @ X490 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X171: subst > term > subst > $o] :
~ ! [X172: term > $o] :
~ ! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) ) )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasinduction = $true )
<=> ! [X309: term,X310: subst > term > subst > $o] :
( ~ ! [X320: subst > term > term] :
( ( ( X310 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X321: subst,X322: term,X323: subst] :
( ( sub @ ( X320 @ X321 @ X322 ) @ X323 )
= ( X320 @ ( comp @ X321 @ X323 ) @ ( sub @ X322 @ X323 ) ) )
| ~ ! [X324: term] :
( ( ( X310 @ id @ X324 @ id )
!= $true )
| ( ( X310 @ id @ ( X320 @ id @ X324 ) @ id )
= $true ) ) )
| ( ( X310 @ id @ X309 @ id )
= $true )
| ~ ! [X325: term,X326: term] :
( ( $true
!= ( X310 @ id @ X326 @ id ) )
| ( ( X310 @ id @ ( ap @ ( sub @ X326 @ id ) @ X325 ) @ id )
= $true )
| ( ( X310 @ id @ X325 @ id )
!= $true ) )
| ~ ! [X316: term,X317: subst,X318: subst,X319: subst] :
( ( ( X310 @ ( comp @ X318 @ X319 ) @ ( sub @ X316 @ X319 ) @ X317 )
= $true )
| ( ( X310 @ X318 @ X316 @ ( comp @ X319 @ X317 ) )
!= $true ) )
| ~ ! [X312: subst,X313: subst,X314: term,X315: subst] :
( ( ( X310 @ X315 @ X314 @ ( comp @ X312 @ X313 ) )
= $true )
| ( $true
!= ( X310 @ ( comp @ X315 @ X312 ) @ ( sub @ X314 @ X312 ) @ X313 ) ) )
| ~ ! [X311: term] :
( ( ( X310 @ id @ X311 @ id )
= $true )
| ( ( var @ ( sub @ X311 @ id ) )
!= $true ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ~ ! [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) )
| ~ ! [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( axmap = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ( ( X483 @ one )
= $true )
| ~ ! [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
= ( X483 @ X485 ) )
| ( ( X481 @ X484 )
!= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ! [X9: term,X10: term > $o,X11: term,X12: subst > term > subst > $o] :
( ~ ! [X14: subst,X15: subst,X16: subst,X17: term] :
( ( ( X12 @ X15 @ X17 @ ( comp @ X16 @ X14 ) )
= $true )
| ( ( X12 @ ( comp @ X15 @ X16 ) @ ( sub @ X17 @ X16 ) @ X14 )
!= $true ) )
| ( ( X10 @ X11 )
!= $true )
| ~ ! [X22: term,X23: term] :
( ( $true
!= ( X12 @ id @ X23 @ id ) )
| ( ( X12 @ id @ ( ap @ ( sub @ X23 @ id ) @ X22 ) @ id )
= $true )
| ( $true
!= ( X12 @ id @ X22 @ id ) ) )
| ( ( X10 @ ( ap @ X11 @ X9 ) )
= $true )
| ~ ! [X13: term] :
( ( X10 @ X13 )
= ( X12 @ id @ X13 @ id ) )
| ~ ! [X18: subst,X19: term,X20: subst,X21: subst] :
( ( ( X12 @ X20 @ X19 @ ( comp @ X18 @ X21 ) )
!= $true )
| ( ( X12 @ ( comp @ X20 @ X18 ) @ ( sub @ X19 @ X18 ) @ X21 )
= $true ) )
| ( ( X10 @ X9 )
!= $true ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( axvarshift = $true )
& ( lamnotap != $true )
& ( ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ~ ! [X250: subst > term > term] :
( ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X251: term] :
( ( ( X246 @ id @ X251 @ id )
!= $true )
| ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true ) )
| ~ ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) ) )
| ~ ! [X255: term] :
( ( ( X247 @ X255 )
!= $true )
| ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
= $true ) )
| ~ ! [X249: term] :
( ( X246 @ id @ X249 @ id )
= ( X247 @ X249 ) )
| ( ( X247 @ ( lam @ X248 ) )
= $true ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X393: term,X394: subst > term > subst > $o] :
( ~ ! [X400: term] :
( ( ( X394 @ id @ ( sub @ X393 @ ( push @ X400 @ id ) ) @ id )
= $true )
| ( ( X394 @ id @ X400 @ id )
!= $true ) )
| ( ( X394 @ id @ ( lam @ ( sub @ X393 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X395: subst > term > term] :
( ~ ! [X396: term] :
( ( ( X394 @ id @ X396 @ id )
!= $true )
| ( ( X394 @ id @ ( X395 @ id @ X396 ) @ id )
= $true ) )
| ~ ! [X397: term,X398: subst,X399: subst] :
( ( X395 @ ( comp @ X398 @ X399 ) @ ( sub @ X397 @ X399 ) )
= ( sub @ ( X395 @ X398 @ X397 ) @ X399 ) )
| ( ( X394 @ id @ ( lam @ ( X395 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ! [X259: term > $o,X260: subst,X261: term] :
~ ! [X262: term > $o] :
~ ! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( axscons = $true )
<=> ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 ) )
& ( ! [X429: term] :
~ ! [X430: subst > term > term] :
( ( X430 @ sh @ one )
!= ( sub @ X429 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem = $true )
<=> ! [X401: subst,X402: term > $o,X403: term] :
( ~ ! [X406: term] :
( ( ( var @ X406 )
!= $true )
| ( ( X402 @ ( sub @ X406 @ X401 ) )
= $true ) )
| ~ ! [X407: term,X408: term] :
( ( ( X402 @ X408 )
!= $true )
| ( ( X402 @ ( ap @ X408 @ X407 ) )
= $true )
| ( ( X402 @ X407 )
!= $true ) )
| ( ( X402 @ ( sub @ X403 @ X401 ) )
= $true )
| ~ ! [X404: term] :
( ~ ! [X405: term] :
( ( ( X402 @ X405 )
!= $true )
| ( ( X402 @ ( sub @ X404 @ ( push @ X405 @ id ) ) )
= $true ) )
| ( ( X402 @ ( lam @ X404 ) )
= $true ) ) ) )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
<=> ( termmset = $true ) )
& ( ( ! [X95: term] :
( ( sub @ X95 @ id )
= X95 )
=> ( ! [X96: term,X97: subst > term > subst > $o] :
( ~ ! [X103: term] :
( ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true )
| ( ( X97 @ id @ X103 @ id )
!= $true ) )
| ~ ! [X98: subst > term > term] :
( ~ ! [X99: term,X100: subst,X101: subst] :
( ( sub @ ( X98 @ X101 @ X99 ) @ X100 )
= ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) ) )
| ~ ! [X102: term] :
( ( $true
!= ( X97 @ id @ X102 @ id ) )
| ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
= $true ) )
| ( ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X104: term,X105: subst > term > subst > $o] :
( ~ ! [X115: subst > term > term] :
( ~ ! [X117: subst,X118: subst,X119: term] :
( ( X115 @ ( comp @ X117 @ X118 ) @ ( sub @ X119 @ X118 ) )
= ( sub @ ( X115 @ X117 @ X119 ) @ X118 ) )
| ~ ! [X116: term] :
( ( ( X105 @ id @ ( X115 @ id @ X116 ) @ id )
= $true )
| ( ( X105 @ id @ X116 @ id )
!= $true ) )
| ( ( X105 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X106: subst,X107: term,X108: subst,X109: subst] :
( ( ( X105 @ ( comp @ X109 @ X108 ) @ ( sub @ X107 @ X108 ) @ X106 )
!= $true )
| ( ( X105 @ X109 @ X107 @ ( comp @ X108 @ X106 ) )
= $true ) )
| ( ( X105 @ id @ ( lam @ X104 ) @ id )
= $true )
| ~ ! [X110: term,X111: subst,X112: subst,X113: subst] :
( ( ( X105 @ X112 @ X110 @ ( comp @ X113 @ X111 ) )
!= $true )
| ( $true
= ( X105 @ ( comp @ X112 @ X113 ) @ ( sub @ X110 @ X113 ) @ X111 ) ) )
| ~ ! [X114: term] :
( ( ( X105 @ id @ X114 @ id )
!= $true )
| ( ( X105 @ id @ ( sub @ X104 @ ( push @ X114 @ id ) ) @ id )
= $true ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
<=> ( laminj = $true ) )
& ( hoasapinj1_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X333: term,X334: subst] :
( ( sub @ one @ ( push @ X333 @ X334 ) )
= X333 )
=> ( ! [X335: subst,X336: term] :
( ( comp @ sh @ ( push @ X336 @ X335 ) )
= X335 )
=> ( ! [X337: subst] :
( ( comp @ X337 @ id )
= X337 )
=> ( ! [X338: term,X339: term > $o] :
( ( $true
= ( X339 @ X338 ) )
| ~ ! [X340: term] :
( ( ( X339 @ X340 )
= $true )
| ( ( var @ X340 )
!= $true ) )
| ~ ! [X341: term] :
( ( ( X339 @ X341 )
!= $true )
| ( $true
= ( X339 @ ( lam @ X341 ) ) ) )
| ~ ! [X342: term,X343: term] :
( ( $true
!= ( X339 @ X342 ) )
| ( ( X339 @ ( ap @ X343 @ X342 ) )
= $true )
| ( ( X339 @ X343 )
!= $true ) ) )
=> ! [X344: subst,X345: term,X346: term > $o] :
( ~ ! [X347: term] :
( ( ( X346 @ ( lam @ X347 ) )
= $true )
| ~ ! [X348: term] :
( ( ( X346 @ ( sub @ X347 @ ( push @ X348 @ id ) ) )
= $true )
| ( ( X346 @ X348 )
!= $true ) ) )
| ~ ! [X351: term] :
( ( ( var @ X351 )
!= $true )
| ( $true
= ( X346 @ ( sub @ X351 @ X344 ) ) ) )
| ~ ! [X349: term,X350: term] :
( ( ( X346 @ X350 )
!= $true )
| ( ( X346 @ X349 )
!= $true )
| ( ( X346 @ ( ap @ X350 @ X349 ) )
= $true ) )
| ( ( X346 @ ( sub @ X345 @ X344 ) )
= $true ) ) ) ) ) ) )
& ! [X486: d_term] : ( d_one = X486 )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X535 @ X532 )
!= ( ap @ X534 @ X533 ) )
| ( X532 = X533 ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) )
& ( ( termmset_lthm = $true )
<=> ( ! [X298: term] :
( ( sub @ X298 @ id )
= X298 )
=> ! [X299: term] :
( ( sub @ X299 @ id )
= X299 ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop_lem1v2_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X457: subst > term > subst > $o,X458: term,X459: term] :
( ( ( X457 @ id @ X458 @ id )
!= $true )
| ~ ! [X462: subst,X463: subst,X464: subst,X465: term] :
( ( $true
= ( X457 @ X463 @ X465 @ ( comp @ X462 @ X464 ) ) )
| ( ( X457 @ ( comp @ X463 @ X462 ) @ ( sub @ X465 @ X462 ) @ X464 )
!= $true ) )
| ( ( X457 @ id @ ( ap @ X458 @ X459 ) @ id )
= $true )
| ~ ! [X460: term,X461: term] :
( ( $true
!= ( X457 @ id @ X460 @ id ) )
| ( ( X457 @ id @ X461 @ id )
!= $true )
| ( ( X457 @ id @ ( ap @ ( sub @ X461 @ id ) @ X460 ) @ id )
= $true ) )
| ( ( X457 @ id @ X459 @ id )
!= $true )
| ~ ! [X466: subst,X467: term,X468: subst,X469: subst] :
( ( ( X457 @ ( comp @ X469 @ X468 ) @ ( sub @ X467 @ X468 ) @ X466 )
= $true )
| ( ( X457 @ X469 @ X467 @ ( comp @ X468 @ X466 ) )
!= $true ) ) ) )
& ( induction2lem_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X241: subst,X242: term,X243: term > $o] :
~ ! [X244: term > $o] :
~ ! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( induction2 = $true )
<=> ! [X120: term > $o,X121: term] :
( ~ ! [X123: term,X124: term] :
( ( ( X120 @ X123 )
!= $true )
| ( ( X120 @ ( ap @ X123 @ X124 ) )
= $true )
| ( ( X120 @ X124 )
!= $true ) )
| ( ( X120 @ X121 )
= $true )
| ~ ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X120 @ X122 )
= $true ) )
| ~ ! [X125: term] :
( ~ ! [X126: term] :
( ( ( X120 @ ( sub @ X125 @ ( push @ X126 @ id ) ) )
= $true )
| ( ( X120 @ X126 )
!= $true ) )
| ( ( X120 @ ( lam @ X125 ) )
= $true ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axvarcons = $true )
<=> ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 ) )
& ( ! [X329: term] :
~ ! [X330: subst > term > term] :
~ ! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( axshiftcons = $true )
<=> ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 ) )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( hoasinduction_lem1_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X0: term,X1: subst > term > subst > $o] :
( ( $true
= ( X1 @ id @ X0 @ id ) )
| ~ ! [X2: term,X3: term] :
( ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ X2 @ id )
!= $true )
| ( ( X1 @ id @ X3 @ id )
!= $true ) )
| ~ ! [X4: subst > term > term] :
( ~ ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X8: term] :
( ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true )
| ( ( X1 @ id @ X8 @ id )
!= $true ) ) ) ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
<=> ( axidr = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( ! [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
= X501 )
=> ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ~ ! [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
= ( X505 @ X507 ) )
| ( $true
= ( X505 @ one ) )
| ( $true
!= ( X504 @ X503 ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( apnotvar = $true )
& ( hoasapnotvar_lthm = $true )
& ( lamnotvar = $true )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
<=> ( apinj2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( ! [X472: term] :
( ( sub @ X472 @ id )
= X472 )
=> ( ! [X473: term,X474: term,X475: term,X476: term] :
( ( X474 = X476 )
| ( ( ap @ X476 @ X473 )
!= ( ap @ X474 @ X475 ) ) )
=> ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X174: term] :
~ ! [X175: subst > term > term] :
~ ! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
=> ( ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 )
=> ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X179: term > $o,X180: term] :
( ~ ! [X181: term] :
( ( ( X179 @ ( lam @ X181 ) )
= $true )
| ~ ! [X182: term] :
( ( ( X179 @ X182 )
!= $true )
| ( ( X179 @ ( sub @ X181 @ ( push @ X182 @ id ) ) )
= $true ) ) )
| ( ( X179 @ X180 )
= $true )
| ~ ! [X183: term,X184: term] :
( ( ( X179 @ X184 )
!= $true )
| ( ( X179 @ ( ap @ X184 @ X183 ) )
= $true )
| ( $true
!= ( X179 @ X183 ) ) )
| ~ ! [X185: term] :
( ( ( X179 @ X185 )
= $true )
| ( ( var @ X185 )
!= $true ) ) )
=> ( ! [X186: term,X187: term,X188: subst > term > subst > $o] :
( ( $true
= ( X188 @ id @ ( ap @ X186 @ X187 ) @ id ) )
| ~ ! [X189: term,X190: term] :
( ( ( X188 @ id @ ( ap @ ( sub @ X189 @ id ) @ X190 ) @ id )
= $true )
| ( ( X188 @ id @ X190 @ id )
!= $true )
| ( ( X188 @ id @ X189 @ id )
!= $true ) )
| ~ ! [X191: term,X192: subst,X193: subst,X194: subst] :
( ( ( X188 @ ( comp @ X194 @ X193 ) @ ( sub @ X191 @ X193 ) @ X192 )
!= $true )
| ( ( X188 @ X194 @ X191 @ ( comp @ X193 @ X192 ) )
= $true ) )
| ( ( X188 @ id @ X187 @ id )
!= $true )
| ~ ! [X195: term,X196: subst,X197: subst,X198: subst] :
( ( ( X188 @ ( comp @ X197 @ X198 ) @ ( sub @ X195 @ X198 ) @ X196 )
= $true )
| ( ( X188 @ X197 @ X195 @ ( comp @ X198 @ X196 ) )
!= $true ) )
| ( ( X188 @ id @ X186 @ id )
!= $true ) )
=> ( ! [X199: term,X200: subst > term > subst > $o] :
( ( ( X200 @ id @ ( lam @ X199 ) @ id )
= $true )
| ~ ! [X205: term] :
( ( ( X200 @ id @ X205 @ id )
!= $true )
| ( ( X200 @ id @ ( sub @ X199 @ ( push @ X205 @ id ) ) @ id )
= $true ) )
| ~ ! [X201: subst,X202: subst,X203: subst,X204: term] :
( ( ( X200 @ ( comp @ X201 @ X202 ) @ ( sub @ X204 @ X202 ) @ X203 )
= $true )
| ( ( X200 @ X201 @ X204 @ ( comp @ X202 @ X203 ) )
!= $true ) )
| ~ ! [X211: subst,X212: term,X213: subst,X214: subst] :
( ( ( X200 @ ( comp @ X213 @ X214 ) @ ( sub @ X212 @ X214 ) @ X211 )
!= $true )
| ( ( X200 @ X213 @ X212 @ ( comp @ X214 @ X211 ) )
= $true ) )
| ~ ! [X206: subst > term > term] :
( ~ ! [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ~ ! [X207: term] :
( ( ( X200 @ id @ X207 @ id )
!= $true )
| ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
= $true ) ) ) )
=> ! [X215: subst > term > subst > $o,X216: term] :
( ~ ! [X231: term,X232: term] :
( ( ( X215 @ id @ X232 @ id )
!= $true )
| ( ( X215 @ id @ X231 @ id )
!= $true )
| ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
= $true ) )
| ~ ! [X217: term] :
( ( ( X215 @ id @ X217 @ id )
= $true )
| ( ( var @ ( sub @ X217 @ id ) )
!= $true ) )
| ~ ! [X227: subst,X228: subst,X229: subst,X230: term] :
( ( ( X215 @ X229 @ X230 @ ( comp @ X228 @ X227 ) )
!= $true )
| ( ( X215 @ ( comp @ X229 @ X228 ) @ ( sub @ X230 @ X228 ) @ X227 )
= $true ) )
| ~ ! [X223: term,X224: subst,X225: subst,X226: subst] :
( ( ( X215 @ ( comp @ X225 @ X226 ) @ ( sub @ X223 @ X226 ) @ X224 )
!= $true )
| ( ( X215 @ X225 @ X223 @ ( comp @ X226 @ X224 ) )
= $true ) )
| ( ( X215 @ id @ X216 @ id )
= $true )
| ~ ! [X218: subst > term > term] :
( ~ ! [X219: term,X220: subst,X221: subst] :
( ( X218 @ ( comp @ X220 @ X221 ) @ ( sub @ X219 @ X221 ) )
= ( sub @ ( X218 @ X220 @ X219 ) @ X221 ) )
| ( ( X215 @ id @ ( lam @ ( X218 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X222: term] :
( ( ( X215 @ id @ X222 @ id )
!= $true )
| ( ( X215 @ id @ ( X218 @ id @ X222 ) @ id )
= $true ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar = $true )
& ( axassoc = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X352: term,X353: term > $o,X354: subst > term > subst > $o] :
( ( ( X353 @ ( lam @ X352 ) )
= $true )
| ~ ! [X366: subst,X367: subst,X368: term,X369: subst] :
( ( ( X354 @ ( comp @ X366 @ X369 ) @ ( sub @ X368 @ X369 ) @ X367 )
= $true )
| ( ( X354 @ X366 @ X368 @ ( comp @ X369 @ X367 ) )
!= $true ) )
| ~ ! [X357: subst,X358: subst,X359: term,X360: subst] :
( ( ( X354 @ ( comp @ X358 @ X360 ) @ ( sub @ X359 @ X360 ) @ X357 )
!= $true )
| ( ( X354 @ X358 @ X359 @ ( comp @ X360 @ X357 ) )
= $true ) )
| ~ ! [X356: term] :
( ( X354 @ id @ X356 @ id )
= ( X353 @ X356 ) )
| ~ ! [X355: term] :
( ( ( X353 @ ( sub @ X352 @ ( push @ X355 @ id ) ) )
= $true )
| ( ( X353 @ X355 )
!= $true ) )
| ~ ! [X361: subst > term > term] :
( ( ( X354 @ id @ ( lam @ ( X361 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X362: subst,X363: subst,X364: term] :
( ( sub @ ( X361 @ X363 @ X364 ) @ X362 )
= ( X361 @ ( comp @ X363 @ X362 ) @ ( sub @ X364 @ X362 ) ) )
| ~ ! [X365: term] :
( ( ( X354 @ id @ ( X361 @ id @ X365 ) @ id )
= $true )
| ( ( X354 @ id @ X365 @ id )
!= $true ) ) ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X43: term] :
( ( sub @ X43 @ id )
= X43 )
=> ( ! [X44: subst > term > subst > $o,X45: term] :
( ~ ! [X51: term] :
( ( ( X44 @ id @ X51 @ id )
!= $true )
| ( ( X44 @ id @ ( sub @ X45 @ ( push @ X51 @ id ) ) @ id )
= $true ) )
| ( ( X44 @ id @ ( lam @ ( sub @ X45 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X46: subst > term > term] :
( ~ ! [X47: term] :
( ( ( X44 @ id @ X47 @ id )
!= $true )
| ( $true
= ( X44 @ id @ ( X46 @ id @ X47 ) @ id ) ) )
| ( ( X44 @ id @ ( lam @ ( X46 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X48: subst,X49: term,X50: subst] :
( ( X46 @ ( comp @ X50 @ X48 ) @ ( sub @ X49 @ X48 ) )
= ( sub @ ( X46 @ X50 @ X49 ) @ X48 ) ) ) )
=> ! [X52: term,X53: subst > term > subst > $o] :
( ~ ! [X59: term] :
( ( $true
!= ( X53 @ id @ X59 @ id ) )
| ( ( X53 @ id @ ( sub @ X52 @ ( push @ X59 @ id ) ) @ id )
= $true ) )
| ~ ! [X54: subst > term > term] :
( ( ( X53 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( ( X53 @ id @ ( X54 @ id @ X55 ) @ id )
= $true ) )
| ~ ! [X56: subst,X57: subst,X58: term] :
( ( X54 @ ( comp @ X57 @ X56 ) @ ( sub @ X58 @ X56 ) )
= ( sub @ ( X54 @ X57 @ X58 ) @ X56 ) ) )
| ( ( X53 @ id @ ( lam @ X52 ) @ id )
= $true ) ) ) ) )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoaslaminj_gthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) ) )
& ( pushprop_lem1_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
<=> ( shinj = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( axclos = $true )
& ( pushprop_lthm_orig = $true )
& ( hoasapinj2_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X508: term] :
( ( sub @ X508 @ id )
= X508 )
=> ! [X509: term > $o,X510: subst > term > subst > $o,X511: term] :
( ~ ! [X512: term,X513: subst,X514: subst,X515: subst] :
( ( ( X510 @ ( comp @ X513 @ X514 ) @ ( sub @ X512 @ X514 ) @ X515 )
= $true )
| ( ( X510 @ X513 @ X512 @ ( comp @ X514 @ X515 ) )
!= $true ) )
| ~ ! [X516: subst,X517: term,X518: subst,X519: subst] :
( ( ( X510 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) @ X519 )
!= $true )
| ( ( X510 @ X516 @ X517 @ ( comp @ X518 @ X519 ) )
= $true ) )
| ~ ! [X521: subst > term > term] :
( ~ ! [X522: term,X523: subst,X524: subst] :
( ( sub @ ( X521 @ X523 @ X522 ) @ X524 )
= ( X521 @ ( comp @ X523 @ X524 ) @ ( sub @ X522 @ X524 ) ) )
| ( ( X510 @ id @ ( lam @ ( X521 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X525: term] :
( ( ( X510 @ id @ X525 @ id )
!= $true )
| ( ( X510 @ id @ ( X521 @ id @ X525 ) @ id )
= $true ) ) )
| ~ ! [X526: term] :
( ( ( X509 @ X526 )
!= $true )
| ( $true
= ( X509 @ ( sub @ X511 @ ( push @ X526 @ id ) ) ) ) )
| ( ( X509 @ ( lam @ X511 ) )
= $true )
| ~ ! [X520: term] :
( ( X509 @ X520 )
= ( X510 @ id @ X520 @ id ) ) ) ) )
& ( ! [X439: term,X440: term > $o] :
( ~ ! [X444: term] :
( ( $true
!= ( var @ X444 ) )
| ( ( X440 @ X444 )
= $true ) )
| ~ ! [X441: term,X442: term] :
( ( ( X440 @ ( ap @ X441 @ X442 ) )
= $true )
| ( ( X440 @ X441 )
!= $true )
| ( ( X440 @ X442 )
!= $true ) )
| ~ ! [X443: term] :
( ( ( X440 @ ( lam @ X443 ) )
= $true )
| ( ( X440 @ X443 )
!= $true ) )
| ( ( X440 @ X439 )
= $true ) )
<=> ( induction = $true ) )
& ( ! [X168: subst > term > subst > $o] :
~ ! [X169: term > $o] :
~ ! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X25: term] :
( ( sub @ X25 @ id )
= X25 )
=> ( ! [X26: term > $o,X27: term,X28: subst] :
( ~ ! [X33: term] :
( ( ( var @ X33 )
!= $true )
| ( ( X26 @ ( sub @ X33 @ X28 ) )
= $true ) )
| ~ ! [X31: term] :
( ( ( X26 @ ( lam @ X31 ) )
= $true )
| ~ ! [X32: term] :
( ( ( X26 @ X32 )
!= $true )
| ( ( X26 @ ( sub @ X31 @ ( push @ X32 @ id ) ) )
= $true ) ) )
| ~ ! [X29: term,X30: term] :
( ( ( X26 @ X29 )
!= $true )
| ( ( X26 @ X30 )
!= $true )
| ( ( X26 @ ( ap @ X29 @ X30 ) )
= $true ) )
| ( ( X26 @ ( sub @ X27 @ X28 ) )
= $true ) )
=> ! [X34: term,X35: term > $o] :
( ~ ! [X40: term] :
( ( ( X35 @ X40 )
= $true )
| ( ( var @ X40 )
!= $true ) )
| ~ ! [X36: term] :
( ~ ! [X37: term] :
( ( $true
= ( X35 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) )
| ( ( X35 @ X37 )
!= $true ) )
| ( ( X35 @ ( lam @ X36 ) )
= $true ) )
| ~ ! [X38: term,X39: term] :
( ( ( X35 @ X38 )
!= $true )
| ( ( X35 @ ( ap @ X39 @ X38 ) )
= $true )
| ( $true
!= ( X35 @ X39 ) ) )
| ( $true
= ( X35 @ X34 ) ) ) ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
<=> ( apinj1 = $true ) )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
= ( d2subst @ X471 ) )
=> ( X470 = X471 ) )
& ( ! [X60: subst > term > subst > $o,X61: term] :
( ( ( X60 @ id @ ( lam @ X61 ) @ id )
= $true )
| ~ ! [X71: subst,X72: subst,X73: subst,X74: term] :
( ( ( X60 @ X73 @ X74 @ ( comp @ X71 @ X72 ) )
!= $true )
| ( ( X60 @ ( comp @ X73 @ X71 ) @ ( sub @ X74 @ X71 ) @ X72 )
= $true ) )
| ~ ! [X67: subst,X68: term,X69: subst,X70: subst] :
( ( ( X60 @ X69 @ X68 @ ( comp @ X70 @ X67 ) )
= $true )
| ( ( X60 @ ( comp @ X69 @ X70 ) @ ( sub @ X68 @ X70 ) @ X67 )
!= $true ) )
| ~ ! [X62: subst > term > term] :
( ~ ! [X63: term,X64: subst,X65: subst] :
( ( sub @ ( X62 @ X65 @ X63 ) @ X64 )
= ( X62 @ ( comp @ X65 @ X64 ) @ ( sub @ X63 @ X64 ) ) )
| ~ ! [X66: term] :
( ( ( X60 @ id @ X66 @ id )
!= $true )
| ( ( X60 @ id @ ( X62 @ id @ X66 ) @ id )
= $true ) )
| ( ( X60 @ id @ ( lam @ ( X62 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X75: term] :
( ( ( X60 @ id @ X75 @ id )
!= $true )
| ( ( X60 @ id @ ( sub @ X61 @ ( push @ X75 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( ! [X264: subst > term > subst > $o] :
~ ! [X265: term > $o] :
~ ! [X266: term] :
( ( X265 @ X266 )
= ( X264 @ id @ X266 @ id ) )
=> ( ! [X267: term > $o,X268: term] :
( ( ( X267 @ X268 )
= $true )
| ~ ! [X269: term,X270: term] :
( ( $true
!= ( X267 @ X269 ) )
| ( ( X267 @ ( ap @ X270 @ X269 ) )
= $true )
| ( ( X267 @ X270 )
!= $true ) )
| ~ ! [X272: term] :
( ~ ! [X273: term] :
( ( $true
!= ( X267 @ X273 ) )
| ( ( X267 @ ( sub @ X272 @ ( push @ X273 @ id ) ) )
= $true ) )
| ( ( X267 @ ( lam @ X272 ) )
= $true ) )
| ~ ! [X271: term] :
( ( ( var @ X271 )
!= $true )
| ( $true
= ( X267 @ X271 ) ) ) )
=> ( ! [X274: term] :
( ( sub @ X274 @ id )
= X274 )
=> ( ! [X275: subst > term > subst > $o,X276: term,X277: term > $o] :
( ( ( X277 @ ( lam @ X276 ) )
= $true )
| ~ ! [X283: term] :
( ( X277 @ X283 )
= ( X275 @ id @ X283 @ id ) )
| ~ ! [X278: subst > term > term] :
( ~ ! [X280: term,X281: subst,X282: subst] :
( ( X278 @ ( comp @ X282 @ X281 ) @ ( sub @ X280 @ X281 ) )
= ( sub @ ( X278 @ X282 @ X280 ) @ X281 ) )
| ( ( X275 @ id @ ( lam @ ( X278 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X279: term] :
( ( ( X275 @ id @ X279 @ id )
!= $true )
| ( ( X275 @ id @ ( X278 @ id @ X279 ) @ id )
= $true ) ) )
| ~ ! [X284: term] :
( ( ( X277 @ X284 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X284 @ id ) ) )
= $true ) ) )
=> ! [X285: term,X286: subst > term > subst > $o] :
( ~ ! [X287: subst > term > term] :
( ( ( X286 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X288: subst,X289: term,X290: subst] :
( ( sub @ ( X287 @ X288 @ X289 ) @ X290 )
= ( X287 @ ( comp @ X288 @ X290 ) @ ( sub @ X289 @ X290 ) ) )
| ~ ! [X291: term] :
( ( ( X286 @ id @ X291 @ id )
!= $true )
| ( ( X286 @ id @ ( X287 @ id @ X291 ) @ id )
= $true ) ) )
| ~ ! [X292: term,X293: term] :
( ( $true
!= ( X286 @ id @ X293 @ id ) )
| ( ( X286 @ id @ ( ap @ ( sub @ X292 @ id ) @ X293 ) @ id )
= $true )
| ( ( X286 @ id @ X292 @ id )
!= $true ) )
| ( ( X286 @ id @ X285 @ id )
= $true ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( ! [X129: subst > term > subst > $o] :
~ ! [X130: term > $o] :
~ ! [X131: term] :
( ( X130 @ X131 )
= ( X129 @ id @ X131 @ id ) )
=> ( ! [X132: term > $o,X133: term] :
( ( ( X132 @ X133 )
= $true )
| ~ ! [X137: term] :
( ( ( X132 @ ( lam @ X137 ) )
= $true )
| ~ ! [X138: term] :
( ( ( X132 @ ( sub @ X137 @ ( push @ X138 @ id ) ) )
= $true )
| ( ( X132 @ X138 )
!= $true ) ) )
| ~ ! [X135: term,X136: term] :
( ( ( X132 @ X135 )
!= $true )
| ( ( X132 @ ( ap @ X135 @ X136 ) )
= $true )
| ( ( X132 @ X136 )
!= $true ) )
| ~ ! [X134: term] :
( ( $true
= ( X132 @ X134 ) )
| ( ( var @ X134 )
!= $true ) ) )
=> ( ! [X139: term] :
( ( sub @ X139 @ id )
= X139 )
=> ( ! [X140: term > $o,X141: term,X142: subst > term > subst > $o] :
( ~ ! [X148: term] :
( ( X140 @ X148 )
= ( X142 @ id @ X148 @ id ) )
| ~ ! [X149: term] :
( ( ( X140 @ ( sub @ X141 @ ( push @ X149 @ id ) ) )
= $true )
| ( ( X140 @ X149 )
!= $true ) )
| ( ( X140 @ ( lam @ X141 ) )
= $true )
| ~ ! [X143: subst > term > term] :
( ( $true
= ( X142 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ~ ! [X144: term] :
( ( ( X142 @ id @ X144 @ id )
!= $true )
| ( ( X142 @ id @ ( X143 @ id @ X144 ) @ id )
= $true ) )
| ~ ! [X145: subst,X146: term,X147: subst] :
( ( X143 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) )
= ( sub @ ( X143 @ X147 @ X146 ) @ X145 ) ) ) )
=> ! [X150: subst > term > subst > $o,X151: term] :
( ~ ! [X155: subst,X156: term,X157: subst,X158: subst] :
( ( ( X150 @ X158 @ X156 @ ( comp @ X155 @ X157 ) )
= $true )
| ( ( X150 @ ( comp @ X158 @ X155 ) @ ( sub @ X156 @ X155 ) @ X157 )
!= $true ) )
| ~ ! [X152: term,X153: term] :
( ( ( X150 @ id @ X153 @ id )
!= $true )
| ( ( X150 @ id @ ( ap @ ( sub @ X152 @ id ) @ X153 ) @ id )
= $true )
| ( ( X150 @ id @ X152 @ id )
!= $true ) )
| ~ ! [X164: subst,X165: subst,X166: subst,X167: term] :
( ( ( X150 @ X166 @ X167 @ ( comp @ X165 @ X164 ) )
!= $true )
| ( ( X150 @ ( comp @ X166 @ X165 ) @ ( sub @ X167 @ X165 ) @ X164 )
= $true ) )
| ( ( X150 @ id @ X151 @ id )
= $true )
| ~ ! [X159: subst > term > term] :
( ~ ! [X163: term] :
( ( $true
!= ( X150 @ id @ X163 @ id ) )
| ( ( X150 @ id @ ( X159 @ id @ X163 ) @ id )
= $true ) )
| ( ( X150 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X160: term,X161: subst,X162: subst] :
( ( sub @ ( X159 @ X162 @ X160 ) @ X161 )
= ( X159 @ ( comp @ X162 @ X161 ) @ ( sub @ X160 @ X161 ) ) ) )
| ~ ! [X154: term] :
( ( ( X150 @ id @ X154 @ id )
= $true )
| ( ( var @ ( sub @ X154 @ id ) )
!= $true ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X0: term,X1: subst > term > subst > $o] :
( ~ ! [X2: term,X3: term] :
( ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ X3 @ id )
!= $true )
| ( ( X1 @ id @ X2 @ id )
!= $true ) )
| ~ ! [X4: subst > term > term] :
( ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ~ ! [X8: term] :
( ( ( X1 @ id @ X8 @ id )
!= $true )
| ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true ) ) )
| ( $true
= ( X1 @ id @ X0 @ id ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( axassoc = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ! [X9: term,X10: term > $o,X11: term,X12: subst > term > subst > $o] :
( ( ( X10 @ X9 )
!= $true )
| ~ ! [X13: term] :
( ( X10 @ X13 )
= ( X12 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X15: subst,X16: subst,X17: term] :
( ( ( X12 @ ( comp @ X15 @ X16 ) @ ( sub @ X17 @ X16 ) @ X14 )
!= $true )
| ( ( X12 @ X15 @ X17 @ ( comp @ X16 @ X14 ) )
= $true ) )
| ( ( X10 @ ( ap @ X11 @ X9 ) )
= $true )
| ( ( X10 @ X11 )
!= $true )
| ~ ! [X18: subst,X19: term,X20: subst,X21: subst] :
( ( ( X12 @ X20 @ X19 @ ( comp @ X18 @ X21 ) )
!= $true )
| ( ( X12 @ ( comp @ X20 @ X18 ) @ ( sub @ X19 @ X18 ) @ X21 )
= $true ) )
| ~ ! [X22: term,X23: term] :
( ( ( X12 @ id @ ( ap @ ( sub @ X23 @ id ) @ X22 ) @ id )
= $true )
| ( $true
!= ( X12 @ id @ X22 @ id ) )
| ( $true
!= ( X12 @ id @ X23 @ id ) ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( axscons = $true )
<=> ! [X24: subst] :
( ( push @ ( sub @ one @ X24 ) @ ( comp @ sh @ X24 ) )
= X24 ) )
& ( ( ! [X25: term] :
( ( sub @ X25 @ id )
= X25 )
=> ( ! [X26: term > $o,X27: term,X28: subst] :
( ~ ! [X29: term,X30: term] :
( ( ( X26 @ X30 )
!= $true )
| ( ( X26 @ ( ap @ X29 @ X30 ) )
= $true )
| ( ( X26 @ X29 )
!= $true ) )
| ~ ! [X31: term] :
( ( ( X26 @ ( lam @ X31 ) )
= $true )
| ~ ! [X32: term] :
( ( ( X26 @ X32 )
!= $true )
| ( ( X26 @ ( sub @ X31 @ ( push @ X32 @ id ) ) )
= $true ) ) )
| ~ ! [X33: term] :
( ( ( X26 @ ( sub @ X33 @ X28 ) )
= $true )
| ( ( var @ X33 )
!= $true ) )
| ( ( X26 @ ( sub @ X27 @ X28 ) )
= $true ) )
=> ! [X34: term,X35: term > $o] :
( ~ ! [X36: term] :
( ~ ! [X37: term] :
( ( $true
= ( X35 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) )
| ( ( X35 @ X37 )
!= $true ) )
| ( ( X35 @ ( lam @ X36 ) )
= $true ) )
| ( $true
= ( X35 @ X34 ) )
| ~ ! [X38: term,X39: term] :
( ( ( X35 @ ( ap @ X39 @ X38 ) )
= $true )
| ( $true
!= ( X35 @ X39 ) )
| ( ( X35 @ X38 )
!= $true ) )
| ~ ! [X40: term] :
( ( ( var @ X40 )
!= $true )
| ( ( X35 @ X40 )
= $true ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( substmonoid = $true )
<=> ( ! [X42: subst] :
( ( comp @ id @ X42 )
= X42 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ulamvarsh = $true )
& ( axvarshift = $true )
& ( ( ! [X43: term] :
( ( sub @ X43 @ id )
= X43 )
=> ( ! [X44: subst > term > subst > $o,X45: term] :
( ~ ! [X46: subst > term > term] :
( ~ ! [X47: term] :
( ( $true
= ( X44 @ id @ ( X46 @ id @ X47 ) @ id ) )
| ( ( X44 @ id @ X47 @ id )
!= $true ) )
| ( ( X44 @ id @ ( lam @ ( X46 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X48: subst,X49: term,X50: subst] :
( ( X46 @ ( comp @ X50 @ X48 ) @ ( sub @ X49 @ X48 ) )
= ( sub @ ( X46 @ X50 @ X49 ) @ X48 ) ) )
| ~ ! [X51: term] :
( ( ( X44 @ id @ ( sub @ X45 @ ( push @ X51 @ id ) ) @ id )
= $true )
| ( ( X44 @ id @ X51 @ id )
!= $true ) )
| ( ( X44 @ id @ ( lam @ ( sub @ X45 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X52: term,X53: subst > term > subst > $o] :
( ~ ! [X54: subst > term > term] :
( ( ( X53 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( ( X53 @ id @ ( X54 @ id @ X55 ) @ id )
= $true ) )
| ~ ! [X56: subst,X57: subst,X58: term] :
( ( X54 @ ( comp @ X57 @ X56 ) @ ( sub @ X58 @ X56 ) )
= ( sub @ ( X54 @ X57 @ X58 ) @ X56 ) ) )
| ~ ! [X59: term] :
( ( ( X53 @ id @ ( sub @ X52 @ ( push @ X59 @ id ) ) @ id )
= $true )
| ( $true
!= ( X53 @ id @ X59 @ id ) ) )
| ( ( X53 @ id @ ( lam @ X52 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X60: subst > term > subst > $o,X61: term] :
( ~ ! [X62: subst > term > term] :
( ~ ! [X63: term,X64: subst,X65: subst] :
( ( sub @ ( X62 @ X65 @ X63 ) @ X64 )
= ( X62 @ ( comp @ X65 @ X64 ) @ ( sub @ X63 @ X64 ) ) )
| ( ( X60 @ id @ ( lam @ ( X62 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X66: term] :
( ( ( X60 @ id @ X66 @ id )
!= $true )
| ( ( X60 @ id @ ( X62 @ id @ X66 ) @ id )
= $true ) ) )
| ~ ! [X67: subst,X68: term,X69: subst,X70: subst] :
( ( ( X60 @ ( comp @ X69 @ X70 ) @ ( sub @ X68 @ X70 ) @ X67 )
!= $true )
| ( ( X60 @ X69 @ X68 @ ( comp @ X70 @ X67 ) )
= $true ) )
| ~ ! [X71: subst,X72: subst,X73: subst,X74: term] :
( ( ( X60 @ X73 @ X74 @ ( comp @ X71 @ X72 ) )
!= $true )
| ( ( X60 @ ( comp @ X73 @ X71 ) @ ( sub @ X74 @ X71 ) @ X72 )
= $true ) )
| ~ ! [X75: term] :
( ( ( X60 @ id @ ( sub @ X61 @ ( push @ X75 @ id ) ) @ id )
= $true )
| ( ( X60 @ id @ X75 @ id )
!= $true ) )
| ( ( X60 @ id @ ( lam @ X61 ) @ id )
= $true ) ) )
& ( ! [X76: subst > term > term,X77: term,X78: term] :
( ( ( ap @ ( sub @ X77 @ id ) @ X78 )
!= ( lam @ ( X76 @ sh @ one ) ) )
| ~ ! [X79: term,X80: subst,X81: subst] :
( ( sub @ ( X76 @ X80 @ X79 ) @ X81 )
= ( X76 @ ( comp @ X80 @ X81 ) @ ( sub @ X79 @ X81 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
=> ( ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 )
=> ( ! [X85: subst] :
( ( comp @ X85 @ id )
= X85 )
& ! [X84: subst] :
( ( comp @ id @ X84 )
= X84 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasapnotvar = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X86: term,X87: term,X88: term,X89: term] :
( ( X88 = X89 )
| ( ( ap @ ( sub @ X86 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X90: term,X91: term > $o,X92: subst,X93: term > $o,X94: term] :
( ( $true
!= ( X93 @ X94 ) )
| ( ( X91 @ ( sub @ X94 @ ( push @ X90 @ X92 ) ) )
= $true ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X95: term] :
( ( sub @ X95 @ id )
= X95 )
=> ( ! [X96: term,X97: subst > term > subst > $o] :
( ~ ! [X98: subst > term > term] :
( ( ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X99: term,X100: subst,X101: subst] :
( ( sub @ ( X98 @ X101 @ X99 ) @ X100 )
= ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) ) )
| ~ ! [X102: term] :
( ( $true
!= ( X97 @ id @ X102 @ id ) )
| ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
= $true ) ) )
| ( ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X103: term] :
( ( ( X97 @ id @ X103 @ id )
!= $true )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) ) )
=> ! [X104: term,X105: subst > term > subst > $o] :
( ~ ! [X106: subst,X107: term,X108: subst,X109: subst] :
( ( ( X105 @ X109 @ X107 @ ( comp @ X108 @ X106 ) )
= $true )
| ( ( X105 @ ( comp @ X109 @ X108 ) @ ( sub @ X107 @ X108 ) @ X106 )
!= $true ) )
| ~ ! [X110: term,X111: subst,X112: subst,X113: subst] :
( ( $true
= ( X105 @ ( comp @ X112 @ X113 ) @ ( sub @ X110 @ X113 ) @ X111 ) )
| ( ( X105 @ X112 @ X110 @ ( comp @ X113 @ X111 ) )
!= $true ) )
| ( ( X105 @ id @ ( lam @ X104 ) @ id )
= $true )
| ~ ! [X114: term] :
( ( ( X105 @ id @ X114 @ id )
!= $true )
| ( ( X105 @ id @ ( sub @ X104 @ ( push @ X114 @ id ) ) @ id )
= $true ) )
| ~ ! [X115: subst > term > term] :
( ( ( X105 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X116: term] :
( ( ( X105 @ id @ X116 @ id )
!= $true )
| ( ( X105 @ id @ ( X115 @ id @ X116 ) @ id )
= $true ) )
| ~ ! [X117: subst,X118: subst,X119: term] :
( ( X115 @ ( comp @ X117 @ X118 ) @ ( sub @ X119 @ X118 ) )
= ( sub @ ( X115 @ X117 @ X119 ) @ X118 ) ) ) ) ) ) )
& ( ( induction2 = $true )
<=> ! [X120: term > $o,X121: term] :
( ~ ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X120 @ X122 )
= $true ) )
| ~ ! [X123: term,X124: term] :
( ( ( X120 @ X123 )
!= $true )
| ( ( X120 @ X124 )
!= $true )
| ( ( X120 @ ( ap @ X123 @ X124 ) )
= $true ) )
| ~ ! [X125: term] :
( ~ ! [X126: term] :
( ( ( X120 @ ( sub @ X125 @ ( push @ X126 @ id ) ) )
= $true )
| ( ( X120 @ X126 )
!= $true ) )
| ( ( X120 @ ( lam @ X125 ) )
= $true ) )
| ( ( X120 @ X121 )
= $true ) ) )
& ( ulamvar1 != $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( axvarcons = $true )
<=> ! [X127: subst,X128: term] :
( ( sub @ one @ ( push @ X128 @ X127 ) )
= X128 ) )
& ( ( ! [X129: subst > term > subst > $o] :
~ ! [X130: term > $o] :
~ ! [X131: term] :
( ( X130 @ X131 )
= ( X129 @ id @ X131 @ id ) )
=> ( ! [X132: term > $o,X133: term] :
( ~ ! [X134: term] :
( ( $true
= ( X132 @ X134 ) )
| ( ( var @ X134 )
!= $true ) )
| ~ ! [X135: term,X136: term] :
( ( ( X132 @ X136 )
!= $true )
| ( ( X132 @ X135 )
!= $true )
| ( ( X132 @ ( ap @ X135 @ X136 ) )
= $true ) )
| ~ ! [X137: term] :
( ~ ! [X138: term] :
( ( ( X132 @ X138 )
!= $true )
| ( ( X132 @ ( sub @ X137 @ ( push @ X138 @ id ) ) )
= $true ) )
| ( ( X132 @ ( lam @ X137 ) )
= $true ) )
| ( ( X132 @ X133 )
= $true ) )
=> ( ! [X139: term] :
( ( sub @ X139 @ id )
= X139 )
=> ( ! [X140: term > $o,X141: term,X142: subst > term > subst > $o] :
( ~ ! [X143: subst > term > term] :
( ( $true
= ( X142 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ~ ! [X144: term] :
( ( ( X142 @ id @ ( X143 @ id @ X144 ) @ id )
= $true )
| ( ( X142 @ id @ X144 @ id )
!= $true ) )
| ~ ! [X145: subst,X146: term,X147: subst] :
( ( X143 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) )
= ( sub @ ( X143 @ X147 @ X146 ) @ X145 ) ) )
| ~ ! [X148: term] :
( ( X140 @ X148 )
= ( X142 @ id @ X148 @ id ) )
| ~ ! [X149: term] :
( ( ( X140 @ X149 )
!= $true )
| ( ( X140 @ ( sub @ X141 @ ( push @ X149 @ id ) ) )
= $true ) )
| ( ( X140 @ ( lam @ X141 ) )
= $true ) )
=> ! [X150: subst > term > subst > $o,X151: term] :
( ~ ! [X152: term,X153: term] :
( ( ( X150 @ id @ ( ap @ ( sub @ X152 @ id ) @ X153 ) @ id )
= $true )
| ( ( X150 @ id @ X153 @ id )
!= $true )
| ( ( X150 @ id @ X152 @ id )
!= $true ) )
| ~ ! [X154: term] :
( ( ( var @ ( sub @ X154 @ id ) )
!= $true )
| ( ( X150 @ id @ X154 @ id )
= $true ) )
| ~ ! [X155: subst,X156: term,X157: subst,X158: subst] :
( ( ( X150 @ X158 @ X156 @ ( comp @ X155 @ X157 ) )
= $true )
| ( ( X150 @ ( comp @ X158 @ X155 ) @ ( sub @ X156 @ X155 ) @ X157 )
!= $true ) )
| ~ ! [X159: subst > term > term] :
( ~ ! [X160: term,X161: subst,X162: subst] :
( ( sub @ ( X159 @ X162 @ X160 ) @ X161 )
= ( X159 @ ( comp @ X162 @ X161 ) @ ( sub @ X160 @ X161 ) ) )
| ( ( X150 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X163: term] :
( ( $true
!= ( X150 @ id @ X163 @ id ) )
| ( ( X150 @ id @ ( X159 @ id @ X163 ) @ id )
= $true ) ) )
| ~ ! [X164: subst,X165: subst,X166: subst,X167: term] :
( ( ( X150 @ X166 @ X167 @ ( comp @ X165 @ X164 ) )
!= $true )
| ( ( X150 @ ( comp @ X166 @ X165 ) @ ( sub @ X167 @ X165 ) @ X164 )
= $true ) )
| ( ( X150 @ id @ X151 @ id )
= $true ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ! [X168: subst > term > subst > $o] :
~ ! [X169: term > $o] :
~ ! [X170: term] :
( ( X168 @ id @ X170 @ id )
= ( X169 @ X170 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X171: subst > term > subst > $o] :
~ ! [X172: term > $o] :
~ ! [X173: term] :
( ( X171 @ id @ X173 @ id )
= ( X172 @ X173 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X174: term] :
~ ! [X175: subst > term > term] :
~ ! [X176: term,X177: subst] :
( ( sub @ X174 @ ( push @ X176 @ X177 ) )
= ( X175 @ X177 @ X176 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ! [X178: term] :
( ( sub @ X178 @ id )
= X178 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X179: term > $o,X180: term] :
( ~ ! [X181: term] :
( ~ ! [X182: term] :
( ( ( X179 @ X182 )
!= $true )
| ( ( X179 @ ( sub @ X181 @ ( push @ X182 @ id ) ) )
= $true ) )
| ( ( X179 @ ( lam @ X181 ) )
= $true ) )
| ~ ! [X183: term,X184: term] :
( ( ( X179 @ X184 )
!= $true )
| ( ( X179 @ ( ap @ X184 @ X183 ) )
= $true )
| ( $true
!= ( X179 @ X183 ) ) )
| ~ ! [X185: term] :
( ( ( var @ X185 )
!= $true )
| ( ( X179 @ X185 )
= $true ) )
| ( ( X179 @ X180 )
= $true ) )
=> ( ! [X186: term,X187: term,X188: subst > term > subst > $o] :
( ( $true
= ( X188 @ id @ ( ap @ X186 @ X187 ) @ id ) )
| ( ( X188 @ id @ X187 @ id )
!= $true )
| ~ ! [X189: term,X190: term] :
( ( ( X188 @ id @ ( ap @ ( sub @ X189 @ id ) @ X190 ) @ id )
= $true )
| ( ( X188 @ id @ X189 @ id )
!= $true )
| ( ( X188 @ id @ X190 @ id )
!= $true ) )
| ( ( X188 @ id @ X186 @ id )
!= $true )
| ~ ! [X191: term,X192: subst,X193: subst,X194: subst] :
( ( ( X188 @ X194 @ X191 @ ( comp @ X193 @ X192 ) )
= $true )
| ( ( X188 @ ( comp @ X194 @ X193 ) @ ( sub @ X191 @ X193 ) @ X192 )
!= $true ) )
| ~ ! [X195: term,X196: subst,X197: subst,X198: subst] :
( ( ( X188 @ X197 @ X195 @ ( comp @ X198 @ X196 ) )
!= $true )
| ( ( X188 @ ( comp @ X197 @ X198 ) @ ( sub @ X195 @ X198 ) @ X196 )
= $true ) ) )
=> ( ! [X199: term,X200: subst > term > subst > $o] :
( ~ ! [X201: subst,X202: subst,X203: subst,X204: term] :
( ( ( X200 @ ( comp @ X201 @ X202 ) @ ( sub @ X204 @ X202 ) @ X203 )
= $true )
| ( ( X200 @ X201 @ X204 @ ( comp @ X202 @ X203 ) )
!= $true ) )
| ( ( X200 @ id @ ( lam @ X199 ) @ id )
= $true )
| ~ ! [X205: term] :
( ( ( X200 @ id @ X205 @ id )
!= $true )
| ( ( X200 @ id @ ( sub @ X199 @ ( push @ X205 @ id ) ) @ id )
= $true ) )
| ~ ! [X206: subst > term > term] :
( ~ ! [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
= $true )
| ( ( X200 @ id @ X207 @ id )
!= $true ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ~ ! [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) )
| ~ ! [X211: subst,X212: term,X213: subst,X214: subst] :
( ( ( X200 @ ( comp @ X213 @ X214 ) @ ( sub @ X212 @ X214 ) @ X211 )
!= $true )
| ( ( X200 @ X213 @ X212 @ ( comp @ X214 @ X211 ) )
= $true ) ) )
=> ! [X215: subst > term > subst > $o,X216: term] :
( ( ( X215 @ id @ X216 @ id )
= $true )
| ~ ! [X217: term] :
( ( ( var @ ( sub @ X217 @ id ) )
!= $true )
| ( ( X215 @ id @ X217 @ id )
= $true ) )
| ~ ! [X218: subst > term > term] :
( ~ ! [X219: term,X220: subst,X221: subst] :
( ( X218 @ ( comp @ X220 @ X221 ) @ ( sub @ X219 @ X221 ) )
= ( sub @ ( X218 @ X220 @ X219 ) @ X221 ) )
| ~ ! [X222: term] :
( ( ( X215 @ id @ X222 @ id )
!= $true )
| ( ( X215 @ id @ ( X218 @ id @ X222 ) @ id )
= $true ) )
| ( ( X215 @ id @ ( lam @ ( X218 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X223: term,X224: subst,X225: subst,X226: subst] :
( ( ( X215 @ X225 @ X223 @ ( comp @ X226 @ X224 ) )
= $true )
| ( ( X215 @ ( comp @ X225 @ X226 ) @ ( sub @ X223 @ X226 ) @ X224 )
!= $true ) )
| ~ ! [X227: subst,X228: subst,X229: subst,X230: term] :
( ( ( X215 @ X229 @ X230 @ ( comp @ X228 @ X227 ) )
!= $true )
| ( ( X215 @ ( comp @ X229 @ X228 ) @ ( sub @ X230 @ X228 ) @ X227 )
= $true ) )
| ~ ! [X231: term,X232: term] :
( ( ( X215 @ id @ X231 @ id )
!= $true )
| ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
= $true )
| ( ( X215 @ id @ X232 @ id )
!= $true ) ) ) ) ) ) )
& ( ! [X233: term,X234: subst > term > subst > $o] :
( ( ( X234 @ id @ ( lam @ X233 ) @ id )
= $true )
| ~ ! [X235: subst > term > term] :
( ~ ! [X236: subst,X237: subst,X238: term] :
( ( X235 @ ( comp @ X236 @ X237 ) @ ( sub @ X238 @ X237 ) )
= ( sub @ ( X235 @ X236 @ X238 ) @ X237 ) )
| ( ( X234 @ id @ ( lam @ ( X235 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X239: term] :
( ( ( X234 @ id @ ( X235 @ id @ X239 ) @ id )
= $true )
| ( ( X234 @ id @ X239 @ id )
!= $true ) ) )
| ~ ! [X240: term] :
( ( ( X234 @ id @ ( sub @ X233 @ ( push @ X240 @ id ) ) @ id )
= $true )
| ( ( X234 @ id @ X240 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X241: subst,X242: term,X243: term > $o] :
~ ! [X244: term > $o] :
~ ! [X245: term] :
( ( X244 @ X245 )
= ( X243 @ ( sub @ X245 @ ( push @ X242 @ X241 ) ) ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
= $true )
| ~ ! [X249: term] :
( ( X246 @ id @ X249 @ id )
= ( X247 @ X249 ) )
| ~ ! [X250: subst > term > term] :
( ~ ! [X251: term] :
( ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true )
| ( ( X246 @ id @ X251 @ id )
!= $true ) )
| ~ ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
| ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X255: term] :
( ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
= $true )
| ( ( X247 @ X255 )
!= $true ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
<=> ( termmset = $true ) )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( ( axidl = $true )
<=> ! [X257: subst] :
( ( comp @ id @ X257 )
= X257 ) )
& ( ! [X258: subst] :
( ( comp @ X258 @ id )
= X258 )
<=> ( axidr = $true ) )
& ( ! [X259: term > $o,X260: subst,X261: term] :
~ ! [X262: term > $o] :
~ ! [X263: term] :
( ( X262 @ X263 )
= ( X259 @ ( sub @ X263 @ ( push @ X261 @ X260 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X264: subst > term > subst > $o] :
~ ! [X265: term > $o] :
~ ! [X266: term] :
( ( X265 @ X266 )
= ( X264 @ id @ X266 @ id ) )
=> ( ! [X267: term > $o,X268: term] :
( ~ ! [X269: term,X270: term] :
( ( ( X267 @ ( ap @ X270 @ X269 ) )
= $true )
| ( ( X267 @ X270 )
!= $true )
| ( $true
!= ( X267 @ X269 ) ) )
| ~ ! [X271: term] :
( ( ( var @ X271 )
!= $true )
| ( $true
= ( X267 @ X271 ) ) )
| ~ ! [X272: term] :
( ~ ! [X273: term] :
( ( $true
!= ( X267 @ X273 ) )
| ( ( X267 @ ( sub @ X272 @ ( push @ X273 @ id ) ) )
= $true ) )
| ( ( X267 @ ( lam @ X272 ) )
= $true ) )
| ( ( X267 @ X268 )
= $true ) )
=> ( ! [X274: term] :
( ( sub @ X274 @ id )
= X274 )
=> ( ! [X275: subst > term > subst > $o,X276: term,X277: term > $o] :
( ~ ! [X278: subst > term > term] :
( ~ ! [X279: term] :
( ( ( X275 @ id @ X279 @ id )
!= $true )
| ( ( X275 @ id @ ( X278 @ id @ X279 ) @ id )
= $true ) )
| ( ( X275 @ id @ ( lam @ ( X278 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X280: term,X281: subst,X282: subst] :
( ( X278 @ ( comp @ X282 @ X281 ) @ ( sub @ X280 @ X281 ) )
= ( sub @ ( X278 @ X282 @ X280 ) @ X281 ) ) )
| ( ( X277 @ ( lam @ X276 ) )
= $true )
| ~ ! [X283: term] :
( ( X277 @ X283 )
= ( X275 @ id @ X283 @ id ) )
| ~ ! [X284: term] :
( ( ( X277 @ ( sub @ X276 @ ( push @ X284 @ id ) ) )
= $true )
| ( ( X277 @ X284 )
!= $true ) ) )
=> ! [X285: term,X286: subst > term > subst > $o] :
( ~ ! [X287: subst > term > term] :
( ~ ! [X288: subst,X289: term,X290: subst] :
( ( sub @ ( X287 @ X288 @ X289 ) @ X290 )
= ( X287 @ ( comp @ X288 @ X290 ) @ ( sub @ X289 @ X290 ) ) )
| ( ( X286 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X291: term] :
( ( ( X286 @ id @ ( X287 @ id @ X291 ) @ id )
= $true )
| ( ( X286 @ id @ X291 @ id )
!= $true ) ) )
| ( ( X286 @ id @ X285 @ id )
= $true )
| ~ ! [X292: term,X293: term] :
( ( ( X286 @ id @ ( ap @ ( sub @ X292 @ id ) @ X293 ) @ id )
= $true )
| ( ( X286 @ id @ X292 @ id )
!= $true )
| ( $true
!= ( X286 @ id @ X293 @ id ) ) ) ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ! [X294: d_term,X295: d_term] :
( ( ( d2term @ X294 )
= ( d2term @ X295 ) )
=> ( X294 = X295 ) )
& ! [X296: subst] :
? [X297: d_subst] :
( ( d2subst @ X297 )
= X296 )
& ( ( termmset_lthm = $true )
<=> ( ! [X298: term] :
( ( sub @ X298 @ id )
= X298 )
=> ! [X299: term] :
( ( sub @ X299 @ id )
= X299 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X300: term,X301: subst] :
( ( sub @ one @ ( push @ X300 @ X301 ) )
= X300 )
=> ( ! [X302: term,X303: subst] :
( ( comp @ sh @ ( push @ X302 @ X303 ) )
= X303 )
=> ! [X304: term,X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ ( sub @ X306 @ ( push @ X304 @ X305 ) ) )
= $true )
| ( ( X307 @ X306 )
!= $true ) ) ) ) )
& ( lamnotvar = $true )
& ( ( hoasinduction = $true )
<=> ! [X309: term,X310: subst > term > subst > $o] :
( ~ ! [X311: term] :
( ( ( X310 @ id @ X311 @ id )
= $true )
| ( ( var @ ( sub @ X311 @ id ) )
!= $true ) )
| ( ( X310 @ id @ X309 @ id )
= $true )
| ~ ! [X312: subst,X313: subst,X314: term,X315: subst] :
( ( ( X310 @ X315 @ X314 @ ( comp @ X312 @ X313 ) )
= $true )
| ( $true
!= ( X310 @ ( comp @ X315 @ X312 ) @ ( sub @ X314 @ X312 ) @ X313 ) ) )
| ~ ! [X316: term,X317: subst,X318: subst,X319: subst] :
( ( ( X310 @ ( comp @ X318 @ X319 ) @ ( sub @ X316 @ X319 ) @ X317 )
= $true )
| ( ( X310 @ X318 @ X316 @ ( comp @ X319 @ X317 ) )
!= $true ) )
| ~ ! [X320: subst > term > term] :
( ( ( X310 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X321: subst,X322: term,X323: subst] :
( ( sub @ ( X320 @ X321 @ X322 ) @ X323 )
= ( X320 @ ( comp @ X321 @ X323 ) @ ( sub @ X322 @ X323 ) ) )
| ~ ! [X324: term] :
( ( ( X310 @ id @ ( X320 @ id @ X324 ) @ id )
= $true )
| ( ( X310 @ id @ X324 @ id )
!= $true ) ) )
| ~ ! [X325: term,X326: term] :
( ( ( X310 @ id @ ( ap @ ( sub @ X326 @ id ) @ X325 ) @ id )
= $true )
| ( ( X310 @ id @ X325 @ id )
!= $true )
| ( $true
!= ( X310 @ id @ X326 @ id ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( pushprop = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X327: term] :
~ ! [X328: subst > term > term] :
( ( sub @ X327 @ ( push @ one @ sh ) )
!= ( X328 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ! [X329: term] :
~ ! [X330: subst > term > term] :
~ ! [X331: term,X332: subst] :
( ( sub @ X329 @ ( push @ X331 @ X332 ) )
= ( X330 @ X332 @ X331 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( induction2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axclos = $true )
& ( ( ! [X333: term,X334: subst] :
( ( sub @ one @ ( push @ X333 @ X334 ) )
= X333 )
=> ( ! [X335: subst,X336: term] :
( ( comp @ sh @ ( push @ X336 @ X335 ) )
= X335 )
=> ( ! [X337: subst] :
( ( comp @ X337 @ id )
= X337 )
=> ( ! [X338: term,X339: term > $o] :
( ~ ! [X340: term] :
( ( ( var @ X340 )
!= $true )
| ( ( X339 @ X340 )
= $true ) )
| ~ ! [X341: term] :
( ( $true
= ( X339 @ ( lam @ X341 ) ) )
| ( ( X339 @ X341 )
!= $true ) )
| ( $true
= ( X339 @ X338 ) )
| ~ ! [X342: term,X343: term] :
( ( $true
!= ( X339 @ X342 ) )
| ( ( X339 @ ( ap @ X343 @ X342 ) )
= $true )
| ( ( X339 @ X343 )
!= $true ) ) )
=> ! [X344: subst,X345: term,X346: term > $o] :
( ~ ! [X347: term] :
( ~ ! [X348: term] :
( ( ( X346 @ ( sub @ X347 @ ( push @ X348 @ id ) ) )
= $true )
| ( ( X346 @ X348 )
!= $true ) )
| ( ( X346 @ ( lam @ X347 ) )
= $true ) )
| ~ ! [X349: term,X350: term] :
( ( ( X346 @ X349 )
!= $true )
| ( ( X346 @ ( ap @ X350 @ X349 ) )
= $true )
| ( ( X346 @ X350 )
!= $true ) )
| ( ( X346 @ ( sub @ X345 @ X344 ) )
= $true )
| ~ ! [X351: term] :
( ( ( var @ X351 )
!= $true )
| ( $true
= ( X346 @ ( sub @ X351 @ X344 ) ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X352: term,X353: term > $o,X354: subst > term > subst > $o] :
( ~ ! [X355: term] :
( ( ( X353 @ ( sub @ X352 @ ( push @ X355 @ id ) ) )
= $true )
| ( ( X353 @ X355 )
!= $true ) )
| ~ ! [X356: term] :
( ( X354 @ id @ X356 @ id )
= ( X353 @ X356 ) )
| ~ ! [X357: subst,X358: subst,X359: term,X360: subst] :
( ( ( X354 @ X358 @ X359 @ ( comp @ X360 @ X357 ) )
= $true )
| ( ( X354 @ ( comp @ X358 @ X360 ) @ ( sub @ X359 @ X360 ) @ X357 )
!= $true ) )
| ( ( X353 @ ( lam @ X352 ) )
= $true )
| ~ ! [X361: subst > term > term] :
( ~ ! [X362: subst,X363: subst,X364: term] :
( ( sub @ ( X361 @ X363 @ X364 ) @ X362 )
= ( X361 @ ( comp @ X363 @ X362 ) @ ( sub @ X364 @ X362 ) ) )
| ( ( X354 @ id @ ( lam @ ( X361 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X365: term] :
( ( ( X354 @ id @ ( X361 @ id @ X365 ) @ id )
= $true )
| ( ( X354 @ id @ X365 @ id )
!= $true ) ) )
| ~ ! [X366: subst,X367: subst,X368: term,X369: subst] :
( ( ( X354 @ X366 @ X368 @ ( comp @ X369 @ X367 ) )
!= $true )
| ( ( X354 @ ( comp @ X366 @ X369 ) @ ( sub @ X368 @ X369 ) @ X367 )
= $true ) ) ) )
& ( ! [X370: term,X371: term,X372: term,X373: term] :
( ( X370 = X372 )
| ( ( ap @ X372 @ X373 )
!= ( ap @ X370 @ X371 ) ) )
<=> ( apinj1 = $true ) )
& ( hoasinduction_gthm = $true )
& ( ! [X374: term,X375: term,X376: term,X377: term] :
( ( ( ap @ ( sub @ X377 @ id ) @ X375 )
!= ( ap @ ( sub @ X374 @ id ) @ X376 ) )
| ( X374 = X377 ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X378: term] :
~ ! [X379: subst > term > term] :
~ ! [X380: term,X381: subst] :
( ( X379 @ X381 @ X380 )
= ( sub @ X378 @ ( push @ X380 @ X381 ) ) )
=> ( ! [X382: term] :
( ( sub @ X382 @ id )
= X382 )
=> ! [X383: term,X384: term > $o,X385: subst > term > subst > $o] :
( ~ ! [X386: term] :
( ( X384 @ X386 )
= ( X385 @ id @ X386 @ id ) )
| ~ ! [X387: subst > term > term] :
( ~ ! [X388: term] :
( ( ( X385 @ id @ X388 @ id )
!= $true )
| ( ( X385 @ id @ ( X387 @ id @ X388 ) @ id )
= $true ) )
| ~ ! [X389: subst,X390: subst,X391: term] :
( ( X387 @ ( comp @ X390 @ X389 ) @ ( sub @ X391 @ X389 ) )
= ( sub @ ( X387 @ X390 @ X391 ) @ X389 ) )
| ( ( X385 @ id @ ( lam @ ( X387 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X392: term] :
( ( ( X384 @ ( sub @ X383 @ ( push @ X392 @ id ) ) )
= $true )
| ( ( X384 @ X392 )
!= $true ) )
| ( ( X384 @ ( lam @ X383 ) )
= $true ) ) ) ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X393: term,X394: subst > term > subst > $o] :
( ( ( X394 @ id @ ( lam @ ( sub @ X393 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X395: subst > term > term] :
( ( ( X394 @ id @ ( lam @ ( X395 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X396: term] :
( ( ( X394 @ id @ X396 @ id )
!= $true )
| ( ( X394 @ id @ ( X395 @ id @ X396 ) @ id )
= $true ) )
| ~ ! [X397: term,X398: subst,X399: subst] :
( ( X395 @ ( comp @ X398 @ X399 ) @ ( sub @ X397 @ X399 ) )
= ( sub @ ( X395 @ X398 @ X397 ) @ X399 ) ) )
| ~ ! [X400: term] :
( ( ( X394 @ id @ X400 @ id )
!= $true )
| ( ( X394 @ id @ ( sub @ X393 @ ( push @ X400 @ id ) ) @ id )
= $true ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X401: subst,X402: term > $o,X403: term] :
( ~ ! [X404: term] :
( ( ( X402 @ ( lam @ X404 ) )
= $true )
| ~ ! [X405: term] :
( ( ( X402 @ X405 )
!= $true )
| ( ( X402 @ ( sub @ X404 @ ( push @ X405 @ id ) ) )
= $true ) ) )
| ~ ! [X406: term] :
( ( ( var @ X406 )
!= $true )
| ( ( X402 @ ( sub @ X406 @ X401 ) )
= $true ) )
| ~ ! [X407: term,X408: term] :
( ( ( X402 @ X407 )
!= $true )
| ( ( X402 @ ( ap @ X408 @ X407 ) )
= $true )
| ( ( X402 @ X408 )
!= $true ) )
| ( ( X402 @ ( sub @ X403 @ X401 ) )
= $true ) ) )
& ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( X409 = X410 )
| ( ( ap @ X411 @ X410 )
!= ( ap @ X412 @ X409 ) ) )
<=> ( apinj2 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X413: subst,X414: term] :
( ( sub @ one @ ( push @ X414 @ X413 ) )
= X414 )
=> ( ! [X415: subst,X416: term] :
( ( comp @ sh @ ( push @ X416 @ X415 ) )
= X415 )
=> ( ! [X417: term,X418: term] :
( ( ( lam @ X418 )
!= ( lam @ X417 ) )
| ( X417 = X418 ) )
=> ! [X419: subst,X420: subst > term > term,X421: subst > term > term,X422: term] :
( ( ( lam @ ( X420 @ sh @ one ) )
!= ( lam @ ( X421 @ sh @ one ) ) )
| ~ ! [X426: subst,X427: subst,X428: term] :
( ( X421 @ ( comp @ X426 @ X427 ) @ ( sub @ X428 @ X427 ) )
= ( sub @ ( X421 @ X426 @ X428 ) @ X427 ) )
| ( ( X420 @ X419 @ X422 )
= ( X421 @ X419 @ X422 ) )
| ~ ! [X423: term,X424: subst,X425: subst] :
( ( X420 @ ( comp @ X425 @ X424 ) @ ( sub @ X423 @ X424 ) )
= ( sub @ ( X420 @ X425 @ X423 ) @ X424 ) ) ) ) ) ) )
& ( ! [X429: term] :
~ ! [X430: subst > term > term] :
( ( X430 @ sh @ one )
!= ( sub @ X429 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X431: term,X432: subst > term > subst > $o] :
( ( ( X432 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X433: subst > term > term] :
( ( ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X434: subst,X435: subst,X436: term] :
( ( sub @ ( X433 @ X434 @ X436 ) @ X435 )
= ( X433 @ ( comp @ X434 @ X435 ) @ ( sub @ X436 @ X435 ) ) )
| ~ ! [X437: term] :
( ( ( X432 @ id @ X437 @ id )
!= $true )
| ( ( X432 @ id @ ( X433 @ id @ X437 ) @ id )
= $true ) ) )
| ~ ! [X438: term] :
( ( ( X432 @ id @ X438 @ id )
!= $true )
| ( ( X432 @ id @ ( sub @ X431 @ ( push @ X438 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X439: term,X440: term > $o] :
( ~ ! [X441: term,X442: term] :
( ( ( X440 @ X441 )
!= $true )
| ( ( X440 @ X442 )
!= $true )
| ( ( X440 @ ( ap @ X441 @ X442 ) )
= $true ) )
| ( ( X440 @ X439 )
= $true )
| ~ ! [X443: term] :
( ( ( X440 @ X443 )
!= $true )
| ( ( X440 @ ( lam @ X443 ) )
= $true ) )
| ~ ! [X444: term] :
( ( ( X440 @ X444 )
= $true )
| ( $true
!= ( var @ X444 ) ) ) )
<=> ( induction = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X445: subst,X446: term,X447: subst > term > term,X448: subst > term > term] :
( ( ( lam @ ( X447 @ sh @ one ) )
!= ( lam @ ( X448 @ sh @ one ) ) )
| ( ( X447 @ X445 @ X446 )
= ( X448 @ X445 @ X446 ) )
| ~ ! [X452: subst,X453: term,X454: subst] :
( ( sub @ ( X447 @ X454 @ X453 ) @ X452 )
= ( X447 @ ( comp @ X454 @ X452 ) @ ( sub @ X453 @ X452 ) ) )
| ~ ! [X449: term,X450: subst,X451: subst] :
( ( sub @ ( X448 @ X450 @ X449 ) @ X451 )
= ( X448 @ ( comp @ X450 @ X451 ) @ ( sub @ X449 @ X451 ) ) ) ) )
& ( ! [X455: term,X456: term] :
( ( X455 = X456 )
| ( ( lam @ X456 )
!= ( lam @ X455 ) ) )
<=> ( laminj = $true ) )
& ( ! [X457: subst > term > subst > $o,X458: term,X459: term] :
( ( ( X457 @ id @ X458 @ id )
!= $true )
| ~ ! [X460: term,X461: term] :
( ( ( X457 @ id @ ( ap @ ( sub @ X461 @ id ) @ X460 ) @ id )
= $true )
| ( ( X457 @ id @ X461 @ id )
!= $true )
| ( $true
!= ( X457 @ id @ X460 @ id ) ) )
| ~ ! [X462: subst,X463: subst,X464: subst,X465: term] :
( ( $true
= ( X457 @ X463 @ X465 @ ( comp @ X462 @ X464 ) ) )
| ( ( X457 @ ( comp @ X463 @ X462 ) @ ( sub @ X465 @ X462 ) @ X464 )
!= $true ) )
| ( ( X457 @ id @ ( ap @ X458 @ X459 ) @ id )
= $true )
| ~ ! [X466: subst,X467: term,X468: subst,X469: subst] :
( ( ( X457 @ ( comp @ X469 @ X468 ) @ ( sub @ X467 @ X468 ) @ X466 )
= $true )
| ( ( X457 @ X469 @ X467 @ ( comp @ X468 @ X466 ) )
!= $true ) )
| ( ( X457 @ id @ X459 @ id )
!= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ! [X470: d_subst,X471: d_subst] :
( ( ( d2subst @ X470 )
= ( d2subst @ X471 ) )
=> ( X470 = X471 ) )
& ( pushprop_lem3v2 = $true )
& ( ( ! [X472: term] :
( ( sub @ X472 @ id )
= X472 )
=> ( ! [X473: term,X474: term,X475: term,X476: term] :
( ( X474 = X476 )
| ( ( ap @ X476 @ X473 )
!= ( ap @ X474 @ X475 ) ) )
=> ! [X477: term,X478: term,X479: term,X480: term] :
( ( X478 = X479 )
| ( ( ap @ ( sub @ X478 @ id ) @ X477 )
!= ( ap @ ( sub @ X479 @ id ) @ X480 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X481: term > $o,X482: subst,X483: term > $o,X484: term] :
( ~ ! [X485: term] :
( ( X481 @ ( sub @ X485 @ ( push @ X484 @ X482 ) ) )
= ( X483 @ X485 ) )
| ( ( X481 @ X484 )
!= $true )
| ( ( X483 @ one )
= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_lem2v2 = $true )
& ! [X486: d_term] : ( d_one = X486 )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslamnotap_gthm = $true )
& ! [X487: term] :
? [X488: d_term] :
( ( d2term @ X488 )
= X487 )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( axapp = $true )
& ( ! [X489: subst > term > subst > $o,X490: term] :
( ~ ! [X491: term] :
( ( ( X489 @ id @ ( sub @ X490 @ ( push @ X491 @ id ) ) @ id )
= $true )
| ( ( X489 @ id @ X491 @ id )
!= $true ) )
| ( ( X489 @ id @ ( lam @ ( sub @ X490 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X492: term,X493: subst > term > term] :
( ~ ! [X494: subst,X495: term,X496: subst] :
( ( X493 @ ( comp @ X496 @ X494 ) @ ( sub @ X495 @ X494 ) )
= ( sub @ X492 @ ( push @ ( sub @ X495 @ X494 ) @ ( comp @ X496 @ X494 ) ) ) )
| ~ ! [X497: subst,X498: term,X499: subst] :
( ( sub @ ( X493 @ X499 @ X498 ) @ X497 )
= ( sub @ ( sub @ X492 @ ( push @ X498 @ X499 ) ) @ X497 ) )
| ~ ! [X500: term] :
( ( ( X489 @ id @ ( X493 @ id @ X500 ) @ id )
= $true )
| ( ( X489 @ id @ X500 @ id )
!= $true ) )
| ( ( X489 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X501: term,X502: subst] :
( ( sub @ one @ ( push @ X501 @ X502 ) )
= X501 )
=> ! [X503: term,X504: term > $o,X505: term > $o,X506: subst] :
( ( $true
!= ( X504 @ X503 ) )
| ~ ! [X507: term] :
( ( X504 @ ( sub @ X507 @ ( push @ X503 @ X506 ) ) )
= ( X505 @ X507 ) )
| ( $true
= ( X505 @ one ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X508: term] :
( ( sub @ X508 @ id )
= X508 )
=> ! [X509: term > $o,X510: subst > term > subst > $o,X511: term] :
( ( ( X509 @ ( lam @ X511 ) )
= $true )
| ~ ! [X512: term,X513: subst,X514: subst,X515: subst] :
( ( ( X510 @ X513 @ X512 @ ( comp @ X514 @ X515 ) )
!= $true )
| ( ( X510 @ ( comp @ X513 @ X514 ) @ ( sub @ X512 @ X514 ) @ X515 )
= $true ) )
| ~ ! [X516: subst,X517: term,X518: subst,X519: subst] :
( ( ( X510 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) @ X519 )
!= $true )
| ( ( X510 @ X516 @ X517 @ ( comp @ X518 @ X519 ) )
= $true ) )
| ~ ! [X520: term] :
( ( X509 @ X520 )
= ( X510 @ id @ X520 @ id ) )
| ~ ! [X521: subst > term > term] :
( ( ( X510 @ id @ ( lam @ ( X521 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X522: term,X523: subst,X524: subst] :
( ( sub @ ( X521 @ X523 @ X522 ) @ X524 )
= ( X521 @ ( comp @ X523 @ X524 ) @ ( sub @ X522 @ X524 ) ) )
| ~ ! [X525: term] :
( ( ( X510 @ id @ ( X521 @ id @ X525 ) @ id )
= $true )
| ( ( X510 @ id @ X525 @ id )
!= $true ) ) )
| ~ ! [X526: term] :
( ( ( X509 @ X526 )
!= $true )
| ( $true
= ( X509 @ ( sub @ X511 @ ( push @ X526 @ id ) ) ) ) ) ) ) )
& ( ! [X527: term,X528: term] :
( ( X527 = X528 )
| ( ( sub @ X528 @ sh )
!= ( sub @ X527 @ sh ) ) )
<=> ( shinj = $true ) )
& ! [X529: d_subst] : ( d_id = X529 )
& ( ( axshiftcons = $true )
<=> ! [X530: subst,X531: term] :
( ( comp @ sh @ ( push @ X531 @ X530 ) )
= X530 ) )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( apnotvar = $true )
& ( termmset_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X535 @ X532 )
!= ( ap @ X534 @ X533 ) )
| ( X532 = X533 ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X0: term,X1: subst > term > subst > $o] :
( ~ ! [X2: term,X3: term] :
( ( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
= $true )
| ( ( X1 @ id @ X3 @ id )
!= $true )
| ( ( X1 @ id @ X2 @ id )
!= $true ) )
| ~ ! [X4: subst > term > term] :
( ( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ~ ! [X8: term] :
( ( ( X1 @ id @ X8 @ id )
!= $true )
| ( ( X1 @ id @ ( X4 @ id @ X8 ) @ id )
= $true ) ) )
| ( $true
= ( X1 @ id @ X0 @ id ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( axassoc = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_gthm = $true )
& ( ! [X14: term,X15: term > $o,X16: term,X17: subst > term > subst > $o] :
( ( ( X15 @ X14 )
!= $true )
| ~ ! [X18: term] :
( ( X15 @ X18 )
= ( X17 @ id @ X18 @ id ) )
| ~ ! [X19: subst,X20: subst,X21: subst,X22: term] :
( ( $true
!= ( X17 @ ( comp @ X20 @ X21 ) @ ( sub @ X22 @ X21 ) @ X19 ) )
| ( ( X17 @ X20 @ X22 @ ( comp @ X21 @ X19 ) )
= $true ) )
| ( ( X15 @ ( ap @ X16 @ X14 ) )
= $true )
| ( ( X15 @ X16 )
!= $true )
| ~ ! [X23: subst,X24: term,X25: subst,X26: subst] :
( ( ( X17 @ X25 @ X24 @ ( comp @ X23 @ X26 ) )
!= $true )
| ( ( X17 @ ( comp @ X25 @ X23 ) @ ( sub @ X24 @ X23 ) @ X26 )
= $true ) )
| ~ ! [X27: term,X28: term] :
( ( ( X17 @ id @ ( ap @ ( sub @ X28 @ id ) @ X27 ) @ id )
= $true )
| ( ( X17 @ id @ X27 @ id )
!= $true )
| ( ( X17 @ id @ X28 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ! [X29: subst] :
( ( push @ ( sub @ one @ X29 ) @ ( comp @ sh @ X29 ) )
= X29 )
<=> ( axscons = $true ) )
& ( ( ! [X30: term] :
( ( sub @ X30 @ id )
= X30 )
=> ( ! [X31: term > $o,X32: term,X33: subst] :
( ~ ! [X34: term,X35: term] :
( ( ( X31 @ X35 )
!= $true )
| ( $true
= ( X31 @ ( ap @ X34 @ X35 ) ) )
| ( ( X31 @ X34 )
!= $true ) )
| ~ ! [X36: term] :
( ( $true
= ( X31 @ ( lam @ X36 ) ) )
| ~ ! [X37: term] :
( ( $true
!= ( X31 @ X37 ) )
| ( ( X31 @ ( sub @ X36 @ ( push @ X37 @ id ) ) )
= $true ) ) )
| ~ ! [X38: term] :
( ( ( X31 @ ( sub @ X38 @ X33 ) )
= $true )
| ( ( var @ X38 )
!= $true ) )
| ( ( X31 @ ( sub @ X32 @ X33 ) )
= $true ) )
=> ! [X39: term,X40: term > $o] :
( ~ ! [X41: term] :
( ~ ! [X42: term] :
( ( $true
= ( X40 @ ( sub @ X41 @ ( push @ X42 @ id ) ) ) )
| ( ( X40 @ X42 )
!= $true ) )
| ( $true
= ( X40 @ ( lam @ X41 ) ) ) )
| ( ( X40 @ X39 )
= $true )
| ~ ! [X43: term,X44: term] :
( ( ( X40 @ ( ap @ X44 @ X43 ) )
= $true )
| ( ( X40 @ X44 )
!= $true )
| ( ( X40 @ X43 )
!= $true ) )
| ~ ! [X45: term] :
( ( ( var @ X45 )
!= $true )
| ( ( X40 @ X45 )
= $true ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( substmonoid = $true )
<=> ( ! [X46: subst] :
( ( comp @ X46 @ id )
= X46 )
& ! [X47: subst] :
( ( comp @ id @ X47 )
= X47 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ulamvarsh = $true )
& ( axvarshift = $true )
& ( ( ! [X48: term] :
( ( sub @ X48 @ id )
= X48 )
=> ( ! [X49: subst > term > subst > $o,X50: term] :
( ~ ! [X51: subst > term > term] :
( ~ ! [X52: term] :
( ( ( X49 @ id @ ( X51 @ id @ X52 ) @ id )
= $true )
| ( ( X49 @ id @ X52 @ id )
!= $true ) )
| ( ( X49 @ id @ ( lam @ ( X51 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X53: subst,X54: term,X55: subst] :
( ( X51 @ ( comp @ X55 @ X53 ) @ ( sub @ X54 @ X53 ) )
= ( sub @ ( X51 @ X55 @ X54 ) @ X53 ) ) )
| ~ ! [X56: term] :
( ( ( X49 @ id @ ( sub @ X50 @ ( push @ X56 @ id ) ) @ id )
= $true )
| ( ( X49 @ id @ X56 @ id )
!= $true ) )
| ( $true
= ( X49 @ id @ ( lam @ ( sub @ X50 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X57: term,X58: subst > term > subst > $o] :
( ~ ! [X59: subst > term > term] :
( ( ( X58 @ id @ ( lam @ ( X59 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X60: term] :
( ( ( X58 @ id @ X60 @ id )
!= $true )
| ( ( X58 @ id @ ( X59 @ id @ X60 ) @ id )
= $true ) )
| ~ ! [X61: subst,X62: subst,X63: term] :
( ( X59 @ ( comp @ X62 @ X61 ) @ ( sub @ X63 @ X61 ) )
= ( sub @ ( X59 @ X62 @ X63 ) @ X61 ) ) )
| ~ ! [X64: term] :
( ( $true
= ( X58 @ id @ ( sub @ X57 @ ( push @ X64 @ id ) ) @ id ) )
| ( ( X58 @ id @ X64 @ id )
!= $true ) )
| ( ( X58 @ id @ ( lam @ X57 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X65: subst > term > subst > $o,X66: term] :
( ~ ! [X67: subst > term > term] :
( ~ ! [X68: term,X69: subst,X70: subst] :
( ( sub @ ( X67 @ X70 @ X68 ) @ X69 )
= ( X67 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) ) )
| ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X71: term] :
( ( $true
!= ( X65 @ id @ X71 @ id ) )
| ( ( X65 @ id @ ( X67 @ id @ X71 ) @ id )
= $true ) ) )
| ~ ! [X72: subst,X73: term,X74: subst,X75: subst] :
( ( ( X65 @ ( comp @ X74 @ X75 ) @ ( sub @ X73 @ X75 ) @ X72 )
!= $true )
| ( ( X65 @ X74 @ X73 @ ( comp @ X75 @ X72 ) )
= $true ) )
| ~ ! [X76: subst,X77: subst,X78: subst,X79: term] :
( ( ( X65 @ X78 @ X79 @ ( comp @ X76 @ X77 ) )
!= $true )
| ( ( X65 @ ( comp @ X78 @ X76 ) @ ( sub @ X79 @ X76 ) @ X77 )
= $true ) )
| ~ ! [X80: term] :
( ( ( X65 @ id @ ( sub @ X66 @ ( push @ X80 @ id ) ) @ id )
= $true )
| ( ( X65 @ id @ X80 @ id )
!= $true ) )
| ( ( X65 @ id @ ( lam @ X66 ) @ id )
= $true ) ) )
& ( ! [X81: subst > term > term,X82: term,X83: term] :
( ~ ! [X84: term,X85: subst,X86: subst] :
( ( X81 @ ( comp @ X85 @ X86 ) @ ( sub @ X84 @ X86 ) )
= ( sub @ ( X81 @ X85 @ X84 ) @ X86 ) )
| ( ( lam @ ( X81 @ sh @ one ) )
!= ( ap @ ( sub @ X82 @ id ) @ X83 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X87: subst] :
( ( comp @ id @ X87 )
= X87 )
=> ( ! [X88: subst] :
( ( comp @ X88 @ id )
= X88 )
=> ( ! [X89: subst] :
( ( comp @ id @ X89 )
= X89 )
& ! [X90: subst] :
( ( comp @ X90 @ id )
= X90 ) ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X91: term,X92: term,X93: term,X94: term] :
( ( ( ap @ ( sub @ X91 @ id ) @ X94 )
!= ( ap @ ( sub @ X92 @ id ) @ X93 ) )
| ( X93 = X94 ) ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X95: term,X96: term > $o,X97: subst,X98: term > $o,X99: term] :
( ( ( X98 @ X99 )
!= $true )
| ( ( X96 @ ( sub @ X99 @ ( push @ X95 @ X97 ) ) )
= $true ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
=> ( ! [X101: term,X102: subst > term > subst > $o] :
( ~ ! [X103: subst > term > term] :
( ( ( X102 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X104: term,X105: subst,X106: subst] :
( ( X103 @ ( comp @ X106 @ X105 ) @ ( sub @ X104 @ X105 ) )
= ( sub @ ( X103 @ X106 @ X104 ) @ X105 ) )
| ~ ! [X107: term] :
( ( ( X102 @ id @ X107 @ id )
!= $true )
| ( ( X102 @ id @ ( X103 @ id @ X107 ) @ id )
= $true ) ) )
| ( ( X102 @ id @ ( lam @ ( sub @ X101 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X108: term] :
( ( ( X102 @ id @ X108 @ id )
!= $true )
| ( ( X102 @ id @ ( sub @ X101 @ ( push @ X108 @ id ) ) @ id )
= $true ) ) )
=> ! [X109: term,X110: subst > term > subst > $o] :
( ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( ( X110 @ X114 @ X112 @ ( comp @ X113 @ X111 ) )
= $true )
| ( $true
!= ( X110 @ ( comp @ X114 @ X113 ) @ ( sub @ X112 @ X113 ) @ X111 ) ) )
| ~ ! [X115: term,X116: subst,X117: subst,X118: subst] :
( ( ( X110 @ ( comp @ X117 @ X118 ) @ ( sub @ X115 @ X118 ) @ X116 )
= $true )
| ( ( X110 @ X117 @ X115 @ ( comp @ X118 @ X116 ) )
!= $true ) )
| ( ( X110 @ id @ ( lam @ X109 ) @ id )
= $true )
| ~ ! [X119: term] :
( ( ( X110 @ id @ X119 @ id )
!= $true )
| ( $true
= ( X110 @ id @ ( sub @ X109 @ ( push @ X119 @ id ) ) @ id ) ) )
| ~ ! [X120: subst > term > term] :
( ( ( X110 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X121: term] :
( ( ( X110 @ id @ X121 @ id )
!= $true )
| ( ( X110 @ id @ ( X120 @ id @ X121 ) @ id )
= $true ) )
| ~ ! [X122: subst,X123: subst,X124: term] :
( ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) )
= ( sub @ ( X120 @ X122 @ X124 ) @ X123 ) ) ) ) ) ) )
& ( ( induction2 = $true )
<=> ! [X125: term > $o,X126: term] :
( ~ ! [X127: term] :
( ( ( var @ X127 )
!= $true )
| ( $true
= ( X125 @ X127 ) ) )
| ~ ! [X128: term,X129: term] :
( ( ( X125 @ X128 )
!= $true )
| ( ( X125 @ X129 )
!= $true )
| ( $true
= ( X125 @ ( ap @ X128 @ X129 ) ) ) )
| ~ ! [X130: term] :
( ~ ! [X131: term] :
( ( ( X125 @ ( sub @ X130 @ ( push @ X131 @ id ) ) )
= $true )
| ( ( X125 @ X131 )
!= $true ) )
| ( $true
= ( X125 @ ( lam @ X130 ) ) ) )
| ( ( X125 @ X126 )
= $true ) ) )
& ( ulamvar1 != $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X132: subst,X133: term] :
( ( sub @ one @ ( push @ X133 @ X132 ) )
= X133 )
<=> ( axvarcons = $true ) )
& ( ( ! [X134: subst > term > subst > $o] :
~ ! [X135: term > $o] :
~ ! [X136: term] :
( ( X134 @ id @ X136 @ id )
= ( X135 @ X136 ) )
=> ( ! [X137: term > $o,X138: term] :
( ~ ! [X139: term] :
( ( $true
= ( X137 @ X139 ) )
| ( ( var @ X139 )
!= $true ) )
| ~ ! [X140: term,X141: term] :
( ( ( X137 @ X141 )
!= $true )
| ( ( X137 @ X140 )
!= $true )
| ( ( X137 @ ( ap @ X140 @ X141 ) )
= $true ) )
| ~ ! [X142: term] :
( ~ ! [X143: term] :
( ( ( X137 @ X143 )
!= $true )
| ( ( X137 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) )
| ( ( X137 @ ( lam @ X142 ) )
= $true ) )
| ( $true
= ( X137 @ X138 ) ) )
=> ( ! [X144: term] :
( ( sub @ X144 @ id )
= X144 )
=> ( ! [X145: term > $o,X146: term,X147: subst > term > subst > $o] :
( ~ ! [X148: subst > term > term] :
( ( ( X147 @ id @ ( lam @ ( X148 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X149: term] :
( ( ( X147 @ id @ ( X148 @ id @ X149 ) @ id )
= $true )
| ( ( X147 @ id @ X149 @ id )
!= $true ) )
| ~ ! [X150: subst,X151: term,X152: subst] :
( ( sub @ ( X148 @ X152 @ X151 ) @ X150 )
= ( X148 @ ( comp @ X152 @ X150 ) @ ( sub @ X151 @ X150 ) ) ) )
| ~ ! [X153: term] :
( ( X147 @ id @ X153 @ id )
= ( X145 @ X153 ) )
| ~ ! [X154: term] :
( ( $true
!= ( X145 @ X154 ) )
| ( ( X145 @ ( sub @ X146 @ ( push @ X154 @ id ) ) )
= $true ) )
| ( $true
= ( X145 @ ( lam @ X146 ) ) ) )
=> ! [X155: subst > term > subst > $o,X156: term] :
( ~ ! [X157: term,X158: term] :
( ( ( X155 @ id @ ( ap @ ( sub @ X157 @ id ) @ X158 ) @ id )
= $true )
| ( ( X155 @ id @ X158 @ id )
!= $true )
| ( ( X155 @ id @ X157 @ id )
!= $true ) )
| ~ ! [X159: term] :
( ( $true
!= ( var @ ( sub @ X159 @ id ) ) )
| ( ( X155 @ id @ X159 @ id )
= $true ) )
| ~ ! [X160: subst,X161: term,X162: subst,X163: subst] :
( ( ( X155 @ X163 @ X161 @ ( comp @ X160 @ X162 ) )
= $true )
| ( ( X155 @ ( comp @ X163 @ X160 ) @ ( sub @ X161 @ X160 ) @ X162 )
!= $true ) )
| ~ ! [X164: subst > term > term] :
( ~ ! [X165: term,X166: subst,X167: subst] :
( ( X164 @ ( comp @ X167 @ X166 ) @ ( sub @ X165 @ X166 ) )
= ( sub @ ( X164 @ X167 @ X165 ) @ X166 ) )
| ( ( X155 @ id @ ( lam @ ( X164 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X168: term] :
( ( ( X155 @ id @ X168 @ id )
!= $true )
| ( ( X155 @ id @ ( X164 @ id @ X168 ) @ id )
= $true ) ) )
| ~ ! [X169: subst,X170: subst,X171: subst,X172: term] :
( ( ( X155 @ X171 @ X172 @ ( comp @ X170 @ X169 ) )
!= $true )
| ( ( X155 @ ( comp @ X171 @ X170 ) @ ( sub @ X172 @ X170 ) @ X169 )
= $true ) )
| ( ( X155 @ id @ X156 @ id )
= $true ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X173: subst > term > subst > $o] :
~ ! [X174: term > $o] :
~ ! [X175: term] :
( ( X173 @ id @ X175 @ id )
= ( X174 @ X175 ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X176: subst > term > subst > $o] :
~ ! [X177: term > $o] :
~ ! [X178: term] :
( ( X176 @ id @ X178 @ id )
= ( X177 @ X178 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X179: term] :
~ ! [X180: subst > term > term] :
~ ! [X181: term,X182: subst] :
( ( X180 @ X182 @ X181 )
= ( sub @ X179 @ ( push @ X181 @ X182 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( axvarid = $true )
<=> ! [X183: term] :
( ( sub @ X183 @ id )
= X183 ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X184: term > $o,X185: term] :
( ~ ! [X186: term] :
( ~ ! [X187: term] :
( ( ( X184 @ X187 )
!= $true )
| ( ( X184 @ ( sub @ X186 @ ( push @ X187 @ id ) ) )
= $true ) )
| ( ( X184 @ ( lam @ X186 ) )
= $true ) )
| ~ ! [X188: term,X189: term] :
( ( $true
!= ( X184 @ X189 ) )
| ( ( X184 @ ( ap @ X189 @ X188 ) )
= $true )
| ( ( X184 @ X188 )
!= $true ) )
| ~ ! [X190: term] :
( ( ( var @ X190 )
!= $true )
| ( ( X184 @ X190 )
= $true ) )
| ( ( X184 @ X185 )
= $true ) )
=> ( ! [X191: term,X192: term,X193: subst > term > subst > $o] :
( ( ( X193 @ id @ ( ap @ X191 @ X192 ) @ id )
= $true )
| ( ( X193 @ id @ X192 @ id )
!= $true )
| ~ ! [X194: term,X195: term] :
( ( ( X193 @ id @ ( ap @ ( sub @ X194 @ id ) @ X195 ) @ id )
= $true )
| ( $true
!= ( X193 @ id @ X194 @ id ) )
| ( ( X193 @ id @ X195 @ id )
!= $true ) )
| ( $true
!= ( X193 @ id @ X191 @ id ) )
| ~ ! [X196: term,X197: subst,X198: subst,X199: subst] :
( ( ( X193 @ X199 @ X196 @ ( comp @ X198 @ X197 ) )
= $true )
| ( ( X193 @ ( comp @ X199 @ X198 ) @ ( sub @ X196 @ X198 ) @ X197 )
!= $true ) )
| ~ ! [X200: term,X201: subst,X202: subst,X203: subst] :
( ( ( X193 @ X202 @ X200 @ ( comp @ X203 @ X201 ) )
!= $true )
| ( ( X193 @ ( comp @ X202 @ X203 ) @ ( sub @ X200 @ X203 ) @ X201 )
= $true ) ) )
=> ( ! [X204: term,X205: subst > term > subst > $o] :
( ~ ! [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X205 @ ( comp @ X206 @ X207 ) @ ( sub @ X209 @ X207 ) @ X208 )
= $true )
| ( ( X205 @ X206 @ X209 @ ( comp @ X207 @ X208 ) )
!= $true ) )
| ( $true
= ( X205 @ id @ ( lam @ X204 ) @ id ) )
| ~ ! [X210: term] :
( ( ( X205 @ id @ X210 @ id )
!= $true )
| ( ( X205 @ id @ ( sub @ X204 @ ( push @ X210 @ id ) ) @ id )
= $true ) )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: term] :
( ( ( X205 @ id @ ( X211 @ id @ X212 ) @ id )
= $true )
| ( ( X205 @ id @ X212 @ id )
!= $true ) )
| ( ( X205 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X213: term,X214: subst,X215: subst] :
( ( sub @ ( X211 @ X215 @ X213 ) @ X214 )
= ( X211 @ ( comp @ X215 @ X214 ) @ ( sub @ X213 @ X214 ) ) ) )
| ~ ! [X216: subst,X217: term,X218: subst,X219: subst] :
( ( ( X205 @ ( comp @ X218 @ X219 ) @ ( sub @ X217 @ X219 ) @ X216 )
!= $true )
| ( ( X205 @ X218 @ X217 @ ( comp @ X219 @ X216 ) )
= $true ) ) )
=> ! [X220: subst > term > subst > $o,X221: term] :
( ( ( X220 @ id @ X221 @ id )
= $true )
| ~ ! [X222: term] :
( ( ( var @ ( sub @ X222 @ id ) )
!= $true )
| ( ( X220 @ id @ X222 @ id )
= $true ) )
| ~ ! [X223: subst > term > term] :
( ~ ! [X224: term,X225: subst,X226: subst] :
( ( sub @ ( X223 @ X225 @ X224 ) @ X226 )
= ( X223 @ ( comp @ X225 @ X226 ) @ ( sub @ X224 @ X226 ) ) )
| ~ ! [X227: term] :
( ( ( X220 @ id @ X227 @ id )
!= $true )
| ( ( X220 @ id @ ( X223 @ id @ X227 ) @ id )
= $true ) )
| ( ( X220 @ id @ ( lam @ ( X223 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X228: term,X229: subst,X230: subst,X231: subst] :
( ( ( X220 @ X230 @ X228 @ ( comp @ X231 @ X229 ) )
= $true )
| ( ( X220 @ ( comp @ X230 @ X231 ) @ ( sub @ X228 @ X231 ) @ X229 )
!= $true ) )
| ~ ! [X232: subst,X233: subst,X234: subst,X235: term] :
( ( ( X220 @ X234 @ X235 @ ( comp @ X233 @ X232 ) )
!= $true )
| ( ( X220 @ ( comp @ X234 @ X233 ) @ ( sub @ X235 @ X233 ) @ X232 )
= $true ) )
| ~ ! [X236: term,X237: term] :
( ( ( X220 @ id @ X236 @ id )
!= $true )
| ( ( X220 @ id @ ( ap @ ( sub @ X237 @ id ) @ X236 ) @ id )
= $true )
| ( $true
!= ( X220 @ id @ X237 @ id ) ) ) ) ) ) ) )
& ( ! [X238: term,X239: subst > term > subst > $o] :
( ( ( X239 @ id @ ( lam @ X238 ) @ id )
= $true )
| ~ ! [X240: subst > term > term] :
( ~ ! [X241: subst,X242: subst,X243: term] :
( ( X240 @ ( comp @ X241 @ X242 ) @ ( sub @ X243 @ X242 ) )
= ( sub @ ( X240 @ X241 @ X243 ) @ X242 ) )
| ( ( X239 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X244: term] :
( ( ( X239 @ id @ ( X240 @ id @ X244 ) @ id )
= $true )
| ( ( X239 @ id @ X244 @ id )
!= $true ) ) )
| ~ ! [X245: term] :
( ( ( X239 @ id @ ( sub @ X238 @ ( push @ X245 @ id ) ) @ id )
= $true )
| ( ( X239 @ id @ X245 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X246: subst,X247: term,X248: term > $o] :
~ ! [X249: term > $o] :
~ ! [X250: term] :
( ( X248 @ ( sub @ X250 @ ( push @ X247 @ X246 ) ) )
= ( X249 @ X250 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X251: subst > term > subst > $o,X252: term > $o,X253: term] :
( ( ( X252 @ ( lam @ X253 ) )
= $true )
| ~ ! [X254: term] :
( ( X251 @ id @ X254 @ id )
= ( X252 @ X254 ) )
| ~ ! [X255: subst > term > term] :
( ~ ! [X256: term] :
( ( ( X251 @ id @ ( X255 @ id @ X256 ) @ id )
= $true )
| ( ( X251 @ id @ X256 @ id )
!= $true ) )
| ~ ! [X257: subst,X258: term,X259: subst] :
( ( X255 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X255 @ X257 @ X258 ) @ X259 ) )
| ( ( X251 @ id @ ( lam @ ( X255 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X260: term] :
( ( ( X252 @ ( sub @ X253 @ ( push @ X260 @ id ) ) )
= $true )
| ( ( X252 @ X260 )
!= $true ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( termmset = $true )
<=> ! [X261: term] :
( ( sub @ X261 @ id )
= X261 ) )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( ( axidl = $true )
<=> ! [X262: subst] :
( ( comp @ id @ X262 )
= X262 ) )
& ( ! [X263: subst] :
( ( comp @ X263 @ id )
= X263 )
<=> ( axidr = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X264: term > $o,X265: subst,X266: term] :
~ ! [X267: term > $o] :
~ ! [X268: term] :
( ( X267 @ X268 )
= ( X264 @ ( sub @ X268 @ ( push @ X266 @ X265 ) ) ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X269: subst > term > subst > $o] :
~ ! [X270: term > $o] :
~ ! [X271: term] :
( ( X269 @ id @ X271 @ id )
= ( X270 @ X271 ) )
=> ( ! [X272: term > $o,X273: term] :
( ~ ! [X274: term,X275: term] :
( ( ( X272 @ ( ap @ X275 @ X274 ) )
= $true )
| ( ( X272 @ X275 )
!= $true )
| ( ( X272 @ X274 )
!= $true ) )
| ~ ! [X276: term] :
( ( ( var @ X276 )
!= $true )
| ( $true
= ( X272 @ X276 ) ) )
| ~ ! [X277: term] :
( ~ ! [X278: term] :
( ( $true
!= ( X272 @ X278 ) )
| ( ( X272 @ ( sub @ X277 @ ( push @ X278 @ id ) ) )
= $true ) )
| ( ( X272 @ ( lam @ X277 ) )
= $true ) )
| ( ( X272 @ X273 )
= $true ) )
=> ( ! [X279: term] :
( ( sub @ X279 @ id )
= X279 )
=> ( ! [X280: subst > term > subst > $o,X281: term,X282: term > $o] :
( ~ ! [X283: subst > term > term] :
( ~ ! [X284: term] :
( ( ( X280 @ id @ X284 @ id )
!= $true )
| ( ( X280 @ id @ ( X283 @ id @ X284 ) @ id )
= $true ) )
| ( ( X280 @ id @ ( lam @ ( X283 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X285: term,X286: subst,X287: subst] :
( ( X283 @ ( comp @ X287 @ X286 ) @ ( sub @ X285 @ X286 ) )
= ( sub @ ( X283 @ X287 @ X285 ) @ X286 ) ) )
| ( ( X282 @ ( lam @ X281 ) )
= $true )
| ~ ! [X288: term] :
( ( X282 @ X288 )
= ( X280 @ id @ X288 @ id ) )
| ~ ! [X289: term] :
( ( ( X282 @ ( sub @ X281 @ ( push @ X289 @ id ) ) )
= $true )
| ( ( X282 @ X289 )
!= $true ) ) )
=> ! [X290: term,X291: subst > term > subst > $o] :
( ~ ! [X292: subst > term > term] :
( ~ ! [X293: subst,X294: term,X295: subst] :
( ( X292 @ ( comp @ X293 @ X295 ) @ ( sub @ X294 @ X295 ) )
= ( sub @ ( X292 @ X293 @ X294 ) @ X295 ) )
| ( ( X291 @ id @ ( lam @ ( X292 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X296: term] :
( ( ( X291 @ id @ ( X292 @ id @ X296 ) @ id )
= $true )
| ( ( X291 @ id @ X296 @ id )
!= $true ) ) )
| ( ( X291 @ id @ X290 @ id )
= $true )
| ~ ! [X297: term,X298: term] :
( ( ( X291 @ id @ ( ap @ ( sub @ X297 @ id ) @ X298 ) @ id )
= $true )
| ( ( X291 @ id @ X297 @ id )
!= $true )
| ( ( X291 @ id @ X298 @ id )
!= $true ) ) ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ! [X299: d_term,X300: d_term] :
( ( ( d2term @ X299 )
= ( d2term @ X300 ) )
=> ( X299 = X300 ) )
& ! [X301: subst] :
? [X302: d_subst] :
( ( d2subst @ X302 )
= X301 )
& ( ( ! [X303: term] :
( ( sub @ X303 @ id )
= X303 )
=> ! [X304: term] :
( ( sub @ X304 @ id )
= X304 ) )
<=> ( termmset_lthm = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X305: term,X306: subst] :
( ( sub @ one @ ( push @ X305 @ X306 ) )
= X305 )
=> ( ! [X307: term,X308: subst] :
( ( comp @ sh @ ( push @ X307 @ X308 ) )
= X308 )
=> ! [X309: term,X310: subst,X311: term,X312: term > $o,X313: term > $o] :
( ( ( X313 @ ( sub @ X311 @ ( push @ X309 @ X310 ) ) )
= $true )
| ( ( X312 @ X311 )
!= $true ) ) ) ) )
& ( lamnotvar = $true )
& ( ( hoasinduction = $true )
<=> ! [X314: term,X315: subst > term > subst > $o] :
( ~ ! [X316: term] :
( ( ( X315 @ id @ X316 @ id )
= $true )
| ( ( var @ ( sub @ X316 @ id ) )
!= $true ) )
| ( ( X315 @ id @ X314 @ id )
= $true )
| ~ ! [X317: subst,X318: subst,X319: term,X320: subst] :
( ( ( X315 @ X320 @ X319 @ ( comp @ X317 @ X318 ) )
= $true )
| ( ( X315 @ ( comp @ X320 @ X317 ) @ ( sub @ X319 @ X317 ) @ X318 )
!= $true ) )
| ~ ! [X321: term,X322: subst,X323: subst,X324: subst] :
( ( ( X315 @ ( comp @ X323 @ X324 ) @ ( sub @ X321 @ X324 ) @ X322 )
= $true )
| ( ( X315 @ X323 @ X321 @ ( comp @ X324 @ X322 ) )
!= $true ) )
| ~ ! [X325: subst > term > term] :
( ( $true
= ( X315 @ id @ ( lam @ ( X325 @ sh @ one ) ) @ id ) )
| ~ ! [X326: subst,X327: term,X328: subst] :
( ( X325 @ ( comp @ X326 @ X328 ) @ ( sub @ X327 @ X328 ) )
= ( sub @ ( X325 @ X326 @ X327 ) @ X328 ) )
| ~ ! [X329: term] :
( ( $true
= ( X315 @ id @ ( X325 @ id @ X329 ) @ id ) )
| ( ( X315 @ id @ X329 @ id )
!= $true ) ) )
| ~ ! [X330: term,X331: term] :
( ( ( X315 @ id @ ( ap @ ( sub @ X331 @ id ) @ X330 ) @ id )
= $true )
| ( ( X315 @ id @ X330 @ id )
!= $true )
| ( ( X315 @ id @ X331 @ id )
!= $true ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( pushprop = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X332: term] :
~ ! [X333: subst > term > term] :
( ( sub @ X332 @ ( push @ one @ sh ) )
!= ( X333 @ sh @ one ) ) )
& ( ! [X334: term] :
~ ! [X335: subst > term > term] :
~ ! [X336: term,X337: subst] :
( ( X335 @ X337 @ X336 )
= ( sub @ X334 @ ( push @ X336 @ X337 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( induction2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axclos = $true )
& ( ( ! [X338: term,X339: subst] :
( ( sub @ one @ ( push @ X338 @ X339 ) )
= X338 )
=> ( ! [X340: subst,X341: term] :
( ( comp @ sh @ ( push @ X341 @ X340 ) )
= X340 )
=> ( ! [X342: subst] :
( ( comp @ X342 @ id )
= X342 )
=> ( ! [X343: term,X344: term > $o] :
( ~ ! [X345: term] :
( ( ( var @ X345 )
!= $true )
| ( ( X344 @ X345 )
= $true ) )
| ~ ! [X346: term] :
( ( ( X344 @ ( lam @ X346 ) )
= $true )
| ( ( X344 @ X346 )
!= $true ) )
| ( $true
= ( X344 @ X343 ) )
| ~ ! [X347: term,X348: term] :
( ( ( X344 @ X347 )
!= $true )
| ( $true
= ( X344 @ ( ap @ X348 @ X347 ) ) )
| ( ( X344 @ X348 )
!= $true ) ) )
=> ! [X349: subst,X350: term,X351: term > $o] :
( ~ ! [X352: term] :
( ~ ! [X353: term] :
( ( ( X351 @ ( sub @ X352 @ ( push @ X353 @ id ) ) )
= $true )
| ( ( X351 @ X353 )
!= $true ) )
| ( ( X351 @ ( lam @ X352 ) )
= $true ) )
| ~ ! [X354: term,X355: term] :
( ( ( X351 @ X354 )
!= $true )
| ( ( X351 @ ( ap @ X355 @ X354 ) )
= $true )
| ( ( X351 @ X355 )
!= $true ) )
| ( ( X351 @ ( sub @ X350 @ X349 ) )
= $true )
| ~ ! [X356: term] :
( ( ( var @ X356 )
!= $true )
| ( ( X351 @ ( sub @ X356 @ X349 ) )
= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X357: term,X358: term > $o,X359: subst > term > subst > $o] :
( ~ ! [X360: term] :
( ( ( X358 @ ( sub @ X357 @ ( push @ X360 @ id ) ) )
= $true )
| ( ( X358 @ X360 )
!= $true ) )
| ~ ! [X361: term] :
( ( X359 @ id @ X361 @ id )
= ( X358 @ X361 ) )
| ~ ! [X362: subst,X363: subst,X364: term,X365: subst] :
( ( ( X359 @ X363 @ X364 @ ( comp @ X365 @ X362 ) )
= $true )
| ( ( X359 @ ( comp @ X363 @ X365 ) @ ( sub @ X364 @ X365 ) @ X362 )
!= $true ) )
| ( $true
= ( X358 @ ( lam @ X357 ) ) )
| ~ ! [X366: subst > term > term] :
( ~ ! [X367: subst,X368: subst,X369: term] :
( ( sub @ ( X366 @ X368 @ X369 ) @ X367 )
= ( X366 @ ( comp @ X368 @ X367 ) @ ( sub @ X369 @ X367 ) ) )
| ( ( X359 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X370: term] :
( ( $true
= ( X359 @ id @ ( X366 @ id @ X370 ) @ id ) )
| ( $true
!= ( X359 @ id @ X370 @ id ) ) ) )
| ~ ! [X371: subst,X372: subst,X373: term,X374: subst] :
( ( ( X359 @ X371 @ X373 @ ( comp @ X374 @ X372 ) )
!= $true )
| ( ( X359 @ ( comp @ X371 @ X374 ) @ ( sub @ X373 @ X374 ) @ X372 )
= $true ) ) ) )
& ( ( apinj1 = $true )
<=> ! [X375: term,X376: term,X377: term,X378: term] :
( ( ( ap @ X375 @ X376 )
!= ( ap @ X377 @ X378 ) )
| ( X375 = X377 ) ) )
& ( hoasinduction_gthm = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X379: term,X380: term,X381: term,X382: term] :
( ( X379 = X382 )
| ( ( ap @ ( sub @ X379 @ id ) @ X381 )
!= ( ap @ ( sub @ X382 @ id ) @ X380 ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X383: term] :
~ ! [X384: subst > term > term] :
~ ! [X385: term,X386: subst] :
( ( X384 @ X386 @ X385 )
= ( sub @ X383 @ ( push @ X385 @ X386 ) ) )
=> ( ! [X387: term] :
( ( sub @ X387 @ id )
= X387 )
=> ! [X388: term,X389: term > $o,X390: subst > term > subst > $o] :
( ~ ! [X391: term] :
( ( X390 @ id @ X391 @ id )
= ( X389 @ X391 ) )
| ~ ! [X392: subst > term > term] :
( ~ ! [X393: term] :
( ( ( X390 @ id @ X393 @ id )
!= $true )
| ( ( X390 @ id @ ( X392 @ id @ X393 ) @ id )
= $true ) )
| ~ ! [X394: subst,X395: subst,X396: term] :
( ( X392 @ ( comp @ X395 @ X394 ) @ ( sub @ X396 @ X394 ) )
= ( sub @ ( X392 @ X395 @ X396 ) @ X394 ) )
| ( ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X397: term] :
( ( ( X389 @ ( sub @ X388 @ ( push @ X397 @ id ) ) )
= $true )
| ( ( X389 @ X397 )
!= $true ) )
| ( ( X389 @ ( lam @ X388 ) )
= $true ) ) ) ) )
& ( axabs = $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X398: term,X399: subst > term > subst > $o] :
( ( ( X399 @ id @ ( lam @ ( sub @ X398 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X400: subst > term > term] :
( ( ( X399 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X401: term] :
( ( ( X399 @ id @ X401 @ id )
!= $true )
| ( ( X399 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
| ~ ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X403 @ X404 ) @ ( sub @ X402 @ X404 ) )
= ( sub @ ( X400 @ X403 @ X402 ) @ X404 ) ) )
| ~ ! [X405: term] :
( ( ( X399 @ id @ X405 @ id )
!= $true )
| ( ( X399 @ id @ ( sub @ X398 @ ( push @ X405 @ id ) ) @ id )
= $true ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X406: subst,X407: term > $o,X408: term] :
( ~ ! [X409: term] :
( ( ( X407 @ ( lam @ X409 ) )
= $true )
| ~ ! [X410: term] :
( ( ( X407 @ X410 )
!= $true )
| ( ( X407 @ ( sub @ X409 @ ( push @ X410 @ id ) ) )
= $true ) ) )
| ~ ! [X411: term] :
( ( ( var @ X411 )
!= $true )
| ( $true
= ( X407 @ ( sub @ X411 @ X406 ) ) ) )
| ~ ! [X412: term,X413: term] :
( ( ( X407 @ X412 )
!= $true )
| ( ( X407 @ ( ap @ X413 @ X412 ) )
= $true )
| ( ( X407 @ X413 )
!= $true ) )
| ( ( X407 @ ( sub @ X408 @ X406 ) )
= $true ) ) )
& ( ( apinj2 = $true )
<=> ! [X414: term,X415: term,X416: term,X417: term] :
( ( ( ap @ X417 @ X414 )
!= ( ap @ X416 @ X415 ) )
| ( X414 = X415 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X418: subst,X419: term] :
( ( sub @ one @ ( push @ X419 @ X418 ) )
= X419 )
=> ( ! [X420: subst,X421: term] :
( ( comp @ sh @ ( push @ X421 @ X420 ) )
= X420 )
=> ( ! [X422: term,X423: term] :
( ( ( lam @ X423 )
!= ( lam @ X422 ) )
| ( X422 = X423 ) )
=> ! [X424: subst,X425: subst > term > term,X426: subst > term > term,X427: term] :
( ~ ! [X428: term,X429: subst,X430: subst] :
( ( sub @ ( X425 @ X430 @ X428 ) @ X429 )
= ( X425 @ ( comp @ X430 @ X429 ) @ ( sub @ X428 @ X429 ) ) )
| ~ ! [X431: subst,X432: subst,X433: term] :
( ( sub @ ( X426 @ X431 @ X433 ) @ X432 )
= ( X426 @ ( comp @ X431 @ X432 ) @ ( sub @ X433 @ X432 ) ) )
| ( ( lam @ ( X425 @ sh @ one ) )
!= ( lam @ ( X426 @ sh @ one ) ) )
| ( ( X425 @ X424 @ X427 )
= ( X426 @ X424 @ X427 ) ) ) ) ) ) )
& ( ! [X434: term] :
~ ! [X435: subst > term > term] :
( ( sub @ X434 @ ( push @ one @ sh ) )
!= ( X435 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X436: term,X437: subst > term > subst > $o] :
( ( ( X437 @ id @ ( lam @ ( sub @ X436 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X438: subst > term > term] :
( ( ( X437 @ id @ ( lam @ ( X438 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X439: subst,X440: subst,X441: term] :
( ( X438 @ ( comp @ X439 @ X440 ) @ ( sub @ X441 @ X440 ) )
= ( sub @ ( X438 @ X439 @ X441 ) @ X440 ) )
| ~ ! [X442: term] :
( ( ( X437 @ id @ X442 @ id )
!= $true )
| ( ( X437 @ id @ ( X438 @ id @ X442 ) @ id )
= $true ) ) )
| ~ ! [X443: term] :
( ( ( X437 @ id @ X443 @ id )
!= $true )
| ( ( X437 @ id @ ( sub @ X436 @ ( push @ X443 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X444: term,X445: term > $o] :
( ~ ! [X446: term,X447: term] :
( ( ( X445 @ X446 )
!= $true )
| ( ( X445 @ X447 )
!= $true )
| ( ( X445 @ ( ap @ X446 @ X447 ) )
= $true ) )
| ( ( X445 @ X444 )
= $true )
| ~ ! [X448: term] :
( ( ( X445 @ X448 )
!= $true )
| ( ( X445 @ ( lam @ X448 ) )
= $true ) )
| ~ ! [X449: term] :
( ( $true
= ( X445 @ X449 ) )
| ( ( var @ X449 )
!= $true ) ) )
<=> ( induction = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X450: subst,X451: term,X452: subst > term > term,X453: subst > term > term] :
( ~ ! [X454: term,X455: subst,X456: subst] :
( ( sub @ ( X453 @ X455 @ X454 ) @ X456 )
= ( X453 @ ( comp @ X455 @ X456 ) @ ( sub @ X454 @ X456 ) ) )
| ( ( lam @ ( X453 @ sh @ one ) )
!= ( lam @ ( X452 @ sh @ one ) ) )
| ~ ! [X457: subst,X458: term,X459: subst] :
( ( X452 @ ( comp @ X459 @ X457 ) @ ( sub @ X458 @ X457 ) )
= ( sub @ ( X452 @ X459 @ X458 ) @ X457 ) )
| ( ( X452 @ X450 @ X451 )
= ( X453 @ X450 @ X451 ) ) ) )
& ( ( laminj = $true )
<=> ! [X460: term,X461: term] :
( ( X460 = X461 )
| ( ( lam @ X460 )
!= ( lam @ X461 ) ) ) )
& ( ! [X462: subst > term > subst > $o,X463: term,X464: term] :
( ( ( X462 @ id @ X463 @ id )
!= $true )
| ~ ! [X465: term,X466: term] :
( ( ( X462 @ id @ ( ap @ ( sub @ X466 @ id ) @ X465 ) @ id )
= $true )
| ( ( X462 @ id @ X466 @ id )
!= $true )
| ( ( X462 @ id @ X465 @ id )
!= $true ) )
| ~ ! [X467: subst,X468: subst,X469: subst,X470: term] :
( ( ( X462 @ X468 @ X470 @ ( comp @ X467 @ X469 ) )
= $true )
| ( ( X462 @ ( comp @ X468 @ X467 ) @ ( sub @ X470 @ X467 ) @ X469 )
!= $true ) )
| ( ( X462 @ id @ ( ap @ X463 @ X464 ) @ id )
= $true )
| ~ ! [X471: subst,X472: term,X473: subst,X474: subst] :
( ( ( X462 @ ( comp @ X474 @ X473 ) @ ( sub @ X472 @ X473 ) @ X471 )
= $true )
| ( ( X462 @ X474 @ X472 @ ( comp @ X473 @ X471 ) )
!= $true ) )
| ( $true
!= ( X462 @ id @ X464 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ! [X475: d_subst,X476: d_subst] :
( ( ( d2subst @ X476 )
= ( d2subst @ X475 ) )
=> ( X475 = X476 ) )
& ( pushprop_lem3v2 = $true )
& ( ( ! [X477: term] :
( ( sub @ X477 @ id )
= X477 )
=> ( ! [X478: term,X479: term,X480: term,X481: term] :
( ( ( ap @ X479 @ X480 )
!= ( ap @ X481 @ X478 ) )
| ( X479 = X481 ) )
=> ! [X482: term,X483: term,X484: term,X485: term] :
( ( ( ap @ ( sub @ X483 @ id ) @ X482 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X483 = X484 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X486: term > $o,X487: subst,X488: term > $o,X489: term] :
( ~ ! [X490: term] :
( ( X486 @ ( sub @ X490 @ ( push @ X489 @ X487 ) ) )
= ( X488 @ X490 ) )
| ( ( X486 @ X489 )
!= $true )
| ( $true
= ( X488 @ one ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_lem2v2 = $true )
& ! [X491: d_term] : ( d_one = X491 )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslamnotap_gthm = $true )
& ! [X492: term] :
? [X493: d_term] :
( ( d2term @ X493 )
= X492 )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( axapp = $true )
& ( ! [X497: subst > term > subst > $o,X498: term] :
( ~ ! [X499: term] :
( ( ( X497 @ id @ ( sub @ X498 @ ( push @ X499 @ id ) ) @ id )
= $true )
| ( ( X497 @ id @ X499 @ id )
!= $true ) )
| ( ( X497 @ id @ ( lam @ ( sub @ X498 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X500: term,X501: subst > term > term] :
( ~ ! [X502: subst,X503: term,X504: subst] :
( ( X501 @ ( comp @ X504 @ X502 ) @ ( sub @ X503 @ X502 ) )
= ( sub @ X500 @ ( push @ ( sub @ X503 @ X502 ) @ ( comp @ X504 @ X502 ) ) ) )
| ~ ! [X505: subst,X506: term,X507: subst] :
( ( sub @ ( X501 @ X507 @ X506 ) @ X505 )
= ( sub @ ( sub @ X500 @ ( push @ X506 @ X507 ) ) @ X505 ) )
| ~ ! [X508: term] :
( ( $true
= ( X497 @ id @ ( X501 @ id @ X508 ) @ id ) )
| ( ( X497 @ id @ X508 @ id )
!= $true ) )
| ( ( X497 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X509: term,X510: subst] :
( ( sub @ one @ ( push @ X509 @ X510 ) )
= X509 )
=> ! [X511: term,X512: term > $o,X513: term > $o,X514: subst] :
( ( $true
!= ( X512 @ X511 ) )
| ~ ! [X515: term] :
( ( X513 @ X515 )
= ( X512 @ ( sub @ X515 @ ( push @ X511 @ X514 ) ) ) )
| ( ( X513 @ one )
= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ! [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ( ( X517 @ ( lam @ X519 ) )
= $true )
| ~ ! [X520: term,X521: subst,X522: subst,X523: subst] :
( ( $true
!= ( X518 @ X521 @ X520 @ ( comp @ X522 @ X523 ) ) )
| ( $true
= ( X518 @ ( comp @ X521 @ X522 ) @ ( sub @ X520 @ X522 ) @ X523 ) ) )
| ~ ! [X524: subst,X525: term,X526: subst,X527: subst] :
( ( $true
!= ( X518 @ ( comp @ X524 @ X526 ) @ ( sub @ X525 @ X526 ) @ X527 ) )
| ( ( X518 @ X524 @ X525 @ ( comp @ X526 @ X527 ) )
= $true ) )
| ~ ! [X528: term] :
( ( X518 @ id @ X528 @ id )
= ( X517 @ X528 ) )
| ~ ! [X529: subst > term > term] :
( ( ( X518 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X530: term,X531: subst,X532: subst] :
( ( sub @ ( X529 @ X531 @ X530 ) @ X532 )
= ( X529 @ ( comp @ X531 @ X532 ) @ ( sub @ X530 @ X532 ) ) )
| ~ ! [X533: term] :
( ( ( X518 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X518 @ id @ X533 @ id )
!= $true ) ) )
| ~ ! [X534: term] :
( ( ( X517 @ X534 )
!= $true )
| ( ( X517 @ ( sub @ X519 @ ( push @ X534 @ id ) ) )
= $true ) ) ) ) )
& ( ! [X535: term,X536: term] :
( ( ( sub @ X535 @ sh )
!= ( sub @ X536 @ sh ) )
| ( X535 = X536 ) )
<=> ( shinj = $true ) )
& ! [X537: d_subst] : ( d_id = X537 )
& ( ( axshiftcons = $true )
<=> ! [X538: subst,X539: term] :
( ( comp @ sh @ ( push @ X539 @ X538 ) )
= X538 ) )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( apnotvar = $true )
& ( termmset_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( X542 = X543 )
| ( ( ap @ X544 @ X543 )
!= ( ap @ X545 @ X542 ) ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( X546 = X548 )
| ( ( ap @ ( sub @ X549 @ id ) @ X548 )
!= ( ap @ ( sub @ X547 @ id ) @ X546 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( hoasinduction_no_psi_cond
<=> ! [X0: term,X1: subst > term > subst > $o] :
( ~ ! [X2: term,X3: term] :
( ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id )
| ~ ( X1 @ id @ X3 @ id )
| ~ ( X1 @ id @ X2 @ id ) )
| ~ ! [X4: subst > term > term] :
( ( X1 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
| ~ ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
| ~ ! [X8: term] :
( ~ ( X1 @ id @ X8 @ id )
| ( X1 @ id @ ( X4 @ id @ X8 ) @ id ) ) )
| ( X1 @ id @ X0 @ id ) ) )
& hoasinduction_lem2_gthm
& ( pushprop_p_and_p_prime
= ( ^ [X9: term,X10: subst,X11: term > $o,X12: term > $o] :
! [X13: term] :
( ( X12 @ X13 )
= ( X11 @ ( sub @ X13 @ ( push @ X9 @ X10 ) ) ) ) ) )
& axassoc
& pushprop_lem2v2_gthm
& pushprop_gthm
& ( ! [X14: term,X15: term > $o,X16: term,X17: subst > term > subst > $o] :
( ~ ( X15 @ X14 )
| ~ ! [X18: term] :
( ( X15 @ X18 )
= ( X17 @ id @ X18 @ id ) )
| ~ ! [X19: subst,X20: subst,X21: subst,X22: term] :
( ~ ( X17 @ ( comp @ X20 @ X21 ) @ ( sub @ X22 @ X21 ) @ X19 )
| ( X17 @ X20 @ X22 @ ( comp @ X21 @ X19 ) ) )
| ( X15 @ ( ap @ X16 @ X14 ) )
| ~ ( X15 @ X16 )
| ~ ! [X23: subst,X24: term,X25: subst,X26: subst] :
( ~ ( X17 @ X25 @ X24 @ ( comp @ X23 @ X26 ) )
| ( X17 @ ( comp @ X25 @ X23 ) @ ( sub @ X24 @ X23 ) @ X26 ) )
| ~ ! [X27: term,X28: term] :
( ( X17 @ id @ ( ap @ ( sub @ X28 @ id ) @ X27 ) @ id )
| ~ ( X17 @ id @ X27 @ id )
| ~ ( X17 @ id @ X28 @ id ) ) )
<=> hoasinduction_lem2v2 )
& hoasinduction_lem2_lthm
& ( ! [X29: subst] :
( ( push @ ( sub @ one @ X29 ) @ ( comp @ sh @ X29 ) )
= X29 )
<=> axscons )
& ( ( ! [X30: term] :
( ( sub @ X30 @ id )
= X30 )
=> ( ! [X31: term > $o,X32: term,X33: subst] :
( ~ ! [X34: term,X35: term] :
( ~ ( X31 @ X35 )
| ( X31 @ ( ap @ X34 @ X35 ) )
| ~ ( X31 @ X34 ) )
| ~ ! [X36: term] :
( ( X31 @ ( lam @ X36 ) )
| ~ ! [X37: term] :
( ~ ( X31 @ X37 )
| ( X31 @ ( sub @ X36 @ ( push @ X37 @ id ) ) ) ) )
| ~ ! [X38: term] :
( ( X31 @ ( sub @ X38 @ X33 ) )
| ~ ( var @ X38 ) )
| ( X31 @ ( sub @ X32 @ X33 ) ) )
=> ! [X39: term,X40: term > $o] :
( ~ ! [X41: term] :
( ~ ! [X42: term] :
( ( X40 @ ( sub @ X41 @ ( push @ X42 @ id ) ) )
| ~ ( X40 @ X42 ) )
| ( X40 @ ( lam @ X41 ) ) )
| ( X40 @ X39 )
| ~ ! [X43: term,X44: term] :
( ( X40 @ ( ap @ X44 @ X43 ) )
| ~ ( X40 @ X44 )
| ~ ( X40 @ X43 ) )
| ~ ! [X45: term] :
( ~ ( var @ X45 )
| ( X40 @ X45 ) ) ) ) )
<=> induction2_lthm )
& hoasinduction_lem3a_gthm
& ( ( d2subst @ d_id )
= sh )
& ( substmonoid
<=> ( ! [X46: subst] :
( ( comp @ X46 @ id )
= X46 )
& ! [X47: subst] :
( ( comp @ id @ X47 )
= X47 ) ) )
& hoasinduction_lem1v2
& ulamvarsh
& axvarshift
& ( ( ! [X48: term] :
( ( sub @ X48 @ id )
= X48 )
=> ( ! [X49: subst > term > subst > $o,X50: term] :
( ~ ! [X51: subst > term > term] :
( ~ ! [X52: term] :
( ( X49 @ id @ ( X51 @ id @ X52 ) @ id )
| ~ ( X49 @ id @ X52 @ id ) )
| ( X49 @ id @ ( lam @ ( X51 @ sh @ one ) ) @ id )
| ~ ! [X53: subst,X54: term,X55: subst] :
( ( X51 @ ( comp @ X55 @ X53 ) @ ( sub @ X54 @ X53 ) )
= ( sub @ ( X51 @ X55 @ X54 ) @ X53 ) ) )
| ~ ! [X56: term] :
( ( X49 @ id @ ( sub @ X50 @ ( push @ X56 @ id ) ) @ id )
| ~ ( X49 @ id @ X56 @ id ) )
| ( X49 @ id @ ( lam @ ( sub @ X50 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X57: term,X58: subst > term > subst > $o] :
( ~ ! [X59: subst > term > term] :
( ( X58 @ id @ ( lam @ ( X59 @ sh @ one ) ) @ id )
| ~ ! [X60: term] :
( ~ ( X58 @ id @ X60 @ id )
| ( X58 @ id @ ( X59 @ id @ X60 ) @ id ) )
| ~ ! [X61: subst,X62: subst,X63: term] :
( ( X59 @ ( comp @ X62 @ X61 ) @ ( sub @ X63 @ X61 ) )
= ( sub @ ( X59 @ X62 @ X63 ) @ X61 ) ) )
| ~ ! [X64: term] :
( ( X58 @ id @ ( sub @ X57 @ ( push @ X64 @ id ) ) @ id )
| ~ ( X58 @ id @ X64 @ id ) )
| ( X58 @ id @ ( lam @ X57 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& hoasapinj2_gthm
& hoasinduction_lem1_gthm
& ( hoasinduction_lem3
<=> ! [X65: subst > term > subst > $o,X66: term] :
( ~ ! [X67: subst > term > term] :
( ~ ! [X68: term,X69: subst,X70: subst] :
( ( sub @ ( X67 @ X70 @ X68 ) @ X69 )
= ( X67 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) ) )
| ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
| ~ ! [X71: term] :
( ~ ( X65 @ id @ X71 @ id )
| ( X65 @ id @ ( X67 @ id @ X71 ) @ id ) ) )
| ~ ! [X72: subst,X73: term,X74: subst,X75: subst] :
( ~ ( X65 @ ( comp @ X74 @ X75 ) @ ( sub @ X73 @ X75 ) @ X72 )
| ( X65 @ X74 @ X73 @ ( comp @ X75 @ X72 ) ) )
| ~ ! [X76: subst,X77: subst,X78: subst,X79: term] :
( ~ ( X65 @ X78 @ X79 @ ( comp @ X76 @ X77 ) )
| ( X65 @ ( comp @ X78 @ X76 ) @ ( sub @ X79 @ X76 ) @ X77 ) )
| ~ ! [X80: term] :
( ( X65 @ id @ ( sub @ X66 @ ( push @ X80 @ id ) ) @ id )
| ~ ( X65 @ id @ X80 @ id ) )
| ( X65 @ id @ ( lam @ X66 ) @ id ) ) )
& ( ! [X81: subst > term > term,X82: term,X83: term] :
( ~ ! [X84: term,X85: subst,X86: subst] :
( ( X81 @ ( comp @ X85 @ X86 ) @ ( sub @ X84 @ X86 ) )
= ( sub @ ( X81 @ X85 @ X84 ) @ X86 ) )
| ( ( lam @ ( X81 @ sh @ one ) )
!= ( ap @ ( sub @ X82 @ id ) @ X83 ) ) )
<=> hoaslamnotap )
& hoasapinj1_gthm
& ( substmonoid_lthm
<=> ( ! [X87: subst] :
( ( comp @ id @ X87 )
= X87 )
=> ( ! [X88: subst] :
( ( comp @ X88 @ id )
= X88 )
=> ( ! [X89: subst] :
( ( comp @ id @ X89 )
= X89 )
& ! [X90: subst] :
( ( comp @ X90 @ id )
= X90 ) ) ) ) )
& hoasapnotvar
& ( hoasapinj2
<=> ! [X91: term,X92: term,X93: term,X94: term] :
( ( ( ap @ ( sub @ X91 @ id ) @ X94 )
!= ( ap @ ( sub @ X92 @ id ) @ X93 ) )
| ( X93 = X94 ) ) )
& ( pushprop_lem1
<=> ! [X95: term,X96: term > $o,X97: subst,X98: term > $o,X99: term] :
( ~ ( X98 @ X99 )
| ( X96 @ ( sub @ X99 @ ( push @ X95 @ X97 ) ) ) ) )
& pushprop_lem2v2_lthm
& hoasinduction_lem1_lthm
& ( hoasinduction_lem3_lthm
<=> ( ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
=> ( ! [X101: term,X102: subst > term > subst > $o] :
( ~ ! [X103: subst > term > term] :
( ( X102 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id )
| ~ ! [X104: term,X105: subst,X106: subst] :
( ( X103 @ ( comp @ X106 @ X105 ) @ ( sub @ X104 @ X105 ) )
= ( sub @ ( X103 @ X106 @ X104 ) @ X105 ) )
| ~ ! [X107: term] :
( ~ ( X102 @ id @ X107 @ id )
| ( X102 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
| ( X102 @ id @ ( lam @ ( sub @ X101 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X108: term] :
( ~ ( X102 @ id @ X108 @ id )
| ( X102 @ id @ ( sub @ X101 @ ( push @ X108 @ id ) ) @ id ) ) )
=> ! [X109: term,X110: subst > term > subst > $o] :
( ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( X110 @ X114 @ X112 @ ( comp @ X113 @ X111 ) )
| ~ ( X110 @ ( comp @ X114 @ X113 ) @ ( sub @ X112 @ X113 ) @ X111 ) )
| ~ ! [X115: term,X116: subst,X117: subst,X118: subst] :
( ( X110 @ ( comp @ X117 @ X118 ) @ ( sub @ X115 @ X118 ) @ X116 )
| ~ ( X110 @ X117 @ X115 @ ( comp @ X118 @ X116 ) ) )
| ( X110 @ id @ ( lam @ X109 ) @ id )
| ~ ! [X119: term] :
( ~ ( X110 @ id @ X119 @ id )
| ( X110 @ id @ ( sub @ X109 @ ( push @ X119 @ id ) ) @ id ) )
| ~ ! [X120: subst > term > term] :
( ( X110 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id )
| ~ ! [X121: term] :
( ~ ( X110 @ id @ X121 @ id )
| ( X110 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ~ ! [X122: subst,X123: subst,X124: term] :
( ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) )
= ( sub @ ( X120 @ X122 @ X124 ) @ X123 ) ) ) ) ) ) )
& ( induction2
<=> ! [X125: term > $o,X126: term] :
( ~ ! [X127: term] :
( ~ ( var @ X127 )
| ( X125 @ X127 ) )
| ~ ! [X128: term,X129: term] :
( ~ ( X125 @ X128 )
| ~ ( X125 @ X129 )
| ( X125 @ ( ap @ X128 @ X129 ) ) )
| ~ ! [X130: term] :
( ~ ! [X131: term] :
( ( X125 @ ( sub @ X130 @ ( push @ X131 @ id ) ) )
| ~ ( X125 @ X131 ) )
| ( X125 @ ( lam @ X130 ) ) )
| ( X125 @ X126 ) ) )
& ~ ulamvar1
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& hoasinduction_lem1v2_gthm
& ( ! [X132: subst,X133: term] :
( ( sub @ one @ ( push @ X133 @ X132 ) )
= X133 )
<=> axvarcons )
& ( ( ! [X134: subst > term > subst > $o] :
~ ! [X135: term > $o] :
~ ! [X136: term] :
( ( X134 @ id @ X136 @ id )
= ( X135 @ X136 ) )
=> ( ! [X137: term > $o,X138: term] :
( ~ ! [X139: term] :
( ( X137 @ X139 )
| ~ ( var @ X139 ) )
| ~ ! [X140: term,X141: term] :
( ~ ( X137 @ X141 )
| ~ ( X137 @ X140 )
| ( X137 @ ( ap @ X140 @ X141 ) ) )
| ~ ! [X142: term] :
( ~ ! [X143: term] :
( ~ ( X137 @ X143 )
| ( X137 @ ( sub @ X142 @ ( push @ X143 @ id ) ) ) )
| ( X137 @ ( lam @ X142 ) ) )
| ( X137 @ X138 ) )
=> ( ! [X144: term] :
( ( sub @ X144 @ id )
= X144 )
=> ( ! [X145: term > $o,X146: term,X147: subst > term > subst > $o] :
( ~ ! [X148: subst > term > term] :
( ( X147 @ id @ ( lam @ ( X148 @ sh @ one ) ) @ id )
| ~ ! [X149: term] :
( ( X147 @ id @ ( X148 @ id @ X149 ) @ id )
| ~ ( X147 @ id @ X149 @ id ) )
| ~ ! [X150: subst,X151: term,X152: subst] :
( ( sub @ ( X148 @ X152 @ X151 ) @ X150 )
= ( X148 @ ( comp @ X152 @ X150 ) @ ( sub @ X151 @ X150 ) ) ) )
| ~ ! [X153: term] :
( ( X147 @ id @ X153 @ id )
= ( X145 @ X153 ) )
| ~ ! [X154: term] :
( ~ ( X145 @ X154 )
| ( X145 @ ( sub @ X146 @ ( push @ X154 @ id ) ) ) )
| ( X145 @ ( lam @ X146 ) ) )
=> ! [X155: subst > term > subst > $o,X156: term] :
( ~ ! [X157: term,X158: term] :
( ( X155 @ id @ ( ap @ ( sub @ X157 @ id ) @ X158 ) @ id )
| ~ ( X155 @ id @ X158 @ id )
| ~ ( X155 @ id @ X157 @ id ) )
| ~ ! [X159: term] :
( ~ ( var @ ( sub @ X159 @ id ) )
| ( X155 @ id @ X159 @ id ) )
| ~ ! [X160: subst,X161: term,X162: subst,X163: subst] :
( ( X155 @ X163 @ X161 @ ( comp @ X160 @ X162 ) )
| ~ ( X155 @ ( comp @ X163 @ X160 ) @ ( sub @ X161 @ X160 ) @ X162 ) )
| ~ ! [X164: subst > term > term] :
( ~ ! [X165: term,X166: subst,X167: subst] :
( ( X164 @ ( comp @ X167 @ X166 ) @ ( sub @ X165 @ X166 ) )
= ( sub @ ( X164 @ X167 @ X165 ) @ X166 ) )
| ( X155 @ id @ ( lam @ ( X164 @ sh @ one ) ) @ id )
| ~ ! [X168: term] :
( ~ ( X155 @ id @ X168 @ id )
| ( X155 @ id @ ( X164 @ id @ X168 ) @ id ) ) )
| ~ ! [X169: subst,X170: subst,X171: subst,X172: term] :
( ~ ( X155 @ X171 @ X172 @ ( comp @ X170 @ X169 ) )
| ( X155 @ ( comp @ X171 @ X170 ) @ ( sub @ X172 @ X170 ) @ X169 ) )
| ( X155 @ id @ X156 @ id ) ) ) ) ) )
<=> hoasinduction_lthm_3 )
& ( hoasinduction_lem0_lthm
<=> ! [X173: subst > term > subst > $o] :
~ ! [X174: term > $o] :
~ ! [X175: term] :
( ( X173 @ id @ X175 @ id )
= ( X174 @ X175 ) ) )
& hoasinduction_lem3_gthm
& hoaslamnotvar_gthm
& pushprop_lem1v2_gthm
& hoasinduction_lem1
& ( hoasinduction_lem0
<=> ! [X176: subst > term > subst > $o] :
~ ! [X177: term > $o] :
~ ! [X178: term] :
( ( X176 @ id @ X178 @ id )
= ( X177 @ X178 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X179: term] :
~ ! [X180: subst > term > term] :
~ ! [X181: term,X182: subst] :
( ( X180 @ X182 @ X181 )
= ( sub @ X179 @ ( push @ X181 @ X182 ) ) )
<=> hoasinduction_lem3v2_f )
& ( axvarid
<=> ! [X183: term] :
( ( sub @ X183 @ id )
= X183 ) )
& ( hoasinduction_lthm
<=> ( ! [X184: term > $o,X185: term] :
( ~ ! [X186: term] :
( ~ ! [X187: term] :
( ~ ( X184 @ X187 )
| ( X184 @ ( sub @ X186 @ ( push @ X187 @ id ) ) ) )
| ( X184 @ ( lam @ X186 ) ) )
| ~ ! [X188: term,X189: term] :
( ~ ( X184 @ X189 )
| ( X184 @ ( ap @ X189 @ X188 ) )
| ~ ( X184 @ X188 ) )
| ~ ! [X190: term] :
( ~ ( var @ X190 )
| ( X184 @ X190 ) )
| ( X184 @ X185 ) )
=> ( ! [X191: term,X192: term,X193: subst > term > subst > $o] :
( ( X193 @ id @ ( ap @ X191 @ X192 ) @ id )
| ~ ( X193 @ id @ X192 @ id )
| ~ ! [X194: term,X195: term] :
( ( X193 @ id @ ( ap @ ( sub @ X194 @ id ) @ X195 ) @ id )
| ~ ( X193 @ id @ X194 @ id )
| ~ ( X193 @ id @ X195 @ id ) )
| ~ ( X193 @ id @ X191 @ id )
| ~ ! [X196: term,X197: subst,X198: subst,X199: subst] :
( ( X193 @ X199 @ X196 @ ( comp @ X198 @ X197 ) )
| ~ ( X193 @ ( comp @ X199 @ X198 ) @ ( sub @ X196 @ X198 ) @ X197 ) )
| ~ ! [X200: term,X201: subst,X202: subst,X203: subst] :
( ~ ( X193 @ X202 @ X200 @ ( comp @ X203 @ X201 ) )
| ( X193 @ ( comp @ X202 @ X203 ) @ ( sub @ X200 @ X203 ) @ X201 ) ) )
=> ( ! [X204: term,X205: subst > term > subst > $o] :
( ~ ! [X206: subst,X207: subst,X208: subst,X209: term] :
( ( X205 @ ( comp @ X206 @ X207 ) @ ( sub @ X209 @ X207 ) @ X208 )
| ~ ( X205 @ X206 @ X209 @ ( comp @ X207 @ X208 ) ) )
| ( X205 @ id @ ( lam @ X204 ) @ id )
| ~ ! [X210: term] :
( ~ ( X205 @ id @ X210 @ id )
| ( X205 @ id @ ( sub @ X204 @ ( push @ X210 @ id ) ) @ id ) )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: term] :
( ( X205 @ id @ ( X211 @ id @ X212 ) @ id )
| ~ ( X205 @ id @ X212 @ id ) )
| ( X205 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id )
| ~ ! [X213: term,X214: subst,X215: subst] :
( ( sub @ ( X211 @ X215 @ X213 ) @ X214 )
= ( X211 @ ( comp @ X215 @ X214 ) @ ( sub @ X213 @ X214 ) ) ) )
| ~ ! [X216: subst,X217: term,X218: subst,X219: subst] :
( ~ ( X205 @ ( comp @ X218 @ X219 ) @ ( sub @ X217 @ X219 ) @ X216 )
| ( X205 @ X218 @ X217 @ ( comp @ X219 @ X216 ) ) ) )
=> ! [X220: subst > term > subst > $o,X221: term] :
( ( X220 @ id @ X221 @ id )
| ~ ! [X222: term] :
( ~ ( var @ ( sub @ X222 @ id ) )
| ( X220 @ id @ X222 @ id ) )
| ~ ! [X223: subst > term > term] :
( ~ ! [X224: term,X225: subst,X226: subst] :
( ( sub @ ( X223 @ X225 @ X224 ) @ X226 )
= ( X223 @ ( comp @ X225 @ X226 ) @ ( sub @ X224 @ X226 ) ) )
| ~ ! [X227: term] :
( ~ ( X220 @ id @ X227 @ id )
| ( X220 @ id @ ( X223 @ id @ X227 ) @ id ) )
| ( X220 @ id @ ( lam @ ( X223 @ sh @ one ) ) @ id ) )
| ~ ! [X228: term,X229: subst,X230: subst,X231: subst] :
( ( X220 @ X230 @ X228 @ ( comp @ X231 @ X229 ) )
| ~ ( X220 @ ( comp @ X230 @ X231 ) @ ( sub @ X228 @ X231 ) @ X229 ) )
| ~ ! [X232: subst,X233: subst,X234: subst,X235: term] :
( ~ ( X220 @ X234 @ X235 @ ( comp @ X233 @ X232 ) )
| ( X220 @ ( comp @ X234 @ X233 ) @ ( sub @ X235 @ X233 ) @ X232 ) )
| ~ ! [X236: term,X237: term] :
( ~ ( X220 @ id @ X236 @ id )
| ( X220 @ id @ ( ap @ ( sub @ X237 @ id ) @ X236 ) @ id )
| ~ ( X220 @ id @ X237 @ id ) ) ) ) ) ) )
& ( ! [X238: term,X239: subst > term > subst > $o] :
( ( X239 @ id @ ( lam @ X238 ) @ id )
| ~ ! [X240: subst > term > term] :
( ~ ! [X241: subst,X242: subst,X243: term] :
( ( X240 @ ( comp @ X241 @ X242 ) @ ( sub @ X243 @ X242 ) )
= ( sub @ ( X240 @ X241 @ X243 ) @ X242 ) )
| ( X239 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
| ~ ! [X244: term] :
( ( X239 @ id @ ( X240 @ id @ X244 ) @ id )
| ~ ( X239 @ id @ X244 @ id ) ) )
| ~ ! [X245: term] :
( ( X239 @ id @ ( sub @ X238 @ ( push @ X245 @ id ) ) @ id )
| ~ ( X239 @ id @ X245 @ id ) ) )
<=> hoasinduction_lem3a )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X246: subst,X247: term,X248: term > $o] :
~ ! [X249: term > $o] :
~ ! [X250: term] :
( ( X248 @ ( sub @ X250 @ ( push @ X247 @ X246 ) ) )
= ( X249 @ X250 ) )
<=> pushprop_lem0_lthm )
& ( hoasinduction_lem3v2a
<=> ! [X251: subst > term > subst > $o,X252: term > $o,X253: term] :
( ( X252 @ ( lam @ X253 ) )
| ~ ! [X254: term] :
( ( X251 @ id @ X254 @ id )
= ( X252 @ X254 ) )
| ~ ! [X255: subst > term > term] :
( ~ ! [X256: term] :
( ( X251 @ id @ ( X255 @ id @ X256 ) @ id )
| ~ ( X251 @ id @ X256 @ id ) )
| ~ ! [X257: subst,X258: term,X259: subst] :
( ( X255 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X255 @ X257 @ X258 ) @ X259 ) )
| ( X251 @ id @ ( lam @ ( X255 @ sh @ one ) ) @ id ) )
| ~ ! [X260: term] :
( ( X252 @ ( sub @ X253 @ ( push @ X260 @ id ) ) )
| ~ ( X252 @ X260 ) ) ) )
& hoaslaminj_gthm
& ( termmset
<=> ! [X261: term] :
( ( sub @ X261 @ id )
= X261 ) )
& ~ lamnotap
& ulamvarind
& ( axidl
<=> ! [X262: subst] :
( ( comp @ id @ X262 )
= X262 ) )
& ( ! [X263: subst] :
( ( comp @ X263 @ id )
= X263 )
<=> axidr )
& ( pushprop_lem0
<=> ! [X264: term > $o,X265: subst,X266: term] :
~ ! [X267: term > $o] :
~ ! [X268: term] :
( ( X267 @ X268 )
= ( X264 @ ( sub @ X268 @ ( push @ X266 @ X265 ) ) ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X269: subst > term > subst > $o] :
~ ! [X270: term > $o] :
~ ! [X271: term] :
( ( X269 @ id @ X271 @ id )
= ( X270 @ X271 ) )
=> ( ! [X272: term > $o,X273: term] :
( ~ ! [X274: term,X275: term] :
( ( X272 @ ( ap @ X275 @ X274 ) )
| ~ ( X272 @ X275 )
| ~ ( X272 @ X274 ) )
| ~ ! [X276: term] :
( ~ ( var @ X276 )
| ( X272 @ X276 ) )
| ~ ! [X277: term] :
( ~ ! [X278: term] :
( ~ ( X272 @ X278 )
| ( X272 @ ( sub @ X277 @ ( push @ X278 @ id ) ) ) )
| ( X272 @ ( lam @ X277 ) ) )
| ( X272 @ X273 ) )
=> ( ! [X279: term] :
( ( sub @ X279 @ id )
= X279 )
=> ( ! [X280: subst > term > subst > $o,X281: term,X282: term > $o] :
( ~ ! [X283: subst > term > term] :
( ~ ! [X284: term] :
( ~ ( X280 @ id @ X284 @ id )
| ( X280 @ id @ ( X283 @ id @ X284 ) @ id ) )
| ( X280 @ id @ ( lam @ ( X283 @ sh @ one ) ) @ id )
| ~ ! [X285: term,X286: subst,X287: subst] :
( ( X283 @ ( comp @ X287 @ X286 ) @ ( sub @ X285 @ X286 ) )
= ( sub @ ( X283 @ X287 @ X285 ) @ X286 ) ) )
| ( X282 @ ( lam @ X281 ) )
| ~ ! [X288: term] :
( ( X282 @ X288 )
= ( X280 @ id @ X288 @ id ) )
| ~ ! [X289: term] :
( ( X282 @ ( sub @ X281 @ ( push @ X289 @ id ) ) )
| ~ ( X282 @ X289 ) ) )
=> ! [X290: term,X291: subst > term > subst > $o] :
( ~ ! [X292: subst > term > term] :
( ~ ! [X293: subst,X294: term,X295: subst] :
( ( X292 @ ( comp @ X293 @ X295 ) @ ( sub @ X294 @ X295 ) )
= ( sub @ ( X292 @ X293 @ X294 ) @ X295 ) )
| ( X291 @ id @ ( lam @ ( X292 @ sh @ one ) ) @ id )
| ~ ! [X296: term] :
( ( X291 @ id @ ( X292 @ id @ X296 ) @ id )
| ~ ( X291 @ id @ X296 @ id ) ) )
| ( X291 @ id @ X290 @ id )
| ~ ! [X297: term,X298: term] :
( ( X291 @ id @ ( ap @ ( sub @ X297 @ id ) @ X298 ) @ id )
| ~ ( X291 @ id @ X297 @ id )
| ~ ( X291 @ id @ X298 @ id ) ) ) ) ) ) ) )
& hoasapnotvar_gthm
& pushprop_lthm
& pushprop_lem3v2_lthm
& ! [X299: d_term,X300: d_term] :
( ( ( d2term @ X299 )
= ( d2term @ X300 ) )
=> ( X299 = X300 ) )
& ! [X301: subst] :
? [X302: d_subst] :
( ( d2subst @ X302 )
= X301 )
& ( ( ! [X303: term] :
( ( sub @ X303 @ id )
= X303 )
=> ! [X304: term] :
( ( sub @ X304 @ id )
= X304 ) )
<=> termmset_lthm )
& hoaslamnotap_lthm
& ( pushprop_lem1_lthm
<=> ( ! [X305: term,X306: subst] :
( ( sub @ one @ ( push @ X305 @ X306 ) )
= X305 )
=> ( ! [X307: term,X308: subst] :
( ( comp @ sh @ ( push @ X307 @ X308 ) )
= X308 )
=> ! [X309: term,X310: subst,X311: term,X312: term > $o,X313: term > $o] :
( ( X313 @ ( sub @ X311 @ ( push @ X309 @ X310 ) ) )
| ~ ( X312 @ X311 ) ) ) ) )
& lamnotvar
& ( hoasinduction
<=> ! [X314: term,X315: subst > term > subst > $o] :
( ~ ! [X316: term] :
( ( X315 @ id @ X316 @ id )
| ~ ( var @ ( sub @ X316 @ id ) ) )
| ( X315 @ id @ X314 @ id )
| ~ ! [X317: subst,X318: subst,X319: term,X320: subst] :
( ( X315 @ X320 @ X319 @ ( comp @ X317 @ X318 ) )
| ~ ( X315 @ ( comp @ X320 @ X317 ) @ ( sub @ X319 @ X317 ) @ X318 ) )
| ~ ! [X321: term,X322: subst,X323: subst,X324: subst] :
( ( X315 @ ( comp @ X323 @ X324 ) @ ( sub @ X321 @ X324 ) @ X322 )
| ~ ( X315 @ X323 @ X321 @ ( comp @ X324 @ X322 ) ) )
| ~ ! [X325: subst > term > term] :
( ( X315 @ id @ ( lam @ ( X325 @ sh @ one ) ) @ id )
| ~ ! [X326: subst,X327: term,X328: subst] :
( ( X325 @ ( comp @ X326 @ X328 ) @ ( sub @ X327 @ X328 ) )
= ( sub @ ( X325 @ X326 @ X327 ) @ X328 ) )
| ~ ! [X329: term] :
( ( X315 @ id @ ( X325 @ id @ X329 ) @ id )
| ~ ( X315 @ id @ X329 @ id ) ) )
| ~ ! [X330: term,X331: term] :
( ( X315 @ id @ ( ap @ ( sub @ X331 @ id ) @ X330 ) @ id )
| ~ ( X315 @ id @ X330 @ id )
| ~ ( X315 @ id @ X331 @ id ) ) ) )
& pushprop_lem0_gthm
& pushprop
& ~ ( var @ ( d2term @ d_one ) )
& ( hoasinduction_lem3b
<=> ! [X332: term] :
~ ! [X333: subst > term > term] :
( ( sub @ X332 @ ( push @ one @ sh ) )
!= ( X333 @ sh @ one ) ) )
& ( ! [X334: term] :
~ ! [X335: subst > term > term] :
~ ! [X336: term,X337: subst] :
( ( X335 @ X337 @ X336 )
= ( sub @ X334 @ ( push @ X336 @ X337 ) ) )
<=> hoasinduction_lem3v2_f_lthm )
& induction2_gthm
& hoaslamnotvar_lthm
& axclos
& ( ( ! [X338: term,X339: subst] :
( ( sub @ one @ ( push @ X338 @ X339 ) )
= X338 )
=> ( ! [X340: subst,X341: term] :
( ( comp @ sh @ ( push @ X341 @ X340 ) )
= X340 )
=> ( ! [X342: subst] :
( ( comp @ X342 @ id )
= X342 )
=> ( ! [X343: term,X344: term > $o] :
( ~ ! [X345: term] :
( ~ ( var @ X345 )
| ( X344 @ X345 ) )
| ~ ! [X346: term] :
( ( X344 @ ( lam @ X346 ) )
| ~ ( X344 @ X346 ) )
| ( X344 @ X343 )
| ~ ! [X347: term,X348: term] :
( ~ ( X344 @ X347 )
| ( X344 @ ( ap @ X348 @ X347 ) )
| ~ ( X344 @ X348 ) ) )
=> ! [X349: subst,X350: term,X351: term > $o] :
( ~ ! [X352: term] :
( ~ ! [X353: term] :
( ( X351 @ ( sub @ X352 @ ( push @ X353 @ id ) ) )
| ~ ( X351 @ X353 ) )
| ( X351 @ ( lam @ X352 ) ) )
| ~ ! [X354: term,X355: term] :
( ~ ( X351 @ X354 )
| ( X351 @ ( ap @ X355 @ X354 ) )
| ~ ( X351 @ X355 ) )
| ( X351 @ ( sub @ X350 @ X349 ) )
| ~ ! [X356: term] :
( ~ ( var @ X356 )
| ( X351 @ ( sub @ X356 @ X349 ) ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoaslamnotvar
& ( hoasinduction_lem3v2
<=> ! [X357: term,X358: term > $o,X359: subst > term > subst > $o] :
( ~ ! [X360: term] :
( ( X358 @ ( sub @ X357 @ ( push @ X360 @ id ) ) )
| ~ ( X358 @ X360 ) )
| ~ ! [X361: term] :
( ( X359 @ id @ X361 @ id )
= ( X358 @ X361 ) )
| ~ ! [X362: subst,X363: subst,X364: term,X365: subst] :
( ( X359 @ X363 @ X364 @ ( comp @ X365 @ X362 ) )
| ~ ( X359 @ ( comp @ X363 @ X365 ) @ ( sub @ X364 @ X365 ) @ X362 ) )
| ( X358 @ ( lam @ X357 ) )
| ~ ! [X366: subst > term > term] :
( ~ ! [X367: subst,X368: subst,X369: term] :
( ( sub @ ( X366 @ X368 @ X369 ) @ X367 )
= ( X366 @ ( comp @ X368 @ X367 ) @ ( sub @ X369 @ X367 ) ) )
| ( X359 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id )
| ~ ! [X370: term] :
( ( X359 @ id @ ( X366 @ id @ X370 ) @ id )
| ~ ( X359 @ id @ X370 @ id ) ) )
| ~ ! [X371: subst,X372: subst,X373: term,X374: subst] :
( ~ ( X359 @ X371 @ X373 @ ( comp @ X374 @ X372 ) )
| ( X359 @ ( comp @ X371 @ X374 ) @ ( sub @ X373 @ X374 ) @ X372 ) ) ) )
& ( apinj1
<=> ! [X375: term,X376: term,X377: term,X378: term] :
( ( ( ap @ X375 @ X376 )
!= ( ap @ X377 @ X378 ) )
| ( X375 = X377 ) ) )
& hoasinduction_gthm
& ( hoasapinj1
<=> ! [X379: term,X380: term,X381: term,X382: term] :
( ( X379 = X382 )
| ( ( ap @ ( sub @ X379 @ id ) @ X381 )
!= ( ap @ ( sub @ X382 @ id ) @ X380 ) ) ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X383: term] :
~ ! [X384: subst > term > term] :
~ ! [X385: term,X386: subst] :
( ( X384 @ X386 @ X385 )
= ( sub @ X383 @ ( push @ X385 @ X386 ) ) )
=> ( ! [X387: term] :
( ( sub @ X387 @ id )
= X387 )
=> ! [X388: term,X389: term > $o,X390: subst > term > subst > $o] :
( ~ ! [X391: term] :
( ( X390 @ id @ X391 @ id )
= ( X389 @ X391 ) )
| ~ ! [X392: subst > term > term] :
( ~ ! [X393: term] :
( ~ ( X390 @ id @ X393 @ id )
| ( X390 @ id @ ( X392 @ id @ X393 ) @ id ) )
| ~ ! [X394: subst,X395: subst,X396: term] :
( ( X392 @ ( comp @ X395 @ X394 ) @ ( sub @ X396 @ X394 ) )
= ( sub @ ( X392 @ X395 @ X396 ) @ X394 ) )
| ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
| ~ ! [X397: term] :
( ( X389 @ ( sub @ X388 @ ( push @ X397 @ id ) ) )
| ~ ( X389 @ X397 ) )
| ( X389 @ ( lam @ X388 ) ) ) ) ) )
& axabs
& ( hoasinduction_lem3aa
<=> ! [X398: term,X399: subst > term > subst > $o] :
( ( X399 @ id @ ( lam @ ( sub @ X398 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X400: subst > term > term] :
( ( X399 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
| ~ ! [X401: term] :
( ~ ( X399 @ id @ X401 @ id )
| ( X399 @ id @ ( X400 @ id @ X401 ) @ id ) )
| ~ ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X403 @ X404 ) @ ( sub @ X402 @ X404 ) )
= ( sub @ ( X400 @ X403 @ X402 ) @ X404 ) ) )
| ~ ! [X405: term] :
( ~ ( X399 @ id @ X405 @ id )
| ( X399 @ id @ ( sub @ X398 @ ( push @ X405 @ id ) ) @ id ) ) ) )
& ( induction2lem
<=> ! [X406: subst,X407: term > $o,X408: term] :
( ~ ! [X409: term] :
( ( X407 @ ( lam @ X409 ) )
| ~ ! [X410: term] :
( ~ ( X407 @ X410 )
| ( X407 @ ( sub @ X409 @ ( push @ X410 @ id ) ) ) ) )
| ~ ! [X411: term] :
( ~ ( var @ X411 )
| ( X407 @ ( sub @ X411 @ X406 ) ) )
| ~ ! [X412: term,X413: term] :
( ~ ( X407 @ X412 )
| ( X407 @ ( ap @ X413 @ X412 ) )
| ~ ( X407 @ X413 ) )
| ( X407 @ ( sub @ X408 @ X406 ) ) ) )
& ( apinj2
<=> ! [X414: term,X415: term,X416: term,X417: term] :
( ( ( ap @ X417 @ X414 )
!= ( ap @ X416 @ X415 ) )
| ( X414 = X415 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoaslaminj_lthm
<=> ( ! [X418: subst,X419: term] :
( ( sub @ one @ ( push @ X419 @ X418 ) )
= X419 )
=> ( ! [X420: subst,X421: term] :
( ( comp @ sh @ ( push @ X421 @ X420 ) )
= X420 )
=> ( ! [X422: term,X423: term] :
( ( ( lam @ X423 )
!= ( lam @ X422 ) )
| ( X422 = X423 ) )
=> ! [X424: subst,X425: subst > term > term,X426: subst > term > term,X427: term] :
( ~ ! [X428: term,X429: subst,X430: subst] :
( ( sub @ ( X425 @ X430 @ X428 ) @ X429 )
= ( X425 @ ( comp @ X430 @ X429 ) @ ( sub @ X428 @ X429 ) ) )
| ~ ! [X431: subst,X432: subst,X433: term] :
( ( sub @ ( X426 @ X431 @ X433 ) @ X432 )
= ( X426 @ ( comp @ X431 @ X432 ) @ ( sub @ X433 @ X432 ) ) )
| ( ( lam @ ( X425 @ sh @ one ) )
!= ( lam @ ( X426 @ sh @ one ) ) )
| ( ( X425 @ X424 @ X427 )
= ( X426 @ X424 @ X427 ) ) ) ) ) ) )
& ( ! [X434: term] :
~ ! [X435: subst > term > term] :
( ( sub @ X434 @ ( push @ one @ sh ) )
!= ( X435 @ sh @ one ) )
<=> hoasinduction_lem3b_lthm )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& induction2lem_gthm
& ( ! [X436: term,X437: subst > term > subst > $o] :
( ( X437 @ id @ ( lam @ ( sub @ X436 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X438: subst > term > term] :
( ( X437 @ id @ ( lam @ ( X438 @ sh @ one ) ) @ id )
| ~ ! [X439: subst,X440: subst,X441: term] :
( ( X438 @ ( comp @ X439 @ X440 ) @ ( sub @ X441 @ X440 ) )
= ( sub @ ( X438 @ X439 @ X441 ) @ X440 ) )
| ~ ! [X442: term] :
( ~ ( X437 @ id @ X442 @ id )
| ( X437 @ id @ ( X438 @ id @ X442 ) @ id ) ) )
| ~ ! [X443: term] :
( ~ ( X437 @ id @ X443 @ id )
| ( X437 @ id @ ( sub @ X436 @ ( push @ X443 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ( ! [X444: term,X445: term > $o] :
( ~ ! [X446: term,X447: term] :
( ~ ( X445 @ X446 )
| ~ ( X445 @ X447 )
| ( X445 @ ( ap @ X446 @ X447 ) ) )
| ( X445 @ X444 )
| ~ ! [X448: term] :
( ~ ( X445 @ X448 )
| ( X445 @ ( lam @ X448 ) ) )
| ~ ! [X449: term] :
( ( X445 @ X449 )
| ~ ( var @ X449 ) ) )
<=> induction )
& ( ( d2subst @ d_id )
= id )
& substmonoid_gthm
& ( hoaslaminj
<=> ! [X450: subst,X451: term,X452: subst > term > term,X453: subst > term > term] :
( ~ ! [X454: term,X455: subst,X456: subst] :
( ( sub @ ( X453 @ X455 @ X454 ) @ X456 )
= ( X453 @ ( comp @ X455 @ X456 ) @ ( sub @ X454 @ X456 ) ) )
| ( ( lam @ ( X453 @ sh @ one ) )
!= ( lam @ ( X452 @ sh @ one ) ) )
| ~ ! [X457: subst,X458: term,X459: subst] :
( ( X452 @ ( comp @ X459 @ X457 ) @ ( sub @ X458 @ X457 ) )
= ( sub @ ( X452 @ X459 @ X458 ) @ X457 ) )
| ( ( X452 @ X450 @ X451 )
= ( X453 @ X450 @ X451 ) ) ) )
& ( laminj
<=> ! [X460: term,X461: term] :
( ( X460 = X461 )
| ( ( lam @ X460 )
!= ( lam @ X461 ) ) ) )
& ( ! [X462: subst > term > subst > $o,X463: term,X464: term] :
( ~ ( X462 @ id @ X463 @ id )
| ~ ! [X465: term,X466: term] :
( ( X462 @ id @ ( ap @ ( sub @ X466 @ id ) @ X465 ) @ id )
| ~ ( X462 @ id @ X466 @ id )
| ~ ( X462 @ id @ X465 @ id ) )
| ~ ! [X467: subst,X468: subst,X469: subst,X470: term] :
( ( X462 @ X468 @ X470 @ ( comp @ X467 @ X469 ) )
| ~ ( X462 @ ( comp @ X468 @ X467 ) @ ( sub @ X470 @ X467 ) @ X469 ) )
| ( X462 @ id @ ( ap @ X463 @ X464 ) @ id )
| ~ ! [X471: subst,X472: term,X473: subst,X474: subst] :
( ( X462 @ ( comp @ X474 @ X473 ) @ ( sub @ X472 @ X473 ) @ X471 )
| ~ ( X462 @ X474 @ X472 @ ( comp @ X473 @ X471 ) ) )
| ~ ( X462 @ id @ X464 @ id ) )
<=> hoasinduction_lem2 )
& ! [X475: d_subst,X476: d_subst] :
( ( ( d2subst @ X476 )
= ( d2subst @ X475 ) )
=> ( X475 = X476 ) )
& pushprop_lem3v2
& ( ( ! [X477: term] :
( ( sub @ X477 @ id )
= X477 )
=> ( ! [X478: term,X479: term,X480: term,X481: term] :
( ( ( ap @ X479 @ X480 )
!= ( ap @ X481 @ X478 ) )
| ( X479 = X481 ) )
=> ! [X482: term,X483: term,X484: term,X485: term] :
( ( ( ap @ ( sub @ X483 @ id ) @ X482 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X483 = X484 ) ) ) )
<=> hoasapinj1_lthm )
& ( ! [X486: term > $o,X487: subst,X488: term > $o,X489: term] :
( ~ ! [X490: term] :
( ( X486 @ ( sub @ X490 @ ( push @ X489 @ X487 ) ) )
= ( X488 @ X490 ) )
| ~ ( X486 @ X489 )
| ( X488 @ one ) )
<=> pushprop_lem1v2 )
& pushprop_lem2v2
& ! [X491: d_term] : ( d_one = X491 )
& hoasinduction_lem3b_gthm
& axmap
& hoaslamnotap_gthm
& ! [X492: term] :
? [X493: d_term] :
( ( d2term @ X493 )
= X492 )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ^ [X494: subst > term > subst > $o,X495: term > $o] :
! [X496: term] :
( ( X494 @ id @ X496 @ id )
= ( X495 @ X496 ) ) )
= hoasinduction_p_and_p_prime )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& axapp
& ( ! [X497: subst > term > subst > $o,X498: term] :
( ~ ! [X499: term] :
( ( X497 @ id @ ( sub @ X498 @ ( push @ X499 @ id ) ) @ id )
| ~ ( X497 @ id @ X499 @ id ) )
| ( X497 @ id @ ( lam @ ( sub @ X498 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X500: term,X501: subst > term > term] :
( ~ ! [X502: subst,X503: term,X504: subst] :
( ( X501 @ ( comp @ X504 @ X502 ) @ ( sub @ X503 @ X502 ) )
= ( sub @ X500 @ ( push @ ( sub @ X503 @ X502 ) @ ( comp @ X504 @ X502 ) ) ) )
| ~ ! [X505: subst,X506: term,X507: subst] :
( ( sub @ ( X501 @ X507 @ X506 ) @ X505 )
= ( sub @ ( sub @ X500 @ ( push @ X506 @ X507 ) ) @ X505 ) )
| ~ ! [X508: term] :
( ( X497 @ id @ ( X501 @ id @ X508 ) @ id )
| ~ ( X497 @ id @ X508 @ id ) )
| ( X497 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aaa )
& hoasinduction_lem3v2_gthm
& ( ( ! [X509: term,X510: subst] :
( ( sub @ one @ ( push @ X509 @ X510 ) )
= X509 )
=> ! [X511: term,X512: term > $o,X513: term > $o,X514: subst] :
( ~ ( X512 @ X511 )
| ~ ! [X515: term] :
( ( X513 @ X515 )
= ( X512 @ ( sub @ X515 @ ( push @ X511 @ X514 ) ) ) )
| ( X513 @ one ) ) )
<=> pushprop_lem1v2_lthm )
& pushprop_lem1_gthm
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ! [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ( X517 @ ( lam @ X519 ) )
| ~ ! [X520: term,X521: subst,X522: subst,X523: subst] :
( ~ ( X518 @ X521 @ X520 @ ( comp @ X522 @ X523 ) )
| ( X518 @ ( comp @ X521 @ X522 ) @ ( sub @ X520 @ X522 ) @ X523 ) )
| ~ ! [X524: subst,X525: term,X526: subst,X527: subst] :
( ~ ( X518 @ ( comp @ X524 @ X526 ) @ ( sub @ X525 @ X526 ) @ X527 )
| ( X518 @ X524 @ X525 @ ( comp @ X526 @ X527 ) ) )
| ~ ! [X528: term] :
( ( X518 @ id @ X528 @ id )
= ( X517 @ X528 ) )
| ~ ! [X529: subst > term > term] :
( ( X518 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
| ~ ! [X530: term,X531: subst,X532: subst] :
( ( sub @ ( X529 @ X531 @ X530 ) @ X532 )
= ( X529 @ ( comp @ X531 @ X532 ) @ ( sub @ X530 @ X532 ) ) )
| ~ ! [X533: term] :
( ( X518 @ id @ ( X529 @ id @ X533 ) @ id )
| ~ ( X518 @ id @ X533 @ id ) ) )
| ~ ! [X534: term] :
( ~ ( X517 @ X534 )
| ( X517 @ ( sub @ X519 @ ( push @ X534 @ id ) ) ) ) ) ) )
& ( ! [X535: term,X536: term] :
( ( ( sub @ X535 @ sh )
!= ( sub @ X536 @ sh ) )
| ( X535 = X536 ) )
<=> shinj )
& ! [X537: d_subst] : ( d_id = X537 )
& ( axshiftcons
<=> ! [X538: subst,X539: term] :
( ( comp @ sh @ ( push @ X539 @ X538 ) )
= X538 ) )
& hoasapnotvar_lthm
& hoasinduction_lem2v2_gthm
& ( hoaslam
= ( ^ [X540: subst,X541: subst > term > term] : ( d2term @ d_one ) ) )
& apnotvar
& termmset_gthm
& pushprop_lthm_orig
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( X542 = X543 )
| ( ( ap @ X544 @ X543 )
!= ( ap @ X545 @ X542 ) ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( X546 = X548 )
| ( ( ap @ ( sub @ X549 @ id ) @ X548 )
!= ( ap @ ( sub @ X547 @ id ) @ X546 ) ) ) )
<=> hoasapinj2_lthm ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( hoasinduction_no_psi_cond
<=> ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ X30 @ id ) ) )
& hoasinduction_lem2_gthm
& ( pushprop_p_and_p_prime
= ( ^ [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) )
& axassoc
& pushprop_lem2v2_gthm
& pushprop_gthm
& ( ! [X45: term,X11: term > $o,X44: term,X10: subst > term > subst > $o] :
( ~ ( X11 @ X45 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ( X11 @ X44 )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
<=> hoasinduction_lem2v2 )
& hoasinduction_lem2_lthm
& ( ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 )
<=> axscons )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: term > $o,X16: term,X17: subst] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) ) ) )
<=> induction2_lthm )
& hoasinduction_lem3a_gthm
& ( ( d2subst @ d_id )
= sh )
& ( substmonoid
<=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) ) )
& hoasinduction_lem1v2
& ulamvarsh
& axvarshift
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X43: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ X43 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& hoasapinj2_gthm
& hoasinduction_lem1_gthm
& ( hoasinduction_lem3
<=> ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id ) ) )
& ( ! [X18: subst > term > term,X46: term,X47: term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) ) )
<=> hoaslamnotap )
& hoasapinj1_gthm
& ( substmonoid_lthm
<=> ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) ) ) ) )
& hoasapnotvar
& ( hoasapinj2
<=> ! [X15: term,X13: term,X19: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
& ( pushprop_lem1
<=> ! [X15: term,X26: term > $o,X14: subst,X10: term > $o,X13: term] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) )
& pushprop_lem2v2_lthm
& hoasinduction_lem1_lthm
& ( hoasinduction_lem3_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) )
& ( induction2
<=> ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) ) )
& ~ ulamvar1
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& hoasinduction_lem1v2_gthm
& ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X29: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ( X11 @ ( lam @ X29 ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) )
<=> hoasinduction_lthm_3 )
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& hoasinduction_lem3_gthm
& hoaslamnotvar_gthm
& pushprop_lem1v2_gthm
& hoasinduction_lem1
& ( hoasinduction_lem0
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& ( axvarid
<=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) )
& ( hoasinduction_lthm
<=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( X10 @ X22 ) )
=> ( ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X25: subst,X26: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) )
=> ( ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ( X10 @ id @ X28 @ id )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) ) ) ) )
& ( ! [X43: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_lem3a )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X14: subst,X13: term,X10: term > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0_lthm )
& ( hoasinduction_lem3v2a
<=> ! [X10: subst > term > subst > $o,X11: term > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) ) )
& hoaslaminj_gthm
& ( termmset
<=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) )
& ~ lamnotap
& ulamvarind
& ( axidl
<=> ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
& ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
<=> axidr )
& ( pushprop_lem0
<=> ! [X10: term > $o,X14: subst,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) )
=> ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ( X10 @ id @ X30 @ id )
| ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) ) ) ) ) )
& hoasapnotvar_gthm
& pushprop_lthm
& pushprop_lem3v2_lthm
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) )
<=> termmset_lthm )
& hoaslamnotap_lthm
& ( pushprop_lem1_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X15: term,X14: subst,X13: term,X10: term > $o,X26: term > $o] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) ) ) ) )
& lamnotvar
& ( hoasinduction
<=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
& pushprop_lem0_gthm
& pushprop
& ~ ( var @ ( d2term @ d_one ) )
& ( hoasinduction_lem3b
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f_lthm )
& induction2_gthm
& hoaslamnotvar_lthm
& axclos
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ X21 )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) ) )
=> ! [X17: subst,X16: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoaslamnotvar
& ( hoasinduction_lem3v2
<=> ! [X48: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) )
& ( apinj1
<=> ! [X15: term,X20: term,X13: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) ) )
& hoasinduction_gthm
& ( hoasapinj1
<=> ! [X15: term,X19: term,X20: term,X13: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X29: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X29 ) ) ) ) ) )
& axabs
& ( hoasinduction_lem3aa
<=> ! [X42: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) ) )
& ( induction2lem
<=> ! [X17: subst,X10: term > $o,X16: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) ) )
& ( apinj2
<=> ! [X20: term,X19: term,X13: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoaslaminj_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X13: term,X15: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
=> ! [X32: subst,X18: subst > term > term,X31: subst > term > term,X33: term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) ) ) ) ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& induction2lem_gthm
& ( ! [X42: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ( ! [X21: term,X10: term > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X21 )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) ) )
<=> induction )
& ( ( d2subst @ d_id )
= id )
& substmonoid_gthm
& ( hoaslaminj
<=> ! [X32: subst,X33: term,X18: subst > term > term,X31: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) ) ) )
& ( laminj
<=> ! [X15: term,X13: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) ) )
& ( ! [X10: subst > term > subst > $o,X23: term,X24: term] :
( ~ ( X10 @ id @ X23 @ id )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X26: subst,X14: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X10 @ id @ X24 @ id ) )
<=> hoasinduction_lem2 )
& ! [X7: d_subst,X6: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& pushprop_lem3v2
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X19: term,X15: term,X20: term,X13: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
=> ! [X19: term,X13: term,X15: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) ) )
<=> hoasapinj1_lthm )
& ( ! [X10: term > $o,X14: subst,X11: term > $o,X13: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ~ ( X10 @ X13 )
| ( X11 @ one ) )
<=> pushprop_lem1v2 )
& pushprop_lem2v2
& ! [X1: d_term] : ( d_one = X1 )
& hoasinduction_lem3b_gthm
& axmap
& hoaslamnotap_gthm
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
= hoasinduction_p_and_p_prime )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& axapp
& ( ! [X10: subst > term > subst > $o,X34: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X35: term,X18: subst > term > term] :
( ~ ! [X41: subst,X40: term,X39: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) )
| ~ ! [X38: subst,X37: term,X36: subst] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aaa )
& hoasinduction_lem3v2_gthm
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X13: term,X10: term > $o,X11: term > $o,X14: subst] :
( ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ( X11 @ one ) ) )
<=> pushprop_lem1v2_lthm )
& pushprop_lem1_gthm
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X11: term > $o,X10: subst > term > subst > $o,X48: term] :
( ( X11 @ ( lam @ X48 ) )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X14: subst,X13: term,X26: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) ) ) ) )
& ( ! [X13: term,X15: term] :
( ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) )
| ( X13 = X15 ) )
<=> shinj )
& ! [X5: d_subst] : ( d_id = X5 )
& ( axshiftcons
<=> ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 ) )
& hoasapnotvar_lthm
& hoasinduction_lem2v2_gthm
& ( hoaslam
= ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) ) )
& apnotvar
& termmset_gthm
& pushprop_lthm_orig
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X20: term,X19: term,X13: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X19: term,X13: term,X20: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
<=> hoasapinj2_lthm ) ),
file('/export/starexec/sandbox2/tmp/tmp.eLR4iSdWK1/DTF2THF_2254.p',alg444_1) ).
thf(f1057,plain,
! [X258: term] :
( ( d2term @ ( sK580 @ X258 ) )
= X258 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f4190,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP11 @ X0 )
!= $true )
| ( ( d2term @ d_one )
!= ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4189,f4091]) ).
thf(f4189,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP11 @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4100,f4179]) ).
thf(f4179,plain,
! [X2: term,X0: subst > term > subst > $o,X1: term] :
( ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4133,f4171]) ).
thf(f4171,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( sP13 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f1511,f4091]) ).
thf(f1511,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( sK365 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
!= ( sP13 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f927,f1127,f1127]) ).
thf(f1127,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f927,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( sK365 @ X0 ) @ id ) )
| ( $true
!= ( sP13 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f387]) ).
thf(f387,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP13 @ X0 ) )
| ! [X1: term,X2: term] :
( ( ( X0 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true )
| ( ( X0 @ id @ X1 @ id )
!= $true ) ) )
& ( ( ( ( X0 @ id @ ( ap @ ( sub @ ( sK366 @ X0 ) @ id ) @ ( sK365 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK366 @ X0 ) @ id )
= $true )
& ( $true
= ( X0 @ id @ ( sK365 @ X0 ) @ id ) ) )
| ( $true
!= ( sP13 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK365,sK366])],[f385,f386]) ).
thf(f386,plain,
! [X0: subst > term > subst > $o] :
( ? [X3: term,X4: term] :
( ( ( X0 @ id @ ( ap @ ( sub @ X4 @ id ) @ X3 ) @ id )
!= $true )
& ( ( X0 @ id @ X4 @ id )
= $true )
& ( ( X0 @ id @ X3 @ id )
= $true ) )
=> ( ( ( X0 @ id @ ( ap @ ( sub @ ( sK366 @ X0 ) @ id ) @ ( sK365 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK366 @ X0 ) @ id )
= $true )
& ( $true
= ( X0 @ id @ ( sK365 @ X0 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f385,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP13 @ X0 ) )
| ! [X1: term,X2: term] :
( ( ( X0 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true )
| ( ( X0 @ id @ X1 @ id )
!= $true ) ) )
& ( ? [X3: term,X4: term] :
( ( ( X0 @ id @ ( ap @ ( sub @ X4 @ id ) @ X3 ) @ id )
!= $true )
& ( ( X0 @ id @ X4 @ id )
= $true )
& ( ( X0 @ id @ X3 @ id )
= $true ) )
| ( $true
!= ( sP13 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f384]) ).
thf(f384,plain,
! [X215: subst > term > subst > $o] :
( ( ( ( sP13 @ X215 )
= $true )
| ! [X231: term,X232: term] :
( ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
= $true )
| ( ( X215 @ id @ X232 @ id )
!= $true )
| ( ( X215 @ id @ X231 @ id )
!= $true ) ) )
& ( ? [X231: term,X232: term] :
( ( ( X215 @ id @ ( ap @ ( sub @ X232 @ id ) @ X231 ) @ id )
!= $true )
& ( ( X215 @ id @ X232 @ id )
= $true )
& ( ( X215 @ id @ X231 @ id )
= $true ) )
| ( ( sP13 @ X215 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f4133,plain,
! [X2: term,X0: subst > term > subst > $o,X1: term] :
( ( $true
= ( sP13 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(backward_demodulation,[status(thm)],[f1508,f4091]) ).
thf(f1508,plain,
! [X2: term,X0: subst > term > subst > $o,X1: term] :
( ( ( X0 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( ap @ ( sub @ X2 @ ( d2subst @ d_id ) ) @ X1 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( sP13 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f930,f1127,f1127,f1127,f1127,f1127,f1127,f1127]) ).
thf(f930,plain,
! [X2: term,X0: subst > term > subst > $o,X1: term] :
( ( $true
= ( sP13 @ X0 ) )
| ( ( X0 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true )
| ( ( X0 @ id @ X1 @ id )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f387]) ).
thf(f4100,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK370 @ X6 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( sP11 @ X0 )
!= $true )
| ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1519,f4091]) ).
thf(f1519,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ( ( sP11 @ X0 )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X6 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK370 @ X6 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f935,f1127,f1127,f1127,f1248,f1150,f1127]) ).
thf(f1150,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1248,plain,
( ( d2subst @ d_id )
= sh ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f935,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ( ( X0 @ id @ ( sK370 @ X6 @ X0 ) @ id )
= $true )
| ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
= $true )
| ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) )
| ( ( sP11 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
thf(f397,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP11 @ X0 )
= $true )
| ( ! [X2: term] :
( ( ( X0 @ id @ ( sK369 @ X0 @ id @ X2 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true ) )
& ( ( X0 @ id @ ( lam @ ( sK369 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X3: term,X4: subst,X5: subst] :
( ( sub @ ( sK369 @ X0 @ X5 @ X3 ) @ X4 )
= ( sK369 @ X0 @ ( comp @ X5 @ X4 ) @ ( sub @ X3 @ X4 ) ) ) ) )
& ( ! [X6: subst > term > term] :
( ( ( ( X0 @ id @ ( X6 @ id @ ( sK370 @ X6 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK370 @ X6 @ X0 ) @ id )
= $true ) )
| ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
= $true )
| ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) ) )
| ( ( sP11 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK369,sK370,sK371,sK372,sK373])],[f393,f396,f395,f394]) ).
thf(f394,plain,
! [X0: subst > term > subst > $o] :
( ? [X1: subst > term > term] :
( ! [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
& ! [X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X5 @ X4 ) @ ( sub @ X3 @ X4 ) )
= ( sub @ ( X1 @ X5 @ X3 ) @ X4 ) ) )
=> ( ! [X2: term] :
( ( ( X0 @ id @ ( sK369 @ X0 @ id @ X2 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true ) )
& ( ( X0 @ id @ ( lam @ ( sK369 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X5: subst,X4: subst,X3: term] :
( ( sub @ ( sK369 @ X0 @ X5 @ X3 ) @ X4 )
= ( sK369 @ X0 @ ( comp @ X5 @ X4 ) @ ( sub @ X3 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f395,plain,
! [X0: subst > term > subst > $o,X6: subst > term > term] :
( ? [X7: term] :
( ( ( X0 @ id @ ( X6 @ id @ X7 ) @ id )
!= $true )
& ( ( X0 @ id @ X7 @ id )
= $true ) )
=> ( ( ( X0 @ id @ ( X6 @ id @ ( sK370 @ X6 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK370 @ X6 @ X0 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f396,plain,
! [X6: subst > term > term] :
( ? [X8: term,X9: subst,X10: subst] :
( ( sub @ ( X6 @ X10 @ X8 ) @ X9 )
!= ( X6 @ ( comp @ X10 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
=> ( ( X6 @ ( comp @ ( sK373 @ X6 ) @ ( sK372 @ X6 ) ) @ ( sub @ ( sK371 @ X6 ) @ ( sK372 @ X6 ) ) )
!= ( sub @ ( X6 @ ( sK373 @ X6 ) @ ( sK371 @ X6 ) ) @ ( sK372 @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f393,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP11 @ X0 )
= $true )
| ? [X1: subst > term > term] :
( ! [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
& ! [X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X5 @ X4 ) @ ( sub @ X3 @ X4 ) )
= ( sub @ ( X1 @ X5 @ X3 ) @ X4 ) ) ) )
& ( ! [X6: subst > term > term] :
( ? [X7: term] :
( ( ( X0 @ id @ ( X6 @ id @ X7 ) @ id )
!= $true )
& ( ( X0 @ id @ X7 @ id )
= $true ) )
| ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
= $true )
| ? [X8: term,X9: subst,X10: subst] :
( ( sub @ ( X6 @ X10 @ X8 ) @ X9 )
!= ( X6 @ ( comp @ X10 @ X9 ) @ ( sub @ X8 @ X9 ) ) ) )
| ( ( sP11 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f392]) ).
thf(f392,plain,
! [X200: subst > term > subst > $o] :
( ( ( ( sP11 @ X200 )
= $true )
| ? [X206: subst > term > term] :
( ! [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
= $true )
| ( ( X200 @ id @ X207 @ id )
!= $true ) )
& ( $true
!= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
& ! [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) ) )
& ( ! [X206: subst > term > term] :
( ? [X207: term] :
( ( ( X200 @ id @ ( X206 @ id @ X207 ) @ id )
!= $true )
& ( ( X200 @ id @ X207 @ id )
= $true ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ? [X208: term,X209: subst,X210: subst] :
( ( X206 @ ( comp @ X210 @ X209 ) @ ( sub @ X208 @ X209 ) )
!= ( sub @ ( X206 @ X210 @ X208 ) @ X209 ) ) )
| ( ( sP11 @ X200 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f4138,plain,
! [X2: term,X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP11 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(backward_demodulation,[status(thm)],[f1516,f4091]) ).
thf(f1516,plain,
! [X2: term,X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK369 @ X0 @ ( d2subst @ d_id ) @ X2 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP11 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f939,f1127,f1127,f1127,f1127,f1127]) ).
thf(f939,plain,
! [X2: term,X0: subst > term > subst > $o] :
( ( ( sP11 @ X0 )
= $true )
| ( ( X0 @ id @ ( sK369 @ X0 @ id @ X2 ) @ id )
= $true )
| ( ( X0 @ id @ X2 @ id )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
thf(f5349,plain,
( ! [X4: subst > term > term] :
( ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290 ),
inference(forward_demodulation,[status(thm)],[f5348,f4091]) ).
thf(f5348,plain,
( ! [X4: subst > term > term] :
( ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290 ),
inference(subsumption_resolution,[status(thm)],[f5347,f4091]) ).
thf(f5347,plain,
( ! [X4: subst > term > term] :
( ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( d2term @ d_one )
!= ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) ) )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_290 ),
inference(forward_demodulation,[status(thm)],[f3133,f4091]) ).
thf(f6673,plain,
spl591_483,
inference(avatar_contradiction_clause,[status(thm)],[f6672]) ).
thf(f6672,plain,
( $false
| spl591_483 ),
inference(subsumption_resolution,[status(thm)],[f6655,f4091]) ).
thf(f6655,plain,
( ( ( d2term @ d_one )
!= sK461 )
| spl591_483 ),
inference(superposition,[status(thm)],[f3986,f4091]) ).
thf(f3986,plain,
( ( sK461
!= ( sub @ sK461 @ ( d2subst @ d_id ) ) )
| spl591_483 ),
inference(avatar_component_clause,[status(thm)],[f3984]) ).
thf(f3984,definition,
( spl591_483
<=> ( sK461
= ( sub @ sK461 @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_483])],[avatar_definition]) ).
thf(f5462,plain,
( ~ spl591_2
| ~ spl591_40
| spl591_151 ),
inference(avatar_contradiction_clause,[status(thm)],[f5461]) ).
thf(f5461,plain,
( $false
| ~ spl591_2
| ~ spl591_40
| spl591_151 ),
inference(subsumption_resolution,[status(thm)],[f5460,f2548]) ).
thf(f2548,plain,
( ( sK561 != sK562 )
| spl591_151 ),
inference(avatar_component_clause,[status(thm)],[f2546]) ).
thf(f2546,definition,
( spl591_151
<=> ( sK561 = sK562 ) ),
introduced(definition,[new_symbols(naming,[spl591_151])],[avatar_definition]) ).
thf(f5460,plain,
( ( sK561 = sK562 )
| ~ spl591_2
| ~ spl591_40 ),
inference(forward_demodulation,[status(thm)],[f5459,f1926]) ).
thf(f1926,plain,
( ! [X86: term] :
( ( sub @ X86 @ ( d2subst @ d_id ) )
= X86 )
| ~ spl591_2 ),
inference(avatar_component_clause,[status(thm)],[f1925]) ).
thf(f1925,definition,
( spl591_2
<=> ! [X86: term] :
( ( sub @ X86 @ ( d2subst @ d_id ) )
= X86 ) ),
introduced(definition,[new_symbols(naming,[spl591_2])],[avatar_definition]) ).
thf(f5459,plain,
( ( ( sub @ sK561 @ ( d2subst @ d_id ) )
= sK562 )
| ~ spl591_2
| ~ spl591_40 ),
inference(forward_demodulation,[status(thm)],[f2083,f1926]) ).
thf(f2083,plain,
( ( ( sub @ sK561 @ ( d2subst @ d_id ) )
= ( sub @ sK562 @ ( d2subst @ d_id ) ) )
| ~ spl591_40 ),
inference(avatar_component_clause,[status(thm)],[f2081]) ).
thf(f2081,definition,
( spl591_40
<=> ( ( sub @ sK561 @ ( d2subst @ d_id ) )
= ( sub @ sK562 @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_40])],[avatar_definition]) ).
thf(f4579,plain,
( spl591_2
| ~ spl591_484 ),
inference(avatar_split_clause,[status(thm)],[f1600,f3988,f1925]) ).
thf(f3988,definition,
( spl591_484
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_484])],[avatar_definition]) ).
thf(f1600,plain,
! [X14: term] :
( ( axvarid != $true )
| ( ( sub @ X14 @ ( d2subst @ d_id ) )
= X14 ) ),
inference(definition_unfolding,[status(thm)],[f1247,f1127]) ).
thf(f1247,plain,
! [X14: term] :
( ( ( sub @ X14 @ id )
= X14 )
| ( axvarid != $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f4464,plain,
( spl591_536
| ~ spl591_39 ),
inference(avatar_split_clause,[status(thm)],[f4460,f2077,f4462]) ).
thf(f2077,definition,
( spl591_39
<=> ( shinj = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_39])],[avatar_definition]) ).
thf(f4460,plain,
! [X218: term,X219: term] :
( ( shinj != $true )
| ( X218 = X219 ) ),
inference(subsumption_resolution,[status(thm)],[f4459,f4091]) ).
thf(f4459,plain,
! [X218: term,X219: term] :
( ( shinj != $true )
| ( X218 = X219 )
| ( ( d2term @ d_one )
!= ( sub @ X218 @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1644,f4091]) ).
thf(f1644,plain,
! [X218: term,X219: term] :
( ( shinj != $true )
| ( X218 = X219 )
| ( ( sub @ X218 @ ( d2subst @ d_id ) )
!= ( sub @ X219 @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1101,f1248,f1248]) ).
thf(f1101,plain,
! [X218: term,X219: term] :
( ( X218 = X219 )
| ( ( sub @ X219 @ sh )
!= ( sub @ X218 @ sh ) )
| ( shinj != $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f4364,plain,
( spl591_516
| spl591_523 ),
inference(avatar_split_clause,[status(thm)],[f4363,f4357,f4324]) ).
thf(f4363,plain,
( ( hoasinduction_lem3v2a = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4362,f4091]) ).
thf(f4362,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $false )
| ( ( d2term @ d_one )
!= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4361,f4091]) ).
thf(f4361,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $false )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f1717,f4219]) ).
thf(f1717,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $false )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f1716]) ).
thf(f1716,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1714]) ).
thf(f1714,plain,
! [X1: subst > term > term] :
( ( $false
= ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction_lem3v2a = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1713]) ).
thf(f1713,plain,
! [X1: subst > term > term] :
( ( $false
= ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) )
@ ( sK597 @ X1 ) )
= $false )
| ( hoasinduction_lem3v2a = $false ) ),
inference(sigma_clausification,[status(thm)],[f1712]) ).
thf(f1712,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) ) ) )
| ( hoasinduction_lem3v2a = $false )
| ( $false
= ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) ) @ ( d2subst @ d_id ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1711]) ).
thf(f1711,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) )
@ ( sK596 @ X1 ) ) )
| ( hoasinduction_lem3v2a = $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1710]) ).
thf(f1710,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1709]) ).
thf(f1709,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ Y0 ) @ Y1 ) ) )
@ ( sK595 @ X1 ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( hoasinduction_lem3v2a = $false ) ),
inference(sigma_clausification,[status(thm)],[f1708]) ).
thf(f1708,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y1 ) @ ( sub @ Y0 @ Y1 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ Y0 ) @ Y1 ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( hoasinduction_lem3v2a = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1707]) ).
thf(f1707,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( X1 @ Y0 @ Y1 ) @ Y2 ) ) ) )
@ ( sK594 @ X1 ) ) )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1706]) ).
thf(f1706,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1705]) ).
thf(f1705,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
= $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1704]) ).
thf(f1704,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $false )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1703]) ).
thf(f1703,plain,
! [X1: subst > term > term] :
( ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
@ X1 )
= $true )
| ( hoasinduction_lem3v2a = $false ) ),
inference(pi_clausification,[status(thm)],[f1702]) ).
thf(f1702,plain,
( ( $true
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1700]) ).
thf(f1700,plain,
( ( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( sK593 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ Y1 )
=> ( sK593 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK593 @ ( lam @ Y0 ) ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1699]) ).
thf(f1699,plain,
( ( $false
= ( ^ [Y0: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) )
@ sK593 ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(sigma_clausification,[status(thm)],[f1698]) ).
thf(f1698,plain,
( ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1697]) ).
thf(f1697,plain,
( ( hoasinduction_lem3v2a = $false )
| ( ( ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) )
@ sK592 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1696]) ).
thf(f1696,plain,
( ( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1694]) ).
thf(f1694,plain,
( hoasinduction_lem3v2a
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1262]) ).
thf(f1262,plain,
( hoasinduction_lem3v2a
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id )
@ ( ^ [Y3: subst,Y4: subst > term > term] : ( d2term @ d_one )
@ ( d2subst @ d_id )
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ ( d2subst @ d_id ) ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( d2subst @ d_id ) @ Y4 @ ( d2subst @ d_id ) )
= ( Y3 @ Y4 ) ) )
@ Y0
@ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f546,f1127,f1127,f1127,f1127,f1127,f1127,f1195,f1127,f1127,f1261,f1127]) ).
thf(f1261,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1207,f1127,f1127]) ).
thf(f1207,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1195,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f546,plain,
( hoasinduction_lem3v2a
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( hoasinduction_lem3v2a
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( hoasinduction_lem3v2a
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: term > $o,X1: subst > term > subst > $o] :
( ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( X2 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) )
= ( sub @ ( X2 @ X5 @ X4 ) @ X3 ) )
=> ( ! [X6: term] :
( ( X1 @ id @ X6 @ id )
=> ( X1 @ id @ ( X2 @ id @ X6 ) @ id ) )
=> ( X1 @ id
@ ( hoaslam @ id
@ ^ [X7: subst,X8: term] : ( X2 @ X7 @ X8 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X1 @ X0 )
=> ! [X9: term] :
( ! [X10: term] :
( ( X0 @ X10 )
=> ( X0 @ ( sub @ X9 @ ( push @ X10 @ id ) ) ) )
=> ( X0 @ ( lam @ X9 ) ) ) ) )
= hoasinduction_lem3v2a ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X11: term > $o,X10: subst > term > subst > $o] :
( ( ! [X18: subst > term > term] :
( ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ( ! [X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
=> ! [X13: term] :
( ! [X15: term] :
( ( X11 @ X15 )
=> ( X11 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
=> ( X11 @ ( lam @ X13 ) ) ) ) )
= hoasinduction_lem3v2a ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X11: term > $o,X10: subst > term > subst > $o] :
( ( ! [X18: subst > term > term] :
( ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ( ! [X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
=> ! [X13: term] :
( ! [X15: term] :
( ( X11 @ X15 )
=> ( X11 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
=> ( X11 @ ( lam @ X13 ) ) ) ) )
= hoasinduction_lem3v2a ),
file('/export/starexec/sandbox2/tmp/tmp.eLR4iSdWK1/DTF2THF_2254.p',hoasinduction_lem3v2a) ).
thf(f4348,plain,
( spl591_516
| spl591_521 ),
inference(avatar_split_clause,[status(thm)],[f1725,f4346,f4324]) ).
thf(f1725,plain,
! [X1: term] :
( ( hoasinduction_lem3v2a = $false )
| ( $true
= ( sK593 @ X1 ) )
| ( $false
= ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1723]) ).
thf(f1723,plain,
! [X1: term] :
( ( hoasinduction_lem3v2a = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) )
= ( sK593 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1722]) ).
thf(f1722,plain,
! [X1: term] :
( ( ( ( sK592 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) )
= ( sK593 @ X1 ) )
= $true )
| ( hoasinduction_lem3v2a = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1721]) ).
thf(f1721,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( sK593 @ Y0 ) )
@ X1 ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(pi_clausification,[status(thm)],[f1720]) ).
thf(f1720,plain,
( ( hoasinduction_lem3v2a = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( sK593 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1701]) ).
thf(f1701,plain,
( ( hoasinduction_lem3v2a = $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( sK593 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ Y1 )
=> ( sK593 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK593 @ ( lam @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1700]) ).
thf(f4331,plain,
( spl591_516
| spl591_517 ),
inference(avatar_split_clause,[status(thm)],[f1728,f4328,f4324]) ).
thf(f1728,plain,
( ( $false
= ( sK593 @ ( lam @ sK598 ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1727]) ).
thf(f1727,plain,
( ( hoasinduction_lem3v2a = $false )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK593 @ Y0 )
=> ( sK593 @ ( sub @ sK598 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK593 @ ( lam @ sK598 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1726]) ).
thf(f1726,plain,
( ( hoasinduction_lem3v2a = $false )
| ( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ Y1 )
=> ( sK593 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK593 @ ( lam @ Y0 ) ) )
@ sK598 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1719]) ).
thf(f1719,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ Y1 )
=> ( sK593 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK593 @ ( lam @ Y0 ) ) ) ) )
| ( hoasinduction_lem3v2a = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1701]) ).
thf(f4291,plain,
( spl591_125
| spl591_514
| spl591_509 ),
inference(avatar_split_clause,[status(thm)],[f4287,f4251,f4289,f2435]) ).
thf(f4287,plain,
! [X2: term > $o,X1: subst > term > subst > $o,X4: term] :
( ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(subsumption_resolution,[status(thm)],[f4286,f4197]) ).
thf(f4197,plain,
! [X2: term,X0: term > $o,X1: term] :
( ( ( X0 @ ( d2term @ d_one ) )
= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4118,f4165]) ).
thf(f4165,plain,
! [X0: term > $o] :
( ( ( sP29 @ X0 )
!= $true )
| ( ( X0 @ ( d2term @ d_one ) )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f796,f4091]) ).
thf(f796,plain,
! [X0: term > $o] :
( ( ( X0 @ ( sK257 @ X0 ) )
= $true )
| ( ( sP29 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
thf(f280,plain,
! [X0: term > $o] :
( ( ( ( sP29 @ X0 )
= $true )
| ! [X1: term,X2: term] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ ( ap @ X2 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ( ( ( X0 @ ( sK257 @ X0 ) )
= $true )
& ( ( X0 @ ( ap @ ( sK257 @ X0 ) @ ( sK256 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK256 @ X0 ) )
= $true ) )
| ( ( sP29 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK256,sK257])],[f278,f279]) ).
thf(f279,plain,
! [X0: term > $o] :
( ? [X3: term,X4: term] :
( ( ( X0 @ X4 )
= $true )
& ( ( X0 @ ( ap @ X4 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
=> ( ( ( X0 @ ( sK257 @ X0 ) )
= $true )
& ( ( X0 @ ( ap @ ( sK257 @ X0 ) @ ( sK256 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK256 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f278,plain,
! [X0: term > $o] :
( ( ( ( sP29 @ X0 )
= $true )
| ! [X1: term,X2: term] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ ( ap @ X2 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ? [X3: term,X4: term] :
( ( ( X0 @ X4 )
= $true )
& ( ( X0 @ ( ap @ X4 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
| ( ( sP29 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f277]) ).
thf(f277,plain,
! [X35: term > $o] :
( ( ( ( sP29 @ X35 )
= $true )
| ! [X38: term,X39: term] :
( ( $true
!= ( X35 @ X39 ) )
| ( ( X35 @ ( ap @ X39 @ X38 ) )
= $true )
| ( ( X35 @ X38 )
!= $true ) ) )
& ( ? [X38: term,X39: term] :
( ( $true
= ( X35 @ X39 ) )
& ( ( X35 @ ( ap @ X39 @ X38 ) )
!= $true )
& ( ( X35 @ X38 )
= $true ) )
| ( ( sP29 @ X35 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
thf(f4118,plain,
! [X2: term,X0: term > $o,X1: term] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( sP29 @ X0 )
= $true )
| ( ( X0 @ ( d2term @ d_one ) )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f797,f4091]) ).
thf(f797,plain,
! [X2: term,X0: term > $o,X1: term] :
( ( ( sP29 @ X0 )
= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( ap @ X2 @ X1 ) )
= $true )
| ( ( X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
thf(f4286,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( hoasinduction_lem3v2a = $true )
| ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4285,f4091]) ).
thf(f4285,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X2 @ ( sK603 @ X1 @ X2 ) )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(subsumption_resolution,[status(thm)],[f4284,f4219]) ).
thf(f4284,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X2 @ ( sK603 @ X1 @ X2 ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(forward_demodulation,[status(thm)],[f4283,f4091]) ).
thf(f4283,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X2 @ ( sK603 @ X1 @ X2 ) )
= $true )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(forward_demodulation,[status(thm)],[f1794,f4091]) ).
thf(f1794,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( $false
= ( X2 @ ( sub @ X3 @ ( push @ ( sK604 @ X3 @ X2 ) @ ( d2subst @ d_id ) ) ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X2 @ ( sK603 @ X1 @ X2 ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1793]) ).
thf(f1793,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X2 @ ( sub @ X3 @ ( push @ ( sK604 @ X3 @ X2 ) @ ( d2subst @ d_id ) ) ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1788]) ).
thf(f1788,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( hoasinduction_lem3v2a = $true )
| ( ( ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) ) )
= $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ ( sub @ X3 @ ( push @ ( sK604 @ X3 @ X2 ) @ ( d2subst @ d_id ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1787]) ).
thf(f1787,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( ( ( X2 @ ( sK604 @ X3 @ X2 ) )
=> ( X2 @ ( sub @ X3 @ ( push @ ( sK604 @ X3 @ X2 ) @ ( d2subst @ d_id ) ) ) ) )
= $false )
| ( ( ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1786]) ).
thf(f1786,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) ) )
= $true )
| ( $false
= ( ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) )
@ ( sK604 @ X3 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1785]) ).
thf(f1785,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
= $false )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( ( ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) ) )
= $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1784]) ).
thf(f1784,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( ( X1 @ ( d2subst @ d_id ) @ X4 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ X4 ) @ ( d2subst @ d_id ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1783]) ).
thf(f1783,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o,X4: term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true )
| ( ( ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1782]) ).
thf(f1782,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f1781]) ).
thf(f1781,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( ( X1 @ ( d2subst @ d_id ) @ ( sK603 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= ( X2 @ ( sK603 @ X1 @ X2 ) ) )
= $false )
| ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1780]) ).
thf(f1780,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) )
@ ( sK603 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1779]) ).
thf(f1779,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
= $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1777]) ).
thf(f1777,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
= $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1776]) ).
thf(f1776,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1775]) ).
thf(f1775,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1740]) ).
thf(f1740,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1739]) ).
thf(f1739,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK599 @ X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( sK599 @ X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( sK599 @ X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1738]) ).
thf(f1738,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
@ ( sK599 @ X1 ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1737]) ).
thf(f1737,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
= $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1736]) ).
thf(f1736,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) )
= ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1735]) ).
thf(f1735,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( ( ^ [Y0: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) )
@ X2 )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(pi_clausification,[status(thm)],[f1734]) ).
thf(f1734,plain,
! [X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1733]) ).
thf(f1733,plain,
! [X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( ( ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1695]) ).
thf(f1695,plain,
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) )
= ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
= ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1694]) ).
thf(f4282,plain,
( spl591_509
| spl591_512
| spl591_125 ),
inference(avatar_split_clause,[status(thm)],[f4281,f2435,f4266,f4251]) ).
thf(f4281,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f4280]) ).
thf(f4280,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(forward_demodulation,[status(thm)],[f4279,f4091]) ).
thf(f4279,plain,
! [X2: term > $o,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4278,f4197]) ).
thf(f4278,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $true
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4277,f4091]) ).
thf(f4277,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( $false
= ( X2 @ ( d2term @ d_one ) ) )
| ( ( X2 @ ( sK606 @ X3 @ X2 ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1805,f4091]) ).
thf(f1805,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( X2 @ ( sK605 @ X1 @ X2 ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X2 @ ( sK606 @ X3 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1803]) ).
thf(f1803,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X2 @ ( sK606 @ X3 @ X2 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK605 @ X1 @ X2 ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1801]) ).
thf(f1801,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( $false
= ( ( X2 @ ( sK606 @ X3 @ X2 ) )
=> ( X2 @ ( sub @ X3 @ ( push @ ( sK606 @ X3 @ X2 ) @ ( d2subst @ d_id ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK605 @ X1 @ X2 ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1800]) ).
thf(f1800,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) )
@ ( sK606 @ X3 @ X2 ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK605 @ X1 @ X2 ) ) )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(sigma_clausification,[status(thm)],[f1799]) ).
thf(f1799,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
= $false )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
!= ( X2 @ ( sK605 @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1798]) ).
thf(f1798,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= ( X2 @ ( sK605 @ X1 @ X2 ) ) ) )
| ( ( X2 @ ( lam @ X3 ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1797]) ).
thf(f1797,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true )
| ( $false
= ( ( X1 @ ( d2subst @ d_id ) @ ( sK605 @ X1 @ X2 ) @ ( d2subst @ d_id ) )
= ( X2 @ ( sK605 @ X1 @ X2 ) ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1796]) ).
thf(f1796,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( $false
= ( ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) )
@ ( sK605 @ X1 @ X2 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1778]) ).
thf(f1778,plain,
! [X2: term > $o,X3: term,X1: subst > term > subst > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
= ( X2 @ Y0 ) ) )
= $false )
| ( $false
= ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ X3 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( X2 @ ( lam @ X3 ) ) )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1777]) ).
thf(f3991,plain,
( ~ spl591_483
| spl591_484 ),
inference(avatar_split_clause,[status(thm)],[f1601,f3988,f3984]) ).
thf(f1601,plain,
( ( sK461
!= ( sub @ sK461 @ ( d2subst @ d_id ) ) )
| ( axvarid = $true ) ),
inference(definition_unfolding,[status(thm)],[f1246,f1127]) ).
thf(f1246,plain,
( ( axvarid = $true )
| ( sK461
!= ( sub @ sK461 @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3809,plain,
( spl591_444
| spl591_124 ),
inference(avatar_split_clause,[status(thm)],[f1828,f2431,f3807]) ).
thf(f2431,definition,
( spl591_124
<=> ( sP2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_124])],[avatar_definition]) ).
thf(f1828,plain,
! [X3: term] :
( ( ( sK429 @ X3 )
= $true )
| ( $false
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) )
| ( sP2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1572]) ).
thf(f1572,plain,
! [X3: term] :
( ( ( sK429 @ X3 )
= ( sK428 @ ( d2subst @ d_id ) @ X3 @ ( d2subst @ d_id ) ) )
| ( sP2 = $true ) ),
inference(definition_unfolding,[status(thm)],[f1015,f1127,f1127]) ).
thf(f1015,plain,
! [X3: term] :
( ( sP2 = $true )
| ( ( sK429 @ X3 )
= ( sK428 @ id @ X3 @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f457]) ).
thf(f457,plain,
( ( ( sP2 = $true )
| ( ( ( sK429 @ ( lam @ sK430 ) )
!= $true )
& ! [X3: term] :
( ( sK429 @ X3 )
= ( sK428 @ id @ X3 @ id ) )
& ! [X4: subst > term > term] :
( ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) )
| ( ( ( sK428 @ id @ ( sK434 @ X4 ) @ id )
= $true )
& ( ( sK428 @ id @ ( X4 @ id @ ( sK434 @ X4 ) ) @ id )
!= $true ) )
| ( ( sK428 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ! [X9: term] :
( ( ( sK429 @ X9 )
!= $true )
| ( ( sK429 @ ( sub @ sK430 @ ( push @ X9 @ id ) ) )
= $true ) ) ) )
& ( ! [X10: subst > term > subst > $o,X11: term > $o,X12: term] :
( ( ( X11 @ ( lam @ X12 ) )
= $true )
| ( ( X11 @ ( sK435 @ X11 @ X10 ) )
!= ( X10 @ id @ ( sK435 @ X11 @ X10 ) @ id ) )
| ( ! [X15: subst,X16: term,X17: subst] :
( ( sK436 @ X10 @ ( comp @ X15 @ X17 ) @ ( sub @ X16 @ X17 ) )
= ( sub @ ( sK436 @ X10 @ X15 @ X16 ) @ X17 ) )
& ! [X18: term] :
( ( ( X10 @ id @ X18 @ id )
!= $true )
| ( ( X10 @ id @ ( sK436 @ X10 @ id @ X18 ) @ id )
= $true ) )
& ( ( X10 @ id @ ( lam @ ( sK436 @ X10 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( ( X11 @ ( sK437 @ X12 @ X11 ) )
= $true )
& ( ( X11 @ ( sub @ X12 @ ( push @ ( sK437 @ X12 @ X11 ) @ id ) ) )
!= $true ) ) )
| ( sP2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK428,sK429,sK430,sK431,sK432,sK433,sK434,sK435,sK436,sK437])],[f450,f456,f455,f454,f453,f452,f451]) ).
thf(f451,plain,
( ? [X0: subst > term > subst > $o,X1: term > $o,X2: term] :
( ( $true
!= ( X1 @ ( lam @ X2 ) ) )
& ! [X3: term] :
( ( X0 @ id @ X3 @ id )
= ( X1 @ X3 ) )
& ! [X4: subst > term > term] :
( ? [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
!= ( sub @ ( X4 @ X5 @ X6 ) @ X7 ) )
| ? [X8: term] :
( ( ( X0 @ id @ X8 @ id )
= $true )
& ( ( X0 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true ) )
| ( ( X0 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ! [X9: term] :
( ( ( X1 @ X9 )
!= $true )
| ( ( X1 @ ( sub @ X2 @ ( push @ X9 @ id ) ) )
= $true ) ) )
=> ( ( ( sK429 @ ( lam @ sK430 ) )
!= $true )
& ! [X3: term] :
( ( sK429 @ X3 )
= ( sK428 @ id @ X3 @ id ) )
& ! [X4: subst > term > term] :
( ? [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
!= ( sub @ ( X4 @ X5 @ X6 ) @ X7 ) )
| ? [X8: term] :
( ( ( sK428 @ id @ X8 @ id )
= $true )
& ( ( sK428 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true ) )
| ( ( sK428 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ! [X9: term] :
( ( ( sK429 @ X9 )
!= $true )
| ( ( sK429 @ ( sub @ sK430 @ ( push @ X9 @ id ) ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f452,plain,
! [X4: subst > term > term] :
( ? [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
!= ( sub @ ( X4 @ X5 @ X6 ) @ X7 ) )
=> ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f453,plain,
! [X4: subst > term > term] :
( ? [X8: term] :
( ( ( sK428 @ id @ X8 @ id )
= $true )
& ( ( sK428 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true ) )
=> ( ( ( sK428 @ id @ ( sK434 @ X4 ) @ id )
= $true )
& ( ( sK428 @ id @ ( X4 @ id @ ( sK434 @ X4 ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f454,plain,
! [X10: subst > term > subst > $o,X11: term > $o] :
( ? [X13: term] :
( ( X10 @ id @ X13 @ id )
!= ( X11 @ X13 ) )
=> ( ( X11 @ ( sK435 @ X11 @ X10 ) )
!= ( X10 @ id @ ( sK435 @ X11 @ X10 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f455,plain,
! [X10: subst > term > subst > $o] :
( ? [X14: subst > term > term] :
( ! [X15: subst,X16: term,X17: subst] :
( ( X14 @ ( comp @ X15 @ X17 ) @ ( sub @ X16 @ X17 ) )
= ( sub @ ( X14 @ X15 @ X16 ) @ X17 ) )
& ! [X18: term] :
( ( ( X10 @ id @ X18 @ id )
!= $true )
| ( ( X10 @ id @ ( X14 @ id @ X18 ) @ id )
= $true ) )
& ( ( X10 @ id @ ( lam @ ( X14 @ sh @ one ) ) @ id )
!= $true ) )
=> ( ! [X17: subst,X16: term,X15: subst] :
( ( sK436 @ X10 @ ( comp @ X15 @ X17 ) @ ( sub @ X16 @ X17 ) )
= ( sub @ ( sK436 @ X10 @ X15 @ X16 ) @ X17 ) )
& ! [X18: term] :
( ( ( X10 @ id @ X18 @ id )
!= $true )
| ( ( X10 @ id @ ( sK436 @ X10 @ id @ X18 ) @ id )
= $true ) )
& ( ( X10 @ id @ ( lam @ ( sK436 @ X10 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f456,plain,
! [X11: term > $o,X12: term] :
( ? [X19: term] :
( ( ( X11 @ X19 )
= $true )
& ( ( X11 @ ( sub @ X12 @ ( push @ X19 @ id ) ) )
!= $true ) )
=> ( ( ( X11 @ ( sK437 @ X12 @ X11 ) )
= $true )
& ( ( X11 @ ( sub @ X12 @ ( push @ ( sK437 @ X12 @ X11 ) @ id ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f450,plain,
( ( ( sP2 = $true )
| ? [X0: subst > term > subst > $o,X1: term > $o,X2: term] :
( ( $true
!= ( X1 @ ( lam @ X2 ) ) )
& ! [X3: term] :
( ( X0 @ id @ X3 @ id )
= ( X1 @ X3 ) )
& ! [X4: subst > term > term] :
( ? [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
!= ( sub @ ( X4 @ X5 @ X6 ) @ X7 ) )
| ? [X8: term] :
( ( ( X0 @ id @ X8 @ id )
= $true )
& ( ( X0 @ id @ ( X4 @ id @ X8 ) @ id )
!= $true ) )
| ( ( X0 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) )
& ! [X9: term] :
( ( ( X1 @ X9 )
!= $true )
| ( ( X1 @ ( sub @ X2 @ ( push @ X9 @ id ) ) )
= $true ) ) ) )
& ( ! [X10: subst > term > subst > $o,X11: term > $o,X12: term] :
( ( ( X11 @ ( lam @ X12 ) )
= $true )
| ? [X13: term] :
( ( X10 @ id @ X13 @ id )
!= ( X11 @ X13 ) )
| ? [X14: subst > term > term] :
( ! [X15: subst,X16: term,X17: subst] :
( ( X14 @ ( comp @ X15 @ X17 ) @ ( sub @ X16 @ X17 ) )
= ( sub @ ( X14 @ X15 @ X16 ) @ X17 ) )
& ! [X18: term] :
( ( ( X10 @ id @ X18 @ id )
!= $true )
| ( ( X10 @ id @ ( X14 @ id @ X18 ) @ id )
= $true ) )
& ( ( X10 @ id @ ( lam @ ( X14 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X19: term] :
( ( ( X11 @ X19 )
= $true )
& ( ( X11 @ ( sub @ X12 @ ( push @ X19 @ id ) ) )
!= $true ) ) )
| ( sP2 != $true ) ) ),
inference(rectify,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( sP2 = $true )
| ? [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
!= $true )
& ! [X249: term] :
( ( X246 @ id @ X249 @ id )
= ( X247 @ X249 ) )
& ! [X250: subst > term > term] :
( ? [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
!= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
| ? [X251: term] :
( ( ( X246 @ id @ X251 @ id )
= $true )
& ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
!= $true ) )
| ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
= $true ) )
& ! [X255: term] :
( ( ( X247 @ X255 )
!= $true )
| ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
= $true ) ) ) )
& ( ! [X246: subst > term > subst > $o,X247: term > $o,X248: term] :
( ( ( X247 @ ( lam @ X248 ) )
= $true )
| ? [X249: term] :
( ( X246 @ id @ X249 @ id )
!= ( X247 @ X249 ) )
| ? [X250: subst > term > term] :
( ! [X252: subst,X253: term,X254: subst] :
( ( sub @ ( X250 @ X252 @ X253 ) @ X254 )
= ( X250 @ ( comp @ X252 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X251: term] :
( ( ( X246 @ id @ X251 @ id )
!= $true )
| ( ( X246 @ id @ ( X250 @ id @ X251 ) @ id )
= $true ) )
& ( ( X246 @ id @ ( lam @ ( X250 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X255: term] :
( ( ( X247 @ X255 )
= $true )
& ( ( X247 @ ( sub @ X248 @ ( push @ X255 @ id ) ) )
!= $true ) ) )
| ( sP2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f3781,plain,
( spl591_124
| ~ spl591_438 ),
inference(avatar_split_clause,[status(thm)],[f1016,f3778,f2431]) ).
thf(f1016,plain,
( ( sP2 = $true )
| ( ( sK429 @ ( lam @ sK430 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f457]) ).
thf(f3134,plain,
( spl591_290
| spl591_124 ),
inference(avatar_split_clause,[status(thm)],[f1573,f2431,f3132]) ).
thf(f1573,plain,
! [X4: subst > term > term] :
( ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( sK434 @ X4 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK428 @ ( d2subst @ d_id ) @ ( lam @ ( X4 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( sP2 = $true ) ),
inference(definition_unfolding,[status(thm)],[f1014,f1127,f1127,f1127,f1248,f1150,f1127]) ).
thf(f1014,plain,
! [X4: subst > term > term] :
( ( sP2 = $true )
| ( ( X4 @ ( comp @ ( sK431 @ X4 ) @ ( sK433 @ X4 ) ) @ ( sub @ ( sK432 @ X4 ) @ ( sK433 @ X4 ) ) )
!= ( sub @ ( X4 @ ( sK431 @ X4 ) @ ( sK432 @ X4 ) ) @ ( sK433 @ X4 ) ) )
| ( ( sK428 @ id @ ( sK434 @ X4 ) @ id )
= $true )
| ( ( sK428 @ id @ ( lam @ ( X4 @ sh @ one ) ) @ id )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f457]) ).
thf(f2549,plain,
( spl591_39
| ~ spl591_151 ),
inference(avatar_split_clause,[status(thm)],[f1100,f2546,f2077]) ).
thf(f1100,plain,
( ( shinj = $true )
| ( sK561 != sK562 ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f2438,plain,
( ~ spl591_124
| spl591_125 ),
inference(avatar_split_clause,[status(thm)],[f1040,f2435,f2431]) ).
thf(f1040,plain,
( ( sP2 != $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f2084,plain,
( spl591_39
| spl591_40 ),
inference(avatar_split_clause,[status(thm)],[f1645,f2081,f2077]) ).
thf(f1645,plain,
( ( ( sub @ sK561 @ ( d2subst @ d_id ) )
= ( sub @ sK562 @ ( d2subst @ d_id ) ) )
| ( shinj = $true ) ),
inference(definition_unfolding,[status(thm)],[f1099,f1248,f1248]) ).
thf(f1099,plain,
( ( shinj = $true )
| ( ( sub @ sK561 @ sh )
= ( sub @ sK562 @ sh ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:06:15 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.27/0.47 % Domain : Software Verification
% 0.27/0.47 % Problem : Benchmark: ALG444^1, Active target: hoasinduction_lem3v2a
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Kon26]
% 0.27/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : ? v9.3.0
% 0.27/0.47 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.27/0.47 % Number of atoms : 256 ( 129 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 248 ( 128 avg)
% 0.27/0.47 % Number of connectives : 2611 ( 333 ~; 306 |; 129 &;1742 @)
% 0.27/0.47 % ( 56 <=>; 45 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 151 ( 76 avg)
% 0.27/0.47 % Number of types : 5 ( 4 usr)
% 0.27/0.47 % Number of type conns : 228 ( 228 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.27/0.47 % Number of variables : 561 ( 10 ^; 549 !; 2 ?; 561 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments :
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(term_type,type,
% 0.27/0.47 term: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(subst_type,type,
% 0.27/0.47 subst: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(one_decl,type,
% 0.27/0.47 one: term ).
% 0.27/0.47
% 0.27/0.47 thf(ap_decl,type,
% 0.27/0.47 ap: term > term > term ).
% 0.27/0.47
% 0.27/0.47 thf(lam_decl,type,
% 0.27/0.47 lam: term > term ).
% 0.27/0.47
% 0.27/0.47 thf(sub_decl,type,
% 0.27/0.47 sub: term > subst > term ).
% 0.27/0.47
% 0.27/0.47 thf(id_decl,type,
% 0.27/0.47 id: subst ).
% 0.27/0.47
% 0.27/0.47 thf(sh_decl,type,
% 0.27/0.47 sh: subst ).
% 0.27/0.47
% 0.27/0.47 thf(push_decl,type,
% 0.27/0.47 push: term > subst > subst ).
% 0.27/0.47
% 0.27/0.47 thf(comp_decl,type,
% 0.27/0.47 comp: subst > subst > subst ).
% 0.27/0.47
% 0.27/0.47 thf(var_decl,type,
% 0.27/0.47 var: term > $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1v2_decl,type,
% 0.27/0.47 pushprop_lem1v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1_gthm_decl,type,
% 0.27/0.47 pushprop_lem1_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axmap_decl,type,
% 0.27/0.47 axmap: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem0_gthm_decl,type,
% 0.27/0.47 pushprop_lem0_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(shinj_decl,type,
% 0.27/0.47 shinj: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem1v2_decl,type,
% 0.27/0.47 hoasinduction_lem1v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem1v2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasap_decl,type,
% 0.27/0.47 hoasap: subst > term > subst > term > term ).
% 0.27/0.47
% 0.27/0.47 thf(induction2lem_decl,type,
% 0.27/0.47 induction2lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2_f_decl,type,
% 0.27/0.47 hoasinduction_lem3v2_f: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axvarshift_decl,type,
% 0.27/0.47 axvarshift: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj2_decl,type,
% 0.27/0.47 hoasapinj2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapnotvar_gthm_decl,type,
% 0.27/0.47 hoasapnotvar_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj1_decl,type,
% 0.27/0.47 hoasapinj1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ulamvar1_decl,type,
% 0.27/0.47 ulamvar1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction2lem_lthm_decl,type,
% 0.27/0.47 induction2lem_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem3v2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(apnotvar_decl,type,
% 0.27/0.47 apnotvar: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lthm_orig_decl,type,
% 0.27/0.47 pushprop_lthm_orig: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3v2_f_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lthm_decl,type,
% 0.27/0.47 hoasinduction_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.27/0.47 hoasinduction_no_psi_cond_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslaminj_decl,type,
% 0.27/0.47 hoaslaminj: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3aaa_decl,type,
% 0.27/0.47 hoasinduction_lem3aaa: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction2lem_gthm_decl,type,
% 0.27/0.47 induction2lem_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3aa_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3_decl,type,
% 0.27/0.47 hoasinduction_lem3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem2_decl,type,
% 0.27/0.47 hoasinduction_lem2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(termmset_lthm_decl,type,
% 0.27/0.47 termmset_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem1_decl,type,
% 0.27/0.47 hoasinduction_lem1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotap_lthm_decl,type,
% 0.27/0.47 hoaslamnotap_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1v2_lthm_decl,type,
% 0.27/0.47 pushprop_lem1v2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapnotvar_decl,type,
% 0.27/0.47 hoasapnotvar: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem0_decl,type,
% 0.27/0.47 hoasinduction_lem0: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_decl,type,
% 0.27/0.47 hoasinduction: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_gthm_decl,type,
% 0.27/0.47 hoasinduction_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axapp_decl,type,
% 0.27/0.47 axapp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotvar_lthm_decl,type,
% 0.27/0.47 hoaslamnotvar_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem3v2_lthm_decl,type,
% 0.27/0.47 pushprop_lem3v2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3b_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ulamvarind_decl,type,
% 0.27/0.47 ulamvarind: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction_decl,type,
% 0.27/0.47 induction: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3a_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(termmset_gthm_decl,type,
% 0.27/0.47 termmset_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3aa_decl,type,
% 0.27/0.47 hoasinduction_lem3aa: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1v2_gthm_decl,type,
% 0.27/0.47 pushprop_lem1v2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotap_gthm_decl,type,
% 0.27/0.47 hoaslamnotap_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotvar_gthm_decl,type,
% 0.27/0.47 hoaslamnotvar_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem3b_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem2v2_decl,type,
% 0.27/0.47 pushprop_lem2v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem3a_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axclos_decl,type,
% 0.27/0.47 axclos: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axassoc_decl,type,
% 0.27/0.47 axassoc: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem2v2_decl,type,
% 0.27/0.47 hoasinduction_lem2v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lthm_decl,type,
% 0.27/0.47 pushprop_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(apinj2_decl,type,
% 0.27/0.47 apinj2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(apinj1_decl,type,
% 0.27/0.47 apinj1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj2_lthm_decl,type,
% 0.27/0.47 hoasapinj2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2a_decl,type,
% 0.27/0.47 hoasinduction_lem3v2a: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj1_lthm_decl,type,
% 0.27/0.47 hoasapinj1_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslaminj_lthm_decl,type,
% 0.27/0.47 hoaslaminj_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axvarcons_decl,type,
% 0.27/0.47 axvarcons: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslam_decl,type,
% 0.27/0.47 hoaslam: subst > ( subst > term > term ) > term ).
% 0.27/0.47
% 0.27/0.47 thf(axscons_decl,type,
% 0.27/0.47 axscons: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem2v2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axidr_decl,type,
% 0.27/0.47 axidr: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1_decl,type,
% 0.27/0.47 pushprop_lem1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(laminj_decl,type,
% 0.27/0.47 laminj: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem0_decl,type,
% 0.27/0.47 pushprop_lem0: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_gthm_decl,type,
% 0.27/0.47 pushprop_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axabs_decl,type,
% 0.27/0.47 axabs: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3v2a_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem2_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj2_gthm_decl,type,
% 0.27/0.47 hoasapinj2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.27/0.47 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem1_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem1_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lamnotap_decl,type,
% 0.27/0.47 lamnotap: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapinj1_gthm_decl,type,
% 0.27/0.47 hoasapinj1_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotvar_decl,type,
% 0.27/0.47 hoaslamnotvar: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axidl_decl,type,
% 0.27/0.47 axidl: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslaminj_gthm_decl,type,
% 0.27/0.47 hoaslaminj_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction2_lthm_decl,type,
% 0.27/0.47 induction2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem0_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem0_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(substmonoid_lthm_decl,type,
% 0.27/0.47 substmonoid_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_decl,type,
% 0.27/0.47 pushprop: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem3_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem2_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3b_decl,type,
% 0.27/0.47 hoasinduction_lem3b: $o ).
% 0.27/0.47
% 0.27/0.47 thf(substmonoid_decl,type,
% 0.27/0.47 substmonoid: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lamnotvar_decl,type,
% 0.27/0.47 lamnotvar: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3a_decl,type,
% 0.27/0.47 hoasinduction_lem3a: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem1_gthm_decl,type,
% 0.27/0.47 hoasinduction_lem1_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_no_psi_cond_decl,type,
% 0.27/0.47 hoasinduction_no_psi_cond: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction2_gthm_decl,type,
% 0.27/0.47 induction2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem2v2_lthm_decl,type,
% 0.27/0.47 pushprop_lem2v2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasvar_decl,type,
% 0.27/0.47 hoasvar: subst > term > subst > $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoaslamnotap_decl,type,
% 0.27/0.47 hoaslamnotap: $o ).
% 0.27/0.47
% 0.27/0.47 thf(substmonoid_gthm_decl,type,
% 0.27/0.47 substmonoid_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ulamvarsh_decl,type,
% 0.27/0.47 ulamvarsh: $o ).
% 0.27/0.47
% 0.27/0.47 thf(induction2_decl,type,
% 0.27/0.47 induction2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem3v2_decl,type,
% 0.27/0.47 pushprop_lem3v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem2v2_gthm_decl,type,
% 0.27/0.47 pushprop_lem2v2_gthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem1_lthm_decl,type,
% 0.27/0.47 pushprop_lem1_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2_decl,type,
% 0.27/0.47 hoasinduction_lem3v2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(axshiftcons_decl,type,
% 0.27/0.47 axshiftcons: $o ).
% 0.27/0.47
% 0.27/0.47 thf(termmset_decl,type,
% 0.27/0.47 termmset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_lem0_lthm_decl,type,
% 0.27/0.47 pushprop_lem0_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasapnotvar_lthm_decl,type,
% 0.27/0.47 hoasapnotvar_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.27/0.47 hoasinduction_lem3v2_lthm: $o ).
% 0.27/0.47
% 0.27/0.47 thf(pushprop_p_and_p_prime_decl,type,
% 0.27/0.47 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(axvarid_decl,type,
% 0.27/0.47 axvarid: $o ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lthm_3_decl,type,
% 0.27/0.47 hoasinduction_lthm_3: $o ).
% 0.27/0.47
% 0.27/0.47 %----Types of the domains
% 0.27/0.47 thf(d_term_type,type,
% 0.27/0.47 d_term: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(d_subst_type,type,
% 0.27/0.47 d_subst: $tType ).
% 0.27/0.47
% 0.27/0.47 %----Types of the promotion functions
% 0.27/0.47 thf(d2term_decl,type,
% 0.27/0.47 d2term: d_term > term ).
% 0.27/0.47
% 0.27/0.47 thf(d2subst_decl,type,
% 0.27/0.47 d2subst: d_subst > subst ).
% 0.27/0.47
% 0.27/0.47 %----Types of the domain elements
% 0.27/0.47 thf(d_one_decl,type,
% 0.27/0.47 d_one: d_term ).
% 0.27/0.47
% 0.27/0.47 thf(d_id_decl,type,
% 0.27/0.47 d_id: d_subst ).
% 0.27/0.47
% 0.27/0.47 thf(alg444_1,axiom,
% 0.27/0.47 ( ! [T: term] :
% 0.27/0.47 ? [DT: d_term] :
% 0.27/0.47 ( T
% 0.27/0.47 = ( d2term @ DT ) )
% 0.27/0.47 & ! [DT: d_term] : ( DT = d_one )
% 0.27/0.47 & ! [DT1: d_term,DT2: d_term] :
% 0.27/0.47 ( ( ( d2term @ DT1 )
% 0.27/0.47 = ( d2term @ DT2 ) )
% 0.27/0.47 => ( DT1 = DT2 ) )
% 0.27/0.47 & ! [S: subst] :
% 0.27/0.47 ? [DS: d_subst] :
% 0.27/0.47 ( S
% 0.27/0.47 = ( d2subst @ DS ) )
% 0.27/0.47 & ! [DS: d_subst] : ( DS = d_id )
% 0.27/0.47 & ! [DS1: d_subst,DS2: d_subst] :
% 0.27/0.47 ( ( ( d2subst @ DS1 )
% 0.27/0.47 = ( d2subst @ DS2 ) )
% 0.27/0.47 => ( DS1 = DS2 ) )
% 0.27/0.47 & ( one
% 0.27/0.47 = ( d2term @ d_one ) )
% 0.27/0.47 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.27/0.47 = ( d2term @ d_one ) )
% 0.27/0.47 & ( ( lam @ ( d2term @ d_one ) )
% 0.27/0.47 = ( d2term @ d_one ) )
% 0.27/0.47 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.27/0.47 = ( d2term @ d_one ) )
% 0.27/0.47 & ( id
% 0.27/0.47 = ( d2subst @ d_id ) )
% 0.27/0.47 & ( sh
% 0.27/0.47 = ( d2subst @ d_id ) )
% 0.27/0.47 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.27/0.47 = ( d2subst @ d_id ) )
% 0.27/0.47 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.27/0.47 = ( d2subst @ d_id ) )
% 0.27/0.47 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.27/0.47 = ( d2term @ d_one ) )
% 0.27/0.47 & ( hoaslam
% 0.27/0.47 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.27/0.47 & ( hoasinduction_p_and_p_prime
% 0.27/0.47 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.27/0.47 ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) ) ) )
% 0.27/0.47 & ( pushprop_p_and_p_prime
% 0.27/0.47 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.27/0.47 ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.27/0.47 & ~ ( var @ ( d2term @ d_one ) )
% 0.27/0.47 & ( pushprop_lem1v2
% 0.27/0.47 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.27/0.47 | ( Q @ one ) ) )
% 0.27/0.47 & pushprop_lem1_gthm
% 0.27/0.47 & axmap
% 0.27/0.47 & pushprop_lem0_gthm
% 0.27/0.47 & ( shinj
% 0.27/0.47 <=> ! [A: term,B: term] :
% 0.27/0.47 ( ( ( sub @ A @ sh )
% 0.27/0.47 != ( sub @ B @ sh ) )
% 0.27/0.47 | ( A = B ) ) )
% 0.27/0.47 & hoasinduction_lem1v2
% 0.27/0.47 & hoasinduction_lem1v2_gthm
% 0.27/0.47 & ( induction2lem
% 0.27/0.47 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.27/0.47 ( ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( var @ B )
% 0.27/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.27/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.27/0.47 & ( hoasinduction_lem3v2_f
% 0.27/0.47 <=> ! [B: term] :
% 0.27/0.47 ~ ! [F: subst > term > term] :
% 0.27/0.47 ~ ! [A: term,M: subst] :
% 0.27/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.27/0.47 = ( F @ M @ A ) ) )
% 0.27/0.47 & axvarshift
% 0.27/0.47 & ( hoasapinj2
% 0.27/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.27/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.27/0.47 | ( C = D ) ) )
% 0.27/0.47 & hoasapnotvar_gthm
% 0.27/0.47 & ( hoasapinj1
% 0.27/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.27/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.27/0.47 | ( A = B ) ) )
% 0.27/0.47 & ~ ulamvar1
% 0.27/0.47 & ( induction2lem_lthm
% 0.27/0.47 <=> ( ! [A: term,M: subst] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.27/0.47 => ( ! [A: term,M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.27/0.47 => ( ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ M @ id ) )
% 0.27/0.47 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2140 ) )
% 0.27/0.47 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.27/0.47 ( ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( var @ B )
% 0.27/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.27/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.27/0.47 & hoasinduction_lem3v2_gthm
% 0.27/0.47 & apnotvar
% 0.27/0.47 & pushprop_lthm_orig
% 0.27/0.47 & ( hoasinduction_lem3v2_f_lthm
% 0.27/0.47 <=> ! [B: term] :
% 0.27/0.47 ~ ! [F: subst > term > term] :
% 0.27/0.47 ~ ! [A: term,M: subst] :
% 0.27/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.27/0.47 = ( F @ M @ A ) ) )
% 0.27/0.47 & ( hoasinduction_lthm
% 0.27/0.47 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2367 ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.27/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.27/0.47 | ( P @ id @ A @ id ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.27/0.47 & ( hoasinduction_no_psi_cond_lthm
% 0.27/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2367 ) )
% 0.27/0.47 => ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.27/0.47 ( ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.27/0.47 & ( hoaslaminj
% 0.27/0.47 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.27/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.27/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.27/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.27/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.27/0.47 & ( hoasinduction_lem3aaa
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.27/0.47 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.27/0.47 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.27/0.47 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.27/0.47 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.27/0.47 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.27/0.47 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.27/0.47 & induction2lem_gthm
% 0.27/0.47 & ( hoasinduction_lem3aa_lthm
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.27/0.47 & ( hoasinduction_lem3
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.27/0.47 & ( hoasinduction_lem2
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.27/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.27/0.47 & ( termmset_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) ) ) )
% 0.27/0.47 & hoasinduction_lem1
% 0.27/0.47 & hoaslamnotap_lthm
% 0.27/0.47 & ( pushprop_lem1v2_lthm
% 0.27/0.47 <=> ( ! [A: term,M: subst] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.27/0.47 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.27/0.47 | ( Q @ one ) ) ) )
% 0.27/0.47 & hoasapnotvar
% 0.27/0.47 & ( hoasinduction_lem0
% 0.27/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) ) )
% 0.27/0.47 & ( hoasinduction
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.27/0.47 | ( P @ id @ A @ id ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.27/0.47 & hoasinduction_gthm
% 0.27/0.47 & axapp
% 0.27/0.47 & hoaslamnotvar_lthm
% 0.27/0.47 & pushprop_lem3v2_lthm
% 0.27/0.47 & ( hoasinduction_lem3b_lthm
% 0.27/0.47 <=> ! [B: term] :
% 0.27/0.47 ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ( F @ sh @ one )
% 0.27/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.27/0.47 & ulamvarind
% 0.27/0.47 & ( induction
% 0.27/0.47 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2140 ) ) )
% 0.27/0.47 & ( hoasinduction_lem3a_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.27/0.47 & termmset_gthm
% 0.27/0.47 & ( hoasinduction_lem3aa
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.27/0.47 & pushprop_lem1v2_gthm
% 0.27/0.47 & hoaslamnotap_gthm
% 0.27/0.47 & hoaslamnotvar_gthm
% 0.27/0.47 & hoasinduction_lem3b_gthm
% 0.27/0.47 & pushprop_lem2v2
% 0.27/0.47 & hoasinduction_lem3a_gthm
% 0.27/0.47 & axclos
% 0.27/0.47 & axassoc
% 0.27/0.47 & ( hoasinduction_lem2v2
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ( Q @ Bound_variable_2820 )
% 0.27/0.47 | ~ ( Q @ Bound_variable_2822 )
% 0.27/0.47 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.27/0.47 & pushprop_lthm
% 0.27/0.47 & ( apinj2
% 0.27/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ A @ C )
% 0.27/0.47 != ( ap @ B @ D ) )
% 0.27/0.47 | ( C = D ) ) )
% 0.27/0.47 & ( apinj1
% 0.27/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ A @ C )
% 0.27/0.47 != ( ap @ B @ D ) )
% 0.27/0.47 | ( A = B ) ) )
% 0.27/0.47 & ( hoasapinj2_lthm
% 0.27/0.47 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ A @ C )
% 0.27/0.47 != ( ap @ B @ D ) )
% 0.27/0.47 | ( C = D ) )
% 0.27/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.27/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.27/0.47 | ( C = D ) ) ) )
% 0.27/0.47 & ( hoasinduction_lem3v2a
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.27/0.47 & ( hoasapinj1_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ A @ C )
% 0.27/0.47 != ( ap @ B @ D ) )
% 0.27/0.47 | ( A = B ) )
% 0.27/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.27/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.27/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.27/0.47 | ( A = B ) ) ) ) )
% 0.27/0.47 & ( hoaslaminj_lthm
% 0.27/0.47 <=> ( ! [A: term,M: subst] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.27/0.47 => ( ! [A: term,M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.27/0.47 => ( ! [A: term,B: term] :
% 0.27/0.47 ( ( ( lam @ A )
% 0.27/0.47 != ( lam @ B ) )
% 0.27/0.47 | ( A = B ) )
% 0.27/0.47 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.27/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.27/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.27/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.27/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.27/0.47 & ( axvarcons
% 0.27/0.47 <=> ! [A: term,M: subst] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.27/0.47 & ( axscons
% 0.27/0.47 <=> ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.27/0.47 & hoasinduction_lem2v2_gthm
% 0.27/0.47 & ( axidr
% 0.27/0.47 <=> ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ M @ id ) ) )
% 0.27/0.47 & ( pushprop_lem1
% 0.27/0.47 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.27/0.47 & ( laminj
% 0.27/0.47 <=> ! [A: term,B: term] :
% 0.27/0.47 ( ( ( lam @ A )
% 0.27/0.47 != ( lam @ B ) )
% 0.27/0.47 | ( A = B ) ) )
% 0.27/0.47 & ( hoasinduction_lem3_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.27/0.47 & ( pushprop_lem0
% 0.27/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.27/0.47 & pushprop_gthm
% 0.27/0.47 & axabs
% 0.27/0.47 & ( hoasinduction_lem3v2a_lthm
% 0.27/0.47 <=> ( ! [B: term] :
% 0.27/0.47 ~ ! [F: subst > term > term] :
% 0.27/0.47 ~ ! [A: term,M: subst] :
% 0.27/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.27/0.47 = ( F @ M @ A ) )
% 0.27/0.47 => ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.27/0.47 & hoasinduction_lem2_lthm
% 0.27/0.47 & hoasapinj2_gthm
% 0.27/0.47 & hoasinduction_lem1_lthm
% 0.27/0.47 & ~ lamnotap
% 0.27/0.47 & hoasapinj1_gthm
% 0.27/0.47 & hoaslamnotvar
% 0.27/0.47 & ( axidl
% 0.27/0.47 <=> ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ id @ M ) ) )
% 0.27/0.47 & hoaslaminj_gthm
% 0.27/0.47 & ( induction2_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.27/0.47 ( ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( var @ B )
% 0.27/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.27/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.27/0.47 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.27/0.47 & ( hoasinduction_lem0_lthm
% 0.27/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) ) )
% 0.27/0.47 & ( substmonoid_lthm
% 0.27/0.47 <=> ( ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ id @ M ) )
% 0.27/0.47 => ( ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ M @ id ) )
% 0.27/0.47 => ( ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ id @ M ) )
% 0.27/0.47 & ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ M @ id ) ) ) ) ) )
% 0.27/0.47 & pushprop
% 0.27/0.47 & hoasinduction_lem3_gthm
% 0.27/0.47 & hoasinduction_lem2_gthm
% 0.27/0.47 & ( hoasinduction_lem3b
% 0.27/0.47 <=> ! [B: term] :
% 0.27/0.47 ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ( F @ sh @ one )
% 0.27/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.27/0.47 & ( substmonoid
% 0.27/0.47 <=> ( ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ id @ M ) )
% 0.27/0.47 & ! [M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ M @ id ) ) ) )
% 0.27/0.47 & lamnotvar
% 0.27/0.47 & ( hoasinduction_lem3a
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.27/0.47 & hoasinduction_lem1_gthm
% 0.27/0.47 & ( hoasinduction_no_psi_cond
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.27/0.47 ( ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.27/0.47 & induction2_gthm
% 0.27/0.47 & pushprop_lem2v2_lthm
% 0.27/0.47 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.27/0.47 & ( hoaslamnotap
% 0.27/0.47 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.27/0.47 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.27/0.47 & substmonoid_gthm
% 0.27/0.47 & ulamvarsh
% 0.27/0.47 & ( induction2
% 0.27/0.47 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2367 ) ) )
% 0.27/0.47 & pushprop_lem3v2
% 0.27/0.47 & pushprop_lem2v2_gthm
% 0.27/0.47 & ( pushprop_lem1_lthm
% 0.27/0.47 <=> ( ! [A: term,M: subst] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.27/0.47 => ( ! [A: term,M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.27/0.47 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.27/0.47 & ( hoasinduction_lem3v2
% 0.27/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.27/0.47 & ( axshiftcons
% 0.27/0.47 <=> ! [A: term,M: subst] :
% 0.27/0.47 ( M
% 0.27/0.47 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.27/0.47 & ( termmset
% 0.27/0.47 <=> ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) ) )
% 0.27/0.47 & ( pushprop_lem0_lthm
% 0.27/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.27/0.47 & hoasapnotvar_lthm
% 0.27/0.47 & ( hoasinduction_lem3v2_lthm
% 0.27/0.47 <=> ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.27/0.47 & ( axvarid
% 0.27/0.47 <=> ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) ) )
% 0.27/0.47 & ( hoasinduction_lthm_3
% 0.27/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.27/0.47 ~ ! [Q: term > $o] :
% 0.27/0.47 ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.27/0.47 ( ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ A )
% 0.27/0.47 | ( P @ A ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ A )
% 0.27/0.47 | ~ ( P @ B )
% 0.27/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ! [B: term] :
% 0.27/0.47 ( ~ ( P @ B )
% 0.27/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( P @ ( lam @ A ) ) )
% 0.27/0.47 | ( P @ Bound_variable_2367 ) )
% 0.27/0.47 => ( ! [A: term] :
% 0.27/0.47 ( A
% 0.27/0.47 = ( sub @ A @ id ) )
% 0.27/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.27/0.47 ( ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ~ ! [X: term] :
% 0.27/0.47 ( ( Q @ X )
% 0.27/0.47 = ( P @ id @ X @ id ) )
% 0.27/0.47 | ~ ! [B: term] :
% 0.27/0.47 ( ~ ( Q @ B )
% 0.27/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.27/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.27/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.27/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.27/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.27/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.27/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.27/0.47 | ( P @ id @ A @ id ) )
% 0.27/0.47 | ~ ! [A: term,B: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ~ ( P @ id @ B @ id )
% 0.27/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.27/0.47 | ~ ! [F: subst > term > term] :
% 0.27/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 | ~ ! [A: term] :
% 0.27/0.47 ( ~ ( P @ id @ A @ id )
% 0.27/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.27/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(hoasinduction_lem3v2a,conjecture,
% 0.27/0.47 ( hoasinduction_lem3v2a
% 0.27/0.47 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.27/0.47 ( ! [F: subst > term > term] :
% 0.27/0.47 ( ! [M: subst,A: term,N: subst] :
% 0.27/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.27/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.27/0.47 => ( ! [A: term] :
% 0.27/0.47 ( ( P @ id @ A @ id )
% 0.27/0.47 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.27/0.47 => ( P @ id
% 0.27/0.47 @ ( hoaslam @ id
% 0.27/0.47 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.27/0.47 @ id ) ) )
% 0.27/0.47 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.27/0.47 => ! [A: term] :
% 0.27/0.47 ( ! [B: term] :
% 0.27/0.47 ( ( Q @ B )
% 0.27/0.47 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.27/0.47 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.35/1.47 ---- Embedded in THF ---
% 2.35/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.35/1.47 %%% Generated on Tue May 05 09:06:16 EDT 2026
% 2.35/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.35/1.47 %%% Logic specification used:
% 2.35/1.47 %%% thf(spec, logic, $$dhol).
% 2.35/1.47
% 2.35/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eLR4iSdWK1/DTF2DTF2254.p
% See solution above
% 2.35/1.47 ------------------------
% 2.51/1.51 ---- Cleaned THF ---
% 2.51/1.51 thf(term_type,type,
% 2.51/1.51 term: $tType ).
% 2.51/1.51
% 2.51/1.51 thf(subst_type,type,
% 2.51/1.51 subst: $tType ).
% 2.51/1.51
% 2.51/1.51 thf(one_decl,type,
% 2.51/1.51 one: term ).
% 2.51/1.51
% 2.51/1.51 thf(ap_decl,type,
% 2.51/1.51 ap: term > term > term ).
% 2.51/1.51
% 2.51/1.51 thf(lam_decl,type,
% 2.51/1.51 lam: term > term ).
% 2.51/1.51
% 2.51/1.51 thf(sub_decl,type,
% 2.51/1.51 sub: term > subst > term ).
% 2.51/1.51
% 2.51/1.51 thf(id_decl,type,
% 2.51/1.51 id: subst ).
% 2.51/1.51
% 2.51/1.51 thf(sh_decl,type,
% 2.51/1.51 sh: subst ).
% 2.51/1.51
% 2.51/1.51 thf(push_decl,type,
% 2.51/1.51 push: term > subst > subst ).
% 2.51/1.51
% 2.51/1.51 thf(comp_decl,type,
% 2.51/1.51 comp: subst > subst > subst ).
% 2.51/1.51
% 2.51/1.51 thf(var_decl,type,
% 2.51/1.51 var: term > $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1v2_decl,type,
% 2.51/1.51 pushprop_lem1v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1_gthm_decl,type,
% 2.51/1.51 pushprop_lem1_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axmap_decl,type,
% 2.51/1.51 axmap: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem0_gthm_decl,type,
% 2.51/1.51 pushprop_lem0_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(shinj_decl,type,
% 2.51/1.51 shinj: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem1v2_decl,type,
% 2.51/1.51 hoasinduction_lem1v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem1v2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasap_decl,type,
% 2.51/1.51 hoasap: subst > term > subst > term > term ).
% 2.51/1.51
% 2.51/1.51 thf(induction2lem_decl,type,
% 2.51/1.51 induction2lem: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2_f_decl,type,
% 2.51/1.51 hoasinduction_lem3v2_f: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axvarshift_decl,type,
% 2.51/1.51 axvarshift: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj2_decl,type,
% 2.51/1.51 hoasapinj2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapnotvar_gthm_decl,type,
% 2.51/1.51 hoasapnotvar_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj1_decl,type,
% 2.51/1.51 hoasapinj1: $o ).
% 2.51/1.51
% 2.51/1.51 thf(ulamvar1_decl,type,
% 2.51/1.51 ulamvar1: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction2lem_lthm_decl,type,
% 2.51/1.51 induction2lem_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem3v2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(apnotvar_decl,type,
% 2.51/1.51 apnotvar: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lthm_orig_decl,type,
% 2.51/1.51 pushprop_lthm_orig: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3v2_f_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lthm_decl,type,
% 2.51/1.51 hoasinduction_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.51/1.51 hoasinduction_no_psi_cond_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslaminj_decl,type,
% 2.51/1.51 hoaslaminj: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3aaa_decl,type,
% 2.51/1.51 hoasinduction_lem3aaa: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction2lem_gthm_decl,type,
% 2.51/1.51 induction2lem_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3aa_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3_decl,type,
% 2.51/1.51 hoasinduction_lem3: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem2_decl,type,
% 2.51/1.51 hoasinduction_lem2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(termmset_lthm_decl,type,
% 2.51/1.51 termmset_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem1_decl,type,
% 2.51/1.51 hoasinduction_lem1: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotap_lthm_decl,type,
% 2.51/1.51 hoaslamnotap_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1v2_lthm_decl,type,
% 2.51/1.51 pushprop_lem1v2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapnotvar_decl,type,
% 2.51/1.51 hoasapnotvar: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem0_decl,type,
% 2.51/1.51 hoasinduction_lem0: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_decl,type,
% 2.51/1.51 hoasinduction: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_gthm_decl,type,
% 2.51/1.51 hoasinduction_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axapp_decl,type,
% 2.51/1.51 axapp: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotvar_lthm_decl,type,
% 2.51/1.51 hoaslamnotvar_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem3v2_lthm_decl,type,
% 2.51/1.51 pushprop_lem3v2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3b_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(ulamvarind_decl,type,
% 2.51/1.51 ulamvarind: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction_decl,type,
% 2.51/1.51 induction: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3a_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(termmset_gthm_decl,type,
% 2.51/1.51 termmset_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3aa_decl,type,
% 2.51/1.51 hoasinduction_lem3aa: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1v2_gthm_decl,type,
% 2.51/1.51 pushprop_lem1v2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotap_gthm_decl,type,
% 2.51/1.51 hoaslamnotap_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotvar_gthm_decl,type,
% 2.51/1.51 hoaslamnotvar_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem3b_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem2v2_decl,type,
% 2.51/1.51 pushprop_lem2v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem3a_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axclos_decl,type,
% 2.51/1.51 axclos: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axassoc_decl,type,
% 2.51/1.51 axassoc: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem2v2_decl,type,
% 2.51/1.51 hoasinduction_lem2v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lthm_decl,type,
% 2.51/1.51 pushprop_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(apinj2_decl,type,
% 2.51/1.51 apinj2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(apinj1_decl,type,
% 2.51/1.51 apinj1: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj2_lthm_decl,type,
% 2.51/1.51 hoasapinj2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2a_decl,type,
% 2.51/1.51 hoasinduction_lem3v2a: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj1_lthm_decl,type,
% 2.51/1.51 hoasapinj1_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslaminj_lthm_decl,type,
% 2.51/1.51 hoaslaminj_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axvarcons_decl,type,
% 2.51/1.51 axvarcons: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslam_decl,type,
% 2.51/1.51 hoaslam: subst > ( subst > term > term ) > term ).
% 2.51/1.51
% 2.51/1.51 thf(axscons_decl,type,
% 2.51/1.51 axscons: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem2v2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axidr_decl,type,
% 2.51/1.51 axidr: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1_decl,type,
% 2.51/1.51 pushprop_lem1: $o ).
% 2.51/1.51
% 2.51/1.51 thf(laminj_decl,type,
% 2.51/1.51 laminj: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem0_decl,type,
% 2.51/1.51 pushprop_lem0: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_gthm_decl,type,
% 2.51/1.51 pushprop_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axabs_decl,type,
% 2.51/1.51 axabs: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3v2a_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem2_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj2_gthm_decl,type,
% 2.51/1.51 hoasapinj2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.51/1.51 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem1_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem1_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(lamnotap_decl,type,
% 2.51/1.51 lamnotap: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapinj1_gthm_decl,type,
% 2.51/1.51 hoasapinj1_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotvar_decl,type,
% 2.51/1.51 hoaslamnotvar: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axidl_decl,type,
% 2.51/1.51 axidl: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslaminj_gthm_decl,type,
% 2.51/1.51 hoaslaminj_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction2_lthm_decl,type,
% 2.51/1.51 induction2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem0_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem0_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(substmonoid_lthm_decl,type,
% 2.51/1.51 substmonoid_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_decl,type,
% 2.51/1.51 pushprop: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem3_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem2_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3b_decl,type,
% 2.51/1.51 hoasinduction_lem3b: $o ).
% 2.51/1.51
% 2.51/1.51 thf(substmonoid_decl,type,
% 2.51/1.51 substmonoid: $o ).
% 2.51/1.51
% 2.51/1.51 thf(lamnotvar_decl,type,
% 2.51/1.51 lamnotvar: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3a_decl,type,
% 2.51/1.51 hoasinduction_lem3a: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem1_gthm_decl,type,
% 2.51/1.51 hoasinduction_lem1_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_no_psi_cond_decl,type,
% 2.51/1.51 hoasinduction_no_psi_cond: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction2_gthm_decl,type,
% 2.51/1.51 induction2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem2v2_lthm_decl,type,
% 2.51/1.51 pushprop_lem2v2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasvar_decl,type,
% 2.51/1.51 hoasvar: subst > term > subst > $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoaslamnotap_decl,type,
% 2.51/1.51 hoaslamnotap: $o ).
% 2.51/1.51
% 2.51/1.51 thf(substmonoid_gthm_decl,type,
% 2.51/1.51 substmonoid_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(ulamvarsh_decl,type,
% 2.51/1.51 ulamvarsh: $o ).
% 2.51/1.51
% 2.51/1.51 thf(induction2_decl,type,
% 2.51/1.51 induction2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem3v2_decl,type,
% 2.51/1.51 pushprop_lem3v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem2v2_gthm_decl,type,
% 2.51/1.51 pushprop_lem2v2_gthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem1_lthm_decl,type,
% 2.51/1.51 pushprop_lem1_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2_decl,type,
% 2.51/1.51 hoasinduction_lem3v2: $o ).
% 2.51/1.51
% 2.51/1.51 thf(axshiftcons_decl,type,
% 2.51/1.51 axshiftcons: $o ).
% 2.51/1.51
% 2.51/1.51 thf(termmset_decl,type,
% 2.51/1.51 termmset: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_lem0_lthm_decl,type,
% 2.51/1.51 pushprop_lem0_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasapnotvar_lthm_decl,type,
% 2.51/1.51 hoasapnotvar_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.51/1.51 hoasinduction_lem3v2_lthm: $o ).
% 2.51/1.51
% 2.51/1.51 thf(pushprop_p_and_p_prime_decl,type,
% 2.51/1.51 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.51/1.51
% 2.51/1.51 thf(axvarid_decl,type,
% 2.51/1.51 axvarid: $o ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lthm_3_decl,type,
% 2.51/1.51 hoasinduction_lthm_3: $o ).
% 2.51/1.51
% 2.51/1.51 thf(d_term_type,type,
% 2.51/1.51 d_term: $tType ).
% 2.51/1.51
% 2.51/1.51 thf(d_subst_type,type,
% 2.51/1.51 d_subst: $tType ).
% 2.51/1.51
% 2.51/1.51 thf(d2term_decl,type,
% 2.51/1.51 d2term: d_term > term ).
% 2.51/1.51
% 2.51/1.51 thf(d2subst_decl,type,
% 2.51/1.51 d2subst: d_subst > subst ).
% 2.51/1.51
% 2.51/1.51 thf(d_one_decl,type,
% 2.51/1.51 d_one: d_term ).
% 2.51/1.51
% 2.51/1.51 thf(d_id_decl,type,
% 2.51/1.51 d_id: d_subst ).
% 2.51/1.51
% 2.51/1.51 thf(alg444_1,axiom,
% 2.51/1.51 ( ! [T: term] :
% 2.51/1.51 ? [DT: d_term] :
% 2.51/1.51 ( T
% 2.51/1.51 = ( d2term @ DT ) )
% 2.51/1.51 & ! [DT: d_term] : ( DT = d_one )
% 2.51/1.51 & ! [DT1: d_term,DT2: d_term] :
% 2.51/1.51 ( ( ( d2term @ DT1 )
% 2.51/1.51 = ( d2term @ DT2 ) )
% 2.51/1.51 => ( DT1 = DT2 ) )
% 2.51/1.51 & ! [S: subst] :
% 2.51/1.51 ? [DS: d_subst] :
% 2.51/1.51 ( S
% 2.51/1.51 = ( d2subst @ DS ) )
% 2.51/1.51 & ! [DS: d_subst] : ( DS = d_id )
% 2.51/1.51 & ! [DS1: d_subst,DS2: d_subst] :
% 2.51/1.51 ( ( ( d2subst @ DS1 )
% 2.51/1.51 = ( d2subst @ DS2 ) )
% 2.51/1.51 => ( DS1 = DS2 ) )
% 2.51/1.51 & ( one
% 2.51/1.51 = ( d2term @ d_one ) )
% 2.51/1.51 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.51/1.51 = ( d2term @ d_one ) )
% 2.51/1.51 & ( ( lam @ ( d2term @ d_one ) )
% 2.51/1.51 = ( d2term @ d_one ) )
% 2.51/1.51 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.51/1.51 = ( d2term @ d_one ) )
% 2.51/1.51 & ( id
% 2.51/1.51 = ( d2subst @ d_id ) )
% 2.51/1.51 & ( sh
% 2.51/1.51 = ( d2subst @ d_id ) )
% 2.51/1.51 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.51/1.51 = ( d2subst @ d_id ) )
% 2.51/1.51 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.51/1.51 = ( d2subst @ d_id ) )
% 2.51/1.51 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.51/1.51 = ( d2term @ d_one ) )
% 2.51/1.51 & ( hoaslam
% 2.51/1.51 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.51/1.51 & ( hoasinduction_p_and_p_prime
% 2.51/1.51 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.51/1.51 ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) ) ) )
% 2.51/1.51 & ( pushprop_p_and_p_prime
% 2.51/1.51 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.51/1.51 ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.51/1.51 & ~ ( var @ ( d2term @ d_one ) )
% 2.51/1.51 & ( pushprop_lem1v2
% 2.51/1.51 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.51/1.51 | ( Q @ one ) ) )
% 2.51/1.51 & pushprop_lem1_gthm
% 2.51/1.51 & axmap
% 2.51/1.51 & pushprop_lem0_gthm
% 2.51/1.51 & ( shinj
% 2.51/1.51 <=> ! [A: term,B: term] :
% 2.51/1.51 ( ( ( sub @ A @ sh )
% 2.51/1.51 != ( sub @ B @ sh ) )
% 2.51/1.51 | ( A = B ) ) )
% 2.51/1.51 & hoasinduction_lem1v2
% 2.51/1.51 & hoasinduction_lem1v2_gthm
% 2.51/1.51 & ( induction2lem
% 2.51/1.51 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.51/1.51 ( ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( var @ B )
% 2.51/1.51 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.51/1.51 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.51/1.51 & ( hoasinduction_lem3v2_f
% 2.51/1.51 <=> ! [B: term] :
% 2.51/1.51 ~ ! [F: subst > term > term] :
% 2.51/1.51 ~ ! [A: term,M: subst] :
% 2.51/1.51 ( ( sub @ B @ ( push @ A @ M ) )
% 2.51/1.51 = ( F @ M @ A ) ) )
% 2.51/1.51 & axvarshift
% 2.51/1.51 & ( hoasapinj2
% 2.51/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.51/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.51/1.51 | ( C = D ) ) )
% 2.51/1.51 & hoasapnotvar_gthm
% 2.51/1.51 & ( hoasapinj1
% 2.51/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.51/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.51/1.51 | ( A = B ) ) )
% 2.51/1.51 & ~ ulamvar1
% 2.51/1.51 & ( induction2lem_lthm
% 2.51/1.51 <=> ( ! [A: term,M: subst] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.51/1.51 => ( ! [A: term,M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.51/1.51 => ( ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ M @ id ) )
% 2.51/1.51 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2140 ) )
% 2.51/1.51 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.51/1.51 ( ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( var @ B )
% 2.51/1.51 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.51/1.51 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.51/1.51 & hoasinduction_lem3v2_gthm
% 2.51/1.51 & apnotvar
% 2.51/1.51 & pushprop_lthm_orig
% 2.51/1.51 & ( hoasinduction_lem3v2_f_lthm
% 2.51/1.51 <=> ! [B: term] :
% 2.51/1.51 ~ ! [F: subst > term > term] :
% 2.51/1.51 ~ ! [A: term,M: subst] :
% 2.51/1.51 ( ( sub @ B @ ( push @ A @ M ) )
% 2.51/1.51 = ( F @ M @ A ) ) )
% 2.51/1.51 & ( hoasinduction_lthm
% 2.51/1.51 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2367 ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.51/1.51 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ ( sub @ A @ id ) )
% 2.51/1.51 | ( P @ id @ A @ id ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.51/1.51 & ( hoasinduction_no_psi_cond_lthm
% 2.51/1.51 <=> ( ! [P: subst > term > subst > $o] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2367 ) )
% 2.51/1.51 => ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.51/1.51 ( ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.51/1.51 & ( hoaslaminj
% 2.51/1.51 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.51/1.51 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ( ( lam @ ( F @ sh @ one ) )
% 2.51/1.51 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.51/1.51 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.51/1.51 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.51/1.51 & ( hoasinduction_lem3aaa
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.51/1.51 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.51/1.51 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.51/1.51 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.51/1.51 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.51/1.51 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.51/1.51 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.51/1.51 & induction2lem_gthm
% 2.51/1.51 & ( hoasinduction_lem3aa_lthm
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.51/1.51 & ( hoasinduction_lem3
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 2.51/1.51 & ( hoasinduction_lem2
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.51/1.51 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 2.51/1.51 & ( termmset_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) ) ) )
% 2.51/1.51 & hoasinduction_lem1
% 2.51/1.51 & hoaslamnotap_lthm
% 2.51/1.51 & ( pushprop_lem1v2_lthm
% 2.51/1.51 <=> ( ! [A: term,M: subst] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.51/1.51 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.51/1.51 | ( Q @ one ) ) ) )
% 2.51/1.51 & hoasapnotvar
% 2.51/1.51 & ( hoasinduction_lem0
% 2.51/1.51 <=> ! [P: subst > term > subst > $o] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) ) )
% 2.51/1.51 & ( hoasinduction
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ ( sub @ A @ id ) )
% 2.51/1.51 | ( P @ id @ A @ id ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 2.51/1.51 & hoasinduction_gthm
% 2.51/1.51 & axapp
% 2.51/1.51 & hoaslamnotvar_lthm
% 2.51/1.51 & pushprop_lem3v2_lthm
% 2.51/1.51 & ( hoasinduction_lem3b_lthm
% 2.51/1.51 <=> ! [B: term] :
% 2.51/1.51 ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ( F @ sh @ one )
% 2.51/1.51 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.51/1.51 & ulamvarind
% 2.51/1.51 & ( induction
% 2.51/1.51 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2140 ) ) )
% 2.51/1.51 & ( hoasinduction_lem3a_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 2.51/1.51 & termmset_gthm
% 2.51/1.51 & ( hoasinduction_lem3aa
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.51/1.51 & pushprop_lem1v2_gthm
% 2.51/1.51 & hoaslamnotap_gthm
% 2.51/1.51 & hoaslamnotvar_gthm
% 2.51/1.51 & hoasinduction_lem3b_gthm
% 2.51/1.51 & pushprop_lem2v2
% 2.51/1.51 & hoasinduction_lem3a_gthm
% 2.51/1.51 & axclos
% 2.51/1.51 & axassoc
% 2.51/1.51 & ( hoasinduction_lem2v2
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ( Q @ Bound_variable_2820 )
% 2.51/1.51 | ~ ( Q @ Bound_variable_2822 )
% 2.51/1.51 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 2.51/1.51 & pushprop_lthm
% 2.51/1.51 & ( apinj2
% 2.51/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ A @ C )
% 2.51/1.51 != ( ap @ B @ D ) )
% 2.51/1.51 | ( C = D ) ) )
% 2.51/1.51 & ( apinj1
% 2.51/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ A @ C )
% 2.51/1.51 != ( ap @ B @ D ) )
% 2.51/1.51 | ( A = B ) ) )
% 2.51/1.51 & ( hoasapinj2_lthm
% 2.51/1.51 <=> ( ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ A @ C )
% 2.51/1.51 != ( ap @ B @ D ) )
% 2.51/1.51 | ( C = D ) )
% 2.51/1.51 => ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.51/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.51/1.51 | ( C = D ) ) ) )
% 2.51/1.51 & ( hoasinduction_lem3v2a
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 2.51/1.51 & ( hoasapinj1_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ A @ C )
% 2.51/1.51 != ( ap @ B @ D ) )
% 2.51/1.51 | ( A = B ) )
% 2.51/1.51 => ! [A: term,B: term,C: term,D: term] :
% 2.51/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.51/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.51/1.51 | ( A = B ) ) ) ) )
% 2.51/1.51 & ( hoaslaminj_lthm
% 2.51/1.51 <=> ( ! [A: term,M: subst] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.51/1.51 => ( ! [A: term,M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.51/1.51 => ( ! [A: term,B: term] :
% 2.51/1.51 ( ( ( lam @ A )
% 2.51/1.51 != ( lam @ B ) )
% 2.51/1.51 | ( A = B ) )
% 2.51/1.51 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.51/1.51 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ( ( lam @ ( F @ sh @ one ) )
% 2.51/1.51 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.51/1.51 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.51/1.51 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 2.51/1.51 & ( axvarcons
% 2.51/1.51 <=> ! [A: term,M: subst] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 2.51/1.51 & ( axscons
% 2.51/1.51 <=> ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 2.51/1.51 & hoasinduction_lem2v2_gthm
% 2.51/1.51 & ( axidr
% 2.51/1.51 <=> ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ M @ id ) ) )
% 2.51/1.51 & ( pushprop_lem1
% 2.51/1.51 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 2.51/1.51 & ( laminj
% 2.51/1.51 <=> ! [A: term,B: term] :
% 2.51/1.51 ( ( ( lam @ A )
% 2.51/1.51 != ( lam @ B ) )
% 2.51/1.51 | ( A = B ) ) )
% 2.51/1.51 & ( hoasinduction_lem3_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 2.51/1.51 & ( pushprop_lem0
% 2.51/1.51 <=> ! [P: term > $o,A: term,M: subst] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.51/1.51 & pushprop_gthm
% 2.51/1.51 & axabs
% 2.51/1.51 & ( hoasinduction_lem3v2a_lthm
% 2.51/1.51 <=> ( ! [B: term] :
% 2.51/1.51 ~ ! [F: subst > term > term] :
% 2.51/1.51 ~ ! [A: term,M: subst] :
% 2.51/1.51 ( ( sub @ B @ ( push @ A @ M ) )
% 2.51/1.51 = ( F @ M @ A ) )
% 2.51/1.51 => ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 2.51/1.51 & hoasinduction_lem2_lthm
% 2.51/1.51 & hoasapinj2_gthm
% 2.51/1.51 & hoasinduction_lem1_lthm
% 2.51/1.51 & ~ lamnotap
% 2.51/1.51 & hoasapinj1_gthm
% 2.51/1.51 & hoaslamnotvar
% 2.51/1.51 & ( axidl
% 2.51/1.51 <=> ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ id @ M ) ) )
% 2.51/1.51 & hoaslaminj_gthm
% 2.51/1.51 & ( induction2_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.51/1.51 ( ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( var @ B )
% 2.51/1.51 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.51/1.51 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 2.51/1.51 => ! [P: term > $o,Bound_variable_2367: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2367 ) ) ) ) )
% 2.51/1.51 & ( hoasinduction_lem0_lthm
% 2.51/1.51 <=> ! [P: subst > term > subst > $o] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) ) )
% 2.51/1.51 & ( substmonoid_lthm
% 2.51/1.51 <=> ( ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ id @ M ) )
% 2.51/1.51 => ( ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ M @ id ) )
% 2.51/1.51 => ( ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ id @ M ) )
% 2.51/1.51 & ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ M @ id ) ) ) ) ) )
% 2.51/1.51 & pushprop
% 2.51/1.51 & hoasinduction_lem3_gthm
% 2.51/1.51 & hoasinduction_lem2_gthm
% 2.51/1.51 & ( hoasinduction_lem3b
% 2.51/1.51 <=> ! [B: term] :
% 2.51/1.51 ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ( F @ sh @ one )
% 2.51/1.51 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.51/1.51 & ( substmonoid
% 2.51/1.51 <=> ( ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ id @ M ) )
% 2.51/1.51 & ! [M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ M @ id ) ) ) )
% 2.51/1.51 & lamnotvar
% 2.51/1.51 & ( hoasinduction_lem3a
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 2.51/1.51 & hoasinduction_lem1_gthm
% 2.51/1.51 & ( hoasinduction_no_psi_cond
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.51/1.51 ( ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 2.51/1.51 & induction2_gthm
% 2.51/1.51 & pushprop_lem2v2_lthm
% 2.51/1.51 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.51/1.51 & ( hoaslamnotap
% 2.51/1.51 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ( ( lam @ ( F @ sh @ one ) )
% 2.51/1.51 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 2.51/1.51 & substmonoid_gthm
% 2.51/1.51 & ulamvarsh
% 2.51/1.51 & ( induction2
% 2.51/1.51 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2367 ) ) )
% 2.51/1.51 & pushprop_lem3v2
% 2.51/1.51 & pushprop_lem2v2_gthm
% 2.51/1.51 & ( pushprop_lem1_lthm
% 2.51/1.51 <=> ( ! [A: term,M: subst] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.51/1.51 => ( ! [A: term,M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.51/1.51 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 2.51/1.51 & ( hoasinduction_lem3v2
% 2.51/1.51 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 2.51/1.51 & ( axshiftcons
% 2.51/1.51 <=> ! [A: term,M: subst] :
% 2.51/1.51 ( M
% 2.51/1.51 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 2.51/1.51 & ( termmset
% 2.51/1.51 <=> ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) ) )
% 2.51/1.51 & ( pushprop_lem0_lthm
% 2.51/1.51 <=> ! [P: term > $o,A: term,M: subst] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.51/1.51 & hoasapnotvar_lthm
% 2.51/1.51 & ( hoasinduction_lem3v2_lthm
% 2.51/1.51 <=> ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 2.51/1.51 & ( axvarid
% 2.51/1.51 <=> ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) ) )
% 2.51/1.51 & ( hoasinduction_lthm_3
% 2.51/1.51 <=> ( ! [P: subst > term > subst > $o] :
% 2.51/1.51 ~ ! [Q: term > $o] :
% 2.51/1.51 ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.51/1.51 ( ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ A )
% 2.51/1.51 | ( P @ A ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ A )
% 2.51/1.51 | ~ ( P @ B )
% 2.51/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ! [B: term] :
% 2.51/1.51 ( ~ ( P @ B )
% 2.51/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( P @ ( lam @ A ) ) )
% 2.51/1.51 | ( P @ Bound_variable_2367 ) )
% 2.51/1.51 => ( ! [A: term] :
% 2.51/1.51 ( A
% 2.51/1.51 = ( sub @ A @ id ) )
% 2.51/1.51 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.51/1.51 ( ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ~ ! [X: term] :
% 2.51/1.51 ( ( Q @ X )
% 2.51/1.51 = ( P @ id @ X @ id ) )
% 2.51/1.51 | ~ ! [B: term] :
% 2.51/1.51 ( ~ ( Q @ B )
% 2.51/1.51 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.51/1.51 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.51/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.51/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.51/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.51/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.51/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( var @ ( sub @ A @ id ) )
% 2.51/1.51 | ( P @ id @ A @ id ) )
% 2.51/1.51 | ~ ! [A: term,B: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ~ ( P @ id @ B @ id )
% 2.51/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.51/1.51 | ~ ! [F: subst > term > term] :
% 2.51/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 | ~ ! [A: term] :
% 2.51/1.51 ( ~ ( P @ id @ A @ id )
% 2.51/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.51/1.51 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 2.51/1.51
% 2.51/1.51 thf(hoasinduction_lem3v2a,conjecture,
% 2.51/1.51 ( hoasinduction_lem3v2a
% 2.51/1.51 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 2.51/1.51 ( ! [F: subst > term > term] :
% 2.51/1.51 ( ! [M: subst,A: term,N: subst] :
% 2.51/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.51/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.51/1.51 => ( ! [A: term] :
% 2.51/1.51 ( ( P @ id @ A @ id )
% 2.51/1.51 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.51/1.51 => ( P @ id
% 2.51/1.51 @ ( hoaslam @ id
% 2.51/1.51 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 2.51/1.51 @ id ) ) )
% 2.51/1.51 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 2.51/1.51 => ! [A: term] :
% 2.51/1.51 ( ! [B: term] :
% 2.51/1.51 ( ( Q @ B )
% 2.51/1.51 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.51/1.51 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ).
% 2.51/1.51 ------------------------
% 2.51/1.53 % (2356)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/2Mi)
% 2.51/1.53 % (2359)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/18Mi)
% 2.51/1.53 % (2356)Instruction limit reached!
% 2.51/1.53 % (2356)------------------------------
% 2.51/1.53 % (2356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.53 % (2356)Termination reason: Unknown
% 2.51/1.53 % (2356)Termination phase: shuffling
% 2.51/1.53
% 2.51/1.53 % (2356)Memory used [KB]: 1279
% 2.51/1.53 % (2356)Time elapsed: 0.003 s
% 2.51/1.53 % (2356)Instructions burned: 4 (million)
% 2.51/1.53 % (2356)------------------------------
% 2.51/1.53 % (2356)------------------------------
% 2.51/1.54 % (2359)Instruction limit reached!
% 2.51/1.54 % (2359)------------------------------
% 2.51/1.54 % (2359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (2359)Termination reason: Unknown
% 2.51/1.54 % (2359)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (2359)Memory used [KB]: 2046
% 2.51/1.54 % (2359)Time elapsed: 0.007 s
% 2.51/1.54 % (2359)Instructions burned: 18 (million)
% 2.51/1.54 % (2359)------------------------------
% 2.51/1.54 % (2359)------------------------------
% 2.51/1.54 % (2353)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/183Mi)
% 2.51/1.54 % (2355)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_2254 for (2999ds/27Mi)
% 2.51/1.54 % (2354)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_2254 for (2999ds/4Mi)
% 2.51/1.54 % (2358)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_2254 for (2999ds/275Mi)
% 2.51/1.54 % (2357)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_2254 for (2999ds/2Mi)
% 2.51/1.54 % (2357)Instruction limit reached!
% 2.51/1.54 % (2357)------------------------------
% 2.51/1.54 % (2357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (2357)Termination reason: Unknown
% 2.51/1.54 % (2357)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (2357)Memory used [KB]: 1279
% 2.51/1.54 % (2357)Time elapsed: 0.003 s
% 2.51/1.54 % (2357)Instructions burned: 3 (million)
% 2.51/1.54 % (2357)------------------------------
% 2.51/1.54 % (2357)------------------------------
% 2.51/1.54 % (2354)Instruction limit reached!
% 2.51/1.54 % (2354)------------------------------
% 2.51/1.54 % (2354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (2354)Termination reason: Unknown
% 2.51/1.54 % (2354)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (2354)Memory used [KB]: 1279
% 2.51/1.54 % (2354)Time elapsed: 0.005 s
% 2.51/1.54 % (2354)Instructions burned: 5 (million)
% 2.51/1.54 % (2354)------------------------------
% 2.51/1.54 % (2354)------------------------------
% 2.51/1.54 % (2360)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/3Mi)
% 2.51/1.54 % (2360)Instruction limit reached!
% 2.51/1.54 % (2360)------------------------------
% 2.51/1.54 % (2360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (2360)Termination reason: Unknown
% 2.51/1.54 % (2360)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (2360)Memory used [KB]: 1279
% 2.51/1.54 % (2360)Time elapsed: 0.002 s
% 2.51/1.54 % (2360)Instructions burned: 4 (million)
% 2.51/1.54 % (2360)------------------------------
% 2.51/1.54 % (2360)------------------------------
% 2.51/1.55 % (2361)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_2254 for (2999ds/37Mi)
% 2.51/1.55 % (2364)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_2254 for (2999ds/1041Mi)
% 2.51/1.55 % (2355)Instruction limit reached!
% 2.51/1.55 % (2355)------------------------------
% 2.51/1.55 % (2355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.55 % (2355)Termination reason: Unknown
% 2.51/1.55 % (2355)Termination phase: Property scanning
% 2.51/1.55
% 2.51/1.55 % (2355)Memory used [KB]: 2174
% 2.51/1.55 % (2355)Time elapsed: 0.018 s
% 2.51/1.55 % (2355)Instructions burned: 27 (million)
% 2.51/1.55 % (2355)------------------------------
% 2.51/1.55 % (2355)------------------------------
% 2.51/1.56 % (2361)Instruction limit reached!
% 2.51/1.56 % (2361)------------------------------
% 2.51/1.56 % (2361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.56 % (2361)Termination reason: Unknown
% 2.51/1.56 % (2361)Termination phase: shuffling
% 2.51/1.56
% 2.51/1.56 % (2361)Memory used [KB]: 1918
% 2.51/1.56 % (2361)Time elapsed: 0.012 s
% 2.51/1.56 % (2361)Instructions burned: 37 (million)
% 2.51/1.56 % (2361)------------------------------
% 2.51/1.56 % (2361)------------------------------
% 2.51/1.56 % (2362)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_2254 for (2999ds/15Mi)
% 2.51/1.56 % (2363)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_2254 for (2999ds/3Mi)
% 2.51/1.56 % (2363)Instruction limit reached!
% 2.51/1.56 % (2363)------------------------------
% 2.51/1.56 % (2363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.56 % (2363)Termination reason: Unknown
% 2.51/1.56 % (2363)Termination phase: shuffling
% 2.51/1.56
% 2.51/1.56 % (2363)Memory used [KB]: 1279
% 2.51/1.56 % (2363)Time elapsed: 0.004 s
% 2.51/1.56 % (2363)Instructions burned: 4 (million)
% 2.51/1.56 % (2363)------------------------------
% 2.51/1.56 % (2363)------------------------------
% 2.51/1.56 % (2358)Refutation not found, incomplete strategy
% 2.51/1.56 % (2358)------------------------------
% 2.51/1.56 % (2358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.56 % (2358)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.56
% 2.51/1.56
% 2.51/1.56 % (2358)Memory used [KB]: 6652
% 2.51/1.56 % (2358)Time elapsed: 0.026 s
% 2.51/1.56 % (2358)Instructions burned: 41 (million)
% 2.51/1.56 % (2358)------------------------------
% 2.51/1.56 % (2358)------------------------------
% 2.51/1.56 % (2362)Instruction limit reached!
% 2.51/1.56 % (2362)------------------------------
% 2.51/1.56 % (2362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.56 % (2362)Termination reason: Unknown
% 2.51/1.56 % (2362)Termination phase: shuffling
% 2.51/1.56
% 2.51/1.56 % (2362)Memory used [KB]: 1791
% 2.51/1.56 % (2362)Time elapsed: 0.010 s
% 2.51/1.56 % (2362)Instructions burned: 15 (million)
% 2.51/1.56 % (2362)------------------------------
% 2.51/1.56 % (2362)------------------------------
% 2.51/1.57 % (2366)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/16Mi)
% 2.51/1.57 % (2365)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/7Mi)
% 2.51/1.57 % (2366)Instruction limit reached!
% 2.51/1.57 % (2366)------------------------------
% 2.51/1.57 % (2366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.57 % (2366)Termination reason: Unknown
% 2.51/1.57 % (2366)Termination phase: shuffling
% 2.51/1.57
% 2.51/1.57 % (2366)Memory used [KB]: 2046
% 2.51/1.57 % (2366)Time elapsed: 0.006 s
% 2.51/1.57 % (2366)Instructions burned: 17 (million)
% 2.51/1.57 % (2366)------------------------------
% 2.51/1.57 % (2366)------------------------------
% 2.51/1.57 % (2365)Instruction limit reached!
% 2.51/1.57 % (2365)------------------------------
% 2.51/1.57 % (2365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.57 % (2365)Termination reason: Unknown
% 2.51/1.57 % (2365)Termination phase: shuffling
% 2.51/1.57
% 2.51/1.57 % (2365)Memory used [KB]: 1407
% 2.51/1.57 % (2365)Time elapsed: 0.006 s
% 2.51/1.57 % (2365)Instructions burned: 8 (million)
% 2.51/1.57 % (2365)------------------------------
% 2.51/1.57 % (2365)------------------------------
% 2.51/1.58 % (2367)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_2254 for (2999ds/3Mi)
% 2.51/1.58 % (2368)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_2254 for (2999ds/3Mi)
% 2.51/1.58 % (2368)Instruction limit reached!
% 2.51/1.58 % (2368)------------------------------
% 2.51/1.58 % (2368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (2368)Termination reason: Unknown
% 2.51/1.58 % (2368)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (2368)Memory used [KB]: 1279
% 2.51/1.58 % (2368)Time elapsed: 0.003 s
% 2.51/1.58 % (2368)Instructions burned: 5 (million)
% 2.51/1.58 % (2368)------------------------------
% 2.51/1.58 % (2368)------------------------------
% 2.51/1.58 % (2367)Instruction limit reached!
% 2.51/1.58 % (2367)------------------------------
% 2.51/1.58 % (2367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (2367)Termination reason: Unknown
% 2.51/1.58 % (2367)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (2367)Memory used [KB]: 1279
% 2.51/1.58 % (2367)Time elapsed: 0.004 s
% 2.51/1.58 % (2367)Instructions burned: 4 (million)
% 2.51/1.58 % (2367)------------------------------
% 2.51/1.58 % (2367)------------------------------
% 2.51/1.58 % (2370)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/3Mi)
% 2.51/1.58 % (2370)Instruction limit reached!
% 2.51/1.58 % (2370)------------------------------
% 2.51/1.58 % (2370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (2370)Termination reason: Unknown
% 2.51/1.58 % (2370)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (2370)Memory used [KB]: 1279
% 2.51/1.58 % (2370)Time elapsed: 0.002 s
% 2.51/1.58 % (2370)Instructions burned: 4 (million)
% 2.51/1.58 % (2370)------------------------------
% 2.51/1.58 % (2370)------------------------------
% 2.51/1.58 % (2369)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/7Mi)
% 2.51/1.59 % (2369)Instruction limit reached!
% 2.51/1.59 % (2369)------------------------------
% 2.51/1.59 % (2369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (2369)Termination reason: Unknown
% 2.51/1.59 % (2369)Termination phase: shuffling
% 2.51/1.59
% 2.51/1.59 % (2369)Memory used [KB]: 1407
% 2.51/1.59 % (2369)Time elapsed: 0.006 s
% 2.51/1.59 % (2369)Instructions burned: 8 (million)
% 2.51/1.59 % (2369)------------------------------
% 2.51/1.59 % (2369)------------------------------
% 2.51/1.59 % (2372)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/18Mi)
% 2.51/1.59 % (2374)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/6Mi)
% 2.51/1.59 % (2371)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/4Mi)
% 2.51/1.59 % (2374)Instruction limit reached!
% 2.51/1.59 % (2374)------------------------------
% 2.51/1.59 % (2374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (2374)Termination reason: Unknown
% 2.51/1.59 % (2374)Termination phase: shuffling
% 2.51/1.59
% 2.51/1.59 % (2374)Memory used [KB]: 1407
% 2.51/1.59 % (2374)Time elapsed: 0.003 s
% 2.51/1.59 % (2374)Instructions burned: 7 (million)
% 2.51/1.59 % (2374)------------------------------
% 2.51/1.59 % (2374)------------------------------
% 2.51/1.59 % (2372)Instruction limit reached!
% 2.51/1.59 % (2372)------------------------------
% 2.51/1.59 % (2372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (2371)Instruction limit reached!
% 2.51/1.59 % (2371)------------------------------
% 2.51/1.59 % (2371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (2371)Termination reason: Unknown
% 2.51/1.59 % (2371)Termination phase: shuffling
% 2.51/1.59
% 2.51/1.59 % (2371)Memory used [KB]: 1279
% 2.51/1.59 % (2371)Time elapsed: 0.004 s
% 2.51/1.59 % (2371)Instructions burned: 4 (million)
% 2.51/1.59 % (2371)------------------------------
% 2.51/1.59 % (2371)------------------------------
% 2.51/1.59 % (2372)Termination reason: Unknown
% 2.51/1.59 % (2372)Termination phase: shuffling
% 2.51/1.59
% 2.51/1.59 % (2372)Memory used [KB]: 2046
% 2.51/1.59 % (2372)Time elapsed: 0.007 s
% 2.51/1.59 % (2372)Instructions burned: 18 (million)
% 2.51/1.59 % (2372)------------------------------
% 2.51/1.59 % (2372)------------------------------
% 2.51/1.59 % (2373)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/710Mi)
% 2.51/1.60 % (2353)Instruction limit reached!
% 2.51/1.60 % (2353)------------------------------
% 2.51/1.60 % (2353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (2353)Termination reason: Unknown
% 2.51/1.60 % (2353)Termination phase: Property scanning
% 2.51/1.60
% 2.51/1.60 % (2353)Memory used [KB]: 4605
% 2.51/1.60 % (2353)Time elapsed: 0.062 s
% 2.51/1.60 % (2353)Instructions burned: 186 (million)
% 2.51/1.60 % (2353)------------------------------
% 2.51/1.60 % (2353)------------------------------
% 2.54/1.60 % (2376)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_2254 for (2999ds/21Mi)
% 2.54/1.60 % (2375)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_2254 for (2999ds/902Mi)
% 2.54/1.60 % (2377)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/5Mi)
% 2.54/1.61 % (2377)Instruction limit reached!
% 2.54/1.61 % (2377)------------------------------
% 2.54/1.61 % (2377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (2377)Termination reason: Unknown
% 2.54/1.61 % (2377)Termination phase: shuffling
% 2.54/1.61
% 2.54/1.61 % (2377)Memory used [KB]: 1407
% 2.54/1.61 % (2377)Time elapsed: 0.003 s
% 2.54/1.61 % (2377)Instructions burned: 8 (million)
% 2.54/1.61 % (2377)------------------------------
% 2.54/1.61 % (2377)------------------------------
% 2.54/1.61 % (2379)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/377Mi)
% 2.54/1.61 % (2376)Instruction limit reached!
% 2.54/1.61 % (2376)------------------------------
% 2.54/1.61 % (2376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (2376)Termination reason: Unknown
% 2.54/1.61 % (2376)Termination phase: shuffling
% 2.54/1.61
% 2.54/1.61 % (2376)Memory used [KB]: 2174
% 2.54/1.61 % (2376)Time elapsed: 0.008 s
% 2.54/1.61 % (2376)Instructions burned: 23 (million)
% 2.54/1.61 % (2376)------------------------------
% 2.54/1.61 % (2376)------------------------------
% 2.54/1.61 % (2378)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_2254 for (2999ds/6Mi)
% 2.54/1.61 % (2378)Instruction limit reached!
% 2.54/1.61 % (2378)------------------------------
% 2.54/1.61 % (2378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (2378)Termination reason: Unknown
% 2.54/1.61 % (2378)Termination phase: shuffling
% 2.54/1.61
% 2.54/1.61 % (2378)Memory used [KB]: 1407
% 2.54/1.61 % (2378)Time elapsed: 0.005 s
% 2.54/1.61 % (2378)Instructions burned: 6 (million)
% 2.54/1.61 % (2378)------------------------------
% 2.54/1.61 % (2378)------------------------------
% 2.54/1.61 % (2380)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_2254 for (2999ds/779Mi)
% 2.54/1.62 % (2381)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_2254 for (2999ds/19Mi)
% 2.54/1.62 % (2381)Instruction limit reached!
% 2.54/1.62 % (2381)------------------------------
% 2.54/1.62 % (2381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.62 % (2381)Termination reason: Unknown
% 2.54/1.62 % (2381)Termination phase: shuffling
% 2.54/1.62
% 2.54/1.62 % (2381)Memory used [KB]: 1663
% 2.54/1.62 % (2381)Time elapsed: 0.006 s
% 2.54/1.62 % (2381)Instructions burned: 19 (million)
% 2.54/1.62 % (2381)------------------------------
% 2.54/1.62 % (2381)------------------------------
% 2.54/1.63 % (2382)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/879Mi)
% 2.54/1.63 % (2383)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2254 for (2999ds/17Mi)
% 2.54/1.64 % (2383)Instruction limit reached!
% 2.54/1.64 % (2383)------------------------------
% 2.54/1.64 % (2383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.64 % (2383)Termination reason: Unknown
% 2.54/1.64 % (2383)Termination phase: shuffling
% 2.54/1.64
% 2.54/1.64 % (2383)Memory used [KB]: 2046
% 2.54/1.64 % (2383)Time elapsed: 0.007 s
% 2.54/1.64 % (2383)Instructions burned: 19 (million)
% 2.54/1.64 % (2383)------------------------------
% 2.54/1.64 % (2383)------------------------------
% 2.54/1.65 % (2384)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2254 for (2998ds/3Mi)
% 2.54/1.65 % (2384)Instruction limit reached!
% 2.54/1.65 % (2384)------------------------------
% 2.54/1.65 % (2384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.65 % (2384)Termination reason: Unknown
% 2.54/1.65 % (2384)Termination phase: shuffling
% 2.54/1.65
% 2.54/1.65 % (2384)Memory used [KB]: 1279
% 2.54/1.65 % (2384)Time elapsed: 0.002 s
% 2.54/1.65 % (2384)Instructions burned: 3 (million)
% 2.54/1.65 % (2384)------------------------------
% 2.54/1.65 % (2384)------------------------------
% 2.54/1.66 % (2385)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2254 for (2998ds/30Mi)
% 2.54/1.67 % (2385)Instruction limit reached!
% 2.54/1.67 % (2385)------------------------------
% 2.54/1.67 % (2385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.67 % (2385)Termination reason: Unknown
% 2.54/1.67 % (2385)Termination phase: Property scanning
% 2.54/1.67
% 2.54/1.67 % (2385)Memory used [KB]: 2174
% 2.54/1.67 % (2385)Time elapsed: 0.011 s
% 2.54/1.67 % (2385)Instructions burned: 34 (million)
% 2.54/1.67 % (2385)------------------------------
% 2.54/1.67 % (2385)------------------------------
% 2.54/1.67 % (2375)Refutation not found, incomplete strategy
% 2.54/1.67 % (2375)------------------------------
% 2.54/1.67 % (2375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.67 % (2375)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.67
% 2.54/1.67
% 2.54/1.67 % (2375)Memory used [KB]: 9338
% 2.54/1.67 % (2375)Time elapsed: 0.068 s
% 2.54/1.67 % (2375)Instructions burned: 204 (million)
% 2.54/1.67 % (2375)------------------------------
% 2.54/1.67 % (2375)------------------------------
% 2.54/1.68 % (2386)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2254 for (2998ds/127Mi)
% 2.54/1.68 % (2387)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2254 for (2998ds/100Mi)
% 2.54/1.71 % (2387)Instruction limit reached!
% 2.54/1.71 % (2387)------------------------------
% 2.54/1.71 % (2387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (2387)Termination reason: Unknown
% 2.54/1.71 % (2387)Termination phase: Saturation
% 2.54/1.71
% 2.54/1.71 % (2387)Memory used [KB]: 6524
% 2.54/1.71 % (2387)Time elapsed: 0.029 s
% 2.54/1.71 % (2387)Instructions burned: 102 (million)
% 2.54/1.71 % (2387)------------------------------
% 2.54/1.71 % (2387)------------------------------
% 2.54/1.71 % (2386)Instruction limit reached!
% 2.54/1.71 % (2386)------------------------------
% 2.54/1.71 % (2386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (2386)Termination reason: Unknown
% 2.54/1.71 % (2386)Termination phase: Property scanning
% 2.54/1.71
% 2.54/1.71 % (2386)Memory used [KB]: 4221
% 2.54/1.71 % (2386)Time elapsed: 0.036 s
% 2.54/1.71 % (2386)Instructions burned: 129 (million)
% 2.54/1.71 % (2386)------------------------------
% 2.54/1.71 % (2386)------------------------------
% 2.54/1.72 % (2388)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_2254 for (2998ds/3Mi)
% 2.54/1.72 % (2388)Instruction limit reached!
% 2.54/1.72 % (2388)------------------------------
% 2.54/1.72 % (2388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.72 % (2388)Termination reason: Unknown
% 2.54/1.72 % (2388)Termination phase: shuffling
% 2.54/1.72
% 2.54/1.72 % (2388)Memory used [KB]: 1279
% 2.54/1.72 % (2388)Time elapsed: 0.002 s
% 2.54/1.72 % (2388)Instructions burned: 3 (million)
% 2.54/1.72 % (2388)------------------------------
% 2.54/1.72 % (2388)------------------------------
% 2.54/1.72 % (2389)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_2254 for (2998ds/20Mi)
% 2.54/1.72 % (2379)Instruction limit reached!
% 2.54/1.72 % (2379)------------------------------
% 2.54/1.72 % (2379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.72 % (2379)Termination reason: Unknown
% 2.54/1.72 % (2379)Termination phase: Saturation
% 2.54/1.72
% 2.54/1.72 % (2379)Memory used [KB]: 10362
% 2.54/1.72 % (2379)Time elapsed: 0.117 s
% 2.54/1.72 % (2379)Instructions burned: 379 (million)
% 2.54/1.72 % (2379)------------------------------
% 2.54/1.72 % (2379)------------------------------
% 2.54/1.73 % (2389)Instruction limit reached!
% 2.54/1.73 % (2389)------------------------------
% 2.54/1.73 % (2389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.73 % (2389)Termination reason: Unknown
% 2.54/1.73 % (2389)Termination phase: shuffling
% 2.54/1.73
% 2.54/1.73 % (2389)Memory used [KB]: 2174
% 2.54/1.73 % (2389)Time elapsed: 0.008 s
% 2.54/1.73 % (2389)Instructions burned: 22 (million)
% 2.54/1.73 % (2389)------------------------------
% 2.54/1.73 % (2389)------------------------------
% 2.54/1.73 % (2390)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_2254 for (2998ds/86Mi)
% 2.54/1.73 % (2391)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_2254 for (2998ds/107Mi)
% 2.54/1.74 % (2392)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_2254 for (2998ds/39Mi)
% 2.54/1.75 % (2392)Instruction limit reached!
% 2.54/1.75 % (2392)------------------------------
% 2.54/1.75 % (2392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (2392)Termination reason: Unknown
% 2.54/1.75 % (2392)Termination phase: Property scanning
% 2.54/1.75
% 2.54/1.75 % (2392)Memory used [KB]: 1918
% 2.54/1.75 % (2392)Time elapsed: 0.012 s
% 2.54/1.75 % (2392)Instructions burned: 42 (million)
% 2.54/1.75 % (2392)------------------------------
% 2.54/1.75 % (2392)------------------------------
% 2.54/1.76 % (2390)Instruction limit reached!
% 2.54/1.76 % (2390)------------------------------
% 2.54/1.76 % (2390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.76 % (2390)Termination reason: Unknown
% 2.54/1.76 % (2390)Termination phase: Preprocessing 3
% 2.54/1.76
% 2.54/1.76 % (2390)Memory used [KB]: 4093
% 2.54/1.76 % (2390)Time elapsed: 0.029 s
% 2.54/1.76 % (2390)Instructions burned: 86 (million)
% 2.54/1.76 % (2390)------------------------------
% 2.54/1.76 % (2390)------------------------------
% 2.54/1.76 % (2393)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_2254 for (2997ds/448Mi)
% 2.54/1.77 % (2391)Instruction limit reached!
% 2.54/1.77 % (2391)------------------------------
% 2.54/1.77 % (2391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (2391)Termination reason: Unknown
% 2.54/1.77 % (2391)Termination phase: Property scanning
% 2.54/1.77
% 2.54/1.77 % (2391)Memory used [KB]: 4349
% 2.54/1.77 % (2391)Time elapsed: 0.034 s
% 2.54/1.77 % (2391)Instructions burned: 108 (million)
% 2.54/1.77 % (2391)------------------------------
% 2.54/1.77 % (2391)------------------------------
% 2.54/1.77 % (2394)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_2254 for (2997ds/46Mi)
% 2.54/1.78 % (2395)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_2254 for (2997ds/98Mi)
% 2.54/1.78 % (2394)Instruction limit reached!
% 2.54/1.78 % (2394)------------------------------
% 2.54/1.78 % (2394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (2394)Termination reason: Unknown
% 2.54/1.78 % (2394)Termination phase: Preprocessing 1
% 2.54/1.78
% 2.54/1.78 % (2394)Memory used [KB]: 2302
% 2.54/1.78 % (2394)Time elapsed: 0.015 s
% 2.54/1.78 % (2394)Instructions burned: 46 (million)
% 2.54/1.78 % (2394)------------------------------
% 2.54/1.78 % (2394)------------------------------
% 2.54/1.79 % (2396)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_2254 for (2997ds/507Mi)
% 2.54/1.80 % (2380)Instruction limit reached!
% 2.54/1.80 % (2380)------------------------------
% 2.54/1.80 % (2380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.80 % (2380)Termination reason: Unknown
% 2.54/1.80 % (2380)Termination phase: Saturation
% 2.54/1.80
% 2.54/1.80 % (2380)Memory used [KB]: 6780
% 2.54/1.80 % (2380)Time elapsed: 0.183 s
% 2.54/1.80 % (2380)Instructions burned: 779 (million)
% 2.54/1.80 % (2380)------------------------------
% 2.54/1.80 % (2380)------------------------------
% 2.54/1.80 % (2364)Instruction limit reached!
% 2.54/1.80 % (2364)------------------------------
% 2.54/1.80 % (2364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.80 % (2364)Termination reason: Unknown
% 2.54/1.80 % (2364)Termination phase: Saturation
% 2.54/1.80
% 2.54/1.80 % (2364)Memory used [KB]: 7803
% 2.54/1.80 % (2364)Time elapsed: 0.252 s
% 2.54/1.80 % (2364)Instructions burned: 1041 (million)
% 2.54/1.80 % (2364)------------------------------
% 2.54/1.80 % (2364)------------------------------
% 2.54/1.80 % (2395)Instruction limit reached!
% 2.54/1.80 % (2395)------------------------------
% 2.54/1.80 % (2395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.80 % (2395)Termination reason: Unknown
% 2.54/1.80 % (2395)Termination phase: Saturation
% 2.54/1.80
% 2.54/1.80 % (2395)Memory used [KB]: 2046
% 2.54/1.80 % (2395)Time elapsed: 0.028 s
% 2.54/1.80 % (2395)Instructions burned: 100 (million)
% 2.54/1.80 % (2395)------------------------------
% 2.54/1.80 % (2395)------------------------------
% 2.54/1.81 % (2397)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_2254 for (2997ds/149Mi)
% 2.54/1.81 % (2398)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2254 for (2997ds/39Mi)
% 2.54/1.81 % (2399)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_2254 for (2997ds/6Mi)
% 2.54/1.82 % (2399)Instruction limit reached!
% 2.54/1.82 % (2399)------------------------------
% 2.54/1.82 % (2399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (2399)Termination reason: Unknown
% 2.54/1.82 % (2399)Termination phase: shuffling
% 2.54/1.82
% 2.54/1.82 % (2399)Memory used [KB]: 1407
% 2.54/1.82 % (2399)Time elapsed: 0.003 s
% 2.54/1.82 % (2399)Instructions burned: 7 (million)
% 2.54/1.82 % (2399)------------------------------
% 2.54/1.82 % (2399)------------------------------
% 2.54/1.82 % (2398)Instruction limit reached!
% 2.54/1.82 % (2398)------------------------------
% 2.54/1.82 % (2398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (2398)Termination reason: Unknown
% 2.54/1.82 % (2398)Termination phase: shuffling
% 2.54/1.82
% 2.54/1.82 % (2398)Memory used [KB]: 2302
% 2.54/1.82 % (2398)Time elapsed: 0.013 s
% 2.54/1.82 % (2398)Instructions burned: 41 (million)
% 2.54/1.82 % (2398)------------------------------
% 2.54/1.82 % (2398)------------------------------
% 2.54/1.83 % (2373)Instruction limit reached!
% 2.54/1.83 % (2373)------------------------------
% 2.54/1.83 % (2373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.83 % (2373)Termination reason: Unknown
% 2.54/1.83 % (2373)Termination phase: Saturation
% 2.54/1.83
% 2.54/1.83 % (2373)Memory used [KB]: 11769
% 2.54/1.83 % (2373)Time elapsed: 0.233 s
% 2.54/1.83 % (2373)Instructions burned: 710 (million)
% 2.54/1.83 % (2373)------------------------------
% 2.54/1.83 % (2373)------------------------------
% 2.54/1.83 % (2400)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_2254 for (2997ds/1087Mi)
% 2.54/1.83 % (2401)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2254 for (2997ds/47Mi)
% 2.54/1.84 % (2402)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_2254 for (2997ds/44Mi)
% 2.54/1.85 % (2401)Instruction limit reached!
% 2.54/1.85 % (2401)------------------------------
% 2.54/1.85 % (2401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.85 % (2401)Termination reason: Unknown
% 2.54/1.85 % (2401)Termination phase: Naming
% 2.54/1.85
% 2.54/1.85 % (2401)Memory used [KB]: 2686
% 2.54/1.85 % (2401)Time elapsed: 0.015 s
% 2.54/1.85 % (2401)Instructions burned: 48 (million)
% 2.54/1.85 % (2401)------------------------------
% 2.54/1.85 % (2401)------------------------------
% 2.54/1.85 % (2397)Instruction limit reached!
% 2.54/1.85 % (2397)------------------------------
% 2.54/1.85 % (2397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.85 % (2397)Termination reason: Unknown
% 2.54/1.85 % (2397)Termination phase: Property scanning
% 2.54/1.85
% 2.54/1.85 % (2397)Memory used [KB]: 7931
% 2.54/1.85 % (2397)Time elapsed: 0.043 s
% 2.54/1.85 % (2397)Instructions burned: 153 (million)
% 2.54/1.85 % (2397)------------------------------
% 2.54/1.85 % (2397)------------------------------
% 2.54/1.85 % (2402)Instruction limit reached!
% 2.54/1.85 % (2402)------------------------------
% 2.54/1.85 % (2402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.85 % (2402)Termination reason: Unknown
% 2.54/1.85 % (2402)Termination phase: Property scanning
% 2.54/1.85
% 2.54/1.85 % (2402)Memory used [KB]: 1918
% 2.54/1.85 % (2402)Time elapsed: 0.014 s
% 2.54/1.85 % (2402)Instructions burned: 46 (million)
% 2.54/1.85 % (2402)------------------------------
% 2.54/1.85 % (2402)------------------------------
% 2.54/1.86 % (2403)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_2254 for (2996ds/432Mi)
% 2.54/1.86 % (2404)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2254 for (2996ds/62Mi)
% 2.54/1.86 % (2405)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_2254 for (2996ds/31Mi)
% 2.54/1.87 % (2405)Instruction limit reached!
% 2.54/1.87 % (2405)------------------------------
% 2.54/1.87 % (2405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.87 % (2405)Termination reason: Unknown
% 2.54/1.87 % (2405)Termination phase: Property scanning
% 2.54/1.87
% 2.54/1.87 % (2405)Memory used [KB]: 2174
% 2.54/1.87 % (2405)Time elapsed: 0.011 s
% 2.54/1.87 % (2405)Instructions burned: 31 (million)
% 2.54/1.87 % (2405)------------------------------
% 2.54/1.87 % (2405)------------------------------
% 2.54/1.87 % (2404)Instruction limit reached!
% 2.54/1.87 % (2404)------------------------------
% 2.54/1.87 % (2404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.87 % (2404)Termination reason: Unknown
% 2.54/1.87 % (2404)Termination phase: Property scanning
% 2.54/1.87
% 2.54/1.87 % (2404)Memory used [KB]: 1918
% 2.54/1.87 % (2404)Time elapsed: 0.017 s
% 2.54/1.87 % (2404)Instructions burned: 64 (million)
% 2.54/1.87 % (2404)------------------------------
% 2.54/1.87 % (2404)------------------------------
% 2.54/1.88 % (2396)Refutation not found, incomplete strategy
% 2.54/1.88 % (2396)------------------------------
% 2.54/1.88 % (2396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (2396)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.88
% 2.54/1.88
% 2.54/1.88 % (2396)Memory used [KB]: 9978
% 2.54/1.88 % (2396)Time elapsed: 0.087 s
% 2.54/1.88 % (2396)Instructions burned: 279 (million)
% 2.54/1.88 % (2396)------------------------------
% 2.54/1.88 % (2396)------------------------------
% 2.54/1.88 % (2393)Instruction limit reached!
% 2.54/1.88 % (2393)------------------------------
% 2.54/1.88 % (2393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (2393)Termination reason: Unknown
% 2.54/1.88 % (2393)Termination phase: Saturation
% 2.54/1.88
% 2.54/1.88 % (2393)Memory used [KB]: 7291
% 2.54/1.88 % (2393)Time elapsed: 0.141 s
% 2.54/1.88 % (2393)Instructions burned: 451 (million)
% 2.54/1.88 % (2393)------------------------------
% 2.54/1.88 % (2393)------------------------------
% 2.54/1.88 % (2406)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2254 for (2996ds/96Mi)
% 2.54/1.88 % (2407)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_2254 for (2996ds/453Mi)
% 2.54/1.89 % (2408)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_2254 for (2996ds/71Mi)
% 2.54/1.89 % (2409)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2254 for (2996ds/83Mi)
% 2.54/1.91 % (2408)Instruction limit reached!
% 2.54/1.91 % (2408)------------------------------
% 2.54/1.91 % (2408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (2408)Termination reason: Unknown
% 2.54/1.91 % (2408)Termination phase: Preprocessing 3
% 2.54/1.91
% 2.54/1.91 % (2408)Memory used [KB]: 3454
% 2.54/1.91 % (2408)Time elapsed: 0.022 s
% 2.54/1.91 % (2408)Instructions burned: 74 (million)
% 2.54/1.91 % (2408)------------------------------
% 2.54/1.91 % (2408)------------------------------
% 2.54/1.91 % (2406)Instruction limit reached!
% 2.54/1.91 % (2406)------------------------------
% 2.54/1.91 % (2406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (2406)Termination reason: Unknown
% 2.54/1.91 % (2406)Termination phase: Property scanning
% 2.54/1.91
% 2.54/1.91 % (2406)Memory used [KB]: 4221
% 2.54/1.91 % (2406)Time elapsed: 0.032 s
% 2.54/1.91 % (2406)Instructions burned: 96 (million)
% 2.54/1.91 % (2406)------------------------------
% 2.54/1.91 % (2406)------------------------------
% 2.54/1.91 % (2382)Instruction limit reached!
% 2.54/1.91 % (2382)------------------------------
% 2.54/1.91 % (2382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (2382)Termination reason: Unknown
% 2.54/1.91 % (2382)Termination phase: Saturation
% 2.54/1.91
% 2.54/1.91 % (2382)Memory used [KB]: 11897
% 2.54/1.91 % (2382)Time elapsed: 0.286 s
% 2.54/1.91 % (2382)Instructions burned: 879 (million)
% 2.54/1.91 % (2382)------------------------------
% 2.54/1.91 % (2382)------------------------------
% 2.54/1.92 % (2409)Instruction limit reached!
% 2.54/1.92 % (2409)------------------------------
% 2.54/1.92 % (2409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (2409)Termination reason: Unknown
% 2.54/1.92 % (2409)Termination phase: Saturation
% 2.54/1.92
% 2.54/1.92 % (2409)Memory used [KB]: 6908
% 2.54/1.92 % (2409)Time elapsed: 0.028 s
% 2.54/1.92 % (2409)Instructions burned: 84 (million)
% 2.54/1.92 % (2409)------------------------------
% 2.54/1.92 % (2409)------------------------------
% 2.54/1.92 % (2410)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2254 for (2996ds/11Mi)
% 2.54/1.92 % (2411)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_2254 for (2996ds/41Mi)
% 2.54/1.92 % (2410)Instruction limit reached!
% 2.54/1.92 % (2410)------------------------------
% 2.54/1.92 % (2410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (2410)Termination reason: Unknown
% 2.54/1.92 % (2410)Termination phase: shuffling
% 2.54/1.92
% 2.54/1.92 % (2410)Memory used [KB]: 1535
% 2.54/1.92 % (2410)Time elapsed: 0.005 s
% 2.54/1.92 % (2410)Instructions burned: 14 (million)
% 2.54/1.92 % (2410)------------------------------
% 2.54/1.92 % (2410)------------------------------
% 2.54/1.92 % (2412)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2254 for (2995ds/6Mi)
% 2.54/1.93 % (2412)Instruction limit reached!
% 2.54/1.93 % (2412)------------------------------
% 2.54/1.93 % (2412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (2412)Termination reason: Unknown
% 2.54/1.93 % (2412)Termination phase: shuffling
% 2.54/1.93
% 2.54/1.93 % (2412)Memory used [KB]: 1407
% 2.54/1.93 % (2412)Time elapsed: 0.003 s
% 2.54/1.93 % (2412)Instructions burned: 7 (million)
% 2.54/1.93 % (2412)------------------------------
% 2.54/1.93 % (2412)------------------------------
% 2.54/1.93 % (2413)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2254 for (2995ds/150Mi)
% 2.54/1.93 % (2414)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2254 for (2995ds/343Mi)
% 2.54/1.93 % (2411)Instruction limit reached!
% 2.54/1.93 % (2411)------------------------------
% 2.54/1.93 % (2411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (2411)Termination reason: Unknown
% 2.54/1.93 % (2411)Termination phase: Property scanning
% 2.54/1.93
% 2.54/1.93 % (2411)Memory used [KB]: 1918
% 2.54/1.93 % (2411)Time elapsed: 0.014 s
% 2.54/1.93 % (2411)Instructions burned: 44 (million)
% 2.54/1.93 % (2411)------------------------------
% 2.54/1.93 % (2411)------------------------------
% 2.54/1.94 % (2415)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_2254 for (2995ds/109Mi)
% 2.54/1.94 % (2416)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_2254 for (2995ds/253Mi)
% 2.54/1.95 % (2414)Refutation not found, incomplete strategy
% 2.54/1.95 % (2414)------------------------------
% 2.54/1.95 % (2414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.95 % (2414)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.95
% 2.54/1.95
% 2.54/1.95 % (2414)Memory used [KB]: 6780
% 2.54/1.95 % (2414)Time elapsed: 0.016 s
% 2.54/1.95 % (2414)Instructions burned: 52 (million)
% 2.54/1.95 % (2414)------------------------------
% 2.54/1.95 % (2414)------------------------------
% 2.54/1.96 % (2417)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2254 for (2995ds/140Mi)
% 2.54/1.96 % (2403)Instruction limit reached!
% 2.54/1.96 % (2403)------------------------------
% 2.54/1.96 % (2403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.96 % (2403)Termination reason: Unknown
% 2.54/1.96 % (2403)Termination phase: Saturation
% 2.54/1.96
% 2.54/1.96 % (2403)Memory used [KB]: 2558
% 2.54/1.96 % (2403)Time elapsed: 0.129 s
% 2.54/1.96 % (2403)Instructions burned: 432 (million)
% 2.54/1.96 % (2403)------------------------------
% 2.54/1.96 % (2403)------------------------------
% 2.54/1.97 % (2415)Instruction limit reached!
% 2.54/1.97 % (2415)------------------------------
% 2.54/1.97 % (2415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.97 % (2415)Termination reason: Unknown
% 2.54/1.97 % (2415)Termination phase: Property scanning
% 2.54/1.97
% 2.54/1.97 % (2415)Memory used [KB]: 4221
% 2.54/1.97 % (2415)Time elapsed: 0.035 s
% 2.54/1.97 % (2415)Instructions burned: 111 (million)
% 2.54/1.97 % (2415)------------------------------
% 2.54/1.97 % (2415)------------------------------
% 2.54/1.97 % (2418)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_2254 for (2995ds/614Mi)
% 2.54/1.98 % (2413)Instruction limit reached!
% 2.54/1.98 % (2413)------------------------------
% 2.54/1.98 % (2413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (2413)Termination reason: Unknown
% 2.54/1.98 % (2413)Termination phase: Property scanning
% 2.54/1.98
% 2.54/1.98 % (2413)Memory used [KB]: 3965
% 2.54/1.98 % (2413)Time elapsed: 0.055 s
% 2.54/1.98 % (2413)Instructions burned: 151 (million)
% 2.54/1.98 % (2413)------------------------------
% 2.54/1.98 % (2413)------------------------------
% 2.54/1.98 % (2419)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_2254 for (2995ds/202Mi)
% 2.54/1.99 % (2420)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_2254 for (2995ds/339Mi)
% 2.54/1.99 % (2407)Instruction limit reached!
% 2.54/1.99 % (2407)------------------------------
% 2.54/1.99 % (2407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (2407)Termination reason: Unknown
% 2.54/1.99 % (2407)Termination phase: Saturation
% 2.54/1.99
% 2.54/1.99 % (2407)Memory used [KB]: 6652
% 2.54/1.99 % (2407)Time elapsed: 0.109 s
% 2.54/1.99 % (2407)Instructions burned: 453 (million)
% 2.54/1.99 % (2407)------------------------------
% 2.54/1.99 % (2407)------------------------------
% 2.54/2.00 % (2417)Instruction limit reached!
% 2.54/2.00 % (2417)------------------------------
% 2.54/2.00 % (2417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.00 % (2417)Termination reason: Unknown
% 2.54/2.00 % (2417)Termination phase: Property scanning
% 2.54/2.00
% 2.54/2.00 % (2417)Memory used [KB]: 4221
% 2.54/2.00 % (2417)Time elapsed: 0.039 s
% 2.54/2.00 % (2417)Instructions burned: 141 (million)
% 2.54/2.00 % (2417)------------------------------
% 2.54/2.00 % (2417)------------------------------
% 2.54/2.00 % (2421)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_2254 for (2995ds/283Mi)
% 2.54/2.01 % (2422)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2254 for (2995ds/134Mi)
% 5.87/2.02 % (2416)Instruction limit reached!
% 5.87/2.02 % (2416)------------------------------
% 5.87/2.02 % (2416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.02 % (2416)Termination reason: Unknown
% 5.87/2.02 % (2416)Termination phase: Saturation
% 5.87/2.02
% 5.87/2.02 % (2416)Memory used [KB]: 7291
% 5.87/2.02 % (2416)Time elapsed: 0.080 s
% 5.87/2.02 % (2416)Instructions burned: 254 (million)
% 5.87/2.02 % (2416)------------------------------
% 5.87/2.02 % (2416)------------------------------
% 5.87/2.03 % (2423)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2254 for (2994ds/298Mi)
% 5.87/2.04 % (2419)Instruction limit reached!
% 5.87/2.04 % (2419)------------------------------
% 5.87/2.04 % (2419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.04 % (2419)Termination reason: Unknown
% 5.87/2.04 % (2419)Termination phase: Saturation
% 5.87/2.04
% 5.87/2.04 % (2419)Memory used [KB]: 4605
% 5.87/2.04 % (2419)Time elapsed: 0.059 s
% 5.87/2.04 % (2419)Instructions burned: 203 (million)
% 5.87/2.04 % (2419)------------------------------
% 5.87/2.04 % (2419)------------------------------
% 5.87/2.05 % (2422)Instruction limit reached!
% 5.87/2.05 % (2422)------------------------------
% 5.87/2.05 % (2422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.05 % (2422)Termination reason: Unknown
% 5.87/2.05 % (2422)Termination phase: Property scanning
% 5.87/2.05
% 5.87/2.05 % (2422)Memory used [KB]: 4349
% 5.87/2.05 % (2422)Time elapsed: 0.041 s
% 5.87/2.05 % (2422)Instructions burned: 137 (million)
% 5.87/2.05 % (2422)------------------------------
% 5.87/2.05 % (2422)------------------------------
% 5.87/2.05 % (2424)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2254 for (2994ds/192Mi)
% 5.87/2.06 % (2425)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_2254 for (2994ds/258Mi)
% 5.87/2.07 % (2421)Instruction limit reached!
% 5.87/2.07 % (2421)------------------------------
% 5.87/2.07 % (2421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.07 % (2421)Termination reason: Unknown
% 5.87/2.07 % (2421)Termination phase: Saturation
% 5.87/2.07
% 5.87/2.07 % (2421)Memory used [KB]: 6652
% 5.87/2.07 % (2421)Time elapsed: 0.071 s
% 5.87/2.07 % (2421)Instructions burned: 285 (million)
% 5.87/2.07 % (2421)------------------------------
% 5.87/2.07 % (2421)------------------------------
% 5.87/2.08 % (2426)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_2254 for (2994ds/90Mi)
% 5.87/2.09 % (2420)Instruction limit reached!
% 5.87/2.09 % (2420)------------------------------
% 5.87/2.09 % (2420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.09 % (2420)Termination reason: Unknown
% 5.87/2.09 % (2420)Termination phase: Saturation
% 5.87/2.09
% 5.87/2.09 % (2420)Memory used [KB]: 9594
% 5.87/2.09 % (2420)Time elapsed: 0.092 s
% 5.87/2.09 % (2420)Instructions burned: 340 (million)
% 5.87/2.09 % (2420)------------------------------
% 5.87/2.09 % (2420)------------------------------
% 5.87/2.10 % (2424)Instruction limit reached!
% 5.87/2.10 % (2424)------------------------------
% 5.87/2.10 % (2424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.10 % (2424)Termination reason: Unknown
% 5.87/2.10 % (2424)Termination phase: Property scanning
% 5.87/2.10
% 5.87/2.10 % (2424)Memory used [KB]: 4477
% 5.87/2.10 % (2424)Time elapsed: 0.052 s
% 5.87/2.10 % (2424)Instructions burned: 193 (million)
% 5.87/2.10 % (2424)------------------------------
% 5.87/2.10 % (2424)------------------------------
% 5.87/2.10 % (2427)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_2254 for (2994ds/231Mi)
% 5.87/2.11 % (2423)Instruction limit reached!
% 5.87/2.11 % (2423)------------------------------
% 5.87/2.11 % (2423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.11 % (2423)Termination reason: Unknown
% 5.87/2.11 % (2423)Termination phase: Saturation
% 5.87/2.11
% 5.87/2.11 % (2423)Memory used [KB]: 6524
% 5.87/2.11 % (2423)Time elapsed: 0.075 s
% 5.87/2.11 % (2423)Instructions burned: 299 (million)
% 5.87/2.11 % (2423)------------------------------
% 5.87/2.11 % (2423)------------------------------
% 5.87/2.11 % (2426)Instruction limit reached!
% 5.87/2.11 % (2426)------------------------------
% 5.87/2.11 % (2426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.11 % (2426)Termination reason: Unknown
% 5.87/2.11 % (2426)Termination phase: Preprocessing 3
% 5.87/2.11
% 5.87/2.11 % (2426)Memory used [KB]: 4093
% 5.87/2.11 % (2426)Time elapsed: 0.028 s
% 5.87/2.11 % (2426)Instructions burned: 92 (million)
% 5.87/2.11 % (2426)------------------------------
% 5.87/2.11 % (2426)------------------------------
% 5.87/2.11 % (2428)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_2254 for (2994ds/458Mi)
% 6.53/2.12 % (2429)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_2254 for (2994ds/31Mi)
% 6.53/2.12 % (2430)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_2254 for (2994ds/297Mi)
% 6.53/2.12 % (2425)Instruction limit reached!
% 6.53/2.12 % (2425)------------------------------
% 6.53/2.12 % (2425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.12 % (2425)Termination reason: Unknown
% 6.53/2.12 % (2425)Termination phase: Property scanning
% 6.53/2.12
% 6.53/2.12 % (2425)Memory used [KB]: 7803
% 6.53/2.12 % (2425)Time elapsed: 0.068 s
% 6.53/2.12 % (2425)Instructions burned: 258 (million)
% 6.53/2.12 % (2425)------------------------------
% 6.53/2.12 % (2425)------------------------------
% 6.53/2.13 % (2429)Instruction limit reached!
% 6.53/2.13 % (2429)------------------------------
% 6.53/2.13 % (2429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.13 % (2429)Termination reason: Unknown
% 6.53/2.13 % (2429)Termination phase: Property scanning
% 6.53/2.13
% 6.53/2.13 % (2429)Memory used [KB]: 2174
% 6.53/2.13 % (2429)Time elapsed: 0.011 s
% 6.53/2.13 % (2429)Instructions burned: 34 (million)
% 6.53/2.13 % (2429)------------------------------
% 6.53/2.13 % (2429)------------------------------
% 6.53/2.13 % (2431)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_2254 for (2994ds/987Mi)
% 6.53/2.13 % (2432)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_2254 for (2994ds/182Mi)
% 6.53/2.15 % (2418)Instruction limit reached!
% 6.53/2.15 % (2418)------------------------------
% 6.53/2.15 % (2418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.15 % (2418)Termination reason: Unknown
% 6.53/2.15 % (2418)Termination phase: Saturation
% 6.53/2.15
% 6.53/2.15 % (2418)Memory used [KB]: 12281
% 6.53/2.15 % (2418)Time elapsed: 0.180 s
% 6.53/2.15 % (2418)Instructions burned: 616 (million)
% 6.53/2.15 % (2418)------------------------------
% 6.53/2.15 % (2418)------------------------------
% 6.53/2.16 % (2427)Instruction limit reached!
% 6.53/2.16 % (2427)------------------------------
% 6.53/2.16 % (2427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.16 % (2427)Termination reason: Unknown
% 6.53/2.16 % (2427)Termination phase: Saturation
% 6.53/2.16
% 6.53/2.16 % (2427)Memory used [KB]: 7164
% 6.53/2.16 % (2427)Time elapsed: 0.058 s
% 6.53/2.16 % (2427)Instructions burned: 232 (million)
% 6.53/2.16 % (2427)------------------------------
% 6.53/2.16 % (2427)------------------------------
% 6.53/2.16 % (2433)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_2254 for (2993ds/182Mi)
% 6.53/2.17 % (2434)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_2254 for (2993ds/154Mi)
% 6.53/2.17 % (2400)Instruction limit reached!
% 6.53/2.17 % (2400)------------------------------
% 6.53/2.17 % (2400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.17 % (2400)Termination reason: Unknown
% 6.53/2.17 % (2400)Termination phase: Saturation
% 6.53/2.17
% 6.53/2.17 % (2400)Memory used [KB]: 11769
% 6.53/2.17 % (2400)Time elapsed: 0.365 s
% 6.53/2.17 % (2400)Instructions burned: 1089 (million)
% 6.53/2.17 % (2400)------------------------------
% 6.53/2.17 % (2400)------------------------------
% 6.53/2.18 % (2435)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_2254 for (2993ds/79Mi)
% 6.53/2.18 % (2432)Instruction limit reached!
% 6.53/2.18 % (2432)------------------------------
% 6.53/2.18 % (2432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.18 % (2432)Termination reason: Unknown
% 6.53/2.18 % (2432)Termination phase: Property scanning
% 6.53/2.18
% 6.53/2.18 % (2432)Memory used [KB]: 7803
% 6.53/2.18 % (2432)Time elapsed: 0.050 s
% 6.53/2.18 % (2432)Instructions burned: 184 (million)
% 6.53/2.18 % (2432)------------------------------
% 6.53/2.18 % (2432)------------------------------
% 6.53/2.19 % (2436)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_2254 for (2993ds/216Mi)
% 6.86/2.20 % (2430)Instruction limit reached!
% 6.86/2.20 % (2430)------------------------------
% 6.86/2.20 % (2430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.20 % (2430)Termination reason: Unknown
% 6.86/2.20 % (2430)Termination phase: Saturation
% 6.86/2.20
% 6.86/2.20 % (2430)Memory used [KB]: 7164
% 6.86/2.20 % (2435)Instruction limit reached!
% 6.86/2.20 % (2435)------------------------------
% 6.86/2.20 % (2435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.20 % (2435)Termination reason: Unknown
% 6.86/2.20 % (2435)Termination phase: Preprocessing 3
% 6.86/2.20
% 6.86/2.20 % (2435)Memory used [KB]: 3837
% 6.86/2.20 % (2435)Time elapsed: 0.024 s
% 6.86/2.20 % (2435)Instructions burned: 79 (million)
% 6.86/2.20 % (2435)------------------------------
% 6.86/2.20 % (2435)------------------------------
% 6.86/2.20 % (2430)Time elapsed: 0.084 s
% 6.86/2.20 % (2430)Instructions burned: 299 (million)
% 6.86/2.20 % (2430)------------------------------
% 6.86/2.20 % (2430)------------------------------
% 6.86/2.20 % (2434)Instruction limit reached!
% 6.86/2.20 % (2434)------------------------------
% 6.86/2.20 % (2434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.20 % (2434)Termination reason: Unknown
% 6.86/2.20 % (2434)Termination phase: Saturation
% 6.86/2.20
% 6.86/2.20 % (2434)Memory used [KB]: 2430
% 6.86/2.20 % (2434)Time elapsed: 0.040 s
% 6.86/2.20 % (2434)Instructions burned: 155 (million)
% 6.86/2.20 % (2434)------------------------------
% 6.86/2.20 % (2434)------------------------------
% 6.86/2.21 % (2437)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_2254 for (2993ds/114Mi)
% 6.86/2.21 % (2438)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_2254 for (2993ds/922Mi)
% 6.86/2.21 % (2433)Instruction limit reached!
% 6.86/2.21 % (2433)------------------------------
% 6.86/2.21 % (2433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.21 % (2433)Termination reason: Unknown
% 6.86/2.21 % (2433)Termination phase: Saturation
% 6.86/2.21
% 6.86/2.21 % (2433)Memory used [KB]: 9083
% 6.86/2.21 % (2433)Time elapsed: 0.052 s
% 6.86/2.21 % (2433)Instructions burned: 184 (million)
% 6.86/2.21 % (2433)------------------------------
% 6.86/2.21 % (2433)------------------------------
% 6.86/2.21 % (2439)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_2254 for (2993ds/182Mi)
% 6.86/2.22 % (2440)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_2254 for (2993ds/164Mi)
% 6.86/2.24 % (2428)Instruction limit reached!
% 6.86/2.24 % (2428)------------------------------
% 6.86/2.24 % (2428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.24 % (2428)Termination reason: Unknown
% 6.86/2.24 % (2428)Termination phase: Saturation
% 6.86/2.24
% 6.86/2.24 % (2428)Memory used [KB]: 10874
% 6.86/2.24 % (2428)Time elapsed: 0.131 s
% 6.86/2.24 % (2428)Instructions burned: 460 (million)
% 6.86/2.24 % (2428)------------------------------
% 6.86/2.24 % (2428)------------------------------
% 6.86/2.24 % (2437)Instruction limit reached!
% 6.86/2.24 % (2437)------------------------------
% 6.86/2.24 % (2437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.24 % (2437)Termination reason: Unknown
% 6.86/2.24 % (2437)Termination phase: Property scanning
% 6.86/2.24
% 6.86/2.24 % (2437)Memory used [KB]: 4221
% 6.86/2.24 % (2437)Time elapsed: 0.033 s
% 6.86/2.24 % (2437)Instructions burned: 115 (million)
% 6.86/2.24 % (2437)------------------------------
% 6.86/2.24 % (2437)------------------------------
% 6.86/2.25 % (2441)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_2254 for (2992ds/50Mi)
% 6.86/2.25 % (2442)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_2254 for (2992ds/368Mi)
% 6.86/2.25 % (2436)Instruction limit reached!
% 6.86/2.25 % (2436)------------------------------
% 6.86/2.25 % (2436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.25 % (2436)Termination reason: Unknown
% 6.86/2.25 % (2436)Termination phase: Saturation
% 6.86/2.25
% 6.86/2.25 % (2436)Memory used [KB]: 7036
% 6.86/2.25 % (2436)Time elapsed: 0.062 s
% 6.86/2.25 % (2436)Instructions burned: 216 (million)
% 6.86/2.25 % (2436)------------------------------
% 6.86/2.25 % (2436)------------------------------
% 6.86/2.26 % (2439)Instruction limit reached!
% 6.86/2.26 % (2439)------------------------------
% 6.86/2.26 % (2439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.26 % (2439)Termination reason: Unknown
% 6.86/2.26 % (2439)Termination phase: Saturation
% 6.86/2.26
% 6.86/2.26 % (2439)Memory used [KB]: 6652
% 6.86/2.26 % (2439)Time elapsed: 0.046 s
% 6.86/2.26 % (2439)Instructions burned: 184 (million)
% 6.86/2.26 % (2439)------------------------------
% 6.86/2.26 % (2439)------------------------------
% 6.86/2.26 % (2441)Instruction limit reached!
% 6.86/2.26 % (2441)------------------------------
% 6.86/2.26 % (2441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.26 % (2441)Termination reason: Unknown
% 6.86/2.26 % (2441)Termination phase: Property scanning
% 6.86/2.26
% 6.86/2.26 % (2441)Memory used [KB]: 1918
% 6.86/2.26 % (2441)Time elapsed: 0.014 s
% 6.86/2.26 % (2441)Instructions burned: 50 (million)
% 6.86/2.26 % (2441)------------------------------
% 6.86/2.26 % (2441)------------------------------
% 6.86/2.26 % (2443)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_2254 for (2992ds/1021Mi)
% 6.86/2.27 % (2440)Instruction limit reached!
% 6.86/2.27 % (2440)------------------------------
% 6.86/2.27 % (2440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.27 % (2440)Termination reason: Unknown
% 6.86/2.27 % (2440)Termination phase: Saturation
% 6.86/2.27
% 6.86/2.27 % (2440)Memory used [KB]: 2302
% 6.86/2.27 % (2440)Time elapsed: 0.047 s
% 6.86/2.27 % (2440)Instructions burned: 165 (million)
% 6.86/2.27 % (2440)------------------------------
% 6.86/2.27 % (2440)------------------------------
% 6.86/2.27 % (2444)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_2254 for (2992ds/267Mi)
% 6.86/2.27 % (2445)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_2254 for (2992ds/204Mi)
% 6.86/2.28 % (2446)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_2254 for (2992ds/26Mi)
% 6.86/2.28 % (2446)Instruction limit reached!
% 6.86/2.28 % (2446)------------------------------
% 6.86/2.28 % (2446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.28 % (2446)Termination reason: Unknown
% 6.86/2.28 % (2446)Termination phase: shuffling
% 6.86/2.28
% 6.86/2.28 % (2446)Memory used [KB]: 1791
% 6.86/2.28 % (2446)Time elapsed: 0.008 s
% 6.86/2.28 % (2446)Instructions burned: 26 (million)
% 6.86/2.28 % (2446)------------------------------
% 6.86/2.28 % (2446)------------------------------
% 6.86/2.29 % (2447)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_2254 for (2992ds/53Mi)
% 7.51/2.31 % (2447)Instruction limit reached!
% 7.51/2.31 % (2447)------------------------------
% 7.51/2.31 % (2447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.31 % (2447)Termination reason: Unknown
% 7.51/2.31 % (2447)Termination phase: Property scanning
% 7.51/2.31
% 7.51/2.31 % (2447)Memory used [KB]: 1918
% 7.51/2.31 % (2447)Time elapsed: 0.015 s
% 7.51/2.31 % (2447)Instructions burned: 54 (million)
% 7.51/2.31 % (2447)------------------------------
% 7.51/2.31 % (2447)------------------------------
% 7.51/2.32 % (2448)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_2254 for (2992ds/4436Mi)
% 7.51/2.32 % (2445)Instruction limit reached!
% 7.51/2.32 % (2445)------------------------------
% 7.51/2.32 % (2445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.32 % (2445)Termination reason: Unknown
% 7.51/2.33 % (2445)Termination phase: Property scanning
% 7.51/2.33
% 7.51/2.33 % (2445)Memory used [KB]: 4605
% 7.51/2.33 % (2445)Time elapsed: 0.055 s
% 7.51/2.33 % (2445)Instructions burned: 207 (million)
% 7.51/2.33 % (2445)------------------------------
% 7.51/2.33 % (2445)------------------------------
% 7.51/2.33 % (2444)Instruction limit reached!
% 7.51/2.33 % (2444)------------------------------
% 7.51/2.33 % (2444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.33 % (2444)Termination reason: Unknown
% 7.51/2.33 % (2444)Termination phase: Saturation
% 7.51/2.33
% 7.51/2.33 % (2444)Memory used [KB]: 6652
% 7.51/2.33 % (2444)Time elapsed: 0.067 s
% 7.51/2.33 % (2444)Instructions burned: 268 (million)
% 7.51/2.33 % (2444)------------------------------
% 7.51/2.33 % (2444)------------------------------
% 7.51/2.33 % (2449)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_2254 for (2991ds/1539Mi)
% 7.51/2.34 % (2450)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_2254 for (2991ds/408Mi)
% 7.51/2.36 % (2442)Instruction limit reached!
% 7.51/2.36 % (2442)------------------------------
% 7.51/2.36 % (2442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.36 % (2442)Termination reason: Unknown
% 7.51/2.36 % (2442)Termination phase: Saturation
% 7.51/2.36
% 7.51/2.36 % (2442)Memory used [KB]: 11769
% 7.51/2.36 % (2442)Time elapsed: 0.105 s
% 7.51/2.36 % (2442)Instructions burned: 370 (million)
% 7.51/2.36 % (2442)------------------------------
% 7.51/2.36 % (2442)------------------------------
% 7.51/2.37 % (2451)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_2254 for (2991ds/5205Mi)
% 7.51/2.37 % (2431)Instruction limit reached!
% 7.51/2.37 % (2431)------------------------------
% 7.51/2.37 % (2431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.37 % (2431)Termination reason: Unknown
% 7.51/2.37 % (2431)Termination phase: Saturation
% 7.51/2.37
% 7.51/2.37 % (2431)Memory used [KB]: 7803
% 7.51/2.37 % (2431)Time elapsed: 0.242 s
% 7.51/2.37 % (2431)Instructions burned: 989 (million)
% 7.51/2.37 % (2431)------------------------------
% 7.51/2.37 % (2431)------------------------------
% 7.51/2.38 % (2452)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_2254 for (2991ds/1913Mi)
% 8.03/2.46 % (2450)Instruction limit reached!
% 8.03/2.46 % (2450)------------------------------
% 8.03/2.46 % (2450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.46 % (2450)Termination reason: Unknown
% 8.03/2.46 % (2450)Termination phase: Saturation
% 8.03/2.46
% 8.03/2.46 % (2450)Memory used [KB]: 10874
% 8.03/2.46 % (2450)Time elapsed: 0.119 s
% 8.03/2.46 % (2450)Instructions burned: 408 (million)
% 8.03/2.46 % (2450)------------------------------
% 8.03/2.46 % (2450)------------------------------
% 8.03/2.47 % (2453)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_2254 for (2990ds/4350Mi)
% 8.03/2.49 % (2438)Instruction limit reached!
% 8.03/2.49 % (2438)------------------------------
% 8.03/2.49 % (2438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.49 % (2438)Termination reason: Unknown
% 8.03/2.49 % (2438)Termination phase: Saturation
% 8.03/2.49
% 8.03/2.49 % (2438)Memory used [KB]: 13176
% 8.03/2.49 % (2438)Time elapsed: 0.279 s
% 8.03/2.49 % (2438)Instructions burned: 922 (million)
% 8.03/2.49 % (2438)------------------------------
% 8.03/2.49 % (2438)------------------------------
% 8.44/2.50 % (2454)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_2254 for (2990ds/68Mi)
% 8.44/2.52 % (2454)Instruction limit reached!
% 8.44/2.52 % (2454)------------------------------
% 8.44/2.52 % (2454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.52 % (2454)Termination reason: Unknown
% 8.44/2.52 % (2454)Termination phase: Preprocessing 3
% 8.44/2.52
% 8.44/2.52 % (2454)Memory used [KB]: 3198
% 8.44/2.52 % (2454)Time elapsed: 0.022 s
% 8.44/2.52 % (2454)Instructions burned: 71 (million)
% 8.44/2.52 % (2454)------------------------------
% 8.44/2.52 % (2454)------------------------------
% 8.44/2.53 % (2455)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_2254 for (2989ds/358Mi)
% 8.44/2.57 % (2443)Instruction limit reached!
% 8.44/2.57 % (2443)------------------------------
% 8.44/2.57 % (2443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.57 % (2443)Termination reason: Unknown
% 8.44/2.57 % (2443)Termination phase: Saturation
% 8.44/2.57
% 8.44/2.57 % (2443)Memory used [KB]: 12281
% 8.44/2.57 % (2443)Time elapsed: 0.325 s
% 8.44/2.57 % (2443)Instructions burned: 1022 (million)
% 8.44/2.57 % (2443)------------------------------
% 8.44/2.57 % (2443)------------------------------
% 8.44/2.58 % (2456)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_2254 for (2989ds/31Mi)
% 8.44/2.59 % (2456)Instruction limit reached!
% 8.44/2.59 % (2456)------------------------------
% 8.44/2.59 % (2456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.59 % (2456)Termination reason: Unknown
% 8.44/2.59 % (2456)Termination phase: Property scanning
% 8.44/2.59
% 8.44/2.59 % (2456)Memory used [KB]: 2174
% 8.44/2.59 % (2456)Time elapsed: 0.011 s
% 8.44/2.59 % (2456)Instructions burned: 31 (million)
% 8.44/2.59 % (2456)------------------------------
% 8.44/2.59 % (2456)------------------------------
% 8.81/2.60 % (2457)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_2254 for (2989ds/279Mi)
% 8.81/2.63 % (2455)Instruction limit reached!
% 8.81/2.63 % (2455)------------------------------
% 8.81/2.63 % (2455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.81/2.63 % (2455)Termination reason: Unknown
% 8.81/2.63 % (2455)Termination phase: Saturation
% 8.81/2.63
% 8.81/2.63 % (2455)Memory used [KB]: 9722
% 8.81/2.63 % (2455)Time elapsed: 0.104 s
% 8.81/2.63 % (2455)Instructions burned: 360 (million)
% 8.81/2.63 % (2455)------------------------------
% 8.81/2.63 % (2455)------------------------------
% 8.81/2.64 % (2458)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_2254 for (2988ds/258Mi)
% 8.81/2.67 % (2457)Instruction limit reached!
% 8.81/2.67 % (2457)------------------------------
% 8.81/2.67 % (2457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.81/2.67 % (2457)Termination reason: Unknown
% 8.81/2.67 % (2457)Termination phase: Saturation
% 8.81/2.67
% 8.81/2.67 % (2457)Memory used [KB]: 7675
% 8.81/2.67 % (2457)Time elapsed: 0.071 s
% 8.81/2.67 % (2457)Instructions burned: 282 (million)
% 8.81/2.67 % (2457)------------------------------
% 8.81/2.67 % (2457)------------------------------
% 8.81/2.68 % (2459)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_2254 for (2988ds/26Mi)
% 8.81/2.68 % (2459)Instruction limit reached!
% 8.81/2.68 % (2459)------------------------------
% 8.81/2.68 % (2459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.81/2.68 % (2459)Termination reason: Unknown
% 8.81/2.68 % (2459)Termination phase: shuffling
% 8.81/2.68
% 8.81/2.68 % (2459)Memory used [KB]: 1791
% 8.81/2.68 % (2459)Time elapsed: 0.009 s
% 8.81/2.68 % (2459)Instructions burned: 29 (million)
% 8.81/2.68 % (2459)------------------------------
% 8.81/2.68 % (2459)------------------------------
% 8.81/2.69 % (2460)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_2254 for (2988ds/995Mi)
% 9.02/2.72 % (2458)Instruction limit reached!
% 9.02/2.72 % (2458)------------------------------
% 9.02/2.72 % (2458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.72 % (2458)Termination reason: Unknown
% 9.02/2.72 % (2458)Termination phase: Saturation
% 9.02/2.72
% 9.02/2.72 % (2458)Memory used [KB]: 9850
% 9.02/2.72 % (2458)Time elapsed: 0.075 s
% 9.02/2.72 % (2458)Instructions burned: 258 (million)
% 9.02/2.72 % (2458)------------------------------
% 9.02/2.72 % (2458)------------------------------
% 9.02/2.73 % (2461)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_2254 for (2988ds/373Mi)
% 9.02/2.77 % (2449)Instruction limit reached!
% 9.02/2.77 % (2449)------------------------------
% 9.02/2.77 % (2449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.77 % (2449)Termination reason: Unknown
% 9.02/2.77 % (2449)Termination phase: Saturation
% 9.02/2.77
% 9.02/2.77 % (2449)Memory used [KB]: 12153
% 9.02/2.77 % (2449)Time elapsed: 0.438 s
% 9.02/2.77 % (2449)Instructions burned: 1539 (million)
% 9.02/2.77 % (2449)------------------------------
% 9.02/2.77 % (2449)------------------------------
% 9.02/2.78 % (2462)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_2254 for (2987ds/253Mi)
% 9.55/2.83 % (2461)Instruction limit reached!
% 9.55/2.83 % (2461)------------------------------
% 9.55/2.83 % (2461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.83 % (2461)Termination reason: Unknown
% 9.55/2.83 % (2461)Termination phase: Saturation
% 9.55/2.83
% 9.55/2.83 % (2461)Memory used [KB]: 10106
% 9.55/2.83 % (2461)Time elapsed: 0.110 s
% 9.55/2.83 % (2461)Instructions burned: 375 (million)
% 9.55/2.83 % (2461)------------------------------
% 9.55/2.83 % (2461)------------------------------
% 9.55/2.84 % (2463)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_2254 for (2986ds/832Mi)
% 9.55/2.84 % (2462)Instruction limit reached!
% 9.55/2.84 % (2462)------------------------------
% 9.55/2.84 % (2462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.84 % (2462)Termination reason: Unknown
% 9.55/2.84 % (2462)Termination phase: Saturation
% 9.55/2.84
% 9.55/2.84 % (2462)Memory used [KB]: 6780
% 9.55/2.84 % (2462)Time elapsed: 0.064 s
% 9.55/2.84 % (2462)Instructions burned: 256 (million)
% 9.55/2.84 % (2462)------------------------------
% 9.55/2.84 % (2462)------------------------------
% 9.55/2.85 % (2464)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_2254 for (2986ds/668Mi)
% 9.74/2.92 % (2463)Refutation not found, incomplete strategy
% 9.74/2.92 % (2463)------------------------------
% 9.74/2.92 % (2463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.92 % (2463)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.92
% 9.74/2.92
% 9.74/2.92 % (2463)Memory used [KB]: 9850
% 9.74/2.92 % (2463)Time elapsed: 0.076 s
% 9.74/2.92 % (2463)Instructions burned: 270 (million)
% 9.74/2.92 % (2463)------------------------------
% 9.74/2.92 % (2463)------------------------------
% 9.74/2.93 % (2460)Instruction limit reached!
% 9.74/2.93 % (2460)------------------------------
% 9.74/2.93 % (2460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.93 % (2460)Termination reason: Unknown
% 9.74/2.93 % (2460)Termination phase: Saturation
% 9.74/2.93
% 9.74/2.93 % (2460)Memory used [KB]: 6652
% 9.74/2.93 % (2460)Time elapsed: 0.237 s
% 9.74/2.93 % (2460)Instructions burned: 995 (million)
% 9.74/2.93 % (2460)------------------------------
% 9.74/2.93 % (2460)------------------------------
% 9.74/2.93 % (2465)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_2254 for (2985ds/40Mi)
% 9.74/2.94 % (2466)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_2254 for (2985ds/294Mi)
% 9.74/2.94 % (2465)Instruction limit reached!
% 9.74/2.94 % (2465)------------------------------
% 9.74/2.94 % (2465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.94 % (2465)Termination reason: Unknown
% 9.74/2.94 % (2465)Termination phase: Property scanning
% 9.74/2.94
% 9.74/2.94 % (2465)Memory used [KB]: 1918
% 9.74/2.94 % (2465)Time elapsed: 0.012 s
% 9.74/2.94 % (2465)Instructions burned: 40 (million)
% 9.74/2.94 % (2465)------------------------------
% 9.74/2.94 % (2465)------------------------------
% 9.74/2.95 % (2467)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_2254 for (2985ds/187Mi)
% 9.74/2.97 % (2452)Instruction limit reached!
% 9.74/2.97 % (2452)------------------------------
% 9.74/2.97 % (2452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.97 % (2452)Termination reason: Unknown
% 9.74/2.97 % (2452)Termination phase: Saturation
% 9.74/2.97
% 9.74/2.97 % (2452)Memory used [KB]: 5884
% 9.74/2.97 % (2452)Time elapsed: 0.587 s
% 9.74/2.97 % (2452)Instructions burned: 1915 (million)
% 9.74/2.97 % (2452)------------------------------
% 9.74/2.97 % (2452)------------------------------
% 9.74/2.98 % (2468)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_2254 for (2985ds/371Mi)
% 9.74/3.00 % (2467)Instruction limit reached!
% 9.74/3.00 % (2467)------------------------------
% 9.74/3.00 % (2467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/3.00 % (2467)Termination reason: Unknown
% 9.74/3.00 % (2467)Termination phase: Property scanning
% 9.74/3.00
% 9.74/3.00 % (2467)Memory used [KB]: 4605
% 9.74/3.00 % (2467)Time elapsed: 0.053 s
% 9.74/3.00 % (2467)Instructions burned: 188 (million)
% 9.74/3.00 % (2467)------------------------------
% 9.74/3.00 % (2467)------------------------------
% 12.88/3.01 % (2466)Instruction limit reached!
% 12.88/3.01 % (2466)------------------------------
% 12.88/3.01 % (2466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.88/3.01 % (2466)Termination reason: Unknown
% 12.88/3.01 % (2466)Termination phase: Saturation
% 12.88/3.01
% 12.88/3.01 % (2466)Memory used [KB]: 8059
% 12.88/3.01 % (2466)Time elapsed: 0.074 s
% 12.88/3.01 % (2466)Instructions burned: 295 (million)
% 12.88/3.01 % (2466)------------------------------
% 12.88/3.01 % (2466)------------------------------
% 12.88/3.02 % (2464)Instruction limit reached!
% 12.88/3.02 % (2464)------------------------------
% 12.88/3.02 % (2464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.88/3.02 % (2464)Termination reason: Unknown
% 12.88/3.02 % (2464)Termination phase: Saturation
% 12.88/3.02
% 12.88/3.02 % (2464)Memory used [KB]: 11129
% 12.88/3.02 % (2464)Time elapsed: 0.164 s
% 12.88/3.02 % (2464)Instructions burned: 670 (million)
% 12.88/3.02 % (2464)------------------------------
% 12.88/3.02 % (2464)------------------------------
% 12.88/3.02 % (2469)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_2254 for (2985ds/1827Mi)
% 12.88/3.02 % (2470)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_2254 for (2985ds/70Mi)
% 12.88/3.03 % (2471)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_2254 for (2985ds/316Mi)
% 12.88/3.03 % (2468)Refutation not found, incomplete strategy
% 12.88/3.03 % (2468)------------------------------
% 12.88/3.03 % (2468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.88/3.03 % (2468)Termination reason: Refutation not found, incomplete strategy
% 12.88/3.03
% 12.88/3.03
% 12.88/3.03 % (2468)Memory used [KB]: 7164
% 12.88/3.03 % (2468)Time elapsed: 0.053 s
% 12.88/3.03 % (2468)Instructions burned: 121 (million)
% 12.88/3.03 % (2468)------------------------------
% 12.88/3.03 % (2468)------------------------------
% 12.88/3.04 % (2470)Instruction limit reached!
% 12.88/3.04 % (2470)------------------------------
% 12.88/3.04 % (2470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.88/3.04 % (2470)Termination reason: Unknown
% 12.88/3.04 % (2470)Termination phase: Property scanning
% 12.88/3.04
% 12.88/3.04 % (2470)Memory used [KB]: 1918
% 12.88/3.04 % (2470)Time elapsed: 0.020 s
% 12.88/3.04 % (2470)Instructions burned: 74 (million)
% 12.88/3.04 % (2470)------------------------------
% 12.88/3.04 % (2470)------------------------------
% 12.88/3.04 % (2472)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_2254 for (2984ds/932Mi)
% 12.88/3.05 % (2473)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_2254 for (2984ds/4714Mi)
% 12.88/3.11 % (2471)Instruction limit reached!
% 12.88/3.11 % (2471)------------------------------
% 12.88/3.11 % (2471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.88/3.11 % (2471)Termination reason: Unknown
% 12.88/3.11 % (2471)Termination phase: Saturation
% 12.88/3.11
% 12.88/3.11 % (2471)Memory used [KB]: 7164
% 12.88/3.11 % (2471)Time elapsed: 0.082 s
% 12.88/3.11 % (2471)Instructions burned: 317 (million)
% 12.88/3.11 % (2471)------------------------------
% 12.88/3.11 % (2471)------------------------------
% 13.36/3.12 % (2474)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_2254 for (2984ds/8250Mi)
% 13.62/3.27 % (2472)Instruction limit reached!
% 13.62/3.27 % (2472)------------------------------
% 13.62/3.27 % (2472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.62/3.27 % (2472)Termination reason: Unknown
% 13.62/3.27 % (2472)Termination phase: Saturation
% 13.62/3.27
% 13.62/3.27 % (2472)Memory used [KB]: 7803
% 13.62/3.27 % (2472)Time elapsed: 0.231 s
% 13.62/3.27 % (2472)Instructions burned: 933 (million)
% 13.62/3.27 % (2472)------------------------------
% 13.62/3.27 % (2472)------------------------------
% 13.62/3.28 % (2475)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_2254 for (2982ds/770Mi)
% 14.17/3.30 % (2475)Refutation not found, incomplete strategy
% 14.17/3.30 % (2475)------------------------------
% 14.17/3.30 % (2475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.30 % (2475)Termination reason: Refutation not found, incomplete strategy
% 14.17/3.30
% 14.17/3.30
% 14.17/3.30 % (2475)Memory used [KB]: 6652
% 14.17/3.30 % (2475)Time elapsed: 0.014 s
% 14.17/3.30 % (2475)Instructions burned: 41 (million)
% 14.17/3.30 % (2475)------------------------------
% 14.17/3.30 % (2475)------------------------------
% 14.17/3.31 % (2476)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_2254 for (2982ds/794Mi)
% 14.79/3.55 % (2476)Instruction limit reached!
% 14.79/3.55 % (2476)------------------------------
% 14.79/3.55 % (2476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.55 % (2476)Termination reason: Unknown
% 14.79/3.55 % (2476)Termination phase: Saturation
% 14.79/3.55
% 14.79/3.55 % (2476)Memory used [KB]: 8443
% 14.79/3.55 % (2476)Time elapsed: 0.241 s
% 14.79/3.55 % (2476)Instructions burned: 796 (million)
% 14.79/3.55 % (2476)------------------------------
% 14.79/3.55 % (2476)------------------------------
% 14.79/3.56 % (2477)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_2254 for (2979ds/464Mi)
% 14.79/3.58 % (2469)Instruction limit reached!
% 14.79/3.58 % (2469)------------------------------
% 14.79/3.58 % (2469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.58 % (2469)Termination reason: Unknown
% 14.79/3.58 % (2469)Termination phase: Saturation
% 14.79/3.58
% 14.79/3.58 % (2469)Memory used [KB]: 13176
% 14.79/3.58 % (2469)Time elapsed: 0.584 s
% 14.79/3.58 % (2469)Instructions burned: 1830 (million)
% 14.79/3.58 % (2469)------------------------------
% 14.79/3.58 % (2469)------------------------------
% 14.79/3.59 % (2478)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_2254 for (2979ds/1376Mi)
% 15.90/3.63 % (2451)Instruction limit reached!
% 15.90/3.63 % (2451)------------------------------
% 15.90/3.63 % (2451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.90/3.63 % (2451)Termination reason: Unknown
% 15.90/3.63 % (2451)Termination phase: Saturation
% 15.90/3.63
% 15.90/3.63 % (2451)Memory used [KB]: 8315
% 15.90/3.63 % (2451)Time elapsed: 1.262 s
% 15.90/3.63 % (2451)Instructions burned: 5205 (million)
% 15.90/3.63 % (2451)------------------------------
% 15.90/3.63 % (2451)------------------------------
% 15.90/3.64 % (2479)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_2254 for (2979ds/906Mi)
% 15.90/3.64 % (2448)Instruction limit reached!
% 15.90/3.64 % (2448)------------------------------
% 15.90/3.64 % (2448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.90/3.64 % (2448)Termination reason: Unknown
% 15.90/3.64 % (2448)Termination phase: Saturation
% 15.90/3.64
% 15.90/3.64 % (2448)Memory used [KB]: 14711
% 15.90/3.64 % (2448)Time elapsed: 1.326 s
% 15.90/3.64 % (2448)Instructions burned: 4439 (million)
% 15.90/3.64 % (2448)------------------------------
% 15.90/3.64 % (2448)------------------------------
% 15.90/3.65 % (2480)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_2254 for (2978ds/434Mi)
% 15.90/3.66 % (2453)Instruction limit reached!
% 15.90/3.66 % (2453)------------------------------
% 15.90/3.66 % (2453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.90/3.66 % (2453)Termination reason: Unknown
% 15.90/3.66 % (2453)Termination phase: Saturation
% 15.90/3.66
% 15.90/3.66 % (2453)Memory used [KB]: 15735
% 15.90/3.66 % (2453)Time elapsed: 1.193 s
% 15.90/3.66 % (2453)Instructions burned: 4352 (million)
% 15.90/3.66 % (2453)------------------------------
% 15.90/3.66 % (2453)------------------------------
% 15.90/3.68 % (2481)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_2254 for (2978ds/865Mi)
% 15.90/3.69 % (2477)Instruction limit reached!
% 15.90/3.69 % (2477)------------------------------
% 15.90/3.69 % (2477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.90/3.69 % (2477)Termination reason: Unknown
% 15.90/3.69 % (2477)Termination phase: Saturation
% 15.90/3.69
% 15.90/3.69 % (2477)Memory used [KB]: 11257
% 15.90/3.69 % (2477)Time elapsed: 0.134 s
% 15.90/3.69 % (2477)Instructions burned: 464 (million)
% 15.90/3.69 % (2477)------------------------------
% 15.90/3.69 % (2477)------------------------------
% 16.22/3.70 % (2482)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_2254 for (2978ds/593Mi)
% 16.22/3.72 % (2480)Refutation not found, incomplete strategy
% 16.22/3.72 % (2480)------------------------------
% 16.22/3.72 % (2480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.22/3.72 % (2480)Termination reason: Refutation not found, incomplete strategy
% 16.22/3.72
% 16.22/3.72
% 16.22/3.72 % (2480)Memory used [KB]: 7291
% 16.22/3.72 % (2480)Time elapsed: 0.066 s
% 16.22/3.72 % (2480)Instructions burned: 215 (million)
% 16.22/3.72 % (2480)------------------------------
% 16.22/3.72 % (2480)------------------------------
% 16.22/3.73 % (2483)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_2254 for (2978ds/443Mi)
% 16.29/3.85 % (2482)Instruction limit reached!
% 16.29/3.85 % (2482)------------------------------
% 16.29/3.85 % (2482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.85 % (2482)Termination reason: Unknown
% 16.29/3.85 % (2482)Termination phase: Saturation
% 16.29/3.85
% 16.29/3.85 % (2482)Memory used [KB]: 6908
% 16.29/3.85 % (2482)Time elapsed: 0.147 s
% 16.29/3.85 % (2482)Instructions burned: 594 (million)
% 16.29/3.85 % (2482)------------------------------
% 16.29/3.85 % (2482)------------------------------
% 16.29/3.85 % (2483)Instruction limit reached!
% 16.29/3.85 % (2483)------------------------------
% 16.29/3.85 % (2483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.85 % (2483)Termination reason: Unknown
% 16.29/3.85 % (2483)Termination phase: Saturation
% 16.29/3.85
% 16.29/3.85 % (2483)Memory used [KB]: 11897
% 16.29/3.85 % (2483)Time elapsed: 0.127 s
% 16.29/3.85 % (2483)Instructions burned: 446 (million)
% 16.29/3.85 % (2483)------------------------------
% 16.29/3.85 % (2483)------------------------------
% 16.29/3.86 % (2484)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_2254 for (2976ds/594Mi)
% 16.29/3.86 % (2485)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_2254 for (2976ds/327Mi)
% 16.29/3.88 % (2481)Instruction limit reached!
% 16.29/3.88 % (2481)------------------------------
% 16.29/3.88 % (2481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.88 % (2481)Termination reason: Unknown
% 16.29/3.88 % (2481)Termination phase: Saturation
% 16.29/3.88
% 16.29/3.88 % (2481)Memory used [KB]: 7036
% 16.29/3.88 % (2481)Time elapsed: 0.211 s
% 16.29/3.88 % (2481)Instructions burned: 868 (million)
% 16.29/3.88 % (2481)------------------------------
% 16.29/3.88 % (2481)------------------------------
% 16.29/3.90 % (2486)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_2254 for (2976ds/5411Mi)
% 16.80/3.91 % (2486)Refutation not found, incomplete strategy
% 16.80/3.91 % (2486)------------------------------
% 16.80/3.91 % (2486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.91 % (2486)Termination reason: Refutation not found, incomplete strategy
% 16.80/3.91
% 16.80/3.91
% 16.80/3.91 % (2486)Memory used [KB]: 6780
% 16.80/3.91 % (2486)Time elapsed: 0.014 s
% 16.80/3.91 % (2486)Instructions burned: 41 (million)
% 16.80/3.91 % (2486)------------------------------
% 16.80/3.91 % (2486)------------------------------
% 16.80/3.92 % (2479)Instruction limit reached!
% 16.80/3.92 % (2479)------------------------------
% 16.80/3.92 % (2479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.92 % (2479)Termination reason: Unknown
% 16.80/3.92 % (2479)Termination phase: Saturation
% 16.80/3.92
% 16.80/3.92 % (2479)Memory used [KB]: 16247
% 16.80/3.92 % (2479)Time elapsed: 0.282 s
% 16.80/3.92 % (2479)Instructions burned: 907 (million)
% 16.80/3.92 % (2479)------------------------------
% 16.80/3.92 % (2479)------------------------------
% 16.80/3.92 % (2487)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_2254 for (2976ds/1762Mi)
% 16.80/3.93 % (2488)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_2254 for (2976ds/96Mi)
% 16.80/3.93 % (2478)Instruction limit reached!
% 16.80/3.93 % (2478)------------------------------
% 16.80/3.93 % (2478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.93 % (2478)Termination reason: Unknown
% 16.80/3.93 % (2478)Termination phase: Saturation
% 16.80/3.93
% 16.80/3.93 % (2478)Memory used [KB]: 7419
% 16.80/3.93 % (2478)Time elapsed: 0.343 s
% 16.80/3.93 % (2478)Instructions burned: 1376 (million)
% 16.80/3.93 % (2478)------------------------------
% 16.80/3.93 % (2478)------------------------------
% 16.80/3.95 % (2489)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_2254 for (2975ds/503Mi)
% 16.80/3.95 % (2488)Instruction limit reached!
% 16.80/3.95 % (2488)------------------------------
% 16.80/3.95 % (2488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.95 % (2488)Termination reason: Unknown
% 16.80/3.95 % (2488)Termination phase: Saturation
% 16.80/3.95
% 16.80/3.95 % (2488)Memory used [KB]: 6524
% 16.80/3.95 % (2488)Time elapsed: 0.025 s
% 16.80/3.95 % (2488)Instructions burned: 96 (million)
% 16.80/3.95 % (2488)------------------------------
% 16.80/3.95 % (2488)------------------------------
% 16.80/3.96 % (2490)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_2254 for (2975ds/90Mi)
% 16.80/3.96 % (2485)Instruction limit reached!
% 16.80/3.96 % (2485)------------------------------
% 16.80/3.96 % (2485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.96 % (2485)Termination reason: Unknown
% 16.80/3.96 % (2485)Termination phase: Saturation
% 16.80/3.96
% 16.80/3.96 % (2485)Memory used [KB]: 10490
% 16.80/3.96 % (2485)Time elapsed: 0.099 s
% 16.80/3.96 % (2485)Instructions burned: 327 (million)
% 16.80/3.96 % (2485)------------------------------
% 16.80/3.96 % (2485)------------------------------
% 16.80/3.97 % (2491)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_2254 for (2975ds/593Mi)
% 16.80/3.98 % (2489)Refutation not found, incomplete strategy
% 16.80/3.98 % (2489)------------------------------
% 16.80/3.98 % (2489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.98 % (2489)Termination reason: Refutation not found, incomplete strategy
% 16.80/3.98
% 16.80/3.98
% 16.80/3.98 % (2489)Memory used [KB]: 6780
% 16.80/3.98 % (2489)Time elapsed: 0.028 s
% 16.80/3.98 % (2489)Instructions burned: 54 (million)
% 16.80/3.98 % (2489)------------------------------
% 16.80/3.98 % (2489)------------------------------
% 16.80/3.99 % (2492)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_2254 for (2975ds/1512Mi)
% 16.80/3.99 % (2490)Instruction limit reached!
% 16.80/3.99 % (2490)------------------------------
% 16.80/3.99 % (2490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.99 % (2490)Termination reason: Unknown
% 16.80/3.99 % (2490)Termination phase: Preprocessing 3
% 16.80/3.99
% 16.80/3.99 % (2490)Memory used [KB]: 3965
% 16.80/3.99 % (2490)Time elapsed: 0.027 s
% 16.80/3.99 % (2490)Instructions burned: 90 (million)
% 16.80/3.99 % (2490)------------------------------
% 16.80/3.99 % (2490)------------------------------
% 16.80/4.00 % (2493)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_2254 for (2975ds/569Mi)
% 19.82/4.03 % (2484)Instruction limit reached!
% 19.82/4.03 % (2484)------------------------------
% 19.82/4.03 % (2484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.82/4.03 % (2484)Termination reason: Unknown
% 19.82/4.03 % (2484)Termination phase: Saturation
% 19.82/4.03
% 19.82/4.03 % (2484)Memory used [KB]: 9850
% 19.82/4.03 % (2484)Time elapsed: 0.174 s
% 19.82/4.03 % (2484)Instructions burned: 596 (million)
% 19.82/4.03 % (2484)------------------------------
% 19.82/4.03 % (2484)------------------------------
% 19.82/4.04 % (2494)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_2254 for (2975ds/501Mi)
% 19.82/4.06 % (2492)Refutation not found, incomplete strategy
% 19.82/4.06 % (2492)------------------------------
% 19.82/4.06 % (2492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.82/4.06 % (2492)Termination reason: Refutation not found, incomplete strategy
% 19.82/4.06
% 19.82/4.06
% 19.82/4.06 % (2492)Memory used [KB]: 9722
% 19.82/4.06 % (2492)Time elapsed: 0.100 s
% 19.82/4.06 % (2492)Instructions burned: 262 (million)
% 19.82/4.06 % (2492)------------------------------
% 19.82/4.06 % (2492)------------------------------
% 19.82/4.07 % (2495)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_2254 for (2974ds/562Mi)
% 20.45/4.14 % (2493)Instruction limit reached!
% 20.45/4.14 % (2493)------------------------------
% 20.45/4.14 % (2493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.45/4.14 % (2493)Termination reason: Unknown
% 20.45/4.14 % (2493)Termination phase: Saturation
% 20.45/4.14
% 20.45/4.14 % (2493)Memory used [KB]: 6652
% 20.45/4.14 % (2493)Time elapsed: 0.140 s
% 20.45/4.14 % (2493)Instructions burned: 571 (million)
% 20.45/4.14 % (2493)------------------------------
% 20.45/4.14 % (2493)------------------------------
% 20.45/4.15 % (2496)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_2254 for (2973ds/406Mi)
% 20.45/4.18 % (2494)Instruction limit reached!
% 20.45/4.18 % (2494)------------------------------
% 20.45/4.18 % (2494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.45/4.18 % (2494)Termination reason: Unknown
% 20.45/4.18 % (2494)Termination phase: Saturation
% 20.45/4.18
% 20.45/4.18 % (2494)Memory used [KB]: 11001
% 20.45/4.18 % (2494)Time elapsed: 0.165 s
% 20.45/4.18 % (2494)Instructions burned: 502 (million)
% 20.45/4.18 % (2494)------------------------------
% 20.45/4.18 % (2494)------------------------------
% 20.45/4.18 % (2491)Instruction limit reached!
% 20.45/4.18 % (2491)------------------------------
% 20.45/4.18 % (2491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.45/4.18 % (2491)Termination reason: Unknown
% 20.45/4.18 % (2491)Termination phase: Saturation
% 20.45/4.18
% 20.45/4.18 % (2491)Memory used [KB]: 11513
% 20.45/4.18 % (2491)Time elapsed: 0.199 s
% 20.45/4.18 % (2491)Instructions burned: 593 (million)
% 20.45/4.18 % (2491)------------------------------
% 20.45/4.18 % (2491)------------------------------
% 20.45/4.19 % (2497)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_2254 for (2973ds/582Mi)
% 20.45/4.19 % (2498)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_2254 for (2973ds/456Mi)
% 20.45/4.19 % (2473)Instruction limit reached!
% 20.45/4.19 % (2473)------------------------------
% 20.45/4.19 % (2473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.45/4.19 % (2473)Termination reason: Unknown
% 20.45/4.19 % (2473)Termination phase: Saturation
% 20.45/4.19
% 20.45/4.19 % (2473)Memory used [KB]: 8187
% 20.45/4.19 % (2473)Time elapsed: 1.144 s
% 20.45/4.19 % (2473)Instructions burned: 4714 (million)
% 20.45/4.19 % (2473)------------------------------
% 20.45/4.19 % (2473)------------------------------
% 20.97/4.20 % (2500)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_2254 for (2973ds/393Mi)
% 20.97/4.21 % (2495)Instruction limit reached!
% 20.97/4.21 % (2495)------------------------------
% 20.97/4.21 % (2495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.21 % (2495)Termination reason: Unknown
% 20.97/4.21 % (2495)Termination phase: Saturation
% 20.97/4.21
% 20.97/4.21 % (2495)Memory used [KB]: 7164
% 20.97/4.21 % (2495)Time elapsed: 0.141 s
% 20.97/4.21 % (2495)Instructions burned: 563 (million)
% 20.97/4.21 % (2495)------------------------------
% 20.97/4.21 % (2495)------------------------------
% 20.97/4.22 % (2501)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_2254 for (2973ds/1335Mi)
% 20.97/4.25 % (2501)Refutation not found, incomplete strategy
% 20.97/4.25 % (2501)------------------------------
% 20.97/4.25 % (2501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.25 % (2501)Termination reason: Refutation not found, incomplete strategy
% 20.97/4.25
% 20.97/4.25
% 20.97/4.25 % (2501)Memory used [KB]: 6652
% 20.97/4.25 % (2501)Time elapsed: 0.024 s
% 20.97/4.25 % (2501)Instructions burned: 90 (million)
% 20.97/4.25 % (2501)------------------------------
% 20.97/4.25 % (2501)------------------------------
% 20.97/4.26 % (2502)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_2254 for (2972ds/3373Mi)
% 20.97/4.26 % (2496)Instruction limit reached!
% 20.97/4.26 % (2496)------------------------------
% 20.97/4.26 % (2496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.26 % (2496)Termination reason: Unknown
% 20.97/4.26 % (2496)Termination phase: Saturation
% 20.97/4.26
% 20.97/4.26 % (2496)Memory used [KB]: 10234
% 20.97/4.26 % (2496)Time elapsed: 0.118 s
% 20.97/4.26 % (2496)Instructions burned: 409 (million)
% 20.97/4.26 % (2496)------------------------------
% 20.97/4.26 % (2496)------------------------------
% 20.97/4.27 % (2503)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_2254 for (2972ds/474Mi)
% 21.49/4.30 % (2500)Instruction limit reached!
% 21.49/4.30 % (2500)------------------------------
% 21.49/4.30 % (2500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.30 % (2500)Termination reason: Unknown
% 21.49/4.30 % (2500)Termination phase: Saturation
% 21.49/4.30
% 21.49/4.30 % (2500)Memory used [KB]: 6652
% 21.49/4.30 % (2500)Time elapsed: 0.096 s
% 21.49/4.30 % (2500)Instructions burned: 393 (million)
% 21.49/4.30 % (2500)------------------------------
% 21.49/4.30 % (2500)------------------------------
% 21.49/4.31 % (2504)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_2254 for (2972ds/157Mi)
% 21.49/4.32 % (2498)Instruction limit reached!
% 21.49/4.32 % (2498)------------------------------
% 21.49/4.32 % (2498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.32 % (2498)Termination reason: Unknown
% 21.49/4.32 % (2498)Termination phase: Saturation
% 21.49/4.32
% 21.49/4.32 % (2498)Memory used [KB]: 11513
% 21.49/4.32 % (2498)Time elapsed: 0.131 s
% 21.49/4.32 % (2498)Instructions burned: 457 (million)
% 21.49/4.32 % (2498)------------------------------
% 21.49/4.32 % (2498)------------------------------
% 21.49/4.33 % (2505)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/590Mi)
% 21.49/4.35 % (2504)Instruction limit reached!
% 21.49/4.35 % (2504)------------------------------
% 21.49/4.35 % (2504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.35 % (2504)Termination reason: Unknown
% 21.49/4.35 % (2504)Termination phase: Saturation
% 21.49/4.35
% 21.49/4.35 % (2504)Memory used [KB]: 6524
% 21.49/4.35 % (2504)Time elapsed: 0.040 s
% 21.49/4.35 % (2504)Instructions burned: 158 (million)
% 21.49/4.35 % (2504)------------------------------
% 21.49/4.35 % (2504)------------------------------
% 21.49/4.36 % (2487)Instruction limit reached!
% 21.49/4.36 % (2487)------------------------------
% 21.49/4.36 % (2487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.36 % (2487)Termination reason: Unknown
% 21.49/4.36 % (2487)Termination phase: Saturation
% 21.49/4.36
% 21.49/4.36 % (2487)Memory used [KB]: 15479
% 21.49/4.36 % (2487)Time elapsed: 0.461 s
% 21.49/4.36 % (2487)Instructions burned: 1763 (million)
% 21.49/4.36 % (2487)------------------------------
% 21.49/4.36 % (2487)------------------------------
% 21.49/4.36 % (2506)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/104Mi)
% 21.49/4.36 % (2497)Instruction limit reached!
% 21.49/4.36 % (2497)------------------------------
% 21.49/4.36 % (2497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.36 % (2497)Termination reason: Unknown
% 21.49/4.36 % (2497)Termination phase: Saturation
% 21.49/4.36
% 21.49/4.36 % (2497)Memory used [KB]: 10106
% 21.49/4.36 % (2497)Time elapsed: 0.175 s
% 21.49/4.36 % (2497)Instructions burned: 585 (million)
% 21.49/4.36 % (2497)------------------------------
% 21.49/4.36 % (2497)------------------------------
% 21.49/4.37 % (2507)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/414Mi)
% 21.49/4.37 % (2508)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/715Mi)
% 21.49/4.39 % (2506)Instruction limit reached!
% 21.49/4.39 % (2506)------------------------------
% 21.49/4.39 % (2506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.39 % (2506)Termination reason: Unknown
% 21.49/4.39 % (2506)Termination phase: Property scanning
% 21.49/4.39
% 21.49/4.39 % (2506)Memory used [KB]: 4221
% 21.49/4.39 % (2506)Time elapsed: 0.031 s
% 21.49/4.39 % (2506)Instructions burned: 106 (million)
% 21.49/4.39 % (2506)------------------------------
% 21.49/4.39 % (2506)------------------------------
% 21.49/4.39 % (2503)Instruction limit reached!
% 21.49/4.39 % (2503)------------------------------
% 21.49/4.39 % (2503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.39 % (2503)Termination reason: Unknown
% 21.49/4.39 % (2503)Termination phase: Saturation
% 21.49/4.39
% 21.49/4.39 % (2503)Memory used [KB]: 7419
% 21.49/4.39 % (2503)Time elapsed: 0.118 s
% 21.49/4.39 % (2503)Instructions burned: 479 (million)
% 21.49/4.39 % (2503)------------------------------
% 21.49/4.39 % (2503)------------------------------
% 21.49/4.40 % (2509)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/961Mi)
% 22.30/4.40 % (2510)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_2254 for (2971ds/1213Mi)
% 22.30/4.47 % (2507)Instruction limit reached!
% 22.30/4.47 % (2507)------------------------------
% 22.30/4.47 % (2507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.47 % (2507)Termination reason: Unknown
% 22.30/4.47 % (2507)Termination phase: Saturation
% 22.30/4.47
% 22.30/4.47 % (2507)Memory used [KB]: 6652
% 22.30/4.47 % (2507)Time elapsed: 0.103 s
% 22.30/4.47 % (2507)Instructions burned: 417 (million)
% 22.30/4.47 % (2507)------------------------------
% 22.30/4.47 % (2507)------------------------------
% 22.30/4.48 % (2511)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_2254 for (2970ds/1979Mi)
% 22.30/4.49 % (2505)Instruction limit reached!
% 22.30/4.49 % (2505)------------------------------
% 22.30/4.49 % (2505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.49 % (2505)Termination reason: Unknown
% 22.30/4.49 % (2505)Termination phase: Saturation
% 22.30/4.49
% 22.30/4.49 % (2505)Memory used [KB]: 11001
% 22.30/4.49 % (2505)Time elapsed: 0.159 s
% 22.30/4.49 % (2505)Instructions burned: 590 (million)
% 22.30/4.49 % (2505)------------------------------
% 22.30/4.49 % (2505)------------------------------
% 22.68/4.50 % (2512)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_2254 for (2970ds/481Mi)
% 22.68/4.58 % (2508)Instruction limit reached!
% 22.68/4.58 % (2508)------------------------------
% 22.68/4.58 % (2508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.68/4.58 % (2508)Termination reason: Unknown
% 22.68/4.58 % (2508)Termination phase: Saturation
% 22.68/4.58
% 22.68/4.58 % (2508)Memory used [KB]: 6268
% 22.68/4.58 % (2508)Time elapsed: 0.207 s
% 22.68/4.58 % (2508)Instructions burned: 715 (million)
% 22.68/4.58 % (2508)------------------------------
% 22.68/4.58 % (2508)------------------------------
% 22.68/4.59 % (2513)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_2254 for (2969ds/783Mi)
% 22.99/4.62 % (2512)Instruction limit reached!
% 22.99/4.62 % (2512)------------------------------
% 22.99/4.62 % (2512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.99/4.62 % (2512)Termination reason: Unknown
% 22.99/4.62 % (2512)Termination phase: Saturation
% 22.99/4.62
% 22.99/4.62 % (2512)Memory used [KB]: 7291
% 22.99/4.62 % (2512)Time elapsed: 0.119 s
% 22.99/4.62 % (2512)Instructions burned: 482 (million)
% 22.99/4.62 % (2512)------------------------------
% 22.99/4.62 % (2512)------------------------------
% 22.99/4.63 % (2514)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_2254 for (2969ds/432Mi)
% 22.99/4.68 % (2509)Instruction limit reached!
% 22.99/4.68 % (2509)------------------------------
% 22.99/4.68 % (2509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.99/4.68 % (2509)Termination reason: Unknown
% 22.99/4.68 % (2509)Termination phase: Saturation
% 22.99/4.68
% 22.99/4.68 % (2509)Memory used [KB]: 12665
% 22.99/4.68 % (2509)Time elapsed: 0.289 s
% 22.99/4.68 % (2509)Instructions burned: 963 (million)
% 22.99/4.68 % (2509)------------------------------
% 22.99/4.68 % (2509)------------------------------
% 22.99/4.69 % (2515)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_2254 for (2968ds/1670Mi)
% 23.52/4.75 % (2514)Instruction limit reached!
% 23.52/4.75 % (2514)------------------------------
% 23.52/4.75 % (2514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.52/4.75 % (2514)Termination reason: Unknown
% 23.52/4.75 % (2514)Termination phase: Saturation
% 23.52/4.75
% 23.52/4.75 % (2514)Memory used [KB]: 7803
% 23.52/4.75 % (2514)Time elapsed: 0.126 s
% 23.52/4.75 % (2514)Instructions burned: 433 (million)
% 23.52/4.75 % (2514)------------------------------
% 23.52/4.75 % (2514)------------------------------
% 23.52/4.76 % (2516)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_2254 for (2967ds/90Mi)
% 23.52/4.76 % (2510)Instruction limit reached!
% 23.52/4.76 % (2510)------------------------------
% 23.52/4.76 % (2510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.52/4.76 % (2510)Termination reason: Unknown
% 23.52/4.76 % (2510)Termination phase: Saturation
% 23.52/4.76
% 23.52/4.76 % (2510)Memory used [KB]: 12281
% 23.52/4.76 % (2510)Time elapsed: 0.365 s
% 23.52/4.76 % (2510)Instructions burned: 1214 (million)
% 23.52/4.76 % (2510)------------------------------
% 23.52/4.76 % (2510)------------------------------
% 23.52/4.77 % (2517)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_2254 for (2967ds/346Mi)
% 23.52/4.79 % (2516)Instruction limit reached!
% 23.52/4.79 % (2516)------------------------------
% 23.52/4.79 % (2516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.52/4.79 % (2516)Termination reason: Unknown
% 23.52/4.79 % (2516)Termination phase: Preprocessing 3
% 23.52/4.79
% 23.52/4.79 % (2516)Memory used [KB]: 4093
% 23.52/4.79 % (2516)Time elapsed: 0.027 s
% 23.52/4.79 % (2516)Instructions burned: 90 (million)
% 23.52/4.79 % (2516)------------------------------
% 23.52/4.79 % (2516)------------------------------
% 24.17/4.80 % (2518)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_2254 for (2967ds/401Mi)
% 24.17/4.80 % (2513)Instruction limit reached!
% 24.17/4.80 % (2513)------------------------------
% 24.17/4.80 % (2513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.17/4.80 % (2513)Termination reason: Unknown
% 24.17/4.80 % (2513)Termination phase: Saturation
% 24.17/4.80
% 24.17/4.80 % (2513)Memory used [KB]: 8187
% 24.17/4.80 % (2513)Time elapsed: 0.211 s
% 24.17/4.80 % (2513)Instructions burned: 785 (million)
% 24.17/4.80 % (2513)------------------------------
% 24.17/4.80 % (2513)------------------------------
% 24.17/4.81 % (2519)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_2254 for (2967ds/6454Mi)
% 24.17/4.86 % (2517)Instruction limit reached!
% 24.17/4.86 % (2517)------------------------------
% 24.17/4.86 % (2517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.17/4.86 % (2517)Termination reason: Unknown
% 24.17/4.86 % (2517)Termination phase: Saturation
% 24.17/4.86
% 24.17/4.86 % (2517)Memory used [KB]: 7291
% 24.17/4.86 % (2517)Time elapsed: 0.085 s
% 24.17/4.86 % (2517)Instructions burned: 347 (million)
% 24.17/4.86 % (2517)------------------------------
% 24.17/4.86 % (2517)------------------------------
% 24.17/4.87 % (2520)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_2254 for (2966ds/283Mi)
% 24.58/4.90 % (2518)Instruction limit reached!
% 24.58/4.90 % (2518)------------------------------
% 24.58/4.90 % (2518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/4.90 % (2518)Termination reason: Unknown
% 24.58/4.90 % (2518)Termination phase: Saturation
% 24.58/4.90
% 24.58/4.90 % (2518)Memory used [KB]: 6908
% 24.58/4.90 % (2518)Time elapsed: 0.102 s
% 24.58/4.90 % (2518)Instructions burned: 402 (million)
% 24.58/4.90 % (2518)------------------------------
% 24.58/4.90 % (2518)------------------------------
% 24.58/4.91 % (2521)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_2254 for (2966ds/865Mi)
% 24.58/4.94 % (2520)Instruction limit reached!
% 24.58/4.94 % (2520)------------------------------
% 24.58/4.94 % (2520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/4.94 % (2520)Termination reason: Unknown
% 24.58/4.94 % (2520)Termination phase: Saturation
% 24.58/4.94
% 24.58/4.94 % (2520)Memory used [KB]: 10106
% 24.58/4.94 % (2520)Time elapsed: 0.077 s
% 24.58/4.94 % (2520)Instructions burned: 283 (million)
% 24.58/4.94 % (2520)------------------------------
% 24.58/4.94 % (2520)------------------------------
% 24.58/4.95 % (2522)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_2254 for (2965ds/4528Mi)
% 24.58/4.96 % (2522)Refutation not found, incomplete strategy
% 24.58/4.96 % (2522)------------------------------
% 24.58/4.96 % (2522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/4.96 % (2522)Termination reason: Refutation not found, incomplete strategy
% 24.58/4.96
% 24.58/4.96
% 24.58/4.96 % (2522)Memory used [KB]: 2174
% 24.58/4.96 % (2522)Time elapsed: 0.013 s
% 24.58/4.96 % (2522)Instructions burned: 39 (million)
% 24.58/4.96 % (2522)------------------------------
% 24.58/4.96 % (2522)------------------------------
% 24.58/4.97 % (2523)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_2254 for (2965ds/1001Mi)
% 24.58/5.01 % (2521)Refutation not found, incomplete strategy
% 24.58/5.01 % (2521)------------------------------
% 24.58/5.01 % (2521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/5.01 % (2521)Termination reason: Refutation not found, incomplete strategy
% 24.58/5.01
% 24.58/5.01
% 24.58/5.01 % (2521)Memory used [KB]: 10746
% 24.58/5.01 % (2521)Time elapsed: 0.124 s
% 24.58/5.01 % (2521)Instructions burned: 359 (million)
% 24.58/5.01 % (2521)------------------------------
% 24.58/5.01 % (2521)------------------------------
% 26.85/5.02 % (2524)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_2254 for (2965ds/102Mi)
% 26.85/5.05 % (2524)Instruction limit reached!
% 26.85/5.05 % (2524)------------------------------
% 26.85/5.05 % (2524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.85/5.05 % (2524)Termination reason: Unknown
% 26.85/5.05 % (2524)Termination phase: Saturation
% 26.85/5.05
% 26.85/5.05 % (2524)Memory used [KB]: 6524
% 26.85/5.05 % (2524)Time elapsed: 0.028 s
% 26.85/5.05 % (2524)Instructions burned: 105 (million)
% 26.85/5.05 % (2524)------------------------------
% 26.85/5.05 % (2524)------------------------------
% 26.85/5.06 % (2525)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_2254 for (2964ds/952Mi)
% 26.85/5.06 % (2511)Instruction limit reached!
% 26.85/5.06 % (2511)------------------------------
% 26.85/5.06 % (2511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.85/5.06 % (2511)Termination reason: Unknown
% 26.85/5.06 % (2511)Termination phase: Saturation
% 26.85/5.06
% 26.85/5.06 % (2511)Memory used [KB]: 12792
% 26.85/5.06 % (2511)Time elapsed: 0.586 s
% 26.85/5.06 % (2511)Instructions burned: 1980 (million)
% 26.85/5.06 % (2511)------------------------------
% 26.85/5.06 % (2511)------------------------------
% 26.85/5.07 % (2526)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_2254 for (2964ds/578Mi)
% 26.85/5.09 % (2515)Instruction limit reached!
% 26.85/5.09 % (2515)------------------------------
% 26.85/5.09 % (2515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.85/5.09 % (2515)Termination reason: Unknown
% 26.85/5.09 % (2515)Termination phase: Saturation
% 26.85/5.09
% 26.85/5.09 % (2515)Memory used [KB]: 6652
% 26.85/5.09 % (2515)Time elapsed: 0.398 s
% 26.85/5.09 % (2515)Instructions burned: 1671 (million)
% 26.85/5.09 % (2515)------------------------------
% 26.85/5.09 % (2515)------------------------------
% 26.85/5.10 % (2527)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_2254 for (2964ds/643Mi)
% 27.81/5.22 % (2526)Instruction limit reached!
% 27.81/5.22 % (2526)------------------------------
% 27.81/5.22 % (2526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.81/5.22 % (2526)Termination reason: Unknown
% 27.81/5.22 % (2526)Termination phase: Saturation
% 27.81/5.22
% 27.81/5.22 % (2526)Memory used [KB]: 8315
% 27.81/5.22 % (2526)Time elapsed: 0.153 s
% 27.81/5.22 % (2526)Instructions burned: 580 (million)
% 27.81/5.22 % (2526)------------------------------
% 27.81/5.22 % (2526)------------------------------
% 27.81/5.23 % (2528)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_2254 for (2962ds/865Mi)
% 27.81/5.25 % (2502)Instruction limit reached!
% 27.81/5.25 % (2502)------------------------------
% 27.81/5.25 % (2502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.81/5.25 % (2502)Termination reason: Unknown
% 27.81/5.25 % (2502)Termination phase: Saturation
% 27.81/5.25
% 27.81/5.25 % (2502)Memory used [KB]: 15351
% 27.81/5.25 % (2502)Time elapsed: 0.991 s
% 27.81/5.25 % (2502)Instructions burned: 3376 (million)
% 27.81/5.25 % (2502)------------------------------
% 27.81/5.25 % (2502)------------------------------
% 27.81/5.25 % (2527)Instruction limit reached!
% 27.81/5.25 % (2527)------------------------------
% 27.81/5.25 % (2527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.81/5.25 % (2527)Termination reason: Unknown
% 27.81/5.25 % (2527)Termination phase: Saturation
% 27.81/5.25
% 27.81/5.25 % (2527)Memory used [KB]: 6652
% 27.81/5.25 % (2527)Time elapsed: 0.153 s
% 27.81/5.25 % (2527)Instructions burned: 646 (million)
% 27.81/5.25 % (2527)------------------------------
% 27.81/5.25 % (2527)------------------------------
% 27.81/5.26 % (2529)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_2254 for (2962ds/1174Mi)
% 27.81/5.26 % (2523)Instruction limit reached!
% 27.81/5.26 % (2523)------------------------------
% 27.81/5.26 % (2523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.81/5.26 % (2523)Termination reason: Unknown
% 27.81/5.26 % (2523)Termination phase: Saturation
% 27.81/5.26
% 27.81/5.26 % (2523)Memory used [KB]: 15735
% 27.81/5.26 % (2523)Time elapsed: 0.308 s
% 27.81/5.26 % (2523)Instructions burned: 1001 (million)
% 27.81/5.26 % (2523)------------------------------
% 27.81/5.26 % (2523)------------------------------
% 27.81/5.26 % (2530)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_2254 for (2962ds/644Mi)
% 27.81/5.27 % (2531)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_2254 for (2962ds/1201Mi)
% 27.81/5.29 % (2519)First to succeed.
% 28.46/5.33 % (2519)Refutation found. Thanks to Tanya!
% 28.46/5.33 % SZS status Theorem for DTF2THF_2254
% 28.46/5.33 % SZS output start Proof for DTF2THF_2254
% 28.46/5.33 thf(type_def_5, type, term: $tType).
% 28.46/5.33 thf(type_def_7, type, subst: $tType).
% 28.46/5.33 thf(type_def_8, type, d_term: $tType).
% 28.46/5.33 thf(type_def_9, type, d_subst: $tType).
% 28.46/5.33 thf(func_def_0, type, term: $tType).
% 28.46/5.33 thf(func_def_1, type, subst: $tType).
% 28.46/5.33 thf(func_def_2, type, one: term).
% 28.46/5.33 thf(func_def_3, type, ap: term > term > term).
% 28.46/5.33 thf(func_def_4, type, lam: term > term).
% 28.46/5.33 thf(func_def_5, type, sub: term > subst > term).
% 28.46/5.33 thf(func_def_6, type, id: subst).
% 28.46/5.33 thf(func_def_7, type, sh: subst).
% 28.46/5.33 thf(func_def_8, type, push: term > subst > subst).
% 28.46/5.33 thf(func_def_9, type, comp: subst > subst > subst).
% 28.46/5.33 thf(func_def_10, type, var: term > $o).
% 28.46/5.33 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 28.46/5.33 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 28.46/5.33 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 28.46/5.33 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 28.46/5.33 thf(func_def_124, type, d_term: $tType).
% 28.46/5.33 thf(func_def_125, type, d_subst: $tType).
% 28.46/5.33 thf(func_def_126, type, d2term: d_term > term).
% 28.46/5.33 thf(func_def_127, type, d2subst: d_subst > subst).
% 28.46/5.33 thf(func_def_128, type, d_one: d_term).
% 28.46/5.33 thf(func_def_129, type, d_id: d_subst).
% 28.46/5.33 thf(func_def_142, type, sP0: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_145, type, sP3: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_146, type, sP4: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_150, type, sP8: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_152, type, sP10: (term > $o) > $o).
% 28.46/5.33 thf(func_def_153, type, sP11: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_154, type, sP12: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_155, type, sP13: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_156, type, sP14: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_157, type, sP15: (term > $o) > $o).
% 28.46/5.33 thf(func_def_162, type, sP20: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_163, type, sP21: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_165, type, sP23: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_166, type, sP24: (term > $o) > $o).
% 28.46/5.33 thf(func_def_171, type, sP29: (term > $o) > $o).
% 28.46/5.33 thf(func_def_172, type, sP30: (term > $o) > $o).
% 28.46/5.33 thf(func_def_175, type, sP33: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_178, type, sP36: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_179, type, sP37: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_180, type, sP38: (term > $o) > $o).
% 28.46/5.33 thf(func_def_184, type, sP42: (term > $o) > $o).
% 28.46/5.33 thf(func_def_186, type, sP44: (term > $o) > $o).
% 28.46/5.33 thf(func_def_189, type, sP47: (term > $o) > $o).
% 28.46/5.33 thf(func_def_190, type, sP48: (term > $o) > $o).
% 28.46/5.33 thf(func_def_193, type, sP51: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_196, type, sP54: (subst > term > subst > $o) > $o).
% 28.46/5.33 thf(func_def_201, type, sK59: term).
% 28.46/5.33 thf(func_def_202, type, sK60: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_203, type, sK61: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_204, type, sK62: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_205, type, sK63: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_206, type, sK64: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_207, type, sK65: term).
% 28.46/5.33 thf(func_def_208, type, sK66: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_209, type, sK67: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_210, type, sK68: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_211, type, sK69: term > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_212, type, sK70: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_213, type, sK71: term).
% 28.46/5.33 thf(func_def_214, type, sK72: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_215, type, sK73: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_216, type, sK74: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_217, type, sK75: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_218, type, sK76: term).
% 28.46/5.33 thf(func_def_219, type, sK77: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_220, type, sK78: term).
% 28.46/5.33 thf(func_def_221, type, sK79: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_222, type, sK80: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_223, type, sK81: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_224, type, sK82: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_225, type, sK83: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_226, type, sK84: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_227, type, sK85: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_228, type, sK86: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_229, type, sK87: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_230, type, sK88: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_231, type, sK89: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_232, type, sK90: term).
% 28.46/5.33 thf(func_def_233, type, sK91: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_234, type, sK92: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_235, type, sK93: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_236, type, sK94: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_237, type, sK95: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_238, type, sK96: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_239, type, sK97: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_240, type, sK98: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_241, type, sK99: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_242, type, sK100: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_243, type, sK101: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_244, type, sK102: term).
% 28.46/5.33 thf(func_def_245, type, sK103: (subst > term > term) > term > subst).
% 28.46/5.33 thf(func_def_246, type, sK104: (subst > term > term) > term > term).
% 28.46/5.33 thf(func_def_247, type, sK105: (subst > term > term) > term > subst).
% 28.46/5.33 thf(func_def_248, type, sK106: (subst > term > term) > term > subst).
% 28.46/5.33 thf(func_def_249, type, sK107: (subst > term > term) > term > term).
% 28.46/5.33 thf(func_def_250, type, sK108: (subst > term > term) > term > subst).
% 28.46/5.33 thf(func_def_251, type, sK109: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_252, type, sK110: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_253, type, sK111: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_254, type, sK112: term > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_255, type, sK113: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_256, type, sK114: term).
% 28.46/5.33 thf(func_def_257, type, sK115: term).
% 28.46/5.33 thf(func_def_258, type, sK116: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_259, type, sK117: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_260, type, sK118: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_261, type, sK119: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_262, type, sK120: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_263, type, sK121: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_264, type, sK122: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_265, type, sK123: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_266, type, sK124: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_267, type, sK125: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_268, type, sK126: (term > $o) > term).
% 28.46/5.33 thf(func_def_269, type, sK127: (term > $o) > term).
% 28.46/5.33 thf(func_def_270, type, sK128: subst).
% 28.46/5.33 thf(func_def_271, type, sK129: term).
% 28.46/5.33 thf(func_def_272, type, sK130: subst).
% 28.46/5.33 thf(func_def_273, type, sK131: term).
% 28.46/5.33 thf(func_def_274, type, sK132: subst).
% 28.46/5.33 thf(func_def_275, type, sK133: term).
% 28.46/5.33 thf(func_def_276, type, sK134: term > $o).
% 28.46/5.33 thf(func_def_277, type, sK135: subst).
% 28.46/5.33 thf(func_def_278, type, sK136: term).
% 28.46/5.33 thf(func_def_279, type, sK137: term > $o).
% 28.46/5.33 thf(func_def_280, type, sK138: term > term).
% 28.46/5.33 thf(func_def_281, type, sK139: (term > $o) > subst > term).
% 28.46/5.33 thf(func_def_282, type, sK140: (term > $o) > term).
% 28.46/5.33 thf(func_def_283, type, sK141: (term > $o) > term).
% 28.46/5.33 thf(func_def_284, type, sK142: (term > $o) > term).
% 28.46/5.33 thf(func_def_285, type, sK143: (term > $o) > term).
% 28.46/5.33 thf(func_def_286, type, sK144: (term > $o) > term).
% 28.46/5.33 thf(func_def_287, type, sK145: subst).
% 28.46/5.33 thf(func_def_288, type, sK146: subst > term > term).
% 28.46/5.33 thf(func_def_289, type, sK147: subst > term > term).
% 28.46/5.33 thf(func_def_290, type, sK148: term).
% 28.46/5.33 thf(func_def_291, type, sK149: subst).
% 28.46/5.33 thf(func_def_292, type, sK150: term).
% 28.46/5.33 thf(func_def_293, type, sK151: subst).
% 28.46/5.33 thf(func_def_294, type, sK152: term).
% 28.46/5.33 thf(func_def_295, type, sK153: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_296, type, sK154: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_297, type, sK155: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_298, type, sK156: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_299, type, sK157: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_300, type, sK158: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_301, type, sK159: term).
% 28.46/5.33 thf(func_def_302, type, sK160: term).
% 28.46/5.33 thf(func_def_303, type, sK161: subst).
% 28.46/5.33 thf(func_def_304, type, sK162: term > $o).
% 28.46/5.33 thf(func_def_305, type, sK163: term).
% 28.46/5.33 thf(func_def_306, type, sK164: term > term).
% 28.46/5.33 thf(func_def_307, type, sK165: (term > $o) > term).
% 28.46/5.33 thf(func_def_308, type, sK166: (term > $o) > subst > term).
% 28.46/5.33 thf(func_def_309, type, sK167: (term > $o) > term).
% 28.46/5.33 thf(func_def_310, type, sK168: (term > $o) > term).
% 28.46/5.33 thf(func_def_311, type, sK169: term > $o).
% 28.46/5.33 thf(func_def_312, type, sK170: term).
% 28.46/5.33 thf(func_def_313, type, sK171: term > term).
% 28.46/5.33 thf(func_def_314, type, sK172: (term > $o) > term).
% 28.46/5.33 thf(func_def_315, type, sK173: (term > $o) > term).
% 28.46/5.33 thf(func_def_316, type, sK174: (term > $o) > term).
% 28.46/5.33 thf(func_def_317, type, sK175: (term > $o) > term).
% 28.46/5.33 thf(func_def_318, type, sK176: (term > $o) > term).
% 28.46/5.33 thf(func_def_319, type, sK177: (term > $o) > term).
% 28.46/5.33 thf(func_def_320, type, sK178: (subst > term > subst > $o) > term > $o).
% 28.46/5.33 thf(func_def_321, type, sK179: term > $o).
% 28.46/5.33 thf(func_def_322, type, sK180: term).
% 28.46/5.33 thf(func_def_323, type, sK181: term > term).
% 28.46/5.33 thf(func_def_324, type, sK182: term).
% 28.46/5.33 thf(func_def_325, type, sK183: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_326, type, sK184: (term > $o) > term).
% 28.46/5.33 thf(func_def_327, type, sK185: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_328, type, sK186: term).
% 28.46/5.33 thf(func_def_329, type, sK187: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_330, type, sK188: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_331, type, sK189: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_332, type, sK190: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_333, type, sK191: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_334, type, sK192: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_335, type, sK193: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_336, type, sK194: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_337, type, sK195: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_338, type, sK196: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_339, type, sK197: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_340, type, sK198: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_341, type, sK199: term > $o).
% 28.46/5.33 thf(func_def_342, type, sK200: term).
% 28.46/5.33 thf(func_def_343, type, sK201: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_344, type, sK202: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_345, type, sK203: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_346, type, sK204: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_347, type, sK205: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_348, type, sK206: (term > $o) > term).
% 28.46/5.33 thf(func_def_349, type, sK207: (term > $o) > term).
% 28.46/5.33 thf(func_def_350, type, sK208: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_351, type, sK209: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_352, type, sK210: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_353, type, sK211: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_354, type, sK212: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_355, type, sK213: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_356, type, sK214: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_357, type, sK215: term).
% 28.46/5.33 thf(func_def_358, type, sK216: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_359, type, sK217: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_360, type, sK218: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_361, type, sK219: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_362, type, sK220: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_363, type, sK221: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_364, type, sK222: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_365, type, sK223: term > $o).
% 28.46/5.33 thf(func_def_366, type, sK224: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_367, type, sK225: term).
% 28.46/5.33 thf(func_def_368, type, sK226: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_369, type, sK227: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_370, type, sK228: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_371, type, sK229: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_372, type, sK230: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_373, type, sK231: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_374, type, sK232: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_375, type, sK233: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_376, type, sK234: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_377, type, sK235: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_378, type, sK236: term).
% 28.46/5.33 thf(func_def_379, type, sK237: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_380, type, sK238: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_381, type, sK239: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_382, type, sK240: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_383, type, sK241: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_384, type, sK242: (term > $o) > term).
% 28.46/5.33 thf(func_def_385, type, sK243: subst > (term > $o) > term).
% 28.46/5.33 thf(func_def_386, type, sK244: term > $o).
% 28.46/5.33 thf(func_def_387, type, sK245: term).
% 28.46/5.33 thf(func_def_388, type, sK246: subst).
% 28.46/5.33 thf(func_def_389, type, sK247: term > term).
% 28.46/5.33 thf(func_def_390, type, sK248: term).
% 28.46/5.33 thf(func_def_391, type, sK249: term).
% 28.46/5.33 thf(func_def_392, type, sK250: term > $o).
% 28.46/5.33 thf(func_def_393, type, sK251: term > term).
% 28.46/5.33 thf(func_def_394, type, sK252: (term > $o) > term).
% 28.46/5.33 thf(func_def_395, type, sK253: (term > $o) > term).
% 28.46/5.33 thf(func_def_396, type, sK254: (term > $o) > term).
% 28.46/5.33 thf(func_def_397, type, sK255: (term > $o) > term).
% 28.46/5.33 thf(func_def_398, type, sK256: (term > $o) > term).
% 28.46/5.33 thf(func_def_399, type, sK257: (term > $o) > term).
% 28.46/5.33 thf(func_def_400, type, sK258: term).
% 28.46/5.33 thf(func_def_401, type, sK259: term > $o).
% 28.46/5.33 thf(func_def_402, type, sK260: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_403, type, sK261: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_404, type, sK262: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_405, type, sK263: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_406, type, sK264: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_407, type, sK265: term > subst > term > term).
% 28.46/5.33 thf(func_def_408, type, sK266: term).
% 28.46/5.33 thf(func_def_409, type, sK267: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_410, type, sK268: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_411, type, sK269: (term > $o) > term > term).
% 28.46/5.33 thf(func_def_412, type, sK270: term).
% 28.46/5.33 thf(func_def_413, type, sK271: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_414, type, sK272: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_415, type, sK273: term).
% 28.46/5.33 thf(func_def_416, type, sK274: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_417, type, sK275: (subst > term > subst > $o) > term > $o).
% 28.46/5.33 thf(func_def_418, type, sK276: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_419, type, sK277: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_420, type, sK278: term).
% 28.46/5.33 thf(func_def_421, type, sK279: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_422, type, sK280: (term > $o) > term).
% 28.46/5.33 thf(func_def_423, type, sK281: (term > $o) > term).
% 28.46/5.33 thf(func_def_424, type, sK282: (term > $o) > term).
% 28.46/5.33 thf(func_def_425, type, sK283: term > $o).
% 28.46/5.33 thf(func_def_426, type, sK284: term).
% 28.46/5.33 thf(func_def_427, type, sK285: term > term).
% 28.46/5.33 thf(func_def_428, type, sK286: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_429, type, sK287: (term > $o) > term > term).
% 28.46/5.33 thf(func_def_430, type, sK288: (term > $o) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_431, type, sK289: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_432, type, sK290: term).
% 28.46/5.33 thf(func_def_433, type, sK291: term > $o).
% 28.46/5.33 thf(func_def_434, type, sK292: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_435, type, sK293: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_436, type, sK294: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_437, type, sK295: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_438, type, sK296: (term > $o) > term).
% 28.46/5.33 thf(func_def_439, type, sK297: (term > $o) > term).
% 28.46/5.33 thf(func_def_440, type, sK298: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_441, type, sK299: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_442, type, sK300: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_443, type, sK301: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_444, type, sK302: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_445, type, sK303: term).
% 28.46/5.33 thf(func_def_446, type, sK304: term > $o).
% 28.46/5.33 thf(func_def_447, type, sK305: term).
% 28.46/5.33 thf(func_def_448, type, sK306: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_449, type, sK307: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_450, type, sK308: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_451, type, sK309: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_452, type, sK310: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_453, type, sK311: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_454, type, sK312: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_455, type, sK313: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_456, type, sK314: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_457, type, sK315: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_458, type, sK316: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_459, type, sK317: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_460, type, sK318: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_461, type, sK319: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_462, type, sK320: (term > $o) > term).
% 28.46/5.33 thf(func_def_463, type, sK321: (term > $o) > term).
% 28.46/5.33 thf(func_def_464, type, sK322: term > $o).
% 28.46/5.33 thf(func_def_465, type, sK323: term).
% 28.46/5.33 thf(func_def_466, type, sK324: term > term).
% 28.46/5.33 thf(func_def_467, type, sK325: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_468, type, sK326: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_469, type, sK327: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_470, type, sK328: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_471, type, sK329: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_472, type, sK330: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_473, type, sK331: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_474, type, sK332: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_475, type, sK333: term).
% 28.46/5.33 thf(func_def_476, type, sK334: term).
% 28.46/5.33 thf(func_def_477, type, sK335: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_478, type, sK336: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_479, type, sK337: term).
% 28.46/5.33 thf(func_def_480, type, sK338: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_481, type, sK339: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_482, type, sK340: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_483, type, sK341: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_484, type, sK342: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_485, type, sK343: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_486, type, sK344: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_487, type, sK345: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_488, type, sK346: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_489, type, sK347: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_490, type, sK348: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_491, type, sK349: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_492, type, sK350: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_493, type, sK351: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_494, type, sK352: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_495, type, sK353: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_496, type, sK354: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_497, type, sK355: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_498, type, sK356: term).
% 28.46/5.33 thf(func_def_499, type, sK357: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_500, type, sK358: (term > $o) > term).
% 28.46/5.33 thf(func_def_501, type, sK359: (term > $o) > term).
% 28.46/5.33 thf(func_def_502, type, sK360: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_503, type, sK361: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_504, type, sK362: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_505, type, sK363: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_506, type, sK364: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_507, type, sK365: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_508, type, sK366: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_509, type, sK367: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_510, type, sK368: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_511, type, sK369: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_512, type, sK370: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_513, type, sK371: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_514, type, sK372: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_515, type, sK373: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_516, type, sK374: (term > $o) > term).
% 28.46/5.33 thf(func_def_517, type, sK375: (term > $o) > term).
% 28.46/5.33 thf(func_def_518, type, sK376: term).
% 28.46/5.33 thf(func_def_519, type, sK377: term > $o).
% 28.46/5.33 thf(func_def_520, type, sK378: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_521, type, sK379: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_522, type, sK380: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_523, type, sK381: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_524, type, sK382: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_525, type, sK383: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_526, type, sK384: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_527, type, sK385: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_528, type, sK386: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_529, type, sK387: (term > $o) > term > term).
% 28.46/5.33 thf(func_def_530, type, sK388: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_531, type, sK389: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_532, type, sK390: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_533, type, sK391: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_534, type, sK392: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_535, type, sK393: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_536, type, sK394: term).
% 28.46/5.33 thf(func_def_537, type, sK395: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_538, type, sK396: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_539, type, sK397: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_540, type, sK398: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_541, type, sK399: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_542, type, sK400: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_543, type, sK401: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_544, type, sK402: term).
% 28.46/5.33 thf(func_def_545, type, sK403: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_546, type, sK404: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_547, type, sK405: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_548, type, sK406: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_549, type, sK407: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_550, type, sK408: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_551, type, sK409: (subst > term > subst > $o) > term > term).
% 28.46/5.33 thf(func_def_552, type, sK410: term).
% 28.46/5.33 thf(func_def_553, type, sK411: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_554, type, sK412: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_555, type, sK413: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_556, type, sK414: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_557, type, sK415: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_558, type, sK416: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_559, type, sK417: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_560, type, sK418: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_561, type, sK419: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_562, type, sK420: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_563, type, sK421: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_564, type, sK422: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_565, type, sK423: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_566, type, sK424: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_567, type, sK425: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_568, type, sK426: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_569, type, sK427: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_570, type, sK428: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_571, type, sK429: term > $o).
% 28.46/5.33 thf(func_def_572, type, sK430: term).
% 28.46/5.33 thf(func_def_573, type, sK431: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_574, type, sK432: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_575, type, sK433: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_576, type, sK434: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_577, type, sK435: (term > $o) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_578, type, sK436: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_579, type, sK437: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_580, type, sK438: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_581, type, sK439: term).
% 28.46/5.33 thf(func_def_582, type, sK440: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_583, type, sK441: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_584, type, sK442: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_585, type, sK443: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_586, type, sK444: term > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_587, type, sK445: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_588, type, sK446: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_589, type, sK447: (subst > term > subst > $o) > subst).
% 28.46/5.33 thf(func_def_590, type, sK448: (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_591, type, sK449: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_592, type, sK450: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_593, type, sK451: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_594, type, sK452: (subst > term > term) > (subst > term > subst > $o) > term).
% 28.46/5.33 thf(func_def_595, type, sK453: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_596, type, sK454: term).
% 28.46/5.33 thf(func_def_597, type, sK455: term).
% 28.46/5.33 thf(func_def_598, type, sK456: term).
% 28.46/5.33 thf(func_def_599, type, sK457: term).
% 28.46/5.33 thf(func_def_600, type, sK458: subst).
% 28.46/5.33 thf(func_def_601, type, sK459: term).
% 28.46/5.33 thf(func_def_602, type, sK460: term).
% 28.46/5.33 thf(func_def_603, type, sK461: term).
% 28.46/5.33 thf(func_def_604, type, sK462: subst).
% 28.46/5.33 thf(func_def_605, type, sK463: term).
% 28.46/5.33 thf(func_def_606, type, sK464: term).
% 28.46/5.33 thf(func_def_607, type, sK465: term > $o).
% 28.46/5.33 thf(func_def_608, type, sK466: subst).
% 28.46/5.33 thf(func_def_609, type, sK467: term > $o).
% 28.46/5.33 thf(func_def_610, type, sK468: term).
% 28.46/5.33 thf(func_def_611, type, sK469: subst).
% 28.46/5.33 thf(func_def_612, type, sK470: subst).
% 28.46/5.33 thf(func_def_613, type, sK471: term).
% 28.46/5.33 thf(func_def_614, type, sK472: subst).
% 28.46/5.33 thf(func_def_615, type, sK473: term).
% 28.46/5.33 thf(func_def_616, type, sK474: subst).
% 28.46/5.33 thf(func_def_617, type, sK475: term).
% 28.46/5.33 thf(func_def_618, type, sK476: subst).
% 28.46/5.33 thf(func_def_619, type, sK477: term).
% 28.46/5.33 thf(func_def_620, type, sK478: term > $o).
% 28.46/5.33 thf(func_def_621, type, sK479: term > $o).
% 28.46/5.33 thf(func_def_622, type, sK480: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_623, type, sK481: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_624, type, sK482: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_625, type, sK483: subst > term > term).
% 28.46/5.33 thf(func_def_626, type, sK484: term).
% 28.46/5.33 thf(func_def_627, type, sK485: term).
% 28.46/5.33 thf(func_def_628, type, sK486: term).
% 28.46/5.33 thf(func_def_629, type, sK487: term).
% 28.46/5.33 thf(func_def_630, type, sK488: term).
% 28.46/5.33 thf(func_def_631, type, sK489: term).
% 28.46/5.33 thf(func_def_632, type, sK490: term).
% 28.46/5.33 thf(func_def_633, type, sK491: term).
% 28.46/5.33 thf(func_def_634, type, sK492: term).
% 28.46/5.33 thf(func_def_635, type, sK493: term).
% 28.46/5.33 thf(func_def_636, type, sK494: term).
% 28.46/5.33 thf(func_def_637, type, sK495: term).
% 28.46/5.33 thf(func_def_638, type, sK496: term > subst > term > term).
% 28.46/5.33 thf(func_def_639, type, sK497: term).
% 28.46/5.33 thf(func_def_640, type, sK498: term > subst > term > term).
% 28.46/5.33 thf(func_def_641, type, sK499: term).
% 28.46/5.33 thf(func_def_642, type, sK500: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_643, type, sK501: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_644, type, sK502: subst > (term > $o) > (term > $o) > term > term).
% 28.46/5.33 thf(func_def_645, type, sK503: term).
% 28.46/5.33 thf(func_def_646, type, sK504: subst).
% 28.46/5.33 thf(func_def_647, type, sK505: term).
% 28.46/5.33 thf(func_def_648, type, sK506: term > $o).
% 28.46/5.33 thf(func_def_649, type, sK507: term > $o).
% 28.46/5.33 thf(func_def_650, type, sK508: subst).
% 28.46/5.33 thf(func_def_651, type, sK509: (subst > term > subst > $o) > term > $o).
% 28.46/5.33 thf(func_def_652, type, sK510: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_653, type, sK511: (term > $o) > term).
% 28.46/5.33 thf(func_def_654, type, sK512: term).
% 28.46/5.33 thf(func_def_655, type, sK513: term).
% 28.46/5.33 thf(func_def_656, type, sK514: term).
% 28.46/5.33 thf(func_def_657, type, sK515: term).
% 28.46/5.33 thf(func_def_658, type, sK516: term > $o).
% 28.46/5.33 thf(func_def_659, type, sK517: subst).
% 28.46/5.33 thf(func_def_660, type, sK518: term).
% 28.46/5.33 thf(func_def_661, type, sK519: (term > $o) > term).
% 28.46/5.33 thf(func_def_662, type, sK520: term > subst > (term > $o) > term > $o).
% 28.46/5.33 thf(func_def_663, type, sK521: subst).
% 28.46/5.33 thf(func_def_664, type, sK522: subst).
% 28.46/5.33 thf(func_def_665, type, sK523: subst).
% 28.46/5.33 thf(func_def_666, type, sK524: subst).
% 28.46/5.33 thf(func_def_667, type, sK525: subst).
% 28.46/5.33 thf(func_def_668, type, sK526: term > (term > $o) > subst > (term > $o) > term).
% 28.46/5.33 thf(func_def_669, type, sK527: term > $o).
% 28.46/5.33 thf(func_def_670, type, sK528: subst).
% 28.46/5.33 thf(func_def_671, type, sK529: term > $o).
% 28.46/5.33 thf(func_def_672, type, sK530: term).
% 28.46/5.33 thf(func_def_673, type, sK531: term).
% 28.46/5.33 thf(func_def_674, type, sK532: term).
% 28.46/5.33 thf(func_def_675, type, sK533: term).
% 28.46/5.33 thf(func_def_676, type, sK534: term).
% 28.46/5.33 thf(func_def_677, type, sK535: term).
% 28.46/5.33 thf(func_def_678, type, sK536: term > subst > term > term).
% 28.46/5.33 thf(func_def_679, type, sK537: term).
% 28.46/5.33 thf(func_def_680, type, sK538: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_681, type, sK539: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_682, type, sK540: term > subst > term > term).
% 28.46/5.33 thf(func_def_683, type, sK541: subst).
% 28.46/5.33 thf(func_def_684, type, sK542: term).
% 28.46/5.33 thf(func_def_685, type, sK543: term).
% 28.46/5.33 thf(func_def_686, type, sK544: term).
% 28.46/5.33 thf(func_def_687, type, sK545: term).
% 28.46/5.33 thf(func_def_688, type, sK546: term).
% 28.46/5.33 thf(func_def_689, type, sK547: term).
% 28.46/5.33 thf(func_def_690, type, sK548: term).
% 28.46/5.33 thf(func_def_691, type, sK549: term).
% 28.46/5.33 thf(func_def_692, type, sK550: term).
% 28.46/5.33 thf(func_def_693, type, sK551: term).
% 28.46/5.33 thf(func_def_694, type, sK552: subst).
% 28.46/5.33 thf(func_def_695, type, sK553: term).
% 28.46/5.33 thf(func_def_696, type, sK554: term > $o).
% 28.46/5.33 thf(func_def_697, type, sK555: (term > $o) > term).
% 28.46/5.33 thf(func_def_698, type, sK556: (term > $o) > term > subst > term > $o).
% 28.46/5.33 thf(func_def_699, type, sK557: term).
% 28.46/5.33 thf(func_def_700, type, sK558: term).
% 28.46/5.33 thf(func_def_701, type, sK559: term).
% 28.46/5.33 thf(func_def_702, type, sK560: term).
% 28.46/5.33 thf(func_def_703, type, sK561: term).
% 28.46/5.33 thf(func_def_704, type, sK562: term).
% 28.46/5.33 thf(func_def_705, type, sK563: (subst > term > subst > $o) > term > $o).
% 28.46/5.33 thf(func_def_706, type, sK564: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_707, type, sK565: (term > $o) > term).
% 28.46/5.33 thf(func_def_708, type, sK566: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_709, type, sK567: term).
% 28.46/5.33 thf(func_def_710, type, sK568: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_711, type, sK569: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_712, type, sK570: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_713, type, sK571: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_714, type, sK572: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_715, type, sK573: subst).
% 28.46/5.33 thf(func_def_716, type, sK574: subst > d_subst).
% 28.46/5.33 thf(func_def_717, type, sK575: term).
% 28.46/5.33 thf(func_def_718, type, sK576: (term > $o) > term).
% 28.46/5.33 thf(func_def_719, type, sK577: (term > $o) > term).
% 28.46/5.33 thf(func_def_720, type, sK578: term).
% 28.46/5.33 thf(func_def_721, type, sK579: term > $o).
% 28.46/5.33 thf(func_def_722, type, sK580: term > d_term).
% 28.46/5.33 thf(func_def_723, type, sK581: subst).
% 28.46/5.33 thf(func_def_724, type, sK582: term).
% 28.46/5.33 thf(func_def_725, type, sK583: subst > term > term).
% 28.46/5.33 thf(func_def_726, type, sK584: subst > term > term).
% 28.46/5.33 thf(func_def_727, type, sK585: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_728, type, sK586: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_729, type, sK587: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_730, type, sK588: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_731, type, sK589: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_732, type, sK590: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_734, type, sK592: subst > term > subst > $o).
% 28.46/5.33 thf(func_def_735, type, sK593: term > $o).
% 28.46/5.33 thf(func_def_736, type, sK594: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_737, type, sK595: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_738, type, sK596: (subst > term > term) > term).
% 28.46/5.33 thf(func_def_739, type, sK597: (subst > term > term) > subst).
% 28.46/5.33 thf(func_def_740, type, sK598: term).
% 28.46/5.33 thf(func_def_741, type, sK599: (subst > term > subst > $o) > subst > term > term).
% 28.46/5.33 thf(func_def_742, type, sK600: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_743, type, sK601: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_744, type, sK602: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_745, type, sK603: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_746, type, sK604: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_747, type, sK605: (subst > term > subst > $o) > (term > $o) > term).
% 28.46/5.33 thf(func_def_748, type, sK606: term > (term > $o) > term).
% 28.46/5.33 thf(func_def_750, type, ph607: !>[X0: $tType]:(X0)).
% 28.46/5.33 thf(f6955,plain,(
% 28.46/5.33 $false),
% 28.46/5.33 inference(avatar_sat_refutation,[status(thm)],[f2084,f2438,f2549,f3134,f3781,f3809,f3991,f4282,f4291,f4331,f4348,f4364,f4464,f4579,f5462,f6673,f6744,f6750,f6780,f6792,f6951])).
% 28.46/5.33 thf(f6951,plain,(
% 28.46/5.33 ~spl591_290 | ~spl591_512 | ~spl591_514 | ~spl591_536),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f6950])).
% 28.46/5.33 thf(f6950,plain,(
% 28.46/5.33 $false | (~spl591_290 | ~spl591_512 | ~spl591_514 | ~spl591_536)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6949])).
% 28.46/5.33 thf(f6949,plain,(
% 28.46/5.33 ($false = $true) | (~spl591_290 | ~spl591_512 | ~spl591_514 | ~spl591_536)),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f6948,f6888])).
% 28.46/5.33 thf(f6888,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o,X4 : term] : (($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)))) ) | (~spl591_512 | ~spl591_514)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6842])).
% 28.46/5.33 thf(f6842,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o,X4 : term] : (($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ($false = $true)) ) | (~spl591_512 | ~spl591_514)),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f4290,f4267])).
% 28.46/5.33 thf(f4267,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o] : (($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) ) | ~spl591_512),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4266])).
% 28.46/5.33 thf(f4266,definition,(
% 28.46/5.33 spl591_512 <=> ! [X1 : subst > term > subst > $o] : ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_512])],[avatar_definition])).
% 28.46/5.33 thf(f4290,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o,X4 : term] : (((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)))) ) | ~spl591_514),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4289])).
% 28.46/5.33 thf(f4289,definition,(
% 28.46/5.33 spl591_514 <=> ! [X4 : term,X1 : subst > term > subst > $o] : (($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_514])],[avatar_definition])).
% 28.46/5.33 thf(f6948,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true)) ) | (~spl591_290 | ~spl591_512 | ~spl591_514 | ~spl591_536)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6947])).
% 28.46/5.33 thf(f6947,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (($false = $true) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true)) ) | (~spl591_290 | ~spl591_512 | ~spl591_514 | ~spl591_536)),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f6946,f6888])).
% 28.46/5.33 thf(f6946,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true)) ) | (~spl591_290 | ~spl591_536)),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f3133,f4463])).
% 28.46/5.33 thf(f4463,plain,(
% 28.46/5.33 ( ! [X218 : term,X219 : term] : ((X218 = X219)) ) | ~spl591_536),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4462])).
% 28.46/5.33 thf(f4462,definition,(
% 28.46/5.33 spl591_536 <=> ! [X219 : term,X218 : term] : (X218 = X219)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_536])],[avatar_definition])).
% 28.46/5.33 thf(f3133,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true)) ) | ~spl591_290),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f3132])).
% 28.46/5.33 thf(f3132,definition,(
% 28.46/5.33 spl591_290 <=> ! [X4 : subst > term > term] : (((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_290])],[avatar_definition])).
% 28.46/5.33 thf(f6792,plain,(
% 28.46/5.33 ~spl591_519 | ~spl591_521 | ~spl591_523),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f6791])).
% 28.46/5.33 thf(f6791,plain,(
% 28.46/5.33 $false | (~spl591_519 | ~spl591_521 | ~spl591_523)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6788])).
% 28.46/5.33 thf(f6788,plain,(
% 28.46/5.33 ($false = $true) | (~spl591_519 | ~spl591_521 | ~spl591_523)),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f4359,f6783])).
% 28.46/5.33 thf(f6783,plain,(
% 28.46/5.33 ( ! [X1 : term] : (($false = (sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)))) ) | (~spl591_519 | ~spl591_521)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6781])).
% 28.46/5.33 thf(f6781,plain,(
% 28.46/5.33 ( ! [X1 : term] : (($false = $true) | ($false = (sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)))) ) | (~spl591_519 | ~spl591_521)),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f4347,f4339])).
% 28.46/5.33 thf(f4339,plain,(
% 28.46/5.33 ( ! [X1 : term] : (($false = (sK593 @ X1))) ) | ~spl591_519),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4338])).
% 28.46/5.33 thf(f4338,definition,(
% 28.46/5.33 spl591_519 <=> ! [X1 : term] : ($false = (sK593 @ X1))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_519])],[avatar_definition])).
% 28.46/5.33 thf(f4347,plain,(
% 28.46/5.33 ( ! [X1 : term] : (($false = (sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | ($true = (sK593 @ X1))) ) | ~spl591_521),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4346])).
% 28.46/5.33 thf(f4346,definition,(
% 28.46/5.33 spl591_521 <=> ! [X1 : term] : (($true = (sK593 @ X1)) | ($false = (sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_521])],[avatar_definition])).
% 28.46/5.33 thf(f4359,plain,(
% 28.46/5.33 ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ~spl591_523),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4357])).
% 28.46/5.33 thf(f4357,definition,(
% 28.46/5.33 spl591_523 <=> ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_523])],[avatar_definition])).
% 28.46/5.33 thf(f6780,plain,(
% 28.46/5.33 spl591_519 | ~spl591_517 | ~spl591_536),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f6777,f4462,f4328,f4338])).
% 28.46/5.33 thf(f4328,definition,(
% 28.46/5.33 spl591_517 <=> ($false = (sK593 @ (lam @ sK598)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_517])],[avatar_definition])).
% 28.46/5.33 thf(f6777,plain,(
% 28.46/5.33 ( ! [X0 : term] : (($false = (sK593 @ X0))) ) | (~spl591_517 | ~spl591_536)),
% 28.46/5.33 inference(superposition,[status(thm)],[f4330,f4463])).
% 28.46/5.33 thf(f4330,plain,(
% 28.46/5.33 ($false = (sK593 @ (lam @ sK598))) | ~spl591_517),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4328])).
% 28.46/5.33 thf(f6750,plain,(
% 28.46/5.33 ~spl591_125 | ~spl591_516),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f6749])).
% 28.46/5.33 thf(f6749,plain,(
% 28.46/5.33 $false | (~spl591_125 | ~spl591_516)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6748])).
% 28.46/5.33 thf(f6748,plain,(
% 28.46/5.33 ($false = $true) | (~spl591_125 | ~spl591_516)),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f2437,f4326])).
% 28.46/5.33 thf(f4326,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | ~spl591_516),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4324])).
% 28.46/5.33 thf(f4324,definition,(
% 28.46/5.33 spl591_516 <=> (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_516])],[avatar_definition])).
% 28.46/5.33 thf(f2437,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $true) | ~spl591_125),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f2435])).
% 28.46/5.33 thf(f2435,definition,(
% 28.46/5.33 spl591_125 <=> (hoasinduction_lem3v2a = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_125])],[avatar_definition])).
% 28.46/5.33 thf(f6744,plain,(
% 28.46/5.33 ~spl591_290 | spl591_438 | ~spl591_444 | ~spl591_509 | ~spl591_536),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f6743])).
% 28.46/5.33 thf(f6743,plain,(
% 28.46/5.33 $false | (~spl591_290 | spl591_438 | ~spl591_444 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6742])).
% 28.46/5.33 thf(f6742,plain,(
% 28.46/5.33 ($false = $true) | (~spl591_290 | spl591_438 | ~spl591_444 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f5350,f6741])).
% 28.46/5.33 thf(f6741,plain,(
% 28.46/5.33 ( ! [X3 : term] : (($false = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id)))) ) | (spl591_438 | ~spl591_444 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6739])).
% 28.46/5.33 thf(f6739,plain,(
% 28.46/5.33 ( ! [X3 : term] : (($false = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id))) | ($false = $true)) ) | (spl591_438 | ~spl591_444 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f3808,f6731])).
% 28.46/5.33 thf(f6731,plain,(
% 28.46/5.33 ( ! [X0 : term] : (((sK429 @ X0) = $false)) ) | (spl591_438 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(superposition,[status(thm)],[f6123,f4463])).
% 28.46/5.33 thf(f6123,plain,(
% 28.46/5.33 ($false = (sK429 @ (d2term @ d_one))) | (spl591_438 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(trivial_inequality_removal,[status(thm)],[f6120])).
% 28.46/5.33 thf(f6120,plain,(
% 28.46/5.33 ($true != $true) | ($false = (sK429 @ (d2term @ d_one))) | (spl591_438 | ~spl591_509 | ~spl591_536)),
% 28.46/5.33 inference(superposition,[status(thm)],[f6103,f4252])).
% 28.46/5.33 thf(f4252,plain,(
% 28.46/5.33 ( ! [X2 : term > $o] : (($true = (X2 @ (d2term @ d_one))) | ($false = (X2 @ (d2term @ d_one)))) ) | ~spl591_509),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f4251])).
% 28.46/5.33 thf(f4251,definition,(
% 28.46/5.33 spl591_509 <=> ! [X2 : term > $o] : (($false = (X2 @ (d2term @ d_one))) | ($true = (X2 @ (d2term @ d_one))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_509])],[avatar_definition])).
% 28.46/5.33 thf(f6103,plain,(
% 28.46/5.33 ( ! [X0 : term] : (((sK429 @ X0) != $true)) ) | (spl591_438 | ~spl591_536)),
% 28.46/5.33 inference(superposition,[status(thm)],[f3780,f4463])).
% 28.46/5.33 thf(f3780,plain,(
% 28.46/5.33 ((sK429 @ (lam @ sK430)) != $true) | spl591_438),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f3778])).
% 28.46/5.33 thf(f3778,definition,(
% 28.46/5.33 spl591_438 <=> ((sK429 @ (lam @ sK430)) = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_438])],[avatar_definition])).
% 28.46/5.33 thf(f3808,plain,(
% 28.46/5.33 ( ! [X3 : term] : (((sK429 @ X3) = $true) | ($false = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id)))) ) | ~spl591_444),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f3807])).
% 28.46/5.33 thf(f3807,definition,(
% 28.46/5.33 spl591_444 <=> ! [X3 : term] : (((sK429 @ X3) = $true) | ($false = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_444])],[avatar_definition])).
% 28.46/5.33 thf(f5350,plain,(
% 28.46/5.33 ((sK428 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ~spl591_290),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f5349,f4219])).
% 28.46/5.33 thf(f4219,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4138,f4191])).
% 28.46/5.33 thf(f4191,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP11 @ X0) != $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4190,f4091])).
% 28.46/5.33 thf(f4091,plain,(
% 28.46/5.33 ( ! [X258 : term] : (((d2term @ d_one) = X258)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f1057,f1159])).
% 28.46/5.33 thf(f1159,plain,(
% 28.46/5.33 ( ! [X119 : d_term] : ((d_one = X119)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f545,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP58 != $true)) & ((hoasapinj2 = $true) | ((sK457 != sK456) & ((ap @ (sub @ sK454 @ id) @ sK457) = (ap @ (sub @ sK455 @ id) @ sK456)))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X6 = X7) | ((ap @ (sub @ X4 @ id) @ X7) != (ap @ (sub @ X5 @ id) @ X6))) | (hoasapinj2 != $true)) & ((axscons = $true) | (sK458 != (push @ (sub @ one @ sK458) @ (comp @ sh @ sK458)))) & (! [X9 : subst] : ((push @ (sub @ one @ X9) @ (comp @ sh @ X9)) = X9) | (axscons != $true)) & (! [X10 : term,X11 : term] : ((X10 = X11) | ((lam @ X10) != (lam @ X11))) | (laminj != $true)) & ((laminj = $true) | ((sK459 != sK460) & ((lam @ sK460) = (lam @ sK459)))) & ((d2subst @ d_id) = sh) & (! [X14 : term] : ((sub @ X14 @ id) = X14) | (axvarid != $true)) & ((axvarid = $true) | (sK461 != (sub @ sK461 @ id))) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) | (sK462 != (comp @ sh @ (push @ sK463 @ sK462)))) & (! [X18 : subst,X19 : term] : ((comp @ sh @ (push @ X19 @ X18)) = X18) | (axshiftcons != $true)) & ! [X20 : d_subst] : (d_id = X20) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1 = $true) | (((sK465 @ (sub @ sK468 @ (push @ sK464 @ sK466))) != $true) & ((sK467 @ sK468) = $true))) & (! [X26 : term,X27 : term > $o,X28 : subst,X29 : term > $o,X30 : term] : (((X27 @ (sub @ X30 @ (push @ X26 @ X28))) = $true) | ((X29 @ X30) != $true)) | (pushprop_lem1 != $true)) & ((substmonoid = $true) | ((comp @ id @ sK469) != sK469) | ((comp @ sK470 @ id) != sK470)) & ((! [X33 : subst] : ((comp @ id @ X33) = X33) & ! [X34 : subst] : ((comp @ X34 @ id) = X34)) | (substmonoid != $true)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (hoasinduction_lem2_lthm = $true) & ((sK472 != (comp @ sh @ (push @ sK471 @ sK472))) | ((sub @ one @ (push @ sK473 @ sK474)) != sK473) | ! [X39 : term,X40 : subst,X41 : term,X42 : term > $o,X43 : term > $o] : (((X43 @ (sub @ X41 @ (push @ X39 @ X40))) = $true) | ((X42 @ X41) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X44 : term,X45 : subst] : ((comp @ sh @ (push @ X44 @ X45)) = X45) & ! [X46 : term,X47 : subst] : ((sub @ one @ (push @ X46 @ X47)) = X46) & (((sK479 @ (sub @ sK477 @ (push @ sK475 @ sK476))) != $true) & ((sK478 @ sK477) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X53 : subst > term > term,X54 : term,X55 : term] : (((X53 @ (comp @ (sK481 @ X53) @ (sK482 @ X53)) @ (sub @ (sK480 @ X53) @ (sK482 @ X53))) != (sub @ (X53 @ (sK481 @ X53) @ (sK480 @ X53)) @ (sK482 @ X53))) | ((lam @ (X53 @ sh @ one)) != (ap @ (sub @ X54 @ id) @ X55))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X62 : term,X63 : subst,X64 : subst] : ((sK483 @ (comp @ X63 @ X64) @ (sub @ X62 @ X64)) = (sub @ (sK483 @ X63 @ X62) @ X64)) & ((ap @ (sub @ sK484 @ id) @ sK485) = (lam @ (sK483 @ sh @ one))))) & (lamnotvar = $true) & (ulamvarind = $true) & ((hoasinduction_lem3aaa = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2_lthm = $true) & ((sP52 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP52 != $true)) & (hoasinduction_gthm = $true) & ! [X65 : d_subst,X66 : d_subst] : (((d2subst @ X66) != (d2subst @ X65)) | (X65 = X66)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & ((induction2lem_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar = $true) & (((sK486 != sK487) & ((ap @ sK488 @ sK487) = (ap @ sK489 @ sK486))) | ! [X71 : term,X72 : term,X73 : term,X74 : term] : ((X71 = X73) | ((ap @ (sub @ X72 @ id) @ X71) != (ap @ (sub @ X74 @ id) @ X73))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X75 : term,X76 : term,X77 : term,X78 : term] : ((X75 = X76) | ((ap @ X77 @ X76) != (ap @ X78 @ X75))) & ((sK490 != sK492) & ((ap @ (sub @ sK493 @ id) @ sK492) = (ap @ (sub @ sK491 @ id) @ sK490))))) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset_lthm = $true) | (! [X83 : term] : ((sub @ X83 @ id) = X83) & (sK494 != (sub @ sK494 @ id)))) & ((sK495 != (sub @ sK495 @ id)) | ! [X86 : term] : ((sub @ X86 @ id) = X86) | (termmset_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (! [X87 : term] : ((sub @ X87 @ (push @ one @ sh)) = (sK496 @ X87 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X90 : subst > term > term] : ((sub @ sK497 @ (push @ one @ sh)) != (X90 @ sh @ one))) & ((induction2lem = $true) | (sP45 != $true)) & ((sP45 = $true) | (induction2lem != $true)) & (! [X91 : term] : ! [X93 : term,X94 : subst] : ((sK498 @ X91 @ X94 @ X93) = (sub @ X91 @ (push @ X93 @ X94))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X96 : subst > term > term] : ((X96 @ (sK501 @ X96) @ (sK500 @ X96)) != (sub @ sK499 @ (push @ (sK500 @ X96) @ (sK501 @ X96))))) & (hoasinduction_lem3v2_gthm = $true) & (! [X99 : term,X100 : term > $o,X101 : term > $o,X102 : subst] : (((X101 @ one) = $true) | ((X101 @ (sK502 @ X102 @ X101 @ X100 @ X99)) != (X100 @ (sub @ (sK502 @ X102 @ X101 @ X100 @ X99) @ (push @ X99 @ X102)))) | ((X100 @ X99) != $true)) | ((sub @ one @ (push @ sK503 @ sK504)) != sK503) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((($true != (sK507 @ one)) & ! [X110 : term] : ((sK507 @ X110) = (sK506 @ (sub @ X110 @ (push @ sK505 @ sK508)))) & ((sK506 @ sK505) = $true)) & ! [X111 : term,X112 : subst] : ((sub @ one @ (push @ X111 @ X112)) = X111))) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & (! [X113 : subst > term > subst > $o] : ! [X115 : term] : ((sK509 @ X113 @ X115) = (X113 @ id @ X115 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X117 : term > $o] : ((X117 @ (sK511 @ X117)) != (sK510 @ id @ (sK511 @ X117) @ id))) & ((sP43 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP43 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP35 != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X119 : d_term] : (d_one = X119) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X120 : term,X121 : term,X122 : term,X123 : term] : ((X120 = X122) | ((ap @ X120 @ X121) != (ap @ X122 @ X123))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK512 != sK514) & ((ap @ sK512 @ sK513) = (ap @ sK514 @ sK515)))) & ((pushprop_lem0 = $true) | ! [X131 : term > $o] : ((sK516 @ (sub @ (sK519 @ X131) @ (push @ sK518 @ sK517))) != (X131 @ (sK519 @ X131)))) & (! [X133 : term > $o,X134 : subst,X135 : term] : ! [X137 : term] : ((sK520 @ X135 @ X134 @ X133 @ X137) = (X133 @ (sub @ X137 @ (push @ X135 @ X134)))) | (pushprop_lem0 != $true)) & ((axidl = $true) | ((comp @ id @ sK521) != sK521)) & (! [X139 : subst] : ((comp @ id @ X139) = X139) | (axidl != $true)) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((comp @ id @ sK522) != sK522) | ((comp @ sK523 @ id) != sK523) | (! [X142 : subst] : ((comp @ X142 @ id) = X142) & ! [X143 : subst] : ((comp @ id @ X143) = X143)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X144 : subst] : ((comp @ id @ X144) = X144) & ! [X145 : subst] : ((comp @ X145 @ id) = X145) & ((sK524 != (comp @ sK524 @ id)) | (sK525 != (comp @ id @ sK525))))) & (! [X148 : term > $o,X149 : subst,X150 : term > $o,X151 : term] : (((X150 @ one) = $true) | ((X148 @ X151) != $true) | ((X148 @ (sub @ (sK526 @ X151 @ X150 @ X149 @ X148) @ (push @ X151 @ X149))) != (X150 @ (sK526 @ X151 @ X150 @ X149 @ X148)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true != (sK529 @ one)) & ((sK527 @ sK530) = $true) & ! [X157 : term] : ((sK529 @ X157) = (sK527 @ (sub @ X157 @ (push @ sK530 @ sK528)))))) & (axapp = $true) & (! [X158 : term,X159 : term,X160 : term,X161 : term] : (((ap @ (sub @ X158 @ id) @ X160) != (ap @ (sub @ X161 @ id) @ X159)) | (X158 = X161)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | (((ap @ (sub @ sK534 @ id) @ sK532) = (ap @ (sub @ sK531 @ id) @ sK533)) & (sK531 != sK534))) & ((hoasinduction_lem3b = $true) | ! [X167 : subst > term > term] : ((X167 @ sh @ one) != (sub @ sK535 @ (push @ one @ sh)))) & (! [X168 : term] : ((sub @ X168 @ (push @ one @ sh)) = (sK536 @ X168 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (axabs = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X171 : subst > term > term] : ((sub @ sK537 @ (push @ (sK538 @ X171) @ (sK539 @ X171))) != (X171 @ (sK539 @ X171) @ (sK538 @ X171)))) & (! [X174 : term] : ! [X176 : term,X177 : subst] : ((sK540 @ X174 @ X177 @ X176) = (sub @ X174 @ (push @ X176 @ X177))) | (hoasinduction_lem3v2_f != $true)) & ((induction2_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2_lthm != $true)) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & ((axvarcons = $true) | ((sub @ one @ (push @ sK542 @ sK541)) != sK542)) & (! [X180 : subst,X181 : term] : ((sub @ one @ (push @ X181 @ X180)) = X181) | (axvarcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) | (((sK545 != sK544) & ((ap @ (sub @ sK545 @ id) @ sK546) = (ap @ (sub @ sK544 @ id) @ sK543))) & ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X187 = X189) | ((ap @ X189 @ X186) != (ap @ X187 @ X188))) & ! [X190 : term] : ((sub @ X190 @ id) = X190))) & (! [X191 : term,X192 : term,X193 : term,X194 : term] : ((X192 = X193) | ((ap @ (sub @ X193 @ id) @ X194) != (ap @ (sub @ X192 @ id) @ X191))) | ((sK550 != sK548) & ((ap @ sK548 @ sK549) = (ap @ sK550 @ sK547))) | ((sub @ sK551 @ id) != sK551) | (hoasapinj1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X203 : term > $o] : ((X203 @ (sK555 @ X203)) != (sK554 @ (sub @ (sK555 @ X203) @ (push @ sK553 @ sK552))))) & (! [X205 : subst,X206 : term,X207 : term > $o] : ! [X209 : term] : ((sK556 @ X207 @ X206 @ X205 @ X209) = (X207 @ (sub @ X209 @ (push @ X206 @ X205)))) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & ((sP28 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP28 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & ((sP27 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP27 != $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X210 : term,X211 : term,X212 : term,X213 : term] : ((X210 = X211) | ((ap @ X213 @ X210) != (ap @ X212 @ X211))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK557 != sK558) & ((ap @ sK560 @ sK557) = (ap @ sK559 @ sK558)))) & (hoasinduction_lem3_gthm = $true) & (! [X218 : term,X219 : term] : ((X218 = X219) | ((sub @ X219 @ sh) != (sub @ X218 @ sh))) | (shinj != $true)) & ((shinj = $true) | ((sK561 != sK562) & ((sub @ sK561 @ sh) = (sub @ sK562 @ sh)))) & ((hoasinduction_lem2v2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2v2 != $true)) & (! [X222 : subst > term > subst > $o] : ! [X224 : term] : ((X222 @ id @ X224 @ id) = (sK563 @ X222 @ X224)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X226 : term > $o] : ((sK564 @ id @ (sK565 @ X226) @ id) != (X226 @ (sK565 @ X226)))) & (hoaslamnotvar_gthm = $true) & (! [X228 : term,X229 : subst > term > subst > $o] : ((! [X231 : term,X232 : subst,X233 : subst] : ((sK566 @ X229 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)) = (sub @ (sK566 @ X229 @ X233 @ X231) @ X232)) & ! [X234 : term] : (($true = (X229 @ id @ (sK566 @ X229 @ id @ X234) @ id)) | ((X229 @ id @ X234 @ id) != $true)) & ($true != (X229 @ id @ (lam @ (sK566 @ X229 @ sh @ one)) @ id))) | ((X229 @ id @ X228 @ id) = $true) | ($true = (sP20 @ X229))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X237 : subst > term > term] : (((sub @ (X237 @ (sK571 @ X237) @ (sK569 @ X237)) @ (sK570 @ X237)) != (X237 @ (comp @ (sK571 @ X237) @ (sK570 @ X237)) @ (sub @ (sK569 @ X237) @ (sK570 @ X237)))) | (((sK568 @ id @ (X237 @ id @ (sK572 @ X237)) @ id) != $true) & ((sK568 @ id @ (sK572 @ X237) @ id) = $true)) | ($true = (sK568 @ id @ (lam @ (X237 @ sh @ one)) @ id))) & ((sK568 @ id @ sK567 @ id) != $true) & ((sP20 @ sK568) != $true))) & (! [X242 : subst] : ((comp @ X242 @ id) = X242) | (axidr != $true)) & ((axidr = $true) | (sK573 != (comp @ sK573 @ id))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X244 : subst] : ((d2subst @ (sK574 @ X244)) = X244) & (induction2_gthm = $true) & (! [X246 : term] : ((sub @ X246 @ id) = X246) | (termmset != $true)) & ((termmset = $true) | ((sub @ sK575 @ id) != sK575)) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X248 : term,X249 : term > $o] : ((($true != (X249 @ (lam @ (sK576 @ X249)))) & ((X249 @ (sK576 @ X249)) = $true)) | ((X249 @ X248) = $true) | ((sP10 @ X249) = $true) | (((X249 @ (sK577 @ X249)) != $true) & ($true = (var @ (sK577 @ X249))))) | (induction != $true)) & ((induction = $true) | (! [X254 : term] : (((sK579 @ (lam @ X254)) = $true) | ((sK579 @ X254) != $true)) & ($true != (sK579 @ sK578)) & ($true != (sP10 @ sK579)) & ! [X255 : term] : (((sK579 @ X255) = $true) | ((var @ X255) != $true)))) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & (lamnotap != $true) & (termmset_gthm = $true) & ((sP9 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP9 != $true)) & ! [X258 : term] : ((d2term @ (sK580 @ X258)) = X258) & ((hoaslaminj = $true) | (((sK584 @ sK581 @ sK582) != (sK583 @ sK581 @ sK582)) & ((lam @ (sK583 @ sh @ one)) = (lam @ (sK584 @ sh @ one))) & ! [X264 : term,X265 : subst,X266 : subst] : ((sub @ (sK584 @ X265 @ X264) @ X266) = (sK584 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266))) & ! [X267 : subst,X268 : term,X269 : subst] : ((sub @ (sK583 @ X269 @ X268) @ X267) = (sK583 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))))) & (! [X270 : subst,X271 : term,X272 : subst > term > term,X273 : subst > term > term] : (((X273 @ X270 @ X271) = (X272 @ X270 @ X271)) | ((lam @ (X272 @ sh @ one)) != (lam @ (X273 @ sh @ one))) | ((X273 @ (comp @ (sK586 @ X273) @ (sK587 @ X273)) @ (sub @ (sK585 @ X273) @ (sK587 @ X273))) != (sub @ (X273 @ (sK586 @ X273) @ (sK585 @ X273)) @ (sK587 @ X273))) | ((sub @ (X272 @ (sK590 @ X272) @ (sK589 @ X272)) @ (sK588 @ X272)) != (X272 @ (comp @ (sK590 @ X272) @ (sK588 @ X272)) @ (sub @ (sK589 @ X272) @ (sK588 @ X272))))) | (hoaslaminj != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((sP6 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP6 != $true)) & (pushprop_lthm = $true) & (pushprop = $true) & ((hoasinduction = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true))),
% 28.46/5.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474])).
% 28.46/5.33 thf(f474,plain,(
% 28.46/5.33 ? [X0 : term,X1 : term,X2 : term,X3 : term] : ((X2 != X3) & ((ap @ (sub @ X0 @ id) @ X3) = (ap @ (sub @ X1 @ id) @ X2))) => ((sK457 != sK456) & ((ap @ (sub @ sK454 @ id) @ sK457) = (ap @ (sub @ sK455 @ id) @ sK456)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f475,plain,(
% 28.46/5.33 ? [X8 : subst] : ((push @ (sub @ one @ X8) @ (comp @ sh @ X8)) != X8) => (sK458 != (push @ (sub @ one @ sK458) @ (comp @ sh @ sK458)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f476,plain,(
% 28.46/5.33 ? [X12 : term,X13 : term] : ((X12 != X13) & ((lam @ X13) = (lam @ X12))) => ((sK459 != sK460) & ((lam @ sK460) = (lam @ sK459)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f477,plain,(
% 28.46/5.33 ? [X15 : term] : ((sub @ X15 @ id) != X15) => (sK461 != (sub @ sK461 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f478,plain,(
% 28.46/5.33 ? [X16 : subst,X17 : term] : ((comp @ sh @ (push @ X17 @ X16)) != X16) => (sK462 != (comp @ sh @ (push @ sK463 @ sK462)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f479,plain,(
% 28.46/5.33 ? [X21 : term,X22 : term > $o,X23 : subst,X24 : term > $o,X25 : term] : (((X22 @ (sub @ X25 @ (push @ X21 @ X23))) != $true) & ((X24 @ X25) = $true)) => (((sK465 @ (sub @ sK468 @ (push @ sK464 @ sK466))) != $true) & ((sK467 @ sK468) = $true))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f480,plain,(
% 28.46/5.33 ? [X31 : subst] : ((comp @ id @ X31) != X31) => ((comp @ id @ sK469) != sK469)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f481,plain,(
% 28.46/5.33 ? [X32 : subst] : ((comp @ X32 @ id) != X32) => ((comp @ sK470 @ id) != sK470)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f482,plain,(
% 28.46/5.33 ? [X35 : term,X36 : subst] : ((comp @ sh @ (push @ X35 @ X36)) != X36) => (sK472 != (comp @ sh @ (push @ sK471 @ sK472)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f483,plain,(
% 28.46/5.33 ? [X37 : term,X38 : subst] : ((sub @ one @ (push @ X37 @ X38)) != X37) => ((sub @ one @ (push @ sK473 @ sK474)) != sK473)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f484,plain,(
% 28.46/5.33 ? [X48 : term,X49 : subst,X50 : term,X51 : term > $o,X52 : term > $o] : (((X52 @ (sub @ X50 @ (push @ X48 @ X49))) != $true) & ((X51 @ X50) = $true)) => (((sK479 @ (sub @ sK477 @ (push @ sK475 @ sK476))) != $true) & ((sK478 @ sK477) = $true))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f485,plain,(
% 28.46/5.33 ! [X53 : subst > term > term] : (? [X56 : term,X57 : subst,X58 : subst] : ((sub @ (X53 @ X57 @ X56) @ X58) != (X53 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58))) => ((X53 @ (comp @ (sK481 @ X53) @ (sK482 @ X53)) @ (sub @ (sK480 @ X53) @ (sK482 @ X53))) != (sub @ (X53 @ (sK481 @ X53) @ (sK480 @ X53)) @ (sK482 @ X53))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f486,plain,(
% 28.46/5.33 ? [X59 : subst > term > term,X60 : term,X61 : term] : (! [X62 : term,X63 : subst,X64 : subst] : ((sub @ (X59 @ X63 @ X62) @ X64) = (X59 @ (comp @ X63 @ X64) @ (sub @ X62 @ X64))) & ((lam @ (X59 @ sh @ one)) = (ap @ (sub @ X60 @ id) @ X61))) => (! [X64 : subst,X63 : subst,X62 : term] : ((sK483 @ (comp @ X63 @ X64) @ (sub @ X62 @ X64)) = (sub @ (sK483 @ X63 @ X62) @ X64)) & ((ap @ (sub @ sK484 @ id) @ sK485) = (lam @ (sK483 @ sh @ one))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f487,plain,(
% 28.46/5.33 ? [X67 : term,X68 : term,X69 : term,X70 : term] : ((X67 != X68) & ((ap @ X69 @ X68) = (ap @ X70 @ X67))) => ((sK486 != sK487) & ((ap @ sK488 @ sK487) = (ap @ sK489 @ sK486)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f488,plain,(
% 28.46/5.33 ? [X79 : term,X80 : term,X81 : term,X82 : term] : ((X79 != X81) & ((ap @ (sub @ X82 @ id) @ X81) = (ap @ (sub @ X80 @ id) @ X79))) => ((sK490 != sK492) & ((ap @ (sub @ sK493 @ id) @ sK492) = (ap @ (sub @ sK491 @ id) @ sK490)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f489,plain,(
% 28.46/5.33 ? [X84 : term] : ((sub @ X84 @ id) != X84) => (sK494 != (sub @ sK494 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f490,plain,(
% 28.46/5.33 ? [X85 : term] : ((sub @ X85 @ id) != X85) => (sK495 != (sub @ sK495 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f491,plain,(
% 28.46/5.33 ! [X87 : term] : (? [X88 : subst > term > term] : ((sub @ X87 @ (push @ one @ sh)) = (X88 @ sh @ one)) => ((sub @ X87 @ (push @ one @ sh)) = (sK496 @ X87 @ sh @ one)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f492,plain,(
% 28.46/5.33 ? [X89 : term] : ! [X90 : subst > term > term] : ((sub @ X89 @ (push @ one @ sh)) != (X90 @ sh @ one)) => ! [X90 : subst > term > term] : ((sub @ sK497 @ (push @ one @ sh)) != (X90 @ sh @ one))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f493,plain,(
% 28.46/5.33 ! [X91 : term] : (? [X92 : subst > term > term] : ! [X93 : term,X94 : subst] : ((X92 @ X94 @ X93) = (sub @ X91 @ (push @ X93 @ X94))) => ! [X94 : subst,X93 : term] : ((sK498 @ X91 @ X94 @ X93) = (sub @ X91 @ (push @ X93 @ X94))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f494,plain,(
% 28.46/5.33 ? [X95 : term] : ! [X96 : subst > term > term] : ? [X97 : term,X98 : subst] : ((sub @ X95 @ (push @ X97 @ X98)) != (X96 @ X98 @ X97)) => ! [X96 : subst > term > term] : ? [X98 : subst,X97 : term] : ((sub @ sK499 @ (push @ X97 @ X98)) != (X96 @ X98 @ X97))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f495,plain,(
% 28.46/5.33 ! [X96 : subst > term > term] : (? [X98 : subst,X97 : term] : ((sub @ sK499 @ (push @ X97 @ X98)) != (X96 @ X98 @ X97)) => ((X96 @ (sK501 @ X96) @ (sK500 @ X96)) != (sub @ sK499 @ (push @ (sK500 @ X96) @ (sK501 @ X96)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f496,plain,(
% 28.46/5.33 ! [X99 : term,X100 : term > $o,X101 : term > $o,X102 : subst] : (? [X103 : term] : ((X100 @ (sub @ X103 @ (push @ X99 @ X102))) != (X101 @ X103)) => ((X101 @ (sK502 @ X102 @ X101 @ X100 @ X99)) != (X100 @ (sub @ (sK502 @ X102 @ X101 @ X100 @ X99) @ (push @ X99 @ X102)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f497,plain,(
% 28.46/5.33 ? [X104 : term,X105 : subst] : ((sub @ one @ (push @ X104 @ X105)) != X104) => ((sub @ one @ (push @ sK503 @ sK504)) != sK503)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f498,plain,(
% 28.46/5.33 ? [X106 : term,X107 : term > $o,X108 : term > $o,X109 : subst] : (((X108 @ one) != $true) & ! [X110 : term] : ((X108 @ X110) = (X107 @ (sub @ X110 @ (push @ X106 @ X109)))) & ((X107 @ X106) = $true)) => (($true != (sK507 @ one)) & ! [X110 : term] : ((sK507 @ X110) = (sK506 @ (sub @ X110 @ (push @ sK505 @ sK508)))) & ((sK506 @ sK505) = $true))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f499,plain,(
% 28.46/5.33 ! [X113 : subst > term > subst > $o] : (? [X114 : term > $o] : ! [X115 : term] : ((X114 @ X115) = (X113 @ id @ X115 @ id)) => ! [X115 : term] : ((sK509 @ X113 @ X115) = (X113 @ id @ X115 @ id)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f500,plain,(
% 28.46/5.33 ? [X116 : subst > term > subst > $o] : ! [X117 : term > $o] : ? [X118 : term] : ((X117 @ X118) != (X116 @ id @ X118 @ id)) => ! [X117 : term > $o] : ? [X118 : term] : ((sK510 @ id @ X118 @ id) != (X117 @ X118))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f501,plain,(
% 28.46/5.33 ! [X117 : term > $o] : (? [X118 : term] : ((sK510 @ id @ X118 @ id) != (X117 @ X118)) => ((X117 @ (sK511 @ X117)) != (sK510 @ id @ (sK511 @ X117) @ id)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f502,plain,(
% 28.46/5.33 ? [X124 : term,X125 : term,X126 : term,X127 : term] : ((X124 != X126) & ((ap @ X126 @ X127) = (ap @ X124 @ X125))) => ((sK512 != sK514) & ((ap @ sK512 @ sK513) = (ap @ sK514 @ sK515)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f503,plain,(
% 28.46/5.33 ? [X128 : term > $o,X129 : subst,X130 : term] : ! [X131 : term > $o] : ? [X132 : term] : ((X131 @ X132) != (X128 @ (sub @ X132 @ (push @ X130 @ X129)))) => ! [X131 : term > $o] : ? [X132 : term] : ((X131 @ X132) != (sK516 @ (sub @ X132 @ (push @ sK518 @ sK517))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f504,plain,(
% 28.46/5.33 ! [X131 : term > $o] : (? [X132 : term] : ((X131 @ X132) != (sK516 @ (sub @ X132 @ (push @ sK518 @ sK517)))) => ((sK516 @ (sub @ (sK519 @ X131) @ (push @ sK518 @ sK517))) != (X131 @ (sK519 @ X131))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f505,plain,(
% 28.46/5.33 ! [X133 : term > $o,X134 : subst,X135 : term] : (? [X136 : term > $o] : ! [X137 : term] : ((X133 @ (sub @ X137 @ (push @ X135 @ X134))) = (X136 @ X137)) => ! [X137 : term] : ((sK520 @ X135 @ X134 @ X133 @ X137) = (X133 @ (sub @ X137 @ (push @ X135 @ X134)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f506,plain,(
% 28.46/5.33 ? [X138 : subst] : ((comp @ id @ X138) != X138) => ((comp @ id @ sK521) != sK521)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f507,plain,(
% 28.46/5.33 ? [X140 : subst] : ((comp @ id @ X140) != X140) => ((comp @ id @ sK522) != sK522)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f508,plain,(
% 28.46/5.33 ? [X141 : subst] : ((comp @ X141 @ id) != X141) => ((comp @ sK523 @ id) != sK523)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f509,plain,(
% 28.46/5.33 ? [X146 : subst] : ((comp @ X146 @ id) != X146) => (sK524 != (comp @ sK524 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f510,plain,(
% 28.46/5.33 ? [X147 : subst] : ((comp @ id @ X147) != X147) => (sK525 != (comp @ id @ sK525))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f511,plain,(
% 28.46/5.33 ! [X148 : term > $o,X149 : subst,X150 : term > $o,X151 : term] : (? [X152 : term] : ((X150 @ X152) != (X148 @ (sub @ X152 @ (push @ X151 @ X149)))) => ((X148 @ (sub @ (sK526 @ X151 @ X150 @ X149 @ X148) @ (push @ X151 @ X149))) != (X150 @ (sK526 @ X151 @ X150 @ X149 @ X148))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f512,plain,(
% 28.46/5.33 ? [X153 : term > $o,X154 : subst,X155 : term > $o,X156 : term] : (((X155 @ one) != $true) & ((X153 @ X156) = $true) & ! [X157 : term] : ((X153 @ (sub @ X157 @ (push @ X156 @ X154))) = (X155 @ X157))) => (($true != (sK529 @ one)) & ((sK527 @ sK530) = $true) & ! [X157 : term] : ((sK529 @ X157) = (sK527 @ (sub @ X157 @ (push @ sK530 @ sK528)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f513,plain,(
% 28.46/5.33 ? [X162 : term,X163 : term,X164 : term,X165 : term] : (((ap @ (sub @ X165 @ id) @ X163) = (ap @ (sub @ X162 @ id) @ X164)) & (X162 != X165)) => (((ap @ (sub @ sK534 @ id) @ sK532) = (ap @ (sub @ sK531 @ id) @ sK533)) & (sK531 != sK534))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f514,plain,(
% 28.46/5.33 ? [X166 : term] : ! [X167 : subst > term > term] : ((X167 @ sh @ one) != (sub @ X166 @ (push @ one @ sh))) => ! [X167 : subst > term > term] : ((X167 @ sh @ one) != (sub @ sK535 @ (push @ one @ sh)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f515,plain,(
% 28.46/5.33 ! [X168 : term] : (? [X169 : subst > term > term] : ((sub @ X168 @ (push @ one @ sh)) = (X169 @ sh @ one)) => ((sub @ X168 @ (push @ one @ sh)) = (sK536 @ X168 @ sh @ one)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f516,plain,(
% 28.46/5.33 ? [X170 : term] : ! [X171 : subst > term > term] : ? [X172 : term,X173 : subst] : ((X171 @ X173 @ X172) != (sub @ X170 @ (push @ X172 @ X173))) => ! [X171 : subst > term > term] : ? [X173 : subst,X172 : term] : ((X171 @ X173 @ X172) != (sub @ sK537 @ (push @ X172 @ X173)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f517,plain,(
% 28.46/5.33 ! [X171 : subst > term > term] : (? [X173 : subst,X172 : term] : ((X171 @ X173 @ X172) != (sub @ sK537 @ (push @ X172 @ X173))) => ((sub @ sK537 @ (push @ (sK538 @ X171) @ (sK539 @ X171))) != (X171 @ (sK539 @ X171) @ (sK538 @ X171))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f518,plain,(
% 28.46/5.33 ! [X174 : term] : (? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) => ! [X177 : subst,X176 : term] : ((sK540 @ X174 @ X177 @ X176) = (sub @ X174 @ (push @ X176 @ X177))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f519,plain,(
% 28.46/5.33 ? [X178 : subst,X179 : term] : ((sub @ one @ (push @ X179 @ X178)) != X179) => ((sub @ one @ (push @ sK542 @ sK541)) != sK542)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f520,plain,(
% 28.46/5.33 ? [X182 : term,X183 : term,X184 : term,X185 : term] : ((X183 != X184) & ((ap @ (sub @ X184 @ id) @ X185) = (ap @ (sub @ X183 @ id) @ X182))) => ((sK545 != sK544) & ((ap @ (sub @ sK545 @ id) @ sK546) = (ap @ (sub @ sK544 @ id) @ sK543)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f521,plain,(
% 28.46/5.33 ? [X195 : term,X196 : term,X197 : term,X198 : term] : ((X196 != X198) & ((ap @ X196 @ X197) = (ap @ X198 @ X195))) => ((sK550 != sK548) & ((ap @ sK548 @ sK549) = (ap @ sK550 @ sK547)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f522,plain,(
% 28.46/5.33 ? [X199 : term] : ((sub @ X199 @ id) != X199) => ((sub @ sK551 @ id) != sK551)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f523,plain,(
% 28.46/5.33 ? [X200 : subst,X201 : term,X202 : term > $o] : ! [X203 : term > $o] : ? [X204 : term] : ((X202 @ (sub @ X204 @ (push @ X201 @ X200))) != (X203 @ X204)) => ! [X203 : term > $o] : ? [X204 : term] : ((sK554 @ (sub @ X204 @ (push @ sK553 @ sK552))) != (X203 @ X204))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f524,plain,(
% 28.46/5.33 ! [X203 : term > $o] : (? [X204 : term] : ((sK554 @ (sub @ X204 @ (push @ sK553 @ sK552))) != (X203 @ X204)) => ((X203 @ (sK555 @ X203)) != (sK554 @ (sub @ (sK555 @ X203) @ (push @ sK553 @ sK552)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f525,plain,(
% 28.46/5.33 ! [X205 : subst,X206 : term,X207 : term > $o] : (? [X208 : term > $o] : ! [X209 : term] : ((X207 @ (sub @ X209 @ (push @ X206 @ X205))) = (X208 @ X209)) => ! [X209 : term] : ((sK556 @ X207 @ X206 @ X205 @ X209) = (X207 @ (sub @ X209 @ (push @ X206 @ X205)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f526,plain,(
% 28.46/5.33 ? [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 != X215) & ((ap @ X216 @ X215) = (ap @ X217 @ X214))) => ((sK557 != sK558) & ((ap @ sK560 @ sK557) = (ap @ sK559 @ sK558)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f527,plain,(
% 28.46/5.33 ? [X220 : term,X221 : term] : ((X220 != X221) & ((sub @ X221 @ sh) = (sub @ X220 @ sh))) => ((sK561 != sK562) & ((sub @ sK561 @ sh) = (sub @ sK562 @ sh)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f528,plain,(
% 28.46/5.33 ! [X222 : subst > term > subst > $o] : (? [X223 : term > $o] : ! [X224 : term] : ((X223 @ X224) = (X222 @ id @ X224 @ id)) => ! [X224 : term] : ((X222 @ id @ X224 @ id) = (sK563 @ X222 @ X224)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f529,plain,(
% 28.46/5.33 ? [X225 : subst > term > subst > $o] : ! [X226 : term > $o] : ? [X227 : term] : ((X226 @ X227) != (X225 @ id @ X227 @ id)) => ! [X226 : term > $o] : ? [X227 : term] : ((X226 @ X227) != (sK564 @ id @ X227 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f530,plain,(
% 28.46/5.33 ! [X226 : term > $o] : (? [X227 : term] : ((X226 @ X227) != (sK564 @ id @ X227 @ id)) => ((sK564 @ id @ (sK565 @ X226) @ id) != (X226 @ (sK565 @ X226))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f531,plain,(
% 28.46/5.33 ! [X229 : subst > term > subst > $o] : (? [X230 : subst > term > term] : (! [X231 : term,X232 : subst,X233 : subst] : ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)) = (sub @ (X230 @ X233 @ X231) @ X232)) & ! [X234 : term] : (((X229 @ id @ (X230 @ id @ X234) @ id) = $true) | ((X229 @ id @ X234 @ id) != $true)) & ((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id) != $true)) => (! [X233 : subst,X232 : subst,X231 : term] : ((sK566 @ X229 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)) = (sub @ (sK566 @ X229 @ X233 @ X231) @ X232)) & ! [X234 : term] : (($true = (X229 @ id @ (sK566 @ X229 @ id @ X234) @ id)) | ((X229 @ id @ X234 @ id) != $true)) & ($true != (X229 @ id @ (lam @ (sK566 @ X229 @ sh @ one)) @ id))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f532,plain,(
% 28.46/5.33 ? [X235 : term,X236 : subst > term > subst > $o] : (! [X237 : subst > term > term] : (? [X238 : term,X239 : subst,X240 : subst] : ((sub @ (X237 @ X240 @ X238) @ X239) != (X237 @ (comp @ X240 @ X239) @ (sub @ X238 @ X239))) | ? [X241 : term] : (((X236 @ id @ (X237 @ id @ X241) @ id) != $true) & ((X236 @ id @ X241 @ id) = $true)) | ((X236 @ id @ (lam @ (X237 @ sh @ one)) @ id) = $true)) & ((X236 @ id @ X235 @ id) != $true) & ((sP20 @ X236) != $true)) => (! [X237 : subst > term > term] : (? [X238 : term,X239 : subst,X240 : subst] : ((sub @ (X237 @ X240 @ X238) @ X239) != (X237 @ (comp @ X240 @ X239) @ (sub @ X238 @ X239))) | ? [X241 : term] : (($true != (sK568 @ id @ (X237 @ id @ X241) @ id)) & ((sK568 @ id @ X241 @ id) = $true)) | ($true = (sK568 @ id @ (lam @ (X237 @ sh @ one)) @ id))) & ((sK568 @ id @ sK567 @ id) != $true) & ((sP20 @ sK568) != $true))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f533,plain,(
% 28.46/5.33 ! [X237 : subst > term > term] : (? [X238 : term,X239 : subst,X240 : subst] : ((sub @ (X237 @ X240 @ X238) @ X239) != (X237 @ (comp @ X240 @ X239) @ (sub @ X238 @ X239))) => ((sub @ (X237 @ (sK571 @ X237) @ (sK569 @ X237)) @ (sK570 @ X237)) != (X237 @ (comp @ (sK571 @ X237) @ (sK570 @ X237)) @ (sub @ (sK569 @ X237) @ (sK570 @ X237)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f534,plain,(
% 28.46/5.33 ! [X237 : subst > term > term] : (? [X241 : term] : (($true != (sK568 @ id @ (X237 @ id @ X241) @ id)) & ((sK568 @ id @ X241 @ id) = $true)) => (((sK568 @ id @ (X237 @ id @ (sK572 @ X237)) @ id) != $true) & ((sK568 @ id @ (sK572 @ X237) @ id) = $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f535,plain,(
% 28.46/5.33 ? [X243 : subst] : ((comp @ X243 @ id) != X243) => (sK573 != (comp @ sK573 @ id))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f536,plain,(
% 28.46/5.33 ! [X244 : subst] : (? [X245 : d_subst] : ((d2subst @ X245) = X244) => ((d2subst @ (sK574 @ X244)) = X244))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f537,plain,(
% 28.46/5.33 ? [X247 : term] : ((sub @ X247 @ id) != X247) => ((sub @ sK575 @ id) != sK575)),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f538,plain,(
% 28.46/5.33 ! [X249 : term > $o] : (? [X250 : term] : (((X249 @ (lam @ X250)) != $true) & ((X249 @ X250) = $true)) => (($true != (X249 @ (lam @ (sK576 @ X249)))) & ((X249 @ (sK576 @ X249)) = $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f539,plain,(
% 28.46/5.33 ! [X249 : term > $o] : (? [X251 : term] : (((X249 @ X251) != $true) & ($true = (var @ X251))) => (((X249 @ (sK577 @ X249)) != $true) & ($true = (var @ (sK577 @ X249)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f540,plain,(
% 28.46/5.33 ? [X252 : term,X253 : term > $o] : (! [X254 : term] : (((X253 @ (lam @ X254)) = $true) | ((X253 @ X254) != $true)) & ((X253 @ X252) != $true) & ((sP10 @ X253) != $true) & ! [X255 : term] : (($true = (X253 @ X255)) | ((var @ X255) != $true))) => (! [X254 : term] : (((sK579 @ (lam @ X254)) = $true) | ((sK579 @ X254) != $true)) & ($true != (sK579 @ sK578)) & ($true != (sP10 @ sK579)) & ! [X255 : term] : (((sK579 @ X255) = $true) | ((var @ X255) != $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f541,plain,(
% 28.46/5.33 ! [X258 : term] : (? [X259 : d_term] : ((d2term @ X259) = X258) => ((d2term @ (sK580 @ X258)) = X258))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f542,plain,(
% 28.46/5.33 ? [X260 : subst,X261 : term,X262 : subst > term > term,X263 : subst > term > term] : (((X263 @ X260 @ X261) != (X262 @ X260 @ X261)) & ((lam @ (X262 @ sh @ one)) = (lam @ (X263 @ sh @ one))) & ! [X264 : term,X265 : subst,X266 : subst] : ((X263 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266)) = (sub @ (X263 @ X265 @ X264) @ X266)) & ! [X267 : subst,X268 : term,X269 : subst] : ((X262 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267)) = (sub @ (X262 @ X269 @ X268) @ X267))) => (((sK584 @ sK581 @ sK582) != (sK583 @ sK581 @ sK582)) & ((lam @ (sK583 @ sh @ one)) = (lam @ (sK584 @ sh @ one))) & ! [X266 : subst,X265 : subst,X264 : term] : ((sub @ (sK584 @ X265 @ X264) @ X266) = (sK584 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266))) & ! [X269 : subst,X268 : term,X267 : subst] : ((sub @ (sK583 @ X269 @ X268) @ X267) = (sK583 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f543,plain,(
% 28.46/5.33 ! [X273 : subst > term > term] : (? [X274 : term,X275 : subst,X276 : subst] : ((X273 @ (comp @ X275 @ X276) @ (sub @ X274 @ X276)) != (sub @ (X273 @ X275 @ X274) @ X276)) => ((X273 @ (comp @ (sK586 @ X273) @ (sK587 @ X273)) @ (sub @ (sK585 @ X273) @ (sK587 @ X273))) != (sub @ (X273 @ (sK586 @ X273) @ (sK585 @ X273)) @ (sK587 @ X273))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f544,plain,(
% 28.46/5.33 ! [X272 : subst > term > term] : (? [X277 : subst,X278 : term,X279 : subst] : ((sub @ (X272 @ X279 @ X278) @ X277) != (X272 @ (comp @ X279 @ X277) @ (sub @ X278 @ X277))) => ((sub @ (X272 @ (sK590 @ X272) @ (sK589 @ X272)) @ (sK588 @ X272)) != (X272 @ (comp @ (sK590 @ X272) @ (sK588 @ X272)) @ (sub @ (sK589 @ X272) @ (sK588 @ X272)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f473,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP58 != $true)) & ((hoasapinj2 = $true) | ? [X0 : term,X1 : term,X2 : term,X3 : term] : ((X2 != X3) & ((ap @ (sub @ X0 @ id) @ X3) = (ap @ (sub @ X1 @ id) @ X2)))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X6 = X7) | ((ap @ (sub @ X4 @ id) @ X7) != (ap @ (sub @ X5 @ id) @ X6))) | (hoasapinj2 != $true)) & ((axscons = $true) | ? [X8 : subst] : ((push @ (sub @ one @ X8) @ (comp @ sh @ X8)) != X8)) & (! [X9 : subst] : ((push @ (sub @ one @ X9) @ (comp @ sh @ X9)) = X9) | (axscons != $true)) & (! [X10 : term,X11 : term] : ((X10 = X11) | ((lam @ X10) != (lam @ X11))) | (laminj != $true)) & ((laminj = $true) | ? [X12 : term,X13 : term] : ((X12 != X13) & ((lam @ X13) = (lam @ X12)))) & ((d2subst @ d_id) = sh) & (! [X14 : term] : ((sub @ X14 @ id) = X14) | (axvarid != $true)) & ((axvarid = $true) | ? [X15 : term] : ((sub @ X15 @ id) != X15)) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) | ? [X16 : subst,X17 : term] : ((comp @ sh @ (push @ X17 @ X16)) != X16)) & (! [X18 : subst,X19 : term] : ((comp @ sh @ (push @ X19 @ X18)) = X18) | (axshiftcons != $true)) & ! [X20 : d_subst] : (d_id = X20) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1 = $true) | ? [X21 : term,X22 : term > $o,X23 : subst,X24 : term > $o,X25 : term] : (((X22 @ (sub @ X25 @ (push @ X21 @ X23))) != $true) & ((X24 @ X25) = $true))) & (! [X26 : term,X27 : term > $o,X28 : subst,X29 : term > $o,X30 : term] : (((X27 @ (sub @ X30 @ (push @ X26 @ X28))) = $true) | ((X29 @ X30) != $true)) | (pushprop_lem1 != $true)) & ((substmonoid = $true) | ? [X31 : subst] : ((comp @ id @ X31) != X31) | ? [X32 : subst] : ((comp @ X32 @ id) != X32)) & ((! [X33 : subst] : ((comp @ id @ X33) = X33) & ! [X34 : subst] : ((comp @ X34 @ id) = X34)) | (substmonoid != $true)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (hoasinduction_lem2_lthm = $true) & (? [X35 : term,X36 : subst] : ((comp @ sh @ (push @ X35 @ X36)) != X36) | ? [X37 : term,X38 : subst] : ((sub @ one @ (push @ X37 @ X38)) != X37) | ! [X39 : term,X40 : subst,X41 : term,X42 : term > $o,X43 : term > $o] : (((X43 @ (sub @ X41 @ (push @ X39 @ X40))) = $true) | ((X42 @ X41) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X44 : term,X45 : subst] : ((comp @ sh @ (push @ X44 @ X45)) = X45) & ! [X46 : term,X47 : subst] : ((sub @ one @ (push @ X46 @ X47)) = X46) & ? [X48 : term,X49 : subst,X50 : term,X51 : term > $o,X52 : term > $o] : (((X52 @ (sub @ X50 @ (push @ X48 @ X49))) != $true) & ((X51 @ X50) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X53 : subst > term > term,X54 : term,X55 : term] : (? [X56 : term,X57 : subst,X58 : subst] : ((sub @ (X53 @ X57 @ X56) @ X58) != (X53 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58))) | ((lam @ (X53 @ sh @ one)) != (ap @ (sub @ X54 @ id) @ X55))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X59 : subst > term > term,X60 : term,X61 : term] : (! [X62 : term,X63 : subst,X64 : subst] : ((sub @ (X59 @ X63 @ X62) @ X64) = (X59 @ (comp @ X63 @ X64) @ (sub @ X62 @ X64))) & ((lam @ (X59 @ sh @ one)) = (ap @ (sub @ X60 @ id) @ X61)))) & (lamnotvar = $true) & (ulamvarind = $true) & ((hoasinduction_lem3aaa = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2_lthm = $true) & ((sP52 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP52 != $true)) & (hoasinduction_gthm = $true) & ! [X65 : d_subst,X66 : d_subst] : (((d2subst @ X66) != (d2subst @ X65)) | (X65 = X66)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & ((induction2lem_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar = $true) & (? [X67 : term,X68 : term,X69 : term,X70 : term] : ((X67 != X68) & ((ap @ X69 @ X68) = (ap @ X70 @ X67))) | ! [X71 : term,X72 : term,X73 : term,X74 : term] : ((X71 = X73) | ((ap @ (sub @ X72 @ id) @ X71) != (ap @ (sub @ X74 @ id) @ X73))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X75 : term,X76 : term,X77 : term,X78 : term] : ((X75 = X76) | ((ap @ X77 @ X76) != (ap @ X78 @ X75))) & ? [X79 : term,X80 : term,X81 : term,X82 : term] : ((X79 != X81) & ((ap @ (sub @ X82 @ id) @ X81) = (ap @ (sub @ X80 @ id) @ X79))))) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset_lthm = $true) | (! [X83 : term] : ((sub @ X83 @ id) = X83) & ? [X84 : term] : ((sub @ X84 @ id) != X84))) & (? [X85 : term] : ((sub @ X85 @ id) != X85) | ! [X86 : term] : ((sub @ X86 @ id) = X86) | (termmset_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (! [X87 : term] : ? [X88 : subst > term > term] : ((sub @ X87 @ (push @ one @ sh)) = (X88 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X89 : term] : ! [X90 : subst > term > term] : ((sub @ X89 @ (push @ one @ sh)) != (X90 @ sh @ one))) & ((induction2lem = $true) | (sP45 != $true)) & ((sP45 = $true) | (induction2lem != $true)) & (! [X91 : term] : ? [X92 : subst > term > term] : ! [X93 : term,X94 : subst] : ((X92 @ X94 @ X93) = (sub @ X91 @ (push @ X93 @ X94))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X95 : term] : ! [X96 : subst > term > term] : ? [X97 : term,X98 : subst] : ((sub @ X95 @ (push @ X97 @ X98)) != (X96 @ X98 @ X97))) & (hoasinduction_lem3v2_gthm = $true) & (! [X99 : term,X100 : term > $o,X101 : term > $o,X102 : subst] : (((X101 @ one) = $true) | ? [X103 : term] : ((X100 @ (sub @ X103 @ (push @ X99 @ X102))) != (X101 @ X103)) | ((X100 @ X99) != $true)) | ? [X104 : term,X105 : subst] : ((sub @ one @ (push @ X104 @ X105)) != X104) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X106 : term,X107 : term > $o,X108 : term > $o,X109 : subst] : (((X108 @ one) != $true) & ! [X110 : term] : ((X108 @ X110) = (X107 @ (sub @ X110 @ (push @ X106 @ X109)))) & ((X107 @ X106) = $true)) & ! [X111 : term,X112 : subst] : ((sub @ one @ (push @ X111 @ X112)) = X111))) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & (! [X113 : subst > term > subst > $o] : ? [X114 : term > $o] : ! [X115 : term] : ((X114 @ X115) = (X113 @ id @ X115 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X116 : subst > term > subst > $o] : ! [X117 : term > $o] : ? [X118 : term] : ((X117 @ X118) != (X116 @ id @ X118 @ id))) & ((sP43 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP43 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP35 != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X119 : d_term] : (d_one = X119) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X120 : term,X121 : term,X122 : term,X123 : term] : ((X120 = X122) | ((ap @ X120 @ X121) != (ap @ X122 @ X123))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X124 : term,X125 : term,X126 : term,X127 : term] : ((X124 != X126) & ((ap @ X126 @ X127) = (ap @ X124 @ X125)))) & ((pushprop_lem0 = $true) | ? [X128 : term > $o,X129 : subst,X130 : term] : ! [X131 : term > $o] : ? [X132 : term] : ((X131 @ X132) != (X128 @ (sub @ X132 @ (push @ X130 @ X129))))) & (! [X133 : term > $o,X134 : subst,X135 : term] : ? [X136 : term > $o] : ! [X137 : term] : ((X133 @ (sub @ X137 @ (push @ X135 @ X134))) = (X136 @ X137)) | (pushprop_lem0 != $true)) & ((axidl = $true) | ? [X138 : subst] : ((comp @ id @ X138) != X138)) & (! [X139 : subst] : ((comp @ id @ X139) = X139) | (axidl != $true)) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (? [X140 : subst] : ((comp @ id @ X140) != X140) | ? [X141 : subst] : ((comp @ X141 @ id) != X141) | (! [X142 : subst] : ((comp @ X142 @ id) = X142) & ! [X143 : subst] : ((comp @ id @ X143) = X143)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X144 : subst] : ((comp @ id @ X144) = X144) & ! [X145 : subst] : ((comp @ X145 @ id) = X145) & (? [X146 : subst] : ((comp @ X146 @ id) != X146) | ? [X147 : subst] : ((comp @ id @ X147) != X147)))) & (! [X148 : term > $o,X149 : subst,X150 : term > $o,X151 : term] : (((X150 @ one) = $true) | ((X148 @ X151) != $true) | ? [X152 : term] : ((X150 @ X152) != (X148 @ (sub @ X152 @ (push @ X151 @ X149))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X153 : term > $o,X154 : subst,X155 : term > $o,X156 : term] : (((X155 @ one) != $true) & ((X153 @ X156) = $true) & ! [X157 : term] : ((X153 @ (sub @ X157 @ (push @ X156 @ X154))) = (X155 @ X157)))) & (axapp = $true) & (! [X158 : term,X159 : term,X160 : term,X161 : term] : (((ap @ (sub @ X158 @ id) @ X160) != (ap @ (sub @ X161 @ id) @ X159)) | (X158 = X161)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X162 : term,X163 : term,X164 : term,X165 : term] : (((ap @ (sub @ X165 @ id) @ X163) = (ap @ (sub @ X162 @ id) @ X164)) & (X162 != X165))) & ((hoasinduction_lem3b = $true) | ? [X166 : term] : ! [X167 : subst > term > term] : ((X167 @ sh @ one) != (sub @ X166 @ (push @ one @ sh)))) & (! [X168 : term] : ? [X169 : subst > term > term] : ((sub @ X168 @ (push @ one @ sh)) = (X169 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (axabs = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X170 : term] : ! [X171 : subst > term > term] : ? [X172 : term,X173 : subst] : ((X171 @ X173 @ X172) != (sub @ X170 @ (push @ X172 @ X173)))) & (! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) | (hoasinduction_lem3v2_f != $true)) & ((induction2_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2_lthm != $true)) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & ((axvarcons = $true) | ? [X178 : subst,X179 : term] : ((sub @ one @ (push @ X179 @ X178)) != X179)) & (! [X180 : subst,X181 : term] : ((sub @ one @ (push @ X181 @ X180)) = X181) | (axvarcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X182 : term,X183 : term,X184 : term,X185 : term] : ((X183 != X184) & ((ap @ (sub @ X184 @ id) @ X185) = (ap @ (sub @ X183 @ id) @ X182))) & ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X187 = X189) | ((ap @ X189 @ X186) != (ap @ X187 @ X188))) & ! [X190 : term] : ((sub @ X190 @ id) = X190))) & (! [X191 : term,X192 : term,X193 : term,X194 : term] : ((X192 = X193) | ((ap @ (sub @ X193 @ id) @ X194) != (ap @ (sub @ X192 @ id) @ X191))) | ? [X195 : term,X196 : term,X197 : term,X198 : term] : ((X196 != X198) & ((ap @ X196 @ X197) = (ap @ X198 @ X195))) | ? [X199 : term] : ((sub @ X199 @ id) != X199) | (hoasapinj1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X200 : subst,X201 : term,X202 : term > $o] : ! [X203 : term > $o] : ? [X204 : term] : ((X202 @ (sub @ X204 @ (push @ X201 @ X200))) != (X203 @ X204))) & (! [X205 : subst,X206 : term,X207 : term > $o] : ? [X208 : term > $o] : ! [X209 : term] : ((X207 @ (sub @ X209 @ (push @ X206 @ X205))) = (X208 @ X209)) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & ((sP28 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP28 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & ((sP27 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP27 != $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X210 : term,X211 : term,X212 : term,X213 : term] : ((X210 = X211) | ((ap @ X213 @ X210) != (ap @ X212 @ X211))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 != X215) & ((ap @ X216 @ X215) = (ap @ X217 @ X214)))) & (hoasinduction_lem3_gthm = $true) & (! [X218 : term,X219 : term] : ((X218 = X219) | ((sub @ X219 @ sh) != (sub @ X218 @ sh))) | (shinj != $true)) & ((shinj = $true) | ? [X220 : term,X221 : term] : ((X220 != X221) & ((sub @ X221 @ sh) = (sub @ X220 @ sh)))) & ((hoasinduction_lem2v2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2v2 != $true)) & (! [X222 : subst > term > subst > $o] : ? [X223 : term > $o] : ! [X224 : term] : ((X223 @ X224) = (X222 @ id @ X224 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X225 : subst > term > subst > $o] : ! [X226 : term > $o] : ? [X227 : term] : ((X226 @ X227) != (X225 @ id @ X227 @ id))) & (hoaslamnotvar_gthm = $true) & (! [X228 : term,X229 : subst > term > subst > $o] : (? [X230 : subst > term > term] : (! [X231 : term,X232 : subst,X233 : subst] : ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)) = (sub @ (X230 @ X233 @ X231) @ X232)) & ! [X234 : term] : (((X229 @ id @ (X230 @ id @ X234) @ id) = $true) | ((X229 @ id @ X234 @ id) != $true)) & ((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id) != $true)) | ((X229 @ id @ X228 @ id) = $true) | ($true = (sP20 @ X229))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X235 : term,X236 : subst > term > subst > $o] : (! [X237 : subst > term > term] : (? [X238 : term,X239 : subst,X240 : subst] : ((sub @ (X237 @ X240 @ X238) @ X239) != (X237 @ (comp @ X240 @ X239) @ (sub @ X238 @ X239))) | ? [X241 : term] : (((X236 @ id @ (X237 @ id @ X241) @ id) != $true) & ((X236 @ id @ X241 @ id) = $true)) | ((X236 @ id @ (lam @ (X237 @ sh @ one)) @ id) = $true)) & ((X236 @ id @ X235 @ id) != $true) & ((sP20 @ X236) != $true))) & (! [X242 : subst] : ((comp @ X242 @ id) = X242) | (axidr != $true)) & ((axidr = $true) | ? [X243 : subst] : ((comp @ X243 @ id) != X243)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X244 : subst] : ? [X245 : d_subst] : ((d2subst @ X245) = X244) & (induction2_gthm = $true) & (! [X246 : term] : ((sub @ X246 @ id) = X246) | (termmset != $true)) & ((termmset = $true) | ? [X247 : term] : ((sub @ X247 @ id) != X247)) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X248 : term,X249 : term > $o] : (? [X250 : term] : (((X249 @ (lam @ X250)) != $true) & ((X249 @ X250) = $true)) | ((X249 @ X248) = $true) | ((sP10 @ X249) = $true) | ? [X251 : term] : (((X249 @ X251) != $true) & ($true = (var @ X251)))) | (induction != $true)) & ((induction = $true) | ? [X252 : term,X253 : term > $o] : (! [X254 : term] : (((X253 @ (lam @ X254)) = $true) | ((X253 @ X254) != $true)) & ((X253 @ X252) != $true) & ((sP10 @ X253) != $true) & ! [X255 : term] : (($true = (X253 @ X255)) | ((var @ X255) != $true)))) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & (lamnotap != $true) & (termmset_gthm = $true) & ((sP9 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP9 != $true)) & ! [X258 : term] : ? [X259 : d_term] : ((d2term @ X259) = X258) & ((hoaslaminj = $true) | ? [X260 : subst,X261 : term,X262 : subst > term > term,X263 : subst > term > term] : (((X263 @ X260 @ X261) != (X262 @ X260 @ X261)) & ((lam @ (X262 @ sh @ one)) = (lam @ (X263 @ sh @ one))) & ! [X264 : term,X265 : subst,X266 : subst] : ((X263 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266)) = (sub @ (X263 @ X265 @ X264) @ X266)) & ! [X267 : subst,X268 : term,X269 : subst] : ((X262 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267)) = (sub @ (X262 @ X269 @ X268) @ X267)))) & (! [X270 : subst,X271 : term,X272 : subst > term > term,X273 : subst > term > term] : (((X273 @ X270 @ X271) = (X272 @ X270 @ X271)) | ((lam @ (X272 @ sh @ one)) != (lam @ (X273 @ sh @ one))) | ? [X274 : term,X275 : subst,X276 : subst] : ((X273 @ (comp @ X275 @ X276) @ (sub @ X274 @ X276)) != (sub @ (X273 @ X275 @ X274) @ X276)) | ? [X277 : subst,X278 : term,X279 : subst] : ((sub @ (X272 @ X279 @ X278) @ X277) != (X272 @ (comp @ X279 @ X277) @ (sub @ X278 @ X277)))) | (hoaslaminj != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((sP6 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP6 != $true)) & (pushprop_lthm = $true) & (pushprop = $true) & ((hoasinduction = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true))),
% 28.46/5.33 inference(rectify,[status(thm)],[f472])).
% 28.46/5.33 thf(f472,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP58 != $true)) & ((hoasapinj2 = $true) | ? [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 != X89) & ((ap @ (sub @ X86 @ id) @ X89) = (ap @ (sub @ X87 @ id) @ X88)))) & (! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88))) | (hoasapinj2 != $true)) & ((axscons = $true) | ? [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) != X24)) & (! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24) | (axscons != $true)) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) | (laminj != $true)) & ((laminj = $true) | ? [X455 : term,X456 : term] : ((X455 != X456) & ((lam @ X456) = (lam @ X455)))) & ((d2subst @ d_id) = sh) & (! [X178 : term] : ((sub @ X178 @ id) = X178) | (axvarid != $true)) & ((axvarid = $true) | ? [X178 : term] : ((sub @ X178 @ id) != X178)) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) | ? [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) != X530)) & (! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530) | (axshiftcons != $true)) & ! [X529 : d_subst] : (d_id = X529) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1 = $true) | ? [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) != $true) & ($true = (X93 @ X94)))) & (! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94))) | (pushprop_lem1 != $true)) & ((substmonoid = $true) | ? [X42 : subst] : ((comp @ id @ X42) != X42) | ? [X41 : subst] : ((comp @ X41 @ id) != X41)) & ((! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41)) | (substmonoid != $true)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (hoasinduction_lem2_lthm = $true) & (? [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) != X303) | ? [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) != X300) | ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) = X303) & ! [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) = X300) & ? [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) != $true) & ((X307 @ X306) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (? [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) != (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) | ((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X76 : subst > term > term,X77 : term,X78 : term] : (! [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) = (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) & ((ap @ (sub @ X77 @ id) @ X78) = (lam @ (X76 @ sh @ one))))) & (lamnotvar = $true) & (ulamvarind = $true) & ((hoasinduction_lem3aaa = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2_lthm = $true) & ((sP52 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP52 != $true)) & (hoasinduction_gthm = $true) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) != (d2subst @ X471)) | (X470 = X471)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & ((induction2lem_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar = $true) & (? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X533) & ((ap @ X535 @ X532) = (ap @ X534 @ X533))) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 = X533) | ((ap @ X535 @ X532) != (ap @ X534 @ X533))) & ? [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 != X538) & ((ap @ (sub @ X539 @ id) @ X538) = (ap @ (sub @ X537 @ id) @ X536))))) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset_lthm = $true) | (! [X298 : term] : ((sub @ X298 @ id) = X298) & ? [X299 : term] : ((sub @ X299 @ id) != X299))) & (? [X298 : term] : ((sub @ X298 @ id) != X298) | ! [X299 : term] : ((sub @ X299 @ id) = X299) | (termmset_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (! [X429 : term] : ? [X430 : subst > term > term] : ((X430 @ sh @ one) = (sub @ X429 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X429 : term] : ! [X430 : subst > term > term] : ((X430 @ sh @ one) != (sub @ X429 @ (push @ one @ sh)))) & ((induction2lem = $true) | (sP45 != $true)) & ((sP45 = $true) | (induction2lem != $true)) & (! [X329 : term] : ? [X330 : subst > term > term] : ! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X329 : term] : ! [X330 : subst > term > term] : ? [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) != (X330 @ X332 @ X331))) & (hoasinduction_lem3v2_gthm = $true) & (! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true = (X505 @ one)) | ? [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) != (X505 @ X507)) | ($true != (X504 @ X503))) | ? [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) != X501) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true != (X505 @ one)) & ! [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) = (X505 @ X507)) & ($true = (X504 @ X503))) & ! [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) = X501))) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & (! [X168 : subst > term > subst > $o] : ? [X169 : term > $o] : ! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X168 : subst > term > subst > $o] : ! [X169 : term > $o] : ? [X170 : term] : ((X168 @ id @ X170 @ id) != (X169 @ X170))) & ((sP43 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP43 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP35 != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X486 : d_term] : (d_one = X486) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 != X372) & ((ap @ X372 @ X373) = (ap @ X370 @ X371)))) & ((pushprop_lem0 = $true) | ? [X259 : term > $o,X260 : subst,X261 : term] : ! [X262 : term > $o] : ? [X263 : term] : ((X262 @ X263) != (X259 @ (sub @ X263 @ (push @ X261 @ X260))))) & (! [X259 : term > $o,X260 : subst,X261 : term] : ? [X262 : term > $o] : ! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260)))) | (pushprop_lem0 != $true)) & ((axidl = $true) | ? [X257 : subst] : ((comp @ id @ X257) != X257)) & (! [X257 : subst] : ((comp @ id @ X257) = X257) | (axidl != $true)) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (? [X82 : subst] : ((comp @ id @ X82) != X82) | ? [X83 : subst] : ((comp @ X83 @ id) != X83) | (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X82 : subst] : ((comp @ id @ X82) = X82) & ! [X83 : subst] : ((comp @ X83 @ id) = X83) & (? [X85 : subst] : ((comp @ X85 @ id) != X85) | ? [X84 : subst] : ((comp @ id @ X84) != X84)))) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ((X481 @ X484) != $true) | ? [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) != (X483 @ X485))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) != $true) & ((X481 @ X484) = $true) & ! [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) = (X483 @ X485)))) & (axapp = $true) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) = (ap @ (sub @ X374 @ id) @ X376)) & (X374 != X377))) & ((hoasinduction_lem3b = $true) | ? [X327 : term] : ! [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) != (X328 @ sh @ one))) & (! [X327 : term] : ? [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) = (X328 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (axabs = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X174 : term] : ! [X175 : subst > term > term] : ? [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) != (X175 @ X177 @ X176))) & (! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) | (hoasinduction_lem3v2_f != $true)) & ((induction2_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2_lthm != $true)) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & ((axvarcons = $true) | ? [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) != X128)) & (! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128) | (axvarcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 != X479) & ((ap @ (sub @ X478 @ id) @ X477) = (ap @ (sub @ X479 @ id) @ X480))) & ! [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 = X476) | ((ap @ X476 @ X473) != (ap @ X474 @ X475))) & ! [X472 : term] : ((sub @ X472 @ id) = X472))) & (! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))) | ? [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 != X476) & ((ap @ X476 @ X473) = (ap @ X474 @ X475))) | ? [X472 : term] : ((sub @ X472 @ id) != X472) | (hoasapinj1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X241 : subst,X242 : term,X243 : term > $o] : ! [X244 : term > $o] : ? [X245 : term] : ((X244 @ X245) != (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (! [X241 : subst,X242 : term,X243 : term > $o] : ? [X244 : term > $o] : ! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241)))) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & ((sP28 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP28 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & ((sP27 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP27 != $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 != X410) & ((ap @ X411 @ X410) = (ap @ X412 @ X409)))) & (hoasinduction_lem3_gthm = $true) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) | (shinj != $true)) & ((shinj = $true) | ? [X527 : term,X528 : term] : ((X527 != X528) & ((sub @ X528 @ sh) = (sub @ X527 @ sh)))) & ((hoasinduction_lem2v2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2v2 != $true)) & (! [X171 : subst > term > subst > $o] : ? [X172 : term > $o] : ! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X171 : subst > term > subst > $o] : ! [X172 : term > $o] : ? [X173 : term] : ((X171 @ id @ X173 @ id) != (X172 @ X173))) & (hoaslamnotvar_gthm = $true) & (! [X0 : term,X1 : subst > term > subst > $o] : (? [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true)) & ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) != $true)) | ($true = (X1 @ id @ X0 @ id)) | ((sP20 @ X1) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X0 : term,X1 : subst > term > subst > $o] : (! [X4 : subst > term > term] : (? [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) != (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ? [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) != $true) & ((X1 @ id @ X8 @ id) = $true)) | ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ($true != (X1 @ id @ X0 @ id)) & ((sP20 @ X1) != $true))) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) | (axidr != $true)) & ((axidr = $true) | ? [X258 : subst] : ((comp @ X258 @ id) != X258)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & (induction2_gthm = $true) & (! [X256 : term] : ((sub @ X256 @ id) = X256) | (termmset != $true)) & ((termmset = $true) | ? [X256 : term] : ((sub @ X256 @ id) != X256)) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X439 : term,X440 : term > $o] : (? [X443 : term] : (((X440 @ (lam @ X443)) != $true) & ((X440 @ X443) = $true)) | ((X440 @ X439) = $true) | ((sP10 @ X440) = $true) | ? [X444 : term] : (((X440 @ X444) != $true) & ($true = (var @ X444)))) | (induction != $true)) & ((induction = $true) | ? [X439 : term,X440 : term > $o] : (! [X443 : term] : (((X440 @ (lam @ X443)) = $true) | ((X440 @ X443) != $true)) & ((X440 @ X439) != $true) & ((sP10 @ X440) != $true) & ! [X444 : term] : (((X440 @ X444) = $true) | ($true != (var @ X444))))) & ! [X294 : d_term,X295 : d_term] : ((X294 = X295) | ((d2term @ X294) != (d2term @ X295))) & (lamnotap != $true) & (termmset_gthm = $true) & ((sP9 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP9 != $true)) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & ((hoaslaminj = $true) | ? [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) != (X448 @ X445 @ X446)) & ((lam @ (X447 @ sh @ one)) = (lam @ (X448 @ sh @ one))) & ! [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) = (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) & ! [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) = (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))))) & (! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ? [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) != (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) | ? [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) != (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452)))) | (hoaslaminj != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((sP6 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP6 != $true)) & (pushprop_lthm = $true) & (pushprop = $true) & ((hoasinduction = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true))),
% 28.46/5.33 inference(flattening,[status(thm)],[f471])).
% 28.46/5.33 thf(f471,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (((sP58 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP58 != $true))) & (((hoasapinj2 = $true) | ? [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 != X89) & ((ap @ (sub @ X86 @ id) @ X89) = (ap @ (sub @ X87 @ id) @ X88)))) & (! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88))) | (hoasapinj2 != $true))) & (((axscons = $true) | ? [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) != X24)) & (! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24) | (axscons != $true))) & ((! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) | (laminj != $true)) & ((laminj = $true) | ? [X455 : term,X456 : term] : ((X455 != X456) & ((lam @ X456) = (lam @ X455))))) & ((d2subst @ d_id) = sh) & ((! [X178 : term] : ((sub @ X178 @ id) = X178) | (axvarid != $true)) & ((axvarid = $true) | ? [X178 : term] : ((sub @ X178 @ id) != X178))) & (hoasapnotvar_gthm = $true) & (((axshiftcons = $true) | ? [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) != X530)) & (! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530) | (axshiftcons != $true))) & ! [X529 : d_subst] : (d_id = X529) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & (((pushprop_lem1 = $true) | ? [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) != $true) & ($true = (X93 @ X94)))) & (! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94))) | (pushprop_lem1 != $true))) & (((substmonoid = $true) | (? [X42 : subst] : ((comp @ id @ X42) != X42) | ? [X41 : subst] : ((comp @ X41 @ id) != X41))) & ((! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41)) | (substmonoid != $true))) & ((($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56))) & (hoasinduction_lem2_lthm = $true) & (((? [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) != X303) | ? [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) != X300) | ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) = X303) & ! [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) = X300) & ? [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) != $true) & ((X307 @ X306) = $true))))) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((! [X76 : subst > term > term,X77 : term,X78 : term] : (? [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) != (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) | ((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X76 : subst > term > term,X77 : term,X78 : term] : (! [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) = (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) & ((ap @ (sub @ X77 @ id) @ X78) = (lam @ (X76 @ sh @ one)))))) & (lamnotvar = $true) & (ulamvarind = $true) & (((hoasinduction_lem3aaa = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3aaa != $true))) & (pushprop_lem3v2_lthm = $true) & (((sP52 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP52 != $true))) & (hoasinduction_gthm = $true) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) != (d2subst @ X471)) | (X470 = X471)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & (((induction2lem_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (induction2lem_lthm != $true))) & (hoaslamnotvar = $true) & (((? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X533) & ((ap @ X535 @ X532) = (ap @ X534 @ X533))) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 = X533) | ((ap @ X535 @ X532) != (ap @ X534 @ X533))) & ? [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 != X538) & ((ap @ (sub @ X539 @ id) @ X538) = (ap @ (sub @ X537 @ id) @ X536)))))) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((termmset_lthm = $true) | (! [X298 : term] : ((sub @ X298 @ id) = X298) & ? [X299 : term] : ((sub @ X299 @ id) != X299))) & ((? [X298 : term] : ((sub @ X298 @ id) != X298) | ! [X299 : term] : ((sub @ X299 @ id) = X299)) | (termmset_lthm != $true))) & (hoasinduction_lem3a_gthm = $true) & ((($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46))) & ((! [X429 : term] : ? [X430 : subst > term > term] : ((X430 @ sh @ one) = (sub @ X429 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X429 : term] : ! [X430 : subst > term > term] : ((X430 @ sh @ one) != (sub @ X429 @ (push @ one @ sh))))) & (((induction2lem = $true) | (sP45 != $true)) & ((sP45 = $true) | (induction2lem != $true))) & ((! [X329 : term] : ? [X330 : subst > term > term] : ! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X329 : term] : ! [X330 : subst > term > term] : ? [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) != (X330 @ X332 @ X331)))) & (hoasinduction_lem3v2_gthm = $true) & (((! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true = (X505 @ one)) | ? [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) != (X505 @ X507)) | ($true != (X504 @ X503))) | ? [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) != X501)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true != (X505 @ one)) & ! [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) = (X505 @ X507)) & ($true = (X504 @ X503))) & ! [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) = X501)))) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & ((! [X168 : subst > term > subst > $o] : ? [X169 : term > $o] : ! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X168 : subst > term > subst > $o] : ! [X169 : term > $o] : ? [X170 : term] : ((X168 @ id @ X170 @ id) != (X169 @ X170)))) & (((sP43 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP43 != $true))) & (((hoasinduction_lthm_3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lthm_3 != $true))) & (((sP35 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP35 != $true))) & (((hoasinduction_lem3v2_lthm = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3v2_lthm != $true))) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X486 : d_term] : (d_one = X486) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 != X372) & ((ap @ X372 @ X373) = (ap @ X370 @ X371))))) & (((pushprop_lem0 = $true) | ? [X259 : term > $o,X260 : subst,X261 : term] : ! [X262 : term > $o] : ? [X263 : term] : ((X262 @ X263) != (X259 @ (sub @ X263 @ (push @ X261 @ X260))))) & (! [X259 : term > $o,X260 : subst,X261 : term] : ? [X262 : term > $o] : ! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260)))) | (pushprop_lem0 != $true))) & (((axidl = $true) | ? [X257 : subst] : ((comp @ id @ X257) != X257)) & (! [X257 : subst] : ((comp @ id @ X257) = X257) | (axidl != $true))) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((? [X82 : subst] : ((comp @ id @ X82) != X82) | ? [X83 : subst] : ((comp @ X83 @ id) != X83) | (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X82 : subst] : ((comp @ id @ X82) = X82) & ! [X83 : subst] : ((comp @ X83 @ id) = X83) & (? [X85 : subst] : ((comp @ X85 @ id) != X85) | ? [X84 : subst] : ((comp @ id @ X84) != X84))))) & ((! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ((X481 @ X484) != $true) | ? [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) != (X483 @ X485))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) != $true) & ((X481 @ X484) = $true) & ! [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) = (X483 @ X485))))) & (axapp = $true) & ((! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) = (ap @ (sub @ X374 @ id) @ X376)) & (X374 != X377)))) & (((hoasinduction_lem3b = $true) | ? [X327 : term] : ! [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) != (X328 @ sh @ one))) & (! [X327 : term] : ? [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) = (X328 @ sh @ one)) | (hoasinduction_lem3b != $true))) & (axabs = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X174 : term] : ! [X175 : subst > term > term] : ? [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) != (X175 @ X177 @ X176))) & (! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) | (hoasinduction_lem3v2_f != $true))) & (((induction2_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2_lthm != $true))) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & (((axvarcons = $true) | ? [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) != X128)) & (! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128) | (axvarcons != $true))) & (hoaslamnotap_gthm = $true) & (((hoasapinj1_lthm = $true) | (? [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 != X479) & ((ap @ (sub @ X478 @ id) @ X477) = (ap @ (sub @ X479 @ id) @ X480))) & ! [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 = X476) | ((ap @ X476 @ X473) != (ap @ X474 @ X475))) & ! [X472 : term] : ((sub @ X472 @ id) = X472))) & ((! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))) | ? [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 != X476) & ((ap @ X476 @ X473) = (ap @ X474 @ X475))) | ? [X472 : term] : ((sub @ X472 @ id) != X472)) | (hoasapinj1_lthm != $true))) & (((pushprop_lem0_lthm = $true) | ? [X241 : subst,X242 : term,X243 : term > $o] : ! [X244 : term > $o] : ? [X245 : term] : ((X244 @ X245) != (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (! [X241 : subst,X242 : term,X243 : term > $o] : ? [X244 : term > $o] : ! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241)))) | (pushprop_lem0_lthm != $true))) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & (((sP28 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP28 != $true))) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & (((sP27 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP27 != $true))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 != X410) & ((ap @ X411 @ X410) = (ap @ X412 @ X409))))) & (hoasinduction_lem3_gthm = $true) & ((! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) | (shinj != $true)) & ((shinj = $true) | ? [X527 : term,X528 : term] : ((X527 != X528) & ((sub @ X528 @ sh) = (sub @ X527 @ sh))))) & (((hoasinduction_lem2v2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2v2 != $true))) & ((! [X171 : subst > term > subst > $o] : ? [X172 : term > $o] : ! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X171 : subst > term > subst > $o] : ! [X172 : term > $o] : ? [X173 : term] : ((X171 @ id @ X173 @ id) != (X172 @ X173)))) & (hoaslamnotvar_gthm = $true) & ((! [X0 : term,X1 : subst > term > subst > $o] : (? [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true)) & ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) != $true)) | ($true = (X1 @ id @ X0 @ id)) | ((sP20 @ X1) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X0 : term,X1 : subst > term > subst > $o] : (! [X4 : subst > term > term] : (? [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) != (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ? [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) != $true) & ((X1 @ id @ X8 @ id) = $true)) | ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ($true != (X1 @ id @ X0 @ id)) & ((sP20 @ X1) != $true)))) & ((! [X258 : subst] : ((comp @ X258 @ id) = X258) | (axidr != $true)) & ((axidr = $true) | ? [X258 : subst] : ((comp @ X258 @ id) != X258))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasinduction_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lthm != $true))) & (hoasinduction_lem2v2_gthm = $true) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & (induction2_gthm = $true) & ((! [X256 : term] : ((sub @ X256 @ id) = X256) | (termmset != $true)) & ((termmset = $true) | ? [X256 : term] : ((sub @ X256 @ id) != X256))) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((! [X439 : term,X440 : term > $o] : (? [X443 : term] : (((X440 @ (lam @ X443)) != $true) & ((X440 @ X443) = $true)) | ((X440 @ X439) = $true) | ((sP10 @ X440) = $true) | ? [X444 : term] : (((X440 @ X444) != $true) & ($true = (var @ X444)))) | (induction != $true)) & ((induction = $true) | ? [X439 : term,X440 : term > $o] : (! [X443 : term] : (((X440 @ (lam @ X443)) = $true) | ((X440 @ X443) != $true)) & ((X440 @ X439) != $true) & ((sP10 @ X440) != $true) & ! [X444 : term] : (((X440 @ X444) = $true) | ($true != (var @ X444)))))) & ! [X294 : d_term,X295 : d_term] : ((X294 = X295) | ((d2term @ X294) != (d2term @ X295))) & (lamnotap != $true) & (termmset_gthm = $true) & (((sP9 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP9 != $true))) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & (((hoaslaminj = $true) | ? [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) != (X448 @ X445 @ X446)) & ((lam @ (X447 @ sh @ one)) = (lam @ (X448 @ sh @ one))) & ! [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) = (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) & ! [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) = (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))))) & (! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ? [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) != (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) | ? [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) != (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452)))) | (hoaslaminj != $true))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & (((hoasinduction_lem3aa_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (((sP6 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP6 != $true))) & (pushprop_lthm = $true) & (pushprop = $true) & (((hoasinduction = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction != $true))) & (((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true))) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true)))),
% 28.46/5.33 inference(nnf_transformation,[status(thm)],[f73])).
% 28.46/5.33 thf(f73,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & ((sP58 = $true) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)))) & ((axscons = $true) <=> ! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24)) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) <=> (laminj = $true)) & ((d2subst @ d_id) = sh) & (! [X178 : term] : ((sub @ X178 @ id) = X178) <=> (axvarid = $true)) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530)) & ! [X529 : d_subst] : (d_id = X529) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94)))) & ((substmonoid = $true) <=> (! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41))) & (($true = sP56) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & ((? [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) != X303) | ? [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) != X300) | ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true))) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (? [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) != (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) | ((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one)))) <=> (hoaslamnotap = $true)) & (lamnotvar = $true) & (ulamvarind = $true) & ((hoasinduction_lem3aaa = $true) <=> (sP53 = $true)) & (pushprop_lem3v2_lthm = $true) & ((sP52 = $true) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_gthm = $true) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) != (d2subst @ X471)) | (X470 = X471)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & ((induction2lem_lthm = $true) <=> (sP50 = $true)) & (hoaslamnotvar = $true) & ((? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X533) & ((ap @ X535 @ X532) = (ap @ X534 @ X533))) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536)))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset_lthm = $true) <=> (? [X298 : term] : ((sub @ X298 @ id) != X298) | ! [X299 : term] : ((sub @ X299 @ id) = X299))) & (hoasinduction_lem3a_gthm = $true) & (($true = sP46) <=> (hoaslaminj_lthm = $true)) & (! [X429 : term] : ? [X430 : subst > term > term] : ((X430 @ sh @ one) = (sub @ X429 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> (sP45 = $true)) & (! [X329 : term] : ? [X330 : subst > term > term] : ! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true = (X505 @ one)) | ? [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) != (X505 @ X507)) | ($true != (X504 @ X503))) | ? [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) != X501)) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & (! [X168 : subst > term > subst > $o] : ? [X169 : term > $o] : ! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) <=> (hoasinduction_lem0_lthm = $true)) & ((sP43 = $true) <=> (induction2 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (sP41 = $true)) & ((sP35 = $true) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP34 = $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X486 : d_term] : (d_one = X486) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) <=> (apinj1 = $true)) & ((pushprop_lem0 = $true) <=> ! [X259 : term > $o,X260 : subst,X261 : term] : ? [X262 : term > $o] : ! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260))))) & ((axidl = $true) <=> ! [X257 : subst] : ((comp @ id @ X257) = X257)) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((? [X82 : subst] : ((comp @ id @ X82) != X82) | ? [X83 : subst] : ((comp @ X83 @ id) != X83) | (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84))) <=> (substmonoid_lthm = $true)) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ((X481 @ X484) != $true) | ? [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) != (X483 @ X485))) <=> (pushprop_lem1v2 = $true)) & (axapp = $true) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X327 : term] : ? [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) = (X328 @ sh @ one))) & (axabs = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176))) & ((induction2_lthm = $true) <=> (sP32 = $true)) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & ((axvarcons = $true) <=> ! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))) | ? [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 != X476) & ((ap @ X476 @ X473) = (ap @ X474 @ X475))) | ? [X472 : term] : ((sub @ X472 @ id) != X472))) & ((pushprop_lem0_lthm = $true) <=> ! [X241 : subst,X242 : term,X243 : term > $o] : ? [X244 : term > $o] : ! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & ((sP28 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & ((sP27 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) <=> (apinj2 = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) <=> (shinj = $true)) & ((hoasinduction_lem2v2 = $true) <=> (sP22 = $true)) & (! [X171 : subst > term > subst > $o] : ? [X172 : term > $o] : ! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173)) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar_gthm = $true) & (! [X0 : term,X1 : subst > term > subst > $o] : (? [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true)) & ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) != $true)) | ($true = (X1 @ id @ X0 @ id)) | ((sP20 @ X1) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) <=> (axidr = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lthm = $true) <=> (sP19 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & (induction2_gthm = $true) & (! [X256 : term] : ((sub @ X256 @ id) = X256) <=> (termmset = $true)) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X439 : term,X440 : term > $o] : (? [X443 : term] : (((X440 @ (lam @ X443)) != $true) & ((X440 @ X443) = $true)) | ((X440 @ X439) = $true) | ((sP10 @ X440) = $true) | ? [X444 : term] : (((X440 @ X444) != $true) & ($true = (var @ X444)))) <=> (induction = $true)) & ! [X294 : d_term,X295 : d_term] : ((X294 = X295) | ((d2term @ X294) != (d2term @ X295))) & (lamnotap != $true) & (termmset_gthm = $true) & ((sP9 = $true) <=> (hoasinduction_lem3v2 = $true)) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & ((hoaslaminj = $true) <=> ! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ? [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) != (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) | ? [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) != (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP7 = $true)) & ((sP6 = $true) <=> (hoasinduction_lem3a = $true)) & (pushprop_lthm = $true) & (pushprop = $true) & ((hoasinduction = $true) <=> (sP5 = $true)) & ((hoasinduction_lem3v2a = $true) <=> (sP2 = $true)) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((sP1 = $true) <=> (hoasinduction_lem3 = $true))),
% 28.46/5.33 inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 28.46/5.33 thf(f14,plain,(
% 28.46/5.33 ! [X60 : subst > term > subst > $o] : (((sP0 @ X60) = $true) <=> ? [X62 : subst > term > term] : (! [X63 : term,X64 : subst,X65 : subst] : ((sub @ (X62 @ X65 @ X63) @ X64) = (X62 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64))) & ! [X66 : term] : (((X60 @ id @ X66 @ id) != $true) | ((X60 @ id @ (X62 @ id @ X66) @ id) = $true)) & ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f15,plain,(
% 28.46/5.33 (sP1 = $true) <=> ! [X60 : subst > term > subst > $o,X61 : term] : (? [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (((X60 @ X69 @ X68 @ (comp @ X70 @ X67)) != $true) & ((X60 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X67) = $true)) | ((X60 @ id @ (lam @ X61) @ id) = $true) | ? [X75 : term] : (((X60 @ id @ (sub @ X61 @ (push @ X75 @ id)) @ id) != $true) & ((X60 @ id @ X75 @ id) = $true)) | ? [X71 : subst,X72 : subst,X73 : subst,X74 : term] : (((X60 @ (comp @ X73 @ X71) @ (sub @ X74 @ X71) @ X72) != $true) & ((X60 @ X73 @ X74 @ (comp @ X71 @ X72)) = $true)) | ((sP0 @ X60) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f16,plain,(
% 28.46/5.33 (sP2 = $true) <=> ! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) = $true) | ? [X249 : term] : ((X246 @ id @ X249 @ id) != (X247 @ X249)) | ? [X250 : subst > term > term] : (! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) & ! [X251 : term] : (((X246 @ id @ X251 @ id) != $true) | ((X246 @ id @ (X250 @ id @ X251) @ id) = $true)) & ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) != $true)) | ? [X255 : term] : (((X247 @ X255) = $true) & ((X247 @ (sub @ X248 @ (push @ X255 @ id))) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f17,plain,(
% 28.46/5.33 ! [X310 : subst > term > subst > $o] : (((sP3 @ X310) = $true) <=> ? [X325 : term,X326 : term] : (($true = (X310 @ id @ X326 @ id)) & ((X310 @ id @ X325 @ id) = $true) & ((X310 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f18,plain,(
% 28.46/5.33 ! [X310 : subst > term > subst > $o] : (((sP4 @ X310) = $true) <=> ? [X320 : subst > term > term] : (! [X324 : term] : (((X310 @ id @ X324 @ id) != $true) | ((X310 @ id @ (X320 @ id @ X324) @ id) = $true)) & ! [X321 : subst,X322 : term,X323 : subst] : ((sub @ (X320 @ X321 @ X322) @ X323) = (X320 @ (comp @ X321 @ X323) @ (sub @ X322 @ X323))) & ((X310 @ id @ (lam @ (X320 @ sh @ one)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f19,plain,(
% 28.46/5.33 (sP5 = $true) <=> ! [X309 : term,X310 : subst > term > subst > $o] : (((sP4 @ X310) = $true) | ? [X312 : subst,X313 : subst,X314 : term,X315 : subst] : (($true = (X310 @ (comp @ X315 @ X312) @ (sub @ X314 @ X312) @ X313)) & ((X310 @ X315 @ X314 @ (comp @ X312 @ X313)) != $true)) | ? [X311 : term] : (((var @ (sub @ X311 @ id)) = $true) & ((X310 @ id @ X311 @ id) != $true)) | ? [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (((X310 @ X318 @ X316 @ (comp @ X319 @ X317)) = $true) & ((X310 @ (comp @ X318 @ X319) @ (sub @ X316 @ X319) @ X317) != $true)) | ((X310 @ id @ X309 @ id) = $true) | ((sP3 @ X310) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f20,plain,(
% 28.46/5.33 (sP6 = $true) <=> ! [X233 : term,X234 : subst > term > subst > $o] : (? [X235 : subst > term > term] : (! [X239 : term] : (((X234 @ id @ (X235 @ id @ X239) @ id) = $true) | ((X234 @ id @ X239 @ id) != $true)) & ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id) != $true) & ! [X236 : subst,X237 : subst,X238 : term] : ((X235 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237)) = (sub @ (X235 @ X236 @ X238) @ X237))) | ((X234 @ id @ (lam @ X233) @ id) = $true) | ? [X240 : term] : (((X234 @ id @ (sub @ X233 @ (push @ X240 @ id)) @ id) != $true) & ((X234 @ id @ X240 @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f21,plain,(
% 28.46/5.33 (sP7 = $true) <=> ! [X431 : term,X432 : subst > term > subst > $o] : (? [X433 : subst > term > term] : (! [X434 : subst,X435 : subst,X436 : term] : ((sub @ (X433 @ X434 @ X436) @ X435) = (X433 @ (comp @ X434 @ X435) @ (sub @ X436 @ X435))) & ((X432 @ id @ (lam @ (X433 @ sh @ one)) @ id) != $true) & ! [X437 : term] : (((X432 @ id @ (X433 @ id @ X437) @ id) = $true) | ((X432 @ id @ X437 @ id) != $true))) | ((X432 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true) | ? [X438 : term] : (((X432 @ id @ (sub @ X431 @ (push @ X438 @ id)) @ id) != $true) & ((X432 @ id @ X438 @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f22,plain,(
% 28.46/5.33 ! [X354 : subst > term > subst > $o] : (((sP8 @ X354) = $true) <=> ? [X361 : subst > term > term] : (! [X365 : term] : (((X354 @ id @ (X361 @ id @ X365) @ id) = $true) | ((X354 @ id @ X365 @ id) != $true)) & ((X354 @ id @ (lam @ (X361 @ sh @ one)) @ id) != $true) & ! [X362 : subst,X363 : subst,X364 : term] : ((sub @ (X361 @ X363 @ X364) @ X362) = (X361 @ (comp @ X363 @ X362) @ (sub @ X364 @ X362)))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f23,plain,(
% 28.46/5.33 (sP9 = $true) <=> ! [X352 : term,X353 : term > $o,X354 : subst > term > subst > $o] : (? [X366 : subst,X367 : subst,X368 : term,X369 : subst] : (((X354 @ X366 @ X368 @ (comp @ X369 @ X367)) = $true) & ((X354 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) != $true)) | ? [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (((X354 @ (comp @ X358 @ X360) @ (sub @ X359 @ X360) @ X357) = $true) & ((X354 @ X358 @ X359 @ (comp @ X360 @ X357)) != $true)) | ? [X355 : term] : (((X353 @ (sub @ X352 @ (push @ X355 @ id))) != $true) & ((X353 @ X355) = $true)) | ((sP8 @ X354) = $true) | ? [X356 : term] : ((X354 @ id @ X356 @ id) != (X353 @ X356)) | ((X353 @ (lam @ X352)) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f24,plain,(
% 28.46/5.33 ! [X440 : term > $o] : (((sP10 @ X440) = $true) <=> ? [X441 : term,X442 : term] : (((X440 @ X442) = $true) & ((X440 @ X441) = $true) & ((X440 @ (ap @ X441 @ X442)) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f25,plain,(
% 28.46/5.33 ! [X200 : subst > term > subst > $o] : (((sP11 @ X200) = $true) <=> ! [X206 : subst > term > term] : (? [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) != $true) & ((X200 @ id @ X207 @ id) = $true)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ? [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) != (sub @ (X206 @ X210 @ X208) @ X209))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f26,plain,(
% 28.46/5.33 ! [X188 : subst > term > subst > $o] : (((sP12 @ X188) = $true) <=> ! [X189 : term,X190 : term] : (((X188 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id) = $true) | ((X188 @ id @ X190 @ id) != $true) | ((X188 @ id @ X189 @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f27,plain,(
% 28.46/5.33 ! [X215 : subst > term > subst > $o] : (((sP13 @ X215) = $true) <=> ? [X231 : term,X232 : term] : (((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) != $true) & ((X215 @ id @ X232 @ id) = $true) & ((X215 @ id @ X231 @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f28,plain,(
% 28.46/5.33 ! [X215 : subst > term > subst > $o] : (((sP14 @ X215) = $true) <=> ? [X218 : subst > term > term] : (((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id) != $true) & ! [X222 : term] : (((X215 @ id @ X222 @ id) != $true) | ((X215 @ id @ (X218 @ id @ X222) @ id) = $true)) & ! [X219 : term,X220 : subst,X221 : subst] : ((X218 @ (comp @ X220 @ X221) @ (sub @ X219 @ X221)) = (sub @ (X218 @ X220 @ X219) @ X221))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f29,plain,(
% 28.46/5.33 ! [X179 : term > $o] : (((sP15 @ X179) = $true) <=> ! [X183 : term,X184 : term] : (((X179 @ X184) != $true) | ((X179 @ (ap @ X184 @ X183)) = $true) | ($true != (X179 @ X183))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f30,plain,(
% 28.46/5.33 (sP16 = $true) <=> ? [X199 : term,X200 : subst > term > subst > $o] : (! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (((X200 @ (comp @ X213 @ X214) @ (sub @ X212 @ X214) @ X211) != $true) | ((X200 @ X213 @ X212 @ (comp @ X214 @ X211)) = $true)) & ! [X201 : subst,X202 : subst,X203 : subst,X204 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X204 @ X202) @ X203) = $true) | ((X200 @ X201 @ X204 @ (comp @ X202 @ X203)) != $true)) & ! [X205 : term] : (((X200 @ id @ X205 @ id) != $true) | ((X200 @ id @ (sub @ X199 @ (push @ X205 @ id)) @ id) = $true)) & ((X200 @ id @ (lam @ X199) @ id) != $true) & ((sP11 @ X200) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f31,plain,(
% 28.46/5.33 (sP17 = $true) <=> ! [X215 : subst > term > subst > $o,X216 : term] : (? [X217 : term] : (((var @ (sub @ X217 @ id)) = $true) & ((X215 @ id @ X217 @ id) != $true)) | ? [X227 : subst,X228 : subst,X229 : subst,X230 : term] : (((X215 @ X229 @ X230 @ (comp @ X228 @ X227)) = $true) & ((X215 @ (comp @ X229 @ X228) @ (sub @ X230 @ X228) @ X227) != $true)) | ? [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (((X215 @ X225 @ X223 @ (comp @ X226 @ X224)) != $true) & ((X215 @ (comp @ X225 @ X226) @ (sub @ X223 @ X226) @ X224) = $true)) | ((sP14 @ X215) = $true) | ((X215 @ id @ X216 @ id) = $true) | ((sP13 @ X215) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f32,plain,(
% 28.46/5.33 (sP18 = $true) <=> ? [X186 : term,X187 : term,X188 : subst > term > subst > $o] : (! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : (((X188 @ (comp @ X194 @ X193) @ (sub @ X191 @ X193) @ X192) != $true) | ((X188 @ X194 @ X191 @ (comp @ X193 @ X192)) = $true)) & ((X188 @ id @ X187 @ id) = $true) & ((sP12 @ X188) = $true) & ($true != (X188 @ id @ (ap @ X186 @ X187) @ id)) & ((X188 @ id @ X186 @ id) = $true) & ! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (((X188 @ (comp @ X197 @ X198) @ (sub @ X195 @ X198) @ X196) = $true) | ((X188 @ X197 @ X195 @ (comp @ X198 @ X196)) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f33,plain,(
% 28.46/5.33 (sP19 = $true) <=> (? [X179 : term > $o,X180 : term] : (((sP15 @ X179) = $true) & ! [X181 : term] : (? [X182 : term] : (((X179 @ (sub @ X181 @ (push @ X182 @ id))) != $true) & ((X179 @ X182) = $true)) | ((X179 @ (lam @ X181)) = $true)) & ((X179 @ X180) != $true) & ! [X185 : term] : (((X179 @ X185) = $true) | ((var @ X185) != $true))) | (sP17 = $true) | (sP18 = $true) | (sP16 = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f34,plain,(
% 28.46/5.33 ! [X1 : subst > term > subst > $o] : (((sP20 @ X1) = $true) <=> ? [X2 : term,X3 : term] : (((X1 @ id @ X3 @ id) = $true) & ((X1 @ id @ X2 @ id) = $true) & ((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f35,plain,(
% 28.46/5.33 ! [X12 : subst > term > subst > $o] : (((sP21 @ X12) = $true) <=> ? [X22 : term,X23 : term] : (($true = (X12 @ id @ X23 @ id)) & ((X12 @ id @ (ap @ (sub @ X23 @ id) @ X22) @ id) != $true) & ($true = (X12 @ id @ X22 @ id))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f36,plain,(
% 28.46/5.33 (sP22 = $true) <=> ! [X9 : term,X10 : term > $o,X11 : term,X12 : subst > term > subst > $o] : (((X10 @ (ap @ X11 @ X9)) = $true) | ? [X14 : subst,X15 : subst,X16 : subst,X17 : term] : (((X12 @ X15 @ X17 @ (comp @ X16 @ X14)) != $true) & ((X12 @ (comp @ X15 @ X16) @ (sub @ X17 @ X16) @ X14) = $true)) | ((X10 @ X9) != $true) | ? [X13 : term] : ((X10 @ X13) != (X12 @ id @ X13 @ id)) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : (((X12 @ X20 @ X19 @ (comp @ X18 @ X21)) = $true) & ((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21) != $true)) | ((X10 @ X11) != $true) | ((sP21 @ X12) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f37,plain,(
% 28.46/5.33 ! [X286 : subst > term > subst > $o] : (((sP23 @ X286) = $true) <=> ? [X287 : subst > term > term] : (((X286 @ id @ (lam @ (X287 @ sh @ one)) @ id) != $true) & ! [X291 : term] : (((X286 @ id @ X291 @ id) != $true) | ((X286 @ id @ (X287 @ id @ X291) @ id) = $true)) & ! [X288 : subst,X289 : term,X290 : subst] : ((sub @ (X287 @ X288 @ X289) @ X290) = (X287 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f38,plain,(
% 28.46/5.33 ! [X267 : term > $o] : (((sP24 @ X267) = $true) <=> ! [X269 : term,X270 : term] : (($true != (X267 @ X269)) | ((X267 @ (ap @ X270 @ X269)) = $true) | ((X267 @ X270) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f39,plain,(
% 28.46/5.33 ($true = sP25) <=> ? [X275 : subst > term > subst > $o,X276 : term,X277 : term > $o] : (! [X278 : subst > term > term] : (((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id) = $true) | ? [X280 : term,X281 : subst,X282 : subst] : ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)) != (sub @ (X278 @ X282 @ X280) @ X281)) | ? [X279 : term] : (((X275 @ id @ (X278 @ id @ X279) @ id) != $true) & ((X275 @ id @ X279 @ id) = $true))) & ((X277 @ (lam @ X276)) != $true) & ! [X284 : term] : (((X277 @ X284) != $true) | ((X277 @ (sub @ X276 @ (push @ X284 @ id))) = $true)) & ! [X283 : term] : ((X277 @ X283) = (X275 @ id @ X283 @ id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f40,plain,(
% 28.46/5.33 ($true = sP26) <=> ? [X267 : term > $o,X268 : term] : (! [X272 : term] : (? [X273 : term] : (((X267 @ (sub @ X272 @ (push @ X273 @ id))) != $true) & ($true = (X267 @ X273))) | ((X267 @ (lam @ X272)) = $true)) & ((sP24 @ X267) = $true) & ((X267 @ X268) != $true) & ! [X271 : term] : (((var @ X271) != $true) | ($true = (X267 @ X271))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f41,plain,(
% 28.46/5.33 (sP27 = $true) <=> (($true = sP26) | ! [X285 : term,X286 : subst > term > subst > $o] : (? [X292 : term,X293 : term] : (($true = (X286 @ id @ X293 @ id)) & ((X286 @ id @ X292 @ id) = $true) & ((X286 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id) != $true)) | ((X286 @ id @ X285 @ id) = $true) | ((sP23 @ X286) = $true)) | ($true = sP25) | ? [X274 : term] : ((sub @ X274 @ id) != X274) | ? [X264 : subst > term > subst > $o] : ! [X265 : term > $o] : ? [X266 : term] : ((X265 @ X266) != (X264 @ id @ X266 @ id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f42,plain,(
% 28.46/5.33 (sP28 = $true) <=> (? [X382 : term] : ((sub @ X382 @ id) != X382) | ! [X383 : term,X384 : term > $o,X385 : subst > term > subst > $o] : (? [X387 : subst > term > term] : (! [X389 : subst,X390 : subst,X391 : term] : ((X387 @ (comp @ X390 @ X389) @ (sub @ X391 @ X389)) = (sub @ (X387 @ X390 @ X391) @ X389)) & ((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id) != $true) & ! [X388 : term] : (((X385 @ id @ X388 @ id) != $true) | ((X385 @ id @ (X387 @ id @ X388) @ id) = $true))) | ? [X386 : term] : ((X384 @ X386) != (X385 @ id @ X386 @ id)) | ? [X392 : term] : (((X384 @ (sub @ X383 @ (push @ X392 @ id))) != $true) & ((X384 @ X392) = $true)) | ((X384 @ (lam @ X383)) = $true)) | ? [X378 : term] : ! [X379 : subst > term > term] : ? [X380 : term,X381 : subst] : ((X379 @ X381 @ X380) != (sub @ X378 @ (push @ X380 @ X381))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f43,plain,(
% 28.46/5.33 ! [X35 : term > $o] : (((sP29 @ X35) = $true) <=> ? [X38 : term,X39 : term] : (($true = (X35 @ X39)) & ((X35 @ (ap @ X39 @ X38)) != $true) & ((X35 @ X38) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f44,plain,(
% 28.46/5.33 ! [X26 : term > $o] : (((sP30 @ X26) = $true) <=> ! [X29 : term,X30 : term] : (((X26 @ X29) != $true) | ((X26 @ X30) != $true) | ((X26 @ (ap @ X29 @ X30)) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f45,plain,(
% 28.46/5.33 (sP31 = $true) <=> ! [X34 : term,X35 : term > $o] : (((sP29 @ X35) = $true) | ($true = (X35 @ X34)) | ? [X36 : term] : (! [X37 : term] : (($true = (X35 @ (sub @ X36 @ (push @ X37 @ id)))) | ((X35 @ X37) != $true)) & ((X35 @ (lam @ X36)) != $true)) | ? [X40 : term] : (((var @ X40) = $true) & ((X35 @ X40) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f46,plain,(
% 28.46/5.33 (sP32 = $true) <=> (? [X26 : term > $o,X27 : term,X28 : subst] : (! [X31 : term] : (? [X32 : term] : (((X26 @ (sub @ X31 @ (push @ X32 @ id))) != $true) & ((X26 @ X32) = $true)) | ((X26 @ (lam @ X31)) = $true)) & ((sP30 @ X26) = $true) & ((X26 @ (sub @ X27 @ X28)) != $true) & ! [X33 : term] : (((var @ X33) != $true) | ((X26 @ (sub @ X33 @ X28)) = $true))) | (sP31 = $true) | ? [X25 : term] : ((sub @ X25 @ id) != X25))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f47,plain,(
% 28.46/5.33 ! [X510 : subst > term > subst > $o] : (((sP33 @ X510) = $true) <=> ? [X521 : subst > term > term] : (! [X522 : term,X523 : subst,X524 : subst] : ((sub @ (X521 @ X523 @ X522) @ X524) = (X521 @ (comp @ X523 @ X524) @ (sub @ X522 @ X524))) & ((X510 @ id @ (lam @ (X521 @ sh @ one)) @ id) != $true) & ! [X525 : term] : (((X510 @ id @ X525 @ id) != $true) | ((X510 @ id @ (X521 @ id @ X525) @ id) = $true))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f48,plain,(
% 28.46/5.33 (sP34 = $true) <=> (! [X509 : term > $o,X510 : subst > term > subst > $o,X511 : term] : (? [X526 : term] : (($true != (X509 @ (sub @ X511 @ (push @ X526 @ id)))) & ((X509 @ X526) = $true)) | ((X509 @ (lam @ X511)) = $true) | ? [X520 : term] : ((X509 @ X520) != (X510 @ id @ X520 @ id)) | ? [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (((X510 @ X513 @ X512 @ (comp @ X514 @ X515)) = $true) & ((X510 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515) != $true)) | ? [X516 : subst,X517 : term,X518 : subst,X519 : subst] : (((X510 @ X516 @ X517 @ (comp @ X518 @ X519)) != $true) & ((X510 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518) @ X519) = $true)) | ((sP33 @ X510) = $true)) | ? [X508 : term] : ((sub @ X508 @ id) != X508))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f49,plain,(
% 28.46/5.33 (sP35 = $true) <=> ! [X393 : term,X394 : subst > term > subst > $o] : (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id) = $true) | ? [X400 : term] : (((X394 @ id @ (sub @ X393 @ (push @ X400 @ id)) @ id) != $true) & ((X394 @ id @ X400 @ id) = $true)) | ? [X395 : subst > term > term] : (! [X397 : term,X398 : subst,X399 : subst] : ((X395 @ (comp @ X398 @ X399) @ (sub @ X397 @ X399)) = (sub @ (X395 @ X398 @ X397) @ X399)) & ! [X396 : term] : (((X394 @ id @ X396 @ id) != $true) | ((X394 @ id @ (X395 @ id @ X396) @ id) = $true)) & ((X394 @ id @ (lam @ (X395 @ sh @ one)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f50,plain,(
% 28.46/5.33 ! [X150 : subst > term > subst > $o] : (((sP36 @ X150) = $true) <=> ? [X152 : term,X153 : term] : (((X150 @ id @ (ap @ (sub @ X152 @ id) @ X153) @ id) != $true) & ((X150 @ id @ X153 @ id) = $true) & ((X150 @ id @ X152 @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f51,plain,(
% 28.46/5.33 ! [X150 : subst > term > subst > $o] : (((sP37 @ X150) = $true) <=> ? [X159 : subst > term > term] : (! [X163 : term] : (($true != (X150 @ id @ X163 @ id)) | ((X150 @ id @ (X159 @ id @ X163) @ id) = $true)) & ! [X160 : term,X161 : subst,X162 : subst] : ((sub @ (X159 @ X162 @ X160) @ X161) = (X159 @ (comp @ X162 @ X161) @ (sub @ X160 @ X161))) & ((X150 @ id @ (lam @ (X159 @ sh @ one)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f52,plain,(
% 28.46/5.33 ! [X132 : term > $o] : (((sP38 @ X132) = $true) <=> ! [X135 : term,X136 : term] : (((X132 @ X135) != $true) | ((X132 @ (ap @ X135 @ X136)) = $true) | ((X132 @ X136) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f53,plain,(
% 28.46/5.33 (sP39 = $true) <=> ? [X140 : term > $o,X141 : term,X142 : subst > term > subst > $o] : (! [X143 : subst > term > term] : (($true = (X142 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ? [X144 : term] : (((X142 @ id @ (X143 @ id @ X144) @ id) != $true) & ((X142 @ id @ X144 @ id) = $true)) | ? [X145 : subst,X146 : term,X147 : subst] : ((X143 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145)) != (sub @ (X143 @ X147 @ X146) @ X145))) & ((X140 @ (lam @ X141)) != $true) & ! [X149 : term] : (((X140 @ (sub @ X141 @ (push @ X149 @ id))) = $true) | ((X140 @ X149) != $true)) & ! [X148 : term] : ((X140 @ X148) = (X142 @ id @ X148 @ id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f54,plain,(
% 28.46/5.33 ($true = sP40) <=> ! [X150 : subst > term > subst > $o,X151 : term] : (? [X154 : term] : (((var @ (sub @ X154 @ id)) = $true) & ((X150 @ id @ X154 @ id) != $true)) | ? [X164 : subst,X165 : subst,X166 : subst,X167 : term] : (((X150 @ (comp @ X166 @ X165) @ (sub @ X167 @ X165) @ X164) != $true) & ((X150 @ X166 @ X167 @ (comp @ X165 @ X164)) = $true)) | ((sP37 @ X150) = $true) | ? [X155 : subst,X156 : term,X157 : subst,X158 : subst] : (((X150 @ (comp @ X158 @ X155) @ (sub @ X156 @ X155) @ X157) = $true) & ((X150 @ X158 @ X156 @ (comp @ X155 @ X157)) != $true)) | ((sP36 @ X150) = $true) | ((X150 @ id @ X151 @ id) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f55,plain,(
% 28.46/5.33 (sP41 = $true) <=> (? [X132 : term > $o,X133 : term] : (((sP38 @ X132) = $true) & ! [X137 : term] : (((X132 @ (lam @ X137)) = $true) | ? [X138 : term] : (((X132 @ (sub @ X137 @ (push @ X138 @ id))) != $true) & ((X132 @ X138) = $true))) & ! [X134 : term] : (($true = (X132 @ X134)) | ((var @ X134) != $true)) & ((X132 @ X133) != $true)) | ($true = sP40) | ? [X139 : term] : ((sub @ X139 @ id) != X139) | (sP39 = $true) | ? [X129 : subst > term > subst > $o] : ! [X130 : term > $o] : ? [X131 : term] : ((X130 @ X131) != (X129 @ id @ X131 @ id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f56,plain,(
% 28.46/5.33 ! [X120 : term > $o] : (((sP42 @ X120) = $true) <=> ? [X123 : term,X124 : term] : (((X120 @ (ap @ X123 @ X124)) != $true) & ((X120 @ X124) = $true) & ((X120 @ X123) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f57,plain,(
% 28.46/5.33 (sP43 = $true) <=> ! [X120 : term > $o,X121 : term] : (? [X125 : term] : (((X120 @ (lam @ X125)) != $true) & ! [X126 : term] : (((X120 @ (sub @ X125 @ (push @ X126 @ id))) = $true) | ((X120 @ X126) != $true))) | ((sP42 @ X120) = $true) | ((X120 @ X121) = $true) | ? [X122 : term] : (((X120 @ X122) != $true) & ((var @ X122) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f58,plain,(
% 28.46/5.33 ! [X402 : term > $o] : (((sP44 @ X402) = $true) <=> ? [X407 : term,X408 : term] : (((X402 @ X407) = $true) & ((X402 @ X408) = $true) & ((X402 @ (ap @ X408 @ X407)) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f59,plain,(
% 28.46/5.33 (sP45 = $true) <=> ! [X401 : subst,X402 : term > $o,X403 : term] : (? [X404 : term] : (((X402 @ (lam @ X404)) != $true) & ! [X405 : term] : (((X402 @ X405) != $true) | ((X402 @ (sub @ X404 @ (push @ X405 @ id))) = $true))) | ((sP44 @ X402) = $true) | ((X402 @ (sub @ X403 @ X401)) = $true) | ? [X406 : term] : (((X402 @ (sub @ X406 @ X401)) != $true) & ((var @ X406) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f60,plain,(
% 28.46/5.33 ($true = sP46) <=> (? [X415 : subst,X416 : term] : ((comp @ sh @ (push @ X416 @ X415)) != X415) | ? [X413 : subst,X414 : term] : ((sub @ one @ (push @ X414 @ X413)) != X414) | ! [X419 : subst,X420 : subst > term > term,X421 : subst > term > term,X422 : term] : (? [X426 : subst,X427 : subst,X428 : term] : ((X421 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)) != (sub @ (X421 @ X426 @ X428) @ X427)) | ((lam @ (X420 @ sh @ one)) != (lam @ (X421 @ sh @ one))) | ? [X423 : term,X424 : subst,X425 : subst] : ((X420 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424)) != (sub @ (X420 @ X425 @ X423) @ X424)) | ((X420 @ X419 @ X422) = (X421 @ X419 @ X422))) | ? [X417 : term,X418 : term] : (((lam @ X418) = (lam @ X417)) & (X417 != X418)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f61,plain,(
% 28.46/5.33 ! [X346 : term > $o] : (((sP47 @ X346) = $true) <=> ? [X349 : term,X350 : term] : (((X346 @ X349) = $true) & ((X346 @ (ap @ X350 @ X349)) != $true) & ((X346 @ X350) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f62,plain,(
% 28.46/5.33 ! [X339 : term > $o] : (((sP48 @ X339) = $true) <=> ! [X342 : term,X343 : term] : (($true != (X339 @ X342)) | ((X339 @ (ap @ X343 @ X342)) = $true) | ((X339 @ X343) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f63,plain,(
% 28.46/5.33 (sP49 = $true) <=> ! [X344 : subst,X345 : term,X346 : term > $o] : (((sP47 @ X346) = $true) | ? [X351 : term] : (((var @ X351) = $true) & ($true != (X346 @ (sub @ X351 @ X344)))) | ? [X347 : term] : (! [X348 : term] : (((X346 @ (sub @ X347 @ (push @ X348 @ id))) = $true) | ((X346 @ X348) != $true)) & ((X346 @ (lam @ X347)) != $true)) | ((X346 @ (sub @ X345 @ X344)) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f64,plain,(
% 28.46/5.33 (sP50 = $true) <=> (? [X335 : subst,X336 : term] : ((comp @ sh @ (push @ X336 @ X335)) != X335) | ? [X337 : subst] : ((comp @ X337 @ id) != X337) | ? [X333 : term,X334 : subst] : ((sub @ one @ (push @ X333 @ X334)) != X333) | ? [X338 : term,X339 : term > $o] : (((sP48 @ X339) = $true) & ($true != (X339 @ X338)) & ! [X341 : term] : (((X339 @ X341) != $true) | ($true = (X339 @ (lam @ X341)))) & ! [X340 : term] : (((X339 @ X340) = $true) | ((var @ X340) != $true))) | (sP49 = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f65,plain,(
% 28.46/5.33 ! [X457 : subst > term > subst > $o] : (($true = (sP51 @ X457)) <=> ? [X460 : term,X461 : term] : (($true = (X457 @ id @ X460 @ id)) & ((X457 @ id @ X461 @ id) = $true) & ((X457 @ id @ (ap @ (sub @ X461 @ id) @ X460) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f66,plain,(
% 28.46/5.33 (sP52 = $true) <=> ! [X457 : subst > term > subst > $o,X458 : term,X459 : term] : (($true = (sP51 @ X457)) | ((X457 @ id @ X458 @ id) != $true) | ((X457 @ id @ X459 @ id) != $true) | ? [X466 : subst,X467 : term,X468 : subst,X469 : subst] : (((X457 @ X469 @ X467 @ (comp @ X468 @ X466)) = $true) & ((X457 @ (comp @ X469 @ X468) @ (sub @ X467 @ X468) @ X466) != $true)) | ? [X462 : subst,X463 : subst,X464 : subst,X465 : term] : (((X457 @ (comp @ X463 @ X462) @ (sub @ X465 @ X462) @ X464) = $true) & ($true != (X457 @ X463 @ X465 @ (comp @ X462 @ X464)))) | ((X457 @ id @ (ap @ X458 @ X459) @ id) = $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f67,plain,(
% 28.46/5.33 (sP53 = $true) <=> ! [X489 : subst > term > subst > $o,X490 : term] : (? [X492 : term,X493 : subst > term > term] : (((X489 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X497 : subst,X498 : term,X499 : subst] : ((sub @ (X493 @ X499 @ X498) @ X497) = (sub @ (sub @ X492 @ (push @ X498 @ X499)) @ X497)) & ! [X494 : subst,X495 : term,X496 : subst] : ((X493 @ (comp @ X496 @ X494) @ (sub @ X495 @ X494)) = (sub @ X492 @ (push @ (sub @ X495 @ X494) @ (comp @ X496 @ X494)))) & ! [X500 : term] : (((X489 @ id @ X500 @ id) != $true) | ((X489 @ id @ (X493 @ id @ X500) @ id) = $true))) | ((X489 @ id @ (lam @ (sub @ X490 @ (push @ one @ sh))) @ id) = $true) | ? [X491 : term] : (((X489 @ id @ X491 @ id) = $true) & ((X489 @ id @ (sub @ X490 @ (push @ X491 @ id)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f68,plain,(
% 28.46/5.33 ! [X105 : subst > term > subst > $o] : (($true = (sP54 @ X105)) <=> ? [X115 : subst > term > term] : (! [X116 : term] : (((X105 @ id @ (X115 @ id @ X116) @ id) = $true) | ((X105 @ id @ X116 @ id) != $true)) & ((X105 @ id @ (lam @ (X115 @ sh @ one)) @ id) != $true) & ! [X117 : subst,X118 : subst,X119 : term] : ((X115 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118)) = (sub @ (X115 @ X117 @ X119) @ X118))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f69,plain,(
% 28.46/5.33 (sP55 = $true) <=> ? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true) | ((X97 @ id @ X103 @ id) != $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ((X97 @ id @ (lam @ (X98 @ sh @ one)) @ id) = $true) | ? [X99 : term,X100 : subst,X101 : subst] : ((sub @ (X98 @ X101 @ X99) @ X100) != (X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)))) & ((X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id) != $true))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f70,plain,(
% 28.46/5.33 ($true = sP56) <=> ((sP55 = $true) | ? [X95 : term] : ((sub @ X95 @ id) != X95) | ! [X104 : term,X105 : subst > term > subst > $o] : (? [X114 : term] : (((X105 @ id @ X114 @ id) = $true) & ((X105 @ id @ (sub @ X104 @ (push @ X114 @ id)) @ id) != $true)) | ? [X110 : term,X111 : subst,X112 : subst,X113 : subst] : (((X105 @ X112 @ X110 @ (comp @ X113 @ X111)) = $true) & ($true != (X105 @ (comp @ X112 @ X113) @ (sub @ X110 @ X113) @ X111))) | ? [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (((X105 @ X109 @ X107 @ (comp @ X108 @ X106)) != $true) & ((X105 @ (comp @ X109 @ X108) @ (sub @ X107 @ X108) @ X106) = $true)) | ($true = (sP54 @ X105)) | ((X105 @ id @ (lam @ X104) @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f71,plain,(
% 28.46/5.33 (sP57 = $true) <=> ? [X44 : subst > term > subst > $o,X45 : term] : (! [X46 : subst > term > term] : (((X44 @ id @ (lam @ (X46 @ sh @ one)) @ id) = $true) | ? [X47 : term] : (((X44 @ id @ X47 @ id) = $true) & ($true != (X44 @ id @ (X46 @ id @ X47) @ id))) | ? [X48 : subst,X49 : term,X50 : subst] : ((X46 @ (comp @ X50 @ X48) @ (sub @ X49 @ X48)) != (sub @ (X46 @ X50 @ X49) @ X48))) & ((X44 @ id @ (lam @ (sub @ X45 @ (push @ one @ sh))) @ id) != $true) & ! [X51 : term] : (((X44 @ id @ X51 @ id) != $true) | ((X44 @ id @ (sub @ X45 @ (push @ X51 @ id)) @ id) = $true)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f72,plain,(
% 28.46/5.33 (sP58 = $true) <=> (? [X43 : term] : ((sub @ X43 @ id) != X43) | (sP57 = $true) | ! [X52 : term,X53 : subst > term > subst > $o] : (? [X59 : term] : (($true = (X53 @ id @ X59 @ id)) & ((X53 @ id @ (sub @ X52 @ (push @ X59 @ id)) @ id) != $true)) | ((X53 @ id @ (lam @ X52) @ id) = $true) | ? [X54 : subst > term > term] : (! [X55 : term] : (($true != (X53 @ id @ X55 @ id)) | ((X53 @ id @ (X54 @ id @ X55) @ id) = $true)) & ! [X56 : subst,X57 : subst,X58 : term] : ((X54 @ (comp @ X57 @ X56) @ (sub @ X58 @ X56)) = (sub @ (X54 @ X57 @ X58) @ X56)) & ((X53 @ id @ (lam @ (X54 @ sh @ one)) @ id) != $true))))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 28.46/5.33 thf(f13,plain,(
% 28.46/5.33 (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & ((? [X43 : term] : ((sub @ X43 @ id) != X43) | ? [X44 : subst > term > subst > $o,X45 : term] : (! [X46 : subst > term > term] : (((X44 @ id @ (lam @ (X46 @ sh @ one)) @ id) = $true) | ? [X47 : term] : (((X44 @ id @ X47 @ id) = $true) & ($true != (X44 @ id @ (X46 @ id @ X47) @ id))) | ? [X48 : subst,X49 : term,X50 : subst] : ((X46 @ (comp @ X50 @ X48) @ (sub @ X49 @ X48)) != (sub @ (X46 @ X50 @ X49) @ X48))) & ((X44 @ id @ (lam @ (sub @ X45 @ (push @ one @ sh))) @ id) != $true) & ! [X51 : term] : (((X44 @ id @ X51 @ id) != $true) | ((X44 @ id @ (sub @ X45 @ (push @ X51 @ id)) @ id) = $true))) | ! [X52 : term,X53 : subst > term > subst > $o] : (? [X59 : term] : (($true = (X53 @ id @ X59 @ id)) & ((X53 @ id @ (sub @ X52 @ (push @ X59 @ id)) @ id) != $true)) | ((X53 @ id @ (lam @ X52) @ id) = $true) | ? [X54 : subst > term > term] : (! [X55 : term] : (($true != (X53 @ id @ X55 @ id)) | ((X53 @ id @ (X54 @ id @ X55) @ id) = $true)) & ! [X56 : subst,X57 : subst,X58 : term] : ((X54 @ (comp @ X57 @ X56) @ (sub @ X58 @ X56)) = (sub @ (X54 @ X57 @ X58) @ X56)) & ((X53 @ id @ (lam @ (X54 @ sh @ one)) @ id) != $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)))) & ((axscons = $true) <=> ! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24)) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) <=> (laminj = $true)) & ((d2subst @ d_id) = sh) & (! [X178 : term] : ((sub @ X178 @ id) = X178) <=> (axvarid = $true)) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530)) & ! [X529 : d_subst] : (d_id = X529) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94)))) & ((substmonoid = $true) <=> (! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41))) & ((? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true) | ((X97 @ id @ X103 @ id) != $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ((X97 @ id @ (lam @ (X98 @ sh @ one)) @ id) = $true) | ? [X99 : term,X100 : subst,X101 : subst] : ((sub @ (X98 @ X101 @ X99) @ X100) != (X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)))) & ((X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id) != $true)) | ? [X95 : term] : ((sub @ X95 @ id) != X95) | ! [X104 : term,X105 : subst > term > subst > $o] : (? [X114 : term] : (((X105 @ id @ X114 @ id) = $true) & ((X105 @ id @ (sub @ X104 @ (push @ X114 @ id)) @ id) != $true)) | ? [X110 : term,X111 : subst,X112 : subst,X113 : subst] : (((X105 @ X112 @ X110 @ (comp @ X113 @ X111)) = $true) & ($true != (X105 @ (comp @ X112 @ X113) @ (sub @ X110 @ X113) @ X111))) | ? [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (((X105 @ X109 @ X107 @ (comp @ X108 @ X106)) != $true) & ((X105 @ (comp @ X109 @ X108) @ (sub @ X107 @ X108) @ X106) = $true)) | ? [X115 : subst > term > term] : (! [X116 : term] : (((X105 @ id @ (X115 @ id @ X116) @ id) = $true) | ((X105 @ id @ X116 @ id) != $true)) & ((X105 @ id @ (lam @ (X115 @ sh @ one)) @ id) != $true) & ! [X117 : subst,X118 : subst,X119 : term] : ((X115 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118)) = (sub @ (X115 @ X117 @ X119) @ X118))) | ((X105 @ id @ (lam @ X104) @ id) = $true))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & ((? [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) != X303) | ? [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) != X300) | ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true))) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (? [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) != (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) | ((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one)))) <=> (hoaslamnotap = $true)) & (lamnotvar = $true) & (ulamvarind = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X489 : subst > term > subst > $o,X490 : term] : (? [X492 : term,X493 : subst > term > term] : (((X489 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X497 : subst,X498 : term,X499 : subst] : ((sub @ (X493 @ X499 @ X498) @ X497) = (sub @ (sub @ X492 @ (push @ X498 @ X499)) @ X497)) & ! [X494 : subst,X495 : term,X496 : subst] : ((X493 @ (comp @ X496 @ X494) @ (sub @ X495 @ X494)) = (sub @ X492 @ (push @ (sub @ X495 @ X494) @ (comp @ X496 @ X494)))) & ! [X500 : term] : (((X489 @ id @ X500 @ id) != $true) | ((X489 @ id @ (X493 @ id @ X500) @ id) = $true))) | ((X489 @ id @ (lam @ (sub @ X490 @ (push @ one @ sh))) @ id) = $true) | ? [X491 : term] : (((X489 @ id @ X491 @ id) = $true) & ((X489 @ id @ (sub @ X490 @ (push @ X491 @ id)) @ id) != $true)))) & (pushprop_lem3v2_lthm = $true) & (! [X457 : subst > term > subst > $o,X458 : term,X459 : term] : (? [X460 : term,X461 : term] : (($true = (X457 @ id @ X460 @ id)) & ((X457 @ id @ X461 @ id) = $true) & ((X457 @ id @ (ap @ (sub @ X461 @ id) @ X460) @ id) != $true)) | ((X457 @ id @ X458 @ id) != $true) | ((X457 @ id @ X459 @ id) != $true) | ? [X466 : subst,X467 : term,X468 : subst,X469 : subst] : (((X457 @ X469 @ X467 @ (comp @ X468 @ X466)) = $true) & ((X457 @ (comp @ X469 @ X468) @ (sub @ X467 @ X468) @ X466) != $true)) | ? [X462 : subst,X463 : subst,X464 : subst,X465 : term] : (((X457 @ (comp @ X463 @ X462) @ (sub @ X465 @ X462) @ X464) = $true) & ($true != (X457 @ X463 @ X465 @ (comp @ X462 @ X464)))) | ((X457 @ id @ (ap @ X458 @ X459) @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_gthm = $true) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) != (d2subst @ X471)) | (X470 = X471)) & (pushprop_lem3v2 = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_lthm = $true) & ((var @ (d2term @ d_one)) != $true) & ((induction2lem_lthm = $true) <=> (? [X335 : subst,X336 : term] : ((comp @ sh @ (push @ X336 @ X335)) != X335) | ? [X337 : subst] : ((comp @ X337 @ id) != X337) | ? [X333 : term,X334 : subst] : ((sub @ one @ (push @ X333 @ X334)) != X333) | ? [X338 : term,X339 : term > $o] : (! [X342 : term,X343 : term] : (($true != (X339 @ X342)) | ((X339 @ (ap @ X343 @ X342)) = $true) | ((X339 @ X343) != $true)) & ($true != (X339 @ X338)) & ! [X341 : term] : (((X339 @ X341) != $true) | ($true = (X339 @ (lam @ X341)))) & ! [X340 : term] : (((X339 @ X340) = $true) | ((var @ X340) != $true))) | ! [X344 : subst,X345 : term,X346 : term > $o] : (? [X349 : term,X350 : term] : (((X346 @ X349) = $true) & ((X346 @ (ap @ X350 @ X349)) != $true) & ((X346 @ X350) = $true)) | ? [X351 : term] : (((var @ X351) = $true) & ($true != (X346 @ (sub @ X351 @ X344)))) | ? [X347 : term] : (! [X348 : term] : (((X346 @ (sub @ X347 @ (push @ X348 @ id))) = $true) | ((X346 @ X348) != $true)) & ((X346 @ (lam @ X347)) != $true)) | ((X346 @ (sub @ X345 @ X344)) = $true)))) & (hoaslamnotvar = $true) & ((? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X533) & ((ap @ X535 @ X532) = (ap @ X534 @ X533))) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536)))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset_lthm = $true) <=> (? [X298 : term] : ((sub @ X298 @ id) != X298) | ! [X299 : term] : ((sub @ X299 @ id) = X299))) & (hoasinduction_lem3a_gthm = $true) & ((? [X415 : subst,X416 : term] : ((comp @ sh @ (push @ X416 @ X415)) != X415) | ? [X413 : subst,X414 : term] : ((sub @ one @ (push @ X414 @ X413)) != X414) | ! [X419 : subst,X420 : subst > term > term,X421 : subst > term > term,X422 : term] : (? [X426 : subst,X427 : subst,X428 : term] : ((X421 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)) != (sub @ (X421 @ X426 @ X428) @ X427)) | ((lam @ (X420 @ sh @ one)) != (lam @ (X421 @ sh @ one))) | ? [X423 : term,X424 : subst,X425 : subst] : ((X420 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424)) != (sub @ (X420 @ X425 @ X423) @ X424)) | ((X420 @ X419 @ X422) = (X421 @ X419 @ X422))) | ? [X417 : term,X418 : term] : (((lam @ X418) = (lam @ X417)) & (X417 != X418))) <=> (hoaslaminj_lthm = $true)) & (! [X429 : term] : ? [X430 : subst > term > term] : ((X430 @ sh @ one) = (sub @ X429 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> ! [X401 : subst,X402 : term > $o,X403 : term] : (? [X404 : term] : (((X402 @ (lam @ X404)) != $true) & ! [X405 : term] : (((X402 @ X405) != $true) | ((X402 @ (sub @ X404 @ (push @ X405 @ id))) = $true))) | ? [X407 : term,X408 : term] : (((X402 @ X407) = $true) & ((X402 @ X408) = $true) & ((X402 @ (ap @ X408 @ X407)) != $true)) | ((X402 @ (sub @ X403 @ X401)) = $true) | ? [X406 : term] : (((X402 @ (sub @ X406 @ X401)) != $true) & ((var @ X406) = $true)))) & (! [X329 : term] : ? [X330 : subst > term > term] : ! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true = (X505 @ one)) | ? [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) != (X505 @ X507)) | ($true != (X504 @ X503))) | ? [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) != X501)) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (axmap = $true) & (ulamvar1 != $true) & (! [X168 : subst > term > subst > $o] : ? [X169 : term > $o] : ! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) <=> (hoasinduction_lem0_lthm = $true)) & (! [X120 : term > $o,X121 : term] : (? [X125 : term] : (((X120 @ (lam @ X125)) != $true) & ! [X126 : term] : (((X120 @ (sub @ X125 @ (push @ X126 @ id))) = $true) | ((X120 @ X126) != $true))) | ? [X123 : term,X124 : term] : (((X120 @ (ap @ X123 @ X124)) != $true) & ((X120 @ X124) = $true) & ((X120 @ X123) = $true)) | ((X120 @ X121) = $true) | ? [X122 : term] : (((X120 @ X122) != $true) & ((var @ X122) = $true))) <=> (induction2 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (? [X132 : term > $o,X133 : term] : (! [X135 : term,X136 : term] : (((X132 @ X135) != $true) | ((X132 @ (ap @ X135 @ X136)) = $true) | ((X132 @ X136) != $true)) & ! [X137 : term] : (((X132 @ (lam @ X137)) = $true) | ? [X138 : term] : (((X132 @ (sub @ X137 @ (push @ X138 @ id))) != $true) & ((X132 @ X138) = $true))) & ! [X134 : term] : (($true = (X132 @ X134)) | ((var @ X134) != $true)) & ((X132 @ X133) != $true)) | ! [X150 : subst > term > subst > $o,X151 : term] : (? [X154 : term] : (((var @ (sub @ X154 @ id)) = $true) & ((X150 @ id @ X154 @ id) != $true)) | ? [X164 : subst,X165 : subst,X166 : subst,X167 : term] : (((X150 @ (comp @ X166 @ X165) @ (sub @ X167 @ X165) @ X164) != $true) & ((X150 @ X166 @ X167 @ (comp @ X165 @ X164)) = $true)) | ? [X159 : subst > term > term] : (! [X163 : term] : (($true != (X150 @ id @ X163 @ id)) | ((X150 @ id @ (X159 @ id @ X163) @ id) = $true)) & ! [X160 : term,X161 : subst,X162 : subst] : ((sub @ (X159 @ X162 @ X160) @ X161) = (X159 @ (comp @ X162 @ X161) @ (sub @ X160 @ X161))) & ((X150 @ id @ (lam @ (X159 @ sh @ one)) @ id) != $true)) | ? [X155 : subst,X156 : term,X157 : subst,X158 : subst] : (((X150 @ (comp @ X158 @ X155) @ (sub @ X156 @ X155) @ X157) = $true) & ((X150 @ X158 @ X156 @ (comp @ X155 @ X157)) != $true)) | ? [X152 : term,X153 : term] : (((X150 @ id @ (ap @ (sub @ X152 @ id) @ X153) @ id) != $true) & ((X150 @ id @ X153 @ id) = $true) & ((X150 @ id @ X152 @ id) = $true)) | ((X150 @ id @ X151 @ id) = $true)) | ? [X139 : term] : ((sub @ X139 @ id) != X139) | ? [X140 : term > $o,X141 : term,X142 : subst > term > subst > $o] : (! [X143 : subst > term > term] : (($true = (X142 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ? [X144 : term] : (((X142 @ id @ (X143 @ id @ X144) @ id) != $true) & ((X142 @ id @ X144 @ id) = $true)) | ? [X145 : subst,X146 : term,X147 : subst] : ((X143 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145)) != (sub @ (X143 @ X147 @ X146) @ X145))) & ((X140 @ (lam @ X141)) != $true) & ! [X149 : term] : (((X140 @ (sub @ X141 @ (push @ X149 @ id))) = $true) | ((X140 @ X149) != $true)) & ! [X148 : term] : ((X140 @ X148) = (X142 @ id @ X148 @ id))) | ? [X129 : subst > term > subst > $o] : ! [X130 : term > $o] : ? [X131 : term] : ((X130 @ X131) != (X129 @ id @ X131 @ id)))) & (! [X393 : term,X394 : subst > term > subst > $o] : (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id) = $true) | ? [X400 : term] : (((X394 @ id @ (sub @ X393 @ (push @ X400 @ id)) @ id) != $true) & ((X394 @ id @ X400 @ id) = $true)) | ? [X395 : subst > term > term] : (! [X397 : term,X398 : subst,X399 : subst] : ((X395 @ (comp @ X398 @ X399) @ (sub @ X397 @ X399)) = (sub @ (X395 @ X398 @ X397) @ X399)) & ! [X396 : term] : (((X394 @ id @ X396 @ id) != $true) | ((X394 @ id @ (X395 @ id @ X396) @ id) = $true)) & ((X394 @ id @ (lam @ (X395 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X509 : term > $o,X510 : subst > term > subst > $o,X511 : term] : (? [X526 : term] : (($true != (X509 @ (sub @ X511 @ (push @ X526 @ id)))) & ((X509 @ X526) = $true)) | ((X509 @ (lam @ X511)) = $true) | ? [X520 : term] : ((X509 @ X520) != (X510 @ id @ X520 @ id)) | ? [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (((X510 @ X513 @ X512 @ (comp @ X514 @ X515)) = $true) & ((X510 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515) != $true)) | ? [X516 : subst,X517 : term,X518 : subst,X519 : subst] : (((X510 @ X516 @ X517 @ (comp @ X518 @ X519)) != $true) & ((X510 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518) @ X519) = $true)) | ? [X521 : subst > term > term] : (! [X522 : term,X523 : subst,X524 : subst] : ((sub @ (X521 @ X523 @ X522) @ X524) = (X521 @ (comp @ X523 @ X524) @ (sub @ X522 @ X524))) & ((X510 @ id @ (lam @ (X521 @ sh @ one)) @ id) != $true) & ! [X525 : term] : (((X510 @ id @ X525 @ id) != $true) | ((X510 @ id @ (X521 @ id @ X525) @ id) = $true)))) | ? [X508 : term] : ((sub @ X508 @ id) != X508))) & (hoaslaminj_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axvarshift = $true) & (axassoc = $true) & ! [X486 : d_term] : (d_one = X486) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) <=> (apinj1 = $true)) & ((pushprop_lem0 = $true) <=> ! [X259 : term > $o,X260 : subst,X261 : term] : ? [X262 : term > $o] : ! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260))))) & ((axidl = $true) <=> ! [X257 : subst] : ((comp @ id @ X257) = X257)) & (one = (d2term @ d_one)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((? [X82 : subst] : ((comp @ id @ X82) != X82) | ? [X83 : subst] : ((comp @ X83 @ id) != X83) | (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84))) <=> (substmonoid_lthm = $true)) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ((X481 @ X484) != $true) | ? [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) != (X483 @ X485))) <=> (pushprop_lem1v2 = $true)) & (axapp = $true) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X327 : term] : ? [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) = (X328 @ sh @ one))) & (axabs = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176))) & ((induction2_lthm = $true) <=> (? [X26 : term > $o,X27 : term,X28 : subst] : (! [X31 : term] : (? [X32 : term] : (((X26 @ (sub @ X31 @ (push @ X32 @ id))) != $true) & ((X26 @ X32) = $true)) | ((X26 @ (lam @ X31)) = $true)) & ! [X29 : term,X30 : term] : (((X26 @ X29) != $true) | ((X26 @ X30) != $true) | ((X26 @ (ap @ X29 @ X30)) = $true)) & ((X26 @ (sub @ X27 @ X28)) != $true) & ! [X33 : term] : (((var @ X33) != $true) | ((X26 @ (sub @ X33 @ X28)) = $true))) | ! [X34 : term,X35 : term > $o] : (? [X38 : term,X39 : term] : (($true = (X35 @ X39)) & ((X35 @ (ap @ X39 @ X38)) != $true) & ((X35 @ X38) = $true)) | ($true = (X35 @ X34)) | ? [X36 : term] : (! [X37 : term] : (($true = (X35 @ (sub @ X36 @ (push @ X37 @ id)))) | ((X35 @ X37) != $true)) & ((X35 @ (lam @ X36)) != $true)) | ? [X40 : term] : (((var @ X40) = $true) & ((X35 @ X40) != $true))) | ? [X25 : term] : ((sub @ X25 @ id) != X25))) & ((d2subst @ d_id) = id) & (induction2lem_gthm = $true) & ((axvarcons = $true) <=> ! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))) | ? [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 != X476) & ((ap @ X476 @ X473) = (ap @ X474 @ X475))) | ? [X472 : term] : ((sub @ X472 @ id) != X472))) & ((pushprop_lem0_lthm = $true) <=> ! [X241 : subst,X242 : term,X243 : term > $o] : ? [X244 : term > $o] : ! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (hoasinduction_lem2_gthm = $true) & (substmonoid_gthm = $true) & ((? [X382 : term] : ((sub @ X382 @ id) != X382) | ! [X383 : term,X384 : term > $o,X385 : subst > term > subst > $o] : (? [X387 : subst > term > term] : (! [X389 : subst,X390 : subst,X391 : term] : ((X387 @ (comp @ X390 @ X389) @ (sub @ X391 @ X389)) = (sub @ (X387 @ X390 @ X391) @ X389)) & ((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id) != $true) & ! [X388 : term] : (((X385 @ id @ X388 @ id) != $true) | ((X385 @ id @ (X387 @ id @ X388) @ id) = $true))) | ? [X386 : term] : ((X384 @ X386) != (X385 @ id @ X386 @ id)) | ? [X392 : term] : (((X384 @ (sub @ X383 @ (push @ X392 @ id))) != $true) & ((X384 @ X392) = $true)) | ((X384 @ (lam @ X383)) = $true)) | ? [X378 : term] : ! [X379 : subst > term > term] : ? [X380 : term,X381 : subst] : ((X379 @ X381 @ X380) != (sub @ X378 @ (push @ X380 @ X381)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar = $true) & ((? [X267 : term > $o,X268 : term] : (! [X272 : term] : (? [X273 : term] : (((X267 @ (sub @ X272 @ (push @ X273 @ id))) != $true) & ($true = (X267 @ X273))) | ((X267 @ (lam @ X272)) = $true)) & ! [X269 : term,X270 : term] : (($true != (X267 @ X269)) | ((X267 @ (ap @ X270 @ X269)) = $true) | ((X267 @ X270) != $true)) & ((X267 @ X268) != $true) & ! [X271 : term] : (((var @ X271) != $true) | ($true = (X267 @ X271)))) | ! [X285 : term,X286 : subst > term > subst > $o] : (? [X292 : term,X293 : term] : (($true = (X286 @ id @ X293 @ id)) & ((X286 @ id @ X292 @ id) = $true) & ((X286 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id) != $true)) | ((X286 @ id @ X285 @ id) = $true) | ? [X287 : subst > term > term] : (((X286 @ id @ (lam @ (X287 @ sh @ one)) @ id) != $true) & ! [X291 : term] : (((X286 @ id @ X291 @ id) != $true) | ((X286 @ id @ (X287 @ id @ X291) @ id) = $true)) & ! [X288 : subst,X289 : term,X290 : subst] : ((sub @ (X287 @ X288 @ X289) @ X290) = (X287 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))) | ? [X275 : subst > term > subst > $o,X276 : term,X277 : term > $o] : (! [X278 : subst > term > term] : (((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id) = $true) | ? [X280 : term,X281 : subst,X282 : subst] : ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)) != (sub @ (X278 @ X282 @ X280) @ X281)) | ? [X279 : term] : (((X275 @ id @ (X278 @ id @ X279) @ id) != $true) & ((X275 @ id @ X279 @ id) = $true))) & ((X277 @ (lam @ X276)) != $true) & ! [X284 : term] : (((X277 @ X284) != $true) | ((X277 @ (sub @ X276 @ (push @ X284 @ id))) = $true)) & ! [X283 : term] : ((X277 @ X283) = (X275 @ id @ X283 @ id))) | ? [X274 : term] : ((sub @ X274 @ id) != X274) | ? [X264 : subst > term > subst > $o] : ! [X265 : term > $o] : ? [X266 : term] : ((X265 @ X266) != (X264 @ id @ X266 @ id))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) <=> (apinj2 = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) <=> (shinj = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X9 : term,X10 : term > $o,X11 : term,X12 : subst > term > subst > $o] : (((X10 @ (ap @ X11 @ X9)) = $true) | ? [X14 : subst,X15 : subst,X16 : subst,X17 : term] : (((X12 @ X15 @ X17 @ (comp @ X16 @ X14)) != $true) & ((X12 @ (comp @ X15 @ X16) @ (sub @ X17 @ X16) @ X14) = $true)) | ((X10 @ X9) != $true) | ? [X13 : term] : ((X10 @ X13) != (X12 @ id @ X13 @ id)) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : (((X12 @ X20 @ X19 @ (comp @ X18 @ X21)) = $true) & ((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21) != $true)) | ((X10 @ X11) != $true) | ? [X22 : term,X23 : term] : (($true = (X12 @ id @ X23 @ id)) & ((X12 @ id @ (ap @ (sub @ X23 @ id) @ X22) @ id) != $true) & ($true = (X12 @ id @ X22 @ id))))) & (! [X171 : subst > term > subst > $o] : ? [X172 : term > $o] : ! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173)) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar_gthm = $true) & (! [X0 : term,X1 : subst > term > subst > $o] : (? [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true)) & ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) != $true)) | ($true = (X1 @ id @ X0 @ id)) | ? [X2 : term,X3 : term] : (((X1 @ id @ X3 @ id) = $true) & ((X1 @ id @ X2 @ id) = $true) & ((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) <=> (axidr = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lthm = $true) <=> (? [X179 : term > $o,X180 : term] : (! [X183 : term,X184 : term] : (((X179 @ X184) != $true) | ((X179 @ (ap @ X184 @ X183)) = $true) | ($true != (X179 @ X183))) & ! [X181 : term] : (? [X182 : term] : (((X179 @ (sub @ X181 @ (push @ X182 @ id))) != $true) & ((X179 @ X182) = $true)) | ((X179 @ (lam @ X181)) = $true)) & ((X179 @ X180) != $true) & ! [X185 : term] : (((X179 @ X185) = $true) | ((var @ X185) != $true))) | ! [X215 : subst > term > subst > $o,X216 : term] : (? [X217 : term] : (((var @ (sub @ X217 @ id)) = $true) & ((X215 @ id @ X217 @ id) != $true)) | ? [X227 : subst,X228 : subst,X229 : subst,X230 : term] : (((X215 @ X229 @ X230 @ (comp @ X228 @ X227)) = $true) & ((X215 @ (comp @ X229 @ X228) @ (sub @ X230 @ X228) @ X227) != $true)) | ? [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (((X215 @ X225 @ X223 @ (comp @ X226 @ X224)) != $true) & ((X215 @ (comp @ X225 @ X226) @ (sub @ X223 @ X226) @ X224) = $true)) | ? [X218 : subst > term > term] : (((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id) != $true) & ! [X222 : term] : (((X215 @ id @ X222 @ id) != $true) | ((X215 @ id @ (X218 @ id @ X222) @ id) = $true)) & ! [X219 : term,X220 : subst,X221 : subst] : ((X218 @ (comp @ X220 @ X221) @ (sub @ X219 @ X221)) = (sub @ (X218 @ X220 @ X219) @ X221))) | ((X215 @ id @ X216 @ id) = $true) | ? [X231 : term,X232 : term] : (((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) != $true) & ((X215 @ id @ X232 @ id) = $true) & ((X215 @ id @ X231 @ id) = $true))) | ? [X186 : term,X187 : term,X188 : subst > term > subst > $o] : (! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : (((X188 @ (comp @ X194 @ X193) @ (sub @ X191 @ X193) @ X192) != $true) | ((X188 @ X194 @ X191 @ (comp @ X193 @ X192)) = $true)) & ((X188 @ id @ X187 @ id) = $true) & ! [X189 : term,X190 : term] : (((X188 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id) = $true) | ((X188 @ id @ X190 @ id) != $true) | ((X188 @ id @ X189 @ id) != $true)) & ($true != (X188 @ id @ (ap @ X186 @ X187) @ id)) & ((X188 @ id @ X186 @ id) = $true) & ! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (((X188 @ (comp @ X197 @ X198) @ (sub @ X195 @ X198) @ X196) = $true) | ((X188 @ X197 @ X195 @ (comp @ X198 @ X196)) != $true))) | ? [X199 : term,X200 : subst > term > subst > $o] : (! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (((X200 @ (comp @ X213 @ X214) @ (sub @ X212 @ X214) @ X211) != $true) | ((X200 @ X213 @ X212 @ (comp @ X214 @ X211)) = $true)) & ! [X201 : subst,X202 : subst,X203 : subst,X204 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X204 @ X202) @ X203) = $true) | ((X200 @ X201 @ X204 @ (comp @ X202 @ X203)) != $true)) & ! [X205 : term] : (((X200 @ id @ X205 @ id) != $true) | ((X200 @ id @ (sub @ X199 @ (push @ X205 @ id)) @ id) = $true)) & ((X200 @ id @ (lam @ X199) @ id) != $true) & ! [X206 : subst > term > term] : (? [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) != $true) & ((X200 @ id @ X207 @ id) = $true)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ? [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) != (sub @ (X206 @ X210 @ X208) @ X209)))))) & (hoasinduction_lem2v2_gthm = $true) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & (induction2_gthm = $true) & (! [X256 : term] : ((sub @ X256 @ id) = X256) <=> (termmset = $true)) & (pushprop_lem1_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X439 : term,X440 : term > $o] : (? [X443 : term] : (((X440 @ (lam @ X443)) != $true) & ((X440 @ X443) = $true)) | ((X440 @ X439) = $true) | ? [X441 : term,X442 : term] : (((X440 @ X442) = $true) & ((X440 @ X441) = $true) & ((X440 @ (ap @ X441 @ X442)) != $true)) | ? [X444 : term] : (((X440 @ X444) != $true) & ($true = (var @ X444)))) <=> (induction = $true)) & ! [X294 : d_term,X295 : d_term] : ((X294 = X295) | ((d2term @ X294) != (d2term @ X295))) & (lamnotap != $true) & (termmset_gthm = $true) & (! [X352 : term,X353 : term > $o,X354 : subst > term > subst > $o] : (? [X366 : subst,X367 : subst,X368 : term,X369 : subst] : (((X354 @ X366 @ X368 @ (comp @ X369 @ X367)) = $true) & ((X354 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) != $true)) | ? [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (((X354 @ (comp @ X358 @ X360) @ (sub @ X359 @ X360) @ X357) = $true) & ((X354 @ X358 @ X359 @ (comp @ X360 @ X357)) != $true)) | ? [X355 : term] : (((X353 @ (sub @ X352 @ (push @ X355 @ id))) != $true) & ((X353 @ X355) = $true)) | ? [X361 : subst > term > term] : (! [X365 : term] : (((X354 @ id @ (X361 @ id @ X365) @ id) = $true) | ((X354 @ id @ X365 @ id) != $true)) & ((X354 @ id @ (lam @ (X361 @ sh @ one)) @ id) != $true) & ! [X362 : subst,X363 : subst,X364 : term] : ((sub @ (X361 @ X363 @ X364) @ X362) = (X361 @ (comp @ X363 @ X362) @ (sub @ X364 @ X362)))) | ? [X356 : term] : ((X354 @ id @ X356 @ id) != (X353 @ X356)) | ((X353 @ (lam @ X352)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & ((hoaslaminj = $true) <=> ! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ? [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) != (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) | ? [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) != (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X431 : term,X432 : subst > term > subst > $o] : (? [X433 : subst > term > term] : (! [X434 : subst,X435 : subst,X436 : term] : ((sub @ (X433 @ X434 @ X436) @ X435) = (X433 @ (comp @ X434 @ X435) @ (sub @ X436 @ X435))) & ((X432 @ id @ (lam @ (X433 @ sh @ one)) @ id) != $true) & ! [X437 : term] : (((X432 @ id @ (X433 @ id @ X437) @ id) = $true) | ((X432 @ id @ X437 @ id) != $true))) | ((X432 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true) | ? [X438 : term] : (((X432 @ id @ (sub @ X431 @ (push @ X438 @ id)) @ id) != $true) & ((X432 @ id @ X438 @ id) = $true)))) & (! [X233 : term,X234 : subst > term > subst > $o] : (? [X235 : subst > term > term] : (! [X239 : term] : (((X234 @ id @ (X235 @ id @ X239) @ id) = $true) | ((X234 @ id @ X239 @ id) != $true)) & ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id) != $true) & ! [X236 : subst,X237 : subst,X238 : term] : ((X235 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237)) = (sub @ (X235 @ X236 @ X238) @ X237))) | ((X234 @ id @ (lam @ X233) @ id) = $true) | ? [X240 : term] : (((X234 @ id @ (sub @ X233 @ (push @ X240 @ id)) @ id) != $true) & ((X234 @ id @ X240 @ id) = $true))) <=> (hoasinduction_lem3a = $true)) & (pushprop_lthm = $true) & (pushprop = $true) & ((hoasinduction = $true) <=> ! [X309 : term,X310 : subst > term > subst > $o] : (? [X320 : subst > term > term] : (! [X324 : term] : (((X310 @ id @ X324 @ id) != $true) | ((X310 @ id @ (X320 @ id @ X324) @ id) = $true)) & ! [X321 : subst,X322 : term,X323 : subst] : ((sub @ (X320 @ X321 @ X322) @ X323) = (X320 @ (comp @ X321 @ X323) @ (sub @ X322 @ X323))) & ((X310 @ id @ (lam @ (X320 @ sh @ one)) @ id) != $true)) | ? [X312 : subst,X313 : subst,X314 : term,X315 : subst] : (($true = (X310 @ (comp @ X315 @ X312) @ (sub @ X314 @ X312) @ X313)) & ((X310 @ X315 @ X314 @ (comp @ X312 @ X313)) != $true)) | ? [X311 : term] : (((var @ (sub @ X311 @ id)) = $true) & ((X310 @ id @ X311 @ id) != $true)) | ? [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (((X310 @ X318 @ X316 @ (comp @ X319 @ X317)) = $true) & ((X310 @ (comp @ X318 @ X319) @ (sub @ X316 @ X319) @ X317) != $true)) | ((X310 @ id @ X309 @ id) = $true) | ? [X325 : term,X326 : term] : (($true = (X310 @ id @ X326 @ id)) & ((X310 @ id @ X325 @ id) = $true) & ((X310 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) != $true)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) = $true) | ? [X249 : term] : ((X246 @ id @ X249 @ id) != (X247 @ X249)) | ? [X250 : subst > term > term] : (! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) & ! [X251 : term] : (((X246 @ id @ X251 @ id) != $true) | ((X246 @ id @ (X250 @ id @ X251) @ id) = $true)) & ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) != $true)) | ? [X255 : term] : (((X247 @ X255) = $true) & ((X247 @ (sub @ X248 @ (push @ X255 @ id))) != $true)))) & (apnotvar = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X60 : subst > term > subst > $o,X61 : term] : (? [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (((X60 @ X69 @ X68 @ (comp @ X70 @ X67)) != $true) & ((X60 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X67) = $true)) | ((X60 @ id @ (lam @ X61) @ id) = $true) | ? [X75 : term] : (((X60 @ id @ (sub @ X61 @ (push @ X75 @ id)) @ id) != $true) & ((X60 @ id @ X75 @ id) = $true)) | ? [X71 : subst,X72 : subst,X73 : subst,X74 : term] : (((X60 @ (comp @ X73 @ X71) @ (sub @ X74 @ X71) @ X72) != $true) & ((X60 @ X73 @ X74 @ (comp @ X71 @ X72)) = $true)) | ? [X62 : subst > term > term] : (! [X63 : term,X64 : subst,X65 : subst] : ((sub @ (X62 @ X65 @ X63) @ X64) = (X62 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64))) & ! [X66 : term] : (((X60 @ id @ X66 @ id) != $true) | ((X60 @ id @ (X62 @ id @ X66) @ id) = $true)) & ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3 = $true))),
% 28.46/5.33 inference(flattening,[status(thm)],[f12])).
% 28.46/5.33 thf(f12,plain,(
% 28.46/5.33 ! [X294 : d_term,X295 : d_term] : ((X294 = X295) | ((d2term @ X294) != (d2term @ X295))) & (axabs = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true)) | ? [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) != X303)) | ? [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) != X300))) & (hoaslamnotap_lthm = $true) & (! [X233 : term,X234 : subst > term > subst > $o] : (? [X235 : subst > term > term] : (! [X239 : term] : (((X234 @ id @ (X235 @ id @ X239) @ id) = $true) | ((X234 @ id @ X239 @ id) != $true)) & ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id) != $true) & ! [X236 : subst,X237 : subst,X238 : term] : ((X235 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237)) = (sub @ (X235 @ X236 @ X238) @ X237))) | ((X234 @ id @ (lam @ X233) @ id) = $true) | ? [X240 : term] : (((X234 @ id @ (sub @ X233 @ (push @ X240 @ id)) @ id) != $true) & ((X234 @ id @ X240 @ id) = $true))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X431 : term,X432 : subst > term > subst > $o] : (? [X433 : subst > term > term] : (! [X434 : subst,X435 : subst,X436 : term] : ((sub @ (X433 @ X434 @ X436) @ X435) = (X433 @ (comp @ X434 @ X435) @ (sub @ X436 @ X435))) & ((X432 @ id @ (lam @ (X433 @ sh @ one)) @ id) != $true) & ! [X437 : term] : (((X432 @ id @ (X433 @ id @ X437) @ id) = $true) | ((X432 @ id @ X437 @ id) != $true))) | ((X432 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true) | ? [X438 : term] : (((X432 @ id @ (sub @ X431 @ (push @ X438 @ id)) @ id) != $true) & ((X432 @ id @ X438 @ id) = $true)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2 = $true) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (? [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) != (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81))) | ((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one)))) <=> (hoaslamnotap = $true)) & (! [X178 : term] : ((sub @ X178 @ id) = X178) <=> (axvarid = $true)) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoaslaminj_lthm = $true) <=> (((! [X419 : subst,X420 : subst > term > term,X421 : subst > term > term,X422 : term] : (? [X426 : subst,X427 : subst,X428 : term] : ((X421 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)) != (sub @ (X421 @ X426 @ X428) @ X427)) | ((lam @ (X420 @ sh @ one)) != (lam @ (X421 @ sh @ one))) | ? [X423 : term,X424 : subst,X425 : subst] : ((X420 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424)) != (sub @ (X420 @ X425 @ X423) @ X424)) | ((X420 @ X419 @ X422) = (X421 @ X419 @ X422))) | ? [X417 : term,X418 : term] : (((lam @ X418) = (lam @ X417)) & (X417 != X418))) | ? [X415 : subst,X416 : term] : ((comp @ sh @ (push @ X416 @ X415)) != X415)) | ? [X413 : subst,X414 : term] : ((sub @ one @ (push @ X414 @ X413)) != X414))) & (ulamvarsh = $true) & (pushprop_lem2v2_gthm = $true) & (((! [X383 : term,X384 : term > $o,X385 : subst > term > subst > $o] : (? [X387 : subst > term > term] : (! [X389 : subst,X390 : subst,X391 : term] : ((X387 @ (comp @ X390 @ X389) @ (sub @ X391 @ X389)) = (sub @ (X387 @ X390 @ X391) @ X389)) & ((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id) != $true) & ! [X388 : term] : (((X385 @ id @ X388 @ id) != $true) | ((X385 @ id @ (X387 @ id @ X388) @ id) = $true))) | ? [X386 : term] : ((X384 @ X386) != (X385 @ id @ X386 @ id)) | ? [X392 : term] : (((X384 @ (sub @ X383 @ (push @ X392 @ id))) != $true) & ((X384 @ X392) = $true)) | ((X384 @ (lam @ X383)) = $true)) | ? [X382 : term] : ((sub @ X382 @ id) != X382)) | ? [X378 : term] : ! [X379 : subst > term > term] : ? [X380 : term,X381 : subst] : ((X379 @ X381 @ X380) != (sub @ X378 @ (push @ X380 @ X381)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvarind = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X327 : term] : ? [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) = (X328 @ sh @ one))) & ! [X529 : d_subst] : (d_id = X529) & (hoaslamnotvar_lthm = $true) & ((d2subst @ d_id) = sh) & ((axidl = $true) <=> ! [X257 : subst] : ((comp @ id @ X257) = X257)) & (termmset_gthm = $true) & (pushprop = $true) & (one = (d2term @ d_one)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94)))) & (hoasapnotvar = $true) & ((hoasapinj2 = $true) <=> ! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X489 : subst > term > subst > $o,X490 : term] : (? [X492 : term,X493 : subst > term > term] : (((X489 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X497 : subst,X498 : term,X499 : subst] : ((sub @ (X493 @ X499 @ X498) @ X497) = (sub @ (sub @ X492 @ (push @ X498 @ X499)) @ X497)) & ! [X494 : subst,X495 : term,X496 : subst] : ((X493 @ (comp @ X496 @ X494) @ (sub @ X495 @ X494)) = (sub @ X492 @ (push @ (sub @ X495 @ X494) @ (comp @ X496 @ X494)))) & ! [X500 : term] : (((X489 @ id @ X500 @ id) != $true) | ((X489 @ id @ (X493 @ id @ X500) @ id) = $true))) | ((X489 @ id @ (lam @ (sub @ X490 @ (push @ one @ sh))) @ id) = $true) | ? [X491 : term] : (((X489 @ id @ X491 @ id) = $true) & ((X489 @ id @ (sub @ X490 @ (push @ X491 @ id)) @ id) != $true)))) & (! [X171 : subst > term > subst > $o] : ? [X172 : term > $o] : ! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173)) <=> (hoasinduction_lem0 = $true)) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) <=> (hoasapinj1 = $true)) & ((hoasinduction = $true) <=> ! [X309 : term,X310 : subst > term > subst > $o] : (? [X320 : subst > term > term] : (! [X324 : term] : (((X310 @ id @ X324 @ id) != $true) | ((X310 @ id @ (X320 @ id @ X324) @ id) = $true)) & ! [X321 : subst,X322 : term,X323 : subst] : ((sub @ (X320 @ X321 @ X322) @ X323) = (X320 @ (comp @ X321 @ X323) @ (sub @ X322 @ X323))) & ((X310 @ id @ (lam @ (X320 @ sh @ one)) @ id) != $true)) | ? [X312 : subst,X313 : subst,X314 : term,X315 : subst] : (($true = (X310 @ (comp @ X315 @ X312) @ (sub @ X314 @ X312) @ X313)) & ((X310 @ X315 @ X314 @ (comp @ X312 @ X313)) != $true)) | ? [X311 : term] : (((var @ (sub @ X311 @ id)) = $true) & ((X310 @ id @ X311 @ id) != $true)) | ? [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (((X310 @ X318 @ X316 @ (comp @ X319 @ X317)) = $true) & ((X310 @ (comp @ X318 @ X319) @ (sub @ X316 @ X319) @ X317) != $true)) | ((X310 @ id @ X309 @ id) = $true) | ? [X325 : term,X326 : term] : (($true = (X310 @ id @ X326 @ id)) & ((X310 @ id @ X325 @ id) = $true) & ((X310 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) != $true)))) & ((hoaslaminj = $true) <=> ! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ? [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) != (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))) | ? [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) != (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axmap = $true) & (hoasinduction_lem1_lthm = $true) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ((X481 @ X484) != $true) | ? [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) != (X483 @ X485))) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X9 : term,X10 : term > $o,X11 : term,X12 : subst > term > subst > $o] : (((X10 @ (ap @ X11 @ X9)) = $true) | ? [X14 : subst,X15 : subst,X16 : subst,X17 : term] : (((X12 @ X15 @ X17 @ (comp @ X16 @ X14)) != $true) & ((X12 @ (comp @ X15 @ X16) @ (sub @ X17 @ X16) @ X14) = $true)) | ((X10 @ X9) != $true) | ? [X13 : term] : ((X10 @ X13) != (X12 @ id @ X13 @ id)) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : (((X12 @ X20 @ X19 @ (comp @ X18 @ X21)) = $true) & ((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21) != $true)) | ((X10 @ X11) != $true) | ? [X22 : term,X23 : term] : (($true = (X12 @ id @ X23 @ id)) & ((X12 @ id @ (ap @ (sub @ X23 @ id) @ X22) @ id) != $true) & ($true = (X12 @ id @ X22 @ id))))) & (axvarshift = $true) & (lamnotap != $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) = $true) | ? [X249 : term] : ((X246 @ id @ X249 @ id) != (X247 @ X249)) | ? [X250 : subst > term > term] : (! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) & ! [X251 : term] : (((X246 @ id @ X251 @ id) != $true) | ((X246 @ id @ (X250 @ id @ X251) @ id) = $true)) & ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) != $true)) | ? [X255 : term] : (((X247 @ X255) = $true) & ((X247 @ (sub @ X248 @ (push @ X255 @ id))) != $true)))) & (! [X393 : term,X394 : subst > term > subst > $o] : (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id) = $true) | ? [X400 : term] : (((X394 @ id @ (sub @ X393 @ (push @ X400 @ id)) @ id) != $true) & ((X394 @ id @ X400 @ id) = $true)) | ? [X395 : subst > term > term] : (! [X397 : term,X398 : subst,X399 : subst] : ((X395 @ (comp @ X398 @ X399) @ (sub @ X397 @ X399)) = (sub @ (X395 @ X398 @ X397) @ X399)) & ! [X396 : term] : (((X394 @ id @ X396 @ id) != $true) | ((X394 @ id @ (X395 @ id @ X396) @ id) = $true)) & ((X394 @ id @ (lam @ (X395 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem2v2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X259 : term > $o,X260 : subst,X261 : term] : ? [X262 : term > $o] : ! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260))))) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((axscons = $true) <=> ! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24)) & (! [X429 : term] : ? [X430 : subst > term > term] : ((X430 @ sh @ one) = (sub @ X429 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> ! [X401 : subst,X402 : term > $o,X403 : term] : (? [X404 : term] : (((X402 @ (lam @ X404)) != $true) & ! [X405 : term] : (((X402 @ X405) != $true) | ((X402 @ (sub @ X404 @ (push @ X405 @ id))) = $true))) | ? [X407 : term,X408 : term] : (((X402 @ X407) = $true) & ((X402 @ X408) = $true) & ((X402 @ (ap @ X408 @ X407)) != $true)) | ((X402 @ (sub @ X403 @ X401)) = $true) | ? [X406 : term] : (((X402 @ (sub @ X406 @ X401)) != $true) & ((var @ X406) = $true)))) & (! [X256 : term] : ((sub @ X256 @ id) = X256) <=> (termmset = $true)) & (((! [X104 : term,X105 : subst > term > subst > $o] : (? [X114 : term] : (((X105 @ id @ X114 @ id) = $true) & ((X105 @ id @ (sub @ X104 @ (push @ X114 @ id)) @ id) != $true)) | ? [X110 : term,X111 : subst,X112 : subst,X113 : subst] : (((X105 @ X112 @ X110 @ (comp @ X113 @ X111)) = $true) & ($true != (X105 @ (comp @ X112 @ X113) @ (sub @ X110 @ X113) @ X111))) | ? [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (((X105 @ X109 @ X107 @ (comp @ X108 @ X106)) != $true) & ((X105 @ (comp @ X109 @ X108) @ (sub @ X107 @ X108) @ X106) = $true)) | ? [X115 : subst > term > term] : (! [X116 : term] : (((X105 @ id @ (X115 @ id @ X116) @ id) = $true) | ((X105 @ id @ X116 @ id) != $true)) & ((X105 @ id @ (lam @ (X115 @ sh @ one)) @ id) != $true) & ! [X117 : subst,X118 : subst,X119 : term] : ((X115 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118)) = (sub @ (X115 @ X117 @ X119) @ X118))) | ((X105 @ id @ (lam @ X104) @ id) = $true)) | ? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true) | ((X97 @ id @ X103 @ id) != $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ((X97 @ id @ (lam @ (X98 @ sh @ one)) @ id) = $true) | ? [X99 : term,X100 : subst,X101 : subst] : ((sub @ (X98 @ X101 @ X99) @ X100) != (X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)))) & ((X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id) != $true))) | ? [X95 : term] : ((sub @ X95 @ id) != X95)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) <=> (laminj = $true)) & (hoasapinj1_gthm = $true) & (pushprop_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X344 : subst,X345 : term,X346 : term > $o] : (? [X349 : term,X350 : term] : (((X346 @ X349) = $true) & ((X346 @ (ap @ X350 @ X349)) != $true) & ((X346 @ X350) = $true)) | ? [X351 : term] : (((var @ X351) = $true) & ($true != (X346 @ (sub @ X351 @ X344)))) | ? [X347 : term] : (! [X348 : term] : (((X346 @ (sub @ X347 @ (push @ X348 @ id))) = $true) | ((X346 @ X348) != $true)) & ((X346 @ (lam @ X347)) != $true)) | ((X346 @ (sub @ X345 @ X344)) = $true)) | ? [X338 : term,X339 : term > $o] : (! [X342 : term,X343 : term] : (($true != (X339 @ X342)) | ((X339 @ (ap @ X343 @ X342)) = $true) | ((X339 @ X343) != $true)) & ($true != (X339 @ X338)) & ! [X341 : term] : (((X339 @ X341) != $true) | ($true = (X339 @ (lam @ X341)))) & ! [X340 : term] : (((X339 @ X340) = $true) | ((var @ X340) != $true)))) | ? [X337 : subst] : ((comp @ X337 @ id) != X337)) | ? [X335 : subst,X336 : term] : ((comp @ sh @ (push @ X336 @ X335)) != X335)) | ? [X333 : term,X334 : subst] : ((sub @ one @ (push @ X333 @ X334)) != X333))) & ! [X486 : d_term] : (d_one = X486) & ((? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X533) & ((ap @ X535 @ X532) = (ap @ X534 @ X533))) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536)))) <=> (hoasapinj2_lthm = $true)) & ((termmset_lthm = $true) <=> (? [X298 : term] : ((sub @ X298 @ id) != X298) | ! [X299 : term] : ((sub @ X299 @ id) = X299))) & ((var @ (d2term @ d_one)) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lthm = $true) & (! [X457 : subst > term > subst > $o,X458 : term,X459 : term] : (? [X460 : term,X461 : term] : (($true = (X457 @ id @ X460 @ id)) & ((X457 @ id @ X461 @ id) = $true) & ((X457 @ id @ (ap @ (sub @ X461 @ id) @ X460) @ id) != $true)) | ((X457 @ id @ X458 @ id) != $true) | ((X457 @ id @ X459 @ id) != $true) | ? [X466 : subst,X467 : term,X468 : subst,X469 : subst] : (((X457 @ X469 @ X467 @ (comp @ X468 @ X466)) = $true) & ((X457 @ (comp @ X469 @ X468) @ (sub @ X467 @ X468) @ X466) != $true)) | ? [X462 : subst,X463 : subst,X464 : subst,X465 : term] : (((X457 @ (comp @ X463 @ X462) @ (sub @ X465 @ X462) @ X464) = $true) & ($true != (X457 @ X463 @ X465 @ (comp @ X462 @ X464)))) | ((X457 @ id @ (ap @ X458 @ X459) @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & (induction2lem_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) <=> ! [X241 : subst,X242 : term,X243 : term > $o] : ? [X244 : term > $o] : ! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (hoasapnotvar_gthm = $true) & (! [X120 : term > $o,X121 : term] : (? [X125 : term] : (((X120 @ (lam @ X125)) != $true) & ! [X126 : term] : (((X120 @ (sub @ X125 @ (push @ X126 @ id))) = $true) | ((X120 @ X126) != $true))) | ? [X123 : term,X124 : term] : (((X120 @ (ap @ X123 @ X124)) != $true) & ((X120 @ X124) = $true) & ((X120 @ X123) = $true)) | ((X120 @ X121) = $true) | ? [X122 : term] : (((X120 @ X122) != $true) & ((var @ X122) = $true))) <=> (induction2 = $true)) & (pushprop_lem3v2_lthm = $true) & ((axvarcons = $true) <=> ! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128)) & (! [X329 : term] : ? [X330 : subst > term > term] : ! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((axshiftcons = $true) <=> ! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530)) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & (hoasinduction_lem1_gthm = $true) & (axapp = $true) & (! [X0 : term,X1 : subst > term > subst > $o] : (? [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true)) & ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) != $true)) | ($true = (X1 @ id @ X0 @ id)) | ? [X2 : term,X3 : term] : (((X1 @ id @ X3 @ id) = $true) & ((X1 @ id @ X2 @ id) = $true) & ((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) <=> (axidr = $true)) & (pushprop_lem2v2_lthm = $true) & ((! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (($true = (X505 @ one)) | ? [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) != (X505 @ X507)) | ($true != (X504 @ X503))) | ? [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) != X501)) <=> (pushprop_lem1v2_lthm = $true)) & (apnotvar = $true) & (hoasapnotvar_lthm = $true) & (lamnotvar = $true) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) <=> (apinj2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))) | ? [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 != X476) & ((ap @ X476 @ X473) = (ap @ X474 @ X475)))) | ? [X472 : term] : ((sub @ X472 @ id) != X472)) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X174 : term] : ? [X175 : subst > term > term] : ! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176))) & ((((! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84)) | ? [X83 : subst] : ((comp @ X83 @ id) != X83)) | ? [X82 : subst] : ((comp @ id @ X82) != X82)) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((((! [X215 : subst > term > subst > $o,X216 : term] : (? [X217 : term] : (((var @ (sub @ X217 @ id)) = $true) & ((X215 @ id @ X217 @ id) != $true)) | ? [X227 : subst,X228 : subst,X229 : subst,X230 : term] : (((X215 @ X229 @ X230 @ (comp @ X228 @ X227)) = $true) & ((X215 @ (comp @ X229 @ X228) @ (sub @ X230 @ X228) @ X227) != $true)) | ? [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (((X215 @ X225 @ X223 @ (comp @ X226 @ X224)) != $true) & ((X215 @ (comp @ X225 @ X226) @ (sub @ X223 @ X226) @ X224) = $true)) | ? [X218 : subst > term > term] : (((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id) != $true) & ! [X222 : term] : (((X215 @ id @ X222 @ id) != $true) | ((X215 @ id @ (X218 @ id @ X222) @ id) = $true)) & ! [X219 : term,X220 : subst,X221 : subst] : ((X218 @ (comp @ X220 @ X221) @ (sub @ X219 @ X221)) = (sub @ (X218 @ X220 @ X219) @ X221))) | ((X215 @ id @ X216 @ id) = $true) | ? [X231 : term,X232 : term] : (((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) != $true) & ((X215 @ id @ X232 @ id) = $true) & ((X215 @ id @ X231 @ id) = $true))) | ? [X199 : term,X200 : subst > term > subst > $o] : (! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (((X200 @ (comp @ X213 @ X214) @ (sub @ X212 @ X214) @ X211) != $true) | ((X200 @ X213 @ X212 @ (comp @ X214 @ X211)) = $true)) & ! [X201 : subst,X202 : subst,X203 : subst,X204 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X204 @ X202) @ X203) = $true) | ((X200 @ X201 @ X204 @ (comp @ X202 @ X203)) != $true)) & ! [X205 : term] : (((X200 @ id @ X205 @ id) != $true) | ((X200 @ id @ (sub @ X199 @ (push @ X205 @ id)) @ id) = $true)) & ((X200 @ id @ (lam @ X199) @ id) != $true) & ! [X206 : subst > term > term] : (? [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) != $true) & ((X200 @ id @ X207 @ id) = $true)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ? [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) != (sub @ (X206 @ X210 @ X208) @ X209))))) | ? [X186 : term,X187 : term,X188 : subst > term > subst > $o] : (! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : (((X188 @ (comp @ X194 @ X193) @ (sub @ X191 @ X193) @ X192) != $true) | ((X188 @ X194 @ X191 @ (comp @ X193 @ X192)) = $true)) & ((X188 @ id @ X187 @ id) = $true) & ! [X189 : term,X190 : term] : (((X188 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id) = $true) | ((X188 @ id @ X190 @ id) != $true) | ((X188 @ id @ X189 @ id) != $true)) & ($true != (X188 @ id @ (ap @ X186 @ X187) @ id)) & ((X188 @ id @ X186 @ id) = $true) & ! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (((X188 @ (comp @ X197 @ X198) @ (sub @ X195 @ X198) @ X196) = $true) | ((X188 @ X197 @ X195 @ (comp @ X198 @ X196)) != $true)))) | ? [X179 : term > $o,X180 : term] : (! [X183 : term,X184 : term] : (((X179 @ X184) != $true) | ((X179 @ (ap @ X184 @ X183)) = $true) | ($true != (X179 @ X183))) & ! [X181 : term] : (? [X182 : term] : (((X179 @ (sub @ X181 @ (push @ X182 @ id))) != $true) & ((X179 @ X182) = $true)) | ((X179 @ (lam @ X181)) = $true)) & ((X179 @ X180) != $true) & ! [X185 : term] : (((X179 @ X185) = $true) | ((var @ X185) != $true)))) <=> (hoasinduction_lthm = $true)) & (substmonoid_gthm = $true) & (hoaslamnotvar = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (! [X352 : term,X353 : term > $o,X354 : subst > term > subst > $o] : (? [X366 : subst,X367 : subst,X368 : term,X369 : subst] : (((X354 @ X366 @ X368 @ (comp @ X369 @ X367)) = $true) & ((X354 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) != $true)) | ? [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (((X354 @ (comp @ X358 @ X360) @ (sub @ X359 @ X360) @ X357) = $true) & ((X354 @ X358 @ X359 @ (comp @ X360 @ X357)) != $true)) | ? [X355 : term] : (((X353 @ (sub @ X352 @ (push @ X355 @ id))) != $true) & ((X353 @ X355) = $true)) | ? [X361 : subst > term > term] : (! [X365 : term] : (((X354 @ id @ (X361 @ id @ X365) @ id) = $true) | ((X354 @ id @ X365 @ id) != $true)) & ((X354 @ id @ (lam @ (X361 @ sh @ one)) @ id) != $true) & ! [X362 : subst,X363 : subst,X364 : term] : ((sub @ (X361 @ X363 @ X364) @ X362) = (X361 @ (comp @ X363 @ X362) @ (sub @ X364 @ X362)))) | ? [X356 : term] : ((X354 @ id @ X356 @ id) != (X353 @ X356)) | ((X353 @ (lam @ X352)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X52 : term,X53 : subst > term > subst > $o] : (? [X59 : term] : (($true = (X53 @ id @ X59 @ id)) & ((X53 @ id @ (sub @ X52 @ (push @ X59 @ id)) @ id) != $true)) | ((X53 @ id @ (lam @ X52) @ id) = $true) | ? [X54 : subst > term > term] : (! [X55 : term] : (($true != (X53 @ id @ X55 @ id)) | ((X53 @ id @ (X54 @ id @ X55) @ id) = $true)) & ! [X56 : subst,X57 : subst,X58 : term] : ((X54 @ (comp @ X57 @ X56) @ (sub @ X58 @ X56)) = (sub @ (X54 @ X57 @ X58) @ X56)) & ((X53 @ id @ (lam @ (X54 @ sh @ one)) @ id) != $true))) | ? [X44 : subst > term > subst > $o,X45 : term] : (! [X46 : subst > term > term] : (((X44 @ id @ (lam @ (X46 @ sh @ one)) @ id) = $true) | ? [X47 : term] : (((X44 @ id @ X47 @ id) = $true) & ($true != (X44 @ id @ (X46 @ id @ X47) @ id))) | ? [X48 : subst,X49 : term,X50 : subst] : ((X46 @ (comp @ X50 @ X48) @ (sub @ X49 @ X48)) != (sub @ (X46 @ X50 @ X49) @ X48))) & ((X44 @ id @ (lam @ (sub @ X45 @ (push @ one @ sh))) @ id) != $true) & ! [X51 : term] : (((X44 @ id @ X51 @ id) != $true) | ((X44 @ id @ (sub @ X45 @ (push @ X51 @ id)) @ id) = $true)))) | ? [X43 : term] : ((sub @ X43 @ id) != X43))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoaslaminj_gthm = $true) & ((substmonoid = $true) <=> (! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41))) & (pushprop_lem1_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) <=> (shinj = $true)) & (hoasinduction_lem3_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X509 : term > $o,X510 : subst > term > subst > $o,X511 : term] : (? [X526 : term] : (($true != (X509 @ (sub @ X511 @ (push @ X526 @ id)))) & ((X509 @ X526) = $true)) | ((X509 @ (lam @ X511)) = $true) | ? [X520 : term] : ((X509 @ X520) != (X510 @ id @ X520 @ id)) | ? [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (((X510 @ X513 @ X512 @ (comp @ X514 @ X515)) = $true) & ((X510 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515) != $true)) | ? [X516 : subst,X517 : term,X518 : subst,X519 : subst] : (((X510 @ X516 @ X517 @ (comp @ X518 @ X519)) != $true) & ((X510 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518) @ X519) = $true)) | ? [X521 : subst > term > term] : (! [X522 : term,X523 : subst,X524 : subst] : ((sub @ (X521 @ X523 @ X522) @ X524) = (X521 @ (comp @ X523 @ X524) @ (sub @ X522 @ X524))) & ((X510 @ id @ (lam @ (X521 @ sh @ one)) @ id) != $true) & ! [X525 : term] : (((X510 @ id @ X525 @ id) != $true) | ((X510 @ id @ (X521 @ id @ X525) @ id) = $true)))) | ? [X508 : term] : ((sub @ X508 @ id) != X508))) & (! [X439 : term,X440 : term > $o] : (? [X443 : term] : (((X440 @ (lam @ X443)) != $true) & ((X440 @ X443) = $true)) | ((X440 @ X439) = $true) | ? [X441 : term,X442 : term] : (((X440 @ X442) = $true) & ((X440 @ X441) = $true) & ((X440 @ (ap @ X441 @ X442)) != $true)) | ? [X444 : term] : (((X440 @ X444) != $true) & ($true = (var @ X444)))) <=> (induction = $true)) & (! [X168 : subst > term > subst > $o] : ? [X169 : term > $o] : ! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) <=> (hoasinduction_lem0_lthm = $true)) & ((induction2_lthm = $true) <=> ((! [X34 : term,X35 : term > $o] : (? [X38 : term,X39 : term] : (($true = (X35 @ X39)) & ((X35 @ (ap @ X39 @ X38)) != $true) & ((X35 @ X38) = $true)) | ($true = (X35 @ X34)) | ? [X36 : term] : (! [X37 : term] : (($true = (X35 @ (sub @ X36 @ (push @ X37 @ id)))) | ((X35 @ X37) != $true)) & ((X35 @ (lam @ X36)) != $true)) | ? [X40 : term] : (((var @ X40) = $true) & ((X35 @ X40) != $true))) | ? [X26 : term > $o,X27 : term,X28 : subst] : (! [X31 : term] : (? [X32 : term] : (((X26 @ (sub @ X31 @ (push @ X32 @ id))) != $true) & ((X26 @ X32) = $true)) | ((X26 @ (lam @ X31)) = $true)) & ! [X29 : term,X30 : term] : (((X26 @ X29) != $true) | ((X26 @ X30) != $true) | ((X26 @ (ap @ X29 @ X30)) = $true)) & ((X26 @ (sub @ X27 @ X28)) != $true) & ! [X33 : term] : (((var @ X33) != $true) | ((X26 @ (sub @ X33 @ X28)) = $true)))) | ? [X25 : term] : ((sub @ X25 @ id) != X25))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) <=> (apinj1 = $true)) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) != (d2subst @ X471)) | (X470 = X471)) & (! [X60 : subst > term > subst > $o,X61 : term] : (? [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (((X60 @ X69 @ X68 @ (comp @ X70 @ X67)) != $true) & ((X60 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X67) = $true)) | ((X60 @ id @ (lam @ X61) @ id) = $true) | ? [X75 : term] : (((X60 @ id @ (sub @ X61 @ (push @ X75 @ id)) @ id) != $true) & ((X60 @ id @ X75 @ id) = $true)) | ? [X71 : subst,X72 : subst,X73 : subst,X74 : term] : (((X60 @ (comp @ X73 @ X71) @ (sub @ X74 @ X71) @ X72) != $true) & ((X60 @ X73 @ X74 @ (comp @ X71 @ X72)) = $true)) | ? [X62 : subst > term > term] : (! [X63 : term,X64 : subst,X65 : subst] : ((sub @ (X62 @ X65 @ X63) @ X64) = (X62 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64))) & ! [X66 : term] : (((X60 @ id @ X66 @ id) != $true) | ((X60 @ id @ (X62 @ id @ X66) @ id) = $true)) & ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3 = $true)) & (((((! [X285 : term,X286 : subst > term > subst > $o] : (? [X292 : term,X293 : term] : (($true = (X286 @ id @ X293 @ id)) & ((X286 @ id @ X292 @ id) = $true) & ((X286 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id) != $true)) | ((X286 @ id @ X285 @ id) = $true) | ? [X287 : subst > term > term] : (((X286 @ id @ (lam @ (X287 @ sh @ one)) @ id) != $true) & ! [X291 : term] : (((X286 @ id @ X291 @ id) != $true) | ((X286 @ id @ (X287 @ id @ X291) @ id) = $true)) & ! [X288 : subst,X289 : term,X290 : subst] : ((sub @ (X287 @ X288 @ X289) @ X290) = (X287 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))) | ? [X275 : subst > term > subst > $o,X276 : term,X277 : term > $o] : (! [X278 : subst > term > term] : (((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id) = $true) | ? [X280 : term,X281 : subst,X282 : subst] : ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)) != (sub @ (X278 @ X282 @ X280) @ X281)) | ? [X279 : term] : (((X275 @ id @ (X278 @ id @ X279) @ id) != $true) & ((X275 @ id @ X279 @ id) = $true))) & ((X277 @ (lam @ X276)) != $true) & ! [X284 : term] : (((X277 @ X284) != $true) | ((X277 @ (sub @ X276 @ (push @ X284 @ id))) = $true)) & ! [X283 : term] : ((X277 @ X283) = (X275 @ id @ X283 @ id)))) | ? [X274 : term] : ((sub @ X274 @ id) != X274)) | ? [X267 : term > $o,X268 : term] : (! [X272 : term] : (? [X273 : term] : (((X267 @ (sub @ X272 @ (push @ X273 @ id))) != $true) & ($true = (X267 @ X273))) | ((X267 @ (lam @ X272)) = $true)) & ! [X269 : term,X270 : term] : (($true != (X267 @ X269)) | ((X267 @ (ap @ X270 @ X269)) = $true) | ((X267 @ X270) != $true)) & ((X267 @ X268) != $true) & ! [X271 : term] : (((var @ X271) != $true) | ($true = (X267 @ X271))))) | ? [X264 : subst > term > subst > $o] : ! [X265 : term > $o] : ? [X266 : term] : ((X265 @ X266) != (X264 @ id @ X266 @ id))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((((! [X150 : subst > term > subst > $o,X151 : term] : (? [X154 : term] : (((var @ (sub @ X154 @ id)) = $true) & ((X150 @ id @ X154 @ id) != $true)) | ? [X164 : subst,X165 : subst,X166 : subst,X167 : term] : (((X150 @ (comp @ X166 @ X165) @ (sub @ X167 @ X165) @ X164) != $true) & ((X150 @ X166 @ X167 @ (comp @ X165 @ X164)) = $true)) | ? [X159 : subst > term > term] : (! [X163 : term] : (($true != (X150 @ id @ X163 @ id)) | ((X150 @ id @ (X159 @ id @ X163) @ id) = $true)) & ! [X160 : term,X161 : subst,X162 : subst] : ((sub @ (X159 @ X162 @ X160) @ X161) = (X159 @ (comp @ X162 @ X161) @ (sub @ X160 @ X161))) & ((X150 @ id @ (lam @ (X159 @ sh @ one)) @ id) != $true)) | ? [X155 : subst,X156 : term,X157 : subst,X158 : subst] : (((X150 @ (comp @ X158 @ X155) @ (sub @ X156 @ X155) @ X157) = $true) & ((X150 @ X158 @ X156 @ (comp @ X155 @ X157)) != $true)) | ? [X152 : term,X153 : term] : (((X150 @ id @ (ap @ (sub @ X152 @ id) @ X153) @ id) != $true) & ((X150 @ id @ X153 @ id) = $true) & ((X150 @ id @ X152 @ id) = $true)) | ((X150 @ id @ X151 @ id) = $true)) | ? [X140 : term > $o,X141 : term,X142 : subst > term > subst > $o] : (! [X143 : subst > term > term] : (($true = (X142 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ? [X144 : term] : (((X142 @ id @ (X143 @ id @ X144) @ id) != $true) & ((X142 @ id @ X144 @ id) = $true)) | ? [X145 : subst,X146 : term,X147 : subst] : ((X143 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145)) != (sub @ (X143 @ X147 @ X146) @ X145))) & ((X140 @ (lam @ X141)) != $true) & ! [X149 : term] : (((X140 @ (sub @ X141 @ (push @ X149 @ id))) = $true) | ((X140 @ X149) != $true)) & ! [X148 : term] : ((X140 @ X148) = (X142 @ id @ X148 @ id)))) | ? [X139 : term] : ((sub @ X139 @ id) != X139)) | ? [X132 : term > $o,X133 : term] : (! [X135 : term,X136 : term] : (((X132 @ X135) != $true) | ((X132 @ (ap @ X135 @ X136)) = $true) | ((X132 @ X136) != $true)) & ! [X137 : term] : (((X132 @ (lam @ X137)) = $true) | ? [X138 : term] : (((X132 @ (sub @ X137 @ (push @ X138 @ id))) != $true) & ((X132 @ X138) = $true))) & ! [X134 : term] : (($true = (X132 @ X134)) | ((var @ X134) != $true)) & ((X132 @ X133) != $true))) | ? [X129 : subst > term > subst > $o] : ! [X130 : term > $o] : ? [X131 : term] : ((X130 @ X131) != (X129 @ id @ X131 @ id))) <=> (hoasinduction_lthm_3 = $true))),
% 28.46/5.33 inference(ennf_transformation,[status(thm)],[f11])).
% 28.46/5.33 thf(f11,plain,(
% 28.46/5.33 ! [X294 : d_term,X295 : d_term] : (((d2term @ X294) = (d2term @ X295)) => (X294 = X295)) & (axabs = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) = X300) => (! [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) = X303) => ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ((X307 @ X306) != $true))))) & (hoaslamnotap_lthm = $true) & (! [X233 : term,X234 : subst > term > subst > $o] : (~! [X240 : term] : (((X234 @ id @ (sub @ X233 @ (push @ X240 @ id)) @ id) = $true) | ((X234 @ id @ X240 @ id) != $true)) | ~! [X235 : subst > term > term] : (~! [X239 : term] : (((X234 @ id @ (X235 @ id @ X239) @ id) = $true) | ((X234 @ id @ X239 @ id) != $true)) | ~! [X236 : subst,X237 : subst,X238 : term] : ((X235 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237)) = (sub @ (X235 @ X236 @ X238) @ X237)) | ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id) = $true)) | ((X234 @ id @ (lam @ X233) @ id) = $true)) <=> (hoasinduction_lem3a = $true)) & (! [X431 : term,X432 : subst > term > subst > $o] : (~! [X438 : term] : (((X432 @ id @ (sub @ X431 @ (push @ X438 @ id)) @ id) = $true) | ((X432 @ id @ X438 @ id) != $true)) | ~! [X433 : subst > term > term] : (~! [X434 : subst,X435 : subst,X436 : term] : ((sub @ (X433 @ X434 @ X436) @ X435) = (X433 @ (comp @ X434 @ X435) @ (sub @ X436 @ X435))) | ((X432 @ id @ (lam @ (X433 @ sh @ one)) @ id) = $true) | ~! [X437 : term] : (((X432 @ id @ (X433 @ id @ X437) @ id) = $true) | ((X432 @ id @ X437 @ id) != $true))) | ((X432 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2 = $true) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one))) | ~! [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) = (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81)))) <=> (hoaslamnotap = $true)) & (! [X178 : term] : ((sub @ X178 @ id) = X178) <=> (axvarid = $true)) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoaslaminj_lthm = $true) <=> (! [X413 : subst,X414 : term] : ((sub @ one @ (push @ X414 @ X413)) = X414) => (! [X415 : subst,X416 : term] : ((comp @ sh @ (push @ X416 @ X415)) = X415) => (! [X417 : term,X418 : term] : (((lam @ X418) != (lam @ X417)) | (X417 = X418)) => ! [X419 : subst,X420 : subst > term > term,X421 : subst > term > term,X422 : term] : (((lam @ (X420 @ sh @ one)) != (lam @ (X421 @ sh @ one))) | ~! [X426 : subst,X427 : subst,X428 : term] : ((X421 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)) = (sub @ (X421 @ X426 @ X428) @ X427)) | ((X420 @ X419 @ X422) = (X421 @ X419 @ X422)) | ~! [X423 : term,X424 : subst,X425 : subst] : ((X420 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424)) = (sub @ (X420 @ X425 @ X423) @ X424))))))) & (ulamvarsh = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X378 : term] : ~! [X379 : subst > term > term] : ~! [X380 : term,X381 : subst] : ((X379 @ X381 @ X380) = (sub @ X378 @ (push @ X380 @ X381))) => (! [X382 : term] : ((sub @ X382 @ id) = X382) => ! [X383 : term,X384 : term > $o,X385 : subst > term > subst > $o] : (~! [X392 : term] : (((X384 @ X392) != $true) | ((X384 @ (sub @ X383 @ (push @ X392 @ id))) = $true)) | ~! [X386 : term] : ((X384 @ X386) = (X385 @ id @ X386 @ id)) | ((X384 @ (lam @ X383)) = $true) | ~! [X387 : subst > term > term] : (((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id) = $true) | ~! [X388 : term] : (((X385 @ id @ X388 @ id) != $true) | ((X385 @ id @ (X387 @ id @ X388) @ id) = $true)) | ~! [X389 : subst,X390 : subst,X391 : term] : ((X387 @ (comp @ X390 @ X389) @ (sub @ X391 @ X389)) = (sub @ (X387 @ X390 @ X391) @ X389)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvarind = $true) & (induction2_gthm = $true) & (! [X327 : term] : ~! [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) != (X328 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ! [X529 : d_subst] : (d_id = X529) & (hoaslamnotvar_lthm = $true) & ((d2subst @ d_id) = sh) & ((axidl = $true) <=> ! [X257 : subst] : ((comp @ id @ X257) = X257)) & (termmset_gthm = $true) & (pushprop = $true) & (one = (d2term @ d_one)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true) | ($true != (X93 @ X94)))) & (hoasapnotvar = $true) & ((hoasapinj2 = $true) <=> ! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)))) & (! [X489 : subst > term > subst > $o,X490 : term] : (~! [X491 : term] : (((X489 @ id @ X491 @ id) != $true) | ((X489 @ id @ (sub @ X490 @ (push @ X491 @ id)) @ id) = $true)) | ~! [X492 : term,X493 : subst > term > term] : (~! [X500 : term] : (((X489 @ id @ X500 @ id) != $true) | ((X489 @ id @ (X493 @ id @ X500) @ id) = $true)) | ((X489 @ id @ (lam @ (X493 @ sh @ one)) @ id) = $true) | ~! [X497 : subst,X498 : term,X499 : subst] : ((sub @ (X493 @ X499 @ X498) @ X497) = (sub @ (sub @ X492 @ (push @ X498 @ X499)) @ X497)) | ~! [X494 : subst,X495 : term,X496 : subst] : ((X493 @ (comp @ X496 @ X494) @ (sub @ X495 @ X494)) = (sub @ X492 @ (push @ (sub @ X495 @ X494) @ (comp @ X496 @ X494))))) | ((X489 @ id @ (lam @ (sub @ X490 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X171 : subst > term > subst > $o] : ~! [X172 : term > $o] : ~! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173))) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) <=> (hoasapinj1 = $true)) & ((hoasinduction = $true) <=> ! [X309 : term,X310 : subst > term > subst > $o] : (~! [X320 : subst > term > term] : (((X310 @ id @ (lam @ (X320 @ sh @ one)) @ id) = $true) | ~! [X321 : subst,X322 : term,X323 : subst] : ((sub @ (X320 @ X321 @ X322) @ X323) = (X320 @ (comp @ X321 @ X323) @ (sub @ X322 @ X323))) | ~! [X324 : term] : (((X310 @ id @ X324 @ id) != $true) | ((X310 @ id @ (X320 @ id @ X324) @ id) = $true))) | ((X310 @ id @ X309 @ id) = $true) | ~! [X325 : term,X326 : term] : (($true != (X310 @ id @ X326 @ id)) | ((X310 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) = $true) | ((X310 @ id @ X325 @ id) != $true)) | ~! [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (((X310 @ (comp @ X318 @ X319) @ (sub @ X316 @ X319) @ X317) = $true) | ((X310 @ X318 @ X316 @ (comp @ X319 @ X317)) != $true)) | ~! [X312 : subst,X313 : subst,X314 : term,X315 : subst] : (((X310 @ X315 @ X314 @ (comp @ X312 @ X313)) = $true) | ($true != (X310 @ (comp @ X315 @ X312) @ (sub @ X314 @ X312) @ X313))) | ~! [X311 : term] : (((X310 @ id @ X311 @ id) = $true) | ((var @ (sub @ X311 @ id)) != $true)))) & ((hoaslaminj = $true) <=> ! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ~! [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) = (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))) | ~! [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) = (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axmap = $true) & (hoasinduction_lem1_lthm = $true) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (((X483 @ one) = $true) | ~! [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) = (X483 @ X485)) | ((X481 @ X484) != $true)) <=> (pushprop_lem1v2 = $true)) & (! [X9 : term,X10 : term > $o,X11 : term,X12 : subst > term > subst > $o] : (~! [X14 : subst,X15 : subst,X16 : subst,X17 : term] : (((X12 @ X15 @ X17 @ (comp @ X16 @ X14)) = $true) | ((X12 @ (comp @ X15 @ X16) @ (sub @ X17 @ X16) @ X14) != $true)) | ((X10 @ X11) != $true) | ~! [X22 : term,X23 : term] : (($true != (X12 @ id @ X23 @ id)) | ((X12 @ id @ (ap @ (sub @ X23 @ id) @ X22) @ id) = $true) | ($true != (X12 @ id @ X22 @ id))) | ((X10 @ (ap @ X11 @ X9)) = $true) | ~! [X13 : term] : ((X10 @ X13) = (X12 @ id @ X13 @ id)) | ~! [X18 : subst,X19 : term,X20 : subst,X21 : subst] : (((X12 @ X20 @ X19 @ (comp @ X18 @ X21)) != $true) | ((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21) = $true)) | ((X10 @ X9) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (axvarshift = $true) & (lamnotap != $true) & (! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (~! [X250 : subst > term > term] : (((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) = $true) | ~! [X251 : term] : (((X246 @ id @ X251 @ id) != $true) | ((X246 @ id @ (X250 @ id @ X251) @ id) = $true)) | ~! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254)))) | ~! [X255 : term] : (((X247 @ X255) != $true) | ((X247 @ (sub @ X248 @ (push @ X255 @ id))) = $true)) | ~! [X249 : term] : ((X246 @ id @ X249 @ id) = (X247 @ X249)) | ((X247 @ (lam @ X248)) = $true)) <=> (hoasinduction_lem3v2a = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X393 : term,X394 : subst > term > subst > $o] : (~! [X400 : term] : (((X394 @ id @ (sub @ X393 @ (push @ X400 @ id)) @ id) = $true) | ((X394 @ id @ X400 @ id) != $true)) | ((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id) = $true) | ~! [X395 : subst > term > term] : (~! [X396 : term] : (((X394 @ id @ X396 @ id) != $true) | ((X394 @ id @ (X395 @ id @ X396) @ id) = $true)) | ~! [X397 : term,X398 : subst,X399 : subst] : ((X395 @ (comp @ X398 @ X399) @ (sub @ X397 @ X399)) = (sub @ (X395 @ X398 @ X397) @ X399)) | ((X394 @ id @ (lam @ (X395 @ sh @ one)) @ id) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem2v2_gthm = $true) & (! [X259 : term > $o,X260 : subst,X261 : term] : ~! [X262 : term > $o] : ~! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260)))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((axscons = $true) <=> ! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24)) & (! [X429 : term] : ~! [X430 : subst > term > term] : ((X430 @ sh @ one) != (sub @ X429 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> ! [X401 : subst,X402 : term > $o,X403 : term] : (~! [X406 : term] : (((var @ X406) != $true) | ((X402 @ (sub @ X406 @ X401)) = $true)) | ~! [X407 : term,X408 : term] : (((X402 @ X408) != $true) | ((X402 @ (ap @ X408 @ X407)) = $true) | ((X402 @ X407) != $true)) | ((X402 @ (sub @ X403 @ X401)) = $true) | ~! [X404 : term] : (~! [X405 : term] : (((X402 @ X405) != $true) | ((X402 @ (sub @ X404 @ (push @ X405 @ id))) = $true)) | ((X402 @ (lam @ X404)) = $true)))) & (! [X256 : term] : ((sub @ X256 @ id) = X256) <=> (termmset = $true)) & ((! [X95 : term] : ((sub @ X95 @ id) = X95) => (! [X96 : term,X97 : subst > term > subst > $o] : (~! [X103 : term] : (((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true) | ((X97 @ id @ X103 @ id) != $true)) | ~! [X98 : subst > term > term] : (~! [X99 : term,X100 : subst,X101 : subst] : ((sub @ (X98 @ X101 @ X99) @ X100) = (X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100))) | ~! [X102 : term] : (($true != (X97 @ id @ X102 @ id)) | ((X97 @ id @ (X98 @ id @ X102) @ id) = $true)) | ((X97 @ id @ (lam @ (X98 @ sh @ one)) @ id) = $true)) | ((X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id) = $true)) => ! [X104 : term,X105 : subst > term > subst > $o] : (~! [X115 : subst > term > term] : (~! [X117 : subst,X118 : subst,X119 : term] : ((X115 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118)) = (sub @ (X115 @ X117 @ X119) @ X118)) | ~! [X116 : term] : (((X105 @ id @ (X115 @ id @ X116) @ id) = $true) | ((X105 @ id @ X116 @ id) != $true)) | ((X105 @ id @ (lam @ (X115 @ sh @ one)) @ id) = $true)) | ~! [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (((X105 @ (comp @ X109 @ X108) @ (sub @ X107 @ X108) @ X106) != $true) | ((X105 @ X109 @ X107 @ (comp @ X108 @ X106)) = $true)) | ((X105 @ id @ (lam @ X104) @ id) = $true) | ~! [X110 : term,X111 : subst,X112 : subst,X113 : subst] : (((X105 @ X112 @ X110 @ (comp @ X113 @ X111)) != $true) | ($true = (X105 @ (comp @ X112 @ X113) @ (sub @ X110 @ X113) @ X111))) | ~! [X114 : term] : (((X105 @ id @ X114 @ id) != $true) | ((X105 @ id @ (sub @ X104 @ (push @ X114 @ id)) @ id) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) <=> (laminj = $true)) & (hoasapinj1_gthm = $true) & (pushprop_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X333 : term,X334 : subst] : ((sub @ one @ (push @ X333 @ X334)) = X333) => (! [X335 : subst,X336 : term] : ((comp @ sh @ (push @ X336 @ X335)) = X335) => (! [X337 : subst] : ((comp @ X337 @ id) = X337) => (! [X338 : term,X339 : term > $o] : (($true = (X339 @ X338)) | ~! [X340 : term] : (((X339 @ X340) = $true) | ((var @ X340) != $true)) | ~! [X341 : term] : (((X339 @ X341) != $true) | ($true = (X339 @ (lam @ X341)))) | ~! [X342 : term,X343 : term] : (($true != (X339 @ X342)) | ((X339 @ (ap @ X343 @ X342)) = $true) | ((X339 @ X343) != $true))) => ! [X344 : subst,X345 : term,X346 : term > $o] : (~! [X347 : term] : (((X346 @ (lam @ X347)) = $true) | ~! [X348 : term] : (((X346 @ (sub @ X347 @ (push @ X348 @ id))) = $true) | ((X346 @ X348) != $true))) | ~! [X351 : term] : (((var @ X351) != $true) | ($true = (X346 @ (sub @ X351 @ X344)))) | ~! [X349 : term,X350 : term] : (((X346 @ X350) != $true) | ((X346 @ X349) != $true) | ((X346 @ (ap @ X350 @ X349)) = $true)) | ((X346 @ (sub @ X345 @ X344)) = $true))))))) & ! [X486 : d_term] : (d_one = X486) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X535 @ X532) != (ap @ X534 @ X533)) | (X532 = X533)) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))))) & ((termmset_lthm = $true) <=> (! [X298 : term] : ((sub @ X298 @ id) = X298) => ! [X299 : term] : ((sub @ X299 @ id) = X299))) & ((var @ (d2term @ d_one)) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X457 : subst > term > subst > $o,X458 : term,X459 : term] : (((X457 @ id @ X458 @ id) != $true) | ~! [X462 : subst,X463 : subst,X464 : subst,X465 : term] : (($true = (X457 @ X463 @ X465 @ (comp @ X462 @ X464))) | ((X457 @ (comp @ X463 @ X462) @ (sub @ X465 @ X462) @ X464) != $true)) | ((X457 @ id @ (ap @ X458 @ X459) @ id) = $true) | ~! [X460 : term,X461 : term] : (($true != (X457 @ id @ X460 @ id)) | ((X457 @ id @ X461 @ id) != $true) | ((X457 @ id @ (ap @ (sub @ X461 @ id) @ X460) @ id) = $true)) | ((X457 @ id @ X459 @ id) != $true) | ~! [X466 : subst,X467 : term,X468 : subst,X469 : subst] : (((X457 @ (comp @ X469 @ X468) @ (sub @ X467 @ X468) @ X466) = $true) | ((X457 @ X469 @ X467 @ (comp @ X468 @ X466)) != $true)))) & (induction2lem_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) <=> ! [X241 : subst,X242 : term,X243 : term > $o] : ~! [X244 : term > $o] : ~! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & (hoasapnotvar_gthm = $true) & ((induction2 = $true) <=> ! [X120 : term > $o,X121 : term] : (~! [X123 : term,X124 : term] : (((X120 @ X123) != $true) | ((X120 @ (ap @ X123 @ X124)) = $true) | ((X120 @ X124) != $true)) | ((X120 @ X121) = $true) | ~! [X122 : term] : (((var @ X122) != $true) | ((X120 @ X122) = $true)) | ~! [X125 : term] : (~! [X126 : term] : (((X120 @ (sub @ X125 @ (push @ X126 @ id))) = $true) | ((X120 @ X126) != $true)) | ((X120 @ (lam @ X125)) = $true)))) & (pushprop_lem3v2_lthm = $true) & ((axvarcons = $true) <=> ! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128)) & (! [X329 : term] : ~! [X330 : subst > term > term] : ~! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((axshiftcons = $true) <=> ! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530)) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & (hoasinduction_lem1_gthm = $true) & (axapp = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X0 : term,X1 : subst > term > subst > $o] : (($true = (X1 @ id @ X0 @ id)) | ~! [X2 : term,X3 : term] : (((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) = $true) | ((X1 @ id @ X2 @ id) != $true) | ((X1 @ id @ X3 @ id) != $true)) | ~! [X4 : subst > term > term] : (~! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true) | ~! [X8 : term] : (((X1 @ id @ (X4 @ id @ X8) @ id) = $true) | ((X1 @ id @ X8 @ id) != $true))))) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) <=> (axidr = $true)) & (pushprop_lem2v2_lthm = $true) & ((! [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) = X501) => ! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (~! [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) = (X505 @ X507)) | ($true = (X505 @ one)) | ($true != (X504 @ X503)))) <=> (pushprop_lem1v2_lthm = $true)) & (apnotvar = $true) & (hoasapnotvar_lthm = $true) & (lamnotvar = $true) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) <=> (apinj2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((! [X472 : term] : ((sub @ X472 @ id) = X472) => (! [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 = X476) | ((ap @ X476 @ X473) != (ap @ X474 @ X475))) => ! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))))) <=> (hoasapinj1_lthm = $true)) & (! [X174 : term] : ~! [X175 : subst > term > term] : ~! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) <=> (hoasinduction_lem3v2_f = $true)) & ((! [X82 : subst] : ((comp @ id @ X82) = X82) => (! [X83 : subst] : ((comp @ X83 @ id) = X83) => (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((! [X179 : term > $o,X180 : term] : (~! [X181 : term] : (((X179 @ (lam @ X181)) = $true) | ~! [X182 : term] : (((X179 @ X182) != $true) | ((X179 @ (sub @ X181 @ (push @ X182 @ id))) = $true))) | ((X179 @ X180) = $true) | ~! [X183 : term,X184 : term] : (((X179 @ X184) != $true) | ((X179 @ (ap @ X184 @ X183)) = $true) | ($true != (X179 @ X183))) | ~! [X185 : term] : (((X179 @ X185) = $true) | ((var @ X185) != $true))) => (! [X186 : term,X187 : term,X188 : subst > term > subst > $o] : (($true = (X188 @ id @ (ap @ X186 @ X187) @ id)) | ~! [X189 : term,X190 : term] : (((X188 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id) = $true) | ((X188 @ id @ X190 @ id) != $true) | ((X188 @ id @ X189 @ id) != $true)) | ~! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : (((X188 @ (comp @ X194 @ X193) @ (sub @ X191 @ X193) @ X192) != $true) | ((X188 @ X194 @ X191 @ (comp @ X193 @ X192)) = $true)) | ((X188 @ id @ X187 @ id) != $true) | ~! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (((X188 @ (comp @ X197 @ X198) @ (sub @ X195 @ X198) @ X196) = $true) | ((X188 @ X197 @ X195 @ (comp @ X198 @ X196)) != $true)) | ((X188 @ id @ X186 @ id) != $true)) => (! [X199 : term,X200 : subst > term > subst > $o] : (((X200 @ id @ (lam @ X199) @ id) = $true) | ~! [X205 : term] : (((X200 @ id @ X205 @ id) != $true) | ((X200 @ id @ (sub @ X199 @ (push @ X205 @ id)) @ id) = $true)) | ~! [X201 : subst,X202 : subst,X203 : subst,X204 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X204 @ X202) @ X203) = $true) | ((X200 @ X201 @ X204 @ (comp @ X202 @ X203)) != $true)) | ~! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (((X200 @ (comp @ X213 @ X214) @ (sub @ X212 @ X214) @ X211) != $true) | ((X200 @ X213 @ X212 @ (comp @ X214 @ X211)) = $true)) | ~! [X206 : subst > term > term] : (~! [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) = (sub @ (X206 @ X210 @ X208) @ X209)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ~! [X207 : term] : (((X200 @ id @ X207 @ id) != $true) | ((X200 @ id @ (X206 @ id @ X207) @ id) = $true)))) => ! [X215 : subst > term > subst > $o,X216 : term] : (~! [X231 : term,X232 : term] : (((X215 @ id @ X232 @ id) != $true) | ((X215 @ id @ X231 @ id) != $true) | ((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) = $true)) | ~! [X217 : term] : (((X215 @ id @ X217 @ id) = $true) | ((var @ (sub @ X217 @ id)) != $true)) | ~! [X227 : subst,X228 : subst,X229 : subst,X230 : term] : (((X215 @ X229 @ X230 @ (comp @ X228 @ X227)) != $true) | ((X215 @ (comp @ X229 @ X228) @ (sub @ X230 @ X228) @ X227) = $true)) | ~! [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (((X215 @ (comp @ X225 @ X226) @ (sub @ X223 @ X226) @ X224) != $true) | ((X215 @ X225 @ X223 @ (comp @ X226 @ X224)) = $true)) | ((X215 @ id @ X216 @ id) = $true) | ~! [X218 : subst > term > term] : (~! [X219 : term,X220 : subst,X221 : subst] : ((X218 @ (comp @ X220 @ X221) @ (sub @ X219 @ X221)) = (sub @ (X218 @ X220 @ X219) @ X221)) | ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id) = $true) | ~! [X222 : term] : (((X215 @ id @ X222 @ id) != $true) | ((X215 @ id @ (X218 @ id @ X222) @ id) = $true))))))) <=> (hoasinduction_lthm = $true)) & (substmonoid_gthm = $true) & (hoaslamnotvar = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X352 : term,X353 : term > $o,X354 : subst > term > subst > $o] : (((X353 @ (lam @ X352)) = $true) | ~! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : (((X354 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) = $true) | ((X354 @ X366 @ X368 @ (comp @ X369 @ X367)) != $true)) | ~! [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (((X354 @ (comp @ X358 @ X360) @ (sub @ X359 @ X360) @ X357) != $true) | ((X354 @ X358 @ X359 @ (comp @ X360 @ X357)) = $true)) | ~! [X356 : term] : ((X354 @ id @ X356 @ id) = (X353 @ X356)) | ~! [X355 : term] : (((X353 @ (sub @ X352 @ (push @ X355 @ id))) = $true) | ((X353 @ X355) != $true)) | ~! [X361 : subst > term > term] : (((X354 @ id @ (lam @ (X361 @ sh @ one)) @ id) = $true) | ~! [X362 : subst,X363 : subst,X364 : term] : ((sub @ (X361 @ X363 @ X364) @ X362) = (X361 @ (comp @ X363 @ X362) @ (sub @ X364 @ X362))) | ~! [X365 : term] : (((X354 @ id @ (X361 @ id @ X365) @ id) = $true) | ((X354 @ id @ X365 @ id) != $true))))) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X43 : term] : ((sub @ X43 @ id) = X43) => (! [X44 : subst > term > subst > $o,X45 : term] : (~! [X51 : term] : (((X44 @ id @ X51 @ id) != $true) | ((X44 @ id @ (sub @ X45 @ (push @ X51 @ id)) @ id) = $true)) | ((X44 @ id @ (lam @ (sub @ X45 @ (push @ one @ sh))) @ id) = $true) | ~! [X46 : subst > term > term] : (~! [X47 : term] : (((X44 @ id @ X47 @ id) != $true) | ($true = (X44 @ id @ (X46 @ id @ X47) @ id))) | ((X44 @ id @ (lam @ (X46 @ sh @ one)) @ id) = $true) | ~! [X48 : subst,X49 : term,X50 : subst] : ((X46 @ (comp @ X50 @ X48) @ (sub @ X49 @ X48)) = (sub @ (X46 @ X50 @ X49) @ X48)))) => ! [X52 : term,X53 : subst > term > subst > $o] : (~! [X59 : term] : (($true != (X53 @ id @ X59 @ id)) | ((X53 @ id @ (sub @ X52 @ (push @ X59 @ id)) @ id) = $true)) | ~! [X54 : subst > term > term] : (((X53 @ id @ (lam @ (X54 @ sh @ one)) @ id) = $true) | ~! [X55 : term] : (($true != (X53 @ id @ X55 @ id)) | ((X53 @ id @ (X54 @ id @ X55) @ id) = $true)) | ~! [X56 : subst,X57 : subst,X58 : term] : ((X54 @ (comp @ X57 @ X56) @ (sub @ X58 @ X56)) = (sub @ (X54 @ X57 @ X58) @ X56))) | ((X53 @ id @ (lam @ X52) @ id) = $true))))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoaslaminj_gthm = $true) & ((substmonoid = $true) <=> (! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41))) & (pushprop_lem1_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) <=> (shinj = $true)) & (hoasinduction_lem3_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X508 : term] : ((sub @ X508 @ id) = X508) => ! [X509 : term > $o,X510 : subst > term > subst > $o,X511 : term] : (~! [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (((X510 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515) = $true) | ((X510 @ X513 @ X512 @ (comp @ X514 @ X515)) != $true)) | ~! [X516 : subst,X517 : term,X518 : subst,X519 : subst] : (((X510 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518) @ X519) != $true) | ((X510 @ X516 @ X517 @ (comp @ X518 @ X519)) = $true)) | ~! [X521 : subst > term > term] : (~! [X522 : term,X523 : subst,X524 : subst] : ((sub @ (X521 @ X523 @ X522) @ X524) = (X521 @ (comp @ X523 @ X524) @ (sub @ X522 @ X524))) | ((X510 @ id @ (lam @ (X521 @ sh @ one)) @ id) = $true) | ~! [X525 : term] : (((X510 @ id @ X525 @ id) != $true) | ((X510 @ id @ (X521 @ id @ X525) @ id) = $true))) | ~! [X526 : term] : (((X509 @ X526) != $true) | ($true = (X509 @ (sub @ X511 @ (push @ X526 @ id))))) | ((X509 @ (lam @ X511)) = $true) | ~! [X520 : term] : ((X509 @ X520) = (X510 @ id @ X520 @ id))))) & (! [X439 : term,X440 : term > $o] : (~! [X444 : term] : (($true != (var @ X444)) | ((X440 @ X444) = $true)) | ~! [X441 : term,X442 : term] : (((X440 @ (ap @ X441 @ X442)) = $true) | ((X440 @ X441) != $true) | ((X440 @ X442) != $true)) | ~! [X443 : term] : (((X440 @ (lam @ X443)) = $true) | ((X440 @ X443) != $true)) | ((X440 @ X439) = $true)) <=> (induction = $true)) & (! [X168 : subst > term > subst > $o] : ~! [X169 : term > $o] : ~! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) <=> (hoasinduction_lem0_lthm = $true)) & ((induction2_lthm = $true) <=> (! [X25 : term] : ((sub @ X25 @ id) = X25) => (! [X26 : term > $o,X27 : term,X28 : subst] : (~! [X33 : term] : (((var @ X33) != $true) | ((X26 @ (sub @ X33 @ X28)) = $true)) | ~! [X31 : term] : (((X26 @ (lam @ X31)) = $true) | ~! [X32 : term] : (((X26 @ X32) != $true) | ((X26 @ (sub @ X31 @ (push @ X32 @ id))) = $true))) | ~! [X29 : term,X30 : term] : (((X26 @ X29) != $true) | ((X26 @ X30) != $true) | ((X26 @ (ap @ X29 @ X30)) = $true)) | ((X26 @ (sub @ X27 @ X28)) = $true)) => ! [X34 : term,X35 : term > $o] : (~! [X40 : term] : (((X35 @ X40) = $true) | ((var @ X40) != $true)) | ~! [X36 : term] : (~! [X37 : term] : (($true = (X35 @ (sub @ X36 @ (push @ X37 @ id)))) | ((X35 @ X37) != $true)) | ((X35 @ (lam @ X36)) = $true)) | ~! [X38 : term,X39 : term] : (((X35 @ X38) != $true) | ((X35 @ (ap @ X39 @ X38)) = $true) | ($true != (X35 @ X39))) | ($true = (X35 @ X34)))))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) <=> (apinj1 = $true)) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) = (d2subst @ X471)) => (X470 = X471)) & (! [X60 : subst > term > subst > $o,X61 : term] : (((X60 @ id @ (lam @ X61) @ id) = $true) | ~! [X71 : subst,X72 : subst,X73 : subst,X74 : term] : (((X60 @ X73 @ X74 @ (comp @ X71 @ X72)) != $true) | ((X60 @ (comp @ X73 @ X71) @ (sub @ X74 @ X71) @ X72) = $true)) | ~! [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (((X60 @ X69 @ X68 @ (comp @ X70 @ X67)) = $true) | ((X60 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X67) != $true)) | ~! [X62 : subst > term > term] : (~! [X63 : term,X64 : subst,X65 : subst] : ((sub @ (X62 @ X65 @ X63) @ X64) = (X62 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64))) | ~! [X66 : term] : (((X60 @ id @ X66 @ id) != $true) | ((X60 @ id @ (X62 @ id @ X66) @ id) = $true)) | ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) = $true)) | ~! [X75 : term] : (((X60 @ id @ X75 @ id) != $true) | ((X60 @ id @ (sub @ X61 @ (push @ X75 @ id)) @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & ((! [X264 : subst > term > subst > $o] : ~! [X265 : term > $o] : ~! [X266 : term] : ((X265 @ X266) = (X264 @ id @ X266 @ id)) => (! [X267 : term > $o,X268 : term] : (((X267 @ X268) = $true) | ~! [X269 : term,X270 : term] : (($true != (X267 @ X269)) | ((X267 @ (ap @ X270 @ X269)) = $true) | ((X267 @ X270) != $true)) | ~! [X272 : term] : (~! [X273 : term] : (($true != (X267 @ X273)) | ((X267 @ (sub @ X272 @ (push @ X273 @ id))) = $true)) | ((X267 @ (lam @ X272)) = $true)) | ~! [X271 : term] : (((var @ X271) != $true) | ($true = (X267 @ X271)))) => (! [X274 : term] : ((sub @ X274 @ id) = X274) => (! [X275 : subst > term > subst > $o,X276 : term,X277 : term > $o] : (((X277 @ (lam @ X276)) = $true) | ~! [X283 : term] : ((X277 @ X283) = (X275 @ id @ X283 @ id)) | ~! [X278 : subst > term > term] : (~! [X280 : term,X281 : subst,X282 : subst] : ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)) = (sub @ (X278 @ X282 @ X280) @ X281)) | ((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id) = $true) | ~! [X279 : term] : (((X275 @ id @ X279 @ id) != $true) | ((X275 @ id @ (X278 @ id @ X279) @ id) = $true))) | ~! [X284 : term] : (((X277 @ X284) != $true) | ((X277 @ (sub @ X276 @ (push @ X284 @ id))) = $true))) => ! [X285 : term,X286 : subst > term > subst > $o] : (~! [X287 : subst > term > term] : (((X286 @ id @ (lam @ (X287 @ sh @ one)) @ id) = $true) | ~! [X288 : subst,X289 : term,X290 : subst] : ((sub @ (X287 @ X288 @ X289) @ X290) = (X287 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))) | ~! [X291 : term] : (((X286 @ id @ X291 @ id) != $true) | ((X286 @ id @ (X287 @ id @ X291) @ id) = $true))) | ~! [X292 : term,X293 : term] : (($true != (X286 @ id @ X293 @ id)) | ((X286 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id) = $true) | ((X286 @ id @ X292 @ id) != $true)) | ((X286 @ id @ X285 @ id) = $true)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X129 : subst > term > subst > $o] : ~! [X130 : term > $o] : ~! [X131 : term] : ((X130 @ X131) = (X129 @ id @ X131 @ id)) => (! [X132 : term > $o,X133 : term] : (((X132 @ X133) = $true) | ~! [X137 : term] : (((X132 @ (lam @ X137)) = $true) | ~! [X138 : term] : (((X132 @ (sub @ X137 @ (push @ X138 @ id))) = $true) | ((X132 @ X138) != $true))) | ~! [X135 : term,X136 : term] : (((X132 @ X135) != $true) | ((X132 @ (ap @ X135 @ X136)) = $true) | ((X132 @ X136) != $true)) | ~! [X134 : term] : (($true = (X132 @ X134)) | ((var @ X134) != $true))) => (! [X139 : term] : ((sub @ X139 @ id) = X139) => (! [X140 : term > $o,X141 : term,X142 : subst > term > subst > $o] : (~! [X148 : term] : ((X140 @ X148) = (X142 @ id @ X148 @ id)) | ~! [X149 : term] : (((X140 @ (sub @ X141 @ (push @ X149 @ id))) = $true) | ((X140 @ X149) != $true)) | ((X140 @ (lam @ X141)) = $true) | ~! [X143 : subst > term > term] : (($true = (X142 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ~! [X144 : term] : (((X142 @ id @ X144 @ id) != $true) | ((X142 @ id @ (X143 @ id @ X144) @ id) = $true)) | ~! [X145 : subst,X146 : term,X147 : subst] : ((X143 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145)) = (sub @ (X143 @ X147 @ X146) @ X145)))) => ! [X150 : subst > term > subst > $o,X151 : term] : (~! [X155 : subst,X156 : term,X157 : subst,X158 : subst] : (((X150 @ X158 @ X156 @ (comp @ X155 @ X157)) = $true) | ((X150 @ (comp @ X158 @ X155) @ (sub @ X156 @ X155) @ X157) != $true)) | ~! [X152 : term,X153 : term] : (((X150 @ id @ X153 @ id) != $true) | ((X150 @ id @ (ap @ (sub @ X152 @ id) @ X153) @ id) = $true) | ((X150 @ id @ X152 @ id) != $true)) | ~! [X164 : subst,X165 : subst,X166 : subst,X167 : term] : (((X150 @ X166 @ X167 @ (comp @ X165 @ X164)) != $true) | ((X150 @ (comp @ X166 @ X165) @ (sub @ X167 @ X165) @ X164) = $true)) | ((X150 @ id @ X151 @ id) = $true) | ~! [X159 : subst > term > term] : (~! [X163 : term] : (($true != (X150 @ id @ X163 @ id)) | ((X150 @ id @ (X159 @ id @ X163) @ id) = $true)) | ((X150 @ id @ (lam @ (X159 @ sh @ one)) @ id) = $true) | ~! [X160 : term,X161 : subst,X162 : subst] : ((sub @ (X159 @ X162 @ X160) @ X161) = (X159 @ (comp @ X162 @ X161) @ (sub @ X160 @ X161)))) | ~! [X154 : term] : (((X150 @ id @ X154 @ id) = $true) | ((var @ (sub @ X154 @ id)) != $true))))))) <=> (hoasinduction_lthm_3 = $true))),
% 28.46/5.33 inference(flattening,[status(thm)],[f10])).
% 28.46/5.33 thf(f10,plain,(
% 28.46/5.33 ((hoasinduction_no_psi_cond = $true) <=> ! [X0 : term,X1 : subst > term > subst > $o] : (~! [X2 : term,X3 : term] : (((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) = $true) | ~((X1 @ id @ X3 @ id) = $true) | ~((X1 @ id @ X2 @ id) = $true)) | ~! [X4 : subst > term > term] : (((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true) | ~! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ~! [X8 : term] : (~((X1 @ id @ X8 @ id) = $true) | ((X1 @ id @ (X4 @ id @ X8) @ id) = $true))) | ($true = (X1 @ id @ X0 @ id)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axassoc = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_gthm = $true) & (! [X9 : term,X10 : term > $o,X11 : term,X12 : subst > term > subst > $o] : (~((X10 @ X9) = $true) | ~! [X13 : term] : ((X10 @ X13) = (X12 @ id @ X13 @ id)) | ~! [X14 : subst,X15 : subst,X16 : subst,X17 : term] : (~((X12 @ (comp @ X15 @ X16) @ (sub @ X17 @ X16) @ X14) = $true) | ((X12 @ X15 @ X17 @ (comp @ X16 @ X14)) = $true)) | ((X10 @ (ap @ X11 @ X9)) = $true) | ~((X10 @ X11) = $true) | ~! [X18 : subst,X19 : term,X20 : subst,X21 : subst] : (~((X12 @ X20 @ X19 @ (comp @ X18 @ X21)) = $true) | ((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21) = $true)) | ~! [X22 : term,X23 : term] : (((X12 @ id @ (ap @ (sub @ X23 @ id) @ X22) @ id) = $true) | ~($true = (X12 @ id @ X22 @ id)) | ~($true = (X12 @ id @ X23 @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem2_lthm = $true) & ((axscons = $true) <=> ! [X24 : subst] : ((push @ (sub @ one @ X24) @ (comp @ sh @ X24)) = X24)) & ((! [X25 : term] : ((sub @ X25 @ id) = X25) => (! [X26 : term > $o,X27 : term,X28 : subst] : (~! [X29 : term,X30 : term] : (~((X26 @ X30) = $true) | ((X26 @ (ap @ X29 @ X30)) = $true) | ~((X26 @ X29) = $true)) | ~! [X31 : term] : (((X26 @ (lam @ X31)) = $true) | ~! [X32 : term] : (~((X26 @ X32) = $true) | ((X26 @ (sub @ X31 @ (push @ X32 @ id))) = $true))) | ~! [X33 : term] : (((X26 @ (sub @ X33 @ X28)) = $true) | ~((var @ X33) = $true)) | ((X26 @ (sub @ X27 @ X28)) = $true)) => ! [X34 : term,X35 : term > $o] : (~! [X36 : term] : (~! [X37 : term] : (($true = (X35 @ (sub @ X36 @ (push @ X37 @ id)))) | ~((X35 @ X37) = $true)) | ((X35 @ (lam @ X36)) = $true)) | ($true = (X35 @ X34)) | ~! [X38 : term,X39 : term] : (((X35 @ (ap @ X39 @ X38)) = $true) | ~($true = (X35 @ X39)) | ~((X35 @ X38) = $true)) | ~! [X40 : term] : (~((var @ X40) = $true) | ((X35 @ X40) = $true))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = sh) & ((substmonoid = $true) <=> (! [X42 : subst] : ((comp @ id @ X42) = X42) & ! [X41 : subst] : ((comp @ X41 @ id) = X41))) & (hoasinduction_lem1v2 = $true) & (ulamvarsh = $true) & (axvarshift = $true) & ((! [X43 : term] : ((sub @ X43 @ id) = X43) => (! [X44 : subst > term > subst > $o,X45 : term] : (~! [X46 : subst > term > term] : (~! [X47 : term] : (($true = (X44 @ id @ (X46 @ id @ X47) @ id)) | ~((X44 @ id @ X47 @ id) = $true)) | ((X44 @ id @ (lam @ (X46 @ sh @ one)) @ id) = $true) | ~! [X48 : subst,X49 : term,X50 : subst] : ((X46 @ (comp @ X50 @ X48) @ (sub @ X49 @ X48)) = (sub @ (X46 @ X50 @ X49) @ X48))) | ~! [X51 : term] : (((X44 @ id @ (sub @ X45 @ (push @ X51 @ id)) @ id) = $true) | ~((X44 @ id @ X51 @ id) = $true)) | ((X44 @ id @ (lam @ (sub @ X45 @ (push @ one @ sh))) @ id) = $true)) => ! [X52 : term,X53 : subst > term > subst > $o] : (~! [X54 : subst > term > term] : (((X53 @ id @ (lam @ (X54 @ sh @ one)) @ id) = $true) | ~! [X55 : term] : (~($true = (X53 @ id @ X55 @ id)) | ((X53 @ id @ (X54 @ id @ X55) @ id) = $true)) | ~! [X56 : subst,X57 : subst,X58 : term] : ((X54 @ (comp @ X57 @ X56) @ (sub @ X58 @ X56)) = (sub @ (X54 @ X57 @ X58) @ X56))) | ~! [X59 : term] : (((X53 @ id @ (sub @ X52 @ (push @ X59 @ id)) @ id) = $true) | ~($true = (X53 @ id @ X59 @ id))) | ((X53 @ id @ (lam @ X52) @ id) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X60 : subst > term > subst > $o,X61 : term] : (~! [X62 : subst > term > term] : (~! [X63 : term,X64 : subst,X65 : subst] : ((sub @ (X62 @ X65 @ X63) @ X64) = (X62 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64))) | ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) = $true) | ~! [X66 : term] : (~((X60 @ id @ X66 @ id) = $true) | ((X60 @ id @ (X62 @ id @ X66) @ id) = $true))) | ~! [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (~((X60 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X67) = $true) | ((X60 @ X69 @ X68 @ (comp @ X70 @ X67)) = $true)) | ~! [X71 : subst,X72 : subst,X73 : subst,X74 : term] : (~((X60 @ X73 @ X74 @ (comp @ X71 @ X72)) = $true) | ((X60 @ (comp @ X73 @ X71) @ (sub @ X74 @ X71) @ X72) = $true)) | ~! [X75 : term] : (((X60 @ id @ (sub @ X61 @ (push @ X75 @ id)) @ id) = $true) | ~((X60 @ id @ X75 @ id) = $true)) | ((X60 @ id @ (lam @ X61) @ id) = $true))) & (! [X76 : subst > term > term,X77 : term,X78 : term] : (((ap @ (sub @ X77 @ id) @ X78) != (lam @ (X76 @ sh @ one))) | ~! [X79 : term,X80 : subst,X81 : subst] : ((sub @ (X76 @ X80 @ X79) @ X81) = (X76 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81)))) <=> (hoaslamnotap = $true)) & (hoasapinj1_gthm = $true) & ((! [X82 : subst] : ((comp @ id @ X82) = X82) => (! [X83 : subst] : ((comp @ X83 @ id) = X83) => (! [X85 : subst] : ((comp @ X85 @ id) = X85) & ! [X84 : subst] : ((comp @ id @ X84) = X84)))) <=> (substmonoid_lthm = $true)) & (hoasapnotvar = $true) & ((hoasapinj2 = $true) <=> ! [X86 : term,X87 : term,X88 : term,X89 : term] : ((X88 = X89) | ((ap @ (sub @ X86 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)))) & ((pushprop_lem1 = $true) <=> ! [X90 : term,X91 : term > $o,X92 : subst,X93 : term > $o,X94 : term] : (~($true = (X93 @ X94)) | ((X91 @ (sub @ X94 @ (push @ X90 @ X92))) = $true))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X95 : term] : ((sub @ X95 @ id) = X95) => (! [X96 : term,X97 : subst > term > subst > $o] : (~! [X98 : subst > term > term] : (((X97 @ id @ (lam @ (X98 @ sh @ one)) @ id) = $true) | ~! [X99 : term,X100 : subst,X101 : subst] : ((sub @ (X98 @ X101 @ X99) @ X100) = (X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100))) | ~! [X102 : term] : (~($true = (X97 @ id @ X102 @ id)) | ((X97 @ id @ (X98 @ id @ X102) @ id) = $true))) | ((X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id) = $true) | ~! [X103 : term] : (~((X97 @ id @ X103 @ id) = $true) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true))) => ! [X104 : term,X105 : subst > term > subst > $o] : (~! [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (((X105 @ X109 @ X107 @ (comp @ X108 @ X106)) = $true) | ~((X105 @ (comp @ X109 @ X108) @ (sub @ X107 @ X108) @ X106) = $true)) | ~! [X110 : term,X111 : subst,X112 : subst,X113 : subst] : (($true = (X105 @ (comp @ X112 @ X113) @ (sub @ X110 @ X113) @ X111)) | ~((X105 @ X112 @ X110 @ (comp @ X113 @ X111)) = $true)) | ((X105 @ id @ (lam @ X104) @ id) = $true) | ~! [X114 : term] : (~((X105 @ id @ X114 @ id) = $true) | ((X105 @ id @ (sub @ X104 @ (push @ X114 @ id)) @ id) = $true)) | ~! [X115 : subst > term > term] : (((X105 @ id @ (lam @ (X115 @ sh @ one)) @ id) = $true) | ~! [X116 : term] : (~((X105 @ id @ X116 @ id) = $true) | ((X105 @ id @ (X115 @ id @ X116) @ id) = $true)) | ~! [X117 : subst,X118 : subst,X119 : term] : ((X115 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118)) = (sub @ (X115 @ X117 @ X119) @ X118))))))) & ((induction2 = $true) <=> ! [X120 : term > $o,X121 : term] : (~! [X122 : term] : (~((var @ X122) = $true) | ((X120 @ X122) = $true)) | ~! [X123 : term,X124 : term] : (~((X120 @ X123) = $true) | ~((X120 @ X124) = $true) | ((X120 @ (ap @ X123 @ X124)) = $true)) | ~! [X125 : term] : (~! [X126 : term] : (((X120 @ (sub @ X125 @ (push @ X126 @ id))) = $true) | ~((X120 @ X126) = $true)) | ((X120 @ (lam @ X125)) = $true)) | ((X120 @ X121) = $true))) & ~(ulamvar1 = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axvarcons = $true) <=> ! [X127 : subst,X128 : term] : ((sub @ one @ (push @ X128 @ X127)) = X128)) & ((! [X129 : subst > term > subst > $o] : ~! [X130 : term > $o] : ~! [X131 : term] : ((X130 @ X131) = (X129 @ id @ X131 @ id)) => (! [X132 : term > $o,X133 : term] : (~! [X134 : term] : (($true = (X132 @ X134)) | ~((var @ X134) = $true)) | ~! [X135 : term,X136 : term] : (~((X132 @ X136) = $true) | ~((X132 @ X135) = $true) | ((X132 @ (ap @ X135 @ X136)) = $true)) | ~! [X137 : term] : (~! [X138 : term] : (~((X132 @ X138) = $true) | ((X132 @ (sub @ X137 @ (push @ X138 @ id))) = $true)) | ((X132 @ (lam @ X137)) = $true)) | ((X132 @ X133) = $true)) => (! [X139 : term] : ((sub @ X139 @ id) = X139) => (! [X140 : term > $o,X141 : term,X142 : subst > term > subst > $o] : (~! [X143 : subst > term > term] : (($true = (X142 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ~! [X144 : term] : (((X142 @ id @ (X143 @ id @ X144) @ id) = $true) | ~((X142 @ id @ X144 @ id) = $true)) | ~! [X145 : subst,X146 : term,X147 : subst] : ((X143 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145)) = (sub @ (X143 @ X147 @ X146) @ X145))) | ~! [X148 : term] : ((X140 @ X148) = (X142 @ id @ X148 @ id)) | ~! [X149 : term] : (~((X140 @ X149) = $true) | ((X140 @ (sub @ X141 @ (push @ X149 @ id))) = $true)) | ((X140 @ (lam @ X141)) = $true)) => ! [X150 : subst > term > subst > $o,X151 : term] : (~! [X152 : term,X153 : term] : (((X150 @ id @ (ap @ (sub @ X152 @ id) @ X153) @ id) = $true) | ~((X150 @ id @ X153 @ id) = $true) | ~((X150 @ id @ X152 @ id) = $true)) | ~! [X154 : term] : (~((var @ (sub @ X154 @ id)) = $true) | ((X150 @ id @ X154 @ id) = $true)) | ~! [X155 : subst,X156 : term,X157 : subst,X158 : subst] : (((X150 @ X158 @ X156 @ (comp @ X155 @ X157)) = $true) | ~((X150 @ (comp @ X158 @ X155) @ (sub @ X156 @ X155) @ X157) = $true)) | ~! [X159 : subst > term > term] : (~! [X160 : term,X161 : subst,X162 : subst] : ((sub @ (X159 @ X162 @ X160) @ X161) = (X159 @ (comp @ X162 @ X161) @ (sub @ X160 @ X161))) | ((X150 @ id @ (lam @ (X159 @ sh @ one)) @ id) = $true) | ~! [X163 : term] : (~($true = (X150 @ id @ X163 @ id)) | ((X150 @ id @ (X159 @ id @ X163) @ id) = $true))) | ~! [X164 : subst,X165 : subst,X166 : subst,X167 : term] : (~((X150 @ X166 @ X167 @ (comp @ X165 @ X164)) = $true) | ((X150 @ (comp @ X166 @ X165) @ (sub @ X167 @ X165) @ X164) = $true)) | ((X150 @ id @ X151 @ id) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X168 : subst > term > subst > $o] : ~! [X169 : term > $o] : ~! [X170 : term] : ((X168 @ id @ X170 @ id) = (X169 @ X170)) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X171 : subst > term > subst > $o] : ~! [X172 : term > $o] : ~! [X173 : term] : ((X171 @ id @ X173 @ id) = (X172 @ X173))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X174 : term] : ~! [X175 : subst > term > term] : ~! [X176 : term,X177 : subst] : ((sub @ X174 @ (push @ X176 @ X177)) = (X175 @ X177 @ X176)) <=> (hoasinduction_lem3v2_f = $true)) & (! [X178 : term] : ((sub @ X178 @ id) = X178) <=> (axvarid = $true)) & ((hoasinduction_lthm = $true) <=> (! [X179 : term > $o,X180 : term] : (~! [X181 : term] : (~! [X182 : term] : (~((X179 @ X182) = $true) | ((X179 @ (sub @ X181 @ (push @ X182 @ id))) = $true)) | ((X179 @ (lam @ X181)) = $true)) | ~! [X183 : term,X184 : term] : (~((X179 @ X184) = $true) | ((X179 @ (ap @ X184 @ X183)) = $true) | ~($true = (X179 @ X183))) | ~! [X185 : term] : (~((var @ X185) = $true) | ((X179 @ X185) = $true)) | ((X179 @ X180) = $true)) => (! [X186 : term,X187 : term,X188 : subst > term > subst > $o] : (($true = (X188 @ id @ (ap @ X186 @ X187) @ id)) | ~((X188 @ id @ X187 @ id) = $true) | ~! [X189 : term,X190 : term] : (((X188 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id) = $true) | ~((X188 @ id @ X189 @ id) = $true) | ~((X188 @ id @ X190 @ id) = $true)) | ~((X188 @ id @ X186 @ id) = $true) | ~! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : (((X188 @ X194 @ X191 @ (comp @ X193 @ X192)) = $true) | ~((X188 @ (comp @ X194 @ X193) @ (sub @ X191 @ X193) @ X192) = $true)) | ~! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (~((X188 @ X197 @ X195 @ (comp @ X198 @ X196)) = $true) | ((X188 @ (comp @ X197 @ X198) @ (sub @ X195 @ X198) @ X196) = $true))) => (! [X199 : term,X200 : subst > term > subst > $o] : (~! [X201 : subst,X202 : subst,X203 : subst,X204 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X204 @ X202) @ X203) = $true) | ~((X200 @ X201 @ X204 @ (comp @ X202 @ X203)) = $true)) | ((X200 @ id @ (lam @ X199) @ id) = $true) | ~! [X205 : term] : (~((X200 @ id @ X205 @ id) = $true) | ((X200 @ id @ (sub @ X199 @ (push @ X205 @ id)) @ id) = $true)) | ~! [X206 : subst > term > term] : (~! [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) = $true) | ~((X200 @ id @ X207 @ id) = $true)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ~! [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) = (sub @ (X206 @ X210 @ X208) @ X209))) | ~! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (~((X200 @ (comp @ X213 @ X214) @ (sub @ X212 @ X214) @ X211) = $true) | ((X200 @ X213 @ X212 @ (comp @ X214 @ X211)) = $true))) => ! [X215 : subst > term > subst > $o,X216 : term] : (((X215 @ id @ X216 @ id) = $true) | ~! [X217 : term] : (~((var @ (sub @ X217 @ id)) = $true) | ((X215 @ id @ X217 @ id) = $true)) | ~! [X218 : subst > term > term] : (~! [X219 : term,X220 : subst,X221 : subst] : ((X218 @ (comp @ X220 @ X221) @ (sub @ X219 @ X221)) = (sub @ (X218 @ X220 @ X219) @ X221)) | ~! [X222 : term] : (~((X215 @ id @ X222 @ id) = $true) | ((X215 @ id @ (X218 @ id @ X222) @ id) = $true)) | ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id) = $true)) | ~! [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (((X215 @ X225 @ X223 @ (comp @ X226 @ X224)) = $true) | ~((X215 @ (comp @ X225 @ X226) @ (sub @ X223 @ X226) @ X224) = $true)) | ~! [X227 : subst,X228 : subst,X229 : subst,X230 : term] : (~((X215 @ X229 @ X230 @ (comp @ X228 @ X227)) = $true) | ((X215 @ (comp @ X229 @ X228) @ (sub @ X230 @ X228) @ X227) = $true)) | ~! [X231 : term,X232 : term] : (~((X215 @ id @ X231 @ id) = $true) | ((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) = $true) | ~((X215 @ id @ X232 @ id) = $true))))))) & (! [X233 : term,X234 : subst > term > subst > $o] : (((X234 @ id @ (lam @ X233) @ id) = $true) | ~! [X235 : subst > term > term] : (~! [X236 : subst,X237 : subst,X238 : term] : ((X235 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237)) = (sub @ (X235 @ X236 @ X238) @ X237)) | ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id) = $true) | ~! [X239 : term] : (((X234 @ id @ (X235 @ id @ X239) @ id) = $true) | ~((X234 @ id @ X239 @ id) = $true))) | ~! [X240 : term] : (((X234 @ id @ (sub @ X233 @ (push @ X240 @ id)) @ id) = $true) | ~((X234 @ id @ X240 @ id) = $true))) <=> (hoasinduction_lem3a = $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((pushprop_lem0_lthm = $true) <=> ! [X241 : subst,X242 : term,X243 : term > $o] : ~! [X244 : term > $o] : ~! [X245 : term] : ((X244 @ X245) = (X243 @ (sub @ X245 @ (push @ X242 @ X241))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) = $true) | ~! [X249 : term] : ((X246 @ id @ X249 @ id) = (X247 @ X249)) | ~! [X250 : subst > term > term] : (~! [X251 : term] : (((X246 @ id @ (X250 @ id @ X251) @ id) = $true) | ~((X246 @ id @ X251 @ id) = $true)) | ~! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) | ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) = $true)) | ~! [X255 : term] : (((X247 @ (sub @ X248 @ (push @ X255 @ id))) = $true) | ~((X247 @ X255) = $true)))) & (hoaslaminj_gthm = $true) & (! [X256 : term] : ((sub @ X256 @ id) = X256) <=> (termmset = $true)) & ~(lamnotap = $true) & (ulamvarind = $true) & ((axidl = $true) <=> ! [X257 : subst] : ((comp @ id @ X257) = X257)) & (! [X258 : subst] : ((comp @ X258 @ id) = X258) <=> (axidr = $true)) & (! [X259 : term > $o,X260 : subst,X261 : term] : ~! [X262 : term > $o] : ~! [X263 : term] : ((X262 @ X263) = (X259 @ (sub @ X263 @ (push @ X261 @ X260)))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X264 : subst > term > subst > $o] : ~! [X265 : term > $o] : ~! [X266 : term] : ((X265 @ X266) = (X264 @ id @ X266 @ id)) => (! [X267 : term > $o,X268 : term] : (~! [X269 : term,X270 : term] : (((X267 @ (ap @ X270 @ X269)) = $true) | ~((X267 @ X270) = $true) | ~($true = (X267 @ X269))) | ~! [X271 : term] : (~((var @ X271) = $true) | ($true = (X267 @ X271))) | ~! [X272 : term] : (~! [X273 : term] : (~($true = (X267 @ X273)) | ((X267 @ (sub @ X272 @ (push @ X273 @ id))) = $true)) | ((X267 @ (lam @ X272)) = $true)) | ((X267 @ X268) = $true)) => (! [X274 : term] : ((sub @ X274 @ id) = X274) => (! [X275 : subst > term > subst > $o,X276 : term,X277 : term > $o] : (~! [X278 : subst > term > term] : (~! [X279 : term] : (~((X275 @ id @ X279 @ id) = $true) | ((X275 @ id @ (X278 @ id @ X279) @ id) = $true)) | ((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id) = $true) | ~! [X280 : term,X281 : subst,X282 : subst] : ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)) = (sub @ (X278 @ X282 @ X280) @ X281))) | ((X277 @ (lam @ X276)) = $true) | ~! [X283 : term] : ((X277 @ X283) = (X275 @ id @ X283 @ id)) | ~! [X284 : term] : (((X277 @ (sub @ X276 @ (push @ X284 @ id))) = $true) | ~((X277 @ X284) = $true))) => ! [X285 : term,X286 : subst > term > subst > $o] : (~! [X287 : subst > term > term] : (~! [X288 : subst,X289 : term,X290 : subst] : ((sub @ (X287 @ X288 @ X289) @ X290) = (X287 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))) | ((X286 @ id @ (lam @ (X287 @ sh @ one)) @ id) = $true) | ~! [X291 : term] : (((X286 @ id @ (X287 @ id @ X291) @ id) = $true) | ~((X286 @ id @ X291 @ id) = $true))) | ((X286 @ id @ X285 @ id) = $true) | ~! [X292 : term,X293 : term] : (((X286 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id) = $true) | ~((X286 @ id @ X292 @ id) = $true) | ~($true = (X286 @ id @ X293 @ id))))))))) & (hoasapnotvar_gthm = $true) & (pushprop_lthm = $true) & (pushprop_lem3v2_lthm = $true) & ! [X294 : d_term,X295 : d_term] : (((d2term @ X294) = (d2term @ X295)) => (X294 = X295)) & ! [X296 : subst] : ? [X297 : d_subst] : ((d2subst @ X297) = X296) & ((termmset_lthm = $true) <=> (! [X298 : term] : ((sub @ X298 @ id) = X298) => ! [X299 : term] : ((sub @ X299 @ id) = X299))) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X300 : term,X301 : subst] : ((sub @ one @ (push @ X300 @ X301)) = X300) => (! [X302 : term,X303 : subst] : ((comp @ sh @ (push @ X302 @ X303)) = X303) => ! [X304 : term,X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ (sub @ X306 @ (push @ X304 @ X305))) = $true) | ~((X307 @ X306) = $true))))) & (lamnotvar = $true) & ((hoasinduction = $true) <=> ! [X309 : term,X310 : subst > term > subst > $o] : (~! [X311 : term] : (((X310 @ id @ X311 @ id) = $true) | ~((var @ (sub @ X311 @ id)) = $true)) | ((X310 @ id @ X309 @ id) = $true) | ~! [X312 : subst,X313 : subst,X314 : term,X315 : subst] : (((X310 @ X315 @ X314 @ (comp @ X312 @ X313)) = $true) | ~($true = (X310 @ (comp @ X315 @ X312) @ (sub @ X314 @ X312) @ X313))) | ~! [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (((X310 @ (comp @ X318 @ X319) @ (sub @ X316 @ X319) @ X317) = $true) | ~((X310 @ X318 @ X316 @ (comp @ X319 @ X317)) = $true)) | ~! [X320 : subst > term > term] : (((X310 @ id @ (lam @ (X320 @ sh @ one)) @ id) = $true) | ~! [X321 : subst,X322 : term,X323 : subst] : ((sub @ (X320 @ X321 @ X322) @ X323) = (X320 @ (comp @ X321 @ X323) @ (sub @ X322 @ X323))) | ~! [X324 : term] : (((X310 @ id @ (X320 @ id @ X324) @ id) = $true) | ~((X310 @ id @ X324 @ id) = $true))) | ~! [X325 : term,X326 : term] : (((X310 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) = $true) | ~((X310 @ id @ X325 @ id) = $true) | ~($true = (X310 @ id @ X326 @ id))))) & (pushprop_lem0_gthm = $true) & (pushprop = $true) & ~((var @ (d2term @ d_one)) = $true) & (! [X327 : term] : ~! [X328 : subst > term > term] : ((sub @ X327 @ (push @ one @ sh)) != (X328 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (! [X329 : term] : ~! [X330 : subst > term > term] : ~! [X331 : term,X332 : subst] : ((sub @ X329 @ (push @ X331 @ X332)) = (X330 @ X332 @ X331)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (induction2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axclos = $true) & ((! [X333 : term,X334 : subst] : ((sub @ one @ (push @ X333 @ X334)) = X333) => (! [X335 : subst,X336 : term] : ((comp @ sh @ (push @ X336 @ X335)) = X335) => (! [X337 : subst] : ((comp @ X337 @ id) = X337) => (! [X338 : term,X339 : term > $o] : (~! [X340 : term] : (~((var @ X340) = $true) | ((X339 @ X340) = $true)) | ~! [X341 : term] : (($true = (X339 @ (lam @ X341))) | ~((X339 @ X341) = $true)) | ($true = (X339 @ X338)) | ~! [X342 : term,X343 : term] : (~($true = (X339 @ X342)) | ((X339 @ (ap @ X343 @ X342)) = $true) | ~((X339 @ X343) = $true))) => ! [X344 : subst,X345 : term,X346 : term > $o] : (~! [X347 : term] : (~! [X348 : term] : (((X346 @ (sub @ X347 @ (push @ X348 @ id))) = $true) | ~((X346 @ X348) = $true)) | ((X346 @ (lam @ X347)) = $true)) | ~! [X349 : term,X350 : term] : (~((X346 @ X349) = $true) | ((X346 @ (ap @ X350 @ X349)) = $true) | ~((X346 @ X350) = $true)) | ((X346 @ (sub @ X345 @ X344)) = $true) | ~! [X351 : term] : (~((var @ X351) = $true) | ($true = (X346 @ (sub @ X351 @ X344))))))))) <=> (induction2lem_lthm = $true)) & (hoaslamnotvar = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X352 : term,X353 : term > $o,X354 : subst > term > subst > $o] : (~! [X355 : term] : (((X353 @ (sub @ X352 @ (push @ X355 @ id))) = $true) | ~((X353 @ X355) = $true)) | ~! [X356 : term] : ((X354 @ id @ X356 @ id) = (X353 @ X356)) | ~! [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (((X354 @ X358 @ X359 @ (comp @ X360 @ X357)) = $true) | ~((X354 @ (comp @ X358 @ X360) @ (sub @ X359 @ X360) @ X357) = $true)) | ((X353 @ (lam @ X352)) = $true) | ~! [X361 : subst > term > term] : (~! [X362 : subst,X363 : subst,X364 : term] : ((sub @ (X361 @ X363 @ X364) @ X362) = (X361 @ (comp @ X363 @ X362) @ (sub @ X364 @ X362))) | ((X354 @ id @ (lam @ (X361 @ sh @ one)) @ id) = $true) | ~! [X365 : term] : (((X354 @ id @ (X361 @ id @ X365) @ id) = $true) | ~((X354 @ id @ X365 @ id) = $true))) | ~! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : (~((X354 @ X366 @ X368 @ (comp @ X369 @ X367)) = $true) | ((X354 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) = $true)))) & (! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | ((ap @ X372 @ X373) != (ap @ X370 @ X371))) <=> (apinj1 = $true)) & (hoasinduction_gthm = $true) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : (((ap @ (sub @ X377 @ id) @ X375) != (ap @ (sub @ X374 @ id) @ X376)) | (X374 = X377)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X378 : term] : ~! [X379 : subst > term > term] : ~! [X380 : term,X381 : subst] : ((X379 @ X381 @ X380) = (sub @ X378 @ (push @ X380 @ X381))) => (! [X382 : term] : ((sub @ X382 @ id) = X382) => ! [X383 : term,X384 : term > $o,X385 : subst > term > subst > $o] : (~! [X386 : term] : ((X384 @ X386) = (X385 @ id @ X386 @ id)) | ~! [X387 : subst > term > term] : (~! [X388 : term] : (~((X385 @ id @ X388 @ id) = $true) | ((X385 @ id @ (X387 @ id @ X388) @ id) = $true)) | ~! [X389 : subst,X390 : subst,X391 : term] : ((X387 @ (comp @ X390 @ X389) @ (sub @ X391 @ X389)) = (sub @ (X387 @ X390 @ X391) @ X389)) | ((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id) = $true)) | ~! [X392 : term] : (((X384 @ (sub @ X383 @ (push @ X392 @ id))) = $true) | ~((X384 @ X392) = $true)) | ((X384 @ (lam @ X383)) = $true))))) & (axabs = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X393 : term,X394 : subst > term > subst > $o] : (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id) = $true) | ~! [X395 : subst > term > term] : (((X394 @ id @ (lam @ (X395 @ sh @ one)) @ id) = $true) | ~! [X396 : term] : (~((X394 @ id @ X396 @ id) = $true) | ((X394 @ id @ (X395 @ id @ X396) @ id) = $true)) | ~! [X397 : term,X398 : subst,X399 : subst] : ((X395 @ (comp @ X398 @ X399) @ (sub @ X397 @ X399)) = (sub @ (X395 @ X398 @ X397) @ X399))) | ~! [X400 : term] : (~((X394 @ id @ X400 @ id) = $true) | ((X394 @ id @ (sub @ X393 @ (push @ X400 @ id)) @ id) = $true)))) & ((induction2lem = $true) <=> ! [X401 : subst,X402 : term > $o,X403 : term] : (~! [X404 : term] : (((X402 @ (lam @ X404)) = $true) | ~! [X405 : term] : (~((X402 @ X405) = $true) | ((X402 @ (sub @ X404 @ (push @ X405 @ id))) = $true))) | ~! [X406 : term] : (~((var @ X406) = $true) | ((X402 @ (sub @ X406 @ X401)) = $true)) | ~! [X407 : term,X408 : term] : (~((X402 @ X407) = $true) | ((X402 @ (ap @ X408 @ X407)) = $true) | ~((X402 @ X408) = $true)) | ((X402 @ (sub @ X403 @ X401)) = $true))) & (! [X409 : term,X410 : term,X411 : term,X412 : term] : ((X409 = X410) | ((ap @ X411 @ X410) != (ap @ X412 @ X409))) <=> (apinj2 = $true)) & (one = (d2term @ d_one)) & ((hoaslaminj_lthm = $true) <=> (! [X413 : subst,X414 : term] : ((sub @ one @ (push @ X414 @ X413)) = X414) => (! [X415 : subst,X416 : term] : ((comp @ sh @ (push @ X416 @ X415)) = X415) => (! [X417 : term,X418 : term] : (((lam @ X418) != (lam @ X417)) | (X417 = X418)) => ! [X419 : subst,X420 : subst > term > term,X421 : subst > term > term,X422 : term] : (((lam @ (X420 @ sh @ one)) != (lam @ (X421 @ sh @ one))) | ~! [X426 : subst,X427 : subst,X428 : term] : ((X421 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)) = (sub @ (X421 @ X426 @ X428) @ X427)) | ((X420 @ X419 @ X422) = (X421 @ X419 @ X422)) | ~! [X423 : term,X424 : subst,X425 : subst] : ((X420 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424)) = (sub @ (X420 @ X425 @ X423) @ X424))))))) & (! [X429 : term] : ~! [X430 : subst > term > term] : ((X430 @ sh @ one) != (sub @ X429 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (induction2lem_gthm = $true) & (! [X431 : term,X432 : subst > term > subst > $o] : (((X432 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true) | ~! [X433 : subst > term > term] : (((X432 @ id @ (lam @ (X433 @ sh @ one)) @ id) = $true) | ~! [X434 : subst,X435 : subst,X436 : term] : ((sub @ (X433 @ X434 @ X436) @ X435) = (X433 @ (comp @ X434 @ X435) @ (sub @ X436 @ X435))) | ~! [X437 : term] : (~((X432 @ id @ X437 @ id) = $true) | ((X432 @ id @ (X433 @ id @ X437) @ id) = $true))) | ~! [X438 : term] : (~((X432 @ id @ X438 @ id) = $true) | ((X432 @ id @ (sub @ X431 @ (push @ X438 @ id)) @ id) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X439 : term,X440 : term > $o] : (~! [X441 : term,X442 : term] : (~((X440 @ X441) = $true) | ~((X440 @ X442) = $true) | ((X440 @ (ap @ X441 @ X442)) = $true)) | ((X440 @ X439) = $true) | ~! [X443 : term] : (~((X440 @ X443) = $true) | ((X440 @ (lam @ X443)) = $true)) | ~! [X444 : term] : (((X440 @ X444) = $true) | ~($true = (var @ X444)))) <=> (induction = $true)) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & ((hoaslaminj = $true) <=> ! [X445 : subst,X446 : term,X447 : subst > term > term,X448 : subst > term > term] : (((lam @ (X447 @ sh @ one)) != (lam @ (X448 @ sh @ one))) | ((X447 @ X445 @ X446) = (X448 @ X445 @ X446)) | ~! [X452 : subst,X453 : term,X454 : subst] : ((sub @ (X447 @ X454 @ X453) @ X452) = (X447 @ (comp @ X454 @ X452) @ (sub @ X453 @ X452))) | ~! [X449 : term,X450 : subst,X451 : subst] : ((sub @ (X448 @ X450 @ X449) @ X451) = (X448 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451))))) & (! [X455 : term,X456 : term] : ((X455 = X456) | ((lam @ X456) != (lam @ X455))) <=> (laminj = $true)) & (! [X457 : subst > term > subst > $o,X458 : term,X459 : term] : (~((X457 @ id @ X458 @ id) = $true) | ~! [X460 : term,X461 : term] : (((X457 @ id @ (ap @ (sub @ X461 @ id) @ X460) @ id) = $true) | ~((X457 @ id @ X461 @ id) = $true) | ~($true = (X457 @ id @ X460 @ id))) | ~! [X462 : subst,X463 : subst,X464 : subst,X465 : term] : (($true = (X457 @ X463 @ X465 @ (comp @ X462 @ X464))) | ~((X457 @ (comp @ X463 @ X462) @ (sub @ X465 @ X462) @ X464) = $true)) | ((X457 @ id @ (ap @ X458 @ X459) @ id) = $true) | ~! [X466 : subst,X467 : term,X468 : subst,X469 : subst] : (((X457 @ (comp @ X469 @ X468) @ (sub @ X467 @ X468) @ X466) = $true) | ~((X457 @ X469 @ X467 @ (comp @ X468 @ X466)) = $true)) | ~((X457 @ id @ X459 @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & ! [X470 : d_subst,X471 : d_subst] : (((d2subst @ X470) = (d2subst @ X471)) => (X470 = X471)) & (pushprop_lem3v2 = $true) & ((! [X472 : term] : ((sub @ X472 @ id) = X472) => (! [X473 : term,X474 : term,X475 : term,X476 : term] : ((X474 = X476) | ((ap @ X476 @ X473) != (ap @ X474 @ X475))) => ! [X477 : term,X478 : term,X479 : term,X480 : term] : ((X478 = X479) | ((ap @ (sub @ X478 @ id) @ X477) != (ap @ (sub @ X479 @ id) @ X480))))) <=> (hoasapinj1_lthm = $true)) & (! [X481 : term > $o,X482 : subst,X483 : term > $o,X484 : term] : (~! [X485 : term] : ((X481 @ (sub @ X485 @ (push @ X484 @ X482))) = (X483 @ X485)) | ~((X481 @ X484) = $true) | ((X483 @ one) = $true)) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem2v2 = $true) & ! [X486 : d_term] : (d_one = X486) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslamnotap_gthm = $true) & ! [X487 : term] : ? [X488 : d_term] : ((d2term @ X488) = X487) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (axapp = $true) & (! [X489 : subst > term > subst > $o,X490 : term] : (~! [X491 : term] : (((X489 @ id @ (sub @ X490 @ (push @ X491 @ id)) @ id) = $true) | ~((X489 @ id @ X491 @ id) = $true)) | ((X489 @ id @ (lam @ (sub @ X490 @ (push @ one @ sh))) @ id) = $true) | ~! [X492 : term,X493 : subst > term > term] : (~! [X494 : subst,X495 : term,X496 : subst] : ((X493 @ (comp @ X496 @ X494) @ (sub @ X495 @ X494)) = (sub @ X492 @ (push @ (sub @ X495 @ X494) @ (comp @ X496 @ X494)))) | ~! [X497 : subst,X498 : term,X499 : subst] : ((sub @ (X493 @ X499 @ X498) @ X497) = (sub @ (sub @ X492 @ (push @ X498 @ X499)) @ X497)) | ~! [X500 : term] : (((X489 @ id @ (X493 @ id @ X500) @ id) = $true) | ~((X489 @ id @ X500 @ id) = $true)) | ((X489 @ id @ (lam @ (X493 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X501 : term,X502 : subst] : ((sub @ one @ (push @ X501 @ X502)) = X501) => ! [X503 : term,X504 : term > $o,X505 : term > $o,X506 : subst] : (~($true = (X504 @ X503)) | ~! [X507 : term] : ((X504 @ (sub @ X507 @ (push @ X503 @ X506))) = (X505 @ X507)) | ($true = (X505 @ one)))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X508 : term] : ((sub @ X508 @ id) = X508) => ! [X509 : term > $o,X510 : subst > term > subst > $o,X511 : term] : (((X509 @ (lam @ X511)) = $true) | ~! [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (~((X510 @ X513 @ X512 @ (comp @ X514 @ X515)) = $true) | ((X510 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515) = $true)) | ~! [X516 : subst,X517 : term,X518 : subst,X519 : subst] : (~((X510 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518) @ X519) = $true) | ((X510 @ X516 @ X517 @ (comp @ X518 @ X519)) = $true)) | ~! [X520 : term] : ((X509 @ X520) = (X510 @ id @ X520 @ id)) | ~! [X521 : subst > term > term] : (((X510 @ id @ (lam @ (X521 @ sh @ one)) @ id) = $true) | ~! [X522 : term,X523 : subst,X524 : subst] : ((sub @ (X521 @ X523 @ X522) @ X524) = (X521 @ (comp @ X523 @ X524) @ (sub @ X522 @ X524))) | ~! [X525 : term] : (((X510 @ id @ (X521 @ id @ X525) @ id) = $true) | ~((X510 @ id @ X525 @ id) = $true))) | ~! [X526 : term] : (~((X509 @ X526) = $true) | ($true = (X509 @ (sub @ X511 @ (push @ X526 @ id)))))))) & (! [X527 : term,X528 : term] : ((X527 = X528) | ((sub @ X528 @ sh) != (sub @ X527 @ sh))) <=> (shinj = $true)) & ! [X529 : d_subst] : (d_id = X529) & ((axshiftcons = $true) <=> ! [X530 : subst,X531 : term] : ((comp @ sh @ (push @ X531 @ X530)) = X530)) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (apnotvar = $true) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X535 @ X532) != (ap @ X534 @ X533)) | (X532 = X533)) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536)))))),
% 28.46/5.33 inference(rectify,[status(thm)],[f8])).
% 28.46/5.33 thf(f8,plain,(
% 28.46/5.33 ((hoasinduction_no_psi_cond = $true) <=> ! [X0 : term,X1 : subst > term > subst > $o] : (~! [X2 : term,X3 : term] : (((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) = $true) | ~((X1 @ id @ X3 @ id) = $true) | ~((X1 @ id @ X2 @ id) = $true)) | ~! [X4 : subst > term > term] : (((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true) | ~! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ~! [X8 : term] : (~((X1 @ id @ X8 @ id) = $true) | ((X1 @ id @ (X4 @ id @ X8) @ id) = $true))) | ($true = (X1 @ id @ X0 @ id)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axassoc = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_gthm = $true) & (! [X14 : term,X15 : term > $o,X16 : term,X17 : subst > term > subst > $o] : (~((X15 @ X14) = $true) | ~! [X18 : term] : ((X15 @ X18) = (X17 @ id @ X18 @ id)) | ~! [X19 : subst,X20 : subst,X21 : subst,X22 : term] : (~($true = (X17 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21) @ X19)) | ((X17 @ X20 @ X22 @ (comp @ X21 @ X19)) = $true)) | ((X15 @ (ap @ X16 @ X14)) = $true) | ~((X15 @ X16) = $true) | ~! [X23 : subst,X24 : term,X25 : subst,X26 : subst] : (~((X17 @ X25 @ X24 @ (comp @ X23 @ X26)) = $true) | ((X17 @ (comp @ X25 @ X23) @ (sub @ X24 @ X23) @ X26) = $true)) | ~! [X27 : term,X28 : term] : (((X17 @ id @ (ap @ (sub @ X28 @ id) @ X27) @ id) = $true) | ~((X17 @ id @ X27 @ id) = $true) | ~((X17 @ id @ X28 @ id) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X29 : subst] : ((push @ (sub @ one @ X29) @ (comp @ sh @ X29)) = X29) <=> (axscons = $true)) & ((! [X30 : term] : ((sub @ X30 @ id) = X30) => (! [X31 : term > $o,X32 : term,X33 : subst] : (~! [X34 : term,X35 : term] : (~((X31 @ X35) = $true) | ($true = (X31 @ (ap @ X34 @ X35))) | ~((X31 @ X34) = $true)) | ~! [X36 : term] : (($true = (X31 @ (lam @ X36))) | ~! [X37 : term] : (~($true = (X31 @ X37)) | ((X31 @ (sub @ X36 @ (push @ X37 @ id))) = $true))) | ~! [X38 : term] : (((X31 @ (sub @ X38 @ X33)) = $true) | ~((var @ X38) = $true)) | ((X31 @ (sub @ X32 @ X33)) = $true)) => ! [X39 : term,X40 : term > $o] : (~! [X41 : term] : (~! [X42 : term] : (($true = (X40 @ (sub @ X41 @ (push @ X42 @ id)))) | ~((X40 @ X42) = $true)) | ($true = (X40 @ (lam @ X41)))) | ((X40 @ X39) = $true) | ~! [X43 : term,X44 : term] : (((X40 @ (ap @ X44 @ X43)) = $true) | ~((X40 @ X44) = $true) | ~((X40 @ X43) = $true)) | ~! [X45 : term] : (~((var @ X45) = $true) | ((X40 @ X45) = $true))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = sh) & ((substmonoid = $true) <=> (! [X46 : subst] : ((comp @ X46 @ id) = X46) & ! [X47 : subst] : ((comp @ id @ X47) = X47))) & (hoasinduction_lem1v2 = $true) & (ulamvarsh = $true) & (axvarshift = $true) & ((! [X48 : term] : ((sub @ X48 @ id) = X48) => (! [X49 : subst > term > subst > $o,X50 : term] : (~! [X51 : subst > term > term] : (~! [X52 : term] : (((X49 @ id @ (X51 @ id @ X52) @ id) = $true) | ~((X49 @ id @ X52 @ id) = $true)) | ((X49 @ id @ (lam @ (X51 @ sh @ one)) @ id) = $true) | ~! [X53 : subst,X54 : term,X55 : subst] : ((X51 @ (comp @ X55 @ X53) @ (sub @ X54 @ X53)) = (sub @ (X51 @ X55 @ X54) @ X53))) | ~! [X56 : term] : (((X49 @ id @ (sub @ X50 @ (push @ X56 @ id)) @ id) = $true) | ~((X49 @ id @ X56 @ id) = $true)) | ($true = (X49 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id))) => ! [X57 : term,X58 : subst > term > subst > $o] : (~! [X59 : subst > term > term] : (((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id) = $true) | ~! [X60 : term] : (~((X58 @ id @ X60 @ id) = $true) | ((X58 @ id @ (X59 @ id @ X60) @ id) = $true)) | ~! [X61 : subst,X62 : subst,X63 : term] : ((X59 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)) = (sub @ (X59 @ X62 @ X63) @ X61))) | ~! [X64 : term] : (($true = (X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id)) | ~((X58 @ id @ X64 @ id) = $true)) | ((X58 @ id @ (lam @ X57) @ id) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X65 : subst > term > subst > $o,X66 : term] : (~! [X67 : subst > term > term] : (~! [X68 : term,X69 : subst,X70 : subst] : ((sub @ (X67 @ X70 @ X68) @ X69) = (X67 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69))) | ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) = $true) | ~! [X71 : term] : (~($true = (X65 @ id @ X71 @ id)) | ((X65 @ id @ (X67 @ id @ X71) @ id) = $true))) | ~! [X72 : subst,X73 : term,X74 : subst,X75 : subst] : (~((X65 @ (comp @ X74 @ X75) @ (sub @ X73 @ X75) @ X72) = $true) | ((X65 @ X74 @ X73 @ (comp @ X75 @ X72)) = $true)) | ~! [X76 : subst,X77 : subst,X78 : subst,X79 : term] : (~((X65 @ X78 @ X79 @ (comp @ X76 @ X77)) = $true) | ((X65 @ (comp @ X78 @ X76) @ (sub @ X79 @ X76) @ X77) = $true)) | ~! [X80 : term] : (((X65 @ id @ (sub @ X66 @ (push @ X80 @ id)) @ id) = $true) | ~((X65 @ id @ X80 @ id) = $true)) | ((X65 @ id @ (lam @ X66) @ id) = $true))) & (! [X81 : subst > term > term,X82 : term,X83 : term] : (~! [X84 : term,X85 : subst,X86 : subst] : ((X81 @ (comp @ X85 @ X86) @ (sub @ X84 @ X86)) = (sub @ (X81 @ X85 @ X84) @ X86)) | ((lam @ (X81 @ sh @ one)) != (ap @ (sub @ X82 @ id) @ X83))) <=> (hoaslamnotap = $true)) & (hoasapinj1_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X87 : subst] : ((comp @ id @ X87) = X87) => (! [X88 : subst] : ((comp @ X88 @ id) = X88) => (! [X89 : subst] : ((comp @ id @ X89) = X89) & ! [X90 : subst] : ((comp @ X90 @ id) = X90))))) & (hoasapnotvar = $true) & ((hoasapinj2 = $true) <=> ! [X91 : term,X92 : term,X93 : term,X94 : term] : (((ap @ (sub @ X91 @ id) @ X94) != (ap @ (sub @ X92 @ id) @ X93)) | (X93 = X94))) & ((pushprop_lem1 = $true) <=> ! [X95 : term,X96 : term > $o,X97 : subst,X98 : term > $o,X99 : term] : (~((X98 @ X99) = $true) | ((X96 @ (sub @ X99 @ (push @ X95 @ X97))) = $true))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X100 : term] : ((sub @ X100 @ id) = X100) => (! [X101 : term,X102 : subst > term > subst > $o] : (~! [X103 : subst > term > term] : (((X102 @ id @ (lam @ (X103 @ sh @ one)) @ id) = $true) | ~! [X104 : term,X105 : subst,X106 : subst] : ((X103 @ (comp @ X106 @ X105) @ (sub @ X104 @ X105)) = (sub @ (X103 @ X106 @ X104) @ X105)) | ~! [X107 : term] : (~((X102 @ id @ X107 @ id) = $true) | ((X102 @ id @ (X103 @ id @ X107) @ id) = $true))) | ((X102 @ id @ (lam @ (sub @ X101 @ (push @ one @ sh))) @ id) = $true) | ~! [X108 : term] : (~((X102 @ id @ X108 @ id) = $true) | ((X102 @ id @ (sub @ X101 @ (push @ X108 @ id)) @ id) = $true))) => ! [X109 : term,X110 : subst > term > subst > $o] : (~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (((X110 @ X114 @ X112 @ (comp @ X113 @ X111)) = $true) | ~($true = (X110 @ (comp @ X114 @ X113) @ (sub @ X112 @ X113) @ X111))) | ~! [X115 : term,X116 : subst,X117 : subst,X118 : subst] : (((X110 @ (comp @ X117 @ X118) @ (sub @ X115 @ X118) @ X116) = $true) | ~((X110 @ X117 @ X115 @ (comp @ X118 @ X116)) = $true)) | ((X110 @ id @ (lam @ X109) @ id) = $true) | ~! [X119 : term] : (~((X110 @ id @ X119 @ id) = $true) | ($true = (X110 @ id @ (sub @ X109 @ (push @ X119 @ id)) @ id))) | ~! [X120 : subst > term > term] : (((X110 @ id @ (lam @ (X120 @ sh @ one)) @ id) = $true) | ~! [X121 : term] : (~((X110 @ id @ X121 @ id) = $true) | ((X110 @ id @ (X120 @ id @ X121) @ id) = $true)) | ~! [X122 : subst,X123 : subst,X124 : term] : ((X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)) = (sub @ (X120 @ X122 @ X124) @ X123))))))) & ((induction2 = $true) <=> ! [X125 : term > $o,X126 : term] : (~! [X127 : term] : (~((var @ X127) = $true) | ($true = (X125 @ X127))) | ~! [X128 : term,X129 : term] : (~((X125 @ X128) = $true) | ~((X125 @ X129) = $true) | ($true = (X125 @ (ap @ X128 @ X129)))) | ~! [X130 : term] : (~! [X131 : term] : (((X125 @ (sub @ X130 @ (push @ X131 @ id))) = $true) | ~((X125 @ X131) = $true)) | ($true = (X125 @ (lam @ X130)))) | ((X125 @ X126) = $true))) & ~(ulamvar1 = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X132 : subst,X133 : term] : ((sub @ one @ (push @ X133 @ X132)) = X133) <=> (axvarcons = $true)) & ((! [X134 : subst > term > subst > $o] : ~! [X135 : term > $o] : ~! [X136 : term] : ((X134 @ id @ X136 @ id) = (X135 @ X136)) => (! [X137 : term > $o,X138 : term] : (~! [X139 : term] : (($true = (X137 @ X139)) | ~((var @ X139) = $true)) | ~! [X140 : term,X141 : term] : (~((X137 @ X141) = $true) | ~((X137 @ X140) = $true) | ((X137 @ (ap @ X140 @ X141)) = $true)) | ~! [X142 : term] : (~! [X143 : term] : (~((X137 @ X143) = $true) | ((X137 @ (sub @ X142 @ (push @ X143 @ id))) = $true)) | ((X137 @ (lam @ X142)) = $true)) | ($true = (X137 @ X138))) => (! [X144 : term] : ((sub @ X144 @ id) = X144) => (! [X145 : term > $o,X146 : term,X147 : subst > term > subst > $o] : (~! [X148 : subst > term > term] : (((X147 @ id @ (lam @ (X148 @ sh @ one)) @ id) = $true) | ~! [X149 : term] : (((X147 @ id @ (X148 @ id @ X149) @ id) = $true) | ~((X147 @ id @ X149 @ id) = $true)) | ~! [X150 : subst,X151 : term,X152 : subst] : ((sub @ (X148 @ X152 @ X151) @ X150) = (X148 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150)))) | ~! [X153 : term] : ((X147 @ id @ X153 @ id) = (X145 @ X153)) | ~! [X154 : term] : (~($true = (X145 @ X154)) | ((X145 @ (sub @ X146 @ (push @ X154 @ id))) = $true)) | ($true = (X145 @ (lam @ X146)))) => ! [X155 : subst > term > subst > $o,X156 : term] : (~! [X157 : term,X158 : term] : (((X155 @ id @ (ap @ (sub @ X157 @ id) @ X158) @ id) = $true) | ~((X155 @ id @ X158 @ id) = $true) | ~((X155 @ id @ X157 @ id) = $true)) | ~! [X159 : term] : (~($true = (var @ (sub @ X159 @ id))) | ((X155 @ id @ X159 @ id) = $true)) | ~! [X160 : subst,X161 : term,X162 : subst,X163 : subst] : (((X155 @ X163 @ X161 @ (comp @ X160 @ X162)) = $true) | ~((X155 @ (comp @ X163 @ X160) @ (sub @ X161 @ X160) @ X162) = $true)) | ~! [X164 : subst > term > term] : (~! [X165 : term,X166 : subst,X167 : subst] : ((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166)) = (sub @ (X164 @ X167 @ X165) @ X166)) | ((X155 @ id @ (lam @ (X164 @ sh @ one)) @ id) = $true) | ~! [X168 : term] : (~((X155 @ id @ X168 @ id) = $true) | ((X155 @ id @ (X164 @ id @ X168) @ id) = $true))) | ~! [X169 : subst,X170 : subst,X171 : subst,X172 : term] : (~((X155 @ X171 @ X172 @ (comp @ X170 @ X169)) = $true) | ((X155 @ (comp @ X171 @ X170) @ (sub @ X172 @ X170) @ X169) = $true)) | ((X155 @ id @ X156 @ id) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X173 : subst > term > subst > $o] : ~! [X174 : term > $o] : ~! [X175 : term] : ((X173 @ id @ X175 @ id) = (X174 @ X175))) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X176 : subst > term > subst > $o] : ~! [X177 : term > $o] : ~! [X178 : term] : ((X176 @ id @ X178 @ id) = (X177 @ X178))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X179 : term] : ~! [X180 : subst > term > term] : ~! [X181 : term,X182 : subst] : ((X180 @ X182 @ X181) = (sub @ X179 @ (push @ X181 @ X182))) <=> (hoasinduction_lem3v2_f = $true)) & ((axvarid = $true) <=> ! [X183 : term] : ((sub @ X183 @ id) = X183)) & ((hoasinduction_lthm = $true) <=> (! [X184 : term > $o,X185 : term] : (~! [X186 : term] : (~! [X187 : term] : (~((X184 @ X187) = $true) | ((X184 @ (sub @ X186 @ (push @ X187 @ id))) = $true)) | ((X184 @ (lam @ X186)) = $true)) | ~! [X188 : term,X189 : term] : (~($true = (X184 @ X189)) | ((X184 @ (ap @ X189 @ X188)) = $true) | ~((X184 @ X188) = $true)) | ~! [X190 : term] : (~((var @ X190) = $true) | ((X184 @ X190) = $true)) | ((X184 @ X185) = $true)) => (! [X191 : term,X192 : term,X193 : subst > term > subst > $o] : (((X193 @ id @ (ap @ X191 @ X192) @ id) = $true) | ~((X193 @ id @ X192 @ id) = $true) | ~! [X194 : term,X195 : term] : (((X193 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id) = $true) | ~($true = (X193 @ id @ X194 @ id)) | ~((X193 @ id @ X195 @ id) = $true)) | ~($true = (X193 @ id @ X191 @ id)) | ~! [X196 : term,X197 : subst,X198 : subst,X199 : subst] : (((X193 @ X199 @ X196 @ (comp @ X198 @ X197)) = $true) | ~((X193 @ (comp @ X199 @ X198) @ (sub @ X196 @ X198) @ X197) = $true)) | ~! [X200 : term,X201 : subst,X202 : subst,X203 : subst] : (~((X193 @ X202 @ X200 @ (comp @ X203 @ X201)) = $true) | ((X193 @ (comp @ X202 @ X203) @ (sub @ X200 @ X203) @ X201) = $true))) => (! [X204 : term,X205 : subst > term > subst > $o] : (~! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (((X205 @ (comp @ X206 @ X207) @ (sub @ X209 @ X207) @ X208) = $true) | ~((X205 @ X206 @ X209 @ (comp @ X207 @ X208)) = $true)) | ($true = (X205 @ id @ (lam @ X204) @ id)) | ~! [X210 : term] : (~((X205 @ id @ X210 @ id) = $true) | ((X205 @ id @ (sub @ X204 @ (push @ X210 @ id)) @ id) = $true)) | ~! [X211 : subst > term > term] : (~! [X212 : term] : (((X205 @ id @ (X211 @ id @ X212) @ id) = $true) | ~((X205 @ id @ X212 @ id) = $true)) | ((X205 @ id @ (lam @ (X211 @ sh @ one)) @ id) = $true) | ~! [X213 : term,X214 : subst,X215 : subst] : ((sub @ (X211 @ X215 @ X213) @ X214) = (X211 @ (comp @ X215 @ X214) @ (sub @ X213 @ X214)))) | ~! [X216 : subst,X217 : term,X218 : subst,X219 : subst] : (~((X205 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X216) = $true) | ((X205 @ X218 @ X217 @ (comp @ X219 @ X216)) = $true))) => ! [X220 : subst > term > subst > $o,X221 : term] : (((X220 @ id @ X221 @ id) = $true) | ~! [X222 : term] : (~((var @ (sub @ X222 @ id)) = $true) | ((X220 @ id @ X222 @ id) = $true)) | ~! [X223 : subst > term > term] : (~! [X224 : term,X225 : subst,X226 : subst] : ((sub @ (X223 @ X225 @ X224) @ X226) = (X223 @ (comp @ X225 @ X226) @ (sub @ X224 @ X226))) | ~! [X227 : term] : (~((X220 @ id @ X227 @ id) = $true) | ((X220 @ id @ (X223 @ id @ X227) @ id) = $true)) | ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id) = $true)) | ~! [X228 : term,X229 : subst,X230 : subst,X231 : subst] : (((X220 @ X230 @ X228 @ (comp @ X231 @ X229)) = $true) | ~((X220 @ (comp @ X230 @ X231) @ (sub @ X228 @ X231) @ X229) = $true)) | ~! [X232 : subst,X233 : subst,X234 : subst,X235 : term] : (~((X220 @ X234 @ X235 @ (comp @ X233 @ X232)) = $true) | ((X220 @ (comp @ X234 @ X233) @ (sub @ X235 @ X233) @ X232) = $true)) | ~! [X236 : term,X237 : term] : (~((X220 @ id @ X236 @ id) = $true) | ((X220 @ id @ (ap @ (sub @ X237 @ id) @ X236) @ id) = $true) | ~($true = (X220 @ id @ X237 @ id)))))))) & (! [X238 : term,X239 : subst > term > subst > $o] : (((X239 @ id @ (lam @ X238) @ id) = $true) | ~! [X240 : subst > term > term] : (~! [X241 : subst,X242 : subst,X243 : term] : ((X240 @ (comp @ X241 @ X242) @ (sub @ X243 @ X242)) = (sub @ (X240 @ X241 @ X243) @ X242)) | ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id) = $true) | ~! [X244 : term] : (((X239 @ id @ (X240 @ id @ X244) @ id) = $true) | ~((X239 @ id @ X244 @ id) = $true))) | ~! [X245 : term] : (((X239 @ id @ (sub @ X238 @ (push @ X245 @ id)) @ id) = $true) | ~((X239 @ id @ X245 @ id) = $true))) <=> (hoasinduction_lem3a = $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X246 : subst,X247 : term,X248 : term > $o] : ~! [X249 : term > $o] : ~! [X250 : term] : ((X248 @ (sub @ X250 @ (push @ X247 @ X246))) = (X249 @ X250)) <=> (pushprop_lem0_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X251 : subst > term > subst > $o,X252 : term > $o,X253 : term] : (((X252 @ (lam @ X253)) = $true) | ~! [X254 : term] : ((X251 @ id @ X254 @ id) = (X252 @ X254)) | ~! [X255 : subst > term > term] : (~! [X256 : term] : (((X251 @ id @ (X255 @ id @ X256) @ id) = $true) | ~((X251 @ id @ X256 @ id) = $true)) | ~! [X257 : subst,X258 : term,X259 : subst] : ((X255 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X255 @ X257 @ X258) @ X259)) | ((X251 @ id @ (lam @ (X255 @ sh @ one)) @ id) = $true)) | ~! [X260 : term] : (((X252 @ (sub @ X253 @ (push @ X260 @ id))) = $true) | ~((X252 @ X260) = $true)))) & (hoaslaminj_gthm = $true) & ((termmset = $true) <=> ! [X261 : term] : ((sub @ X261 @ id) = X261)) & ~(lamnotap = $true) & (ulamvarind = $true) & ((axidl = $true) <=> ! [X262 : subst] : ((comp @ id @ X262) = X262)) & (! [X263 : subst] : ((comp @ X263 @ id) = X263) <=> (axidr = $true)) & ((pushprop_lem0 = $true) <=> ! [X264 : term > $o,X265 : subst,X266 : term] : ~! [X267 : term > $o] : ~! [X268 : term] : ((X267 @ X268) = (X264 @ (sub @ X268 @ (push @ X266 @ X265))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X269 : subst > term > subst > $o] : ~! [X270 : term > $o] : ~! [X271 : term] : ((X269 @ id @ X271 @ id) = (X270 @ X271)) => (! [X272 : term > $o,X273 : term] : (~! [X274 : term,X275 : term] : (((X272 @ (ap @ X275 @ X274)) = $true) | ~((X272 @ X275) = $true) | ~((X272 @ X274) = $true)) | ~! [X276 : term] : (~((var @ X276) = $true) | ($true = (X272 @ X276))) | ~! [X277 : term] : (~! [X278 : term] : (~($true = (X272 @ X278)) | ((X272 @ (sub @ X277 @ (push @ X278 @ id))) = $true)) | ((X272 @ (lam @ X277)) = $true)) | ((X272 @ X273) = $true)) => (! [X279 : term] : ((sub @ X279 @ id) = X279) => (! [X280 : subst > term > subst > $o,X281 : term,X282 : term > $o] : (~! [X283 : subst > term > term] : (~! [X284 : term] : (~((X280 @ id @ X284 @ id) = $true) | ((X280 @ id @ (X283 @ id @ X284) @ id) = $true)) | ((X280 @ id @ (lam @ (X283 @ sh @ one)) @ id) = $true) | ~! [X285 : term,X286 : subst,X287 : subst] : ((X283 @ (comp @ X287 @ X286) @ (sub @ X285 @ X286)) = (sub @ (X283 @ X287 @ X285) @ X286))) | ((X282 @ (lam @ X281)) = $true) | ~! [X288 : term] : ((X282 @ X288) = (X280 @ id @ X288 @ id)) | ~! [X289 : term] : (((X282 @ (sub @ X281 @ (push @ X289 @ id))) = $true) | ~((X282 @ X289) = $true))) => ! [X290 : term,X291 : subst > term > subst > $o] : (~! [X292 : subst > term > term] : (~! [X293 : subst,X294 : term,X295 : subst] : ((X292 @ (comp @ X293 @ X295) @ (sub @ X294 @ X295)) = (sub @ (X292 @ X293 @ X294) @ X295)) | ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id) = $true) | ~! [X296 : term] : (((X291 @ id @ (X292 @ id @ X296) @ id) = $true) | ~((X291 @ id @ X296 @ id) = $true))) | ((X291 @ id @ X290 @ id) = $true) | ~! [X297 : term,X298 : term] : (((X291 @ id @ (ap @ (sub @ X297 @ id) @ X298) @ id) = $true) | ~((X291 @ id @ X297 @ id) = $true) | ~((X291 @ id @ X298 @ id) = $true)))))))) & (hoasapnotvar_gthm = $true) & (pushprop_lthm = $true) & (pushprop_lem3v2_lthm = $true) & ! [X299 : d_term,X300 : d_term] : (((d2term @ X299) = (d2term @ X300)) => (X299 = X300)) & ! [X301 : subst] : ? [X302 : d_subst] : ((d2subst @ X302) = X301) & ((! [X303 : term] : ((sub @ X303 @ id) = X303) => ! [X304 : term] : ((sub @ X304 @ id) = X304)) <=> (termmset_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X305 : term,X306 : subst] : ((sub @ one @ (push @ X305 @ X306)) = X305) => (! [X307 : term,X308 : subst] : ((comp @ sh @ (push @ X307 @ X308)) = X308) => ! [X309 : term,X310 : subst,X311 : term,X312 : term > $o,X313 : term > $o] : (((X313 @ (sub @ X311 @ (push @ X309 @ X310))) = $true) | ~((X312 @ X311) = $true))))) & (lamnotvar = $true) & ((hoasinduction = $true) <=> ! [X314 : term,X315 : subst > term > subst > $o] : (~! [X316 : term] : (((X315 @ id @ X316 @ id) = $true) | ~((var @ (sub @ X316 @ id)) = $true)) | ((X315 @ id @ X314 @ id) = $true) | ~! [X317 : subst,X318 : subst,X319 : term,X320 : subst] : (((X315 @ X320 @ X319 @ (comp @ X317 @ X318)) = $true) | ~((X315 @ (comp @ X320 @ X317) @ (sub @ X319 @ X317) @ X318) = $true)) | ~! [X321 : term,X322 : subst,X323 : subst,X324 : subst] : (((X315 @ (comp @ X323 @ X324) @ (sub @ X321 @ X324) @ X322) = $true) | ~((X315 @ X323 @ X321 @ (comp @ X324 @ X322)) = $true)) | ~! [X325 : subst > term > term] : (($true = (X315 @ id @ (lam @ (X325 @ sh @ one)) @ id)) | ~! [X326 : subst,X327 : term,X328 : subst] : ((X325 @ (comp @ X326 @ X328) @ (sub @ X327 @ X328)) = (sub @ (X325 @ X326 @ X327) @ X328)) | ~! [X329 : term] : (($true = (X315 @ id @ (X325 @ id @ X329) @ id)) | ~((X315 @ id @ X329 @ id) = $true))) | ~! [X330 : term,X331 : term] : (((X315 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id) = $true) | ~((X315 @ id @ X330 @ id) = $true) | ~((X315 @ id @ X331 @ id) = $true)))) & (pushprop_lem0_gthm = $true) & (pushprop = $true) & ~((var @ (d2term @ d_one)) = $true) & ((hoasinduction_lem3b = $true) <=> ! [X332 : term] : ~! [X333 : subst > term > term] : ((sub @ X332 @ (push @ one @ sh)) != (X333 @ sh @ one))) & (! [X334 : term] : ~! [X335 : subst > term > term] : ~! [X336 : term,X337 : subst] : ((X335 @ X337 @ X336) = (sub @ X334 @ (push @ X336 @ X337))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (induction2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axclos = $true) & ((! [X338 : term,X339 : subst] : ((sub @ one @ (push @ X338 @ X339)) = X338) => (! [X340 : subst,X341 : term] : ((comp @ sh @ (push @ X341 @ X340)) = X340) => (! [X342 : subst] : ((comp @ X342 @ id) = X342) => (! [X343 : term,X344 : term > $o] : (~! [X345 : term] : (~((var @ X345) = $true) | ((X344 @ X345) = $true)) | ~! [X346 : term] : (((X344 @ (lam @ X346)) = $true) | ~((X344 @ X346) = $true)) | ($true = (X344 @ X343)) | ~! [X347 : term,X348 : term] : (~((X344 @ X347) = $true) | ($true = (X344 @ (ap @ X348 @ X347))) | ~((X344 @ X348) = $true))) => ! [X349 : subst,X350 : term,X351 : term > $o] : (~! [X352 : term] : (~! [X353 : term] : (((X351 @ (sub @ X352 @ (push @ X353 @ id))) = $true) | ~((X351 @ X353) = $true)) | ((X351 @ (lam @ X352)) = $true)) | ~! [X354 : term,X355 : term] : (~((X351 @ X354) = $true) | ((X351 @ (ap @ X355 @ X354)) = $true) | ~((X351 @ X355) = $true)) | ((X351 @ (sub @ X350 @ X349)) = $true) | ~! [X356 : term] : (~((var @ X356) = $true) | ((X351 @ (sub @ X356 @ X349)) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoaslamnotvar = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X357 : term,X358 : term > $o,X359 : subst > term > subst > $o] : (~! [X360 : term] : (((X358 @ (sub @ X357 @ (push @ X360 @ id))) = $true) | ~((X358 @ X360) = $true)) | ~! [X361 : term] : ((X359 @ id @ X361 @ id) = (X358 @ X361)) | ~! [X362 : subst,X363 : subst,X364 : term,X365 : subst] : (((X359 @ X363 @ X364 @ (comp @ X365 @ X362)) = $true) | ~((X359 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365) @ X362) = $true)) | ($true = (X358 @ (lam @ X357))) | ~! [X366 : subst > term > term] : (~! [X367 : subst,X368 : subst,X369 : term] : ((sub @ (X366 @ X368 @ X369) @ X367) = (X366 @ (comp @ X368 @ X367) @ (sub @ X369 @ X367))) | ((X359 @ id @ (lam @ (X366 @ sh @ one)) @ id) = $true) | ~! [X370 : term] : (($true = (X359 @ id @ (X366 @ id @ X370) @ id)) | ~($true = (X359 @ id @ X370 @ id)))) | ~! [X371 : subst,X372 : subst,X373 : term,X374 : subst] : (~((X359 @ X371 @ X373 @ (comp @ X374 @ X372)) = $true) | ((X359 @ (comp @ X371 @ X374) @ (sub @ X373 @ X374) @ X372) = $true)))) & ((apinj1 = $true) <=> ! [X375 : term,X376 : term,X377 : term,X378 : term] : (((ap @ X375 @ X376) != (ap @ X377 @ X378)) | (X375 = X377))) & (hoasinduction_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X379 : term,X380 : term,X381 : term,X382 : term] : ((X379 = X382) | ((ap @ (sub @ X379 @ id) @ X381) != (ap @ (sub @ X382 @ id) @ X380)))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X383 : term] : ~! [X384 : subst > term > term] : ~! [X385 : term,X386 : subst] : ((X384 @ X386 @ X385) = (sub @ X383 @ (push @ X385 @ X386))) => (! [X387 : term] : ((sub @ X387 @ id) = X387) => ! [X388 : term,X389 : term > $o,X390 : subst > term > subst > $o] : (~! [X391 : term] : ((X390 @ id @ X391 @ id) = (X389 @ X391)) | ~! [X392 : subst > term > term] : (~! [X393 : term] : (~((X390 @ id @ X393 @ id) = $true) | ((X390 @ id @ (X392 @ id @ X393) @ id) = $true)) | ~! [X394 : subst,X395 : subst,X396 : term] : ((X392 @ (comp @ X395 @ X394) @ (sub @ X396 @ X394)) = (sub @ (X392 @ X395 @ X396) @ X394)) | ((X390 @ id @ (lam @ (X392 @ sh @ one)) @ id) = $true)) | ~! [X397 : term] : (((X389 @ (sub @ X388 @ (push @ X397 @ id))) = $true) | ~((X389 @ X397) = $true)) | ((X389 @ (lam @ X388)) = $true))))) & (axabs = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X398 : term,X399 : subst > term > subst > $o] : (((X399 @ id @ (lam @ (sub @ X398 @ (push @ one @ sh))) @ id) = $true) | ~! [X400 : subst > term > term] : (((X399 @ id @ (lam @ (X400 @ sh @ one)) @ id) = $true) | ~! [X401 : term] : (~((X399 @ id @ X401 @ id) = $true) | ((X399 @ id @ (X400 @ id @ X401) @ id) = $true)) | ~! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X403 @ X404) @ (sub @ X402 @ X404)) = (sub @ (X400 @ X403 @ X402) @ X404))) | ~! [X405 : term] : (~((X399 @ id @ X405 @ id) = $true) | ((X399 @ id @ (sub @ X398 @ (push @ X405 @ id)) @ id) = $true)))) & ((induction2lem = $true) <=> ! [X406 : subst,X407 : term > $o,X408 : term] : (~! [X409 : term] : (((X407 @ (lam @ X409)) = $true) | ~! [X410 : term] : (~((X407 @ X410) = $true) | ((X407 @ (sub @ X409 @ (push @ X410 @ id))) = $true))) | ~! [X411 : term] : (~((var @ X411) = $true) | ($true = (X407 @ (sub @ X411 @ X406)))) | ~! [X412 : term,X413 : term] : (~((X407 @ X412) = $true) | ((X407 @ (ap @ X413 @ X412)) = $true) | ~((X407 @ X413) = $true)) | ((X407 @ (sub @ X408 @ X406)) = $true))) & ((apinj2 = $true) <=> ! [X414 : term,X415 : term,X416 : term,X417 : term] : (((ap @ X417 @ X414) != (ap @ X416 @ X415)) | (X414 = X415))) & (one = (d2term @ d_one)) & ((hoaslaminj_lthm = $true) <=> (! [X418 : subst,X419 : term] : ((sub @ one @ (push @ X419 @ X418)) = X419) => (! [X420 : subst,X421 : term] : ((comp @ sh @ (push @ X421 @ X420)) = X420) => (! [X422 : term,X423 : term] : (((lam @ X423) != (lam @ X422)) | (X422 = X423)) => ! [X424 : subst,X425 : subst > term > term,X426 : subst > term > term,X427 : term] : (~! [X428 : term,X429 : subst,X430 : subst] : ((sub @ (X425 @ X430 @ X428) @ X429) = (X425 @ (comp @ X430 @ X429) @ (sub @ X428 @ X429))) | ~! [X431 : subst,X432 : subst,X433 : term] : ((sub @ (X426 @ X431 @ X433) @ X432) = (X426 @ (comp @ X431 @ X432) @ (sub @ X433 @ X432))) | ((lam @ (X425 @ sh @ one)) != (lam @ (X426 @ sh @ one))) | ((X425 @ X424 @ X427) = (X426 @ X424 @ X427))))))) & (! [X434 : term] : ~! [X435 : subst > term > term] : ((sub @ X434 @ (push @ one @ sh)) != (X435 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (induction2lem_gthm = $true) & (! [X436 : term,X437 : subst > term > subst > $o] : (((X437 @ id @ (lam @ (sub @ X436 @ (push @ one @ sh))) @ id) = $true) | ~! [X438 : subst > term > term] : (((X437 @ id @ (lam @ (X438 @ sh @ one)) @ id) = $true) | ~! [X439 : subst,X440 : subst,X441 : term] : ((X438 @ (comp @ X439 @ X440) @ (sub @ X441 @ X440)) = (sub @ (X438 @ X439 @ X441) @ X440)) | ~! [X442 : term] : (~((X437 @ id @ X442 @ id) = $true) | ((X437 @ id @ (X438 @ id @ X442) @ id) = $true))) | ~! [X443 : term] : (~((X437 @ id @ X443 @ id) = $true) | ((X437 @ id @ (sub @ X436 @ (push @ X443 @ id)) @ id) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X444 : term,X445 : term > $o] : (~! [X446 : term,X447 : term] : (~((X445 @ X446) = $true) | ~((X445 @ X447) = $true) | ((X445 @ (ap @ X446 @ X447)) = $true)) | ((X445 @ X444) = $true) | ~! [X448 : term] : (~((X445 @ X448) = $true) | ((X445 @ (lam @ X448)) = $true)) | ~! [X449 : term] : (($true = (X445 @ X449)) | ~((var @ X449) = $true))) <=> (induction = $true)) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & ((hoaslaminj = $true) <=> ! [X450 : subst,X451 : term,X452 : subst > term > term,X453 : subst > term > term] : (~! [X454 : term,X455 : subst,X456 : subst] : ((sub @ (X453 @ X455 @ X454) @ X456) = (X453 @ (comp @ X455 @ X456) @ (sub @ X454 @ X456))) | ((lam @ (X453 @ sh @ one)) != (lam @ (X452 @ sh @ one))) | ~! [X457 : subst,X458 : term,X459 : subst] : ((X452 @ (comp @ X459 @ X457) @ (sub @ X458 @ X457)) = (sub @ (X452 @ X459 @ X458) @ X457)) | ((X452 @ X450 @ X451) = (X453 @ X450 @ X451)))) & ((laminj = $true) <=> ! [X460 : term,X461 : term] : ((X460 = X461) | ((lam @ X460) != (lam @ X461)))) & (! [X462 : subst > term > subst > $o,X463 : term,X464 : term] : (~((X462 @ id @ X463 @ id) = $true) | ~! [X465 : term,X466 : term] : (((X462 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id) = $true) | ~((X462 @ id @ X466 @ id) = $true) | ~((X462 @ id @ X465 @ id) = $true)) | ~! [X467 : subst,X468 : subst,X469 : subst,X470 : term] : (((X462 @ X468 @ X470 @ (comp @ X467 @ X469)) = $true) | ~((X462 @ (comp @ X468 @ X467) @ (sub @ X470 @ X467) @ X469) = $true)) | ((X462 @ id @ (ap @ X463 @ X464) @ id) = $true) | ~! [X471 : subst,X472 : term,X473 : subst,X474 : subst] : (((X462 @ (comp @ X474 @ X473) @ (sub @ X472 @ X473) @ X471) = $true) | ~((X462 @ X474 @ X472 @ (comp @ X473 @ X471)) = $true)) | ~($true = (X462 @ id @ X464 @ id))) <=> (hoasinduction_lem2 = $true)) & ! [X475 : d_subst,X476 : d_subst] : (((d2subst @ X476) = (d2subst @ X475)) => (X475 = X476)) & (pushprop_lem3v2 = $true) & ((! [X477 : term] : ((sub @ X477 @ id) = X477) => (! [X478 : term,X479 : term,X480 : term,X481 : term] : (((ap @ X479 @ X480) != (ap @ X481 @ X478)) | (X479 = X481)) => ! [X482 : term,X483 : term,X484 : term,X485 : term] : (((ap @ (sub @ X483 @ id) @ X482) != (ap @ (sub @ X484 @ id) @ X485)) | (X483 = X484)))) <=> (hoasapinj1_lthm = $true)) & (! [X486 : term > $o,X487 : subst,X488 : term > $o,X489 : term] : (~! [X490 : term] : ((X486 @ (sub @ X490 @ (push @ X489 @ X487))) = (X488 @ X490)) | ~((X486 @ X489) = $true) | ($true = (X488 @ one))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem2v2 = $true) & ! [X491 : d_term] : (d_one = X491) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslamnotap_gthm = $true) & ! [X492 : term] : ? [X493 : d_term] : ((d2term @ X493) = X492) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (axapp = $true) & (! [X497 : subst > term > subst > $o,X498 : term] : (~! [X499 : term] : (((X497 @ id @ (sub @ X498 @ (push @ X499 @ id)) @ id) = $true) | ~((X497 @ id @ X499 @ id) = $true)) | ((X497 @ id @ (lam @ (sub @ X498 @ (push @ one @ sh))) @ id) = $true) | ~! [X500 : term,X501 : subst > term > term] : (~! [X502 : subst,X503 : term,X504 : subst] : ((X501 @ (comp @ X504 @ X502) @ (sub @ X503 @ X502)) = (sub @ X500 @ (push @ (sub @ X503 @ X502) @ (comp @ X504 @ X502)))) | ~! [X505 : subst,X506 : term,X507 : subst] : ((sub @ (X501 @ X507 @ X506) @ X505) = (sub @ (sub @ X500 @ (push @ X506 @ X507)) @ X505)) | ~! [X508 : term] : (($true = (X497 @ id @ (X501 @ id @ X508) @ id)) | ~((X497 @ id @ X508 @ id) = $true)) | ((X497 @ id @ (lam @ (X501 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X509 : term,X510 : subst] : ((sub @ one @ (push @ X509 @ X510)) = X509) => ! [X511 : term,X512 : term > $o,X513 : term > $o,X514 : subst] : (~($true = (X512 @ X511)) | ~! [X515 : term] : ((X513 @ X515) = (X512 @ (sub @ X515 @ (push @ X511 @ X514)))) | ((X513 @ one) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X516 : term] : ((sub @ X516 @ id) = X516) => ! [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (((X517 @ (lam @ X519)) = $true) | ~! [X520 : term,X521 : subst,X522 : subst,X523 : subst] : (~($true = (X518 @ X521 @ X520 @ (comp @ X522 @ X523))) | ($true = (X518 @ (comp @ X521 @ X522) @ (sub @ X520 @ X522) @ X523))) | ~! [X524 : subst,X525 : term,X526 : subst,X527 : subst] : (~($true = (X518 @ (comp @ X524 @ X526) @ (sub @ X525 @ X526) @ X527)) | ((X518 @ X524 @ X525 @ (comp @ X526 @ X527)) = $true)) | ~! [X528 : term] : ((X518 @ id @ X528 @ id) = (X517 @ X528)) | ~! [X529 : subst > term > term] : (((X518 @ id @ (lam @ (X529 @ sh @ one)) @ id) = $true) | ~! [X530 : term,X531 : subst,X532 : subst] : ((sub @ (X529 @ X531 @ X530) @ X532) = (X529 @ (comp @ X531 @ X532) @ (sub @ X530 @ X532))) | ~! [X533 : term] : (((X518 @ id @ (X529 @ id @ X533) @ id) = $true) | ~((X518 @ id @ X533 @ id) = $true))) | ~! [X534 : term] : (~((X517 @ X534) = $true) | ((X517 @ (sub @ X519 @ (push @ X534 @ id))) = $true))))) & (! [X535 : term,X536 : term] : (((sub @ X535 @ sh) != (sub @ X536 @ sh)) | (X535 = X536)) <=> (shinj = $true)) & ! [X537 : d_subst] : (d_id = X537) & ((axshiftcons = $true) <=> ! [X538 : subst,X539 : term] : ((comp @ sh @ (push @ X539 @ X538)) = X538)) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (apnotvar = $true) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X542 : term,X543 : term,X544 : term,X545 : term] : ((X542 = X543) | ((ap @ X544 @ X543) != (ap @ X545 @ X542))) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X546 = X548) | ((ap @ (sub @ X549 @ id) @ X548) != (ap @ (sub @ X547 @ id) @ X546)))) <=> (hoasapinj2_lthm = $true))),
% 28.46/5.33 inference(fool_elimination,[status(thm)],[f7])).
% 28.46/5.33 thf(f7,plain,(
% 28.46/5.33 (hoasinduction_no_psi_cond <=> ! [X0 : term,X1 : subst > term > subst > $o] : (~! [X2 : term,X3 : term] : ((X1 @ id @ (ap @ (sub @ X2 @ id) @ X3) @ id) | ~(X1 @ id @ X3 @ id) | ~(X1 @ id @ X2 @ id)) | ~! [X4 : subst > term > term] : ((X1 @ id @ (lam @ (X4 @ sh @ one)) @ id) | ~! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X7 @ X5) @ X6) = (X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) | ~! [X8 : term] : (~(X1 @ id @ X8 @ id) | (X1 @ id @ (X4 @ id @ X8) @ id))) | (X1 @ id @ X0 @ id))) & hoasinduction_lem2_gthm & (pushprop_p_and_p_prime = (^[X9 : term, X10 : subst, X11 : term > $o, X12 : term > $o] : (! [X13 : term] : ((X12 @ X13) = (X11 @ (sub @ X13 @ (push @ X9 @ X10))))))) & axassoc & pushprop_lem2v2_gthm & pushprop_gthm & (! [X14 : term,X15 : term > $o,X16 : term,X17 : subst > term > subst > $o] : (~(X15 @ X14) | ~! [X18 : term] : ((X15 @ X18) = (X17 @ id @ X18 @ id)) | ~! [X19 : subst,X20 : subst,X21 : subst,X22 : term] : (~(X17 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21) @ X19) | (X17 @ X20 @ X22 @ (comp @ X21 @ X19))) | (X15 @ (ap @ X16 @ X14)) | ~(X15 @ X16) | ~! [X23 : subst,X24 : term,X25 : subst,X26 : subst] : (~(X17 @ X25 @ X24 @ (comp @ X23 @ X26)) | (X17 @ (comp @ X25 @ X23) @ (sub @ X24 @ X23) @ X26)) | ~! [X27 : term,X28 : term] : ((X17 @ id @ (ap @ (sub @ X28 @ id) @ X27) @ id) | ~(X17 @ id @ X27 @ id) | ~(X17 @ id @ X28 @ id))) <=> hoasinduction_lem2v2) & hoasinduction_lem2_lthm & (! [X29 : subst] : ((push @ (sub @ one @ X29) @ (comp @ sh @ X29)) = X29) <=> axscons) & ((! [X30 : term] : ((sub @ X30 @ id) = X30) => (! [X31 : term > $o,X32 : term,X33 : subst] : (~! [X34 : term,X35 : term] : (~(X31 @ X35) | (X31 @ (ap @ X34 @ X35)) | ~(X31 @ X34)) | ~! [X36 : term] : ((X31 @ (lam @ X36)) | ~! [X37 : term] : (~(X31 @ X37) | (X31 @ (sub @ X36 @ (push @ X37 @ id))))) | ~! [X38 : term] : ((X31 @ (sub @ X38 @ X33)) | ~(var @ X38)) | (X31 @ (sub @ X32 @ X33))) => ! [X39 : term,X40 : term > $o] : (~! [X41 : term] : (~! [X42 : term] : ((X40 @ (sub @ X41 @ (push @ X42 @ id))) | ~(X40 @ X42)) | (X40 @ (lam @ X41))) | (X40 @ X39) | ~! [X43 : term,X44 : term] : ((X40 @ (ap @ X44 @ X43)) | ~(X40 @ X44) | ~(X40 @ X43)) | ~! [X45 : term] : (~(var @ X45) | (X40 @ X45))))) <=> induction2_lthm) & hoasinduction_lem3a_gthm & ((d2subst @ d_id) = sh) & (substmonoid <=> (! [X46 : subst] : ((comp @ X46 @ id) = X46) & ! [X47 : subst] : ((comp @ id @ X47) = X47))) & hoasinduction_lem1v2 & ulamvarsh & axvarshift & ((! [X48 : term] : ((sub @ X48 @ id) = X48) => (! [X49 : subst > term > subst > $o,X50 : term] : (~! [X51 : subst > term > term] : (~! [X52 : term] : ((X49 @ id @ (X51 @ id @ X52) @ id) | ~(X49 @ id @ X52 @ id)) | (X49 @ id @ (lam @ (X51 @ sh @ one)) @ id) | ~! [X53 : subst,X54 : term,X55 : subst] : ((X51 @ (comp @ X55 @ X53) @ (sub @ X54 @ X53)) = (sub @ (X51 @ X55 @ X54) @ X53))) | ~! [X56 : term] : ((X49 @ id @ (sub @ X50 @ (push @ X56 @ id)) @ id) | ~(X49 @ id @ X56 @ id)) | (X49 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)) => ! [X57 : term,X58 : subst > term > subst > $o] : (~! [X59 : subst > term > term] : ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id) | ~! [X60 : term] : (~(X58 @ id @ X60 @ id) | (X58 @ id @ (X59 @ id @ X60) @ id)) | ~! [X61 : subst,X62 : subst,X63 : term] : ((X59 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)) = (sub @ (X59 @ X62 @ X63) @ X61))) | ~! [X64 : term] : ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id) | ~(X58 @ id @ X64 @ id)) | (X58 @ id @ (lam @ X57) @ id)))) <=> hoasinduction_lem3a_lthm) & hoasapinj2_gthm & hoasinduction_lem1_gthm & (hoasinduction_lem3 <=> ! [X65 : subst > term > subst > $o,X66 : term] : (~! [X67 : subst > term > term] : (~! [X68 : term,X69 : subst,X70 : subst] : ((sub @ (X67 @ X70 @ X68) @ X69) = (X67 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69))) | (X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) | ~! [X71 : term] : (~(X65 @ id @ X71 @ id) | (X65 @ id @ (X67 @ id @ X71) @ id))) | ~! [X72 : subst,X73 : term,X74 : subst,X75 : subst] : (~(X65 @ (comp @ X74 @ X75) @ (sub @ X73 @ X75) @ X72) | (X65 @ X74 @ X73 @ (comp @ X75 @ X72))) | ~! [X76 : subst,X77 : subst,X78 : subst,X79 : term] : (~(X65 @ X78 @ X79 @ (comp @ X76 @ X77)) | (X65 @ (comp @ X78 @ X76) @ (sub @ X79 @ X76) @ X77)) | ~! [X80 : term] : ((X65 @ id @ (sub @ X66 @ (push @ X80 @ id)) @ id) | ~(X65 @ id @ X80 @ id)) | (X65 @ id @ (lam @ X66) @ id))) & (! [X81 : subst > term > term,X82 : term,X83 : term] : (~! [X84 : term,X85 : subst,X86 : subst] : ((X81 @ (comp @ X85 @ X86) @ (sub @ X84 @ X86)) = (sub @ (X81 @ X85 @ X84) @ X86)) | ((lam @ (X81 @ sh @ one)) != (ap @ (sub @ X82 @ id) @ X83))) <=> hoaslamnotap) & hoasapinj1_gthm & (substmonoid_lthm <=> (! [X87 : subst] : ((comp @ id @ X87) = X87) => (! [X88 : subst] : ((comp @ X88 @ id) = X88) => (! [X89 : subst] : ((comp @ id @ X89) = X89) & ! [X90 : subst] : ((comp @ X90 @ id) = X90))))) & hoasapnotvar & (hoasapinj2 <=> ! [X91 : term,X92 : term,X93 : term,X94 : term] : (((ap @ (sub @ X91 @ id) @ X94) != (ap @ (sub @ X92 @ id) @ X93)) | (X93 = X94))) & (pushprop_lem1 <=> ! [X95 : term,X96 : term > $o,X97 : subst,X98 : term > $o,X99 : term] : (~(X98 @ X99) | (X96 @ (sub @ X99 @ (push @ X95 @ X97))))) & pushprop_lem2v2_lthm & hoasinduction_lem1_lthm & (hoasinduction_lem3_lthm <=> (! [X100 : term] : ((sub @ X100 @ id) = X100) => (! [X101 : term,X102 : subst > term > subst > $o] : (~! [X103 : subst > term > term] : ((X102 @ id @ (lam @ (X103 @ sh @ one)) @ id) | ~! [X104 : term,X105 : subst,X106 : subst] : ((X103 @ (comp @ X106 @ X105) @ (sub @ X104 @ X105)) = (sub @ (X103 @ X106 @ X104) @ X105)) | ~! [X107 : term] : (~(X102 @ id @ X107 @ id) | (X102 @ id @ (X103 @ id @ X107) @ id))) | (X102 @ id @ (lam @ (sub @ X101 @ (push @ one @ sh))) @ id) | ~! [X108 : term] : (~(X102 @ id @ X108 @ id) | (X102 @ id @ (sub @ X101 @ (push @ X108 @ id)) @ id))) => ! [X109 : term,X110 : subst > term > subst > $o] : (~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : ((X110 @ X114 @ X112 @ (comp @ X113 @ X111)) | ~(X110 @ (comp @ X114 @ X113) @ (sub @ X112 @ X113) @ X111)) | ~! [X115 : term,X116 : subst,X117 : subst,X118 : subst] : ((X110 @ (comp @ X117 @ X118) @ (sub @ X115 @ X118) @ X116) | ~(X110 @ X117 @ X115 @ (comp @ X118 @ X116))) | (X110 @ id @ (lam @ X109) @ id) | ~! [X119 : term] : (~(X110 @ id @ X119 @ id) | (X110 @ id @ (sub @ X109 @ (push @ X119 @ id)) @ id)) | ~! [X120 : subst > term > term] : ((X110 @ id @ (lam @ (X120 @ sh @ one)) @ id) | ~! [X121 : term] : (~(X110 @ id @ X121 @ id) | (X110 @ id @ (X120 @ id @ X121) @ id)) | ~! [X122 : subst,X123 : subst,X124 : term] : ((X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)) = (sub @ (X120 @ X122 @ X124) @ X123))))))) & (induction2 <=> ! [X125 : term > $o,X126 : term] : (~! [X127 : term] : (~(var @ X127) | (X125 @ X127)) | ~! [X128 : term,X129 : term] : (~(X125 @ X128) | ~(X125 @ X129) | (X125 @ (ap @ X128 @ X129))) | ~! [X130 : term] : (~! [X131 : term] : ((X125 @ (sub @ X130 @ (push @ X131 @ id))) | ~(X125 @ X131)) | (X125 @ (lam @ X130))) | (X125 @ X126))) & ~ulamvar1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1v2_gthm & (! [X132 : subst,X133 : term] : ((sub @ one @ (push @ X133 @ X132)) = X133) <=> axvarcons) & ((! [X134 : subst > term > subst > $o] : ~! [X135 : term > $o] : ~! [X136 : term] : ((X134 @ id @ X136 @ id) = (X135 @ X136)) => (! [X137 : term > $o,X138 : term] : (~! [X139 : term] : ((X137 @ X139) | ~(var @ X139)) | ~! [X140 : term,X141 : term] : (~(X137 @ X141) | ~(X137 @ X140) | (X137 @ (ap @ X140 @ X141))) | ~! [X142 : term] : (~! [X143 : term] : (~(X137 @ X143) | (X137 @ (sub @ X142 @ (push @ X143 @ id)))) | (X137 @ (lam @ X142))) | (X137 @ X138)) => (! [X144 : term] : ((sub @ X144 @ id) = X144) => (! [X145 : term > $o,X146 : term,X147 : subst > term > subst > $o] : (~! [X148 : subst > term > term] : ((X147 @ id @ (lam @ (X148 @ sh @ one)) @ id) | ~! [X149 : term] : ((X147 @ id @ (X148 @ id @ X149) @ id) | ~(X147 @ id @ X149 @ id)) | ~! [X150 : subst,X151 : term,X152 : subst] : ((sub @ (X148 @ X152 @ X151) @ X150) = (X148 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150)))) | ~! [X153 : term] : ((X147 @ id @ X153 @ id) = (X145 @ X153)) | ~! [X154 : term] : (~(X145 @ X154) | (X145 @ (sub @ X146 @ (push @ X154 @ id)))) | (X145 @ (lam @ X146))) => ! [X155 : subst > term > subst > $o,X156 : term] : (~! [X157 : term,X158 : term] : ((X155 @ id @ (ap @ (sub @ X157 @ id) @ X158) @ id) | ~(X155 @ id @ X158 @ id) | ~(X155 @ id @ X157 @ id)) | ~! [X159 : term] : (~(var @ (sub @ X159 @ id)) | (X155 @ id @ X159 @ id)) | ~! [X160 : subst,X161 : term,X162 : subst,X163 : subst] : ((X155 @ X163 @ X161 @ (comp @ X160 @ X162)) | ~(X155 @ (comp @ X163 @ X160) @ (sub @ X161 @ X160) @ X162)) | ~! [X164 : subst > term > term] : (~! [X165 : term,X166 : subst,X167 : subst] : ((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166)) = (sub @ (X164 @ X167 @ X165) @ X166)) | (X155 @ id @ (lam @ (X164 @ sh @ one)) @ id) | ~! [X168 : term] : (~(X155 @ id @ X168 @ id) | (X155 @ id @ (X164 @ id @ X168) @ id))) | ~! [X169 : subst,X170 : subst,X171 : subst,X172 : term] : (~(X155 @ X171 @ X172 @ (comp @ X170 @ X169)) | (X155 @ (comp @ X171 @ X170) @ (sub @ X172 @ X170) @ X169)) | (X155 @ id @ X156 @ id)))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem0_lthm <=> ! [X173 : subst > term > subst > $o] : ~! [X174 : term > $o] : ~! [X175 : term] : ((X173 @ id @ X175 @ id) = (X174 @ X175))) & hoasinduction_lem3_gthm & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & hoasinduction_lem1 & (hoasinduction_lem0 <=> ! [X176 : subst > term > subst > $o] : ~! [X177 : term > $o] : ~! [X178 : term] : ((X176 @ id @ X178 @ id) = (X177 @ X178))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X179 : term] : ~! [X180 : subst > term > term] : ~! [X181 : term,X182 : subst] : ((X180 @ X182 @ X181) = (sub @ X179 @ (push @ X181 @ X182))) <=> hoasinduction_lem3v2_f) & (axvarid <=> ! [X183 : term] : ((sub @ X183 @ id) = X183)) & (hoasinduction_lthm <=> (! [X184 : term > $o,X185 : term] : (~! [X186 : term] : (~! [X187 : term] : (~(X184 @ X187) | (X184 @ (sub @ X186 @ (push @ X187 @ id)))) | (X184 @ (lam @ X186))) | ~! [X188 : term,X189 : term] : (~(X184 @ X189) | (X184 @ (ap @ X189 @ X188)) | ~(X184 @ X188)) | ~! [X190 : term] : (~(var @ X190) | (X184 @ X190)) | (X184 @ X185)) => (! [X191 : term,X192 : term,X193 : subst > term > subst > $o] : ((X193 @ id @ (ap @ X191 @ X192) @ id) | ~(X193 @ id @ X192 @ id) | ~! [X194 : term,X195 : term] : ((X193 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id) | ~(X193 @ id @ X194 @ id) | ~(X193 @ id @ X195 @ id)) | ~(X193 @ id @ X191 @ id) | ~! [X196 : term,X197 : subst,X198 : subst,X199 : subst] : ((X193 @ X199 @ X196 @ (comp @ X198 @ X197)) | ~(X193 @ (comp @ X199 @ X198) @ (sub @ X196 @ X198) @ X197)) | ~! [X200 : term,X201 : subst,X202 : subst,X203 : subst] : (~(X193 @ X202 @ X200 @ (comp @ X203 @ X201)) | (X193 @ (comp @ X202 @ X203) @ (sub @ X200 @ X203) @ X201))) => (! [X204 : term,X205 : subst > term > subst > $o] : (~! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : ((X205 @ (comp @ X206 @ X207) @ (sub @ X209 @ X207) @ X208) | ~(X205 @ X206 @ X209 @ (comp @ X207 @ X208))) | (X205 @ id @ (lam @ X204) @ id) | ~! [X210 : term] : (~(X205 @ id @ X210 @ id) | (X205 @ id @ (sub @ X204 @ (push @ X210 @ id)) @ id)) | ~! [X211 : subst > term > term] : (~! [X212 : term] : ((X205 @ id @ (X211 @ id @ X212) @ id) | ~(X205 @ id @ X212 @ id)) | (X205 @ id @ (lam @ (X211 @ sh @ one)) @ id) | ~! [X213 : term,X214 : subst,X215 : subst] : ((sub @ (X211 @ X215 @ X213) @ X214) = (X211 @ (comp @ X215 @ X214) @ (sub @ X213 @ X214)))) | ~! [X216 : subst,X217 : term,X218 : subst,X219 : subst] : (~(X205 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X216) | (X205 @ X218 @ X217 @ (comp @ X219 @ X216)))) => ! [X220 : subst > term > subst > $o,X221 : term] : ((X220 @ id @ X221 @ id) | ~! [X222 : term] : (~(var @ (sub @ X222 @ id)) | (X220 @ id @ X222 @ id)) | ~! [X223 : subst > term > term] : (~! [X224 : term,X225 : subst,X226 : subst] : ((sub @ (X223 @ X225 @ X224) @ X226) = (X223 @ (comp @ X225 @ X226) @ (sub @ X224 @ X226))) | ~! [X227 : term] : (~(X220 @ id @ X227 @ id) | (X220 @ id @ (X223 @ id @ X227) @ id)) | (X220 @ id @ (lam @ (X223 @ sh @ one)) @ id)) | ~! [X228 : term,X229 : subst,X230 : subst,X231 : subst] : ((X220 @ X230 @ X228 @ (comp @ X231 @ X229)) | ~(X220 @ (comp @ X230 @ X231) @ (sub @ X228 @ X231) @ X229)) | ~! [X232 : subst,X233 : subst,X234 : subst,X235 : term] : (~(X220 @ X234 @ X235 @ (comp @ X233 @ X232)) | (X220 @ (comp @ X234 @ X233) @ (sub @ X235 @ X233) @ X232)) | ~! [X236 : term,X237 : term] : (~(X220 @ id @ X236 @ id) | (X220 @ id @ (ap @ (sub @ X237 @ id) @ X236) @ id) | ~(X220 @ id @ X237 @ id))))))) & (! [X238 : term,X239 : subst > term > subst > $o] : ((X239 @ id @ (lam @ X238) @ id) | ~! [X240 : subst > term > term] : (~! [X241 : subst,X242 : subst,X243 : term] : ((X240 @ (comp @ X241 @ X242) @ (sub @ X243 @ X242)) = (sub @ (X240 @ X241 @ X243) @ X242)) | (X239 @ id @ (lam @ (X240 @ sh @ one)) @ id) | ~! [X244 : term] : ((X239 @ id @ (X240 @ id @ X244) @ id) | ~(X239 @ id @ X244 @ id))) | ~! [X245 : term] : ((X239 @ id @ (sub @ X238 @ (push @ X245 @ id)) @ id) | ~(X239 @ id @ X245 @ id))) <=> hoasinduction_lem3a) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X246 : subst,X247 : term,X248 : term > $o] : ~! [X249 : term > $o] : ~! [X250 : term] : ((X248 @ (sub @ X250 @ (push @ X247 @ X246))) = (X249 @ X250)) <=> pushprop_lem0_lthm) & (hoasinduction_lem3v2a <=> ! [X251 : subst > term > subst > $o,X252 : term > $o,X253 : term] : ((X252 @ (lam @ X253)) | ~! [X254 : term] : ((X251 @ id @ X254 @ id) = (X252 @ X254)) | ~! [X255 : subst > term > term] : (~! [X256 : term] : ((X251 @ id @ (X255 @ id @ X256) @ id) | ~(X251 @ id @ X256 @ id)) | ~! [X257 : subst,X258 : term,X259 : subst] : ((X255 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X255 @ X257 @ X258) @ X259)) | (X251 @ id @ (lam @ (X255 @ sh @ one)) @ id)) | ~! [X260 : term] : ((X252 @ (sub @ X253 @ (push @ X260 @ id))) | ~(X252 @ X260)))) & hoaslaminj_gthm & (termmset <=> ! [X261 : term] : ((sub @ X261 @ id) = X261)) & ~lamnotap & ulamvarind & (axidl <=> ! [X262 : subst] : ((comp @ id @ X262) = X262)) & (! [X263 : subst] : ((comp @ X263 @ id) = X263) <=> axidr) & (pushprop_lem0 <=> ! [X264 : term > $o,X265 : subst,X266 : term] : ~! [X267 : term > $o] : ~! [X268 : term] : ((X267 @ X268) = (X264 @ (sub @ X268 @ (push @ X266 @ X265))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X269 : subst > term > subst > $o] : ~! [X270 : term > $o] : ~! [X271 : term] : ((X269 @ id @ X271 @ id) = (X270 @ X271)) => (! [X272 : term > $o,X273 : term] : (~! [X274 : term,X275 : term] : ((X272 @ (ap @ X275 @ X274)) | ~(X272 @ X275) | ~(X272 @ X274)) | ~! [X276 : term] : (~(var @ X276) | (X272 @ X276)) | ~! [X277 : term] : (~! [X278 : term] : (~(X272 @ X278) | (X272 @ (sub @ X277 @ (push @ X278 @ id)))) | (X272 @ (lam @ X277))) | (X272 @ X273)) => (! [X279 : term] : ((sub @ X279 @ id) = X279) => (! [X280 : subst > term > subst > $o,X281 : term,X282 : term > $o] : (~! [X283 : subst > term > term] : (~! [X284 : term] : (~(X280 @ id @ X284 @ id) | (X280 @ id @ (X283 @ id @ X284) @ id)) | (X280 @ id @ (lam @ (X283 @ sh @ one)) @ id) | ~! [X285 : term,X286 : subst,X287 : subst] : ((X283 @ (comp @ X287 @ X286) @ (sub @ X285 @ X286)) = (sub @ (X283 @ X287 @ X285) @ X286))) | (X282 @ (lam @ X281)) | ~! [X288 : term] : ((X282 @ X288) = (X280 @ id @ X288 @ id)) | ~! [X289 : term] : ((X282 @ (sub @ X281 @ (push @ X289 @ id))) | ~(X282 @ X289))) => ! [X290 : term,X291 : subst > term > subst > $o] : (~! [X292 : subst > term > term] : (~! [X293 : subst,X294 : term,X295 : subst] : ((X292 @ (comp @ X293 @ X295) @ (sub @ X294 @ X295)) = (sub @ (X292 @ X293 @ X294) @ X295)) | (X291 @ id @ (lam @ (X292 @ sh @ one)) @ id) | ~! [X296 : term] : ((X291 @ id @ (X292 @ id @ X296) @ id) | ~(X291 @ id @ X296 @ id))) | (X291 @ id @ X290 @ id) | ~! [X297 : term,X298 : term] : ((X291 @ id @ (ap @ (sub @ X297 @ id) @ X298) @ id) | ~(X291 @ id @ X297 @ id) | ~(X291 @ id @ X298 @ id)))))))) & hoasapnotvar_gthm & pushprop_lthm & pushprop_lem3v2_lthm & ! [X299 : d_term,X300 : d_term] : (((d2term @ X299) = (d2term @ X300)) => (X299 = X300)) & ! [X301 : subst] : ? [X302 : d_subst] : ((d2subst @ X302) = X301) & ((! [X303 : term] : ((sub @ X303 @ id) = X303) => ! [X304 : term] : ((sub @ X304 @ id) = X304)) <=> termmset_lthm) & hoaslamnotap_lthm & (pushprop_lem1_lthm <=> (! [X305 : term,X306 : subst] : ((sub @ one @ (push @ X305 @ X306)) = X305) => (! [X307 : term,X308 : subst] : ((comp @ sh @ (push @ X307 @ X308)) = X308) => ! [X309 : term,X310 : subst,X311 : term,X312 : term > $o,X313 : term > $o] : ((X313 @ (sub @ X311 @ (push @ X309 @ X310))) | ~(X312 @ X311))))) & lamnotvar & (hoasinduction <=> ! [X314 : term,X315 : subst > term > subst > $o] : (~! [X316 : term] : ((X315 @ id @ X316 @ id) | ~(var @ (sub @ X316 @ id))) | (X315 @ id @ X314 @ id) | ~! [X317 : subst,X318 : subst,X319 : term,X320 : subst] : ((X315 @ X320 @ X319 @ (comp @ X317 @ X318)) | ~(X315 @ (comp @ X320 @ X317) @ (sub @ X319 @ X317) @ X318)) | ~! [X321 : term,X322 : subst,X323 : subst,X324 : subst] : ((X315 @ (comp @ X323 @ X324) @ (sub @ X321 @ X324) @ X322) | ~(X315 @ X323 @ X321 @ (comp @ X324 @ X322))) | ~! [X325 : subst > term > term] : ((X315 @ id @ (lam @ (X325 @ sh @ one)) @ id) | ~! [X326 : subst,X327 : term,X328 : subst] : ((X325 @ (comp @ X326 @ X328) @ (sub @ X327 @ X328)) = (sub @ (X325 @ X326 @ X327) @ X328)) | ~! [X329 : term] : ((X315 @ id @ (X325 @ id @ X329) @ id) | ~(X315 @ id @ X329 @ id))) | ~! [X330 : term,X331 : term] : ((X315 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id) | ~(X315 @ id @ X330 @ id) | ~(X315 @ id @ X331 @ id)))) & pushprop_lem0_gthm & pushprop & ~(var @ (d2term @ d_one)) & (hoasinduction_lem3b <=> ! [X332 : term] : ~! [X333 : subst > term > term] : ((sub @ X332 @ (push @ one @ sh)) != (X333 @ sh @ one))) & (! [X334 : term] : ~! [X335 : subst > term > term] : ~! [X336 : term,X337 : subst] : ((X335 @ X337 @ X336) = (sub @ X334 @ (push @ X336 @ X337))) <=> hoasinduction_lem3v2_f_lthm) & induction2_gthm & hoaslamnotvar_lthm & axclos & ((! [X338 : term,X339 : subst] : ((sub @ one @ (push @ X338 @ X339)) = X338) => (! [X340 : subst,X341 : term] : ((comp @ sh @ (push @ X341 @ X340)) = X340) => (! [X342 : subst] : ((comp @ X342 @ id) = X342) => (! [X343 : term,X344 : term > $o] : (~! [X345 : term] : (~(var @ X345) | (X344 @ X345)) | ~! [X346 : term] : ((X344 @ (lam @ X346)) | ~(X344 @ X346)) | (X344 @ X343) | ~! [X347 : term,X348 : term] : (~(X344 @ X347) | (X344 @ (ap @ X348 @ X347)) | ~(X344 @ X348))) => ! [X349 : subst,X350 : term,X351 : term > $o] : (~! [X352 : term] : (~! [X353 : term] : ((X351 @ (sub @ X352 @ (push @ X353 @ id))) | ~(X351 @ X353)) | (X351 @ (lam @ X352))) | ~! [X354 : term,X355 : term] : (~(X351 @ X354) | (X351 @ (ap @ X355 @ X354)) | ~(X351 @ X355)) | (X351 @ (sub @ X350 @ X349)) | ~! [X356 : term] : (~(var @ X356) | (X351 @ (sub @ X356 @ X349)))))))) <=> induction2lem_lthm) & hoaslamnotvar & (hoasinduction_lem3v2 <=> ! [X357 : term,X358 : term > $o,X359 : subst > term > subst > $o] : (~! [X360 : term] : ((X358 @ (sub @ X357 @ (push @ X360 @ id))) | ~(X358 @ X360)) | ~! [X361 : term] : ((X359 @ id @ X361 @ id) = (X358 @ X361)) | ~! [X362 : subst,X363 : subst,X364 : term,X365 : subst] : ((X359 @ X363 @ X364 @ (comp @ X365 @ X362)) | ~(X359 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365) @ X362)) | (X358 @ (lam @ X357)) | ~! [X366 : subst > term > term] : (~! [X367 : subst,X368 : subst,X369 : term] : ((sub @ (X366 @ X368 @ X369) @ X367) = (X366 @ (comp @ X368 @ X367) @ (sub @ X369 @ X367))) | (X359 @ id @ (lam @ (X366 @ sh @ one)) @ id) | ~! [X370 : term] : ((X359 @ id @ (X366 @ id @ X370) @ id) | ~(X359 @ id @ X370 @ id))) | ~! [X371 : subst,X372 : subst,X373 : term,X374 : subst] : (~(X359 @ X371 @ X373 @ (comp @ X374 @ X372)) | (X359 @ (comp @ X371 @ X374) @ (sub @ X373 @ X374) @ X372)))) & (apinj1 <=> ! [X375 : term,X376 : term,X377 : term,X378 : term] : (((ap @ X375 @ X376) != (ap @ X377 @ X378)) | (X375 = X377))) & hoasinduction_gthm & (hoasapinj1 <=> ! [X379 : term,X380 : term,X381 : term,X382 : term] : ((X379 = X382) | ((ap @ (sub @ X379 @ id) @ X381) != (ap @ (sub @ X382 @ id) @ X380)))) & (hoasinduction_lem3v2a_lthm <=> (! [X383 : term] : ~! [X384 : subst > term > term] : ~! [X385 : term,X386 : subst] : ((X384 @ X386 @ X385) = (sub @ X383 @ (push @ X385 @ X386))) => (! [X387 : term] : ((sub @ X387 @ id) = X387) => ! [X388 : term,X389 : term > $o,X390 : subst > term > subst > $o] : (~! [X391 : term] : ((X390 @ id @ X391 @ id) = (X389 @ X391)) | ~! [X392 : subst > term > term] : (~! [X393 : term] : (~(X390 @ id @ X393 @ id) | (X390 @ id @ (X392 @ id @ X393) @ id)) | ~! [X394 : subst,X395 : subst,X396 : term] : ((X392 @ (comp @ X395 @ X394) @ (sub @ X396 @ X394)) = (sub @ (X392 @ X395 @ X396) @ X394)) | (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) | ~! [X397 : term] : ((X389 @ (sub @ X388 @ (push @ X397 @ id))) | ~(X389 @ X397)) | (X389 @ (lam @ X388)))))) & axabs & (hoasinduction_lem3aa <=> ! [X398 : term,X399 : subst > term > subst > $o] : ((X399 @ id @ (lam @ (sub @ X398 @ (push @ one @ sh))) @ id) | ~! [X400 : subst > term > term] : ((X399 @ id @ (lam @ (X400 @ sh @ one)) @ id) | ~! [X401 : term] : (~(X399 @ id @ X401 @ id) | (X399 @ id @ (X400 @ id @ X401) @ id)) | ~! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X403 @ X404) @ (sub @ X402 @ X404)) = (sub @ (X400 @ X403 @ X402) @ X404))) | ~! [X405 : term] : (~(X399 @ id @ X405 @ id) | (X399 @ id @ (sub @ X398 @ (push @ X405 @ id)) @ id)))) & (induction2lem <=> ! [X406 : subst,X407 : term > $o,X408 : term] : (~! [X409 : term] : ((X407 @ (lam @ X409)) | ~! [X410 : term] : (~(X407 @ X410) | (X407 @ (sub @ X409 @ (push @ X410 @ id))))) | ~! [X411 : term] : (~(var @ X411) | (X407 @ (sub @ X411 @ X406))) | ~! [X412 : term,X413 : term] : (~(X407 @ X412) | (X407 @ (ap @ X413 @ X412)) | ~(X407 @ X413)) | (X407 @ (sub @ X408 @ X406)))) & (apinj2 <=> ! [X414 : term,X415 : term,X416 : term,X417 : term] : (((ap @ X417 @ X414) != (ap @ X416 @ X415)) | (X414 = X415))) & (one = (d2term @ d_one)) & (hoaslaminj_lthm <=> (! [X418 : subst,X419 : term] : ((sub @ one @ (push @ X419 @ X418)) = X419) => (! [X420 : subst,X421 : term] : ((comp @ sh @ (push @ X421 @ X420)) = X420) => (! [X422 : term,X423 : term] : (((lam @ X423) != (lam @ X422)) | (X422 = X423)) => ! [X424 : subst,X425 : subst > term > term,X426 : subst > term > term,X427 : term] : (~! [X428 : term,X429 : subst,X430 : subst] : ((sub @ (X425 @ X430 @ X428) @ X429) = (X425 @ (comp @ X430 @ X429) @ (sub @ X428 @ X429))) | ~! [X431 : subst,X432 : subst,X433 : term] : ((sub @ (X426 @ X431 @ X433) @ X432) = (X426 @ (comp @ X431 @ X432) @ (sub @ X433 @ X432))) | ((lam @ (X425 @ sh @ one)) != (lam @ (X426 @ sh @ one))) | ((X425 @ X424 @ X427) = (X426 @ X424 @ X427))))))) & (! [X434 : term] : ~! [X435 : subst > term > term] : ((sub @ X434 @ (push @ one @ sh)) != (X435 @ sh @ one)) <=> hoasinduction_lem3b_lthm) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & induction2lem_gthm & (! [X436 : term,X437 : subst > term > subst > $o] : ((X437 @ id @ (lam @ (sub @ X436 @ (push @ one @ sh))) @ id) | ~! [X438 : subst > term > term] : ((X437 @ id @ (lam @ (X438 @ sh @ one)) @ id) | ~! [X439 : subst,X440 : subst,X441 : term] : ((X438 @ (comp @ X439 @ X440) @ (sub @ X441 @ X440)) = (sub @ (X438 @ X439 @ X441) @ X440)) | ~! [X442 : term] : (~(X437 @ id @ X442 @ id) | (X437 @ id @ (X438 @ id @ X442) @ id))) | ~! [X443 : term] : (~(X437 @ id @ X443 @ id) | (X437 @ id @ (sub @ X436 @ (push @ X443 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (! [X444 : term,X445 : term > $o] : (~! [X446 : term,X447 : term] : (~(X445 @ X446) | ~(X445 @ X447) | (X445 @ (ap @ X446 @ X447))) | (X445 @ X444) | ~! [X448 : term] : (~(X445 @ X448) | (X445 @ (lam @ X448))) | ~! [X449 : term] : ((X445 @ X449) | ~(var @ X449))) <=> induction) & ((d2subst @ d_id) = id) & substmonoid_gthm & (hoaslaminj <=> ! [X450 : subst,X451 : term,X452 : subst > term > term,X453 : subst > term > term] : (~! [X454 : term,X455 : subst,X456 : subst] : ((sub @ (X453 @ X455 @ X454) @ X456) = (X453 @ (comp @ X455 @ X456) @ (sub @ X454 @ X456))) | ((lam @ (X453 @ sh @ one)) != (lam @ (X452 @ sh @ one))) | ~! [X457 : subst,X458 : term,X459 : subst] : ((X452 @ (comp @ X459 @ X457) @ (sub @ X458 @ X457)) = (sub @ (X452 @ X459 @ X458) @ X457)) | ((X452 @ X450 @ X451) = (X453 @ X450 @ X451)))) & (laminj <=> ! [X460 : term,X461 : term] : ((X460 = X461) | ((lam @ X460) != (lam @ X461)))) & (! [X462 : subst > term > subst > $o,X463 : term,X464 : term] : (~(X462 @ id @ X463 @ id) | ~! [X465 : term,X466 : term] : ((X462 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id) | ~(X462 @ id @ X466 @ id) | ~(X462 @ id @ X465 @ id)) | ~! [X467 : subst,X468 : subst,X469 : subst,X470 : term] : ((X462 @ X468 @ X470 @ (comp @ X467 @ X469)) | ~(X462 @ (comp @ X468 @ X467) @ (sub @ X470 @ X467) @ X469)) | (X462 @ id @ (ap @ X463 @ X464) @ id) | ~! [X471 : subst,X472 : term,X473 : subst,X474 : subst] : ((X462 @ (comp @ X474 @ X473) @ (sub @ X472 @ X473) @ X471) | ~(X462 @ X474 @ X472 @ (comp @ X473 @ X471))) | ~(X462 @ id @ X464 @ id)) <=> hoasinduction_lem2) & ! [X475 : d_subst,X476 : d_subst] : (((d2subst @ X476) = (d2subst @ X475)) => (X475 = X476)) & pushprop_lem3v2 & ((! [X477 : term] : ((sub @ X477 @ id) = X477) => (! [X478 : term,X479 : term,X480 : term,X481 : term] : (((ap @ X479 @ X480) != (ap @ X481 @ X478)) | (X479 = X481)) => ! [X482 : term,X483 : term,X484 : term,X485 : term] : (((ap @ (sub @ X483 @ id) @ X482) != (ap @ (sub @ X484 @ id) @ X485)) | (X483 = X484)))) <=> hoasapinj1_lthm) & (! [X486 : term > $o,X487 : subst,X488 : term > $o,X489 : term] : (~! [X490 : term] : ((X486 @ (sub @ X490 @ (push @ X489 @ X487))) = (X488 @ X490)) | ~(X486 @ X489) | (X488 @ one)) <=> pushprop_lem1v2) & pushprop_lem2v2 & ! [X491 : d_term] : (d_one = X491) & hoasinduction_lem3b_gthm & axmap & hoaslamnotap_gthm & ! [X492 : term] : ? [X493 : d_term] : ((d2term @ X493) = X492) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((^[X494 : subst > term > subst > $o, X495 : term > $o] : (! [X496 : term] : ((X494 @ id @ X496 @ id) = (X495 @ X496)))) = hoasinduction_p_and_p_prime) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & axapp & (! [X497 : subst > term > subst > $o,X498 : term] : (~! [X499 : term] : ((X497 @ id @ (sub @ X498 @ (push @ X499 @ id)) @ id) | ~(X497 @ id @ X499 @ id)) | (X497 @ id @ (lam @ (sub @ X498 @ (push @ one @ sh))) @ id) | ~! [X500 : term,X501 : subst > term > term] : (~! [X502 : subst,X503 : term,X504 : subst] : ((X501 @ (comp @ X504 @ X502) @ (sub @ X503 @ X502)) = (sub @ X500 @ (push @ (sub @ X503 @ X502) @ (comp @ X504 @ X502)))) | ~! [X505 : subst,X506 : term,X507 : subst] : ((sub @ (X501 @ X507 @ X506) @ X505) = (sub @ (sub @ X500 @ (push @ X506 @ X507)) @ X505)) | ~! [X508 : term] : ((X497 @ id @ (X501 @ id @ X508) @ id) | ~(X497 @ id @ X508 @ id)) | (X497 @ id @ (lam @ (X501 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & hoasinduction_lem3v2_gthm & ((! [X509 : term,X510 : subst] : ((sub @ one @ (push @ X509 @ X510)) = X509) => ! [X511 : term,X512 : term > $o,X513 : term > $o,X514 : subst] : (~(X512 @ X511) | ~! [X515 : term] : ((X513 @ X515) = (X512 @ (sub @ X515 @ (push @ X511 @ X514)))) | (X513 @ one))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & (hoasinduction_lem3v2_lthm <=> (! [X516 : term] : ((sub @ X516 @ id) = X516) => ! [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : ((X517 @ (lam @ X519)) | ~! [X520 : term,X521 : subst,X522 : subst,X523 : subst] : (~(X518 @ X521 @ X520 @ (comp @ X522 @ X523)) | (X518 @ (comp @ X521 @ X522) @ (sub @ X520 @ X522) @ X523)) | ~! [X524 : subst,X525 : term,X526 : subst,X527 : subst] : (~(X518 @ (comp @ X524 @ X526) @ (sub @ X525 @ X526) @ X527) | (X518 @ X524 @ X525 @ (comp @ X526 @ X527))) | ~! [X528 : term] : ((X518 @ id @ X528 @ id) = (X517 @ X528)) | ~! [X529 : subst > term > term] : ((X518 @ id @ (lam @ (X529 @ sh @ one)) @ id) | ~! [X530 : term,X531 : subst,X532 : subst] : ((sub @ (X529 @ X531 @ X530) @ X532) = (X529 @ (comp @ X531 @ X532) @ (sub @ X530 @ X532))) | ~! [X533 : term] : ((X518 @ id @ (X529 @ id @ X533) @ id) | ~(X518 @ id @ X533 @ id))) | ~! [X534 : term] : (~(X517 @ X534) | (X517 @ (sub @ X519 @ (push @ X534 @ id))))))) & (! [X535 : term,X536 : term] : (((sub @ X535 @ sh) != (sub @ X536 @ sh)) | (X535 = X536)) <=> shinj) & ! [X537 : d_subst] : (d_id = X537) & (axshiftcons <=> ! [X538 : subst,X539 : term] : ((comp @ sh @ (push @ X539 @ X538)) = X538)) & hoasapnotvar_lthm & hoasinduction_lem2v2_gthm & (hoaslam = (^[X540 : subst, X541 : subst > term > term] : (d2term @ d_one))) & apnotvar & termmset_gthm & pushprop_lthm_orig & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X542 : term,X543 : term,X544 : term,X545 : term] : ((X542 = X543) | ((ap @ X544 @ X543) != (ap @ X545 @ X542))) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X546 = X548) | ((ap @ (sub @ X549 @ id) @ X548) != (ap @ (sub @ X547 @ id) @ X546)))) <=> hoasapinj2_lthm)),
% 28.46/5.33 inference(rectify,[status(thm)],[f1])).
% 28.46/5.33 thf(f1,axiom,(
% 28.46/5.33 (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X30 @ id))) & hoasinduction_lem2_gthm & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : term > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & axassoc & pushprop_lem2v2_gthm & pushprop_gthm & (! [X45 : term,X11 : term > $o,X44 : term,X10 : subst > term > subst > $o] : (~(X11 @ X45) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X44) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id))) <=> hoasinduction_lem2v2) & hoasinduction_lem2_lthm & (! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14) <=> axscons) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : term > $o,X16 : term,X17 : subst] : (~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))))) <=> induction2_lthm) & hoasinduction_lem3a_gthm & ((d2subst @ d_id) = sh) & (substmonoid <=> (! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14))) & hoasinduction_lem1v2 & ulamvarsh & axvarshift & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & hoasapinj2_gthm & hoasinduction_lem1_gthm & (hoasinduction_lem3 <=> ! [X10 : subst > term > subst > $o,X27 : term] : (~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id))) & (! [X18 : subst > term > term,X46 : term,X47 : term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47))) <=> hoaslamnotap) & hoasapinj1_gthm & (substmonoid_lthm <=> (! [X14 : subst] : ((comp @ id @ X14) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14))))) & hoasapnotvar & (hoasapinj2 <=> ! [X15 : term,X13 : term,X19 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) & (pushprop_lem1 <=> ! [X15 : term,X26 : term > $o,X14 : subst,X10 : term > $o,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & pushprop_lem2v2_lthm & hoasinduction_lem1_lthm & (hoasinduction_lem3_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X27 : term,X10 : subst > term > subst > $o] : (~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) & (induction2 <=> ! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22))) & ~ulamvar1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1v2_gthm & (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X29 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))) => ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id)))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & hoasinduction_lem3_gthm & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & hoasinduction_lem1 & (hoasinduction_lem0 <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & (axvarid <=> ! [X13 : term] : ((sub @ X13 @ id) = X13)) & (hoasinduction_lthm <=> (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22)) => (! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~(X10 @ id @ X23 @ id) | ~! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X27 : term,X10 : subst > term > subst > $o] : (~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : subst > term > subst > $o,X28 : term] : ((X10 @ id @ X28 @ id) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id))))))) & (! [X43 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3a) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X14 : subst,X13 : term,X10 : term > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0_lthm) & (hoasinduction_lem3v2a <=> ! [X10 : subst > term > subst > $o,X11 : term > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))) & hoaslaminj_gthm & (termmset <=> ! [X13 : term] : ((sub @ X13 @ id) = X13)) & ~lamnotap & ulamvarind & (axidl <=> ! [X14 : subst] : ((comp @ id @ X14) = X14)) & (! [X14 : subst] : ((comp @ X14 @ id) = X14) <=> axidr) & (pushprop_lem0 <=> ! [X10 : term > $o,X14 : subst,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X30 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ X30 @ id) | ~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)))))))) & hoasapnotvar_gthm & pushprop_lthm & pushprop_lem3v2_lthm & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13)) <=> termmset_lthm) & hoaslamnotap_lthm & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X15 : term,X14 : subst,X13 : term,X10 : term > $o,X26 : term > $o] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & lamnotvar & (hoasinduction <=> ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & pushprop_lem0_gthm & pushprop & ~(var @ (d2term @ d_one)) & (hoasinduction_lem3b <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f_lthm) & induction2_gthm & hoaslamnotvar_lthm & axclos & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X21 : term,X10 : term > $o] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => ! [X17 : subst,X16 : term,X10 : term > $o] : (~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17)) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))))))) <=> induction2lem_lthm) & hoaslamnotvar & (hoasinduction_lem3v2 <=> ! [X48 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (apinj1 <=> ! [X15 : term,X20 : term,X13 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15))) & hoasinduction_gthm & (hoasapinj1 <=> ! [X15 : term,X19 : term,X20 : term,X13 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X29 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)))))) & axabs & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)))) & (induction2lem <=> ! [X17 : subst,X10 : term > $o,X16 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17)))) & (apinj2 <=> ! [X20 : term,X19 : term,X13 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20))) & (one = (d2term @ d_one)) & (hoaslaminj_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X13 : term,X15 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) => ! [X32 : subst,X18 : subst > term > term,X31 : subst > term > term,X33 : term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33))))))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & induction2lem_gthm & (! [X42 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (! [X21 : term,X10 : term > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X21) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) <=> induction) & ((d2subst @ d_id) = id) & substmonoid_gthm & (hoaslaminj <=> ! [X32 : subst,X33 : term,X18 : subst > term > term,X31 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)))) & (laminj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15)))) & (! [X10 : subst > term > subst > $o,X23 : term,X24 : term] : (~(X10 @ id @ X23 @ id) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id)) <=> hoasinduction_lem2) & ! [X7 : d_subst,X6 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & pushprop_lem3v2 & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X19 : term,X15 : term,X20 : term,X13 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) => ! [X19 : term,X13 : term,X15 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)))) <=> hoasapinj1_lthm) & (! [X10 : term > $o,X14 : subst,X11 : term > $o,X13 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | ~(X10 @ X13) | (X11 @ one)) <=> pushprop_lem1v2) & pushprop_lem2v2 & ! [X1 : d_term] : (d_one = X1) & hoasinduction_lem3b_gthm & axmap & hoaslamnotap_gthm & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) = hoasinduction_p_and_p_prime) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & axapp & (! [X10 : subst > term > subst > $o,X34 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X35 : term,X18 : subst > term > term] : (~! [X41 : subst,X40 : term,X39 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))) | ~! [X38 : subst,X37 : term,X36 : subst] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & hoasinduction_lem3v2_gthm & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X13 : term,X10 : term > $o,X11 : term > $o,X14 : subst] : (~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X11 : term > $o,X10 : subst > term > subst > $o,X48 : term] : ((X11 @ (lam @ X48)) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id))))))) & (! [X13 : term,X15 : term] : (((sub @ X13 @ sh) != (sub @ X15 @ sh)) | (X13 = X15)) <=> shinj) & ! [X5 : d_subst] : (d_id = X5) & (axshiftcons <=> ! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14)) & hoasapnotvar_lthm & hoasinduction_lem2v2_gthm & (hoaslam = (^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one))) & apnotvar & termmset_gthm & pushprop_lthm_orig & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X19 = X20) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X19 : term,X13 : term,X20 : term,X15 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj2_lthm)),
% 28.46/5.33 file('/export/starexec/sandbox2/tmp/tmp.eLR4iSdWK1/DTF2THF_2254.p',alg444_1)).
% 28.46/5.33 thf(f1057,plain,(
% 28.46/5.33 ( ! [X258 : term] : (((d2term @ (sK580 @ X258)) = X258)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f4190,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP11 @ X0) != $true) | ((d2term @ d_one) != (X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4189,f4091])).
% 28.46/5.33 thf(f4189,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6))) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP11 @ X0) != $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4100,f4179])).
% 28.46/5.33 thf(f4179,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o,X1 : term] : (((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4133,f4171])).
% 28.46/5.33 thf(f4171,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o] : (($true != (sP13 @ X0)) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f1511,f4091])).
% 28.46/5.33 thf(f1511,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (sK365 @ X0) @ (d2subst @ d_id)) = $true) | ($true != (sP13 @ X0))) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f927,f1127,f1127])).
% 28.46/5.33 thf(f1127,plain,(
% 28.46/5.33 ((d2subst @ d_id) = id)),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f927,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (sK365 @ X0) @ id)) | ($true != (sP13 @ X0))) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f387])).
% 28.46/5.33 thf(f387,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : ((($true = (sP13 @ X0)) | ! [X1 : term,X2 : term] : (((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true) | ((X0 @ id @ X1 @ id) != $true))) & ((((X0 @ id @ (ap @ (sub @ (sK366 @ X0) @ id) @ (sK365 @ X0)) @ id) != $true) & ((X0 @ id @ (sK366 @ X0) @ id) = $true) & ($true = (X0 @ id @ (sK365 @ X0) @ id))) | ($true != (sP13 @ X0))))),
% 28.46/5.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK365,sK366])],[f385,f386])).
% 28.46/5.33 thf(f386,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : (? [X3 : term,X4 : term] : (((X0 @ id @ (ap @ (sub @ X4 @ id) @ X3) @ id) != $true) & ((X0 @ id @ X4 @ id) = $true) & ((X0 @ id @ X3 @ id) = $true)) => (((X0 @ id @ (ap @ (sub @ (sK366 @ X0) @ id) @ (sK365 @ X0)) @ id) != $true) & ((X0 @ id @ (sK366 @ X0) @ id) = $true) & ($true = (X0 @ id @ (sK365 @ X0) @ id))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f385,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : ((($true = (sP13 @ X0)) | ! [X1 : term,X2 : term] : (((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true) | ((X0 @ id @ X1 @ id) != $true))) & (? [X3 : term,X4 : term] : (((X0 @ id @ (ap @ (sub @ X4 @ id) @ X3) @ id) != $true) & ((X0 @ id @ X4 @ id) = $true) & ((X0 @ id @ X3 @ id) = $true)) | ($true != (sP13 @ X0))))),
% 28.46/5.33 inference(rectify,[status(thm)],[f384])).
% 28.46/5.33 thf(f384,plain,(
% 28.46/5.33 ! [X215 : subst > term > subst > $o] : ((((sP13 @ X215) = $true) | ! [X231 : term,X232 : term] : (((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) = $true) | ((X215 @ id @ X232 @ id) != $true) | ((X215 @ id @ X231 @ id) != $true))) & (? [X231 : term,X232 : term] : (((X215 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id) != $true) & ((X215 @ id @ X232 @ id) = $true) & ((X215 @ id @ X231 @ id) = $true)) | ((sP13 @ X215) != $true)))),
% 28.46/5.33 inference(nnf_transformation,[status(thm)],[f27])).
% 28.46/5.33 thf(f4133,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o,X1 : term] : (($true = (sP13 @ X0)) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)) != $true)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f1508,f4091])).
% 28.46/5.33 thf(f1508,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o,X1 : term] : (((X0 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ (ap @ (sub @ X2 @ (d2subst @ d_id)) @ X1) @ (d2subst @ d_id)) = $true) | ($true = (sP13 @ X0))) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f930,f1127,f1127,f1127,f1127,f1127,f1127,f1127])).
% 28.46/5.33 thf(f930,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o,X1 : term] : (($true = (sP13 @ X0)) | ((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true) | ((X0 @ id @ X1 @ id) != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f387])).
% 28.46/5.33 thf(f4100,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (sK370 @ X6 @ X0) @ (d2subst @ d_id))) | ((sP11 @ X0) != $true) | ((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6)))) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f1519,f4091])).
% 28.46/5.33 thf(f1519,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (((sP11 @ X0) != $true) | ((X0 @ (d2subst @ d_id) @ (lam @ (X6 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (sK370 @ X6 @ X0) @ (d2subst @ d_id))) | ((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6)))) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f935,f1127,f1127,f1127,f1248,f1150,f1127])).
% 28.46/5.33 thf(f1150,plain,(
% 28.46/5.33 (one = (d2term @ d_one))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f1248,plain,(
% 28.46/5.33 ((d2subst @ d_id) = sh)),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f935,plain,(
% 28.46/5.33 ( ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (((X0 @ id @ (sK370 @ X6 @ X0) @ id) = $true) | ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) = $true) | ((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6))) | ((sP11 @ X0) != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f397])).
% 28.46/5.33 thf(f397,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : ((((sP11 @ X0) = $true) | (! [X2 : term] : (((X0 @ id @ (sK369 @ X0 @ id @ X2) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true)) & ((X0 @ id @ (lam @ (sK369 @ X0 @ sh @ one)) @ id) != $true) & ! [X3 : term,X4 : subst,X5 : subst] : ((sub @ (sK369 @ X0 @ X5 @ X3) @ X4) = (sK369 @ X0 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4))))) & (! [X6 : subst > term > term] : ((((X0 @ id @ (X6 @ id @ (sK370 @ X6 @ X0)) @ id) != $true) & ((X0 @ id @ (sK370 @ X6 @ X0) @ id) = $true)) | ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) = $true) | ((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6)))) | ((sP11 @ X0) != $true)))),
% 28.46/5.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK369,sK370,sK371,sK372,sK373])],[f393,f396,f395,f394])).
% 28.46/5.33 thf(f394,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : (? [X1 : subst > term > term] : (! [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true)) & ($true != (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) & ! [X3 : term,X4 : subst,X5 : subst] : ((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4)) = (sub @ (X1 @ X5 @ X3) @ X4))) => (! [X2 : term] : (((X0 @ id @ (sK369 @ X0 @ id @ X2) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true)) & ((X0 @ id @ (lam @ (sK369 @ X0 @ sh @ one)) @ id) != $true) & ! [X5 : subst,X4 : subst,X3 : term] : ((sub @ (sK369 @ X0 @ X5 @ X3) @ X4) = (sK369 @ X0 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4)))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f395,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o,X6 : subst > term > term] : (? [X7 : term] : (((X0 @ id @ (X6 @ id @ X7) @ id) != $true) & ((X0 @ id @ X7 @ id) = $true)) => (((X0 @ id @ (X6 @ id @ (sK370 @ X6 @ X0)) @ id) != $true) & ((X0 @ id @ (sK370 @ X6 @ X0) @ id) = $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f396,plain,(
% 28.46/5.33 ! [X6 : subst > term > term] : (? [X8 : term,X9 : subst,X10 : subst] : ((sub @ (X6 @ X10 @ X8) @ X9) != (X6 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9))) => ((X6 @ (comp @ (sK373 @ X6) @ (sK372 @ X6)) @ (sub @ (sK371 @ X6) @ (sK372 @ X6))) != (sub @ (X6 @ (sK373 @ X6) @ (sK371 @ X6)) @ (sK372 @ X6))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f393,plain,(
% 28.46/5.33 ! [X0 : subst > term > subst > $o] : ((((sP11 @ X0) = $true) | ? [X1 : subst > term > term] : (! [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true)) & ($true != (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) & ! [X3 : term,X4 : subst,X5 : subst] : ((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4)) = (sub @ (X1 @ X5 @ X3) @ X4)))) & (! [X6 : subst > term > term] : (? [X7 : term] : (((X0 @ id @ (X6 @ id @ X7) @ id) != $true) & ((X0 @ id @ X7 @ id) = $true)) | ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) = $true) | ? [X8 : term,X9 : subst,X10 : subst] : ((sub @ (X6 @ X10 @ X8) @ X9) != (X6 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9)))) | ((sP11 @ X0) != $true)))),
% 28.46/5.33 inference(rectify,[status(thm)],[f392])).
% 28.46/5.33 thf(f392,plain,(
% 28.46/5.33 ! [X200 : subst > term > subst > $o] : ((((sP11 @ X200) = $true) | ? [X206 : subst > term > term] : (! [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) = $true) | ((X200 @ id @ X207 @ id) != $true)) & ($true != (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) & ! [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) = (sub @ (X206 @ X210 @ X208) @ X209)))) & (! [X206 : subst > term > term] : (? [X207 : term] : (((X200 @ id @ (X206 @ id @ X207) @ id) != $true) & ((X200 @ id @ X207 @ id) = $true)) | ($true = (X200 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ? [X208 : term,X209 : subst,X210 : subst] : ((X206 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209)) != (sub @ (X206 @ X210 @ X208) @ X209))) | ((sP11 @ X200) != $true)))),
% 28.46/5.33 inference(nnf_transformation,[status(thm)],[f25])).
% 28.46/5.33 thf(f4138,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP11 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f1516,f4091])).
% 28.46/5.33 thf(f1516,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((X0 @ (d2subst @ d_id) @ (sK369 @ X0 @ (d2subst @ d_id) @ X2) @ (d2subst @ d_id)) = $true) | ((sP11 @ X0) = $true)) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f939,f1127,f1127,f1127,f1127,f1127])).
% 28.46/5.33 thf(f939,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : subst > term > subst > $o] : (((sP11 @ X0) = $true) | ((X0 @ id @ (sK369 @ X0 @ id @ X2) @ id) = $true) | ((X0 @ id @ X2 @ id) != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f397])).
% 28.46/5.33 thf(f5349,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) ) | ~spl591_290),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f5348,f4091])).
% 28.46/5.33 thf(f5348,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true)) ) | ~spl591_290),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f5347,f4091])).
% 28.46/5.33 thf(f5347,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true) | ((d2term @ d_one) != (X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4)))) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true)) ) | ~spl591_290),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f3133,f4091])).
% 28.46/5.33 thf(f6673,plain,(
% 28.46/5.33 spl591_483),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f6672])).
% 28.46/5.33 thf(f6672,plain,(
% 28.46/5.33 $false | spl591_483),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f6655,f4091])).
% 28.46/5.33 thf(f6655,plain,(
% 28.46/5.33 ((d2term @ d_one) != sK461) | spl591_483),
% 28.46/5.33 inference(superposition,[status(thm)],[f3986,f4091])).
% 28.46/5.33 thf(f3986,plain,(
% 28.46/5.33 (sK461 != (sub @ sK461 @ (d2subst @ d_id))) | spl591_483),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f3984])).
% 28.46/5.33 thf(f3984,definition,(
% 28.46/5.33 spl591_483 <=> (sK461 = (sub @ sK461 @ (d2subst @ d_id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_483])],[avatar_definition])).
% 28.46/5.33 thf(f5462,plain,(
% 28.46/5.33 ~spl591_2 | ~spl591_40 | spl591_151),
% 28.46/5.33 inference(avatar_contradiction_clause,[status(thm)],[f5461])).
% 28.46/5.33 thf(f5461,plain,(
% 28.46/5.33 $false | (~spl591_2 | ~spl591_40 | spl591_151)),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f5460,f2548])).
% 28.46/5.33 thf(f2548,plain,(
% 28.46/5.33 (sK561 != sK562) | spl591_151),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f2546])).
% 28.46/5.33 thf(f2546,definition,(
% 28.46/5.33 spl591_151 <=> (sK561 = sK562)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_151])],[avatar_definition])).
% 28.46/5.33 thf(f5460,plain,(
% 28.46/5.33 (sK561 = sK562) | (~spl591_2 | ~spl591_40)),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f5459,f1926])).
% 28.46/5.33 thf(f1926,plain,(
% 28.46/5.33 ( ! [X86 : term] : (((sub @ X86 @ (d2subst @ d_id)) = X86)) ) | ~spl591_2),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f1925])).
% 28.46/5.33 thf(f1925,definition,(
% 28.46/5.33 spl591_2 <=> ! [X86 : term] : ((sub @ X86 @ (d2subst @ d_id)) = X86)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_2])],[avatar_definition])).
% 28.46/5.33 thf(f5459,plain,(
% 28.46/5.33 ((sub @ sK561 @ (d2subst @ d_id)) = sK562) | (~spl591_2 | ~spl591_40)),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f2083,f1926])).
% 28.46/5.33 thf(f2083,plain,(
% 28.46/5.33 ((sub @ sK561 @ (d2subst @ d_id)) = (sub @ sK562 @ (d2subst @ d_id))) | ~spl591_40),
% 28.46/5.33 inference(avatar_component_clause,[status(thm)],[f2081])).
% 28.46/5.33 thf(f2081,definition,(
% 28.46/5.33 spl591_40 <=> ((sub @ sK561 @ (d2subst @ d_id)) = (sub @ sK562 @ (d2subst @ d_id)))),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_40])],[avatar_definition])).
% 28.46/5.33 thf(f4579,plain,(
% 28.46/5.33 spl591_2 | ~spl591_484),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1600,f3988,f1925])).
% 28.46/5.33 thf(f3988,definition,(
% 28.46/5.33 spl591_484 <=> (axvarid = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_484])],[avatar_definition])).
% 28.46/5.33 thf(f1600,plain,(
% 28.46/5.33 ( ! [X14 : term] : ((axvarid != $true) | ((sub @ X14 @ (d2subst @ d_id)) = X14)) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1247,f1127])).
% 28.46/5.33 thf(f1247,plain,(
% 28.46/5.33 ( ! [X14 : term] : (((sub @ X14 @ id) = X14) | (axvarid != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f4464,plain,(
% 28.46/5.33 spl591_536 | ~spl591_39),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f4460,f2077,f4462])).
% 28.46/5.33 thf(f2077,definition,(
% 28.46/5.33 spl591_39 <=> (shinj = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_39])],[avatar_definition])).
% 28.46/5.33 thf(f4460,plain,(
% 28.46/5.33 ( ! [X218 : term,X219 : term] : ((shinj != $true) | (X218 = X219)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4459,f4091])).
% 28.46/5.33 thf(f4459,plain,(
% 28.46/5.33 ( ! [X218 : term,X219 : term] : ((shinj != $true) | (X218 = X219) | ((d2term @ d_one) != (sub @ X218 @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f1644,f4091])).
% 28.46/5.33 thf(f1644,plain,(
% 28.46/5.33 ( ! [X218 : term,X219 : term] : ((shinj != $true) | (X218 = X219) | ((sub @ X218 @ (d2subst @ d_id)) != (sub @ X219 @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1101,f1248,f1248])).
% 28.46/5.33 thf(f1101,plain,(
% 28.46/5.33 ( ! [X218 : term,X219 : term] : ((X218 = X219) | ((sub @ X219 @ sh) != (sub @ X218 @ sh)) | (shinj != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f4364,plain,(
% 28.46/5.33 spl591_516 | spl591_523),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f4363,f4357,f4324])).
% 28.46/5.33 thf(f4363,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4362,f4091])).
% 28.46/5.33 thf(f4362,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $false) | ((d2term @ d_one) != (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4361,f4091])).
% 28.46/5.33 thf(f4361,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $false) | ((sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))))) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f1717,f4219])).
% 28.46/5.33 thf(f1717,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $false) | ((sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1)))) | ((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(equality_proxy_clausification,[status(thm)],[f1716])).
% 28.46/5.33 thf(f1716,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) = $true) | ($false = ((X1 @ (comp @ (sK594 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)))) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1714])).
% 28.46/5.33 thf(f1714,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (($false = ((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK596 @ X1)) @ (d2subst @ d_id)))) | (hoasinduction_lem3v2a = $false) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = ((X1 @ (comp @ (sK594 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1))))) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1713])).
% 28.46/5.33 thf(f1713,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (($false = ((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK596 @ X1)) @ (d2subst @ d_id)))) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (((^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ Y0))) @ (sK597 @ X1)) = $false) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1712])).
% 28.46/5.33 thf(f1712,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = (!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ Y0))))) | (hoasinduction_lem3v2a = $false) | ($false = ((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK596 @ X1)) @ (d2subst @ d_id))))) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1711])).
% 28.46/5.33 thf(f1711,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id)))) @ (sK596 @ X1))) | (hoasinduction_lem3v2a = $false) | ($false = (!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ Y0))))) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1710])).
% 28.46/5.33 thf(f1710,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | ($false = (!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK595 @ X1)) @ Y0))))) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1709])).
% 28.46/5.33 thf(f1709,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y1) @ (sub @ Y0 @ Y1)) = (sub @ (X1 @ (sK594 @ X1) @ Y0) @ Y1))))) @ (sK595 @ X1))) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1708])).
% 28.46/5.33 thf(f1708,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y1) @ (sub @ Y0 @ Y1)) = (sub @ (X1 @ (sK594 @ X1) @ Y0) @ Y1))))))) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | (hoasinduction_lem3v2a = $false) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1707])).
% 28.46/5.33 thf(f1707,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3v2a = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | ($false = ((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))) @ (sK594 @ X1))) | ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1706])).
% 28.46/5.33 thf(f1706,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $false) | ($false = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))))) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1705])).
% 28.46/5.33 thf(f1705,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3v2a = $false) | (((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) | ($false = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2)))))))))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1704])).
% 28.46/5.33 thf(f1704,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3v2a = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1703])).
% 28.46/5.33 thf(f1703,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > term] : ((((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) @ X1) = $true) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1702])).
% 28.46/5.33 thf(f1702,plain,(
% 28.46/5.33 ($true = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1700])).
% 28.46/5.33 thf(f1700,plain,(
% 28.46/5.33 ($false = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (sK593 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) => (sK593 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK593 @ (lam @ Y0)))))))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1699])).
% 28.46/5.33 thf(f1699,plain,(
% 28.46/5.33 ($false = ((^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((sK592 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) = (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y1)))))))) @ sK593)) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1698])).
% 28.46/5.33 thf(f1698,plain,(
% 28.46/5.33 ($false = (!! @ (term > $o) @ (^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((sK592 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) = (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y1)))))))))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1697])).
% 28.46/5.33 thf(f1697,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | (((^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2)))))))))) @ sK592) = $false)),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1696])).
% 28.46/5.33 thf(f1696,plain,(
% 28.46/5.33 ($false = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2)))))))))))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1694])).
% 28.46/5.33 thf(f1694,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2))))))))))))),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1262])).
% 28.46/5.33 thf(f1262,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ (d2subst @ d_id) @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ (d2subst @ d_id)))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (d2subst @ d_id) @ Y4 @ (d2subst @ d_id)) = (Y3 @ Y4))))))) @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2))))))))))))),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f546,f1127,f1127,f1127,f1127,f1127,f1127,f1195,f1127,f1127,f1261,f1127])).
% 28.46/5.33 thf(f1261,plain,(
% 28.46/5.33 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2))))))))),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1207,f1127,f1127])).
% 28.46/5.33 thf(f1207,plain,(
% 28.46/5.33 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2))))))))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f1195,plain,(
% 28.46/5.33 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f546,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2))))))))))))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f9])).
% 28.46/5.33 thf(f9,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2))))))))))))),
% 28.46/5.33 inference(flattening,[status(thm)],[f6])).
% 28.46/5.33 thf(f6,plain,(
% 28.46/5.33 ~(hoasinduction_lem3v2a = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2))))))))))))),
% 28.46/5.33 inference(fool_elimination,[status(thm)],[f5])).
% 28.46/5.33 thf(f5,plain,(
% 28.46/5.33 ~(! [X0 : term > $o,X1 : subst > term > subst > $o] : (! [X2 : subst > term > term] : (! [X3 : subst,X4 : term,X5 : subst] : ((X2 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3)) = (sub @ (X2 @ X5 @ X4) @ X3)) => (! [X6 : term] : ((X1 @ id @ X6 @ id) => (X1 @ id @ (X2 @ id @ X6) @ id)) => (X1 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : (X2 @ X7 @ X8))) @ id))) => ((hoasinduction_p_and_p_prime @ X1 @ X0) => ! [X9 : term] : (! [X10 : term] : ((X0 @ X10) => (X0 @ (sub @ X9 @ (push @ X10 @ id)))) => (X0 @ (lam @ X9))))) = hoasinduction_lem3v2a)),
% 28.46/5.33 inference(rectify,[status(thm)],[f3])).
% 28.46/5.33 thf(f3,negated_conjecture,(
% 28.46/5.33 ~(! [X11 : term > $o,X10 : subst > term > subst > $o] : (! [X18 : subst > term > term] : (! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ((hoasinduction_p_and_p_prime @ X10 @ X11) => ! [X13 : term] : (! [X15 : term] : ((X11 @ X15) => (X11 @ (sub @ X13 @ (push @ X15 @ id)))) => (X11 @ (lam @ X13))))) = hoasinduction_lem3v2a)),
% 28.46/5.33 inference(negated_conjecture,[status(cth)],[f2])).
% 28.46/5.33 thf(f2,conjecture,(
% 28.46/5.33 (! [X11 : term > $o,X10 : subst > term > subst > $o] : (! [X18 : subst > term > term] : (! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ((hoasinduction_p_and_p_prime @ X10 @ X11) => ! [X13 : term] : (! [X15 : term] : ((X11 @ X15) => (X11 @ (sub @ X13 @ (push @ X15 @ id)))) => (X11 @ (lam @ X13))))) = hoasinduction_lem3v2a)),
% 28.46/5.33 file('/export/starexec/sandbox2/tmp/tmp.eLR4iSdWK1/DTF2THF_2254.p',hoasinduction_lem3v2a)).
% 28.46/5.33 thf(f4348,plain,(
% 28.46/5.33 spl591_516 | spl591_521),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1725,f4346,f4324])).
% 28.46/5.33 thf(f1725,plain,(
% 28.46/5.33 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | ($true = (sK593 @ X1)) | ($false = (sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1723])).
% 28.46/5.33 thf(f1723,plain,(
% 28.46/5.33 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | ((sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)) = (sK593 @ X1))) )),
% 28.46/5.33 inference(equality_proxy_clausification,[status(thm)],[f1722])).
% 28.46/5.33 thf(f1722,plain,(
% 28.46/5.33 ( ! [X1 : term] : ((((sK592 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)) = (sK593 @ X1)) = $true) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1721])).
% 28.46/5.33 thf(f1721,plain,(
% 28.46/5.33 ( ! [X1 : term] : (($true = ((^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (sK593 @ Y0))) @ X1)) | (hoasinduction_lem3v2a = $false)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1720])).
% 28.46/5.33 thf(f1720,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (sK593 @ Y0)))) = $true)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1701])).
% 28.46/5.33 thf(f1701,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | (((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (sK593 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) => (sK593 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK593 @ (lam @ Y0)))))) = $false)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1700])).
% 28.46/5.33 thf(f4331,plain,(
% 28.46/5.33 spl591_516 | spl591_517),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1728,f4328,f4324])).
% 28.46/5.33 thf(f1728,plain,(
% 28.46/5.33 ($false = (sK593 @ (lam @ sK598))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1727])).
% 28.46/5.33 thf(f1727,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK593 @ Y0) => (sK593 @ (sub @ sK598 @ (push @ Y0 @ (d2subst @ d_id))))))) => (sK593 @ (lam @ sK598))))),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1726])).
% 28.46/5.33 thf(f1726,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $false) | (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) => (sK593 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK593 @ (lam @ Y0)))) @ sK598) = $false)),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1719])).
% 28.46/5.33 thf(f1719,plain,(
% 28.46/5.33 ($false = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) => (sK593 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK593 @ (lam @ Y0)))))) | (hoasinduction_lem3v2a = $false)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1701])).
% 28.46/5.33 thf(f4291,plain,(
% 28.46/5.33 spl591_125 | spl591_514 | spl591_509),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f4287,f4251,f4289,f2435])).
% 28.46/5.33 thf(f4287,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o,X4 : term] : (($true = (X2 @ (d2term @ d_one))) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ($false = (X2 @ (d2term @ d_one))) | ((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4286,f4197])).
% 28.46/5.33 thf(f4197,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : term > $o,X1 : term] : (((X0 @ (d2term @ d_one)) = $true) | ((X0 @ X1) != $true) | ((X0 @ X2) != $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4118,f4165])).
% 28.46/5.33 thf(f4165,plain,(
% 28.46/5.33 ( ! [X0 : term > $o] : (((sP29 @ X0) != $true) | ((X0 @ (d2term @ d_one)) = $true)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f796,f4091])).
% 28.46/5.33 thf(f796,plain,(
% 28.46/5.33 ( ! [X0 : term > $o] : (((X0 @ (sK257 @ X0)) = $true) | ((sP29 @ X0) != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f280])).
% 28.46/5.33 thf(f280,plain,(
% 28.46/5.33 ! [X0 : term > $o] : ((((sP29 @ X0) = $true) | ! [X1 : term,X2 : term] : (((X0 @ X2) != $true) | ((X0 @ (ap @ X2 @ X1)) = $true) | ((X0 @ X1) != $true))) & ((((X0 @ (sK257 @ X0)) = $true) & ((X0 @ (ap @ (sK257 @ X0) @ (sK256 @ X0))) != $true) & ((X0 @ (sK256 @ X0)) = $true)) | ((sP29 @ X0) != $true)))),
% 28.46/5.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK256,sK257])],[f278,f279])).
% 28.46/5.33 thf(f279,plain,(
% 28.46/5.33 ! [X0 : term > $o] : (? [X3 : term,X4 : term] : (((X0 @ X4) = $true) & ((X0 @ (ap @ X4 @ X3)) != $true) & ((X0 @ X3) = $true)) => (((X0 @ (sK257 @ X0)) = $true) & ((X0 @ (ap @ (sK257 @ X0) @ (sK256 @ X0))) != $true) & ((X0 @ (sK256 @ X0)) = $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f278,plain,(
% 28.46/5.33 ! [X0 : term > $o] : ((((sP29 @ X0) = $true) | ! [X1 : term,X2 : term] : (((X0 @ X2) != $true) | ((X0 @ (ap @ X2 @ X1)) = $true) | ((X0 @ X1) != $true))) & (? [X3 : term,X4 : term] : (((X0 @ X4) = $true) & ((X0 @ (ap @ X4 @ X3)) != $true) & ((X0 @ X3) = $true)) | ((sP29 @ X0) != $true)))),
% 28.46/5.33 inference(rectify,[status(thm)],[f277])).
% 28.46/5.33 thf(f277,plain,(
% 28.46/5.33 ! [X35 : term > $o] : ((((sP29 @ X35) = $true) | ! [X38 : term,X39 : term] : (($true != (X35 @ X39)) | ((X35 @ (ap @ X39 @ X38)) = $true) | ((X35 @ X38) != $true))) & (? [X38 : term,X39 : term] : (($true = (X35 @ X39)) & ((X35 @ (ap @ X39 @ X38)) != $true) & ((X35 @ X38) = $true)) | ((sP29 @ X35) != $true)))),
% 28.46/5.33 inference(nnf_transformation,[status(thm)],[f43])).
% 28.46/5.33 thf(f4118,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : term > $o,X1 : term] : (((X0 @ X1) != $true) | ((X0 @ X2) != $true) | ((sP29 @ X0) = $true) | ((X0 @ (d2term @ d_one)) = $true)) )),
% 28.46/5.33 inference(backward_demodulation,[status(thm)],[f797,f4091])).
% 28.46/5.33 thf(f797,plain,(
% 28.46/5.33 ( ! [X2 : term,X0 : term > $o,X1 : term] : (((sP29 @ X0) = $true) | ((X0 @ X1) != $true) | ((X0 @ (ap @ X2 @ X1)) = $true) | ((X0 @ X2) != $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f280])).
% 28.46/5.33 thf(f4286,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : ((hoasinduction_lem3v2a = $true) | ($true = (X2 @ (d2term @ d_one))) | ((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ((X2 @ (lam @ X3)) = $true) | ($false = (X2 @ (d2term @ d_one)))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4285,f4091])).
% 28.46/5.33 thf(f4285,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X2 @ (lam @ X3)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ($false = (X2 @ (d2term @ d_one))) | ((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((X2 @ (sK603 @ X1 @ X2)) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4284,f4219])).
% 28.46/5.33 thf(f4284,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (($false = (X2 @ (d2term @ d_one))) | ((X2 @ (sK603 @ X1 @ X2)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((X2 @ (lam @ X3)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4283,f4091])).
% 28.46/5.33 thf(f4283,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) = $true) | ((X2 @ (sK603 @ X1 @ X2)) = $true) | ($false = (X2 @ (d2term @ d_one))) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ((X2 @ (lam @ X3)) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f1794,f4091])).
% 28.46/5.33 thf(f1794,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (($false = (X2 @ (sub @ X3 @ (push @ (sK604 @ X3 @ X2) @ (d2subst @ d_id))))) | (hoasinduction_lem3v2a = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id)) = $true) | ((X2 @ (lam @ X3)) = $true) | ((X2 @ (sK603 @ X1 @ X2)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1793])).
% 28.46/5.33 thf(f1793,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | ($false = (X2 @ (sub @ X3 @ (push @ (sK604 @ X3 @ X2) @ (d2subst @ d_id))))) | ($false = (X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id))) | ((X2 @ (lam @ X3)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id)) = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1788])).
% 28.46/5.33 thf(f1788,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : ((hoasinduction_lem3v2a = $true) | (((X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id))) = $true) | ((X2 @ (lam @ X3)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | ($false = (X2 @ (sub @ X3 @ (push @ (sK604 @ X3 @ X2) @ (d2subst @ d_id)))))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1787])).
% 28.46/5.33 thf(f1787,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X2 @ (lam @ X3)) = $true) | (hoasinduction_lem3v2a = $true) | (((X2 @ (sK604 @ X3 @ X2)) => (X2 @ (sub @ X3 @ (push @ (sK604 @ X3 @ X2) @ (d2subst @ d_id))))) = $false) | (((X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id))) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2)))) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1786])).
% 28.46/5.33 thf(f1786,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X2 @ (lam @ X3)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | (((X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id))) = $true) | ($false = ((^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id)))))) @ (sK604 @ X3 @ X2)))) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1785])).
% 28.46/5.33 thf(f1785,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : ((hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) = $false) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (((X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id))) = $true) | ((X2 @ (lam @ X3)) = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1784])).
% 28.46/5.33 thf(f1784,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : ((((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | (((X1 @ (d2subst @ d_id) @ X4 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ X4) @ (d2subst @ d_id))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1783])).
% 28.46/5.33 thf(f1783,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o,X4 : term] : (((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true) | (((^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id)))) @ X4) = $true)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1782])).
% 28.46/5.33 thf(f1782,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $true) | ((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true)) )),
% 28.46/5.33 inference(equality_proxy_clausification,[status(thm)],[f1781])).
% 28.46/5.33 thf(f1781,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : ((((X1 @ (d2subst @ d_id) @ (sK603 @ X1 @ X2) @ (d2subst @ d_id)) = (X2 @ (sK603 @ X1 @ X2))) = $false) | (hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $true) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1780])).
% 28.46/5.33 thf(f1780,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = ((^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0))) @ (sK603 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $true) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1779])).
% 28.46/5.33 thf(f1779,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) = $false) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1777])).
% 28.46/5.33 thf(f1777,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) | (hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) = $false) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1776])).
% 28.46/5.33 thf(f1776,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) = $false) | (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0)))) @ X3) = $true)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1775])).
% 28.46/5.33 thf(f1775,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0))))) = $true) | ($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) | ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) = $false)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1740])).
% 28.46/5.33 thf(f1740,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0)))))) = $true) | ($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1739])).
% 28.46/5.33 thf(f1739,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sK599 @ X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (sK599 @ X1 @ Y0 @ Y1) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (sK599 @ X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) | (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0)))))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1738])).
% 28.46/5.33 thf(f1738,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ($false = ((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) @ (sK599 @ X1))) | (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0)))))) = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1737])).
% 28.46/5.33 thf(f1737,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) = $false) | (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0)))))) = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1736])).
% 28.46/5.33 thf(f1736,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => (X2 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (X2 @ (lam @ Y0))))))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1735])).
% 28.46/5.33 thf(f1735,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : ((((^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((X1 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) = (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y1)))))))) @ X2) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1734])).
% 28.46/5.33 thf(f1734,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ((!! @ (term > $o) @ (^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((X1 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (X1 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) = (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y1))))))))) = $true)) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1733])).
% 28.46/5.33 thf(f1733,plain,(
% 28.46/5.33 ( ! [X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | (((^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2)))))))))) @ X1) = $true)) )),
% 28.46/5.33 inference(pi_clausification,[status(thm)],[f1695])).
% 28.46/5.33 thf(f1695,plain,(
% 28.46/5.33 (hoasinduction_lem3v2a = $true) | ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y3 @ Y5) @ (sub @ Y4 @ Y5)) = (sub @ (Y2 @ Y3 @ Y4) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) = (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y1 @ (lam @ Y2))))))))))) = $true)),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1694])).
% 28.46/5.33 thf(f4282,plain,(
% 28.46/5.33 spl591_509 | spl591_512 | spl591_125),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f4281,f2435,f4266,f4251])).
% 28.46/5.33 thf(f4281,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : (($true = (X2 @ (d2term @ d_one))) | (hoasinduction_lem3v2a = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($false = (X2 @ (d2term @ d_one)))) )),
% 28.46/5.33 inference(duplicate_literal_removal,[status(thm)],[f4280])).
% 28.46/5.33 thf(f4280,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : (($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (X2 @ (d2term @ d_one))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($false = (X2 @ (d2term @ d_one))) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4279,f4091])).
% 28.46/5.33 thf(f4279,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X1 : subst > term > subst > $o] : (($false = (X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id))) | (hoasinduction_lem3v2a = $true) | ($false = (X2 @ (d2term @ d_one))) | ($true = (X2 @ (d2term @ d_one))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(subsumption_resolution,[status(thm)],[f4278,f4197])).
% 28.46/5.33 thf(f4278,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($true = (X2 @ (d2term @ d_one))) | ((X2 @ (lam @ X3)) = $true) | (hoasinduction_lem3v2a = $true) | ($false = (X2 @ (d2term @ d_one))) | ($false = (X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f4277,f4091])).
% 28.46/5.33 thf(f4277,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem3v2a = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X2 @ (lam @ X3)) = $true) | ($false = (X2 @ (d2term @ d_one))) | ((X2 @ (sK606 @ X3 @ X2)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(forward_demodulation,[status(thm)],[f1805,f4091])).
% 28.46/5.33 thf(f1805,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = (X2 @ (sK605 @ X1 @ X2))) | ($false = (X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id))) | (hoasinduction_lem3v2a = $true) | ((X2 @ (lam @ X3)) = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X2 @ (sK606 @ X3 @ X2)) = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1803])).
% 28.46/5.33 thf(f1803,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (((X2 @ (lam @ X3)) = $true) | ((X2 @ (sK606 @ X3 @ X2)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK605 @ X1 @ X2))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1801])).
% 28.46/5.33 thf(f1801,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (((X2 @ (lam @ X3)) = $true) | ($false = ((X2 @ (sK606 @ X3 @ X2)) => (X2 @ (sub @ X3 @ (push @ (sK606 @ X3 @ X2) @ (d2subst @ d_id)))))) | (hoasinduction_lem3v2a = $true) | ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK605 @ X1 @ X2))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1800])).
% 28.46/5.33 thf(f1800,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = ((^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id)))))) @ (sK606 @ X3 @ X2))) | ((X2 @ (lam @ X3)) = $true) | ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK605 @ X1 @ X2))) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1799])).
% 28.46/5.33 thf(f1799,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction_lem3v2a = $true) | ((X2 @ (lam @ X3)) = $true) | ((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) = $false) | ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) != (X2 @ (sK605 @ X1 @ X2)))) )),
% 28.46/5.33 inference(equality_proxy_clausification,[status(thm)],[f1798])).
% 28.46/5.33 thf(f1798,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) = (X2 @ (sK605 @ X1 @ X2)))) | ((X2 @ (lam @ X3)) = $true) | ((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) = $false) | (hoasinduction_lem3v2a = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1797])).
% 28.46/5.33 thf(f1797,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : ((((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true) | ($false = ((X1 @ (d2subst @ d_id) @ (sK605 @ X1 @ X2) @ (d2subst @ d_id)) = (X2 @ (sK605 @ X1 @ X2)))) | (hoasinduction_lem3v2a = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 28.46/5.33 inference(beta_eta_normalization,[status(thm)],[f1796])).
% 28.46/5.33 thf(f1796,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (($false = ((^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0))) @ (sK605 @ X1 @ X2))) | (hoasinduction_lem3v2a = $true) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true)) )),
% 28.46/5.33 inference(sigma_clausification,[status(thm)],[f1778])).
% 28.46/5.33 thf(f1778,plain,(
% 28.46/5.33 ( ! [X2 : term > $o,X3 : term,X1 : subst > term > subst > $o] : (((!! @ term @ (^[Y0 : term]: ((X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) = (X2 @ Y0)))) = $false) | ($false = (X1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => (X2 @ (sub @ X3 @ (push @ Y0 @ (d2subst @ d_id))))))) => (X2 @ (lam @ X3))) = $true) | (hoasinduction_lem3v2a = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1777])).
% 28.46/5.33 thf(f3991,plain,(
% 28.46/5.33 ~spl591_483 | spl591_484),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1601,f3988,f3984])).
% 28.46/5.33 thf(f1601,plain,(
% 28.46/5.33 (sK461 != (sub @ sK461 @ (d2subst @ d_id))) | (axvarid = $true)),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1246,f1127])).
% 28.46/5.33 thf(f1246,plain,(
% 28.46/5.33 (axvarid = $true) | (sK461 != (sub @ sK461 @ id))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f3809,plain,(
% 28.46/5.33 spl591_444 | spl591_124),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1828,f2431,f3807])).
% 28.46/5.33 thf(f2431,definition,(
% 28.46/5.33 spl591_124 <=> (sP2 = $true)),
% 28.46/5.33 introduced(definition,[new_symbols(naming,[spl591_124])],[avatar_definition])).
% 28.46/5.33 thf(f1828,plain,(
% 28.46/5.33 ( ! [X3 : term] : (((sK429 @ X3) = $true) | ($false = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id))) | (sP2 = $true)) )),
% 28.46/5.33 inference(binary_proxy_clausification,[status(thm)],[f1572])).
% 28.46/5.33 thf(f1572,plain,(
% 28.46/5.33 ( ! [X3 : term] : (((sK429 @ X3) = (sK428 @ (d2subst @ d_id) @ X3 @ (d2subst @ d_id))) | (sP2 = $true)) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1015,f1127,f1127])).
% 28.46/5.33 thf(f1015,plain,(
% 28.46/5.33 ( ! [X3 : term] : ((sP2 = $true) | ((sK429 @ X3) = (sK428 @ id @ X3 @ id))) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f457])).
% 28.46/5.33 thf(f457,plain,(
% 28.46/5.33 ((sP2 = $true) | (((sK429 @ (lam @ sK430)) != $true) & ! [X3 : term] : ((sK429 @ X3) = (sK428 @ id @ X3 @ id)) & ! [X4 : subst > term > term] : (((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))) | (((sK428 @ id @ (sK434 @ X4) @ id) = $true) & ((sK428 @ id @ (X4 @ id @ (sK434 @ X4)) @ id) != $true)) | ((sK428 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ! [X9 : term] : (((sK429 @ X9) != $true) | ((sK429 @ (sub @ sK430 @ (push @ X9 @ id))) = $true)))) & (! [X10 : subst > term > subst > $o,X11 : term > $o,X12 : term] : (((X11 @ (lam @ X12)) = $true) | ((X11 @ (sK435 @ X11 @ X10)) != (X10 @ id @ (sK435 @ X11 @ X10) @ id)) | (! [X15 : subst,X16 : term,X17 : subst] : ((sK436 @ X10 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)) = (sub @ (sK436 @ X10 @ X15 @ X16) @ X17)) & ! [X18 : term] : (((X10 @ id @ X18 @ id) != $true) | ((X10 @ id @ (sK436 @ X10 @ id @ X18) @ id) = $true)) & ((X10 @ id @ (lam @ (sK436 @ X10 @ sh @ one)) @ id) != $true)) | (((X11 @ (sK437 @ X12 @ X11)) = $true) & ((X11 @ (sub @ X12 @ (push @ (sK437 @ X12 @ X11) @ id))) != $true))) | (sP2 != $true))),
% 28.46/5.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK428,sK429,sK430,sK431,sK432,sK433,sK434,sK435,sK436,sK437])],[f450,f456,f455,f454,f453,f452,f451])).
% 28.46/5.33 thf(f451,plain,(
% 28.46/5.33 ? [X0 : subst > term > subst > $o,X1 : term > $o,X2 : term] : (($true != (X1 @ (lam @ X2))) & ! [X3 : term] : ((X0 @ id @ X3 @ id) = (X1 @ X3)) & ! [X4 : subst > term > term] : (? [X5 : subst,X6 : term,X7 : subst] : ((X4 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7)) != (sub @ (X4 @ X5 @ X6) @ X7)) | ? [X8 : term] : (((X0 @ id @ X8 @ id) = $true) & ((X0 @ id @ (X4 @ id @ X8) @ id) != $true)) | ((X0 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ! [X9 : term] : (((X1 @ X9) != $true) | ((X1 @ (sub @ X2 @ (push @ X9 @ id))) = $true))) => (((sK429 @ (lam @ sK430)) != $true) & ! [X3 : term] : ((sK429 @ X3) = (sK428 @ id @ X3 @ id)) & ! [X4 : subst > term > term] : (? [X5 : subst,X6 : term,X7 : subst] : ((X4 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7)) != (sub @ (X4 @ X5 @ X6) @ X7)) | ? [X8 : term] : (((sK428 @ id @ X8 @ id) = $true) & ((sK428 @ id @ (X4 @ id @ X8) @ id) != $true)) | ((sK428 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ! [X9 : term] : (((sK429 @ X9) != $true) | ((sK429 @ (sub @ sK430 @ (push @ X9 @ id))) = $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f452,plain,(
% 28.46/5.33 ! [X4 : subst > term > term] : (? [X5 : subst,X6 : term,X7 : subst] : ((X4 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7)) != (sub @ (X4 @ X5 @ X6) @ X7)) => ((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f453,plain,(
% 28.46/5.33 ! [X4 : subst > term > term] : (? [X8 : term] : (((sK428 @ id @ X8 @ id) = $true) & ((sK428 @ id @ (X4 @ id @ X8) @ id) != $true)) => (((sK428 @ id @ (sK434 @ X4) @ id) = $true) & ((sK428 @ id @ (X4 @ id @ (sK434 @ X4)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f454,plain,(
% 28.46/5.33 ! [X10 : subst > term > subst > $o,X11 : term > $o] : (? [X13 : term] : ((X10 @ id @ X13 @ id) != (X11 @ X13)) => ((X11 @ (sK435 @ X11 @ X10)) != (X10 @ id @ (sK435 @ X11 @ X10) @ id)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f455,plain,(
% 28.46/5.33 ! [X10 : subst > term > subst > $o] : (? [X14 : subst > term > term] : (! [X15 : subst,X16 : term,X17 : subst] : ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)) = (sub @ (X14 @ X15 @ X16) @ X17)) & ! [X18 : term] : (((X10 @ id @ X18 @ id) != $true) | ((X10 @ id @ (X14 @ id @ X18) @ id) = $true)) & ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) != $true)) => (! [X17 : subst,X16 : term,X15 : subst] : ((sK436 @ X10 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)) = (sub @ (sK436 @ X10 @ X15 @ X16) @ X17)) & ! [X18 : term] : (((X10 @ id @ X18 @ id) != $true) | ((X10 @ id @ (sK436 @ X10 @ id @ X18) @ id) = $true)) & ((X10 @ id @ (lam @ (sK436 @ X10 @ sh @ one)) @ id) != $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f456,plain,(
% 28.46/5.33 ! [X11 : term > $o,X12 : term] : (? [X19 : term] : (((X11 @ X19) = $true) & ((X11 @ (sub @ X12 @ (push @ X19 @ id))) != $true)) => (((X11 @ (sK437 @ X12 @ X11)) = $true) & ((X11 @ (sub @ X12 @ (push @ (sK437 @ X12 @ X11) @ id))) != $true)))),
% 28.46/5.33 introduced(definition,[],[choice_axiom])).
% 28.46/5.33 thf(f450,plain,(
% 28.46/5.33 ((sP2 = $true) | ? [X0 : subst > term > subst > $o,X1 : term > $o,X2 : term] : (($true != (X1 @ (lam @ X2))) & ! [X3 : term] : ((X0 @ id @ X3 @ id) = (X1 @ X3)) & ! [X4 : subst > term > term] : (? [X5 : subst,X6 : term,X7 : subst] : ((X4 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7)) != (sub @ (X4 @ X5 @ X6) @ X7)) | ? [X8 : term] : (((X0 @ id @ X8 @ id) = $true) & ((X0 @ id @ (X4 @ id @ X8) @ id) != $true)) | ((X0 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) & ! [X9 : term] : (((X1 @ X9) != $true) | ((X1 @ (sub @ X2 @ (push @ X9 @ id))) = $true)))) & (! [X10 : subst > term > subst > $o,X11 : term > $o,X12 : term] : (((X11 @ (lam @ X12)) = $true) | ? [X13 : term] : ((X10 @ id @ X13 @ id) != (X11 @ X13)) | ? [X14 : subst > term > term] : (! [X15 : subst,X16 : term,X17 : subst] : ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)) = (sub @ (X14 @ X15 @ X16) @ X17)) & ! [X18 : term] : (((X10 @ id @ X18 @ id) != $true) | ((X10 @ id @ (X14 @ id @ X18) @ id) = $true)) & ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) != $true)) | ? [X19 : term] : (((X11 @ X19) = $true) & ((X11 @ (sub @ X12 @ (push @ X19 @ id))) != $true))) | (sP2 != $true))),
% 28.46/5.33 inference(rectify,[status(thm)],[f449])).
% 28.46/5.33 thf(f449,plain,(
% 28.46/5.33 ((sP2 = $true) | ? [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) != $true) & ! [X249 : term] : ((X246 @ id @ X249 @ id) = (X247 @ X249)) & ! [X250 : subst > term > term] : (? [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) != (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) | ? [X251 : term] : (((X246 @ id @ X251 @ id) = $true) & ((X246 @ id @ (X250 @ id @ X251) @ id) != $true)) | ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) = $true)) & ! [X255 : term] : (((X247 @ X255) != $true) | ((X247 @ (sub @ X248 @ (push @ X255 @ id))) = $true)))) & (! [X246 : subst > term > subst > $o,X247 : term > $o,X248 : term] : (((X247 @ (lam @ X248)) = $true) | ? [X249 : term] : ((X246 @ id @ X249 @ id) != (X247 @ X249)) | ? [X250 : subst > term > term] : (! [X252 : subst,X253 : term,X254 : subst] : ((sub @ (X250 @ X252 @ X253) @ X254) = (X250 @ (comp @ X252 @ X254) @ (sub @ X253 @ X254))) & ! [X251 : term] : (((X246 @ id @ X251 @ id) != $true) | ((X246 @ id @ (X250 @ id @ X251) @ id) = $true)) & ((X246 @ id @ (lam @ (X250 @ sh @ one)) @ id) != $true)) | ? [X255 : term] : (((X247 @ X255) = $true) & ((X247 @ (sub @ X248 @ (push @ X255 @ id))) != $true))) | (sP2 != $true))),
% 28.46/5.33 inference(nnf_transformation,[status(thm)],[f16])).
% 28.46/5.33 thf(f3781,plain,(
% 28.46/5.33 spl591_124 | ~spl591_438),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1016,f3778,f2431])).
% 28.46/5.33 thf(f1016,plain,(
% 28.46/5.33 (sP2 = $true) | ((sK429 @ (lam @ sK430)) != $true)),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f457])).
% 28.46/5.33 thf(f3134,plain,(
% 28.46/5.33 spl591_290 | spl591_124),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1573,f2431,f3132])).
% 28.46/5.33 thf(f1573,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : (((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))) | ((sK428 @ (d2subst @ d_id) @ (sK434 @ X4) @ (d2subst @ d_id)) = $true) | ((sK428 @ (d2subst @ d_id) @ (lam @ (X4 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | (sP2 = $true)) )),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1014,f1127,f1127,f1127,f1248,f1150,f1127])).
% 28.46/5.33 thf(f1014,plain,(
% 28.46/5.33 ( ! [X4 : subst > term > term] : ((sP2 = $true) | ((X4 @ (comp @ (sK431 @ X4) @ (sK433 @ X4)) @ (sub @ (sK432 @ X4) @ (sK433 @ X4))) != (sub @ (X4 @ (sK431 @ X4) @ (sK432 @ X4)) @ (sK433 @ X4))) | ((sK428 @ id @ (sK434 @ X4) @ id) = $true) | ((sK428 @ id @ (lam @ (X4 @ sh @ one)) @ id) = $true)) )),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f457])).
% 28.46/5.33 thf(f2549,plain,(
% 28.46/5.33 spl591_39 | ~spl591_151),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1100,f2546,f2077])).
% 28.46/5.33 thf(f1100,plain,(
% 28.46/5.33 (shinj = $true) | (sK561 != sK562)),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f2438,plain,(
% 28.46/5.33 ~spl591_124 | spl591_125),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1040,f2435,f2431])).
% 28.46/5.33 thf(f1040,plain,(
% 28.46/5.33 (sP2 != $true) | (hoasinduction_lem3v2a = $true)),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 thf(f2084,plain,(
% 28.46/5.33 spl591_39 | spl591_40),
% 28.46/5.33 inference(avatar_split_clause,[status(thm)],[f1645,f2081,f2077])).
% 28.46/5.33 thf(f1645,plain,(
% 28.46/5.33 ((sub @ sK561 @ (d2subst @ d_id)) = (sub @ sK562 @ (d2subst @ d_id))) | (shinj = $true)),
% 28.46/5.33 inference(definition_unfolding,[status(thm)],[f1099,f1248,f1248])).
% 28.46/5.33 thf(f1099,plain,(
% 28.46/5.33 (shinj = $true) | ((sub @ sK561 @ sh) = (sub @ sK562 @ sh))),
% 28.46/5.33 inference(cnf_transformation,[status(thm)],[f545])).
% 28.46/5.33 % SZS output end Proof for DTF2THF_2254
% 28.46/5.33 % (2519)------------------------------
% 28.46/5.33 % (2519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.46/5.33 % (2519)Termination reason: Refutation
% 28.46/5.33
% 28.46/5.33 % (2519)Memory used [KB]: 14456
% 28.46/5.33 % (2519)Time elapsed: 0.521 s
% 28.46/5.33 % (2519)Instructions burned: 1414 (million)
% 28.46/5.33 % (2519)------------------------------
% 28.46/5.33 % (2519)------------------------------
% 28.46/5.33 % (2352)Success in time 3.82 s
%------------------------------------------------------------------------------