%------------------------------------------------------------------------------
% 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 : n024.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 06:58:47 PM UTC 2026
% Result : Theorem 42.64s 7.44s
% Output : Refutation 42.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 153
% Syntax : Number of formulae : 306 ( 26 unt; 0 typ; 22 def)
% Number of atoms : 11744 (5553 equ; 0 cnn)
% Maximal formula atoms : 530 ( 38 avg)
% Number of connectives : 27054 (3197 ~;2953 |;2430 &;17633 @)
% ( 529 <=>; 260 =>; 0 <=; 0 <~>)
% Maximal formula depth : 188 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2158 (2158 >; 0 *; 0 +; 0 <<)
% Number of symbols : 748 ( 743 usr; 315 con; 0-4 aty)
% ( 41 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 5890 ( 173 ^;4360 !;1357 ?;5890 :)
% 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_143,type,
sP1: ( subst > term > subst > $o ) > $o ).
thf(func_def_147,type,
sP5: ( subst > term > subst > $o ) > $o ).
thf(func_def_148,type,
sP6: ( subst > term > subst > $o ) > $o ).
thf(func_def_149,type,
sP7: ( term > $o ) > $o ).
thf(func_def_154,type,
sP12: ( term > $o ) > $o ).
thf(func_def_156,type,
sP14: ( term > $o ) > $o ).
thf(func_def_158,type,
sP16: ( subst > term > subst > $o ) > $o ).
thf(func_def_160,type,
sP18: ( term > $o ) > $o ).
thf(func_def_161,type,
sP19: ( term > $o ) > $o ).
thf(func_def_164,type,
sP22: ( term > $o ) > $o ).
thf(func_def_165,type,
sP23: ( term > $o ) > $o ).
thf(func_def_168,type,
sP26: ( term > $o ) > $o ).
thf(func_def_170,type,
sP28: ( subst > term > subst > $o ) > $o ).
thf(func_def_171,type,
sP29: ( subst > term > subst > $o ) > $o ).
thf(func_def_173,type,
sP31: ( subst > term > subst > $o ) > $o ).
thf(func_def_177,type,
sP35: ( subst > term > subst > $o ) > $o ).
thf(func_def_179,type,
sP37: ( subst > term > subst > $o ) > $o ).
thf(func_def_180,type,
sP38: ( subst > term > subst > $o ) > $o ).
thf(func_def_182,type,
sP40: ( term > $o ) > $o ).
thf(func_def_183,type,
sP41: ( subst > term > subst > $o ) > $o ).
thf(func_def_188,type,
sP46: ( subst > term > subst > $o ) > $o ).
thf(func_def_191,type,
sP49: ( subst > term > subst > $o ) > $o ).
thf(func_def_192,type,
sP50: ( subst > term > subst > $o ) > $o ).
thf(func_def_193,type,
sP51: ( subst > term > subst > $o ) > $o ).
thf(func_def_194,type,
sP52: ( subst > term > subst > $o ) > $o ).
thf(func_def_195,type,
sP53: ( term > $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 ) > term ).
thf(func_def_206,type,
sK64: ( subst > term > term ) > subst ).
thf(func_def_207,type,
sK65: ( subst > term > subst > $o ) > term > term ).
thf(func_def_208,type,
sK66: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_209,type,
sK67: ( term > $o ) > term ).
thf(func_def_210,type,
sK68: ( term > $o ) > term ).
thf(func_def_211,type,
sK69: term > $o ).
thf(func_def_212,type,
sK70: term ).
thf(func_def_213,type,
sK71: term > term ).
thf(func_def_214,type,
sK72: ( subst > term > subst > $o ) > term ).
thf(func_def_215,type,
sK73: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK74: ( subst > term > subst > $o ) > subst ).
thf(func_def_217,type,
sK75: ( subst > term > subst > $o ) > subst ).
thf(func_def_218,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_219,type,
sK77: ( subst > term > subst > $o ) > subst ).
thf(func_def_220,type,
sK78: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK79: ( subst > term > subst > $o ) > term ).
thf(func_def_222,type,
sK80: subst > term > subst > $o ).
thf(func_def_223,type,
sK81: term ).
thf(func_def_224,type,
sK82: term ).
thf(func_def_225,type,
sK83: term ).
thf(func_def_226,type,
sK84: subst > term > subst > $o ).
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 ) > subst ).
thf(func_def_231,type,
sK89: ( subst > term > subst > $o ) > subst ).
thf(func_def_232,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK91: ( subst > term > subst > $o ) > term ).
thf(func_def_234,type,
sK92: ( subst > term > subst > $o ) > subst ).
thf(func_def_235,type,
sK93: ( subst > term > subst > $o ) > term ).
thf(func_def_236,type,
sK94: ( subst > term > subst > $o ) > subst ).
thf(func_def_237,type,
sK95: ( subst > term > subst > $o ) > subst ).
thf(func_def_238,type,
sK96: ( subst > term > subst > $o ) > term ).
thf(func_def_239,type,
sK97: ( subst > term > subst > $o ) > subst ).
thf(func_def_240,type,
sK98: term > ( subst > term > subst > $o ) > term ).
thf(func_def_241,type,
sK99: ( subst > term > subst > $o ) > subst ).
thf(func_def_242,type,
sK100: ( subst > term > subst > $o ) > term ).
thf(func_def_243,type,
sK101: ( subst > term > subst > $o ) > subst ).
thf(func_def_244,type,
sK102: ( subst > term > subst > $o ) > subst ).
thf(func_def_245,type,
sK103: subst > term > subst > $o ).
thf(func_def_246,type,
sK104: term ).
thf(func_def_247,type,
sK105: ( term > $o ) > term ).
thf(func_def_248,type,
sK106: ( term > $o ) > term ).
thf(func_def_249,type,
sK107: ( subst > term > subst > $o ) > term ).
thf(func_def_250,type,
sK108: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK109: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_252,type,
sK110: ( subst > term > term ) > subst ).
thf(func_def_253,type,
sK111: ( subst > term > term ) > term ).
thf(func_def_254,type,
sK112: ( subst > term > term ) > subst ).
thf(func_def_255,type,
sK113: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_256,type,
sK114: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_257,type,
sK115: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_258,type,
sK116: ( subst > term > term ) > term ).
thf(func_def_259,type,
sK117: ( subst > term > term ) > subst ).
thf(func_def_260,type,
sK118: ( subst > term > term ) > subst ).
thf(func_def_261,type,
sK119: ( subst > term > subst > $o ) > term ).
thf(func_def_262,type,
sK120: ( subst > term > subst > $o ) > term ).
thf(func_def_263,type,
sK121: subst > term > subst > $o ).
thf(func_def_264,type,
sK122: term ).
thf(func_def_265,type,
sK123: term ).
thf(func_def_266,type,
sK124: ( subst > term > subst > $o ) > subst ).
thf(func_def_267,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK126: ( subst > term > subst > $o ) > term ).
thf(func_def_269,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK128: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK131: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK132: term > ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK133: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_276,type,
sK134: ( subst > term > subst > $o ) > term > term ).
thf(func_def_277,type,
sK135: term ).
thf(func_def_278,type,
sK136: subst > term > subst > $o ).
thf(func_def_279,type,
sK137: ( subst > term > term ) > term ).
thf(func_def_280,type,
sK138: ( subst > term > term ) > subst ).
thf(func_def_281,type,
sK139: ( subst > term > term ) > subst ).
thf(func_def_282,type,
sK140: ( subst > term > term ) > term ).
thf(func_def_283,type,
sK141: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_284,type,
sK142: ( subst > term > term ) > term ).
thf(func_def_285,type,
sK143: ( subst > term > term ) > subst ).
thf(func_def_286,type,
sK144: ( subst > term > term ) > subst ).
thf(func_def_287,type,
sK145: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_288,type,
sK146: subst > term > term ).
thf(func_def_289,type,
sK147: term ).
thf(func_def_290,type,
sK148: subst ).
thf(func_def_291,type,
sK149: subst > term > term ).
thf(func_def_292,type,
sK150: term ).
thf(func_def_293,type,
sK151: term ).
thf(func_def_294,type,
sK152: term ).
thf(func_def_295,type,
sK153: subst ).
thf(func_def_296,type,
sK154: term ).
thf(func_def_297,type,
sK155: subst ).
thf(func_def_298,type,
sK156: ( subst > term > term ) > subst ).
thf(func_def_299,type,
sK157: ( subst > term > term ) > term ).
thf(func_def_300,type,
sK158: ( subst > term > term ) > subst ).
thf(func_def_301,type,
sK159: ( subst > term > term ) > subst ).
thf(func_def_302,type,
sK160: ( subst > term > term ) > term ).
thf(func_def_303,type,
sK161: ( subst > term > term ) > subst ).
thf(func_def_304,type,
sK162: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_305,type,
sK163: subst > term > subst > $o ).
thf(func_def_306,type,
sK164: term ).
thf(func_def_307,type,
sK165: subst > term > subst > $o ).
thf(func_def_308,type,
sK166: ( term > $o ) > term ).
thf(func_def_309,type,
sK167: term ).
thf(func_def_310,type,
sK168: ( subst > term > subst > $o ) > term ).
thf(func_def_311,type,
sK169: ( subst > term > subst > $o ) > term ).
thf(func_def_312,type,
sK170: ( term > $o ) > term ).
thf(func_def_313,type,
sK171: ( term > $o ) > term ).
thf(func_def_314,type,
sK172: term > $o ).
thf(func_def_315,type,
sK173: term ).
thf(func_def_316,type,
sK174: term > term ).
thf(func_def_317,type,
sK175: ( term > $o ) > term > term ).
thf(func_def_318,type,
sK176: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_319,type,
sK177: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_320,type,
sK178: term ).
thf(func_def_321,type,
sK179: term > $o ).
thf(func_def_322,type,
sK180: subst > term > subst > $o ).
thf(func_def_323,type,
sK181: ( subst > term > term ) > term ).
thf(func_def_324,type,
sK182: ( subst > term > term ) > subst ).
thf(func_def_325,type,
sK183: ( subst > term > term ) > subst ).
thf(func_def_326,type,
sK184: ( subst > term > term ) > term ).
thf(func_def_327,type,
sK185: ( subst > term > term ) > subst ).
thf(func_def_328,type,
sK186: ( subst > term > term ) > subst ).
thf(func_def_329,type,
sK187: ( subst > term > term ) > term ).
thf(func_def_330,type,
sK188: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_331,type,
sK189: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_332,type,
sK190: ( term > $o ) > term ).
thf(func_def_333,type,
sK191: ( term > $o ) > term ).
thf(func_def_334,type,
sK192: subst > term > subst > $o ).
thf(func_def_335,type,
sK193: term ).
thf(func_def_336,type,
sK194: ( subst > term > subst > $o ) > term ).
thf(func_def_337,type,
sK195: ( subst > term > subst > $o ) > term ).
thf(func_def_338,type,
sK196: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK197: ( subst > term > subst > $o ) > subst ).
thf(func_def_340,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK199: ( subst > term > subst > $o ) > subst ).
thf(func_def_342,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_343,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_344,type,
sK202: ( subst > term > subst > $o ) > term ).
thf(func_def_345,type,
sK203: ( subst > term > term ) > subst ).
thf(func_def_346,type,
sK204: ( subst > term > term ) > subst ).
thf(func_def_347,type,
sK205: ( subst > term > term ) > term ).
thf(func_def_348,type,
sK206: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_349,type,
sK207: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_350,type,
sK208: ( subst > term > subst > $o ) > term ).
thf(func_def_351,type,
sK209: ( subst > term > subst > $o ) > term ).
thf(func_def_352,type,
sK210: term > $o ).
thf(func_def_353,type,
sK211: term ).
thf(func_def_354,type,
sK212: subst > term > subst > $o ).
thf(func_def_355,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_356,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_357,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK216: ( subst > term > subst > $o ) > term ).
thf(func_def_359,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_360,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_361,type,
sK219: ( subst > term > subst > $o ) > term ).
thf(func_def_362,type,
sK220: ( subst > term > subst > $o ) > subst ).
thf(func_def_363,type,
sK221: term > ( term > $o ) > term ).
thf(func_def_364,type,
sK222: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_365,type,
sK223: ( subst > term > term ) > subst ).
thf(func_def_366,type,
sK224: ( subst > term > term ) > subst ).
thf(func_def_367,type,
sK225: ( subst > term > term ) > term ).
thf(func_def_368,type,
sK226: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_369,type,
sK227: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_370,type,
sK228: term > $o ).
thf(func_def_371,type,
sK229: term ).
thf(func_def_372,type,
sK230: subst > term > subst > $o ).
thf(func_def_373,type,
sK231: ( subst > term > term ) > subst ).
thf(func_def_374,type,
sK232: ( subst > term > term ) > term ).
thf(func_def_375,type,
sK233: ( subst > term > term ) > subst ).
thf(func_def_376,type,
sK234: ( subst > term > term ) > term ).
thf(func_def_377,type,
sK235: term > ( term > $o ) > term ).
thf(func_def_378,type,
sK236: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_379,type,
sK237: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_380,type,
sK238: term ).
thf(func_def_381,type,
sK239: subst > term > subst > $o ).
thf(func_def_382,type,
sK240: ( subst > term > term ) > subst ).
thf(func_def_383,type,
sK241: ( subst > term > term ) > subst ).
thf(func_def_384,type,
sK242: ( subst > term > term ) > term ).
thf(func_def_385,type,
sK243: ( subst > term > term ) > term ).
thf(func_def_386,type,
sK244: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_387,type,
sK245: ( subst > term > subst > $o ) > term > term ).
thf(func_def_388,type,
sK246: term ).
thf(func_def_389,type,
sK247: term > $o ).
thf(func_def_390,type,
sK248: term ).
thf(func_def_391,type,
sK249: subst > term > subst > $o ).
thf(func_def_392,type,
sK250: ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK251: ( subst > term > subst > $o ) > subst ).
thf(func_def_394,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_395,type,
sK253: ( subst > term > subst > $o ) > subst ).
thf(func_def_396,type,
sK254: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_397,type,
sK255: ( subst > term > subst > $o ) > subst ).
thf(func_def_398,type,
sK256: ( subst > term > subst > $o ) > subst ).
thf(func_def_399,type,
sK257: ( subst > term > subst > $o ) > term ).
thf(func_def_400,type,
sK258: ( subst > term > subst > $o ) > subst ).
thf(func_def_401,type,
sK259: ( subst > term > subst > $o ) > term ).
thf(func_def_402,type,
sK260: ( subst > term > subst > $o ) > term ).
thf(func_def_403,type,
sK261: term ).
thf(func_def_404,type,
sK262: term ).
thf(func_def_405,type,
sK263: subst > term > subst > $o ).
thf(func_def_406,type,
sK264: ( subst > term > subst > $o ) > subst ).
thf(func_def_407,type,
sK265: ( subst > term > subst > $o ) > subst ).
thf(func_def_408,type,
sK266: ( subst > term > subst > $o ) > subst ).
thf(func_def_409,type,
sK267: ( subst > term > subst > $o ) > term ).
thf(func_def_410,type,
sK268: ( subst > term > subst > $o ) > subst ).
thf(func_def_411,type,
sK269: ( subst > term > subst > $o ) > term ).
thf(func_def_412,type,
sK270: ( subst > term > subst > $o ) > subst ).
thf(func_def_413,type,
sK271: ( subst > term > subst > $o ) > subst ).
thf(func_def_414,type,
sK272: ( subst > term > subst > $o ) > term ).
thf(func_def_415,type,
sK273: ( subst > term > subst > $o ) > term ).
thf(func_def_416,type,
sK274: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_417,type,
sK275: ( subst > term > term ) > subst ).
thf(func_def_418,type,
sK276: ( subst > term > term ) > term ).
thf(func_def_419,type,
sK277: ( subst > term > term ) > subst ).
thf(func_def_420,type,
sK278: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_421,type,
sK279: term ).
thf(func_def_422,type,
sK280: term > $o ).
thf(func_def_423,type,
sK281: term > term ).
thf(func_def_424,type,
sK282: ( term > $o ) > term ).
thf(func_def_425,type,
sK283: ( term > $o ) > term ).
thf(func_def_426,type,
sK284: ( term > $o ) > term ).
thf(func_def_427,type,
sK285: ( term > $o ) > term ).
thf(func_def_428,type,
sK286: ( term > $o ) > term ).
thf(func_def_429,type,
sK287: subst > ( term > $o ) > term ).
thf(func_def_430,type,
sK288: term > $o ).
thf(func_def_431,type,
sK289: subst ).
thf(func_def_432,type,
sK290: term ).
thf(func_def_433,type,
sK291: term > term ).
thf(func_def_434,type,
sK292: term ).
thf(func_def_435,type,
sK293: term ).
thf(func_def_436,type,
sK294: term > $o ).
thf(func_def_437,type,
sK295: 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: ( term > $o ) > term ).
thf(func_def_441,type,
sK299: ( term > $o ) > term ).
thf(func_def_442,type,
sK300: ( term > $o ) > term ).
thf(func_def_443,type,
sK301: ( term > $o ) > term ).
thf(func_def_444,type,
sK302: ( term > $o ) > term ).
thf(func_def_445,type,
sK303: ( term > $o ) > term ).
thf(func_def_446,type,
sK304: subst ).
thf(func_def_447,type,
sK305: term ).
thf(func_def_448,type,
sK306: term > $o ).
thf(func_def_449,type,
sK307: term ).
thf(func_def_450,type,
sK308: subst ).
thf(func_def_451,type,
sK309: term ).
thf(func_def_452,type,
sK310: subst ).
thf(func_def_453,type,
sK311: term > $o ).
thf(func_def_454,type,
sK312: term ).
thf(func_def_455,type,
sK313: subst ).
thf(func_def_456,type,
sK314: term > term ).
thf(func_def_457,type,
sK315: ( term > $o ) > term ).
thf(func_def_458,type,
sK316: subst > ( term > $o ) > term ).
thf(func_def_459,type,
sK317: ( term > $o ) > term ).
thf(func_def_460,type,
sK318: ( term > $o ) > term ).
thf(func_def_461,type,
sK319: ( term > $o ) > term ).
thf(func_def_462,type,
sK320: ( term > $o ) > term ).
thf(func_def_463,type,
sK321: term ).
thf(func_def_464,type,
sK322: subst > term > subst > $o ).
thf(func_def_465,type,
sK323: term > $o ).
thf(func_def_466,type,
sK324: 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 > $o ) > term > term ).
thf(func_def_476,type,
sK334: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_477,type,
sK335: ( subst > term > term ) > subst ).
thf(func_def_478,type,
sK336: ( subst > term > term ) > term ).
thf(func_def_479,type,
sK337: ( subst > term > term ) > subst ).
thf(func_def_480,type,
sK338: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_481,type,
sK339: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_482,type,
sK340: subst ).
thf(func_def_483,type,
sK341: term > $o ).
thf(func_def_484,type,
sK342: term ).
thf(func_def_485,type,
sK343: term > term ).
thf(func_def_486,type,
sK344: ( term > $o ) > subst > term ).
thf(func_def_487,type,
sK345: ( term > $o ) > term ).
thf(func_def_488,type,
sK346: ( term > $o ) > term ).
thf(func_def_489,type,
sK347: ( term > $o ) > term ).
thf(func_def_490,type,
sK348: subst > term > subst > $o ).
thf(func_def_491,type,
sK349: term ).
thf(func_def_492,type,
sK350: term > ( subst > term > term ) > subst ).
thf(func_def_493,type,
sK351: term > ( subst > term > term ) > term ).
thf(func_def_494,type,
sK352: term > ( subst > term > term ) > subst ).
thf(func_def_495,type,
sK353: term > ( subst > term > term ) > subst ).
thf(func_def_496,type,
sK354: term > ( subst > term > term ) > subst ).
thf(func_def_497,type,
sK355: term > ( subst > term > term ) > term ).
thf(func_def_498,type,
sK356: ( subst > term > term ) > term ).
thf(func_def_499,type,
sK357: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_500,type,
sK358: ( subst > term > subst > $o ) > term ).
thf(func_def_501,type,
sK359: term > ( subst > term > subst > $o ) > term ).
thf(func_def_502,type,
sK360: ( term > $o ) > term ).
thf(func_def_503,type,
sK361: ( term > $o ) > term ).
thf(func_def_504,type,
sK362: term ).
thf(func_def_505,type,
sK363: term > $o ).
thf(func_def_506,type,
sK364: subst > term > subst > $o ).
thf(func_def_507,type,
sK365: ( subst > term > term ) > term ).
thf(func_def_508,type,
sK366: ( subst > term > term ) > subst ).
thf(func_def_509,type,
sK367: ( subst > term > term ) > term ).
thf(func_def_510,type,
sK368: ( subst > term > term ) > subst ).
thf(func_def_511,type,
sK369: term > subst > term > term ).
thf(func_def_512,type,
sK370: ( term > $o ) > term > term ).
thf(func_def_513,type,
sK371: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_514,type,
sK372: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_515,type,
sK373: term ).
thf(func_def_516,type,
sK374: ( subst > term > term ) > term ).
thf(func_def_517,type,
sK375: ( subst > term > term ) > subst ).
thf(func_def_518,type,
sK376: term ).
thf(func_def_519,type,
sK377: ( term > $o ) > term ).
thf(func_def_520,type,
sK378: ( term > $o ) > term ).
thf(func_def_521,type,
sK379: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_522,type,
sK380: term ).
thf(func_def_523,type,
sK381: term ).
thf(func_def_524,type,
sK382: term > $o ).
thf(func_def_525,type,
sK383: term > term ).
thf(func_def_526,type,
sK384: subst > term > subst > $o ).
thf(func_def_527,type,
sK385: ( term > $o ) > term ).
thf(func_def_528,type,
sK386: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_529,type,
sK387: term > ( term > $o ) > term ).
thf(func_def_530,type,
sK388: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_531,type,
sK389: term > $o ).
thf(func_def_532,type,
sK390: subst > term > subst > $o ).
thf(func_def_533,type,
sK391: term ).
thf(func_def_534,type,
sK392: ( subst > term > term ) > term ).
thf(func_def_535,type,
sK393: ( subst > term > term ) > subst ).
thf(func_def_536,type,
sK394: ( subst > term > term ) > subst ).
thf(func_def_537,type,
sK395: ( subst > term > term ) > term ).
thf(func_def_538,type,
sK396: term ).
thf(func_def_539,type,
sK397: subst > term > subst > $o ).
thf(func_def_540,type,
sK398: ( subst > term > subst > $o ) > subst ).
thf(func_def_541,type,
sK399: ( subst > term > subst > $o ) > subst ).
thf(func_def_542,type,
sK400: ( subst > term > subst > $o ) > term ).
thf(func_def_543,type,
sK401: ( subst > term > subst > $o ) > subst ).
thf(func_def_544,type,
sK402: ( subst > term > subst > $o ) > term ).
thf(func_def_545,type,
sK403: ( subst > term > subst > $o ) > subst ).
thf(func_def_546,type,
sK404: ( subst > term > subst > $o ) > subst ).
thf(func_def_547,type,
sK405: ( subst > term > subst > $o ) > term ).
thf(func_def_548,type,
sK406: ( subst > term > subst > $o ) > subst ).
thf(func_def_549,type,
sK407: ( term > $o ) > term ).
thf(func_def_550,type,
sK408: ( term > $o ) > term ).
thf(func_def_551,type,
sK409: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_552,type,
sK410: ( subst > term > term ) > term ).
thf(func_def_553,type,
sK411: ( subst > term > term ) > subst ).
thf(func_def_554,type,
sK412: ( subst > term > term ) > subst ).
thf(func_def_555,type,
sK413: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_556,type,
sK414: ( subst > term > subst > $o ) > term ).
thf(func_def_557,type,
sK415: ( subst > term > subst > $o ) > term ).
thf(func_def_558,type,
sK416: subst > term > subst > $o ).
thf(func_def_559,type,
sK417: term ).
thf(func_def_560,type,
sK418: ( subst > term > term ) > term ).
thf(func_def_561,type,
sK419: ( subst > term > term ) > subst ).
thf(func_def_562,type,
sK420: ( subst > term > term ) > subst ).
thf(func_def_563,type,
sK421: ( subst > term > term ) > term ).
thf(func_def_564,type,
sK422: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_565,type,
sK423: term > ( subst > term > subst > $o ) > term ).
thf(func_def_566,type,
sK424: term ).
thf(func_def_567,type,
sK425: term > ( subst > term > subst > $o ) > term ).
thf(func_def_568,type,
sK426: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_569,type,
sK427: subst > term > subst > $o ).
thf(func_def_570,type,
sK428: term ).
thf(func_def_571,type,
sK429: ( subst > term > term ) > term ).
thf(func_def_572,type,
sK430: ( subst > term > term ) > subst ).
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 > subst > $o ).
thf(func_def_576,type,
sK434: term ).
thf(func_def_577,type,
sK435: ( subst > term > subst > $o ) > term ).
thf(func_def_578,type,
sK436: ( subst > term > subst > $o ) > subst ).
thf(func_def_579,type,
sK437: ( subst > term > subst > $o ) > subst ).
thf(func_def_580,type,
sK438: ( subst > term > subst > $o ) > subst ).
thf(func_def_581,type,
sK439: term > ( subst > term > subst > $o ) > term ).
thf(func_def_582,type,
sK440: ( subst > term > subst > $o ) > subst ).
thf(func_def_583,type,
sK441: ( subst > term > subst > $o ) > subst ).
thf(func_def_584,type,
sK442: ( subst > term > subst > $o ) > subst ).
thf(func_def_585,type,
sK443: ( subst > term > subst > $o ) > term ).
thf(func_def_586,type,
sK444: ( subst > term > term ) > subst ).
thf(func_def_587,type,
sK445: ( subst > term > term ) > term ).
thf(func_def_588,type,
sK446: ( subst > term > term ) > subst ).
thf(func_def_589,type,
sK447: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_590,type,
sK448: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_591,type,
sK449: term ).
thf(func_def_592,type,
sK450: subst > term > subst > $o ).
thf(func_def_593,type,
sK451: ( subst > term > term ) > subst ).
thf(func_def_594,type,
sK452: ( subst > term > term ) > term ).
thf(func_def_595,type,
sK453: ( subst > term > term ) > subst ).
thf(func_def_596,type,
sK454: ( subst > term > term ) > term ).
thf(func_def_597,type,
sK455: ( subst > term > subst > $o ) > term > term ).
thf(func_def_598,type,
sK456: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_599,type,
sK457: term ).
thf(func_def_600,type,
sK458: subst > term > term ).
thf(func_def_601,type,
sK459: subst > term > term ).
thf(func_def_602,type,
sK460: subst ).
thf(func_def_603,type,
sK461: ( subst > term > term ) > subst ).
thf(func_def_604,type,
sK462: ( subst > term > term ) > term ).
thf(func_def_605,type,
sK463: ( subst > term > term ) > subst ).
thf(func_def_606,type,
sK464: ( subst > term > term ) > subst ).
thf(func_def_607,type,
sK465: ( subst > term > term ) > term ).
thf(func_def_608,type,
sK466: ( subst > term > term ) > subst ).
thf(func_def_609,type,
sK467: term ).
thf(func_def_610,type,
sK468: term ).
thf(func_def_611,type,
sK469: term > subst > term > term ).
thf(func_def_612,type,
sK470: term ).
thf(func_def_613,type,
sK471: term ).
thf(func_def_614,type,
sK472: term ).
thf(func_def_615,type,
sK473: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_616,type,
sK474: subst > term > subst > $o ).
thf(func_def_617,type,
sK475: ( term > $o ) > term ).
thf(func_def_618,type,
sK476: term > $o ).
thf(func_def_619,type,
sK477: subst ).
thf(func_def_620,type,
sK478: term ).
thf(func_def_621,type,
sK479: ( term > $o ) > term ).
thf(func_def_622,type,
sK480: term > subst > ( term > $o ) > term > $o ).
thf(func_def_623,type,
sK481: term > subst > term > term ).
thf(func_def_624,type,
sK482: term ).
thf(func_def_625,type,
sK483: subst ).
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: ( subst > term > subst > $o ) > term ).
thf(func_def_631,type,
sK489: ( subst > term > subst > $o ) > term ).
thf(func_def_632,type,
sK490: subst > term > subst > $o ).
thf(func_def_633,type,
sK491: term ).
thf(func_def_634,type,
sK492: term > subst > term > term ).
thf(func_def_635,type,
sK493: term ).
thf(func_def_636,type,
sK494: ( subst > term > term ) > subst ).
thf(func_def_637,type,
sK495: ( subst > term > term ) > term ).
thf(func_def_638,type,
sK496: term > subst > term > term ).
thf(func_def_639,type,
sK497: term ).
thf(func_def_640,type,
sK498: ( subst > term > term ) > subst ).
thf(func_def_641,type,
sK499: ( subst > term > term ) > term ).
thf(func_def_642,type,
sK500: term ).
thf(func_def_643,type,
sK501: term ).
thf(func_def_644,type,
sK502: term ).
thf(func_def_645,type,
sK503: term ).
thf(func_def_646,type,
sK504: term ).
thf(func_def_647,type,
sK505: term ).
thf(func_def_648,type,
sK506: term ).
thf(func_def_649,type,
sK507: term ).
thf(func_def_650,type,
sK508: term ).
thf(func_def_651,type,
sK509: term ).
thf(func_def_652,type,
sK510: term ).
thf(func_def_653,type,
sK511: term ).
thf(func_def_654,type,
sK512: term ).
thf(func_def_655,type,
sK513: subst ).
thf(func_def_656,type,
sK514: ( term > $o ) > term > subst > term > $o ).
thf(func_def_657,type,
sK515: subst ).
thf(func_def_658,type,
sK516: term ).
thf(func_def_659,type,
sK517: term > $o ).
thf(func_def_660,type,
sK518: ( term > $o ) > term ).
thf(func_def_661,type,
sK519: term ).
thf(func_def_662,type,
sK520: term ).
thf(func_def_663,type,
sK521: term ).
thf(func_def_664,type,
sK522: term ).
thf(func_def_665,type,
sK523: term > d_term ).
thf(func_def_666,type,
sK524: term > $o ).
thf(func_def_667,type,
sK525: subst ).
thf(func_def_668,type,
sK526: term > $o ).
thf(func_def_669,type,
sK527: term ).
thf(func_def_670,type,
sK528: term > ( term > $o ) > subst > ( term > $o ) > term ).
thf(func_def_671,type,
sK529: subst ).
thf(func_def_672,type,
sK530: term ).
thf(func_def_673,type,
sK531: subst > d_subst ).
thf(func_def_674,type,
sK532: subst ).
thf(func_def_675,type,
sK533: term ).
thf(func_def_676,type,
sK534: subst > term > subst > $o ).
thf(func_def_677,type,
sK535: ( term > $o ) > term ).
thf(func_def_678,type,
sK536: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_679,type,
sK537: ( subst > term > term ) > subst ).
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 ).
thf(func_def_683,type,
sK541: term ).
thf(func_def_684,type,
sK542: subst > term > term ).
thf(func_def_685,type,
sK543: term ).
thf(func_def_686,type,
sK544: term > $o ).
thf(func_def_687,type,
sK545: ( term > $o ) > term ).
thf(func_def_688,type,
sK546: ( term > $o ) > term ).
thf(func_def_689,type,
sK547: term ).
thf(func_def_690,type,
sK548: subst ).
thf(func_def_691,type,
sK549: subst ).
thf(func_def_692,type,
sK550: term ).
thf(func_def_693,type,
sK551: term > $o ).
thf(func_def_694,type,
sK552: term ).
thf(func_def_695,type,
sK553: subst ).
thf(func_def_696,type,
sK554: term ).
thf(func_def_697,type,
sK555: term > $o ).
thf(func_def_698,type,
sK556: subst ).
thf(func_def_699,type,
sK557: term ).
thf(func_def_700,type,
sK558: term > $o ).
thf(func_def_701,type,
sK559: term > $o ).
thf(func_def_702,type,
sK560: subst ).
thf(func_def_703,type,
sK561: term ).
thf(func_def_704,type,
sK562: term ).
thf(func_def_705,type,
sK563: term ).
thf(func_def_706,type,
sK564: term ).
thf(func_def_707,type,
sK565: term ).
thf(func_def_708,type,
sK566: term ).
thf(func_def_709,type,
sK567: term ).
thf(func_def_710,type,
sK568: term ).
thf(func_def_711,type,
sK569: term ).
thf(func_def_712,type,
sK570: term ).
thf(func_def_713,type,
sK571: term ).
thf(func_def_714,type,
sK572: term ).
thf(func_def_715,type,
sK573: term ).
thf(func_def_716,type,
sK574: subst ).
thf(func_def_717,type,
sK575: subst ).
thf(func_def_718,type,
sK576: subst ).
thf(func_def_719,type,
sK577: subst ).
thf(func_def_720,type,
sK578: term > $o ).
thf(func_def_721,type,
sK579: term > $o ).
thf(func_def_722,type,
sK580: subst ).
thf(func_def_723,type,
sK581: term ).
thf(func_def_724,type,
sK582: term > subst > ( term > $o ) > ( term > $o ) > term ).
thf(func_def_725,type,
sK583: term ).
thf(func_def_726,type,
sK584: term ).
thf(func_def_727,type,
sK585: subst ).
thf(func_def_728,type,
sK586: term ).
thf(func_def_729,type,
sK587: term ).
thf(func_def_730,type,
sK588: term ).
thf(func_def_731,type,
sK589: subst ).
thf(func_def_732,type,
sK590: subst ).
thf(func_def_734,type,
sK592: subst > term > subst > $o ).
thf(func_def_735,type,
sK593: ( term > $o ) > term ).
thf(func_def_736,type,
sK594: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_738,type,
ph595:
!>[X0: $tType] : X0 ).
thf(f7182,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2578,f2582,f2656,f2664,f2668,f2765,f3013,f3280,f3450,f3991,f5251,f5631,f5707,f5886,f5908,f5958,f6210,f6458,f6606,f6665,f6756,f6945,f7026,f7168]) ).
thf(f7168,plain,
( ~ spl591_197
| ~ spl591_504
| ~ spl591_697 ),
inference(avatar_contradiction_clause,[status(thm)],[f7167]) ).
thf(f7167,plain,
( $false
| ~ spl591_197
| ~ spl591_504
| ~ spl591_697 ),
inference(trivial_inequality_removal,[status(thm)],[f7166]) ).
thf(f7166,plain,
( ( $true = $false )
| ~ spl591_197
| ~ spl591_504
| ~ spl591_697 ),
inference(forward_demodulation,[status(thm)],[f7165,f7068]) ).
thf(f7068,plain,
( ! [X34: term,X32: subst > term > subst > $o] :
( $false
= ( X32 @ ( d2subst @ d_id ) @ X34 @ ( d2subst @ d_id ) ) )
| ~ spl591_504
| ~ spl591_697 ),
inference(subsumption_resolution,[status(thm)],[f3990,f6664]) ).
thf(f6664,plain,
( ! [X189: term,X186: term > $o] :
( $true
!= ( X186 @ X189 ) )
| ~ spl591_697 ),
inference(avatar_component_clause,[status(thm)],[f6663]) ).
thf(f6663,definition,
( spl591_697
<=> ! [X189: term,X186: term > $o] :
( $true
!= ( X186 @ X189 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_697])],[avatar_definition]) ).
thf(f3990,plain,
( ! [X34: term,X32: subst > term > subst > $o] :
( ( $false
= ( X32 @ ( d2subst @ d_id ) @ X34 @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK473 @ X32 @ X34 ) ) )
| ~ spl591_504 ),
inference(avatar_component_clause,[status(thm)],[f3989]) ).
thf(f3989,definition,
( spl591_504
<=> ! [X34: term,X32: subst > term > subst > $o] :
( ( $true
= ( sK473 @ X32 @ X34 ) )
| ( $false
= ( X32 @ ( d2subst @ d_id ) @ X34 @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_504])],[avatar_definition]) ).
thf(f7165,plain,
( ! [X1: term > $o] :
( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) ) )
| ~ spl591_197
| ~ spl591_697 ),
inference(subsumption_resolution,[status(thm)],[f2659,f6664]) ).
thf(f2659,plain,
( ! [X1: term > $o] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X1 @ ( sK593 @ X1 ) ) ) )
| ~ spl591_197 ),
inference(avatar_component_clause,[status(thm)],[f2658]) ).
thf(f2658,definition,
( spl591_197
<=> ! [X1: term > $o] :
( ( $true
= ( X1 @ ( sK593 @ X1 ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_197])],[avatar_definition]) ).
thf(f7026,plain,
spl591_279,
inference(avatar_contradiction_clause,[status(thm)],[f7025]) ).
thf(f7025,plain,
( $false
| spl591_279 ),
inference(subsumption_resolution,[status(thm)],[f3012,f6107]) ).
thf(f6107,plain,
! [X0: subst,X1: subst] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f4142,f4142]) ).
thf(f4142,plain,
! [X152: subst] :
( ( d2subst @ d_id )
= X152 ),
inference(forward_demodulation,[status(thm)],[f1127,f1132]) ).
thf(f1132,plain,
! [X151: d_subst] : ( d_id = X151 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( ( hoasinduction_lem3aa = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP57 )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
| ( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( sK459 @ X4 @ X5 ) @ X6 )
= ( sK459 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( lam @ ( sK459 @ sh @ one ) )
= ( lam @ ( sK458 @ sh @ one ) ) )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( sK458 @ X9 @ X8 ) @ X7 )
= ( sK458 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) ) )
& ( ( sK459 @ sK460 @ sK457 )
!= ( sK458 @ sK460 @ sK457 ) ) ) )
& ( ! [X10: term,X11: subst > term > term,X12: subst > term > term,X13: subst] :
( ( ( X12 @ ( comp @ ( sK461 @ X12 ) @ ( sK463 @ X12 ) ) @ ( sub @ ( sK462 @ X12 ) @ ( sK463 @ X12 ) ) )
!= ( sub @ ( X12 @ ( sK461 @ X12 ) @ ( sK462 @ X12 ) ) @ ( sK463 @ X12 ) ) )
| ( ( lam @ ( X12 @ sh @ one ) )
!= ( lam @ ( X11 @ sh @ one ) ) )
| ( ( sub @ ( X11 @ ( sK466 @ X11 ) @ ( sK465 @ X11 ) ) @ ( sK464 @ X11 ) )
!= ( X11 @ ( comp @ ( sK466 @ X11 ) @ ( sK464 @ X11 ) ) @ ( sub @ ( sK465 @ X11 ) @ ( sK464 @ X11 ) ) ) )
| ( ( X12 @ X13 @ X10 )
= ( X11 @ X13 @ X10 ) ) )
| ( hoaslaminj != $true ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
| ( sK467
!= ( sub @ sK467 @ id ) ) )
& ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ( axvarid != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X23: subst > term > term] :
( ( sub @ sK468 @ ( push @ one @ sh ) )
!= ( X23 @ sh @ one ) ) )
& ( ! [X24: term] :
( ( sK469 @ X24 @ sh @ one )
= ( sub @ X24 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP48 ) )
& ( ( $true = sP48 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( $true = sP45 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP45 ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
| ( sK470
!= ( sub @ sK470 @ id ) ) )
& ( ! [X27: term] :
( ( sub @ X27 @ id )
= X27 )
| ( termmset != $true ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP44 ) )
& ( ( $true = sP44 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( $true = sP39 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP39 ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X28: term,X29: term] :
( ( X28 = X29 )
| ( ( lam @ X29 )
!= ( lam @ X28 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ( ( sK472 != sK471 )
& ( ( lam @ sK472 )
= ( lam @ sK471 ) ) ) )
& ( ( $true = sP36 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP36 ) )
& ( axapp = $true )
& ( ( $true = sP34 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP34 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X32: subst > term > subst > $o,X34: term] :
( ( sK473 @ X32 @ X34 )
= ( X32 @ id @ X34 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ! [X36: term > $o] :
( ( sK474 @ id @ ( sK475 @ X36 ) @ id )
!= ( X36 @ ( sK475 @ X36 ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X41: term > $o] :
( ( X41 @ ( sK479 @ X41 ) )
!= ( sK476 @ ( sub @ ( sK479 @ X41 ) @ ( push @ sK478 @ sK477 ) ) ) ) )
& ( ! [X43: term > $o,X44: subst,X45: term,X47: term] :
( ( sK480 @ X45 @ X44 @ X43 @ X47 )
= ( X43 @ ( sub @ X47 @ ( push @ X45 @ X44 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ! [X48: term] :
( ( sK481 @ X48 @ sh @ one )
= ( sub @ X48 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X51: subst > term > term] :
( ( X51 @ sh @ one )
!= ( sub @ sK482 @ ( push @ one @ sh ) ) ) )
& ( ! [X52: subst] :
( ( push @ ( sub @ one @ X52 ) @ ( comp @ sh @ X52 ) )
= X52 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ( sK483
!= ( push @ ( sub @ one @ sK483 ) @ ( comp @ sh @ sK483 ) ) ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X54: term,X55: term,X56: term,X57: term] :
( ( ( ap @ X57 @ X55 )
!= ( ap @ X56 @ X54 ) )
| ( X56 = X57 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ( ( ( ap @ sK487 @ sK485 )
= ( ap @ sK486 @ sK484 ) )
& ( sK486 != sK487 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( $true = sP33 )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP33 ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2 != $true ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X62: subst > term > subst > $o,X63: term] :
( ( ( $true
= ( X62 @ id @ ( sK488 @ X62 ) @ id ) )
& ( $true
!= ( X62 @ id @ ( ap @ ( sub @ ( sK488 @ X62 ) @ id ) @ ( sK489 @ X62 ) ) @ id ) )
& ( ( X62 @ id @ ( sK489 @ X62 ) @ id )
= $true ) )
| ( $true
= ( sP28 @ X62 ) )
| ( $true
= ( X62 @ id @ X63 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X68: term,X69: term] :
( ( $true
!= ( sK490 @ id @ X68 @ id ) )
| ( ( sK490 @ id @ ( ap @ ( sub @ X68 @ id ) @ X69 ) @ id )
= $true )
| ( $true
!= ( sK490 @ id @ X69 @ id ) ) )
& ( $true
!= ( sP28 @ sK490 ) )
& ( ( sK490 @ id @ sK491 @ id )
!= $true ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
| ( $true != sP27 ) )
& ( ( $true = sP27 )
| ( induction2 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X70: term,X72: subst,X73: term] :
( ( sub @ X70 @ ( push @ X73 @ X72 ) )
= ( sK492 @ X70 @ X72 @ X73 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X75: subst > term > term] :
( ( X75 @ ( sK494 @ X75 ) @ ( sK495 @ X75 ) )
!= ( sub @ sK493 @ ( push @ ( sK495 @ X75 ) @ ( sK494 @ X75 ) ) ) ) )
& ( ( $true = sP25 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP25 ) )
& ( ! [X78: term,X80: subst,X81: term] :
( ( sub @ X78 @ ( push @ X81 @ X80 ) )
= ( sK496 @ X78 @ X80 @ X81 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X83: subst > term > term] :
( ( X83 @ ( sK498 @ X83 ) @ ( sK499 @ X83 ) )
!= ( sub @ sK497 @ ( push @ ( sK499 @ X83 ) @ ( sK498 @ X83 ) ) ) ) )
& ( ( hoasapinj2 = $true )
| ( ( sK502 != sK500 )
& ( ( ap @ ( sub @ sK503 @ id ) @ sK500 )
= ( ap @ ( sub @ sK501 @ id ) @ sK502 ) ) ) )
& ( ! [X90: term,X91: term,X92: term,X93: term] :
( ( X90 = X92 )
| ( ( ap @ ( sub @ X93 @ id ) @ X90 )
!= ( ap @ ( sub @ X91 @ id ) @ X92 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( $true = sP21 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP21 ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ( sK504 != sK507 )
& ( ( ap @ sK507 @ sK505 )
= ( ap @ sK504 @ sK506 ) ) )
| ( ( sub @ sK508 @ id )
!= sK508 )
| ! [X99: term,X100: term,X101: term,X102: term] :
( ( ( ap @ ( sub @ X102 @ id ) @ X100 )
!= ( ap @ ( sub @ X101 @ id ) @ X99 ) )
| ( X101 = X102 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X103: term,X104: term,X105: term,X106: term] :
( ( X103 = X106 )
| ( ( ap @ X106 @ X104 )
!= ( ap @ X103 @ X105 ) ) )
& ! [X107: term] :
( ( sub @ X107 @ id )
= X107 )
& ( ( ap @ ( sub @ sK511 @ id ) @ sK509 )
= ( ap @ ( sub @ sK512 @ id ) @ sK510 ) )
& ( sK511 != sK512 ) ) )
& ! [X112: d_term,X113: d_term] :
( ( ( d2term @ X113 )
!= ( d2term @ X112 ) )
| ( X112 = X113 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X114: d_term] : ( d_one = X114 )
& ( pushprop_lem3v2 = $true )
& ( ! [X115: subst] :
( ( comp @ id @ X115 )
= X115 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ( sK513
!= ( comp @ id @ sK513 ) ) )
& ( ! [X117: subst,X118: term,X119: term > $o,X121: term] :
( ( X119 @ ( sub @ X121 @ ( push @ X118 @ X117 ) ) )
= ( sK514 @ X119 @ X118 @ X117 @ X121 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ! [X125: term > $o] :
( ( X125 @ ( sK518 @ X125 ) )
!= ( sK517 @ ( sub @ ( sK518 @ X125 ) @ ( push @ sK516 @ sK515 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X127: term,X128: term,X129: term,X130: term] :
( ( ( ap @ X127 @ X130 )
!= ( ap @ X128 @ X129 ) )
| ( X129 = X130 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( ( ap @ sK520 @ sK521 )
= ( ap @ sK519 @ sK522 ) )
& ( sK522 != sK521 ) ) )
& ! [X135: term] :
( ( d2term @ ( sK523 @ X135 ) )
= X135 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ( $true
!= ( sK526 @ one ) )
& ( ( sK524 @ sK527 )
= $true )
& ! [X141: term] :
( ( sK526 @ X141 )
= ( sK524 @ ( sub @ X141 @ ( push @ sK527 @ sK525 ) ) ) )
& ! [X142: subst,X143: term] :
( ( sub @ one @ ( push @ X143 @ X142 ) )
= X143 ) ) )
& ( ! [X144: term > $o,X145: subst,X146: term > $o,X147: term] :
( ( $true
= ( X146 @ one ) )
| ( $true
!= ( X144 @ X147 ) )
| ( ( X146 @ ( sK528 @ X147 @ X146 @ X145 @ X144 ) )
!= ( X144 @ ( sub @ ( sK528 @ X147 @ X146 @ X145 @ X144 ) @ ( push @ X147 @ X145 ) ) ) ) )
| ( ( sub @ one @ ( push @ sK530 @ sK529 ) )
!= sK530 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP17 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP17 ) )
& ( ( $true = sP15 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP15 ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X151: d_subst] : ( d_id = X151 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X152: subst] :
( ( d2subst @ ( sK531 @ X152 ) )
= X152 )
& ( pushprop_gthm = $true )
& ( ! [X154: subst,X155: term] :
( ( comp @ sh @ ( push @ X155 @ X154 ) )
= X154 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK533 @ sK532 ) )
!= sK532 ) )
& ! [X158: d_subst,X159: d_subst] :
( ( X158 = X159 )
| ( ( d2subst @ X159 )
!= ( d2subst @ X158 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X161: term > $o] :
( ( X161 @ ( sK535 @ X161 ) )
!= ( sK534 @ id @ ( sK535 @ X161 ) @ id ) ) )
& ( ! [X163: subst > term > subst > $o,X165: term] :
( ( sK536 @ X163 @ X165 )
= ( X163 @ id @ X165 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( $true = sP13 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP13 ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X166: term,X167: term,X168: subst > term > term] :
( ( ( lam @ ( X168 @ sh @ one ) )
!= ( ap @ ( sub @ X167 @ id ) @ X166 ) )
| ( ( sub @ ( X168 @ ( sK537 @ X168 ) @ ( sK538 @ X168 ) ) @ ( sK539 @ X168 ) )
!= ( X168 @ ( comp @ ( sK537 @ X168 ) @ ( sK539 @ X168 ) ) @ ( sub @ ( sK538 @ X168 ) @ ( sK539 @ X168 ) ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ( ( ( ap @ ( sub @ sK541 @ id ) @ sK540 )
= ( lam @ ( sK542 @ sh @ one ) ) )
& ! [X175: subst,X176: term,X177: subst] :
( ( sK542 @ ( comp @ X175 @ X177 ) @ ( sub @ X176 @ X177 ) )
= ( sub @ ( sK542 @ X175 @ X176 ) @ X177 ) ) ) )
& ( ( induction = $true )
| ( ! [X180: term] :
( ( $true
= ( sK544 @ ( lam @ X180 ) ) )
| ( $true
!= ( sK544 @ X180 ) ) )
& ( $true
!= ( sP12 @ sK544 ) )
& ( $true
!= ( sK544 @ sK543 ) )
& ! [X181: term] :
( ( $true
!= ( var @ X181 ) )
| ( $true
= ( sK544 @ X181 ) ) ) ) )
& ( ! [X182: term,X183: term > $o] :
( ( ( $true
!= ( X183 @ ( lam @ ( sK545 @ X183 ) ) ) )
& ( $true
= ( X183 @ ( sK545 @ X183 ) ) ) )
| ( $true
= ( sP12 @ X183 ) )
| ( $true
= ( X183 @ X182 ) )
| ( ( $true
= ( var @ ( sK546 @ X183 ) ) )
& ( $true
!= ( X183 @ ( sK546 @ X183 ) ) ) ) )
| ( induction != $true ) )
& ( ! [X186: term > $o,X187: term,X188: subst,X189: term,X190: term > $o] :
( ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) )
| ( $true
!= ( X186 @ X189 ) ) )
| ( sK547
!= ( sub @ one @ ( push @ sK547 @ sK548 ) ) )
| ( sK549
!= ( comp @ sh @ ( push @ sK550 @ sK549 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ( ( sK555 @ ( sub @ sK554 @ ( push @ sK552 @ sK553 ) ) )
!= $true )
& ( ( sK551 @ sK554 )
= $true )
& ! [X200: term,X201: subst] :
( ( sub @ one @ ( push @ X200 @ X201 ) )
= X200 )
& ! [X202: subst,X203: term] :
( ( comp @ sh @ ( push @ X203 @ X202 ) )
= X202 ) ) )
& ( ! [X204: subst] :
( ( comp @ X204 @ id )
= X204 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ( sK556
!= ( comp @ sK556 @ id ) ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X206: term,X207: term > $o,X208: term > $o,X209: subst,X210: term] :
( ( $true
= ( X207 @ ( sub @ X206 @ ( push @ X210 @ X209 ) ) ) )
| ( $true
!= ( X208 @ X206 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK558 @ ( sub @ sK557 @ ( push @ sK561 @ sK560 ) ) )
!= $true )
& ( $true
= ( sK559 @ sK557 ) ) ) )
& ( ( hoasapinj1 = $true )
| ( ( sK563 != sK562 )
& ( ( ap @ ( sub @ sK563 @ id ) @ sK564 )
= ( ap @ ( sub @ sK562 @ id ) @ sK565 ) ) ) )
& ( ! [X220: term,X221: term,X222: term,X223: term] :
( ( X220 = X221 )
| ( ( ap @ ( sub @ X220 @ id ) @ X223 )
!= ( ap @ ( sub @ X221 @ id ) @ X222 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ( sK569 != sK567 )
& ( ( ap @ ( sub @ sK566 @ id ) @ sK569 )
= ( ap @ ( sub @ sK568 @ id ) @ sK567 ) )
& ! [X228: term,X229: term,X230: term,X231: term] :
( ( ( ap @ X228 @ X229 )
!= ( ap @ X230 @ X231 ) )
| ( X229 = X231 ) ) ) )
& ( ! [X232: term,X233: term,X234: term,X235: term] :
( ( X233 = X235 )
| ( ( ap @ ( sub @ X234 @ id ) @ X233 )
!= ( ap @ ( sub @ X232 @ id ) @ X235 ) ) )
| ( ( ( ap @ sK570 @ sK571 )
= ( ap @ sK572 @ sK573 ) )
& ( sK573 != sK571 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( $true = sP11 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP11 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( $true = sP10 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP10 ) )
& ( 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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ( sK574
!= ( comp @ sK574 @ id ) )
| ( ( comp @ id @ sK575 )
!= sK575 )
| ( ! [X242: subst] :
( ( comp @ X242 @ id )
= X242 )
& ! [X243: subst] :
( ( comp @ id @ X243 )
= X243 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X244: subst] :
( ( comp @ X244 @ id )
= X244 )
& ! [X245: subst] :
( ( comp @ id @ X245 )
= X245 )
& ( ( ( comp @ sK576 @ id )
!= sK576 )
| ( ( comp @ id @ sK577 )
!= sK577 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
| ( ! [X252: term] :
( ( sK579 @ X252 )
= ( sK578 @ ( sub @ X252 @ ( push @ sK581 @ sK580 ) ) ) )
& ( ( sK578 @ sK581 )
= $true )
& ( $true
!= ( sK579 @ one ) ) ) )
& ( ! [X253: term > $o,X254: term > $o,X255: subst,X256: term] :
( ( ( X254 @ ( sK582 @ X256 @ X255 @ X254 @ X253 ) )
!= ( X253 @ ( sub @ ( sK582 @ X256 @ X255 @ X254 @ X253 ) @ ( push @ X256 @ X255 ) ) ) )
| ( $true
!= ( X253 @ X256 ) )
| ( $true
= ( X254 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ! [X258: term,X259: term] :
( ( ( sub @ X259 @ sh )
!= ( sub @ X258 @ sh ) )
| ( X258 = X259 ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ( ( ( sub @ sK583 @ sh )
= ( sub @ sK584 @ sh ) )
& ( sK584 != sK583 ) ) )
& ( ! [X262: subst,X263: term] :
( ( sub @ one @ ( push @ X263 @ X262 ) )
= X263 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ( sK586
!= ( sub @ one @ ( push @ sK586 @ sK585 ) ) ) )
& ( ! [X266: term] :
( ( sub @ X266 @ id )
= X266 )
| ( ( sub @ sK587 @ id )
!= sK587 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ( ( sub @ sK588 @ id )
!= sK588 )
& ! [X269: term] :
( ( sub @ X269 @ id )
= X269 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP2 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP2 ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP0 != $true ) )
& ( ( sP0 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( substmonoid = $true )
| ( ( comp @ id @ sK589 )
!= sK589 )
| ( sK590
!= ( comp @ sK590 @ id ) ) )
& ( ( ! [X272: subst] :
( ( comp @ id @ X272 )
= X272 )
& ! [X273: subst] :
( ( comp @ X273 @ id )
= X273 ) )
| ( substmonoid != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[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])],[f475,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]) ).
thf(f476,plain,
( ? [X0: term,X1: subst > term > term,X2: subst > term > term,X3: subst] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X2 @ X4 @ X5 ) @ X6 )
= ( X2 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( lam @ ( X2 @ sh @ one ) )
= ( lam @ ( X1 @ sh @ one ) ) )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( X1 @ X9 @ X8 ) @ X7 )
= ( X1 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) ) )
& ( ( X2 @ X3 @ X0 )
!= ( X1 @ X3 @ X0 ) ) )
=> ( ! [X6: subst,X5: term,X4: subst] :
( ( sub @ ( sK459 @ X4 @ X5 ) @ X6 )
= ( sK459 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( lam @ ( sK459 @ sh @ one ) )
= ( lam @ ( sK458 @ sh @ one ) ) )
& ! [X9: subst,X8: term,X7: subst] :
( ( sub @ ( sK458 @ X9 @ X8 ) @ X7 )
= ( sK458 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) ) )
& ( ( sK459 @ sK460 @ sK457 )
!= ( sK458 @ sK460 @ sK457 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
! [X12: subst > term > term] :
( ? [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X14 @ X15 ) @ X16 )
!= ( X12 @ ( comp @ X14 @ X16 ) @ ( sub @ X15 @ X16 ) ) )
=> ( ( X12 @ ( comp @ ( sK461 @ X12 ) @ ( sK463 @ X12 ) ) @ ( sub @ ( sK462 @ X12 ) @ ( sK463 @ X12 ) ) )
!= ( sub @ ( X12 @ ( sK461 @ X12 ) @ ( sK462 @ X12 ) ) @ ( sK463 @ X12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
! [X11: subst > term > term] :
( ? [X17: subst,X18: term,X19: subst] :
( ( sub @ ( X11 @ X19 @ X18 ) @ X17 )
!= ( X11 @ ( comp @ X19 @ X17 ) @ ( sub @ X18 @ X17 ) ) )
=> ( ( sub @ ( X11 @ ( sK466 @ X11 ) @ ( sK465 @ X11 ) ) @ ( sK464 @ X11 ) )
!= ( X11 @ ( comp @ ( sK466 @ X11 ) @ ( sK464 @ X11 ) ) @ ( sub @ ( sK465 @ X11 ) @ ( sK464 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 )
=> ( sK467
!= ( sub @ sK467 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
( ? [X22: term] :
! [X23: subst > term > term] :
( ( sub @ X22 @ ( push @ one @ sh ) )
!= ( X23 @ sh @ one ) )
=> ! [X23: subst > term > term] :
( ( sub @ sK468 @ ( push @ one @ sh ) )
!= ( X23 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
! [X24: term] :
( ? [X25: subst > term > term] :
( ( X25 @ sh @ one )
= ( sub @ X24 @ ( push @ one @ sh ) ) )
=> ( ( sK469 @ X24 @ sh @ one )
= ( sub @ X24 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ? [X26: term] :
( ( sub @ X26 @ id )
!= X26 )
=> ( sK470
!= ( sub @ sK470 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
( ? [X30: term,X31: term] :
( ( X30 != X31 )
& ( ( lam @ X31 )
= ( lam @ X30 ) ) )
=> ( ( sK472 != sK471 )
& ( ( lam @ sK472 )
= ( lam @ sK471 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
! [X32: subst > term > subst > $o] :
( ? [X33: term > $o] :
! [X34: term] :
( ( X33 @ X34 )
= ( X32 @ id @ X34 @ id ) )
=> ! [X34: term] :
( ( sK473 @ X32 @ X34 )
= ( X32 @ id @ X34 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
( ? [X35: subst > term > subst > $o] :
! [X36: term > $o] :
? [X37: term] :
( ( X36 @ X37 )
!= ( X35 @ id @ X37 @ id ) )
=> ! [X36: term > $o] :
? [X37: term] :
( ( X36 @ X37 )
!= ( sK474 @ id @ X37 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
! [X36: term > $o] :
( ? [X37: term] :
( ( X36 @ X37 )
!= ( sK474 @ id @ X37 @ id ) )
=> ( ( sK474 @ id @ ( sK475 @ X36 ) @ id )
!= ( X36 @ ( sK475 @ X36 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
( ? [X38: term > $o,X39: subst,X40: term] :
! [X41: term > $o] :
? [X42: term] :
( ( X38 @ ( sub @ X42 @ ( push @ X40 @ X39 ) ) )
!= ( X41 @ X42 ) )
=> ! [X41: term > $o] :
? [X42: term] :
( ( sK476 @ ( sub @ X42 @ ( push @ sK478 @ sK477 ) ) )
!= ( X41 @ X42 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
! [X41: term > $o] :
( ? [X42: term] :
( ( sK476 @ ( sub @ X42 @ ( push @ sK478 @ sK477 ) ) )
!= ( X41 @ X42 ) )
=> ( ( X41 @ ( sK479 @ X41 ) )
!= ( sK476 @ ( sub @ ( sK479 @ X41 ) @ ( push @ sK478 @ sK477 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
! [X43: term > $o,X44: subst,X45: term] :
( ? [X46: term > $o] :
! [X47: term] :
( ( X43 @ ( sub @ X47 @ ( push @ X45 @ X44 ) ) )
= ( X46 @ X47 ) )
=> ! [X47: term] :
( ( sK480 @ X45 @ X44 @ X43 @ X47 )
= ( X43 @ ( sub @ X47 @ ( push @ X45 @ X44 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
! [X48: term] :
( ? [X49: subst > term > term] :
( ( X49 @ sh @ one )
= ( sub @ X48 @ ( push @ one @ sh ) ) )
=> ( ( sK481 @ X48 @ sh @ one )
= ( sub @ X48 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
( ? [X50: term] :
! [X51: subst > term > term] :
( ( sub @ X50 @ ( push @ one @ sh ) )
!= ( X51 @ sh @ one ) )
=> ! [X51: subst > term > term] :
( ( X51 @ sh @ one )
!= ( sub @ sK482 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
( ? [X53: subst] :
( ( push @ ( sub @ one @ X53 ) @ ( comp @ sh @ X53 ) )
!= X53 )
=> ( sK483
!= ( push @ ( sub @ one @ sK483 ) @ ( comp @ sh @ sK483 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
( ? [X58: term,X59: term,X60: term,X61: term] :
( ( ( ap @ X60 @ X58 )
= ( ap @ X61 @ X59 ) )
& ( X60 != X61 ) )
=> ( ( ( ap @ sK487 @ sK485 )
= ( ap @ sK486 @ sK484 ) )
& ( sK486 != sK487 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
! [X62: subst > term > subst > $o] :
( ? [X64: term,X65: term] :
( ( $true
= ( X62 @ id @ X64 @ id ) )
& ( $true
!= ( X62 @ id @ ( ap @ ( sub @ X64 @ id ) @ X65 ) @ id ) )
& ( $true
= ( X62 @ id @ X65 @ id ) ) )
=> ( ( $true
= ( X62 @ id @ ( sK488 @ X62 ) @ id ) )
& ( $true
!= ( X62 @ id @ ( ap @ ( sub @ ( sK488 @ X62 ) @ id ) @ ( sK489 @ X62 ) ) @ id ) )
& ( ( X62 @ id @ ( sK489 @ X62 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
( ? [X66: subst > term > subst > $o,X67: term] :
( ! [X68: term,X69: term] :
( ( ( X66 @ id @ X68 @ id )
!= $true )
| ( $true
= ( X66 @ id @ ( ap @ ( sub @ X68 @ id ) @ X69 ) @ id ) )
| ( $true
!= ( X66 @ id @ X69 @ id ) ) )
& ( $true
!= ( sP28 @ X66 ) )
& ( ( X66 @ id @ X67 @ id )
!= $true ) )
=> ( ! [X69: term,X68: term] :
( ( $true
!= ( sK490 @ id @ X68 @ id ) )
| ( ( sK490 @ id @ ( ap @ ( sub @ X68 @ id ) @ X69 ) @ id )
= $true )
| ( $true
!= ( sK490 @ id @ X69 @ id ) ) )
& ( $true
!= ( sP28 @ sK490 ) )
& ( ( sK490 @ id @ sK491 @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
! [X70: term] :
( ? [X71: subst > term > term] :
! [X72: subst,X73: term] :
( ( X71 @ X72 @ X73 )
= ( sub @ X70 @ ( push @ X73 @ X72 ) ) )
=> ! [X73: term,X72: subst] :
( ( sub @ X70 @ ( push @ X73 @ X72 ) )
= ( sK492 @ X70 @ X72 @ X73 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
( ? [X74: term] :
! [X75: subst > term > term] :
? [X76: subst,X77: term] :
( ( X75 @ X76 @ X77 )
!= ( sub @ X74 @ ( push @ X77 @ X76 ) ) )
=> ! [X75: subst > term > term] :
? [X77: term,X76: subst] :
( ( X75 @ X76 @ X77 )
!= ( sub @ sK493 @ ( push @ X77 @ X76 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
! [X75: subst > term > term] :
( ? [X77: term,X76: subst] :
( ( X75 @ X76 @ X77 )
!= ( sub @ sK493 @ ( push @ X77 @ X76 ) ) )
=> ( ( X75 @ ( sK494 @ X75 ) @ ( sK495 @ X75 ) )
!= ( sub @ sK493 @ ( push @ ( sK495 @ X75 ) @ ( sK494 @ X75 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
! [X78: term] :
( ? [X79: subst > term > term] :
! [X80: subst,X81: term] :
( ( X79 @ X80 @ X81 )
= ( sub @ X78 @ ( push @ X81 @ X80 ) ) )
=> ! [X81: term,X80: subst] :
( ( sub @ X78 @ ( push @ X81 @ X80 ) )
= ( sK496 @ X78 @ X80 @ X81 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
( ? [X82: term] :
! [X83: subst > term > term] :
? [X84: subst,X85: term] :
( ( X83 @ X84 @ X85 )
!= ( sub @ X82 @ ( push @ X85 @ X84 ) ) )
=> ! [X83: subst > term > term] :
? [X85: term,X84: subst] :
( ( sub @ sK497 @ ( push @ X85 @ X84 ) )
!= ( X83 @ X84 @ X85 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
! [X83: subst > term > term] :
( ? [X85: term,X84: subst] :
( ( sub @ sK497 @ ( push @ X85 @ X84 ) )
!= ( X83 @ X84 @ X85 ) )
=> ( ( X83 @ ( sK498 @ X83 ) @ ( sK499 @ X83 ) )
!= ( sub @ sK497 @ ( push @ ( sK499 @ X83 ) @ ( sK498 @ X83 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
( ? [X86: term,X87: term,X88: term,X89: term] :
( ( X86 != X88 )
& ( ( ap @ ( sub @ X89 @ id ) @ X86 )
= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) )
=> ( ( sK502 != sK500 )
& ( ( ap @ ( sub @ sK503 @ id ) @ sK500 )
= ( ap @ ( sub @ sK501 @ id ) @ sK502 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
( ? [X94: term,X95: term,X96: term,X97: term] :
( ( X94 != X97 )
& ( ( ap @ X94 @ X96 )
= ( ap @ X97 @ X95 ) ) )
=> ( ( sK504 != sK507 )
& ( ( ap @ sK507 @ sK505 )
= ( ap @ sK504 @ sK506 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
=> ( ( sub @ sK508 @ id )
!= sK508 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
( ? [X108: term,X109: term,X110: term,X111: term] :
( ( ( ap @ ( sub @ X110 @ id ) @ X108 )
= ( ap @ ( sub @ X111 @ id ) @ X109 ) )
& ( X110 != X111 ) )
=> ( ( ( ap @ ( sub @ sK511 @ id ) @ sK509 )
= ( ap @ ( sub @ sK512 @ id ) @ sK510 ) )
& ( sK511 != sK512 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
( ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 )
=> ( sK513
!= ( comp @ id @ sK513 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
! [X117: subst,X118: term,X119: term > $o] :
( ? [X120: term > $o] :
! [X121: term] :
( ( X120 @ X121 )
= ( X119 @ ( sub @ X121 @ ( push @ X118 @ X117 ) ) ) )
=> ! [X121: term] :
( ( X119 @ ( sub @ X121 @ ( push @ X118 @ X117 ) ) )
= ( sK514 @ X119 @ X118 @ X117 @ X121 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X122: subst,X123: term,X124: term > $o] :
! [X125: term > $o] :
? [X126: term] :
( ( X124 @ ( sub @ X126 @ ( push @ X123 @ X122 ) ) )
!= ( X125 @ X126 ) )
=> ! [X125: term > $o] :
? [X126: term] :
( ( sK517 @ ( sub @ X126 @ ( push @ sK516 @ sK515 ) ) )
!= ( X125 @ X126 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
! [X125: term > $o] :
( ? [X126: term] :
( ( sK517 @ ( sub @ X126 @ ( push @ sK516 @ sK515 ) ) )
!= ( X125 @ X126 ) )
=> ( ( X125 @ ( sK518 @ X125 ) )
!= ( sK517 @ ( sub @ ( sK518 @ X125 ) @ ( push @ sK516 @ sK515 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
( ? [X131: term,X132: term,X133: term,X134: term] :
( ( ( ap @ X131 @ X134 )
= ( ap @ X132 @ X133 ) )
& ( X133 != X134 ) )
=> ( ( ( ap @ sK520 @ sK521 )
= ( ap @ sK519 @ sK522 ) )
& ( sK522 != sK521 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
! [X135: term] :
( ? [X136: d_term] :
( ( d2term @ X136 )
= X135 )
=> ( ( d2term @ ( sK523 @ X135 ) )
= X135 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
( ? [X137: term > $o,X138: subst,X139: term > $o,X140: term] :
( ( $true
!= ( X139 @ one ) )
& ( $true
= ( X137 @ X140 ) )
& ! [X141: term] :
( ( X139 @ X141 )
= ( X137 @ ( sub @ X141 @ ( push @ X140 @ X138 ) ) ) ) )
=> ( ( $true
!= ( sK526 @ one ) )
& ( ( sK524 @ sK527 )
= $true )
& ! [X141: term] :
( ( sK526 @ X141 )
= ( sK524 @ ( sub @ X141 @ ( push @ sK527 @ sK525 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
! [X144: term > $o,X145: subst,X146: term > $o,X147: term] :
( ? [X148: term] :
( ( X144 @ ( sub @ X148 @ ( push @ X147 @ X145 ) ) )
!= ( X146 @ X148 ) )
=> ( ( X146 @ ( sK528 @ X147 @ X146 @ X145 @ X144 ) )
!= ( X144 @ ( sub @ ( sK528 @ X147 @ X146 @ X145 @ X144 ) @ ( push @ X147 @ X145 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ? [X149: subst,X150: term] :
( ( sub @ one @ ( push @ X150 @ X149 ) )
!= X150 )
=> ( ( sub @ one @ ( push @ sK530 @ sK529 ) )
!= sK530 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
! [X152: subst] :
( ? [X153: d_subst] :
( ( d2subst @ X153 )
= X152 )
=> ( ( d2subst @ ( sK531 @ X152 ) )
= X152 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
( ? [X156: subst,X157: term] :
( ( comp @ sh @ ( push @ X157 @ X156 ) )
!= X156 )
=> ( ( comp @ sh @ ( push @ sK533 @ sK532 ) )
!= sK532 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
( ? [X160: subst > term > subst > $o] :
! [X161: term > $o] :
? [X162: term] :
( ( X160 @ id @ X162 @ id )
!= ( X161 @ X162 ) )
=> ! [X161: term > $o] :
? [X162: term] :
( ( sK534 @ id @ X162 @ id )
!= ( X161 @ X162 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
! [X161: term > $o] :
( ? [X162: term] :
( ( sK534 @ id @ X162 @ id )
!= ( X161 @ X162 ) )
=> ( ( X161 @ ( sK535 @ X161 ) )
!= ( sK534 @ id @ ( sK535 @ X161 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
! [X163: subst > term > subst > $o] :
( ? [X164: term > $o] :
! [X165: term] :
( ( X164 @ X165 )
= ( X163 @ id @ X165 @ id ) )
=> ! [X165: term] :
( ( sK536 @ X163 @ X165 )
= ( X163 @ id @ X165 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
! [X168: subst > term > term] :
( ? [X169: subst,X170: term,X171: subst] :
( ( X168 @ ( comp @ X169 @ X171 ) @ ( sub @ X170 @ X171 ) )
!= ( sub @ ( X168 @ X169 @ X170 ) @ X171 ) )
=> ( ( sub @ ( X168 @ ( sK537 @ X168 ) @ ( sK538 @ X168 ) ) @ ( sK539 @ X168 ) )
!= ( X168 @ ( comp @ ( sK537 @ X168 ) @ ( sK539 @ X168 ) ) @ ( sub @ ( sK538 @ X168 ) @ ( sK539 @ X168 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X172: term,X173: term,X174: subst > term > term] :
( ( ( ap @ ( sub @ X173 @ id ) @ X172 )
= ( lam @ ( X174 @ sh @ one ) ) )
& ! [X175: subst,X176: term,X177: subst] :
( ( X174 @ ( comp @ X175 @ X177 ) @ ( sub @ X176 @ X177 ) )
= ( sub @ ( X174 @ X175 @ X176 ) @ X177 ) ) )
=> ( ( ( ap @ ( sub @ sK541 @ id ) @ sK540 )
= ( lam @ ( sK542 @ sh @ one ) ) )
& ! [X177: subst,X176: term,X175: subst] :
( ( sK542 @ ( comp @ X175 @ X177 ) @ ( sub @ X176 @ X177 ) )
= ( sub @ ( sK542 @ X175 @ X176 ) @ X177 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
( ? [X178: term,X179: term > $o] :
( ! [X180: term] :
( ( $true
= ( X179 @ ( lam @ X180 ) ) )
| ( ( X179 @ X180 )
!= $true ) )
& ( $true
!= ( sP12 @ X179 ) )
& ( ( X179 @ X178 )
!= $true )
& ! [X181: term] :
( ( $true
!= ( var @ X181 ) )
| ( $true
= ( X179 @ X181 ) ) ) )
=> ( ! [X180: term] :
( ( $true
= ( sK544 @ ( lam @ X180 ) ) )
| ( $true
!= ( sK544 @ X180 ) ) )
& ( $true
!= ( sP12 @ sK544 ) )
& ( $true
!= ( sK544 @ sK543 ) )
& ! [X181: term] :
( ( $true
!= ( var @ X181 ) )
| ( $true
= ( sK544 @ X181 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
! [X183: term > $o] :
( ? [X184: term] :
( ( ( X183 @ ( lam @ X184 ) )
!= $true )
& ( ( X183 @ X184 )
= $true ) )
=> ( ( $true
!= ( X183 @ ( lam @ ( sK545 @ X183 ) ) ) )
& ( $true
= ( X183 @ ( sK545 @ X183 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
! [X183: term > $o] :
( ? [X185: term] :
( ( $true
= ( var @ X185 ) )
& ( $true
!= ( X183 @ X185 ) ) )
=> ( ( $true
= ( var @ ( sK546 @ X183 ) ) )
& ( $true
!= ( X183 @ ( sK546 @ X183 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
( ? [X191: term,X192: subst] :
( ( sub @ one @ ( push @ X191 @ X192 ) )
!= X191 )
=> ( sK547
!= ( sub @ one @ ( push @ sK547 @ sK548 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
( ? [X193: subst,X194: term] :
( ( comp @ sh @ ( push @ X194 @ X193 ) )
!= X193 )
=> ( sK549
!= ( comp @ sh @ ( push @ sK550 @ sK549 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
( ? [X195: term > $o,X196: term,X197: subst,X198: term,X199: term > $o] :
( ( $true
!= ( X199 @ ( sub @ X198 @ ( push @ X196 @ X197 ) ) ) )
& ( $true
= ( X195 @ X198 ) ) )
=> ( ( ( sK555 @ ( sub @ sK554 @ ( push @ sK552 @ sK553 ) ) )
!= $true )
& ( ( sK551 @ sK554 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
( ? [X205: subst] :
( ( comp @ X205 @ id )
!= X205 )
=> ( sK556
!= ( comp @ sK556 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
( ? [X211: term,X212: term > $o,X213: term > $o,X214: subst,X215: term] :
( ( ( X212 @ ( sub @ X211 @ ( push @ X215 @ X214 ) ) )
!= $true )
& ( $true
= ( X213 @ X211 ) ) )
=> ( ( ( sK558 @ ( sub @ sK557 @ ( push @ sK561 @ sK560 ) ) )
!= $true )
& ( $true
= ( sK559 @ sK557 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
( ? [X216: term,X217: term,X218: term,X219: term] :
( ( X216 != X217 )
& ( ( ap @ ( sub @ X216 @ id ) @ X219 )
= ( ap @ ( sub @ X217 @ id ) @ X218 ) ) )
=> ( ( sK563 != sK562 )
& ( ( ap @ ( sub @ sK563 @ id ) @ sK564 )
= ( ap @ ( sub @ sK562 @ id ) @ sK565 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
( ? [X224: term,X225: term,X226: term,X227: term] :
( ( X225 != X227 )
& ( ( ap @ ( sub @ X224 @ id ) @ X227 )
= ( ap @ ( sub @ X226 @ id ) @ X225 ) ) )
=> ( ( sK569 != sK567 )
& ( ( ap @ ( sub @ sK566 @ id ) @ sK569 )
= ( ap @ ( sub @ sK568 @ id ) @ sK567 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X236: term,X237: term,X238: term,X239: term] :
( ( ( ap @ X238 @ X239 )
= ( ap @ X236 @ X237 ) )
& ( X237 != X239 ) )
=> ( ( ( ap @ sK570 @ sK571 )
= ( ap @ sK572 @ sK573 ) )
& ( sK573 != sK571 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
( ? [X240: subst] :
( ( comp @ X240 @ id )
!= X240 )
=> ( sK574
!= ( comp @ sK574 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
( ? [X241: subst] :
( ( comp @ id @ X241 )
!= X241 )
=> ( ( comp @ id @ sK575 )
!= sK575 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
( ? [X246: subst] :
( ( comp @ X246 @ id )
!= X246 )
=> ( ( comp @ sK576 @ id )
!= sK576 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
( ? [X247: subst] :
( ( comp @ id @ X247 )
!= X247 )
=> ( ( comp @ id @ sK577 )
!= sK577 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
( ? [X248: term > $o,X249: term > $o,X250: subst,X251: term] :
( ! [X252: term] :
( ( X249 @ X252 )
= ( X248 @ ( sub @ X252 @ ( push @ X251 @ X250 ) ) ) )
& ( $true
= ( X248 @ X251 ) )
& ( $true
!= ( X249 @ one ) ) )
=> ( ! [X252: term] :
( ( sK579 @ X252 )
= ( sK578 @ ( sub @ X252 @ ( push @ sK581 @ sK580 ) ) ) )
& ( ( sK578 @ sK581 )
= $true )
& ( $true
!= ( sK579 @ one ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
! [X253: term > $o,X254: term > $o,X255: subst,X256: term] :
( ? [X257: term] :
( ( X254 @ X257 )
!= ( X253 @ ( sub @ X257 @ ( push @ X256 @ X255 ) ) ) )
=> ( ( X254 @ ( sK582 @ X256 @ X255 @ X254 @ X253 ) )
!= ( X253 @ ( sub @ ( sK582 @ X256 @ X255 @ X254 @ X253 ) @ ( push @ X256 @ X255 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
( ? [X260: term,X261: term] :
( ( ( sub @ X260 @ sh )
= ( sub @ X261 @ sh ) )
& ( X260 != X261 ) )
=> ( ( ( sub @ sK583 @ sh )
= ( sub @ sK584 @ sh ) )
& ( sK584 != sK583 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
( ? [X264: subst,X265: term] :
( ( sub @ one @ ( push @ X265 @ X264 ) )
!= X265 )
=> ( sK586
!= ( sub @ one @ ( push @ sK586 @ sK585 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
( ? [X267: term] :
( ( sub @ X267 @ id )
!= X267 )
=> ( ( sub @ sK587 @ id )
!= sK587 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
( ? [X268: term] :
( ( sub @ X268 @ id )
!= X268 )
=> ( ( sub @ sK588 @ id )
!= sK588 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
( ? [X270: subst] :
( ( comp @ id @ X270 )
!= X270 )
=> ( ( comp @ id @ sK589 )
!= sK589 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
( ? [X271: subst] :
( ( comp @ X271 @ id )
!= X271 )
=> ( sK590
!= ( comp @ sK590 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
( ( ( hoasinduction_lem3aa = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP57 )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
| ? [X0: term,X1: subst > term > term,X2: subst > term > term,X3: subst] :
( ! [X4: subst,X5: term,X6: subst] :
( ( sub @ ( X2 @ X4 @ X5 ) @ X6 )
= ( X2 @ ( comp @ X4 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( lam @ ( X2 @ sh @ one ) )
= ( lam @ ( X1 @ sh @ one ) ) )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( X1 @ X9 @ X8 ) @ X7 )
= ( X1 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) ) )
& ( ( X2 @ X3 @ X0 )
!= ( X1 @ X3 @ X0 ) ) ) )
& ( ! [X10: term,X11: subst > term > term,X12: subst > term > term,X13: subst] :
( ? [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X14 @ X15 ) @ X16 )
!= ( X12 @ ( comp @ X14 @ X16 ) @ ( sub @ X15 @ X16 ) ) )
| ( ( lam @ ( X12 @ sh @ one ) )
!= ( lam @ ( X11 @ sh @ one ) ) )
| ? [X17: subst,X18: term,X19: subst] :
( ( sub @ ( X11 @ X19 @ X18 ) @ X17 )
!= ( X11 @ ( comp @ X19 @ X17 ) @ ( sub @ X18 @ X17 ) ) )
| ( ( X12 @ X13 @ X10 )
= ( X11 @ X13 @ X10 ) ) )
| ( hoaslaminj != $true ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 ) )
& ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ( axvarid != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X22: term] :
! [X23: subst > term > term] :
( ( sub @ X22 @ ( push @ one @ sh ) )
!= ( X23 @ sh @ one ) ) )
& ( ! [X24: term] :
? [X25: subst > term > term] :
( ( X25 @ sh @ one )
= ( sub @ X24 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP48 ) )
& ( ( $true = sP48 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( $true = sP45 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP45 ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
| ? [X26: term] :
( ( sub @ X26 @ id )
!= X26 ) )
& ( ! [X27: term] :
( ( sub @ X27 @ id )
= X27 )
| ( termmset != $true ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP44 ) )
& ( ( $true = sP44 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( $true = sP39 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP39 ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X28: term,X29: term] :
( ( X28 = X29 )
| ( ( lam @ X29 )
!= ( lam @ X28 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X30: term,X31: term] :
( ( X30 != X31 )
& ( ( lam @ X31 )
= ( lam @ X30 ) ) ) )
& ( ( $true = sP36 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP36 ) )
& ( axapp = $true )
& ( ( $true = sP34 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP34 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X32: subst > term > subst > $o] :
? [X33: term > $o] :
! [X34: term] :
( ( X33 @ X34 )
= ( X32 @ id @ X34 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X35: subst > term > subst > $o] :
! [X36: term > $o] :
? [X37: term] :
( ( X36 @ X37 )
!= ( X35 @ id @ X37 @ id ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X38: term > $o,X39: subst,X40: term] :
! [X41: term > $o] :
? [X42: term] :
( ( X38 @ ( sub @ X42 @ ( push @ X40 @ X39 ) ) )
!= ( X41 @ X42 ) ) )
& ( ! [X43: term > $o,X44: subst,X45: term] :
? [X46: term > $o] :
! [X47: term] :
( ( X43 @ ( sub @ X47 @ ( push @ X45 @ X44 ) ) )
= ( X46 @ X47 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ! [X48: term] :
? [X49: subst > term > term] :
( ( X49 @ sh @ one )
= ( sub @ X48 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X50: term] :
! [X51: subst > term > term] :
( ( sub @ X50 @ ( push @ one @ sh ) )
!= ( X51 @ sh @ one ) ) )
& ( ! [X52: subst] :
( ( push @ ( sub @ one @ X52 ) @ ( comp @ sh @ X52 ) )
= X52 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X53: subst] :
( ( push @ ( sub @ one @ X53 ) @ ( comp @ sh @ X53 ) )
!= X53 ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X54: term,X55: term,X56: term,X57: term] :
( ( ( ap @ X57 @ X55 )
!= ( ap @ X56 @ X54 ) )
| ( X56 = X57 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X58: term,X59: term,X60: term,X61: term] :
( ( ( ap @ X60 @ X58 )
= ( ap @ X61 @ X59 ) )
& ( X60 != X61 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( $true = sP33 )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP33 ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2 != $true ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X62: subst > term > subst > $o,X63: term] :
( ? [X64: term,X65: term] :
( ( $true
= ( X62 @ id @ X64 @ id ) )
& ( $true
!= ( X62 @ id @ ( ap @ ( sub @ X64 @ id ) @ X65 ) @ id ) )
& ( $true
= ( X62 @ id @ X65 @ id ) ) )
| ( $true
= ( sP28 @ X62 ) )
| ( $true
= ( X62 @ id @ X63 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X66: subst > term > subst > $o,X67: term] :
( ! [X68: term,X69: term] :
( ( ( X66 @ id @ X68 @ id )
!= $true )
| ( $true
= ( X66 @ id @ ( ap @ ( sub @ X68 @ id ) @ X69 ) @ id ) )
| ( $true
!= ( X66 @ id @ X69 @ id ) ) )
& ( $true
!= ( sP28 @ X66 ) )
& ( ( X66 @ id @ X67 @ id )
!= $true ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
| ( $true != sP27 ) )
& ( ( $true = sP27 )
| ( induction2 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X70: term] :
? [X71: subst > term > term] :
! [X72: subst,X73: term] :
( ( X71 @ X72 @ X73 )
= ( sub @ X70 @ ( push @ X73 @ X72 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X74: term] :
! [X75: subst > term > term] :
? [X76: subst,X77: term] :
( ( X75 @ X76 @ X77 )
!= ( sub @ X74 @ ( push @ X77 @ X76 ) ) ) )
& ( ( $true = sP25 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP25 ) )
& ( ! [X78: term] :
? [X79: subst > term > term] :
! [X80: subst,X81: term] :
( ( X79 @ X80 @ X81 )
= ( sub @ X78 @ ( push @ X81 @ X80 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X82: term] :
! [X83: subst > term > term] :
? [X84: subst,X85: term] :
( ( X83 @ X84 @ X85 )
!= ( sub @ X82 @ ( push @ X85 @ X84 ) ) ) )
& ( ( hoasapinj2 = $true )
| ? [X86: term,X87: term,X88: term,X89: term] :
( ( X86 != X88 )
& ( ( ap @ ( sub @ X89 @ id ) @ X86 )
= ( ap @ ( sub @ X87 @ id ) @ X88 ) ) ) )
& ( ! [X90: term,X91: term,X92: term,X93: term] :
( ( X90 = X92 )
| ( ( ap @ ( sub @ X93 @ id ) @ X90 )
!= ( ap @ ( sub @ X91 @ id ) @ X92 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( $true = sP21 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP21 ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ? [X94: term,X95: term,X96: term,X97: term] :
( ( X94 != X97 )
& ( ( ap @ X94 @ X96 )
= ( ap @ X97 @ X95 ) ) )
| ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ! [X99: term,X100: term,X101: term,X102: term] :
( ( ( ap @ ( sub @ X102 @ id ) @ X100 )
!= ( ap @ ( sub @ X101 @ id ) @ X99 ) )
| ( X101 = X102 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X103: term,X104: term,X105: term,X106: term] :
( ( X103 = X106 )
| ( ( ap @ X106 @ X104 )
!= ( ap @ X103 @ X105 ) ) )
& ! [X107: term] :
( ( sub @ X107 @ id )
= X107 )
& ? [X108: term,X109: term,X110: term,X111: term] :
( ( ( ap @ ( sub @ X110 @ id ) @ X108 )
= ( ap @ ( sub @ X111 @ id ) @ X109 ) )
& ( X110 != X111 ) ) ) )
& ! [X112: d_term,X113: d_term] :
( ( ( d2term @ X113 )
!= ( d2term @ X112 ) )
| ( X112 = X113 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X114: d_term] : ( d_one = X114 )
& ( pushprop_lem3v2 = $true )
& ( ! [X115: subst] :
( ( comp @ id @ X115 )
= X115 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 ) )
& ( ! [X117: subst,X118: term,X119: term > $o] :
? [X120: term > $o] :
! [X121: term] :
( ( X120 @ X121 )
= ( X119 @ ( sub @ X121 @ ( push @ X118 @ X117 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X122: subst,X123: term,X124: term > $o] :
! [X125: term > $o] :
? [X126: term] :
( ( X124 @ ( sub @ X126 @ ( push @ X123 @ X122 ) ) )
!= ( X125 @ X126 ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X127: term,X128: term,X129: term,X130: term] :
( ( ( ap @ X127 @ X130 )
!= ( ap @ X128 @ X129 ) )
| ( X129 = X130 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X131: term,X132: term,X133: term,X134: term] :
( ( ( ap @ X131 @ X134 )
= ( ap @ X132 @ X133 ) )
& ( X133 != X134 ) ) )
& ! [X135: term] :
? [X136: d_term] :
( ( d2term @ X136 )
= X135 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X137: term > $o,X138: subst,X139: term > $o,X140: term] :
( ( $true
!= ( X139 @ one ) )
& ( $true
= ( X137 @ X140 ) )
& ! [X141: term] :
( ( X139 @ X141 )
= ( X137 @ ( sub @ X141 @ ( push @ X140 @ X138 ) ) ) ) )
& ! [X142: subst,X143: term] :
( ( sub @ one @ ( push @ X143 @ X142 ) )
= X143 ) ) )
& ( ! [X144: term > $o,X145: subst,X146: term > $o,X147: term] :
( ( $true
= ( X146 @ one ) )
| ( $true
!= ( X144 @ X147 ) )
| ? [X148: term] :
( ( X144 @ ( sub @ X148 @ ( push @ X147 @ X145 ) ) )
!= ( X146 @ X148 ) ) )
| ? [X149: subst,X150: term] :
( ( sub @ one @ ( push @ X150 @ X149 ) )
!= X150 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP17 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP17 ) )
& ( ( $true = sP15 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP15 ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X151: d_subst] : ( d_id = X151 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X152: subst] :
? [X153: d_subst] :
( ( d2subst @ X153 )
= X152 )
& ( pushprop_gthm = $true )
& ( ! [X154: subst,X155: term] :
( ( comp @ sh @ ( push @ X155 @ X154 ) )
= X154 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X156: subst,X157: term] :
( ( comp @ sh @ ( push @ X157 @ X156 ) )
!= X156 ) )
& ! [X158: d_subst,X159: d_subst] :
( ( X158 = X159 )
| ( ( d2subst @ X159 )
!= ( d2subst @ X158 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X160: subst > term > subst > $o] :
! [X161: term > $o] :
? [X162: term] :
( ( X160 @ id @ X162 @ id )
!= ( X161 @ X162 ) ) )
& ( ! [X163: subst > term > subst > $o] :
? [X164: term > $o] :
! [X165: term] :
( ( X164 @ X165 )
= ( X163 @ id @ X165 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( $true = sP13 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP13 ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X166: term,X167: term,X168: subst > term > term] :
( ( ( lam @ ( X168 @ sh @ one ) )
!= ( ap @ ( sub @ X167 @ id ) @ X166 ) )
| ? [X169: subst,X170: term,X171: subst] :
( ( X168 @ ( comp @ X169 @ X171 ) @ ( sub @ X170 @ X171 ) )
!= ( sub @ ( X168 @ X169 @ X170 ) @ X171 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X172: term,X173: term,X174: subst > term > term] :
( ( ( ap @ ( sub @ X173 @ id ) @ X172 )
= ( lam @ ( X174 @ sh @ one ) ) )
& ! [X175: subst,X176: term,X177: subst] :
( ( X174 @ ( comp @ X175 @ X177 ) @ ( sub @ X176 @ X177 ) )
= ( sub @ ( X174 @ X175 @ X176 ) @ X177 ) ) ) )
& ( ( induction = $true )
| ? [X178: term,X179: term > $o] :
( ! [X180: term] :
( ( $true
= ( X179 @ ( lam @ X180 ) ) )
| ( ( X179 @ X180 )
!= $true ) )
& ( $true
!= ( sP12 @ X179 ) )
& ( ( X179 @ X178 )
!= $true )
& ! [X181: term] :
( ( $true
!= ( var @ X181 ) )
| ( $true
= ( X179 @ X181 ) ) ) ) )
& ( ! [X182: term,X183: term > $o] :
( ? [X184: term] :
( ( ( X183 @ ( lam @ X184 ) )
!= $true )
& ( ( X183 @ X184 )
= $true ) )
| ( $true
= ( sP12 @ X183 ) )
| ( $true
= ( X183 @ X182 ) )
| ? [X185: term] :
( ( $true
= ( var @ X185 ) )
& ( $true
!= ( X183 @ X185 ) ) ) )
| ( induction != $true ) )
& ( ! [X186: term > $o,X187: term,X188: subst,X189: term,X190: term > $o] :
( ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) )
| ( $true
!= ( X186 @ X189 ) ) )
| ? [X191: term,X192: subst] :
( ( sub @ one @ ( push @ X191 @ X192 ) )
!= X191 )
| ? [X193: subst,X194: term] :
( ( comp @ sh @ ( push @ X194 @ X193 ) )
!= X193 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X195: term > $o,X196: term,X197: subst,X198: term,X199: term > $o] :
( ( $true
!= ( X199 @ ( sub @ X198 @ ( push @ X196 @ X197 ) ) ) )
& ( $true
= ( X195 @ X198 ) ) )
& ! [X200: term,X201: subst] :
( ( sub @ one @ ( push @ X200 @ X201 ) )
= X200 )
& ! [X202: subst,X203: term] :
( ( comp @ sh @ ( push @ X203 @ X202 ) )
= X202 ) ) )
& ( ! [X204: subst] :
( ( comp @ X204 @ id )
= X204 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X205: subst] :
( ( comp @ X205 @ id )
!= X205 ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X206: term,X207: term > $o,X208: term > $o,X209: subst,X210: term] :
( ( $true
= ( X207 @ ( sub @ X206 @ ( push @ X210 @ X209 ) ) ) )
| ( $true
!= ( X208 @ X206 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X211: term,X212: term > $o,X213: term > $o,X214: subst,X215: term] :
( ( ( X212 @ ( sub @ X211 @ ( push @ X215 @ X214 ) ) )
!= $true )
& ( $true
= ( X213 @ X211 ) ) ) )
& ( ( hoasapinj1 = $true )
| ? [X216: term,X217: term,X218: term,X219: term] :
( ( X216 != X217 )
& ( ( ap @ ( sub @ X216 @ id ) @ X219 )
= ( ap @ ( sub @ X217 @ id ) @ X218 ) ) ) )
& ( ! [X220: term,X221: term,X222: term,X223: term] :
( ( X220 = X221 )
| ( ( ap @ ( sub @ X220 @ id ) @ X223 )
!= ( ap @ ( sub @ X221 @ id ) @ X222 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X224: term,X225: term,X226: term,X227: term] :
( ( X225 != X227 )
& ( ( ap @ ( sub @ X224 @ id ) @ X227 )
= ( ap @ ( sub @ X226 @ id ) @ X225 ) ) )
& ! [X228: term,X229: term,X230: term,X231: term] :
( ( ( ap @ X228 @ X229 )
!= ( ap @ X230 @ X231 ) )
| ( X229 = X231 ) ) ) )
& ( ! [X232: term,X233: term,X234: term,X235: term] :
( ( X233 = X235 )
| ( ( ap @ ( sub @ X234 @ id ) @ X233 )
!= ( ap @ ( sub @ X232 @ id ) @ X235 ) ) )
| ? [X236: term,X237: term,X238: term,X239: term] :
( ( ( ap @ X238 @ X239 )
= ( ap @ X236 @ X237 ) )
& ( X237 != X239 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( $true = sP11 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP11 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( $true = sP10 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP10 ) )
& ( 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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ? [X240: subst] :
( ( comp @ X240 @ id )
!= X240 )
| ? [X241: subst] :
( ( comp @ id @ X241 )
!= X241 )
| ( ! [X242: subst] :
( ( comp @ X242 @ id )
= X242 )
& ! [X243: subst] :
( ( comp @ id @ X243 )
= X243 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X244: subst] :
( ( comp @ X244 @ id )
= X244 )
& ! [X245: subst] :
( ( comp @ id @ X245 )
= X245 )
& ( ? [X246: subst] :
( ( comp @ X246 @ id )
!= X246 )
| ? [X247: subst] :
( ( comp @ id @ X247 )
!= X247 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
| ? [X248: term > $o,X249: term > $o,X250: subst,X251: term] :
( ! [X252: term] :
( ( X249 @ X252 )
= ( X248 @ ( sub @ X252 @ ( push @ X251 @ X250 ) ) ) )
& ( $true
= ( X248 @ X251 ) )
& ( $true
!= ( X249 @ one ) ) ) )
& ( ! [X253: term > $o,X254: term > $o,X255: subst,X256: term] :
( ? [X257: term] :
( ( X254 @ X257 )
!= ( X253 @ ( sub @ X257 @ ( push @ X256 @ X255 ) ) ) )
| ( $true
!= ( X253 @ X256 ) )
| ( $true
= ( X254 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ! [X258: term,X259: term] :
( ( ( sub @ X259 @ sh )
!= ( sub @ X258 @ sh ) )
| ( X258 = X259 ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X260: term,X261: term] :
( ( ( sub @ X260 @ sh )
= ( sub @ X261 @ sh ) )
& ( X260 != X261 ) ) )
& ( ! [X262: subst,X263: term] :
( ( sub @ one @ ( push @ X263 @ X262 ) )
= X263 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X264: subst,X265: term] :
( ( sub @ one @ ( push @ X265 @ X264 ) )
!= X265 ) )
& ( ! [X266: term] :
( ( sub @ X266 @ id )
= X266 )
| ? [X267: term] :
( ( sub @ X267 @ id )
!= X267 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X268: term] :
( ( sub @ X268 @ id )
!= X268 )
& ! [X269: term] :
( ( sub @ X269 @ id )
= X269 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP2 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP2 ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP0 != $true ) )
& ( ( sP0 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( substmonoid = $true )
| ? [X270: subst] :
( ( comp @ id @ X270 )
!= X270 )
| ? [X271: subst] :
( ( comp @ X271 @ id )
!= X271 ) )
& ( ( ! [X272: subst] :
( ( comp @ id @ X272 )
= X272 )
& ! [X273: subst] :
( ( comp @ X273 @ id )
= X273 ) )
| ( substmonoid != $true ) ) ),
inference(rectify,[status(thm)],[f474]) ).
thf(f474,plain,
( ( ( hoasinduction_lem3aa = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP57 )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
| ? [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ! [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
& ( ( lam @ ( X417 @ sh @ one ) )
= ( lam @ ( X416 @ sh @ one ) ) )
& ! [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
& ( ( X416 @ X418 @ X415 )
!= ( X417 @ X418 @ X415 ) ) ) )
& ( ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ? [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
!= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) )
| ? [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
!= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) ) )
| ( hoaslaminj != $true ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
| ? [X73: term] :
( ( sub @ X73 @ id )
!= X73 ) )
& ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
| ( axvarid != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X216: term] :
! [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
!= ( X217 @ sh @ one ) ) )
& ( ! [X216: term] :
? [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
= ( X217 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP48 ) )
& ( ( $true = sP48 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( $true = sP45 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP45 ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
| ? [X344: term] :
( ( sub @ X344 @ id )
!= X344 ) )
& ( ! [X344: term] :
( ( sub @ X344 @ id )
= X344 )
| ( termmset != $true ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP44 ) )
& ( ( $true = sP44 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( $true = sP39 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP39 ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X440: term,X441: term] :
( ( X440 != X441 )
& ( ( lam @ X440 )
= ( lam @ X441 ) ) ) )
& ( ( $true = sP36 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP36 ) )
& ( axapp = $true )
& ( ( $true = sP34 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP34 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X397: subst > term > subst > $o] :
? [X398: term > $o] :
! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X397: subst > term > subst > $o] :
! [X398: term > $o] :
? [X399: term] :
( ( X398 @ X399 )
!= ( X397 @ id @ X399 @ id ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X273: term > $o,X274: subst,X275: term] :
! [X276: term > $o] :
? [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
!= ( X276 @ X277 ) ) )
& ( ! [X273: term > $o,X274: subst,X275: term] :
? [X276: term > $o] :
! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ! [X49: term] :
? [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
= ( X50 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X49: term] :
! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) ) )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
!= X243 ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
= ( ap @ X136 @ X134 ) )
& ( X136 != X137 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( $true = sP33 )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP33 ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2 != $true ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
= $true )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X203 @ id @ X206 @ id ) ) )
| ( $true
= ( sP28 @ X203 ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X203: subst > term > subst > $o,X204: term] :
( ! [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
!= $true )
| ( $true
= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
| ( $true
!= ( X203 @ id @ X206 @ id ) ) )
& ( $true
!= ( sP28 @ X203 ) )
& ( $true
!= ( X203 @ id @ X204 @ id ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
| ( $true != sP27 ) )
& ( ( $true = sP27 )
| ( induction2 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X111: term] :
? [X112: subst > term > term] :
! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X111: term] :
! [X112: subst > term > term] :
? [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
!= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& ( ( $true = sP25 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP25 ) )
& ( ! [X19: term] :
? [X20: subst > term > term] :
! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X19: term] :
! [X20: subst > term > term] :
? [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
!= ( sub @ X19 @ ( push @ X22 @ X21 ) ) ) )
& ( ( hoasapinj2 = $true )
| ? [X95: term,X96: term,X97: term,X98: term] :
( ( X95 != X97 )
& ( ( ap @ ( sub @ X96 @ id ) @ X97 )
= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( $true = sP21 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP21 ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ? [X219: term,X220: term,X221: term,X222: term] :
( ( X219 != X222 )
& ( ( ap @ X222 @ X220 )
= ( ap @ X219 @ X221 ) ) )
| ? [X218: term] :
( ( sub @ X218 @ id )
!= X218 )
| ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X219: term,X220: term,X221: term,X222: term] :
( ( X219 = X222 )
| ( ( ap @ X222 @ X220 )
!= ( ap @ X219 @ X221 ) ) )
& ! [X218: term] :
( ( sub @ X218 @ id )
= X218 )
& ? [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
& ( X225 != X226 ) ) ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
!= ( d2term @ X408 ) )
| ( X407 = X408 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_lem3v2 = $true )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X70: subst] :
( ( comp @ id @ X70 )
!= X70 ) )
& ( ! [X196: subst,X197: term,X198: term > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X196: subst,X197: term,X198: term > $o] :
! [X199: term > $o] :
? [X200: term] :
( ( X199 @ X200 )
!= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
= ( ap @ X213 @ X214 ) )
& ( X214 != X215 ) ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
!= $true )
& ( $true
= ( X402 @ X405 ) )
& ! [X406: term] :
( ( X404 @ X406 )
= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
& ! [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
= X401 ) ) )
& ( ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ( $true
!= ( X402 @ X405 ) )
| ? [X406: term] :
( ( X404 @ X406 )
!= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
| ? [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
!= X401 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP17 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP17 ) )
& ( ( $true = sP15 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP15 ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( pushprop_gthm = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
!= X71 ) )
& ! [X51: d_subst,X52: d_subst] :
( ( X51 = X52 )
| ( ( d2subst @ X52 )
!= ( d2subst @ X51 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X252: subst > term > subst > $o] :
! [X253: term > $o] :
? [X254: term] :
( ( X253 @ X254 )
!= ( X252 @ id @ X254 @ id ) ) )
& ( ! [X252: subst > term > subst > $o] :
? [X253: term > $o] :
! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( $true = sP13 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP13 ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
| ? [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
!= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
& ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) ) )
& ( ( induction = $true )
| ? [X409: term,X410: term > $o] :
( ! [X411: term] :
( ( $true
= ( X410 @ ( lam @ X411 ) ) )
| ( $true
!= ( X410 @ X411 ) ) )
& ( $true
!= ( sP12 @ X410 ) )
& ( $true
!= ( X410 @ X409 ) )
& ! [X412: term] :
( ( ( var @ X412 )
!= $true )
| ( $true
= ( X410 @ X412 ) ) ) ) )
& ( ! [X409: term,X410: term > $o] :
( ? [X411: term] :
( ( $true
!= ( X410 @ ( lam @ X411 ) ) )
& ( $true
= ( X410 @ X411 ) ) )
| ( $true
= ( sP12 @ X410 ) )
| ( $true
= ( X410 @ X409 ) )
| ? [X412: term] :
( ( ( var @ X412 )
= $true )
& ( $true
!= ( X410 @ X412 ) ) ) )
| ( induction != $true ) )
& ( ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) )
| ? [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
!= X335 )
| ? [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
!= X337 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
!= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
& ( $true
= ( X339 @ X342 ) ) )
& ! [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
= X335 )
& ! [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
= X337 ) ) )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X539: subst] :
( ( comp @ X539 @ id )
!= X539 ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
!= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
& ( $true
= ( X67 @ X65 ) ) ) )
& ( ( hoasapinj1 = $true )
| ? [X37: term,X38: term,X39: term,X40: term] :
( ( X37 != X38 )
& ( ( ap @ ( sub @ X38 @ id ) @ X39 )
= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X248: term,X249: term,X250: term,X251: term] :
( ( X249 != X251 )
& ( ( ap @ ( sub @ X248 @ id ) @ X251 )
= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
& ! [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
!= ( ap @ X246 @ X247 ) )
| ( X245 = X247 ) ) ) )
& ( ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
| ? [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
= ( ap @ X246 @ X247 ) )
& ( X245 != X247 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( $true = sP11 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP11 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( $true = sP10 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP10 ) )
& ( 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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ? [X139: subst] :
( ( comp @ X139 @ id )
!= X139 )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 )
| ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
& ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
& ( ? [X141: subst] :
( ( comp @ X141 @ id )
!= X141 )
| ? [X140: subst] :
( ( comp @ id @ X140 )
!= X140 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
| ? [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
& ( $true
= ( X99 @ X102 ) )
& ( $true
!= ( X100 @ one ) ) ) )
& ( ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ? [X103: term] :
( ( X100 @ X103 )
!= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
!= ( X99 @ X102 ) )
| ( $true
= ( X100 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
= ( sub @ X256 @ sh ) )
& ( X255 != X256 ) ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
!= X75 ) )
& ( ! [X202: term] :
( ( sub @ X202 @ id )
= X202 )
| ? [X201: term] :
( ( sub @ X201 @ id )
!= X201 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X202: term] :
( ( sub @ X202 @ id )
!= X202 )
& ! [X201: term] :
( ( sub @ X201 @ id )
= X201 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP2 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP2 ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP0 != $true ) )
& ( ( sP0 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( substmonoid = $true )
| ? [X443: subst] :
( ( comp @ id @ X443 )
!= X443 )
| ? [X442: subst] :
( ( comp @ X442 @ id )
!= X442 ) )
& ( ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) )
| ( substmonoid != $true ) ) ),
inference(flattening,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ( hoasinduction_lem3aa = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP57 )
| ( hoasinduction_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
| ? [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ! [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
& ( ( lam @ ( X417 @ sh @ one ) )
= ( lam @ ( X416 @ sh @ one ) ) )
& ! [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
& ( ( X416 @ X418 @ X415 )
!= ( X417 @ X418 @ X415 ) ) ) )
& ( ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ? [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
!= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) )
| ? [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
!= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) ) )
| ( hoaslaminj != $true ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
| ? [X73: term] :
( ( sub @ X73 @ id )
!= X73 ) )
& ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
| ( axvarid != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X216: term] :
! [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
!= ( X217 @ sh @ one ) ) )
& ( ! [X216: term] :
? [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
= ( X217 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP48 ) )
& ( ( $true = sP48 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( $true = sP45 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP45 ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
| ? [X344: term] :
( ( sub @ X344 @ id )
!= X344 ) )
& ( ! [X344: term] :
( ( sub @ X344 @ id )
= X344 )
| ( termmset != $true ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP44 ) )
& ( ( $true = sP44 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( $true = sP39 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP39 ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X440: term,X441: term] :
( ( X440 != X441 )
& ( ( lam @ X440 )
= ( lam @ X441 ) ) ) )
& ( ( $true = sP36 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP36 ) )
& ( axapp = $true )
& ( ( $true = sP34 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP34 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X397: subst > term > subst > $o] :
? [X398: term > $o] :
! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X397: subst > term > subst > $o] :
! [X398: term > $o] :
? [X399: term] :
( ( X398 @ X399 )
!= ( X397 @ id @ X399 @ id ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X273: term > $o,X274: subst,X275: term] :
! [X276: term > $o] :
? [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
!= ( X276 @ X277 ) ) )
& ( ! [X273: term > $o,X274: subst,X275: term] :
? [X276: term > $o] :
! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ! [X49: term] :
? [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
= ( X50 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X49: term] :
! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) ) )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
!= X243 ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
= ( ap @ X136 @ X134 ) )
& ( X136 != X137 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( $true = sP33 )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP33 ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2 != $true ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
= $true )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X203 @ id @ X206 @ id ) ) )
| ( $true
= ( sP28 @ X203 ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X203: subst > term > subst > $o,X204: term] :
( ! [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
!= $true )
| ( $true
= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
| ( $true
!= ( X203 @ id @ X206 @ id ) ) )
& ( $true
!= ( sP28 @ X203 ) )
& ( $true
!= ( X203 @ id @ X204 @ id ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
| ( $true != sP27 ) )
& ( ( $true = sP27 )
| ( induction2 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X111: term] :
? [X112: subst > term > term] :
! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X111: term] :
! [X112: subst > term > term] :
? [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
!= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& ( ( $true = sP25 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP25 ) )
& ( ! [X19: term] :
? [X20: subst > term > term] :
! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X19: term] :
! [X20: subst > term > term] :
? [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
!= ( sub @ X19 @ ( push @ X22 @ X21 ) ) ) )
& ( ( hoasapinj2 = $true )
| ? [X95: term,X96: term,X97: term,X98: term] :
( ( X95 != X97 )
& ( ( ap @ ( sub @ X96 @ id ) @ X97 )
= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( $true = sP21 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP21 ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ? [X219: term,X220: term,X221: term,X222: term] :
( ( X219 != X222 )
& ( ( ap @ X222 @ X220 )
= ( ap @ X219 @ X221 ) ) )
| ? [X218: term] :
( ( sub @ X218 @ id )
!= X218 )
| ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X219: term,X220: term,X221: term,X222: term] :
( ( X219 = X222 )
| ( ( ap @ X222 @ X220 )
!= ( ap @ X219 @ X221 ) ) )
& ! [X218: term] :
( ( sub @ X218 @ id )
= X218 )
& ? [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
& ( X225 != X226 ) ) ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
!= ( d2term @ X408 ) )
| ( X407 = X408 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_lem3v2 = $true )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X70: subst] :
( ( comp @ id @ X70 )
!= X70 ) )
& ( ! [X196: subst,X197: term,X198: term > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X196: subst,X197: term,X198: term > $o] :
! [X199: term > $o] :
? [X200: term] :
( ( X199 @ X200 )
!= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
= ( ap @ X213 @ X214 ) )
& ( X214 != X215 ) ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
!= $true )
& ( $true
= ( X402 @ X405 ) )
& ! [X406: term] :
( ( X404 @ X406 )
= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
& ! [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
= X401 ) ) )
& ( ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ( $true
!= ( X402 @ X405 ) )
| ? [X406: term] :
( ( X404 @ X406 )
!= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
| ? [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
!= X401 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP17 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP17 ) )
& ( ( $true = sP15 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP15 ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( pushprop_gthm = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
!= X71 ) )
& ! [X51: d_subst,X52: d_subst] :
( ( X51 = X52 )
| ( ( d2subst @ X52 )
!= ( d2subst @ X51 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X252: subst > term > subst > $o] :
! [X253: term > $o] :
? [X254: term] :
( ( X253 @ X254 )
!= ( X252 @ id @ X254 @ id ) ) )
& ( ! [X252: subst > term > subst > $o] :
? [X253: term > $o] :
! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( $true = sP13 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP13 ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
| ? [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
!= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
& ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) ) )
& ( ( induction = $true )
| ? [X409: term,X410: term > $o] :
( ! [X411: term] :
( ( $true
= ( X410 @ ( lam @ X411 ) ) )
| ( $true
!= ( X410 @ X411 ) ) )
& ( $true
!= ( sP12 @ X410 ) )
& ( $true
!= ( X410 @ X409 ) )
& ! [X412: term] :
( ( ( var @ X412 )
!= $true )
| ( $true
= ( X410 @ X412 ) ) ) ) )
& ( ! [X409: term,X410: term > $o] :
( ? [X411: term] :
( ( $true
!= ( X410 @ ( lam @ X411 ) ) )
& ( $true
= ( X410 @ X411 ) ) )
| ( $true
= ( sP12 @ X410 ) )
| ( $true
= ( X410 @ X409 ) )
| ? [X412: term] :
( ( ( var @ X412 )
= $true )
& ( $true
!= ( X410 @ X412 ) ) ) )
| ( induction != $true ) )
& ( ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) )
| ? [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
!= X335 )
| ? [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
!= X337 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
!= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
& ( $true
= ( X339 @ X342 ) ) )
& ! [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
= X335 )
& ! [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
= X337 ) ) )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X539: subst] :
( ( comp @ X539 @ id )
!= X539 ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
!= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
& ( $true
= ( X67 @ X65 ) ) ) )
& ( ( hoasapinj1 = $true )
| ? [X37: term,X38: term,X39: term,X40: term] :
( ( X37 != X38 )
& ( ( ap @ ( sub @ X38 @ id ) @ X39 )
= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X248: term,X249: term,X250: term,X251: term] :
( ( X249 != X251 )
& ( ( ap @ ( sub @ X248 @ id ) @ X251 )
= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
& ! [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
!= ( ap @ X246 @ X247 ) )
| ( X245 = X247 ) ) ) )
& ( ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
| ? [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
= ( ap @ X246 @ X247 ) )
& ( X245 != X247 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( $true = sP11 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP11 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( $true = sP10 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP10 ) )
& ( 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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ? [X139: subst] :
( ( comp @ X139 @ id )
!= X139 )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 )
| ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
& ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
& ( ? [X141: subst] :
( ( comp @ X141 @ id )
!= X141 )
| ? [X140: subst] :
( ( comp @ id @ X140 )
!= X140 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
| ? [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
& ( $true
= ( X99 @ X102 ) )
& ( $true
!= ( X100 @ one ) ) ) )
& ( ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ? [X103: term] :
( ( X100 @ X103 )
!= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
!= ( X99 @ X102 ) )
| ( $true
= ( X100 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
| ( shinj != $true ) )
& ( ( shinj = $true )
| ? [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
= ( sub @ X256 @ sh ) )
& ( X255 != X256 ) ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
!= X75 ) )
& ( ! [X202: term] :
( ( sub @ X202 @ id )
= X202 )
| ? [X201: term] :
( ( sub @ X201 @ id )
!= X201 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X202: term] :
( ( sub @ X202 @ id )
!= X202 )
& ! [X201: term] :
( ( sub @ X201 @ id )
= X201 ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP2 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP2 ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP0 != $true ) )
& ( ( sP0 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( substmonoid = $true )
| ? [X443: subst] :
( ( comp @ id @ X443 )
!= X443 )
| ? [X442: subst] :
( ( comp @ X442 @ id )
!= X442 ) )
& ( ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) )
| ( substmonoid != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( hoasinduction_lem3aa = $true )
<=> ( $true = sP58 ) )
& ( ( hoasinduction_lthm = $true )
<=> ( $true = sP57 ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ? [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
!= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) )
| ? [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
!= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) ) ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X216: term] :
? [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
= ( X217 @ sh @ one ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( $true = sP48 ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( $true = sP45 )
<=> ( hoaslaminj_lthm = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
<=> ! [X344: term] :
( ( sub @ X344 @ id )
= X344 ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( $true = sP44 ) )
& ( ( $true = sP39 )
<=> ( hoasinduction = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
<=> ( laminj = $true ) )
& ( ( $true = sP36 )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( axapp = $true )
& ( ( $true = sP34 )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X397: subst > term > subst > $o] :
? [X398: term > $o] :
! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X273: term > $o,X274: subst,X275: term] :
? [X276: term > $o] :
! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) ) )
& ( ! [X49: term] :
? [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
<=> ( axscons = $true ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( $true = sP33 )
<=> ( hoasinduction_lem3a = $true ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ( $true = sP32 ) )
& ( ( hoasinduction_lem2 = $true )
<=> ( $true = sP30 ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
= $true )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X203 @ id @ X206 @ id ) ) )
| ( $true
= ( sP28 @ X203 ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
<=> ( $true = sP27 ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X111: term] :
? [X112: subst > term > term] :
! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( $true = sP25 )
<=> ( induction2_lthm = $true ) )
& ( ! [X19: term] :
? [X20: subst > term > term] :
! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ( $true = sP21 )
<=> ( induction2lem_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ? [X219: term,X220: term,X221: term,X222: term] :
( ( X219 != X222 )
& ( ( ap @ X222 @ X220 )
= ( ap @ X219 @ X221 ) ) )
| ? [X218: term] :
( ( sub @ X218 @ id )
!= X218 )
| ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
!= ( d2term @ X408 ) )
| ( X407 = X408 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_lem3v2 = $true )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ! [X196: subst,X197: term,X198: term > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( induction2lem_gthm = $true )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ( $true
!= ( X402 @ X405 ) )
| ? [X406: term] :
( ( X404 @ X406 )
!= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
| ? [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
!= X401 ) ) )
& ( ( $true = sP17 )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( $true = sP15 )
<=> ( induction2lem = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( pushprop_gthm = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ! [X51: d_subst,X52: d_subst] :
( ( X51 = X52 )
| ( ( d2subst @ X52 )
!= ( d2subst @ X51 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X252: subst > term > subst > $o] :
? [X253: term > $o] :
! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( $true = sP13 )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
| ? [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
!= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( induction = $true )
<=> ! [X409: term,X410: term > $o] :
( ? [X411: term] :
( ( $true
!= ( X410 @ ( lam @ X411 ) ) )
& ( $true
= ( X410 @ X411 ) ) )
| ( $true
= ( sP12 @ X410 ) )
| ( $true
= ( X410 @ X409 ) )
| ? [X412: term] :
( ( ( var @ X412 )
= $true )
& ( $true
!= ( X410 @ X412 ) ) ) ) )
& ( ( ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) )
| ? [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
!= X335 )
| ? [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
!= X337 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
<=> ( axidr = $true ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
| ? [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
= ( ap @ X246 @ X247 ) )
& ( X245 != X247 ) ) ) )
& ( ( $true = sP11 )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( $true = sP10 )
<=> ( hoasinduction_lthm_3 = $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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ( ? [X139: subst] :
( ( comp @ X139 @ id )
!= X139 )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 )
| ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ? [X103: term] :
( ( X100 @ X103 )
!= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
!= ( X99 @ X102 ) )
| ( $true
= ( X100 @ one ) ) ) )
& ( ( $true = sP4 )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
<=> ( shinj = $true ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ( ! [X202: term] :
( ( sub @ X202 @ id )
= X202 )
| ? [X201: term] :
( ( sub @ X201 @ id )
!= X201 ) )
<=> ( termmset_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP2 )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ( sP0 = $true ) )
& ( ( substmonoid = $true )
<=> ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) ) ) ),
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,
( ( sP0 = $true )
<=> ! [X501: term,X502: subst > term > subst > $o] :
( ? [X508: term] :
( ( $true
!= ( X502 @ id @ ( sub @ X501 @ ( push @ X508 @ id ) ) @ id ) )
& ( $true
= ( X502 @ id @ X508 @ id ) ) )
| ( ( X502 @ id @ ( lam @ ( sub @ X501 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X503: subst > term > term] :
( ! [X504: subst,X505: term,X506: subst] :
( ( X503 @ ( comp @ X506 @ X504 ) @ ( sub @ X505 @ X504 ) )
= ( sub @ ( X503 @ X506 @ X505 ) @ X504 ) )
& ! [X507: term] :
( ( $true
= ( X502 @ id @ ( X503 @ id @ X507 ) @ id ) )
| ( $true
!= ( X502 @ id @ X507 @ id ) ) )
& ( ( X502 @ id @ ( lam @ ( X503 @ sh @ one ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
! [X523: subst > term > subst > $o] :
( ( $true
= ( sP1 @ X523 ) )
<=> ? [X530: subst > term > term] :
( ( $true
!= ( X523 @ id @ ( lam @ ( X530 @ sh @ one ) ) @ id ) )
& ! [X531: subst,X532: term,X533: subst] :
( ( sub @ ( X530 @ X531 @ X532 ) @ X533 )
= ( X530 @ ( comp @ X531 @ X533 ) @ ( sub @ X532 @ X533 ) ) )
& ! [X534: term] :
( ( $true
!= ( X523 @ id @ X534 @ id ) )
| ( $true
= ( X523 @ id @ ( X530 @ id @ X534 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( $true = sP2 )
<=> ! [X523: subst > term > subst > $o,X524: term] :
( ? [X535: term,X536: subst,X537: subst,X538: subst] :
( ( $true
!= ( X523 @ X538 @ X535 @ ( comp @ X536 @ X537 ) ) )
& ( $true
= ( X523 @ ( comp @ X538 @ X536 ) @ ( sub @ X535 @ X536 ) @ X537 ) ) )
| ( $true
= ( X523 @ id @ ( lam @ X524 ) @ id ) )
| ? [X525: term] :
( ( $true
!= ( X523 @ id @ ( sub @ X524 @ ( push @ X525 @ id ) ) @ id ) )
& ( $true
= ( X523 @ id @ X525 @ id ) ) )
| ( $true
= ( sP1 @ X523 ) )
| ? [X526: subst,X527: subst,X528: subst,X529: term] :
( ( ( X523 @ ( comp @ X527 @ X526 ) @ ( sub @ X529 @ X526 ) @ X528 )
!= $true )
& ( $true
= ( X523 @ X527 @ X529 @ ( comp @ X526 @ X528 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( $true = sP3 )
<=> ? [X3: subst > term > subst > $o,X4: term] :
( ( $true
!= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: term] :
( ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X3 @ id @ X10 @ id ) ) )
& ! [X5: subst > term > term] :
( ? [X9: term] :
( ( $true
!= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) )
& ( $true
= ( X3 @ id @ X9 @ id ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) )
| ? [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
!= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
( ( $true = sP4 )
<=> ( ! [X11: subst > term > subst > $o,X12: term] :
( ? [X13: subst > term > term] :
( ( $true
!= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
& ! [X17: term] :
( ( $true
!= ( X11 @ id @ X17 @ id ) )
| ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) ) )
& ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) ) )
| ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ? [X18: term] :
( ( $true
= ( X11 @ id @ X18 @ id ) )
& ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) )
| ? [X2: term] :
( ( sub @ X2 @ id )
!= X2 )
| ( $true = sP3 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X484: subst > term > subst > $o] :
( ( $true
= ( sP5 @ X484 ) )
<=> ? [X493: term,X494: term] :
( ( $true
= ( X484 @ id @ X494 @ id ) )
& ( $true
= ( X484 @ id @ X493 @ id ) )
& ( $true
!= ( X484 @ id @ ( ap @ ( sub @ X493 @ id ) @ X494 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
! [X484: subst > term > subst > $o] :
( ( $true
= ( sP6 @ X484 ) )
<=> ? [X496: subst > term > term] :
( ! [X500: term] :
( ( $true
!= ( X484 @ id @ X500 @ id ) )
| ( $true
= ( X484 @ id @ ( X496 @ id @ X500 ) @ id ) ) )
& ( $true
!= ( X484 @ id @ ( lam @ ( X496 @ sh @ one ) ) @ id ) )
& ! [X497: term,X498: subst,X499: subst] :
( ( X496 @ ( comp @ X499 @ X498 ) @ ( sub @ X497 @ X498 ) )
= ( sub @ ( X496 @ X499 @ X497 ) @ X498 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
! [X466: term > $o] :
( ( $true
= ( sP7 @ X466 ) )
<=> ! [X467: term,X468: term] :
( ( ( X466 @ X468 )
!= $true )
| ( $true
!= ( X466 @ X467 ) )
| ( $true
= ( X466 @ ( ap @ X468 @ X467 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
( ( $true = sP8 )
<=> ! [X483: term,X484: subst > term > subst > $o] :
( ( $true
= ( X484 @ id @ X483 @ id ) )
| ( $true
= ( sP6 @ X484 ) )
| ? [X489: subst,X490: subst,X491: term,X492: subst] :
( ( $true
!= ( X484 @ ( comp @ X489 @ X492 ) @ ( sub @ X491 @ X492 ) @ X490 ) )
& ( $true
= ( X484 @ X489 @ X491 @ ( comp @ X492 @ X490 ) ) ) )
| ? [X495: term] :
( ( $true
= ( var @ ( sub @ X495 @ id ) ) )
& ( $true
!= ( X484 @ id @ X495 @ id ) ) )
| ? [X485: subst,X486: subst,X487: term,X488: subst] :
( ( $true
= ( X484 @ ( comp @ X485 @ X488 ) @ ( sub @ X487 @ X488 ) @ X486 ) )
& ( $true
!= ( X484 @ X485 @ X487 @ ( comp @ X488 @ X486 ) ) ) )
| ( $true
= ( sP5 @ X484 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
( ( sP9 = $true )
<=> ? [X473: term > $o,X474: subst > term > subst > $o,X475: term] :
( ! [X478: subst > term > term] :
( ? [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X481 @ X482 ) @ ( sub @ X480 @ X482 ) )
!= ( sub @ ( X478 @ X481 @ X480 ) @ X482 ) )
| ? [X479: term] :
( ( $true
= ( X474 @ id @ X479 @ id ) )
& ( $true
!= ( X474 @ id @ ( X478 @ id @ X479 ) @ id ) ) )
| ( $true
= ( X474 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( X473 @ ( lam @ X475 ) ) )
& ! [X476: term] :
( ( $true
= ( X473 @ ( sub @ X475 @ ( push @ X476 @ id ) ) ) )
| ( ( X473 @ X476 )
!= $true ) )
& ! [X477: term] :
( ( X474 @ id @ X477 @ id )
= ( X473 @ X477 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
( ( $true = sP10 )
<=> ( ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 )
| ? [X465: term,X466: term > $o] :
( ! [X470: term] :
( ( $true
= ( X466 @ ( lam @ X470 ) ) )
| ? [X471: term] :
( ( ( X466 @ ( sub @ X470 @ ( push @ X471 @ id ) ) )
!= $true )
& ( $true
= ( X466 @ X471 ) ) ) )
& ( $true
!= ( X466 @ X465 ) )
& ! [X469: term] :
( ( ( X466 @ X469 )
= $true )
| ( $true
!= ( var @ X469 ) ) )
& ( $true
= ( sP7 @ X466 ) ) )
| ( sP9 = $true )
| ( $true = sP8 )
| ? [X462: subst > term > subst > $o] :
! [X463: term > $o] :
? [X464: term] :
( ( X462 @ id @ X464 @ id )
!= ( X463 @ X464 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( $true = sP11 )
<=> ( ! [X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ? [X439: term] :
( ( $true
= ( X431 @ X439 ) )
& ( $true
!= ( X431 @ ( sub @ X430 @ ( push @ X439 @ id ) ) ) ) )
| ? [X438: term] :
( ( X432 @ id @ X438 @ id )
!= ( X431 @ X438 ) )
| ( $true
= ( X431 @ ( lam @ X430 ) ) )
| ? [X433: subst > term > term] :
( ! [X434: term] :
( ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( $true
= ( X432 @ id @ ( X433 @ id @ X434 ) @ id ) ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id ) )
& ! [X435: subst,X436: term,X437: subst] :
( ( X433 @ ( comp @ X437 @ X435 ) @ ( sub @ X436 @ X435 ) )
= ( sub @ ( X433 @ X437 @ X436 ) @ X435 ) ) ) )
| ? [X425: term] :
! [X426: subst > term > term] :
? [X427: term,X428: subst] :
( ( sub @ X425 @ ( push @ X427 @ X428 ) )
!= ( X426 @ X428 @ X427 ) )
| ? [X429: term] :
( ( sub @ X429 @ id )
!= X429 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
! [X410: term > $o] :
( ( $true
= ( sP12 @ X410 ) )
<=> ? [X413: term,X414: term] :
( ( $true
= ( X410 @ X414 ) )
& ( $true
= ( X410 @ X413 ) )
& ( $true
!= ( X410 @ ( ap @ X414 @ X413 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( $true = sP13 )
<=> ! [X53: subst > term > subst > $o,X54: term] :
( ? [X56: subst > term > term,X57: term] :
( ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
& ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) )
& ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) )
& ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X55: term] :
( ( $true
!= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) )
& ( $true
= ( X53 @ id @ X55 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X516: term > $o] :
( ( $true
= ( sP14 @ X516 ) )
<=> ? [X519: term,X520: term] :
( ( $true
= ( X516 @ X519 ) )
& ( $true
= ( X516 @ X520 ) )
& ( $true
!= ( X516 @ ( ap @ X520 @ X519 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
( ( $true = sP15 )
<=> ! [X515: subst,X516: term > $o,X517: term] :
( ? [X518: term] :
( ( $true
= ( var @ X518 ) )
& ( $true
!= ( X516 @ ( sub @ X518 @ X515 ) ) ) )
| ? [X521: term] :
( ! [X522: term] :
( ( $true
!= ( X516 @ X522 ) )
| ( $true
= ( X516 @ ( sub @ X521 @ ( push @ X522 @ id ) ) ) ) )
& ( $true
!= ( X516 @ ( lam @ X521 ) ) ) )
| ( $true
= ( X516 @ ( sub @ X517 @ X515 ) ) )
| ( $true
= ( sP14 @ X516 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
! [X78: subst > term > subst > $o] :
( ( $true
= ( sP16 @ X78 ) )
<=> ? [X90: subst > term > term] :
( ( $true
!= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) )
& ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
& ! [X94: term] :
( ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) )
| ( $true
!= ( X78 @ id @ X94 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
( ( $true = sP17 )
<=> ( ? [X76: term] :
( ( sub @ X76 @ id )
!= X76 )
| ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ? [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
& ( $true
!= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) )
| ( $true
= ( sP16 @ X78 ) )
| ? [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) )
& ( $true
= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ? [X89: term] :
( ( $true
= ( X79 @ X89 ) )
& ( $true
!= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ? [X80: term] :
( ( X78 @ id @ X80 @ id )
!= ( X79 @ X80 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
! [X126: term > $o] :
( ( ( sP18 @ X126 )
= $true )
<=> ? [X129: term,X130: term] :
( ( $true
= ( X126 @ X129 ) )
& ( $true
= ( X126 @ X130 ) )
& ( ( X126 @ ( ap @ X130 @ X129 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
! [X120: term > $o] :
( ( $true
= ( sP19 @ X120 ) )
<=> ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
( ( $true = sP20 )
<=> ! [X126: term > $o,X127: term,X128: subst] :
( ? [X131: term] :
( ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) )
& ( $true
!= ( X126 @ ( lam @ X131 ) ) ) )
| ? [X133: term] :
( ( $true
!= ( X126 @ ( sub @ X133 @ X128 ) ) )
& ( $true
= ( var @ X133 ) ) )
| ( ( sP18 @ X126 )
= $true )
| ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
( ( $true = sP21 )
<=> ( ? [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
!= X116 )
| ? [X120: term > $o,X121: term] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( $true
= ( X120 @ X122 ) ) )
& ( $true
!= ( X120 @ X121 ) )
& ( $true
= ( sP19 @ X120 ) )
& ! [X125: term] :
( ( $true
= ( X120 @ ( lam @ X125 ) ) )
| ( $true
!= ( X120 @ X125 ) ) ) )
| ( $true = sP20 )
| ? [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
!= X117 )
| ? [X119: subst] :
( ( comp @ X119 @ id )
!= X119 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
! [X237: term > $o] :
( ( $true
= ( sP22 @ X237 ) )
<=> ? [X239: term,X240: term] :
( ( $true
= ( X237 @ X240 ) )
& ( $true
!= ( X237 @ ( ap @ X240 @ X239 ) ) )
& ( $true
= ( X237 @ X239 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
! [X228: term > $o] :
( ( $true
= ( sP23 @ X228 ) )
<=> ! [X234: term,X235: term] :
( ( $true
= ( X228 @ ( ap @ X234 @ X235 ) ) )
| ( $true
!= ( X228 @ X235 ) )
| ( $true
!= ( X228 @ X234 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
( ( $true = sP24 )
<=> ! [X236: term,X237: term > $o] :
( ? [X238: term] :
( ( $true
= ( var @ X238 ) )
& ( $true
!= ( X237 @ X238 ) ) )
| ( $true
= ( sP22 @ X237 ) )
| ( $true
= ( X237 @ X236 ) )
| ? [X241: term] :
( ! [X242: term] :
( ( $true
!= ( X237 @ X242 ) )
| ( $true
= ( X237 @ ( sub @ X241 @ ( push @ X242 @ id ) ) ) ) )
& ( $true
!= ( X237 @ ( lam @ X241 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
( ( $true = sP25 )
<=> ( ? [X228: term > $o,X229: subst,X230: term] :
( ( $true
= ( sP23 @ X228 ) )
& ! [X232: term] :
( ? [X233: term] :
( ( $true
= ( X228 @ X233 ) )
& ( $true
!= ( X228 @ ( sub @ X232 @ ( push @ X233 @ id ) ) ) ) )
| ( $true
= ( X228 @ ( lam @ X232 ) ) ) )
& ! [X231: term] :
( ( $true
!= ( var @ X231 ) )
| ( $true
= ( X228 @ ( sub @ X231 @ X229 ) ) ) )
& ( $true
!= ( X228 @ ( sub @ X230 @ X229 ) ) ) )
| ( $true = sP24 )
| ? [X227: term] :
( ( sub @ X227 @ id )
!= X227 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
! [X105: term > $o] :
( ( $true
= ( sP26 @ X105 ) )
<=> ? [X109: term,X110: term] :
( ( $true
= ( X105 @ X110 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X110 ) ) )
& ( ( X105 @ X109 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
( ( $true = sP27 )
<=> ! [X104: term,X105: term > $o] :
( ( $true
= ( sP26 @ X105 ) )
| ? [X106: term] :
( ! [X107: term] :
( ( ( X105 @ X107 )
!= $true )
| ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) ) )
& ( $true
!= ( X105 @ ( lam @ X106 ) ) ) )
| ? [X108: term] :
( ( $true
!= ( X105 @ X108 ) )
& ( ( var @ X108 )
= $true ) )
| ( $true
= ( X105 @ X104 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
! [X203: subst > term > subst > $o] :
( ( $true
= ( sP28 @ X203 ) )
<=> ? [X207: subst > term > term] :
( ( $true
!= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) )
& ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
& ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
! [X26: subst > term > subst > $o] :
( ( $true
= ( sP29 @ X26 ) )
<=> ? [X31: term,X32: term] :
( ( $true
= ( X26 @ id @ X31 @ id ) )
& ( $true
= ( X26 @ id @ X32 @ id ) )
& ( $true
!= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( $true = sP30 )
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ? [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) )
& ( $true
!= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) ) )
| ? [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
& ( $true
!= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ( $true
!= ( X26 @ id @ X25 @ id ) )
| ( $true
= ( sP29 @ X26 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
! [X281: subst > term > subst > $o] :
( ( ( sP31 @ X281 )
= $true )
<=> ? [X282: term,X283: term] :
( ( $true
= ( X281 @ id @ X282 @ id ) )
& ( ( X281 @ id @ ( ap @ ( sub @ X283 @ id ) @ X282 ) @ id )
!= $true )
& ( $true
= ( X281 @ id @ X283 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
( ( $true = sP32 )
<=> ! [X278: term,X279: term > $o,X280: term,X281: subst > term > subst > $o] :
( ( $true
!= ( X279 @ X280 ) )
| ( $true
!= ( X279 @ X278 ) )
| ( $true
= ( X279 @ ( ap @ X278 @ X280 ) ) )
| ? [X288: term,X289: subst,X290: subst,X291: subst] :
( ( $true
!= ( X281 @ ( comp @ X289 @ X291 ) @ ( sub @ X288 @ X291 ) @ X290 ) )
& ( ( X281 @ X289 @ X288 @ ( comp @ X291 @ X290 ) )
= $true ) )
| ? [X292: term] :
( ( X279 @ X292 )
!= ( X281 @ id @ X292 @ id ) )
| ( ( sP31 @ X281 )
= $true )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X281 @ ( comp @ X284 @ X287 ) @ ( sub @ X286 @ X287 ) @ X285 ) )
& ( $true
!= ( X281 @ X284 @ X286 @ ( comp @ X287 @ X285 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
( ( $true = sP33 )
<=> ! [X41: term,X42: subst > term > subst > $o] :
( ? [X43: subst > term > term] :
( ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
& ( $true
!= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
& ! [X47: term] :
( ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) )
| ( ( X42 @ id @ X47 @ id )
!= $true ) ) )
| ? [X48: term] :
( ( $true
= ( X42 @ id @ X48 @ id ) )
& ( $true
!= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) )
| ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
( ( $true = sP34 )
<=> ! [X295: term > $o,X296: term,X297: subst > term > subst > $o] :
( ? [X304: term] :
( ( $true
!= ( X295 @ ( sub @ X296 @ ( push @ X304 @ id ) ) ) )
& ( ( X295 @ X304 )
= $true ) )
| ? [X298: subst > term > term] :
( ! [X300: subst,X301: term,X302: subst] :
( ( sub @ ( X298 @ X302 @ X301 ) @ X300 )
= ( X298 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) ) )
& ( $true
!= ( X297 @ id @ ( lam @ ( X298 @ sh @ one ) ) @ id ) )
& ! [X299: term] :
( ( ( X297 @ id @ X299 @ id )
!= $true )
| ( $true
= ( X297 @ id @ ( X298 @ id @ X299 ) @ id ) ) ) )
| ? [X303: term] :
( ( X295 @ X303 )
!= ( X297 @ id @ X303 @ id ) )
| ( $true
= ( X295 @ ( lam @ X296 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
! [X347: subst > term > subst > $o] :
( ( $true
= ( sP35 @ X347 ) )
<=> ? [X349: subst > term > term] :
( ( $true
!= ( X347 @ id @ ( lam @ ( X349 @ sh @ one ) ) @ id ) )
& ! [X351: subst,X352: subst,X353: term] :
( ( X349 @ ( comp @ X351 @ X352 ) @ ( sub @ X353 @ X352 ) )
= ( sub @ ( X349 @ X351 @ X353 ) @ X352 ) )
& ! [X350: term] :
( ( ( X347 @ id @ X350 @ id )
!= $true )
| ( $true
= ( X347 @ id @ ( X349 @ id @ X350 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
( ( $true = sP36 )
<=> ! [X345: term > $o,X346: term,X347: subst > term > subst > $o] :
( ? [X354: subst,X355: subst,X356: subst,X357: term] :
( ( ( X347 @ ( comp @ X354 @ X356 ) @ ( sub @ X357 @ X356 ) @ X355 )
= $true )
& ( $true
!= ( X347 @ X354 @ X357 @ ( comp @ X356 @ X355 ) ) ) )
| ? [X359: subst,X360: subst,X361: term,X362: subst] :
( ( $true
!= ( X347 @ ( comp @ X359 @ X360 ) @ ( sub @ X361 @ X360 ) @ X362 ) )
& ( $true
= ( X347 @ X359 @ X361 @ ( comp @ X360 @ X362 ) ) ) )
| ? [X348: term] :
( ( $true
= ( X345 @ X348 ) )
& ( ( X345 @ ( sub @ X346 @ ( push @ X348 @ id ) ) )
!= $true ) )
| ( ( X345 @ ( lam @ X346 ) )
= $true )
| ( $true
= ( sP35 @ X347 ) )
| ? [X358: term] :
( ( X345 @ X358 )
!= ( X347 @ id @ X358 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
! [X444: subst > term > subst > $o] :
( ( $true
= ( sP37 @ X444 ) )
<=> ? [X446: term,X447: term] :
( ( $true
= ( X444 @ id @ X447 @ id ) )
& ( ( X444 @ id @ ( ap @ ( sub @ X447 @ id ) @ X446 ) @ id )
!= $true )
& ( $true
= ( X444 @ id @ X446 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
! [X444: subst > term > subst > $o] :
( ( $true
= ( sP38 @ X444 ) )
<=> ? [X449: subst > term > term] :
( ! [X451: subst,X452: subst,X453: term] :
( ( sub @ ( X449 @ X452 @ X453 ) @ X451 )
= ( X449 @ ( comp @ X452 @ X451 ) @ ( sub @ X453 @ X451 ) ) )
& ! [X450: term] :
( ( $true
= ( X444 @ id @ ( X449 @ id @ X450 ) @ id ) )
| ( $true
!= ( X444 @ id @ X450 @ id ) ) )
& ( $true
!= ( X444 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
( ( $true = sP39 )
<=> ! [X444: subst > term > subst > $o,X445: term] :
( ? [X448: term] :
( ( $true
= ( var @ ( sub @ X448 @ id ) ) )
& ( $true
!= ( X444 @ id @ X448 @ id ) ) )
| ? [X458: term,X459: subst,X460: subst,X461: subst] :
( ( ( X444 @ X460 @ X458 @ ( comp @ X461 @ X459 ) )
!= $true )
& ( $true
= ( X444 @ ( comp @ X460 @ X461 ) @ ( sub @ X458 @ X461 ) @ X459 ) ) )
| ? [X454: subst,X455: subst,X456: subst,X457: term] :
( ( $true
!= ( X444 @ ( comp @ X454 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) )
& ( $true
= ( X444 @ X454 @ X457 @ ( comp @ X455 @ X456 ) ) ) )
| ( ( X444 @ id @ X445 @ id )
= $true )
| ( $true
= ( sP38 @ X444 ) )
| ( $true
= ( sP37 @ X444 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X308: term > $o] :
( ( $true
= ( sP40 @ X308 ) )
<=> ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) )
| ( $true
!= ( X308 @ X311 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
! [X326: subst > term > subst > $o] :
( ( $true
= ( sP41 @ X326 ) )
<=> ? [X330: subst > term > term] :
( ! [X331: subst,X332: subst,X333: term] :
( ( X330 @ ( comp @ X331 @ X332 ) @ ( sub @ X333 @ X332 ) )
= ( sub @ ( X330 @ X331 @ X333 ) @ X332 ) )
& ( $true
!= ( X326 @ id @ ( lam @ ( X330 @ sh @ one ) ) @ id ) )
& ! [X334: term] :
( ( $true
!= ( X326 @ id @ X334 @ id ) )
| ( $true
= ( X326 @ id @ ( X330 @ id @ X334 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
( ( sP42 = $true )
<=> ? [X316: term,X317: term > $o,X318: subst > term > subst > $o] :
( ! [X325: term] :
( ( $true
= ( X317 @ ( sub @ X316 @ ( push @ X325 @ id ) ) ) )
| ( $true
!= ( X317 @ X325 ) ) )
& ! [X320: subst > term > term] :
( ? [X324: term] :
( ( $true
!= ( X318 @ id @ ( X320 @ id @ X324 ) @ id ) )
& ( $true
= ( X318 @ id @ X324 @ id ) ) )
| ( $true
= ( X318 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id ) )
| ? [X321: subst,X322: subst,X323: term] :
( ( sub @ ( X320 @ X321 @ X323 ) @ X322 )
!= ( X320 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) )
& ( ( X317 @ ( lam @ X316 ) )
!= $true )
& ! [X319: term] :
( ( X318 @ id @ X319 @ id )
= ( X317 @ X319 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
( ( $true = sP43 )
<=> ? [X308: term > $o,X309: term] :
( ! [X313: term] :
( ( $true
= ( X308 @ ( lam @ X313 ) ) )
| ? [X314: term] :
( ( $true
= ( X308 @ X314 ) )
& ( $true
!= ( X308 @ ( sub @ X313 @ ( push @ X314 @ id ) ) ) ) ) )
& ( $true
= ( sP40 @ X308 ) )
& ! [X310: term] :
( ( $true
= ( X308 @ X310 ) )
| ( ( var @ X310 )
!= $true ) )
& ( $true
!= ( X308 @ X309 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
( ( $true = sP44 )
<=> ( ? [X305: subst > term > subst > $o] :
! [X306: term > $o] :
? [X307: term] :
( ( X306 @ X307 )
!= ( X305 @ id @ X307 @ id ) )
| ? [X315: term] :
( ( sub @ X315 @ id )
!= X315 )
| ( sP42 = $true )
| ! [X326: subst > term > subst > $o,X327: term] :
( ? [X328: term,X329: term] :
( ( $true
= ( X326 @ id @ X329 @ id ) )
& ( $true
= ( X326 @ id @ X328 @ id ) )
& ( $true
!= ( X326 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id ) ) )
| ( $true
= ( sP41 @ X326 ) )
| ( $true
= ( X326 @ id @ X327 @ id ) ) )
| ( $true = sP43 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
( ( $true = sP45 )
<=> ( ? [X261: term,X262: term] :
( ( X261 != X262 )
& ( ( lam @ X262 )
= ( lam @ X261 ) ) )
| ? [X257: term,X258: subst] :
( ( sub @ one @ ( push @ X257 @ X258 ) )
!= X257 )
| ? [X259: term,X260: subst] :
( ( comp @ sh @ ( push @ X259 @ X260 ) )
!= X260 )
| ! [X263: subst > term > term,X264: term,X265: subst,X266: subst > term > term] :
( ( ( lam @ ( X266 @ sh @ one ) )
!= ( lam @ ( X263 @ sh @ one ) ) )
| ? [X267: subst,X268: term,X269: subst] :
( ( sub @ ( X263 @ X269 @ X268 ) @ X267 )
!= ( X263 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) )
| ( ( X263 @ X265 @ X264 )
= ( X266 @ X265 @ X264 ) )
| ? [X270: subst,X271: term,X272: subst] :
( ( sub @ ( X266 @ X270 @ X271 ) @ X272 )
!= ( X266 @ ( comp @ X270 @ X272 ) @ ( sub @ X271 @ X272 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
! [X372: subst > term > subst > $o] :
( ( $true
= ( sP46 @ X372 ) )
<=> ? [X379: subst > term > term] :
( ( $true
!= ( X372 @ id @ ( lam @ ( X379 @ sh @ one ) ) @ id ) )
& ! [X380: term] :
( ( $true
!= ( X372 @ id @ X380 @ id ) )
| ( $true
= ( X372 @ id @ ( X379 @ id @ X380 ) @ id ) ) )
& ! [X381: term,X382: subst,X383: subst] :
( ( X379 @ ( comp @ X382 @ X383 ) @ ( sub @ X381 @ X383 ) )
= ( sub @ ( X379 @ X382 @ X381 ) @ X383 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
( ( $true = sP47 )
<=> ? [X364: term,X365: subst > term > subst > $o] :
( ! [X366: subst > term > term] :
( ? [X367: term,X368: subst,X369: subst] :
( ( X366 @ ( comp @ X369 @ X368 ) @ ( sub @ X367 @ X368 ) )
!= ( sub @ ( X366 @ X369 @ X367 ) @ X368 ) )
| ? [X370: term] :
( ( $true
!= ( X365 @ id @ ( X366 @ id @ X370 ) @ id ) )
& ( $true
= ( X365 @ id @ X370 @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id ) ) )
& ! [X371: term] :
( ( $true
!= ( X365 @ id @ X371 @ id ) )
| ( $true
= ( X365 @ id @ ( sub @ X364 @ ( push @ X371 @ id ) ) @ id ) ) )
& ( $true
!= ( X365 @ id @ ( lam @ ( sub @ X364 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
( ( $true = sP48 )
<=> ( ( $true = sP47 )
| ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 )
| ! [X372: subst > term > subst > $o,X373: term] :
( ( $true
= ( sP46 @ X372 ) )
| ? [X384: subst,X385: subst,X386: term,X387: subst] :
( ( $true
= ( X372 @ ( comp @ X387 @ X384 ) @ ( sub @ X386 @ X384 ) @ X385 ) )
& ( ( X372 @ X387 @ X386 @ ( comp @ X384 @ X385 ) )
!= $true ) )
| ( $true
= ( X372 @ id @ ( lam @ X373 ) @ id ) )
| ? [X374: subst,X375: subst,X376: subst,X377: term] :
( ( $true
= ( X372 @ X376 @ X377 @ ( comp @ X374 @ X375 ) ) )
& ( ( X372 @ ( comp @ X376 @ X374 ) @ ( sub @ X377 @ X374 ) @ X375 )
!= $true ) )
| ? [X378: term] :
( ( $true
= ( X372 @ id @ X378 @ id ) )
& ( $true
!= ( X372 @ id @ ( sub @ X373 @ ( push @ X378 @ id ) ) @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
! [X149: subst > term > subst > $o] :
( ( $true
= ( sP49 @ X149 ) )
<=> ! [X156: term,X157: term] :
( ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) )
| ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
! [X162: subst > term > subst > $o] :
( ( ( sP50 @ X162 )
= $true )
<=> ! [X173: subst > term > term] :
( ? [X174: term] :
( ( $true
= ( X162 @ id @ X174 @ id ) )
& ( $true
!= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) ) )
| ? [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
!= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
! [X179: subst > term > subst > $o] :
( ( $true
= ( sP51 @ X179 ) )
<=> ? [X191: subst > term > term] :
( ! [X195: term] :
( ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) )
| ( $true
!= ( X179 @ id @ X195 @ id ) ) )
& ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
!= $true )
& ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
! [X179: subst > term > subst > $o] :
( ( $true
= ( sP52 @ X179 ) )
<=> ? [X181: term,X182: term] :
( ( $true
= ( X179 @ id @ X181 @ id ) )
& ( ( X179 @ id @ X182 @ id )
= $true )
& ( $true
!= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
! [X142: term > $o] :
( ( $true
= ( sP53 @ X142 ) )
<=> ! [X145: term,X146: term] :
( ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) )
| ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
( ( $true = sP54 )
<=> ? [X162: subst > term > subst > $o,X163: term] :
( ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) )
| ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) ) )
& ( $true
!= ( X162 @ id @ ( lam @ X163 ) @ id ) )
& ( ( sP50 @ X162 )
= $true )
& ! [X164: term] :
( ( $true
!= ( X162 @ id @ X164 @ id ) )
| ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) ) )
& ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
( ( $true = sP55 )
<=> ! [X178: term,X179: subst > term > subst > $o] :
( ? [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
!= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) )
& ( $true
= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) ) )
| ( $true
= ( sP52 @ X179 ) )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
!= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) )
& ( $true
= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) ) )
| ( $true
= ( sP51 @ X179 ) )
| ? [X180: term] :
( ( $true
= ( var @ ( sub @ X180 @ id ) ) )
& ( $true
!= ( X179 @ id @ X180 @ id ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( $true = sP56 )
<=> ? [X149: subst > term > subst > $o,X150: term,X151: term] :
( ( $true
= ( sP49 @ X149 ) )
& ( $true
= ( X149 @ id @ X151 @ id ) )
& ( $true
!= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
& ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
& ( $true
= ( X149 @ id @ X150 @ id ) )
& ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true )
| ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
( ( $true = sP57 )
<=> ( ? [X142: term > $o,X143: term] :
( ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
& ! [X147: term] :
( ( $true
= ( X142 @ ( lam @ X147 ) ) )
| ? [X148: term] :
( ( $true
= ( X142 @ X148 ) )
& ( $true
!= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) ) ) )
& ( $true
= ( sP53 @ X142 ) )
& ( $true
!= ( X142 @ X143 ) ) )
| ( $true = sP55 )
| ( $true = sP54 )
| ( $true = sP56 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( $true = sP58 )
<=> ! [X389: term,X390: subst > term > subst > $o] :
( ? [X391: term] :
( ( $true
= ( X390 @ id @ X391 @ id ) )
& ( ( X390 @ id @ ( sub @ X389 @ ( push @ X391 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X390 @ id @ ( lam @ ( sub @ X389 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X392: subst > term > term] :
( ( $true
!= ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
& ! [X396: term] :
( ( $true
= ( X390 @ id @ ( X392 @ id @ X396 ) @ id ) )
| ( $true
!= ( X390 @ id @ X396 @ id ) ) )
& ! [X393: subst,X394: term,X395: subst] :
( ( X392 @ ( comp @ X395 @ X393 ) @ ( sub @ X394 @ X393 ) )
= ( sub @ ( X392 @ X395 @ X394 ) @ X393 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( ( hoasinduction_lem3aa = $true )
<=> ! [X389: term,X390: subst > term > subst > $o] :
( ? [X391: term] :
( ( $true
= ( X390 @ id @ X391 @ id ) )
& ( ( X390 @ id @ ( sub @ X389 @ ( push @ X391 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X390 @ id @ ( lam @ ( sub @ X389 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X392: subst > term > term] :
( ( $true
!= ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
& ! [X396: term] :
( ( $true
= ( X390 @ id @ ( X392 @ id @ X396 ) @ id ) )
| ( $true
!= ( X390 @ id @ X396 @ id ) ) )
& ! [X393: subst,X394: term,X395: subst] :
( ( X392 @ ( comp @ X395 @ X393 ) @ ( sub @ X394 @ X393 ) )
= ( sub @ ( X392 @ X395 @ X394 ) @ X393 ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ? [X142: term > $o,X143: term] :
( ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
& ! [X147: term] :
( ( $true
= ( X142 @ ( lam @ X147 ) ) )
| ? [X148: term] :
( ( $true
= ( X142 @ X148 ) )
& ( $true
!= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) ) ) )
& ! [X145: term,X146: term] :
( ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) )
| ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) ) )
& ( $true
!= ( X142 @ X143 ) ) )
| ! [X178: term,X179: subst > term > subst > $o] :
( ? [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
!= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) )
& ( $true
= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) ) )
| ? [X181: term,X182: term] :
( ( $true
= ( X179 @ id @ X181 @ id ) )
& ( ( X179 @ id @ X182 @ id )
= $true )
& ( $true
!= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) ) )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
!= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) )
& ( $true
= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) ) )
| ? [X191: subst > term > term] :
( ! [X195: term] :
( ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) )
| ( $true
!= ( X179 @ id @ X195 @ id ) ) )
& ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
!= $true )
& ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) ) )
| ? [X180: term] :
( ( $true
= ( var @ ( sub @ X180 @ id ) ) )
& ( $true
!= ( X179 @ id @ X180 @ id ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true ) )
| ? [X162: subst > term > subst > $o,X163: term] :
( ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) )
| ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) ) )
& ( $true
!= ( X162 @ id @ ( lam @ X163 ) @ id ) )
& ! [X173: subst > term > term] :
( ? [X174: term] :
( ( $true
= ( X162 @ id @ X174 @ id ) )
& ( $true
!= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) ) )
| ? [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
!= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) )
& ! [X164: term] :
( ( $true
!= ( X162 @ id @ X164 @ id ) )
| ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) ) )
& ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) ) )
| ? [X149: subst > term > subst > $o,X150: term,X151: term] :
( ! [X156: term,X157: term] :
( ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) )
| ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) ) )
& ( $true
= ( X149 @ id @ X151 @ id ) )
& ( $true
!= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
& ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
& ( $true
= ( X149 @ id @ X150 @ id ) )
& ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true )
| ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) ) ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ? [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
!= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) )
| ? [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
!= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) ) ) )
& ( lamnotap != $true )
& ( apnotvar = $true )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X216: term] :
? [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
= ( X217 @ sh @ one ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ? [X364: term,X365: subst > term > subst > $o] :
( ! [X366: subst > term > term] :
( ? [X367: term,X368: subst,X369: subst] :
( ( X366 @ ( comp @ X369 @ X368 ) @ ( sub @ X367 @ X368 ) )
!= ( sub @ ( X366 @ X369 @ X367 ) @ X368 ) )
| ? [X370: term] :
( ( $true
!= ( X365 @ id @ ( X366 @ id @ X370 ) @ id ) )
& ( $true
= ( X365 @ id @ X370 @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id ) ) )
& ! [X371: term] :
( ( $true
!= ( X365 @ id @ X371 @ id ) )
| ( $true
= ( X365 @ id @ ( sub @ X364 @ ( push @ X371 @ id ) ) @ id ) ) )
& ( $true
!= ( X365 @ id @ ( lam @ ( sub @ X364 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 )
| ! [X372: subst > term > subst > $o,X373: term] :
( ? [X379: subst > term > term] :
( ( $true
!= ( X372 @ id @ ( lam @ ( X379 @ sh @ one ) ) @ id ) )
& ! [X380: term] :
( ( $true
!= ( X372 @ id @ X380 @ id ) )
| ( $true
= ( X372 @ id @ ( X379 @ id @ X380 ) @ id ) ) )
& ! [X381: term,X382: subst,X383: subst] :
( ( X379 @ ( comp @ X382 @ X383 ) @ ( sub @ X381 @ X383 ) )
= ( sub @ ( X379 @ X382 @ X381 ) @ X383 ) ) )
| ? [X384: subst,X385: subst,X386: term,X387: subst] :
( ( $true
= ( X372 @ ( comp @ X387 @ X384 ) @ ( sub @ X386 @ X384 ) @ X385 ) )
& ( ( X372 @ X387 @ X386 @ ( comp @ X384 @ X385 ) )
!= $true ) )
| ( $true
= ( X372 @ id @ ( lam @ X373 ) @ id ) )
| ? [X374: subst,X375: subst,X376: subst,X377: term] :
( ( $true
= ( X372 @ X376 @ X377 @ ( comp @ X374 @ X375 ) ) )
& ( ( X372 @ ( comp @ X376 @ X374 ) @ ( sub @ X377 @ X374 ) @ X375 )
!= $true ) )
| ? [X378: term] :
( ( $true
= ( X372 @ id @ X378 @ id ) )
& ( $true
!= ( X372 @ id @ ( sub @ X373 @ ( push @ X378 @ id ) ) @ id ) ) ) ) ) )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( ? [X261: term,X262: term] :
( ( X261 != X262 )
& ( ( lam @ X262 )
= ( lam @ X261 ) ) )
| ? [X257: term,X258: subst] :
( ( sub @ one @ ( push @ X257 @ X258 ) )
!= X257 )
| ? [X259: term,X260: subst] :
( ( comp @ sh @ ( push @ X259 @ X260 ) )
!= X260 )
| ! [X263: subst > term > term,X264: term,X265: subst,X266: subst > term > term] :
( ( ( lam @ ( X266 @ sh @ one ) )
!= ( lam @ ( X263 @ sh @ one ) ) )
| ? [X267: subst,X268: term,X269: subst] :
( ( sub @ ( X263 @ X269 @ X268 ) @ X267 )
!= ( X263 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) )
| ( ( X263 @ X265 @ X264 )
= ( X266 @ X265 @ X264 ) )
| ? [X270: subst,X271: term,X272: subst] :
( ( sub @ ( X266 @ X270 @ X271 ) @ X272 )
!= ( X266 @ ( comp @ X270 @ X272 ) @ ( sub @ X271 @ X272 ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( termmset = $true )
<=> ! [X344: term] :
( ( sub @ X344 @ id )
= X344 ) )
& ( axassoc = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ? [X305: subst > term > subst > $o] :
! [X306: term > $o] :
? [X307: term] :
( ( X306 @ X307 )
!= ( X305 @ id @ X307 @ id ) )
| ? [X315: term] :
( ( sub @ X315 @ id )
!= X315 )
| ? [X316: term,X317: term > $o,X318: subst > term > subst > $o] :
( ! [X325: term] :
( ( $true
= ( X317 @ ( sub @ X316 @ ( push @ X325 @ id ) ) ) )
| ( $true
!= ( X317 @ X325 ) ) )
& ! [X320: subst > term > term] :
( ? [X324: term] :
( ( $true
!= ( X318 @ id @ ( X320 @ id @ X324 ) @ id ) )
& ( $true
= ( X318 @ id @ X324 @ id ) ) )
| ( $true
= ( X318 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id ) )
| ? [X321: subst,X322: subst,X323: term] :
( ( sub @ ( X320 @ X321 @ X323 ) @ X322 )
!= ( X320 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) )
& ( ( X317 @ ( lam @ X316 ) )
!= $true )
& ! [X319: term] :
( ( X318 @ id @ X319 @ id )
= ( X317 @ X319 ) ) )
| ! [X326: subst > term > subst > $o,X327: term] :
( ? [X328: term,X329: term] :
( ( $true
= ( X326 @ id @ X329 @ id ) )
& ( $true
= ( X326 @ id @ X328 @ id ) )
& ( $true
!= ( X326 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id ) ) )
| ? [X330: subst > term > term] :
( ! [X331: subst,X332: subst,X333: term] :
( ( X330 @ ( comp @ X331 @ X332 ) @ ( sub @ X333 @ X332 ) )
= ( sub @ ( X330 @ X331 @ X333 ) @ X332 ) )
& ( $true
!= ( X326 @ id @ ( lam @ ( X330 @ sh @ one ) ) @ id ) )
& ! [X334: term] :
( ( $true
!= ( X326 @ id @ X334 @ id ) )
| ( $true
= ( X326 @ id @ ( X330 @ id @ X334 ) @ id ) ) ) )
| ( $true
= ( X326 @ id @ X327 @ id ) ) )
| ? [X308: term > $o,X309: term] :
( ! [X313: term] :
( ( $true
= ( X308 @ ( lam @ X313 ) ) )
| ? [X314: term] :
( ( $true
= ( X308 @ X314 ) )
& ( $true
!= ( X308 @ ( sub @ X313 @ ( push @ X314 @ id ) ) ) ) ) )
& ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) )
| ( $true
!= ( X308 @ X311 ) ) )
& ! [X310: term] :
( ( $true
= ( X308 @ X310 ) )
| ( ( var @ X310 )
!= $true ) )
& ( $true
!= ( X308 @ X309 ) ) ) ) )
& ( ! [X444: subst > term > subst > $o,X445: term] :
( ? [X448: term] :
( ( $true
= ( var @ ( sub @ X448 @ id ) ) )
& ( $true
!= ( X444 @ id @ X448 @ id ) ) )
| ? [X458: term,X459: subst,X460: subst,X461: subst] :
( ( ( X444 @ X460 @ X458 @ ( comp @ X461 @ X459 ) )
!= $true )
& ( $true
= ( X444 @ ( comp @ X460 @ X461 ) @ ( sub @ X458 @ X461 ) @ X459 ) ) )
| ? [X454: subst,X455: subst,X456: subst,X457: term] :
( ( $true
!= ( X444 @ ( comp @ X454 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) )
& ( $true
= ( X444 @ X454 @ X457 @ ( comp @ X455 @ X456 ) ) ) )
| ( ( X444 @ id @ X445 @ id )
= $true )
| ? [X449: subst > term > term] :
( ! [X451: subst,X452: subst,X453: term] :
( ( sub @ ( X449 @ X452 @ X453 ) @ X451 )
= ( X449 @ ( comp @ X452 @ X451 ) @ ( sub @ X453 @ X451 ) ) )
& ! [X450: term] :
( ( $true
= ( X444 @ id @ ( X449 @ id @ X450 ) @ id ) )
| ( $true
!= ( X444 @ id @ X450 @ id ) ) )
& ( $true
!= ( X444 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id ) ) )
| ? [X446: term,X447: term] :
( ( $true
= ( X444 @ id @ X447 @ id ) )
& ( ( X444 @ id @ ( ap @ ( sub @ X447 @ id ) @ X446 ) @ id )
!= $true )
& ( $true
= ( X444 @ id @ X446 @ id ) ) ) )
<=> ( hoasinduction = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
<=> ( laminj = $true ) )
& ( ! [X345: term > $o,X346: term,X347: subst > term > subst > $o] :
( ? [X354: subst,X355: subst,X356: subst,X357: term] :
( ( ( X347 @ ( comp @ X354 @ X356 ) @ ( sub @ X357 @ X356 ) @ X355 )
= $true )
& ( $true
!= ( X347 @ X354 @ X357 @ ( comp @ X356 @ X355 ) ) ) )
| ? [X359: subst,X360: subst,X361: term,X362: subst] :
( ( $true
!= ( X347 @ ( comp @ X359 @ X360 ) @ ( sub @ X361 @ X360 ) @ X362 ) )
& ( $true
= ( X347 @ X359 @ X361 @ ( comp @ X360 @ X362 ) ) ) )
| ? [X348: term] :
( ( $true
= ( X345 @ X348 ) )
& ( ( X345 @ ( sub @ X346 @ ( push @ X348 @ id ) ) )
!= $true ) )
| ( ( X345 @ ( lam @ X346 ) )
= $true )
| ? [X349: subst > term > term] :
( ( $true
!= ( X347 @ id @ ( lam @ ( X349 @ sh @ one ) ) @ id ) )
& ! [X351: subst,X352: subst,X353: term] :
( ( X349 @ ( comp @ X351 @ X352 ) @ ( sub @ X353 @ X352 ) )
= ( sub @ ( X349 @ X351 @ X353 ) @ X352 ) )
& ! [X350: term] :
( ( ( X347 @ id @ X350 @ id )
!= $true )
| ( $true
= ( X347 @ id @ ( X349 @ id @ X350 ) @ id ) ) ) )
| ? [X358: term] :
( ( X345 @ X358 )
!= ( X347 @ id @ X358 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( axapp = $true )
& ( ! [X295: term > $o,X296: term,X297: subst > term > subst > $o] :
( ? [X304: term] :
( ( $true
!= ( X295 @ ( sub @ X296 @ ( push @ X304 @ id ) ) ) )
& ( ( X295 @ X304 )
= $true ) )
| ? [X298: subst > term > term] :
( ! [X300: subst,X301: term,X302: subst] :
( ( sub @ ( X298 @ X302 @ X301 ) @ X300 )
= ( X298 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) ) )
& ( $true
!= ( X297 @ id @ ( lam @ ( X298 @ sh @ one ) ) @ id ) )
& ! [X299: term] :
( ( ( X297 @ id @ X299 @ id )
!= $true )
| ( $true
= ( X297 @ id @ ( X298 @ id @ X299 ) @ id ) ) ) )
| ? [X303: term] :
( ( X295 @ X303 )
!= ( X297 @ id @ X303 @ id ) )
| ( $true
= ( X295 @ ( lam @ X296 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X397: subst > term > subst > $o] :
? [X398: term > $o] :
! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X273: term > $o,X274: subst,X275: term] :
? [X276: term > $o] :
! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) ) )
& ( ! [X49: term] :
? [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
<=> ( axscons = $true ) )
& ( induction2_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasapnotvar = $true )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= sh )
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ? [X43: subst > term > term] :
( ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
& ( $true
!= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
& ! [X47: term] :
( ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) )
| ( ( X42 @ id @ X47 @ id )
!= $true ) ) )
| ? [X48: term] :
( ( $true
= ( X42 @ id @ X48 @ id ) )
& ( $true
!= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) )
| ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( axvarshift = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X278: term,X279: term > $o,X280: term,X281: subst > term > subst > $o] :
( ( $true
!= ( X279 @ X280 ) )
| ( $true
!= ( X279 @ X278 ) )
| ( $true
= ( X279 @ ( ap @ X278 @ X280 ) ) )
| ? [X288: term,X289: subst,X290: subst,X291: subst] :
( ( $true
!= ( X281 @ ( comp @ X289 @ X291 ) @ ( sub @ X288 @ X291 ) @ X290 ) )
& ( ( X281 @ X289 @ X288 @ ( comp @ X291 @ X290 ) )
= $true ) )
| ? [X292: term] :
( ( X279 @ X292 )
!= ( X281 @ id @ X292 @ id ) )
| ? [X282: term,X283: term] :
( ( $true
= ( X281 @ id @ X282 @ id ) )
& ( ( X281 @ id @ ( ap @ ( sub @ X283 @ id ) @ X282 ) @ id )
!= $true )
& ( $true
= ( X281 @ id @ X283 @ id ) ) )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X281 @ ( comp @ X284 @ X287 ) @ ( sub @ X286 @ X287 ) @ X285 ) )
& ( $true
!= ( X281 @ X284 @ X286 @ ( comp @ X287 @ X285 ) ) ) ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ? [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) )
& ( $true
!= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) ) )
| ? [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
& ( $true
!= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ( $true
!= ( X26 @ id @ X25 @ id ) )
| ? [X31: term,X32: term] :
( ( $true
= ( X26 @ id @ X31 @ id ) )
& ( $true
= ( X26 @ id @ X32 @ id ) )
& ( $true
!= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) ) ) ) )
& ( hoasinduction_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
= $true )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X203 @ id @ X206 @ id ) ) )
| ? [X207: subst > term > term] :
( ( $true
!= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) )
& ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
& ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( induction2 = $true )
<=> ! [X104: term,X105: term > $o] :
( ? [X109: term,X110: term] :
( ( $true
= ( X105 @ X110 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X110 ) ) )
& ( ( X105 @ X109 )
= $true ) )
| ? [X106: term] :
( ! [X107: term] :
( ( ( X105 @ X107 )
!= $true )
| ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) ) )
& ( $true
!= ( X105 @ ( lam @ X106 ) ) ) )
| ? [X108: term] :
( ( $true
!= ( X105 @ X108 ) )
& ( ( var @ X108 )
= $true ) )
| ( $true
= ( X105 @ X104 ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X111: term] :
? [X112: subst > term > term] :
! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( ? [X228: term > $o,X229: subst,X230: term] :
( ! [X234: term,X235: term] :
( ( $true
= ( X228 @ ( ap @ X234 @ X235 ) ) )
| ( $true
!= ( X228 @ X235 ) )
| ( $true
!= ( X228 @ X234 ) ) )
& ! [X232: term] :
( ? [X233: term] :
( ( $true
= ( X228 @ X233 ) )
& ( $true
!= ( X228 @ ( sub @ X232 @ ( push @ X233 @ id ) ) ) ) )
| ( $true
= ( X228 @ ( lam @ X232 ) ) ) )
& ! [X231: term] :
( ( $true
!= ( var @ X231 ) )
| ( $true
= ( X228 @ ( sub @ X231 @ X229 ) ) ) )
& ( $true
!= ( X228 @ ( sub @ X230 @ X229 ) ) ) )
| ! [X236: term,X237: term > $o] :
( ? [X238: term] :
( ( $true
= ( var @ X238 ) )
& ( $true
!= ( X237 @ X238 ) ) )
| ? [X239: term,X240: term] :
( ( $true
= ( X237 @ X240 ) )
& ( $true
!= ( X237 @ ( ap @ X240 @ X239 ) ) )
& ( $true
= ( X237 @ X239 ) ) )
| ( $true
= ( X237 @ X236 ) )
| ? [X241: term] :
( ! [X242: term] :
( ( $true
!= ( X237 @ X242 ) )
| ( $true
= ( X237 @ ( sub @ X241 @ ( push @ X242 @ id ) ) ) ) )
& ( $true
!= ( X237 @ ( lam @ X241 ) ) ) ) )
| ? [X227: term] :
( ( sub @ X227 @ id )
!= X227 ) )
<=> ( induction2_lthm = $true ) )
& ( ! [X19: term] :
? [X20: subst > term > term] :
! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ( ? [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
!= X116 )
| ? [X120: term > $o,X121: term] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( $true
= ( X120 @ X122 ) ) )
& ( $true
!= ( X120 @ X121 ) )
& ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) )
& ! [X125: term] :
( ( $true
= ( X120 @ ( lam @ X125 ) ) )
| ( $true
!= ( X120 @ X125 ) ) ) )
| ! [X126: term > $o,X127: term,X128: subst] :
( ? [X131: term] :
( ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) )
& ( $true
!= ( X126 @ ( lam @ X131 ) ) ) )
| ? [X133: term] :
( ( $true
!= ( X126 @ ( sub @ X133 @ X128 ) ) )
& ( $true
= ( var @ X133 ) ) )
| ? [X129: term,X130: term] :
( ( $true
= ( X126 @ X129 ) )
& ( $true
= ( X126 @ X130 ) )
& ( ( X126 @ ( ap @ X130 @ X129 ) )
!= $true ) )
| ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) ) )
| ? [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
!= X117 )
| ? [X119: subst] :
( ( comp @ X119 @ id )
!= X119 ) )
<=> ( induction2lem_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ? [X219: term,X220: term,X221: term,X222: term] :
( ( X219 != X222 )
& ( ( ap @ X222 @ X220 )
= ( ap @ X219 @ X221 ) ) )
| ? [X218: term] :
( ( sub @ X218 @ id )
!= X218 )
| ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
!= ( d2term @ X408 ) )
| ( X407 = X408 ) )
& ( hoasapinj1_gthm = $true )
& ( lamnotvar = $true )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_lem3v2 = $true )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ! [X196: subst,X197: term,X198: term > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( induction2lem_gthm = $true )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( pushprop = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ( $true
!= ( X402 @ X405 ) )
| ? [X406: term] :
( ( X404 @ X406 )
!= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
| ? [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
!= X401 ) ) )
& ( ( ? [X76: term] :
( ( sub @ X76 @ id )
!= X76 )
| ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ? [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
& ( $true
!= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) )
| ? [X90: subst > term > term] :
( ( $true
!= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) )
& ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
& ! [X94: term] :
( ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) )
| ( $true
!= ( X78 @ id @ X94 @ id ) ) ) )
| ? [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) )
& ( $true
= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ? [X89: term] :
( ( $true
= ( X79 @ X89 ) )
& ( $true
!= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ? [X80: term] :
( ( X78 @ id @ X80 @ id )
!= ( X79 @ X80 ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X515: subst,X516: term > $o,X517: term] :
( ? [X518: term] :
( ( $true
= ( var @ X518 ) )
& ( $true
!= ( X516 @ ( sub @ X518 @ X515 ) ) ) )
| ? [X521: term] :
( ! [X522: term] :
( ( $true
!= ( X516 @ X522 ) )
| ( $true
= ( X516 @ ( sub @ X521 @ ( push @ X522 @ id ) ) ) ) )
& ( $true
!= ( X516 @ ( lam @ X521 ) ) ) )
| ( $true
= ( X516 @ ( sub @ X517 @ X515 ) ) )
| ? [X519: term,X520: term] :
( ( $true
= ( X516 @ X519 ) )
& ( $true
= ( X516 @ X520 ) )
& ( $true
!= ( X516 @ ( ap @ X520 @ X519 ) ) ) ) )
<=> ( induction2lem = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( axmap = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( pushprop_gthm = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ! [X51: d_subst,X52: d_subst] :
( ( X51 = X52 )
| ( ( d2subst @ X52 )
!= ( d2subst @ X51 ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X252: subst > term > subst > $o] :
? [X253: term > $o] :
! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ! [X53: subst > term > subst > $o,X54: term] :
( ? [X56: subst > term > term,X57: term] :
( ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
& ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) )
& ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) )
& ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X55: term] :
( ( $true
!= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) )
& ( $true
= ( X53 @ id @ X55 @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( axabs = $true )
& ( hoaslaminj_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
| ? [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
!= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( induction = $true )
<=> ! [X409: term,X410: term > $o] :
( ? [X411: term] :
( ( $true
!= ( X410 @ ( lam @ X411 ) ) )
& ( $true
= ( X410 @ X411 ) ) )
| ? [X413: term,X414: term] :
( ( $true
= ( X410 @ X414 ) )
& ( $true
= ( X410 @ X413 ) )
& ( $true
!= ( X410 @ ( ap @ X414 @ X413 ) ) ) )
| ( $true
= ( X410 @ X409 ) )
| ? [X412: term] :
( ( ( var @ X412 )
= $true )
& ( $true
!= ( X410 @ X412 ) ) ) ) )
& ( ( ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) )
| ? [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
!= X335 )
| ? [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
!= X337 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
<=> ( axidr = $true ) )
& ( termmset_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ulamvarsh = $true )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
| ? [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
= ( ap @ X246 @ X247 ) )
& ( X245 != X247 ) ) ) )
& ( ( ! [X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ? [X439: term] :
( ( $true
= ( X431 @ X439 ) )
& ( $true
!= ( X431 @ ( sub @ X430 @ ( push @ X439 @ id ) ) ) ) )
| ? [X438: term] :
( ( X432 @ id @ X438 @ id )
!= ( X431 @ X438 ) )
| ( $true
= ( X431 @ ( lam @ X430 ) ) )
| ? [X433: subst > term > term] :
( ! [X434: term] :
( ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( $true
= ( X432 @ id @ ( X433 @ id @ X434 ) @ id ) ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id ) )
& ! [X435: subst,X436: term,X437: subst] :
( ( X433 @ ( comp @ X437 @ X435 ) @ ( sub @ X436 @ X435 ) )
= ( sub @ ( X433 @ X437 @ X436 ) @ X435 ) ) ) )
| ? [X425: term] :
! [X426: subst > term > term] :
? [X427: term,X428: subst] :
( ( sub @ X425 @ ( push @ X427 @ X428 ) )
!= ( X426 @ X428 @ X427 ) )
| ? [X429: term] :
( ( sub @ X429 @ id )
!= X429 ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 )
| ? [X465: term,X466: term > $o] :
( ! [X470: term] :
( ( $true
= ( X466 @ ( lam @ X470 ) ) )
| ? [X471: term] :
( ( ( X466 @ ( sub @ X470 @ ( push @ X471 @ id ) ) )
!= $true )
& ( $true
= ( X466 @ X471 ) ) ) )
& ( $true
!= ( X466 @ X465 ) )
& ! [X469: term] :
( ( ( X466 @ X469 )
= $true )
| ( $true
!= ( var @ X469 ) ) )
& ! [X467: term,X468: term] :
( ( ( X466 @ X468 )
!= $true )
| ( $true
!= ( X466 @ X467 ) )
| ( $true
= ( X466 @ ( ap @ X468 @ X467 ) ) ) ) )
| ? [X473: term > $o,X474: subst > term > subst > $o,X475: term] :
( ! [X478: subst > term > term] :
( ? [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X481 @ X482 ) @ ( sub @ X480 @ X482 ) )
!= ( sub @ ( X478 @ X481 @ X480 ) @ X482 ) )
| ? [X479: term] :
( ( $true
= ( X474 @ id @ X479 @ id ) )
& ( $true
!= ( X474 @ id @ ( X478 @ id @ X479 ) @ id ) ) )
| ( $true
= ( X474 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( X473 @ ( lam @ X475 ) ) )
& ! [X476: term] :
( ( $true
= ( X473 @ ( sub @ X475 @ ( push @ X476 @ id ) ) ) )
| ( ( X473 @ X476 )
!= $true ) )
& ! [X477: term] :
( ( X474 @ id @ X477 @ id )
= ( X473 @ X477 ) ) )
| ! [X483: term,X484: subst > term > subst > $o] :
( ( $true
= ( X484 @ id @ X483 @ id ) )
| ? [X496: subst > term > term] :
( ! [X500: term] :
( ( $true
!= ( X484 @ id @ X500 @ id ) )
| ( $true
= ( X484 @ id @ ( X496 @ id @ X500 ) @ id ) ) )
& ( $true
!= ( X484 @ id @ ( lam @ ( X496 @ sh @ one ) ) @ id ) )
& ! [X497: term,X498: subst,X499: subst] :
( ( X496 @ ( comp @ X499 @ X498 ) @ ( sub @ X497 @ X498 ) )
= ( sub @ ( X496 @ X499 @ X497 ) @ X498 ) ) )
| ? [X489: subst,X490: subst,X491: term,X492: subst] :
( ( $true
!= ( X484 @ ( comp @ X489 @ X492 ) @ ( sub @ X491 @ X492 ) @ X490 ) )
& ( $true
= ( X484 @ X489 @ X491 @ ( comp @ X492 @ X490 ) ) ) )
| ? [X495: term] :
( ( $true
= ( var @ ( sub @ X495 @ id ) ) )
& ( $true
!= ( X484 @ id @ X495 @ id ) ) )
| ? [X485: subst,X486: subst,X487: term,X488: subst] :
( ( $true
= ( X484 @ ( comp @ X485 @ X488 ) @ ( sub @ X487 @ X488 ) @ X486 ) )
& ( $true
!= ( X484 @ X485 @ X487 @ ( comp @ X488 @ X486 ) ) ) )
| ? [X493: term,X494: term] :
( ( $true
= ( X484 @ id @ X494 @ id ) )
& ( $true
= ( X484 @ id @ X493 @ id ) )
& ( $true
!= ( X484 @ id @ ( ap @ ( sub @ X493 @ id ) @ X494 ) @ id ) ) ) )
| ? [X462: subst > term > subst > $o] :
! [X463: term > $o] :
? [X464: term] :
( ( X462 @ id @ X464 @ id )
!= ( X463 @ X464 ) ) )
<=> ( hoasinduction_lthm_3 = $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 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ( ? [X139: subst] :
( ( comp @ X139 @ id )
!= X139 )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 )
| ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ? [X103: term] :
( ( X100 @ X103 )
!= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
!= ( X99 @ X102 ) )
| ( $true
= ( X100 @ one ) ) ) )
& ( ( ! [X11: subst > term > subst > $o,X12: term] :
( ? [X13: subst > term > term] :
( ( $true
!= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
& ! [X17: term] :
( ( $true
!= ( X11 @ id @ X17 @ id ) )
| ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) ) )
& ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) ) )
| ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ? [X18: term] :
( ( $true
= ( X11 @ id @ X18 @ id ) )
& ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) )
| ? [X2: term] :
( ( sub @ X2 @ id )
!= X2 )
| ? [X3: subst > term > subst > $o,X4: term] :
( ( $true
!= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: term] :
( ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X3 @ id @ X10 @ id ) ) )
& ! [X5: subst > term > term] :
( ? [X9: term] :
( ( $true
!= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) )
& ( $true
= ( X3 @ id @ X9 @ id ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) )
| ? [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
!= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
<=> ( shinj = $true ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ( ! [X202: term] :
( ( sub @ X202 @ id )
= X202 )
| ? [X201: term] :
( ( sub @ X201 @ id )
!= X201 ) )
<=> ( termmset_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ! [X523: subst > term > subst > $o,X524: term] :
( ? [X535: term,X536: subst,X537: subst,X538: subst] :
( ( $true
!= ( X523 @ X538 @ X535 @ ( comp @ X536 @ X537 ) ) )
& ( $true
= ( X523 @ ( comp @ X538 @ X536 ) @ ( sub @ X535 @ X536 ) @ X537 ) ) )
| ( $true
= ( X523 @ id @ ( lam @ X524 ) @ id ) )
| ? [X525: term] :
( ( $true
!= ( X523 @ id @ ( sub @ X524 @ ( push @ X525 @ id ) ) @ id ) )
& ( $true
= ( X523 @ id @ X525 @ id ) ) )
| ? [X530: subst > term > term] :
( ( $true
!= ( X523 @ id @ ( lam @ ( X530 @ sh @ one ) ) @ id ) )
& ! [X531: subst,X532: term,X533: subst] :
( ( sub @ ( X530 @ X531 @ X532 ) @ X533 )
= ( X530 @ ( comp @ X531 @ X533 ) @ ( sub @ X532 @ X533 ) ) )
& ! [X534: term] :
( ( $true
!= ( X523 @ id @ X534 @ id ) )
| ( $true
= ( X523 @ id @ ( X530 @ id @ X534 ) @ id ) ) ) )
| ? [X526: subst,X527: subst,X528: subst,X529: term] :
( ( ( X523 @ ( comp @ X527 @ X526 ) @ ( sub @ X529 @ X526 ) @ X528 )
!= $true )
& ( $true
= ( X523 @ X527 @ X529 @ ( comp @ X526 @ X528 ) ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X501: term,X502: subst > term > subst > $o] :
( ? [X508: term] :
( ( $true
!= ( X502 @ id @ ( sub @ X501 @ ( push @ X508 @ id ) ) @ id ) )
& ( $true
= ( X502 @ id @ X508 @ id ) ) )
| ( ( X502 @ id @ ( lam @ ( sub @ X501 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X503: subst > term > term] :
( ! [X504: subst,X505: term,X506: subst] :
( ( X503 @ ( comp @ X506 @ X504 ) @ ( sub @ X505 @ X504 ) )
= ( sub @ ( X503 @ X506 @ X505 ) @ X504 ) )
& ! [X507: term] :
( ( $true
= ( X502 @ id @ ( X503 @ id @ X507 ) @ id ) )
| ( $true
!= ( X502 @ id @ X507 @ id ) ) )
& ( ( X502 @ id @ ( lam @ ( X503 @ sh @ one ) ) @ id )
!= $true ) ) ) )
& ( ( substmonoid = $true )
<=> ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( d2subst @ d_id )
= sh )
& ( ! [X515: subst,X516: term > $o,X517: term] :
( ? [X518: term] :
( ( $true
= ( var @ X518 ) )
& ( $true
!= ( X516 @ ( sub @ X518 @ X515 ) ) ) )
| ? [X521: term] :
( ! [X522: term] :
( ( $true
!= ( X516 @ X522 ) )
| ( $true
= ( X516 @ ( sub @ X521 @ ( push @ X522 @ id ) ) ) ) )
& ( $true
!= ( X516 @ ( lam @ X521 ) ) ) )
| ( $true
= ( X516 @ ( sub @ X517 @ X515 ) ) )
| ? [X519: term,X520: term] :
( ( $true
= ( X516 @ X519 ) )
& ( $true
= ( X516 @ X520 ) )
& ( $true
!= ( X516 @ ( ap @ X520 @ X519 ) ) ) ) )
<=> ( induction2lem = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ! [X523: subst > term > subst > $o,X524: term] :
( ? [X535: term,X536: subst,X537: subst,X538: subst] :
( ( $true
!= ( X523 @ X538 @ X535 @ ( comp @ X536 @ X537 ) ) )
& ( $true
= ( X523 @ ( comp @ X538 @ X536 ) @ ( sub @ X535 @ X536 ) @ X537 ) ) )
| ( $true
= ( X523 @ id @ ( lam @ X524 ) @ id ) )
| ? [X525: term] :
( ( $true
!= ( X523 @ id @ ( sub @ X524 @ ( push @ X525 @ id ) ) @ id ) )
& ( $true
= ( X523 @ id @ X525 @ id ) ) )
| ? [X530: subst > term > term] :
( ( $true
!= ( X523 @ id @ ( lam @ ( X530 @ sh @ one ) ) @ id ) )
& ! [X531: subst,X532: term,X533: subst] :
( ( sub @ ( X530 @ X531 @ X532 ) @ X533 )
= ( X530 @ ( comp @ X531 @ X533 ) @ ( sub @ X532 @ X533 ) ) )
& ! [X534: term] :
( ( $true
!= ( X523 @ id @ X534 @ id ) )
| ( $true
= ( X523 @ id @ ( X530 @ id @ X534 ) @ id ) ) ) )
| ? [X526: subst,X527: subst,X528: subst,X529: term] :
( ( ( X523 @ ( comp @ X527 @ X526 ) @ ( sub @ X529 @ X526 ) @ X528 )
!= $true )
& ( $true
= ( X523 @ X527 @ X529 @ ( comp @ X526 @ X528 ) ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( axabs = $true )
& ( pushprop_lem0_gthm = $true )
& ( ! [X49: term] :
? [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X345: term > $o,X346: term,X347: subst > term > subst > $o] :
( ? [X354: subst,X355: subst,X356: subst,X357: term] :
( ( ( X347 @ ( comp @ X354 @ X356 ) @ ( sub @ X357 @ X356 ) @ X355 )
= $true )
& ( $true
!= ( X347 @ X354 @ X357 @ ( comp @ X356 @ X355 ) ) ) )
| ? [X359: subst,X360: subst,X361: term,X362: subst] :
( ( $true
!= ( X347 @ ( comp @ X359 @ X360 ) @ ( sub @ X361 @ X360 ) @ X362 ) )
& ( $true
= ( X347 @ X359 @ X361 @ ( comp @ X360 @ X362 ) ) ) )
| ? [X348: term] :
( ( $true
= ( X345 @ X348 ) )
& ( ( X345 @ ( sub @ X346 @ ( push @ X348 @ id ) ) )
!= $true ) )
| ( ( X345 @ ( lam @ X346 ) )
= $true )
| ? [X349: subst > term > term] :
( ( $true
!= ( X347 @ id @ ( lam @ ( X349 @ sh @ one ) ) @ id ) )
& ! [X351: subst,X352: subst,X353: term] :
( ( X349 @ ( comp @ X351 @ X352 ) @ ( sub @ X353 @ X352 ) )
= ( sub @ ( X349 @ X351 @ X353 ) @ X352 ) )
& ! [X350: term] :
( ( ( X347 @ id @ X350 @ id )
!= $true )
| ( $true
= ( X347 @ id @ ( X349 @ id @ X350 ) @ id ) ) ) )
| ? [X358: term] :
( ( X345 @ X358 )
!= ( X347 @ id @ X358 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X126: term > $o,X127: term,X128: subst] :
( ? [X131: term] :
( ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) )
& ( $true
!= ( X126 @ ( lam @ X131 ) ) ) )
| ? [X133: term] :
( ( $true
!= ( X126 @ ( sub @ X133 @ X128 ) ) )
& ( $true
= ( var @ X133 ) ) )
| ? [X129: term,X130: term] :
( ( $true
= ( X126 @ X129 ) )
& ( $true
= ( X126 @ X130 ) )
& ( ( X126 @ ( ap @ X130 @ X129 ) )
!= $true ) )
| ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) ) )
| ? [X120: term > $o,X121: term] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( $true
= ( X120 @ X122 ) ) )
& ( $true
!= ( X120 @ X121 ) )
& ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) )
& ! [X125: term] :
( ( $true
= ( X120 @ ( lam @ X125 ) ) )
| ( $true
!= ( X120 @ X125 ) ) ) )
| ? [X119: subst] :
( ( comp @ X119 @ id )
!= X119 )
| ? [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
!= X117 )
| ? [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
!= X116 ) ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( termmset_gthm = $true )
& ( axassoc = $true )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) )
| ? [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
!= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( induction2_gthm = $true )
& ( ulamvarsh = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X295: term > $o,X296: term,X297: subst > term > subst > $o] :
( ? [X304: term] :
( ( $true
!= ( X295 @ ( sub @ X296 @ ( push @ X304 @ id ) ) ) )
& ( ( X295 @ X304 )
= $true ) )
| ? [X298: subst > term > term] :
( ! [X300: subst,X301: term,X302: subst] :
( ( sub @ ( X298 @ X302 @ X301 ) @ X300 )
= ( X298 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) ) )
& ( $true
!= ( X297 @ id @ ( lam @ ( X298 @ sh @ one ) ) @ id ) )
& ! [X299: term] :
( ( ( X297 @ id @ X299 @ id )
!= $true )
| ( $true
= ( X297 @ id @ ( X298 @ id @ X299 ) @ id ) ) ) )
| ? [X303: term] :
( ( X295 @ X303 )
!= ( X297 @ id @ X303 @ id ) )
| ( $true
= ( X295 @ ( lam @ X296 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( induction2 = $true )
<=> ! [X104: term,X105: term > $o] :
( ? [X109: term,X110: term] :
( ( $true
= ( X105 @ X110 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X110 ) ) )
& ( ( X105 @ X109 )
= $true ) )
| ? [X106: term] :
( ! [X107: term] :
( ( ( X105 @ X107 )
!= $true )
| ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) ) )
& ( $true
!= ( X105 @ ( lam @ X106 ) ) ) )
| ? [X108: term] :
( ( $true
!= ( X105 @ X108 ) )
& ( ( var @ X108 )
= $true ) )
| ( $true
= ( X105 @ X104 ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X19: term] :
? [X20: subst > term > term] :
! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X389: term,X390: subst > term > subst > $o] :
( ? [X391: term] :
( ( $true
= ( X390 @ id @ X391 @ id ) )
& ( ( X390 @ id @ ( sub @ X389 @ ( push @ X391 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X390 @ id @ ( lam @ ( sub @ X389 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X392: subst > term > term] :
( ( $true
!= ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
& ! [X396: term] :
( ( $true
= ( X390 @ id @ ( X392 @ id @ X396 ) @ id ) )
| ( $true
!= ( X390 @ id @ X396 @ id ) ) )
& ! [X393: subst,X394: term,X395: subst] :
( ( X392 @ ( comp @ X395 @ X393 ) @ ( sub @ X394 @ X393 ) )
= ( sub @ ( X392 @ X395 @ X394 ) @ X393 ) ) ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X501: term,X502: subst > term > subst > $o] :
( ? [X508: term] :
( ( $true
!= ( X502 @ id @ ( sub @ X501 @ ( push @ X508 @ id ) ) @ id ) )
& ( $true
= ( X502 @ id @ X508 @ id ) ) )
| ( ( X502 @ id @ ( lam @ ( sub @ X501 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X503: subst > term > term] :
( ! [X504: subst,X505: term,X506: subst] :
( ( X503 @ ( comp @ X506 @ X504 ) @ ( sub @ X505 @ X504 ) )
= ( sub @ ( X503 @ X506 @ X505 ) @ X504 ) )
& ! [X507: term] :
( ( $true
= ( X502 @ id @ ( X503 @ id @ X507 ) @ id ) )
| ( $true
!= ( X502 @ id @ X507 @ id ) ) )
& ( ( X502 @ id @ ( lam @ ( X503 @ sh @ one ) ) @ id )
!= $true ) ) ) )
& ( ( ! [X202: term] :
( ( sub @ X202 @ id )
= X202 )
| ? [X201: term] :
( ( sub @ X201 @ id )
!= X201 ) )
<=> ( termmset_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X178: term,X179: subst > term > subst > $o] :
( ? [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
!= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) )
& ( $true
= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) ) )
| ? [X181: term,X182: term] :
( ( $true
= ( X179 @ id @ X181 @ id ) )
& ( ( X179 @ id @ X182 @ id )
= $true )
& ( $true
!= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) ) )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
!= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) )
& ( $true
= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) ) )
| ? [X191: subst > term > term] :
( ! [X195: term] :
( ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) )
| ( $true
!= ( X179 @ id @ X195 @ id ) ) )
& ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
!= $true )
& ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) ) )
| ? [X180: term] :
( ( $true
= ( var @ ( sub @ X180 @ id ) ) )
& ( $true
!= ( X179 @ id @ X180 @ id ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true ) )
| ? [X162: subst > term > subst > $o,X163: term] :
( ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) )
| ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) ) )
& ( $true
!= ( X162 @ id @ ( lam @ X163 ) @ id ) )
& ! [X173: subst > term > term] :
( ? [X174: term] :
( ( $true
= ( X162 @ id @ X174 @ id ) )
& ( $true
!= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) ) )
| ? [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
!= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) )
& ! [X164: term] :
( ( $true
!= ( X162 @ id @ X164 @ id ) )
| ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) ) )
& ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) ) )
| ? [X149: subst > term > subst > $o,X150: term,X151: term] :
( ! [X156: term,X157: term] :
( ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) )
| ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) ) )
& ( $true
= ( X149 @ id @ X151 @ id ) )
& ( $true
!= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
& ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
& ( $true
= ( X149 @ id @ X150 @ id ) )
& ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true )
| ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) ) ) )
| ? [X142: term > $o,X143: term] :
( ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
& ! [X147: term] :
( ( $true
= ( X142 @ ( lam @ X147 ) ) )
| ? [X148: term] :
( ( $true
= ( X142 @ X148 ) )
& ( $true
!= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) ) ) )
& ! [X145: term,X146: term] :
( ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) )
| ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) ) )
& ( $true
!= ( X142 @ X143 ) ) ) ) )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoasapnotvar = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X273: term > $o,X274: subst,X275: term] :
? [X276: term > $o] :
! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ? [X43: subst > term > term] :
( ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
& ( $true
!= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
& ! [X47: term] :
( ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) )
| ( ( X42 @ id @ X47 @ id )
!= $true ) ) )
| ? [X48: term] :
( ( $true
= ( X42 @ id @ X48 @ id ) )
& ( $true
!= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) )
| ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslaminj_gthm = $true )
& ( axmap = $true )
& ( axvarshift = $true )
& ( ! [X196: subst,X197: term,X198: term > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( pushprop = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ? [X103: term] :
( ( X100 @ X103 )
!= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
!= ( X99 @ X102 ) )
| ( $true
= ( X100 @ one ) ) ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
!= ( d2term @ X408 ) )
| ( X407 = X408 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
<=> ( axscons = $true ) )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( ( X203 @ id @ X205 @ id )
= $true )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X203 @ id @ X206 @ id ) ) )
| ? [X207: subst > term > term] :
( ( $true
!= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) )
& ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
& ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( lamnotap != $true )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
<=> ( shinj = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X372: subst > term > subst > $o,X373: term] :
( ? [X379: subst > term > term] :
( ( $true
!= ( X372 @ id @ ( lam @ ( X379 @ sh @ one ) ) @ id ) )
& ! [X380: term] :
( ( $true
!= ( X372 @ id @ X380 @ id ) )
| ( $true
= ( X372 @ id @ ( X379 @ id @ X380 ) @ id ) ) )
& ! [X381: term,X382: subst,X383: subst] :
( ( X379 @ ( comp @ X382 @ X383 ) @ ( sub @ X381 @ X383 ) )
= ( sub @ ( X379 @ X382 @ X381 ) @ X383 ) ) )
| ? [X384: subst,X385: subst,X386: term,X387: subst] :
( ( $true
= ( X372 @ ( comp @ X387 @ X384 ) @ ( sub @ X386 @ X384 ) @ X385 ) )
& ( ( X372 @ X387 @ X386 @ ( comp @ X384 @ X385 ) )
!= $true ) )
| ( $true
= ( X372 @ id @ ( lam @ X373 ) @ id ) )
| ? [X374: subst,X375: subst,X376: subst,X377: term] :
( ( $true
= ( X372 @ X376 @ X377 @ ( comp @ X374 @ X375 ) ) )
& ( ( X372 @ ( comp @ X376 @ X374 ) @ ( sub @ X377 @ X374 ) @ X375 )
!= $true ) )
| ? [X378: term] :
( ( $true
= ( X372 @ id @ X378 @ id ) )
& ( $true
!= ( X372 @ id @ ( sub @ X373 @ ( push @ X378 @ id ) ) @ id ) ) ) )
| ? [X364: term,X365: subst > term > subst > $o] :
( ! [X366: subst > term > term] :
( ? [X367: term,X368: subst,X369: subst] :
( ( X366 @ ( comp @ X369 @ X368 ) @ ( sub @ X367 @ X368 ) )
!= ( sub @ ( X366 @ X369 @ X367 ) @ X368 ) )
| ? [X370: term] :
( ( $true
!= ( X365 @ id @ ( X366 @ id @ X370 ) @ id ) )
& ( $true
= ( X365 @ id @ X370 @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id ) ) )
& ! [X371: term] :
( ( $true
!= ( X365 @ id @ X371 @ id ) )
| ( $true
= ( X365 @ id @ ( sub @ X364 @ ( push @ X371 @ id ) ) @ id ) ) )
& ( $true
!= ( X365 @ id @ ( lam @ ( sub @ X364 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 ) ) )
& ( ( induction = $true )
<=> ! [X409: term,X410: term > $o] :
( ? [X411: term] :
( ( $true
!= ( X410 @ ( lam @ X411 ) ) )
& ( $true
= ( X410 @ X411 ) ) )
| ? [X413: term,X414: term] :
( ( $true
= ( X410 @ X414 ) )
& ( $true
= ( X410 @ X413 ) )
& ( $true
!= ( X410 @ ( ap @ X414 @ X413 ) ) ) )
| ( $true
= ( X410 @ X409 ) )
| ? [X412: term] :
( ( ( var @ X412 )
= $true )
& ( $true
!= ( X410 @ X412 ) ) ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ? [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) )
& ( $true
!= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) ) )
| ? [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
& ( $true
!= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ( $true
!= ( X26 @ id @ X25 @ id ) )
| ? [X31: term,X32: term] :
( ( $true
= ( X26 @ id @ X31 @ id ) )
& ( $true
= ( X26 @ id @ X32 @ id ) )
& ( $true
!= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ( $true
!= ( X402 @ X405 ) )
| ? [X406: term] :
( ( X404 @ X406 )
!= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) )
| ? [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
!= X401 ) ) )
& ( hoasapnotvar_gthm = $true )
& ( axapp = $true )
& ( ! [X444: subst > term > subst > $o,X445: term] :
( ? [X448: term] :
( ( $true
= ( var @ ( sub @ X448 @ id ) ) )
& ( $true
!= ( X444 @ id @ X448 @ id ) ) )
| ? [X458: term,X459: subst,X460: subst,X461: subst] :
( ( ( X444 @ X460 @ X458 @ ( comp @ X461 @ X459 ) )
!= $true )
& ( $true
= ( X444 @ ( comp @ X460 @ X461 ) @ ( sub @ X458 @ X461 ) @ X459 ) ) )
| ? [X454: subst,X455: subst,X456: subst,X457: term] :
( ( $true
!= ( X444 @ ( comp @ X454 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) )
& ( $true
= ( X444 @ X454 @ X457 @ ( comp @ X455 @ X456 ) ) ) )
| ( ( X444 @ id @ X445 @ id )
= $true )
| ? [X449: subst > term > term] :
( ! [X451: subst,X452: subst,X453: term] :
( ( sub @ ( X449 @ X452 @ X453 ) @ X451 )
= ( X449 @ ( comp @ X452 @ X451 ) @ ( sub @ X453 @ X451 ) ) )
& ! [X450: term] :
( ( $true
= ( X444 @ id @ ( X449 @ id @ X450 ) @ id ) )
| ( $true
!= ( X444 @ id @ X450 @ id ) ) )
& ( $true
!= ( X444 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id ) ) )
| ? [X446: term,X447: term] :
( ( $true
= ( X444 @ id @ X447 @ id ) )
& ( ( X444 @ id @ ( ap @ ( sub @ X447 @ id ) @ X446 ) @ id )
!= $true )
& ( $true
= ( X444 @ id @ X446 @ id ) ) ) )
<=> ( hoasinduction = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( ! [X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ? [X439: term] :
( ( $true
= ( X431 @ X439 ) )
& ( $true
!= ( X431 @ ( sub @ X430 @ ( push @ X439 @ id ) ) ) ) )
| ? [X438: term] :
( ( X432 @ id @ X438 @ id )
!= ( X431 @ X438 ) )
| ( $true
= ( X431 @ ( lam @ X430 ) ) )
| ? [X433: subst > term > term] :
( ! [X434: term] :
( ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( $true
= ( X432 @ id @ ( X433 @ id @ X434 ) @ id ) ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id ) )
& ! [X435: subst,X436: term,X437: subst] :
( ( X433 @ ( comp @ X437 @ X435 ) @ ( sub @ X436 @ X435 ) )
= ( sub @ ( X433 @ X437 @ X436 ) @ X435 ) ) ) )
| ? [X429: term] :
( ( sub @ X429 @ id )
!= X429 )
| ? [X425: term] :
! [X426: subst > term > term] :
? [X427: term,X428: subst] :
( ( sub @ X425 @ ( push @ X427 @ X428 ) )
!= ( X426 @ X428 @ X427 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X263: subst > term > term,X264: term,X265: subst,X266: subst > term > term] :
( ( ( lam @ ( X266 @ sh @ one ) )
!= ( lam @ ( X263 @ sh @ one ) ) )
| ? [X267: subst,X268: term,X269: subst] :
( ( sub @ ( X263 @ X269 @ X268 ) @ X267 )
!= ( X263 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) )
| ( ( X263 @ X265 @ X264 )
= ( X266 @ X265 @ X264 ) )
| ? [X270: subst,X271: term,X272: subst] :
( ( sub @ ( X266 @ X270 @ X271 ) @ X272 )
!= ( X266 @ ( comp @ X270 @ X272 ) @ ( sub @ X271 @ X272 ) ) ) )
| ? [X261: term,X262: term] :
( ( X261 != X262 )
& ( ( lam @ X262 )
= ( lam @ X261 ) ) )
| ? [X259: term,X260: subst] :
( ( comp @ sh @ ( push @ X259 @ X260 ) )
!= X260 )
| ? [X257: term,X258: subst] :
( ( sub @ one @ ( push @ X257 @ X258 ) )
!= X257 ) ) )
& ( apnotvar = $true )
& ( ! [X111: term] :
? [X112: subst > term > term] :
! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X236: term,X237: term > $o] :
( ? [X238: term] :
( ( $true
= ( var @ X238 ) )
& ( $true
!= ( X237 @ X238 ) ) )
| ? [X239: term,X240: term] :
( ( $true
= ( X237 @ X240 ) )
& ( $true
!= ( X237 @ ( ap @ X240 @ X239 ) ) )
& ( $true
= ( X237 @ X239 ) ) )
| ( $true
= ( X237 @ X236 ) )
| ? [X241: term] :
( ! [X242: term] :
( ( $true
!= ( X237 @ X242 ) )
| ( $true
= ( X237 @ ( sub @ X241 @ ( push @ X242 @ id ) ) ) ) )
& ( $true
!= ( X237 @ ( lam @ X241 ) ) ) ) )
| ? [X228: term > $o,X229: subst,X230: term] :
( ! [X234: term,X235: term] :
( ( $true
= ( X228 @ ( ap @ X234 @ X235 ) ) )
| ( $true
!= ( X228 @ X235 ) )
| ( $true
!= ( X228 @ X234 ) ) )
& ! [X232: term] :
( ? [X233: term] :
( ( $true
= ( X228 @ X233 ) )
& ( $true
!= ( X228 @ ( sub @ X232 @ ( push @ X233 @ id ) ) ) ) )
| ( $true
= ( X228 @ ( lam @ X232 ) ) ) )
& ! [X231: term] :
( ( $true
!= ( var @ X231 ) )
| ( $true
= ( X228 @ ( sub @ X231 @ X229 ) ) ) )
& ( $true
!= ( X228 @ ( sub @ X230 @ X229 ) ) ) )
| ? [X227: term] :
( ( sub @ X227 @ id )
!= X227 ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvarind = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ? [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
!= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) )
| ? [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
!= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) ) ) )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
<=> ( laminj = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X326: subst > term > subst > $o,X327: term] :
( ? [X328: term,X329: term] :
( ( $true
= ( X326 @ id @ X329 @ id ) )
& ( $true
= ( X326 @ id @ X328 @ id ) )
& ( $true
!= ( X326 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id ) ) )
| ? [X330: subst > term > term] :
( ! [X331: subst,X332: subst,X333: term] :
( ( X330 @ ( comp @ X331 @ X332 ) @ ( sub @ X333 @ X332 ) )
= ( sub @ ( X330 @ X331 @ X333 ) @ X332 ) )
& ( $true
!= ( X326 @ id @ ( lam @ ( X330 @ sh @ one ) ) @ id ) )
& ! [X334: term] :
( ( $true
!= ( X326 @ id @ X334 @ id ) )
| ( $true
= ( X326 @ id @ ( X330 @ id @ X334 ) @ id ) ) ) )
| ( $true
= ( X326 @ id @ X327 @ id ) ) )
| ? [X316: term,X317: term > $o,X318: subst > term > subst > $o] :
( ! [X325: term] :
( ( $true
= ( X317 @ ( sub @ X316 @ ( push @ X325 @ id ) ) ) )
| ( $true
!= ( X317 @ X325 ) ) )
& ! [X320: subst > term > term] :
( ? [X324: term] :
( ( $true
!= ( X318 @ id @ ( X320 @ id @ X324 ) @ id ) )
& ( $true
= ( X318 @ id @ X324 @ id ) ) )
| ( $true
= ( X318 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id ) )
| ? [X321: subst,X322: subst,X323: term] :
( ( sub @ ( X320 @ X321 @ X323 ) @ X322 )
!= ( X320 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) )
& ( ( X317 @ ( lam @ X316 ) )
!= $true )
& ! [X319: term] :
( ( X318 @ id @ X319 @ id )
= ( X317 @ X319 ) ) )
| ? [X315: term] :
( ( sub @ X315 @ id )
!= X315 )
| ? [X308: term > $o,X309: term] :
( ! [X313: term] :
( ( $true
= ( X308 @ ( lam @ X313 ) ) )
| ? [X314: term] :
( ( $true
= ( X308 @ X314 ) )
& ( $true
!= ( X308 @ ( sub @ X313 @ ( push @ X314 @ id ) ) ) ) ) )
& ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) )
| ( $true
!= ( X308 @ X311 ) ) )
& ! [X310: term] :
( ( $true
= ( X308 @ X310 ) )
| ( ( var @ X310 )
!= $true ) )
& ( $true
!= ( X308 @ X309 ) ) )
| ? [X305: subst > term > subst > $o] :
! [X306: term > $o] :
? [X307: term] :
( ( X306 @ X307 )
!= ( X305 @ id @ X307 @ id ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( termmset = $true )
<=> ! [X344: term] :
( ( sub @ X344 @ id )
= X344 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) )
| ? [X139: subst] :
( ( comp @ X139 @ id )
!= X139 )
| ? [X138: subst] :
( ( comp @ id @ X138 )
!= X138 ) ) )
& ( induction2lem_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) )
| ? [X219: term,X220: term,X221: term,X222: term] :
( ( X219 != X222 )
& ( ( ap @ X222 @ X220 )
= ( ap @ X219 @ X221 ) ) )
| ? [X218: term] :
( ( sub @ X218 @ id )
!= X218 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoaslamnotvar = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X483: term,X484: subst > term > subst > $o] :
( ( $true
= ( X484 @ id @ X483 @ id ) )
| ? [X496: subst > term > term] :
( ! [X500: term] :
( ( $true
!= ( X484 @ id @ X500 @ id ) )
| ( $true
= ( X484 @ id @ ( X496 @ id @ X500 ) @ id ) ) )
& ( $true
!= ( X484 @ id @ ( lam @ ( X496 @ sh @ one ) ) @ id ) )
& ! [X497: term,X498: subst,X499: subst] :
( ( X496 @ ( comp @ X499 @ X498 ) @ ( sub @ X497 @ X498 ) )
= ( sub @ ( X496 @ X499 @ X497 ) @ X498 ) ) )
| ? [X489: subst,X490: subst,X491: term,X492: subst] :
( ( $true
!= ( X484 @ ( comp @ X489 @ X492 ) @ ( sub @ X491 @ X492 ) @ X490 ) )
& ( $true
= ( X484 @ X489 @ X491 @ ( comp @ X492 @ X490 ) ) ) )
| ? [X495: term] :
( ( $true
= ( var @ ( sub @ X495 @ id ) ) )
& ( $true
!= ( X484 @ id @ X495 @ id ) ) )
| ? [X485: subst,X486: subst,X487: term,X488: subst] :
( ( $true
= ( X484 @ ( comp @ X485 @ X488 ) @ ( sub @ X487 @ X488 ) @ X486 ) )
& ( $true
!= ( X484 @ X485 @ X487 @ ( comp @ X488 @ X486 ) ) ) )
| ? [X493: term,X494: term] :
( ( $true
= ( X484 @ id @ X494 @ id ) )
& ( $true
= ( X484 @ id @ X493 @ id ) )
& ( $true
!= ( X484 @ id @ ( ap @ ( sub @ X493 @ id ) @ X494 ) @ id ) ) ) )
| ? [X473: term > $o,X474: subst > term > subst > $o,X475: term] :
( ! [X478: subst > term > term] :
( ? [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X481 @ X482 ) @ ( sub @ X480 @ X482 ) )
!= ( sub @ ( X478 @ X481 @ X480 ) @ X482 ) )
| ? [X479: term] :
( ( $true
= ( X474 @ id @ X479 @ id ) )
& ( $true
!= ( X474 @ id @ ( X478 @ id @ X479 ) @ id ) ) )
| ( $true
= ( X474 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( X473 @ ( lam @ X475 ) ) )
& ! [X476: term] :
( ( $true
= ( X473 @ ( sub @ X475 @ ( push @ X476 @ id ) ) ) )
| ( ( X473 @ X476 )
!= $true ) )
& ! [X477: term] :
( ( X474 @ id @ X477 @ id )
= ( X473 @ X477 ) ) )
| ? [X472: term] :
( ( sub @ X472 @ id )
!= X472 )
| ? [X465: term,X466: term > $o] :
( ! [X470: term] :
( ( $true
= ( X466 @ ( lam @ X470 ) ) )
| ? [X471: term] :
( ( ( X466 @ ( sub @ X470 @ ( push @ X471 @ id ) ) )
!= $true )
& ( $true
= ( X466 @ X471 ) ) ) )
& ( $true
!= ( X466 @ X465 ) )
& ! [X469: term] :
( ( ( X466 @ X469 )
= $true )
| ( $true
!= ( var @ X469 ) ) )
& ! [X467: term,X468: term] :
( ( ( X466 @ X468 )
!= $true )
| ( $true
!= ( X466 @ X467 ) )
| ( $true
= ( X466 @ ( ap @ X468 @ X467 ) ) ) ) )
| ? [X462: subst > term > subst > $o] :
! [X463: term > $o] :
? [X464: term] :
( ( X462 @ id @ X464 @ id )
!= ( X463 @ X464 ) ) ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ! [X53: subst > term > subst > $o,X54: term] :
( ? [X56: subst > term > term,X57: term] :
( ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
& ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) )
& ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) )
& ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X55: term] :
( ( $true
!= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) )
& ( $true
= ( X53 @ id @ X55 @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( substmonoid_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( ! [X11: subst > term > subst > $o,X12: term] :
( ? [X13: subst > term > term] :
( ( $true
!= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
& ! [X17: term] :
( ( $true
!= ( X11 @ id @ X17 @ id ) )
| ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) ) )
& ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) ) )
| ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ? [X18: term] :
( ( $true
= ( X11 @ id @ X18 @ id ) )
& ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) )
| ? [X3: subst > term > subst > $o,X4: term] :
( ( $true
!= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: term] :
( ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X3 @ id @ X10 @ id ) ) )
& ! [X5: subst > term > term] :
( ? [X9: term] :
( ( $true
!= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) )
& ( $true
= ( X3 @ id @ X9 @ id ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) )
| ? [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
!= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) ) ) )
| ? [X2: term] :
( ( sub @ X2 @ id )
!= X2 ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X278: term,X279: term > $o,X280: term,X281: subst > term > subst > $o] :
( ( $true
!= ( X279 @ X280 ) )
| ( $true
!= ( X279 @ X278 ) )
| ( $true
= ( X279 @ ( ap @ X278 @ X280 ) ) )
| ? [X288: term,X289: subst,X290: subst,X291: subst] :
( ( $true
!= ( X281 @ ( comp @ X289 @ X291 ) @ ( sub @ X288 @ X291 ) @ X290 ) )
& ( ( X281 @ X289 @ X288 @ ( comp @ X291 @ X290 ) )
= $true ) )
| ? [X292: term] :
( ( X279 @ X292 )
!= ( X281 @ id @ X292 @ id ) )
| ? [X282: term,X283: term] :
( ( $true
= ( X281 @ id @ X282 @ id ) )
& ( ( X281 @ id @ ( ap @ ( sub @ X283 @ id ) @ X282 ) @ id )
!= $true )
& ( $true
= ( X281 @ id @ X283 @ id ) ) )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X281 @ ( comp @ X284 @ X287 ) @ ( sub @ X286 @ X287 ) @ X285 ) )
& ( $true
!= ( X281 @ X284 @ X286 @ ( comp @ X287 @ X285 ) ) ) ) ) )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_gthm = $true )
& ( axclos = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X252: subst > term > subst > $o] :
? [X253: term > $o] :
! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
<=> ( axidr = $true ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) )
| ? [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
!= X337 )
| ? [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
!= X335 ) ) )
& ( lamnotvar = $true )
& ( pushprop_lem1_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X51: d_subst,X52: d_subst] :
( ( X51 = X52 )
| ( ( d2subst @ X52 )
!= ( d2subst @ X51 ) ) )
& ( ( ? [X76: term] :
( ( sub @ X76 @ id )
!= X76 )
| ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ? [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
& ( $true
!= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) )
| ? [X90: subst > term > term] :
( ( $true
!= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) )
& ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
& ! [X94: term] :
( ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) )
| ( $true
!= ( X78 @ id @ X94 @ id ) ) ) )
| ? [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) )
& ( $true
= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ? [X89: term] :
( ( $true
= ( X79 @ X89 ) )
& ( $true
!= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ? [X80: term] :
( ( X78 @ id @ X80 @ id )
!= ( X79 @ X80 ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $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 ) ) ) ) ) ) )
& ( ! [X397: subst > term > subst > $o] :
? [X398: term > $o] :
! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) )
| ? [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
= ( ap @ X246 @ X247 ) )
& ( X245 != X247 ) ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X216: term] :
? [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
= ( X217 @ sh @ one ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( pushprop_lthm_orig = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( d2subst @ d_id )
= sh )
& ( ( induction2lem = $true )
<=> ! [X515: subst,X516: term > $o,X517: term] :
( ~ ! [X519: term,X520: term] :
( ( $true
= ( X516 @ ( ap @ X520 @ X519 ) ) )
| ( $true
!= ( X516 @ X520 ) )
| ( $true
!= ( X516 @ X519 ) ) )
| ( $true
= ( X516 @ ( sub @ X517 @ X515 ) ) )
| ~ ! [X518: term] :
( ( $true
= ( X516 @ ( sub @ X518 @ X515 ) ) )
| ( $true
!= ( var @ X518 ) ) )
| ~ ! [X521: term] :
( ~ ! [X522: term] :
( ( $true
!= ( X516 @ X522 ) )
| ( $true
= ( X516 @ ( sub @ X521 @ ( push @ X522 @ id ) ) ) ) )
| ( $true
= ( X516 @ ( lam @ X521 ) ) ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X523: subst > term > subst > $o,X524: term] :
( ~ ! [X526: subst,X527: subst,X528: subst,X529: term] :
( ( $true
!= ( X523 @ X527 @ X529 @ ( comp @ X526 @ X528 ) ) )
| ( ( X523 @ ( comp @ X527 @ X526 ) @ ( sub @ X529 @ X526 ) @ X528 )
= $true ) )
| ~ ! [X535: term,X536: subst,X537: subst,X538: subst] :
( ( $true
!= ( X523 @ ( comp @ X538 @ X536 ) @ ( sub @ X535 @ X536 ) @ X537 ) )
| ( $true
= ( X523 @ X538 @ X535 @ ( comp @ X536 @ X537 ) ) ) )
| ( $true
= ( X523 @ id @ ( lam @ X524 ) @ id ) )
| ~ ! [X530: subst > term > term] :
( ~ ! [X534: term] :
( ( $true
!= ( X523 @ id @ X534 @ id ) )
| ( $true
= ( X523 @ id @ ( X530 @ id @ X534 ) @ id ) ) )
| ( $true
= ( X523 @ id @ ( lam @ ( X530 @ sh @ one ) ) @ id ) )
| ~ ! [X531: subst,X532: term,X533: subst] :
( ( sub @ ( X530 @ X531 @ X532 ) @ X533 )
= ( X530 @ ( comp @ X531 @ X533 ) @ ( sub @ X532 @ X533 ) ) ) )
| ~ ! [X525: term] :
( ( $true
= ( X523 @ id @ ( sub @ X524 @ ( push @ X525 @ id ) ) @ id ) )
| ( $true
!= ( X523 @ id @ X525 @ id ) ) ) ) )
& ( axabs = $true )
& ( pushprop_lem0_gthm = $true )
& ( ! [X49: term] :
~ ! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X345: term > $o,X346: term,X347: subst > term > subst > $o] :
( ~ ! [X349: subst > term > term] :
( ~ ! [X350: term] :
( ( ( X347 @ id @ X350 @ id )
!= $true )
| ( $true
= ( X347 @ id @ ( X349 @ id @ X350 ) @ id ) ) )
| ( $true
= ( X347 @ id @ ( lam @ ( X349 @ sh @ one ) ) @ id ) )
| ~ ! [X351: subst,X352: subst,X353: term] :
( ( X349 @ ( comp @ X351 @ X352 ) @ ( sub @ X353 @ X352 ) )
= ( sub @ ( X349 @ X351 @ X353 ) @ X352 ) ) )
| ( ( X345 @ ( lam @ X346 ) )
= $true )
| ~ ! [X354: subst,X355: subst,X356: subst,X357: term] :
( ( $true
= ( X347 @ X354 @ X357 @ ( comp @ X356 @ X355 ) ) )
| ( ( X347 @ ( comp @ X354 @ X356 ) @ ( sub @ X357 @ X356 ) @ X355 )
!= $true ) )
| ~ ! [X359: subst,X360: subst,X361: term,X362: subst] :
( ( $true
!= ( X347 @ X359 @ X361 @ ( comp @ X360 @ X362 ) ) )
| ( $true
= ( X347 @ ( comp @ X359 @ X360 ) @ ( sub @ X361 @ X360 ) @ X362 ) ) )
| ~ ! [X348: term] :
( ( $true
!= ( X345 @ X348 ) )
| ( ( X345 @ ( sub @ X346 @ ( push @ X348 @ id ) ) )
= $true ) )
| ~ ! [X358: term] :
( ( X345 @ X358 )
= ( X347 @ id @ X358 @ id ) ) ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
= X116 )
=> ( ! [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
= X117 )
=> ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
=> ( ! [X120: term > $o,X121: term] :
( ~ ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( $true
= ( X120 @ X122 ) ) )
| ~ ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) )
| ( $true
= ( X120 @ X121 ) )
| ~ ! [X125: term] :
( ( $true
= ( X120 @ ( lam @ X125 ) ) )
| ( $true
!= ( X120 @ X125 ) ) ) )
=> ! [X126: term > $o,X127: term,X128: subst] :
( ~ ! [X133: term] :
( ( $true
= ( X126 @ ( sub @ X133 @ X128 ) ) )
| ( $true
!= ( var @ X133 ) ) )
| ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) )
| ~ ! [X129: term,X130: term] :
( ( $true
!= ( X126 @ X130 ) )
| ( $true
!= ( X126 @ X129 ) )
| ( ( X126 @ ( ap @ X130 @ X129 ) )
= $true ) )
| ~ ! [X131: term] :
( ( $true
= ( X126 @ ( lam @ X131 ) ) )
| ~ ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) ) ) ) ) ) ) ) )
& ( pushprop_lem3v2 = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( termmset_gthm = $true )
& ( axassoc = $true )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ~ ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
| ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( induction2_gthm = $true )
& ( ulamvarsh = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X295: term > $o,X296: term,X297: subst > term > subst > $o] :
( ~ ! [X304: term] :
( ( $true
= ( X295 @ ( sub @ X296 @ ( push @ X304 @ id ) ) ) )
| ( ( X295 @ X304 )
!= $true ) )
| ~ ! [X303: term] :
( ( X295 @ X303 )
= ( X297 @ id @ X303 @ id ) )
| ~ ! [X298: subst > term > term] :
( ~ ! [X300: subst,X301: term,X302: subst] :
( ( sub @ ( X298 @ X302 @ X301 ) @ X300 )
= ( X298 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) ) )
| ( $true
= ( X297 @ id @ ( lam @ ( X298 @ sh @ one ) ) @ id ) )
| ~ ! [X299: term] :
( ( ( X297 @ id @ X299 @ id )
!= $true )
| ( $true
= ( X297 @ id @ ( X298 @ id @ X299 ) @ id ) ) ) )
| ( $true
= ( X295 @ ( lam @ X296 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_gthm = $true )
& ( ! [X104: term,X105: term > $o] :
( ~ ! [X109: term,X110: term] :
( ( $true
= ( X105 @ ( ap @ X109 @ X110 ) ) )
| ( ( X105 @ X109 )
!= $true )
| ( $true
!= ( X105 @ X110 ) ) )
| ( $true
= ( X105 @ X104 ) )
| ~ ! [X106: term] :
( ( $true
= ( X105 @ ( lam @ X106 ) ) )
| ~ ! [X107: term] :
( ( ( X105 @ X107 )
!= $true )
| ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) ) ) )
| ~ ! [X108: term] :
( ( $true
= ( X105 @ X108 ) )
| ( ( var @ X108 )
!= $true ) ) )
<=> ( induction2 = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X19: term] :
~ ! [X20: subst > term > term] :
~ ! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) ) )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X389: term,X390: subst > term > subst > $o] :
( ~ ! [X392: subst > term > term] :
( ( $true
= ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
| ~ ! [X396: term] :
( ( $true
= ( X390 @ id @ ( X392 @ id @ X396 ) @ id ) )
| ( $true
!= ( X390 @ id @ X396 @ id ) ) )
| ~ ! [X393: subst,X394: term,X395: subst] :
( ( X392 @ ( comp @ X395 @ X393 ) @ ( sub @ X394 @ X393 ) )
= ( sub @ ( X392 @ X395 @ X394 ) @ X393 ) ) )
| ~ ! [X391: term] :
( ( ( X390 @ id @ ( sub @ X389 @ ( push @ X391 @ id ) ) @ id )
= $true )
| ( $true
!= ( X390 @ id @ X391 @ id ) ) )
| ( $true
= ( X390 @ id @ ( lam @ ( sub @ X389 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X501: term,X502: subst > term > subst > $o] :
( ~ ! [X503: subst > term > term] :
( ( ( X502 @ id @ ( lam @ ( X503 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X504: subst,X505: term,X506: subst] :
( ( X503 @ ( comp @ X506 @ X504 ) @ ( sub @ X505 @ X504 ) )
= ( sub @ ( X503 @ X506 @ X505 ) @ X504 ) )
| ~ ! [X507: term] :
( ( $true
= ( X502 @ id @ ( X503 @ id @ X507 ) @ id ) )
| ( $true
!= ( X502 @ id @ X507 @ id ) ) ) )
| ~ ! [X508: term] :
( ( $true
!= ( X502 @ id @ X508 @ id ) )
| ( $true
= ( X502 @ id @ ( sub @ X501 @ ( push @ X508 @ id ) ) @ id ) ) )
| ( ( X502 @ id @ ( lam @ ( sub @ X501 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( ! [X201: term] :
( ( sub @ X201 @ id )
= X201 )
=> ! [X202: term] :
( ( sub @ X202 @ id )
= X202 ) )
<=> ( termmset_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X142: term > $o,X143: term] :
( ~ ! [X145: term,X146: term] :
( ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) )
| ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) ) )
| ( $true
= ( X142 @ X143 ) )
| ~ ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
| ~ ! [X147: term] :
( ~ ! [X148: term] :
( ( $true
= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) )
| ( $true
!= ( X142 @ X148 ) ) )
| ( $true
= ( X142 @ ( lam @ X147 ) ) ) ) )
=> ( ! [X149: subst > term > subst > $o,X150: term,X151: term] :
( ( $true
!= ( X149 @ id @ X150 @ id ) )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
| ( $true
= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
| ~ ! [X156: term,X157: term] :
( ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) )
| ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) ) )
| ~ ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true )
| ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) ) )
| ( $true
!= ( X149 @ id @ X151 @ id ) ) )
=> ( ! [X162: subst > term > subst > $o,X163: term] :
( ~ ! [X164: term] :
( ( $true
!= ( X162 @ id @ X164 @ id ) )
| ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) ) )
| ~ ! [X173: subst > term > term] :
( ~ ! [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) )
| ~ ! [X174: term] :
( ( $true
= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) )
| ( $true
!= ( X162 @ id @ X174 @ id ) ) ) )
| ~ ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) )
| ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) ) )
| ( $true
= ( X162 @ id @ ( lam @ X163 ) @ id ) )
| ~ ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) ) )
=> ! [X178: term,X179: subst > term > subst > $o] :
( ~ ! [X191: subst > term > term] :
( ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) )
| ~ ! [X195: term] :
( ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) )
| ( $true
!= ( X179 @ id @ X195 @ id ) ) ) )
| ~ ! [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
!= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) )
| ( $true
= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) ) )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) )
| ( $true
!= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) ) )
| ~ ! [X181: term,X182: term] :
( ( $true
= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) )
| ( ( X179 @ id @ X182 @ id )
!= $true )
| ( $true
!= ( X179 @ id @ X181 @ id ) ) )
| ~ ! [X180: term] :
( ( $true
= ( X179 @ id @ X180 @ id ) )
| ( $true
!= ( var @ ( sub @ X180 @ id ) ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true ) ) ) ) ) )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoasapnotvar = $true )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X273: term > $o,X274: subst,X275: term] :
~ ! [X276: term > $o] :
~ ! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ~ ! [X43: subst > term > term] :
( ~ ! [X47: term] :
( ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) )
| ( ( X42 @ id @ X47 @ id )
!= $true ) )
| ( $true
= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
| ~ ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) ) )
| ~ ! [X48: term] :
( ( $true
= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) )
| ( $true
!= ( X42 @ id @ X48 @ id ) ) )
| ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslaminj_gthm = $true )
& ( axmap = $true )
& ( axvarshift = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X196: subst,X197: term,X198: term > $o] :
~ ! [X199: term > $o] :
~ ! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( pushprop = $true )
& ( ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ( $true
!= ( X99 @ X102 ) )
| ~ ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
= ( X100 @ one ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
= ( d2term @ X408 ) )
=> ( X407 = X408 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
<=> ( axscons = $true ) )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ( $true
= ( X203 @ id @ X204 @ id ) )
| ~ ! [X205: term,X206: term] :
( ( $true
= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
| ( ( X203 @ id @ X205 @ id )
!= $true )
| ( $true
!= ( X203 @ id @ X206 @ id ) ) )
| ~ ! [X207: subst > term > term] :
( ~ ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
| ~ ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) )
| ( $true
= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( lamnotap != $true )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
<=> ( shinj = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
=> ( ! [X364: term,X365: subst > term > subst > $o] :
( ( $true
= ( X365 @ id @ ( lam @ ( sub @ X364 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X366: subst > term > term] :
( ~ ! [X367: term,X368: subst,X369: subst] :
( ( X366 @ ( comp @ X369 @ X368 ) @ ( sub @ X367 @ X368 ) )
= ( sub @ ( X366 @ X369 @ X367 ) @ X368 ) )
| ~ ! [X370: term] :
( ( $true
!= ( X365 @ id @ X370 @ id ) )
| ( $true
= ( X365 @ id @ ( X366 @ id @ X370 ) @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id ) ) )
| ~ ! [X371: term] :
( ( $true
!= ( X365 @ id @ X371 @ id ) )
| ( $true
= ( X365 @ id @ ( sub @ X364 @ ( push @ X371 @ id ) ) @ id ) ) ) )
=> ! [X372: subst > term > subst > $o,X373: term] :
( ~ ! [X384: subst,X385: subst,X386: term,X387: subst] :
( ( ( X372 @ X387 @ X386 @ ( comp @ X384 @ X385 ) )
= $true )
| ( $true
!= ( X372 @ ( comp @ X387 @ X384 ) @ ( sub @ X386 @ X384 ) @ X385 ) ) )
| ( $true
= ( X372 @ id @ ( lam @ X373 ) @ id ) )
| ~ ! [X374: subst,X375: subst,X376: subst,X377: term] :
( ( ( X372 @ ( comp @ X376 @ X374 ) @ ( sub @ X377 @ X374 ) @ X375 )
= $true )
| ( $true
!= ( X372 @ X376 @ X377 @ ( comp @ X374 @ X375 ) ) ) )
| ~ ! [X378: term] :
( ( $true
!= ( X372 @ id @ X378 @ id ) )
| ( $true
= ( X372 @ id @ ( sub @ X373 @ ( push @ X378 @ id ) ) @ id ) ) )
| ~ ! [X379: subst > term > term] :
( ~ ! [X380: term] :
( ( $true
!= ( X372 @ id @ X380 @ id ) )
| ( $true
= ( X372 @ id @ ( X379 @ id @ X380 ) @ id ) ) )
| ( $true
= ( X372 @ id @ ( lam @ ( X379 @ sh @ one ) ) @ id ) )
| ~ ! [X381: term,X382: subst,X383: subst] :
( ( X379 @ ( comp @ X382 @ X383 ) @ ( sub @ X381 @ X383 ) )
= ( sub @ ( X379 @ X382 @ X381 ) @ X383 ) ) ) ) ) ) )
& ( ( induction = $true )
<=> ! [X409: term,X410: term > $o] :
( ( $true
= ( X410 @ X409 ) )
| ~ ! [X411: term] :
( ( $true
!= ( X410 @ X411 ) )
| ( $true
= ( X410 @ ( lam @ X411 ) ) ) )
| ~ ! [X413: term,X414: term] :
( ( $true
!= ( X410 @ X414 ) )
| ( $true
= ( X410 @ ( ap @ X414 @ X413 ) ) )
| ( $true
!= ( X410 @ X413 ) ) )
| ~ ! [X412: term] :
( ( $true
= ( X410 @ X412 ) )
| ( ( var @ X412 )
!= $true ) ) ) )
& ( ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ( $true
!= ( X26 @ id @ X25 @ id ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) )
| ~ ! [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
!= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) )
| ( $true
= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) ) )
| ~ ! [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
!= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
| ( $true
= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ~ ! [X31: term,X32: term] :
( ( $true
!= ( X26 @ id @ X31 @ id ) )
| ( $true
!= ( X26 @ id @ X32 @ id ) )
| ( $true
= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( ! [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
= X401 )
=> ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( $true
!= ( X402 @ X405 ) )
| ( ( X404 @ one )
= $true )
| ~ ! [X406: term] :
( ( X404 @ X406 )
= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction = $true )
<=> ! [X444: subst > term > subst > $o,X445: term] :
( ~ ! [X448: term] :
( ( $true
= ( X444 @ id @ X448 @ id ) )
| ( $true
!= ( var @ ( sub @ X448 @ id ) ) ) )
| ~ ! [X458: term,X459: subst,X460: subst,X461: subst] :
( ( ( X444 @ X460 @ X458 @ ( comp @ X461 @ X459 ) )
= $true )
| ( $true
!= ( X444 @ ( comp @ X460 @ X461 ) @ ( sub @ X458 @ X461 ) @ X459 ) ) )
| ( ( X444 @ id @ X445 @ id )
= $true )
| ~ ! [X446: term,X447: term] :
( ( $true
!= ( X444 @ id @ X446 @ id ) )
| ( ( X444 @ id @ ( ap @ ( sub @ X447 @ id ) @ X446 ) @ id )
= $true )
| ( $true
!= ( X444 @ id @ X447 @ id ) ) )
| ~ ! [X454: subst,X455: subst,X456: subst,X457: term] :
( ( $true
= ( X444 @ ( comp @ X454 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) )
| ( $true
!= ( X444 @ X454 @ X457 @ ( comp @ X455 @ X456 ) ) ) )
| ~ ! [X449: subst > term > term] :
( ~ ! [X450: term] :
( ( $true
= ( X444 @ id @ ( X449 @ id @ X450 ) @ id ) )
| ( $true
!= ( X444 @ id @ X450 @ id ) ) )
| ( $true
= ( X444 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id ) )
| ~ ! [X451: subst,X452: subst,X453: term] :
( ( sub @ ( X449 @ X452 @ X453 ) @ X451 )
= ( X449 @ ( comp @ X452 @ X451 ) @ ( sub @ X453 @ X451 ) ) ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( ! [X425: term] :
~ ! [X426: subst > term > term] :
~ ! [X427: term,X428: subst] :
( ( sub @ X425 @ ( push @ X427 @ X428 ) )
= ( X426 @ X428 @ X427 ) )
=> ( ! [X429: term] :
( ( sub @ X429 @ id )
= X429 )
=> ! [X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ~ ! [X433: subst > term > term] :
( ( $true
= ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id ) )
| ~ ! [X435: subst,X436: term,X437: subst] :
( ( X433 @ ( comp @ X437 @ X435 ) @ ( sub @ X436 @ X435 ) )
= ( sub @ ( X433 @ X437 @ X436 ) @ X435 ) )
| ~ ! [X434: term] :
( ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( $true
= ( X432 @ id @ ( X433 @ id @ X434 ) @ id ) ) ) )
| ( $true
= ( X431 @ ( lam @ X430 ) ) )
| ~ ! [X438: term] :
( ( X432 @ id @ X438 @ id )
= ( X431 @ X438 ) )
| ~ ! [X439: term] :
( ( $true
!= ( X431 @ X439 ) )
| ( $true
= ( X431 @ ( sub @ X430 @ ( push @ X439 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X257: term,X258: subst] :
( ( sub @ one @ ( push @ X257 @ X258 ) )
= X257 )
=> ( ! [X259: term,X260: subst] :
( ( comp @ sh @ ( push @ X259 @ X260 ) )
= X260 )
=> ( ! [X261: term,X262: term] :
( ( ( lam @ X262 )
!= ( lam @ X261 ) )
| ( X261 = X262 ) )
=> ! [X263: subst > term > term,X264: term,X265: subst,X266: subst > term > term] :
( ~ ! [X270: subst,X271: term,X272: subst] :
( ( sub @ ( X266 @ X270 @ X271 ) @ X272 )
= ( X266 @ ( comp @ X270 @ X272 ) @ ( sub @ X271 @ X272 ) ) )
| ( ( X263 @ X265 @ X264 )
= ( X266 @ X265 @ X264 ) )
| ~ ! [X267: subst,X268: term,X269: subst] :
( ( sub @ ( X263 @ X269 @ X268 ) @ X267 )
= ( X263 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) )
| ( ( lam @ ( X266 @ sh @ one ) )
!= ( lam @ ( X263 @ sh @ one ) ) ) ) ) ) ) )
& ( apnotvar = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X111: term] :
~ ! [X112: subst > term > term] :
~ ! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X227: term] :
( ( sub @ X227 @ id )
= X227 )
=> ( ! [X228: term > $o,X229: subst,X230: term] :
( ~ ! [X232: term] :
( ( $true
= ( X228 @ ( lam @ X232 ) ) )
| ~ ! [X233: term] :
( ( $true
!= ( X228 @ X233 ) )
| ( $true
= ( X228 @ ( sub @ X232 @ ( push @ X233 @ id ) ) ) ) ) )
| ( $true
= ( X228 @ ( sub @ X230 @ X229 ) ) )
| ~ ! [X231: term] :
( ( $true
!= ( var @ X231 ) )
| ( $true
= ( X228 @ ( sub @ X231 @ X229 ) ) ) )
| ~ ! [X234: term,X235: term] :
( ( $true
= ( X228 @ ( ap @ X234 @ X235 ) ) )
| ( $true
!= ( X228 @ X235 ) )
| ( $true
!= ( X228 @ X234 ) ) ) )
=> ! [X236: term,X237: term > $o] :
( ~ ! [X241: term] :
( ~ ! [X242: term] :
( ( $true
!= ( X237 @ X242 ) )
| ( $true
= ( X237 @ ( sub @ X241 @ ( push @ X242 @ id ) ) ) ) )
| ( $true
= ( X237 @ ( lam @ X241 ) ) ) )
| ( $true
= ( X237 @ X236 ) )
| ~ ! [X238: term] :
( ( $true
= ( X237 @ X238 ) )
| ( $true
!= ( var @ X238 ) ) )
| ~ ! [X239: term,X240: term] :
( ( $true
!= ( X237 @ X240 ) )
| ( $true
!= ( X237 @ X239 ) )
| ( $true
= ( X237 @ ( ap @ X240 @ X239 ) ) ) ) ) ) ) )
& ! [X23: d_subst] : ( d_id = X23 )
& ( ulamvarind = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ~ ! [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) )
| ~ ! [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) ) ) )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
<=> ( laminj = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X305: subst > term > subst > $o] :
~ ! [X306: term > $o] :
~ ! [X307: term] :
( ( X306 @ X307 )
= ( X305 @ id @ X307 @ id ) )
=> ( ! [X308: term > $o,X309: term] :
( ~ ! [X313: term] :
( ~ ! [X314: term] :
( ( $true
!= ( X308 @ X314 ) )
| ( $true
= ( X308 @ ( sub @ X313 @ ( push @ X314 @ id ) ) ) ) )
| ( $true
= ( X308 @ ( lam @ X313 ) ) ) )
| ~ ! [X310: term] :
( ( $true
= ( X308 @ X310 ) )
| ( ( var @ X310 )
!= $true ) )
| ( $true
= ( X308 @ X309 ) )
| ~ ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) )
| ( $true
!= ( X308 @ X311 ) ) ) )
=> ( ! [X315: term] :
( ( sub @ X315 @ id )
= X315 )
=> ( ! [X316: term,X317: term > $o,X318: subst > term > subst > $o] :
( ~ ! [X325: term] :
( ( $true
= ( X317 @ ( sub @ X316 @ ( push @ X325 @ id ) ) ) )
| ( $true
!= ( X317 @ X325 ) ) )
| ~ ! [X320: subst > term > term] :
( ( $true
= ( X318 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id ) )
| ~ ! [X324: term] :
( ( $true
= ( X318 @ id @ ( X320 @ id @ X324 ) @ id ) )
| ( $true
!= ( X318 @ id @ X324 @ id ) ) )
| ~ ! [X321: subst,X322: subst,X323: term] :
( ( sub @ ( X320 @ X321 @ X323 ) @ X322 )
= ( X320 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) )
| ~ ! [X319: term] :
( ( X318 @ id @ X319 @ id )
= ( X317 @ X319 ) )
| ( ( X317 @ ( lam @ X316 ) )
= $true ) )
=> ! [X326: subst > term > subst > $o,X327: term] :
( ( $true
= ( X326 @ id @ X327 @ id ) )
| ~ ! [X328: term,X329: term] :
( ( $true
!= ( X326 @ id @ X329 @ id ) )
| ( $true
!= ( X326 @ id @ X328 @ id ) )
| ( $true
= ( X326 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id ) ) )
| ~ ! [X330: subst > term > term] :
( ( $true
= ( X326 @ id @ ( lam @ ( X330 @ sh @ one ) ) @ id ) )
| ~ ! [X334: term] :
( ( $true
!= ( X326 @ id @ X334 @ id ) )
| ( $true
= ( X326 @ id @ ( X330 @ id @ X334 ) @ id ) ) )
| ~ ! [X331: subst,X332: subst,X333: term] :
( ( X330 @ ( comp @ X331 @ X332 ) @ ( sub @ X333 @ X332 ) )
= ( sub @ ( X330 @ X331 @ X333 ) @ X332 ) ) ) ) ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( termmset = $true )
<=> ! [X344: term] :
( ( sub @ X344 @ id )
= X344 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
=> ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
=> ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X218: term] :
( ( sub @ X218 @ id )
= X218 )
=> ( ! [X219: term,X220: term,X221: term,X222: term] :
( ( X219 = X222 )
| ( ( ap @ X222 @ X220 )
!= ( ap @ X219 @ X221 ) ) )
=> ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoaslamnotvar = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X462: subst > term > subst > $o] :
~ ! [X463: term > $o] :
~ ! [X464: term] :
( ( X462 @ id @ X464 @ id )
= ( X463 @ X464 ) )
=> ( ! [X465: term,X466: term > $o] :
( ~ ! [X469: term] :
( ( ( X466 @ X469 )
= $true )
| ( $true
!= ( var @ X469 ) ) )
| ~ ! [X470: term] :
( ( $true
= ( X466 @ ( lam @ X470 ) ) )
| ~ ! [X471: term] :
( ( ( X466 @ ( sub @ X470 @ ( push @ X471 @ id ) ) )
= $true )
| ( $true
!= ( X466 @ X471 ) ) ) )
| ( $true
= ( X466 @ X465 ) )
| ~ ! [X467: term,X468: term] :
( ( ( X466 @ X468 )
!= $true )
| ( $true
!= ( X466 @ X467 ) )
| ( $true
= ( X466 @ ( ap @ X468 @ X467 ) ) ) ) )
=> ( ! [X472: term] :
( ( sub @ X472 @ id )
= X472 )
=> ( ! [X473: term > $o,X474: subst > term > subst > $o,X475: term] :
( ~ ! [X477: term] :
( ( X474 @ id @ X477 @ id )
= ( X473 @ X477 ) )
| ( $true
= ( X473 @ ( lam @ X475 ) ) )
| ~ ! [X476: term] :
( ( $true
= ( X473 @ ( sub @ X475 @ ( push @ X476 @ id ) ) ) )
| ( ( X473 @ X476 )
!= $true ) )
| ~ ! [X478: subst > term > term] :
( ~ ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X481 @ X482 ) @ ( sub @ X480 @ X482 ) )
= ( sub @ ( X478 @ X481 @ X480 ) @ X482 ) )
| ~ ! [X479: term] :
( ( $true
= ( X474 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X474 @ id @ X479 @ id ) ) )
| ( $true
= ( X474 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) ) )
=> ! [X483: term,X484: subst > term > subst > $o] :
( ~ ! [X489: subst,X490: subst,X491: term,X492: subst] :
( ( $true
= ( X484 @ ( comp @ X489 @ X492 ) @ ( sub @ X491 @ X492 ) @ X490 ) )
| ( $true
!= ( X484 @ X489 @ X491 @ ( comp @ X492 @ X490 ) ) ) )
| ( $true
= ( X484 @ id @ X483 @ id ) )
| ~ ! [X485: subst,X486: subst,X487: term,X488: subst] :
( ( $true
= ( X484 @ X485 @ X487 @ ( comp @ X488 @ X486 ) ) )
| ( $true
!= ( X484 @ ( comp @ X485 @ X488 ) @ ( sub @ X487 @ X488 ) @ X486 ) ) )
| ~ ! [X496: subst > term > term] :
( ~ ! [X497: term,X498: subst,X499: subst] :
( ( X496 @ ( comp @ X499 @ X498 ) @ ( sub @ X497 @ X498 ) )
= ( sub @ ( X496 @ X499 @ X497 ) @ X498 ) )
| ~ ! [X500: term] :
( ( $true
!= ( X484 @ id @ X500 @ id ) )
| ( $true
= ( X484 @ id @ ( X496 @ id @ X500 ) @ id ) ) )
| ( $true
= ( X484 @ id @ ( lam @ ( X496 @ sh @ one ) ) @ id ) ) )
| ~ ! [X495: term] :
( ( $true
= ( X484 @ id @ X495 @ id ) )
| ( $true
!= ( var @ ( sub @ X495 @ id ) ) ) )
| ~ ! [X493: term,X494: term] :
( ( $true
!= ( X484 @ id @ X493 @ id ) )
| ( $true
= ( X484 @ id @ ( ap @ ( sub @ X493 @ id ) @ X494 ) @ id ) )
| ( $true
!= ( X484 @ id @ X494 @ id ) ) ) ) ) ) ) ) )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ! [X53: subst > term > subst > $o,X54: term] :
( ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X56: subst > term > term,X57: term] :
( ~ ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
| ~ ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) )
| ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) ) )
| ~ ! [X55: term] :
( ( $true
!= ( X53 @ id @ X55 @ id ) )
| ( $true
= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( substmonoid_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( ! [X2: term] :
( ( sub @ X2 @ id )
= X2 )
=> ( ! [X3: subst > term > subst > $o,X4: term] :
( ~ ! [X10: term] :
( ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X3 @ id @ X10 @ id ) ) )
| ~ ! [X5: subst > term > term] :
( ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) )
| ~ ! [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) )
| ~ ! [X9: term] :
( ( $true
!= ( X3 @ id @ X9 @ id ) )
| ( $true
= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X11: subst > term > subst > $o,X12: term] :
( ~ ! [X18: term] :
( ( $true
= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) )
| ( $true
!= ( X11 @ id @ X18 @ id ) ) )
| ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ~ ! [X13: subst > term > term] :
( ( $true
= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
| ~ ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) )
| ~ ! [X17: term] :
( ( $true
!= ( X11 @ id @ X17 @ id ) )
| ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X278: term,X279: term > $o,X280: term,X281: subst > term > subst > $o] :
( ~ ! [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
!= ( X281 @ ( comp @ X284 @ X287 ) @ ( sub @ X286 @ X287 ) @ X285 ) )
| ( $true
= ( X281 @ X284 @ X286 @ ( comp @ X287 @ X285 ) ) ) )
| ( $true
= ( X279 @ ( ap @ X278 @ X280 ) ) )
| ~ ! [X282: term,X283: term] :
( ( ( X281 @ id @ ( ap @ ( sub @ X283 @ id ) @ X282 ) @ id )
= $true )
| ( $true
!= ( X281 @ id @ X283 @ id ) )
| ( $true
!= ( X281 @ id @ X282 @ id ) ) )
| ( $true
!= ( X279 @ X280 ) )
| ~ ! [X292: term] :
( ( X279 @ X292 )
= ( X281 @ id @ X292 @ id ) )
| ~ ! [X288: term,X289: subst,X290: subst,X291: subst] :
( ( ( X281 @ X289 @ X288 @ ( comp @ X291 @ X290 ) )
!= $true )
| ( $true
= ( X281 @ ( comp @ X289 @ X291 ) @ ( sub @ X288 @ X291 ) @ X290 ) ) )
| ( $true
!= ( X279 @ X278 ) ) ) )
& ! [X388: d_term] : ( d_one = X388 )
& ( pushprop_gthm = $true )
& ( axclos = $true )
& ( ! [X252: subst > term > subst > $o] :
~ ! [X253: term > $o] :
~ ! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
<=> ( axidr = $true ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
= X335 )
=> ( ! [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
= X337 )
=> ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) )
| ( $true
!= ( X339 @ X342 ) ) ) ) ) )
& ( lamnotvar = $true )
& ( pushprop_lem1_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X51: d_subst,X52: d_subst] :
( ( ( d2subst @ X52 )
= ( d2subst @ X51 ) )
=> ( X51 = X52 ) )
& ( ( ! [X76: term] :
( ( sub @ X76 @ id )
= X76 )
=> ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ~ ! [X90: subst > term > term] :
( ~ ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
| ~ ! [X94: term] :
( ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) )
| ( $true
!= ( X78 @ id @ X94 @ id ) ) )
| ( $true
= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) ) )
| ~ ! [X89: term] :
( ( $true
!= ( X79 @ X89 ) )
| ( $true
= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ~ ! [X80: term] :
( ( X78 @ id @ X80 @ id )
= ( X79 @ X80 ) )
| ~ ! [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) )
| ( $true
= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) ) )
| ~ ! [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
!= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
| ( $true
= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $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 ) ) ) ) ) ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X397: subst > term > subst > $o] :
~ ! [X398: term > $o] :
~ ! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
!= ( ap @ X246 @ X247 ) )
| ( X245 = X247 ) )
=> ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) ) ) )
& ( ! [X216: term] :
~ ! [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
!= ( X217 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( pushprop_lthm_orig = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( termmset_gthm = $true )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( ( ! [X2: term] :
( ( sub @ X2 @ id )
= X2 )
=> ( ! [X3: subst > term > subst > $o,X4: term] :
( ~ ! [X5: subst > term > term] :
( ~ ! [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) )
| ~ ! [X9: term] :
( ( $true
= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) )
| ( $true
!= ( X3 @ id @ X9 @ id ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) ) )
| ~ ! [X10: term] :
( ( $true
!= ( X3 @ id @ X10 @ id ) )
| ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X11: subst > term > subst > $o,X12: term] :
( ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ~ ! [X13: subst > term > term] :
( ( $true
= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
| ~ ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) )
| ~ ! [X17: term] :
( ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) )
| ( $true
!= ( X11 @ id @ X17 @ id ) ) ) )
| ~ ! [X18: term] :
( ( $true
!= ( X11 @ id @ X18 @ id ) )
| ( $true
= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X19: term] :
~ ! [X20: subst > term > term] :
~ ! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) ) )
& ( hoasapinj2_gthm = $true )
& ! [X23: d_subst] : ( d_id = X23 )
& ( pushprop_lem1v2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ~ ! [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
!= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
| ( $true
= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
| ( $true
!= ( X26 @ id @ X31 @ id ) )
| ( $true
!= ( X26 @ id @ X32 @ id ) ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ( $true
!= ( X26 @ id @ X25 @ id ) )
| ~ ! [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) )
| ( $true
!= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) ) )
| ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( lamnotap != $true )
& ( pushprop_lthm_orig = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) )
| ~ ! [X43: subst > term > term] :
( ~ ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
| ( $true
= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
| ~ ! [X47: term] :
( ( ( X42 @ id @ X47 @ id )
!= $true )
| ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) ) ) )
| ~ ! [X48: term] :
( ( $true
!= ( X42 @ id @ X48 @ id ) )
| ( $true
= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ! [X49: term] :
~ ! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ! [X51: d_subst,X52: d_subst] :
( ( ( d2subst @ X52 )
= ( d2subst @ X51 ) )
=> ( X51 = X52 ) )
& ( pushprop_lem3v2 = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X53: subst > term > subst > $o,X54: term] :
( ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X55: term] :
( ( $true
= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) )
| ( $true
!= ( X53 @ id @ X55 @ id ) ) )
| ~ ! [X56: subst > term > term,X57: term] :
( ~ ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
| ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) )
| ~ ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) ) ) ) )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( hoaslamnotvar = $true )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X76: term] :
( ( sub @ X76 @ id )
= X76 )
=> ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ~ ! [X80: term] :
( ( X78 @ id @ X80 @ id )
= ( X79 @ X80 ) )
| ~ ! [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
!= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
| ( $true
= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) )
| ~ ! [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) )
| ( $true
= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) ) )
| ~ ! [X89: term] :
( ( $true
!= ( X79 @ X89 ) )
| ( $true
= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ~ ! [X90: subst > term > term] :
( ~ ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
| ~ ! [X94: term] :
( ( $true
!= ( X78 @ id @ X94 @ id ) )
| ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) ) )
| ( $true
= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) ) ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ~ ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
= ( X100 @ one ) )
| ( $true
!= ( X99 @ X102 ) ) ) )
& ( ( induction2 = $true )
<=> ! [X104: term,X105: term > $o] :
( ~ ! [X106: term] :
( ( $true
= ( X105 @ ( lam @ X106 ) ) )
| ~ ! [X107: term] :
( ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) )
| ( ( X105 @ X107 )
!= $true ) ) )
| ~ ! [X108: term] :
( ( ( var @ X108 )
!= $true )
| ( $true
= ( X105 @ X108 ) ) )
| ( $true
= ( X105 @ X104 ) )
| ~ ! [X109: term,X110: term] :
( ( $true
= ( X105 @ ( ap @ X109 @ X110 ) ) )
| ( $true
!= ( X105 @ X110 ) )
| ( ( X105 @ X109 )
!= $true ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( axmap = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X111: term] :
~ ! [X112: subst > term > term] :
~ ! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
= X116 )
=> ( ! [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
= X117 )
=> ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
=> ( ! [X120: term > $o,X121: term] :
( ( $true
= ( X120 @ X121 ) )
| ~ ! [X122: term] :
( ( $true
= ( X120 @ X122 ) )
| ( ( var @ X122 )
!= $true ) )
| ~ ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) )
| ~ ! [X125: term] :
( ( $true
!= ( X120 @ X125 ) )
| ( $true
= ( X120 @ ( lam @ X125 ) ) ) ) )
=> ! [X126: term > $o,X127: term,X128: subst] :
( ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) )
| ~ ! [X129: term,X130: term] :
( ( ( X126 @ ( ap @ X130 @ X129 ) )
= $true )
| ( $true
!= ( X126 @ X129 ) )
| ( $true
!= ( X126 @ X130 ) ) )
| ~ ! [X131: term] :
( ( $true
= ( X126 @ ( lam @ X131 ) ) )
| ~ ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) ) )
| ~ ! [X133: term] :
( ( $true
!= ( var @ X133 ) )
| ( $true
= ( X126 @ ( sub @ X133 @ X128 ) ) ) ) ) ) ) ) ) )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
=> ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
=> ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) ) ) ) )
& ( apnotvar = $true )
& ( ( ! [X142: term > $o,X143: term] :
( ( $true
= ( X142 @ X143 ) )
| ~ ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
| ~ ! [X145: term,X146: term] :
( ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) )
| ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) ) )
| ~ ! [X147: term] :
( ( $true
= ( X142 @ ( lam @ X147 ) ) )
| ~ ! [X148: term] :
( ( $true
= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) )
| ( $true
!= ( X142 @ X148 ) ) ) ) )
=> ( ! [X149: subst > term > subst > $o,X150: term,X151: term] :
( ( $true
!= ( X149 @ id @ X151 @ id ) )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
| ~ ! [X156: term,X157: term] :
( ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) )
| ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) ) )
| ( $true
= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
| ( $true
!= ( X149 @ id @ X150 @ id ) )
| ~ ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) )
| ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true ) ) )
=> ( ! [X162: subst > term > subst > $o,X163: term] :
( ( $true
= ( X162 @ id @ ( lam @ X163 ) @ id ) )
| ~ ! [X164: term] :
( ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) )
| ( $true
!= ( X162 @ id @ X164 @ id ) ) )
| ~ ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) )
| ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) ) )
| ~ ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) )
| ~ ! [X173: subst > term > term] :
( ~ ! [X174: term] :
( ( $true
= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) )
| ( $true
!= ( X162 @ id @ X174 @ id ) ) )
| ~ ! [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) ) )
=> ! [X178: term,X179: subst > term > subst > $o] :
( ~ ! [X180: term] :
( ( $true
= ( X179 @ id @ X180 @ id ) )
| ( $true
!= ( var @ ( sub @ X180 @ id ) ) ) )
| ~ ! [X181: term,X182: term] :
( ( ( X179 @ id @ X182 @ id )
!= $true )
| ( $true
= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) )
| ( $true
!= ( X179 @ id @ X181 @ id ) ) )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
!= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) )
| ( $true
= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) ) )
| ~ ! [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) )
| ( $true
!= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true )
| ~ ! [X191: subst > term > term] :
( ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) )
| ~ ! [X195: term] :
( ( $true
!= ( X179 @ id @ X195 @ id ) )
| ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop = $true )
& ( pushprop_lem1_gthm = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X196: subst,X197: term,X198: term > $o] :
~ ! [X199: term > $o] :
~ ! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( ( ! [X201: term] :
( ( sub @ X201 @ id )
= X201 )
=> ! [X202: term] :
( ( sub @ X202 @ id )
= X202 ) )
<=> ( termmset_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ~ ! [X205: term,X206: term] :
( ( $true
!= ( X203 @ id @ X206 @ id ) )
| ( $true
= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
| ( ( X203 @ id @ X205 @ id )
!= $true ) )
| ~ ! [X207: subst > term > term] :
( ( $true
= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) )
| ~ ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
| ~ ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ulamvar1 != $true )
& ( hoasapnotvar = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ! [X216: term] :
~ ! [X217: subst > term > term] :
( ( sub @ X216 @ ( push @ one @ sh ) )
!= ( X217 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X218: term] :
( ( sub @ X218 @ id )
= X218 )
=> ( ! [X219: term,X220: term,X221: term,X222: term] :
( ( X219 = X222 )
| ( ( ap @ X222 @ X220 )
!= ( ap @ X219 @ X221 ) ) )
=> ! [X223: term,X224: term,X225: term,X226: term] :
( ( ( ap @ ( sub @ X226 @ id ) @ X224 )
!= ( ap @ ( sub @ X225 @ id ) @ X223 ) )
| ( X225 = X226 ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( induction2_lthm = $true )
<=> ( ! [X227: term] :
( ( sub @ X227 @ id )
= X227 )
=> ( ! [X228: term > $o,X229: subst,X230: term] :
( ~ ! [X231: term] :
( ( $true
!= ( var @ X231 ) )
| ( $true
= ( X228 @ ( sub @ X231 @ X229 ) ) ) )
| ~ ! [X232: term] :
( ~ ! [X233: term] :
( ( $true
= ( X228 @ ( sub @ X232 @ ( push @ X233 @ id ) ) ) )
| ( $true
!= ( X228 @ X233 ) ) )
| ( $true
= ( X228 @ ( lam @ X232 ) ) ) )
| ( $true
= ( X228 @ ( sub @ X230 @ X229 ) ) )
| ~ ! [X234: term,X235: term] :
( ( $true
!= ( X228 @ X235 ) )
| ( $true
= ( X228 @ ( ap @ X234 @ X235 ) ) )
| ( $true
!= ( X228 @ X234 ) ) ) )
=> ! [X236: term,X237: term > $o] :
( ~ ! [X238: term] :
( ( $true
= ( X237 @ X238 ) )
| ( $true
!= ( var @ X238 ) ) )
| ~ ! [X239: term,X240: term] :
( ( $true
!= ( X237 @ X240 ) )
| ( $true
= ( X237 @ ( ap @ X240 @ X239 ) ) )
| ( $true
!= ( X237 @ X239 ) ) )
| ~ ! [X241: term] :
( ~ ! [X242: term] :
( ( $true
!= ( X237 @ X242 ) )
| ( $true
= ( X237 @ ( sub @ X241 @ ( push @ X242 @ id ) ) ) ) )
| ( $true
= ( X237 @ ( lam @ X241 ) ) ) )
| ( $true
= ( X237 @ X236 ) ) ) ) ) )
& ( ! [X243: subst] :
( ( push @ ( sub @ one @ X243 ) @ ( comp @ sh @ X243 ) )
= X243 )
<=> ( axscons = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X244: term,X245: term,X246: term,X247: term] :
( ( ( ap @ X244 @ X245 )
!= ( ap @ X246 @ X247 ) )
| ( X245 = X247 ) )
=> ! [X248: term,X249: term,X250: term,X251: term] :
( ( X249 = X251 )
| ( ( ap @ ( sub @ X248 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X249 ) ) ) ) )
& ( ! [X252: subst > term > subst > $o] :
~ ! [X253: term > $o] :
~ ! [X254: term] :
( ( X253 @ X254 )
= ( X252 @ id @ X254 @ id ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ! [X255: term,X256: term] :
( ( ( sub @ X255 @ sh )
!= ( sub @ X256 @ sh ) )
| ( X255 = X256 ) )
<=> ( shinj = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X257: term,X258: subst] :
( ( sub @ one @ ( push @ X257 @ X258 ) )
= X257 )
=> ( ! [X259: term,X260: subst] :
( ( comp @ sh @ ( push @ X259 @ X260 ) )
= X260 )
=> ( ! [X261: term,X262: term] :
( ( ( lam @ X262 )
!= ( lam @ X261 ) )
| ( X261 = X262 ) )
=> ! [X263: subst > term > term,X264: term,X265: subst,X266: subst > term > term] :
( ~ ! [X270: subst,X271: term,X272: subst] :
( ( sub @ ( X266 @ X270 @ X271 ) @ X272 )
= ( X266 @ ( comp @ X270 @ X272 ) @ ( sub @ X271 @ X272 ) ) )
| ( ( X263 @ X265 @ X264 )
= ( X266 @ X265 @ X264 ) )
| ~ ! [X267: subst,X268: term,X269: subst] :
( ( sub @ ( X263 @ X269 @ X268 ) @ X267 )
= ( X263 @ ( comp @ X269 @ X267 ) @ ( sub @ X268 @ X267 ) ) )
| ( ( lam @ ( X266 @ sh @ one ) )
!= ( lam @ ( X263 @ sh @ one ) ) ) ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X273: term > $o,X274: subst,X275: term] :
~ ! [X276: term > $o] :
~ ! [X277: term] :
( ( X273 @ ( sub @ X277 @ ( push @ X275 @ X274 ) ) )
= ( X276 @ X277 ) ) )
& ( axapp = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X278: term,X279: term > $o,X280: term,X281: subst > term > subst > $o] :
( ~ ! [X282: term,X283: term] :
( ( ( X281 @ id @ ( ap @ ( sub @ X283 @ id ) @ X282 ) @ id )
= $true )
| ( $true
!= ( X281 @ id @ X282 @ id ) )
| ( $true
!= ( X281 @ id @ X283 @ id ) ) )
| ( $true
!= ( X279 @ X280 ) )
| ( $true
= ( X279 @ ( ap @ X278 @ X280 ) ) )
| ~ ! [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
!= ( X281 @ ( comp @ X284 @ X287 ) @ ( sub @ X286 @ X287 ) @ X285 ) )
| ( $true
= ( X281 @ X284 @ X286 @ ( comp @ X287 @ X285 ) ) ) )
| ~ ! [X288: term,X289: subst,X290: subst,X291: subst] :
( ( $true
= ( X281 @ ( comp @ X289 @ X291 ) @ ( sub @ X288 @ X291 ) @ X290 ) )
| ( ( X281 @ X289 @ X288 @ ( comp @ X291 @ X290 ) )
!= $true ) )
| ~ ! [X292: term] :
( ( X279 @ X292 )
= ( X281 @ id @ X292 @ id ) )
| ( $true
!= ( X279 @ X278 ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasapinj1_gthm = $true )
& ! [X293: term] :
? [X294: d_term] :
( ( d2term @ X294 )
= X293 )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X295: term > $o,X296: term,X297: subst > term > subst > $o] :
( ~ ! [X298: subst > term > term] :
( ~ ! [X299: term] :
( ( ( X297 @ id @ X299 @ id )
!= $true )
| ( $true
= ( X297 @ id @ ( X298 @ id @ X299 ) @ id ) ) )
| ( $true
= ( X297 @ id @ ( lam @ ( X298 @ sh @ one ) ) @ id ) )
| ~ ! [X300: subst,X301: term,X302: subst] :
( ( sub @ ( X298 @ X302 @ X301 ) @ X300 )
= ( X298 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) ) ) )
| ( $true
= ( X295 @ ( lam @ X296 ) ) )
| ~ ! [X303: term] :
( ( X295 @ X303 )
= ( X297 @ id @ X303 @ id ) )
| ~ ! [X304: term] :
( ( ( X295 @ X304 )
!= $true )
| ( $true
= ( X295 @ ( sub @ X296 @ ( push @ X304 @ id ) ) ) ) ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( ! [X305: subst > term > subst > $o] :
~ ! [X306: term > $o] :
~ ! [X307: term] :
( ( X306 @ X307 )
= ( X305 @ id @ X307 @ id ) )
=> ( ! [X308: term > $o,X309: term] :
( ~ ! [X310: term] :
( ( ( var @ X310 )
!= $true )
| ( $true
= ( X308 @ X310 ) ) )
| ~ ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
!= ( X308 @ X311 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) ) )
| ( $true
= ( X308 @ X309 ) )
| ~ ! [X313: term] :
( ~ ! [X314: term] :
( ( $true
= ( X308 @ ( sub @ X313 @ ( push @ X314 @ id ) ) ) )
| ( $true
!= ( X308 @ X314 ) ) )
| ( $true
= ( X308 @ ( lam @ X313 ) ) ) ) )
=> ( ! [X315: term] :
( ( sub @ X315 @ id )
= X315 )
=> ( ! [X316: term,X317: term > $o,X318: subst > term > subst > $o] :
( ~ ! [X319: term] :
( ( X318 @ id @ X319 @ id )
= ( X317 @ X319 ) )
| ( ( X317 @ ( lam @ X316 ) )
= $true )
| ~ ! [X320: subst > term > term] :
( ~ ! [X321: subst,X322: subst,X323: term] :
( ( sub @ ( X320 @ X321 @ X323 ) @ X322 )
= ( X320 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) ) )
| ( $true
= ( X318 @ id @ ( lam @ ( X320 @ sh @ one ) ) @ id ) )
| ~ ! [X324: term] :
( ( $true
!= ( X318 @ id @ X324 @ id ) )
| ( $true
= ( X318 @ id @ ( X320 @ id @ X324 ) @ id ) ) ) )
| ~ ! [X325: term] :
( ( $true
= ( X317 @ ( sub @ X316 @ ( push @ X325 @ id ) ) ) )
| ( $true
!= ( X317 @ X325 ) ) ) )
=> ! [X326: subst > term > subst > $o,X327: term] :
( ~ ! [X328: term,X329: term] :
( ( $true
!= ( X326 @ id @ X328 @ id ) )
| ( $true
!= ( X326 @ id @ X329 @ id ) )
| ( $true
= ( X326 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id ) ) )
| ( $true
= ( X326 @ id @ X327 @ id ) )
| ~ ! [X330: subst > term > term] :
( ~ ! [X331: subst,X332: subst,X333: term] :
( ( X330 @ ( comp @ X331 @ X332 ) @ ( sub @ X333 @ X332 ) )
= ( sub @ ( X330 @ X331 @ X333 ) @ X332 ) )
| ~ ! [X334: term] :
( ( $true
!= ( X326 @ id @ X334 @ id ) )
| ( $true
= ( X326 @ id @ ( X330 @ id @ X334 ) @ id ) ) )
| ( $true
= ( X326 @ id @ ( lam @ ( X330 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( ! [X335: term,X336: subst] :
( ( sub @ one @ ( push @ X335 @ X336 ) )
= X335 )
=> ( ! [X337: subst,X338: term] :
( ( comp @ sh @ ( push @ X338 @ X337 ) )
= X337 )
=> ! [X339: term > $o,X340: term,X341: subst,X342: term,X343: term > $o] :
( ( $true
!= ( X339 @ X342 ) )
| ( $true
= ( X343 @ ( sub @ X342 @ ( push @ X340 @ X341 ) ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( axassoc = $true )
& ( ( termmset = $true )
<=> ! [X344: term] :
( ( sub @ X344 @ id )
= X344 ) )
& ( hoasapnotvar_gthm = $true )
& ( ulamvarsh = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X345: term > $o,X346: term,X347: subst > term > subst > $o] :
( ~ ! [X348: term] :
( ( $true
!= ( X345 @ X348 ) )
| ( ( X345 @ ( sub @ X346 @ ( push @ X348 @ id ) ) )
= $true ) )
| ~ ! [X349: subst > term > term] :
( ~ ! [X350: term] :
( ( $true
= ( X347 @ id @ ( X349 @ id @ X350 ) @ id ) )
| ( ( X347 @ id @ X350 @ id )
!= $true ) )
| ( $true
= ( X347 @ id @ ( lam @ ( X349 @ sh @ one ) ) @ id ) )
| ~ ! [X351: subst,X352: subst,X353: term] :
( ( X349 @ ( comp @ X351 @ X352 ) @ ( sub @ X353 @ X352 ) )
= ( sub @ ( X349 @ X351 @ X353 ) @ X352 ) ) )
| ~ ! [X354: subst,X355: subst,X356: subst,X357: term] :
( ( $true
= ( X347 @ X354 @ X357 @ ( comp @ X356 @ X355 ) ) )
| ( ( X347 @ ( comp @ X354 @ X356 ) @ ( sub @ X357 @ X356 ) @ X355 )
!= $true ) )
| ~ ! [X358: term] :
( ( X345 @ X358 )
= ( X347 @ id @ X358 @ id ) )
| ~ ! [X359: subst,X360: subst,X361: term,X362: subst] :
( ( $true
= ( X347 @ ( comp @ X359 @ X360 ) @ ( sub @ X361 @ X360 ) @ X362 ) )
| ( $true
!= ( X347 @ X359 @ X361 @ ( comp @ X360 @ X362 ) ) ) )
| ( ( X345 @ ( lam @ X346 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
=> ( ! [X364: term,X365: subst > term > subst > $o] :
( ~ ! [X366: subst > term > term] :
( ~ ! [X367: term,X368: subst,X369: subst] :
( ( X366 @ ( comp @ X369 @ X368 ) @ ( sub @ X367 @ X368 ) )
= ( sub @ ( X366 @ X369 @ X367 ) @ X368 ) )
| ~ ! [X370: term] :
( ( $true
!= ( X365 @ id @ X370 @ id ) )
| ( $true
= ( X365 @ id @ ( X366 @ id @ X370 ) @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X366 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( sub @ X364 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X371: term] :
( ( $true
!= ( X365 @ id @ X371 @ id ) )
| ( $true
= ( X365 @ id @ ( sub @ X364 @ ( push @ X371 @ id ) ) @ id ) ) ) )
=> ! [X372: subst > term > subst > $o,X373: term] :
( ( $true
= ( X372 @ id @ ( lam @ X373 ) @ id ) )
| ~ ! [X374: subst,X375: subst,X376: subst,X377: term] :
( ( $true
!= ( X372 @ X376 @ X377 @ ( comp @ X374 @ X375 ) ) )
| ( ( X372 @ ( comp @ X376 @ X374 ) @ ( sub @ X377 @ X374 ) @ X375 )
= $true ) )
| ~ ! [X378: term] :
( ( $true
= ( X372 @ id @ ( sub @ X373 @ ( push @ X378 @ id ) ) @ id ) )
| ( $true
!= ( X372 @ id @ X378 @ id ) ) )
| ~ ! [X379: subst > term > term] :
( ( $true
= ( X372 @ id @ ( lam @ ( X379 @ sh @ one ) ) @ id ) )
| ~ ! [X380: term] :
( ( $true
!= ( X372 @ id @ X380 @ id ) )
| ( $true
= ( X372 @ id @ ( X379 @ id @ X380 ) @ id ) ) )
| ~ ! [X381: term,X382: subst,X383: subst] :
( ( X379 @ ( comp @ X382 @ X383 ) @ ( sub @ X381 @ X383 ) )
= ( sub @ ( X379 @ X382 @ X381 ) @ X383 ) ) )
| ~ ! [X384: subst,X385: subst,X386: term,X387: subst] :
( ( $true
!= ( X372 @ ( comp @ X387 @ X384 ) @ ( sub @ X386 @ X384 ) @ X385 ) )
| ( ( X372 @ X387 @ X386 @ ( comp @ X384 @ X385 ) )
= $true ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ! [X388: d_term] : ( d_one = X388 )
& ( ! [X389: term,X390: subst > term > subst > $o] :
( ( $true
= ( X390 @ id @ ( lam @ ( sub @ X389 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X391: term] :
( ( $true
!= ( X390 @ id @ X391 @ id ) )
| ( ( X390 @ id @ ( sub @ X389 @ ( push @ X391 @ id ) ) @ id )
= $true ) )
| ~ ! [X392: subst > term > term] :
( ( $true
= ( X390 @ id @ ( lam @ ( X392 @ sh @ one ) ) @ id ) )
| ~ ! [X393: subst,X394: term,X395: subst] :
( ( X392 @ ( comp @ X395 @ X393 ) @ ( sub @ X394 @ X393 ) )
= ( sub @ ( X392 @ X395 @ X394 ) @ X393 ) )
| ~ ! [X396: term] :
( ( $true
= ( X390 @ id @ ( X392 @ id @ X396 ) @ id ) )
| ( $true
!= ( X390 @ id @ X396 @ id ) ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X397: subst > term > subst > $o] :
~ ! [X398: term > $o] :
~ ! [X399: term] :
( ( X398 @ X399 )
= ( X397 @ id @ X399 @ id ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X400: subst,X401: term] :
( ( sub @ one @ ( push @ X401 @ X400 ) )
= X401 )
=> ! [X402: term > $o,X403: subst,X404: term > $o,X405: term] :
( ( ( X404 @ one )
= $true )
| ~ ! [X406: term] :
( ( X404 @ X406 )
= ( X402 @ ( sub @ X406 @ ( push @ X405 @ X403 ) ) ) )
| ( $true
!= ( X402 @ X405 ) ) ) ) )
& ! [X407: d_term,X408: d_term] :
( ( ( d2term @ X407 )
= ( d2term @ X408 ) )
=> ( X407 = X408 ) )
& ( ( induction = $true )
<=> ! [X409: term,X410: term > $o] :
( ~ ! [X411: term] :
( ( $true
!= ( X410 @ X411 ) )
| ( $true
= ( X410 @ ( lam @ X411 ) ) ) )
| ( $true
= ( X410 @ X409 ) )
| ~ ! [X412: term] :
( ( ( var @ X412 )
!= $true )
| ( $true
= ( X410 @ X412 ) ) )
| ~ ! [X413: term,X414: term] :
( ( $true
= ( X410 @ ( ap @ X414 @ X413 ) ) )
| ( $true
!= ( X410 @ X414 ) )
| ( $true
!= ( X410 @ X413 ) ) ) ) )
& ( lamnotvar = $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 ) ) ) ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X415: term,X416: subst > term > term,X417: subst > term > term,X418: subst] :
( ~ ! [X419: subst,X420: term,X421: subst] :
( ( X417 @ ( comp @ X419 @ X421 ) @ ( sub @ X420 @ X421 ) )
= ( sub @ ( X417 @ X419 @ X420 ) @ X421 ) )
| ( ( X416 @ X418 @ X415 )
= ( X417 @ X418 @ X415 ) )
| ~ ! [X422: subst,X423: term,X424: subst] :
( ( sub @ ( X416 @ X424 @ X423 ) @ X422 )
= ( X416 @ ( comp @ X424 @ X422 ) @ ( sub @ X423 @ X422 ) ) )
| ( ( lam @ ( X417 @ sh @ one ) )
!= ( lam @ ( X416 @ sh @ one ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X425: term] :
~ ! [X426: subst > term > term] :
~ ! [X427: term,X428: subst] :
( ( sub @ X425 @ ( push @ X427 @ X428 ) )
= ( X426 @ X428 @ X427 ) )
=> ( ! [X429: term] :
( ( sub @ X429 @ id )
= X429 )
=> ! [X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ( $true
= ( X431 @ ( lam @ X430 ) ) )
| ~ ! [X433: subst > term > term] :
( ~ ! [X434: term] :
( ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( $true
= ( X432 @ id @ ( X433 @ id @ X434 ) @ id ) ) )
| ~ ! [X435: subst,X436: term,X437: subst] :
( ( X433 @ ( comp @ X437 @ X435 ) @ ( sub @ X436 @ X435 ) )
= ( sub @ ( X433 @ X437 @ X436 ) @ X435 ) )
| ( $true
= ( X432 @ id @ ( lam @ ( X433 @ sh @ one ) ) @ id ) ) )
| ~ ! [X438: term] :
( ( X432 @ id @ X438 @ id )
= ( X431 @ X438 ) )
| ~ ! [X439: term] :
( ( $true
= ( X431 @ ( sub @ X430 @ ( push @ X439 @ id ) ) ) )
| ( $true
!= ( X431 @ X439 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X440: term,X441: term] :
( ( X440 = X441 )
| ( ( lam @ X440 )
!= ( lam @ X441 ) ) )
<=> ( laminj = $true ) )
& ( ulamvarind = $true )
& ( ( substmonoid = $true )
<=> ( ! [X443: subst] :
( ( comp @ id @ X443 )
= X443 )
& ! [X442: subst] :
( ( comp @ X442 @ id )
= X442 ) ) )
& ( ( hoasinduction = $true )
<=> ! [X444: subst > term > subst > $o,X445: term] :
( ~ ! [X446: term,X447: term] :
( ( $true
!= ( X444 @ id @ X447 @ id ) )
| ( ( X444 @ id @ ( ap @ ( sub @ X447 @ id ) @ X446 ) @ id )
= $true )
| ( $true
!= ( X444 @ id @ X446 @ id ) ) )
| ~ ! [X448: term] :
( ( $true
= ( X444 @ id @ X448 @ id ) )
| ( $true
!= ( var @ ( sub @ X448 @ id ) ) ) )
| ~ ! [X449: subst > term > term] :
( ( $true
= ( X444 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id ) )
| ~ ! [X450: term] :
( ( $true
= ( X444 @ id @ ( X449 @ id @ X450 ) @ id ) )
| ( $true
!= ( X444 @ id @ X450 @ id ) ) )
| ~ ! [X451: subst,X452: subst,X453: term] :
( ( sub @ ( X449 @ X452 @ X453 ) @ X451 )
= ( X449 @ ( comp @ X452 @ X451 ) @ ( sub @ X453 @ X451 ) ) ) )
| ~ ! [X454: subst,X455: subst,X456: subst,X457: term] :
( ( $true
!= ( X444 @ X454 @ X457 @ ( comp @ X455 @ X456 ) ) )
| ( $true
= ( X444 @ ( comp @ X454 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X444 @ id @ X445 @ id )
= $true )
| ~ ! [X458: term,X459: subst,X460: subst,X461: subst] :
( ( ( X444 @ X460 @ X458 @ ( comp @ X461 @ X459 ) )
= $true )
| ( $true
!= ( X444 @ ( comp @ X460 @ X461 ) @ ( sub @ X458 @ X461 ) @ X459 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X462: subst > term > subst > $o] :
~ ! [X463: term > $o] :
~ ! [X464: term] :
( ( X462 @ id @ X464 @ id )
= ( X463 @ X464 ) )
=> ( ! [X465: term,X466: term > $o] :
( ~ ! [X467: term,X468: term] :
( ( $true
!= ( X466 @ X467 ) )
| ( ( X466 @ X468 )
!= $true )
| ( $true
= ( X466 @ ( ap @ X468 @ X467 ) ) ) )
| ~ ! [X469: term] :
( ( $true
!= ( var @ X469 ) )
| ( ( X466 @ X469 )
= $true ) )
| ~ ! [X470: term] :
( ~ ! [X471: term] :
( ( ( X466 @ ( sub @ X470 @ ( push @ X471 @ id ) ) )
= $true )
| ( $true
!= ( X466 @ X471 ) ) )
| ( $true
= ( X466 @ ( lam @ X470 ) ) ) )
| ( $true
= ( X466 @ X465 ) ) )
=> ( ! [X472: term] :
( ( sub @ X472 @ id )
= X472 )
=> ( ! [X473: term > $o,X474: subst > term > subst > $o,X475: term] :
( ( $true
= ( X473 @ ( lam @ X475 ) ) )
| ~ ! [X476: term] :
( ( $true
= ( X473 @ ( sub @ X475 @ ( push @ X476 @ id ) ) ) )
| ( ( X473 @ X476 )
!= $true ) )
| ~ ! [X477: term] :
( ( X474 @ id @ X477 @ id )
= ( X473 @ X477 ) )
| ~ ! [X478: subst > term > term] :
( ( $true
= ( X474 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) )
| ~ ! [X479: term] :
( ( $true
= ( X474 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X474 @ id @ X479 @ id ) ) )
| ~ ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X481 @ X482 ) @ ( sub @ X480 @ X482 ) )
= ( sub @ ( X478 @ X481 @ X480 ) @ X482 ) ) ) )
=> ! [X483: term,X484: subst > term > subst > $o] :
( ~ ! [X485: subst,X486: subst,X487: term,X488: subst] :
( ( $true
= ( X484 @ X485 @ X487 @ ( comp @ X488 @ X486 ) ) )
| ( $true
!= ( X484 @ ( comp @ X485 @ X488 ) @ ( sub @ X487 @ X488 ) @ X486 ) ) )
| ~ ! [X489: subst,X490: subst,X491: term,X492: subst] :
( ( $true
= ( X484 @ ( comp @ X489 @ X492 ) @ ( sub @ X491 @ X492 ) @ X490 ) )
| ( $true
!= ( X484 @ X489 @ X491 @ ( comp @ X492 @ X490 ) ) ) )
| ( $true
= ( X484 @ id @ X483 @ id ) )
| ~ ! [X493: term,X494: term] :
( ( $true
!= ( X484 @ id @ X494 @ id ) )
| ( $true
= ( X484 @ id @ ( ap @ ( sub @ X493 @ id ) @ X494 ) @ id ) )
| ( $true
!= ( X484 @ id @ X493 @ id ) ) )
| ~ ! [X495: term] :
( ( $true
= ( X484 @ id @ X495 @ id ) )
| ( $true
!= ( var @ ( sub @ X495 @ id ) ) ) )
| ~ ! [X496: subst > term > term] :
( ( $true
= ( X484 @ id @ ( lam @ ( X496 @ sh @ one ) ) @ id ) )
| ~ ! [X497: term,X498: subst,X499: subst] :
( ( X496 @ ( comp @ X499 @ X498 ) @ ( sub @ X497 @ X498 ) )
= ( sub @ ( X496 @ X499 @ X497 ) @ X498 ) )
| ~ ! [X500: term] :
( ( $true
!= ( X484 @ id @ X500 @ id ) )
| ( $true
= ( X484 @ id @ ( X496 @ id @ X500 ) @ id ) ) ) ) ) ) ) ) ) )
& ( ! [X501: term,X502: subst > term > subst > $o] :
( ~ ! [X503: subst > term > term] :
( ~ ! [X504: subst,X505: term,X506: subst] :
( ( X503 @ ( comp @ X506 @ X504 ) @ ( sub @ X505 @ X504 ) )
= ( sub @ ( X503 @ X506 @ X505 ) @ X504 ) )
| ~ ! [X507: term] :
( ( $true
!= ( X502 @ id @ X507 @ id ) )
| ( $true
= ( X502 @ id @ ( X503 @ id @ X507 ) @ id ) ) )
| ( ( X502 @ id @ ( lam @ ( X503 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X502 @ id @ ( lam @ ( sub @ X501 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X508: term] :
( ( $true
!= ( X502 @ id @ X508 @ id ) )
| ( $true
= ( X502 @ id @ ( sub @ X501 @ ( push @ X508 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X509: term,X510: term,X511: subst > term > term] :
( ~ ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X511 @ X512 @ X513 ) @ X514 )
= ( X511 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
| ( ( lam @ ( X511 @ sh @ one ) )
!= ( ap @ ( sub @ X510 @ id ) @ X509 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axclos = $true )
& ( ! [X515: subst,X516: term > $o,X517: term] :
( ~ ! [X518: term] :
( ( $true
= ( X516 @ ( sub @ X518 @ X515 ) ) )
| ( $true
!= ( var @ X518 ) ) )
| ~ ! [X519: term,X520: term] :
( ( $true
!= ( X516 @ X519 ) )
| ( $true
= ( X516 @ ( ap @ X520 @ X519 ) ) )
| ( $true
!= ( X516 @ X520 ) ) )
| ~ ! [X521: term] :
( ~ ! [X522: term] :
( ( $true
= ( X516 @ ( sub @ X521 @ ( push @ X522 @ id ) ) ) )
| ( $true
!= ( X516 @ X522 ) ) )
| ( $true
= ( X516 @ ( lam @ X521 ) ) ) )
| ( $true
= ( X516 @ ( sub @ X517 @ X515 ) ) ) )
<=> ( induction2lem = $true ) )
& ( ! [X523: subst > term > subst > $o,X524: term] :
( ~ ! [X525: term] :
( ( $true
!= ( X523 @ id @ X525 @ id ) )
| ( $true
= ( X523 @ id @ ( sub @ X524 @ ( push @ X525 @ id ) ) @ id ) ) )
| ~ ! [X526: subst,X527: subst,X528: subst,X529: term] :
( ( $true
!= ( X523 @ X527 @ X529 @ ( comp @ X526 @ X528 ) ) )
| ( ( X523 @ ( comp @ X527 @ X526 ) @ ( sub @ X529 @ X526 ) @ X528 )
= $true ) )
| ( $true
= ( X523 @ id @ ( lam @ X524 ) @ id ) )
| ~ ! [X530: subst > term > term] :
( ~ ! [X531: subst,X532: term,X533: subst] :
( ( sub @ ( X530 @ X531 @ X532 ) @ X533 )
= ( X530 @ ( comp @ X531 @ X533 ) @ ( sub @ X532 @ X533 ) ) )
| ( $true
= ( X523 @ id @ ( lam @ ( X530 @ sh @ one ) ) @ id ) )
| ~ ! [X534: term] :
( ( $true
!= ( X523 @ id @ X534 @ id ) )
| ( $true
= ( X523 @ id @ ( X530 @ id @ X534 ) @ id ) ) ) )
| ~ ! [X535: term,X536: subst,X537: subst,X538: subst] :
( ( $true
= ( X523 @ X538 @ X535 @ ( comp @ X536 @ X537 ) ) )
| ( $true
!= ( X523 @ ( comp @ X538 @ X536 ) @ ( sub @ X535 @ X536 ) @ X537 ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ! [X539: subst] :
( ( comp @ X539 @ id )
= X539 )
<=> ( axidr = $true ) )
& ( axvarshift = $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( termmset_gthm = $true )
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( ( ! [X2: term] :
( ( sub @ X2 @ id )
= X2 )
=> ( ! [X3: subst > term > subst > $o,X4: term] :
( ~ ! [X5: subst > term > term] :
( ~ ! [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) )
| ~ ! [X9: term] :
( ( $true
= ( X3 @ id @ ( X5 @ id @ X9 ) @ id ) )
| ( $true
!= ( X3 @ id @ X9 @ id ) ) )
| ( $true
= ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) ) )
| ~ ! [X10: term] :
( ( $true
!= ( X3 @ id @ X10 @ id ) )
| ( ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X11: subst > term > subst > $o,X12: term] :
( ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ~ ! [X13: subst > term > term] :
( ( $true
= ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id ) )
| ~ ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) )
| ~ ! [X17: term] :
( ( $true
= ( X11 @ id @ ( X13 @ id @ X17 ) @ id ) )
| ( $true
!= ( X11 @ id @ X17 @ id ) ) ) )
| ~ ! [X18: term] :
( ( $true
!= ( X11 @ id @ X18 @ id ) )
| ( $true
= ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X19: term] :
~ ! [X20: subst > term > term] :
~ ! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) ) )
& ( hoasapinj2_gthm = $true )
& ! [X23: d_subst] : ( d_id = X23 )
& ( pushprop_lem1v2_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ~ ! [X27: subst,X28: term,X29: subst,X30: subst] :
( ( $true
!= ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 ) )
| ( $true
= ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) ) )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
| ( $true
!= ( X26 @ id @ X31 @ id ) )
| ( $true
!= ( X26 @ id @ X32 @ id ) ) )
| ( ( X26 @ id @ X24 @ id )
!= $true )
| ( $true
!= ( X26 @ id @ X25 @ id ) )
| ~ ! [X33: subst,X34: subst,X35: subst,X36: term] :
( ( $true
= ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 ) )
| ( $true
!= ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) ) )
| ( $true
= ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( lamnotap != $true )
& ( pushprop_lthm_orig = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ( $true
= ( X42 @ id @ ( lam @ X41 ) @ id ) )
| ~ ! [X43: subst > term > term] :
( ~ ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
| ( $true
= ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id ) )
| ~ ! [X47: term] :
( ( ( X42 @ id @ X47 @ id )
!= $true )
| ( $true
= ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) ) ) )
| ~ ! [X48: term] :
( ( $true
!= ( X42 @ id @ X48 @ id ) )
| ( $true
= ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ! [X49: term] :
~ ! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ! [X51: d_subst,X52: d_subst] :
( ( ( d2subst @ X52 )
= ( d2subst @ X51 ) )
=> ( X51 = X52 ) )
& ( pushprop_lem3v2 = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X53: subst > term > subst > $o,X54: term] :
( ( $true
= ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X55: term] :
( ( $true
= ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id ) )
| ( $true
!= ( X53 @ id @ X55 @ id ) ) )
| ~ ! [X56: subst > term > term,X57: term] :
( ~ ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
| ( ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X61: term] :
( ( $true
= ( X53 @ id @ ( X56 @ id @ X61 ) @ id ) )
| ( $true
!= ( X53 @ id @ X61 @ id ) ) )
| ~ ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) ) ) ) )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( $true
= ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) ) )
| ( $true
!= ( X67 @ X65 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 )
<=> ( axidl = $true ) )
& ( ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 )
<=> ( axshiftcons = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
<=> ! [X73: term] :
( ( sub @ X73 @ id )
= X73 ) )
& ( hoaslamnotvar = $true )
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X76: term] :
( ( sub @ X76 @ id )
= X76 )
=> ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ~ ! [X80: term] :
( ( X78 @ id @ X80 @ id )
= ( X79 @ X80 ) )
| ~ ! [X81: term,X82: subst,X83: subst,X84: subst] :
( ( $true
!= ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) ) )
| ( $true
= ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) ) )
| ~ ! [X85: term,X86: subst,X87: subst,X88: subst] :
( ( $true
!= ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 ) )
| ( $true
= ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) ) )
| ~ ! [X89: term] :
( ( $true
!= ( X79 @ X89 ) )
| ( $true
= ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) ) )
| ( $true
= ( X79 @ ( lam @ X77 ) ) )
| ~ ! [X90: subst > term > term] :
( ~ ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
| ~ ! [X94: term] :
( ( $true
!= ( X78 @ id @ X94 @ id ) )
| ( $true
= ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) ) )
| ( $true
= ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) ) ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X95: term,X96: term,X97: term,X98: term] :
( ( X95 = X97 )
| ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ~ ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( $true
= ( X100 @ one ) )
| ( $true
!= ( X99 @ X102 ) ) ) )
& ( ( induction2 = $true )
<=> ! [X104: term,X105: term > $o] :
( ~ ! [X106: term] :
( ( $true
= ( X105 @ ( lam @ X106 ) ) )
| ~ ! [X107: term] :
( ( $true
= ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) ) )
| ( ( X105 @ X107 )
!= $true ) ) )
| ~ ! [X108: term] :
( ( ( var @ X108 )
!= $true )
| ( $true
= ( X105 @ X108 ) ) )
| ( $true
= ( X105 @ X104 ) )
| ~ ! [X109: term,X110: term] :
( ( $true
= ( X105 @ ( ap @ X109 @ X110 ) ) )
| ( $true
!= ( X105 @ X110 ) )
| ( ( X105 @ X109 )
!= $true ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( axmap = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X111: term] :
~ ! [X112: subst > term > term] :
~ ! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
= X116 )
=> ( ! [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
= X117 )
=> ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
=> ( ! [X120: term > $o,X121: term] :
( ( $true
= ( X120 @ X121 ) )
| ~ ! [X122: term] :
( ( $true
= ( X120 @ X122 ) )
| ( ( var @ X122 )
!= $true ) )
| ~ ! [X123: term,X124: term] :
( ( $true
!= ( X120 @ X123 ) )
| ( $true
!= ( X120 @ X124 ) )
| ( $true
= ( X120 @ ( ap @ X124 @ X123 ) ) ) )
| ~ ! [X125: term] :
( ( $true
!= ( X120 @ X125 ) )
| ( $true
= ( X120 @ ( lam @ X125 ) ) ) ) )
=> ! [X126: term > $o,X127: term,X128: subst] :
( ( $true
= ( X126 @ ( sub @ X127 @ X128 ) ) )
| ~ ! [X129: term,X130: term] :
( ( ( X126 @ ( ap @ X130 @ X129 ) )
= $true )
| ( $true
!= ( X126 @ X129 ) )
| ( $true
!= ( X126 @ X130 ) ) )
| ~ ! [X131: term] :
( ( $true
= ( X126 @ ( lam @ X131 ) ) )
| ~ ! [X132: term] :
( ( $true
!= ( X126 @ X132 ) )
| ( $true
= ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) ) )
| ~ ! [X133: term] :
( ( $true
!= ( var @ X133 ) )
| ( $true
= ( X126 @ ( sub @ X133 @ X128 ) ) ) ) ) ) ) ) ) )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> ( apinj1 = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
=> ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
=> ( ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 )
& ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 ) ) ) ) )
& ( apnotvar = $true )
& ( ( ! [X142: term > $o,X143: term] :
( ( $true
= ( X142 @ X143 ) )
| ~ ! [X144: term] :
( ( $true
= ( X142 @ X144 ) )
| ( ( var @ X144 )
!= $true ) )
| ~ ! [X145: term,X146: term] :
( ( $true
!= ( X142 @ X145 ) )
| ( $true
!= ( X142 @ X146 ) )
| ( $true
= ( X142 @ ( ap @ X145 @ X146 ) ) ) )
| ~ ! [X147: term] :
( ( $true
= ( X142 @ ( lam @ X147 ) ) )
| ~ ! [X148: term] :
( ( $true
= ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) ) )
| ( $true
!= ( X142 @ X148 ) ) ) ) )
=> ( ! [X149: subst > term > subst > $o,X150: term,X151: term] :
( ( $true
!= ( X149 @ id @ X151 @ id ) )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( $true
!= ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) ) )
| ( $true
= ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) ) )
| ~ ! [X156: term,X157: term] :
( ( $true
= ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id ) )
| ( ( X149 @ id @ X157 @ id )
!= $true )
| ( $true
!= ( X149 @ id @ X156 @ id ) ) )
| ( $true
= ( X149 @ id @ ( ap @ X151 @ X150 ) @ id ) )
| ( $true
!= ( X149 @ id @ X150 @ id ) )
| ~ ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ( $true
!= ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 ) )
| ( ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) )
= $true ) ) )
=> ( ! [X162: subst > term > subst > $o,X163: term] :
( ( $true
= ( X162 @ id @ ( lam @ X163 ) @ id ) )
| ~ ! [X164: term] :
( ( $true
= ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id ) )
| ( $true
!= ( X162 @ id @ X164 @ id ) ) )
| ~ ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ( $true
!= ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) ) )
| ( $true
= ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) ) )
| ~ ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ( $true
!= ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 ) )
| ( ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) )
= $true ) )
| ~ ! [X173: subst > term > term] :
( ~ ! [X174: term] :
( ( $true
= ( X162 @ id @ ( X173 @ id @ X174 ) @ id ) )
| ( $true
!= ( X162 @ id @ X174 @ id ) ) )
| ~ ! [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( $true
= ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) ) )
=> ! [X178: term,X179: subst > term > subst > $o] :
( ~ ! [X180: term] :
( ( $true
= ( X179 @ id @ X180 @ id ) )
| ( $true
!= ( var @ ( sub @ X180 @ id ) ) ) )
| ~ ! [X181: term,X182: term] :
( ( ( X179 @ id @ X182 @ id )
!= $true )
| ( $true
= ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id ) )
| ( $true
!= ( X179 @ id @ X181 @ id ) ) )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ( $true
!= ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) ) )
| ( $true
= ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) ) )
| ~ ! [X187: term,X188: subst,X189: subst,X190: subst] :
( ( $true
= ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) ) )
| ( $true
!= ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) ) )
| ( ( X179 @ id @ X178 @ id )
= $true )
| ~ ! [X191: subst > term > term] :
( ( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) )
| ~ ! [X195: term] :
( ( $true
!= ( X179 @ id @ X195 @ id ) )
| ( $true
= ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop = $true )
& ( pushprop_lem1_gthm = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X196: subst,X197: term,X198: term > $o] :
~ ! [X199: term > $o] :
~ ! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( ( ! [X201: term] :
( ( sub @ X201 @ id )
= X201 )
=> ! [X202: term] :
( ( sub @ X202 @ id )
= X202 ) )
<=> ( termmset_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ~ ! [X205: term,X206: term] :
( ( $true
!= ( X203 @ id @ X206 @ id ) )
| ( $true
= ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id ) )
| ( ( X203 @ id @ X205 @ id )
!= $true ) )
| ~ ! [X207: subst > term > term] :
( ( $true
= ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id ) )
| ~ ! [X208: term] :
( ( $true
!= ( X203 @ id @ X208 @ id ) )
| ( $true
= ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) ) )
| ~ ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) )
| ( $true
= ( X203 @ id @ X204 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) )
<=> ( apinj2 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ulamvar1 != $true )
& ( hoasapnotvar = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X218: term] :
~ ! [X219: subst > term > term] :
( ( X219 @ sh @ one )
!= ( sub @ X218 @ ( push @ one @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X220: term] :
( ( sub @ X220 @ id )
= X220 )
=> ( ! [X221: term,X222: term,X223: term,X224: term] :
( ( ( ap @ X224 @ X222 )
!= ( ap @ X221 @ X223 ) )
| ( X221 = X224 ) )
=> ! [X225: term,X226: term,X227: term,X228: term] :
( ( X227 = X228 )
| ( ( ap @ ( sub @ X227 @ id ) @ X225 )
!= ( ap @ ( sub @ X228 @ id ) @ X226 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( induction2_lthm = $true )
<=> ( ! [X229: term] :
( ( sub @ X229 @ id )
= X229 )
=> ( ! [X230: term > $o,X231: subst,X232: term] :
( ~ ! [X233: term] :
( ( $true
!= ( var @ X233 ) )
| ( $true
= ( X230 @ ( sub @ X233 @ X231 ) ) ) )
| ~ ! [X234: term] :
( ~ ! [X235: term] :
( ( $true
= ( X230 @ ( sub @ X234 @ ( push @ X235 @ id ) ) ) )
| ( $true
!= ( X230 @ X235 ) ) )
| ( ( X230 @ ( lam @ X234 ) )
= $true ) )
| ( ( X230 @ ( sub @ X232 @ X231 ) )
= $true )
| ~ ! [X236: term,X237: term] :
( ( $true
!= ( X230 @ X237 ) )
| ( $true
= ( X230 @ ( ap @ X236 @ X237 ) ) )
| ( $true
!= ( X230 @ X236 ) ) ) )
=> ! [X238: term,X239: term > $o] :
( ~ ! [X240: term] :
( ( $true
= ( X239 @ X240 ) )
| ( $true
!= ( var @ X240 ) ) )
| ~ ! [X241: term,X242: term] :
( ( $true
!= ( X239 @ X242 ) )
| ( ( X239 @ ( ap @ X242 @ X241 ) )
= $true )
| ( $true
!= ( X239 @ X241 ) ) )
| ~ ! [X243: term] :
( ~ ! [X244: term] :
( ( $true
!= ( X239 @ X244 ) )
| ( $true
= ( X239 @ ( sub @ X243 @ ( push @ X244 @ id ) ) ) ) )
| ( $true
= ( X239 @ ( lam @ X243 ) ) ) )
| ( $true
= ( X239 @ X238 ) ) ) ) ) )
& ( ( axscons = $true )
<=> ! [X245: subst] :
( ( push @ ( sub @ one @ X245 ) @ ( comp @ sh @ X245 ) )
= X245 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X246: term,X247: term,X248: term,X249: term] :
( ( X247 = X249 )
| ( ( ap @ X248 @ X249 )
!= ( ap @ X246 @ X247 ) ) )
=> ! [X250: term,X251: term,X252: term,X253: term] :
( ( ( ap @ ( sub @ X252 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X253 ) )
| ( X251 = X253 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X254: subst > term > subst > $o] :
~ ! [X255: term > $o] :
~ ! [X256: term] :
( ( X254 @ id @ X256 @ id )
= ( X255 @ X256 ) ) )
& ( ! [X257: term,X258: term] :
( ( ( sub @ X257 @ sh )
!= ( sub @ X258 @ sh ) )
| ( X257 = X258 ) )
<=> ( shinj = $true ) )
& ( ( ! [X259: term,X260: subst] :
( ( sub @ one @ ( push @ X259 @ X260 ) )
= X259 )
=> ( ! [X261: term,X262: subst] :
( ( comp @ sh @ ( push @ X261 @ X262 ) )
= X262 )
=> ( ! [X263: term,X264: term] :
( ( X263 = X264 )
| ( ( lam @ X263 )
!= ( lam @ X264 ) ) )
=> ! [X265: subst > term > term,X266: term,X267: subst,X268: subst > term > term] :
( ( ( lam @ ( X265 @ sh @ one ) )
!= ( lam @ ( X268 @ sh @ one ) ) )
| ( ( X265 @ X267 @ X266 )
= ( X268 @ X267 @ X266 ) )
| ~ ! [X269: subst,X270: term,X271: subst] :
( ( X265 @ ( comp @ X271 @ X269 ) @ ( sub @ X270 @ X269 ) )
= ( sub @ ( X265 @ X271 @ X270 ) @ X269 ) )
| ~ ! [X272: subst,X273: term,X274: subst] :
( ( X268 @ ( comp @ X272 @ X274 ) @ ( sub @ X273 @ X274 ) )
= ( sub @ ( X268 @ X272 @ X273 ) @ X274 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X275: term > $o,X276: subst,X277: term] :
~ ! [X278: term > $o] :
~ ! [X279: term] :
( ( X275 @ ( sub @ X279 @ ( push @ X277 @ X276 ) ) )
= ( X278 @ X279 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( axapp = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X280: term,X281: term > $o,X282: term,X283: subst > term > subst > $o] :
( ~ ! [X284: term,X285: term] :
( ( $true
= ( X283 @ id @ ( ap @ ( sub @ X285 @ id ) @ X284 ) @ id ) )
| ( $true
!= ( X283 @ id @ X284 @ id ) )
| ( ( X283 @ id @ X285 @ id )
!= $true ) )
| ( $true
!= ( X281 @ X282 ) )
| ( $true
= ( X281 @ ( ap @ X280 @ X282 ) ) )
| ~ ! [X286: subst,X287: subst,X288: term,X289: subst] :
( ( $true
!= ( X283 @ ( comp @ X286 @ X289 ) @ ( sub @ X288 @ X289 ) @ X287 ) )
| ( $true
= ( X283 @ X286 @ X288 @ ( comp @ X289 @ X287 ) ) ) )
| ~ ! [X290: term,X291: subst,X292: subst,X293: subst] :
( ( ( X283 @ ( comp @ X291 @ X293 ) @ ( sub @ X290 @ X293 ) @ X292 )
= $true )
| ( $true
!= ( X283 @ X291 @ X290 @ ( comp @ X293 @ X292 ) ) ) )
| ~ ! [X294: term] :
( ( X283 @ id @ X294 @ id )
= ( X281 @ X294 ) )
| ( $true
!= ( X281 @ X280 ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasapinj1_gthm = $true )
& ! [X295: term] :
? [X296: d_term] :
( ( d2term @ X296 )
= X295 )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X297: term > $o,X298: term,X299: subst > term > subst > $o] :
( ~ ! [X300: subst > term > term] :
( ~ ! [X301: term] :
( ( $true
!= ( X299 @ id @ X301 @ id ) )
| ( $true
= ( X299 @ id @ ( X300 @ id @ X301 ) @ id ) ) )
| ( $true
= ( X299 @ id @ ( lam @ ( X300 @ sh @ one ) ) @ id ) )
| ~ ! [X302: subst,X303: term,X304: subst] :
( ( X300 @ ( comp @ X304 @ X302 ) @ ( sub @ X303 @ X302 ) )
= ( sub @ ( X300 @ X304 @ X303 ) @ X302 ) ) )
| ( $true
= ( X297 @ ( lam @ X298 ) ) )
| ~ ! [X305: term] :
( ( X297 @ X305 )
= ( X299 @ id @ X305 @ id ) )
| ~ ! [X306: term] :
( ( $true
!= ( X297 @ X306 ) )
| ( ( X297 @ ( sub @ X298 @ ( push @ X306 @ id ) ) )
= $true ) ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( ! [X307: subst > term > subst > $o] :
~ ! [X308: term > $o] :
~ ! [X309: term] :
( ( X308 @ X309 )
= ( X307 @ id @ X309 @ id ) )
=> ( ! [X310: term > $o,X311: term] :
( ~ ! [X312: term] :
( ( $true
!= ( var @ X312 ) )
| ( $true
= ( X310 @ X312 ) ) )
| ~ ! [X313: term,X314: term] :
( ( $true
!= ( X310 @ X314 ) )
| ( $true
!= ( X310 @ X313 ) )
| ( $true
= ( X310 @ ( ap @ X313 @ X314 ) ) ) )
| ( $true
= ( X310 @ X311 ) )
| ~ ! [X315: term] :
( ~ ! [X316: term] :
( ( $true
= ( X310 @ ( sub @ X315 @ ( push @ X316 @ id ) ) ) )
| ( $true
!= ( X310 @ X316 ) ) )
| ( $true
= ( X310 @ ( lam @ X315 ) ) ) ) )
=> ( ! [X317: term] :
( ( sub @ X317 @ id )
= X317 )
=> ( ! [X318: term,X319: term > $o,X320: subst > term > subst > $o] :
( ~ ! [X321: term] :
( ( X320 @ id @ X321 @ id )
= ( X319 @ X321 ) )
| ( $true
= ( X319 @ ( lam @ X318 ) ) )
| ~ ! [X322: subst > term > term] :
( ~ ! [X323: subst,X324: subst,X325: term] :
( ( sub @ ( X322 @ X323 @ X325 ) @ X324 )
= ( X322 @ ( comp @ X323 @ X324 ) @ ( sub @ X325 @ X324 ) ) )
| ( $true
= ( X320 @ id @ ( lam @ ( X322 @ sh @ one ) ) @ id ) )
| ~ ! [X326: term] :
( ( $true
!= ( X320 @ id @ X326 @ id ) )
| ( ( X320 @ id @ ( X322 @ id @ X326 ) @ id )
= $true ) ) )
| ~ ! [X327: term] :
( ( $true
= ( X319 @ ( sub @ X318 @ ( push @ X327 @ id ) ) ) )
| ( $true
!= ( X319 @ X327 ) ) ) )
=> ! [X328: subst > term > subst > $o,X329: term] :
( ~ ! [X330: term,X331: term] :
( ( $true
!= ( X328 @ id @ X330 @ id ) )
| ( $true
!= ( X328 @ id @ X331 @ id ) )
| ( $true
= ( X328 @ id @ ( ap @ ( sub @ X331 @ id ) @ X330 ) @ id ) ) )
| ( $true
= ( X328 @ id @ X329 @ id ) )
| ~ ! [X332: subst > term > term] :
( ~ ! [X333: subst,X334: subst,X335: term] :
( ( sub @ ( X332 @ X333 @ X335 ) @ X334 )
= ( X332 @ ( comp @ X333 @ X334 ) @ ( sub @ X335 @ X334 ) ) )
| ~ ! [X336: term] :
( ( $true
!= ( X328 @ id @ X336 @ id ) )
| ( $true
= ( X328 @ id @ ( X332 @ id @ X336 ) @ id ) ) )
| ( $true
= ( X328 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( ! [X337: term,X338: subst] :
( ( sub @ one @ ( push @ X337 @ X338 ) )
= X337 )
=> ( ! [X339: subst,X340: term] :
( ( comp @ sh @ ( push @ X340 @ X339 ) )
= X339 )
=> ! [X341: term > $o,X342: term,X343: subst,X344: term,X345: term > $o] :
( ( $true
!= ( X341 @ X344 ) )
| ( $true
= ( X345 @ ( sub @ X344 @ ( push @ X342 @ X343 ) ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( axassoc = $true )
& ( ( termmset = $true )
<=> ! [X346: term] :
( ( sub @ X346 @ id )
= X346 ) )
& ( hoasapnotvar_gthm = $true )
& ( ulamvarsh = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X347: term > $o,X348: term,X349: subst > term > subst > $o] :
( ~ ! [X350: term] :
( ( $true
!= ( X347 @ X350 ) )
| ( $true
= ( X347 @ ( sub @ X348 @ ( push @ X350 @ id ) ) ) ) )
| ~ ! [X351: subst > term > term] :
( ~ ! [X352: term] :
( ( ( X349 @ id @ ( X351 @ id @ X352 ) @ id )
= $true )
| ( $true
!= ( X349 @ id @ X352 @ id ) ) )
| ( $true
= ( X349 @ id @ ( lam @ ( X351 @ sh @ one ) ) @ id ) )
| ~ ! [X353: subst,X354: subst,X355: term] :
( ( sub @ ( X351 @ X353 @ X355 ) @ X354 )
= ( X351 @ ( comp @ X353 @ X354 ) @ ( sub @ X355 @ X354 ) ) ) )
| ~ ! [X356: subst,X357: subst,X358: subst,X359: term] :
( ( $true
= ( X349 @ X356 @ X359 @ ( comp @ X358 @ X357 ) ) )
| ( $true
!= ( X349 @ ( comp @ X356 @ X358 ) @ ( sub @ X359 @ X358 ) @ X357 ) ) )
| ~ ! [X360: term] :
( ( X347 @ X360 )
= ( X349 @ id @ X360 @ id ) )
| ~ ! [X361: subst,X362: subst,X363: term,X364: subst] :
( ( $true
= ( X349 @ ( comp @ X361 @ X362 ) @ ( sub @ X363 @ X362 ) @ X364 ) )
| ( $true
!= ( X349 @ X361 @ X363 @ ( comp @ X362 @ X364 ) ) ) )
| ( $true
= ( X347 @ ( lam @ X348 ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( ! [X365: term] :
( ( sub @ X365 @ id )
= X365 )
=> ( ! [X366: term,X367: subst > term > subst > $o] :
( ~ ! [X368: subst > term > term] :
( ~ ! [X369: term,X370: subst,X371: subst] :
( ( X368 @ ( comp @ X371 @ X370 ) @ ( sub @ X369 @ X370 ) )
= ( sub @ ( X368 @ X371 @ X369 ) @ X370 ) )
| ~ ! [X372: term] :
( ( $true
!= ( X367 @ id @ X372 @ id ) )
| ( $true
= ( X367 @ id @ ( X368 @ id @ X372 ) @ id ) ) )
| ( $true
= ( X367 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) ) )
| ( ( X367 @ id @ ( lam @ ( sub @ X366 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X373: term] :
( ( $true
!= ( X367 @ id @ X373 @ id ) )
| ( $true
= ( X367 @ id @ ( sub @ X366 @ ( push @ X373 @ id ) ) @ id ) ) ) )
=> ! [X374: subst > term > subst > $o,X375: term] :
( ( $true
= ( X374 @ id @ ( lam @ X375 ) @ id ) )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ( $true
!= ( X374 @ X378 @ X379 @ ( comp @ X376 @ X377 ) ) )
| ( ( X374 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
= $true ) )
| ~ ! [X380: term] :
( ( $true
= ( X374 @ id @ ( sub @ X375 @ ( push @ X380 @ id ) ) @ id ) )
| ( $true
!= ( X374 @ id @ X380 @ id ) ) )
| ~ ! [X381: subst > term > term] :
( ( $true
= ( X374 @ id @ ( lam @ ( X381 @ sh @ one ) ) @ id ) )
| ~ ! [X382: term] :
( ( $true
!= ( X374 @ id @ X382 @ id ) )
| ( $true
= ( X374 @ id @ ( X381 @ id @ X382 ) @ id ) ) )
| ~ ! [X383: term,X384: subst,X385: subst] :
( ( sub @ ( X381 @ X384 @ X383 ) @ X385 )
= ( X381 @ ( comp @ X384 @ X385 ) @ ( sub @ X383 @ X385 ) ) ) )
| ~ ! [X386: subst,X387: subst,X388: term,X389: subst] :
( ( $true
!= ( X374 @ ( comp @ X389 @ X386 ) @ ( sub @ X388 @ X386 ) @ X387 ) )
| ( $true
= ( X374 @ X389 @ X388 @ ( comp @ X386 @ X387 ) ) ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ! [X390: d_term] : ( d_one = X390 )
& ( ! [X391: term,X392: subst > term > subst > $o] :
( ( $true
= ( X392 @ id @ ( lam @ ( sub @ X391 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X393: term] :
( ( $true
!= ( X392 @ id @ X393 @ id ) )
| ( $true
= ( X392 @ id @ ( sub @ X391 @ ( push @ X393 @ id ) ) @ id ) ) )
| ~ ! [X394: subst > term > term] :
( ( ( X392 @ id @ ( lam @ ( X394 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X395: subst,X396: term,X397: subst] :
( ( X394 @ ( comp @ X397 @ X395 ) @ ( sub @ X396 @ X395 ) )
= ( sub @ ( X394 @ X397 @ X396 ) @ X395 ) )
| ~ ! [X398: term] :
( ( $true
= ( X392 @ id @ ( X394 @ id @ X398 ) @ id ) )
| ( $true
!= ( X392 @ id @ X398 @ id ) ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X399: subst > term > subst > $o] :
~ ! [X400: term > $o] :
~ ! [X401: term] :
( ( X399 @ id @ X401 @ id )
= ( X400 @ X401 ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X402: subst,X403: term] :
( ( sub @ one @ ( push @ X403 @ X402 ) )
= X403 )
=> ! [X404: term > $o,X405: subst,X406: term > $o,X407: term] :
( ( $true
= ( X406 @ one ) )
| ~ ! [X408: term] :
( ( X406 @ X408 )
= ( X404 @ ( sub @ X408 @ ( push @ X407 @ X405 ) ) ) )
| ( $true
!= ( X404 @ X407 ) ) ) ) )
& ! [X409: d_term,X410: d_term] :
( ( ( d2term @ X409 )
= ( d2term @ X410 ) )
=> ( X409 = X410 ) )
& ( ( induction = $true )
<=> ! [X411: term,X412: term > $o] :
( ~ ! [X413: term] :
( ( $true
!= ( X412 @ X413 ) )
| ( $true
= ( X412 @ ( lam @ X413 ) ) ) )
| ( $true
= ( X412 @ X411 ) )
| ~ ! [X414: term] :
( ( $true
!= ( var @ X414 ) )
| ( $true
= ( X412 @ X414 ) ) )
| ~ ! [X415: term,X416: term] :
( ( $true
= ( X412 @ ( ap @ X416 @ X415 ) ) )
| ( $true
!= ( X412 @ X416 ) )
| ( $true
!= ( X412 @ X415 ) ) ) ) )
& ( lamnotvar = $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 ) ) ) ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X422: term,X423: subst > term > term,X424: subst > term > term,X425: subst] :
( ( ( lam @ ( X424 @ sh @ one ) )
!= ( lam @ ( X423 @ sh @ one ) ) )
| ( ( X423 @ X425 @ X422 )
= ( X424 @ X425 @ X422 ) )
| ~ ! [X426: subst,X427: term,X428: subst] :
( ( X424 @ ( comp @ X426 @ X428 ) @ ( sub @ X427 @ X428 ) )
= ( sub @ ( X424 @ X426 @ X427 ) @ X428 ) )
| ~ ! [X429: subst,X430: term,X431: subst] :
( ( sub @ ( X423 @ X431 @ X430 ) @ X429 )
= ( X423 @ ( comp @ X431 @ X429 ) @ ( sub @ X430 @ X429 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X432: term] :
~ ! [X433: subst > term > term] :
~ ! [X434: term,X435: subst] :
( ( X433 @ X435 @ X434 )
= ( sub @ X432 @ ( push @ X434 @ X435 ) ) )
=> ( ! [X436: term] :
( ( sub @ X436 @ id )
= X436 )
=> ! [X437: term,X438: term > $o,X439: subst > term > subst > $o] :
( ( $true
= ( X438 @ ( lam @ X437 ) ) )
| ~ ! [X440: subst > term > term] :
( ~ ! [X441: term] :
( ( ( X439 @ id @ X441 @ id )
!= $true )
| ( $true
= ( X439 @ id @ ( X440 @ id @ X441 ) @ id ) ) )
| ~ ! [X442: subst,X443: term,X444: subst] :
( ( sub @ ( X440 @ X444 @ X443 ) @ X442 )
= ( X440 @ ( comp @ X444 @ X442 ) @ ( sub @ X443 @ X442 ) ) )
| ( ( X439 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X445: term] :
( ( X439 @ id @ X445 @ id )
= ( X438 @ X445 ) )
| ~ ! [X446: term] :
( ( ( X438 @ ( sub @ X437 @ ( push @ X446 @ id ) ) )
= $true )
| ( $true
!= ( X438 @ X446 ) ) ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X447: term,X448: term] :
( ( ( lam @ X447 )
!= ( lam @ X448 ) )
| ( X447 = X448 ) )
<=> ( laminj = $true ) )
& ( ulamvarind = $true )
& ( ( substmonoid = $true )
<=> ( ! [X449: subst] :
( ( comp @ X449 @ id )
= X449 )
& ! [X450: subst] :
( ( comp @ id @ X450 )
= X450 ) ) )
& ( ( hoasinduction = $true )
<=> ! [X451: subst > term > subst > $o,X452: term] :
( ~ ! [X453: term,X454: term] :
( ( $true
!= ( X451 @ id @ X454 @ id ) )
| ( $true
= ( X451 @ id @ ( ap @ ( sub @ X454 @ id ) @ X453 ) @ id ) )
| ( ( X451 @ id @ X453 @ id )
!= $true ) )
| ~ ! [X455: term] :
( ( $true
= ( X451 @ id @ X455 @ id ) )
| ( ( var @ ( sub @ X455 @ id ) )
!= $true ) )
| ~ ! [X456: subst > term > term] :
( ( $true
= ( X451 @ id @ ( lam @ ( X456 @ sh @ one ) ) @ id ) )
| ~ ! [X457: term] :
( ( $true
= ( X451 @ id @ ( X456 @ id @ X457 ) @ id ) )
| ( $true
!= ( X451 @ id @ X457 @ id ) ) )
| ~ ! [X458: subst,X459: subst,X460: term] :
( ( sub @ ( X456 @ X459 @ X460 ) @ X458 )
= ( X456 @ ( comp @ X459 @ X458 ) @ ( sub @ X460 @ X458 ) ) ) )
| ~ ! [X461: subst,X462: subst,X463: subst,X464: term] :
( ( $true
!= ( X451 @ X461 @ X464 @ ( comp @ X462 @ X463 ) ) )
| ( $true
= ( X451 @ ( comp @ X461 @ X462 ) @ ( sub @ X464 @ X462 ) @ X463 ) ) )
| ( $true
= ( X451 @ id @ X452 @ id ) )
| ~ ! [X465: term,X466: subst,X467: subst,X468: subst] :
( ( $true
= ( X451 @ X467 @ X465 @ ( comp @ X468 @ X466 ) ) )
| ( $true
!= ( X451 @ ( comp @ X467 @ X468 ) @ ( sub @ X465 @ X468 ) @ X466 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X472: subst > term > subst > $o] :
~ ! [X473: term > $o] :
~ ! [X474: term] :
( ( X473 @ X474 )
= ( X472 @ id @ X474 @ id ) )
=> ( ! [X475: term,X476: term > $o] :
( ~ ! [X477: term,X478: term] :
( ( $true
!= ( X476 @ X477 ) )
| ( $true
!= ( X476 @ X478 ) )
| ( $true
= ( X476 @ ( ap @ X478 @ X477 ) ) ) )
| ~ ! [X479: term] :
( ( $true
!= ( var @ X479 ) )
| ( $true
= ( X476 @ X479 ) ) )
| ~ ! [X480: term] :
( ~ ! [X481: term] :
( ( $true
= ( X476 @ ( sub @ X480 @ ( push @ X481 @ id ) ) ) )
| ( $true
!= ( X476 @ X481 ) ) )
| ( $true
= ( X476 @ ( lam @ X480 ) ) ) )
| ( $true
= ( X476 @ X475 ) ) )
=> ( ! [X482: term] :
( ( sub @ X482 @ id )
= X482 )
=> ( ! [X483: term > $o,X484: subst > term > subst > $o,X485: term] :
( ( $true
= ( X483 @ ( lam @ X485 ) ) )
| ~ ! [X486: term] :
( ( $true
= ( X483 @ ( sub @ X485 @ ( push @ X486 @ id ) ) ) )
| ( $true
!= ( X483 @ X486 ) ) )
| ~ ! [X487: term] :
( ( X483 @ X487 )
= ( X484 @ id @ X487 @ id ) )
| ~ ! [X488: subst > term > term] :
( ( $true
= ( X484 @ id @ ( lam @ ( X488 @ sh @ one ) ) @ id ) )
| ~ ! [X489: term] :
( ( $true
= ( X484 @ id @ ( X488 @ id @ X489 ) @ id ) )
| ( ( X484 @ id @ X489 @ id )
!= $true ) )
| ~ ! [X490: term,X491: subst,X492: subst] :
( ( X488 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) )
= ( sub @ ( X488 @ X491 @ X490 ) @ X492 ) ) ) )
=> ! [X493: term,X494: subst > term > subst > $o] :
( ~ ! [X495: subst,X496: subst,X497: term,X498: subst] :
( ( ( X494 @ X495 @ X497 @ ( comp @ X498 @ X496 ) )
= $true )
| ( $true
!= ( X494 @ ( comp @ X495 @ X498 ) @ ( sub @ X497 @ X498 ) @ X496 ) ) )
| ~ ! [X499: subst,X500: subst,X501: term,X502: subst] :
( ( $true
= ( X494 @ ( comp @ X499 @ X502 ) @ ( sub @ X501 @ X502 ) @ X500 ) )
| ( $true
!= ( X494 @ X499 @ X501 @ ( comp @ X502 @ X500 ) ) ) )
| ( $true
= ( X494 @ id @ X493 @ id ) )
| ~ ! [X503: term,X504: term] :
( ( $true
!= ( X494 @ id @ X504 @ id ) )
| ( $true
= ( X494 @ id @ ( ap @ ( sub @ X503 @ id ) @ X504 ) @ id ) )
| ( $true
!= ( X494 @ id @ X503 @ id ) ) )
| ~ ! [X505: term] :
( ( $true
= ( X494 @ id @ X505 @ id ) )
| ( $true
!= ( var @ ( sub @ X505 @ id ) ) ) )
| ~ ! [X506: subst > term > term] :
( ( $true
= ( X494 @ id @ ( lam @ ( X506 @ sh @ one ) ) @ id ) )
| ~ ! [X507: term,X508: subst,X509: subst] :
( ( X506 @ ( comp @ X509 @ X508 ) @ ( sub @ X507 @ X508 ) )
= ( sub @ ( X506 @ X509 @ X507 ) @ X508 ) )
| ~ ! [X510: term] :
( ( $true
!= ( X494 @ id @ X510 @ id ) )
| ( $true
= ( X494 @ id @ ( X506 @ id @ X510 ) @ id ) ) ) ) ) ) ) ) ) )
& ( ! [X511: term,X512: subst > term > subst > $o] :
( ~ ! [X513: subst > term > term] :
( ~ ! [X514: subst,X515: term,X516: subst] :
( ( X513 @ ( comp @ X516 @ X514 ) @ ( sub @ X515 @ X514 ) )
= ( sub @ ( X513 @ X516 @ X515 ) @ X514 ) )
| ~ ! [X517: term] :
( ( ( X512 @ id @ X517 @ id )
!= $true )
| ( $true
= ( X512 @ id @ ( X513 @ id @ X517 ) @ id ) ) )
| ( $true
= ( X512 @ id @ ( lam @ ( X513 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X512 @ id @ ( lam @ ( sub @ X511 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X518: term] :
( ( $true
!= ( X512 @ id @ X518 @ id ) )
| ( $true
= ( X512 @ id @ ( sub @ X511 @ ( push @ X518 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X519: term,X520: term,X521: subst > term > term] :
( ~ ! [X522: subst,X523: term,X524: subst] :
( ( sub @ ( X521 @ X522 @ X523 ) @ X524 )
= ( X521 @ ( comp @ X522 @ X524 ) @ ( sub @ X523 @ X524 ) ) )
| ( ( lam @ ( X521 @ sh @ one ) )
!= ( ap @ ( sub @ X520 @ id ) @ X519 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( axclos = $true )
& ( ! [X525: subst,X526: term > $o,X527: term] :
( ~ ! [X528: term] :
( ( $true
= ( X526 @ ( sub @ X528 @ X525 ) ) )
| ( $true
!= ( var @ X528 ) ) )
| ~ ! [X529: term,X530: term] :
( ( $true
!= ( X526 @ X529 ) )
| ( ( X526 @ ( ap @ X530 @ X529 ) )
= $true )
| ( $true
!= ( X526 @ X530 ) ) )
| ~ ! [X531: term] :
( ~ ! [X532: term] :
( ( $true
= ( X526 @ ( sub @ X531 @ ( push @ X532 @ id ) ) ) )
| ( $true
!= ( X526 @ X532 ) ) )
| ( ( X526 @ ( lam @ X531 ) )
= $true ) )
| ( $true
= ( X526 @ ( sub @ X527 @ X525 ) ) ) )
<=> ( induction2lem = $true ) )
& ( ! [X533: subst > term > subst > $o,X534: term] :
( ~ ! [X535: term] :
( ( $true
!= ( X533 @ id @ X535 @ id ) )
| ( $true
= ( X533 @ id @ ( sub @ X534 @ ( push @ X535 @ id ) ) @ id ) ) )
| ~ ! [X536: subst,X537: subst,X538: subst,X539: term] :
( ( $true
!= ( X533 @ X537 @ X539 @ ( comp @ X536 @ X538 ) ) )
| ( $true
= ( X533 @ ( comp @ X537 @ X536 ) @ ( sub @ X539 @ X536 ) @ X538 ) ) )
| ( $true
= ( X533 @ id @ ( lam @ X534 ) @ id ) )
| ~ ! [X540: subst > term > term] :
( ~ ! [X541: subst,X542: term,X543: subst] :
( ( X540 @ ( comp @ X541 @ X543 ) @ ( sub @ X542 @ X543 ) )
= ( sub @ ( X540 @ X541 @ X542 ) @ X543 ) )
| ( $true
= ( X533 @ id @ ( lam @ ( X540 @ sh @ one ) ) @ id ) )
| ~ ! [X544: term] :
( ( $true
!= ( X533 @ id @ X544 @ id ) )
| ( $true
= ( X533 @ id @ ( X540 @ id @ X544 ) @ id ) ) ) )
| ~ ! [X545: term,X546: subst,X547: subst,X548: subst] :
( ( $true
= ( X533 @ X548 @ X545 @ ( comp @ X546 @ X547 ) ) )
| ( $true
!= ( X533 @ ( comp @ X548 @ X546 ) @ ( sub @ X545 @ X546 ) @ X547 ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( axidr = $true )
<=> ! [X549: subst] :
( ( comp @ X549 @ id )
= X549 ) )
& ( axvarshift = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( termmset_gthm
& ! [X0: subst] :
? [X1: d_subst] :
( ( d2subst @ X1 )
= X0 )
& ( ( ! [X2: term] :
( ( sub @ X2 @ id )
= X2 )
=> ( ! [X3: subst > term > subst > $o,X4: term] :
( ~ ! [X5: subst > term > term] :
( ~ ! [X6: subst,X7: subst,X8: term] :
( ( X5 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) )
= ( sub @ ( X5 @ X7 @ X8 ) @ X6 ) )
| ~ ! [X9: term] :
( ( X3 @ id @ ( X5 @ id @ X9 ) @ id )
| ~ ( X3 @ id @ X9 @ id ) )
| ( X3 @ id @ ( lam @ ( X5 @ sh @ one ) ) @ id ) )
| ~ ! [X10: term] :
( ~ ( X3 @ id @ X10 @ id )
| ( X3 @ id @ ( sub @ X4 @ ( push @ X10 @ id ) ) @ id ) )
| ( X3 @ id @ ( lam @ ( sub @ X4 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X11: subst > term > subst > $o,X12: term] :
( ( X11 @ id @ ( lam @ X12 ) @ id )
| ~ ! [X13: subst > term > term] :
( ( X11 @ id @ ( lam @ ( X13 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X15: subst,X16: term] :
( ( X13 @ ( comp @ X15 @ X14 ) @ ( sub @ X16 @ X14 ) )
= ( sub @ ( X13 @ X15 @ X16 ) @ X14 ) )
| ~ ! [X17: term] :
( ( X11 @ id @ ( X13 @ id @ X17 ) @ id )
| ~ ( X11 @ id @ X17 @ id ) ) )
| ~ ! [X18: term] :
( ~ ( X11 @ id @ X18 @ id )
| ( X11 @ id @ ( sub @ X12 @ ( push @ X18 @ id ) ) @ id ) ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( ! [X19: term] :
~ ! [X20: subst > term > term] :
~ ! [X21: subst,X22: term] :
( ( X20 @ X21 @ X22 )
= ( sub @ X19 @ ( push @ X22 @ X21 ) ) )
<=> hoasinduction_lem3v2_f_lthm )
& hoasapinj2_gthm
& ! [X23: d_subst] : ( d_id = X23 )
& pushprop_lem1v2_gthm
& hoasinduction_lem1v2
& ( hoasinduction_lem2
<=> ! [X24: term,X25: term,X26: subst > term > subst > $o] :
( ~ ! [X27: subst,X28: term,X29: subst,X30: subst] :
( ~ ( X26 @ ( comp @ X29 @ X30 ) @ ( sub @ X28 @ X30 ) @ X27 )
| ( X26 @ X29 @ X28 @ ( comp @ X30 @ X27 ) ) )
| ~ ! [X31: term,X32: term] :
( ( X26 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id )
| ~ ( X26 @ id @ X31 @ id )
| ~ ( X26 @ id @ X32 @ id ) )
| ~ ( X26 @ id @ X24 @ id )
| ~ ( X26 @ id @ X25 @ id )
| ~ ! [X33: subst,X34: subst,X35: subst,X36: term] :
( ( X26 @ ( comp @ X33 @ X34 ) @ ( sub @ X36 @ X34 ) @ X35 )
| ~ ( X26 @ X33 @ X36 @ ( comp @ X34 @ X35 ) ) )
| ( X26 @ id @ ( ap @ X24 @ X25 ) @ id ) ) )
& hoaslamnotap_gthm
& ( hoasapinj1
<=> ! [X37: term,X38: term,X39: term,X40: term] :
( ( X37 = X38 )
| ( ( ap @ ( sub @ X38 @ id ) @ X39 )
!= ( ap @ ( sub @ X37 @ id ) @ X40 ) ) ) )
& hoasinduction_lem1
& ~ lamnotap
& pushprop_lthm_orig
& hoaslaminj_gthm
& ( ! [X41: term,X42: subst > term > subst > $o] :
( ( X42 @ id @ ( lam @ X41 ) @ id )
| ~ ! [X43: subst > term > term] :
( ~ ! [X44: subst,X45: subst,X46: term] :
( ( X43 @ ( comp @ X44 @ X45 ) @ ( sub @ X46 @ X45 ) )
= ( sub @ ( X43 @ X44 @ X46 ) @ X45 ) )
| ( X42 @ id @ ( lam @ ( X43 @ sh @ one ) ) @ id )
| ~ ! [X47: term] :
( ~ ( X42 @ id @ X47 @ id )
| ( X42 @ id @ ( X43 @ id @ X47 ) @ id ) ) )
| ~ ! [X48: term] :
( ~ ( X42 @ id @ X48 @ id )
| ( X42 @ id @ ( sub @ X41 @ ( push @ X48 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3a )
& ( hoasinduction_lem3b
<=> ! [X49: term] :
~ ! [X50: subst > term > term] :
( ( sub @ X49 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) ) )
& ! [X51: d_subst,X52: d_subst] :
( ( ( d2subst @ X52 )
= ( d2subst @ X51 ) )
=> ( X51 = X52 ) )
& pushprop_lem3v2
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3aaa
<=> ! [X53: subst > term > subst > $o,X54: term] :
( ( X53 @ id @ ( lam @ ( sub @ X54 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X55: term] :
( ( X53 @ id @ ( sub @ X54 @ ( push @ X55 @ id ) ) @ id )
| ~ ( X53 @ id @ X55 @ id ) )
| ~ ! [X56: subst > term > term,X57: term] :
( ~ ! [X58: subst,X59: term,X60: subst] :
( ( sub @ ( X56 @ X58 @ X59 ) @ X60 )
= ( sub @ ( sub @ X57 @ ( push @ X59 @ X58 ) ) @ X60 ) )
| ( X53 @ id @ ( lam @ ( X56 @ sh @ one ) ) @ id )
| ~ ! [X61: term] :
( ( X53 @ id @ ( X56 @ id @ X61 ) @ id )
| ~ ( X53 @ id @ X61 @ id ) )
| ~ ! [X62: subst,X63: subst,X64: term] :
( ( X56 @ ( comp @ X62 @ X63 ) @ ( sub @ X64 @ X63 ) )
= ( sub @ X57 @ ( push @ ( sub @ X64 @ X63 ) @ ( comp @ X62 @ X63 ) ) ) ) ) ) )
& ( ! [X65: term,X66: term > $o,X67: term > $o,X68: subst,X69: term] :
( ( X66 @ ( sub @ X65 @ ( push @ X69 @ X68 ) ) )
| ~ ( X67 @ X65 ) )
<=> pushprop_lem1 )
& ( axidl
<=> ! [X70: subst] :
( ( comp @ id @ X70 )
= X70 ) )
& ( axshiftcons
<=> ! [X71: subst,X72: term] :
( ( comp @ sh @ ( push @ X72 @ X71 ) )
= X71 ) )
& ( ( d2subst @ d_id )
= sh )
& hoasinduction_lem3b_gthm
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
<=> axvarid )
& hoaslamnotvar
& ( ! [X74: subst,X75: term] :
( ( sub @ one @ ( push @ X75 @ X74 ) )
= X75 )
<=> axvarcons )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X76: term] :
( ( sub @ X76 @ id )
= X76 )
=> ! [X77: term,X78: subst > term > subst > $o,X79: term > $o] :
( ~ ! [X80: term] :
( ( X78 @ id @ X80 @ id )
= ( X79 @ X80 ) )
| ~ ! [X81: term,X82: subst,X83: subst,X84: subst] :
( ~ ( X78 @ X82 @ X81 @ ( comp @ X83 @ X84 ) )
| ( X78 @ ( comp @ X82 @ X83 ) @ ( sub @ X81 @ X83 ) @ X84 ) )
| ~ ! [X85: term,X86: subst,X87: subst,X88: subst] :
( ~ ( X78 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) @ X88 )
| ( X78 @ X87 @ X85 @ ( comp @ X86 @ X88 ) ) )
| ~ ! [X89: term] :
( ~ ( X79 @ X89 )
| ( X79 @ ( sub @ X77 @ ( push @ X89 @ id ) ) ) )
| ( X79 @ ( lam @ X77 ) )
| ~ ! [X90: subst > term > term] :
( ~ ! [X91: subst,X92: term,X93: subst] :
( ( sub @ ( X90 @ X91 @ X92 ) @ X93 )
= ( X90 @ ( comp @ X91 @ X93 ) @ ( sub @ X92 @ X93 ) ) )
| ~ ! [X94: term] :
( ~ ( X78 @ id @ X94 @ id )
| ( X78 @ id @ ( X90 @ id @ X94 ) @ id ) )
| ( X78 @ id @ ( lam @ ( X90 @ sh @ one ) ) @ id ) ) ) ) )
& hoasinduction_lem1_lthm
& ( ! [X95: term,X96: term,X97: term,X98: term] :
( ( ( ap @ ( sub @ X96 @ id ) @ X97 )
!= ( ap @ ( sub @ X98 @ id ) @ X95 ) )
| ( X95 = X97 ) )
<=> hoasapinj2 )
& ( pushprop_lem1v2
<=> ! [X99: term > $o,X100: term > $o,X101: subst,X102: term] :
( ~ ! [X103: term] :
( ( X100 @ X103 )
= ( X99 @ ( sub @ X103 @ ( push @ X102 @ X101 ) ) ) )
| ( X100 @ one )
| ~ ( X99 @ X102 ) ) )
& ( induction2
<=> ! [X104: term,X105: term > $o] :
( ~ ! [X106: term] :
( ( X105 @ ( lam @ X106 ) )
| ~ ! [X107: term] :
( ( X105 @ ( sub @ X106 @ ( push @ X107 @ id ) ) )
| ~ ( X105 @ X107 ) ) )
| ~ ! [X108: term] :
( ~ ( var @ X108 )
| ( X105 @ X108 ) )
| ( X105 @ X104 )
| ~ ! [X109: term,X110: term] :
( ( X105 @ ( ap @ X109 @ X110 ) )
| ~ ( X105 @ X110 )
| ~ ( X105 @ X109 ) ) ) )
& hoasinduction_lem1_gthm
& axmap
& pushprop_lthm
& ( hoasinduction_lem3v2_f
<=> ! [X111: term] :
~ ! [X112: subst > term > term] :
~ ! [X113: subst,X114: term] :
( ( X112 @ X113 @ X114 )
= ( sub @ X111 @ ( push @ X114 @ X113 ) ) ) )
& pushprop_gthm
& pushprop_lem2v2
& ( induction2lem_lthm
<=> ( ! [X115: subst,X116: term] :
( ( sub @ one @ ( push @ X116 @ X115 ) )
= X116 )
=> ( ! [X117: subst,X118: term] :
( ( comp @ sh @ ( push @ X118 @ X117 ) )
= X117 )
=> ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
=> ( ! [X120: term > $o,X121: term] :
( ( X120 @ X121 )
| ~ ! [X122: term] :
( ( X120 @ X122 )
| ~ ( var @ X122 ) )
| ~ ! [X123: term,X124: term] :
( ~ ( X120 @ X123 )
| ~ ( X120 @ X124 )
| ( X120 @ ( ap @ X124 @ X123 ) ) )
| ~ ! [X125: term] :
( ~ ( X120 @ X125 )
| ( X120 @ ( lam @ X125 ) ) ) )
=> ! [X126: term > $o,X127: term,X128: subst] :
( ( X126 @ ( sub @ X127 @ X128 ) )
| ~ ! [X129: term,X130: term] :
( ( X126 @ ( ap @ X130 @ X129 ) )
| ~ ( X126 @ X129 )
| ~ ( X126 @ X130 ) )
| ~ ! [X131: term] :
( ( X126 @ ( lam @ X131 ) )
| ~ ! [X132: term] :
( ~ ( X126 @ X132 )
| ( X126 @ ( sub @ X131 @ ( push @ X132 @ id ) ) ) ) )
| ~ ! [X133: term] :
( ~ ( var @ X133 )
| ( X126 @ ( sub @ X133 @ X128 ) ) ) ) ) ) ) ) )
& ( ! [X134: term,X135: term,X136: term,X137: term] :
( ( ( ap @ X137 @ X135 )
!= ( ap @ X136 @ X134 ) )
| ( X136 = X137 ) )
<=> apinj1 )
& hoaslamnotap_lthm
& ( ( ! [X138: subst] :
( ( comp @ id @ X138 )
= X138 )
=> ( ! [X139: subst] :
( ( comp @ X139 @ id )
= X139 )
=> ( ! [X140: subst] :
( ( comp @ id @ X140 )
= X140 )
& ! [X141: subst] :
( ( comp @ X141 @ id )
= X141 ) ) ) )
<=> substmonoid_lthm )
& apnotvar
& ( ( ! [X142: term > $o,X143: term] :
( ( X142 @ X143 )
| ~ ! [X144: term] :
( ( X142 @ X144 )
| ~ ( var @ X144 ) )
| ~ ! [X145: term,X146: term] :
( ~ ( X142 @ X145 )
| ~ ( X142 @ X146 )
| ( X142 @ ( ap @ X145 @ X146 ) ) )
| ~ ! [X147: term] :
( ( X142 @ ( lam @ X147 ) )
| ~ ! [X148: term] :
( ( X142 @ ( sub @ X147 @ ( push @ X148 @ id ) ) )
| ~ ( X142 @ X148 ) ) ) )
=> ( ! [X149: subst > term > subst > $o,X150: term,X151: term] :
( ~ ( X149 @ id @ X151 @ id )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ~ ( X149 @ X155 @ X152 @ ( comp @ X153 @ X154 ) )
| ( X149 @ ( comp @ X155 @ X153 ) @ ( sub @ X152 @ X153 ) @ X154 ) )
| ~ ! [X156: term,X157: term] :
( ( X149 @ id @ ( ap @ ( sub @ X157 @ id ) @ X156 ) @ id )
| ~ ( X149 @ id @ X157 @ id )
| ~ ( X149 @ id @ X156 @ id ) )
| ( X149 @ id @ ( ap @ X151 @ X150 ) @ id )
| ~ ( X149 @ id @ X150 @ id )
| ~ ! [X158: subst,X159: subst,X160: subst,X161: term] :
( ~ ( X149 @ ( comp @ X158 @ X160 ) @ ( sub @ X161 @ X160 ) @ X159 )
| ( X149 @ X158 @ X161 @ ( comp @ X160 @ X159 ) ) ) )
=> ( ! [X162: subst > term > subst > $o,X163: term] :
( ( X162 @ id @ ( lam @ X163 ) @ id )
| ~ ! [X164: term] :
( ( X162 @ id @ ( sub @ X163 @ ( push @ X164 @ id ) ) @ id )
| ~ ( X162 @ id @ X164 @ id ) )
| ~ ! [X165: subst,X166: subst,X167: term,X168: subst] :
( ~ ( X162 @ X165 @ X167 @ ( comp @ X168 @ X166 ) )
| ( X162 @ ( comp @ X165 @ X168 ) @ ( sub @ X167 @ X168 ) @ X166 ) )
| ~ ! [X169: subst,X170: term,X171: subst,X172: subst] :
( ~ ( X162 @ ( comp @ X171 @ X172 ) @ ( sub @ X170 @ X172 ) @ X169 )
| ( X162 @ X171 @ X170 @ ( comp @ X172 @ X169 ) ) )
| ~ ! [X173: subst > term > term] :
( ~ ! [X174: term] :
( ( X162 @ id @ ( X173 @ id @ X174 ) @ id )
| ~ ( X162 @ id @ X174 @ id ) )
| ~ ! [X175: term,X176: subst,X177: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X177 )
= ( X173 @ ( comp @ X176 @ X177 ) @ ( sub @ X175 @ X177 ) ) )
| ( X162 @ id @ ( lam @ ( X173 @ sh @ one ) ) @ id ) ) )
=> ! [X178: term,X179: subst > term > subst > $o] :
( ~ ! [X180: term] :
( ( X179 @ id @ X180 @ id )
| ~ ( var @ ( sub @ X180 @ id ) ) )
| ~ ! [X181: term,X182: term] :
( ~ ( X179 @ id @ X182 @ id )
| ( X179 @ id @ ( ap @ ( sub @ X181 @ id ) @ X182 ) @ id )
| ~ ( X179 @ id @ X181 @ id ) )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ~ ( X179 @ X184 @ X185 @ ( comp @ X186 @ X183 ) )
| ( X179 @ ( comp @ X184 @ X186 ) @ ( sub @ X185 @ X186 ) @ X183 ) )
| ~ ! [X187: term,X188: subst,X189: subst,X190: subst] :
( ( X179 @ X188 @ X187 @ ( comp @ X189 @ X190 ) )
| ~ ( X179 @ ( comp @ X188 @ X189 ) @ ( sub @ X187 @ X189 ) @ X190 ) )
| ( X179 @ id @ X178 @ id )
| ~ ! [X191: subst > term > term] :
( ( X179 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( X191 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X192 ) )
| ~ ! [X195: term] :
( ~ ( X179 @ id @ X195 @ id )
| ( X179 @ id @ ( X191 @ id @ X195 ) @ id ) ) ) ) ) ) )
<=> hoasinduction_lthm )
& induction2lem_gthm
& hoasinduction_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& pushprop_lem2v2_lthm
& pushprop
& pushprop_lem1_gthm
& induction2_gthm
& hoasinduction_lem2_gthm
& ( pushprop_lem0
<=> ! [X196: subst,X197: term,X198: term > $o] :
~ ! [X199: term > $o] :
~ ! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ ( sub @ X200 @ ( push @ X197 @ X196 ) ) ) ) )
& ( termmset_lthm
<=> ( ! [X201: term] :
( ( sub @ X201 @ id )
= X201 )
=> ! [X202: term] :
( ( sub @ X202 @ id )
= X202 ) ) )
& hoaslamnotvar_lthm
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ~ ! [X205: term,X206: term] :
( ~ ( X203 @ id @ X206 @ id )
| ( X203 @ id @ ( ap @ ( sub @ X205 @ id ) @ X206 ) @ id )
| ~ ( X203 @ id @ X205 @ id ) )
| ~ ! [X207: subst > term > term] :
( ( X203 @ id @ ( lam @ ( X207 @ sh @ one ) ) @ id )
| ~ ! [X208: term] :
( ~ ( X203 @ id @ X208 @ id )
| ( X203 @ id @ ( X207 @ id @ X208 ) @ id ) )
| ~ ! [X209: subst,X210: term,X211: subst] :
( ( X207 @ ( comp @ X209 @ X211 ) @ ( sub @ X210 @ X211 ) )
= ( sub @ ( X207 @ X209 @ X210 ) @ X211 ) ) )
| ( X203 @ id @ X204 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( apinj2
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ X212 @ X215 )
!= ( ap @ X213 @ X214 ) )
| ( X214 = X215 ) ) )
& pushprop_lem3v2_lthm
& ~ ulamvar1
& hoasapnotvar
& ( ( ^ [X216: subst,X217: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& hoasapnotvar_lthm
& ( hoasinduction_lem3b_lthm
<=> ! [X218: term] :
~ ! [X219: subst > term > term] :
( ( X219 @ sh @ one )
!= ( sub @ X218 @ ( push @ one @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X220: term] :
( ( sub @ X220 @ id )
= X220 )
=> ( ! [X221: term,X222: term,X223: term,X224: term] :
( ( ( ap @ X224 @ X222 )
!= ( ap @ X221 @ X223 ) )
| ( X221 = X224 ) )
=> ! [X225: term,X226: term,X227: term,X228: term] :
( ( X227 = X228 )
| ( ( ap @ ( sub @ X227 @ id ) @ X225 )
!= ( ap @ ( sub @ X228 @ id ) @ X226 ) ) ) ) )
<=> hoasapinj1_lthm )
& hoasinduction_lem3a_gthm
& substmonoid_gthm
& ( ( d2subst @ d_id )
= id )
& ( induction2_lthm
<=> ( ! [X229: term] :
( ( sub @ X229 @ id )
= X229 )
=> ( ! [X230: term > $o,X231: subst,X232: term] :
( ~ ! [X233: term] :
( ~ ( var @ X233 )
| ( X230 @ ( sub @ X233 @ X231 ) ) )
| ~ ! [X234: term] :
( ~ ! [X235: term] :
( ( X230 @ ( sub @ X234 @ ( push @ X235 @ id ) ) )
| ~ ( X230 @ X235 ) )
| ( X230 @ ( lam @ X234 ) ) )
| ( X230 @ ( sub @ X232 @ X231 ) )
| ~ ! [X236: term,X237: term] :
( ~ ( X230 @ X237 )
| ( X230 @ ( ap @ X236 @ X237 ) )
| ~ ( X230 @ X236 ) ) )
=> ! [X238: term,X239: term > $o] :
( ~ ! [X240: term] :
( ( X239 @ X240 )
| ~ ( var @ X240 ) )
| ~ ! [X241: term,X242: term] :
( ~ ( X239 @ X242 )
| ( X239 @ ( ap @ X242 @ X241 ) )
| ~ ( X239 @ X241 ) )
| ~ ! [X243: term] :
( ~ ! [X244: term] :
( ~ ( X239 @ X244 )
| ( X239 @ ( sub @ X243 @ ( push @ X244 @ id ) ) ) )
| ( X239 @ ( lam @ X243 ) ) )
| ( X239 @ X238 ) ) ) ) )
& ( axscons
<=> ! [X245: subst] :
( ( push @ ( sub @ one @ X245 ) @ ( comp @ sh @ X245 ) )
= X245 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoasinduction_lem2_lthm
& axabs
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X246: term,X247: term,X248: term,X249: term] :
( ( X247 = X249 )
| ( ( ap @ X248 @ X249 )
!= ( ap @ X246 @ X247 ) ) )
=> ! [X250: term,X251: term,X252: term,X253: term] :
( ( ( ap @ ( sub @ X252 @ id ) @ X251 )
!= ( ap @ ( sub @ X250 @ id ) @ X253 ) )
| ( X251 = X253 ) ) )
<=> hoasapinj2_lthm )
& ( hoasinduction_lem0_lthm
<=> ! [X254: subst > term > subst > $o] :
~ ! [X255: term > $o] :
~ ! [X256: term] :
( ( X254 @ id @ X256 @ id )
= ( X255 @ X256 ) ) )
& ( ! [X257: term,X258: term] :
( ( ( sub @ X257 @ sh )
!= ( sub @ X258 @ sh ) )
| ( X257 = X258 ) )
<=> shinj )
& ( ( ! [X259: term,X260: subst] :
( ( sub @ one @ ( push @ X259 @ X260 ) )
= X259 )
=> ( ! [X261: term,X262: subst] :
( ( comp @ sh @ ( push @ X261 @ X262 ) )
= X262 )
=> ( ! [X263: term,X264: term] :
( ( X263 = X264 )
| ( ( lam @ X263 )
!= ( lam @ X264 ) ) )
=> ! [X265: subst > term > term,X266: term,X267: subst,X268: subst > term > term] :
( ( ( lam @ ( X265 @ sh @ one ) )
!= ( lam @ ( X268 @ sh @ one ) ) )
| ( ( X265 @ X267 @ X266 )
= ( X268 @ X267 @ X266 ) )
| ~ ! [X269: subst,X270: term,X271: subst] :
( ( X265 @ ( comp @ X271 @ X269 ) @ ( sub @ X270 @ X269 ) )
= ( sub @ ( X265 @ X271 @ X270 ) @ X269 ) )
| ~ ! [X272: subst,X273: term,X274: subst] :
( ( X268 @ ( comp @ X272 @ X274 ) @ ( sub @ X273 @ X274 ) )
= ( sub @ ( X268 @ X272 @ X273 ) @ X274 ) ) ) ) ) )
<=> hoaslaminj_lthm )
& ( ! [X275: term > $o,X276: subst,X277: term] :
~ ! [X278: term > $o] :
~ ! [X279: term] :
( ( X275 @ ( sub @ X279 @ ( push @ X277 @ X276 ) ) )
= ( X278 @ X279 ) )
<=> pushprop_lem0_lthm )
& axapp
& ( hoasinduction_lem2v2
<=> ! [X280: term,X281: term > $o,X282: term,X283: subst > term > subst > $o] :
( ~ ! [X284: term,X285: term] :
( ( X283 @ id @ ( ap @ ( sub @ X285 @ id ) @ X284 ) @ id )
| ~ ( X283 @ id @ X284 @ id )
| ~ ( X283 @ id @ X285 @ id ) )
| ~ ( X281 @ X282 )
| ( X281 @ ( ap @ X280 @ X282 ) )
| ~ ! [X286: subst,X287: subst,X288: term,X289: subst] :
( ~ ( X283 @ ( comp @ X286 @ X289 ) @ ( sub @ X288 @ X289 ) @ X287 )
| ( X283 @ X286 @ X288 @ ( comp @ X289 @ X287 ) ) )
| ~ ! [X290: term,X291: subst,X292: subst,X293: subst] :
( ( X283 @ ( comp @ X291 @ X293 ) @ ( sub @ X290 @ X293 ) @ X292 )
| ~ ( X283 @ X291 @ X290 @ ( comp @ X293 @ X292 ) ) )
| ~ ! [X294: term] :
( ( X283 @ id @ X294 @ id )
= ( X281 @ X294 ) )
| ~ ( X281 @ X280 ) ) )
& ~ ( var @ ( d2term @ d_one ) )
& hoasapinj1_gthm
& ! [X295: term] :
? [X296: d_term] :
( ( d2term @ X296 )
= X295 )
& ( hoasinduction_lem3v2a
<=> ! [X297: term > $o,X298: term,X299: subst > term > subst > $o] :
( ~ ! [X300: subst > term > term] :
( ~ ! [X301: term] :
( ~ ( X299 @ id @ X301 @ id )
| ( X299 @ id @ ( X300 @ id @ X301 ) @ id ) )
| ( X299 @ id @ ( lam @ ( X300 @ sh @ one ) ) @ id )
| ~ ! [X302: subst,X303: term,X304: subst] :
( ( X300 @ ( comp @ X304 @ X302 ) @ ( sub @ X303 @ X302 ) )
= ( sub @ ( X300 @ X304 @ X303 ) @ X302 ) ) )
| ( X297 @ ( lam @ X298 ) )
| ~ ! [X305: term] :
( ( X297 @ X305 )
= ( X299 @ id @ X305 @ id ) )
| ~ ! [X306: term] :
( ~ ( X297 @ X306 )
| ( X297 @ ( sub @ X298 @ ( push @ X306 @ id ) ) ) ) ) )
& hoasinduction_lem1v2_gthm
& hoasinduction_lem3_gthm
& ( ( ! [X307: subst > term > subst > $o] :
~ ! [X308: term > $o] :
~ ! [X309: term] :
( ( X308 @ X309 )
= ( X307 @ id @ X309 @ id ) )
=> ( ! [X310: term > $o,X311: term] :
( ~ ! [X312: term] :
( ~ ( var @ X312 )
| ( X310 @ X312 ) )
| ~ ! [X313: term,X314: term] :
( ~ ( X310 @ X314 )
| ~ ( X310 @ X313 )
| ( X310 @ ( ap @ X313 @ X314 ) ) )
| ( X310 @ X311 )
| ~ ! [X315: term] :
( ~ ! [X316: term] :
( ( X310 @ ( sub @ X315 @ ( push @ X316 @ id ) ) )
| ~ ( X310 @ X316 ) )
| ( X310 @ ( lam @ X315 ) ) ) )
=> ( ! [X317: term] :
( ( sub @ X317 @ id )
= X317 )
=> ( ! [X318: term,X319: term > $o,X320: subst > term > subst > $o] :
( ~ ! [X321: term] :
( ( X320 @ id @ X321 @ id )
= ( X319 @ X321 ) )
| ( X319 @ ( lam @ X318 ) )
| ~ ! [X322: subst > term > term] :
( ~ ! [X323: subst,X324: subst,X325: term] :
( ( sub @ ( X322 @ X323 @ X325 ) @ X324 )
= ( X322 @ ( comp @ X323 @ X324 ) @ ( sub @ X325 @ X324 ) ) )
| ( X320 @ id @ ( lam @ ( X322 @ sh @ one ) ) @ id )
| ~ ! [X326: term] :
( ~ ( X320 @ id @ X326 @ id )
| ( X320 @ id @ ( X322 @ id @ X326 ) @ id ) ) )
| ~ ! [X327: term] :
( ( X319 @ ( sub @ X318 @ ( push @ X327 @ id ) ) )
| ~ ( X319 @ X327 ) ) )
=> ! [X328: subst > term > subst > $o,X329: term] :
( ~ ! [X330: term,X331: term] :
( ~ ( X328 @ id @ X330 @ id )
| ~ ( X328 @ id @ X331 @ id )
| ( X328 @ id @ ( ap @ ( sub @ X331 @ id ) @ X330 ) @ id ) )
| ( X328 @ id @ X329 @ id )
| ~ ! [X332: subst > term > term] :
( ~ ! [X333: subst,X334: subst,X335: term] :
( ( sub @ ( X332 @ X333 @ X335 ) @ X334 )
= ( X332 @ ( comp @ X333 @ X334 ) @ ( sub @ X335 @ X334 ) ) )
| ~ ! [X336: term] :
( ~ ( X328 @ id @ X336 @ id )
| ( X328 @ id @ ( X332 @ id @ X336 ) @ id ) )
| ( X328 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& ( ( ! [X337: term,X338: subst] :
( ( sub @ one @ ( push @ X337 @ X338 ) )
= X337 )
=> ( ! [X339: subst,X340: term] :
( ( comp @ sh @ ( push @ X340 @ X339 ) )
= X339 )
=> ! [X341: term > $o,X342: term,X343: subst,X344: term,X345: term > $o] :
( ~ ( X341 @ X344 )
| ( X345 @ ( sub @ X344 @ ( push @ X342 @ X343 ) ) ) ) ) )
<=> pushprop_lem1_lthm )
& axassoc
& ( termmset
<=> ! [X346: term] :
( ( sub @ X346 @ id )
= X346 ) )
& hoasapnotvar_gthm
& ulamvarsh
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X347: term > $o,X348: term,X349: subst > term > subst > $o] :
( ~ ! [X350: term] :
( ~ ( X347 @ X350 )
| ( X347 @ ( sub @ X348 @ ( push @ X350 @ id ) ) ) )
| ~ ! [X351: subst > term > term] :
( ~ ! [X352: term] :
( ( X349 @ id @ ( X351 @ id @ X352 ) @ id )
| ~ ( X349 @ id @ X352 @ id ) )
| ( X349 @ id @ ( lam @ ( X351 @ sh @ one ) ) @ id )
| ~ ! [X353: subst,X354: subst,X355: term] :
( ( sub @ ( X351 @ X353 @ X355 ) @ X354 )
= ( X351 @ ( comp @ X353 @ X354 ) @ ( sub @ X355 @ X354 ) ) ) )
| ~ ! [X356: subst,X357: subst,X358: subst,X359: term] :
( ( X349 @ X356 @ X359 @ ( comp @ X358 @ X357 ) )
| ~ ( X349 @ ( comp @ X356 @ X358 ) @ ( sub @ X359 @ X358 ) @ X357 ) )
| ~ ! [X360: term] :
( ( X347 @ X360 )
= ( X349 @ id @ X360 @ id ) )
| ~ ! [X361: subst,X362: subst,X363: term,X364: subst] :
( ( X349 @ ( comp @ X361 @ X362 ) @ ( sub @ X363 @ X362 ) @ X364 )
| ~ ( X349 @ X361 @ X363 @ ( comp @ X362 @ X364 ) ) )
| ( X347 @ ( lam @ X348 ) ) )
<=> hoasinduction_lem3v2 )
& ( ( ! [X365: term] :
( ( sub @ X365 @ id )
= X365 )
=> ( ! [X366: term,X367: subst > term > subst > $o] :
( ~ ! [X368: subst > term > term] :
( ~ ! [X369: term,X370: subst,X371: subst] :
( ( X368 @ ( comp @ X371 @ X370 ) @ ( sub @ X369 @ X370 ) )
= ( sub @ ( X368 @ X371 @ X369 ) @ X370 ) )
| ~ ! [X372: term] :
( ~ ( X367 @ id @ X372 @ id )
| ( X367 @ id @ ( X368 @ id @ X372 ) @ id ) )
| ( X367 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) )
| ( X367 @ id @ ( lam @ ( sub @ X366 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X373: term] :
( ~ ( X367 @ id @ X373 @ id )
| ( X367 @ id @ ( sub @ X366 @ ( push @ X373 @ id ) ) @ id ) ) )
=> ! [X374: subst > term > subst > $o,X375: term] :
( ( X374 @ id @ ( lam @ X375 ) @ id )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ~ ( X374 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
| ( X374 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 ) )
| ~ ! [X380: term] :
( ( X374 @ id @ ( sub @ X375 @ ( push @ X380 @ id ) ) @ id )
| ~ ( X374 @ id @ X380 @ id ) )
| ~ ! [X381: subst > term > term] :
( ( X374 @ id @ ( lam @ ( X381 @ sh @ one ) ) @ id )
| ~ ! [X382: term] :
( ~ ( X374 @ id @ X382 @ id )
| ( X374 @ id @ ( X381 @ id @ X382 ) @ id ) )
| ~ ! [X383: term,X384: subst,X385: subst] :
( ( sub @ ( X381 @ X384 @ X383 ) @ X385 )
= ( X381 @ ( comp @ X384 @ X385 ) @ ( sub @ X383 @ X385 ) ) ) )
| ~ ! [X386: subst,X387: subst,X388: term,X389: subst] :
( ~ ( X374 @ ( comp @ X389 @ X386 ) @ ( sub @ X388 @ X386 ) @ X387 )
| ( X374 @ X389 @ X388 @ ( comp @ X386 @ X387 ) ) ) ) ) )
<=> hoasinduction_lem3_lthm )
& ! [X390: d_term] : ( d_one = X390 )
& ( ! [X391: term,X392: subst > term > subst > $o] :
( ( X392 @ id @ ( lam @ ( sub @ X391 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X393: term] :
( ~ ( X392 @ id @ X393 @ id )
| ( X392 @ id @ ( sub @ X391 @ ( push @ X393 @ id ) ) @ id ) )
| ~ ! [X394: subst > term > term] :
( ( X392 @ id @ ( lam @ ( X394 @ sh @ one ) ) @ id )
| ~ ! [X395: subst,X396: term,X397: subst] :
( ( X394 @ ( comp @ X397 @ X395 ) @ ( sub @ X396 @ X395 ) )
= ( sub @ ( X394 @ X397 @ X396 ) @ X395 ) )
| ~ ! [X398: term] :
( ( X392 @ id @ ( X394 @ id @ X398 ) @ id )
| ~ ( X392 @ id @ X398 @ id ) ) ) )
<=> hoasinduction_lem3aa )
& ( hoasinduction_lem0
<=> ! [X399: subst > term > subst > $o] :
~ ! [X400: term > $o] :
~ ! [X401: term] :
( ( X399 @ id @ X401 @ id )
= ( X400 @ X401 ) ) )
& ( pushprop_lem1v2_lthm
<=> ( ! [X402: subst,X403: term] :
( ( sub @ one @ ( push @ X403 @ X402 ) )
= X403 )
=> ! [X404: term > $o,X405: subst,X406: term > $o,X407: term] :
( ( X406 @ one )
| ~ ! [X408: term] :
( ( X406 @ X408 )
= ( X404 @ ( sub @ X408 @ ( push @ X407 @ X405 ) ) ) )
| ~ ( X404 @ X407 ) ) ) )
& ! [X409: d_term,X410: d_term] :
( ( ( d2term @ X409 )
= ( d2term @ X410 ) )
=> ( X409 = X410 ) )
& ( induction
<=> ! [X411: term,X412: term > $o] :
( ~ ! [X413: term] :
( ~ ( X412 @ X413 )
| ( X412 @ ( lam @ X413 ) ) )
| ( X412 @ X411 )
| ~ ! [X414: term] :
( ~ ( var @ X414 )
| ( X412 @ X414 ) )
| ~ ! [X415: term,X416: term] :
( ( X412 @ ( ap @ X416 @ X415 ) )
| ~ ( X412 @ X416 )
| ~ ( X412 @ X415 ) ) ) )
& lamnotvar
& ( pushprop_p_and_p_prime
= ( ^ [X417: term,X418: subst,X419: term > $o,X420: term > $o] :
! [X421: term] :
( ( X420 @ X421 )
= ( X419 @ ( sub @ X421 @ ( push @ X417 @ X418 ) ) ) ) ) )
& ( hoaslaminj
<=> ! [X422: term,X423: subst > term > term,X424: subst > term > term,X425: subst] :
( ( ( lam @ ( X424 @ sh @ one ) )
!= ( lam @ ( X423 @ sh @ one ) ) )
| ( ( X423 @ X425 @ X422 )
= ( X424 @ X425 @ X422 ) )
| ~ ! [X426: subst,X427: term,X428: subst] :
( ( X424 @ ( comp @ X426 @ X428 ) @ ( sub @ X427 @ X428 ) )
= ( sub @ ( X424 @ X426 @ X427 ) @ X428 ) )
| ~ ! [X429: subst,X430: term,X431: subst] :
( ( sub @ ( X423 @ X431 @ X430 ) @ X429 )
= ( X423 @ ( comp @ X431 @ X429 ) @ ( sub @ X430 @ X429 ) ) ) ) )
& pushprop_lem0_gthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& hoasinduction_lem2v2_gthm
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X432: term] :
~ ! [X433: subst > term > term] :
~ ! [X434: term,X435: subst] :
( ( X433 @ X435 @ X434 )
= ( sub @ X432 @ ( push @ X434 @ X435 ) ) )
=> ( ! [X436: term] :
( ( sub @ X436 @ id )
= X436 )
=> ! [X437: term,X438: term > $o,X439: subst > term > subst > $o] :
( ( X438 @ ( lam @ X437 ) )
| ~ ! [X440: subst > term > term] :
( ~ ! [X441: term] :
( ~ ( X439 @ id @ X441 @ id )
| ( X439 @ id @ ( X440 @ id @ X441 ) @ id ) )
| ~ ! [X442: subst,X443: term,X444: subst] :
( ( sub @ ( X440 @ X444 @ X443 ) @ X442 )
= ( X440 @ ( comp @ X444 @ X442 ) @ ( sub @ X443 @ X442 ) ) )
| ( X439 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id ) )
| ~ ! [X445: term] :
( ( X439 @ id @ X445 @ id )
= ( X438 @ X445 ) )
| ~ ! [X446: term] :
( ( X438 @ ( sub @ X437 @ ( push @ X446 @ id ) ) )
| ~ ( X438 @ X446 ) ) ) ) ) )
& hoaslamnotvar_gthm
& ( ! [X447: term,X448: term] :
( ( ( lam @ X447 )
!= ( lam @ X448 ) )
| ( X447 = X448 ) )
<=> laminj )
& ulamvarind
& ( substmonoid
<=> ( ! [X449: subst] :
( ( comp @ X449 @ id )
= X449 )
& ! [X450: subst] :
( ( comp @ id @ X450 )
= X450 ) ) )
& ( hoasinduction
<=> ! [X451: subst > term > subst > $o,X452: term] :
( ~ ! [X453: term,X454: term] :
( ~ ( X451 @ id @ X454 @ id )
| ( X451 @ id @ ( ap @ ( sub @ X454 @ id ) @ X453 ) @ id )
| ~ ( X451 @ id @ X453 @ id ) )
| ~ ! [X455: term] :
( ( X451 @ id @ X455 @ id )
| ~ ( var @ ( sub @ X455 @ id ) ) )
| ~ ! [X456: subst > term > term] :
( ( X451 @ id @ ( lam @ ( X456 @ sh @ one ) ) @ id )
| ~ ! [X457: term] :
( ( X451 @ id @ ( X456 @ id @ X457 ) @ id )
| ~ ( X451 @ id @ X457 @ id ) )
| ~ ! [X458: subst,X459: subst,X460: term] :
( ( sub @ ( X456 @ X459 @ X460 ) @ X458 )
= ( X456 @ ( comp @ X459 @ X458 ) @ ( sub @ X460 @ X458 ) ) ) )
| ~ ! [X461: subst,X462: subst,X463: subst,X464: term] :
( ~ ( X451 @ X461 @ X464 @ ( comp @ X462 @ X463 ) )
| ( X451 @ ( comp @ X461 @ X462 ) @ ( sub @ X464 @ X462 ) @ X463 ) )
| ( X451 @ id @ X452 @ id )
| ~ ! [X465: term,X466: subst,X467: subst,X468: subst] :
( ( X451 @ X467 @ X465 @ ( comp @ X468 @ X466 ) )
| ~ ( X451 @ ( comp @ X467 @ X468 ) @ ( sub @ X465 @ X468 ) @ X466 ) ) ) )
& ( ( ^ [X469: subst > term > subst > $o,X470: term > $o] :
! [X471: term] :
( ( X470 @ X471 )
= ( X469 @ id @ X471 @ id ) ) )
= hoasinduction_p_and_p_prime )
& hoasinduction_lem3v2_gthm
& ( hoasinduction_lthm_3
<=> ( ! [X472: subst > term > subst > $o] :
~ ! [X473: term > $o] :
~ ! [X474: term] :
( ( X473 @ X474 )
= ( X472 @ id @ X474 @ id ) )
=> ( ! [X475: term,X476: term > $o] :
( ~ ! [X477: term,X478: term] :
( ~ ( X476 @ X477 )
| ~ ( X476 @ X478 )
| ( X476 @ ( ap @ X478 @ X477 ) ) )
| ~ ! [X479: term] :
( ~ ( var @ X479 )
| ( X476 @ X479 ) )
| ~ ! [X480: term] :
( ~ ! [X481: term] :
( ( X476 @ ( sub @ X480 @ ( push @ X481 @ id ) ) )
| ~ ( X476 @ X481 ) )
| ( X476 @ ( lam @ X480 ) ) )
| ( X476 @ X475 ) )
=> ( ! [X482: term] :
( ( sub @ X482 @ id )
= X482 )
=> ( ! [X483: term > $o,X484: subst > term > subst > $o,X485: term] :
( ( X483 @ ( lam @ X485 ) )
| ~ ! [X486: term] :
( ( X483 @ ( sub @ X485 @ ( push @ X486 @ id ) ) )
| ~ ( X483 @ X486 ) )
| ~ ! [X487: term] :
( ( X483 @ X487 )
= ( X484 @ id @ X487 @ id ) )
| ~ ! [X488: subst > term > term] :
( ( X484 @ id @ ( lam @ ( X488 @ sh @ one ) ) @ id )
| ~ ! [X489: term] :
( ( X484 @ id @ ( X488 @ id @ X489 ) @ id )
| ~ ( X484 @ id @ X489 @ id ) )
| ~ ! [X490: term,X491: subst,X492: subst] :
( ( X488 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) )
= ( sub @ ( X488 @ X491 @ X490 ) @ X492 ) ) ) )
=> ! [X493: term,X494: subst > term > subst > $o] :
( ~ ! [X495: subst,X496: subst,X497: term,X498: subst] :
( ( X494 @ X495 @ X497 @ ( comp @ X498 @ X496 ) )
| ~ ( X494 @ ( comp @ X495 @ X498 ) @ ( sub @ X497 @ X498 ) @ X496 ) )
| ~ ! [X499: subst,X500: subst,X501: term,X502: subst] :
( ( X494 @ ( comp @ X499 @ X502 ) @ ( sub @ X501 @ X502 ) @ X500 )
| ~ ( X494 @ X499 @ X501 @ ( comp @ X502 @ X500 ) ) )
| ( X494 @ id @ X493 @ id )
| ~ ! [X503: term,X504: term] :
( ~ ( X494 @ id @ X504 @ id )
| ( X494 @ id @ ( ap @ ( sub @ X503 @ id ) @ X504 ) @ id )
| ~ ( X494 @ id @ X503 @ id ) )
| ~ ! [X505: term] :
( ( X494 @ id @ X505 @ id )
| ~ ( var @ ( sub @ X505 @ id ) ) )
| ~ ! [X506: subst > term > term] :
( ( X494 @ id @ ( lam @ ( X506 @ sh @ one ) ) @ id )
| ~ ! [X507: term,X508: subst,X509: subst] :
( ( X506 @ ( comp @ X509 @ X508 ) @ ( sub @ X507 @ X508 ) )
= ( sub @ ( X506 @ X509 @ X507 ) @ X508 ) )
| ~ ! [X510: term] :
( ~ ( X494 @ id @ X510 @ id )
| ( X494 @ id @ ( X506 @ id @ X510 ) @ id ) ) ) ) ) ) ) ) )
& ( ! [X511: term,X512: subst > term > subst > $o] :
( ~ ! [X513: subst > term > term] :
( ~ ! [X514: subst,X515: term,X516: subst] :
( ( X513 @ ( comp @ X516 @ X514 ) @ ( sub @ X515 @ X514 ) )
= ( sub @ ( X513 @ X516 @ X515 ) @ X514 ) )
| ~ ! [X517: term] :
( ~ ( X512 @ id @ X517 @ id )
| ( X512 @ id @ ( X513 @ id @ X517 ) @ id ) )
| ( X512 @ id @ ( lam @ ( X513 @ sh @ one ) ) @ id ) )
| ( X512 @ id @ ( lam @ ( sub @ X511 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X518: term] :
( ~ ( X512 @ id @ X518 @ id )
| ( X512 @ id @ ( sub @ X511 @ ( push @ X518 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ( ! [X519: term,X520: term,X521: subst > term > term] :
( ~ ! [X522: subst,X523: term,X524: subst] :
( ( sub @ ( X521 @ X522 @ X523 ) @ X524 )
= ( X521 @ ( comp @ X522 @ X524 ) @ ( sub @ X523 @ X524 ) ) )
| ( ( lam @ ( X521 @ sh @ one ) )
!= ( ap @ ( sub @ X520 @ id ) @ X519 ) ) )
<=> hoaslamnotap )
& pushprop_lem2v2_gthm
& axclos
& ( ! [X525: subst,X526: term > $o,X527: term] :
( ~ ! [X528: term] :
( ( X526 @ ( sub @ X528 @ X525 ) )
| ~ ( var @ X528 ) )
| ~ ! [X529: term,X530: term] :
( ~ ( X526 @ X529 )
| ( X526 @ ( ap @ X530 @ X529 ) )
| ~ ( X526 @ X530 ) )
| ~ ! [X531: term] :
( ~ ! [X532: term] :
( ( X526 @ ( sub @ X531 @ ( push @ X532 @ id ) ) )
| ~ ( X526 @ X532 ) )
| ( X526 @ ( lam @ X531 ) ) )
| ( X526 @ ( sub @ X527 @ X525 ) ) )
<=> induction2lem )
& ( ! [X533: subst > term > subst > $o,X534: term] :
( ~ ! [X535: term] :
( ~ ( X533 @ id @ X535 @ id )
| ( X533 @ id @ ( sub @ X534 @ ( push @ X535 @ id ) ) @ id ) )
| ~ ! [X536: subst,X537: subst,X538: subst,X539: term] :
( ~ ( X533 @ X537 @ X539 @ ( comp @ X536 @ X538 ) )
| ( X533 @ ( comp @ X537 @ X536 ) @ ( sub @ X539 @ X536 ) @ X538 ) )
| ( X533 @ id @ ( lam @ X534 ) @ id )
| ~ ! [X540: subst > term > term] :
( ~ ! [X541: subst,X542: term,X543: subst] :
( ( X540 @ ( comp @ X541 @ X543 ) @ ( sub @ X542 @ X543 ) )
= ( sub @ ( X540 @ X541 @ X542 ) @ X543 ) )
| ( X533 @ id @ ( lam @ ( X540 @ sh @ one ) ) @ id )
| ~ ! [X544: term] :
( ~ ( X533 @ id @ X544 @ id )
| ( X533 @ id @ ( X540 @ id @ X544 ) @ id ) ) )
| ~ ! [X545: term,X546: subst,X547: subst,X548: subst] :
( ( X533 @ X548 @ X545 @ ( comp @ X546 @ X547 ) )
| ~ ( X533 @ ( comp @ X548 @ X546 ) @ ( sub @ X545 @ X546 ) @ X547 ) ) )
<=> hoasinduction_lem3 )
& ( axidr
<=> ! [X549: subst] :
( ( comp @ X549 @ id )
= X549 ) )
& axvarshift ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( termmset_gthm
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X10: subst > term > subst > $o,X43: term] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( 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] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id ) ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f_lthm )
& hoasapinj2_gthm
& ! [X5: d_subst] : ( d_id = X5 )
& pushprop_lem1v2_gthm
& hoasinduction_lem1v2
& ( hoasinduction_lem2
<=> ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id ) ) )
& hoaslamnotap_gthm
& ( hoasapinj1
<=> ! [X13: term,X15: term,X20: term,X19: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
& hoasinduction_lem1
& ~ lamnotap
& pushprop_lthm_orig
& hoaslaminj_gthm
& ( ! [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 @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3a )
& ( hoasinduction_lem3b
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& ! [X7: d_subst,X6: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& pushprop_lem3v2
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3aaa
<=> ! [X10: subst > term > subst > $o,X34: term] :
( ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term,X35: term] :
( ~ ! [X36: subst,X37: term,X38: subst] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X39: subst,X41: subst,X40: term] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) ) ) ) )
& ( ! [X13: term,X26: term > $o,X10: term > $o,X14: subst,X15: term] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) )
<=> pushprop_lem1 )
& ( axidl
<=> ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
& ( axshiftcons
<=> ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 ) )
& ( ( d2subst @ d_id )
= sh )
& hoasinduction_lem3b_gthm
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& hoaslamnotvar
& ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X48: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,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 ) ) ) ) )
& hoasinduction_lem1_lthm
& ( ! [X19: term,X15: term,X20: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) )
<=> hoasapinj2 )
& ( pushprop_lem1v2
<=> ! [X10: term > $o,X11: term > $o,X14: subst,X13: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ( X11 @ one )
| ~ ( X10 @ X13 ) ) )
& ( induction2
<=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) ) ) )
& hoasinduction_lem1_gthm
& axmap
& pushprop_lthm
& ( hoasinduction_lem3v2_f
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) ) )
& pushprop_gthm
& pushprop_lem2v2
& ( induction2lem_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X10: term > $o,X21: term] :
( ( X10 @ X21 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) ) )
=> ! [X10: term > $o,X16: term,X17: subst] :
( ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) ) ) ) ) ) ) )
& ( ! [X19: term,X20: term,X13: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
<=> apinj1 )
& hoaslamnotap_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 ) ) ) )
<=> substmonoid_lthm )
& apnotvar
& ( ( ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) ) )
=> ( ! [X10: subst > term > subst > $o,X24: term,X23: term] :
( ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X26: subst,X25: subst,X14: 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 @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) )
=> ( ! [X10: subst > term > subst > $o,X27: term] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X18: subst > term > term] :
( ( 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 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) ) ) ) ) )
<=> hoasinduction_lthm )
& induction2lem_gthm
& hoasinduction_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& pushprop_lem2v2_lthm
& pushprop
& pushprop_lem1_gthm
& induction2_gthm
& hoasinduction_lem2_gthm
& ( pushprop_lem0
<=> ! [X14: subst,X13: term,X10: term > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& hoaslamnotvar_lthm
& ( ! [X10: subst > term > subst > $o,X30: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ 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,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ X30 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( apinj2
<=> ! [X15: term,X13: term,X19: term,X20: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) ) )
& pushprop_lem3v2_lthm
& ~ ulamvar1
& hoasapnotvar
& ( ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& hoasapnotvar_lthm
& ( hoasinduction_lem3b_lthm
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X13: term,X20: term,X19: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
=> ! [X19: term,X20: term,X13: term,X15: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) ) )
<=> hoasapinj1_lthm )
& hoasinduction_lem3a_gthm
& substmonoid_gthm
& ( ( d2subst @ d_id )
= id )
& ( induction2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: term > $o,X17: subst,X16: term] :
( ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) ) )
=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) ) ) ) )
& ( axscons
<=> ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoasinduction_lem2_lthm
& axabs
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X15: term,X20: term,X13: term,X19: term] :
( ( X19 = X20 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X15: term,X19: term,X13: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
<=> hoasapinj2_lthm )
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( ! [X13: term,X15: term] :
( ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) )
| ( X13 = X15 ) )
<=> shinj )
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X15: term,X13: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) )
=> ! [X18: subst > term > term,X33: term,X32: subst,X31: subst > term > term] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) )
<=> hoaslaminj_lthm )
& ( ! [X10: term > $o,X14: subst,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0_lthm )
& axapp
& ( hoasinduction_lem2v2
<=> ! [X44: term,X11: term > $o,X45: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ( X11 @ X45 )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X14: subst,X25: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ( X11 @ X44 ) ) )
& ~ ( var @ ( d2term @ d_one ) )
& hoasapinj1_gthm
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( hoasinduction_lem3v2a
<=> ! [X11: term > $o,X29: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ 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 ) ) ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) ) )
& hoasinduction_lem1v2_gthm
& hoasinduction_lem3_gthm
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ 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 ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [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 @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) )
=> ! [X10: subst > term > subst > $o,X30: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ( X10 @ id @ X30 @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [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 ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X10: term > $o,X15: term,X14: subst,X13: term,X26: term > $o] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) ) )
<=> pushprop_lem1_lthm )
& axassoc
& ( termmset
<=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) )
& hoasapnotvar_gthm
& ulamvarsh
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X11: term > $o,X48: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( 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 ) ) ) )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X14: subst,X26: subst,X13: term,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X11 @ ( lam @ X48 ) ) )
<=> hoasinduction_lem3v2 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [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 @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X10: subst > term > subst > $o,X27: term] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [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 ) )
| ~ ! [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 ) ) ) )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) ) )
<=> hoasinduction_lem3_lthm )
& ! [X1: d_term] : ( d_one = X1 )
& ( ! [X42: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ( 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 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
<=> hoasinduction_lem3aa )
& ( hoasinduction_lem0
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( pushprop_lem1v2_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X10: term > $o,X14: subst,X11: term > $o,X13: term] :
( ( X11 @ one )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ~ ( X10 @ X13 ) ) ) )
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& ( induction
<=> ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X21 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) ) ) )
& lamnotvar
& ( 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 ) ) ) ) ) )
& ( hoaslaminj
<=> ! [X33: term,X18: subst > term > term,X31: subst > term > term,X32: subst] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
& pushprop_lem0_gthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& hoasinduction_lem2v2_gthm
& ( 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] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) ) ) ) )
& hoaslamnotvar_gthm
& ( ! [X15: term,X13: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
<=> laminj )
& ulamvarind
& ( substmonoid
<=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) ) )
& ( hoasinduction
<=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [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,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) )
& ( ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
= hoasinduction_p_and_p_prime )
& hoasinduction_lem3v2_gthm
& ( hoasinduction_lthm_3
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ 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 ) ) ) ) ) ) ) ) )
& ( ! [X42: term,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 @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ( ! [X47: term,X46: term,X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) ) )
<=> hoaslamnotap )
& pushprop_lem2v2_gthm
& axclos
& ( ! [X17: subst,X10: term > $o,X16: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
<=> induction2lem )
& ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ 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 @ ( lam @ X27 ) @ id )
| ~ ! [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 @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X13: term,X26: subst,X25: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) )
<=> hoasinduction_lem3 )
& ( axidr
<=> ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
& axvarshift ),
file('/export/starexec/sandbox2/tmp/tmp.C6YnWq5B3d/DTF2THF_12223.p',alg444_1) ).
thf(f1127,plain,
! [X152: subst] :
( ( d2subst @ ( sK531 @ X152 ) )
= X152 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3012,plain,
( ( sK549
!= ( comp @ ( d2subst @ d_id ) @ ( push @ sK550 @ sK549 ) ) )
| spl591_279 ),
inference(avatar_component_clause,[status(thm)],[f3010]) ).
thf(f3010,definition,
( spl591_279
<=> ( sK549
= ( comp @ ( d2subst @ d_id ) @ ( push @ sK550 @ sK549 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_279])],[avatar_definition]) ).
thf(f6945,plain,
( ~ spl591_196
| ~ spl591_697 ),
inference(avatar_contradiction_clause,[status(thm)],[f6944]) ).
thf(f6944,plain,
( $false
| ~ spl591_196
| ~ spl591_697 ),
inference(subsumption_resolution,[status(thm)],[f1082,f6862]) ).
thf(f6862,plain,
( ! [X2: term,X5: subst > term > subst > $o] :
( $true
= ( X5 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) ) )
| ~ spl591_196
| ~ spl591_697 ),
inference(subsumption_resolution,[status(thm)],[f6056,f6664]) ).
thf(f6056,plain,
( ! [X2: term,X5: subst > term > subst > $o] :
( ( $true
= ( sK594
@ ^ [Y0: subst,Y1: term,Y2: subst] :
~ ( X5 @ Y0 @ Y1 @ Y2 )
@ X2 ) )
| ( $true
= ( X5 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_196 ),
inference(not_proxy_clausification,[status(thm)],[f6055]) ).
thf(f6055,plain,
( ! [X2: term,X5: subst > term > subst > $o] :
( ( ( ~ ( X5 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) ) )
= $false )
| ( $true
= ( sK594
@ ^ [Y0: subst,Y1: term,Y2: subst] :
~ ( X5 @ Y0 @ Y1 @ Y2 )
@ X2 ) ) )
| ~ spl591_196 ),
inference(beta_eta_normalization,[status(thm)],[f6041]) ).
thf(f6041,plain,
( ! [X2: term,X5: subst > term > subst > $o] :
( ( $true
= ( sK594
@ ^ [Y0: subst,Y1: term,Y2: subst] :
~ ( X5 @ Y0 @ Y1 @ Y2 )
@ X2 ) )
| ( $false
= ( ^ [Y0: subst,Y1: term,Y2: subst] :
~ ( X5 @ Y0 @ Y1 @ Y2 )
@ ( d2subst @ d_id )
@ X2
@ ( d2subst @ d_id ) ) ) )
| ~ spl591_196 ),
inference(primitive_instantiation,[status(thm)],[f2655]) ).
thf(f2655,plain,
( ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
= $false )
| ( $true
= ( sK594 @ X1 @ X2 ) ) )
| ~ spl591_196 ),
inference(avatar_component_clause,[status(thm)],[f2654]) ).
thf(f2654,definition,
( spl591_196
<=> ! [X2: term,X1: subst > term > subst > $o] :
( ( ( X1 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
= $false )
| ( $true
= ( sK594 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_196])],[avatar_definition]) ).
thf(f1082,plain,
( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f6756,plain,
( ~ spl591_341
| ~ spl591_661 ),
inference(avatar_contradiction_clause,[status(thm)],[f6755]) ).
thf(f6755,plain,
( $false
| ~ spl591_341
| ~ spl591_661 ),
inference(subsumption_resolution,[status(thm)],[f3279,f6742]) ).
thf(f6742,plain,
( ! [X3: term,X0: term > $o,X4: term] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
!= ( X0 @ X4 ) ) )
| ~ spl591_661 ),
inference(trivial_inequality_removal,[status(thm)],[f6728]) ).
thf(f6728,plain,
( ! [X3: term,X0: term > $o,X4: term] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true = $false )
| ( $true
!= ( X0 @ X3 ) ) )
| ~ spl591_661 ),
inference(backward_demodulation,[status(thm)],[f4949,f5250]) ).
thf(f5250,plain,
( ! [X36: term > $o] :
( $false
= ( X36 @ ( d2term @ d_one ) ) )
| ~ spl591_661 ),
inference(avatar_component_clause,[status(thm)],[f5249]) ).
thf(f5249,definition,
( spl591_661
<=> ! [X36: term > $o] :
( $false
= ( X36 @ ( d2term @ d_one ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_661])],[avatar_definition]) ).
thf(f4949,plain,
! [X3: term,X0: term > $o,X4: term] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
!= ( X0 @ X3 ) )
| ( $true
= ( X0 @ ( d2term @ d_one ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4845,f4896]) ).
thf(f4896,plain,
! [X0: term > $o] :
( ( $true
= ( X0 @ ( d2term @ d_one ) ) )
| ( $true
= ( sP40 @ X0 ) ) ),
inference(backward_demodulation,[status(thm)],[f702,f4807]) ).
thf(f4807,plain,
! [X135: term] :
( ( d2term @ d_one )
= X135 ),
inference(forward_demodulation,[status(thm)],[f1145,f1155]) ).
thf(f1155,plain,
! [X114: d_term] : ( d_one = X114 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1145,plain,
! [X135: term] :
( ( d2term @ ( sK523 @ X135 ) )
= X135 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f702,plain,
! [X0: term > $o] :
( ( ( X0 @ ( sK190 @ X0 ) )
= $true )
| ( $true
= ( sP40 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
thf(f202,plain,
! [X0: term > $o] :
( ( ( $true
= ( sP40 @ X0 ) )
| ( ( $true
= ( X0 @ ( sK191 @ X0 ) ) )
& ( $true
!= ( X0 @ ( ap @ ( sK190 @ X0 ) @ ( sK191 @ X0 ) ) ) )
& ( ( X0 @ ( sK190 @ X0 ) )
= $true ) ) )
& ( ! [X3: term,X4: term] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X0 @ ( ap @ X3 @ X4 ) ) )
| ( $true
!= ( X0 @ X3 ) ) )
| ( $true
!= ( sP40 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191])],[f200,f201]) ).
thf(f201,plain,
! [X0: term > $o] :
( ? [X1: term,X2: term] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X0 @ ( ap @ X1 @ X2 ) ) )
& ( $true
= ( X0 @ X1 ) ) )
=> ( ( $true
= ( X0 @ ( sK191 @ X0 ) ) )
& ( $true
!= ( X0 @ ( ap @ ( sK190 @ X0 ) @ ( sK191 @ X0 ) ) ) )
& ( ( X0 @ ( sK190 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f200,plain,
! [X0: term > $o] :
( ( ( $true
= ( sP40 @ X0 ) )
| ? [X1: term,X2: term] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X0 @ ( ap @ X1 @ X2 ) ) )
& ( $true
= ( X0 @ X1 ) ) ) )
& ( ! [X3: term,X4: term] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X0 @ ( ap @ X3 @ X4 ) ) )
| ( $true
!= ( X0 @ X3 ) ) )
| ( $true
!= ( sP40 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f199]) ).
thf(f199,plain,
! [X308: term > $o] :
( ( ( $true
= ( sP40 @ X308 ) )
| ? [X311: term,X312: term] :
( ( $true
= ( X308 @ X312 ) )
& ( $true
!= ( X308 @ ( ap @ X311 @ X312 ) ) )
& ( $true
= ( X308 @ X311 ) ) ) )
& ( ! [X311: term,X312: term] :
( ( $true
!= ( X308 @ X312 ) )
| ( $true
= ( X308 @ ( ap @ X311 @ X312 ) ) )
| ( $true
!= ( X308 @ X311 ) ) )
| ( $true
!= ( sP40 @ X308 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
thf(f4845,plain,
! [X3: term,X0: term > $o,X4: term] :
( ( $true
!= ( sP40 @ X0 ) )
| ( $true
= ( X0 @ ( d2term @ d_one ) ) )
| ( $true
!= ( X0 @ X4 ) )
| ( $true
!= ( X0 @ X3 ) ) ),
inference(backward_demodulation,[status(thm)],[f701,f4807]) ).
thf(f701,plain,
! [X3: term,X0: term > $o,X4: term] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
!= ( sP40 @ X0 ) )
| ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X0 @ ( ap @ X3 @ X4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
thf(f3279,plain,
( ( ( sK551 @ sK554 )
= $true )
| ~ spl591_341 ),
inference(avatar_component_clause,[status(thm)],[f3277]) ).
thf(f3277,definition,
( spl591_341
<=> ( ( sK551 @ sK554 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_341])],[avatar_definition]) ).
thf(f6665,plain,
( spl591_645
| spl591_697
| ~ spl591_278 ),
inference(avatar_split_clause,[status(thm)],[f6264,f3007,f6663,f5046]) ).
thf(f5046,definition,
( spl591_645
<=> ! [X125: term > $o] :
( $true
= ( X125 @ ( d2term @ d_one ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_645])],[avatar_definition]) ).
thf(f3007,definition,
( spl591_278
<=> ! [X189: term,X188: subst,X187: term,X186: term > $o,X190: term > $o] :
( ( $true
!= ( X186 @ X189 ) )
| ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_278])],[avatar_definition]) ).
thf(f6264,plain,
( ! [X189: term,X186: term > $o,X190: term > $o] :
( ( ( X190 @ ( d2term @ d_one ) )
= $true )
| ( $true
!= ( X186 @ X189 ) ) )
| ~ spl591_278 ),
inference(forward_demodulation,[status(thm)],[f3008,f4807]) ).
thf(f3008,plain,
( ! [X188: subst,X189: term,X186: term > $o,X187: term,X190: term > $o] :
( ( $true
!= ( X186 @ X189 ) )
| ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) ) )
| ~ spl591_278 ),
inference(avatar_component_clause,[status(thm)],[f3007]) ).
thf(f6606,plain,
( spl591_645
| ~ spl591_178
| ~ spl591_660 ),
inference(avatar_split_clause,[status(thm)],[f6605,f5245,f2576,f5046]) ).
thf(f2576,definition,
( spl591_178
<=> ! [X36: term > $o] :
( ( $true
= ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X36 @ ( sK475 @ X36 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_178])],[avatar_definition]) ).
thf(f5245,definition,
( spl591_660
<=> ( ( sK474 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl591_660])],[avatar_definition]) ).
thf(f6605,plain,
( ! [X36: term > $o] :
( $true
= ( X36 @ ( d2term @ d_one ) ) )
| ~ spl591_178
| ~ spl591_660 ),
inference(trivial_inequality_removal,[status(thm)],[f6604]) ).
thf(f6604,plain,
( ! [X36: term > $o] :
( ( $true = $false )
| ( $true
= ( X36 @ ( d2term @ d_one ) ) ) )
| ~ spl591_178
| ~ spl591_660 ),
inference(forward_demodulation,[status(thm)],[f6603,f5247]) ).
thf(f5247,plain,
( ( ( sK474 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $false )
| ~ spl591_660 ),
inference(avatar_component_clause,[status(thm)],[f5245]) ).
thf(f6603,plain,
( ! [X36: term > $o] :
( ( $true
= ( X36 @ ( d2term @ d_one ) ) )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_178 ),
inference(forward_demodulation,[status(thm)],[f6602,f4807]) ).
thf(f6602,plain,
( ! [X36: term > $o] :
( ( $true
= ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X36 @ ( d2term @ d_one ) ) ) )
| ~ spl591_178 ),
inference(forward_demodulation,[status(thm)],[f2577,f4807]) ).
thf(f2577,plain,
( ! [X36: term > $o] :
( ( $true
= ( X36 @ ( sK475 @ X36 ) ) )
| ( $true
= ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) ) ) )
| ~ spl591_178 ),
inference(avatar_component_clause,[status(thm)],[f2576]) ).
thf(f6458,plain,
~ spl591_645,
inference(avatar_contradiction_clause,[status(thm)],[f6457]) ).
thf(f6457,plain,
( $false
| ~ spl591_645 ),
inference(trivial_inequality_removal,[status(thm)],[f6456]) ).
thf(f6456,plain,
( ( $true = $false )
| ~ spl591_645 ),
inference(beta_eta_normalization,[status(thm)],[f6382]) ).
thf(f6382,plain,
( ( $true
= ( ^ [Y0: term] : $false
@ ( d2term @ d_one ) ) )
| ~ spl591_645 ),
inference(primitive_instantiation,[status(thm)],[f5047]) ).
thf(f5047,plain,
( ! [X125: term > $o] :
( $true
= ( X125 @ ( d2term @ d_one ) ) )
| ~ spl591_645 ),
inference(avatar_component_clause,[status(thm)],[f5046]) ).
thf(f6210,plain,
spl591_220,
inference(avatar_contradiction_clause,[status(thm)],[f6209]) ).
thf(f6209,plain,
( $false
| spl591_220 ),
inference(subsumption_resolution,[status(thm)],[f6182,f6114]) ).
thf(f6114,plain,
! [X0: term,X1: term] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f4807,f4807]) ).
thf(f6182,plain,
( ! [X0: term] : ( sK583 != X0 )
| spl591_220 ),
inference(superposition,[status(thm)],[f2760,f6114]) ).
thf(f2760,plain,
( ( sK584 != sK583 )
| spl591_220 ),
inference(avatar_component_clause,[status(thm)],[f2758]) ).
thf(f2758,definition,
( spl591_220
<=> ( sK584 = sK583 ) ),
introduced(definition,[new_symbols(naming,[spl591_220])],[avatar_definition]) ).
thf(f5958,plain,
( ~ spl591_686
| ~ spl591_687 ),
inference(avatar_contradiction_clause,[status(thm)],[f5957]) ).
thf(f5957,plain,
( $false
| ~ spl591_686
| ~ spl591_687 ),
inference(trivial_inequality_removal,[status(thm)],[f5956]) ).
thf(f5956,plain,
( ( $true = $false )
| ~ spl591_686
| ~ spl591_687 ),
inference(forward_demodulation,[status(thm)],[f5907,f5885]) ).
thf(f5885,plain,
( ( $false
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl591_686 ),
inference(avatar_component_clause,[status(thm)],[f5883]) ).
thf(f5883,definition,
( spl591_686
<=> ( $false
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_686])],[avatar_definition]) ).
thf(f5907,plain,
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl591_687 ),
inference(avatar_component_clause,[status(thm)],[f5905]) ).
thf(f5905,definition,
( spl591_687
<=> ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_687])],[avatar_definition]) ).
thf(f5908,plain,
( spl591_687
| spl591_645
| ~ spl591_197 ),
inference(avatar_split_clause,[status(thm)],[f5903,f2658,f5046,f5905]) ).
thf(f5903,plain,
( ! [X1: term > $o] :
( ( $true
= ( X1 @ ( d2term @ d_one ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ~ spl591_197 ),
inference(forward_demodulation,[status(thm)],[f5902,f4807]) ).
thf(f5902,plain,
( ! [X1: term > $o] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X1 @ ( sK593 @ X1 ) ) ) )
| ~ spl591_197 ),
inference(forward_demodulation,[status(thm)],[f2659,f4807]) ).
thf(f5886,plain,
( spl591_686
| spl591_661
| ~ spl591_199 ),
inference(avatar_split_clause,[status(thm)],[f5881,f2666,f5249,f5883]) ).
thf(f2666,definition,
( spl591_199
<=> ! [X1: term > $o] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) )
= $false )
| ( ( X1 @ ( sK593 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl591_199])],[avatar_definition]) ).
thf(f5881,plain,
( ! [X1: term > $o] :
( ( $false
= ( X1 @ ( d2term @ d_one ) ) )
| ( $false
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ~ spl591_199 ),
inference(forward_demodulation,[status(thm)],[f5880,f4807]) ).
thf(f5880,plain,
( ! [X1: term > $o] :
( ( $false
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( sK593 @ X1 ) )
= $false ) )
| ~ spl591_199 ),
inference(forward_demodulation,[status(thm)],[f2667,f4807]) ).
thf(f2667,plain,
( ! [X1: term > $o] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) )
= $false )
| ( ( X1 @ ( sK593 @ X1 ) )
= $false ) )
| ~ spl591_199 ),
inference(avatar_component_clause,[status(thm)],[f2666]) ).
thf(f5707,plain,
( ~ spl591_177
| ~ spl591_198 ),
inference(avatar_contradiction_clause,[status(thm)],[f5706]) ).
thf(f5706,plain,
( $false
| ~ spl591_177
| ~ spl591_198 ),
inference(trivial_inequality_removal,[status(thm)],[f5705]) ).
thf(f5705,plain,
( ( $true = $false )
| ~ spl591_177
| ~ spl591_198 ),
inference(forward_demodulation,[status(thm)],[f2574,f2663]) ).
thf(f2663,plain,
( ( hoasinduction_lem0 = $false )
| ~ spl591_198 ),
inference(avatar_component_clause,[status(thm)],[f2661]) ).
thf(f2661,definition,
( spl591_198
<=> ( hoasinduction_lem0 = $false ) ),
introduced(definition,[new_symbols(naming,[spl591_198])],[avatar_definition]) ).
thf(f2574,plain,
( ( hoasinduction_lem0 = $true )
| ~ spl591_177 ),
inference(avatar_component_clause,[status(thm)],[f2572]) ).
thf(f2572,definition,
( spl591_177
<=> ( hoasinduction_lem0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_177])],[avatar_definition]) ).
thf(f5631,plain,
( spl591_277
| ~ spl591_380 ),
inference(avatar_contradiction_clause,[status(thm)],[f5630]) ).
thf(f5630,plain,
( $false
| spl591_277
| ~ spl591_380 ),
inference(subsumption_resolution,[status(thm)],[f3005,f5616]) ).
thf(f5616,plain,
( ! [X259: term,X258: term] : ( X258 = X259 )
| ~ spl591_380 ),
inference(subsumption_resolution,[status(thm)],[f5615,f4807]) ).
thf(f5615,plain,
( ! [X259: term,X258: term] :
( ( ( d2term @ d_one )
!= ( sub @ X258 @ ( d2subst @ d_id ) ) )
| ( X258 = X259 ) )
| ~ spl591_380 ),
inference(forward_demodulation,[status(thm)],[f3449,f4807]) ).
thf(f3449,plain,
( ! [X259: term,X258: term] :
( ( ( sub @ X258 @ ( d2subst @ d_id ) )
!= ( sub @ X259 @ ( d2subst @ d_id ) ) )
| ( X258 = X259 ) )
| ~ spl591_380 ),
inference(avatar_component_clause,[status(thm)],[f3448]) ).
thf(f3448,definition,
( spl591_380
<=> ! [X259: term,X258: term] :
( ( X258 = X259 )
| ( ( sub @ X258 @ ( d2subst @ d_id ) )
!= ( sub @ X259 @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_380])],[avatar_definition]) ).
thf(f3005,plain,
( ( sK547
!= ( sub @ ( d2term @ d_one ) @ ( push @ sK547 @ sK548 ) ) )
| spl591_277 ),
inference(avatar_component_clause,[status(thm)],[f3003]) ).
thf(f3003,definition,
( spl591_277
<=> ( sK547
= ( sub @ ( d2term @ d_one ) @ ( push @ sK547 @ sK548 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_277])],[avatar_definition]) ).
thf(f5251,plain,
( spl591_660
| spl591_661
| ~ spl591_179 ),
inference(avatar_split_clause,[status(thm)],[f5243,f2580,f5249,f5245]) ).
thf(f2580,definition,
( spl591_179
<=> ! [X36: term > $o] :
( ( $false
= ( X36 @ ( sK475 @ X36 ) ) )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl591_179])],[avatar_definition]) ).
thf(f5243,plain,
( ! [X36: term > $o] :
( ( $false
= ( X36 @ ( d2term @ d_one ) ) )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $false ) )
| ~ spl591_179 ),
inference(forward_demodulation,[status(thm)],[f5242,f4807]) ).
thf(f5242,plain,
( ! [X36: term > $o] :
( ( ( sK474 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $false )
| ( $false
= ( X36 @ ( sK475 @ X36 ) ) ) )
| ~ spl591_179 ),
inference(forward_demodulation,[status(thm)],[f2581,f4807]) ).
thf(f2581,plain,
( ! [X36: term > $o] :
( ( $false
= ( X36 @ ( sK475 @ X36 ) ) )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) )
= $false ) )
| ~ spl591_179 ),
inference(avatar_component_clause,[status(thm)],[f2580]) ).
thf(f3991,plain,
( spl591_504
| ~ spl591_177 ),
inference(avatar_split_clause,[status(thm)],[f1691,f2572,f3989]) ).
thf(f1691,plain,
! [X34: term,X32: subst > term > subst > $o] :
( ( $true
= ( sK473 @ X32 @ X34 ) )
| ( hoasinduction_lem0 != $true )
| ( $false
= ( X32 @ ( d2subst @ d_id ) @ X34 @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1603]) ).
thf(f1603,plain,
! [X34: term,X32: subst > term > subst > $o] :
( ( hoasinduction_lem0 != $true )
| ( ( sK473 @ X32 @ X34 )
= ( X32 @ ( d2subst @ d_id ) @ X34 @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1215,f1092,f1092]) ).
thf(f1092,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1215,plain,
! [X34: term,X32: subst > term > subst > $o] :
( ( ( sK473 @ X32 @ X34 )
= ( X32 @ id @ X34 @ id ) )
| ( hoasinduction_lem0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3450,plain,
( spl591_380
| ~ spl591_221 ),
inference(avatar_split_clause,[status(thm)],[f1648,f2762,f3448]) ).
thf(f2762,definition,
( spl591_221
<=> ( shinj = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_221])],[avatar_definition]) ).
thf(f1648,plain,
! [X259: term,X258: term] :
( ( shinj != $true )
| ( X258 = X259 )
| ( ( sub @ X258 @ ( d2subst @ d_id ) )
!= ( sub @ X259 @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1053,f1200,f1200]) ).
thf(f1200,plain,
( ( d2subst @ d_id )
= sh ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1053,plain,
! [X259: term,X258: term] :
( ( ( sub @ X259 @ sh )
!= ( sub @ X258 @ sh ) )
| ( X258 = X259 )
| ( shinj != $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3280,plain,
( spl591_341
| spl591_115 ),
inference(avatar_split_clause,[status(thm)],[f1099,f2305,f3277]) ).
thf(f2305,definition,
( spl591_115
<=> ( pushprop_lem1_lthm = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_115])],[avatar_definition]) ).
thf(f1099,plain,
( ( pushprop_lem1_lthm = $true )
| ( ( sK551 @ sK554 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3013,plain,
( ~ spl591_115
| ~ spl591_277
| spl591_278
| ~ spl591_279 ),
inference(avatar_split_clause,[status(thm)],[f1631,f3010,f3007,f3003,f2305]) ).
thf(f1631,plain,
! [X188: subst,X189: term,X186: term > $o,X187: term,X190: term > $o] :
( ( sK547
!= ( sub @ ( d2term @ d_one ) @ ( push @ sK547 @ sK548 ) ) )
| ( $true
!= ( X186 @ X189 ) )
| ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) )
| ( pushprop_lem1_lthm != $true )
| ( sK549
!= ( comp @ ( d2subst @ d_id ) @ ( push @ sK550 @ sK549 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1101,f1201,f1200]) ).
thf(f1201,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1101,plain,
! [X188: subst,X189: term,X186: term > $o,X187: term,X190: term > $o] :
( ( $true
= ( X190 @ ( sub @ X189 @ ( push @ X187 @ X188 ) ) ) )
| ( $true
!= ( X186 @ X189 ) )
| ( sK547
!= ( sub @ one @ ( push @ sK547 @ sK548 ) ) )
| ( sK549
!= ( comp @ sh @ ( push @ sK550 @ sK549 ) ) )
| ( pushprop_lem1_lthm != $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f2765,plain,
( ~ spl591_220
| spl591_221 ),
inference(avatar_split_clause,[status(thm)],[f1051,f2762,f2758]) ).
thf(f1051,plain,
( ( shinj = $true )
| ( sK584 != sK583 ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f2668,plain,
( spl591_199
| spl591_198 ),
inference(avatar_split_clause,[status(thm)],[f1786,f2661,f2666]) ).
thf(f1786,plain,
! [X1: term > $o] :
( ( hoasinduction_lem0 = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) )
= $false )
| ( ( X1 @ ( sK593 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1784]) ).
thf(f1784,plain,
! [X1: term > $o] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) )
!= ( X1 @ ( sK593 @ X1 ) ) )
| ( hoasinduction_lem0 = $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f1783]) ).
thf(f1783,plain,
! [X1: term > $o] :
( ( hoasinduction_lem0 = $false )
| ( ( ( X1 @ ( sK593 @ X1 ) )
= ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1782]) ).
thf(f1782,plain,
! [X1: term > $o] :
( ( ( ^ [Y0: term] :
( ( X1 @ Y0 )
= ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) )
@ ( sK593 @ X1 ) )
= $false )
| ( hoasinduction_lem0 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1781]) ).
thf(f1781,plain,
! [X1: term > $o] :
( ( hoasinduction_lem0 = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ Y0 )
= ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1780]) ).
thf(f1780,plain,
! [X1: term > $o] :
( ( $false
= ( ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
= ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
@ X1 ) )
| ( hoasinduction_lem0 = $false ) ),
inference(pi_clausification,[status(thm)],[f1779]) ).
thf(f1779,plain,
( ( hoasinduction_lem0 = $false )
| ( $false
= ( ?? @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
= ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1778]) ).
thf(f1778,plain,
( ( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) )
@ sK592 ) )
| ( hoasinduction_lem0 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1777]) ).
thf(f1777,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
= $false )
| ( hoasinduction_lem0 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1775]) ).
thf(f1775,plain,
( hoasinduction_lem0
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1658]) ).
thf(f1658,plain,
( hoasinduction_lem0
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( d2subst @ d_id ) @ Y4 @ ( d2subst @ d_id ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1260,f1261]) ).
thf(f1261,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1119,f1092,f1092]) ).
thf(f1119,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1260,plain,
( hoasinduction_lem0
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] : ( hoasinduction_p_and_p_prime @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( hoasinduction_lem0
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] : ( hoasinduction_p_and_p_prime @ Y0 @ Y1 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( hoasinduction_lem0
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] : ( hoasinduction_p_and_p_prime @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: subst > term > subst > $o] :
? [X1: term > $o] :
( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
= hoasinduction_lem0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X10: subst > term > subst > $o] :
? [X11: term > $o] :
( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
= hoasinduction_lem0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X10: subst > term > subst > $o] :
? [X11: term > $o] :
( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
= hoasinduction_lem0 ),
file('/export/starexec/sandbox2/tmp/tmp.C6YnWq5B3d/DTF2THF_12223.p',hoasinduction_lem0) ).
thf(f2664,plain,
( spl591_197
| spl591_198 ),
inference(avatar_split_clause,[status(thm)],[f1785,f2661,f2658]) ).
thf(f1785,plain,
! [X1: term > $o] :
( ( hoasinduction_lem0 = $false )
| ( $true
= ( X1 @ ( sK593 @ X1 ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK593 @ X1 ) @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1784]) ).
thf(f2656,plain,
( spl591_177
| spl591_196 ),
inference(avatar_split_clause,[status(thm)],[f1795,f2654,f2572]) ).
thf(f1795,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( X1 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
= $false )
| ( $true
= ( sK594 @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1793]) ).
thf(f1793,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( X1 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
= ( sK594 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1792]) ).
thf(f1792,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( ( sK594 @ X1 @ X2 )
= ( X1 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction_lem0 = $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1791]) ).
thf(f1791,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( ^ [Y0: term] :
( ( sK594 @ X1 @ Y0 )
= ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1790]) ).
thf(f1790,plain,
! [X1: subst > term > subst > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK594 @ X1 @ Y0 )
= ( X1 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1789]) ).
thf(f1789,plain,
! [X1: subst > term > subst > $o] :
( ( hoasinduction_lem0 = $true )
| ( $true
= ( ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
= ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
@ ( sK594 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1788]) ).
thf(f1788,plain,
! [X1: subst > term > subst > $o] :
( ( $true
= ( ?? @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
= ( X1 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
| ( hoasinduction_lem0 = $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1787]) ).
thf(f1787,plain,
! [X1: subst > term > subst > $o] :
( ( ( ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) )
@ X1 )
= $true )
| ( hoasinduction_lem0 = $true ) ),
inference(pi_clausification,[status(thm)],[f1776]) ).
thf(f1776,plain,
( ( hoasinduction_lem0 = $true )
| ( $true
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ?? @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1775]) ).
thf(f2582,plain,
( spl591_179
| spl591_177 ),
inference(avatar_split_clause,[status(thm)],[f1799,f2572,f2580]) ).
thf(f1799,plain,
! [X36: term > $o] :
( ( $false
= ( X36 @ ( sK475 @ X36 ) ) )
| ( hoasinduction_lem0 = $true )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1604]) ).
thf(f1604,plain,
! [X36: term > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) )
!= ( X36 @ ( sK475 @ X36 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1214,f1092,f1092]) ).
thf(f1214,plain,
! [X36: term > $o] :
( ( hoasinduction_lem0 = $true )
| ( ( sK474 @ id @ ( sK475 @ X36 ) @ id )
!= ( X36 @ ( sK475 @ X36 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f2578,plain,
( spl591_177
| spl591_178 ),
inference(avatar_split_clause,[status(thm)],[f1798,f2576,f2572]) ).
thf(f1798,plain,
! [X36: term > $o] :
( ( hoasinduction_lem0 = $true )
| ( $true
= ( sK474 @ ( d2subst @ d_id ) @ ( sK475 @ X36 ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X36 @ ( sK475 @ X36 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.26 % Computer : n024.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8042.1875MB
% 0.09/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue May 5 04:02:41 EDT 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.32 ---- Original DTF file ---
% 0.09/0.33 thf(spec,logic,$$dhol).
% 0.09/0.33 %------------------------------------------------------------------------------
% 0.09/0.33 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.09/0.33 % Domain : Software Verification
% 0.09/0.33 % Problem : Benchmark: ALG444^1, Active target: hoasinduction_lem0
% 0.09/0.33 % Version : Especial.
% 0.09/0.33 % English :
% 0.09/0.33
% 0.09/0.33 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.09/0.33 % Source : [Kon26]
% 0.09/0.33 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.09/0.33
% 0.09/0.33 % Status : Theorem
% 0.09/0.33 % Rating : ? v9.3.0
% 0.09/0.33 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.09/0.33 % Number of atoms : 255 ( 128 equ; 0 cnn)
% 0.09/0.33 % Maximal formula atoms : 248 ( 127 avg)
% 0.09/0.33 % Number of connectives : 2571 ( 333 ~; 306 |; 129 &;1709 @)
% 0.09/0.33 % ( 56 <=>; 38 =>; 0 <=; 0 <~>)
% 0.09/0.33 % Maximal formula depth : 151 ( 76 avg)
% 0.09/0.33 % Number of types : 5 ( 4 usr)
% 0.09/0.33 % Number of type conns : 226 ( 226 >; 0 *; 0 +; 0 <<)
% 0.09/0.33 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.09/0.33 % Number of variables : 552 ( 8 ^; 541 !; 3 ?; 552 :)
% 0.09/0.33 % SPC : TH0_THM_EQU_NAR
% 0.09/0.33
% 0.09/0.33 % Comments :
% 0.09/0.33 %------------------------------------------------------------------------------
% 0.09/0.33 thf(term_type,type,
% 0.09/0.33 term: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(subst_type,type,
% 0.09/0.33 subst: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(one_decl,type,
% 0.09/0.33 one: term ).
% 0.09/0.33
% 0.09/0.33 thf(ap_decl,type,
% 0.09/0.33 ap: term > term > term ).
% 0.09/0.33
% 0.09/0.33 thf(lam_decl,type,
% 0.09/0.33 lam: term > term ).
% 0.09/0.33
% 0.09/0.33 thf(sub_decl,type,
% 0.09/0.33 sub: term > subst > term ).
% 0.09/0.33
% 0.09/0.33 thf(id_decl,type,
% 0.09/0.33 id: subst ).
% 0.09/0.33
% 0.09/0.33 thf(sh_decl,type,
% 0.09/0.33 sh: subst ).
% 0.09/0.33
% 0.09/0.33 thf(push_decl,type,
% 0.09/0.33 push: term > subst > subst ).
% 0.09/0.33
% 0.09/0.33 thf(comp_decl,type,
% 0.09/0.33 comp: subst > subst > subst ).
% 0.09/0.33
% 0.09/0.33 thf(var_decl,type,
% 0.09/0.33 var: term > $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1v2_decl,type,
% 0.09/0.33 pushprop_lem1v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1_gthm_decl,type,
% 0.09/0.33 pushprop_lem1_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axmap_decl,type,
% 0.09/0.33 axmap: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem0_gthm_decl,type,
% 0.09/0.33 pushprop_lem0_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(shinj_decl,type,
% 0.09/0.33 shinj: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem1v2_decl,type,
% 0.09/0.33 hoasinduction_lem1v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem1v2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasap_decl,type,
% 0.09/0.33 hoasap: subst > term > subst > term > term ).
% 0.09/0.33
% 0.09/0.33 thf(induction2lem_decl,type,
% 0.09/0.33 induction2lem: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2_f_decl,type,
% 0.09/0.33 hoasinduction_lem3v2_f: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axvarshift_decl,type,
% 0.09/0.33 axvarshift: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj2_decl,type,
% 0.09/0.33 hoasapinj2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapnotvar_gthm_decl,type,
% 0.09/0.33 hoasapnotvar_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj1_decl,type,
% 0.09/0.33 hoasapinj1: $o ).
% 0.09/0.33
% 0.09/0.33 thf(ulamvar1_decl,type,
% 0.09/0.33 ulamvar1: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction2lem_lthm_decl,type,
% 0.09/0.33 induction2lem_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem3v2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(apnotvar_decl,type,
% 0.09/0.33 apnotvar: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lthm_orig_decl,type,
% 0.09/0.33 pushprop_lthm_orig: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3v2_f_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lthm_decl,type,
% 0.09/0.33 hoasinduction_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.09/0.33 hoasinduction_no_psi_cond_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslaminj_decl,type,
% 0.09/0.33 hoaslaminj: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3aaa_decl,type,
% 0.09/0.33 hoasinduction_lem3aaa: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction2lem_gthm_decl,type,
% 0.09/0.33 induction2lem_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3aa_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3_decl,type,
% 0.09/0.33 hoasinduction_lem3: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem2_decl,type,
% 0.09/0.33 hoasinduction_lem2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(termmset_lthm_decl,type,
% 0.09/0.33 termmset_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem1_decl,type,
% 0.09/0.33 hoasinduction_lem1: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotap_lthm_decl,type,
% 0.09/0.33 hoaslamnotap_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1v2_lthm_decl,type,
% 0.09/0.33 pushprop_lem1v2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapnotvar_decl,type,
% 0.09/0.33 hoasapnotvar: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem0_decl,type,
% 0.09/0.33 hoasinduction_lem0: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_decl,type,
% 0.09/0.33 hoasinduction: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_gthm_decl,type,
% 0.09/0.33 hoasinduction_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axapp_decl,type,
% 0.09/0.33 axapp: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotvar_lthm_decl,type,
% 0.09/0.33 hoaslamnotvar_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem3v2_lthm_decl,type,
% 0.09/0.33 pushprop_lem3v2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3b_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(ulamvarind_decl,type,
% 0.09/0.33 ulamvarind: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction_decl,type,
% 0.09/0.33 induction: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3a_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(termmset_gthm_decl,type,
% 0.09/0.33 termmset_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3aa_decl,type,
% 0.09/0.33 hoasinduction_lem3aa: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1v2_gthm_decl,type,
% 0.09/0.33 pushprop_lem1v2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotap_gthm_decl,type,
% 0.09/0.33 hoaslamnotap_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotvar_gthm_decl,type,
% 0.09/0.33 hoaslamnotvar_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem3b_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem2v2_decl,type,
% 0.09/0.33 pushprop_lem2v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem3a_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axclos_decl,type,
% 0.09/0.33 axclos: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axassoc_decl,type,
% 0.09/0.33 axassoc: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem2v2_decl,type,
% 0.09/0.33 hoasinduction_lem2v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lthm_decl,type,
% 0.09/0.33 pushprop_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(apinj2_decl,type,
% 0.09/0.33 apinj2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(apinj1_decl,type,
% 0.09/0.33 apinj1: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj2_lthm_decl,type,
% 0.09/0.33 hoasapinj2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2a_decl,type,
% 0.09/0.33 hoasinduction_lem3v2a: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj1_lthm_decl,type,
% 0.09/0.33 hoasapinj1_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslaminj_lthm_decl,type,
% 0.09/0.33 hoaslaminj_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axvarcons_decl,type,
% 0.09/0.33 axvarcons: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslam_decl,type,
% 0.09/0.33 hoaslam: subst > ( subst > term > term ) > term ).
% 0.09/0.33
% 0.09/0.33 thf(axscons_decl,type,
% 0.09/0.33 axscons: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem2v2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axidr_decl,type,
% 0.09/0.33 axidr: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1_decl,type,
% 0.09/0.33 pushprop_lem1: $o ).
% 0.09/0.33
% 0.09/0.33 thf(laminj_decl,type,
% 0.09/0.33 laminj: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem0_decl,type,
% 0.09/0.33 pushprop_lem0: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_gthm_decl,type,
% 0.09/0.33 pushprop_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axabs_decl,type,
% 0.09/0.33 axabs: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3v2a_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem2_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj2_gthm_decl,type,
% 0.09/0.33 hoasapinj2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.09/0.33 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem1_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem1_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(lamnotap_decl,type,
% 0.09/0.33 lamnotap: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapinj1_gthm_decl,type,
% 0.09/0.33 hoasapinj1_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotvar_decl,type,
% 0.09/0.33 hoaslamnotvar: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axidl_decl,type,
% 0.09/0.33 axidl: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslaminj_gthm_decl,type,
% 0.09/0.33 hoaslaminj_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction2_lthm_decl,type,
% 0.09/0.33 induction2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem0_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem0_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(substmonoid_lthm_decl,type,
% 0.09/0.33 substmonoid_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_decl,type,
% 0.09/0.33 pushprop: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem3_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem2_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3b_decl,type,
% 0.09/0.33 hoasinduction_lem3b: $o ).
% 0.09/0.33
% 0.09/0.33 thf(substmonoid_decl,type,
% 0.09/0.33 substmonoid: $o ).
% 0.09/0.33
% 0.09/0.33 thf(lamnotvar_decl,type,
% 0.09/0.33 lamnotvar: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3a_decl,type,
% 0.09/0.33 hoasinduction_lem3a: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem1_gthm_decl,type,
% 0.09/0.33 hoasinduction_lem1_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_no_psi_cond_decl,type,
% 0.09/0.33 hoasinduction_no_psi_cond: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction2_gthm_decl,type,
% 0.09/0.33 induction2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem2v2_lthm_decl,type,
% 0.09/0.33 pushprop_lem2v2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasvar_decl,type,
% 0.09/0.33 hoasvar: subst > term > subst > $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoaslamnotap_decl,type,
% 0.09/0.33 hoaslamnotap: $o ).
% 0.09/0.33
% 0.09/0.33 thf(substmonoid_gthm_decl,type,
% 0.09/0.33 substmonoid_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(ulamvarsh_decl,type,
% 0.09/0.33 ulamvarsh: $o ).
% 0.09/0.33
% 0.09/0.33 thf(induction2_decl,type,
% 0.09/0.33 induction2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem3v2_decl,type,
% 0.09/0.33 pushprop_lem3v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem2v2_gthm_decl,type,
% 0.09/0.33 pushprop_lem2v2_gthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem1_lthm_decl,type,
% 0.09/0.33 pushprop_lem1_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2_decl,type,
% 0.09/0.33 hoasinduction_lem3v2: $o ).
% 0.09/0.33
% 0.09/0.33 thf(axshiftcons_decl,type,
% 0.09/0.33 axshiftcons: $o ).
% 0.09/0.33
% 0.09/0.33 thf(termmset_decl,type,
% 0.09/0.33 termmset: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_lem0_lthm_decl,type,
% 0.09/0.33 pushprop_lem0_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasapnotvar_lthm_decl,type,
% 0.09/0.33 hoasapnotvar_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.09/0.33 hoasinduction_lem3v2_lthm: $o ).
% 0.09/0.33
% 0.09/0.33 thf(pushprop_p_and_p_prime_decl,type,
% 0.09/0.33 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.09/0.33
% 0.09/0.33 thf(axvarid_decl,type,
% 0.09/0.33 axvarid: $o ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lthm_3_decl,type,
% 0.09/0.33 hoasinduction_lthm_3: $o ).
% 0.09/0.33
% 0.09/0.33 %----Types of the domains
% 0.09/0.33 thf(d_term_type,type,
% 0.09/0.33 d_term: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(d_subst_type,type,
% 0.09/0.33 d_subst: $tType ).
% 0.09/0.33
% 0.09/0.33 %----Types of the promotion functions
% 0.09/0.33 thf(d2term_decl,type,
% 0.09/0.33 d2term: d_term > term ).
% 0.09/0.33
% 0.09/0.33 thf(d2subst_decl,type,
% 0.09/0.33 d2subst: d_subst > subst ).
% 0.09/0.33
% 0.09/0.33 %----Types of the domain elements
% 0.09/0.33 thf(d_one_decl,type,
% 0.09/0.33 d_one: d_term ).
% 0.09/0.33
% 0.09/0.33 thf(d_id_decl,type,
% 0.09/0.33 d_id: d_subst ).
% 0.09/0.33
% 0.09/0.33 thf(alg444_1,axiom,
% 0.09/0.33 ( ! [T: term] :
% 0.09/0.33 ? [DT: d_term] :
% 0.09/0.33 ( T
% 0.09/0.33 = ( d2term @ DT ) )
% 0.09/0.33 & ! [DT: d_term] : ( DT = d_one )
% 0.09/0.33 & ! [DT1: d_term,DT2: d_term] :
% 0.09/0.33 ( ( ( d2term @ DT1 )
% 0.09/0.33 = ( d2term @ DT2 ) )
% 0.09/0.33 => ( DT1 = DT2 ) )
% 0.09/0.33 & ! [S: subst] :
% 0.09/0.33 ? [DS: d_subst] :
% 0.09/0.33 ( S
% 0.09/0.33 = ( d2subst @ DS ) )
% 0.09/0.33 & ! [DS: d_subst] : ( DS = d_id )
% 0.09/0.33 & ! [DS1: d_subst,DS2: d_subst] :
% 0.09/0.33 ( ( ( d2subst @ DS1 )
% 0.09/0.33 = ( d2subst @ DS2 ) )
% 0.09/0.33 => ( DS1 = DS2 ) )
% 0.09/0.33 & ( one
% 0.09/0.33 = ( d2term @ d_one ) )
% 0.09/0.33 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.09/0.33 = ( d2term @ d_one ) )
% 0.09/0.33 & ( ( lam @ ( d2term @ d_one ) )
% 0.09/0.33 = ( d2term @ d_one ) )
% 0.09/0.33 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.09/0.33 = ( d2term @ d_one ) )
% 0.09/0.33 & ( id
% 0.09/0.33 = ( d2subst @ d_id ) )
% 0.09/0.33 & ( sh
% 0.09/0.33 = ( d2subst @ d_id ) )
% 0.09/0.33 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.09/0.33 = ( d2subst @ d_id ) )
% 0.09/0.33 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.09/0.33 = ( d2subst @ d_id ) )
% 0.09/0.33 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.09/0.33 = ( d2term @ d_one ) )
% 0.09/0.33 & ( hoaslam
% 0.09/0.33 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.09/0.33 & ( hoasinduction_p_and_p_prime
% 0.09/0.33 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.09/0.33 ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) ) ) )
% 0.09/0.33 & ( pushprop_p_and_p_prime
% 0.09/0.33 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.09/0.33 ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.09/0.33 & ~ ( var @ ( d2term @ d_one ) )
% 0.09/0.33 & ( pushprop_lem1v2
% 0.09/0.33 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.09/0.33 | ( Q @ one ) ) )
% 0.09/0.33 & pushprop_lem1_gthm
% 0.09/0.33 & axmap
% 0.09/0.33 & pushprop_lem0_gthm
% 0.09/0.33 & ( shinj
% 0.09/0.33 <=> ! [A: term,B: term] :
% 0.09/0.33 ( ( ( sub @ A @ sh )
% 0.09/0.33 != ( sub @ B @ sh ) )
% 0.09/0.33 | ( A = B ) ) )
% 0.09/0.33 & hoasinduction_lem1v2
% 0.09/0.33 & hoasinduction_lem1v2_gthm
% 0.09/0.33 & ( induction2lem
% 0.09/0.33 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.09/0.33 ( ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( var @ B )
% 0.09/0.33 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.09/0.33 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.09/0.33 & ( hoasinduction_lem3v2_f
% 0.09/0.33 <=> ! [B: term] :
% 0.09/0.33 ~ ! [F: subst > term > term] :
% 0.09/0.33 ~ ! [A: term,M: subst] :
% 0.09/0.33 ( ( sub @ B @ ( push @ A @ M ) )
% 0.09/0.33 = ( F @ M @ A ) ) )
% 0.09/0.33 & axvarshift
% 0.09/0.33 & ( hoasapinj2
% 0.09/0.33 <=> ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.09/0.33 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.09/0.33 | ( C = D ) ) )
% 0.09/0.33 & hoasapnotvar_gthm
% 0.09/0.33 & ( hoasapinj1
% 0.09/0.33 <=> ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.09/0.33 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.09/0.33 | ( A = B ) ) )
% 0.09/0.33 & ~ ulamvar1
% 0.09/0.33 & ( induction2lem_lthm
% 0.09/0.33 <=> ( ! [A: term,M: subst] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.09/0.33 => ( ! [A: term,M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.09/0.33 => ( ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ M @ id ) )
% 0.09/0.33 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2140 ) )
% 0.09/0.33 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.09/0.33 ( ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( var @ B )
% 0.09/0.33 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.09/0.33 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.09/0.33 & hoasinduction_lem3v2_gthm
% 0.09/0.33 & apnotvar
% 0.09/0.33 & pushprop_lthm_orig
% 0.09/0.33 & ( hoasinduction_lem3v2_f_lthm
% 0.09/0.33 <=> ! [B: term] :
% 0.09/0.33 ~ ! [F: subst > term > term] :
% 0.09/0.33 ~ ! [A: term,M: subst] :
% 0.09/0.33 ( ( sub @ B @ ( push @ A @ M ) )
% 0.09/0.33 = ( F @ M @ A ) ) )
% 0.09/0.33 & ( hoasinduction_lthm
% 0.09/0.33 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2367 ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.09/0.33 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ ( sub @ A @ id ) )
% 0.09/0.33 | ( P @ id @ A @ id ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.09/0.33 & ( hoasinduction_no_psi_cond_lthm
% 0.09/0.33 <=> ( ! [P: subst > term > subst > $o] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2367 ) )
% 0.09/0.33 => ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.09/0.33 ( ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.09/0.33 & ( hoaslaminj
% 0.09/0.33 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.09/0.33 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ( ( lam @ ( F @ sh @ one ) )
% 0.09/0.33 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.09/0.33 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.09/0.33 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.09/0.33 & ( hoasinduction_lem3aaa
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.09/0.33 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.09/0.33 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.09/0.33 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.09/0.33 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.09/0.33 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.09/0.33 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.09/0.33 & induction2lem_gthm
% 0.09/0.33 & ( hoasinduction_lem3aa_lthm
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.09/0.33 & ( hoasinduction_lem3
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.09/0.33 & ( hoasinduction_lem2
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.09/0.33 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.09/0.33 & ( termmset_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) ) ) )
% 0.09/0.33 & hoasinduction_lem1
% 0.09/0.33 & hoaslamnotap_lthm
% 0.09/0.33 & ( pushprop_lem1v2_lthm
% 0.09/0.33 <=> ( ! [A: term,M: subst] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.09/0.33 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.09/0.33 | ( Q @ one ) ) ) )
% 0.09/0.33 & hoasapnotvar
% 0.09/0.33 & ( hoasinduction_lem0
% 0.09/0.33 <=> ! [P: subst > term > subst > $o] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) ) )
% 0.09/0.33 & ( hoasinduction
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ ( sub @ A @ id ) )
% 0.09/0.33 | ( P @ id @ A @ id ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.09/0.33 & hoasinduction_gthm
% 0.09/0.33 & axapp
% 0.09/0.33 & hoaslamnotvar_lthm
% 0.09/0.33 & pushprop_lem3v2_lthm
% 0.09/0.33 & ( hoasinduction_lem3b_lthm
% 0.09/0.33 <=> ! [B: term] :
% 0.09/0.33 ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ( F @ sh @ one )
% 0.09/0.33 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.09/0.33 & ulamvarind
% 0.09/0.33 & ( induction
% 0.09/0.33 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2140 ) ) )
% 0.09/0.33 & ( hoasinduction_lem3a_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.09/0.33 & termmset_gthm
% 0.09/0.33 & ( hoasinduction_lem3aa
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.09/0.33 & pushprop_lem1v2_gthm
% 0.09/0.33 & hoaslamnotap_gthm
% 0.09/0.33 & hoaslamnotvar_gthm
% 0.09/0.33 & hoasinduction_lem3b_gthm
% 0.09/0.33 & pushprop_lem2v2
% 0.09/0.33 & hoasinduction_lem3a_gthm
% 0.09/0.33 & axclos
% 0.09/0.33 & axassoc
% 0.09/0.33 & ( hoasinduction_lem2v2
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ( Q @ Bound_variable_2820 )
% 0.09/0.33 | ~ ( Q @ Bound_variable_2822 )
% 0.09/0.33 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.09/0.33 & pushprop_lthm
% 0.09/0.33 & ( apinj2
% 0.09/0.33 <=> ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ A @ C )
% 0.09/0.33 != ( ap @ B @ D ) )
% 0.09/0.33 | ( C = D ) ) )
% 0.09/0.33 & ( apinj1
% 0.09/0.33 <=> ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ A @ C )
% 0.09/0.33 != ( ap @ B @ D ) )
% 0.09/0.33 | ( A = B ) ) )
% 0.09/0.33 & ( hoasapinj2_lthm
% 0.09/0.33 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ A @ C )
% 0.09/0.33 != ( ap @ B @ D ) )
% 0.09/0.33 | ( C = D ) )
% 0.09/0.33 => ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.09/0.33 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.09/0.33 | ( C = D ) ) ) )
% 0.09/0.33 & ( hoasinduction_lem3v2a
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.09/0.33 & ( hoasapinj1_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ A @ C )
% 0.09/0.33 != ( ap @ B @ D ) )
% 0.09/0.33 | ( A = B ) )
% 0.09/0.33 => ! [A: term,B: term,C: term,D: term] :
% 0.09/0.33 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.09/0.33 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.09/0.33 | ( A = B ) ) ) ) )
% 0.09/0.33 & ( hoaslaminj_lthm
% 0.09/0.33 <=> ( ! [A: term,M: subst] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.09/0.33 => ( ! [A: term,M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.09/0.33 => ( ! [A: term,B: term] :
% 0.09/0.33 ( ( ( lam @ A )
% 0.09/0.33 != ( lam @ B ) )
% 0.09/0.33 | ( A = B ) )
% 0.09/0.33 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.09/0.33 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ( ( lam @ ( F @ sh @ one ) )
% 0.09/0.33 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.09/0.33 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.09/0.33 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.09/0.33 & ( axvarcons
% 0.09/0.33 <=> ! [A: term,M: subst] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.09/0.33 & ( axscons
% 0.09/0.33 <=> ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.09/0.33 & hoasinduction_lem2v2_gthm
% 0.09/0.33 & ( axidr
% 0.09/0.33 <=> ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ M @ id ) ) )
% 0.09/0.33 & ( pushprop_lem1
% 0.09/0.33 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.09/0.33 & ( laminj
% 0.09/0.33 <=> ! [A: term,B: term] :
% 0.09/0.33 ( ( ( lam @ A )
% 0.09/0.33 != ( lam @ B ) )
% 0.09/0.33 | ( A = B ) ) )
% 0.09/0.33 & ( hoasinduction_lem3_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.09/0.33 & ( pushprop_lem0
% 0.09/0.33 <=> ! [P: term > $o,A: term,M: subst] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.09/0.33 & pushprop_gthm
% 0.09/0.33 & axabs
% 0.09/0.33 & ( hoasinduction_lem3v2a_lthm
% 0.09/0.33 <=> ( ! [B: term] :
% 0.09/0.33 ~ ! [F: subst > term > term] :
% 0.09/0.33 ~ ! [A: term,M: subst] :
% 0.09/0.33 ( ( sub @ B @ ( push @ A @ M ) )
% 0.09/0.33 = ( F @ M @ A ) )
% 0.09/0.33 => ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.09/0.33 & hoasinduction_lem2_lthm
% 0.09/0.33 & hoasapinj2_gthm
% 0.09/0.33 & hoasinduction_lem1_lthm
% 0.09/0.33 & ~ lamnotap
% 0.09/0.33 & hoasapinj1_gthm
% 0.09/0.33 & hoaslamnotvar
% 0.09/0.33 & ( axidl
% 0.09/0.33 <=> ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ id @ M ) ) )
% 0.09/0.33 & hoaslaminj_gthm
% 0.09/0.33 & ( induction2_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.09/0.33 ( ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( var @ B )
% 0.09/0.33 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.09/0.33 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.09/0.33 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.09/0.33 & ( hoasinduction_lem0_lthm
% 0.09/0.33 <=> ! [P: subst > term > subst > $o] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) ) )
% 0.09/0.33 & ( substmonoid_lthm
% 0.09/0.33 <=> ( ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ id @ M ) )
% 0.09/0.33 => ( ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ M @ id ) )
% 0.09/0.33 => ( ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ id @ M ) )
% 0.09/0.33 & ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ M @ id ) ) ) ) ) )
% 0.09/0.33 & pushprop
% 0.09/0.33 & hoasinduction_lem3_gthm
% 0.09/0.33 & hoasinduction_lem2_gthm
% 0.09/0.33 & ( hoasinduction_lem3b
% 0.09/0.33 <=> ! [B: term] :
% 0.09/0.33 ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ( F @ sh @ one )
% 0.09/0.33 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.09/0.33 & ( substmonoid
% 0.09/0.33 <=> ( ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ id @ M ) )
% 0.09/0.33 & ! [M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ M @ id ) ) ) )
% 0.09/0.33 & lamnotvar
% 0.09/0.33 & ( hoasinduction_lem3a
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.09/0.33 & hoasinduction_lem1_gthm
% 0.09/0.33 & ( hoasinduction_no_psi_cond
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.09/0.33 ( ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.09/0.33 & induction2_gthm
% 0.09/0.33 & pushprop_lem2v2_lthm
% 0.09/0.33 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.09/0.33 & ( hoaslamnotap
% 0.09/0.33 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ( ( lam @ ( F @ sh @ one ) )
% 0.09/0.33 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.09/0.33 & substmonoid_gthm
% 0.09/0.33 & ulamvarsh
% 0.09/0.33 & ( induction2
% 0.09/0.33 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2367 ) ) )
% 0.09/0.33 & pushprop_lem3v2
% 0.09/0.33 & pushprop_lem2v2_gthm
% 0.09/0.33 & ( pushprop_lem1_lthm
% 0.09/0.33 <=> ( ! [A: term,M: subst] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.09/0.33 => ( ! [A: term,M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.09/0.33 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.09/0.33 & ( hoasinduction_lem3v2
% 0.09/0.33 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.09/0.33 & ( axshiftcons
% 0.09/0.33 <=> ! [A: term,M: subst] :
% 0.09/0.33 ( M
% 0.09/0.33 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.09/0.33 & ( termmset
% 0.09/0.33 <=> ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) ) )
% 0.09/0.33 & ( pushprop_lem0_lthm
% 0.09/0.33 <=> ! [P: term > $o,A: term,M: subst] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.09/0.33 & hoasapnotvar_lthm
% 0.09/0.33 & ( hoasinduction_lem3v2_lthm
% 0.09/0.33 <=> ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.09/0.33 & ( axvarid
% 0.09/0.33 <=> ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) ) )
% 0.09/0.33 & ( hoasinduction_lthm_3
% 0.09/0.33 <=> ( ! [P: subst > term > subst > $o] :
% 0.09/0.33 ~ ! [Q: term > $o] :
% 0.09/0.33 ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.09/0.33 ( ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ A )
% 0.09/0.33 | ( P @ A ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ A )
% 0.09/0.33 | ~ ( P @ B )
% 0.09/0.33 | ( P @ ( ap @ A @ B ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ! [B: term] :
% 0.09/0.33 ( ~ ( P @ B )
% 0.09/0.33 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( P @ ( lam @ A ) ) )
% 0.09/0.33 | ( P @ Bound_variable_2367 ) )
% 0.09/0.33 => ( ! [A: term] :
% 0.09/0.33 ( A
% 0.09/0.33 = ( sub @ A @ id ) )
% 0.09/0.33 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.09/0.33 ( ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ~ ! [X: term] :
% 0.09/0.33 ( ( Q @ X )
% 0.09/0.33 = ( P @ id @ X @ id ) )
% 0.09/0.33 | ~ ! [B: term] :
% 0.09/0.33 ( ~ ( Q @ B )
% 0.09/0.33 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.09/0.33 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.09/0.33 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.09/0.33 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.09/0.33 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.09/0.33 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.09/0.33 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( var @ ( sub @ A @ id ) )
% 0.09/0.33 | ( P @ id @ A @ id ) )
% 0.09/0.33 | ~ ! [A: term,B: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ~ ( P @ id @ B @ id )
% 0.09/0.33 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.09/0.33 | ~ ! [F: subst > term > term] :
% 0.09/0.33 ( ~ ! [M: subst,A: term,N: subst] :
% 0.09/0.33 ( ( sub @ ( F @ M @ A ) @ N )
% 0.09/0.33 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.09/0.33 | ~ ! [A: term] :
% 0.09/0.33 ( ~ ( P @ id @ A @ id )
% 0.09/0.33 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.09/0.33 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.09/0.33 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(hoasinduction_lem0,conjecture,
% 0.09/0.33 ( hoasinduction_lem0
% 0.09/0.33 = ( ! [P: subst > term > subst > $o] :
% 0.09/0.33 ? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ) ).
% 0.09/0.33
% 0.09/0.33 %------------------------------------------------------------------------------
% 0.09/0.33 ------------------------
% 0.16/1.50 ---- Embedded in THF ---
% 0.16/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.16/1.50 %%% Generated on Tue May 05 04:02:42 EDT 2026
% 0.16/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.16/1.50 %%% Logic specification used:
% 0.16/1.50 %%% thf(spec, logic, $$dhol).
% 0.16/1.50
% 0.16/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.C6YnWq5B3d/DTF2DTF12223.p
% See solution above
% 0.16/1.50 ------------------------
% 0.16/1.54 ---- Cleaned THF ---
% 0.16/1.54 thf(term_type,type,
% 0.16/1.54 term: $tType ).
% 0.16/1.54
% 0.16/1.54 thf(subst_type,type,
% 0.16/1.54 subst: $tType ).
% 0.16/1.54
% 0.16/1.54 thf(one_decl,type,
% 0.16/1.54 one: term ).
% 0.16/1.54
% 0.16/1.54 thf(ap_decl,type,
% 0.16/1.54 ap: term > term > term ).
% 0.16/1.54
% 0.16/1.54 thf(lam_decl,type,
% 0.16/1.54 lam: term > term ).
% 0.16/1.54
% 0.16/1.54 thf(sub_decl,type,
% 0.16/1.54 sub: term > subst > term ).
% 0.16/1.54
% 0.16/1.54 thf(id_decl,type,
% 0.16/1.54 id: subst ).
% 0.16/1.54
% 0.16/1.54 thf(sh_decl,type,
% 0.16/1.54 sh: subst ).
% 0.16/1.54
% 0.16/1.54 thf(push_decl,type,
% 0.16/1.54 push: term > subst > subst ).
% 0.16/1.54
% 0.16/1.54 thf(comp_decl,type,
% 0.16/1.54 comp: subst > subst > subst ).
% 0.16/1.54
% 0.16/1.54 thf(var_decl,type,
% 0.16/1.54 var: term > $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1v2_decl,type,
% 0.16/1.54 pushprop_lem1v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1_gthm_decl,type,
% 0.16/1.54 pushprop_lem1_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axmap_decl,type,
% 0.16/1.54 axmap: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem0_gthm_decl,type,
% 0.16/1.54 pushprop_lem0_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(shinj_decl,type,
% 0.16/1.54 shinj: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem1v2_decl,type,
% 0.16/1.54 hoasinduction_lem1v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem1v2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasap_decl,type,
% 0.16/1.54 hoasap: subst > term > subst > term > term ).
% 0.16/1.54
% 0.16/1.54 thf(induction2lem_decl,type,
% 0.16/1.54 induction2lem: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2_f_decl,type,
% 0.16/1.54 hoasinduction_lem3v2_f: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axvarshift_decl,type,
% 0.16/1.54 axvarshift: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj2_decl,type,
% 0.16/1.54 hoasapinj2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapnotvar_gthm_decl,type,
% 0.16/1.54 hoasapnotvar_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj1_decl,type,
% 0.16/1.54 hoasapinj1: $o ).
% 0.16/1.54
% 0.16/1.54 thf(ulamvar1_decl,type,
% 0.16/1.54 ulamvar1: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction2lem_lthm_decl,type,
% 0.16/1.54 induction2lem_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem3v2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(apnotvar_decl,type,
% 0.16/1.54 apnotvar: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lthm_orig_decl,type,
% 0.16/1.54 pushprop_lthm_orig: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3v2_f_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lthm_decl,type,
% 0.16/1.54 hoasinduction_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.16/1.54 hoasinduction_no_psi_cond_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslaminj_decl,type,
% 0.16/1.54 hoaslaminj: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3aaa_decl,type,
% 0.16/1.54 hoasinduction_lem3aaa: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction2lem_gthm_decl,type,
% 0.16/1.54 induction2lem_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3aa_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3_decl,type,
% 0.16/1.54 hoasinduction_lem3: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem2_decl,type,
% 0.16/1.54 hoasinduction_lem2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(termmset_lthm_decl,type,
% 0.16/1.54 termmset_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem1_decl,type,
% 0.16/1.54 hoasinduction_lem1: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotap_lthm_decl,type,
% 0.16/1.54 hoaslamnotap_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1v2_lthm_decl,type,
% 0.16/1.54 pushprop_lem1v2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapnotvar_decl,type,
% 0.16/1.54 hoasapnotvar: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem0_decl,type,
% 0.16/1.54 hoasinduction_lem0: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_decl,type,
% 0.16/1.54 hoasinduction: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_gthm_decl,type,
% 0.16/1.54 hoasinduction_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axapp_decl,type,
% 0.16/1.54 axapp: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotvar_lthm_decl,type,
% 0.16/1.54 hoaslamnotvar_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem3v2_lthm_decl,type,
% 0.16/1.54 pushprop_lem3v2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3b_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(ulamvarind_decl,type,
% 0.16/1.54 ulamvarind: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction_decl,type,
% 0.16/1.54 induction: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3a_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(termmset_gthm_decl,type,
% 0.16/1.54 termmset_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3aa_decl,type,
% 0.16/1.54 hoasinduction_lem3aa: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1v2_gthm_decl,type,
% 0.16/1.54 pushprop_lem1v2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotap_gthm_decl,type,
% 0.16/1.54 hoaslamnotap_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotvar_gthm_decl,type,
% 0.16/1.54 hoaslamnotvar_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem3b_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem2v2_decl,type,
% 0.16/1.54 pushprop_lem2v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem3a_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axclos_decl,type,
% 0.16/1.54 axclos: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axassoc_decl,type,
% 0.16/1.54 axassoc: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem2v2_decl,type,
% 0.16/1.54 hoasinduction_lem2v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lthm_decl,type,
% 0.16/1.54 pushprop_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(apinj2_decl,type,
% 0.16/1.54 apinj2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(apinj1_decl,type,
% 0.16/1.54 apinj1: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj2_lthm_decl,type,
% 0.16/1.54 hoasapinj2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2a_decl,type,
% 0.16/1.54 hoasinduction_lem3v2a: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj1_lthm_decl,type,
% 0.16/1.54 hoasapinj1_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslaminj_lthm_decl,type,
% 0.16/1.54 hoaslaminj_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axvarcons_decl,type,
% 0.16/1.54 axvarcons: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslam_decl,type,
% 0.16/1.54 hoaslam: subst > ( subst > term > term ) > term ).
% 0.16/1.54
% 0.16/1.54 thf(axscons_decl,type,
% 0.16/1.54 axscons: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem2v2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axidr_decl,type,
% 0.16/1.54 axidr: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1_decl,type,
% 0.16/1.54 pushprop_lem1: $o ).
% 0.16/1.54
% 0.16/1.54 thf(laminj_decl,type,
% 0.16/1.54 laminj: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem0_decl,type,
% 0.16/1.54 pushprop_lem0: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_gthm_decl,type,
% 0.16/1.54 pushprop_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axabs_decl,type,
% 0.16/1.54 axabs: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3v2a_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem2_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj2_gthm_decl,type,
% 0.16/1.54 hoasapinj2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.16/1.54 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem1_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem1_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(lamnotap_decl,type,
% 0.16/1.54 lamnotap: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapinj1_gthm_decl,type,
% 0.16/1.54 hoasapinj1_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotvar_decl,type,
% 0.16/1.54 hoaslamnotvar: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axidl_decl,type,
% 0.16/1.54 axidl: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslaminj_gthm_decl,type,
% 0.16/1.54 hoaslaminj_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction2_lthm_decl,type,
% 0.16/1.54 induction2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem0_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem0_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(substmonoid_lthm_decl,type,
% 0.16/1.54 substmonoid_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_decl,type,
% 0.16/1.54 pushprop: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem3_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem2_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3b_decl,type,
% 0.16/1.54 hoasinduction_lem3b: $o ).
% 0.16/1.54
% 0.16/1.54 thf(substmonoid_decl,type,
% 0.16/1.54 substmonoid: $o ).
% 0.16/1.54
% 0.16/1.54 thf(lamnotvar_decl,type,
% 0.16/1.54 lamnotvar: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3a_decl,type,
% 0.16/1.54 hoasinduction_lem3a: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem1_gthm_decl,type,
% 0.16/1.54 hoasinduction_lem1_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_no_psi_cond_decl,type,
% 0.16/1.54 hoasinduction_no_psi_cond: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction2_gthm_decl,type,
% 0.16/1.54 induction2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem2v2_lthm_decl,type,
% 0.16/1.54 pushprop_lem2v2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasvar_decl,type,
% 0.16/1.54 hoasvar: subst > term > subst > $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoaslamnotap_decl,type,
% 0.16/1.54 hoaslamnotap: $o ).
% 0.16/1.54
% 0.16/1.54 thf(substmonoid_gthm_decl,type,
% 0.16/1.54 substmonoid_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(ulamvarsh_decl,type,
% 0.16/1.54 ulamvarsh: $o ).
% 0.16/1.54
% 0.16/1.54 thf(induction2_decl,type,
% 0.16/1.54 induction2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem3v2_decl,type,
% 0.16/1.54 pushprop_lem3v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem2v2_gthm_decl,type,
% 0.16/1.54 pushprop_lem2v2_gthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem1_lthm_decl,type,
% 0.16/1.54 pushprop_lem1_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2_decl,type,
% 0.16/1.54 hoasinduction_lem3v2: $o ).
% 0.16/1.54
% 0.16/1.54 thf(axshiftcons_decl,type,
% 0.16/1.54 axshiftcons: $o ).
% 0.16/1.54
% 0.16/1.54 thf(termmset_decl,type,
% 0.16/1.54 termmset: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_lem0_lthm_decl,type,
% 0.16/1.54 pushprop_lem0_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasapnotvar_lthm_decl,type,
% 0.16/1.54 hoasapnotvar_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.16/1.54 hoasinduction_lem3v2_lthm: $o ).
% 0.16/1.54
% 0.16/1.54 thf(pushprop_p_and_p_prime_decl,type,
% 0.16/1.54 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.16/1.54
% 0.16/1.54 thf(axvarid_decl,type,
% 0.16/1.54 axvarid: $o ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lthm_3_decl,type,
% 0.16/1.54 hoasinduction_lthm_3: $o ).
% 0.16/1.54
% 0.16/1.54 thf(d_term_type,type,
% 0.16/1.54 d_term: $tType ).
% 0.16/1.54
% 0.16/1.54 thf(d_subst_type,type,
% 0.16/1.54 d_subst: $tType ).
% 0.16/1.54
% 0.16/1.54 thf(d2term_decl,type,
% 0.16/1.54 d2term: d_term > term ).
% 0.16/1.54
% 0.16/1.54 thf(d2subst_decl,type,
% 0.16/1.54 d2subst: d_subst > subst ).
% 0.16/1.54
% 0.16/1.54 thf(d_one_decl,type,
% 0.16/1.54 d_one: d_term ).
% 0.16/1.54
% 0.16/1.54 thf(d_id_decl,type,
% 0.16/1.54 d_id: d_subst ).
% 0.16/1.54
% 0.16/1.54 thf(alg444_1,axiom,
% 0.16/1.54 ( ! [T: term] :
% 0.16/1.54 ? [DT: d_term] :
% 0.16/1.54 ( T
% 0.16/1.54 = ( d2term @ DT ) )
% 0.16/1.54 & ! [DT: d_term] : ( DT = d_one )
% 0.16/1.54 & ! [DT1: d_term,DT2: d_term] :
% 0.16/1.54 ( ( ( d2term @ DT1 )
% 0.16/1.54 = ( d2term @ DT2 ) )
% 0.16/1.54 => ( DT1 = DT2 ) )
% 0.16/1.54 & ! [S: subst] :
% 0.16/1.54 ? [DS: d_subst] :
% 0.16/1.54 ( S
% 0.16/1.54 = ( d2subst @ DS ) )
% 0.16/1.54 & ! [DS: d_subst] : ( DS = d_id )
% 0.16/1.54 & ! [DS1: d_subst,DS2: d_subst] :
% 0.16/1.54 ( ( ( d2subst @ DS1 )
% 0.16/1.54 = ( d2subst @ DS2 ) )
% 0.16/1.54 => ( DS1 = DS2 ) )
% 0.16/1.54 & ( one
% 0.16/1.54 = ( d2term @ d_one ) )
% 0.16/1.54 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.16/1.54 = ( d2term @ d_one ) )
% 0.16/1.54 & ( ( lam @ ( d2term @ d_one ) )
% 0.16/1.54 = ( d2term @ d_one ) )
% 0.16/1.54 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.16/1.54 = ( d2term @ d_one ) )
% 0.16/1.54 & ( id
% 0.16/1.54 = ( d2subst @ d_id ) )
% 0.16/1.54 & ( sh
% 0.16/1.54 = ( d2subst @ d_id ) )
% 0.16/1.54 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.16/1.54 = ( d2subst @ d_id ) )
% 0.16/1.54 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.16/1.54 = ( d2subst @ d_id ) )
% 0.16/1.54 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.16/1.54 = ( d2term @ d_one ) )
% 0.16/1.54 & ( hoaslam
% 0.16/1.54 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.16/1.54 & ( hoasinduction_p_and_p_prime
% 0.16/1.54 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.16/1.54 ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) ) ) )
% 0.16/1.54 & ( pushprop_p_and_p_prime
% 0.16/1.54 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.16/1.54 ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.16/1.54 & ~ ( var @ ( d2term @ d_one ) )
% 0.16/1.54 & ( pushprop_lem1v2
% 0.16/1.54 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.16/1.54 | ( Q @ one ) ) )
% 0.16/1.54 & pushprop_lem1_gthm
% 0.16/1.54 & axmap
% 0.16/1.54 & pushprop_lem0_gthm
% 0.16/1.54 & ( shinj
% 0.16/1.54 <=> ! [A: term,B: term] :
% 0.16/1.54 ( ( ( sub @ A @ sh )
% 0.16/1.54 != ( sub @ B @ sh ) )
% 0.16/1.54 | ( A = B ) ) )
% 0.16/1.54 & hoasinduction_lem1v2
% 0.16/1.54 & hoasinduction_lem1v2_gthm
% 0.16/1.54 & ( induction2lem
% 0.16/1.54 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.16/1.54 ( ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( var @ B )
% 0.16/1.54 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.16/1.54 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.16/1.54 & ( hoasinduction_lem3v2_f
% 0.16/1.54 <=> ! [B: term] :
% 0.16/1.54 ~ ! [F: subst > term > term] :
% 0.16/1.54 ~ ! [A: term,M: subst] :
% 0.16/1.54 ( ( sub @ B @ ( push @ A @ M ) )
% 0.16/1.54 = ( F @ M @ A ) ) )
% 0.16/1.54 & axvarshift
% 0.16/1.54 & ( hoasapinj2
% 0.16/1.54 <=> ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.16/1.54 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.16/1.54 | ( C = D ) ) )
% 0.16/1.54 & hoasapnotvar_gthm
% 0.16/1.54 & ( hoasapinj1
% 0.16/1.54 <=> ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.16/1.54 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.16/1.54 | ( A = B ) ) )
% 0.16/1.54 & ~ ulamvar1
% 0.16/1.54 & ( induction2lem_lthm
% 0.16/1.54 <=> ( ! [A: term,M: subst] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.16/1.54 => ( ! [A: term,M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.16/1.54 => ( ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ M @ id ) )
% 0.16/1.54 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2140 ) )
% 0.16/1.54 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.16/1.54 ( ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( var @ B )
% 0.16/1.54 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.16/1.54 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.16/1.54 & hoasinduction_lem3v2_gthm
% 0.16/1.54 & apnotvar
% 0.16/1.54 & pushprop_lthm_orig
% 0.16/1.54 & ( hoasinduction_lem3v2_f_lthm
% 0.16/1.54 <=> ! [B: term] :
% 0.16/1.54 ~ ! [F: subst > term > term] :
% 0.16/1.54 ~ ! [A: term,M: subst] :
% 0.16/1.54 ( ( sub @ B @ ( push @ A @ M ) )
% 0.16/1.54 = ( F @ M @ A ) ) )
% 0.16/1.54 & ( hoasinduction_lthm
% 0.16/1.54 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2367 ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.16/1.54 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ ( sub @ A @ id ) )
% 0.16/1.54 | ( P @ id @ A @ id ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.16/1.54 & ( hoasinduction_no_psi_cond_lthm
% 0.16/1.54 <=> ( ! [P: subst > term > subst > $o] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2367 ) )
% 0.16/1.54 => ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.16/1.54 ( ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.16/1.54 & ( hoaslaminj
% 0.16/1.54 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.16/1.54 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ( ( lam @ ( F @ sh @ one ) )
% 0.16/1.54 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.16/1.54 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.16/1.54 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.16/1.54 & ( hoasinduction_lem3aaa
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.16/1.54 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.16/1.54 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.16/1.54 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.16/1.54 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.16/1.54 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.16/1.54 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.16/1.54 & induction2lem_gthm
% 0.16/1.54 & ( hoasinduction_lem3aa_lthm
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.16/1.54 & ( hoasinduction_lem3
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.16/1.54 & ( hoasinduction_lem2
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.16/1.54 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.16/1.54 & ( termmset_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) ) ) )
% 0.16/1.54 & hoasinduction_lem1
% 0.16/1.54 & hoaslamnotap_lthm
% 0.16/1.54 & ( pushprop_lem1v2_lthm
% 0.16/1.54 <=> ( ! [A: term,M: subst] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.16/1.54 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.16/1.54 | ( Q @ one ) ) ) )
% 0.16/1.54 & hoasapnotvar
% 0.16/1.54 & ( hoasinduction_lem0
% 0.16/1.54 <=> ! [P: subst > term > subst > $o] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) ) )
% 0.16/1.54 & ( hoasinduction
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ ( sub @ A @ id ) )
% 0.16/1.54 | ( P @ id @ A @ id ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.16/1.54 & hoasinduction_gthm
% 0.16/1.54 & axapp
% 0.16/1.54 & hoaslamnotvar_lthm
% 0.16/1.54 & pushprop_lem3v2_lthm
% 0.16/1.54 & ( hoasinduction_lem3b_lthm
% 0.16/1.54 <=> ! [B: term] :
% 0.16/1.54 ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ( F @ sh @ one )
% 0.16/1.54 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.16/1.54 & ulamvarind
% 0.16/1.54 & ( induction
% 0.16/1.54 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2140 ) ) )
% 0.16/1.54 & ( hoasinduction_lem3a_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.16/1.54 & termmset_gthm
% 0.16/1.54 & ( hoasinduction_lem3aa
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.16/1.54 & pushprop_lem1v2_gthm
% 0.16/1.54 & hoaslamnotap_gthm
% 0.16/1.54 & hoaslamnotvar_gthm
% 0.16/1.54 & hoasinduction_lem3b_gthm
% 0.16/1.54 & pushprop_lem2v2
% 0.16/1.54 & hoasinduction_lem3a_gthm
% 0.16/1.54 & axclos
% 0.16/1.54 & axassoc
% 0.16/1.54 & ( hoasinduction_lem2v2
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ( Q @ Bound_variable_2820 )
% 0.16/1.54 | ~ ( Q @ Bound_variable_2822 )
% 0.16/1.54 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.16/1.54 & pushprop_lthm
% 0.16/1.54 & ( apinj2
% 0.16/1.54 <=> ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ A @ C )
% 0.16/1.54 != ( ap @ B @ D ) )
% 0.16/1.54 | ( C = D ) ) )
% 0.16/1.54 & ( apinj1
% 0.16/1.54 <=> ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ A @ C )
% 0.16/1.54 != ( ap @ B @ D ) )
% 0.16/1.54 | ( A = B ) ) )
% 0.16/1.54 & ( hoasapinj2_lthm
% 0.16/1.54 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ A @ C )
% 0.16/1.54 != ( ap @ B @ D ) )
% 0.16/1.54 | ( C = D ) )
% 0.16/1.54 => ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.16/1.54 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.16/1.54 | ( C = D ) ) ) )
% 0.16/1.54 & ( hoasinduction_lem3v2a
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.16/1.54 & ( hoasapinj1_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ A @ C )
% 0.16/1.54 != ( ap @ B @ D ) )
% 0.16/1.54 | ( A = B ) )
% 0.16/1.54 => ! [A: term,B: term,C: term,D: term] :
% 0.16/1.54 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.16/1.54 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.16/1.54 | ( A = B ) ) ) ) )
% 0.16/1.54 & ( hoaslaminj_lthm
% 0.16/1.54 <=> ( ! [A: term,M: subst] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.16/1.54 => ( ! [A: term,M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.16/1.54 => ( ! [A: term,B: term] :
% 0.16/1.54 ( ( ( lam @ A )
% 0.16/1.54 != ( lam @ B ) )
% 0.16/1.54 | ( A = B ) )
% 0.16/1.54 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.16/1.54 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ( ( lam @ ( F @ sh @ one ) )
% 0.16/1.54 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.16/1.54 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.16/1.54 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.16/1.54 & ( axvarcons
% 0.16/1.54 <=> ! [A: term,M: subst] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.16/1.54 & ( axscons
% 0.16/1.54 <=> ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.16/1.54 & hoasinduction_lem2v2_gthm
% 0.16/1.54 & ( axidr
% 0.16/1.54 <=> ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ M @ id ) ) )
% 0.16/1.54 & ( pushprop_lem1
% 0.16/1.54 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.16/1.54 & ( laminj
% 0.16/1.54 <=> ! [A: term,B: term] :
% 0.16/1.54 ( ( ( lam @ A )
% 0.16/1.54 != ( lam @ B ) )
% 0.16/1.54 | ( A = B ) ) )
% 0.16/1.54 & ( hoasinduction_lem3_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.16/1.54 & ( pushprop_lem0
% 0.16/1.54 <=> ! [P: term > $o,A: term,M: subst] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.16/1.54 & pushprop_gthm
% 0.16/1.54 & axabs
% 0.16/1.54 & ( hoasinduction_lem3v2a_lthm
% 0.16/1.54 <=> ( ! [B: term] :
% 0.16/1.54 ~ ! [F: subst > term > term] :
% 0.16/1.54 ~ ! [A: term,M: subst] :
% 0.16/1.54 ( ( sub @ B @ ( push @ A @ M ) )
% 0.16/1.54 = ( F @ M @ A ) )
% 0.16/1.54 => ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.16/1.54 & hoasinduction_lem2_lthm
% 0.16/1.54 & hoasapinj2_gthm
% 0.16/1.54 & hoasinduction_lem1_lthm
% 0.16/1.54 & ~ lamnotap
% 0.16/1.54 & hoasapinj1_gthm
% 0.16/1.54 & hoaslamnotvar
% 0.16/1.54 & ( axidl
% 0.16/1.54 <=> ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ id @ M ) ) )
% 0.16/1.54 & hoaslaminj_gthm
% 0.16/1.54 & ( induction2_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.16/1.54 ( ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( var @ B )
% 0.16/1.54 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.16/1.54 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.16/1.54 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.16/1.54 & ( hoasinduction_lem0_lthm
% 0.16/1.54 <=> ! [P: subst > term > subst > $o] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) ) )
% 0.16/1.54 & ( substmonoid_lthm
% 0.16/1.54 <=> ( ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ id @ M ) )
% 0.16/1.54 => ( ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ M @ id ) )
% 0.16/1.54 => ( ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ id @ M ) )
% 0.16/1.54 & ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ M @ id ) ) ) ) ) )
% 0.16/1.54 & pushprop
% 0.16/1.54 & hoasinduction_lem3_gthm
% 0.16/1.54 & hoasinduction_lem2_gthm
% 0.16/1.54 & ( hoasinduction_lem3b
% 0.16/1.54 <=> ! [B: term] :
% 0.16/1.54 ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ( F @ sh @ one )
% 0.16/1.54 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.16/1.54 & ( substmonoid
% 0.16/1.54 <=> ( ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ id @ M ) )
% 0.16/1.54 & ! [M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ M @ id ) ) ) )
% 0.16/1.54 & lamnotvar
% 0.16/1.54 & ( hoasinduction_lem3a
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.16/1.54 & hoasinduction_lem1_gthm
% 0.16/1.54 & ( hoasinduction_no_psi_cond
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.16/1.54 ( ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.16/1.54 & induction2_gthm
% 0.16/1.54 & pushprop_lem2v2_lthm
% 0.16/1.54 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.16/1.54 & ( hoaslamnotap
% 0.16/1.54 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ( ( lam @ ( F @ sh @ one ) )
% 0.16/1.54 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.16/1.54 & substmonoid_gthm
% 0.16/1.54 & ulamvarsh
% 0.16/1.54 & ( induction2
% 0.16/1.54 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2367 ) ) )
% 0.16/1.54 & pushprop_lem3v2
% 0.16/1.54 & pushprop_lem2v2_gthm
% 0.16/1.54 & ( pushprop_lem1_lthm
% 0.16/1.54 <=> ( ! [A: term,M: subst] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.16/1.54 => ( ! [A: term,M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.16/1.54 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.16/1.54 & ( hoasinduction_lem3v2
% 0.16/1.54 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.16/1.54 & ( axshiftcons
% 0.16/1.54 <=> ! [A: term,M: subst] :
% 0.16/1.54 ( M
% 0.16/1.54 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.16/1.54 & ( termmset
% 0.16/1.54 <=> ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) ) )
% 0.16/1.54 & ( pushprop_lem0_lthm
% 0.16/1.54 <=> ! [P: term > $o,A: term,M: subst] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.16/1.54 & hoasapnotvar_lthm
% 0.16/1.54 & ( hoasinduction_lem3v2_lthm
% 0.16/1.54 <=> ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.16/1.54 & ( axvarid
% 0.16/1.54 <=> ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) ) )
% 0.16/1.54 & ( hoasinduction_lthm_3
% 0.16/1.54 <=> ( ! [P: subst > term > subst > $o] :
% 0.16/1.54 ~ ! [Q: term > $o] :
% 0.16/1.54 ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.16/1.54 ( ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ A )
% 0.16/1.54 | ( P @ A ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ A )
% 0.16/1.54 | ~ ( P @ B )
% 0.16/1.54 | ( P @ ( ap @ A @ B ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ! [B: term] :
% 0.16/1.54 ( ~ ( P @ B )
% 0.16/1.54 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( P @ ( lam @ A ) ) )
% 0.16/1.54 | ( P @ Bound_variable_2367 ) )
% 0.16/1.54 => ( ! [A: term] :
% 0.16/1.54 ( A
% 0.16/1.54 = ( sub @ A @ id ) )
% 0.16/1.54 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.16/1.54 ( ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ~ ! [X: term] :
% 0.16/1.54 ( ( Q @ X )
% 0.16/1.54 = ( P @ id @ X @ id ) )
% 0.16/1.54 | ~ ! [B: term] :
% 0.16/1.54 ( ~ ( Q @ B )
% 0.16/1.54 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.16/1.54 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.16/1.54 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.16/1.54 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.16/1.54 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.16/1.54 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.16/1.54 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( var @ ( sub @ A @ id ) )
% 0.16/1.54 | ( P @ id @ A @ id ) )
% 0.16/1.54 | ~ ! [A: term,B: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ~ ( P @ id @ B @ id )
% 0.16/1.54 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.16/1.54 | ~ ! [F: subst > term > term] :
% 0.16/1.54 ( ~ ! [M: subst,A: term,N: subst] :
% 0.16/1.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.16/1.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.16/1.54 | ~ ! [A: term] :
% 0.16/1.54 ( ~ ( P @ id @ A @ id )
% 0.16/1.54 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.16/1.54 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.16/1.54 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.16/1.54
% 0.16/1.54 thf(hoasinduction_lem0,conjecture,
% 0.16/1.54 ( hoasinduction_lem0
% 0.16/1.54 = ( ! [P: subst > term > subst > $o] :
% 0.16/1.54 ? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ) ).
% 0.16/1.54 ------------------------
% 0.16/1.57 % (12428)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_12223 for (2999ds/27Mi)
% 0.16/1.57 % (12429)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/2Mi)
% 0.16/1.57 % (12426)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/183Mi)
% 0.16/1.57 % (12427)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_12223 for (2999ds/4Mi)
% 0.16/1.57 % (12432)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/18Mi)
% 0.16/1.57 % (12431)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_12223 for (2999ds/275Mi)
% 0.16/1.57 % (12430)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_12223 for (2999ds/2Mi)
% 0.16/1.57 % (12429)Instruction limit reached!
% 0.16/1.57 % (12429)------------------------------
% 0.16/1.57 % (12429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.57 % (12429)Termination reason: Unknown
% 0.16/1.57 % (12429)Termination phase: shuffling
% 0.16/1.57
% 0.16/1.57 % (12429)Memory used [KB]: 1279
% 0.16/1.57 % (12429)Time elapsed: 0.003 s
% 0.16/1.57 % (12429)Instructions burned: 3 (million)
% 0.16/1.57 % (12429)------------------------------
% 0.16/1.57 % (12429)------------------------------
% 0.16/1.57 % (12430)Instruction limit reached!
% 0.16/1.57 % (12430)------------------------------
% 0.16/1.57 % (12430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.57 % (12430)Termination reason: Unknown
% 0.16/1.57 % (12430)Termination phase: shuffling
% 0.16/1.57
% 0.16/1.57 % (12430)Memory used [KB]: 1279
% 0.16/1.57 % (12430)Time elapsed: 0.003 s
% 0.16/1.57 % (12430)Instructions burned: 3 (million)
% 0.16/1.57 % (12430)------------------------------
% 0.16/1.57 % (12430)------------------------------
% 0.16/1.57 % (12427)Instruction limit reached!
% 0.16/1.57 % (12427)------------------------------
% 0.16/1.57 % (12427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.57 % (12427)Termination reason: Unknown
% 0.16/1.57 % (12427)Termination phase: shuffling
% 0.16/1.57
% 0.16/1.57 % (12427)Memory used [KB]: 1279
% 0.16/1.57 % (12427)Time elapsed: 0.004 s
% 0.16/1.57 % (12427)Instructions burned: 5 (million)
% 0.16/1.57 % (12427)------------------------------
% 0.16/1.57 % (12427)------------------------------
% 0.16/1.58 % (12432)Instruction limit reached!
% 0.16/1.58 % (12432)------------------------------
% 0.16/1.58 % (12432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.58 % (12432)Termination reason: Unknown
% 0.16/1.58 % (12432)Termination phase: shuffling
% 0.16/1.58
% 0.16/1.58 % (12432)Memory used [KB]: 2046
% 0.16/1.58 % (12432)Time elapsed: 0.011 s
% 0.16/1.58 % (12432)Instructions burned: 19 (million)
% 0.16/1.58 % (12432)------------------------------
% 0.16/1.58 % (12432)------------------------------
% 0.16/1.58 % (12428)Instruction limit reached!
% 0.16/1.58 % (12428)------------------------------
% 0.16/1.58 % (12428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.58 % (12428)Termination reason: Unknown
% 0.16/1.58 % (12428)Termination phase: Property scanning
% 0.16/1.58
% 0.16/1.58 % (12428)Memory used [KB]: 2174
% 0.16/1.58 % (12428)Time elapsed: 0.015 s
% 0.16/1.58 % (12428)Instructions burned: 27 (million)
% 0.16/1.58 % (12428)------------------------------
% 0.16/1.58 % (12428)------------------------------
% 0.16/1.59 % (12435)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_12223 for (2999ds/15Mi)
% 0.16/1.59 % (12433)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/3Mi)
% 0.16/1.59 % (12434)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_12223 for (2999ds/37Mi)
% 0.16/1.59 % (12431)Refutation not found, incomplete strategy
% 0.16/1.59 % (12431)------------------------------
% 0.16/1.59 % (12431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.59 % (12431)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.59
% 0.16/1.59
% 0.16/1.59 % (12431)Memory used [KB]: 6652
% 0.16/1.59 % (12431)Time elapsed: 0.020 s
% 0.16/1.59 % (12431)Instructions burned: 37 (million)
% 0.16/1.59 % (12431)------------------------------
% 0.16/1.59 % (12431)------------------------------
% 0.16/1.59 % (12433)Instruction limit reached!
% 0.16/1.59 % (12433)------------------------------
% 0.16/1.59 % (12433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.59 % (12433)Termination reason: Unknown
% 0.16/1.59 % (12433)Termination phase: shuffling
% 0.16/1.59
% 0.16/1.59 % (12433)Memory used [KB]: 1279
% 0.16/1.59 % (12433)Time elapsed: 0.003 s
% 0.16/1.59 % (12433)Instructions burned: 3 (million)
% 0.16/1.59 % (12433)------------------------------
% 0.16/1.59 % (12433)------------------------------
% 0.16/1.59 % (12435)Instruction limit reached!
% 0.16/1.59 % (12435)------------------------------
% 0.16/1.59 % (12435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.16/1.59 % (12435)Termination reason: Unknown
% 0.16/1.59 % (12435)Termination phase: shuffling
% 0.16/1.59
% 0.16/1.59 % (12435)Memory used [KB]: 1791
% 0.16/1.59 % (12435)Time elapsed: 0.009 s
% 0.16/1.59 % (12435)Instructions burned: 15 (million)
% 0.16/1.59 % (12435)------------------------------
% 0.16/1.59 % (12435)------------------------------
% 0.16/1.59 % (12436)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_12223 for (2999ds/3Mi)
% 2.63/1.60 % (12436)Instruction limit reached!
% 2.63/1.60 % (12436)------------------------------
% 2.63/1.60 % (12436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.60 % (12436)Termination reason: Unknown
% 2.63/1.60 % (12436)Termination phase: shuffling
% 2.63/1.60
% 2.63/1.60 % (12436)Memory used [KB]: 1279
% 2.63/1.60 % (12436)Time elapsed: 0.004 s
% 2.63/1.60 % (12436)Instructions burned: 4 (million)
% 2.63/1.60 % (12436)------------------------------
% 2.63/1.60 % (12436)------------------------------
% 2.63/1.60 % (12437)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_12223 for (2999ds/1041Mi)
% 2.63/1.60 % (12438)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/7Mi)
% 2.63/1.60 % (12439)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/16Mi)
% 2.63/1.60 % (12434)Instruction limit reached!
% 2.63/1.60 % (12434)------------------------------
% 2.63/1.60 % (12434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.60 % (12434)Termination reason: Unknown
% 2.63/1.60 % (12434)Termination phase: Property scanning
% 2.63/1.60
% 2.63/1.60 % (12434)Memory used [KB]: 1918
% 2.63/1.60 % (12434)Time elapsed: 0.019 s
% 2.63/1.60 % (12434)Instructions burned: 39 (million)
% 2.63/1.60 % (12434)------------------------------
% 2.63/1.60 % (12434)------------------------------
% 2.63/1.61 % (12438)Instruction limit reached!
% 2.63/1.61 % (12438)------------------------------
% 2.63/1.61 % (12438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.61 % (12438)Termination reason: Unknown
% 2.63/1.61 % (12438)Termination phase: shuffling
% 2.63/1.61
% 2.63/1.61 % (12438)Memory used [KB]: 1535
% 2.63/1.61 % (12438)Time elapsed: 0.005 s
% 2.63/1.61 % (12438)Instructions burned: 8 (million)
% 2.63/1.61 % (12438)------------------------------
% 2.63/1.61 % (12438)------------------------------
% 2.63/1.61 % (12440)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_12223 for (2999ds/3Mi)
% 2.63/1.61 % (12440)Instruction limit reached!
% 2.63/1.61 % (12440)------------------------------
% 2.63/1.61 % (12440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.61 % (12440)Termination reason: Unknown
% 2.63/1.61 % (12440)Termination phase: shuffling
% 2.63/1.61
% 2.63/1.61 % (12440)Memory used [KB]: 1279
% 2.63/1.61 % (12440)Time elapsed: 0.004 s
% 2.63/1.61 % (12440)Instructions burned: 4 (million)
% 2.63/1.61 % (12440)------------------------------
% 2.63/1.61 % (12440)------------------------------
% 2.63/1.61 % (12441)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_12223 for (2999ds/3Mi)
% 2.63/1.61 % (12439)Instruction limit reached!
% 2.63/1.61 % (12439)------------------------------
% 2.63/1.61 % (12439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.61 % (12439)Termination reason: Unknown
% 2.63/1.61 % (12439)Termination phase: shuffling
% 2.63/1.61
% 2.63/1.61 % (12439)Memory used [KB]: 1918
% 2.63/1.61 % (12439)Time elapsed: 0.010 s
% 2.63/1.61 % (12439)Instructions burned: 16 (million)
% 2.63/1.61 % (12439)------------------------------
% 2.63/1.61 % (12439)------------------------------
% 2.63/1.61 % (12441)Instruction limit reached!
% 2.63/1.61 % (12441)------------------------------
% 2.63/1.61 % (12441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.61 % (12441)Termination reason: Unknown
% 2.63/1.61 % (12441)Termination phase: shuffling
% 2.63/1.61
% 2.63/1.61 % (12441)Memory used [KB]: 1279
% 2.63/1.61 % (12441)Time elapsed: 0.003 s
% 2.63/1.61 % (12441)Instructions burned: 3 (million)
% 2.63/1.61 % (12441)------------------------------
% 2.63/1.61 % (12441)------------------------------
% 2.63/1.62 % (12442)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/7Mi)
% 2.63/1.62 % (12443)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/3Mi)
% 2.63/1.62 % (12442)Instruction limit reached!
% 2.63/1.62 % (12442)------------------------------
% 2.63/1.62 % (12442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.62 % (12442)Termination reason: Unknown
% 2.63/1.62 % (12442)Termination phase: shuffling
% 2.63/1.62
% 2.63/1.62 % (12442)Memory used [KB]: 1407
% 2.63/1.62 % (12442)Time elapsed: 0.005 s
% 2.63/1.62 % (12442)Instructions burned: 7 (million)
% 2.63/1.62 % (12442)------------------------------
% 2.63/1.62 % (12442)------------------------------
% 2.63/1.63 % (12443)Instruction limit reached!
% 2.63/1.63 % (12443)------------------------------
% 2.63/1.63 % (12443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.63 % (12443)Termination reason: Unknown
% 2.63/1.63 % (12443)Termination phase: shuffling
% 2.63/1.63
% 2.63/1.63 % (12443)Memory used [KB]: 1279
% 2.63/1.63 % (12443)Time elapsed: 0.003 s
% 2.63/1.63 % (12443)Instructions burned: 4 (million)
% 2.63/1.63 % (12443)------------------------------
% 2.63/1.63 % (12443)------------------------------
% 2.63/1.63 % (12445)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/4Mi)
% 2.63/1.63 % (12446)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/18Mi)
% 2.63/1.63 % (12447)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/710Mi)
% 2.63/1.63 % (12445)Instruction limit reached!
% 2.63/1.63 % (12445)------------------------------
% 2.63/1.63 % (12445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.63 % (12445)Termination reason: Unknown
% 2.63/1.63 % (12445)Termination phase: shuffling
% 2.63/1.63
% 2.63/1.63 % (12445)Memory used [KB]: 1279
% 2.63/1.63 % (12445)Time elapsed: 0.003 s
% 2.63/1.63 % (12445)Instructions burned: 4 (million)
% 2.63/1.63 % (12445)------------------------------
% 2.63/1.63 % (12445)------------------------------
% 2.63/1.64 % (12446)Instruction limit reached!
% 2.63/1.64 % (12446)------------------------------
% 2.63/1.64 % (12446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.64 % (12446)Termination reason: Unknown
% 2.63/1.64 % (12446)Termination phase: shuffling
% 2.63/1.64
% 2.63/1.64 % (12446)Memory used [KB]: 2046
% 2.63/1.64 % (12446)Time elapsed: 0.011 s
% 2.63/1.64 % (12446)Instructions burned: 19 (million)
% 2.63/1.64 % (12446)------------------------------
% 2.63/1.64 % (12446)------------------------------
% 2.63/1.64 % (12448)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/6Mi)
% 2.63/1.64 % (12449)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_12223 for (2999ds/902Mi)
% 2.63/1.64 % (12448)Instruction limit reached!
% 2.63/1.64 % (12448)------------------------------
% 2.63/1.64 % (12448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.64 % (12448)Termination reason: Unknown
% 2.63/1.64 % (12448)Termination phase: shuffling
% 2.63/1.64
% 2.63/1.64 % (12448)Memory used [KB]: 1407
% 2.63/1.64 % (12448)Time elapsed: 0.005 s
% 2.63/1.64 % (12448)Instructions burned: 7 (million)
% 2.63/1.64 % (12448)------------------------------
% 2.63/1.64 % (12448)------------------------------
% 2.63/1.65 % (12450)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_12223 for (2999ds/21Mi)
% 2.63/1.65 % (12426)Instruction limit reached!
% 2.63/1.65 % (12426)------------------------------
% 2.63/1.65 % (12426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.65 % (12426)Termination reason: Unknown
% 2.63/1.65 % (12426)Termination phase: Property scanning
% 2.63/1.65
% 2.63/1.65 % (12426)Memory used [KB]: 4349
% 2.63/1.65 % (12426)Time elapsed: 0.085 s
% 2.63/1.65 % (12426)Instructions burned: 183 (million)
% 2.63/1.65 % (12426)------------------------------
% 2.63/1.65 % (12426)------------------------------
% 2.63/1.65 % (12451)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12223 for (2999ds/5Mi)
% 2.63/1.66 % (12451)Instruction limit reached!
% 2.63/1.66 % (12451)------------------------------
% 2.63/1.66 % (12451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.66 % (12451)Termination reason: Unknown
% 2.63/1.66 % (12451)Termination phase: shuffling
% 2.63/1.66
% 2.63/1.66 % (12451)Memory used [KB]: 1279
% 2.63/1.66 % (12451)Time elapsed: 0.004 s
% 2.63/1.66 % (12451)Instructions burned: 5 (million)
% 2.63/1.66 % (12451)------------------------------
% 2.63/1.66 % (12451)------------------------------
% 2.63/1.66 % (12450)Instruction limit reached!
% 2.63/1.66 % (12450)------------------------------
% 2.63/1.66 % (12450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.66 % (12450)Termination reason: Unknown
% 2.63/1.66 % (12450)Termination phase: shuffling
% 2.63/1.66
% 2.63/1.66 % (12450)Memory used [KB]: 2046
% 2.63/1.66 % (12450)Time elapsed: 0.012 s
% 2.63/1.66 % (12450)Instructions burned: 21 (million)
% 2.63/1.66 % (12450)------------------------------
% 2.63/1.66 % (12450)------------------------------
% 2.63/1.66 % (12452)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_12223 for (2999ds/6Mi)
% 2.63/1.66 % (12452)Instruction limit reached!
% 2.63/1.66 % (12452)------------------------------
% 2.63/1.66 % (12452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.66 % (12452)Termination reason: Unknown
% 2.63/1.66 % (12452)Termination phase: shuffling
% 2.63/1.66
% 2.63/1.66 % (12452)Memory used [KB]: 1407
% 2.63/1.66 % (12452)Time elapsed: 0.005 s
% 2.63/1.66 % (12452)Instructions burned: 7 (million)
% 2.63/1.66 % (12452)------------------------------
% 2.63/1.66 % (12452)------------------------------
% 2.63/1.67 % (12453)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/377Mi)
% 2.63/1.67 % (12455)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_12223 for (2998ds/19Mi)
% 2.63/1.67 % (12454)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_12223 for (2998ds/779Mi)
% 2.63/1.68 % (12456)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/879Mi)
% 2.63/1.68 % (12455)Instruction limit reached!
% 2.63/1.68 % (12455)------------------------------
% 2.63/1.68 % (12455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.68 % (12455)Termination reason: Unknown
% 2.63/1.68 % (12455)Termination phase: shuffling
% 2.63/1.68
% 2.63/1.68 % (12455)Memory used [KB]: 1663
% 2.63/1.68 % (12455)Time elapsed: 0.010 s
% 2.63/1.68 % (12455)Instructions burned: 19 (million)
% 2.63/1.68 % (12455)------------------------------
% 2.63/1.68 % (12455)------------------------------
% 2.63/1.70 % (12457)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/17Mi)
% 2.63/1.71 % (12457)Instruction limit reached!
% 2.63/1.71 % (12457)------------------------------
% 2.63/1.71 % (12457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.71 % (12457)Termination reason: Unknown
% 2.63/1.71 % (12457)Termination phase: shuffling
% 2.63/1.71
% 2.63/1.71 % (12457)Memory used [KB]: 2046
% 2.63/1.71 % (12457)Time elapsed: 0.011 s
% 2.63/1.71 % (12457)Instructions burned: 18 (million)
% 2.63/1.71 % (12457)------------------------------
% 2.63/1.71 % (12457)------------------------------
% 2.63/1.72 % (12458)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/3Mi)
% 2.63/1.72 % (12458)Instruction limit reached!
% 2.63/1.72 % (12458)------------------------------
% 2.63/1.72 % (12458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.72 % (12458)Termination reason: Unknown
% 2.63/1.72 % (12458)Termination phase: shuffling
% 2.63/1.72
% 2.63/1.72 % (12458)Memory used [KB]: 1279
% 2.63/1.72 % (12458)Time elapsed: 0.004 s
% 2.63/1.72 % (12458)Instructions burned: 4 (million)
% 2.63/1.72 % (12458)------------------------------
% 2.63/1.72 % (12458)------------------------------
% 2.63/1.74 % (12449)Refutation not found, incomplete strategy
% 2.63/1.74 % (12449)------------------------------
% 2.63/1.74 % (12449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.74 % (12449)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.74
% 2.63/1.74
% 2.63/1.74 % (12449)Memory used [KB]: 9210
% 2.63/1.74 % (12449)Time elapsed: 0.098 s
% 2.63/1.74 % (12449)Instructions burned: 200 (million)
% 2.63/1.74 % (12449)------------------------------
% 2.63/1.74 % (12449)------------------------------
% 2.63/1.74 % (12459)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/30Mi)
% 2.63/1.76 % (12460)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/127Mi)
% 2.63/1.76 % (12459)Instruction limit reached!
% 2.63/1.76 % (12459)------------------------------
% 2.63/1.76 % (12459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.76 % (12459)Termination reason: Unknown
% 2.63/1.76 % (12459)Termination phase: Property scanning
% 2.63/1.76
% 2.63/1.76 % (12459)Memory used [KB]: 2174
% 2.63/1.76 % (12459)Time elapsed: 0.017 s
% 2.63/1.76 % (12459)Instructions burned: 31 (million)
% 2.63/1.76 % (12459)------------------------------
% 2.63/1.76 % (12459)------------------------------
% 2.63/1.77 % (12461)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12223 for (2998ds/100Mi)
% 2.63/1.81 % (12460)Instruction limit reached!
% 2.63/1.81 % (12460)------------------------------
% 2.63/1.81 % (12460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.81 % (12460)Termination reason: Unknown
% 2.63/1.81 % (12460)Termination phase: Property scanning
% 2.63/1.81
% 2.63/1.81 % (12460)Memory used [KB]: 4221
% 2.63/1.81 % (12460)Time elapsed: 0.061 s
% 2.63/1.81 % (12460)Instructions burned: 127 (million)
% 2.63/1.81 % (12460)------------------------------
% 2.63/1.81 % (12460)------------------------------
% 2.63/1.82 % (12461)Instruction limit reached!
% 2.63/1.82 % (12461)------------------------------
% 2.63/1.82 % (12461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.82 % (12461)Termination reason: Unknown
% 2.63/1.82 % (12461)Termination phase: Saturation
% 2.63/1.82
% 2.63/1.82 % (12461)Memory used [KB]: 6524
% 2.63/1.82 % (12461)Time elapsed: 0.046 s
% 2.63/1.82 % (12461)Instructions burned: 102 (million)
% 2.63/1.82 % (12461)------------------------------
% 2.63/1.82 % (12461)------------------------------
% 2.63/1.83 % (12462)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_12223 for (2997ds/3Mi)
% 2.63/1.83 % (12462)Instruction limit reached!
% 2.63/1.83 % (12462)------------------------------
% 2.63/1.83 % (12462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.83 % (12462)Termination reason: Unknown
% 2.63/1.83 % (12462)Termination phase: shuffling
% 2.63/1.83
% 2.63/1.83 % (12462)Memory used [KB]: 1279
% 2.63/1.83 % (12462)Time elapsed: 0.003 s
% 2.63/1.83 % (12462)Instructions burned: 3 (million)
% 2.63/1.83 % (12462)------------------------------
% 2.63/1.83 % (12462)------------------------------
% 2.63/1.83 % (12463)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_12223 for (2997ds/20Mi)
% 2.63/1.84 % (12463)Instruction limit reached!
% 2.63/1.84 % (12463)------------------------------
% 2.63/1.84 % (12463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.84 % (12463)Termination reason: Unknown
% 2.63/1.84 % (12463)Termination phase: shuffling
% 2.63/1.84
% 2.63/1.84 % (12463)Memory used [KB]: 2174
% 2.63/1.84 % (12463)Time elapsed: 0.012 s
% 2.63/1.84 % (12463)Instructions burned: 21 (million)
% 2.63/1.84 % (12463)------------------------------
% 2.63/1.84 % (12463)------------------------------
% 2.63/1.85 % (12453)Instruction limit reached!
% 2.63/1.85 % (12453)------------------------------
% 2.63/1.85 % (12453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.85 % (12453)Termination reason: Unknown
% 2.63/1.85 % (12453)Termination phase: Saturation
% 2.63/1.85
% 2.63/1.85 % (12453)Memory used [KB]: 10490
% 2.63/1.85 % (12453)Time elapsed: 0.181 s
% 2.63/1.85 % (12453)Instructions burned: 377 (million)
% 2.63/1.85 % (12453)------------------------------
% 2.63/1.85 % (12453)------------------------------
% 2.63/1.85 % (12464)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_12223 for (2997ds/86Mi)
% 2.63/1.86 % (12465)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_12223 for (2996ds/107Mi)
% 2.63/1.87 % (12466)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_12223 for (2996ds/39Mi)
% 2.63/1.88 % (12466)Instruction limit reached!
% 2.63/1.88 % (12466)------------------------------
% 2.63/1.88 % (12466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.88 % (12466)Termination reason: Unknown
% 2.63/1.88 % (12466)Termination phase: Property scanning
% 2.63/1.88
% 2.63/1.88 % (12466)Memory used [KB]: 1918
% 2.63/1.88 % (12466)Time elapsed: 0.019 s
% 2.63/1.88 % (12466)Instructions burned: 40 (million)
% 2.63/1.88 % (12466)------------------------------
% 2.63/1.88 % (12466)------------------------------
% 2.63/1.89 % (12464)Instruction limit reached!
% 2.63/1.89 % (12464)------------------------------
% 2.63/1.89 % (12464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.89 % (12464)Termination reason: Unknown
% 2.63/1.89 % (12464)Termination phase: Preprocessing 3
% 2.63/1.89
% 2.63/1.89 % (12464)Memory used [KB]: 4221
% 2.63/1.89 % (12464)Time elapsed: 0.043 s
% 2.63/1.89 % (12464)Instructions burned: 86 (million)
% 2.63/1.89 % (12464)------------------------------
% 2.63/1.89 % (12464)------------------------------
% 2.63/1.90 % (12467)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_12223 for (2996ds/448Mi)
% 2.63/1.91 % (12468)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_12223 for (2996ds/46Mi)
% 2.63/1.91 % (12465)Instruction limit reached!
% 2.63/1.91 % (12465)------------------------------
% 2.63/1.91 % (12465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.91 % (12465)Termination reason: Unknown
% 2.63/1.91 % (12465)Termination phase: Property scanning
% 2.63/1.91
% 2.63/1.91 % (12465)Memory used [KB]: 4477
% 2.63/1.91 % (12465)Time elapsed: 0.053 s
% 2.63/1.91 % (12465)Instructions burned: 108 (million)
% 2.63/1.91 % (12465)------------------------------
% 2.63/1.91 % (12465)------------------------------
% 2.63/1.93 % (12468)Instruction limit reached!
% 2.63/1.93 % (12468)------------------------------
% 2.63/1.93 % (12468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.93 % (12468)Termination reason: Unknown
% 2.63/1.93 % (12468)Termination phase: Preprocessing 2
% 2.63/1.93
% 2.63/1.93 % (12468)Memory used [KB]: 2430
% 2.63/1.93 % (12468)Time elapsed: 0.024 s
% 2.63/1.93 % (12468)Instructions burned: 46 (million)
% 2.63/1.93 % (12468)------------------------------
% 2.63/1.93 % (12468)------------------------------
% 2.63/1.93 % (12469)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_12223 for (2996ds/98Mi)
% 2.63/1.93 % (12467)Refutation not found, incomplete strategy
% 2.63/1.93 % (12467)------------------------------
% 2.63/1.93 % (12467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.93 % (12467)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.93
% 2.63/1.93
% 2.63/1.93 % (12467)Memory used [KB]: 6524
% 2.63/1.93 % (12467)Time elapsed: 0.034 s
% 2.63/1.93 % (12467)Instructions burned: 77 (million)
% 2.63/1.93 % (12467)------------------------------
% 2.63/1.93 % (12467)------------------------------
% 2.63/1.95 % (12470)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_12223 for (2996ds/507Mi)
% 2.63/1.95 % (12471)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_12223 for (2996ds/149Mi)
% 2.63/1.96 % (12447)Instruction limit reached!
% 2.63/1.96 % (12447)------------------------------
% 2.63/1.96 % (12447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.96 % (12447)Termination reason: Unknown
% 2.63/1.96 % (12447)Termination phase: Saturation
% 2.63/1.96
% 2.63/1.96 % (12447)Memory used [KB]: 11385
% 2.63/1.96 % (12447)Time elapsed: 0.339 s
% 2.63/1.96 % (12447)Instructions burned: 711 (million)
% 2.63/1.96 % (12447)------------------------------
% 2.63/1.96 % (12447)------------------------------
% 2.63/1.97 % (12469)Instruction limit reached!
% 2.63/1.97 % (12469)------------------------------
% 2.63/1.97 % (12469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.97 % (12469)Termination reason: Unknown
% 2.63/1.97 % (12469)Termination phase: Saturation
% 2.63/1.97
% 2.63/1.97 % (12469)Memory used [KB]: 2046
% 2.63/1.97 % (12469)Time elapsed: 0.045 s
% 2.63/1.97 % (12469)Instructions burned: 99 (million)
% 2.63/1.97 % (12469)------------------------------
% 2.63/1.97 % (12469)------------------------------
% 2.63/1.98 % (12454)Instruction limit reached!
% 2.63/1.98 % (12454)------------------------------
% 2.63/1.98 % (12454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.98 % (12454)Termination reason: Unknown
% 2.63/1.98 % (12454)Termination phase: Saturation
% 2.63/1.98
% 2.63/1.98 % (12454)Memory used [KB]: 7164
% 2.63/1.98 % (12454)Time elapsed: 0.307 s
% 2.63/1.98 % (12454)Instructions burned: 779 (million)
% 2.63/1.98 % (12454)------------------------------
% 2.63/1.98 % (12454)------------------------------
% 2.63/1.98 % (12437)Instruction limit reached!
% 2.63/1.98 % (12437)------------------------------
% 2.63/1.98 % (12437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.98 % (12437)Termination reason: Unknown
% 2.63/1.98 % (12437)Termination phase: Saturation
% 2.63/1.98
% 2.63/1.98 % (12437)Memory used [KB]: 7547
% 2.63/1.98 % (12437)Time elapsed: 0.383 s
% 2.63/1.98 % (12437)Instructions burned: 1041 (million)
% 2.63/1.98 % (12437)------------------------------
% 2.63/1.98 % (12437)------------------------------
% 2.63/1.98 % (12472)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12223 for (2995ds/39Mi)
% 2.63/1.99 % (12473)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_12223 for (2995ds/6Mi)
% 2.63/1.99 % (12473)Instruction limit reached!
% 2.63/1.99 % (12473)------------------------------
% 2.63/1.99 % (12473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/1.99 % (12473)Termination reason: Unknown
% 2.63/1.99 % (12473)Termination phase: shuffling
% 2.63/1.99
% 2.63/1.99 % (12473)Memory used [KB]: 1407
% 2.63/1.99 % (12473)Time elapsed: 0.005 s
% 2.63/1.99 % (12473)Instructions burned: 7 (million)
% 2.63/1.99 % (12473)------------------------------
% 2.63/1.99 % (12473)------------------------------
% 2.63/1.99 % (12474)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_12223 for (2995ds/1087Mi)
% 2.63/2.00 % (12475)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12223 for (2995ds/47Mi)
% 2.63/2.00 % (12472)Instruction limit reached!
% 2.63/2.00 % (12472)------------------------------
% 2.63/2.00 % (12472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/2.00 % (12472)Termination reason: Unknown
% 2.63/2.00 % (12472)Termination phase: Preprocessing 1
% 2.63/2.00
% 2.63/2.00 % (12472)Memory used [KB]: 2302
% 2.63/2.00 % (12472)Time elapsed: 0.020 s
% 2.63/2.00 % (12472)Instructions burned: 39 (million)
% 2.63/2.00 % (12472)------------------------------
% 2.63/2.00 % (12472)------------------------------
% 2.63/2.01 % (12476)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_12223 for (2995ds/44Mi)
% 2.63/2.02 % (12471)Instruction limit reached!
% 2.63/2.02 % (12471)------------------------------
% 2.63/2.02 % (12471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/2.02 % (12471)Termination reason: Unknown
% 2.63/2.02 % (12471)Termination phase: Property scanning
% 2.63/2.02
% 2.63/2.02 % (12471)Memory used [KB]: 7803
% 2.63/2.02 % (12471)Time elapsed: 0.071 s
% 2.63/2.02 % (12471)Instructions burned: 151 (million)
% 2.63/2.02 % (12471)------------------------------
% 2.63/2.02 % (12471)------------------------------
% 2.63/2.02 % (12475)Instruction limit reached!
% 2.63/2.02 % (12475)------------------------------
% 2.63/2.02 % (12475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/2.02 % (12475)Termination reason: Unknown
% 2.63/2.02 % (12475)Termination phase: Preprocessing 3
% 2.63/2.02
% 2.63/2.02 % (12475)Memory used [KB]: 2686
% 2.63/2.02 % (12475)Time elapsed: 0.025 s
% 2.63/2.02 % (12475)Instructions burned: 48 (million)
% 2.63/2.02 % (12475)------------------------------
% 2.63/2.02 % (12475)------------------------------
% 2.63/2.03 % (12476)Instruction limit reached!
% 2.63/2.03 % (12476)------------------------------
% 2.63/2.03 % (12476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.63/2.03 % (12476)Termination reason: Unknown
% 2.63/2.03 % (12476)Termination phase: Property scanning
% 2.63/2.03
% 2.63/2.03 % (12476)Memory used [KB]: 1918
% 2.63/2.03 % (12476)Time elapsed: 0.022 s
% 2.63/2.03 % (12476)Instructions burned: 46 (million)
% 2.63/2.03 % (12476)------------------------------
% 2.63/2.03 % (12476)------------------------------
% 5.86/2.03 % (12478)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12223 for (2995ds/62Mi)
% 5.86/2.04 % (12479)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_12223 for (2995ds/31Mi)
% 5.86/2.04 % (12477)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_12223 for (2995ds/432Mi)
% 5.86/2.05 % (12480)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12223 for (2995ds/96Mi)
% 5.86/2.05 % (12479)Instruction limit reached!
% 5.86/2.05 % (12479)------------------------------
% 5.86/2.05 % (12479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.05 % (12479)Termination reason: Unknown
% 5.86/2.05 % (12479)Termination phase: Property scanning
% 5.86/2.05
% 5.86/2.05 % (12479)Memory used [KB]: 2174
% 5.86/2.05 % (12479)Time elapsed: 0.017 s
% 5.86/2.05 % (12479)Instructions burned: 32 (million)
% 5.86/2.05 % (12479)------------------------------
% 5.86/2.05 % (12479)------------------------------
% 5.86/2.06 % (12478)Instruction limit reached!
% 5.86/2.06 % (12478)------------------------------
% 5.86/2.06 % (12478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.06 % (12478)Termination reason: Unknown
% 5.86/2.06 % (12478)Termination phase: Property scanning
% 5.86/2.06
% 5.86/2.06 % (12478)Memory used [KB]: 1918
% 5.86/2.06 % (12478)Time elapsed: 0.029 s
% 5.86/2.06 % (12478)Instructions burned: 63 (million)
% 5.86/2.06 % (12478)------------------------------
% 5.86/2.06 % (12478)------------------------------
% 5.86/2.07 % (12481)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_12223 for (2994ds/453Mi)
% 5.86/2.08 % (12470)Refutation not found, incomplete strategy
% 5.86/2.08 % (12470)------------------------------
% 5.86/2.08 % (12470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.08 % (12470)Termination reason: Refutation not found, incomplete strategy
% 5.86/2.08
% 5.86/2.08
% 5.86/2.08 % (12470)Memory used [KB]: 9850
% 5.86/2.08 % (12470)Time elapsed: 0.131 s
% 5.86/2.08 % (12470)Instructions burned: 273 (million)
% 5.86/2.08 % (12470)------------------------------
% 5.86/2.08 % (12470)------------------------------
% 5.86/2.08 % (12482)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_12223 for (2994ds/71Mi)
% 5.86/2.09 % (12480)Instruction limit reached!
% 5.86/2.09 % (12480)------------------------------
% 5.86/2.09 % (12480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.09 % (12480)Termination reason: Unknown
% 5.86/2.09 % (12480)Termination phase: Property scanning
% 5.86/2.09
% 5.86/2.09 % (12480)Memory used [KB]: 4221
% 5.86/2.09 % (12480)Time elapsed: 0.049 s
% 5.86/2.09 % (12480)Instructions burned: 97 (million)
% 5.86/2.09 % (12480)------------------------------
% 5.86/2.09 % (12480)------------------------------
% 5.86/2.09 % (12483)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12223 for (2994ds/83Mi)
% 5.86/2.11 % (12456)Instruction limit reached!
% 5.86/2.11 % (12456)------------------------------
% 5.86/2.11 % (12456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.11 % (12456)Termination reason: Unknown
% 5.86/2.11 % (12456)Termination phase: Saturation
% 5.86/2.11
% 5.86/2.11 % (12456)Memory used [KB]: 11513
% 5.86/2.11 % (12456)Time elapsed: 0.431 s
% 5.86/2.11 % (12456)Instructions burned: 879 (million)
% 5.86/2.11 % (12456)------------------------------
% 5.86/2.11 % (12456)------------------------------
% 5.86/2.11 % (12484)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12223 for (2994ds/11Mi)
% 5.86/2.11 % (12482)Instruction limit reached!
% 5.86/2.11 % (12482)------------------------------
% 5.86/2.11 % (12482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.11 % (12482)Termination reason: Unknown
% 5.86/2.11 % (12482)Termination phase: Preprocessing 3
% 5.86/2.11
% 5.86/2.11 % (12482)Memory used [KB]: 3454
% 5.86/2.11 % (12482)Time elapsed: 0.036 s
% 5.86/2.11 % (12482)Instructions burned: 72 (million)
% 5.86/2.11 % (12482)------------------------------
% 5.86/2.11 % (12482)------------------------------
% 5.86/2.11 % (12483)Refutation not found, incomplete strategy
% 5.86/2.11 % (12483)------------------------------
% 5.86/2.11 % (12483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.11 % (12483)Termination reason: Refutation not found, incomplete strategy
% 5.86/2.11
% 5.86/2.11
% 5.86/2.11 % (12483)Memory used [KB]: 6652
% 5.86/2.11 % (12483)Time elapsed: 0.021 s
% 5.86/2.11 % (12483)Instructions burned: 40 (million)
% 5.86/2.11 % (12483)------------------------------
% 5.86/2.11 % (12483)------------------------------
% 5.86/2.12 % (12484)Instruction limit reached!
% 5.86/2.12 % (12484)------------------------------
% 5.86/2.12 % (12484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.12 % (12484)Termination reason: Unknown
% 5.86/2.12 % (12484)Termination phase: shuffling
% 5.86/2.12
% 5.86/2.12 % (12484)Memory used [KB]: 1535
% 5.86/2.12 % (12484)Time elapsed: 0.007 s
% 5.86/2.12 % (12484)Instructions burned: 12 (million)
% 5.86/2.12 % (12484)------------------------------
% 5.86/2.12 % (12484)------------------------------
% 5.86/2.13 % (12485)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_12223 for (2994ds/41Mi)
% 5.86/2.13 % (12486)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12223 for (2994ds/6Mi)
% 5.86/2.13 % (12487)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12223 for (2994ds/150Mi)
% 5.86/2.13 % (12488)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12223 for (2994ds/343Mi)
% 5.86/2.13 % (12486)Instruction limit reached!
% 5.86/2.13 % (12486)------------------------------
% 5.86/2.13 % (12486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.13 % (12486)Termination reason: Unknown
% 5.86/2.13 % (12486)Termination phase: shuffling
% 5.86/2.13
% 5.86/2.13 % (12486)Memory used [KB]: 1407
% 5.86/2.13 % (12486)Time elapsed: 0.005 s
% 5.86/2.13 % (12486)Instructions burned: 6 (million)
% 5.86/2.13 % (12486)------------------------------
% 5.86/2.13 % (12486)------------------------------
% 6.39/2.14 % (12485)Instruction limit reached!
% 6.39/2.14 % (12485)------------------------------
% 6.39/2.14 % (12485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (12485)Termination reason: Unknown
% 6.39/2.14 % (12485)Termination phase: Property scanning
% 6.39/2.14
% 6.39/2.14 % (12485)Memory used [KB]: 1918
% 6.39/2.14 % (12485)Time elapsed: 0.020 s
% 6.39/2.14 % (12485)Instructions burned: 42 (million)
% 6.39/2.14 % (12485)------------------------------
% 6.39/2.14 % (12485)------------------------------
% 6.39/2.15 % (12489)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_12223 for (2994ds/109Mi)
% 6.39/2.15 % (12488)Refutation not found, incomplete strategy
% 6.39/2.15 % (12488)------------------------------
% 6.39/2.15 % (12488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.15 % (12488)Termination reason: Refutation not found, incomplete strategy
% 6.39/2.15
% 6.39/2.15
% 6.39/2.15 % (12488)Memory used [KB]: 6652
% 6.39/2.15 % (12488)Time elapsed: 0.021 s
% 6.39/2.15 % (12488)Instructions burned: 42 (million)
% 6.39/2.15 % (12488)------------------------------
% 6.39/2.15 % (12488)------------------------------
% 6.39/2.16 % (12490)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_12223 for (2994ds/253Mi)
% 6.39/2.17 % (12491)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12223 for (2993ds/140Mi)
% 6.39/2.18 % (12477)Instruction limit reached!
% 6.39/2.18 % (12477)------------------------------
% 6.39/2.18 % (12477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.18 % (12477)Termination reason: Unknown
% 6.39/2.18 % (12477)Termination phase: Saturation
% 6.39/2.18
% 6.39/2.18 % (12477)Memory used [KB]: 2558
% 6.39/2.18 % (12477)Time elapsed: 0.174 s
% 6.39/2.18 % (12477)Instructions burned: 434 (million)
% 6.39/2.18 % (12477)------------------------------
% 6.39/2.18 % (12477)------------------------------
% 6.39/2.18 % (12490)Refutation not found, incomplete strategy
% 6.39/2.18 % (12490)------------------------------
% 6.39/2.18 % (12490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.18 % (12490)Termination reason: Refutation not found, incomplete strategy
% 6.39/2.18
% 6.39/2.18
% 6.39/2.18 % (12490)Memory used [KB]: 6652
% 6.39/2.18 % (12490)Time elapsed: 0.020 s
% 6.39/2.18 % (12490)Instructions burned: 37 (million)
% 6.39/2.18 % (12490)------------------------------
% 6.39/2.18 % (12490)------------------------------
% 6.39/2.19 % (12492)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_12223 for (2993ds/614Mi)
% 6.72/2.20 % (12493)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_12223 for (2993ds/202Mi)
% 6.72/2.20 % (12487)Instruction limit reached!
% 6.72/2.20 % (12487)------------------------------
% 6.72/2.20 % (12487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.20 % (12487)Termination reason: Unknown
% 6.72/2.20 % (12487)Termination phase: Property scanning
% 6.72/2.20
% 6.72/2.20 % (12487)Memory used [KB]: 4221
% 6.72/2.20 % (12487)Time elapsed: 0.070 s
% 6.72/2.20 % (12487)Instructions burned: 150 (million)
% 6.72/2.20 % (12487)------------------------------
% 6.72/2.20 % (12487)------------------------------
% 6.72/2.20 % (12489)Instruction limit reached!
% 6.72/2.20 % (12489)------------------------------
% 6.72/2.20 % (12489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.20 % (12489)Termination reason: Unknown
% 6.72/2.20 % (12489)Termination phase: Property scanning
% 6.72/2.20
% 6.72/2.20 % (12489)Memory used [KB]: 4349
% 6.72/2.20 % (12489)Time elapsed: 0.053 s
% 6.72/2.20 % (12489)Instructions burned: 109 (million)
% 6.72/2.20 % (12489)------------------------------
% 6.72/2.20 % (12489)------------------------------
% 6.72/2.21 % (12494)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_12223 for (2993ds/339Mi)
% 6.72/2.21 % (12495)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_12223 for (2993ds/283Mi)
% 6.72/2.23 % (12491)Instruction limit reached!
% 6.72/2.23 % (12491)------------------------------
% 6.72/2.23 % (12491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.23 % (12491)Termination reason: Unknown
% 6.72/2.23 % (12491)Termination phase: Property scanning
% 6.72/2.23
% 6.72/2.23 % (12491)Memory used [KB]: 4221
% 6.72/2.23 % (12491)Time elapsed: 0.066 s
% 6.72/2.23 % (12491)Instructions burned: 140 (million)
% 6.72/2.23 % (12491)------------------------------
% 6.72/2.23 % (12491)------------------------------
% 6.72/2.24 % (12481)Instruction limit reached!
% 6.72/2.24 % (12481)------------------------------
% 6.72/2.24 % (12481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.24 % (12481)Termination reason: Unknown
% 6.72/2.24 % (12481)Termination phase: Saturation
% 6.72/2.24
% 6.72/2.24 % (12481)Memory used [KB]: 6652
% 6.72/2.24 % (12481)Time elapsed: 0.172 s
% 6.72/2.24 % (12481)Instructions burned: 454 (million)
% 6.72/2.24 % (12481)------------------------------
% 6.72/2.24 % (12481)------------------------------
% 6.72/2.25 % (12496)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12223 for (2993ds/134Mi)
% 6.72/2.26 % (12497)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12223 for (2993ds/298Mi)
% 6.72/2.29 % (12493)Instruction limit reached!
% 6.72/2.29 % (12493)------------------------------
% 6.72/2.29 % (12493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.29 % (12493)Termination reason: Unknown
% 6.72/2.29 % (12493)Termination phase: Saturation
% 6.72/2.29
% 6.72/2.29 % (12493)Memory used [KB]: 4477
% 6.72/2.29 % (12493)Time elapsed: 0.095 s
% 6.72/2.29 % (12493)Instructions burned: 202 (million)
% 6.72/2.29 % (12493)------------------------------
% 6.72/2.29 % (12493)------------------------------
% 7.35/2.31 % (12498)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12223 for (2992ds/192Mi)
% 7.35/2.31 % (12496)Instruction limit reached!
% 7.35/2.31 % (12496)------------------------------
% 7.35/2.31 % (12496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.31 % (12496)Termination reason: Unknown
% 7.35/2.31 % (12496)Termination phase: Property scanning
% 7.35/2.31
% 7.35/2.31 % (12496)Memory used [KB]: 4221
% 7.35/2.31 % (12496)Time elapsed: 0.064 s
% 7.35/2.31 % (12496)Instructions burned: 135 (million)
% 7.35/2.31 % (12496)------------------------------
% 7.35/2.31 % (12496)------------------------------
% 7.35/2.32 % (12495)Instruction limit reached!
% 7.35/2.32 % (12495)------------------------------
% 7.35/2.32 % (12495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.32 % (12495)Termination reason: Unknown
% 7.35/2.32 % (12495)Termination phase: Saturation
% 7.35/2.32
% 7.35/2.32 % (12495)Memory used [KB]: 7164
% 7.35/2.32 % (12495)Time elapsed: 0.110 s
% 7.35/2.32 % (12495)Instructions burned: 283 (million)
% 7.35/2.32 % (12495)------------------------------
% 7.35/2.32 % (12495)------------------------------
% 7.35/2.33 % (12499)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_12223 for (2992ds/258Mi)
% 7.35/2.34 % (12500)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_12223 for (2992ds/90Mi)
% 7.35/2.37 % (12494)Instruction limit reached!
% 7.35/2.37 % (12494)------------------------------
% 7.35/2.37 % (12494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.37 % (12494)Termination reason: Unknown
% 7.35/2.37 % (12494)Termination phase: Saturation
% 7.35/2.37
% 7.35/2.37 % (12494)Memory used [KB]: 11513
% 7.35/2.37 % (12494)Time elapsed: 0.160 s
% 7.35/2.37 % (12494)Instructions burned: 340 (million)
% 7.35/2.37 % (12494)------------------------------
% 7.35/2.37 % (12494)------------------------------
% 7.35/2.38 % (12497)Instruction limit reached!
% 7.35/2.38 % (12497)------------------------------
% 7.35/2.38 % (12497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.38 % (12497)Termination reason: Unknown
% 7.35/2.38 % (12497)Termination phase: Saturation
% 7.35/2.38
% 7.35/2.38 % (12497)Memory used [KB]: 6780
% 7.35/2.38 % (12497)Time elapsed: 0.127 s
% 7.35/2.38 % (12497)Instructions burned: 298 (million)
% 7.35/2.38 % (12497)------------------------------
% 7.35/2.38 % (12497)------------------------------
% 7.35/2.38 % (12500)Instruction limit reached!
% 7.35/2.38 % (12500)------------------------------
% 7.35/2.38 % (12500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.38 % (12500)Termination reason: Unknown
% 7.35/2.38 % (12500)Termination phase: Preprocessing 3
% 7.35/2.38
% 7.35/2.38 % (12500)Memory used [KB]: 4093
% 7.35/2.38 % (12500)Time elapsed: 0.045 s
% 7.35/2.38 % (12500)Instructions burned: 91 (million)
% 7.35/2.38 % (12500)------------------------------
% 7.35/2.38 % (12500)------------------------------
% 7.35/2.39 % (12501)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_12223 for (2991ds/231Mi)
% 7.35/2.39 % (12498)Instruction limit reached!
% 7.35/2.39 % (12498)------------------------------
% 7.35/2.39 % (12498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.39 % (12498)Termination reason: Unknown
% 7.35/2.39 % (12498)Termination phase: Property scanning
% 7.35/2.39
% 7.35/2.39 % (12498)Memory used [KB]: 4605
% 7.35/2.39 % (12498)Time elapsed: 0.088 s
% 7.35/2.39 % (12498)Instructions burned: 193 (million)
% 7.35/2.39 % (12498)------------------------------
% 7.35/2.39 % (12498)------------------------------
% 8.14/2.40 % (12502)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_12223 for (2991ds/458Mi)
% 8.14/2.40 % (12503)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_12223 for (2991ds/31Mi)
% 8.14/2.41 % (12504)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_12223 for (2991ds/297Mi)
% 8.14/2.41 % (12503)Instruction limit reached!
% 8.14/2.41 % (12503)------------------------------
% 8.14/2.41 % (12503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.41 % (12503)Termination reason: Unknown
% 8.14/2.41 % (12503)Termination phase: Property scanning
% 8.14/2.41
% 8.14/2.41 % (12503)Memory used [KB]: 2174
% 8.14/2.41 % (12503)Time elapsed: 0.017 s
% 8.14/2.41 % (12503)Instructions burned: 31 (million)
% 8.14/2.41 % (12503)------------------------------
% 8.14/2.41 % (12503)------------------------------
% 8.14/2.43 % (12505)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_12223 for (2991ds/987Mi)
% 8.14/2.44 % (12504)Refutation not found, incomplete strategy
% 8.14/2.44 % (12504)------------------------------
% 8.14/2.44 % (12504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.44 % (12504)Termination reason: Refutation not found, incomplete strategy
% 8.14/2.44
% 8.14/2.44
% 8.14/2.44 % (12504)Memory used [KB]: 6524
% 8.14/2.44 % (12504)Time elapsed: 0.056 s
% 8.14/2.44 % (12504)Instructions burned: 75 (million)
% 8.14/2.44 % (12504)------------------------------
% 8.14/2.44 % (12504)------------------------------
% 8.14/2.44 % (12499)Instruction limit reached!
% 8.14/2.44 % (12499)------------------------------
% 8.14/2.44 % (12499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.44 % (12499)Termination reason: Unknown
% 8.14/2.44 % (12499)Termination phase: Property scanning
% 8.14/2.44
% 8.14/2.44 % (12499)Memory used [KB]: 7803
% 8.14/2.44 % (12499)Time elapsed: 0.117 s
% 8.14/2.44 % (12499)Instructions burned: 259 (million)
% 8.14/2.44 % (12499)------------------------------
% 8.14/2.44 % (12499)------------------------------
% 8.14/2.46 % (12506)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_12223 for (2990ds/182Mi)
% 8.14/2.46 % (12507)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_12223 for (2990ds/182Mi)
% 8.14/2.48 % (12501)Instruction limit reached!
% 8.14/2.48 % (12501)------------------------------
% 8.14/2.48 % (12501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.48 % (12501)Termination reason: Unknown
% 8.14/2.48 % (12501)Termination phase: Saturation
% 8.14/2.48
% 8.14/2.48 % (12501)Memory used [KB]: 7036
% 8.14/2.48 % (12501)Time elapsed: 0.096 s
% 8.14/2.48 % (12501)Instructions burned: 231 (million)
% 8.14/2.48 % (12501)------------------------------
% 8.14/2.48 % (12501)------------------------------
% 8.14/2.49 % (12492)Instruction limit reached!
% 8.14/2.49 % (12492)------------------------------
% 8.14/2.49 % (12492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.49 % (12492)Termination reason: Unknown
% 8.14/2.49 % (12492)Termination phase: Saturation
% 8.14/2.49
% 8.14/2.49 % (12492)Memory used [KB]: 12409
% 8.14/2.49 % (12492)Time elapsed: 0.300 s
% 8.14/2.49 % (12492)Instructions burned: 614 (million)
% 8.14/2.49 % (12492)------------------------------
% 8.14/2.49 % (12492)------------------------------
% 8.87/2.50 % (12508)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_12223 for (2990ds/154Mi)
% 8.87/2.51 % (12509)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_12223 for (2990ds/79Mi)
% 8.87/2.54 % (12474)Instruction limit reached!
% 8.87/2.54 % (12474)------------------------------
% 8.87/2.54 % (12474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.54 % (12474)Termination reason: Unknown
% 8.87/2.54 % (12474)Termination phase: Saturation
% 8.87/2.54
% 8.87/2.54 % (12474)Memory used [KB]: 12281
% 8.87/2.54 % (12474)Time elapsed: 0.545 s
% 8.87/2.54 % (12474)Instructions burned: 1087 (million)
% 8.87/2.54 % (12474)------------------------------
% 8.87/2.54 % (12474)------------------------------
% 8.87/2.54 % (12506)Instruction limit reached!
% 8.87/2.54 % (12506)------------------------------
% 8.87/2.54 % (12506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.54 % (12506)Termination reason: Unknown
% 8.87/2.54 % (12506)Termination phase: Property scanning
% 8.87/2.54
% 8.87/2.54 % (12506)Memory used [KB]: 7803
% 8.87/2.54 % (12506)Time elapsed: 0.085 s
% 8.87/2.54 % (12506)Instructions burned: 182 (million)
% 8.87/2.54 % (12506)------------------------------
% 8.87/2.54 % (12506)------------------------------
% 8.87/2.55 % (12507)Instruction limit reached!
% 8.87/2.55 % (12507)------------------------------
% 8.87/2.55 % (12507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.55 % (12507)Termination reason: Unknown
% 8.87/2.55 % (12507)Termination phase: Saturation
% 8.87/2.55
% 8.87/2.55 % (12507)Memory used [KB]: 9083
% 8.87/2.55 % (12507)Time elapsed: 0.088 s
% 8.87/2.55 % (12507)Instructions burned: 183 (million)
% 8.87/2.55 % (12507)------------------------------
% 8.87/2.55 % (12507)------------------------------
% 8.87/2.55 % (12509)Instruction limit reached!
% 8.87/2.55 % (12509)------------------------------
% 8.87/2.55 % (12509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.55 % (12509)Termination reason: Unknown
% 8.87/2.55 % (12509)Termination phase: Preprocessing 3
% 8.87/2.55
% 8.87/2.55 % (12509)Memory used [KB]: 3837
% 8.87/2.55 % (12509)Time elapsed: 0.040 s
% 8.87/2.55 % (12509)Instructions burned: 79 (million)
% 8.87/2.55 % (12509)------------------------------
% 8.87/2.55 % (12509)------------------------------
% 8.87/2.55 % (12510)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_12223 for (2989ds/216Mi)
% 8.87/2.56 % (12511)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_12223 for (2989ds/114Mi)
% 8.87/2.56 % (12508)Instruction limit reached!
% 8.87/2.56 % (12508)------------------------------
% 8.87/2.56 % (12508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.56 % (12508)Termination reason: Unknown
% 8.87/2.56 % (12508)Termination phase: Saturation
% 8.87/2.56
% 8.87/2.56 % (12508)Memory used [KB]: 2558
% 8.87/2.56 % (12508)Time elapsed: 0.063 s
% 8.87/2.56 % (12508)Instructions burned: 156 (million)
% 8.87/2.56 % (12508)------------------------------
% 8.87/2.56 % (12508)------------------------------
% 8.87/2.56 % (12512)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_12223 for (2989ds/922Mi)
% 8.87/2.56 % (12513)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_12223 for (2989ds/182Mi)
% 8.87/2.58 % (12514)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_12223 for (2989ds/164Mi)
% 8.87/2.59 % (12510)Refutation not found, incomplete strategy
% 8.87/2.59 % (12510)------------------------------
% 8.87/2.59 % (12510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.59 % (12510)Termination reason: Refutation not found, incomplete strategy
% 8.87/2.59
% 8.87/2.59
% 8.87/2.59 % (12510)Memory used [KB]: 6524
% 8.87/2.59 % (12510)Time elapsed: 0.041 s
% 8.87/2.59 % (12510)Instructions burned: 86 (million)
% 8.87/2.59 % (12510)------------------------------
% 8.87/2.59 % (12510)------------------------------
% 9.31/2.61 % (12514)Refutation not found, incomplete strategy
% 9.31/2.61 % (12514)------------------------------
% 9.31/2.61 % (12514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.61 % (12514)Termination reason: Refutation not found, incomplete strategy
% 9.31/2.61
% 9.31/2.61
% 9.31/2.61 % (12514)Memory used [KB]: 2046
% 9.31/2.61 % (12514)Time elapsed: 0.033 s
% 9.31/2.61 % (12514)Instructions burned: 74 (million)
% 9.31/2.61 % (12514)------------------------------
% 9.31/2.61 % (12514)------------------------------
% 9.31/2.61 % (12515)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_12223 for (2989ds/50Mi)
% 9.31/2.61 % (12502)Instruction limit reached!
% 9.31/2.61 % (12502)------------------------------
% 9.31/2.61 % (12502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.61 % (12502)Termination reason: Unknown
% 9.31/2.61 % (12502)Termination phase: Saturation
% 9.31/2.61
% 9.31/2.61 % (12502)Memory used [KB]: 10234
% 9.31/2.61 % (12502)Time elapsed: 0.217 s
% 9.31/2.61 % (12502)Instructions burned: 458 (million)
% 9.31/2.61 % (12502)------------------------------
% 9.31/2.61 % (12502)------------------------------
% 9.31/2.61 % (12511)Instruction limit reached!
% 9.31/2.61 % (12511)------------------------------
% 9.31/2.61 % (12511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.61 % (12511)Termination reason: Unknown
% 9.31/2.61 % (12511)Termination phase: Property scanning
% 9.31/2.61
% 9.31/2.61 % (12511)Memory used [KB]: 4221
% 9.31/2.61 % (12511)Time elapsed: 0.055 s
% 9.31/2.61 % (12511)Instructions burned: 114 (million)
% 9.31/2.61 % (12511)------------------------------
% 9.31/2.61 % (12511)------------------------------
% 9.31/2.63 % (12516)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_12223 for (2989ds/368Mi)
% 9.31/2.63 % (12517)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_12223 for (2989ds/1021Mi)
% 9.31/2.63 % (12518)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_12223 for (2989ds/267Mi)
% 9.31/2.63 % (12515)Instruction limit reached!
% 9.31/2.63 % (12515)------------------------------
% 9.31/2.63 % (12515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.63 % (12515)Termination reason: Unknown
% 9.31/2.63 % (12515)Termination phase: Property scanning
% 9.31/2.63
% 9.31/2.63 % (12515)Memory used [KB]: 1918
% 9.31/2.63 % (12515)Time elapsed: 0.024 s
% 9.31/2.63 % (12515)Instructions burned: 50 (million)
% 9.31/2.63 % (12515)------------------------------
% 9.31/2.63 % (12515)------------------------------
% 9.31/2.64 % (12513)Instruction limit reached!
% 9.31/2.64 % (12513)------------------------------
% 9.31/2.64 % (12513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.64 % (12513)Termination reason: Unknown
% 9.31/2.64 % (12513)Termination phase: Saturation
% 9.31/2.64
% 9.31/2.64 % (12513)Memory used [KB]: 6524
% 9.31/2.64 % (12513)Time elapsed: 0.076 s
% 9.31/2.64 % (12513)Instructions burned: 184 (million)
% 9.31/2.64 % (12513)------------------------------
% 9.31/2.64 % (12513)------------------------------
% 9.31/2.65 % (12519)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_12223 for (2989ds/204Mi)
% 9.31/2.66 % (12520)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_12223 for (2989ds/26Mi)
% 9.31/2.67 % (12520)Instruction limit reached!
% 9.31/2.67 % (12520)------------------------------
% 9.31/2.67 % (12520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.67 % (12520)Termination reason: Unknown
% 9.31/2.67 % (12520)Termination phase: shuffling
% 9.31/2.67
% 9.31/2.67 % (12520)Memory used [KB]: 1791
% 9.31/2.67 % (12520)Time elapsed: 0.014 s
% 9.31/2.67 % (12520)Instructions burned: 26 (million)
% 9.31/2.67 % (12520)------------------------------
% 9.31/2.67 % (12520)------------------------------
% 9.31/2.68 % (12521)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_12223 for (2988ds/53Mi)
% 9.83/2.71 % (12521)Instruction limit reached!
% 9.83/2.71 % (12521)------------------------------
% 9.83/2.71 % (12521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.83/2.71 % (12521)Termination reason: Unknown
% 9.83/2.71 % (12521)Termination phase: Property scanning
% 9.83/2.71
% 9.83/2.71 % (12521)Memory used [KB]: 1918
% 9.83/2.71 % (12521)Time elapsed: 0.025 s
% 9.83/2.71 % (12521)Instructions burned: 54 (million)
% 9.83/2.71 % (12521)------------------------------
% 9.83/2.71 % (12521)------------------------------
% 9.83/2.72 % (12522)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_12223 for (2988ds/4436Mi)
% 9.83/2.73 % (12518)Instruction limit reached!
% 9.83/2.73 % (12518)------------------------------
% 9.83/2.73 % (12518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.83/2.73 % (12518)Termination reason: Unknown
% 9.83/2.73 % (12518)Termination phase: Saturation
% 9.83/2.73
% 9.83/2.73 % (12518)Memory used [KB]: 7419
% 9.83/2.73 % (12518)Time elapsed: 0.104 s
% 9.83/2.73 % (12518)Instructions burned: 269 (million)
% 9.83/2.73 % (12518)------------------------------
% 9.83/2.73 % (12518)------------------------------
% 9.83/2.74 % (12519)Instruction limit reached!
% 9.83/2.74 % (12519)------------------------------
% 9.83/2.74 % (12519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.83/2.74 % (12519)Termination reason: Unknown
% 9.83/2.74 % (12519)Termination phase: Property scanning
% 9.83/2.74
% 9.83/2.74 % (12519)Memory used [KB]: 4477
% 9.83/2.74 % (12519)Time elapsed: 0.094 s
% 9.83/2.74 % (12519)Instructions burned: 205 (million)
% 9.83/2.74 % (12519)------------------------------
% 9.83/2.74 % (12519)------------------------------
% 9.83/2.75 % (12523)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_12223 for (2988ds/1539Mi)
% 9.83/2.76 % (12524)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_12223 for (2988ds/408Mi)
% 10.10/2.80 % (12505)Instruction limit reached!
% 10.10/2.80 % (12505)------------------------------
% 10.10/2.80 % (12505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.80 % (12505)Termination reason: Unknown
% 10.10/2.80 % (12505)Termination phase: Saturation
% 10.10/2.80
% 10.10/2.80 % (12505)Memory used [KB]: 7547
% 10.10/2.80 % (12505)Time elapsed: 0.389 s
% 10.10/2.80 % (12505)Instructions burned: 988 (million)
% 10.10/2.80 % (12505)------------------------------
% 10.10/2.80 % (12505)------------------------------
% 10.10/2.81 % (12516)Instruction limit reached!
% 10.10/2.81 % (12516)------------------------------
% 10.10/2.81 % (12516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.81 % (12516)Termination reason: Unknown
% 10.10/2.81 % (12516)Termination phase: Saturation
% 10.10/2.81
% 10.10/2.81 % (12516)Memory used [KB]: 11641
% 10.10/2.81 % (12516)Time elapsed: 0.182 s
% 10.10/2.81 % (12516)Instructions burned: 369 (million)
% 10.10/2.81 % (12516)------------------------------
% 10.10/2.81 % (12516)------------------------------
% 10.10/2.81 % (12525)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_12223 for (2987ds/5205Mi)
% 10.10/2.82 % (12526)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_12223 for (2987ds/1913Mi)
% 10.67/2.95 % (12524)Instruction limit reached!
% 10.67/2.95 % (12524)------------------------------
% 10.67/2.95 % (12524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.95 % (12524)Termination reason: Unknown
% 10.67/2.95 % (12524)Termination phase: Saturation
% 10.67/2.95
% 10.67/2.95 % (12524)Memory used [KB]: 11129
% 10.67/2.95 % (12524)Time elapsed: 0.198 s
% 10.67/2.95 % (12524)Instructions burned: 408 (million)
% 10.67/2.95 % (12524)------------------------------
% 10.67/2.95 % (12524)------------------------------
% 10.67/2.97 % (12527)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_12223 for (2985ds/4350Mi)
% 10.67/3.02 % (12512)Instruction limit reached!
% 10.67/3.02 % (12512)------------------------------
% 10.67/3.02 % (12512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/3.02 % (12512)Termination reason: Unknown
% 10.67/3.02 % (12512)Termination phase: Saturation
% 10.67/3.02
% 10.67/3.02 % (12512)Memory used [KB]: 12537
% 10.67/3.02 % (12512)Time elapsed: 0.460 s
% 10.67/3.02 % (12512)Instructions burned: 923 (million)
% 10.67/3.02 % (12512)------------------------------
% 10.67/3.02 % (12512)------------------------------
% 12.82/3.04 % (12528)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_12223 for (2985ds/68Mi)
% 12.82/3.07 % (12528)Instruction limit reached!
% 12.82/3.07 % (12528)------------------------------
% 12.82/3.07 % (12528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.07 % (12528)Termination reason: Unknown
% 12.82/3.07 % (12528)Termination phase: Preprocessing 3
% 12.82/3.07
% 12.82/3.07 % (12528)Memory used [KB]: 3070
% 12.82/3.07 % (12528)Time elapsed: 0.035 s
% 12.82/3.07 % (12528)Instructions burned: 69 (million)
% 12.82/3.07 % (12528)------------------------------
% 12.82/3.07 % (12528)------------------------------
% 12.82/3.09 % (12529)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_12223 for (2984ds/358Mi)
% 12.82/3.12 % (12517)Instruction limit reached!
% 12.82/3.12 % (12517)------------------------------
% 12.82/3.12 % (12517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.12 % (12517)Termination reason: Unknown
% 12.82/3.12 % (12517)Termination phase: Saturation
% 12.82/3.12
% 12.82/3.12 % (12517)Memory used [KB]: 12920
% 12.82/3.12 % (12517)Time elapsed: 0.488 s
% 12.82/3.12 % (12517)Instructions burned: 1021 (million)
% 12.82/3.12 % (12517)------------------------------
% 12.82/3.12 % (12517)------------------------------
% 13.51/3.13 % (12530)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_12223 for (2984ds/31Mi)
% 13.51/3.15 % (12530)Instruction limit reached!
% 13.51/3.15 % (12530)------------------------------
% 13.51/3.15 % (12530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.51/3.15 % (12530)Termination reason: Unknown
% 13.51/3.15 % (12530)Termination phase: Property scanning
% 13.51/3.15
% 13.51/3.15 % (12530)Memory used [KB]: 2174
% 13.51/3.15 % (12530)Time elapsed: 0.017 s
% 13.51/3.15 % (12530)Instructions burned: 31 (million)
% 13.51/3.15 % (12530)------------------------------
% 13.51/3.15 % (12530)------------------------------
% 13.51/3.16 % (12531)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_12223 for (2984ds/279Mi)
% 13.89/3.26 % (12529)Instruction limit reached!
% 13.89/3.26 % (12529)------------------------------
% 13.89/3.26 % (12529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.89/3.26 % (12529)Termination reason: Unknown
% 13.89/3.26 % (12529)Termination phase: Saturation
% 13.89/3.26
% 13.89/3.26 % (12529)Memory used [KB]: 9466
% 13.89/3.26 % (12529)Time elapsed: 0.169 s
% 13.89/3.26 % (12529)Instructions burned: 359 (million)
% 13.89/3.26 % (12529)------------------------------
% 13.89/3.26 % (12529)------------------------------
% 13.89/3.27 % (12531)Instruction limit reached!
% 13.89/3.27 % (12531)------------------------------
% 13.89/3.27 % (12531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.89/3.27 % (12531)Termination reason: Unknown
% 13.89/3.27 % (12531)Termination phase: Saturation
% 13.89/3.27
% 13.89/3.27 % (12531)Memory used [KB]: 7547
% 13.89/3.27 % (12531)Time elapsed: 0.111 s
% 13.89/3.27 % (12531)Instructions burned: 281 (million)
% 13.89/3.27 % (12531)------------------------------
% 13.89/3.27 % (12531)------------------------------
% 13.89/3.27 % (12532)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_12223 for (2982ds/258Mi)
% 13.89/3.29 % (12533)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_12223 for (2982ds/26Mi)
% 14.70/3.30 % (12533)Instruction limit reached!
% 14.70/3.30 % (12533)------------------------------
% 14.70/3.30 % (12533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.30 % (12533)Termination reason: Unknown
% 14.70/3.30 % (12533)Termination phase: shuffling
% 14.70/3.30
% 14.70/3.30 % (12533)Memory used [KB]: 1791
% 14.70/3.30 % (12533)Time elapsed: 0.013 s
% 14.70/3.30 % (12533)Instructions burned: 26 (million)
% 14.70/3.30 % (12533)------------------------------
% 14.70/3.30 % (12533)------------------------------
% 14.70/3.32 % (12534)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_12223 for (2982ds/995Mi)
% 15.24/3.40 % (12532)Instruction limit reached!
% 15.24/3.40 % (12532)------------------------------
% 15.24/3.40 % (12532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.24/3.40 % (12532)Termination reason: Unknown
% 15.24/3.40 % (12532)Termination phase: Saturation
% 15.24/3.40
% 15.24/3.40 % (12532)Memory used [KB]: 9722
% 15.24/3.40 % (12532)Time elapsed: 0.127 s
% 15.24/3.40 % (12532)Instructions burned: 259 (million)
% 15.24/3.40 % (12532)------------------------------
% 15.24/3.40 % (12532)------------------------------
% 15.24/3.42 % (12535)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_12223 for (2981ds/373Mi)
% 15.87/3.51 % (12523)Instruction limit reached!
% 15.87/3.51 % (12523)------------------------------
% 15.87/3.51 % (12523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.51 % (12523)Termination reason: Unknown
% 15.87/3.51 % (12523)Termination phase: Saturation
% 15.87/3.51
% 15.87/3.51 % (12523)Memory used [KB]: 12665
% 15.87/3.51 % (12523)Time elapsed: 0.758 s
% 15.87/3.51 % (12523)Instructions burned: 1539 (million)
% 15.87/3.51 % (12523)------------------------------
% 15.87/3.51 % (12523)------------------------------
% 15.87/3.52 % (12536)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_12223 for (2980ds/253Mi)
% 16.29/3.60 % (12535)Instruction limit reached!
% 16.29/3.60 % (12535)------------------------------
% 16.29/3.60 % (12535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.60 % (12535)Termination reason: Unknown
% 16.29/3.60 % (12535)Termination phase: Saturation
% 16.29/3.60
% 16.29/3.60 % (12535)Memory used [KB]: 9978
% 16.29/3.60 % (12535)Time elapsed: 0.204 s
% 16.29/3.60 % (12535)Instructions burned: 374 (million)
% 16.29/3.60 % (12535)------------------------------
% 16.29/3.60 % (12535)------------------------------
% 16.29/3.61 % (12537)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_12223 for (2979ds/832Mi)
% 16.29/3.62 % (12536)Instruction limit reached!
% 16.29/3.62 % (12536)------------------------------
% 16.29/3.62 % (12536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.62 % (12536)Termination reason: Unknown
% 16.29/3.62 % (12536)Termination phase: Saturation
% 16.29/3.62
% 16.29/3.62 % (12536)Memory used [KB]: 6780
% 16.29/3.62 % (12536)Time elapsed: 0.099 s
% 16.29/3.62 % (12536)Instructions burned: 253 (million)
% 16.29/3.62 % (12536)------------------------------
% 16.29/3.62 % (12536)------------------------------
% 16.29/3.64 % (12538)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_12223 for (2979ds/668Mi)
% 16.29/3.68 % (12534)Instruction limit reached!
% 16.29/3.68 % (12534)------------------------------
% 16.29/3.68 % (12534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.68 % (12534)Termination reason: Unknown
% 16.29/3.68 % (12534)Termination phase: Saturation
% 16.29/3.68
% 16.29/3.68 % (12534)Memory used [KB]: 6652
% 16.29/3.68 % (12534)Time elapsed: 0.360 s
% 16.29/3.68 % (12534)Instructions burned: 996 (million)
% 16.29/3.68 % (12534)------------------------------
% 16.29/3.68 % (12534)------------------------------
% 16.29/3.69 % (12539)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_12223 for (2978ds/40Mi)
% 17.37/3.71 % (12539)Instruction limit reached!
% 17.37/3.71 % (12539)------------------------------
% 17.37/3.71 % (12539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.37/3.71 % (12539)Termination reason: Unknown
% 17.37/3.71 % (12539)Termination phase: Property scanning
% 17.37/3.71
% 17.37/3.71 % (12539)Memory used [KB]: 1918
% 17.37/3.71 % (12539)Time elapsed: 0.019 s
% 17.37/3.71 % (12539)Instructions burned: 40 (million)
% 17.37/3.71 % (12539)------------------------------
% 17.37/3.71 % (12539)------------------------------
% 17.37/3.73 % (12540)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_12223 for (2978ds/294Mi)
% 17.37/3.74 % (12537)Refutation not found, incomplete strategy
% 17.37/3.74 % (12537)------------------------------
% 17.37/3.74 % (12537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.37/3.74 % (12537)Termination reason: Refutation not found, incomplete strategy
% 17.37/3.74
% 17.37/3.74
% 17.37/3.74 % (12537)Memory used [KB]: 9594
% 17.37/3.74 % (12537)Time elapsed: 0.147 s
% 17.37/3.74 % (12537)Instructions burned: 264 (million)
% 17.37/3.74 % (12537)------------------------------
% 17.37/3.74 % (12537)------------------------------
% 17.37/3.76 % (12526)Instruction limit reached!
% 17.37/3.76 % (12526)------------------------------
% 17.37/3.76 % (12526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.37/3.76 % (12526)Termination reason: Unknown
% 17.37/3.76 % (12526)Termination phase: Saturation
% 17.37/3.76
% 17.37/3.76 % (12526)Memory used [KB]: 6012
% 17.37/3.76 % (12526)Time elapsed: 0.942 s
% 17.37/3.76 % (12526)Instructions burned: 1913 (million)
% 17.37/3.76 % (12526)------------------------------
% 17.37/3.76 % (12526)------------------------------
% 17.37/3.77 % (12542)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_12223 for (2978ds/187Mi)
% 17.37/3.78 % (12549)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_12223 for (2977ds/371Mi)
% 17.93/3.80 % (12549)Refutation not found, incomplete strategy
% 17.93/3.80 % (12549)------------------------------
% 17.93/3.80 % (12549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/3.80 % (12549)Termination reason: Refutation not found, incomplete strategy
% 17.93/3.80
% 17.93/3.80
% 17.93/3.80 % (12549)Memory used [KB]: 6652
% 17.93/3.80 % (12549)Time elapsed: 0.021 s
% 17.93/3.80 % (12549)Instructions burned: 39 (million)
% 17.93/3.80 % (12549)------------------------------
% 17.93/3.80 % (12549)------------------------------
% 17.93/3.82 % (12559)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_12223 for (2977ds/1827Mi)
% 17.93/3.83 % (12540)Instruction limit reached!
% 17.93/3.83 % (12540)------------------------------
% 17.93/3.83 % (12540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/3.83 % (12540)Termination reason: Unknown
% 17.93/3.83 % (12540)Termination phase: Saturation
% 17.93/3.83
% 17.93/3.83 % (12540)Memory used [KB]: 7547
% 17.93/3.83 % (12540)Time elapsed: 0.106 s
% 17.93/3.83 % (12540)Instructions burned: 296 (million)
% 17.93/3.83 % (12540)------------------------------
% 17.93/3.83 % (12540)------------------------------
% 17.93/3.85 % (12542)Instruction limit reached!
% 17.93/3.85 % (12542)------------------------------
% 17.93/3.85 % (12542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/3.85 % (12542)Termination reason: Unknown
% 17.93/3.85 % (12542)Termination phase: Property scanning
% 17.93/3.85
% 17.93/3.85 % (12542)Memory used [KB]: 4733
% 17.93/3.85 % (12542)Time elapsed: 0.080 s
% 17.93/3.85 % (12542)Instructions burned: 187 (million)
% 17.93/3.85 % (12542)------------------------------
% 17.93/3.85 % (12542)------------------------------
% 17.93/3.85 % (12560)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_12223 for (2977ds/70Mi)
% 17.93/3.86 % (12561)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_12223 for (2976ds/316Mi)
% 17.93/3.88 % (12560)Instruction limit reached!
% 17.93/3.88 % (12560)------------------------------
% 17.93/3.88 % (12560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/3.88 % (12560)Termination reason: Unknown
% 17.93/3.88 % (12560)Termination phase: Property scanning
% 17.93/3.88
% 17.93/3.88 % (12560)Memory used [KB]: 1918
% 17.93/3.88 % (12560)Time elapsed: 0.032 s
% 17.93/3.88 % (12560)Instructions burned: 71 (million)
% 17.93/3.88 % (12560)------------------------------
% 17.93/3.88 % (12560)------------------------------
% 17.93/3.88 % (12538)Instruction limit reached!
% 17.93/3.88 % (12538)------------------------------
% 17.93/3.88 % (12538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.93/3.88 % (12538)Termination reason: Unknown
% 17.93/3.88 % (12538)Termination phase: Saturation
% 17.93/3.88
% 17.93/3.88 % (12538)Memory used [KB]: 11129
% 17.93/3.88 % (12538)Time elapsed: 0.249 s
% 17.93/3.88 % (12538)Instructions burned: 668 (million)
% 17.93/3.88 % (12538)------------------------------
% 17.93/3.88 % (12538)------------------------------
% 17.93/3.90 % (12562)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_12223 for (2976ds/932Mi)
% 18.79/3.90 % (12563)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_12223 for (2976ds/4714Mi)
% 18.79/3.99 % (12561)Instruction limit reached!
% 18.79/3.99 % (12561)------------------------------
% 18.79/3.99 % (12561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.79/3.99 % (12561)Termination reason: Unknown
% 18.79/3.99 % (12561)Termination phase: Saturation
% 18.79/3.99
% 18.79/3.99 % (12561)Memory used [KB]: 7036
% 18.79/3.99 % (12561)Time elapsed: 0.132 s
% 18.79/3.99 % (12561)Instructions burned: 318 (million)
% 18.79/3.99 % (12561)------------------------------
% 18.79/3.99 % (12561)------------------------------
% 18.79/4.01 % (12564)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_12223 for (2975ds/8250Mi)
% 21.03/4.25 % (12562)Instruction limit reached!
% 21.03/4.25 % (12562)------------------------------
% 21.03/4.25 % (12562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.03/4.25 % (12562)Termination reason: Unknown
% 21.03/4.25 % (12562)Termination phase: Saturation
% 21.03/4.25
% 21.03/4.25 % (12562)Memory used [KB]: 8059
% 21.03/4.25 % (12562)Time elapsed: 0.353 s
% 21.03/4.25 % (12562)Instructions burned: 933 (million)
% 21.03/4.25 % (12562)------------------------------
% 21.03/4.25 % (12562)------------------------------
% 21.03/4.26 % (12565)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_12223 for (2972ds/770Mi)
% 21.03/4.28 % (12565)Refutation not found, incomplete strategy
% 21.03/4.28 % (12565)------------------------------
% 21.03/4.28 % (12565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.03/4.28 % (12565)Termination reason: Refutation not found, incomplete strategy
% 21.03/4.28
% 21.03/4.28
% 21.03/4.28 % (12565)Memory used [KB]: 6652
% 21.03/4.28 % (12565)Time elapsed: 0.020 s
% 21.03/4.28 % (12565)Instructions burned: 38 (million)
% 21.03/4.28 % (12565)------------------------------
% 21.03/4.28 % (12565)------------------------------
% 21.73/4.30 % (12566)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_12223 for (2972ds/794Mi)
% 23.54/4.68 % (12566)Instruction limit reached!
% 23.54/4.68 % (12566)------------------------------
% 23.54/4.68 % (12566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.54/4.68 % (12566)Termination reason: Unknown
% 23.54/4.68 % (12566)Termination phase: Saturation
% 23.54/4.68
% 23.54/4.68 % (12566)Memory used [KB]: 7547
% 23.54/4.68 % (12566)Time elapsed: 0.380 s
% 23.54/4.68 % (12566)Instructions burned: 794 (million)
% 23.54/4.68 % (12566)------------------------------
% 23.54/4.68 % (12566)------------------------------
% 23.54/4.70 % (12567)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_12223 for (2968ds/464Mi)
% 24.53/4.70 % (12525)Instruction limit reached!
% 24.53/4.70 % (12525)------------------------------
% 24.53/4.70 % (12525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.53/4.70 % (12525)Termination reason: Unknown
% 24.53/4.70 % (12525)Termination phase: Saturation
% 24.53/4.70
% 24.53/4.70 % (12525)Memory used [KB]: 8315
% 24.53/4.70 % (12525)Time elapsed: 1.891 s
% 24.53/4.70 % (12525)Instructions burned: 5207 (million)
% 24.53/4.70 % (12525)------------------------------
% 24.53/4.70 % (12525)------------------------------
% 24.53/4.72 % (12568)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_12223 for (2968ds/1376Mi)
% 24.53/4.73 % (12559)Instruction limit reached!
% 24.53/4.73 % (12559)------------------------------
% 24.53/4.73 % (12559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.53/4.73 % (12559)Termination reason: Unknown
% 24.53/4.73 % (12559)Termination phase: Saturation
% 24.53/4.73
% 24.53/4.73 % (12559)Memory used [KB]: 13176
% 24.53/4.73 % (12559)Time elapsed: 0.914 s
% 24.53/4.73 % (12559)Instructions burned: 1827 (million)
% 24.53/4.73 % (12559)------------------------------
% 24.53/4.73 % (12559)------------------------------
% 24.53/4.75 % (12569)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_12223 for (2968ds/906Mi)
% 25.38/4.91 % (12567)Instruction limit reached!
% 25.38/4.91 % (12567)------------------------------
% 25.38/4.91 % (12567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.38/4.91 % (12567)Termination reason: Unknown
% 25.38/4.91 % (12567)Termination phase: Saturation
% 25.38/4.91
% 25.38/4.91 % (12567)Memory used [KB]: 11257
% 25.38/4.91 % (12567)Time elapsed: 0.220 s
% 25.38/4.91 % (12567)Instructions burned: 465 (million)
% 25.38/4.91 % (12567)------------------------------
% 25.38/4.91 % (12567)------------------------------
% 25.38/4.91 % (12522)Instruction limit reached!
% 25.38/4.91 % (12522)------------------------------
% 25.38/4.91 % (12522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.38/4.91 % (12522)Termination reason: Unknown
% 25.38/4.91 % (12522)Termination phase: Saturation
% 25.38/4.91
% 25.38/4.91 % (12522)Memory used [KB]: 15095
% 25.38/4.91 % (12522)Time elapsed: 2.192 s
% 25.38/4.91 % (12522)Instructions burned: 4436 (million)
% 25.38/4.91 % (12522)------------------------------
% 25.38/4.91 % (12522)------------------------------
% 25.38/4.93 % (12571)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_12223 for (2966ds/865Mi)
% 25.38/4.93 % (12570)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_12223 for (2966ds/434Mi)
% 25.38/4.95 % (12570)Refutation not found, incomplete strategy
% 25.38/4.95 % (12570)------------------------------
% 25.38/4.95 % (12570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.38/4.95 % (12570)Termination reason: Refutation not found, incomplete strategy
% 25.38/4.95
% 25.38/4.95
% 25.38/4.95 % (12570)Memory used [KB]: 6652
% 25.38/4.95 % (12570)Time elapsed: 0.020 s
% 25.38/4.95 % (12570)Instructions burned: 37 (million)
% 25.38/4.95 % (12570)------------------------------
% 25.38/4.95 % (12570)------------------------------
% 25.38/4.97 % (12572)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_12223 for (2965ds/593Mi)
% 26.82/5.04 % (12527)Instruction limit reached!
% 26.82/5.04 % (12527)------------------------------
% 26.82/5.04 % (12527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.82/5.04 % (12527)Termination reason: Unknown
% 26.82/5.04 % (12527)Termination phase: Saturation
% 26.82/5.04
% 26.82/5.04 % (12527)Memory used [KB]: 18293
% 26.82/5.04 % (12527)Time elapsed: 2.067 s
% 26.82/5.04 % (12527)Instructions burned: 4351 (million)
% 26.82/5.04 % (12527)------------------------------
% 26.82/5.04 % (12527)------------------------------
% 26.82/5.06 % (12573)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_12223 for (2965ds/443Mi)
% 27.45/5.19 % (12572)Instruction limit reached!
% 27.45/5.19 % (12572)------------------------------
% 27.45/5.19 % (12572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.19 % (12572)Termination reason: Unknown
% 27.45/5.19 % (12572)Termination phase: Saturation
% 27.45/5.19
% 27.45/5.19 % (12572)Memory used [KB]: 6908
% 27.45/5.19 % (12572)Time elapsed: 0.223 s
% 27.45/5.19 % (12572)Instructions burned: 595 (million)
% 27.45/5.19 % (12572)------------------------------
% 27.45/5.19 % (12572)------------------------------
% 27.45/5.19 % (12569)Instruction limit reached!
% 27.45/5.19 % (12569)------------------------------
% 27.45/5.19 % (12569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.45/5.19 % (12569)Termination reason: Unknown
% 27.45/5.19 % (12569)Termination phase: Saturation
% 27.45/5.19
% 27.45/5.19 % (12569)Memory used [KB]: 16119
% 27.45/5.19 % (12569)Time elapsed: 0.442 s
% 27.45/5.19 % (12569)Instructions burned: 907 (million)
% 27.45/5.19 % (12569)------------------------------
% 27.45/5.19 % (12569)------------------------------
% 27.88/5.20 % (12574)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_12223 for (2963ds/594Mi)
% 27.88/5.20 % (12575)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_12223 for (2963ds/327Mi)
% 27.88/5.26 % (12568)Instruction limit reached!
% 27.88/5.26 % (12568)------------------------------
% 27.88/5.26 % (12568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.26 % (12568)Termination reason: Unknown
% 27.88/5.26 % (12568)Termination phase: Saturation
% 27.88/5.26
% 27.88/5.26 % (12568)Memory used [KB]: 8059
% 27.88/5.26 % (12568)Time elapsed: 0.541 s
% 27.88/5.26 % (12568)Instructions burned: 1377 (million)
% 27.88/5.26 % (12568)------------------------------
% 27.88/5.26 % (12568)------------------------------
% 27.88/5.26 % (12571)Instruction limit reached!
% 27.88/5.26 % (12571)------------------------------
% 27.88/5.26 % (12571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.26 % (12571)Termination reason: Unknown
% 27.88/5.26 % (12571)Termination phase: Saturation
% 27.88/5.26
% 27.88/5.26 % (12571)Memory used [KB]: 7036
% 27.88/5.26 % (12571)Time elapsed: 0.336 s
% 27.88/5.26 % (12571)Instructions burned: 865 (million)
% 27.88/5.26 % (12571)------------------------------
% 27.88/5.26 % (12571)------------------------------
% 27.88/5.27 % (12573)Instruction limit reached!
% 27.88/5.27 % (12573)------------------------------
% 27.88/5.27 % (12573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.27 % (12573)Termination reason: Unknown
% 27.88/5.27 % (12573)Termination phase: Saturation
% 27.88/5.27
% 27.88/5.27 % (12573)Memory used [KB]: 11257
% 27.88/5.27 % (12573)Time elapsed: 0.216 s
% 27.88/5.27 % (12573)Instructions burned: 444 (million)
% 27.88/5.27 % (12573)------------------------------
% 27.88/5.27 % (12573)------------------------------
% 27.88/5.28 % (12576)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_12223 for (2962ds/5411Mi)
% 27.88/5.28 % (12577)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_12223 for (2962ds/1762Mi)
% 27.88/5.29 % (12578)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_12223 for (2962ds/96Mi)
% 27.88/5.29 % (12576)Refutation not found, incomplete strategy
% 27.88/5.29 % (12576)------------------------------
% 27.88/5.29 % (12576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.29 % (12576)Termination reason: Refutation not found, incomplete strategy
% 27.88/5.29
% 27.88/5.29
% 27.88/5.29 % (12576)Memory used [KB]: 6652
% 27.88/5.29 % (12576)Time elapsed: 0.020 s
% 27.88/5.29 % (12576)Instructions burned: 37 (million)
% 27.88/5.29 % (12576)------------------------------
% 27.88/5.29 % (12576)------------------------------
% 28.49/5.31 % (12579)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_12223 for (2962ds/503Mi)
% 28.49/5.33 % (12578)Instruction limit reached!
% 28.49/5.33 % (12578)------------------------------
% 28.49/5.33 % (12578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.49/5.33 % (12578)Termination reason: Unknown
% 28.49/5.33 % (12578)Termination phase: Saturation
% 28.49/5.33
% 28.49/5.33 % (12578)Memory used [KB]: 6524
% 28.49/5.33 % (12578)Time elapsed: 0.042 s
% 28.49/5.33 % (12578)Instructions burned: 97 (million)
% 28.49/5.33 % (12578)------------------------------
% 28.49/5.33 % (12578)------------------------------
% 28.49/5.33 % (12579)Refutation not found, incomplete strategy
% 28.49/5.33 % (12579)------------------------------
% 28.49/5.33 % (12579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.49/5.33 % (12579)Termination reason: Refutation not found, incomplete strategy
% 28.49/5.33
% 28.49/5.33
% 28.49/5.33 % (12579)Memory used [KB]: 6652
% 28.49/5.33 % (12579)Time elapsed: 0.020 s
% 28.49/5.33 % (12579)Instructions burned: 37 (million)
% 28.49/5.33 % (12579)------------------------------
% 28.49/5.33 % (12579)------------------------------
% 28.49/5.34 % (12580)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_12223 for (2962ds/90Mi)
% 28.49/5.35 % (12581)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_12223 for (2962ds/593Mi)
% 28.49/5.36 % (12575)Instruction limit reached!
% 28.49/5.36 % (12575)------------------------------
% 28.49/5.36 % (12575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.49/5.36 % (12575)Termination reason: Unknown
% 28.49/5.36 % (12575)Termination phase: Saturation
% 28.49/5.36
% 28.49/5.36 % (12575)Memory used [KB]: 10234
% 28.49/5.36 % (12575)Time elapsed: 0.161 s
% 28.49/5.36 % (12575)Instructions burned: 328 (million)
% 28.49/5.36 % (12575)------------------------------
% 28.49/5.36 % (12575)------------------------------
% 28.49/5.38 % (12582)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_12223 for (2961ds/1512Mi)
% 28.49/5.38 % (12580)Instruction limit reached!
% 28.49/5.38 % (12580)------------------------------
% 28.49/5.38 % (12580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.49/5.38 % (12580)Termination reason: Unknown
% 28.49/5.38 % (12580)Termination phase: Preprocessing 3
% 28.49/5.38
% 28.49/5.38 % (12580)Memory used [KB]: 4093
% 28.49/5.38 % (12580)Time elapsed: 0.044 s
% 28.49/5.38 % (12580)Instructions burned: 91 (million)
% 28.49/5.38 % (12580)------------------------------
% 28.49/5.38 % (12580)------------------------------
% 29.02/5.40 % (12583)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_12223 for (2961ds/569Mi)
% 29.02/5.49 % (12574)Instruction limit reached!
% 29.02/5.49 % (12574)------------------------------
% 29.02/5.49 % (12574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.02/5.49 % (12574)Termination reason: Unknown
% 29.02/5.49 % (12574)Termination phase: Saturation
% 29.02/5.49
% 29.02/5.49 % (12574)Memory used [KB]: 9722
% 29.02/5.49 % (12574)Time elapsed: 0.285 s
% 29.02/5.49 % (12574)Instructions burned: 595 (million)
% 29.02/5.49 % (12574)------------------------------
% 29.02/5.49 % (12574)------------------------------
% 29.52/5.51 % (12582)Refutation not found, incomplete strategy
% 29.52/5.51 % (12582)------------------------------
% 29.52/5.51 % (12582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.52/5.51 % (12582)Termination reason: Refutation not found, incomplete strategy
% 29.52/5.51
% 29.52/5.51
% 29.52/5.51 % (12582)Memory used [KB]: 9722
% 29.52/5.51 % (12582)Time elapsed: 0.125 s
% 29.52/5.51 % (12582)Instructions burned: 259 (million)
% 29.52/5.51 % (12582)------------------------------
% 29.52/5.51 % (12582)------------------------------
% 29.52/5.51 % (12584)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_12223 for (2960ds/501Mi)
% 29.52/5.52 % (12585)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_12223 for (2960ds/562Mi)
% 29.86/5.61 % (12583)Instruction limit reached!
% 29.86/5.61 % (12583)------------------------------
% 29.86/5.61 % (12583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.86/5.61 % (12583)Termination reason: Unknown
% 29.86/5.61 % (12583)Termination phase: Saturation
% 29.86/5.61
% 29.86/5.61 % (12583)Memory used [KB]: 6652
% 29.86/5.61 % (12583)Time elapsed: 0.212 s
% 29.86/5.61 % (12583)Instructions burned: 569 (million)
% 29.86/5.61 % (12583)------------------------------
% 29.86/5.61 % (12583)------------------------------
% 29.86/5.63 % (12586)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12223 for (2959ds/406Mi)
% 29.86/5.63 % (12581)Instruction limit reached!
% 29.86/5.63 % (12581)------------------------------
% 29.86/5.63 % (12581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.86/5.63 % (12581)Termination reason: Unknown
% 29.86/5.63 % (12581)Termination phase: Saturation
% 29.86/5.63
% 29.86/5.63 % (12581)Memory used [KB]: 11001
% 29.86/5.63 % (12581)Time elapsed: 0.284 s
% 29.86/5.63 % (12581)Instructions burned: 594 (million)
% 29.86/5.63 % (12581)------------------------------
% 29.86/5.63 % (12581)------------------------------
% 29.86/5.65 % (12592)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_12223 for (2959ds/582Mi)
% 29.86/5.65 % (12563)Instruction limit reached!
% 29.86/5.65 % (12563)------------------------------
% 29.86/5.65 % (12563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.86/5.65 % (12563)Termination reason: Unknown
% 29.86/5.65 % (12563)Termination phase: Saturation
% 29.86/5.65
% 29.86/5.65 % (12563)Memory used [KB]: 9850
% 29.86/5.65 % (12563)Time elapsed: 1.756 s
% 29.86/5.65 % (12563)Instructions burned: 4714 (million)
% 29.86/5.65 % (12563)------------------------------
% 29.86/5.65 % (12563)------------------------------
% 29.86/5.67 % (12609)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_12223 for (2959ds/456Mi)
% 30.56/5.74 % (12584)Instruction limit reached!
% 30.56/5.74 % (12584)------------------------------
% 30.56/5.74 % (12584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.74 % (12584)Termination reason: Unknown
% 30.56/5.74 % (12584)Termination phase: Saturation
% 30.56/5.74
% 30.56/5.74 % (12584)Memory used [KB]: 11129
% 30.56/5.74 % (12584)Time elapsed: 0.234 s
% 30.56/5.74 % (12584)Instructions burned: 502 (million)
% 30.56/5.74 % (12584)------------------------------
% 30.56/5.74 % (12584)------------------------------
% 30.56/5.74 % (12585)Instruction limit reached!
% 30.56/5.74 % (12585)------------------------------
% 30.56/5.74 % (12585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.74 % (12585)Termination reason: Unknown
% 30.56/5.74 % (12585)Termination phase: Saturation
% 30.56/5.74
% 30.56/5.74 % (12585)Memory used [KB]: 7164
% 30.56/5.74 % (12585)Time elapsed: 0.219 s
% 30.56/5.74 % (12585)Instructions burned: 562 (million)
% 30.56/5.74 % (12585)------------------------------
% 30.56/5.74 % (12585)------------------------------
% 30.56/5.76 % (12615)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_12223 for (2958ds/1335Mi)
% 30.56/5.76 % (12614)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_12223 for (2958ds/393Mi)
% 30.56/5.79 % (12615)Refutation not found, incomplete strategy
% 30.56/5.79 % (12615)------------------------------
% 30.56/5.79 % (12615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.79 % (12615)Termination reason: Refutation not found, incomplete strategy
% 30.56/5.79
% 30.56/5.79
% 30.56/5.79 % (12615)Memory used [KB]: 6524
% 30.56/5.79 % (12615)Time elapsed: 0.034 s
% 30.56/5.79 % (12615)Instructions burned: 76 (million)
% 30.56/5.79 % (12615)------------------------------
% 30.56/5.79 % (12615)------------------------------
% 30.56/5.79 % (12586)Instruction limit reached!
% 30.56/5.79 % (12586)------------------------------
% 30.56/5.79 % (12586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.56/5.79 % (12586)Termination reason: Unknown
% 30.56/5.79 % (12586)Termination phase: Saturation
% 30.56/5.79
% 30.56/5.79 % (12586)Memory used [KB]: 10234
% 30.56/5.79 % (12586)Time elapsed: 0.167 s
% 30.56/5.79 % (12586)Instructions burned: 407 (million)
% 30.56/5.79 % (12586)------------------------------
% 30.56/5.79 % (12586)------------------------------
% 31.38/5.81 % (12616)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_12223 for (2957ds/3373Mi)
% 31.38/5.81 % (12617)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_12223 for (2957ds/474Mi)
% 31.38/5.87 % (12592)Instruction limit reached!
% 31.38/5.87 % (12592)------------------------------
% 31.38/5.87 % (12592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.38/5.87 % (12592)Termination reason: Unknown
% 31.38/5.87 % (12592)Termination phase: Saturation
% 31.38/5.87
% 31.38/5.87 % (12592)Memory used [KB]: 9850
% 31.38/5.87 % (12592)Time elapsed: 0.244 s
% 31.38/5.87 % (12592)Instructions burned: 584 (million)
% 31.38/5.87 % (12592)------------------------------
% 31.38/5.87 % (12592)------------------------------
% 31.38/5.88 % (12618)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_12223 for (2956ds/157Mi)
% 31.38/5.88 % (12609)Instruction limit reached!
% 31.38/5.88 % (12609)------------------------------
% 31.38/5.88 % (12609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.38/5.88 % (12609)Termination reason: Unknown
% 31.38/5.88 % (12609)Termination phase: Saturation
% 31.38/5.88
% 31.38/5.88 % (12609)Memory used [KB]: 11513
% 31.38/5.88 % (12609)Time elapsed: 0.212 s
% 31.38/5.88 % (12609)Instructions burned: 458 (million)
% 31.38/5.88 % (12609)------------------------------
% 31.38/5.88 % (12609)------------------------------
% 31.38/5.89 % (12619)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_12223 for (2956ds/590Mi)
% 31.94/5.92 % (12614)Instruction limit reached!
% 31.94/5.92 % (12614)------------------------------
% 31.94/5.92 % (12614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.92 % (12614)Termination reason: Unknown
% 31.94/5.92 % (12614)Termination phase: Saturation
% 31.94/5.92
% 31.94/5.92 % (12614)Memory used [KB]: 6780
% 31.94/5.92 % (12614)Time elapsed: 0.161 s
% 31.94/5.92 % (12614)Instructions burned: 394 (million)
% 31.94/5.92 % (12614)------------------------------
% 31.94/5.92 % (12614)------------------------------
% 31.94/5.93 % (12620)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_12223 for (2956ds/104Mi)
% 31.94/5.94 % (12577)Instruction limit reached!
% 31.94/5.94 % (12577)------------------------------
% 31.94/5.94 % (12577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.94 % (12577)Termination reason: Unknown
% 31.94/5.94 % (12577)Termination phase: Saturation
% 31.94/5.94
% 31.94/5.94 % (12577)Memory used [KB]: 14839
% 31.94/5.94 % (12577)Time elapsed: 0.657 s
% 31.94/5.94 % (12577)Instructions burned: 1765 (million)
% 31.94/5.94 % (12577)------------------------------
% 31.94/5.94 % (12577)------------------------------
% 31.94/5.95 % (12618)Instruction limit reached!
% 31.94/5.95 % (12618)------------------------------
% 31.94/5.95 % (12618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.95 % (12618)Termination reason: Unknown
% 31.94/5.95 % (12618)Termination phase: Saturation
% 31.94/5.95
% 31.94/5.95 % (12618)Memory used [KB]: 6524
% 31.94/5.95 % (12618)Time elapsed: 0.066 s
% 31.94/5.95 % (12618)Instructions burned: 160 (million)
% 31.94/5.95 % (12618)------------------------------
% 31.94/5.95 % (12618)------------------------------
% 31.94/5.95 % (12621)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_12223 for (2955ds/414Mi)
% 31.94/5.96 % (12622)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_12223 for (2955ds/715Mi)
% 31.94/5.98 % (12620)Instruction limit reached!
% 31.94/5.98 % (12620)------------------------------
% 31.94/5.98 % (12620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.98 % (12620)Termination reason: Unknown
% 31.94/5.98 % (12620)Termination phase: Property scanning
% 31.94/5.98
% 31.94/5.98 % (12620)Memory used [KB]: 4093
% 31.94/5.98 % (12620)Time elapsed: 0.051 s
% 31.94/5.98 % (12620)Instructions burned: 104 (million)
% 31.94/5.98 % (12620)------------------------------
% 31.94/5.98 % (12620)------------------------------
% 31.94/5.99 % (12617)Instruction limit reached!
% 31.94/5.99 % (12617)------------------------------
% 31.94/5.99 % (12617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.94/5.99 % (12617)Termination reason: Unknown
% 31.94/5.99 % (12617)Termination phase: Saturation
% 31.94/5.99
% 31.94/5.99 % (12617)Memory used [KB]: 7547
% 31.94/5.99 % (12617)Time elapsed: 0.182 s
% 31.94/5.99 % (12617)Instructions burned: 475 (million)
% 31.94/5.99 % (12617)------------------------------
% 31.94/5.99 % (12617)------------------------------
% 31.94/6.00 % (12623)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_12223 for (2955ds/961Mi)
% 31.94/6.01 % (12624)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_12223 for (2955ds/1213Mi)
% 33.79/6.09 % (12621)Instruction limit reached!
% 33.79/6.09 % (12621)------------------------------
% 33.79/6.09 % (12621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.79/6.09 % (12621)Termination reason: Unknown
% 33.79/6.09 % (12621)Termination phase: Saturation
% 33.79/6.09
% 33.79/6.09 % (12621)Memory used [KB]: 6652
% 33.79/6.09 % (12621)Time elapsed: 0.146 s
% 33.79/6.09 % (12621)Instructions burned: 414 (million)
% 33.79/6.09 % (12621)------------------------------
% 33.79/6.09 % (12621)------------------------------
% 33.79/6.10 % (12625)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_12223 for (2954ds/1979Mi)
% 34.50/6.15 % (12619)Instruction limit reached!
% 34.50/6.15 % (12619)------------------------------
% 34.50/6.15 % (12619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.50/6.15 % (12619)Termination reason: Unknown
% 34.50/6.15 % (12619)Termination phase: Saturation
% 34.50/6.15
% 34.50/6.15 % (12619)Memory used [KB]: 10234
% 34.50/6.15 % (12619)Time elapsed: 0.262 s
% 34.50/6.15 % (12619)Instructions burned: 590 (million)
% 34.50/6.15 % (12619)------------------------------
% 34.50/6.15 % (12619)------------------------------
% 34.50/6.17 % (12626)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_12223 for (2953ds/481Mi)
% 34.90/6.27 % (12622)Instruction limit reached!
% 34.90/6.27 % (12622)------------------------------
% 34.90/6.27 % (12622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.27 % (12622)Termination reason: Unknown
% 34.90/6.27 % (12622)Termination phase: Saturation
% 34.90/6.27
% 34.90/6.27 % (12622)Memory used [KB]: 6012
% 34.90/6.27 % (12622)Time elapsed: 0.315 s
% 34.90/6.27 % (12622)Instructions burned: 716 (million)
% 34.90/6.27 % (12622)------------------------------
% 34.90/6.27 % (12622)------------------------------
% 34.90/6.29 % (12627)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_12223 for (2952ds/783Mi)
% 35.39/6.31 % (12627)Refutation not found, incomplete strategy
% 35.39/6.31 % (12627)------------------------------
% 35.39/6.31 % (12627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.31 % (12627)Termination reason: Refutation not found, incomplete strategy
% 35.39/6.31
% 35.39/6.31
% 35.39/6.31 % (12627)Memory used [KB]: 6652
% 35.39/6.31 % (12627)Time elapsed: 0.021 s
% 35.39/6.31 % (12627)Instructions burned: 37 (million)
% 35.39/6.31 % (12627)------------------------------
% 35.39/6.31 % (12627)------------------------------
% 35.39/6.33 % (12628)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_12223 for (2952ds/432Mi)
% 35.39/6.35 % (12628)Refutation not found, incomplete strategy
% 35.39/6.35 % (12628)------------------------------
% 35.39/6.35 % (12628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.35 % (12628)Termination reason: Refutation not found, incomplete strategy
% 35.39/6.35
% 35.39/6.35
% 35.39/6.35 % (12628)Memory used [KB]: 6652
% 35.39/6.35 % (12628)Time elapsed: 0.020 s
% 35.39/6.35 % (12628)Instructions burned: 38 (million)
% 35.39/6.35 % (12628)------------------------------
% 35.39/6.35 % (12628)------------------------------
% 35.39/6.35 % (12626)Instruction limit reached!
% 35.39/6.35 % (12626)------------------------------
% 35.39/6.35 % (12626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.35 % (12626)Termination reason: Unknown
% 35.39/6.35 % (12626)Termination phase: Saturation
% 35.39/6.35
% 35.39/6.35 % (12626)Memory used [KB]: 7419
% 35.39/6.35 % (12626)Time elapsed: 0.181 s
% 35.39/6.35 % (12626)Instructions burned: 482 (million)
% 35.39/6.35 % (12626)------------------------------
% 35.39/6.35 % (12626)------------------------------
% 35.39/6.36 % (12629)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_12223 for (2951ds/1670Mi)
% 35.39/6.37 % (12630)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_12223 for (2951ds/90Mi)
% 36.06/6.41 % (12630)Instruction limit reached!
% 36.06/6.41 % (12630)------------------------------
% 36.06/6.41 % (12630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.41 % (12630)Termination reason: Unknown
% 36.06/6.41 % (12630)Termination phase: Preprocessing 3
% 36.06/6.41
% 36.06/6.41 % (12630)Memory used [KB]: 4093
% 36.06/6.41 % (12630)Time elapsed: 0.046 s
% 36.06/6.41 % (12630)Instructions burned: 92 (million)
% 36.06/6.41 % (12630)------------------------------
% 36.06/6.41 % (12630)------------------------------
% 36.06/6.42 % (12631)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_12223 for (2951ds/346Mi)
% 36.06/6.46 % (12623)Instruction limit reached!
% 36.06/6.46 % (12623)------------------------------
% 36.06/6.46 % (12623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.46 % (12623)Termination reason: Unknown
% 36.06/6.46 % (12623)Termination phase: Saturation
% 36.06/6.46
% 36.06/6.46 % (12623)Memory used [KB]: 11769
% 36.06/6.46 % (12623)Time elapsed: 0.467 s
% 36.06/6.46 % (12623)Instructions burned: 961 (million)
% 36.06/6.46 % (12623)------------------------------
% 36.06/6.46 % (12623)------------------------------
% 36.06/6.49 % (12632)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_12223 for (2950ds/401Mi)
% 36.49/6.54 % (12631)Instruction limit reached!
% 36.49/6.54 % (12631)------------------------------
% 36.49/6.54 % (12631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.49/6.54 % (12631)Termination reason: Unknown
% 36.49/6.54 % (12631)Termination phase: Saturation
% 36.49/6.54
% 36.49/6.54 % (12631)Memory used [KB]: 7419
% 36.49/6.54 % (12631)Time elapsed: 0.105 s
% 36.49/6.54 % (12631)Instructions burned: 349 (million)
% 36.49/6.54 % (12631)------------------------------
% 36.49/6.54 % (12631)------------------------------
% 36.49/6.55 % (12633)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_12223 for (2950ds/6454Mi)
% 36.91/6.60 % (12624)Instruction limit reached!
% 36.91/6.60 % (12624)------------------------------
% 36.91/6.60 % (12624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.91/6.60 % (12624)Termination reason: Unknown
% 36.91/6.60 % (12624)Termination phase: Saturation
% 36.91/6.60
% 36.91/6.60 % (12624)Memory used [KB]: 12409
% 36.91/6.60 % (12624)Time elapsed: 0.592 s
% 36.91/6.60 % (12624)Instructions burned: 1214 (million)
% 36.91/6.60 % (12624)------------------------------
% 36.91/6.60 % (12624)------------------------------
% 36.91/6.62 % (12634)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_12223 for (2949ds/283Mi)
% 36.91/6.63 % (12632)Instruction limit reached!
% 36.91/6.63 % (12632)------------------------------
% 36.91/6.63 % (12632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.91/6.63 % (12632)Termination reason: Unknown
% 36.91/6.63 % (12632)Termination phase: Saturation
% 36.91/6.63
% 36.91/6.63 % (12632)Memory used [KB]: 6652
% 36.91/6.63 % (12632)Time elapsed: 0.139 s
% 36.91/6.63 % (12632)Instructions burned: 402 (million)
% 36.91/6.63 % (12632)------------------------------
% 36.91/6.63 % (12632)------------------------------
% 36.91/6.64 % (12635)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_12223 for (2949ds/865Mi)
% 37.27/6.75 % (12634)Instruction limit reached!
% 37.27/6.75 % (12634)------------------------------
% 37.27/6.75 % (12634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.27/6.75 % (12634)Termination reason: Unknown
% 37.27/6.75 % (12634)Termination phase: Saturation
% 37.27/6.75
% 37.27/6.75 % (12634)Memory used [KB]: 10234
% 37.27/6.75 % (12634)Time elapsed: 0.136 s
% 37.27/6.75 % (12634)Instructions burned: 284 (million)
% 37.27/6.75 % (12634)------------------------------
% 37.27/6.75 % (12634)------------------------------
% 37.27/6.77 % (12636)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_12223 for (2947ds/4528Mi)
% 37.27/6.78 % (12635)Refutation not found, incomplete strategy
% 37.27/6.78 % (12635)------------------------------
% 37.27/6.78 % (12635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.27/6.78 % (12635)Termination reason: Refutation not found, incomplete strategy
% 37.27/6.78
% 37.27/6.78
% 37.27/6.78 % (12635)Memory used [KB]: 10746
% 37.27/6.78 % (12635)Time elapsed: 0.137 s
% 37.27/6.78 % (12635)Instructions burned: 355 (million)
% 37.27/6.78 % (12635)------------------------------
% 37.27/6.78 % (12635)------------------------------
% 37.27/6.79 % (12636)Refutation not found, incomplete strategy
% 37.27/6.79 % (12636)------------------------------
% 37.27/6.79 % (12636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.27/6.79 % (12636)Termination reason: Refutation not found, incomplete strategy
% 37.27/6.79
% 37.27/6.79
% 37.27/6.79 % (12636)Memory used [KB]: 2174
% 37.27/6.79 % (12636)Time elapsed: 0.020 s
% 37.27/6.79 % (12636)Instructions burned: 37 (million)
% 37.27/6.79 % (12636)------------------------------
% 37.27/6.79 % (12636)------------------------------
% 37.27/6.80 % (12637)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_12223 for (2947ds/1001Mi)
% 37.79/6.81 % (12638)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_12223 for (2947ds/102Mi)
% 37.79/6.85 % (12638)Instruction limit reached!
% 37.79/6.85 % (12638)------------------------------
% 37.79/6.85 % (12638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.79/6.85 % (12638)Termination reason: Unknown
% 37.79/6.85 % (12638)Termination phase: Saturation
% 37.79/6.85
% 37.79/6.85 % (12638)Memory used [KB]: 6524
% 37.79/6.85 % (12638)Time elapsed: 0.042 s
% 37.79/6.85 % (12638)Instructions burned: 103 (million)
% 37.79/6.85 % (12638)------------------------------
% 37.79/6.85 % (12638)------------------------------
% 37.79/6.86 % (12639)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_12223 for (2946ds/952Mi)
% 38.04/6.93 % (12625)Instruction limit reached!
% 38.04/6.93 % (12625)------------------------------
% 38.04/6.93 % (12625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.04/6.93 % (12625)Termination reason: Unknown
% 38.04/6.93 % (12625)Termination phase: Saturation
% 38.04/6.93
% 38.04/6.93 % (12625)Memory used [KB]: 12792
% 38.04/6.93 % (12625)Time elapsed: 0.827 s
% 38.04/6.93 % (12625)Instructions burned: 1980 (million)
% 38.04/6.93 % (12625)------------------------------
% 38.04/6.93 % (12625)------------------------------
% 38.04/6.95 % (12629)Instruction limit reached!
% 38.04/6.95 % (12629)------------------------------
% 38.04/6.95 % (12629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.04/6.95 % (12629)Termination reason: Unknown
% 38.04/6.95 % (12629)Termination phase: Saturation
% 38.04/6.95
% 38.04/6.95 % (12629)Memory used [KB]: 6652
% 38.04/6.95 % (12629)Time elapsed: 0.587 s
% 38.04/6.95 % (12629)Instructions burned: 1671 (million)
% 38.04/6.95 % (12629)------------------------------
% 38.04/6.95 % (12629)------------------------------
% 38.04/6.95 % (12640)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_12223 for (2946ds/578Mi)
% 38.04/6.96 % (12641)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_12223 for (2945ds/643Mi)
% 41.52/7.16 % (12640)Instruction limit reached!
% 41.52/7.16 % (12640)------------------------------
% 41.52/7.16 % (12640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.52/7.16 % (12640)Termination reason: Unknown
% 41.52/7.16 % (12640)Termination phase: Saturation
% 41.52/7.16
% 41.52/7.16 % (12640)Memory used [KB]: 10874
% 41.52/7.16 % (12640)Time elapsed: 0.224 s
% 41.52/7.16 % (12640)Instructions burned: 579 (million)
% 41.52/7.16 % (12640)------------------------------
% 41.52/7.16 % (12640)------------------------------
% 41.52/7.17 % (12642)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_12223 for (2943ds/865Mi)
% 41.52/7.19 % (12641)Instruction limit reached!
% 41.52/7.19 % (12641)------------------------------
% 41.52/7.19 % (12641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.52/7.19 % (12641)Termination reason: Unknown
% 41.52/7.19 % (12641)Termination phase: Saturation
% 41.52/7.19
% 41.52/7.19 % (12641)Memory used [KB]: 6524
% 41.52/7.19 % (12641)Time elapsed: 0.231 s
% 41.52/7.19 % (12641)Instructions burned: 643 (million)
% 41.52/7.19 % (12641)------------------------------
% 41.52/7.19 % (12641)------------------------------
% 41.91/7.21 % (12643)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_12223 for (2943ds/1174Mi)
% 41.91/7.27 % (12639)Instruction limit reached!
% 41.91/7.27 % (12639)------------------------------
% 41.91/7.27 % (12639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.91/7.27 % (12639)Termination reason: Unknown
% 41.91/7.27 % (12639)Termination phase: Saturation
% 41.91/7.27
% 41.91/7.27 % (12639)Memory used [KB]: 12025
% 41.91/7.27 % (12639)Time elapsed: 0.415 s
% 41.91/7.27 % (12639)Instructions burned: 954 (million)
% 41.91/7.27 % (12639)------------------------------
% 41.91/7.27 % (12639)------------------------------
% 41.91/7.27 % (12637)Instruction limit reached!
% 41.91/7.27 % (12637)------------------------------
% 41.91/7.27 % (12637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.91/7.27 % (12637)Termination reason: Unknown
% 41.91/7.27 % (12637)Termination phase: Saturation
% 41.91/7.27
% 41.91/7.27 % (12637)Memory used [KB]: 15735
% 41.91/7.27 % (12637)Time elapsed: 0.481 s
% 41.91/7.27 % (12637)Instructions burned: 1001 (million)
% 41.91/7.27 % (12637)------------------------------
% 41.91/7.27 % (12637)------------------------------
% 41.91/7.29 % (12644)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_12223 for (2942ds/644Mi)
% 42.39/7.30 % (12645)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_12223 for (2942ds/1201Mi)
% 42.39/7.35 % (12616)Instruction limit reached!
% 42.39/7.35 % (12616)------------------------------
% 42.39/7.35 % (12616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.39/7.35 % (12616)Termination reason: Unknown
% 42.39/7.35 % (12616)Termination phase: Saturation
% 42.39/7.35
% 42.39/7.35 % (12616)Memory used [KB]: 15095
% 42.39/7.35 % (12616)Time elapsed: 1.567 s
% 42.39/7.35 % (12616)Instructions burned: 3374 (million)
% 42.39/7.35 % (12616)------------------------------
% 42.39/7.35 % (12616)------------------------------
% 42.39/7.37 % (12646)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_12223 for (2941ds/1046Mi)
% 42.39/7.38 % (12633)First to succeed.
% 42.64/7.44 % (12633)Refutation found. Thanks to Tanya!
% 42.64/7.44 % SZS status Theorem for DTF2THF_12223
% 42.64/7.44 % SZS output start Proof for DTF2THF_12223
% 42.64/7.44 thf(type_def_5, type, term: $tType).
% 42.64/7.44 thf(type_def_7, type, subst: $tType).
% 42.64/7.44 thf(type_def_8, type, d_term: $tType).
% 42.64/7.44 thf(type_def_9, type, d_subst: $tType).
% 42.64/7.44 thf(func_def_0, type, term: $tType).
% 42.64/7.44 thf(func_def_1, type, subst: $tType).
% 42.64/7.44 thf(func_def_2, type, one: term).
% 42.64/7.44 thf(func_def_3, type, ap: term > term > term).
% 42.64/7.44 thf(func_def_4, type, lam: term > term).
% 42.64/7.44 thf(func_def_5, type, sub: term > subst > term).
% 42.64/7.44 thf(func_def_6, type, id: subst).
% 42.64/7.44 thf(func_def_7, type, sh: subst).
% 42.64/7.44 thf(func_def_8, type, push: term > subst > subst).
% 42.64/7.44 thf(func_def_9, type, comp: subst > subst > subst).
% 42.64/7.44 thf(func_def_10, type, var: term > $o).
% 42.64/7.44 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 42.64/7.44 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 42.64/7.44 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 42.64/7.44 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 42.64/7.44 thf(func_def_124, type, d_term: $tType).
% 42.64/7.44 thf(func_def_125, type, d_subst: $tType).
% 42.64/7.44 thf(func_def_126, type, d2term: d_term > term).
% 42.64/7.44 thf(func_def_127, type, d2subst: d_subst > subst).
% 42.64/7.44 thf(func_def_128, type, d_one: d_term).
% 42.64/7.44 thf(func_def_129, type, d_id: d_subst).
% 42.64/7.44 thf(func_def_143, type, sP1: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_147, type, sP5: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_148, type, sP6: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_149, type, sP7: (term > $o) > $o).
% 42.64/7.44 thf(func_def_154, type, sP12: (term > $o) > $o).
% 42.64/7.44 thf(func_def_156, type, sP14: (term > $o) > $o).
% 42.64/7.44 thf(func_def_158, type, sP16: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_160, type, sP18: (term > $o) > $o).
% 42.64/7.44 thf(func_def_161, type, sP19: (term > $o) > $o).
% 42.64/7.44 thf(func_def_164, type, sP22: (term > $o) > $o).
% 42.64/7.44 thf(func_def_165, type, sP23: (term > $o) > $o).
% 42.64/7.44 thf(func_def_168, type, sP26: (term > $o) > $o).
% 42.64/7.44 thf(func_def_170, type, sP28: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_171, type, sP29: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_173, type, sP31: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_177, type, sP35: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_179, type, sP37: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_180, type, sP38: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_182, type, sP40: (term > $o) > $o).
% 42.64/7.44 thf(func_def_183, type, sP41: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_188, type, sP46: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_191, type, sP49: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_192, type, sP50: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_193, type, sP51: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_194, type, sP52: (subst > term > subst > $o) > $o).
% 42.64/7.44 thf(func_def_195, type, sP53: (term > $o) > $o).
% 42.64/7.44 thf(func_def_201, type, sK59: term).
% 42.64/7.44 thf(func_def_202, type, sK60: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_203, type, sK61: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_204, type, sK62: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_205, type, sK63: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_206, type, sK64: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_207, type, sK65: (subst > term > subst > $o) > term > term).
% 42.64/7.44 thf(func_def_208, type, sK66: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_209, type, sK67: (term > $o) > term).
% 42.64/7.44 thf(func_def_210, type, sK68: (term > $o) > term).
% 42.64/7.44 thf(func_def_211, type, sK69: term > $o).
% 42.64/7.44 thf(func_def_212, type, sK70: term).
% 42.64/7.44 thf(func_def_213, type, sK71: term > term).
% 42.64/7.44 thf(func_def_214, type, sK72: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_215, type, sK73: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_216, type, sK74: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_217, type, sK75: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_218, type, sK76: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_219, type, sK77: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_220, type, sK78: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_221, type, sK79: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_222, type, sK80: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_223, type, sK81: term).
% 42.64/7.44 thf(func_def_224, type, sK82: term).
% 42.64/7.44 thf(func_def_225, type, sK83: term).
% 42.64/7.44 thf(func_def_226, type, sK84: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_227, type, sK85: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_228, type, sK86: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_229, type, sK87: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_230, type, sK88: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_231, type, sK89: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_232, type, sK90: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_233, type, sK91: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_234, type, sK92: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_235, type, sK93: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_236, type, sK94: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_237, type, sK95: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_238, type, sK96: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_239, type, sK97: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_240, type, sK98: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_241, type, sK99: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_242, type, sK100: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_243, type, sK101: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_244, type, sK102: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_245, type, sK103: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_246, type, sK104: term).
% 42.64/7.44 thf(func_def_247, type, sK105: (term > $o) > term).
% 42.64/7.44 thf(func_def_248, type, sK106: (term > $o) > term).
% 42.64/7.44 thf(func_def_249, type, sK107: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_250, type, sK108: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_251, type, sK109: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_252, type, sK110: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_253, type, sK111: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_254, type, sK112: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_255, type, sK113: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_256, type, sK114: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_257, type, sK115: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_258, type, sK116: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_259, type, sK117: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_260, type, sK118: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_261, type, sK119: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_262, type, sK120: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_263, type, sK121: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_264, type, sK122: term).
% 42.64/7.44 thf(func_def_265, type, sK123: term).
% 42.64/7.44 thf(func_def_266, type, sK124: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_267, type, sK125: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_268, type, sK126: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_269, type, sK127: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_270, type, sK128: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_271, type, sK129: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_272, type, sK130: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_273, type, sK131: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_274, type, sK132: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_275, type, sK133: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_276, type, sK134: (subst > term > subst > $o) > term > term).
% 42.64/7.44 thf(func_def_277, type, sK135: term).
% 42.64/7.44 thf(func_def_278, type, sK136: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_279, type, sK137: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_280, type, sK138: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_281, type, sK139: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_282, type, sK140: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_283, type, sK141: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_284, type, sK142: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_285, type, sK143: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_286, type, sK144: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_287, type, sK145: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_288, type, sK146: subst > term > term).
% 42.64/7.44 thf(func_def_289, type, sK147: term).
% 42.64/7.44 thf(func_def_290, type, sK148: subst).
% 42.64/7.44 thf(func_def_291, type, sK149: subst > term > term).
% 42.64/7.44 thf(func_def_292, type, sK150: term).
% 42.64/7.44 thf(func_def_293, type, sK151: term).
% 42.64/7.44 thf(func_def_294, type, sK152: term).
% 42.64/7.44 thf(func_def_295, type, sK153: subst).
% 42.64/7.44 thf(func_def_296, type, sK154: term).
% 42.64/7.44 thf(func_def_297, type, sK155: subst).
% 42.64/7.44 thf(func_def_298, type, sK156: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_299, type, sK157: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_300, type, sK158: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_301, type, sK159: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_302, type, sK160: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_303, type, sK161: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_304, type, sK162: (subst > term > subst > $o) > term > $o).
% 42.64/7.44 thf(func_def_305, type, sK163: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_306, type, sK164: term).
% 42.64/7.44 thf(func_def_307, type, sK165: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_308, type, sK166: (term > $o) > term).
% 42.64/7.44 thf(func_def_309, type, sK167: term).
% 42.64/7.44 thf(func_def_310, type, sK168: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_311, type, sK169: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_312, type, sK170: (term > $o) > term).
% 42.64/7.44 thf(func_def_313, type, sK171: (term > $o) > term).
% 42.64/7.44 thf(func_def_314, type, sK172: term > $o).
% 42.64/7.44 thf(func_def_315, type, sK173: term).
% 42.64/7.44 thf(func_def_316, type, sK174: term > term).
% 42.64/7.44 thf(func_def_317, type, sK175: (term > $o) > term > term).
% 42.64/7.44 thf(func_def_318, type, sK176: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_319, type, sK177: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_320, type, sK178: term).
% 42.64/7.44 thf(func_def_321, type, sK179: term > $o).
% 42.64/7.44 thf(func_def_322, type, sK180: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_323, type, sK181: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_324, type, sK182: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_325, type, sK183: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_326, type, sK184: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_327, type, sK185: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_328, type, sK186: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_329, type, sK187: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_330, type, sK188: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_331, type, sK189: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_332, type, sK190: (term > $o) > term).
% 42.64/7.44 thf(func_def_333, type, sK191: (term > $o) > term).
% 42.64/7.44 thf(func_def_334, type, sK192: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_335, type, sK193: term).
% 42.64/7.44 thf(func_def_336, type, sK194: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_337, type, sK195: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_338, type, sK196: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_339, type, sK197: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_340, type, sK198: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_341, type, sK199: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_342, type, sK200: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_343, type, sK201: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_344, type, sK202: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_345, type, sK203: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_346, type, sK204: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_347, type, sK205: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_348, type, sK206: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_349, type, sK207: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_350, type, sK208: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_351, type, sK209: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_352, type, sK210: term > $o).
% 42.64/7.44 thf(func_def_353, type, sK211: term).
% 42.64/7.44 thf(func_def_354, type, sK212: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_355, type, sK213: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_356, type, sK214: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_357, type, sK215: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_358, type, sK216: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_359, type, sK217: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_360, type, sK218: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_361, type, sK219: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_362, type, sK220: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_363, type, sK221: term > (term > $o) > term).
% 42.64/7.44 thf(func_def_364, type, sK222: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_365, type, sK223: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_366, type, sK224: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_367, type, sK225: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_368, type, sK226: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_369, type, sK227: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_370, type, sK228: term > $o).
% 42.64/7.44 thf(func_def_371, type, sK229: term).
% 42.64/7.44 thf(func_def_372, type, sK230: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_373, type, sK231: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_374, type, sK232: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_375, type, sK233: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_376, type, sK234: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_377, type, sK235: term > (term > $o) > term).
% 42.64/7.44 thf(func_def_378, type, sK236: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_379, type, sK237: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_380, type, sK238: term).
% 42.64/7.44 thf(func_def_381, type, sK239: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_382, type, sK240: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_383, type, sK241: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_384, type, sK242: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_385, type, sK243: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_386, type, sK244: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_387, type, sK245: (subst > term > subst > $o) > term > term).
% 42.64/7.44 thf(func_def_388, type, sK246: term).
% 42.64/7.44 thf(func_def_389, type, sK247: term > $o).
% 42.64/7.44 thf(func_def_390, type, sK248: term).
% 42.64/7.44 thf(func_def_391, type, sK249: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_392, type, sK250: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_393, type, sK251: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_394, type, sK252: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_395, type, sK253: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_396, type, sK254: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_397, type, sK255: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_398, type, sK256: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_399, type, sK257: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_400, type, sK258: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_401, type, sK259: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_402, type, sK260: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_403, type, sK261: term).
% 42.64/7.44 thf(func_def_404, type, sK262: term).
% 42.64/7.44 thf(func_def_405, type, sK263: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_406, type, sK264: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_407, type, sK265: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_408, type, sK266: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_409, type, sK267: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_410, type, sK268: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_411, type, sK269: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_412, type, sK270: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_413, type, sK271: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_414, type, sK272: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_415, type, sK273: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_416, type, sK274: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_417, type, sK275: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_418, type, sK276: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_419, type, sK277: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_420, type, sK278: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_421, type, sK279: term).
% 42.64/7.44 thf(func_def_422, type, sK280: term > $o).
% 42.64/7.44 thf(func_def_423, type, sK281: term > term).
% 42.64/7.44 thf(func_def_424, type, sK282: (term > $o) > term).
% 42.64/7.44 thf(func_def_425, type, sK283: (term > $o) > term).
% 42.64/7.44 thf(func_def_426, type, sK284: (term > $o) > term).
% 42.64/7.44 thf(func_def_427, type, sK285: (term > $o) > term).
% 42.64/7.44 thf(func_def_428, type, sK286: (term > $o) > term).
% 42.64/7.44 thf(func_def_429, type, sK287: subst > (term > $o) > term).
% 42.64/7.44 thf(func_def_430, type, sK288: term > $o).
% 42.64/7.44 thf(func_def_431, type, sK289: subst).
% 42.64/7.44 thf(func_def_432, type, sK290: term).
% 42.64/7.44 thf(func_def_433, type, sK291: term > term).
% 42.64/7.44 thf(func_def_434, type, sK292: term).
% 42.64/7.44 thf(func_def_435, type, sK293: term).
% 42.64/7.44 thf(func_def_436, type, sK294: term > $o).
% 42.64/7.44 thf(func_def_437, type, sK295: term > term).
% 42.64/7.44 thf(func_def_438, type, sK296: (term > $o) > term).
% 42.64/7.44 thf(func_def_439, type, sK297: (term > $o) > term).
% 42.64/7.44 thf(func_def_440, type, sK298: (term > $o) > term).
% 42.64/7.44 thf(func_def_441, type, sK299: (term > $o) > term).
% 42.64/7.44 thf(func_def_442, type, sK300: (term > $o) > term).
% 42.64/7.44 thf(func_def_443, type, sK301: (term > $o) > term).
% 42.64/7.44 thf(func_def_444, type, sK302: (term > $o) > term).
% 42.64/7.44 thf(func_def_445, type, sK303: (term > $o) > term).
% 42.64/7.44 thf(func_def_446, type, sK304: subst).
% 42.64/7.44 thf(func_def_447, type, sK305: term).
% 42.64/7.44 thf(func_def_448, type, sK306: term > $o).
% 42.64/7.44 thf(func_def_449, type, sK307: term).
% 42.64/7.44 thf(func_def_450, type, sK308: subst).
% 42.64/7.44 thf(func_def_451, type, sK309: term).
% 42.64/7.44 thf(func_def_452, type, sK310: subst).
% 42.64/7.44 thf(func_def_453, type, sK311: term > $o).
% 42.64/7.44 thf(func_def_454, type, sK312: term).
% 42.64/7.44 thf(func_def_455, type, sK313: subst).
% 42.64/7.44 thf(func_def_456, type, sK314: term > term).
% 42.64/7.44 thf(func_def_457, type, sK315: (term > $o) > term).
% 42.64/7.44 thf(func_def_458, type, sK316: subst > (term > $o) > term).
% 42.64/7.44 thf(func_def_459, type, sK317: (term > $o) > term).
% 42.64/7.44 thf(func_def_460, type, sK318: (term > $o) > term).
% 42.64/7.44 thf(func_def_461, type, sK319: (term > $o) > term).
% 42.64/7.44 thf(func_def_462, type, sK320: (term > $o) > term).
% 42.64/7.44 thf(func_def_463, type, sK321: term).
% 42.64/7.44 thf(func_def_464, type, sK322: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_465, type, sK323: term > $o).
% 42.64/7.44 thf(func_def_466, type, sK324: term).
% 42.64/7.44 thf(func_def_467, type, sK325: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_468, type, sK326: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_469, type, sK327: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_470, type, sK328: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_471, type, sK329: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_472, type, sK330: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_473, type, sK331: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_474, type, sK332: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_475, type, sK333: (term > $o) > term > term).
% 42.64/7.44 thf(func_def_476, type, sK334: (term > $o) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_477, type, sK335: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_478, type, sK336: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_479, type, sK337: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_480, type, sK338: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_481, type, sK339: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_482, type, sK340: subst).
% 42.64/7.44 thf(func_def_483, type, sK341: term > $o).
% 42.64/7.44 thf(func_def_484, type, sK342: term).
% 42.64/7.44 thf(func_def_485, type, sK343: term > term).
% 42.64/7.44 thf(func_def_486, type, sK344: (term > $o) > subst > term).
% 42.64/7.44 thf(func_def_487, type, sK345: (term > $o) > term).
% 42.64/7.44 thf(func_def_488, type, sK346: (term > $o) > term).
% 42.64/7.44 thf(func_def_489, type, sK347: (term > $o) > term).
% 42.64/7.44 thf(func_def_490, type, sK348: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_491, type, sK349: term).
% 42.64/7.44 thf(func_def_492, type, sK350: term > (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_493, type, sK351: term > (subst > term > term) > term).
% 42.64/7.44 thf(func_def_494, type, sK352: term > (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_495, type, sK353: term > (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_496, type, sK354: term > (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_497, type, sK355: term > (subst > term > term) > term).
% 42.64/7.44 thf(func_def_498, type, sK356: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_499, type, sK357: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_500, type, sK358: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_501, type, sK359: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_502, type, sK360: (term > $o) > term).
% 42.64/7.44 thf(func_def_503, type, sK361: (term > $o) > term).
% 42.64/7.44 thf(func_def_504, type, sK362: term).
% 42.64/7.44 thf(func_def_505, type, sK363: term > $o).
% 42.64/7.44 thf(func_def_506, type, sK364: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_507, type, sK365: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_508, type, sK366: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_509, type, sK367: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_510, type, sK368: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_511, type, sK369: term > subst > term > term).
% 42.64/7.44 thf(func_def_512, type, sK370: (term > $o) > term > term).
% 42.64/7.44 thf(func_def_513, type, sK371: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_514, type, sK372: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_515, type, sK373: term).
% 42.64/7.44 thf(func_def_516, type, sK374: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_517, type, sK375: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_518, type, sK376: term).
% 42.64/7.44 thf(func_def_519, type, sK377: (term > $o) > term).
% 42.64/7.44 thf(func_def_520, type, sK378: (term > $o) > term).
% 42.64/7.44 thf(func_def_521, type, sK379: (subst > term > subst > $o) > term > $o).
% 42.64/7.44 thf(func_def_522, type, sK380: term).
% 42.64/7.44 thf(func_def_523, type, sK381: term).
% 42.64/7.44 thf(func_def_524, type, sK382: term > $o).
% 42.64/7.44 thf(func_def_525, type, sK383: term > term).
% 42.64/7.44 thf(func_def_526, type, sK384: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_527, type, sK385: (term > $o) > term).
% 42.64/7.44 thf(func_def_528, type, sK386: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_529, type, sK387: term > (term > $o) > term).
% 42.64/7.44 thf(func_def_530, type, sK388: (subst > term > subst > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_531, type, sK389: term > $o).
% 42.64/7.44 thf(func_def_532, type, sK390: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_533, type, sK391: term).
% 42.64/7.44 thf(func_def_534, type, sK392: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_535, type, sK393: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_536, type, sK394: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_537, type, sK395: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_538, type, sK396: term).
% 42.64/7.44 thf(func_def_539, type, sK397: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_540, type, sK398: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_541, type, sK399: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_542, type, sK400: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_543, type, sK401: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_544, type, sK402: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_545, type, sK403: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_546, type, sK404: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_547, type, sK405: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_548, type, sK406: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_549, type, sK407: (term > $o) > term).
% 42.64/7.44 thf(func_def_550, type, sK408: (term > $o) > term).
% 42.64/7.44 thf(func_def_551, type, sK409: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_552, type, sK410: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_553, type, sK411: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_554, type, sK412: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_555, type, sK413: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_556, type, sK414: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_557, type, sK415: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_558, type, sK416: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_559, type, sK417: term).
% 42.64/7.44 thf(func_def_560, type, sK418: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_561, type, sK419: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_562, type, sK420: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_563, type, sK421: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_564, type, sK422: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_565, type, sK423: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_566, type, sK424: term).
% 42.64/7.44 thf(func_def_567, type, sK425: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_568, type, sK426: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_569, type, sK427: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_570, type, sK428: term).
% 42.64/7.44 thf(func_def_571, type, sK429: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_572, type, sK430: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_573, type, sK431: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_574, type, sK432: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_575, type, sK433: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_576, type, sK434: term).
% 42.64/7.44 thf(func_def_577, type, sK435: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_578, type, sK436: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_579, type, sK437: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_580, type, sK438: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_581, type, sK439: term > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_582, type, sK440: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_583, type, sK441: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_584, type, sK442: (subst > term > subst > $o) > subst).
% 42.64/7.44 thf(func_def_585, type, sK443: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_586, type, sK444: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_587, type, sK445: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_588, type, sK446: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_589, type, sK447: (subst > term > term) > (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_590, type, sK448: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_591, type, sK449: term).
% 42.64/7.44 thf(func_def_592, type, sK450: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_593, type, sK451: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_594, type, sK452: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_595, type, sK453: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_596, type, sK454: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_597, type, sK455: (subst > term > subst > $o) > term > term).
% 42.64/7.44 thf(func_def_598, type, sK456: (subst > term > subst > $o) > subst > term > term).
% 42.64/7.44 thf(func_def_599, type, sK457: term).
% 42.64/7.44 thf(func_def_600, type, sK458: subst > term > term).
% 42.64/7.44 thf(func_def_601, type, sK459: subst > term > term).
% 42.64/7.44 thf(func_def_602, type, sK460: subst).
% 42.64/7.44 thf(func_def_603, type, sK461: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_604, type, sK462: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_605, type, sK463: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_606, type, sK464: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_607, type, sK465: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_608, type, sK466: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_609, type, sK467: term).
% 42.64/7.44 thf(func_def_610, type, sK468: term).
% 42.64/7.44 thf(func_def_611, type, sK469: term > subst > term > term).
% 42.64/7.44 thf(func_def_612, type, sK470: term).
% 42.64/7.44 thf(func_def_613, type, sK471: term).
% 42.64/7.44 thf(func_def_614, type, sK472: term).
% 42.64/7.44 thf(func_def_615, type, sK473: (subst > term > subst > $o) > term > $o).
% 42.64/7.44 thf(func_def_616, type, sK474: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_617, type, sK475: (term > $o) > term).
% 42.64/7.44 thf(func_def_618, type, sK476: term > $o).
% 42.64/7.44 thf(func_def_619, type, sK477: subst).
% 42.64/7.44 thf(func_def_620, type, sK478: term).
% 42.64/7.44 thf(func_def_621, type, sK479: (term > $o) > term).
% 42.64/7.44 thf(func_def_622, type, sK480: term > subst > (term > $o) > term > $o).
% 42.64/7.44 thf(func_def_623, type, sK481: term > subst > term > term).
% 42.64/7.44 thf(func_def_624, type, sK482: term).
% 42.64/7.44 thf(func_def_625, type, sK483: subst).
% 42.64/7.44 thf(func_def_626, type, sK484: term).
% 42.64/7.44 thf(func_def_627, type, sK485: term).
% 42.64/7.44 thf(func_def_628, type, sK486: term).
% 42.64/7.44 thf(func_def_629, type, sK487: term).
% 42.64/7.44 thf(func_def_630, type, sK488: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_631, type, sK489: (subst > term > subst > $o) > term).
% 42.64/7.44 thf(func_def_632, type, sK490: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_633, type, sK491: term).
% 42.64/7.44 thf(func_def_634, type, sK492: term > subst > term > term).
% 42.64/7.44 thf(func_def_635, type, sK493: term).
% 42.64/7.44 thf(func_def_636, type, sK494: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_637, type, sK495: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_638, type, sK496: term > subst > term > term).
% 42.64/7.44 thf(func_def_639, type, sK497: term).
% 42.64/7.44 thf(func_def_640, type, sK498: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_641, type, sK499: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_642, type, sK500: term).
% 42.64/7.44 thf(func_def_643, type, sK501: term).
% 42.64/7.44 thf(func_def_644, type, sK502: term).
% 42.64/7.44 thf(func_def_645, type, sK503: term).
% 42.64/7.44 thf(func_def_646, type, sK504: term).
% 42.64/7.44 thf(func_def_647, type, sK505: term).
% 42.64/7.44 thf(func_def_648, type, sK506: term).
% 42.64/7.44 thf(func_def_649, type, sK507: term).
% 42.64/7.44 thf(func_def_650, type, sK508: term).
% 42.64/7.44 thf(func_def_651, type, sK509: term).
% 42.64/7.44 thf(func_def_652, type, sK510: term).
% 42.64/7.44 thf(func_def_653, type, sK511: term).
% 42.64/7.44 thf(func_def_654, type, sK512: term).
% 42.64/7.44 thf(func_def_655, type, sK513: subst).
% 42.64/7.44 thf(func_def_656, type, sK514: (term > $o) > term > subst > term > $o).
% 42.64/7.44 thf(func_def_657, type, sK515: subst).
% 42.64/7.44 thf(func_def_658, type, sK516: term).
% 42.64/7.44 thf(func_def_659, type, sK517: term > $o).
% 42.64/7.44 thf(func_def_660, type, sK518: (term > $o) > term).
% 42.64/7.44 thf(func_def_661, type, sK519: term).
% 42.64/7.44 thf(func_def_662, type, sK520: term).
% 42.64/7.44 thf(func_def_663, type, sK521: term).
% 42.64/7.44 thf(func_def_664, type, sK522: term).
% 42.64/7.44 thf(func_def_665, type, sK523: term > d_term).
% 42.64/7.44 thf(func_def_666, type, sK524: term > $o).
% 42.64/7.44 thf(func_def_667, type, sK525: subst).
% 42.64/7.44 thf(func_def_668, type, sK526: term > $o).
% 42.64/7.44 thf(func_def_669, type, sK527: term).
% 42.64/7.44 thf(func_def_670, type, sK528: term > (term > $o) > subst > (term > $o) > term).
% 42.64/7.44 thf(func_def_671, type, sK529: subst).
% 42.64/7.44 thf(func_def_672, type, sK530: term).
% 42.64/7.44 thf(func_def_673, type, sK531: subst > d_subst).
% 42.64/7.44 thf(func_def_674, type, sK532: subst).
% 42.64/7.44 thf(func_def_675, type, sK533: term).
% 42.64/7.44 thf(func_def_676, type, sK534: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_677, type, sK535: (term > $o) > term).
% 42.64/7.44 thf(func_def_678, type, sK536: (subst > term > subst > $o) > term > $o).
% 42.64/7.44 thf(func_def_679, type, sK537: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_680, type, sK538: (subst > term > term) > term).
% 42.64/7.44 thf(func_def_681, type, sK539: (subst > term > term) > subst).
% 42.64/7.44 thf(func_def_682, type, sK540: term).
% 42.64/7.44 thf(func_def_683, type, sK541: term).
% 42.64/7.44 thf(func_def_684, type, sK542: subst > term > term).
% 42.64/7.44 thf(func_def_685, type, sK543: term).
% 42.64/7.44 thf(func_def_686, type, sK544: term > $o).
% 42.64/7.44 thf(func_def_687, type, sK545: (term > $o) > term).
% 42.64/7.44 thf(func_def_688, type, sK546: (term > $o) > term).
% 42.64/7.44 thf(func_def_689, type, sK547: term).
% 42.64/7.44 thf(func_def_690, type, sK548: subst).
% 42.64/7.44 thf(func_def_691, type, sK549: subst).
% 42.64/7.44 thf(func_def_692, type, sK550: term).
% 42.64/7.44 thf(func_def_693, type, sK551: term > $o).
% 42.64/7.44 thf(func_def_694, type, sK552: term).
% 42.64/7.44 thf(func_def_695, type, sK553: subst).
% 42.64/7.44 thf(func_def_696, type, sK554: term).
% 42.64/7.44 thf(func_def_697, type, sK555: term > $o).
% 42.64/7.44 thf(func_def_698, type, sK556: subst).
% 42.64/7.44 thf(func_def_699, type, sK557: term).
% 42.64/7.44 thf(func_def_700, type, sK558: term > $o).
% 42.64/7.44 thf(func_def_701, type, sK559: term > $o).
% 42.64/7.44 thf(func_def_702, type, sK560: subst).
% 42.64/7.44 thf(func_def_703, type, sK561: term).
% 42.64/7.44 thf(func_def_704, type, sK562: term).
% 42.64/7.44 thf(func_def_705, type, sK563: term).
% 42.64/7.44 thf(func_def_706, type, sK564: term).
% 42.64/7.44 thf(func_def_707, type, sK565: term).
% 42.64/7.44 thf(func_def_708, type, sK566: term).
% 42.64/7.44 thf(func_def_709, type, sK567: term).
% 42.64/7.44 thf(func_def_710, type, sK568: term).
% 42.64/7.44 thf(func_def_711, type, sK569: term).
% 42.64/7.44 thf(func_def_712, type, sK570: term).
% 42.64/7.44 thf(func_def_713, type, sK571: term).
% 42.64/7.44 thf(func_def_714, type, sK572: term).
% 42.64/7.44 thf(func_def_715, type, sK573: term).
% 42.64/7.44 thf(func_def_716, type, sK574: subst).
% 42.64/7.44 thf(func_def_717, type, sK575: subst).
% 42.64/7.44 thf(func_def_718, type, sK576: subst).
% 42.64/7.44 thf(func_def_719, type, sK577: subst).
% 42.64/7.44 thf(func_def_720, type, sK578: term > $o).
% 42.64/7.44 thf(func_def_721, type, sK579: term > $o).
% 42.64/7.44 thf(func_def_722, type, sK580: subst).
% 42.64/7.44 thf(func_def_723, type, sK581: term).
% 42.64/7.44 thf(func_def_724, type, sK582: term > subst > (term > $o) > (term > $o) > term).
% 42.64/7.44 thf(func_def_725, type, sK583: term).
% 42.64/7.44 thf(func_def_726, type, sK584: term).
% 42.64/7.44 thf(func_def_727, type, sK585: subst).
% 42.64/7.44 thf(func_def_728, type, sK586: term).
% 42.64/7.44 thf(func_def_729, type, sK587: term).
% 42.64/7.44 thf(func_def_730, type, sK588: term).
% 42.64/7.44 thf(func_def_731, type, sK589: subst).
% 42.64/7.44 thf(func_def_732, type, sK590: subst).
% 42.64/7.44 thf(func_def_734, type, sK592: subst > term > subst > $o).
% 42.64/7.44 thf(func_def_735, type, sK593: (term > $o) > term).
% 42.64/7.44 thf(func_def_736, type, sK594: (subst > term > subst > $o) > term > $o).
% 42.64/7.44 thf(func_def_738, type, ph595: !>[X0: $tType]:(X0)).
% 42.64/7.44 thf(f7182,plain,(
% 42.64/7.44 $false),
% 42.64/7.44 inference(avatar_sat_refutation,[status(thm)],[f2578,f2582,f2656,f2664,f2668,f2765,f3013,f3280,f3450,f3991,f5251,f5631,f5707,f5886,f5908,f5958,f6210,f6458,f6606,f6665,f6756,f6945,f7026,f7168])).
% 42.64/7.44 thf(f7168,plain,(
% 42.64/7.44 ~spl591_197 | ~spl591_504 | ~spl591_697),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f7167])).
% 42.64/7.44 thf(f7167,plain,(
% 42.64/7.44 $false | (~spl591_197 | ~spl591_504 | ~spl591_697)),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f7166])).
% 42.64/7.44 thf(f7166,plain,(
% 42.64/7.44 ($true = $false) | (~spl591_197 | ~spl591_504 | ~spl591_697)),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f7165,f7068])).
% 42.64/7.44 thf(f7068,plain,(
% 42.64/7.44 ( ! [X34 : term,X32 : subst > term > subst > $o] : (($false = (X32 @ (d2subst @ d_id) @ X34 @ (d2subst @ d_id)))) ) | (~spl591_504 | ~spl591_697)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f3990,f6664])).
% 42.64/7.44 thf(f6664,plain,(
% 42.64/7.44 ( ! [X189 : term,X186 : term > $o] : (($true != (X186 @ X189))) ) | ~spl591_697),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f6663])).
% 42.64/7.44 thf(f6663,definition,(
% 42.64/7.44 spl591_697 <=> ! [X189 : term,X186 : term > $o] : ($true != (X186 @ X189))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_697])],[avatar_definition])).
% 42.64/7.44 thf(f3990,plain,(
% 42.64/7.44 ( ! [X34 : term,X32 : subst > term > subst > $o] : (($false = (X32 @ (d2subst @ d_id) @ X34 @ (d2subst @ d_id))) | ($true = (sK473 @ X32 @ X34))) ) | ~spl591_504),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3989])).
% 42.64/7.44 thf(f3989,definition,(
% 42.64/7.44 spl591_504 <=> ! [X34 : term,X32 : subst > term > subst > $o] : (($true = (sK473 @ X32 @ X34)) | ($false = (X32 @ (d2subst @ d_id) @ X34 @ (d2subst @ d_id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_504])],[avatar_definition])).
% 42.64/7.44 thf(f7165,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($true = (sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)))) ) | (~spl591_197 | ~spl591_697)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f2659,f6664])).
% 42.64/7.44 thf(f2659,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($true = (sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id))) | ($true = (X1 @ (sK593 @ X1)))) ) | ~spl591_197),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2658])).
% 42.64/7.44 thf(f2658,definition,(
% 42.64/7.44 spl591_197 <=> ! [X1 : term > $o] : (($true = (X1 @ (sK593 @ X1))) | ($true = (sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_197])],[avatar_definition])).
% 42.64/7.44 thf(f7026,plain,(
% 42.64/7.44 spl591_279),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f7025])).
% 42.64/7.44 thf(f7025,plain,(
% 42.64/7.44 $false | spl591_279),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f3012,f6107])).
% 42.64/7.44 thf(f6107,plain,(
% 42.64/7.44 ( ! [X0 : subst,X1 : subst] : ((X0 = X1)) )),
% 42.64/7.44 inference(superposition,[status(thm)],[f4142,f4142])).
% 42.64/7.44 thf(f4142,plain,(
% 42.64/7.44 ( ! [X152 : subst] : (((d2subst @ d_id) = X152)) )),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f1127,f1132])).
% 42.64/7.44 thf(f1132,plain,(
% 42.64/7.44 ( ! [X151 : d_subst] : ((d_id = X151)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f545,plain,(
% 42.64/7.44 ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lthm = $true) | ($true != sP57)) & (($true = sP57) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((hoaslaminj = $true) | (! [X4 : subst,X5 : term,X6 : subst] : ((sub @ (sK459 @ X4 @ X5) @ X6) = (sK459 @ (comp @ X4 @ X6) @ (sub @ X5 @ X6))) & ((lam @ (sK459 @ sh @ one)) = (lam @ (sK458 @ sh @ one))) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (sK458 @ X9 @ X8) @ X7) = (sK458 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7))) & ((sK459 @ sK460 @ sK457) != (sK458 @ sK460 @ sK457)))) & (! [X10 : term,X11 : subst > term > term,X12 : subst > term > term,X13 : subst] : (((X12 @ (comp @ (sK461 @ X12) @ (sK463 @ X12)) @ (sub @ (sK462 @ X12) @ (sK463 @ X12))) != (sub @ (X12 @ (sK461 @ X12) @ (sK462 @ X12)) @ (sK463 @ X12))) | ((lam @ (X12 @ sh @ one)) != (lam @ (X11 @ sh @ one))) | ((sub @ (X11 @ (sK466 @ X11) @ (sK465 @ X11)) @ (sK464 @ X11)) != (X11 @ (comp @ (sK466 @ X11) @ (sK464 @ X11)) @ (sub @ (sK465 @ X11) @ (sK464 @ X11)))) | ((X12 @ X13 @ X10) = (X11 @ X13 @ X10))) | (hoaslaminj != $true)) & (lamnotap != $true) & (apnotvar = $true) & ((axvarid = $true) | (sK467 != (sub @ sK467 @ id))) & (! [X21 : term] : ((sub @ X21 @ id) = X21) | (axvarid != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3b_lthm = $true) | ! [X23 : subst > term > term] : ((sub @ sK468 @ (push @ one @ sh)) != (X23 @ sh @ one))) & (! [X24 : term] : ((sK469 @ X24 @ sh @ one) = (sub @ X24 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP48)) & (($true = sP48) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (($true = sP45) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP45)) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & ((termmset = $true) | (sK470 != (sub @ sK470 @ id))) & (! [X27 : term] : ((sub @ X27 @ id) = X27) | (termmset != $true)) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP39) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP39)) & (hoasapinj2_gthm = $true) & (! [X28 : term,X29 : term] : ((X28 = X29) | ((lam @ X29) != (lam @ X28))) | (laminj != $true)) & ((laminj = $true) | ((sK472 != sK471) & ((lam @ sK472) = (lam @ sK471)))) & (($true = sP36) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP36)) & (axapp = $true) & (($true = sP34) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP34)) & (hoasinduction_lem2_gthm = $true) & (! [X32 : subst > term > subst > $o] : ! [X34 : term] : ((sK473 @ X32 @ X34) = (X32 @ id @ X34 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X36 : term > $o] : ((sK474 @ id @ (sK475 @ X36) @ id) != (X36 @ (sK475 @ X36)))) & ((pushprop_lem0_lthm = $true) | ! [X41 : term > $o] : ((X41 @ (sK479 @ X41)) != (sK476 @ (sub @ (sK479 @ X41) @ (push @ sK478 @ sK477))))) & (! [X43 : term > $o,X44 : subst,X45 : term] : ! [X47 : term] : ((sK480 @ X45 @ X44 @ X43 @ X47) = (X43 @ (sub @ X47 @ (push @ X45 @ X44)))) | (pushprop_lem0_lthm != $true)) & (! [X48 : term] : ((sK481 @ X48 @ sh @ one) = (sub @ X48 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X51 : subst > term > term] : ((X51 @ sh @ one) != (sub @ sK482 @ (push @ one @ sh)))) & (! [X52 : subst] : ((push @ (sub @ one @ X52) @ (comp @ sh @ X52)) = X52) | (axscons != $true)) & ((axscons = $true) | (sK483 != (push @ (sub @ one @ sK483) @ (comp @ sh @ sK483)))) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & (! [X54 : term,X55 : term,X56 : term,X57 : term] : (((ap @ X57 @ X55) != (ap @ X56 @ X54)) | (X56 = X57)) | (apinj1 != $true)) & ((apinj1 = $true) | (((ap @ sK487 @ sK485) = (ap @ sK486 @ sK484)) & (sK486 != sK487))) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & (axvarshift = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X62 : subst > term > subst > $o,X63 : term] : ((($true = (X62 @ id @ (sK488 @ X62) @ id)) & ($true != (X62 @ id @ (ap @ (sub @ (sK488 @ X62) @ id) @ (sK489 @ X62)) @ id)) & ((X62 @ id @ (sK489 @ X62) @ id) = $true)) | ($true = (sP28 @ X62)) | ($true = (X62 @ id @ X63 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X68 : term,X69 : term] : (($true != (sK490 @ id @ X68 @ id)) | ((sK490 @ id @ (ap @ (sub @ X68 @ id) @ X69) @ id) = $true) | ($true != (sK490 @ id @ X69 @ id))) & ($true != (sP28 @ sK490)) & ((sK490 @ id @ sK491 @ id) != $true))) & (hoaslamnotap_lthm = $true) & ((induction2 = $true) | ($true != sP27)) & (($true = sP27) | (induction2 != $true)) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X70 : term] : ! [X72 : subst,X73 : term] : ((sub @ X70 @ (push @ X73 @ X72)) = (sK492 @ X70 @ X72 @ X73)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X75 : subst > term > term] : ((X75 @ (sK494 @ X75) @ (sK495 @ X75)) != (sub @ sK493 @ (push @ (sK495 @ X75) @ (sK494 @ X75))))) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (! [X78 : term] : ! [X80 : subst,X81 : term] : ((sub @ X78 @ (push @ X81 @ X80)) = (sK496 @ X78 @ X80 @ X81)) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X83 : subst > term > term] : ((X83 @ (sK498 @ X83) @ (sK499 @ X83)) != (sub @ sK497 @ (push @ (sK499 @ X83) @ (sK498 @ X83))))) & ((hoasapinj2 = $true) | ((sK502 != sK500) & ((ap @ (sub @ sK503 @ id) @ sK500) = (ap @ (sub @ sK501 @ id) @ sK502)))) & (! [X90 : term,X91 : term,X92 : term,X93 : term] : ((X90 = X92) | ((ap @ (sub @ X93 @ id) @ X90) != (ap @ (sub @ X91 @ id) @ X92))) | (hoasapinj2 != $true)) & (($true = sP21) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP21)) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((sK504 != sK507) & ((ap @ sK507 @ sK505) = (ap @ sK504 @ sK506))) | ((sub @ sK508 @ id) != sK508) | ! [X99 : term,X100 : term,X101 : term,X102 : term] : (((ap @ (sub @ X102 @ id) @ X100) != (ap @ (sub @ X101 @ id) @ X99)) | (X101 = X102)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X103 : term,X104 : term,X105 : term,X106 : term] : ((X103 = X106) | ((ap @ X106 @ X104) != (ap @ X103 @ X105))) & ! [X107 : term] : ((sub @ X107 @ id) = X107) & (((ap @ (sub @ sK511 @ id) @ sK509) = (ap @ (sub @ sK512 @ id) @ sK510)) & (sK511 != sK512)))) & ! [X112 : d_term,X113 : d_term] : (((d2term @ X113) != (d2term @ X112)) | (X112 = X113)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X114 : d_term] : (d_one = X114) & (pushprop_lem3v2 = $true) & (! [X115 : subst] : ((comp @ id @ X115) = X115) | (axidl != $true)) & ((axidl = $true) | (sK513 != (comp @ id @ sK513))) & (! [X117 : subst,X118 : term,X119 : term > $o] : ! [X121 : term] : ((X119 @ (sub @ X121 @ (push @ X118 @ X117))) = (sK514 @ X119 @ X118 @ X117 @ X121)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X125 : term > $o] : ((X125 @ (sK518 @ X125)) != (sK517 @ (sub @ (sK518 @ X125) @ (push @ sK516 @ sK515))))) & (induction2lem_gthm = $true) & (! [X127 : term,X128 : term,X129 : term,X130 : term] : (((ap @ X127 @ X130) != (ap @ X128 @ X129)) | (X129 = X130)) | (apinj2 != $true)) & ((apinj2 = $true) | (((ap @ sK520 @ sK521) = (ap @ sK519 @ sK522)) & (sK522 != sK521))) & ! [X135 : term] : ((d2term @ (sK523 @ X135)) = X135) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | ((($true != (sK526 @ one)) & ((sK524 @ sK527) = $true) & ! [X141 : term] : ((sK526 @ X141) = (sK524 @ (sub @ X141 @ (push @ sK527 @ sK525))))) & ! [X142 : subst,X143 : term] : ((sub @ one @ (push @ X143 @ X142)) = X143))) & (! [X144 : term > $o,X145 : subst,X146 : term > $o,X147 : term] : (($true = (X146 @ one)) | ($true != (X144 @ X147)) | ((X146 @ (sK528 @ X147 @ X146 @ X145 @ X144)) != (X144 @ (sub @ (sK528 @ X147 @ X146 @ X145 @ X144) @ (push @ X147 @ X145))))) | ((sub @ one @ (push @ sK530 @ sK529)) != sK530) | (pushprop_lem1v2_lthm != $true)) & (($true = sP17) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP17)) & (($true = sP15) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP15)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X151 : d_subst] : (d_id = X151) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X152 : subst] : ((d2subst @ (sK531 @ X152)) = X152) & (pushprop_gthm = $true) & (! [X154 : subst,X155 : term] : ((comp @ sh @ (push @ X155 @ X154)) = X154) | (axshiftcons != $true)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK533 @ sK532)) != sK532)) & ! [X158 : d_subst,X159 : d_subst] : ((X158 = X159) | ((d2subst @ X159) != (d2subst @ X158))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X161 : term > $o] : ((X161 @ (sK535 @ X161)) != (sK534 @ id @ (sK535 @ X161) @ id))) & (! [X163 : subst > term > subst > $o] : ! [X165 : term] : ((sK536 @ X163 @ X165) = (X163 @ id @ X165 @ id)) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & (($true = sP13) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP13)) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X166 : term,X167 : term,X168 : subst > term > term] : (((lam @ (X168 @ sh @ one)) != (ap @ (sub @ X167 @ id) @ X166)) | ((sub @ (X168 @ (sK537 @ X168) @ (sK538 @ X168)) @ (sK539 @ X168)) != (X168 @ (comp @ (sK537 @ X168) @ (sK539 @ X168)) @ (sub @ (sK538 @ X168) @ (sK539 @ X168))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (((ap @ (sub @ sK541 @ id) @ sK540) = (lam @ (sK542 @ sh @ one))) & ! [X175 : subst,X176 : term,X177 : subst] : ((sK542 @ (comp @ X175 @ X177) @ (sub @ X176 @ X177)) = (sub @ (sK542 @ X175 @ X176) @ X177)))) & ((induction = $true) | (! [X180 : term] : (($true = (sK544 @ (lam @ X180))) | ($true != (sK544 @ X180))) & ($true != (sP12 @ sK544)) & ($true != (sK544 @ sK543)) & ! [X181 : term] : (($true != (var @ X181)) | ($true = (sK544 @ X181))))) & (! [X182 : term,X183 : term > $o] : ((($true != (X183 @ (lam @ (sK545 @ X183)))) & ($true = (X183 @ (sK545 @ X183)))) | ($true = (sP12 @ X183)) | ($true = (X183 @ X182)) | (($true = (var @ (sK546 @ X183))) & ($true != (X183 @ (sK546 @ X183))))) | (induction != $true)) & (! [X186 : term > $o,X187 : term,X188 : subst,X189 : term,X190 : term > $o] : (($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188)))) | ($true != (X186 @ X189))) | (sK547 != (sub @ one @ (push @ sK547 @ sK548))) | (sK549 != (comp @ sh @ (push @ sK550 @ sK549))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | ((((sK555 @ (sub @ sK554 @ (push @ sK552 @ sK553))) != $true) & ((sK551 @ sK554) = $true)) & ! [X200 : term,X201 : subst] : ((sub @ one @ (push @ X200 @ X201)) = X200) & ! [X202 : subst,X203 : term] : ((comp @ sh @ (push @ X203 @ X202)) = X202))) & (! [X204 : subst] : ((comp @ X204 @ id) = X204) | (axidr != $true)) & ((axidr = $true) | (sK556 != (comp @ sK556 @ id))) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & (! [X206 : term,X207 : term > $o,X208 : term > $o,X209 : subst,X210 : term] : (($true = (X207 @ (sub @ X206 @ (push @ X210 @ X209)))) | ($true != (X208 @ X206))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (((sK558 @ (sub @ sK557 @ (push @ sK561 @ sK560))) != $true) & ($true = (sK559 @ sK557)))) & ((hoasapinj1 = $true) | ((sK563 != sK562) & ((ap @ (sub @ sK563 @ id) @ sK564) = (ap @ (sub @ sK562 @ id) @ sK565)))) & (! [X220 : term,X221 : term,X222 : term,X223 : term] : ((X220 = X221) | ((ap @ (sub @ X220 @ id) @ X223) != (ap @ (sub @ X221 @ id) @ X222))) | (hoasapinj1 != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (((sK569 != sK567) & ((ap @ (sub @ sK566 @ id) @ sK569) = (ap @ (sub @ sK568 @ id) @ sK567))) & ! [X228 : term,X229 : term,X230 : term,X231 : term] : (((ap @ X228 @ X229) != (ap @ X230 @ X231)) | (X229 = X231)))) & (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X233 = X235) | ((ap @ (sub @ X234 @ id) @ X233) != (ap @ (sub @ X232 @ id) @ X235))) | (((ap @ sK570 @ sK571) = (ap @ sK572 @ sK573)) & (sK573 != sK571)) | (hoasapinj2_lthm != $true)) & (($true = sP11) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP11)) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & (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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & ((sK574 != (comp @ sK574 @ id)) | ((comp @ id @ sK575) != sK575) | (! [X242 : subst] : ((comp @ X242 @ id) = X242) & ! [X243 : subst] : ((comp @ id @ X243) = X243)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X244 : subst] : ((comp @ X244 @ id) = X244) & ! [X245 : subst] : ((comp @ id @ X245) = X245) & (((comp @ sK576 @ id) != sK576) | ((comp @ id @ sK577) != sK577)))) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) | (! [X252 : term] : ((sK579 @ X252) = (sK578 @ (sub @ X252 @ (push @ sK581 @ sK580)))) & ((sK578 @ sK581) = $true) & ($true != (sK579 @ one)))) & (! [X253 : term > $o,X254 : term > $o,X255 : subst,X256 : term] : (((X254 @ (sK582 @ X256 @ X255 @ X254 @ X253)) != (X253 @ (sub @ (sK582 @ X256 @ X255 @ X254 @ X253) @ (push @ X256 @ X255)))) | ($true != (X253 @ X256)) | ($true = (X254 @ one))) | (pushprop_lem1v2 != $true)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (! [X258 : term,X259 : term] : (((sub @ X259 @ sh) != (sub @ X258 @ sh)) | (X258 = X259)) | (shinj != $true)) & ((shinj = $true) | (((sub @ sK583 @ sh) = (sub @ sK584 @ sh)) & (sK584 != sK583))) & (! [X262 : subst,X263 : term] : ((sub @ one @ (push @ X263 @ X262)) = X263) | (axvarcons != $true)) & ((axvarcons = $true) | (sK586 != (sub @ one @ (push @ sK586 @ sK585)))) & (! [X266 : term] : ((sub @ X266 @ id) = X266) | ((sub @ sK587 @ id) != sK587) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (((sub @ sK588 @ id) != sK588) & ! [X269 : term] : ((sub @ X269 @ id) = X269))) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & (($true = sP2) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP2)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((substmonoid = $true) | ((comp @ id @ sK589) != sK589) | (sK590 != (comp @ sK590 @ id))) & ((! [X272 : subst] : ((comp @ id @ X272) = X272) & ! [X273 : subst] : ((comp @ X273 @ id) = X273)) | (substmonoid != $true))),
% 42.64/7.44 inference(skolemisation,[status(esa),new_symbols(skolem,[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])],[f475,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])).
% 42.64/7.44 thf(f476,plain,(
% 42.64/7.44 ? [X0 : term,X1 : subst > term > term,X2 : subst > term > term,X3 : subst] : (! [X4 : subst,X5 : term,X6 : subst] : ((sub @ (X2 @ X4 @ X5) @ X6) = (X2 @ (comp @ X4 @ X6) @ (sub @ X5 @ X6))) & ((lam @ (X2 @ sh @ one)) = (lam @ (X1 @ sh @ one))) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (X1 @ X9 @ X8) @ X7) = (X1 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7))) & ((X2 @ X3 @ X0) != (X1 @ X3 @ X0))) => (! [X6 : subst,X5 : term,X4 : subst] : ((sub @ (sK459 @ X4 @ X5) @ X6) = (sK459 @ (comp @ X4 @ X6) @ (sub @ X5 @ X6))) & ((lam @ (sK459 @ sh @ one)) = (lam @ (sK458 @ sh @ one))) & ! [X9 : subst,X8 : term,X7 : subst] : ((sub @ (sK458 @ X9 @ X8) @ X7) = (sK458 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7))) & ((sK459 @ sK460 @ sK457) != (sK458 @ sK460 @ sK457)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f477,plain,(
% 42.64/7.44 ! [X12 : subst > term > term] : (? [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X14 @ X15) @ X16) != (X12 @ (comp @ X14 @ X16) @ (sub @ X15 @ X16))) => ((X12 @ (comp @ (sK461 @ X12) @ (sK463 @ X12)) @ (sub @ (sK462 @ X12) @ (sK463 @ X12))) != (sub @ (X12 @ (sK461 @ X12) @ (sK462 @ X12)) @ (sK463 @ X12))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f478,plain,(
% 42.64/7.44 ! [X11 : subst > term > term] : (? [X17 : subst,X18 : term,X19 : subst] : ((sub @ (X11 @ X19 @ X18) @ X17) != (X11 @ (comp @ X19 @ X17) @ (sub @ X18 @ X17))) => ((sub @ (X11 @ (sK466 @ X11) @ (sK465 @ X11)) @ (sK464 @ X11)) != (X11 @ (comp @ (sK466 @ X11) @ (sK464 @ X11)) @ (sub @ (sK465 @ X11) @ (sK464 @ X11)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f479,plain,(
% 42.64/7.44 ? [X20 : term] : ((sub @ X20 @ id) != X20) => (sK467 != (sub @ sK467 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f480,plain,(
% 42.64/7.44 ? [X22 : term] : ! [X23 : subst > term > term] : ((sub @ X22 @ (push @ one @ sh)) != (X23 @ sh @ one)) => ! [X23 : subst > term > term] : ((sub @ sK468 @ (push @ one @ sh)) != (X23 @ sh @ one))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f481,plain,(
% 42.64/7.44 ! [X24 : term] : (? [X25 : subst > term > term] : ((X25 @ sh @ one) = (sub @ X24 @ (push @ one @ sh))) => ((sK469 @ X24 @ sh @ one) = (sub @ X24 @ (push @ one @ sh))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f482,plain,(
% 42.64/7.44 ? [X26 : term] : ((sub @ X26 @ id) != X26) => (sK470 != (sub @ sK470 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f483,plain,(
% 42.64/7.44 ? [X30 : term,X31 : term] : ((X30 != X31) & ((lam @ X31) = (lam @ X30))) => ((sK472 != sK471) & ((lam @ sK472) = (lam @ sK471)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f484,plain,(
% 42.64/7.44 ! [X32 : subst > term > subst > $o] : (? [X33 : term > $o] : ! [X34 : term] : ((X33 @ X34) = (X32 @ id @ X34 @ id)) => ! [X34 : term] : ((sK473 @ X32 @ X34) = (X32 @ id @ X34 @ id)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f485,plain,(
% 42.64/7.44 ? [X35 : subst > term > subst > $o] : ! [X36 : term > $o] : ? [X37 : term] : ((X36 @ X37) != (X35 @ id @ X37 @ id)) => ! [X36 : term > $o] : ? [X37 : term] : ((X36 @ X37) != (sK474 @ id @ X37 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f486,plain,(
% 42.64/7.44 ! [X36 : term > $o] : (? [X37 : term] : ((X36 @ X37) != (sK474 @ id @ X37 @ id)) => ((sK474 @ id @ (sK475 @ X36) @ id) != (X36 @ (sK475 @ X36))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f487,plain,(
% 42.64/7.44 ? [X38 : term > $o,X39 : subst,X40 : term] : ! [X41 : term > $o] : ? [X42 : term] : ((X38 @ (sub @ X42 @ (push @ X40 @ X39))) != (X41 @ X42)) => ! [X41 : term > $o] : ? [X42 : term] : ((sK476 @ (sub @ X42 @ (push @ sK478 @ sK477))) != (X41 @ X42))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f488,plain,(
% 42.64/7.44 ! [X41 : term > $o] : (? [X42 : term] : ((sK476 @ (sub @ X42 @ (push @ sK478 @ sK477))) != (X41 @ X42)) => ((X41 @ (sK479 @ X41)) != (sK476 @ (sub @ (sK479 @ X41) @ (push @ sK478 @ sK477)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f489,plain,(
% 42.64/7.44 ! [X43 : term > $o,X44 : subst,X45 : term] : (? [X46 : term > $o] : ! [X47 : term] : ((X43 @ (sub @ X47 @ (push @ X45 @ X44))) = (X46 @ X47)) => ! [X47 : term] : ((sK480 @ X45 @ X44 @ X43 @ X47) = (X43 @ (sub @ X47 @ (push @ X45 @ X44)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f490,plain,(
% 42.64/7.44 ! [X48 : term] : (? [X49 : subst > term > term] : ((X49 @ sh @ one) = (sub @ X48 @ (push @ one @ sh))) => ((sK481 @ X48 @ sh @ one) = (sub @ X48 @ (push @ one @ sh))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f491,plain,(
% 42.64/7.44 ? [X50 : term] : ! [X51 : subst > term > term] : ((sub @ X50 @ (push @ one @ sh)) != (X51 @ sh @ one)) => ! [X51 : subst > term > term] : ((X51 @ sh @ one) != (sub @ sK482 @ (push @ one @ sh)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f492,plain,(
% 42.64/7.44 ? [X53 : subst] : ((push @ (sub @ one @ X53) @ (comp @ sh @ X53)) != X53) => (sK483 != (push @ (sub @ one @ sK483) @ (comp @ sh @ sK483)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f493,plain,(
% 42.64/7.44 ? [X58 : term,X59 : term,X60 : term,X61 : term] : (((ap @ X60 @ X58) = (ap @ X61 @ X59)) & (X60 != X61)) => (((ap @ sK487 @ sK485) = (ap @ sK486 @ sK484)) & (sK486 != sK487))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f494,plain,(
% 42.64/7.44 ! [X62 : subst > term > subst > $o] : (? [X64 : term,X65 : term] : (($true = (X62 @ id @ X64 @ id)) & ($true != (X62 @ id @ (ap @ (sub @ X64 @ id) @ X65) @ id)) & ($true = (X62 @ id @ X65 @ id))) => (($true = (X62 @ id @ (sK488 @ X62) @ id)) & ($true != (X62 @ id @ (ap @ (sub @ (sK488 @ X62) @ id) @ (sK489 @ X62)) @ id)) & ((X62 @ id @ (sK489 @ X62) @ id) = $true)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f495,plain,(
% 42.64/7.44 ? [X66 : subst > term > subst > $o,X67 : term] : (! [X68 : term,X69 : term] : (((X66 @ id @ X68 @ id) != $true) | ($true = (X66 @ id @ (ap @ (sub @ X68 @ id) @ X69) @ id)) | ($true != (X66 @ id @ X69 @ id))) & ($true != (sP28 @ X66)) & ((X66 @ id @ X67 @ id) != $true)) => (! [X69 : term,X68 : term] : (($true != (sK490 @ id @ X68 @ id)) | ((sK490 @ id @ (ap @ (sub @ X68 @ id) @ X69) @ id) = $true) | ($true != (sK490 @ id @ X69 @ id))) & ($true != (sP28 @ sK490)) & ((sK490 @ id @ sK491 @ id) != $true))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f496,plain,(
% 42.64/7.44 ! [X70 : term] : (? [X71 : subst > term > term] : ! [X72 : subst,X73 : term] : ((X71 @ X72 @ X73) = (sub @ X70 @ (push @ X73 @ X72))) => ! [X73 : term,X72 : subst] : ((sub @ X70 @ (push @ X73 @ X72)) = (sK492 @ X70 @ X72 @ X73)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f497,plain,(
% 42.64/7.44 ? [X74 : term] : ! [X75 : subst > term > term] : ? [X76 : subst,X77 : term] : ((X75 @ X76 @ X77) != (sub @ X74 @ (push @ X77 @ X76))) => ! [X75 : subst > term > term] : ? [X77 : term,X76 : subst] : ((X75 @ X76 @ X77) != (sub @ sK493 @ (push @ X77 @ X76)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f498,plain,(
% 42.64/7.44 ! [X75 : subst > term > term] : (? [X77 : term,X76 : subst] : ((X75 @ X76 @ X77) != (sub @ sK493 @ (push @ X77 @ X76))) => ((X75 @ (sK494 @ X75) @ (sK495 @ X75)) != (sub @ sK493 @ (push @ (sK495 @ X75) @ (sK494 @ X75)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f499,plain,(
% 42.64/7.44 ! [X78 : term] : (? [X79 : subst > term > term] : ! [X80 : subst,X81 : term] : ((X79 @ X80 @ X81) = (sub @ X78 @ (push @ X81 @ X80))) => ! [X81 : term,X80 : subst] : ((sub @ X78 @ (push @ X81 @ X80)) = (sK496 @ X78 @ X80 @ X81)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f500,plain,(
% 42.64/7.44 ? [X82 : term] : ! [X83 : subst > term > term] : ? [X84 : subst,X85 : term] : ((X83 @ X84 @ X85) != (sub @ X82 @ (push @ X85 @ X84))) => ! [X83 : subst > term > term] : ? [X85 : term,X84 : subst] : ((sub @ sK497 @ (push @ X85 @ X84)) != (X83 @ X84 @ X85))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f501,plain,(
% 42.64/7.44 ! [X83 : subst > term > term] : (? [X85 : term,X84 : subst] : ((sub @ sK497 @ (push @ X85 @ X84)) != (X83 @ X84 @ X85)) => ((X83 @ (sK498 @ X83) @ (sK499 @ X83)) != (sub @ sK497 @ (push @ (sK499 @ X83) @ (sK498 @ X83)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f502,plain,(
% 42.64/7.44 ? [X86 : term,X87 : term,X88 : term,X89 : term] : ((X86 != X88) & ((ap @ (sub @ X89 @ id) @ X86) = (ap @ (sub @ X87 @ id) @ X88))) => ((sK502 != sK500) & ((ap @ (sub @ sK503 @ id) @ sK500) = (ap @ (sub @ sK501 @ id) @ sK502)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f503,plain,(
% 42.64/7.44 ? [X94 : term,X95 : term,X96 : term,X97 : term] : ((X94 != X97) & ((ap @ X94 @ X96) = (ap @ X97 @ X95))) => ((sK504 != sK507) & ((ap @ sK507 @ sK505) = (ap @ sK504 @ sK506)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f504,plain,(
% 42.64/7.44 ? [X98 : term] : ((sub @ X98 @ id) != X98) => ((sub @ sK508 @ id) != sK508)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f505,plain,(
% 42.64/7.44 ? [X108 : term,X109 : term,X110 : term,X111 : term] : (((ap @ (sub @ X110 @ id) @ X108) = (ap @ (sub @ X111 @ id) @ X109)) & (X110 != X111)) => (((ap @ (sub @ sK511 @ id) @ sK509) = (ap @ (sub @ sK512 @ id) @ sK510)) & (sK511 != sK512))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f506,plain,(
% 42.64/7.44 ? [X116 : subst] : ((comp @ id @ X116) != X116) => (sK513 != (comp @ id @ sK513))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f507,plain,(
% 42.64/7.44 ! [X117 : subst,X118 : term,X119 : term > $o] : (? [X120 : term > $o] : ! [X121 : term] : ((X120 @ X121) = (X119 @ (sub @ X121 @ (push @ X118 @ X117)))) => ! [X121 : term] : ((X119 @ (sub @ X121 @ (push @ X118 @ X117))) = (sK514 @ X119 @ X118 @ X117 @ X121)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f508,plain,(
% 42.64/7.44 ? [X122 : subst,X123 : term,X124 : term > $o] : ! [X125 : term > $o] : ? [X126 : term] : ((X124 @ (sub @ X126 @ (push @ X123 @ X122))) != (X125 @ X126)) => ! [X125 : term > $o] : ? [X126 : term] : ((sK517 @ (sub @ X126 @ (push @ sK516 @ sK515))) != (X125 @ X126))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f509,plain,(
% 42.64/7.44 ! [X125 : term > $o] : (? [X126 : term] : ((sK517 @ (sub @ X126 @ (push @ sK516 @ sK515))) != (X125 @ X126)) => ((X125 @ (sK518 @ X125)) != (sK517 @ (sub @ (sK518 @ X125) @ (push @ sK516 @ sK515)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f510,plain,(
% 42.64/7.44 ? [X131 : term,X132 : term,X133 : term,X134 : term] : (((ap @ X131 @ X134) = (ap @ X132 @ X133)) & (X133 != X134)) => (((ap @ sK520 @ sK521) = (ap @ sK519 @ sK522)) & (sK522 != sK521))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f511,plain,(
% 42.64/7.44 ! [X135 : term] : (? [X136 : d_term] : ((d2term @ X136) = X135) => ((d2term @ (sK523 @ X135)) = X135))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f512,plain,(
% 42.64/7.44 ? [X137 : term > $o,X138 : subst,X139 : term > $o,X140 : term] : (($true != (X139 @ one)) & ($true = (X137 @ X140)) & ! [X141 : term] : ((X139 @ X141) = (X137 @ (sub @ X141 @ (push @ X140 @ X138))))) => (($true != (sK526 @ one)) & ((sK524 @ sK527) = $true) & ! [X141 : term] : ((sK526 @ X141) = (sK524 @ (sub @ X141 @ (push @ sK527 @ sK525)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f513,plain,(
% 42.64/7.44 ! [X144 : term > $o,X145 : subst,X146 : term > $o,X147 : term] : (? [X148 : term] : ((X144 @ (sub @ X148 @ (push @ X147 @ X145))) != (X146 @ X148)) => ((X146 @ (sK528 @ X147 @ X146 @ X145 @ X144)) != (X144 @ (sub @ (sK528 @ X147 @ X146 @ X145 @ X144) @ (push @ X147 @ X145)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f514,plain,(
% 42.64/7.44 ? [X149 : subst,X150 : term] : ((sub @ one @ (push @ X150 @ X149)) != X150) => ((sub @ one @ (push @ sK530 @ sK529)) != sK530)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f515,plain,(
% 42.64/7.44 ! [X152 : subst] : (? [X153 : d_subst] : ((d2subst @ X153) = X152) => ((d2subst @ (sK531 @ X152)) = X152))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f516,plain,(
% 42.64/7.44 ? [X156 : subst,X157 : term] : ((comp @ sh @ (push @ X157 @ X156)) != X156) => ((comp @ sh @ (push @ sK533 @ sK532)) != sK532)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f517,plain,(
% 42.64/7.44 ? [X160 : subst > term > subst > $o] : ! [X161 : term > $o] : ? [X162 : term] : ((X160 @ id @ X162 @ id) != (X161 @ X162)) => ! [X161 : term > $o] : ? [X162 : term] : ((sK534 @ id @ X162 @ id) != (X161 @ X162))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f518,plain,(
% 42.64/7.44 ! [X161 : term > $o] : (? [X162 : term] : ((sK534 @ id @ X162 @ id) != (X161 @ X162)) => ((X161 @ (sK535 @ X161)) != (sK534 @ id @ (sK535 @ X161) @ id)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f519,plain,(
% 42.64/7.44 ! [X163 : subst > term > subst > $o] : (? [X164 : term > $o] : ! [X165 : term] : ((X164 @ X165) = (X163 @ id @ X165 @ id)) => ! [X165 : term] : ((sK536 @ X163 @ X165) = (X163 @ id @ X165 @ id)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f520,plain,(
% 42.64/7.44 ! [X168 : subst > term > term] : (? [X169 : subst,X170 : term,X171 : subst] : ((X168 @ (comp @ X169 @ X171) @ (sub @ X170 @ X171)) != (sub @ (X168 @ X169 @ X170) @ X171)) => ((sub @ (X168 @ (sK537 @ X168) @ (sK538 @ X168)) @ (sK539 @ X168)) != (X168 @ (comp @ (sK537 @ X168) @ (sK539 @ X168)) @ (sub @ (sK538 @ X168) @ (sK539 @ X168)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f521,plain,(
% 42.64/7.44 ? [X172 : term,X173 : term,X174 : subst > term > term] : (((ap @ (sub @ X173 @ id) @ X172) = (lam @ (X174 @ sh @ one))) & ! [X175 : subst,X176 : term,X177 : subst] : ((X174 @ (comp @ X175 @ X177) @ (sub @ X176 @ X177)) = (sub @ (X174 @ X175 @ X176) @ X177))) => (((ap @ (sub @ sK541 @ id) @ sK540) = (lam @ (sK542 @ sh @ one))) & ! [X177 : subst,X176 : term,X175 : subst] : ((sK542 @ (comp @ X175 @ X177) @ (sub @ X176 @ X177)) = (sub @ (sK542 @ X175 @ X176) @ X177)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f522,plain,(
% 42.64/7.44 ? [X178 : term,X179 : term > $o] : (! [X180 : term] : (($true = (X179 @ (lam @ X180))) | ((X179 @ X180) != $true)) & ($true != (sP12 @ X179)) & ((X179 @ X178) != $true) & ! [X181 : term] : (($true != (var @ X181)) | ($true = (X179 @ X181)))) => (! [X180 : term] : (($true = (sK544 @ (lam @ X180))) | ($true != (sK544 @ X180))) & ($true != (sP12 @ sK544)) & ($true != (sK544 @ sK543)) & ! [X181 : term] : (($true != (var @ X181)) | ($true = (sK544 @ X181))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f523,plain,(
% 42.64/7.44 ! [X183 : term > $o] : (? [X184 : term] : (((X183 @ (lam @ X184)) != $true) & ((X183 @ X184) = $true)) => (($true != (X183 @ (lam @ (sK545 @ X183)))) & ($true = (X183 @ (sK545 @ X183)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f524,plain,(
% 42.64/7.44 ! [X183 : term > $o] : (? [X185 : term] : (($true = (var @ X185)) & ($true != (X183 @ X185))) => (($true = (var @ (sK546 @ X183))) & ($true != (X183 @ (sK546 @ X183)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f525,plain,(
% 42.64/7.44 ? [X191 : term,X192 : subst] : ((sub @ one @ (push @ X191 @ X192)) != X191) => (sK547 != (sub @ one @ (push @ sK547 @ sK548)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f526,plain,(
% 42.64/7.44 ? [X193 : subst,X194 : term] : ((comp @ sh @ (push @ X194 @ X193)) != X193) => (sK549 != (comp @ sh @ (push @ sK550 @ sK549)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f527,plain,(
% 42.64/7.44 ? [X195 : term > $o,X196 : term,X197 : subst,X198 : term,X199 : term > $o] : (($true != (X199 @ (sub @ X198 @ (push @ X196 @ X197)))) & ($true = (X195 @ X198))) => (((sK555 @ (sub @ sK554 @ (push @ sK552 @ sK553))) != $true) & ((sK551 @ sK554) = $true))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f528,plain,(
% 42.64/7.44 ? [X205 : subst] : ((comp @ X205 @ id) != X205) => (sK556 != (comp @ sK556 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f529,plain,(
% 42.64/7.44 ? [X211 : term,X212 : term > $o,X213 : term > $o,X214 : subst,X215 : term] : (((X212 @ (sub @ X211 @ (push @ X215 @ X214))) != $true) & ($true = (X213 @ X211))) => (((sK558 @ (sub @ sK557 @ (push @ sK561 @ sK560))) != $true) & ($true = (sK559 @ sK557)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f530,plain,(
% 42.64/7.44 ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 != X217) & ((ap @ (sub @ X216 @ id) @ X219) = (ap @ (sub @ X217 @ id) @ X218))) => ((sK563 != sK562) & ((ap @ (sub @ sK563 @ id) @ sK564) = (ap @ (sub @ sK562 @ id) @ sK565)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f531,plain,(
% 42.64/7.44 ? [X224 : term,X225 : term,X226 : term,X227 : term] : ((X225 != X227) & ((ap @ (sub @ X224 @ id) @ X227) = (ap @ (sub @ X226 @ id) @ X225))) => ((sK569 != sK567) & ((ap @ (sub @ sK566 @ id) @ sK569) = (ap @ (sub @ sK568 @ id) @ sK567)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f532,plain,(
% 42.64/7.44 ? [X236 : term,X237 : term,X238 : term,X239 : term] : (((ap @ X238 @ X239) = (ap @ X236 @ X237)) & (X237 != X239)) => (((ap @ sK570 @ sK571) = (ap @ sK572 @ sK573)) & (sK573 != sK571))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f533,plain,(
% 42.64/7.44 ? [X240 : subst] : ((comp @ X240 @ id) != X240) => (sK574 != (comp @ sK574 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f534,plain,(
% 42.64/7.44 ? [X241 : subst] : ((comp @ id @ X241) != X241) => ((comp @ id @ sK575) != sK575)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f535,plain,(
% 42.64/7.44 ? [X246 : subst] : ((comp @ X246 @ id) != X246) => ((comp @ sK576 @ id) != sK576)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f536,plain,(
% 42.64/7.44 ? [X247 : subst] : ((comp @ id @ X247) != X247) => ((comp @ id @ sK577) != sK577)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f537,plain,(
% 42.64/7.44 ? [X248 : term > $o,X249 : term > $o,X250 : subst,X251 : term] : (! [X252 : term] : ((X249 @ X252) = (X248 @ (sub @ X252 @ (push @ X251 @ X250)))) & ($true = (X248 @ X251)) & ($true != (X249 @ one))) => (! [X252 : term] : ((sK579 @ X252) = (sK578 @ (sub @ X252 @ (push @ sK581 @ sK580)))) & ((sK578 @ sK581) = $true) & ($true != (sK579 @ one)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f538,plain,(
% 42.64/7.44 ! [X253 : term > $o,X254 : term > $o,X255 : subst,X256 : term] : (? [X257 : term] : ((X254 @ X257) != (X253 @ (sub @ X257 @ (push @ X256 @ X255)))) => ((X254 @ (sK582 @ X256 @ X255 @ X254 @ X253)) != (X253 @ (sub @ (sK582 @ X256 @ X255 @ X254 @ X253) @ (push @ X256 @ X255)))))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f539,plain,(
% 42.64/7.44 ? [X260 : term,X261 : term] : (((sub @ X260 @ sh) = (sub @ X261 @ sh)) & (X260 != X261)) => (((sub @ sK583 @ sh) = (sub @ sK584 @ sh)) & (sK584 != sK583))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f540,plain,(
% 42.64/7.44 ? [X264 : subst,X265 : term] : ((sub @ one @ (push @ X265 @ X264)) != X265) => (sK586 != (sub @ one @ (push @ sK586 @ sK585)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f541,plain,(
% 42.64/7.44 ? [X267 : term] : ((sub @ X267 @ id) != X267) => ((sub @ sK587 @ id) != sK587)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f542,plain,(
% 42.64/7.44 ? [X268 : term] : ((sub @ X268 @ id) != X268) => ((sub @ sK588 @ id) != sK588)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f543,plain,(
% 42.64/7.44 ? [X270 : subst] : ((comp @ id @ X270) != X270) => ((comp @ id @ sK589) != sK589)),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f544,plain,(
% 42.64/7.44 ? [X271 : subst] : ((comp @ X271 @ id) != X271) => (sK590 != (comp @ sK590 @ id))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f475,plain,(
% 42.64/7.44 ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lthm = $true) | ($true != sP57)) & (($true = sP57) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((hoaslaminj = $true) | ? [X0 : term,X1 : subst > term > term,X2 : subst > term > term,X3 : subst] : (! [X4 : subst,X5 : term,X6 : subst] : ((sub @ (X2 @ X4 @ X5) @ X6) = (X2 @ (comp @ X4 @ X6) @ (sub @ X5 @ X6))) & ((lam @ (X2 @ sh @ one)) = (lam @ (X1 @ sh @ one))) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (X1 @ X9 @ X8) @ X7) = (X1 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7))) & ((X2 @ X3 @ X0) != (X1 @ X3 @ X0)))) & (! [X10 : term,X11 : subst > term > term,X12 : subst > term > term,X13 : subst] : (? [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X14 @ X15) @ X16) != (X12 @ (comp @ X14 @ X16) @ (sub @ X15 @ X16))) | ((lam @ (X12 @ sh @ one)) != (lam @ (X11 @ sh @ one))) | ? [X17 : subst,X18 : term,X19 : subst] : ((sub @ (X11 @ X19 @ X18) @ X17) != (X11 @ (comp @ X19 @ X17) @ (sub @ X18 @ X17))) | ((X12 @ X13 @ X10) = (X11 @ X13 @ X10))) | (hoaslaminj != $true)) & (lamnotap != $true) & (apnotvar = $true) & ((axvarid = $true) | ? [X20 : term] : ((sub @ X20 @ id) != X20)) & (! [X21 : term] : ((sub @ X21 @ id) = X21) | (axvarid != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3b_lthm = $true) | ? [X22 : term] : ! [X23 : subst > term > term] : ((sub @ X22 @ (push @ one @ sh)) != (X23 @ sh @ one))) & (! [X24 : term] : ? [X25 : subst > term > term] : ((X25 @ sh @ one) = (sub @ X24 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP48)) & (($true = sP48) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (($true = sP45) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP45)) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & ((termmset = $true) | ? [X26 : term] : ((sub @ X26 @ id) != X26)) & (! [X27 : term] : ((sub @ X27 @ id) = X27) | (termmset != $true)) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP39) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP39)) & (hoasapinj2_gthm = $true) & (! [X28 : term,X29 : term] : ((X28 = X29) | ((lam @ X29) != (lam @ X28))) | (laminj != $true)) & ((laminj = $true) | ? [X30 : term,X31 : term] : ((X30 != X31) & ((lam @ X31) = (lam @ X30)))) & (($true = sP36) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP36)) & (axapp = $true) & (($true = sP34) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP34)) & (hoasinduction_lem2_gthm = $true) & (! [X32 : subst > term > subst > $o] : ? [X33 : term > $o] : ! [X34 : term] : ((X33 @ X34) = (X32 @ id @ X34 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X35 : subst > term > subst > $o] : ! [X36 : term > $o] : ? [X37 : term] : ((X36 @ X37) != (X35 @ id @ X37 @ id))) & ((pushprop_lem0_lthm = $true) | ? [X38 : term > $o,X39 : subst,X40 : term] : ! [X41 : term > $o] : ? [X42 : term] : ((X38 @ (sub @ X42 @ (push @ X40 @ X39))) != (X41 @ X42))) & (! [X43 : term > $o,X44 : subst,X45 : term] : ? [X46 : term > $o] : ! [X47 : term] : ((X43 @ (sub @ X47 @ (push @ X45 @ X44))) = (X46 @ X47)) | (pushprop_lem0_lthm != $true)) & (! [X48 : term] : ? [X49 : subst > term > term] : ((X49 @ sh @ one) = (sub @ X48 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X50 : term] : ! [X51 : subst > term > term] : ((sub @ X50 @ (push @ one @ sh)) != (X51 @ sh @ one))) & (! [X52 : subst] : ((push @ (sub @ one @ X52) @ (comp @ sh @ X52)) = X52) | (axscons != $true)) & ((axscons = $true) | ? [X53 : subst] : ((push @ (sub @ one @ X53) @ (comp @ sh @ X53)) != X53)) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & (! [X54 : term,X55 : term,X56 : term,X57 : term] : (((ap @ X57 @ X55) != (ap @ X56 @ X54)) | (X56 = X57)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X58 : term,X59 : term,X60 : term,X61 : term] : (((ap @ X60 @ X58) = (ap @ X61 @ X59)) & (X60 != X61))) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & (axvarshift = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X62 : subst > term > subst > $o,X63 : term] : (? [X64 : term,X65 : term] : (($true = (X62 @ id @ X64 @ id)) & ($true != (X62 @ id @ (ap @ (sub @ X64 @ id) @ X65) @ id)) & ($true = (X62 @ id @ X65 @ id))) | ($true = (sP28 @ X62)) | ($true = (X62 @ id @ X63 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X66 : subst > term > subst > $o,X67 : term] : (! [X68 : term,X69 : term] : (((X66 @ id @ X68 @ id) != $true) | ($true = (X66 @ id @ (ap @ (sub @ X68 @ id) @ X69) @ id)) | ($true != (X66 @ id @ X69 @ id))) & ($true != (sP28 @ X66)) & ((X66 @ id @ X67 @ id) != $true))) & (hoaslamnotap_lthm = $true) & ((induction2 = $true) | ($true != sP27)) & (($true = sP27) | (induction2 != $true)) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X70 : term] : ? [X71 : subst > term > term] : ! [X72 : subst,X73 : term] : ((X71 @ X72 @ X73) = (sub @ X70 @ (push @ X73 @ X72))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X74 : term] : ! [X75 : subst > term > term] : ? [X76 : subst,X77 : term] : ((X75 @ X76 @ X77) != (sub @ X74 @ (push @ X77 @ X76)))) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (! [X78 : term] : ? [X79 : subst > term > term] : ! [X80 : subst,X81 : term] : ((X79 @ X80 @ X81) = (sub @ X78 @ (push @ X81 @ X80))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X82 : term] : ! [X83 : subst > term > term] : ? [X84 : subst,X85 : term] : ((X83 @ X84 @ X85) != (sub @ X82 @ (push @ X85 @ X84)))) & ((hoasapinj2 = $true) | ? [X86 : term,X87 : term,X88 : term,X89 : term] : ((X86 != X88) & ((ap @ (sub @ X89 @ id) @ X86) = (ap @ (sub @ X87 @ id) @ X88)))) & (! [X90 : term,X91 : term,X92 : term,X93 : term] : ((X90 = X92) | ((ap @ (sub @ X93 @ id) @ X90) != (ap @ (sub @ X91 @ id) @ X92))) | (hoasapinj2 != $true)) & (($true = sP21) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP21)) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (? [X94 : term,X95 : term,X96 : term,X97 : term] : ((X94 != X97) & ((ap @ X94 @ X96) = (ap @ X97 @ X95))) | ? [X98 : term] : ((sub @ X98 @ id) != X98) | ! [X99 : term,X100 : term,X101 : term,X102 : term] : (((ap @ (sub @ X102 @ id) @ X100) != (ap @ (sub @ X101 @ id) @ X99)) | (X101 = X102)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X103 : term,X104 : term,X105 : term,X106 : term] : ((X103 = X106) | ((ap @ X106 @ X104) != (ap @ X103 @ X105))) & ! [X107 : term] : ((sub @ X107 @ id) = X107) & ? [X108 : term,X109 : term,X110 : term,X111 : term] : (((ap @ (sub @ X110 @ id) @ X108) = (ap @ (sub @ X111 @ id) @ X109)) & (X110 != X111)))) & ! [X112 : d_term,X113 : d_term] : (((d2term @ X113) != (d2term @ X112)) | (X112 = X113)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X114 : d_term] : (d_one = X114) & (pushprop_lem3v2 = $true) & (! [X115 : subst] : ((comp @ id @ X115) = X115) | (axidl != $true)) & ((axidl = $true) | ? [X116 : subst] : ((comp @ id @ X116) != X116)) & (! [X117 : subst,X118 : term,X119 : term > $o] : ? [X120 : term > $o] : ! [X121 : term] : ((X120 @ X121) = (X119 @ (sub @ X121 @ (push @ X118 @ X117)))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X122 : subst,X123 : term,X124 : term > $o] : ! [X125 : term > $o] : ? [X126 : term] : ((X124 @ (sub @ X126 @ (push @ X123 @ X122))) != (X125 @ X126))) & (induction2lem_gthm = $true) & (! [X127 : term,X128 : term,X129 : term,X130 : term] : (((ap @ X127 @ X130) != (ap @ X128 @ X129)) | (X129 = X130)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X131 : term,X132 : term,X133 : term,X134 : term] : (((ap @ X131 @ X134) = (ap @ X132 @ X133)) & (X133 != X134))) & ! [X135 : term] : ? [X136 : d_term] : ((d2term @ X136) = X135) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X137 : term > $o,X138 : subst,X139 : term > $o,X140 : term] : (($true != (X139 @ one)) & ($true = (X137 @ X140)) & ! [X141 : term] : ((X139 @ X141) = (X137 @ (sub @ X141 @ (push @ X140 @ X138))))) & ! [X142 : subst,X143 : term] : ((sub @ one @ (push @ X143 @ X142)) = X143))) & (! [X144 : term > $o,X145 : subst,X146 : term > $o,X147 : term] : (($true = (X146 @ one)) | ($true != (X144 @ X147)) | ? [X148 : term] : ((X144 @ (sub @ X148 @ (push @ X147 @ X145))) != (X146 @ X148))) | ? [X149 : subst,X150 : term] : ((sub @ one @ (push @ X150 @ X149)) != X150) | (pushprop_lem1v2_lthm != $true)) & (($true = sP17) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP17)) & (($true = sP15) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP15)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X151 : d_subst] : (d_id = X151) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X152 : subst] : ? [X153 : d_subst] : ((d2subst @ X153) = X152) & (pushprop_gthm = $true) & (! [X154 : subst,X155 : term] : ((comp @ sh @ (push @ X155 @ X154)) = X154) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X156 : subst,X157 : term] : ((comp @ sh @ (push @ X157 @ X156)) != X156)) & ! [X158 : d_subst,X159 : d_subst] : ((X158 = X159) | ((d2subst @ X159) != (d2subst @ X158))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X160 : subst > term > subst > $o] : ! [X161 : term > $o] : ? [X162 : term] : ((X160 @ id @ X162 @ id) != (X161 @ X162))) & (! [X163 : subst > term > subst > $o] : ? [X164 : term > $o] : ! [X165 : term] : ((X164 @ X165) = (X163 @ id @ X165 @ id)) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & (($true = sP13) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP13)) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X166 : term,X167 : term,X168 : subst > term > term] : (((lam @ (X168 @ sh @ one)) != (ap @ (sub @ X167 @ id) @ X166)) | ? [X169 : subst,X170 : term,X171 : subst] : ((X168 @ (comp @ X169 @ X171) @ (sub @ X170 @ X171)) != (sub @ (X168 @ X169 @ X170) @ X171))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X172 : term,X173 : term,X174 : subst > term > term] : (((ap @ (sub @ X173 @ id) @ X172) = (lam @ (X174 @ sh @ one))) & ! [X175 : subst,X176 : term,X177 : subst] : ((X174 @ (comp @ X175 @ X177) @ (sub @ X176 @ X177)) = (sub @ (X174 @ X175 @ X176) @ X177)))) & ((induction = $true) | ? [X178 : term,X179 : term > $o] : (! [X180 : term] : (($true = (X179 @ (lam @ X180))) | ((X179 @ X180) != $true)) & ($true != (sP12 @ X179)) & ((X179 @ X178) != $true) & ! [X181 : term] : (($true != (var @ X181)) | ($true = (X179 @ X181))))) & (! [X182 : term,X183 : term > $o] : (? [X184 : term] : (((X183 @ (lam @ X184)) != $true) & ((X183 @ X184) = $true)) | ($true = (sP12 @ X183)) | ($true = (X183 @ X182)) | ? [X185 : term] : (($true = (var @ X185)) & ($true != (X183 @ X185)))) | (induction != $true)) & (! [X186 : term > $o,X187 : term,X188 : subst,X189 : term,X190 : term > $o] : (($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188)))) | ($true != (X186 @ X189))) | ? [X191 : term,X192 : subst] : ((sub @ one @ (push @ X191 @ X192)) != X191) | ? [X193 : subst,X194 : term] : ((comp @ sh @ (push @ X194 @ X193)) != X193) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X195 : term > $o,X196 : term,X197 : subst,X198 : term,X199 : term > $o] : (($true != (X199 @ (sub @ X198 @ (push @ X196 @ X197)))) & ($true = (X195 @ X198))) & ! [X200 : term,X201 : subst] : ((sub @ one @ (push @ X200 @ X201)) = X200) & ! [X202 : subst,X203 : term] : ((comp @ sh @ (push @ X203 @ X202)) = X202))) & (! [X204 : subst] : ((comp @ X204 @ id) = X204) | (axidr != $true)) & ((axidr = $true) | ? [X205 : subst] : ((comp @ X205 @ id) != X205)) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & (! [X206 : term,X207 : term > $o,X208 : term > $o,X209 : subst,X210 : term] : (($true = (X207 @ (sub @ X206 @ (push @ X210 @ X209)))) | ($true != (X208 @ X206))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X211 : term,X212 : term > $o,X213 : term > $o,X214 : subst,X215 : term] : (((X212 @ (sub @ X211 @ (push @ X215 @ X214))) != $true) & ($true = (X213 @ X211)))) & ((hoasapinj1 = $true) | ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 != X217) & ((ap @ (sub @ X216 @ id) @ X219) = (ap @ (sub @ X217 @ id) @ X218)))) & (! [X220 : term,X221 : term,X222 : term,X223 : term] : ((X220 = X221) | ((ap @ (sub @ X220 @ id) @ X223) != (ap @ (sub @ X221 @ id) @ X222))) | (hoasapinj1 != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (? [X224 : term,X225 : term,X226 : term,X227 : term] : ((X225 != X227) & ((ap @ (sub @ X224 @ id) @ X227) = (ap @ (sub @ X226 @ id) @ X225))) & ! [X228 : term,X229 : term,X230 : term,X231 : term] : (((ap @ X228 @ X229) != (ap @ X230 @ X231)) | (X229 = X231)))) & (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X233 = X235) | ((ap @ (sub @ X234 @ id) @ X233) != (ap @ (sub @ X232 @ id) @ X235))) | ? [X236 : term,X237 : term,X238 : term,X239 : term] : (((ap @ X238 @ X239) = (ap @ X236 @ X237)) & (X237 != X239)) | (hoasapinj2_lthm != $true)) & (($true = sP11) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP11)) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & (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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (? [X240 : subst] : ((comp @ X240 @ id) != X240) | ? [X241 : subst] : ((comp @ id @ X241) != X241) | (! [X242 : subst] : ((comp @ X242 @ id) = X242) & ! [X243 : subst] : ((comp @ id @ X243) = X243)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X244 : subst] : ((comp @ X244 @ id) = X244) & ! [X245 : subst] : ((comp @ id @ X245) = X245) & (? [X246 : subst] : ((comp @ X246 @ id) != X246) | ? [X247 : subst] : ((comp @ id @ X247) != X247)))) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X248 : term > $o,X249 : term > $o,X250 : subst,X251 : term] : (! [X252 : term] : ((X249 @ X252) = (X248 @ (sub @ X252 @ (push @ X251 @ X250)))) & ($true = (X248 @ X251)) & ($true != (X249 @ one)))) & (! [X253 : term > $o,X254 : term > $o,X255 : subst,X256 : term] : (? [X257 : term] : ((X254 @ X257) != (X253 @ (sub @ X257 @ (push @ X256 @ X255)))) | ($true != (X253 @ X256)) | ($true = (X254 @ one))) | (pushprop_lem1v2 != $true)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (! [X258 : term,X259 : term] : (((sub @ X259 @ sh) != (sub @ X258 @ sh)) | (X258 = X259)) | (shinj != $true)) & ((shinj = $true) | ? [X260 : term,X261 : term] : (((sub @ X260 @ sh) = (sub @ X261 @ sh)) & (X260 != X261))) & (! [X262 : subst,X263 : term] : ((sub @ one @ (push @ X263 @ X262)) = X263) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X264 : subst,X265 : term] : ((sub @ one @ (push @ X265 @ X264)) != X265)) & (! [X266 : term] : ((sub @ X266 @ id) = X266) | ? [X267 : term] : ((sub @ X267 @ id) != X267) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X268 : term] : ((sub @ X268 @ id) != X268) & ! [X269 : term] : ((sub @ X269 @ id) = X269))) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & (($true = sP2) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP2)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((substmonoid = $true) | ? [X270 : subst] : ((comp @ id @ X270) != X270) | ? [X271 : subst] : ((comp @ X271 @ id) != X271)) & ((! [X272 : subst] : ((comp @ id @ X272) = X272) & ! [X273 : subst] : ((comp @ X273 @ id) = X273)) | (substmonoid != $true))),
% 42.64/7.44 inference(rectify,[status(thm)],[f474])).
% 42.64/7.44 thf(f474,plain,(
% 42.64/7.44 ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lthm = $true) | ($true != sP57)) & (($true = sP57) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((hoaslaminj = $true) | ? [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (! [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) = (sub @ (X417 @ X419 @ X420) @ X421)) & ((lam @ (X417 @ sh @ one)) = (lam @ (X416 @ sh @ one))) & ! [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) = (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) & ((X416 @ X418 @ X415) != (X417 @ X418 @ X415)))) & (! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (? [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) != (sub @ (X417 @ X419 @ X420) @ X421)) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))) | ? [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) != (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415))) | (hoaslaminj != $true)) & (lamnotap != $true) & (apnotvar = $true) & ((axvarid = $true) | ? [X73 : term] : ((sub @ X73 @ id) != X73)) & (! [X73 : term] : ((sub @ X73 @ id) = X73) | (axvarid != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3b_lthm = $true) | ? [X216 : term] : ! [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) != (X217 @ sh @ one))) & (! [X216 : term] : ? [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) = (X217 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP48)) & (($true = sP48) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (($true = sP45) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP45)) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & ((termmset = $true) | ? [X344 : term] : ((sub @ X344 @ id) != X344)) & (! [X344 : term] : ((sub @ X344 @ id) = X344) | (termmset != $true)) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP39) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP39)) & (hoasapinj2_gthm = $true) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) | (laminj != $true)) & ((laminj = $true) | ? [X440 : term,X441 : term] : ((X440 != X441) & ((lam @ X440) = (lam @ X441)))) & (($true = sP36) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP36)) & (axapp = $true) & (($true = sP34) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP34)) & (hoasinduction_lem2_gthm = $true) & (! [X397 : subst > term > subst > $o] : ? [X398 : term > $o] : ! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X397 : subst > term > subst > $o] : ! [X398 : term > $o] : ? [X399 : term] : ((X398 @ X399) != (X397 @ id @ X399 @ id))) & ((pushprop_lem0_lthm = $true) | ? [X273 : term > $o,X274 : subst,X275 : term] : ! [X276 : term > $o] : ? [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) != (X276 @ X277))) & (! [X273 : term > $o,X274 : subst,X275 : term] : ? [X276 : term > $o] : ! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277)) | (pushprop_lem0_lthm != $true)) & (! [X49 : term] : ? [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) = (X50 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X49 : term] : ! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one))) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) | (axscons != $true)) & ((axscons = $true) | ? [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) != X243)) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) = (ap @ X136 @ X134)) & (X136 != X137))) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & (axvarshift = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) = $true) & ($true != (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) & ($true = (X203 @ id @ X206 @ id))) | ($true = (sP28 @ X203)) | ($true = (X203 @ id @ X204 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X203 : subst > term > subst > $o,X204 : term] : (! [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) != $true) | ($true = (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) | ($true != (X203 @ id @ X206 @ id))) & ($true != (sP28 @ X203)) & ($true != (X203 @ id @ X204 @ id)))) & (hoaslamnotap_lthm = $true) & ((induction2 = $true) | ($true != sP27)) & (($true = sP27) | (induction2 != $true)) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X111 : term] : ? [X112 : subst > term > term] : ! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X111 : term] : ! [X112 : subst > term > term] : ? [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) != (sub @ X111 @ (push @ X114 @ X113)))) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (! [X19 : term] : ? [X20 : subst > term > term] : ! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X19 : term] : ! [X20 : subst > term > term] : ? [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) != (sub @ X19 @ (push @ X22 @ X21)))) & ((hoasapinj2 = $true) | ? [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 != X97) & ((ap @ (sub @ X96 @ id) @ X97) = (ap @ (sub @ X98 @ id) @ X95)))) & (! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95))) | (hoasapinj2 != $true)) & (($true = sP21) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP21)) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (? [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 != X222) & ((ap @ X222 @ X220) = (ap @ X219 @ X221))) | ? [X218 : term] : ((sub @ X218 @ id) != X218) | ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 = X222) | ((ap @ X222 @ X220) != (ap @ X219 @ X221))) & ! [X218 : term] : ((sub @ X218 @ id) = X218) & ? [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) = (ap @ (sub @ X225 @ id) @ X223)) & (X225 != X226)))) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) != (d2term @ X408)) | (X407 = X408)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X388 : d_term] : (d_one = X388) & (pushprop_lem3v2 = $true) & (! [X70 : subst] : ((comp @ id @ X70) = X70) | (axidl != $true)) & ((axidl = $true) | ? [X70 : subst] : ((comp @ id @ X70) != X70)) & (! [X196 : subst,X197 : term,X198 : term > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196)))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X196 : subst,X197 : term,X198 : term > $o] : ! [X199 : term > $o] : ? [X200 : term] : ((X199 @ X200) != (X198 @ (sub @ X200 @ (push @ X197 @ X196))))) & (induction2lem_gthm = $true) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) = (ap @ X213 @ X214)) & (X214 != X215))) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) != $true) & ($true = (X402 @ X405)) & ! [X406 : term] : ((X404 @ X406) = (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) & ! [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) = X401))) & (! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ($true != (X402 @ X405)) | ? [X406 : term] : ((X404 @ X406) != (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) | ? [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) != X401) | (pushprop_lem1v2_lthm != $true)) & (($true = sP17) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP17)) & (($true = sP15) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP15)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (pushprop_gthm = $true) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) != X71)) & ! [X51 : d_subst,X52 : d_subst] : ((X51 = X52) | ((d2subst @ X52) != (d2subst @ X51))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X252 : subst > term > subst > $o] : ! [X253 : term > $o] : ? [X254 : term] : ((X253 @ X254) != (X252 @ id @ X254 @ id))) & (! [X252 : subst > term > subst > $o] : ? [X253 : term > $o] : ! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id)) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & (($true = sP13) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP13)) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509)) | ? [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) != (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) = (ap @ (sub @ X510 @ id) @ X509)) & ! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) = (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))))) & ((induction = $true) | ? [X409 : term,X410 : term > $o] : (! [X411 : term] : (($true = (X410 @ (lam @ X411))) | ($true != (X410 @ X411))) & ($true != (sP12 @ X410)) & ($true != (X410 @ X409)) & ! [X412 : term] : (((var @ X412) != $true) | ($true = (X410 @ X412))))) & (! [X409 : term,X410 : term > $o] : (? [X411 : term] : (($true != (X410 @ (lam @ X411))) & ($true = (X410 @ X411))) | ($true = (sP12 @ X410)) | ($true = (X410 @ X409)) | ? [X412 : term] : (((var @ X412) = $true) & ($true != (X410 @ X412)))) | (induction != $true)) & (! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342))) | ? [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) != X335) | ? [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) != X337) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true != (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) & ($true = (X339 @ X342))) & ! [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) = X335) & ! [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) = X337))) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) | (axidr != $true)) & ((axidr = $true) | ? [X539 : subst] : ((comp @ X539 @ id) != X539)) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true != (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) & ($true = (X67 @ X65)))) & ((hoasapinj1 = $true) | ? [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 != X38) & ((ap @ (sub @ X38 @ id) @ X39) = (ap @ (sub @ X37 @ id) @ X40)))) & (! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40))) | (hoasapinj1 != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (? [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 != X251) & ((ap @ (sub @ X248 @ id) @ X251) = (ap @ (sub @ X250 @ id) @ X249))) & ! [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) != (ap @ X246 @ X247)) | (X245 = X247)))) & (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) = (ap @ X246 @ X247)) & (X245 != X247)) | (hoasapinj2_lthm != $true)) & (($true = sP11) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP11)) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & (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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (? [X139 : subst] : ((comp @ X139 @ id) != X139) | ? [X138 : subst] : ((comp @ id @ X138) != X138) | (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X139 : subst] : ((comp @ X139 @ id) = X139) & ! [X138 : subst] : ((comp @ id @ X138) = X138) & (? [X141 : subst] : ((comp @ X141 @ id) != X141) | ? [X140 : subst] : ((comp @ id @ X140) != X140)))) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) & ($true = (X99 @ X102)) & ($true != (X100 @ one)))) & (! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (? [X103 : term] : ((X100 @ X103) != (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true != (X99 @ X102)) | ($true = (X100 @ one))) | (pushprop_lem1v2 != $true)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) | (shinj != $true)) & ((shinj = $true) | ? [X255 : term,X256 : term] : (((sub @ X255 @ sh) = (sub @ X256 @ sh)) & (X255 != X256))) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) != X75)) & (! [X202 : term] : ((sub @ X202 @ id) = X202) | ? [X201 : term] : ((sub @ X201 @ id) != X201) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X202 : term] : ((sub @ X202 @ id) != X202) & ! [X201 : term] : ((sub @ X201 @ id) = X201))) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & (($true = sP2) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP2)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((substmonoid = $true) | ? [X443 : subst] : ((comp @ id @ X443) != X443) | ? [X442 : subst] : ((comp @ X442 @ id) != X442)) & ((! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442)) | (substmonoid != $true))),
% 42.64/7.44 inference(flattening,[status(thm)],[f473])).
% 42.64/7.44 thf(f473,plain,(
% 42.64/7.44 (((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true))) & (((hoasinduction_lthm = $true) | ($true != sP57)) & (($true = sP57) | (hoasinduction_lthm != $true))) & (hoasinduction_lem1_lthm = $true) & (((hoaslaminj = $true) | ? [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (! [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) = (sub @ (X417 @ X419 @ X420) @ X421)) & ((lam @ (X417 @ sh @ one)) = (lam @ (X416 @ sh @ one))) & ! [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) = (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) & ((X416 @ X418 @ X415) != (X417 @ X418 @ X415)))) & (! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (? [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) != (sub @ (X417 @ X419 @ X420) @ X421)) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))) | ? [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) != (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415))) | (hoaslaminj != $true))) & (lamnotap != $true) & (apnotvar = $true) & (((axvarid = $true) | ? [X73 : term] : ((sub @ X73 @ id) != X73)) & (! [X73 : term] : ((sub @ X73 @ id) = X73) | (axvarid != $true))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (((hoasinduction_lem3b_lthm = $true) | ? [X216 : term] : ! [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) != (X217 @ sh @ one))) & (! [X216 : term] : ? [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) = (X217 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true))) & (((hoasinduction_lem3_lthm = $true) | ($true != sP48)) & (($true = sP48) | (hoasinduction_lem3_lthm != $true))) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & ((($true = sP45) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP45))) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & (((termmset = $true) | ? [X344 : term] : ((sub @ X344 @ id) != X344)) & (! [X344 : term] : ((sub @ X344 @ id) = X344) | (termmset != $true))) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_no_psi_cond_lthm != $true))) & ((($true = sP39) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP39))) & (hoasapinj2_gthm = $true) & ((! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) | (laminj != $true)) & ((laminj = $true) | ? [X440 : term,X441 : term] : ((X440 != X441) & ((lam @ X440) = (lam @ X441))))) & ((($true = sP36) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP36))) & (axapp = $true) & ((($true = sP34) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP34))) & (hoasinduction_lem2_gthm = $true) & ((! [X397 : subst > term > subst > $o] : ? [X398 : term > $o] : ! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X397 : subst > term > subst > $o] : ! [X398 : term > $o] : ? [X399 : term] : ((X398 @ X399) != (X397 @ id @ X399 @ id)))) & (((pushprop_lem0_lthm = $true) | ? [X273 : term > $o,X274 : subst,X275 : term] : ! [X276 : term > $o] : ? [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) != (X276 @ X277))) & (! [X273 : term > $o,X274 : subst,X275 : term] : ? [X276 : term > $o] : ! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277)) | (pushprop_lem0_lthm != $true))) & ((! [X49 : term] : ? [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) = (X50 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X49 : term] : ! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one)))) & ((! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) | (axscons != $true)) & ((axscons = $true) | ? [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) != X243))) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & ((! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) = (ap @ X136 @ X134)) & (X136 != X137)))) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & ((($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33))) & (axvarshift = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem2v2 != $true))) & (((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true))) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & ((! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) = $true) & ($true != (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) & ($true = (X203 @ id @ X206 @ id))) | ($true = (sP28 @ X203)) | ($true = (X203 @ id @ X204 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X203 : subst > term > subst > $o,X204 : term] : (! [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) != $true) | ($true = (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) | ($true != (X203 @ id @ X206 @ id))) & ($true != (sP28 @ X203)) & ($true != (X203 @ id @ X204 @ id))))) & (hoaslamnotap_lthm = $true) & (((induction2 = $true) | ($true != sP27)) & (($true = sP27) | (induction2 != $true))) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((! [X111 : term] : ? [X112 : subst > term > term] : ! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X111 : term] : ! [X112 : subst > term > term] : ? [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) != (sub @ X111 @ (push @ X114 @ X113))))) & ((($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25))) & ((! [X19 : term] : ? [X20 : subst > term > term] : ! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X19 : term] : ! [X20 : subst > term > term] : ? [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) != (sub @ X19 @ (push @ X22 @ X21))))) & (((hoasapinj2 = $true) | ? [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 != X97) & ((ap @ (sub @ X96 @ id) @ X97) = (ap @ (sub @ X98 @ id) @ X95)))) & (! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95))) | (hoasapinj2 != $true))) & ((($true = sP21) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP21))) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((? [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 != X222) & ((ap @ X222 @ X220) = (ap @ X219 @ X221))) | ? [X218 : term] : ((sub @ X218 @ id) != X218) | ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 = X222) | ((ap @ X222 @ X220) != (ap @ X219 @ X221))) & ! [X218 : term] : ((sub @ X218 @ id) = X218) & ? [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) = (ap @ (sub @ X225 @ id) @ X223)) & (X225 != X226))))) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) != (d2term @ X408)) | (X407 = X408)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X388 : d_term] : (d_one = X388) & (pushprop_lem3v2 = $true) & ((! [X70 : subst] : ((comp @ id @ X70) = X70) | (axidl != $true)) & ((axidl = $true) | ? [X70 : subst] : ((comp @ id @ X70) != X70))) & ((! [X196 : subst,X197 : term,X198 : term > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196)))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X196 : subst,X197 : term,X198 : term > $o] : ! [X199 : term > $o] : ? [X200 : term] : ((X199 @ X200) != (X198 @ (sub @ X200 @ (push @ X197 @ X196)))))) & (induction2lem_gthm = $true) & ((! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) = (ap @ X213 @ X214)) & (X214 != X215)))) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & (((pushprop_lem1v2_lthm = $true) | (? [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) != $true) & ($true = (X402 @ X405)) & ! [X406 : term] : ((X404 @ X406) = (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) & ! [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) = X401))) & ((! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ($true != (X402 @ X405)) | ? [X406 : term] : ((X404 @ X406) != (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) | ? [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) != X401)) | (pushprop_lem1v2_lthm != $true))) & ((($true = sP17) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP17))) & ((($true = sP15) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP15))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (pushprop_gthm = $true) & ((! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) != X71))) & ! [X51 : d_subst,X52 : d_subst] : ((X51 = X52) | ((d2subst @ X52) != (d2subst @ X51))) & (pushprop_lthm_orig = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X252 : subst > term > subst > $o] : ! [X253 : term > $o] : ? [X254 : term] : ((X253 @ X254) != (X252 @ id @ X254 @ id))) & (! [X252 : subst > term > subst > $o] : ? [X253 : term > $o] : ! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id)) | (hoasinduction_lem0_lthm != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & ((($true = sP13) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP13))) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((! [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509)) | ? [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) != (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) = (ap @ (sub @ X510 @ id) @ X509)) & ! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) = (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))))) & (((induction = $true) | ? [X409 : term,X410 : term > $o] : (! [X411 : term] : (($true = (X410 @ (lam @ X411))) | ($true != (X410 @ X411))) & ($true != (sP12 @ X410)) & ($true != (X410 @ X409)) & ! [X412 : term] : (((var @ X412) != $true) | ($true = (X410 @ X412))))) & (! [X409 : term,X410 : term > $o] : (? [X411 : term] : (($true != (X410 @ (lam @ X411))) & ($true = (X410 @ X411))) | ($true = (sP12 @ X410)) | ($true = (X410 @ X409)) | ? [X412 : term] : (((var @ X412) = $true) & ($true != (X410 @ X412)))) | (induction != $true))) & (((! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342))) | ? [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) != X335) | ? [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) != X337)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true != (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) & ($true = (X339 @ X342))) & ! [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) = X335) & ! [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) = X337)))) & ((! [X539 : subst] : ((comp @ X539 @ id) = X539) | (axidr != $true)) & ((axidr = $true) | ? [X539 : subst] : ((comp @ X539 @ id) != X539))) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & ((! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true != (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) & ($true = (X67 @ X65))))) & (((hoasapinj1 = $true) | ? [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 != X38) & ((ap @ (sub @ X38 @ id) @ X39) = (ap @ (sub @ X37 @ id) @ X40)))) & (! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40))) | (hoasapinj1 != $true))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & (((hoasapinj2_lthm = $true) | (? [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 != X251) & ((ap @ (sub @ X248 @ id) @ X251) = (ap @ (sub @ X250 @ id) @ X249))) & ! [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) != (ap @ X246 @ X247)) | (X245 = X247)))) & ((! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) = (ap @ X246 @ X247)) & (X245 != X247))) | (hoasapinj2_lthm != $true))) & ((($true = sP11) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP11))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10))) & (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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (((? [X139 : subst] : ((comp @ X139 @ id) != X139) | ? [X138 : subst] : ((comp @ id @ X138) != X138) | (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X139 : subst] : ((comp @ X139 @ id) = X139) & ! [X138 : subst] : ((comp @ id @ X138) = X138) & (? [X141 : subst] : ((comp @ X141 @ id) != X141) | ? [X140 : subst] : ((comp @ id @ X140) != X140))))) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & (((pushprop_lem1v2 = $true) | ? [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) & ($true = (X99 @ X102)) & ($true != (X100 @ one)))) & (! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (? [X103 : term] : ((X100 @ X103) != (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true != (X99 @ X102)) | ($true = (X100 @ one))) | (pushprop_lem1v2 != $true))) & ((($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4))) & ((! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) | (shinj != $true)) & ((shinj = $true) | ? [X255 : term,X256 : term] : (((sub @ X255 @ sh) = (sub @ X256 @ sh)) & (X255 != X256)))) & ((! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) != X75))) & (((! [X202 : term] : ((sub @ X202 @ id) = X202) | ? [X201 : term] : ((sub @ X201 @ id) != X201)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X202 : term] : ((sub @ X202 @ id) != X202) & ! [X201 : term] : ((sub @ X201 @ id) = X201)))) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & ((($true = sP2) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP2))) & (((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (((substmonoid = $true) | (? [X443 : subst] : ((comp @ id @ X443) != X443) | ? [X442 : subst] : ((comp @ X442 @ id) != X442))) & ((! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442)) | (substmonoid != $true)))),
% 42.64/7.44 inference(nnf_transformation,[status(thm)],[f73])).
% 42.64/7.44 thf(f73,plain,(
% 42.64/7.44 ((hoasinduction_lem3aa = $true) <=> ($true = sP58)) & ((hoasinduction_lthm = $true) <=> ($true = sP57)) & (hoasinduction_lem1_lthm = $true) & ((hoaslaminj = $true) <=> ! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (? [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) != (sub @ (X417 @ X419 @ X420) @ X421)) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))) | ? [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) != (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415)))) & (lamnotap != $true) & (apnotvar = $true) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X216 : term] : ? [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) = (X217 @ sh @ one))) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP48)) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (($true = sP45) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & ((termmset = $true) <=> ! [X344 : term] : ((sub @ X344 @ id) = X344)) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP44)) & (($true = sP39) <=> (hoasinduction = $true)) & (hoasapinj2_gthm = $true) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) <=> (laminj = $true)) & (($true = sP36) <=> (hoasinduction_lem3v2 = $true)) & (axapp = $true) & (($true = sP34) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X397 : subst > term > subst > $o] : ? [X398 : term > $o] : ! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id)) <=> (hoasinduction_lem0 = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X273 : term > $o,X274 : subst,X275 : term] : ? [X276 : term > $o] : ! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277))) & (! [X49 : term] : ? [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) = (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) <=> (axscons = $true)) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & (($true = sP33) <=> (hoasinduction_lem3a = $true)) & (axvarshift = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP32)) & ((hoasinduction_lem2 = $true) <=> ($true = sP30)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) = $true) & ($true != (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) & ($true = (X203 @ id @ X206 @ id))) | ($true = (sP28 @ X203)) | ($true = (X203 @ id @ X204 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (hoaslamnotap_lthm = $true) & ((induction2 = $true) <=> ($true = sP27)) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X111 : term] : ? [X112 : subst > term > term] : ! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113))) <=> (hoasinduction_lem3v2_f = $true)) & (($true = sP25) <=> (induction2_lthm = $true)) & (! [X19 : term] : ? [X20 : subst > term > term] : ! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & (($true = sP21) <=> (induction2lem_lthm = $true)) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & ((? [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 != X222) & ((ap @ X222 @ X220) = (ap @ X219 @ X221))) | ? [X218 : term] : ((sub @ X218 @ id) != X218) | ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226))) <=> (hoasapinj1_lthm = $true)) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) != (d2term @ X408)) | (X407 = X408)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X388 : d_term] : (d_one = X388) & (pushprop_lem3v2 = $true) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & (! [X196 : subst,X197 : term,X198 : term > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196)))) <=> (pushprop_lem0 = $true)) & (induction2lem_gthm = $true) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ($true != (X402 @ X405)) | ? [X406 : term] : ((X404 @ X406) != (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) | ? [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) != X401))) & (($true = sP17) <=> (hoasinduction_lem3v2_lthm = $true)) & (($true = sP15) <=> (induction2lem = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (pushprop_gthm = $true) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ! [X51 : d_subst,X52 : d_subst] : ((X51 = X52) | ((d2subst @ X52) != (d2subst @ X51))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X252 : subst > term > subst > $o] : ? [X253 : term > $o] : ! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & (($true = sP13) <=> (hoasinduction_lem3aaa = $true)) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509)) | ? [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) != (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))) <=> (hoaslamnotap = $true)) & ((induction = $true) <=> ! [X409 : term,X410 : term > $o] : (? [X411 : term] : (($true != (X410 @ (lam @ X411))) & ($true = (X410 @ X411))) | ($true = (sP12 @ X410)) | ($true = (X410 @ X409)) | ? [X412 : term] : (((var @ X412) = $true) & ($true != (X410 @ X412))))) & ((! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342))) | ? [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) != X335) | ? [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) != X337)) <=> (pushprop_lem1_lthm = $true)) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) <=> (axidr = $true)) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) <=> (pushprop_lem1 = $true)) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) = (ap @ X246 @ X247)) & (X245 != X247)))) & (($true = sP11) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (($true = sP10) <=> (hoasinduction_lthm_3 = $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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & ((? [X139 : subst] : ((comp @ X139 @ id) != X139) | ? [X138 : subst] : ((comp @ id @ X138) != X138) | (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (? [X103 : term] : ((X100 @ X103) != (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true != (X99 @ X102)) | ($true = (X100 @ one)))) & (($true = sP4) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) <=> (shinj = $true)) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & ((! [X202 : term] : ((sub @ X202 @ id) = X202) | ? [X201 : term] : ((sub @ X201 @ id) != X201)) <=> (termmset_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & (($true = sP2) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP0 = $true)) & ((substmonoid = $true) <=> (! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442)))),
% 42.64/7.44 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])).
% 42.64/7.44 thf(f14,plain,(
% 42.64/7.44 (sP0 = $true) <=> ! [X501 : term,X502 : subst > term > subst > $o] : (? [X508 : term] : (($true != (X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)) & ($true = (X502 @ id @ X508 @ id))) | ((X502 @ id @ (lam @ (sub @ X501 @ (push @ one @ sh))) @ id) = $true) | ? [X503 : subst > term > term] : (! [X504 : subst,X505 : term,X506 : subst] : ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)) = (sub @ (X503 @ X506 @ X505) @ X504)) & ! [X507 : term] : (($true = (X502 @ id @ (X503 @ id @ X507) @ id)) | ($true != (X502 @ id @ X507 @ id))) & ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id) != $true)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f15,plain,(
% 42.64/7.44 ! [X523 : subst > term > subst > $o] : (($true = (sP1 @ X523)) <=> ? [X530 : subst > term > term] : (($true != (X523 @ id @ (lam @ (X530 @ sh @ one)) @ id)) & ! [X531 : subst,X532 : term,X533 : subst] : ((sub @ (X530 @ X531 @ X532) @ X533) = (X530 @ (comp @ X531 @ X533) @ (sub @ X532 @ X533))) & ! [X534 : term] : (($true != (X523 @ id @ X534 @ id)) | ($true = (X523 @ id @ (X530 @ id @ X534) @ id)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f16,plain,(
% 42.64/7.44 ($true = sP2) <=> ! [X523 : subst > term > subst > $o,X524 : term] : (? [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (($true != (X523 @ X538 @ X535 @ (comp @ X536 @ X537))) & ($true = (X523 @ (comp @ X538 @ X536) @ (sub @ X535 @ X536) @ X537))) | ($true = (X523 @ id @ (lam @ X524) @ id)) | ? [X525 : term] : (($true != (X523 @ id @ (sub @ X524 @ (push @ X525 @ id)) @ id)) & ($true = (X523 @ id @ X525 @ id))) | ($true = (sP1 @ X523)) | ? [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (((X523 @ (comp @ X527 @ X526) @ (sub @ X529 @ X526) @ X528) != $true) & ($true = (X523 @ X527 @ X529 @ (comp @ X526 @ X528)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f17,plain,(
% 42.64/7.44 ($true = sP3) <=> ? [X3 : subst > term > subst > $o,X4 : term] : (($true != (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id)) & ! [X10 : term] : (((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X3 @ id @ X10 @ id))) & ! [X5 : subst > term > term] : (? [X9 : term] : (($true != (X3 @ id @ (X5 @ id @ X9) @ id)) & ($true = (X3 @ id @ X9 @ id))) | ($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id)) | ? [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) != (sub @ (X5 @ X7 @ X8) @ X6))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f18,plain,(
% 42.64/7.44 ($true = sP4) <=> (! [X11 : subst > term > subst > $o,X12 : term] : (? [X13 : subst > term > term] : (($true != (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) & ! [X17 : term] : (($true != (X11 @ id @ X17 @ id)) | ($true = (X11 @ id @ (X13 @ id @ X17) @ id))) & ! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14))) | ($true = (X11 @ id @ (lam @ X12) @ id)) | ? [X18 : term] : (($true = (X11 @ id @ X18 @ id)) & ($true != (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)))) | ? [X2 : term] : ((sub @ X2 @ id) != X2) | ($true = sP3))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f19,plain,(
% 42.64/7.44 ! [X484 : subst > term > subst > $o] : (($true = (sP5 @ X484)) <=> ? [X493 : term,X494 : term] : (($true = (X484 @ id @ X494 @ id)) & ($true = (X484 @ id @ X493 @ id)) & ($true != (X484 @ id @ (ap @ (sub @ X493 @ id) @ X494) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f20,plain,(
% 42.64/7.44 ! [X484 : subst > term > subst > $o] : (($true = (sP6 @ X484)) <=> ? [X496 : subst > term > term] : (! [X500 : term] : (($true != (X484 @ id @ X500 @ id)) | ($true = (X484 @ id @ (X496 @ id @ X500) @ id))) & ($true != (X484 @ id @ (lam @ (X496 @ sh @ one)) @ id)) & ! [X497 : term,X498 : subst,X499 : subst] : ((X496 @ (comp @ X499 @ X498) @ (sub @ X497 @ X498)) = (sub @ (X496 @ X499 @ X497) @ X498))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f21,plain,(
% 42.64/7.44 ! [X466 : term > $o] : (($true = (sP7 @ X466)) <=> ! [X467 : term,X468 : term] : (((X466 @ X468) != $true) | ($true != (X466 @ X467)) | ($true = (X466 @ (ap @ X468 @ X467)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f22,plain,(
% 42.64/7.44 ($true = sP8) <=> ! [X483 : term,X484 : subst > term > subst > $o] : (($true = (X484 @ id @ X483 @ id)) | ($true = (sP6 @ X484)) | ? [X489 : subst,X490 : subst,X491 : term,X492 : subst] : (($true != (X484 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) & ($true = (X484 @ X489 @ X491 @ (comp @ X492 @ X490)))) | ? [X495 : term] : (($true = (var @ (sub @ X495 @ id))) & ($true != (X484 @ id @ X495 @ id))) | ? [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (($true = (X484 @ (comp @ X485 @ X488) @ (sub @ X487 @ X488) @ X486)) & ($true != (X484 @ X485 @ X487 @ (comp @ X488 @ X486)))) | ($true = (sP5 @ X484)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f23,plain,(
% 42.64/7.44 (sP9 = $true) <=> ? [X473 : term > $o,X474 : subst > term > subst > $o,X475 : term] : (! [X478 : subst > term > term] : (? [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X481 @ X482) @ (sub @ X480 @ X482)) != (sub @ (X478 @ X481 @ X480) @ X482)) | ? [X479 : term] : (($true = (X474 @ id @ X479 @ id)) & ($true != (X474 @ id @ (X478 @ id @ X479) @ id))) | ($true = (X474 @ id @ (lam @ (X478 @ sh @ one)) @ id))) & ($true != (X473 @ (lam @ X475))) & ! [X476 : term] : (($true = (X473 @ (sub @ X475 @ (push @ X476 @ id)))) | ((X473 @ X476) != $true)) & ! [X477 : term] : ((X474 @ id @ X477 @ id) = (X473 @ X477)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f24,plain,(
% 42.64/7.44 ($true = sP10) <=> (? [X472 : term] : ((sub @ X472 @ id) != X472) | ? [X465 : term,X466 : term > $o] : (! [X470 : term] : (($true = (X466 @ (lam @ X470))) | ? [X471 : term] : (((X466 @ (sub @ X470 @ (push @ X471 @ id))) != $true) & ($true = (X466 @ X471)))) & ($true != (X466 @ X465)) & ! [X469 : term] : (((X466 @ X469) = $true) | ($true != (var @ X469))) & ($true = (sP7 @ X466))) | (sP9 = $true) | ($true = sP8) | ? [X462 : subst > term > subst > $o] : ! [X463 : term > $o] : ? [X464 : term] : ((X462 @ id @ X464 @ id) != (X463 @ X464)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f25,plain,(
% 42.64/7.44 ($true = sP11) <=> (! [X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (? [X439 : term] : (($true = (X431 @ X439)) & ($true != (X431 @ (sub @ X430 @ (push @ X439 @ id))))) | ? [X438 : term] : ((X432 @ id @ X438 @ id) != (X431 @ X438)) | ($true = (X431 @ (lam @ X430))) | ? [X433 : subst > term > term] : (! [X434 : term] : (($true != (X432 @ id @ X434 @ id)) | ($true = (X432 @ id @ (X433 @ id @ X434) @ id))) & ($true != (X432 @ id @ (lam @ (X433 @ sh @ one)) @ id)) & ! [X435 : subst,X436 : term,X437 : subst] : ((X433 @ (comp @ X437 @ X435) @ (sub @ X436 @ X435)) = (sub @ (X433 @ X437 @ X436) @ X435)))) | ? [X425 : term] : ! [X426 : subst > term > term] : ? [X427 : term,X428 : subst] : ((sub @ X425 @ (push @ X427 @ X428)) != (X426 @ X428 @ X427)) | ? [X429 : term] : ((sub @ X429 @ id) != X429))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f26,plain,(
% 42.64/7.44 ! [X410 : term > $o] : (($true = (sP12 @ X410)) <=> ? [X413 : term,X414 : term] : (($true = (X410 @ X414)) & ($true = (X410 @ X413)) & ($true != (X410 @ (ap @ X414 @ X413)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f27,plain,(
% 42.64/7.44 ($true = sP13) <=> ! [X53 : subst > term > subst > $o,X54 : term] : (? [X56 : subst > term > term,X57 : term] : (! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) & ! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63)))) & ! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ($true != (X53 @ id @ X61 @ id))) & ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) != $true)) | ($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ? [X55 : term] : (($true != (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) & ($true = (X53 @ id @ X55 @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f28,plain,(
% 42.64/7.44 ! [X516 : term > $o] : (($true = (sP14 @ X516)) <=> ? [X519 : term,X520 : term] : (($true = (X516 @ X519)) & ($true = (X516 @ X520)) & ($true != (X516 @ (ap @ X520 @ X519)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f29,plain,(
% 42.64/7.44 ($true = sP15) <=> ! [X515 : subst,X516 : term > $o,X517 : term] : (? [X518 : term] : (($true = (var @ X518)) & ($true != (X516 @ (sub @ X518 @ X515)))) | ? [X521 : term] : (! [X522 : term] : (($true != (X516 @ X522)) | ($true = (X516 @ (sub @ X521 @ (push @ X522 @ id))))) & ($true != (X516 @ (lam @ X521)))) | ($true = (X516 @ (sub @ X517 @ X515))) | ($true = (sP14 @ X516)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f30,plain,(
% 42.64/7.44 ! [X78 : subst > term > subst > $o] : (($true = (sP16 @ X78)) <=> ? [X90 : subst > term > term] : (($true != (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id)) & ! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) & ! [X94 : term] : (($true = (X78 @ id @ (X90 @ id @ X94) @ id)) | ($true != (X78 @ id @ X94 @ id)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f31,plain,(
% 42.64/7.44 ($true = sP17) <=> (? [X76 : term] : ((sub @ X76 @ id) != X76) | ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (? [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (($true = (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) & ($true != (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))) | ($true = (sP16 @ X78)) | ? [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (($true != (X78 @ X87 @ X85 @ (comp @ X86 @ X88))) & ($true = (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88))) | ($true = (X79 @ (lam @ X77))) | ? [X89 : term] : (($true = (X79 @ X89)) & ($true != (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ? [X80 : term] : ((X78 @ id @ X80 @ id) != (X79 @ X80))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f32,plain,(
% 42.64/7.44 ! [X126 : term > $o] : (((sP18 @ X126) = $true) <=> ? [X129 : term,X130 : term] : (($true = (X126 @ X129)) & ($true = (X126 @ X130)) & ((X126 @ (ap @ X130 @ X129)) != $true)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f33,plain,(
% 42.64/7.44 ! [X120 : term > $o] : (($true = (sP19 @ X120)) <=> ! [X123 : term,X124 : term] : (($true != (X120 @ X123)) | ($true != (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f34,plain,(
% 42.64/7.44 ($true = sP20) <=> ! [X126 : term > $o,X127 : term,X128 : subst] : (? [X131 : term] : (! [X132 : term] : (($true != (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id))))) & ($true != (X126 @ (lam @ X131)))) | ? [X133 : term] : (($true != (X126 @ (sub @ X133 @ X128))) & ($true = (var @ X133))) | ((sP18 @ X126) = $true) | ($true = (X126 @ (sub @ X127 @ X128))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f35,plain,(
% 42.64/7.44 ($true = sP21) <=> (? [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) != X116) | ? [X120 : term > $o,X121 : term] : (! [X122 : term] : (((var @ X122) != $true) | ($true = (X120 @ X122))) & ($true != (X120 @ X121)) & ($true = (sP19 @ X120)) & ! [X125 : term] : (($true = (X120 @ (lam @ X125))) | ($true != (X120 @ X125)))) | ($true = sP20) | ? [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) != X117) | ? [X119 : subst] : ((comp @ X119 @ id) != X119))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f36,plain,(
% 42.64/7.44 ! [X237 : term > $o] : (($true = (sP22 @ X237)) <=> ? [X239 : term,X240 : term] : (($true = (X237 @ X240)) & ($true != (X237 @ (ap @ X240 @ X239))) & ($true = (X237 @ X239))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f37,plain,(
% 42.64/7.44 ! [X228 : term > $o] : (($true = (sP23 @ X228)) <=> ! [X234 : term,X235 : term] : (($true = (X228 @ (ap @ X234 @ X235))) | ($true != (X228 @ X235)) | ($true != (X228 @ X234))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f38,plain,(
% 42.64/7.44 ($true = sP24) <=> ! [X236 : term,X237 : term > $o] : (? [X238 : term] : (($true = (var @ X238)) & ($true != (X237 @ X238))) | ($true = (sP22 @ X237)) | ($true = (X237 @ X236)) | ? [X241 : term] : (! [X242 : term] : (($true != (X237 @ X242)) | ($true = (X237 @ (sub @ X241 @ (push @ X242 @ id))))) & ($true != (X237 @ (lam @ X241)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f39,plain,(
% 42.64/7.44 ($true = sP25) <=> (? [X228 : term > $o,X229 : subst,X230 : term] : (($true = (sP23 @ X228)) & ! [X232 : term] : (? [X233 : term] : (($true = (X228 @ X233)) & ($true != (X228 @ (sub @ X232 @ (push @ X233 @ id))))) | ($true = (X228 @ (lam @ X232)))) & ! [X231 : term] : (($true != (var @ X231)) | ($true = (X228 @ (sub @ X231 @ X229)))) & ($true != (X228 @ (sub @ X230 @ X229)))) | ($true = sP24) | ? [X227 : term] : ((sub @ X227 @ id) != X227))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f40,plain,(
% 42.64/7.44 ! [X105 : term > $o] : (($true = (sP26 @ X105)) <=> ? [X109 : term,X110 : term] : (($true = (X105 @ X110)) & ($true != (X105 @ (ap @ X109 @ X110))) & ((X105 @ X109) = $true)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f41,plain,(
% 42.64/7.44 ($true = sP27) <=> ! [X104 : term,X105 : term > $o] : (($true = (sP26 @ X105)) | ? [X106 : term] : (! [X107 : term] : (((X105 @ X107) != $true) | ($true = (X105 @ (sub @ X106 @ (push @ X107 @ id))))) & ($true != (X105 @ (lam @ X106)))) | ? [X108 : term] : (($true != (X105 @ X108)) & ((var @ X108) = $true)) | ($true = (X105 @ X104)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f42,plain,(
% 42.64/7.44 ! [X203 : subst > term > subst > $o] : (($true = (sP28 @ X203)) <=> ? [X207 : subst > term > term] : (($true != (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)) & ! [X208 : term] : (($true != (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) & ! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f43,plain,(
% 42.64/7.44 ! [X26 : subst > term > subst > $o] : (($true = (sP29 @ X26)) <=> ? [X31 : term,X32 : term] : (($true = (X26 @ id @ X31 @ id)) & ($true = (X26 @ id @ X32 @ id)) & ($true != (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f44,plain,(
% 42.64/7.44 ($true = sP30) <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (($true = (X26 @ id @ (ap @ X24 @ X25) @ id)) | ((X26 @ id @ X24 @ id) != $true) | ? [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true = (X26 @ X33 @ X36 @ (comp @ X34 @ X35))) & ($true != (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35))) | ? [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true = (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) & ($true != (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ($true != (X26 @ id @ X25 @ id)) | ($true = (sP29 @ X26)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f45,plain,(
% 42.64/7.44 ! [X281 : subst > term > subst > $o] : (((sP31 @ X281) = $true) <=> ? [X282 : term,X283 : term] : (($true = (X281 @ id @ X282 @ id)) & ((X281 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id) != $true) & ($true = (X281 @ id @ X283 @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f46,plain,(
% 42.64/7.44 ($true = sP32) <=> ! [X278 : term,X279 : term > $o,X280 : term,X281 : subst > term > subst > $o] : (($true != (X279 @ X280)) | ($true != (X279 @ X278)) | ($true = (X279 @ (ap @ X278 @ X280))) | ? [X288 : term,X289 : subst,X290 : subst,X291 : subst] : (($true != (X281 @ (comp @ X289 @ X291) @ (sub @ X288 @ X291) @ X290)) & ((X281 @ X289 @ X288 @ (comp @ X291 @ X290)) = $true)) | ? [X292 : term] : ((X279 @ X292) != (X281 @ id @ X292 @ id)) | ((sP31 @ X281) = $true) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X281 @ (comp @ X284 @ X287) @ (sub @ X286 @ X287) @ X285)) & ($true != (X281 @ X284 @ X286 @ (comp @ X287 @ X285)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f47,plain,(
% 42.64/7.44 ($true = sP33) <=> ! [X41 : term,X42 : subst > term > subst > $o] : (? [X43 : subst > term > term] : (! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) & ($true != (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) & ! [X47 : term] : (($true = (X42 @ id @ (X43 @ id @ X47) @ id)) | ((X42 @ id @ X47 @ id) != $true))) | ? [X48 : term] : (($true = (X42 @ id @ X48 @ id)) & ($true != (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id))) | ($true = (X42 @ id @ (lam @ X41) @ id)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f48,plain,(
% 42.64/7.44 ($true = sP34) <=> ! [X295 : term > $o,X296 : term,X297 : subst > term > subst > $o] : (? [X304 : term] : (($true != (X295 @ (sub @ X296 @ (push @ X304 @ id)))) & ((X295 @ X304) = $true)) | ? [X298 : subst > term > term] : (! [X300 : subst,X301 : term,X302 : subst] : ((sub @ (X298 @ X302 @ X301) @ X300) = (X298 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300))) & ($true != (X297 @ id @ (lam @ (X298 @ sh @ one)) @ id)) & ! [X299 : term] : (((X297 @ id @ X299 @ id) != $true) | ($true = (X297 @ id @ (X298 @ id @ X299) @ id)))) | ? [X303 : term] : ((X295 @ X303) != (X297 @ id @ X303 @ id)) | ($true = (X295 @ (lam @ X296))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f49,plain,(
% 42.64/7.44 ! [X347 : subst > term > subst > $o] : (($true = (sP35 @ X347)) <=> ? [X349 : subst > term > term] : (($true != (X347 @ id @ (lam @ (X349 @ sh @ one)) @ id)) & ! [X351 : subst,X352 : subst,X353 : term] : ((X349 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)) = (sub @ (X349 @ X351 @ X353) @ X352)) & ! [X350 : term] : (((X347 @ id @ X350 @ id) != $true) | ($true = (X347 @ id @ (X349 @ id @ X350) @ id)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f50,plain,(
% 42.64/7.44 ($true = sP36) <=> ! [X345 : term > $o,X346 : term,X347 : subst > term > subst > $o] : (? [X354 : subst,X355 : subst,X356 : subst,X357 : term] : (((X347 @ (comp @ X354 @ X356) @ (sub @ X357 @ X356) @ X355) = $true) & ($true != (X347 @ X354 @ X357 @ (comp @ X356 @ X355)))) | ? [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (($true != (X347 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360) @ X362)) & ($true = (X347 @ X359 @ X361 @ (comp @ X360 @ X362)))) | ? [X348 : term] : (($true = (X345 @ X348)) & ((X345 @ (sub @ X346 @ (push @ X348 @ id))) != $true)) | ((X345 @ (lam @ X346)) = $true) | ($true = (sP35 @ X347)) | ? [X358 : term] : ((X345 @ X358) != (X347 @ id @ X358 @ id)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f51,plain,(
% 42.64/7.44 ! [X444 : subst > term > subst > $o] : (($true = (sP37 @ X444)) <=> ? [X446 : term,X447 : term] : (($true = (X444 @ id @ X447 @ id)) & ((X444 @ id @ (ap @ (sub @ X447 @ id) @ X446) @ id) != $true) & ($true = (X444 @ id @ X446 @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f52,plain,(
% 42.64/7.44 ! [X444 : subst > term > subst > $o] : (($true = (sP38 @ X444)) <=> ? [X449 : subst > term > term] : (! [X451 : subst,X452 : subst,X453 : term] : ((sub @ (X449 @ X452 @ X453) @ X451) = (X449 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451))) & ! [X450 : term] : (($true = (X444 @ id @ (X449 @ id @ X450) @ id)) | ($true != (X444 @ id @ X450 @ id))) & ($true != (X444 @ id @ (lam @ (X449 @ sh @ one)) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f53,plain,(
% 42.64/7.44 ($true = sP39) <=> ! [X444 : subst > term > subst > $o,X445 : term] : (? [X448 : term] : (($true = (var @ (sub @ X448 @ id))) & ($true != (X444 @ id @ X448 @ id))) | ? [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (((X444 @ X460 @ X458 @ (comp @ X461 @ X459)) != $true) & ($true = (X444 @ (comp @ X460 @ X461) @ (sub @ X458 @ X461) @ X459))) | ? [X454 : subst,X455 : subst,X456 : subst,X457 : term] : (($true != (X444 @ (comp @ X454 @ X455) @ (sub @ X457 @ X455) @ X456)) & ($true = (X444 @ X454 @ X457 @ (comp @ X455 @ X456)))) | ((X444 @ id @ X445 @ id) = $true) | ($true = (sP38 @ X444)) | ($true = (sP37 @ X444)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f54,plain,(
% 42.64/7.44 ! [X308 : term > $o] : (($true = (sP40 @ X308)) <=> ! [X311 : term,X312 : term] : (($true != (X308 @ X312)) | ($true = (X308 @ (ap @ X311 @ X312))) | ($true != (X308 @ X311))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f55,plain,(
% 42.64/7.44 ! [X326 : subst > term > subst > $o] : (($true = (sP41 @ X326)) <=> ? [X330 : subst > term > term] : (! [X331 : subst,X332 : subst,X333 : term] : ((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)) = (sub @ (X330 @ X331 @ X333) @ X332)) & ($true != (X326 @ id @ (lam @ (X330 @ sh @ one)) @ id)) & ! [X334 : term] : (($true != (X326 @ id @ X334 @ id)) | ($true = (X326 @ id @ (X330 @ id @ X334) @ id)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f56,plain,(
% 42.64/7.44 (sP42 = $true) <=> ? [X316 : term,X317 : term > $o,X318 : subst > term > subst > $o] : (! [X325 : term] : (($true = (X317 @ (sub @ X316 @ (push @ X325 @ id)))) | ($true != (X317 @ X325))) & ! [X320 : subst > term > term] : (? [X324 : term] : (($true != (X318 @ id @ (X320 @ id @ X324) @ id)) & ($true = (X318 @ id @ X324 @ id))) | ($true = (X318 @ id @ (lam @ (X320 @ sh @ one)) @ id)) | ? [X321 : subst,X322 : subst,X323 : term] : ((sub @ (X320 @ X321 @ X323) @ X322) != (X320 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322)))) & ((X317 @ (lam @ X316)) != $true) & ! [X319 : term] : ((X318 @ id @ X319 @ id) = (X317 @ X319)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f57,plain,(
% 42.64/7.44 ($true = sP43) <=> ? [X308 : term > $o,X309 : term] : (! [X313 : term] : (($true = (X308 @ (lam @ X313))) | ? [X314 : term] : (($true = (X308 @ X314)) & ($true != (X308 @ (sub @ X313 @ (push @ X314 @ id)))))) & ($true = (sP40 @ X308)) & ! [X310 : term] : (($true = (X308 @ X310)) | ((var @ X310) != $true)) & ($true != (X308 @ X309)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f58,plain,(
% 42.64/7.44 ($true = sP44) <=> (? [X305 : subst > term > subst > $o] : ! [X306 : term > $o] : ? [X307 : term] : ((X306 @ X307) != (X305 @ id @ X307 @ id)) | ? [X315 : term] : ((sub @ X315 @ id) != X315) | (sP42 = $true) | ! [X326 : subst > term > subst > $o,X327 : term] : (? [X328 : term,X329 : term] : (($true = (X326 @ id @ X329 @ id)) & ($true = (X326 @ id @ X328 @ id)) & ($true != (X326 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id))) | ($true = (sP41 @ X326)) | ($true = (X326 @ id @ X327 @ id))) | ($true = sP43))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f59,plain,(
% 42.64/7.44 ($true = sP45) <=> (? [X261 : term,X262 : term] : ((X261 != X262) & ((lam @ X262) = (lam @ X261))) | ? [X257 : term,X258 : subst] : ((sub @ one @ (push @ X257 @ X258)) != X257) | ? [X259 : term,X260 : subst] : ((comp @ sh @ (push @ X259 @ X260)) != X260) | ! [X263 : subst > term > term,X264 : term,X265 : subst,X266 : subst > term > term] : (((lam @ (X266 @ sh @ one)) != (lam @ (X263 @ sh @ one))) | ? [X267 : subst,X268 : term,X269 : subst] : ((sub @ (X263 @ X269 @ X268) @ X267) != (X263 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))) | ((X263 @ X265 @ X264) = (X266 @ X265 @ X264)) | ? [X270 : subst,X271 : term,X272 : subst] : ((sub @ (X266 @ X270 @ X271) @ X272) != (X266 @ (comp @ X270 @ X272) @ (sub @ X271 @ X272)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f60,plain,(
% 42.64/7.44 ! [X372 : subst > term > subst > $o] : (($true = (sP46 @ X372)) <=> ? [X379 : subst > term > term] : (($true != (X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)) & ! [X380 : term] : (($true != (X372 @ id @ X380 @ id)) | ($true = (X372 @ id @ (X379 @ id @ X380) @ id))) & ! [X381 : term,X382 : subst,X383 : subst] : ((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383)) = (sub @ (X379 @ X382 @ X381) @ X383))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f61,plain,(
% 42.64/7.44 ($true = sP47) <=> ? [X364 : term,X365 : subst > term > subst > $o] : (! [X366 : subst > term > term] : (? [X367 : term,X368 : subst,X369 : subst] : ((X366 @ (comp @ X369 @ X368) @ (sub @ X367 @ X368)) != (sub @ (X366 @ X369 @ X367) @ X368)) | ? [X370 : term] : (($true != (X365 @ id @ (X366 @ id @ X370) @ id)) & ($true = (X365 @ id @ X370 @ id))) | ($true = (X365 @ id @ (lam @ (X366 @ sh @ one)) @ id))) & ! [X371 : term] : (($true != (X365 @ id @ X371 @ id)) | ($true = (X365 @ id @ (sub @ X364 @ (push @ X371 @ id)) @ id))) & ($true != (X365 @ id @ (lam @ (sub @ X364 @ (push @ one @ sh))) @ id)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f62,plain,(
% 42.64/7.44 ($true = sP48) <=> (($true = sP47) | ? [X363 : term] : ((sub @ X363 @ id) != X363) | ! [X372 : subst > term > subst > $o,X373 : term] : (($true = (sP46 @ X372)) | ? [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (($true = (X372 @ (comp @ X387 @ X384) @ (sub @ X386 @ X384) @ X385)) & ((X372 @ X387 @ X386 @ (comp @ X384 @ X385)) != $true)) | ($true = (X372 @ id @ (lam @ X373) @ id)) | ? [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (($true = (X372 @ X376 @ X377 @ (comp @ X374 @ X375))) & ((X372 @ (comp @ X376 @ X374) @ (sub @ X377 @ X374) @ X375) != $true)) | ? [X378 : term] : (($true = (X372 @ id @ X378 @ id)) & ($true != (X372 @ id @ (sub @ X373 @ (push @ X378 @ id)) @ id)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f63,plain,(
% 42.64/7.44 ! [X149 : subst > term > subst > $o] : (($true = (sP49 @ X149)) <=> ! [X156 : term,X157 : term] : (((X149 @ id @ X157 @ id) != $true) | ($true != (X149 @ id @ X156 @ id)) | ($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f64,plain,(
% 42.64/7.44 ! [X162 : subst > term > subst > $o] : (((sP50 @ X162) = $true) <=> ! [X173 : subst > term > term] : (? [X174 : term] : (($true = (X162 @ id @ X174 @ id)) & ($true != (X162 @ id @ (X173 @ id @ X174) @ id))) | ? [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) != (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f65,plain,(
% 42.64/7.44 ! [X179 : subst > term > subst > $o] : (($true = (sP51 @ X179)) <=> ? [X191 : subst > term > term] : (! [X195 : term] : (($true = (X179 @ id @ (X191 @ id @ X195) @ id)) | ($true != (X179 @ id @ X195 @ id))) & ((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) != $true) & ! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f66,plain,(
% 42.64/7.44 ! [X179 : subst > term > subst > $o] : (($true = (sP52 @ X179)) <=> ? [X181 : term,X182 : term] : (($true = (X179 @ id @ X181 @ id)) & ((X179 @ id @ X182 @ id) = $true) & ($true != (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f67,plain,(
% 42.64/7.44 ! [X142 : term > $o] : (($true = (sP53 @ X142)) <=> ! [X145 : term,X146 : term] : (($true = (X142 @ (ap @ X145 @ X146))) | ($true != (X142 @ X145)) | ($true != (X142 @ X146))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f68,plain,(
% 42.64/7.44 ($true = sP54) <=> ? [X162 : subst > term > subst > $o,X163 : term] : (! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166)) | ($true != (X162 @ X165 @ X167 @ (comp @ X168 @ X166)))) & ($true != (X162 @ id @ (lam @ X163) @ id)) & ((sP50 @ X162) = $true) & ! [X164 : term] : (($true != (X162 @ id @ X164 @ id)) | ($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id))) & ! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (($true != (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f69,plain,(
% 42.64/7.44 ($true = sP55) <=> ! [X178 : term,X179 : subst > term > subst > $o] : (? [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true != (X179 @ X188 @ X187 @ (comp @ X189 @ X190))) & ($true = (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190))) | ($true = (sP52 @ X179)) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (($true != (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183)) & ($true = (X179 @ X184 @ X185 @ (comp @ X186 @ X183)))) | ($true = (sP51 @ X179)) | ? [X180 : term] : (($true = (var @ (sub @ X180 @ id))) & ($true != (X179 @ id @ X180 @ id))) | ((X179 @ id @ X178 @ id) = $true))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f70,plain,(
% 42.64/7.44 ($true = sP56) <=> ? [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (($true = (sP49 @ X149)) & ($true = (X149 @ id @ X151 @ id)) & ($true != (X149 @ id @ (ap @ X151 @ X150) @ id)) & ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true != (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) & ($true = (X149 @ id @ X150 @ id)) & ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true) | ($true != (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f71,plain,(
% 42.64/7.44 ($true = sP57) <=> (? [X142 : term > $o,X143 : term] : (! [X144 : term] : (($true = (X142 @ X144)) | ((var @ X144) != $true)) & ! [X147 : term] : (($true = (X142 @ (lam @ X147))) | ? [X148 : term] : (($true = (X142 @ X148)) & ($true != (X142 @ (sub @ X147 @ (push @ X148 @ id)))))) & ($true = (sP53 @ X142)) & ($true != (X142 @ X143))) | ($true = sP55) | ($true = sP54) | ($true = sP56))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f72,plain,(
% 42.64/7.44 ($true = sP58) <=> ! [X389 : term,X390 : subst > term > subst > $o] : (? [X391 : term] : (($true = (X390 @ id @ X391 @ id)) & ((X390 @ id @ (sub @ X389 @ (push @ X391 @ id)) @ id) != $true)) | ($true = (X390 @ id @ (lam @ (sub @ X389 @ (push @ one @ sh))) @ id)) | ? [X392 : subst > term > term] : (($true != (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) & ! [X396 : term] : (($true = (X390 @ id @ (X392 @ id @ X396) @ id)) | ($true != (X390 @ id @ X396 @ id))) & ! [X393 : subst,X394 : term,X395 : subst] : ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)) = (sub @ (X392 @ X395 @ X394) @ X393))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 42.64/7.44 thf(f13,plain,(
% 42.64/7.44 ((hoasinduction_lem3aa = $true) <=> ! [X389 : term,X390 : subst > term > subst > $o] : (? [X391 : term] : (($true = (X390 @ id @ X391 @ id)) & ((X390 @ id @ (sub @ X389 @ (push @ X391 @ id)) @ id) != $true)) | ($true = (X390 @ id @ (lam @ (sub @ X389 @ (push @ one @ sh))) @ id)) | ? [X392 : subst > term > term] : (($true != (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) & ! [X396 : term] : (($true = (X390 @ id @ (X392 @ id @ X396) @ id)) | ($true != (X390 @ id @ X396 @ id))) & ! [X393 : subst,X394 : term,X395 : subst] : ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)) = (sub @ (X392 @ X395 @ X394) @ X393))))) & ((hoasinduction_lthm = $true) <=> (? [X142 : term > $o,X143 : term] : (! [X144 : term] : (($true = (X142 @ X144)) | ((var @ X144) != $true)) & ! [X147 : term] : (($true = (X142 @ (lam @ X147))) | ? [X148 : term] : (($true = (X142 @ X148)) & ($true != (X142 @ (sub @ X147 @ (push @ X148 @ id)))))) & ! [X145 : term,X146 : term] : (($true = (X142 @ (ap @ X145 @ X146))) | ($true != (X142 @ X145)) | ($true != (X142 @ X146))) & ($true != (X142 @ X143))) | ! [X178 : term,X179 : subst > term > subst > $o] : (? [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true != (X179 @ X188 @ X187 @ (comp @ X189 @ X190))) & ($true = (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190))) | ? [X181 : term,X182 : term] : (($true = (X179 @ id @ X181 @ id)) & ((X179 @ id @ X182 @ id) = $true) & ($true != (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id))) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (($true != (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183)) & ($true = (X179 @ X184 @ X185 @ (comp @ X186 @ X183)))) | ? [X191 : subst > term > term] : (! [X195 : term] : (($true = (X179 @ id @ (X191 @ id @ X195) @ id)) | ($true != (X179 @ id @ X195 @ id))) & ((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) != $true) & ! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192))) | ? [X180 : term] : (($true = (var @ (sub @ X180 @ id))) & ($true != (X179 @ id @ X180 @ id))) | ((X179 @ id @ X178 @ id) = $true)) | ? [X162 : subst > term > subst > $o,X163 : term] : (! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166)) | ($true != (X162 @ X165 @ X167 @ (comp @ X168 @ X166)))) & ($true != (X162 @ id @ (lam @ X163) @ id)) & ! [X173 : subst > term > term] : (? [X174 : term] : (($true = (X162 @ id @ X174 @ id)) & ($true != (X162 @ id @ (X173 @ id @ X174) @ id))) | ? [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) != (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id))) & ! [X164 : term] : (($true != (X162 @ id @ X164 @ id)) | ($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id))) & ! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (($true != (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true))) | ? [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (! [X156 : term,X157 : term] : (((X149 @ id @ X157 @ id) != $true) | ($true != (X149 @ id @ X156 @ id)) | ($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id))) & ($true = (X149 @ id @ X151 @ id)) & ($true != (X149 @ id @ (ap @ X151 @ X150) @ id)) & ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true != (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) & ($true = (X149 @ id @ X150 @ id)) & ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true) | ($true != (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159)))))) & (hoasinduction_lem1_lthm = $true) & ((hoaslaminj = $true) <=> ! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (? [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) != (sub @ (X417 @ X419 @ X420) @ X421)) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))) | ? [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) != (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415)))) & (lamnotap != $true) & (apnotvar = $true) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X216 : term] : ? [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) = (X217 @ sh @ one))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X364 : term,X365 : subst > term > subst > $o] : (! [X366 : subst > term > term] : (? [X367 : term,X368 : subst,X369 : subst] : ((X366 @ (comp @ X369 @ X368) @ (sub @ X367 @ X368)) != (sub @ (X366 @ X369 @ X367) @ X368)) | ? [X370 : term] : (($true != (X365 @ id @ (X366 @ id @ X370) @ id)) & ($true = (X365 @ id @ X370 @ id))) | ($true = (X365 @ id @ (lam @ (X366 @ sh @ one)) @ id))) & ! [X371 : term] : (($true != (X365 @ id @ X371 @ id)) | ($true = (X365 @ id @ (sub @ X364 @ (push @ X371 @ id)) @ id))) & ($true != (X365 @ id @ (lam @ (sub @ X364 @ (push @ one @ sh))) @ id))) | ? [X363 : term] : ((sub @ X363 @ id) != X363) | ! [X372 : subst > term > subst > $o,X373 : term] : (? [X379 : subst > term > term] : (($true != (X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)) & ! [X380 : term] : (($true != (X372 @ id @ X380 @ id)) | ($true = (X372 @ id @ (X379 @ id @ X380) @ id))) & ! [X381 : term,X382 : subst,X383 : subst] : ((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383)) = (sub @ (X379 @ X382 @ X381) @ X383))) | ? [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (($true = (X372 @ (comp @ X387 @ X384) @ (sub @ X386 @ X384) @ X385)) & ((X372 @ X387 @ X386 @ (comp @ X384 @ X385)) != $true)) | ($true = (X372 @ id @ (lam @ X373) @ id)) | ? [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (($true = (X372 @ X376 @ X377 @ (comp @ X374 @ X375))) & ((X372 @ (comp @ X376 @ X374) @ (sub @ X377 @ X374) @ X375) != $true)) | ? [X378 : term] : (($true = (X372 @ id @ X378 @ id)) & ($true != (X372 @ id @ (sub @ X373 @ (push @ X378 @ id)) @ id)))))) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & ((? [X261 : term,X262 : term] : ((X261 != X262) & ((lam @ X262) = (lam @ X261))) | ? [X257 : term,X258 : subst] : ((sub @ one @ (push @ X257 @ X258)) != X257) | ? [X259 : term,X260 : subst] : ((comp @ sh @ (push @ X259 @ X260)) != X260) | ! [X263 : subst > term > term,X264 : term,X265 : subst,X266 : subst > term > term] : (((lam @ (X266 @ sh @ one)) != (lam @ (X263 @ sh @ one))) | ? [X267 : subst,X268 : term,X269 : subst] : ((sub @ (X263 @ X269 @ X268) @ X267) != (X263 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))) | ((X263 @ X265 @ X264) = (X266 @ X265 @ X264)) | ? [X270 : subst,X271 : term,X272 : subst] : ((sub @ (X266 @ X270 @ X271) @ X272) != (X266 @ (comp @ X270 @ X272) @ (sub @ X271 @ X272))))) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (substmonoid_gthm = $true) & ((termmset = $true) <=> ! [X344 : term] : ((sub @ X344 @ id) = X344)) & (axassoc = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X305 : subst > term > subst > $o] : ! [X306 : term > $o] : ? [X307 : term] : ((X306 @ X307) != (X305 @ id @ X307 @ id)) | ? [X315 : term] : ((sub @ X315 @ id) != X315) | ? [X316 : term,X317 : term > $o,X318 : subst > term > subst > $o] : (! [X325 : term] : (($true = (X317 @ (sub @ X316 @ (push @ X325 @ id)))) | ($true != (X317 @ X325))) & ! [X320 : subst > term > term] : (? [X324 : term] : (($true != (X318 @ id @ (X320 @ id @ X324) @ id)) & ($true = (X318 @ id @ X324 @ id))) | ($true = (X318 @ id @ (lam @ (X320 @ sh @ one)) @ id)) | ? [X321 : subst,X322 : subst,X323 : term] : ((sub @ (X320 @ X321 @ X323) @ X322) != (X320 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322)))) & ((X317 @ (lam @ X316)) != $true) & ! [X319 : term] : ((X318 @ id @ X319 @ id) = (X317 @ X319))) | ! [X326 : subst > term > subst > $o,X327 : term] : (? [X328 : term,X329 : term] : (($true = (X326 @ id @ X329 @ id)) & ($true = (X326 @ id @ X328 @ id)) & ($true != (X326 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id))) | ? [X330 : subst > term > term] : (! [X331 : subst,X332 : subst,X333 : term] : ((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)) = (sub @ (X330 @ X331 @ X333) @ X332)) & ($true != (X326 @ id @ (lam @ (X330 @ sh @ one)) @ id)) & ! [X334 : term] : (($true != (X326 @ id @ X334 @ id)) | ($true = (X326 @ id @ (X330 @ id @ X334) @ id)))) | ($true = (X326 @ id @ X327 @ id))) | ? [X308 : term > $o,X309 : term] : (! [X313 : term] : (($true = (X308 @ (lam @ X313))) | ? [X314 : term] : (($true = (X308 @ X314)) & ($true != (X308 @ (sub @ X313 @ (push @ X314 @ id)))))) & ! [X311 : term,X312 : term] : (($true != (X308 @ X312)) | ($true = (X308 @ (ap @ X311 @ X312))) | ($true != (X308 @ X311))) & ! [X310 : term] : (($true = (X308 @ X310)) | ((var @ X310) != $true)) & ($true != (X308 @ X309))))) & (! [X444 : subst > term > subst > $o,X445 : term] : (? [X448 : term] : (($true = (var @ (sub @ X448 @ id))) & ($true != (X444 @ id @ X448 @ id))) | ? [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (((X444 @ X460 @ X458 @ (comp @ X461 @ X459)) != $true) & ($true = (X444 @ (comp @ X460 @ X461) @ (sub @ X458 @ X461) @ X459))) | ? [X454 : subst,X455 : subst,X456 : subst,X457 : term] : (($true != (X444 @ (comp @ X454 @ X455) @ (sub @ X457 @ X455) @ X456)) & ($true = (X444 @ X454 @ X457 @ (comp @ X455 @ X456)))) | ((X444 @ id @ X445 @ id) = $true) | ? [X449 : subst > term > term] : (! [X451 : subst,X452 : subst,X453 : term] : ((sub @ (X449 @ X452 @ X453) @ X451) = (X449 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451))) & ! [X450 : term] : (($true = (X444 @ id @ (X449 @ id @ X450) @ id)) | ($true != (X444 @ id @ X450 @ id))) & ($true != (X444 @ id @ (lam @ (X449 @ sh @ one)) @ id))) | ? [X446 : term,X447 : term] : (($true = (X444 @ id @ X447 @ id)) & ((X444 @ id @ (ap @ (sub @ X447 @ id) @ X446) @ id) != $true) & ($true = (X444 @ id @ X446 @ id)))) <=> (hoasinduction = $true)) & (hoasapinj2_gthm = $true) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) <=> (laminj = $true)) & (! [X345 : term > $o,X346 : term,X347 : subst > term > subst > $o] : (? [X354 : subst,X355 : subst,X356 : subst,X357 : term] : (((X347 @ (comp @ X354 @ X356) @ (sub @ X357 @ X356) @ X355) = $true) & ($true != (X347 @ X354 @ X357 @ (comp @ X356 @ X355)))) | ? [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (($true != (X347 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360) @ X362)) & ($true = (X347 @ X359 @ X361 @ (comp @ X360 @ X362)))) | ? [X348 : term] : (($true = (X345 @ X348)) & ((X345 @ (sub @ X346 @ (push @ X348 @ id))) != $true)) | ((X345 @ (lam @ X346)) = $true) | ? [X349 : subst > term > term] : (($true != (X347 @ id @ (lam @ (X349 @ sh @ one)) @ id)) & ! [X351 : subst,X352 : subst,X353 : term] : ((X349 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)) = (sub @ (X349 @ X351 @ X353) @ X352)) & ! [X350 : term] : (((X347 @ id @ X350 @ id) != $true) | ($true = (X347 @ id @ (X349 @ id @ X350) @ id)))) | ? [X358 : term] : ((X345 @ X358) != (X347 @ id @ X358 @ id))) <=> (hoasinduction_lem3v2 = $true)) & (axapp = $true) & (! [X295 : term > $o,X296 : term,X297 : subst > term > subst > $o] : (? [X304 : term] : (($true != (X295 @ (sub @ X296 @ (push @ X304 @ id)))) & ((X295 @ X304) = $true)) | ? [X298 : subst > term > term] : (! [X300 : subst,X301 : term,X302 : subst] : ((sub @ (X298 @ X302 @ X301) @ X300) = (X298 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300))) & ($true != (X297 @ id @ (lam @ (X298 @ sh @ one)) @ id)) & ! [X299 : term] : (((X297 @ id @ X299 @ id) != $true) | ($true = (X297 @ id @ (X298 @ id @ X299) @ id)))) | ? [X303 : term] : ((X295 @ X303) != (X297 @ id @ X303 @ id)) | ($true = (X295 @ (lam @ X296)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X397 : subst > term > subst > $o] : ? [X398 : term > $o] : ! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id)) <=> (hoasinduction_lem0 = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X273 : term > $o,X274 : subst,X275 : term] : ? [X276 : term > $o] : ! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277))) & (! [X49 : term] : ? [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) = (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) <=> (axscons = $true)) & (induction2_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasapnotvar = $true) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = sh) & (! [X41 : term,X42 : subst > term > subst > $o] : (? [X43 : subst > term > term] : (! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) & ($true != (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) & ! [X47 : term] : (($true = (X42 @ id @ (X43 @ id @ X47) @ id)) | ((X42 @ id @ X47 @ id) != $true))) | ? [X48 : term] : (($true = (X42 @ id @ X48 @ id)) & ($true != (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id))) | ($true = (X42 @ id @ (lam @ X41) @ id))) <=> (hoasinduction_lem3a = $true)) & (axvarshift = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X278 : term,X279 : term > $o,X280 : term,X281 : subst > term > subst > $o] : (($true != (X279 @ X280)) | ($true != (X279 @ X278)) | ($true = (X279 @ (ap @ X278 @ X280))) | ? [X288 : term,X289 : subst,X290 : subst,X291 : subst] : (($true != (X281 @ (comp @ X289 @ X291) @ (sub @ X288 @ X291) @ X290)) & ((X281 @ X289 @ X288 @ (comp @ X291 @ X290)) = $true)) | ? [X292 : term] : ((X279 @ X292) != (X281 @ id @ X292 @ id)) | ? [X282 : term,X283 : term] : (($true = (X281 @ id @ X282 @ id)) & ((X281 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id) != $true) & ($true = (X281 @ id @ X283 @ id))) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X281 @ (comp @ X284 @ X287) @ (sub @ X286 @ X287) @ X285)) & ($true != (X281 @ X284 @ X286 @ (comp @ X287 @ X285)))))) & ((hoasinduction_lem2 = $true) <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (($true = (X26 @ id @ (ap @ X24 @ X25) @ id)) | ((X26 @ id @ X24 @ id) != $true) | ? [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true = (X26 @ X33 @ X36 @ (comp @ X34 @ X35))) & ($true != (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35))) | ? [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true = (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) & ($true != (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ($true != (X26 @ id @ X25 @ id)) | ? [X31 : term,X32 : term] : (($true = (X26 @ id @ X31 @ id)) & ($true = (X26 @ id @ X32 @ id)) & ($true != (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id))))) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) = $true) & ($true != (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) & ($true = (X203 @ id @ X206 @ id))) | ? [X207 : subst > term > term] : (($true != (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)) & ! [X208 : term] : (($true != (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) & ! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))) | ($true = (X203 @ id @ X204 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (hoaslamnotap_lthm = $true) & ((induction2 = $true) <=> ! [X104 : term,X105 : term > $o] : (? [X109 : term,X110 : term] : (($true = (X105 @ X110)) & ($true != (X105 @ (ap @ X109 @ X110))) & ((X105 @ X109) = $true)) | ? [X106 : term] : (! [X107 : term] : (((X105 @ X107) != $true) | ($true = (X105 @ (sub @ X106 @ (push @ X107 @ id))))) & ($true != (X105 @ (lam @ X106)))) | ? [X108 : term] : (($true != (X105 @ X108)) & ((var @ X108) = $true)) | ($true = (X105 @ X104)))) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X111 : term] : ? [X112 : subst > term > term] : ! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113))) <=> (hoasinduction_lem3v2_f = $true)) & ((? [X228 : term > $o,X229 : subst,X230 : term] : (! [X234 : term,X235 : term] : (($true = (X228 @ (ap @ X234 @ X235))) | ($true != (X228 @ X235)) | ($true != (X228 @ X234))) & ! [X232 : term] : (? [X233 : term] : (($true = (X228 @ X233)) & ($true != (X228 @ (sub @ X232 @ (push @ X233 @ id))))) | ($true = (X228 @ (lam @ X232)))) & ! [X231 : term] : (($true != (var @ X231)) | ($true = (X228 @ (sub @ X231 @ X229)))) & ($true != (X228 @ (sub @ X230 @ X229)))) | ! [X236 : term,X237 : term > $o] : (? [X238 : term] : (($true = (var @ X238)) & ($true != (X237 @ X238))) | ? [X239 : term,X240 : term] : (($true = (X237 @ X240)) & ($true != (X237 @ (ap @ X240 @ X239))) & ($true = (X237 @ X239))) | ($true = (X237 @ X236)) | ? [X241 : term] : (! [X242 : term] : (($true != (X237 @ X242)) | ($true = (X237 @ (sub @ X241 @ (push @ X242 @ id))))) & ($true != (X237 @ (lam @ X241))))) | ? [X227 : term] : ((sub @ X227 @ id) != X227)) <=> (induction2_lthm = $true)) & (! [X19 : term] : ? [X20 : subst > term > term] : ! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & ((? [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) != X116) | ? [X120 : term > $o,X121 : term] : (! [X122 : term] : (((var @ X122) != $true) | ($true = (X120 @ X122))) & ($true != (X120 @ X121)) & ! [X123 : term,X124 : term] : (($true != (X120 @ X123)) | ($true != (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))) & ! [X125 : term] : (($true = (X120 @ (lam @ X125))) | ($true != (X120 @ X125)))) | ! [X126 : term > $o,X127 : term,X128 : subst] : (? [X131 : term] : (! [X132 : term] : (($true != (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id))))) & ($true != (X126 @ (lam @ X131)))) | ? [X133 : term] : (($true != (X126 @ (sub @ X133 @ X128))) & ($true = (var @ X133))) | ? [X129 : term,X130 : term] : (($true = (X126 @ X129)) & ($true = (X126 @ X130)) & ((X126 @ (ap @ X130 @ X129)) != $true)) | ($true = (X126 @ (sub @ X127 @ X128)))) | ? [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) != X117) | ? [X119 : subst] : ((comp @ X119 @ id) != X119)) <=> (induction2lem_lthm = $true)) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & ((? [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 != X222) & ((ap @ X222 @ X220) = (ap @ X219 @ X221))) | ? [X218 : term] : ((sub @ X218 @ id) != X218) | ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226))) <=> (hoasapinj1_lthm = $true)) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) != (d2term @ X408)) | (X407 = X408)) & (hoasapinj1_gthm = $true) & (lamnotvar = $true) & ! [X388 : d_term] : (d_one = X388) & (pushprop_lem3v2 = $true) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & (! [X196 : subst,X197 : term,X198 : term > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196)))) <=> (pushprop_lem0 = $true)) & (induction2lem_gthm = $true) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ($true != (X402 @ X405)) | ? [X406 : term] : ((X404 @ X406) != (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) | ? [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) != X401))) & ((? [X76 : term] : ((sub @ X76 @ id) != X76) | ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (? [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (($true = (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) & ($true != (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))) | ? [X90 : subst > term > term] : (($true != (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id)) & ! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) & ! [X94 : term] : (($true = (X78 @ id @ (X90 @ id @ X94) @ id)) | ($true != (X78 @ id @ X94 @ id)))) | ? [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (($true != (X78 @ X87 @ X85 @ (comp @ X86 @ X88))) & ($true = (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88))) | ($true = (X79 @ (lam @ X77))) | ? [X89 : term] : (($true = (X79 @ X89)) & ($true != (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ? [X80 : term] : ((X78 @ id @ X80 @ id) != (X79 @ X80)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X515 : subst,X516 : term > $o,X517 : term] : (? [X518 : term] : (($true = (var @ X518)) & ($true != (X516 @ (sub @ X518 @ X515)))) | ? [X521 : term] : (! [X522 : term] : (($true != (X516 @ X522)) | ($true = (X516 @ (sub @ X521 @ (push @ X522 @ id))))) & ($true != (X516 @ (lam @ X521)))) | ($true = (X516 @ (sub @ X517 @ X515))) | ? [X519 : term,X520 : term] : (($true = (X516 @ X519)) & ($true = (X516 @ X520)) & ($true != (X516 @ (ap @ X520 @ X519))))) <=> (induction2lem = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (pushprop_gthm = $true) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ! [X51 : d_subst,X52 : d_subst] : ((X51 = X52) | ((d2subst @ X52) != (d2subst @ X51))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X252 : subst > term > subst > $o] : ? [X253 : term > $o] : ! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem2_lthm = $true) & (! [X53 : subst > term > subst > $o,X54 : term] : (? [X56 : subst > term > term,X57 : term] : (! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) & ! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63)))) & ! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ($true != (X53 @ id @ X61 @ id))) & ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) != $true)) | ($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ? [X55 : term] : (($true != (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) & ($true = (X53 @ id @ X55 @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (axabs = $true) & (hoaslaminj_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509)) | ? [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) != (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))) <=> (hoaslamnotap = $true)) & ((induction = $true) <=> ! [X409 : term,X410 : term > $o] : (? [X411 : term] : (($true != (X410 @ (lam @ X411))) & ($true = (X410 @ X411))) | ? [X413 : term,X414 : term] : (($true = (X410 @ X414)) & ($true = (X410 @ X413)) & ($true != (X410 @ (ap @ X414 @ X413)))) | ($true = (X410 @ X409)) | ? [X412 : term] : (((var @ X412) = $true) & ($true != (X410 @ X412))))) & ((! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342))) | ? [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) != X335) | ? [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) != X337)) <=> (pushprop_lem1_lthm = $true)) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) <=> (axidr = $true)) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (ulamvarsh = $true) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) <=> (pushprop_lem1 = $true)) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) = (ap @ X246 @ X247)) & (X245 != X247)))) & ((! [X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (? [X439 : term] : (($true = (X431 @ X439)) & ($true != (X431 @ (sub @ X430 @ (push @ X439 @ id))))) | ? [X438 : term] : ((X432 @ id @ X438 @ id) != (X431 @ X438)) | ($true = (X431 @ (lam @ X430))) | ? [X433 : subst > term > term] : (! [X434 : term] : (($true != (X432 @ id @ X434 @ id)) | ($true = (X432 @ id @ (X433 @ id @ X434) @ id))) & ($true != (X432 @ id @ (lam @ (X433 @ sh @ one)) @ id)) & ! [X435 : subst,X436 : term,X437 : subst] : ((X433 @ (comp @ X437 @ X435) @ (sub @ X436 @ X435)) = (sub @ (X433 @ X437 @ X436) @ X435)))) | ? [X425 : term] : ! [X426 : subst > term > term] : ? [X427 : term,X428 : subst] : ((sub @ X425 @ (push @ X427 @ X428)) != (X426 @ X428 @ X427)) | ? [X429 : term] : ((sub @ X429 @ id) != X429)) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((? [X472 : term] : ((sub @ X472 @ id) != X472) | ? [X465 : term,X466 : term > $o] : (! [X470 : term] : (($true = (X466 @ (lam @ X470))) | ? [X471 : term] : (((X466 @ (sub @ X470 @ (push @ X471 @ id))) != $true) & ($true = (X466 @ X471)))) & ($true != (X466 @ X465)) & ! [X469 : term] : (((X466 @ X469) = $true) | ($true != (var @ X469))) & ! [X467 : term,X468 : term] : (((X466 @ X468) != $true) | ($true != (X466 @ X467)) | ($true = (X466 @ (ap @ X468 @ X467))))) | ? [X473 : term > $o,X474 : subst > term > subst > $o,X475 : term] : (! [X478 : subst > term > term] : (? [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X481 @ X482) @ (sub @ X480 @ X482)) != (sub @ (X478 @ X481 @ X480) @ X482)) | ? [X479 : term] : (($true = (X474 @ id @ X479 @ id)) & ($true != (X474 @ id @ (X478 @ id @ X479) @ id))) | ($true = (X474 @ id @ (lam @ (X478 @ sh @ one)) @ id))) & ($true != (X473 @ (lam @ X475))) & ! [X476 : term] : (($true = (X473 @ (sub @ X475 @ (push @ X476 @ id)))) | ((X473 @ X476) != $true)) & ! [X477 : term] : ((X474 @ id @ X477 @ id) = (X473 @ X477))) | ! [X483 : term,X484 : subst > term > subst > $o] : (($true = (X484 @ id @ X483 @ id)) | ? [X496 : subst > term > term] : (! [X500 : term] : (($true != (X484 @ id @ X500 @ id)) | ($true = (X484 @ id @ (X496 @ id @ X500) @ id))) & ($true != (X484 @ id @ (lam @ (X496 @ sh @ one)) @ id)) & ! [X497 : term,X498 : subst,X499 : subst] : ((X496 @ (comp @ X499 @ X498) @ (sub @ X497 @ X498)) = (sub @ (X496 @ X499 @ X497) @ X498))) | ? [X489 : subst,X490 : subst,X491 : term,X492 : subst] : (($true != (X484 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) & ($true = (X484 @ X489 @ X491 @ (comp @ X492 @ X490)))) | ? [X495 : term] : (($true = (var @ (sub @ X495 @ id))) & ($true != (X484 @ id @ X495 @ id))) | ? [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (($true = (X484 @ (comp @ X485 @ X488) @ (sub @ X487 @ X488) @ X486)) & ($true != (X484 @ X485 @ X487 @ (comp @ X488 @ X486)))) | ? [X493 : term,X494 : term] : (($true = (X484 @ id @ X494 @ id)) & ($true = (X484 @ id @ X493 @ id)) & ($true != (X484 @ id @ (ap @ (sub @ X493 @ id) @ X494) @ id)))) | ? [X462 : subst > term > subst > $o] : ! [X463 : term > $o] : ? [X464 : term] : ((X462 @ id @ X464 @ id) != (X463 @ X464))) <=> (hoasinduction_lthm_3 = $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)))))))))))))) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & ((? [X139 : subst] : ((comp @ X139 @ id) != X139) | ? [X138 : subst] : ((comp @ id @ X138) != X138) | (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (? [X103 : term] : ((X100 @ X103) != (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true != (X99 @ X102)) | ($true = (X100 @ one)))) & ((! [X11 : subst > term > subst > $o,X12 : term] : (? [X13 : subst > term > term] : (($true != (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) & ! [X17 : term] : (($true != (X11 @ id @ X17 @ id)) | ($true = (X11 @ id @ (X13 @ id @ X17) @ id))) & ! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14))) | ($true = (X11 @ id @ (lam @ X12) @ id)) | ? [X18 : term] : (($true = (X11 @ id @ X18 @ id)) & ($true != (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)))) | ? [X2 : term] : ((sub @ X2 @ id) != X2) | ? [X3 : subst > term > subst > $o,X4 : term] : (($true != (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id)) & ! [X10 : term] : (((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X3 @ id @ X10 @ id))) & ! [X5 : subst > term > term] : (? [X9 : term] : (($true != (X3 @ id @ (X5 @ id @ X9) @ id)) & ($true = (X3 @ id @ X9 @ id))) | ($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id)) | ? [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) != (sub @ (X5 @ X7 @ X8) @ X6))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) <=> (shinj = $true)) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & ((! [X202 : term] : ((sub @ X202 @ id) = X202) | ? [X201 : term] : ((sub @ X201 @ id) != X201)) <=> (termmset_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X523 : subst > term > subst > $o,X524 : term] : (? [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (($true != (X523 @ X538 @ X535 @ (comp @ X536 @ X537))) & ($true = (X523 @ (comp @ X538 @ X536) @ (sub @ X535 @ X536) @ X537))) | ($true = (X523 @ id @ (lam @ X524) @ id)) | ? [X525 : term] : (($true != (X523 @ id @ (sub @ X524 @ (push @ X525 @ id)) @ id)) & ($true = (X523 @ id @ X525 @ id))) | ? [X530 : subst > term > term] : (($true != (X523 @ id @ (lam @ (X530 @ sh @ one)) @ id)) & ! [X531 : subst,X532 : term,X533 : subst] : ((sub @ (X530 @ X531 @ X532) @ X533) = (X530 @ (comp @ X531 @ X533) @ (sub @ X532 @ X533))) & ! [X534 : term] : (($true != (X523 @ id @ X534 @ id)) | ($true = (X523 @ id @ (X530 @ id @ X534) @ id)))) | ? [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (((X523 @ (comp @ X527 @ X526) @ (sub @ X529 @ X526) @ X528) != $true) & ($true = (X523 @ X527 @ X529 @ (comp @ X526 @ X528))))) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X501 : term,X502 : subst > term > subst > $o] : (? [X508 : term] : (($true != (X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)) & ($true = (X502 @ id @ X508 @ id))) | ((X502 @ id @ (lam @ (sub @ X501 @ (push @ one @ sh))) @ id) = $true) | ? [X503 : subst > term > term] : (! [X504 : subst,X505 : term,X506 : subst] : ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)) = (sub @ (X503 @ X506 @ X505) @ X504)) & ! [X507 : term] : (($true = (X502 @ id @ (X503 @ id @ X507) @ id)) | ($true != (X502 @ id @ X507 @ id))) & ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id) != $true)))) & ((substmonoid = $true) <=> (! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442)))),
% 42.64/7.44 inference(flattening,[status(thm)],[f12])).
% 42.64/7.44 thf(f12,plain,(
% 42.64/7.44 ((d2subst @ d_id) = sh) & (! [X515 : subst,X516 : term > $o,X517 : term] : (? [X518 : term] : (($true = (var @ X518)) & ($true != (X516 @ (sub @ X518 @ X515)))) | ? [X521 : term] : (! [X522 : term] : (($true != (X516 @ X522)) | ($true = (X516 @ (sub @ X521 @ (push @ X522 @ id))))) & ($true != (X516 @ (lam @ X521)))) | ($true = (X516 @ (sub @ X517 @ X515))) | ? [X519 : term,X520 : term] : (($true = (X516 @ X519)) & ($true = (X516 @ X520)) & ($true != (X516 @ (ap @ X520 @ X519))))) <=> (induction2lem = $true)) & (hoaslamnotap_lthm = $true) & (! [X523 : subst > term > subst > $o,X524 : term] : (? [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (($true != (X523 @ X538 @ X535 @ (comp @ X536 @ X537))) & ($true = (X523 @ (comp @ X538 @ X536) @ (sub @ X535 @ X536) @ X537))) | ($true = (X523 @ id @ (lam @ X524) @ id)) | ? [X525 : term] : (($true != (X523 @ id @ (sub @ X524 @ (push @ X525 @ id)) @ id)) & ($true = (X523 @ id @ X525 @ id))) | ? [X530 : subst > term > term] : (($true != (X523 @ id @ (lam @ (X530 @ sh @ one)) @ id)) & ! [X531 : subst,X532 : term,X533 : subst] : ((sub @ (X530 @ X531 @ X532) @ X533) = (X530 @ (comp @ X531 @ X533) @ (sub @ X532 @ X533))) & ! [X534 : term] : (($true != (X523 @ id @ X534 @ id)) | ($true = (X523 @ id @ (X530 @ id @ X534) @ id)))) | ? [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (((X523 @ (comp @ X527 @ X526) @ (sub @ X529 @ X526) @ X528) != $true) & ($true = (X523 @ X527 @ X529 @ (comp @ X526 @ X528))))) <=> (hoasinduction_lem3 = $true)) & (axabs = $true) & (pushprop_lem0_gthm = $true) & (! [X49 : term] : ? [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) = (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = id) & (! [X345 : term > $o,X346 : term,X347 : subst > term > subst > $o] : (? [X354 : subst,X355 : subst,X356 : subst,X357 : term] : (((X347 @ (comp @ X354 @ X356) @ (sub @ X357 @ X356) @ X355) = $true) & ($true != (X347 @ X354 @ X357 @ (comp @ X356 @ X355)))) | ? [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (($true != (X347 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360) @ X362)) & ($true = (X347 @ X359 @ X361 @ (comp @ X360 @ X362)))) | ? [X348 : term] : (($true = (X345 @ X348)) & ((X345 @ (sub @ X346 @ (push @ X348 @ id))) != $true)) | ((X345 @ (lam @ X346)) = $true) | ? [X349 : subst > term > term] : (($true != (X347 @ id @ (lam @ (X349 @ sh @ one)) @ id)) & ! [X351 : subst,X352 : subst,X353 : term] : ((X349 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)) = (sub @ (X349 @ X351 @ X353) @ X352)) & ! [X350 : term] : (((X347 @ id @ X350 @ id) != $true) | ($true = (X347 @ id @ (X349 @ id @ X350) @ id)))) | ? [X358 : term] : ((X345 @ X358) != (X347 @ id @ X358 @ id))) <=> (hoasinduction_lem3v2 = $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & ((induction2lem_lthm = $true) <=> ((((! [X126 : term > $o,X127 : term,X128 : subst] : (? [X131 : term] : (! [X132 : term] : (($true != (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id))))) & ($true != (X126 @ (lam @ X131)))) | ? [X133 : term] : (($true != (X126 @ (sub @ X133 @ X128))) & ($true = (var @ X133))) | ? [X129 : term,X130 : term] : (($true = (X126 @ X129)) & ($true = (X126 @ X130)) & ((X126 @ (ap @ X130 @ X129)) != $true)) | ($true = (X126 @ (sub @ X127 @ X128)))) | ? [X120 : term > $o,X121 : term] : (! [X122 : term] : (((var @ X122) != $true) | ($true = (X120 @ X122))) & ($true != (X120 @ X121)) & ! [X123 : term,X124 : term] : (($true != (X120 @ X123)) | ($true != (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))) & ! [X125 : term] : (($true = (X120 @ (lam @ X125))) | ($true != (X120 @ X125))))) | ? [X119 : subst] : ((comp @ X119 @ id) != X119)) | ? [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) != X117)) | ? [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) != X116))) & (pushprop_lem3v2 = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (termmset_gthm = $true) & (axassoc = $true) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509)) | ? [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) != (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514)))) <=> (hoaslamnotap = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) <=> (pushprop_lem1 = $true)) & (induction2_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem2v2 = $true) & (! [X295 : term > $o,X296 : term,X297 : subst > term > subst > $o] : (? [X304 : term] : (($true != (X295 @ (sub @ X296 @ (push @ X304 @ id)))) & ((X295 @ X304) = $true)) | ? [X298 : subst > term > term] : (! [X300 : subst,X301 : term,X302 : subst] : ((sub @ (X298 @ X302 @ X301) @ X300) = (X298 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300))) & ($true != (X297 @ id @ (lam @ (X298 @ sh @ one)) @ id)) & ! [X299 : term] : (((X297 @ id @ X299 @ id) != $true) | ($true = (X297 @ id @ (X298 @ id @ X299) @ id)))) | ? [X303 : term] : ((X295 @ X303) != (X297 @ id @ X303 @ id)) | ($true = (X295 @ (lam @ X296)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_gthm = $true) & ((induction2 = $true) <=> ! [X104 : term,X105 : term > $o] : (? [X109 : term,X110 : term] : (($true = (X105 @ X110)) & ($true != (X105 @ (ap @ X109 @ X110))) & ((X105 @ X109) = $true)) | ? [X106 : term] : (! [X107 : term] : (((X105 @ X107) != $true) | ($true = (X105 @ (sub @ X106 @ (push @ X107 @ id))))) & ($true != (X105 @ (lam @ X106)))) | ? [X108 : term] : (($true != (X105 @ X108)) & ((var @ X108) = $true)) | ($true = (X105 @ X104)))) & (hoasinduction_lem1_gthm = $true) & (! [X19 : term] : ? [X20 : subst > term > term] : ! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X389 : term,X390 : subst > term > subst > $o] : (? [X391 : term] : (($true = (X390 @ id @ X391 @ id)) & ((X390 @ id @ (sub @ X389 @ (push @ X391 @ id)) @ id) != $true)) | ($true = (X390 @ id @ (lam @ (sub @ X389 @ (push @ one @ sh))) @ id)) | ? [X392 : subst > term > term] : (($true != (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) & ! [X396 : term] : (($true = (X390 @ id @ (X392 @ id @ X396) @ id)) | ($true != (X390 @ id @ X396 @ id))) & ! [X393 : subst,X394 : term,X395 : subst] : ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)) = (sub @ (X392 @ X395 @ X394) @ X393))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X501 : term,X502 : subst > term > subst > $o] : (? [X508 : term] : (($true != (X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)) & ($true = (X502 @ id @ X508 @ id))) | ((X502 @ id @ (lam @ (sub @ X501 @ (push @ one @ sh))) @ id) = $true) | ? [X503 : subst > term > term] : (! [X504 : subst,X505 : term,X506 : subst] : ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)) = (sub @ (X503 @ X506 @ X505) @ X504)) & ! [X507 : term] : (($true = (X502 @ id @ (X503 @ id @ X507) @ id)) | ($true != (X502 @ id @ X507 @ id))) & ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id) != $true)))) & ((! [X202 : term] : ((sub @ X202 @ id) = X202) | ? [X201 : term] : ((sub @ X201 @ id) != X201)) <=> (termmset_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lthm = $true) <=> (((! [X178 : term,X179 : subst > term > subst > $o] : (? [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true != (X179 @ X188 @ X187 @ (comp @ X189 @ X190))) & ($true = (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190))) | ? [X181 : term,X182 : term] : (($true = (X179 @ id @ X181 @ id)) & ((X179 @ id @ X182 @ id) = $true) & ($true != (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id))) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (($true != (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183)) & ($true = (X179 @ X184 @ X185 @ (comp @ X186 @ X183)))) | ? [X191 : subst > term > term] : (! [X195 : term] : (($true = (X179 @ id @ (X191 @ id @ X195) @ id)) | ($true != (X179 @ id @ X195 @ id))) & ((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) != $true) & ! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192))) | ? [X180 : term] : (($true = (var @ (sub @ X180 @ id))) & ($true != (X179 @ id @ X180 @ id))) | ((X179 @ id @ X178 @ id) = $true)) | ? [X162 : subst > term > subst > $o,X163 : term] : (! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166)) | ($true != (X162 @ X165 @ X167 @ (comp @ X168 @ X166)))) & ($true != (X162 @ id @ (lam @ X163) @ id)) & ! [X173 : subst > term > term] : (? [X174 : term] : (($true = (X162 @ id @ X174 @ id)) & ($true != (X162 @ id @ (X173 @ id @ X174) @ id))) | ? [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) != (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id))) & ! [X164 : term] : (($true != (X162 @ id @ X164 @ id)) | ($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id))) & ! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (($true != (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true)))) | ? [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (! [X156 : term,X157 : term] : (((X149 @ id @ X157 @ id) != $true) | ($true != (X149 @ id @ X156 @ id)) | ($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id))) & ($true = (X149 @ id @ X151 @ id)) & ($true != (X149 @ id @ (ap @ X151 @ X150) @ id)) & ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true != (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) & ($true = (X149 @ id @ X150 @ id)) & ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true) | ($true != (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159))))) | ? [X142 : term > $o,X143 : term] : (! [X144 : term] : (($true = (X142 @ X144)) | ((var @ X144) != $true)) & ! [X147 : term] : (($true = (X142 @ (lam @ X147))) | ? [X148 : term] : (($true = (X142 @ X148)) & ($true != (X142 @ (sub @ X147 @ (push @ X148 @ id)))))) & ! [X145 : term,X146 : term] : (($true = (X142 @ (ap @ X145 @ X146))) | ($true != (X142 @ X145)) | ($true != (X142 @ X146))) & ($true != (X142 @ X143))))) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapnotvar = $true) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & ((pushprop_lem0_lthm = $true) <=> ! [X273 : term > $o,X274 : subst,X275 : term] : ? [X276 : term > $o] : ! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277))) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & (! [X41 : term,X42 : subst > term > subst > $o] : (? [X43 : subst > term > term] : (! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) & ($true != (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) & ! [X47 : term] : (($true = (X42 @ id @ (X43 @ id @ X47) @ id)) | ((X42 @ id @ X47 @ id) != $true))) | ? [X48 : term] : (($true = (X42 @ id @ X48 @ id)) & ($true != (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id))) | ($true = (X42 @ id @ (lam @ X41) @ id))) <=> (hoasinduction_lem3a = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (axmap = $true) & (axvarshift = $true) & (! [X196 : subst,X197 : term,X198 : term > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196)))) <=> (pushprop_lem0 = $true)) & (pushprop = $true) & ((pushprop_lem1v2 = $true) <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (? [X103 : term] : ((X100 @ X103) != (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true != (X99 @ X102)) | ($true = (X100 @ one)))) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) != (d2term @ X408)) | (X407 = X408)) & ((var @ (d2term @ d_one)) != $true) & (pushprop_lem2v2_gthm = $true) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) <=> (axscons = $true)) & (! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (((X203 @ id @ X205 @ id) = $true) & ($true != (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) & ($true = (X203 @ id @ X206 @ id))) | ? [X207 : subst > term > term] : (($true != (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)) & ! [X208 : term] : (($true != (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) & ! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))) | ($true = (X203 @ id @ X204 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (lamnotap != $true) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) <=> (shinj = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X372 : subst > term > subst > $o,X373 : term] : (? [X379 : subst > term > term] : (($true != (X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)) & ! [X380 : term] : (($true != (X372 @ id @ X380 @ id)) | ($true = (X372 @ id @ (X379 @ id @ X380) @ id))) & ! [X381 : term,X382 : subst,X383 : subst] : ((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383)) = (sub @ (X379 @ X382 @ X381) @ X383))) | ? [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (($true = (X372 @ (comp @ X387 @ X384) @ (sub @ X386 @ X384) @ X385)) & ((X372 @ X387 @ X386 @ (comp @ X384 @ X385)) != $true)) | ($true = (X372 @ id @ (lam @ X373) @ id)) | ? [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (($true = (X372 @ X376 @ X377 @ (comp @ X374 @ X375))) & ((X372 @ (comp @ X376 @ X374) @ (sub @ X377 @ X374) @ X375) != $true)) | ? [X378 : term] : (($true = (X372 @ id @ X378 @ id)) & ($true != (X372 @ id @ (sub @ X373 @ (push @ X378 @ id)) @ id)))) | ? [X364 : term,X365 : subst > term > subst > $o] : (! [X366 : subst > term > term] : (? [X367 : term,X368 : subst,X369 : subst] : ((X366 @ (comp @ X369 @ X368) @ (sub @ X367 @ X368)) != (sub @ (X366 @ X369 @ X367) @ X368)) | ? [X370 : term] : (($true != (X365 @ id @ (X366 @ id @ X370) @ id)) & ($true = (X365 @ id @ X370 @ id))) | ($true = (X365 @ id @ (lam @ (X366 @ sh @ one)) @ id))) & ! [X371 : term] : (($true != (X365 @ id @ X371 @ id)) | ($true = (X365 @ id @ (sub @ X364 @ (push @ X371 @ id)) @ id))) & ($true != (X365 @ id @ (lam @ (sub @ X364 @ (push @ one @ sh))) @ id)))) | ? [X363 : term] : ((sub @ X363 @ id) != X363))) & ((induction = $true) <=> ! [X409 : term,X410 : term > $o] : (? [X411 : term] : (($true != (X410 @ (lam @ X411))) & ($true = (X410 @ X411))) | ? [X413 : term,X414 : term] : (($true = (X410 @ X414)) & ($true = (X410 @ X413)) & ($true != (X410 @ (ap @ X414 @ X413)))) | ($true = (X410 @ X409)) | ? [X412 : term] : (((var @ X412) = $true) & ($true != (X410 @ X412))))) & ((hoasinduction_lem2 = $true) <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (($true = (X26 @ id @ (ap @ X24 @ X25) @ id)) | ((X26 @ id @ X24 @ id) != $true) | ? [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true = (X26 @ X33 @ X36 @ (comp @ X34 @ X35))) & ($true != (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35))) | ? [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true = (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) & ($true != (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ($true != (X26 @ id @ X25 @ id)) | ? [X31 : term,X32 : term] : (($true = (X26 @ id @ X31 @ id)) & ($true = (X26 @ id @ X32 @ id)) & ($true != (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id))))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ($true != (X402 @ X405)) | ? [X406 : term] : ((X404 @ X406) != (X402 @ (sub @ X406 @ (push @ X405 @ X403))))) | ? [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) != X401))) & (hoasapnotvar_gthm = $true) & (axapp = $true) & (! [X444 : subst > term > subst > $o,X445 : term] : (? [X448 : term] : (($true = (var @ (sub @ X448 @ id))) & ($true != (X444 @ id @ X448 @ id))) | ? [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (((X444 @ X460 @ X458 @ (comp @ X461 @ X459)) != $true) & ($true = (X444 @ (comp @ X460 @ X461) @ (sub @ X458 @ X461) @ X459))) | ? [X454 : subst,X455 : subst,X456 : subst,X457 : term] : (($true != (X444 @ (comp @ X454 @ X455) @ (sub @ X457 @ X455) @ X456)) & ($true = (X444 @ X454 @ X457 @ (comp @ X455 @ X456)))) | ((X444 @ id @ X445 @ id) = $true) | ? [X449 : subst > term > term] : (! [X451 : subst,X452 : subst,X453 : term] : ((sub @ (X449 @ X452 @ X453) @ X451) = (X449 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451))) & ! [X450 : term] : (($true = (X444 @ id @ (X449 @ id @ X450) @ id)) | ($true != (X444 @ id @ X450 @ id))) & ($true != (X444 @ id @ (lam @ (X449 @ sh @ one)) @ id))) | ? [X446 : term,X447 : term] : (($true = (X444 @ id @ X447 @ id)) & ((X444 @ id @ (ap @ (sub @ X447 @ id) @ X446) @ id) != $true) & ($true = (X444 @ id @ X446 @ id)))) <=> (hoasinduction = $true)) & (pushprop_lem3v2_lthm = $true) & (((! [X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (? [X439 : term] : (($true = (X431 @ X439)) & ($true != (X431 @ (sub @ X430 @ (push @ X439 @ id))))) | ? [X438 : term] : ((X432 @ id @ X438 @ id) != (X431 @ X438)) | ($true = (X431 @ (lam @ X430))) | ? [X433 : subst > term > term] : (! [X434 : term] : (($true != (X432 @ id @ X434 @ id)) | ($true = (X432 @ id @ (X433 @ id @ X434) @ id))) & ($true != (X432 @ id @ (lam @ (X433 @ sh @ one)) @ id)) & ! [X435 : subst,X436 : term,X437 : subst] : ((X433 @ (comp @ X437 @ X435) @ (sub @ X436 @ X435)) = (sub @ (X433 @ X437 @ X436) @ X435)))) | ? [X429 : term] : ((sub @ X429 @ id) != X429)) | ? [X425 : term] : ! [X426 : subst > term > term] : ? [X427 : term,X428 : subst] : ((sub @ X425 @ (push @ X427 @ X428)) != (X426 @ X428 @ X427))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> (((! [X263 : subst > term > term,X264 : term,X265 : subst,X266 : subst > term > term] : (((lam @ (X266 @ sh @ one)) != (lam @ (X263 @ sh @ one))) | ? [X267 : subst,X268 : term,X269 : subst] : ((sub @ (X263 @ X269 @ X268) @ X267) != (X263 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))) | ((X263 @ X265 @ X264) = (X266 @ X265 @ X264)) | ? [X270 : subst,X271 : term,X272 : subst] : ((sub @ (X266 @ X270 @ X271) @ X272) != (X266 @ (comp @ X270 @ X272) @ (sub @ X271 @ X272)))) | ? [X261 : term,X262 : term] : ((X261 != X262) & ((lam @ X262) = (lam @ X261)))) | ? [X259 : term,X260 : subst] : ((comp @ sh @ (push @ X259 @ X260)) != X260)) | ? [X257 : term,X258 : subst] : ((sub @ one @ (push @ X257 @ X258)) != X257))) & (apnotvar = $true) & (! [X111 : term] : ? [X112 : subst > term > term] : ! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113))) <=> (hoasinduction_lem3v2_f = $true)) & ((induction2_lthm = $true) <=> ((! [X236 : term,X237 : term > $o] : (? [X238 : term] : (($true = (var @ X238)) & ($true != (X237 @ X238))) | ? [X239 : term,X240 : term] : (($true = (X237 @ X240)) & ($true != (X237 @ (ap @ X240 @ X239))) & ($true = (X237 @ X239))) | ($true = (X237 @ X236)) | ? [X241 : term] : (! [X242 : term] : (($true != (X237 @ X242)) | ($true = (X237 @ (sub @ X241 @ (push @ X242 @ id))))) & ($true != (X237 @ (lam @ X241))))) | ? [X228 : term > $o,X229 : subst,X230 : term] : (! [X234 : term,X235 : term] : (($true = (X228 @ (ap @ X234 @ X235))) | ($true != (X228 @ X235)) | ($true != (X228 @ X234))) & ! [X232 : term] : (? [X233 : term] : (($true = (X228 @ X233)) & ($true != (X228 @ (sub @ X232 @ (push @ X233 @ id))))) | ($true = (X228 @ (lam @ X232)))) & ! [X231 : term] : (($true != (var @ X231)) | ($true = (X228 @ (sub @ X231 @ X229)))) & ($true != (X228 @ (sub @ X230 @ X229))))) | ? [X227 : term] : ((sub @ X227 @ id) != X227))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvarind = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((hoaslaminj = $true) <=> ! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (? [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) != (sub @ (X417 @ X419 @ X420) @ X421)) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))) | ? [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) != (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415)))) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) <=> (laminj = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X326 : subst > term > subst > $o,X327 : term] : (? [X328 : term,X329 : term] : (($true = (X326 @ id @ X329 @ id)) & ($true = (X326 @ id @ X328 @ id)) & ($true != (X326 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id))) | ? [X330 : subst > term > term] : (! [X331 : subst,X332 : subst,X333 : term] : ((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)) = (sub @ (X330 @ X331 @ X333) @ X332)) & ($true != (X326 @ id @ (lam @ (X330 @ sh @ one)) @ id)) & ! [X334 : term] : (($true != (X326 @ id @ X334 @ id)) | ($true = (X326 @ id @ (X330 @ id @ X334) @ id)))) | ($true = (X326 @ id @ X327 @ id))) | ? [X316 : term,X317 : term > $o,X318 : subst > term > subst > $o] : (! [X325 : term] : (($true = (X317 @ (sub @ X316 @ (push @ X325 @ id)))) | ($true != (X317 @ X325))) & ! [X320 : subst > term > term] : (? [X324 : term] : (($true != (X318 @ id @ (X320 @ id @ X324) @ id)) & ($true = (X318 @ id @ X324 @ id))) | ($true = (X318 @ id @ (lam @ (X320 @ sh @ one)) @ id)) | ? [X321 : subst,X322 : subst,X323 : term] : ((sub @ (X320 @ X321 @ X323) @ X322) != (X320 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322)))) & ((X317 @ (lam @ X316)) != $true) & ! [X319 : term] : ((X318 @ id @ X319 @ id) = (X317 @ X319)))) | ? [X315 : term] : ((sub @ X315 @ id) != X315)) | ? [X308 : term > $o,X309 : term] : (! [X313 : term] : (($true = (X308 @ (lam @ X313))) | ? [X314 : term] : (($true = (X308 @ X314)) & ($true != (X308 @ (sub @ X313 @ (push @ X314 @ id)))))) & ! [X311 : term,X312 : term] : (($true != (X308 @ X312)) | ($true = (X308 @ (ap @ X311 @ X312))) | ($true != (X308 @ X311))) & ! [X310 : term] : (($true = (X308 @ X310)) | ((var @ X310) != $true)) & ($true != (X308 @ X309)))) | ? [X305 : subst > term > subst > $o] : ! [X306 : term > $o] : ? [X307 : term] : ((X306 @ X307) != (X305 @ id @ X307 @ id)))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((termmset = $true) <=> ! [X344 : term] : ((sub @ X344 @ id) = X344)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((substmonoid_lthm = $true) <=> (((! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140)) | ? [X139 : subst] : ((comp @ X139 @ id) != X139)) | ? [X138 : subst] : ((comp @ id @ X138) != X138))) & (induction2lem_gthm = $true) & ((hoasapinj1_lthm = $true) <=> ((! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226)) | ? [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 != X222) & ((ap @ X222 @ X220) = (ap @ X219 @ X221)))) | ? [X218 : term] : ((sub @ X218 @ id) != X218))) & (one = (d2term @ d_one)) & (hoaslamnotvar = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X483 : term,X484 : subst > term > subst > $o] : (($true = (X484 @ id @ X483 @ id)) | ? [X496 : subst > term > term] : (! [X500 : term] : (($true != (X484 @ id @ X500 @ id)) | ($true = (X484 @ id @ (X496 @ id @ X500) @ id))) & ($true != (X484 @ id @ (lam @ (X496 @ sh @ one)) @ id)) & ! [X497 : term,X498 : subst,X499 : subst] : ((X496 @ (comp @ X499 @ X498) @ (sub @ X497 @ X498)) = (sub @ (X496 @ X499 @ X497) @ X498))) | ? [X489 : subst,X490 : subst,X491 : term,X492 : subst] : (($true != (X484 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) & ($true = (X484 @ X489 @ X491 @ (comp @ X492 @ X490)))) | ? [X495 : term] : (($true = (var @ (sub @ X495 @ id))) & ($true != (X484 @ id @ X495 @ id))) | ? [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (($true = (X484 @ (comp @ X485 @ X488) @ (sub @ X487 @ X488) @ X486)) & ($true != (X484 @ X485 @ X487 @ (comp @ X488 @ X486)))) | ? [X493 : term,X494 : term] : (($true = (X484 @ id @ X494 @ id)) & ($true = (X484 @ id @ X493 @ id)) & ($true != (X484 @ id @ (ap @ (sub @ X493 @ id) @ X494) @ id)))) | ? [X473 : term > $o,X474 : subst > term > subst > $o,X475 : term] : (! [X478 : subst > term > term] : (? [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X481 @ X482) @ (sub @ X480 @ X482)) != (sub @ (X478 @ X481 @ X480) @ X482)) | ? [X479 : term] : (($true = (X474 @ id @ X479 @ id)) & ($true != (X474 @ id @ (X478 @ id @ X479) @ id))) | ($true = (X474 @ id @ (lam @ (X478 @ sh @ one)) @ id))) & ($true != (X473 @ (lam @ X475))) & ! [X476 : term] : (($true = (X473 @ (sub @ X475 @ (push @ X476 @ id)))) | ((X473 @ X476) != $true)) & ! [X477 : term] : ((X474 @ id @ X477 @ id) = (X473 @ X477)))) | ? [X472 : term] : ((sub @ X472 @ id) != X472)) | ? [X465 : term,X466 : term > $o] : (! [X470 : term] : (($true = (X466 @ (lam @ X470))) | ? [X471 : term] : (((X466 @ (sub @ X470 @ (push @ X471 @ id))) != $true) & ($true = (X466 @ X471)))) & ($true != (X466 @ X465)) & ! [X469 : term] : (((X466 @ X469) = $true) | ($true != (var @ X469))) & ! [X467 : term,X468 : term] : (((X466 @ X468) != $true) | ($true != (X466 @ X467)) | ($true = (X466 @ (ap @ X468 @ X467)))))) | ? [X462 : subst > term > subst > $o] : ! [X463 : term > $o] : ? [X464 : term] : ((X462 @ id @ X464 @ id) != (X463 @ X464)))) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & (! [X53 : subst > term > subst > $o,X54 : term] : (? [X56 : subst > term > term,X57 : term] : (! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) & ! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63)))) & ! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ($true != (X53 @ id @ X61 @ id))) & ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) != $true)) | ($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ? [X55 : term] : (($true != (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) & ($true = (X53 @ id @ X55 @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (substmonoid_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (((! [X11 : subst > term > subst > $o,X12 : term] : (? [X13 : subst > term > term] : (($true != (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) & ! [X17 : term] : (($true != (X11 @ id @ X17 @ id)) | ($true = (X11 @ id @ (X13 @ id @ X17) @ id))) & ! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14))) | ($true = (X11 @ id @ (lam @ X12) @ id)) | ? [X18 : term] : (($true = (X11 @ id @ X18 @ id)) & ($true != (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)))) | ? [X3 : subst > term > subst > $o,X4 : term] : (($true != (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id)) & ! [X10 : term] : (((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X3 @ id @ X10 @ id))) & ! [X5 : subst > term > term] : (? [X9 : term] : (($true != (X3 @ id @ (X5 @ id @ X9) @ id)) & ($true = (X3 @ id @ X9 @ id))) | ($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id)) | ? [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) != (sub @ (X5 @ X7 @ X8) @ X6))))) | ? [X2 : term] : ((sub @ X2 @ id) != X2)) <=> (hoasinduction_lem3a_lthm = $true)) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X278 : term,X279 : term > $o,X280 : term,X281 : subst > term > subst > $o] : (($true != (X279 @ X280)) | ($true != (X279 @ X278)) | ($true = (X279 @ (ap @ X278 @ X280))) | ? [X288 : term,X289 : subst,X290 : subst,X291 : subst] : (($true != (X281 @ (comp @ X289 @ X291) @ (sub @ X288 @ X291) @ X290)) & ((X281 @ X289 @ X288 @ (comp @ X291 @ X290)) = $true)) | ? [X292 : term] : ((X279 @ X292) != (X281 @ id @ X292 @ id)) | ? [X282 : term,X283 : term] : (($true = (X281 @ id @ X282 @ id)) & ((X281 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id) != $true) & ($true = (X281 @ id @ X283 @ id))) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X281 @ (comp @ X284 @ X287) @ (sub @ X286 @ X287) @ X285)) & ($true != (X281 @ X284 @ X286 @ (comp @ X287 @ X285)))))) & ! [X388 : d_term] : (d_one = X388) & (pushprop_gthm = $true) & (axclos = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X252 : subst > term > subst > $o] : ? [X253 : term > $o] : ! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id))) & (hoaslamnotvar_lthm = $true) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) <=> (axidr = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342))) | ? [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) != X337)) | ? [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) != X335))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lthm = $true) & ((substmonoid = $true) <=> (! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442))) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (hoasinduction_lem3v2_gthm = $true) & ! [X51 : d_subst,X52 : d_subst] : ((X51 = X52) | ((d2subst @ X52) != (d2subst @ X51))) & ((? [X76 : term] : ((sub @ X76 @ id) != X76) | ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (? [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (($true = (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) & ($true != (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))) | ? [X90 : subst > term > term] : (($true != (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id)) & ! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) & ! [X94 : term] : (($true = (X78 @ id @ (X90 @ id @ X94) @ id)) | ($true != (X78 @ id @ X94 @ id)))) | ? [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (($true != (X78 @ X87 @ X85 @ (comp @ X86 @ X88))) & ($true = (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88))) | ($true = (X79 @ (lam @ X77))) | ? [X89 : term] : (($true = (X79 @ X89)) & ($true != (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ? [X80 : term] : ((X78 @ id @ X80 @ id) != (X79 @ X80)))) <=> (hoasinduction_lem3v2_lthm = $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)))))))))))))) & (! [X397 : subst > term > subst > $o] : ? [X398 : term > $o] : ! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id)) <=> (hoasinduction_lem0 = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) = (ap @ X246 @ X247)) & (X245 != X247)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X216 : term] : ? [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) = (X217 @ sh @ one))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true)),
% 42.64/7.44 inference(ennf_transformation,[status(thm)],[f11])).
% 42.64/7.44 thf(f11,plain,(
% 42.64/7.44 ((d2subst @ d_id) = sh) & ((induction2lem = $true) <=> ! [X515 : subst,X516 : term > $o,X517 : term] : (~! [X519 : term,X520 : term] : (($true = (X516 @ (ap @ X520 @ X519))) | ($true != (X516 @ X520)) | ($true != (X516 @ X519))) | ($true = (X516 @ (sub @ X517 @ X515))) | ~! [X518 : term] : (($true = (X516 @ (sub @ X518 @ X515))) | ($true != (var @ X518))) | ~! [X521 : term] : (~! [X522 : term] : (($true != (X516 @ X522)) | ($true = (X516 @ (sub @ X521 @ (push @ X522 @ id))))) | ($true = (X516 @ (lam @ X521)))))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X523 : subst > term > subst > $o,X524 : term] : (~! [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (($true != (X523 @ X527 @ X529 @ (comp @ X526 @ X528))) | ((X523 @ (comp @ X527 @ X526) @ (sub @ X529 @ X526) @ X528) = $true)) | ~! [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (($true != (X523 @ (comp @ X538 @ X536) @ (sub @ X535 @ X536) @ X537)) | ($true = (X523 @ X538 @ X535 @ (comp @ X536 @ X537)))) | ($true = (X523 @ id @ (lam @ X524) @ id)) | ~! [X530 : subst > term > term] : (~! [X534 : term] : (($true != (X523 @ id @ X534 @ id)) | ($true = (X523 @ id @ (X530 @ id @ X534) @ id))) | ($true = (X523 @ id @ (lam @ (X530 @ sh @ one)) @ id)) | ~! [X531 : subst,X532 : term,X533 : subst] : ((sub @ (X530 @ X531 @ X532) @ X533) = (X530 @ (comp @ X531 @ X533) @ (sub @ X532 @ X533)))) | ~! [X525 : term] : (($true = (X523 @ id @ (sub @ X524 @ (push @ X525 @ id)) @ id)) | ($true != (X523 @ id @ X525 @ id))))) & (axabs = $true) & (pushprop_lem0_gthm = $true) & (! [X49 : term] : ~! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3v2 = $true) <=> ! [X345 : term > $o,X346 : term,X347 : subst > term > subst > $o] : (~! [X349 : subst > term > term] : (~! [X350 : term] : (((X347 @ id @ X350 @ id) != $true) | ($true = (X347 @ id @ (X349 @ id @ X350) @ id))) | ($true = (X347 @ id @ (lam @ (X349 @ sh @ one)) @ id)) | ~! [X351 : subst,X352 : subst,X353 : term] : ((X349 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)) = (sub @ (X349 @ X351 @ X353) @ X352))) | ((X345 @ (lam @ X346)) = $true) | ~! [X354 : subst,X355 : subst,X356 : subst,X357 : term] : (($true = (X347 @ X354 @ X357 @ (comp @ X356 @ X355))) | ((X347 @ (comp @ X354 @ X356) @ (sub @ X357 @ X356) @ X355) != $true)) | ~! [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (($true != (X347 @ X359 @ X361 @ (comp @ X360 @ X362))) | ($true = (X347 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360) @ X362))) | ~! [X348 : term] : (($true != (X345 @ X348)) | ((X345 @ (sub @ X346 @ (push @ X348 @ id))) = $true)) | ~! [X358 : term] : ((X345 @ X358) = (X347 @ id @ X358 @ id)))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & ((induction2lem_lthm = $true) <=> (! [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) = X116) => (! [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) = X117) => (! [X119 : subst] : ((comp @ X119 @ id) = X119) => (! [X120 : term > $o,X121 : term] : (~! [X122 : term] : (((var @ X122) != $true) | ($true = (X120 @ X122))) | ~! [X123 : term,X124 : term] : (($true != (X120 @ X123)) | ($true != (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))) | ($true = (X120 @ X121)) | ~! [X125 : term] : (($true = (X120 @ (lam @ X125))) | ($true != (X120 @ X125)))) => ! [X126 : term > $o,X127 : term,X128 : subst] : (~! [X133 : term] : (($true = (X126 @ (sub @ X133 @ X128))) | ($true != (var @ X133))) | ($true = (X126 @ (sub @ X127 @ X128))) | ~! [X129 : term,X130 : term] : (($true != (X126 @ X130)) | ($true != (X126 @ X129)) | ((X126 @ (ap @ X130 @ X129)) = $true)) | ~! [X131 : term] : (($true = (X126 @ (lam @ X131))) | ~! [X132 : term] : (($true != (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id)))))))))))) & (pushprop_lem3v2 = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (termmset_gthm = $true) & (axassoc = $true) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (~! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) = (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) | ((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509))) <=> (hoaslamnotap = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ($true != (X67 @ X65))) <=> (pushprop_lem1 = $true)) & (induction2_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem2v2 = $true) & (! [X295 : term > $o,X296 : term,X297 : subst > term > subst > $o] : (~! [X304 : term] : (($true = (X295 @ (sub @ X296 @ (push @ X304 @ id)))) | ((X295 @ X304) != $true)) | ~! [X303 : term] : ((X295 @ X303) = (X297 @ id @ X303 @ id)) | ~! [X298 : subst > term > term] : (~! [X300 : subst,X301 : term,X302 : subst] : ((sub @ (X298 @ X302 @ X301) @ X300) = (X298 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300))) | ($true = (X297 @ id @ (lam @ (X298 @ sh @ one)) @ id)) | ~! [X299 : term] : (((X297 @ id @ X299 @ id) != $true) | ($true = (X297 @ id @ (X298 @ id @ X299) @ id)))) | ($true = (X295 @ (lam @ X296)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_gthm = $true) & (! [X104 : term,X105 : term > $o] : (~! [X109 : term,X110 : term] : (($true = (X105 @ (ap @ X109 @ X110))) | ((X105 @ X109) != $true) | ($true != (X105 @ X110))) | ($true = (X105 @ X104)) | ~! [X106 : term] : (($true = (X105 @ (lam @ X106))) | ~! [X107 : term] : (((X105 @ X107) != $true) | ($true = (X105 @ (sub @ X106 @ (push @ X107 @ id)))))) | ~! [X108 : term] : (($true = (X105 @ X108)) | ((var @ X108) != $true))) <=> (induction2 = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X19 : term] : ~! [X20 : subst > term > term] : ~! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21)))) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X389 : term,X390 : subst > term > subst > $o] : (~! [X392 : subst > term > term] : (($true = (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) | ~! [X396 : term] : (($true = (X390 @ id @ (X392 @ id @ X396) @ id)) | ($true != (X390 @ id @ X396 @ id))) | ~! [X393 : subst,X394 : term,X395 : subst] : ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)) = (sub @ (X392 @ X395 @ X394) @ X393))) | ~! [X391 : term] : (((X390 @ id @ (sub @ X389 @ (push @ X391 @ id)) @ id) = $true) | ($true != (X390 @ id @ X391 @ id))) | ($true = (X390 @ id @ (lam @ (sub @ X389 @ (push @ one @ sh))) @ id)))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X501 : term,X502 : subst > term > subst > $o] : (~! [X503 : subst > term > term] : (((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id) = $true) | ~! [X504 : subst,X505 : term,X506 : subst] : ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)) = (sub @ (X503 @ X506 @ X505) @ X504)) | ~! [X507 : term] : (($true = (X502 @ id @ (X503 @ id @ X507) @ id)) | ($true != (X502 @ id @ X507 @ id)))) | ~! [X508 : term] : (($true != (X502 @ id @ X508 @ id)) | ($true = (X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id))) | ((X502 @ id @ (lam @ (sub @ X501 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & ((! [X201 : term] : ((sub @ X201 @ id) = X201) => ! [X202 : term] : ((sub @ X202 @ id) = X202)) <=> (termmset_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lthm = $true) <=> (! [X142 : term > $o,X143 : term] : (~! [X145 : term,X146 : term] : (($true = (X142 @ (ap @ X145 @ X146))) | ($true != (X142 @ X145)) | ($true != (X142 @ X146))) | ($true = (X142 @ X143)) | ~! [X144 : term] : (($true = (X142 @ X144)) | ((var @ X144) != $true)) | ~! [X147 : term] : (~! [X148 : term] : (($true = (X142 @ (sub @ X147 @ (push @ X148 @ id)))) | ($true != (X142 @ X148))) | ($true = (X142 @ (lam @ X147))))) => (! [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (($true != (X149 @ id @ X150 @ id)) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true != (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) | ($true = (X149 @ id @ (ap @ X151 @ X150) @ id)) | ~! [X156 : term,X157 : term] : (((X149 @ id @ X157 @ id) != $true) | ($true != (X149 @ id @ X156 @ id)) | ($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id))) | ~! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true) | ($true != (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159))) | ($true != (X149 @ id @ X151 @ id))) => (! [X162 : subst > term > subst > $o,X163 : term] : (~! [X164 : term] : (($true != (X162 @ id @ X164 @ id)) | ($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id))) | ~! [X173 : subst > term > term] : (~! [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) = (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id)) | ~! [X174 : term] : (($true = (X162 @ id @ (X173 @ id @ X174) @ id)) | ($true != (X162 @ id @ X174 @ id)))) | ~! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166)) | ($true != (X162 @ X165 @ X167 @ (comp @ X168 @ X166)))) | ($true = (X162 @ id @ (lam @ X163) @ id)) | ~! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (($true != (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true))) => ! [X178 : term,X179 : subst > term > subst > $o] : (~! [X191 : subst > term > term] : (((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) = $true) | ~! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192)) | ~! [X195 : term] : (($true = (X179 @ id @ (X191 @ id @ X195) @ id)) | ($true != (X179 @ id @ X195 @ id)))) | ~! [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true != (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190)) | ($true = (X179 @ X188 @ X187 @ (comp @ X189 @ X190)))) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (($true = (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183)) | ($true != (X179 @ X184 @ X185 @ (comp @ X186 @ X183)))) | ~! [X181 : term,X182 : term] : (($true = (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) | ((X179 @ id @ X182 @ id) != $true) | ($true != (X179 @ id @ X181 @ id))) | ~! [X180 : term] : (($true = (X179 @ id @ X180 @ id)) | ($true != (var @ (sub @ X180 @ id)))) | ((X179 @ id @ X178 @ id) = $true)))))) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapnotvar = $true) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & ((pushprop_lem0_lthm = $true) <=> ! [X273 : term > $o,X274 : subst,X275 : term] : ~! [X276 : term > $o] : ~! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277))) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & (! [X41 : term,X42 : subst > term > subst > $o] : (~! [X43 : subst > term > term] : (~! [X47 : term] : (($true = (X42 @ id @ (X43 @ id @ X47) @ id)) | ((X42 @ id @ X47 @ id) != $true)) | ($true = (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) | ~! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45))) | ~! [X48 : term] : (($true = (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id)) | ($true != (X42 @ id @ X48 @ id))) | ($true = (X42 @ id @ (lam @ X41) @ id))) <=> (hoasinduction_lem3a = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (axmap = $true) & (axvarshift = $true) & ((pushprop_lem0 = $true) <=> ! [X196 : subst,X197 : term,X198 : term > $o] : ~! [X199 : term > $o] : ~! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196))))) & (pushprop = $true) & (! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (($true != (X99 @ X102)) | ~! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true = (X100 @ one))) <=> (pushprop_lem1v2 = $true)) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) = (d2term @ X408)) => (X407 = X408)) & ((var @ (d2term @ d_one)) != $true) & (pushprop_lem2v2_gthm = $true) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) <=> (axscons = $true)) & (! [X203 : subst > term > subst > $o,X204 : term] : (($true = (X203 @ id @ X204 @ id)) | ~! [X205 : term,X206 : term] : (($true = (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) | ((X203 @ id @ X205 @ id) != $true) | ($true != (X203 @ id @ X206 @ id))) | ~! [X207 : subst > term > term] : (~! [X208 : term] : (($true != (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) | ~! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211)) | ($true = (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (lamnotap != $true) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) <=> (shinj = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X363 : term] : ((sub @ X363 @ id) = X363) => (! [X364 : term,X365 : subst > term > subst > $o] : (($true = (X365 @ id @ (lam @ (sub @ X364 @ (push @ one @ sh))) @ id)) | ~! [X366 : subst > term > term] : (~! [X367 : term,X368 : subst,X369 : subst] : ((X366 @ (comp @ X369 @ X368) @ (sub @ X367 @ X368)) = (sub @ (X366 @ X369 @ X367) @ X368)) | ~! [X370 : term] : (($true != (X365 @ id @ X370 @ id)) | ($true = (X365 @ id @ (X366 @ id @ X370) @ id))) | ($true = (X365 @ id @ (lam @ (X366 @ sh @ one)) @ id))) | ~! [X371 : term] : (($true != (X365 @ id @ X371 @ id)) | ($true = (X365 @ id @ (sub @ X364 @ (push @ X371 @ id)) @ id)))) => ! [X372 : subst > term > subst > $o,X373 : term] : (~! [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (((X372 @ X387 @ X386 @ (comp @ X384 @ X385)) = $true) | ($true != (X372 @ (comp @ X387 @ X384) @ (sub @ X386 @ X384) @ X385))) | ($true = (X372 @ id @ (lam @ X373) @ id)) | ~! [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (((X372 @ (comp @ X376 @ X374) @ (sub @ X377 @ X374) @ X375) = $true) | ($true != (X372 @ X376 @ X377 @ (comp @ X374 @ X375)))) | ~! [X378 : term] : (($true != (X372 @ id @ X378 @ id)) | ($true = (X372 @ id @ (sub @ X373 @ (push @ X378 @ id)) @ id))) | ~! [X379 : subst > term > term] : (~! [X380 : term] : (($true != (X372 @ id @ X380 @ id)) | ($true = (X372 @ id @ (X379 @ id @ X380) @ id))) | ($true = (X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)) | ~! [X381 : term,X382 : subst,X383 : subst] : ((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383)) = (sub @ (X379 @ X382 @ X381) @ X383))))))) & ((induction = $true) <=> ! [X409 : term,X410 : term > $o] : (($true = (X410 @ X409)) | ~! [X411 : term] : (($true != (X410 @ X411)) | ($true = (X410 @ (lam @ X411)))) | ~! [X413 : term,X414 : term] : (($true != (X410 @ X414)) | ($true = (X410 @ (ap @ X414 @ X413))) | ($true != (X410 @ X413))) | ~! [X412 : term] : (($true = (X410 @ X412)) | ((var @ X412) != $true)))) & (! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (($true != (X26 @ id @ X25 @ id)) | ((X26 @ id @ X24 @ id) != $true) | ($true = (X26 @ id @ (ap @ X24 @ X25) @ id)) | ~! [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true != (X26 @ X33 @ X36 @ (comp @ X34 @ X35))) | ($true = (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35))) | ~! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true != (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) | ($true = (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ~! [X31 : term,X32 : term] : (($true != (X26 @ id @ X31 @ id)) | ($true != (X26 @ id @ X32 @ id)) | ($true = (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)))) <=> (hoasinduction_lem2 = $true)) & ((! [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) = X401) => ! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (($true != (X402 @ X405)) | ((X404 @ one) = $true) | ~! [X406 : term] : ((X404 @ X406) = (X402 @ (sub @ X406 @ (push @ X405 @ X403)))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasapnotvar_gthm = $true) & (axapp = $true) & ((hoasinduction = $true) <=> ! [X444 : subst > term > subst > $o,X445 : term] : (~! [X448 : term] : (($true = (X444 @ id @ X448 @ id)) | ($true != (var @ (sub @ X448 @ id)))) | ~! [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (((X444 @ X460 @ X458 @ (comp @ X461 @ X459)) = $true) | ($true != (X444 @ (comp @ X460 @ X461) @ (sub @ X458 @ X461) @ X459))) | ((X444 @ id @ X445 @ id) = $true) | ~! [X446 : term,X447 : term] : (($true != (X444 @ id @ X446 @ id)) | ((X444 @ id @ (ap @ (sub @ X447 @ id) @ X446) @ id) = $true) | ($true != (X444 @ id @ X447 @ id))) | ~! [X454 : subst,X455 : subst,X456 : subst,X457 : term] : (($true = (X444 @ (comp @ X454 @ X455) @ (sub @ X457 @ X455) @ X456)) | ($true != (X444 @ X454 @ X457 @ (comp @ X455 @ X456)))) | ~! [X449 : subst > term > term] : (~! [X450 : term] : (($true = (X444 @ id @ (X449 @ id @ X450) @ id)) | ($true != (X444 @ id @ X450 @ id))) | ($true = (X444 @ id @ (lam @ (X449 @ sh @ one)) @ id)) | ~! [X451 : subst,X452 : subst,X453 : term] : ((sub @ (X449 @ X452 @ X453) @ X451) = (X449 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451)))))) & (pushprop_lem3v2_lthm = $true) & ((! [X425 : term] : ~! [X426 : subst > term > term] : ~! [X427 : term,X428 : subst] : ((sub @ X425 @ (push @ X427 @ X428)) = (X426 @ X428 @ X427)) => (! [X429 : term] : ((sub @ X429 @ id) = X429) => ! [X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (~! [X433 : subst > term > term] : (($true = (X432 @ id @ (lam @ (X433 @ sh @ one)) @ id)) | ~! [X435 : subst,X436 : term,X437 : subst] : ((X433 @ (comp @ X437 @ X435) @ (sub @ X436 @ X435)) = (sub @ (X433 @ X437 @ X436) @ X435)) | ~! [X434 : term] : (($true != (X432 @ id @ X434 @ id)) | ($true = (X432 @ id @ (X433 @ id @ X434) @ id)))) | ($true = (X431 @ (lam @ X430))) | ~! [X438 : term] : ((X432 @ id @ X438 @ id) = (X431 @ X438)) | ~! [X439 : term] : (($true != (X431 @ X439)) | ($true = (X431 @ (sub @ X430 @ (push @ X439 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X257 : term,X258 : subst] : ((sub @ one @ (push @ X257 @ X258)) = X257) => (! [X259 : term,X260 : subst] : ((comp @ sh @ (push @ X259 @ X260)) = X260) => (! [X261 : term,X262 : term] : (((lam @ X262) != (lam @ X261)) | (X261 = X262)) => ! [X263 : subst > term > term,X264 : term,X265 : subst,X266 : subst > term > term] : (~! [X270 : subst,X271 : term,X272 : subst] : ((sub @ (X266 @ X270 @ X271) @ X272) = (X266 @ (comp @ X270 @ X272) @ (sub @ X271 @ X272))) | ((X263 @ X265 @ X264) = (X266 @ X265 @ X264)) | ~! [X267 : subst,X268 : term,X269 : subst] : ((sub @ (X263 @ X269 @ X268) @ X267) = (X263 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))) | ((lam @ (X266 @ sh @ one)) != (lam @ (X263 @ sh @ one)))))))) & (apnotvar = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X111 : term] : ~! [X112 : subst > term > term] : ~! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113)))) & ((induction2_lthm = $true) <=> (! [X227 : term] : ((sub @ X227 @ id) = X227) => (! [X228 : term > $o,X229 : subst,X230 : term] : (~! [X232 : term] : (($true = (X228 @ (lam @ X232))) | ~! [X233 : term] : (($true != (X228 @ X233)) | ($true = (X228 @ (sub @ X232 @ (push @ X233 @ id)))))) | ($true = (X228 @ (sub @ X230 @ X229))) | ~! [X231 : term] : (($true != (var @ X231)) | ($true = (X228 @ (sub @ X231 @ X229)))) | ~! [X234 : term,X235 : term] : (($true = (X228 @ (ap @ X234 @ X235))) | ($true != (X228 @ X235)) | ($true != (X228 @ X234)))) => ! [X236 : term,X237 : term > $o] : (~! [X241 : term] : (~! [X242 : term] : (($true != (X237 @ X242)) | ($true = (X237 @ (sub @ X241 @ (push @ X242 @ id))))) | ($true = (X237 @ (lam @ X241)))) | ($true = (X237 @ X236)) | ~! [X238 : term] : (($true = (X237 @ X238)) | ($true != (var @ X238))) | ~! [X239 : term,X240 : term] : (($true != (X237 @ X240)) | ($true != (X237 @ X239)) | ($true = (X237 @ (ap @ X240 @ X239)))))))) & ! [X23 : d_subst] : (d_id = X23) & (ulamvarind = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((hoaslaminj = $true) <=> ! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (~! [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) = (sub @ (X417 @ X419 @ X420) @ X421)) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415)) | ~! [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) = (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))))) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) <=> (laminj = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X305 : subst > term > subst > $o] : ~! [X306 : term > $o] : ~! [X307 : term] : ((X306 @ X307) = (X305 @ id @ X307 @ id)) => (! [X308 : term > $o,X309 : term] : (~! [X313 : term] : (~! [X314 : term] : (($true != (X308 @ X314)) | ($true = (X308 @ (sub @ X313 @ (push @ X314 @ id))))) | ($true = (X308 @ (lam @ X313)))) | ~! [X310 : term] : (($true = (X308 @ X310)) | ((var @ X310) != $true)) | ($true = (X308 @ X309)) | ~! [X311 : term,X312 : term] : (($true != (X308 @ X312)) | ($true = (X308 @ (ap @ X311 @ X312))) | ($true != (X308 @ X311)))) => (! [X315 : term] : ((sub @ X315 @ id) = X315) => (! [X316 : term,X317 : term > $o,X318 : subst > term > subst > $o] : (~! [X325 : term] : (($true = (X317 @ (sub @ X316 @ (push @ X325 @ id)))) | ($true != (X317 @ X325))) | ~! [X320 : subst > term > term] : (($true = (X318 @ id @ (lam @ (X320 @ sh @ one)) @ id)) | ~! [X324 : term] : (($true = (X318 @ id @ (X320 @ id @ X324) @ id)) | ($true != (X318 @ id @ X324 @ id))) | ~! [X321 : subst,X322 : subst,X323 : term] : ((sub @ (X320 @ X321 @ X323) @ X322) = (X320 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322)))) | ~! [X319 : term] : ((X318 @ id @ X319 @ id) = (X317 @ X319)) | ((X317 @ (lam @ X316)) = $true)) => ! [X326 : subst > term > subst > $o,X327 : term] : (($true = (X326 @ id @ X327 @ id)) | ~! [X328 : term,X329 : term] : (($true != (X326 @ id @ X329 @ id)) | ($true != (X326 @ id @ X328 @ id)) | ($true = (X326 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id))) | ~! [X330 : subst > term > term] : (($true = (X326 @ id @ (lam @ (X330 @ sh @ one)) @ id)) | ~! [X334 : term] : (($true != (X326 @ id @ X334 @ id)) | ($true = (X326 @ id @ (X330 @ id @ X334) @ id))) | ~! [X331 : subst,X332 : subst,X333 : term] : ((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)) = (sub @ (X330 @ X331 @ X333) @ X332))))))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((termmset = $true) <=> ! [X344 : term] : ((sub @ X344 @ id) = X344)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((substmonoid_lthm = $true) <=> (! [X138 : subst] : ((comp @ id @ X138) = X138) => (! [X139 : subst] : ((comp @ X139 @ id) = X139) => (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))))) & (induction2lem_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X218 : term] : ((sub @ X218 @ id) = X218) => (! [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 = X222) | ((ap @ X222 @ X220) != (ap @ X219 @ X221))) => ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226))))) & (one = (d2term @ d_one)) & (hoaslamnotvar = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X462 : subst > term > subst > $o] : ~! [X463 : term > $o] : ~! [X464 : term] : ((X462 @ id @ X464 @ id) = (X463 @ X464)) => (! [X465 : term,X466 : term > $o] : (~! [X469 : term] : (((X466 @ X469) = $true) | ($true != (var @ X469))) | ~! [X470 : term] : (($true = (X466 @ (lam @ X470))) | ~! [X471 : term] : (((X466 @ (sub @ X470 @ (push @ X471 @ id))) = $true) | ($true != (X466 @ X471)))) | ($true = (X466 @ X465)) | ~! [X467 : term,X468 : term] : (((X466 @ X468) != $true) | ($true != (X466 @ X467)) | ($true = (X466 @ (ap @ X468 @ X467))))) => (! [X472 : term] : ((sub @ X472 @ id) = X472) => (! [X473 : term > $o,X474 : subst > term > subst > $o,X475 : term] : (~! [X477 : term] : ((X474 @ id @ X477 @ id) = (X473 @ X477)) | ($true = (X473 @ (lam @ X475))) | ~! [X476 : term] : (($true = (X473 @ (sub @ X475 @ (push @ X476 @ id)))) | ((X473 @ X476) != $true)) | ~! [X478 : subst > term > term] : (~! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X481 @ X482) @ (sub @ X480 @ X482)) = (sub @ (X478 @ X481 @ X480) @ X482)) | ~! [X479 : term] : (($true = (X474 @ id @ (X478 @ id @ X479) @ id)) | ($true != (X474 @ id @ X479 @ id))) | ($true = (X474 @ id @ (lam @ (X478 @ sh @ one)) @ id)))) => ! [X483 : term,X484 : subst > term > subst > $o] : (~! [X489 : subst,X490 : subst,X491 : term,X492 : subst] : (($true = (X484 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) | ($true != (X484 @ X489 @ X491 @ (comp @ X492 @ X490)))) | ($true = (X484 @ id @ X483 @ id)) | ~! [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (($true = (X484 @ X485 @ X487 @ (comp @ X488 @ X486))) | ($true != (X484 @ (comp @ X485 @ X488) @ (sub @ X487 @ X488) @ X486))) | ~! [X496 : subst > term > term] : (~! [X497 : term,X498 : subst,X499 : subst] : ((X496 @ (comp @ X499 @ X498) @ (sub @ X497 @ X498)) = (sub @ (X496 @ X499 @ X497) @ X498)) | ~! [X500 : term] : (($true != (X484 @ id @ X500 @ id)) | ($true = (X484 @ id @ (X496 @ id @ X500) @ id))) | ($true = (X484 @ id @ (lam @ (X496 @ sh @ one)) @ id))) | ~! [X495 : term] : (($true = (X484 @ id @ X495 @ id)) | ($true != (var @ (sub @ X495 @ id)))) | ~! [X493 : term,X494 : term] : (($true != (X484 @ id @ X493 @ id)) | ($true = (X484 @ id @ (ap @ (sub @ X493 @ id) @ X494) @ id)) | ($true != (X484 @ id @ X494 @ id))))))))) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & (! [X53 : subst > term > subst > $o,X54 : term] : (($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ~! [X56 : subst > term > term,X57 : term] : (~! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) | ~! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63)))) | ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) = $true) | ~! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ($true != (X53 @ id @ X61 @ id)))) | ~! [X55 : term] : (($true != (X53 @ id @ X55 @ id)) | ($true = (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (substmonoid_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & ((! [X2 : term] : ((sub @ X2 @ id) = X2) => (! [X3 : subst > term > subst > $o,X4 : term] : (~! [X10 : term] : (((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X3 @ id @ X10 @ id))) | ~! [X5 : subst > term > term] : (($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id)) | ~! [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) = (sub @ (X5 @ X7 @ X8) @ X6)) | ~! [X9 : term] : (($true != (X3 @ id @ X9 @ id)) | ($true = (X3 @ id @ (X5 @ id @ X9) @ id)))) | ($true = (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id))) => ! [X11 : subst > term > subst > $o,X12 : term] : (~! [X18 : term] : (($true = (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)) | ($true != (X11 @ id @ X18 @ id))) | ($true = (X11 @ id @ (lam @ X12) @ id)) | ~! [X13 : subst > term > term] : (($true = (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14)) | ~! [X17 : term] : (($true != (X11 @ id @ X17 @ id)) | ($true = (X11 @ id @ (X13 @ id @ X17) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X278 : term,X279 : term > $o,X280 : term,X281 : subst > term > subst > $o] : (~! [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true != (X281 @ (comp @ X284 @ X287) @ (sub @ X286 @ X287) @ X285)) | ($true = (X281 @ X284 @ X286 @ (comp @ X287 @ X285)))) | ($true = (X279 @ (ap @ X278 @ X280))) | ~! [X282 : term,X283 : term] : (((X281 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id) = $true) | ($true != (X281 @ id @ X283 @ id)) | ($true != (X281 @ id @ X282 @ id))) | ($true != (X279 @ X280)) | ~! [X292 : term] : ((X279 @ X292) = (X281 @ id @ X292 @ id)) | ~! [X288 : term,X289 : subst,X290 : subst,X291 : subst] : (((X281 @ X289 @ X288 @ (comp @ X291 @ X290)) != $true) | ($true = (X281 @ (comp @ X289 @ X291) @ (sub @ X288 @ X291) @ X290))) | ($true != (X279 @ X278)))) & ! [X388 : d_term] : (d_one = X388) & (pushprop_gthm = $true) & (axclos = $true) & (! [X252 : subst > term > subst > $o] : ~! [X253 : term > $o] : ~! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id)) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) <=> (axidr = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) = X335) => (! [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) = X337) => ! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341)))) | ($true != (X339 @ X342)))))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lthm = $true) & ((substmonoid = $true) <=> (! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442))) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & (hoasinduction_lem3v2_gthm = $true) & ! [X51 : d_subst,X52 : d_subst] : (((d2subst @ X52) = (d2subst @ X51)) => (X51 = X52)) & ((! [X76 : term] : ((sub @ X76 @ id) = X76) => ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (~! [X90 : subst > term > term] : (~! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) | ~! [X94 : term] : (($true = (X78 @ id @ (X90 @ id @ X94) @ id)) | ($true != (X78 @ id @ X94 @ id))) | ($true = (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id))) | ~! [X89 : term] : (($true != (X79 @ X89)) | ($true = (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ($true = (X79 @ (lam @ X77))) | ~! [X80 : term] : ((X78 @ id @ X80 @ id) = (X79 @ X80)) | ~! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (($true != (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88)) | ($true = (X78 @ X87 @ X85 @ (comp @ X86 @ X88)))) | ~! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (($true != (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) | ($true = (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))))) <=> (hoasinduction_lem3v2_lthm = $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)))))))))))))) & ((hoasinduction_lem0 = $true) <=> ! [X397 : subst > term > subst > $o] : ~! [X398 : term > $o] : ~! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id))) & ((hoasapinj2_lthm = $true) <=> (! [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) != (ap @ X246 @ X247)) | (X245 = X247)) => ! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))))) & (! [X216 : term] : ~! [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) != (X217 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true)),
% 42.64/7.44 inference(flattening,[status(thm)],[f10])).
% 42.64/7.44 thf(f10,plain,(
% 42.64/7.44 (termmset_gthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & ((! [X2 : term] : ((sub @ X2 @ id) = X2) => (! [X3 : subst > term > subst > $o,X4 : term] : (~! [X5 : subst > term > term] : (~! [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) = (sub @ (X5 @ X7 @ X8) @ X6)) | ~! [X9 : term] : (($true = (X3 @ id @ (X5 @ id @ X9) @ id)) | ~($true = (X3 @ id @ X9 @ id))) | ($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | ~! [X10 : term] : (~($true = (X3 @ id @ X10 @ id)) | ((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true)) | ($true = (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id))) => ! [X11 : subst > term > subst > $o,X12 : term] : (($true = (X11 @ id @ (lam @ X12) @ id)) | ~! [X13 : subst > term > term] : (($true = (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14)) | ~! [X17 : term] : (($true = (X11 @ id @ (X13 @ id @ X17) @ id)) | ~($true = (X11 @ id @ X17 @ id)))) | ~! [X18 : term] : (~($true = (X11 @ id @ X18 @ id)) | ($true = (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X19 : term] : ~! [X20 : subst > term > term] : ~! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21)))) & (hoasapinj2_gthm = $true) & ! [X23 : d_subst] : (d_id = X23) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (~! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (~($true = (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) | ($true = (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ~! [X31 : term,X32 : term] : (($true = (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) | ~($true = (X26 @ id @ X31 @ id)) | ~($true = (X26 @ id @ X32 @ id))) | ~((X26 @ id @ X24 @ id) = $true) | ~($true = (X26 @ id @ X25 @ id)) | ~! [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true = (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35)) | ~($true = (X26 @ X33 @ X36 @ (comp @ X34 @ X35)))) | ($true = (X26 @ id @ (ap @ X24 @ X25) @ id)))) & (hoaslamnotap_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & (hoasinduction_lem1 = $true) & ~(lamnotap = $true) & (pushprop_lthm_orig = $true) & (hoaslaminj_gthm = $true) & (! [X41 : term,X42 : subst > term > subst > $o] : (($true = (X42 @ id @ (lam @ X41) @ id)) | ~! [X43 : subst > term > term] : (~! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) | ($true = (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) | ~! [X47 : term] : (~((X42 @ id @ X47 @ id) = $true) | ($true = (X42 @ id @ (X43 @ id @ X47) @ id)))) | ~! [X48 : term] : (~($true = (X42 @ id @ X48 @ id)) | ($true = (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id)))) <=> (hoasinduction_lem3a = $true)) & (! [X49 : term] : ~! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ! [X51 : d_subst,X52 : d_subst] : (((d2subst @ X52) = (d2subst @ X51)) => (X51 = X52)) & (pushprop_lem3v2 = $true) & (one = (d2term @ d_one)) & ((hoasinduction_lem3aaa = $true) <=> ! [X53 : subst > term > subst > $o,X54 : term] : (($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ~! [X55 : term] : (($true = (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) | ~($true = (X53 @ id @ X55 @ id))) | ~! [X56 : subst > term > term,X57 : term] : (~! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) | ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) = $true) | ~! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ~($true = (X53 @ id @ X61 @ id))) | ~! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63))))))) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ~($true = (X67 @ X65))) <=> (pushprop_lem1 = $true)) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & (hoaslamnotvar = $true) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X76 : term] : ((sub @ X76 @ id) = X76) => ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (~! [X80 : term] : ((X78 @ id @ X80 @ id) = (X79 @ X80)) | ~! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (~($true = (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) | ($true = (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))) | ~! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (~($true = (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88)) | ($true = (X78 @ X87 @ X85 @ (comp @ X86 @ X88)))) | ~! [X89 : term] : (~($true = (X79 @ X89)) | ($true = (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ($true = (X79 @ (lam @ X77))) | ~! [X90 : subst > term > term] : (~! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) | ~! [X94 : term] : (~($true = (X78 @ id @ X94 @ id)) | ($true = (X78 @ id @ (X90 @ id @ X94) @ id))) | ($true = (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id)))))) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & ((pushprop_lem1v2 = $true) <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (~! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true = (X100 @ one)) | ~($true = (X99 @ X102)))) & ((induction2 = $true) <=> ! [X104 : term,X105 : term > $o] : (~! [X106 : term] : (($true = (X105 @ (lam @ X106))) | ~! [X107 : term] : (($true = (X105 @ (sub @ X106 @ (push @ X107 @ id)))) | ~((X105 @ X107) = $true))) | ~! [X108 : term] : (~((var @ X108) = $true) | ($true = (X105 @ X108))) | ($true = (X105 @ X104)) | ~! [X109 : term,X110 : term] : (($true = (X105 @ (ap @ X109 @ X110))) | ~($true = (X105 @ X110)) | ~((X105 @ X109) = $true)))) & (hoasinduction_lem1_gthm = $true) & (axmap = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X111 : term] : ~! [X112 : subst > term > term] : ~! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113)))) & (pushprop_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2lem_lthm = $true) <=> (! [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) = X116) => (! [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) = X117) => (! [X119 : subst] : ((comp @ X119 @ id) = X119) => (! [X120 : term > $o,X121 : term] : (($true = (X120 @ X121)) | ~! [X122 : term] : (($true = (X120 @ X122)) | ~((var @ X122) = $true)) | ~! [X123 : term,X124 : term] : (~($true = (X120 @ X123)) | ~($true = (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))) | ~! [X125 : term] : (~($true = (X120 @ X125)) | ($true = (X120 @ (lam @ X125))))) => ! [X126 : term > $o,X127 : term,X128 : subst] : (($true = (X126 @ (sub @ X127 @ X128))) | ~! [X129 : term,X130 : term] : (((X126 @ (ap @ X130 @ X129)) = $true) | ~($true = (X126 @ X129)) | ~($true = (X126 @ X130))) | ~! [X131 : term] : (($true = (X126 @ (lam @ X131))) | ~! [X132 : term] : (~($true = (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id)))))) | ~! [X133 : term] : (~($true = (var @ X133)) | ($true = (X126 @ (sub @ X133 @ X128)))))))))) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (hoaslamnotap_lthm = $true) & ((substmonoid_lthm = $true) <=> (! [X138 : subst] : ((comp @ id @ X138) = X138) => (! [X139 : subst] : ((comp @ X139 @ id) = X139) => (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))))) & (apnotvar = $true) & ((! [X142 : term > $o,X143 : term] : (($true = (X142 @ X143)) | ~! [X144 : term] : (($true = (X142 @ X144)) | ~((var @ X144) = $true)) | ~! [X145 : term,X146 : term] : (~($true = (X142 @ X145)) | ~($true = (X142 @ X146)) | ($true = (X142 @ (ap @ X145 @ X146)))) | ~! [X147 : term] : (($true = (X142 @ (lam @ X147))) | ~! [X148 : term] : (($true = (X142 @ (sub @ X147 @ (push @ X148 @ id)))) | ~($true = (X142 @ X148))))) => (! [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (~($true = (X149 @ id @ X151 @ id)) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (~($true = (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) | ~! [X156 : term,X157 : term] : (($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id)) | ~((X149 @ id @ X157 @ id) = $true) | ~($true = (X149 @ id @ X156 @ id))) | ($true = (X149 @ id @ (ap @ X151 @ X150) @ id)) | ~($true = (X149 @ id @ X150 @ id)) | ~! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (~($true = (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159)) | ((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true))) => (! [X162 : subst > term > subst > $o,X163 : term] : (($true = (X162 @ id @ (lam @ X163) @ id)) | ~! [X164 : term] : (($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id)) | ~($true = (X162 @ id @ X164 @ id))) | ~! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (~($true = (X162 @ X165 @ X167 @ (comp @ X168 @ X166))) | ($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166))) | ~! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (~($true = (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true)) | ~! [X173 : subst > term > term] : (~! [X174 : term] : (($true = (X162 @ id @ (X173 @ id @ X174) @ id)) | ~($true = (X162 @ id @ X174 @ id))) | ~! [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) = (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id)))) => ! [X178 : term,X179 : subst > term > subst > $o] : (~! [X180 : term] : (($true = (X179 @ id @ X180 @ id)) | ~($true = (var @ (sub @ X180 @ id)))) | ~! [X181 : term,X182 : term] : (~((X179 @ id @ X182 @ id) = $true) | ($true = (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) | ~($true = (X179 @ id @ X181 @ id))) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (~($true = (X179 @ X184 @ X185 @ (comp @ X186 @ X183))) | ($true = (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183))) | ~! [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true = (X179 @ X188 @ X187 @ (comp @ X189 @ X190))) | ~($true = (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190))) | ((X179 @ id @ X178 @ id) = $true) | ~! [X191 : subst > term > term] : (((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) = $true) | ~! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192)) | ~! [X195 : term] : (~($true = (X179 @ id @ X195 @ id)) | ($true = (X179 @ id @ (X191 @ id @ X195) @ id)))))))) <=> (hoasinduction_lthm = $true)) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop = $true) & (pushprop_lem1_gthm = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X196 : subst,X197 : term,X198 : term > $o] : ~! [X199 : term > $o] : ~! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196))))) & ((! [X201 : term] : ((sub @ X201 @ id) = X201) => ! [X202 : term] : ((sub @ X202 @ id) = X202)) <=> (termmset_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (~! [X205 : term,X206 : term] : (~($true = (X203 @ id @ X206 @ id)) | ($true = (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) | ~((X203 @ id @ X205 @ id) = $true)) | ~! [X207 : subst > term > term] : (($true = (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)) | ~! [X208 : term] : (~($true = (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) | ~! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))) | ($true = (X203 @ id @ X204 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & ~(ulamvar1 = $true) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_lthm = $true) & (! [X216 : term] : ~! [X217 : subst > term > term] : ((sub @ X216 @ (push @ one @ sh)) != (X217 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasapinj1_lthm = $true) <=> (! [X218 : term] : ((sub @ X218 @ id) = X218) => (! [X219 : term,X220 : term,X221 : term,X222 : term] : ((X219 = X222) | ((ap @ X222 @ X220) != (ap @ X219 @ X221))) => ! [X223 : term,X224 : term,X225 : term,X226 : term] : (((ap @ (sub @ X226 @ id) @ X224) != (ap @ (sub @ X225 @ id) @ X223)) | (X225 = X226))))) & (hoasinduction_lem3a_gthm = $true) & (substmonoid_gthm = $true) & ((d2subst @ d_id) = id) & ((induction2_lthm = $true) <=> (! [X227 : term] : ((sub @ X227 @ id) = X227) => (! [X228 : term > $o,X229 : subst,X230 : term] : (~! [X231 : term] : (~($true = (var @ X231)) | ($true = (X228 @ (sub @ X231 @ X229)))) | ~! [X232 : term] : (~! [X233 : term] : (($true = (X228 @ (sub @ X232 @ (push @ X233 @ id)))) | ~($true = (X228 @ X233))) | ($true = (X228 @ (lam @ X232)))) | ($true = (X228 @ (sub @ X230 @ X229))) | ~! [X234 : term,X235 : term] : (~($true = (X228 @ X235)) | ($true = (X228 @ (ap @ X234 @ X235))) | ~($true = (X228 @ X234)))) => ! [X236 : term,X237 : term > $o] : (~! [X238 : term] : (($true = (X237 @ X238)) | ~($true = (var @ X238))) | ~! [X239 : term,X240 : term] : (~($true = (X237 @ X240)) | ($true = (X237 @ (ap @ X240 @ X239))) | ~($true = (X237 @ X239))) | ~! [X241 : term] : (~! [X242 : term] : (~($true = (X237 @ X242)) | ($true = (X237 @ (sub @ X241 @ (push @ X242 @ id))))) | ($true = (X237 @ (lam @ X241)))) | ($true = (X237 @ X236)))))) & (! [X243 : subst] : ((push @ (sub @ one @ X243) @ (comp @ sh @ X243)) = X243) <=> (axscons = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasapinj2_lthm = $true) <=> (! [X244 : term,X245 : term,X246 : term,X247 : term] : (((ap @ X244 @ X245) != (ap @ X246 @ X247)) | (X245 = X247)) => ! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X249 = X251) | ((ap @ (sub @ X248 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X249))))) & (! [X252 : subst > term > subst > $o] : ~! [X253 : term > $o] : ~! [X254 : term] : ((X253 @ X254) = (X252 @ id @ X254 @ id)) <=> (hoasinduction_lem0_lthm = $true)) & (! [X255 : term,X256 : term] : (((sub @ X255 @ sh) != (sub @ X256 @ sh)) | (X255 = X256)) <=> (shinj = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X257 : term,X258 : subst] : ((sub @ one @ (push @ X257 @ X258)) = X257) => (! [X259 : term,X260 : subst] : ((comp @ sh @ (push @ X259 @ X260)) = X260) => (! [X261 : term,X262 : term] : (((lam @ X262) != (lam @ X261)) | (X261 = X262)) => ! [X263 : subst > term > term,X264 : term,X265 : subst,X266 : subst > term > term] : (~! [X270 : subst,X271 : term,X272 : subst] : ((sub @ (X266 @ X270 @ X271) @ X272) = (X266 @ (comp @ X270 @ X272) @ (sub @ X271 @ X272))) | ((X263 @ X265 @ X264) = (X266 @ X265 @ X264)) | ~! [X267 : subst,X268 : term,X269 : subst] : ((sub @ (X263 @ X269 @ X268) @ X267) = (X263 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267))) | ((lam @ (X266 @ sh @ one)) != (lam @ (X263 @ sh @ one)))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X273 : term > $o,X274 : subst,X275 : term] : ~! [X276 : term > $o] : ~! [X277 : term] : ((X273 @ (sub @ X277 @ (push @ X275 @ X274))) = (X276 @ X277))) & (axapp = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X278 : term,X279 : term > $o,X280 : term,X281 : subst > term > subst > $o] : (~! [X282 : term,X283 : term] : (((X281 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id) = $true) | ~($true = (X281 @ id @ X282 @ id)) | ~($true = (X281 @ id @ X283 @ id))) | ~($true = (X279 @ X280)) | ($true = (X279 @ (ap @ X278 @ X280))) | ~! [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (~($true = (X281 @ (comp @ X284 @ X287) @ (sub @ X286 @ X287) @ X285)) | ($true = (X281 @ X284 @ X286 @ (comp @ X287 @ X285)))) | ~! [X288 : term,X289 : subst,X290 : subst,X291 : subst] : (($true = (X281 @ (comp @ X289 @ X291) @ (sub @ X288 @ X291) @ X290)) | ~((X281 @ X289 @ X288 @ (comp @ X291 @ X290)) = $true)) | ~! [X292 : term] : ((X279 @ X292) = (X281 @ id @ X292 @ id)) | ~($true = (X279 @ X278)))) & ~((var @ (d2term @ d_one)) = $true) & (hoasapinj1_gthm = $true) & ! [X293 : term] : ? [X294 : d_term] : ((d2term @ X294) = X293) & ((hoasinduction_lem3v2a = $true) <=> ! [X295 : term > $o,X296 : term,X297 : subst > term > subst > $o] : (~! [X298 : subst > term > term] : (~! [X299 : term] : (~((X297 @ id @ X299 @ id) = $true) | ($true = (X297 @ id @ (X298 @ id @ X299) @ id))) | ($true = (X297 @ id @ (lam @ (X298 @ sh @ one)) @ id)) | ~! [X300 : subst,X301 : term,X302 : subst] : ((sub @ (X298 @ X302 @ X301) @ X300) = (X298 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300)))) | ($true = (X295 @ (lam @ X296))) | ~! [X303 : term] : ((X295 @ X303) = (X297 @ id @ X303 @ id)) | ~! [X304 : term] : (~((X295 @ X304) = $true) | ($true = (X295 @ (sub @ X296 @ (push @ X304 @ id))))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((! [X305 : subst > term > subst > $o] : ~! [X306 : term > $o] : ~! [X307 : term] : ((X306 @ X307) = (X305 @ id @ X307 @ id)) => (! [X308 : term > $o,X309 : term] : (~! [X310 : term] : (~((var @ X310) = $true) | ($true = (X308 @ X310))) | ~! [X311 : term,X312 : term] : (~($true = (X308 @ X312)) | ~($true = (X308 @ X311)) | ($true = (X308 @ (ap @ X311 @ X312)))) | ($true = (X308 @ X309)) | ~! [X313 : term] : (~! [X314 : term] : (($true = (X308 @ (sub @ X313 @ (push @ X314 @ id)))) | ~($true = (X308 @ X314))) | ($true = (X308 @ (lam @ X313))))) => (! [X315 : term] : ((sub @ X315 @ id) = X315) => (! [X316 : term,X317 : term > $o,X318 : subst > term > subst > $o] : (~! [X319 : term] : ((X318 @ id @ X319 @ id) = (X317 @ X319)) | ((X317 @ (lam @ X316)) = $true) | ~! [X320 : subst > term > term] : (~! [X321 : subst,X322 : subst,X323 : term] : ((sub @ (X320 @ X321 @ X323) @ X322) = (X320 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322))) | ($true = (X318 @ id @ (lam @ (X320 @ sh @ one)) @ id)) | ~! [X324 : term] : (~($true = (X318 @ id @ X324 @ id)) | ($true = (X318 @ id @ (X320 @ id @ X324) @ id)))) | ~! [X325 : term] : (($true = (X317 @ (sub @ X316 @ (push @ X325 @ id)))) | ~($true = (X317 @ X325)))) => ! [X326 : subst > term > subst > $o,X327 : term] : (~! [X328 : term,X329 : term] : (~($true = (X326 @ id @ X328 @ id)) | ~($true = (X326 @ id @ X329 @ id)) | ($true = (X326 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id))) | ($true = (X326 @ id @ X327 @ id)) | ~! [X330 : subst > term > term] : (~! [X331 : subst,X332 : subst,X333 : term] : ((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)) = (sub @ (X330 @ X331 @ X333) @ X332)) | ~! [X334 : term] : (~($true = (X326 @ id @ X334 @ id)) | ($true = (X326 @ id @ (X330 @ id @ X334) @ id))) | ($true = (X326 @ id @ (lam @ (X330 @ sh @ one)) @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X335 : term,X336 : subst] : ((sub @ one @ (push @ X335 @ X336)) = X335) => (! [X337 : subst,X338 : term] : ((comp @ sh @ (push @ X338 @ X337)) = X337) => ! [X339 : term > $o,X340 : term,X341 : subst,X342 : term,X343 : term > $o] : (~($true = (X339 @ X342)) | ($true = (X343 @ (sub @ X342 @ (push @ X340 @ X341))))))) <=> (pushprop_lem1_lthm = $true)) & (axassoc = $true) & ((termmset = $true) <=> ! [X344 : term] : ((sub @ X344 @ id) = X344)) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X345 : term > $o,X346 : term,X347 : subst > term > subst > $o] : (~! [X348 : term] : (~($true = (X345 @ X348)) | ((X345 @ (sub @ X346 @ (push @ X348 @ id))) = $true)) | ~! [X349 : subst > term > term] : (~! [X350 : term] : (($true = (X347 @ id @ (X349 @ id @ X350) @ id)) | ~((X347 @ id @ X350 @ id) = $true)) | ($true = (X347 @ id @ (lam @ (X349 @ sh @ one)) @ id)) | ~! [X351 : subst,X352 : subst,X353 : term] : ((X349 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)) = (sub @ (X349 @ X351 @ X353) @ X352))) | ~! [X354 : subst,X355 : subst,X356 : subst,X357 : term] : (($true = (X347 @ X354 @ X357 @ (comp @ X356 @ X355))) | ~((X347 @ (comp @ X354 @ X356) @ (sub @ X357 @ X356) @ X355) = $true)) | ~! [X358 : term] : ((X345 @ X358) = (X347 @ id @ X358 @ id)) | ~! [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (($true = (X347 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360) @ X362)) | ~($true = (X347 @ X359 @ X361 @ (comp @ X360 @ X362)))) | ((X345 @ (lam @ X346)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & ((! [X363 : term] : ((sub @ X363 @ id) = X363) => (! [X364 : term,X365 : subst > term > subst > $o] : (~! [X366 : subst > term > term] : (~! [X367 : term,X368 : subst,X369 : subst] : ((X366 @ (comp @ X369 @ X368) @ (sub @ X367 @ X368)) = (sub @ (X366 @ X369 @ X367) @ X368)) | ~! [X370 : term] : (~($true = (X365 @ id @ X370 @ id)) | ($true = (X365 @ id @ (X366 @ id @ X370) @ id))) | ($true = (X365 @ id @ (lam @ (X366 @ sh @ one)) @ id))) | ($true = (X365 @ id @ (lam @ (sub @ X364 @ (push @ one @ sh))) @ id)) | ~! [X371 : term] : (~($true = (X365 @ id @ X371 @ id)) | ($true = (X365 @ id @ (sub @ X364 @ (push @ X371 @ id)) @ id)))) => ! [X372 : subst > term > subst > $o,X373 : term] : (($true = (X372 @ id @ (lam @ X373) @ id)) | ~! [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (~($true = (X372 @ X376 @ X377 @ (comp @ X374 @ X375))) | ((X372 @ (comp @ X376 @ X374) @ (sub @ X377 @ X374) @ X375) = $true)) | ~! [X378 : term] : (($true = (X372 @ id @ (sub @ X373 @ (push @ X378 @ id)) @ id)) | ~($true = (X372 @ id @ X378 @ id))) | ~! [X379 : subst > term > term] : (($true = (X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)) | ~! [X380 : term] : (~($true = (X372 @ id @ X380 @ id)) | ($true = (X372 @ id @ (X379 @ id @ X380) @ id))) | ~! [X381 : term,X382 : subst,X383 : subst] : ((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383)) = (sub @ (X379 @ X382 @ X381) @ X383))) | ~! [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (~($true = (X372 @ (comp @ X387 @ X384) @ (sub @ X386 @ X384) @ X385)) | ((X372 @ X387 @ X386 @ (comp @ X384 @ X385)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X388 : d_term] : (d_one = X388) & (! [X389 : term,X390 : subst > term > subst > $o] : (($true = (X390 @ id @ (lam @ (sub @ X389 @ (push @ one @ sh))) @ id)) | ~! [X391 : term] : (~($true = (X390 @ id @ X391 @ id)) | ((X390 @ id @ (sub @ X389 @ (push @ X391 @ id)) @ id) = $true)) | ~! [X392 : subst > term > term] : (($true = (X390 @ id @ (lam @ (X392 @ sh @ one)) @ id)) | ~! [X393 : subst,X394 : term,X395 : subst] : ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)) = (sub @ (X392 @ X395 @ X394) @ X393)) | ~! [X396 : term] : (($true = (X390 @ id @ (X392 @ id @ X396) @ id)) | ~($true = (X390 @ id @ X396 @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X397 : subst > term > subst > $o] : ~! [X398 : term > $o] : ~! [X399 : term] : ((X398 @ X399) = (X397 @ id @ X399 @ id))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X400 : subst,X401 : term] : ((sub @ one @ (push @ X401 @ X400)) = X401) => ! [X402 : term > $o,X403 : subst,X404 : term > $o,X405 : term] : (((X404 @ one) = $true) | ~! [X406 : term] : ((X404 @ X406) = (X402 @ (sub @ X406 @ (push @ X405 @ X403)))) | ~($true = (X402 @ X405))))) & ! [X407 : d_term,X408 : d_term] : (((d2term @ X407) = (d2term @ X408)) => (X407 = X408)) & ((induction = $true) <=> ! [X409 : term,X410 : term > $o] : (~! [X411 : term] : (~($true = (X410 @ X411)) | ($true = (X410 @ (lam @ X411)))) | ($true = (X410 @ X409)) | ~! [X412 : term] : (~((var @ X412) = $true) | ($true = (X410 @ X412))) | ~! [X413 : term,X414 : term] : (($true = (X410 @ (ap @ X414 @ X413))) | ~($true = (X410 @ X414)) | ~($true = (X410 @ X413))))) & (lamnotvar = $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)))))))))))))) & ((hoaslaminj = $true) <=> ! [X415 : term,X416 : subst > term > term,X417 : subst > term > term,X418 : subst] : (~! [X419 : subst,X420 : term,X421 : subst] : ((X417 @ (comp @ X419 @ X421) @ (sub @ X420 @ X421)) = (sub @ (X417 @ X419 @ X420) @ X421)) | ((X416 @ X418 @ X415) = (X417 @ X418 @ X415)) | ~! [X422 : subst,X423 : term,X424 : subst] : ((sub @ (X416 @ X424 @ X423) @ X422) = (X416 @ (comp @ X424 @ X422) @ (sub @ X423 @ X422))) | ((lam @ (X417 @ sh @ one)) != (lam @ (X416 @ sh @ one))))) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X425 : term] : ~! [X426 : subst > term > term] : ~! [X427 : term,X428 : subst] : ((sub @ X425 @ (push @ X427 @ X428)) = (X426 @ X428 @ X427)) => (! [X429 : term] : ((sub @ X429 @ id) = X429) => ! [X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (($true = (X431 @ (lam @ X430))) | ~! [X433 : subst > term > term] : (~! [X434 : term] : (~($true = (X432 @ id @ X434 @ id)) | ($true = (X432 @ id @ (X433 @ id @ X434) @ id))) | ~! [X435 : subst,X436 : term,X437 : subst] : ((X433 @ (comp @ X437 @ X435) @ (sub @ X436 @ X435)) = (sub @ (X433 @ X437 @ X436) @ X435)) | ($true = (X432 @ id @ (lam @ (X433 @ sh @ one)) @ id))) | ~! [X438 : term] : ((X432 @ id @ X438 @ id) = (X431 @ X438)) | ~! [X439 : term] : (($true = (X431 @ (sub @ X430 @ (push @ X439 @ id)))) | ~($true = (X431 @ X439))))))) & (hoaslamnotvar_gthm = $true) & (! [X440 : term,X441 : term] : ((X440 = X441) | ((lam @ X440) != (lam @ X441))) <=> (laminj = $true)) & (ulamvarind = $true) & ((substmonoid = $true) <=> (! [X443 : subst] : ((comp @ id @ X443) = X443) & ! [X442 : subst] : ((comp @ X442 @ id) = X442))) & ((hoasinduction = $true) <=> ! [X444 : subst > term > subst > $o,X445 : term] : (~! [X446 : term,X447 : term] : (~($true = (X444 @ id @ X447 @ id)) | ((X444 @ id @ (ap @ (sub @ X447 @ id) @ X446) @ id) = $true) | ~($true = (X444 @ id @ X446 @ id))) | ~! [X448 : term] : (($true = (X444 @ id @ X448 @ id)) | ~($true = (var @ (sub @ X448 @ id)))) | ~! [X449 : subst > term > term] : (($true = (X444 @ id @ (lam @ (X449 @ sh @ one)) @ id)) | ~! [X450 : term] : (($true = (X444 @ id @ (X449 @ id @ X450) @ id)) | ~($true = (X444 @ id @ X450 @ id))) | ~! [X451 : subst,X452 : subst,X453 : term] : ((sub @ (X449 @ X452 @ X453) @ X451) = (X449 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451)))) | ~! [X454 : subst,X455 : subst,X456 : subst,X457 : term] : (~($true = (X444 @ X454 @ X457 @ (comp @ X455 @ X456))) | ($true = (X444 @ (comp @ X454 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X444 @ id @ X445 @ id) = $true) | ~! [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (((X444 @ X460 @ X458 @ (comp @ X461 @ X459)) = $true) | ~($true = (X444 @ (comp @ X460 @ X461) @ (sub @ X458 @ X461) @ X459))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X462 : subst > term > subst > $o] : ~! [X463 : term > $o] : ~! [X464 : term] : ((X462 @ id @ X464 @ id) = (X463 @ X464)) => (! [X465 : term,X466 : term > $o] : (~! [X467 : term,X468 : term] : (~($true = (X466 @ X467)) | ~((X466 @ X468) = $true) | ($true = (X466 @ (ap @ X468 @ X467)))) | ~! [X469 : term] : (~($true = (var @ X469)) | ((X466 @ X469) = $true)) | ~! [X470 : term] : (~! [X471 : term] : (((X466 @ (sub @ X470 @ (push @ X471 @ id))) = $true) | ~($true = (X466 @ X471))) | ($true = (X466 @ (lam @ X470)))) | ($true = (X466 @ X465))) => (! [X472 : term] : ((sub @ X472 @ id) = X472) => (! [X473 : term > $o,X474 : subst > term > subst > $o,X475 : term] : (($true = (X473 @ (lam @ X475))) | ~! [X476 : term] : (($true = (X473 @ (sub @ X475 @ (push @ X476 @ id)))) | ~((X473 @ X476) = $true)) | ~! [X477 : term] : ((X474 @ id @ X477 @ id) = (X473 @ X477)) | ~! [X478 : subst > term > term] : (($true = (X474 @ id @ (lam @ (X478 @ sh @ one)) @ id)) | ~! [X479 : term] : (($true = (X474 @ id @ (X478 @ id @ X479) @ id)) | ~($true = (X474 @ id @ X479 @ id))) | ~! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X481 @ X482) @ (sub @ X480 @ X482)) = (sub @ (X478 @ X481 @ X480) @ X482)))) => ! [X483 : term,X484 : subst > term > subst > $o] : (~! [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (($true = (X484 @ X485 @ X487 @ (comp @ X488 @ X486))) | ~($true = (X484 @ (comp @ X485 @ X488) @ (sub @ X487 @ X488) @ X486))) | ~! [X489 : subst,X490 : subst,X491 : term,X492 : subst] : (($true = (X484 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) | ~($true = (X484 @ X489 @ X491 @ (comp @ X492 @ X490)))) | ($true = (X484 @ id @ X483 @ id)) | ~! [X493 : term,X494 : term] : (~($true = (X484 @ id @ X494 @ id)) | ($true = (X484 @ id @ (ap @ (sub @ X493 @ id) @ X494) @ id)) | ~($true = (X484 @ id @ X493 @ id))) | ~! [X495 : term] : (($true = (X484 @ id @ X495 @ id)) | ~($true = (var @ (sub @ X495 @ id)))) | ~! [X496 : subst > term > term] : (($true = (X484 @ id @ (lam @ (X496 @ sh @ one)) @ id)) | ~! [X497 : term,X498 : subst,X499 : subst] : ((X496 @ (comp @ X499 @ X498) @ (sub @ X497 @ X498)) = (sub @ (X496 @ X499 @ X497) @ X498)) | ~! [X500 : term] : (~($true = (X484 @ id @ X500 @ id)) | ($true = (X484 @ id @ (X496 @ id @ X500) @ id)))))))))) & (! [X501 : term,X502 : subst > term > subst > $o] : (~! [X503 : subst > term > term] : (~! [X504 : subst,X505 : term,X506 : subst] : ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)) = (sub @ (X503 @ X506 @ X505) @ X504)) | ~! [X507 : term] : (~($true = (X502 @ id @ X507 @ id)) | ($true = (X502 @ id @ (X503 @ id @ X507) @ id))) | ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id) = $true)) | ((X502 @ id @ (lam @ (sub @ X501 @ (push @ one @ sh))) @ id) = $true) | ~! [X508 : term] : (~($true = (X502 @ id @ X508 @ id)) | ($true = (X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X509 : term,X510 : term,X511 : subst > term > term] : (~! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X511 @ X512 @ X513) @ X514) = (X511 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) | ((lam @ (X511 @ sh @ one)) != (ap @ (sub @ X510 @ id) @ X509))) <=> (hoaslamnotap = $true)) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (! [X515 : subst,X516 : term > $o,X517 : term] : (~! [X518 : term] : (($true = (X516 @ (sub @ X518 @ X515))) | ~($true = (var @ X518))) | ~! [X519 : term,X520 : term] : (~($true = (X516 @ X519)) | ($true = (X516 @ (ap @ X520 @ X519))) | ~($true = (X516 @ X520))) | ~! [X521 : term] : (~! [X522 : term] : (($true = (X516 @ (sub @ X521 @ (push @ X522 @ id)))) | ~($true = (X516 @ X522))) | ($true = (X516 @ (lam @ X521)))) | ($true = (X516 @ (sub @ X517 @ X515)))) <=> (induction2lem = $true)) & (! [X523 : subst > term > subst > $o,X524 : term] : (~! [X525 : term] : (~($true = (X523 @ id @ X525 @ id)) | ($true = (X523 @ id @ (sub @ X524 @ (push @ X525 @ id)) @ id))) | ~! [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (~($true = (X523 @ X527 @ X529 @ (comp @ X526 @ X528))) | ((X523 @ (comp @ X527 @ X526) @ (sub @ X529 @ X526) @ X528) = $true)) | ($true = (X523 @ id @ (lam @ X524) @ id)) | ~! [X530 : subst > term > term] : (~! [X531 : subst,X532 : term,X533 : subst] : ((sub @ (X530 @ X531 @ X532) @ X533) = (X530 @ (comp @ X531 @ X533) @ (sub @ X532 @ X533))) | ($true = (X523 @ id @ (lam @ (X530 @ sh @ one)) @ id)) | ~! [X534 : term] : (~($true = (X523 @ id @ X534 @ id)) | ($true = (X523 @ id @ (X530 @ id @ X534) @ id)))) | ~! [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (($true = (X523 @ X538 @ X535 @ (comp @ X536 @ X537))) | ~($true = (X523 @ (comp @ X538 @ X536) @ (sub @ X535 @ X536) @ X537)))) <=> (hoasinduction_lem3 = $true)) & (! [X539 : subst] : ((comp @ X539 @ id) = X539) <=> (axidr = $true)) & (axvarshift = $true)),
% 42.64/7.44 inference(rectify,[status(thm)],[f8])).
% 42.64/7.44 thf(f8,plain,(
% 42.64/7.44 (termmset_gthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & ((! [X2 : term] : ((sub @ X2 @ id) = X2) => (! [X3 : subst > term > subst > $o,X4 : term] : (~! [X5 : subst > term > term] : (~! [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) = (sub @ (X5 @ X7 @ X8) @ X6)) | ~! [X9 : term] : (($true = (X3 @ id @ (X5 @ id @ X9) @ id)) | ~($true = (X3 @ id @ X9 @ id))) | ($true = (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | ~! [X10 : term] : (~($true = (X3 @ id @ X10 @ id)) | ((X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id) = $true)) | ($true = (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id))) => ! [X11 : subst > term > subst > $o,X12 : term] : (($true = (X11 @ id @ (lam @ X12) @ id)) | ~! [X13 : subst > term > term] : (($true = (X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14)) | ~! [X17 : term] : (($true = (X11 @ id @ (X13 @ id @ X17) @ id)) | ~($true = (X11 @ id @ X17 @ id)))) | ~! [X18 : term] : (~($true = (X11 @ id @ X18 @ id)) | ($true = (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X19 : term] : ~! [X20 : subst > term > term] : ~! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21)))) & (hoasapinj2_gthm = $true) & ! [X23 : d_subst] : (d_id = X23) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (~! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (~($true = (X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27)) | ($true = (X26 @ X29 @ X28 @ (comp @ X30 @ X27)))) | ~! [X31 : term,X32 : term] : (($true = (X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) | ~($true = (X26 @ id @ X31 @ id)) | ~($true = (X26 @ id @ X32 @ id))) | ~((X26 @ id @ X24 @ id) = $true) | ~($true = (X26 @ id @ X25 @ id)) | ~! [X33 : subst,X34 : subst,X35 : subst,X36 : term] : (($true = (X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35)) | ~($true = (X26 @ X33 @ X36 @ (comp @ X34 @ X35)))) | ($true = (X26 @ id @ (ap @ X24 @ X25) @ id)))) & (hoaslamnotap_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & (hoasinduction_lem1 = $true) & ~(lamnotap = $true) & (pushprop_lthm_orig = $true) & (hoaslaminj_gthm = $true) & (! [X41 : term,X42 : subst > term > subst > $o] : (($true = (X42 @ id @ (lam @ X41) @ id)) | ~! [X43 : subst > term > term] : (~! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) | ($true = (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id)) | ~! [X47 : term] : (~((X42 @ id @ X47 @ id) = $true) | ($true = (X42 @ id @ (X43 @ id @ X47) @ id)))) | ~! [X48 : term] : (~($true = (X42 @ id @ X48 @ id)) | ($true = (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id)))) <=> (hoasinduction_lem3a = $true)) & (! [X49 : term] : ~! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ! [X51 : d_subst,X52 : d_subst] : (((d2subst @ X52) = (d2subst @ X51)) => (X51 = X52)) & (pushprop_lem3v2 = $true) & (one = (d2term @ d_one)) & ((hoasinduction_lem3aaa = $true) <=> ! [X53 : subst > term > subst > $o,X54 : term] : (($true = (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)) | ~! [X55 : term] : (($true = (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) | ~($true = (X53 @ id @ X55 @ id))) | ~! [X56 : subst > term > term,X57 : term] : (~! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) | ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) = $true) | ~! [X61 : term] : (($true = (X53 @ id @ (X56 @ id @ X61) @ id)) | ~($true = (X53 @ id @ X61 @ id))) | ~! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63))))))) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : (($true = (X66 @ (sub @ X65 @ (push @ X69 @ X68)))) | ~($true = (X67 @ X65))) <=> (pushprop_lem1 = $true)) & (! [X70 : subst] : ((comp @ id @ X70) = X70) <=> (axidl = $true)) & (! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71) <=> (axshiftcons = $true)) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((axvarid = $true) <=> ! [X73 : term] : ((sub @ X73 @ id) = X73)) & (hoaslamnotvar = $true) & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X76 : term] : ((sub @ X76 @ id) = X76) => ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (~! [X80 : term] : ((X78 @ id @ X80 @ id) = (X79 @ X80)) | ~! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (~($true = (X78 @ X82 @ X81 @ (comp @ X83 @ X84))) | ($true = (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84))) | ~! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (~($true = (X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88)) | ($true = (X78 @ X87 @ X85 @ (comp @ X86 @ X88)))) | ~! [X89 : term] : (~($true = (X79 @ X89)) | ($true = (X79 @ (sub @ X77 @ (push @ X89 @ id))))) | ($true = (X79 @ (lam @ X77))) | ~! [X90 : subst > term > term] : (~! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) | ~! [X94 : term] : (~($true = (X78 @ id @ X94 @ id)) | ($true = (X78 @ id @ (X90 @ id @ X94) @ id))) | ($true = (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id)))))) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X97) | ((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)))) & ((pushprop_lem1v2 = $true) <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (~! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | ($true = (X100 @ one)) | ~($true = (X99 @ X102)))) & ((induction2 = $true) <=> ! [X104 : term,X105 : term > $o] : (~! [X106 : term] : (($true = (X105 @ (lam @ X106))) | ~! [X107 : term] : (($true = (X105 @ (sub @ X106 @ (push @ X107 @ id)))) | ~((X105 @ X107) = $true))) | ~! [X108 : term] : (~((var @ X108) = $true) | ($true = (X105 @ X108))) | ($true = (X105 @ X104)) | ~! [X109 : term,X110 : term] : (($true = (X105 @ (ap @ X109 @ X110))) | ~($true = (X105 @ X110)) | ~((X105 @ X109) = $true)))) & (hoasinduction_lem1_gthm = $true) & (axmap = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X111 : term] : ~! [X112 : subst > term > term] : ~! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113)))) & (pushprop_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2lem_lthm = $true) <=> (! [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) = X116) => (! [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) = X117) => (! [X119 : subst] : ((comp @ X119 @ id) = X119) => (! [X120 : term > $o,X121 : term] : (($true = (X120 @ X121)) | ~! [X122 : term] : (($true = (X120 @ X122)) | ~((var @ X122) = $true)) | ~! [X123 : term,X124 : term] : (~($true = (X120 @ X123)) | ~($true = (X120 @ X124)) | ($true = (X120 @ (ap @ X124 @ X123)))) | ~! [X125 : term] : (~($true = (X120 @ X125)) | ($true = (X120 @ (lam @ X125))))) => ! [X126 : term > $o,X127 : term,X128 : subst] : (($true = (X126 @ (sub @ X127 @ X128))) | ~! [X129 : term,X130 : term] : (((X126 @ (ap @ X130 @ X129)) = $true) | ~($true = (X126 @ X129)) | ~($true = (X126 @ X130))) | ~! [X131 : term] : (($true = (X126 @ (lam @ X131))) | ~! [X132 : term] : (~($true = (X126 @ X132)) | ($true = (X126 @ (sub @ X131 @ (push @ X132 @ id)))))) | ~! [X133 : term] : (~($true = (var @ X133)) | ($true = (X126 @ (sub @ X133 @ X128)))))))))) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> (apinj1 = $true)) & (hoaslamnotap_lthm = $true) & ((substmonoid_lthm = $true) <=> (! [X138 : subst] : ((comp @ id @ X138) = X138) => (! [X139 : subst] : ((comp @ X139 @ id) = X139) => (! [X141 : subst] : ((comp @ X141 @ id) = X141) & ! [X140 : subst] : ((comp @ id @ X140) = X140))))) & (apnotvar = $true) & ((! [X142 : term > $o,X143 : term] : (($true = (X142 @ X143)) | ~! [X144 : term] : (($true = (X142 @ X144)) | ~((var @ X144) = $true)) | ~! [X145 : term,X146 : term] : (~($true = (X142 @ X145)) | ~($true = (X142 @ X146)) | ($true = (X142 @ (ap @ X145 @ X146)))) | ~! [X147 : term] : (($true = (X142 @ (lam @ X147))) | ~! [X148 : term] : (($true = (X142 @ (sub @ X147 @ (push @ X148 @ id)))) | ~($true = (X142 @ X148))))) => (! [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (~($true = (X149 @ id @ X151 @ id)) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (~($true = (X149 @ X155 @ X152 @ (comp @ X153 @ X154))) | ($true = (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154))) | ~! [X156 : term,X157 : term] : (($true = (X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id)) | ~((X149 @ id @ X157 @ id) = $true) | ~($true = (X149 @ id @ X156 @ id))) | ($true = (X149 @ id @ (ap @ X151 @ X150) @ id)) | ~($true = (X149 @ id @ X150 @ id)) | ~! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (~($true = (X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159)) | ((X149 @ X158 @ X161 @ (comp @ X160 @ X159)) = $true))) => (! [X162 : subst > term > subst > $o,X163 : term] : (($true = (X162 @ id @ (lam @ X163) @ id)) | ~! [X164 : term] : (($true = (X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id)) | ~($true = (X162 @ id @ X164 @ id))) | ~! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (~($true = (X162 @ X165 @ X167 @ (comp @ X168 @ X166))) | ($true = (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166))) | ~! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (~($true = (X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169)) | ((X162 @ X171 @ X170 @ (comp @ X172 @ X169)) = $true)) | ~! [X173 : subst > term > term] : (~! [X174 : term] : (($true = (X162 @ id @ (X173 @ id @ X174) @ id)) | ~($true = (X162 @ id @ X174 @ id))) | ~! [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) = (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | ($true = (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id)))) => ! [X178 : term,X179 : subst > term > subst > $o] : (~! [X180 : term] : (($true = (X179 @ id @ X180 @ id)) | ~($true = (var @ (sub @ X180 @ id)))) | ~! [X181 : term,X182 : term] : (~((X179 @ id @ X182 @ id) = $true) | ($true = (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) | ~($true = (X179 @ id @ X181 @ id))) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (~($true = (X179 @ X184 @ X185 @ (comp @ X186 @ X183))) | ($true = (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183))) | ~! [X187 : term,X188 : subst,X189 : subst,X190 : subst] : (($true = (X179 @ X188 @ X187 @ (comp @ X189 @ X190))) | ~($true = (X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190))) | ((X179 @ id @ X178 @ id) = $true) | ~! [X191 : subst > term > term] : (((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) = $true) | ~! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192)) | ~! [X195 : term] : (~($true = (X179 @ id @ X195 @ id)) | ($true = (X179 @ id @ (X191 @ id @ X195) @ id)))))))) <=> (hoasinduction_lthm = $true)) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop = $true) & (pushprop_lem1_gthm = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X196 : subst,X197 : term,X198 : term > $o] : ~! [X199 : term > $o] : ~! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196))))) & ((! [X201 : term] : ((sub @ X201 @ id) = X201) => ! [X202 : term] : ((sub @ X202 @ id) = X202)) <=> (termmset_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (~! [X205 : term,X206 : term] : (~($true = (X203 @ id @ X206 @ id)) | ($true = (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id)) | ~((X203 @ id @ X205 @ id) = $true)) | ~! [X207 : subst > term > term] : (($true = (X203 @ id @ (lam @ (X207 @ sh @ one)) @ id)) | ~! [X208 : term] : (~($true = (X203 @ id @ X208 @ id)) | ($true = (X203 @ id @ (X207 @ id @ X208) @ id))) | ~! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))) | ($true = (X203 @ id @ X204 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215)) <=> (apinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & ~(ulamvar1 = $true) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X218 : term] : ~! [X219 : subst > term > term] : ((X219 @ sh @ one) != (sub @ X218 @ (push @ one @ sh)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X220 : term] : ((sub @ X220 @ id) = X220) => (! [X221 : term,X222 : term,X223 : term,X224 : term] : (((ap @ X224 @ X222) != (ap @ X221 @ X223)) | (X221 = X224)) => ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X227 = X228) | ((ap @ (sub @ X227 @ id) @ X225) != (ap @ (sub @ X228 @ id) @ X226))))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (substmonoid_gthm = $true) & ((d2subst @ d_id) = id) & ((induction2_lthm = $true) <=> (! [X229 : term] : ((sub @ X229 @ id) = X229) => (! [X230 : term > $o,X231 : subst,X232 : term] : (~! [X233 : term] : (~($true = (var @ X233)) | ($true = (X230 @ (sub @ X233 @ X231)))) | ~! [X234 : term] : (~! [X235 : term] : (($true = (X230 @ (sub @ X234 @ (push @ X235 @ id)))) | ~($true = (X230 @ X235))) | ((X230 @ (lam @ X234)) = $true)) | ((X230 @ (sub @ X232 @ X231)) = $true) | ~! [X236 : term,X237 : term] : (~($true = (X230 @ X237)) | ($true = (X230 @ (ap @ X236 @ X237))) | ~($true = (X230 @ X236)))) => ! [X238 : term,X239 : term > $o] : (~! [X240 : term] : (($true = (X239 @ X240)) | ~($true = (var @ X240))) | ~! [X241 : term,X242 : term] : (~($true = (X239 @ X242)) | ((X239 @ (ap @ X242 @ X241)) = $true) | ~($true = (X239 @ X241))) | ~! [X243 : term] : (~! [X244 : term] : (~($true = (X239 @ X244)) | ($true = (X239 @ (sub @ X243 @ (push @ X244 @ id))))) | ($true = (X239 @ (lam @ X243)))) | ($true = (X239 @ X238)))))) & ((axscons = $true) <=> ! [X245 : subst] : ((push @ (sub @ one @ X245) @ (comp @ sh @ X245)) = X245)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((! [X246 : term,X247 : term,X248 : term,X249 : term] : ((X247 = X249) | ((ap @ X248 @ X249) != (ap @ X246 @ X247))) => ! [X250 : term,X251 : term,X252 : term,X253 : term] : (((ap @ (sub @ X252 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X253)) | (X251 = X253))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X254 : subst > term > subst > $o] : ~! [X255 : term > $o] : ~! [X256 : term] : ((X254 @ id @ X256 @ id) = (X255 @ X256))) & (! [X257 : term,X258 : term] : (((sub @ X257 @ sh) != (sub @ X258 @ sh)) | (X257 = X258)) <=> (shinj = $true)) & ((! [X259 : term,X260 : subst] : ((sub @ one @ (push @ X259 @ X260)) = X259) => (! [X261 : term,X262 : subst] : ((comp @ sh @ (push @ X261 @ X262)) = X262) => (! [X263 : term,X264 : term] : ((X263 = X264) | ((lam @ X263) != (lam @ X264))) => ! [X265 : subst > term > term,X266 : term,X267 : subst,X268 : subst > term > term] : (((lam @ (X265 @ sh @ one)) != (lam @ (X268 @ sh @ one))) | ((X265 @ X267 @ X266) = (X268 @ X267 @ X266)) | ~! [X269 : subst,X270 : term,X271 : subst] : ((X265 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)) = (sub @ (X265 @ X271 @ X270) @ X269)) | ~! [X272 : subst,X273 : term,X274 : subst] : ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)) = (sub @ (X268 @ X272 @ X273) @ X274)))))) <=> (hoaslaminj_lthm = $true)) & (! [X275 : term > $o,X276 : subst,X277 : term] : ~! [X278 : term > $o] : ~! [X279 : term] : ((X275 @ (sub @ X279 @ (push @ X277 @ X276))) = (X278 @ X279)) <=> (pushprop_lem0_lthm = $true)) & (axapp = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X280 : term,X281 : term > $o,X282 : term,X283 : subst > term > subst > $o] : (~! [X284 : term,X285 : term] : (($true = (X283 @ id @ (ap @ (sub @ X285 @ id) @ X284) @ id)) | ~($true = (X283 @ id @ X284 @ id)) | ~((X283 @ id @ X285 @ id) = $true)) | ~($true = (X281 @ X282)) | ($true = (X281 @ (ap @ X280 @ X282))) | ~! [X286 : subst,X287 : subst,X288 : term,X289 : subst] : (~($true = (X283 @ (comp @ X286 @ X289) @ (sub @ X288 @ X289) @ X287)) | ($true = (X283 @ X286 @ X288 @ (comp @ X289 @ X287)))) | ~! [X290 : term,X291 : subst,X292 : subst,X293 : subst] : (((X283 @ (comp @ X291 @ X293) @ (sub @ X290 @ X293) @ X292) = $true) | ~($true = (X283 @ X291 @ X290 @ (comp @ X293 @ X292)))) | ~! [X294 : term] : ((X283 @ id @ X294 @ id) = (X281 @ X294)) | ~($true = (X281 @ X280)))) & ~((var @ (d2term @ d_one)) = $true) & (hoasapinj1_gthm = $true) & ! [X295 : term] : ? [X296 : d_term] : ((d2term @ X296) = X295) & ((hoasinduction_lem3v2a = $true) <=> ! [X297 : term > $o,X298 : term,X299 : subst > term > subst > $o] : (~! [X300 : subst > term > term] : (~! [X301 : term] : (~($true = (X299 @ id @ X301 @ id)) | ($true = (X299 @ id @ (X300 @ id @ X301) @ id))) | ($true = (X299 @ id @ (lam @ (X300 @ sh @ one)) @ id)) | ~! [X302 : subst,X303 : term,X304 : subst] : ((X300 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302)) = (sub @ (X300 @ X304 @ X303) @ X302))) | ($true = (X297 @ (lam @ X298))) | ~! [X305 : term] : ((X297 @ X305) = (X299 @ id @ X305 @ id)) | ~! [X306 : term] : (~($true = (X297 @ X306)) | ((X297 @ (sub @ X298 @ (push @ X306 @ id))) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((! [X307 : subst > term > subst > $o] : ~! [X308 : term > $o] : ~! [X309 : term] : ((X308 @ X309) = (X307 @ id @ X309 @ id)) => (! [X310 : term > $o,X311 : term] : (~! [X312 : term] : (~($true = (var @ X312)) | ($true = (X310 @ X312))) | ~! [X313 : term,X314 : term] : (~($true = (X310 @ X314)) | ~($true = (X310 @ X313)) | ($true = (X310 @ (ap @ X313 @ X314)))) | ($true = (X310 @ X311)) | ~! [X315 : term] : (~! [X316 : term] : (($true = (X310 @ (sub @ X315 @ (push @ X316 @ id)))) | ~($true = (X310 @ X316))) | ($true = (X310 @ (lam @ X315))))) => (! [X317 : term] : ((sub @ X317 @ id) = X317) => (! [X318 : term,X319 : term > $o,X320 : subst > term > subst > $o] : (~! [X321 : term] : ((X320 @ id @ X321 @ id) = (X319 @ X321)) | ($true = (X319 @ (lam @ X318))) | ~! [X322 : subst > term > term] : (~! [X323 : subst,X324 : subst,X325 : term] : ((sub @ (X322 @ X323 @ X325) @ X324) = (X322 @ (comp @ X323 @ X324) @ (sub @ X325 @ X324))) | ($true = (X320 @ id @ (lam @ (X322 @ sh @ one)) @ id)) | ~! [X326 : term] : (~($true = (X320 @ id @ X326 @ id)) | ((X320 @ id @ (X322 @ id @ X326) @ id) = $true))) | ~! [X327 : term] : (($true = (X319 @ (sub @ X318 @ (push @ X327 @ id)))) | ~($true = (X319 @ X327)))) => ! [X328 : subst > term > subst > $o,X329 : term] : (~! [X330 : term,X331 : term] : (~($true = (X328 @ id @ X330 @ id)) | ~($true = (X328 @ id @ X331 @ id)) | ($true = (X328 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) | ($true = (X328 @ id @ X329 @ id)) | ~! [X332 : subst > term > term] : (~! [X333 : subst,X334 : subst,X335 : term] : ((sub @ (X332 @ X333 @ X335) @ X334) = (X332 @ (comp @ X333 @ X334) @ (sub @ X335 @ X334))) | ~! [X336 : term] : (~($true = (X328 @ id @ X336 @ id)) | ($true = (X328 @ id @ (X332 @ id @ X336) @ id))) | ($true = (X328 @ id @ (lam @ (X332 @ sh @ one)) @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X337 : term,X338 : subst] : ((sub @ one @ (push @ X337 @ X338)) = X337) => (! [X339 : subst,X340 : term] : ((comp @ sh @ (push @ X340 @ X339)) = X339) => ! [X341 : term > $o,X342 : term,X343 : subst,X344 : term,X345 : term > $o] : (~($true = (X341 @ X344)) | ($true = (X345 @ (sub @ X344 @ (push @ X342 @ X343))))))) <=> (pushprop_lem1_lthm = $true)) & (axassoc = $true) & ((termmset = $true) <=> ! [X346 : term] : ((sub @ X346 @ id) = X346)) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X347 : term > $o,X348 : term,X349 : subst > term > subst > $o] : (~! [X350 : term] : (~($true = (X347 @ X350)) | ($true = (X347 @ (sub @ X348 @ (push @ X350 @ id))))) | ~! [X351 : subst > term > term] : (~! [X352 : term] : (((X349 @ id @ (X351 @ id @ X352) @ id) = $true) | ~($true = (X349 @ id @ X352 @ id))) | ($true = (X349 @ id @ (lam @ (X351 @ sh @ one)) @ id)) | ~! [X353 : subst,X354 : subst,X355 : term] : ((sub @ (X351 @ X353 @ X355) @ X354) = (X351 @ (comp @ X353 @ X354) @ (sub @ X355 @ X354)))) | ~! [X356 : subst,X357 : subst,X358 : subst,X359 : term] : (($true = (X349 @ X356 @ X359 @ (comp @ X358 @ X357))) | ~($true = (X349 @ (comp @ X356 @ X358) @ (sub @ X359 @ X358) @ X357))) | ~! [X360 : term] : ((X347 @ X360) = (X349 @ id @ X360 @ id)) | ~! [X361 : subst,X362 : subst,X363 : term,X364 : subst] : (($true = (X349 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362) @ X364)) | ~($true = (X349 @ X361 @ X363 @ (comp @ X362 @ X364)))) | ($true = (X347 @ (lam @ X348)))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X365 : term] : ((sub @ X365 @ id) = X365) => (! [X366 : term,X367 : subst > term > subst > $o] : (~! [X368 : subst > term > term] : (~! [X369 : term,X370 : subst,X371 : subst] : ((X368 @ (comp @ X371 @ X370) @ (sub @ X369 @ X370)) = (sub @ (X368 @ X371 @ X369) @ X370)) | ~! [X372 : term] : (~($true = (X367 @ id @ X372 @ id)) | ($true = (X367 @ id @ (X368 @ id @ X372) @ id))) | ($true = (X367 @ id @ (lam @ (X368 @ sh @ one)) @ id))) | ((X367 @ id @ (lam @ (sub @ X366 @ (push @ one @ sh))) @ id) = $true) | ~! [X373 : term] : (~($true = (X367 @ id @ X373 @ id)) | ($true = (X367 @ id @ (sub @ X366 @ (push @ X373 @ id)) @ id)))) => ! [X374 : subst > term > subst > $o,X375 : term] : (($true = (X374 @ id @ (lam @ X375) @ id)) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (~($true = (X374 @ X378 @ X379 @ (comp @ X376 @ X377))) | ((X374 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) = $true)) | ~! [X380 : term] : (($true = (X374 @ id @ (sub @ X375 @ (push @ X380 @ id)) @ id)) | ~($true = (X374 @ id @ X380 @ id))) | ~! [X381 : subst > term > term] : (($true = (X374 @ id @ (lam @ (X381 @ sh @ one)) @ id)) | ~! [X382 : term] : (~($true = (X374 @ id @ X382 @ id)) | ($true = (X374 @ id @ (X381 @ id @ X382) @ id))) | ~! [X383 : term,X384 : subst,X385 : subst] : ((sub @ (X381 @ X384 @ X383) @ X385) = (X381 @ (comp @ X384 @ X385) @ (sub @ X383 @ X385)))) | ~! [X386 : subst,X387 : subst,X388 : term,X389 : subst] : (~($true = (X374 @ (comp @ X389 @ X386) @ (sub @ X388 @ X386) @ X387)) | ($true = (X374 @ X389 @ X388 @ (comp @ X386 @ X387))))))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X390 : d_term] : (d_one = X390) & (! [X391 : term,X392 : subst > term > subst > $o] : (($true = (X392 @ id @ (lam @ (sub @ X391 @ (push @ one @ sh))) @ id)) | ~! [X393 : term] : (~($true = (X392 @ id @ X393 @ id)) | ($true = (X392 @ id @ (sub @ X391 @ (push @ X393 @ id)) @ id))) | ~! [X394 : subst > term > term] : (((X392 @ id @ (lam @ (X394 @ sh @ one)) @ id) = $true) | ~! [X395 : subst,X396 : term,X397 : subst] : ((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395)) = (sub @ (X394 @ X397 @ X396) @ X395)) | ~! [X398 : term] : (($true = (X392 @ id @ (X394 @ id @ X398) @ id)) | ~($true = (X392 @ id @ X398 @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X399 : subst > term > subst > $o] : ~! [X400 : term > $o] : ~! [X401 : term] : ((X399 @ id @ X401 @ id) = (X400 @ X401))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X402 : subst,X403 : term] : ((sub @ one @ (push @ X403 @ X402)) = X403) => ! [X404 : term > $o,X405 : subst,X406 : term > $o,X407 : term] : (($true = (X406 @ one)) | ~! [X408 : term] : ((X406 @ X408) = (X404 @ (sub @ X408 @ (push @ X407 @ X405)))) | ~($true = (X404 @ X407))))) & ! [X409 : d_term,X410 : d_term] : (((d2term @ X409) = (d2term @ X410)) => (X409 = X410)) & ((induction = $true) <=> ! [X411 : term,X412 : term > $o] : (~! [X413 : term] : (~($true = (X412 @ X413)) | ($true = (X412 @ (lam @ X413)))) | ($true = (X412 @ X411)) | ~! [X414 : term] : (~($true = (var @ X414)) | ($true = (X412 @ X414))) | ~! [X415 : term,X416 : term] : (($true = (X412 @ (ap @ X416 @ X415))) | ~($true = (X412 @ X416)) | ~($true = (X412 @ X415))))) & (lamnotvar = $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)))))))))))))) & ((hoaslaminj = $true) <=> ! [X422 : term,X423 : subst > term > term,X424 : subst > term > term,X425 : subst] : (((lam @ (X424 @ sh @ one)) != (lam @ (X423 @ sh @ one))) | ((X423 @ X425 @ X422) = (X424 @ X425 @ X422)) | ~! [X426 : subst,X427 : term,X428 : subst] : ((X424 @ (comp @ X426 @ X428) @ (sub @ X427 @ X428)) = (sub @ (X424 @ X426 @ X427) @ X428)) | ~! [X429 : subst,X430 : term,X431 : subst] : ((sub @ (X423 @ X431 @ X430) @ X429) = (X423 @ (comp @ X431 @ X429) @ (sub @ X430 @ X429))))) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X432 : term] : ~! [X433 : subst > term > term] : ~! [X434 : term,X435 : subst] : ((X433 @ X435 @ X434) = (sub @ X432 @ (push @ X434 @ X435))) => (! [X436 : term] : ((sub @ X436 @ id) = X436) => ! [X437 : term,X438 : term > $o,X439 : subst > term > subst > $o] : (($true = (X438 @ (lam @ X437))) | ~! [X440 : subst > term > term] : (~! [X441 : term] : (~((X439 @ id @ X441 @ id) = $true) | ($true = (X439 @ id @ (X440 @ id @ X441) @ id))) | ~! [X442 : subst,X443 : term,X444 : subst] : ((sub @ (X440 @ X444 @ X443) @ X442) = (X440 @ (comp @ X444 @ X442) @ (sub @ X443 @ X442))) | ((X439 @ id @ (lam @ (X440 @ sh @ one)) @ id) = $true)) | ~! [X445 : term] : ((X439 @ id @ X445 @ id) = (X438 @ X445)) | ~! [X446 : term] : (((X438 @ (sub @ X437 @ (push @ X446 @ id))) = $true) | ~($true = (X438 @ X446))))))) & (hoaslamnotvar_gthm = $true) & (! [X447 : term,X448 : term] : (((lam @ X447) != (lam @ X448)) | (X447 = X448)) <=> (laminj = $true)) & (ulamvarind = $true) & ((substmonoid = $true) <=> (! [X449 : subst] : ((comp @ X449 @ id) = X449) & ! [X450 : subst] : ((comp @ id @ X450) = X450))) & ((hoasinduction = $true) <=> ! [X451 : subst > term > subst > $o,X452 : term] : (~! [X453 : term,X454 : term] : (~($true = (X451 @ id @ X454 @ id)) | ($true = (X451 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) | ~((X451 @ id @ X453 @ id) = $true)) | ~! [X455 : term] : (($true = (X451 @ id @ X455 @ id)) | ~((var @ (sub @ X455 @ id)) = $true)) | ~! [X456 : subst > term > term] : (($true = (X451 @ id @ (lam @ (X456 @ sh @ one)) @ id)) | ~! [X457 : term] : (($true = (X451 @ id @ (X456 @ id @ X457) @ id)) | ~($true = (X451 @ id @ X457 @ id))) | ~! [X458 : subst,X459 : subst,X460 : term] : ((sub @ (X456 @ X459 @ X460) @ X458) = (X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | ~! [X461 : subst,X462 : subst,X463 : subst,X464 : term] : (~($true = (X451 @ X461 @ X464 @ (comp @ X462 @ X463))) | ($true = (X451 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) | ($true = (X451 @ id @ X452 @ id)) | ~! [X465 : term,X466 : subst,X467 : subst,X468 : subst] : (($true = (X451 @ X467 @ X465 @ (comp @ X468 @ X466))) | ~($true = (X451 @ (comp @ X467 @ X468) @ (sub @ X465 @ X468) @ X466))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X472 : subst > term > subst > $o] : ~! [X473 : term > $o] : ~! [X474 : term] : ((X473 @ X474) = (X472 @ id @ X474 @ id)) => (! [X475 : term,X476 : term > $o] : (~! [X477 : term,X478 : term] : (~($true = (X476 @ X477)) | ~($true = (X476 @ X478)) | ($true = (X476 @ (ap @ X478 @ X477)))) | ~! [X479 : term] : (~($true = (var @ X479)) | ($true = (X476 @ X479))) | ~! [X480 : term] : (~! [X481 : term] : (($true = (X476 @ (sub @ X480 @ (push @ X481 @ id)))) | ~($true = (X476 @ X481))) | ($true = (X476 @ (lam @ X480)))) | ($true = (X476 @ X475))) => (! [X482 : term] : ((sub @ X482 @ id) = X482) => (! [X483 : term > $o,X484 : subst > term > subst > $o,X485 : term] : (($true = (X483 @ (lam @ X485))) | ~! [X486 : term] : (($true = (X483 @ (sub @ X485 @ (push @ X486 @ id)))) | ~($true = (X483 @ X486))) | ~! [X487 : term] : ((X483 @ X487) = (X484 @ id @ X487 @ id)) | ~! [X488 : subst > term > term] : (($true = (X484 @ id @ (lam @ (X488 @ sh @ one)) @ id)) | ~! [X489 : term] : (($true = (X484 @ id @ (X488 @ id @ X489) @ id)) | ~((X484 @ id @ X489 @ id) = $true)) | ~! [X490 : term,X491 : subst,X492 : subst] : ((X488 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492)) = (sub @ (X488 @ X491 @ X490) @ X492)))) => ! [X493 : term,X494 : subst > term > subst > $o] : (~! [X495 : subst,X496 : subst,X497 : term,X498 : subst] : (((X494 @ X495 @ X497 @ (comp @ X498 @ X496)) = $true) | ~($true = (X494 @ (comp @ X495 @ X498) @ (sub @ X497 @ X498) @ X496))) | ~! [X499 : subst,X500 : subst,X501 : term,X502 : subst] : (($true = (X494 @ (comp @ X499 @ X502) @ (sub @ X501 @ X502) @ X500)) | ~($true = (X494 @ X499 @ X501 @ (comp @ X502 @ X500)))) | ($true = (X494 @ id @ X493 @ id)) | ~! [X503 : term,X504 : term] : (~($true = (X494 @ id @ X504 @ id)) | ($true = (X494 @ id @ (ap @ (sub @ X503 @ id) @ X504) @ id)) | ~($true = (X494 @ id @ X503 @ id))) | ~! [X505 : term] : (($true = (X494 @ id @ X505 @ id)) | ~($true = (var @ (sub @ X505 @ id)))) | ~! [X506 : subst > term > term] : (($true = (X494 @ id @ (lam @ (X506 @ sh @ one)) @ id)) | ~! [X507 : term,X508 : subst,X509 : subst] : ((X506 @ (comp @ X509 @ X508) @ (sub @ X507 @ X508)) = (sub @ (X506 @ X509 @ X507) @ X508)) | ~! [X510 : term] : (~($true = (X494 @ id @ X510 @ id)) | ($true = (X494 @ id @ (X506 @ id @ X510) @ id)))))))))) & (! [X511 : term,X512 : subst > term > subst > $o] : (~! [X513 : subst > term > term] : (~! [X514 : subst,X515 : term,X516 : subst] : ((X513 @ (comp @ X516 @ X514) @ (sub @ X515 @ X514)) = (sub @ (X513 @ X516 @ X515) @ X514)) | ~! [X517 : term] : (~((X512 @ id @ X517 @ id) = $true) | ($true = (X512 @ id @ (X513 @ id @ X517) @ id))) | ($true = (X512 @ id @ (lam @ (X513 @ sh @ one)) @ id))) | ($true = (X512 @ id @ (lam @ (sub @ X511 @ (push @ one @ sh))) @ id)) | ~! [X518 : term] : (~($true = (X512 @ id @ X518 @ id)) | ($true = (X512 @ id @ (sub @ X511 @ (push @ X518 @ id)) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X519 : term,X520 : term,X521 : subst > term > term] : (~! [X522 : subst,X523 : term,X524 : subst] : ((sub @ (X521 @ X522 @ X523) @ X524) = (X521 @ (comp @ X522 @ X524) @ (sub @ X523 @ X524))) | ((lam @ (X521 @ sh @ one)) != (ap @ (sub @ X520 @ id) @ X519))) <=> (hoaslamnotap = $true)) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (! [X525 : subst,X526 : term > $o,X527 : term] : (~! [X528 : term] : (($true = (X526 @ (sub @ X528 @ X525))) | ~($true = (var @ X528))) | ~! [X529 : term,X530 : term] : (~($true = (X526 @ X529)) | ((X526 @ (ap @ X530 @ X529)) = $true) | ~($true = (X526 @ X530))) | ~! [X531 : term] : (~! [X532 : term] : (($true = (X526 @ (sub @ X531 @ (push @ X532 @ id)))) | ~($true = (X526 @ X532))) | ((X526 @ (lam @ X531)) = $true)) | ($true = (X526 @ (sub @ X527 @ X525)))) <=> (induction2lem = $true)) & (! [X533 : subst > term > subst > $o,X534 : term] : (~! [X535 : term] : (~($true = (X533 @ id @ X535 @ id)) | ($true = (X533 @ id @ (sub @ X534 @ (push @ X535 @ id)) @ id))) | ~! [X536 : subst,X537 : subst,X538 : subst,X539 : term] : (~($true = (X533 @ X537 @ X539 @ (comp @ X536 @ X538))) | ($true = (X533 @ (comp @ X537 @ X536) @ (sub @ X539 @ X536) @ X538))) | ($true = (X533 @ id @ (lam @ X534) @ id)) | ~! [X540 : subst > term > term] : (~! [X541 : subst,X542 : term,X543 : subst] : ((X540 @ (comp @ X541 @ X543) @ (sub @ X542 @ X543)) = (sub @ (X540 @ X541 @ X542) @ X543)) | ($true = (X533 @ id @ (lam @ (X540 @ sh @ one)) @ id)) | ~! [X544 : term] : (~($true = (X533 @ id @ X544 @ id)) | ($true = (X533 @ id @ (X540 @ id @ X544) @ id)))) | ~! [X545 : term,X546 : subst,X547 : subst,X548 : subst] : (($true = (X533 @ X548 @ X545 @ (comp @ X546 @ X547))) | ~($true = (X533 @ (comp @ X548 @ X546) @ (sub @ X545 @ X546) @ X547)))) <=> (hoasinduction_lem3 = $true)) & ((axidr = $true) <=> ! [X549 : subst] : ((comp @ X549 @ id) = X549)) & (axvarshift = $true)),
% 42.64/7.44 inference(fool_elimination,[status(thm)],[f7])).
% 42.64/7.44 thf(f7,plain,(
% 42.64/7.44 termmset_gthm & ! [X0 : subst] : ? [X1 : d_subst] : ((d2subst @ X1) = X0) & ((! [X2 : term] : ((sub @ X2 @ id) = X2) => (! [X3 : subst > term > subst > $o,X4 : term] : (~! [X5 : subst > term > term] : (~! [X6 : subst,X7 : subst,X8 : term] : ((X5 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6)) = (sub @ (X5 @ X7 @ X8) @ X6)) | ~! [X9 : term] : ((X3 @ id @ (X5 @ id @ X9) @ id) | ~(X3 @ id @ X9 @ id)) | (X3 @ id @ (lam @ (X5 @ sh @ one)) @ id)) | ~! [X10 : term] : (~(X3 @ id @ X10 @ id) | (X3 @ id @ (sub @ X4 @ (push @ X10 @ id)) @ id)) | (X3 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id)) => ! [X11 : subst > term > subst > $o,X12 : term] : ((X11 @ id @ (lam @ X12) @ id) | ~! [X13 : subst > term > term] : ((X11 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~! [X14 : subst,X15 : subst,X16 : term] : ((X13 @ (comp @ X15 @ X14) @ (sub @ X16 @ X14)) = (sub @ (X13 @ X15 @ X16) @ X14)) | ~! [X17 : term] : ((X11 @ id @ (X13 @ id @ X17) @ id) | ~(X11 @ id @ X17 @ id))) | ~! [X18 : term] : (~(X11 @ id @ X18 @ id) | (X11 @ id @ (sub @ X12 @ (push @ X18 @ id)) @ id))))) <=> hoasinduction_lem3a_lthm) & (! [X19 : term] : ~! [X20 : subst > term > term] : ~! [X21 : subst,X22 : term] : ((X20 @ X21 @ X22) = (sub @ X19 @ (push @ X22 @ X21))) <=> hoasinduction_lem3v2_f_lthm) & hoasapinj2_gthm & ! [X23 : d_subst] : (d_id = X23) & pushprop_lem1v2_gthm & hoasinduction_lem1v2 & (hoasinduction_lem2 <=> ! [X24 : term,X25 : term,X26 : subst > term > subst > $o] : (~! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (~(X26 @ (comp @ X29 @ X30) @ (sub @ X28 @ X30) @ X27) | (X26 @ X29 @ X28 @ (comp @ X30 @ X27))) | ~! [X31 : term,X32 : term] : ((X26 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id) | ~(X26 @ id @ X31 @ id) | ~(X26 @ id @ X32 @ id)) | ~(X26 @ id @ X24 @ id) | ~(X26 @ id @ X25 @ id) | ~! [X33 : subst,X34 : subst,X35 : subst,X36 : term] : ((X26 @ (comp @ X33 @ X34) @ (sub @ X36 @ X34) @ X35) | ~(X26 @ X33 @ X36 @ (comp @ X34 @ X35))) | (X26 @ id @ (ap @ X24 @ X25) @ id))) & hoaslamnotap_gthm & (hoasapinj1 <=> ! [X37 : term,X38 : term,X39 : term,X40 : term] : ((X37 = X38) | ((ap @ (sub @ X38 @ id) @ X39) != (ap @ (sub @ X37 @ id) @ X40)))) & hoasinduction_lem1 & ~lamnotap & pushprop_lthm_orig & hoaslaminj_gthm & (! [X41 : term,X42 : subst > term > subst > $o] : ((X42 @ id @ (lam @ X41) @ id) | ~! [X43 : subst > term > term] : (~! [X44 : subst,X45 : subst,X46 : term] : ((X43 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45)) = (sub @ (X43 @ X44 @ X46) @ X45)) | (X42 @ id @ (lam @ (X43 @ sh @ one)) @ id) | ~! [X47 : term] : (~(X42 @ id @ X47 @ id) | (X42 @ id @ (X43 @ id @ X47) @ id))) | ~! [X48 : term] : (~(X42 @ id @ X48 @ id) | (X42 @ id @ (sub @ X41 @ (push @ X48 @ id)) @ id))) <=> hoasinduction_lem3a) & (hoasinduction_lem3b <=> ! [X49 : term] : ~! [X50 : subst > term > term] : ((sub @ X49 @ (push @ one @ sh)) != (X50 @ sh @ one))) & ! [X51 : d_subst,X52 : d_subst] : (((d2subst @ X52) = (d2subst @ X51)) => (X51 = X52)) & pushprop_lem3v2 & (one = (d2term @ d_one)) & (hoasinduction_lem3aaa <=> ! [X53 : subst > term > subst > $o,X54 : term] : ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id) | ~! [X55 : term] : ((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id) | ~(X53 @ id @ X55 @ id)) | ~! [X56 : subst > term > term,X57 : term] : (~! [X58 : subst,X59 : term,X60 : subst] : ((sub @ (X56 @ X58 @ X59) @ X60) = (sub @ (sub @ X57 @ (push @ X59 @ X58)) @ X60)) | (X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) | ~! [X61 : term] : ((X53 @ id @ (X56 @ id @ X61) @ id) | ~(X53 @ id @ X61 @ id)) | ~! [X62 : subst,X63 : subst,X64 : term] : ((X56 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)) = (sub @ X57 @ (push @ (sub @ X64 @ X63) @ (comp @ X62 @ X63))))))) & (! [X65 : term,X66 : term > $o,X67 : term > $o,X68 : subst,X69 : term] : ((X66 @ (sub @ X65 @ (push @ X69 @ X68))) | ~(X67 @ X65)) <=> pushprop_lem1) & (axidl <=> ! [X70 : subst] : ((comp @ id @ X70) = X70)) & (axshiftcons <=> ! [X71 : subst,X72 : term] : ((comp @ sh @ (push @ X72 @ X71)) = X71)) & ((d2subst @ d_id) = sh) & hoasinduction_lem3b_gthm & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X73 : term] : ((sub @ X73 @ id) = X73) <=> axvarid) & hoaslamnotvar & (! [X74 : subst,X75 : term] : ((sub @ one @ (push @ X75 @ X74)) = X75) <=> axvarcons) & (hoasinduction_lem3v2_lthm <=> (! [X76 : term] : ((sub @ X76 @ id) = X76) => ! [X77 : term,X78 : subst > term > subst > $o,X79 : term > $o] : (~! [X80 : term] : ((X78 @ id @ X80 @ id) = (X79 @ X80)) | ~! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : (~(X78 @ X82 @ X81 @ (comp @ X83 @ X84)) | (X78 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84)) | ~! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (~(X78 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86) @ X88) | (X78 @ X87 @ X85 @ (comp @ X86 @ X88))) | ~! [X89 : term] : (~(X79 @ X89) | (X79 @ (sub @ X77 @ (push @ X89 @ id)))) | (X79 @ (lam @ X77)) | ~! [X90 : subst > term > term] : (~! [X91 : subst,X92 : term,X93 : subst] : ((sub @ (X90 @ X91 @ X92) @ X93) = (X90 @ (comp @ X91 @ X93) @ (sub @ X92 @ X93))) | ~! [X94 : term] : (~(X78 @ id @ X94 @ id) | (X78 @ id @ (X90 @ id @ X94) @ id)) | (X78 @ id @ (lam @ (X90 @ sh @ one)) @ id))))) & hoasinduction_lem1_lthm & (! [X95 : term,X96 : term,X97 : term,X98 : term] : (((ap @ (sub @ X96 @ id) @ X97) != (ap @ (sub @ X98 @ id) @ X95)) | (X95 = X97)) <=> hoasapinj2) & (pushprop_lem1v2 <=> ! [X99 : term > $o,X100 : term > $o,X101 : subst,X102 : term] : (~! [X103 : term] : ((X100 @ X103) = (X99 @ (sub @ X103 @ (push @ X102 @ X101)))) | (X100 @ one) | ~(X99 @ X102))) & (induction2 <=> ! [X104 : term,X105 : term > $o] : (~! [X106 : term] : ((X105 @ (lam @ X106)) | ~! [X107 : term] : ((X105 @ (sub @ X106 @ (push @ X107 @ id))) | ~(X105 @ X107))) | ~! [X108 : term] : (~(var @ X108) | (X105 @ X108)) | (X105 @ X104) | ~! [X109 : term,X110 : term] : ((X105 @ (ap @ X109 @ X110)) | ~(X105 @ X110) | ~(X105 @ X109)))) & hoasinduction_lem1_gthm & axmap & pushprop_lthm & (hoasinduction_lem3v2_f <=> ! [X111 : term] : ~! [X112 : subst > term > term] : ~! [X113 : subst,X114 : term] : ((X112 @ X113 @ X114) = (sub @ X111 @ (push @ X114 @ X113)))) & pushprop_gthm & pushprop_lem2v2 & (induction2lem_lthm <=> (! [X115 : subst,X116 : term] : ((sub @ one @ (push @ X116 @ X115)) = X116) => (! [X117 : subst,X118 : term] : ((comp @ sh @ (push @ X118 @ X117)) = X117) => (! [X119 : subst] : ((comp @ X119 @ id) = X119) => (! [X120 : term > $o,X121 : term] : ((X120 @ X121) | ~! [X122 : term] : ((X120 @ X122) | ~(var @ X122)) | ~! [X123 : term,X124 : term] : (~(X120 @ X123) | ~(X120 @ X124) | (X120 @ (ap @ X124 @ X123))) | ~! [X125 : term] : (~(X120 @ X125) | (X120 @ (lam @ X125)))) => ! [X126 : term > $o,X127 : term,X128 : subst] : ((X126 @ (sub @ X127 @ X128)) | ~! [X129 : term,X130 : term] : ((X126 @ (ap @ X130 @ X129)) | ~(X126 @ X129) | ~(X126 @ X130)) | ~! [X131 : term] : ((X126 @ (lam @ X131)) | ~! [X132 : term] : (~(X126 @ X132) | (X126 @ (sub @ X131 @ (push @ X132 @ id))))) | ~! [X133 : term] : (~(var @ X133) | (X126 @ (sub @ X133 @ X128))))))))) & (! [X134 : term,X135 : term,X136 : term,X137 : term] : (((ap @ X137 @ X135) != (ap @ X136 @ X134)) | (X136 = X137)) <=> apinj1) & hoaslamnotap_lthm & ((! [X138 : subst] : ((comp @ id @ X138) = X138) => (! [X139 : subst] : ((comp @ X139 @ id) = X139) => (! [X140 : subst] : ((comp @ id @ X140) = X140) & ! [X141 : subst] : ((comp @ X141 @ id) = X141)))) <=> substmonoid_lthm) & apnotvar & ((! [X142 : term > $o,X143 : term] : ((X142 @ X143) | ~! [X144 : term] : ((X142 @ X144) | ~(var @ X144)) | ~! [X145 : term,X146 : term] : (~(X142 @ X145) | ~(X142 @ X146) | (X142 @ (ap @ X145 @ X146))) | ~! [X147 : term] : ((X142 @ (lam @ X147)) | ~! [X148 : term] : ((X142 @ (sub @ X147 @ (push @ X148 @ id))) | ~(X142 @ X148)))) => (! [X149 : subst > term > subst > $o,X150 : term,X151 : term] : (~(X149 @ id @ X151 @ id) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (~(X149 @ X155 @ X152 @ (comp @ X153 @ X154)) | (X149 @ (comp @ X155 @ X153) @ (sub @ X152 @ X153) @ X154)) | ~! [X156 : term,X157 : term] : ((X149 @ id @ (ap @ (sub @ X157 @ id) @ X156) @ id) | ~(X149 @ id @ X157 @ id) | ~(X149 @ id @ X156 @ id)) | (X149 @ id @ (ap @ X151 @ X150) @ id) | ~(X149 @ id @ X150 @ id) | ~! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : (~(X149 @ (comp @ X158 @ X160) @ (sub @ X161 @ X160) @ X159) | (X149 @ X158 @ X161 @ (comp @ X160 @ X159)))) => (! [X162 : subst > term > subst > $o,X163 : term] : ((X162 @ id @ (lam @ X163) @ id) | ~! [X164 : term] : ((X162 @ id @ (sub @ X163 @ (push @ X164 @ id)) @ id) | ~(X162 @ id @ X164 @ id)) | ~! [X165 : subst,X166 : subst,X167 : term,X168 : subst] : (~(X162 @ X165 @ X167 @ (comp @ X168 @ X166)) | (X162 @ (comp @ X165 @ X168) @ (sub @ X167 @ X168) @ X166)) | ~! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : (~(X162 @ (comp @ X171 @ X172) @ (sub @ X170 @ X172) @ X169) | (X162 @ X171 @ X170 @ (comp @ X172 @ X169))) | ~! [X173 : subst > term > term] : (~! [X174 : term] : ((X162 @ id @ (X173 @ id @ X174) @ id) | ~(X162 @ id @ X174 @ id)) | ~! [X175 : term,X176 : subst,X177 : subst] : ((sub @ (X173 @ X176 @ X175) @ X177) = (X173 @ (comp @ X176 @ X177) @ (sub @ X175 @ X177))) | (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id))) => ! [X178 : term,X179 : subst > term > subst > $o] : (~! [X180 : term] : ((X179 @ id @ X180 @ id) | ~(var @ (sub @ X180 @ id))) | ~! [X181 : term,X182 : term] : (~(X179 @ id @ X182 @ id) | (X179 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id) | ~(X179 @ id @ X181 @ id)) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (~(X179 @ X184 @ X185 @ (comp @ X186 @ X183)) | (X179 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186) @ X183)) | ~! [X187 : term,X188 : subst,X189 : subst,X190 : subst] : ((X179 @ X188 @ X187 @ (comp @ X189 @ X190)) | ~(X179 @ (comp @ X188 @ X189) @ (sub @ X187 @ X189) @ X190)) | (X179 @ id @ X178 @ id) | ~! [X191 : subst > term > term] : ((X179 @ id @ (lam @ (X191 @ sh @ one)) @ id) | ~! [X192 : subst,X193 : term,X194 : subst] : ((X191 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192)) = (sub @ (X191 @ X194 @ X193) @ X192)) | ~! [X195 : term] : (~(X179 @ id @ X195 @ id) | (X179 @ id @ (X191 @ id @ X195) @ id))))))) <=> hoasinduction_lthm) & induction2lem_gthm & hoasinduction_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & pushprop & pushprop_lem1_gthm & induction2_gthm & hoasinduction_lem2_gthm & (pushprop_lem0 <=> ! [X196 : subst,X197 : term,X198 : term > $o] : ~! [X199 : term > $o] : ~! [X200 : term] : ((X199 @ X200) = (X198 @ (sub @ X200 @ (push @ X197 @ X196))))) & (termmset_lthm <=> (! [X201 : term] : ((sub @ X201 @ id) = X201) => ! [X202 : term] : ((sub @ X202 @ id) = X202))) & hoaslamnotvar_lthm & (! [X203 : subst > term > subst > $o,X204 : term] : (~! [X205 : term,X206 : term] : (~(X203 @ id @ X206 @ id) | (X203 @ id @ (ap @ (sub @ X205 @ id) @ X206) @ id) | ~(X203 @ id @ X205 @ id)) | ~! [X207 : subst > term > term] : ((X203 @ id @ (lam @ (X207 @ sh @ one)) @ id) | ~! [X208 : term] : (~(X203 @ id @ X208 @ id) | (X203 @ id @ (X207 @ id @ X208) @ id)) | ~! [X209 : subst,X210 : term,X211 : subst] : ((X207 @ (comp @ X209 @ X211) @ (sub @ X210 @ X211)) = (sub @ (X207 @ X209 @ X210) @ X211))) | (X203 @ id @ X204 @ id)) <=> hoasinduction_no_psi_cond) & (apinj2 <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ X212 @ X215) != (ap @ X213 @ X214)) | (X214 = X215))) & pushprop_lem3v2_lthm & ~ulamvar1 & hoasapnotvar & ((^[X216 : subst, X217 : subst > term > term] : (d2term @ d_one)) = hoaslam) & hoasapnotvar_lthm & (hoasinduction_lem3b_lthm <=> ! [X218 : term] : ~! [X219 : subst > term > term] : ((X219 @ sh @ one) != (sub @ X218 @ (push @ one @ sh)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X220 : term] : ((sub @ X220 @ id) = X220) => (! [X221 : term,X222 : term,X223 : term,X224 : term] : (((ap @ X224 @ X222) != (ap @ X221 @ X223)) | (X221 = X224)) => ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X227 = X228) | ((ap @ (sub @ X227 @ id) @ X225) != (ap @ (sub @ X228 @ id) @ X226))))) <=> hoasapinj1_lthm) & hoasinduction_lem3a_gthm & substmonoid_gthm & ((d2subst @ d_id) = id) & (induction2_lthm <=> (! [X229 : term] : ((sub @ X229 @ id) = X229) => (! [X230 : term > $o,X231 : subst,X232 : term] : (~! [X233 : term] : (~(var @ X233) | (X230 @ (sub @ X233 @ X231))) | ~! [X234 : term] : (~! [X235 : term] : ((X230 @ (sub @ X234 @ (push @ X235 @ id))) | ~(X230 @ X235)) | (X230 @ (lam @ X234))) | (X230 @ (sub @ X232 @ X231)) | ~! [X236 : term,X237 : term] : (~(X230 @ X237) | (X230 @ (ap @ X236 @ X237)) | ~(X230 @ X236))) => ! [X238 : term,X239 : term > $o] : (~! [X240 : term] : ((X239 @ X240) | ~(var @ X240)) | ~! [X241 : term,X242 : term] : (~(X239 @ X242) | (X239 @ (ap @ X242 @ X241)) | ~(X239 @ X241)) | ~! [X243 : term] : (~! [X244 : term] : (~(X239 @ X244) | (X239 @ (sub @ X243 @ (push @ X244 @ id)))) | (X239 @ (lam @ X243))) | (X239 @ X238))))) & (axscons <=> ! [X245 : subst] : ((push @ (sub @ one @ X245) @ (comp @ sh @ X245)) = X245)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & hoasinduction_lem2_lthm & axabs & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((! [X246 : term,X247 : term,X248 : term,X249 : term] : ((X247 = X249) | ((ap @ X248 @ X249) != (ap @ X246 @ X247))) => ! [X250 : term,X251 : term,X252 : term,X253 : term] : (((ap @ (sub @ X252 @ id) @ X251) != (ap @ (sub @ X250 @ id) @ X253)) | (X251 = X253))) <=> hoasapinj2_lthm) & (hoasinduction_lem0_lthm <=> ! [X254 : subst > term > subst > $o] : ~! [X255 : term > $o] : ~! [X256 : term] : ((X254 @ id @ X256 @ id) = (X255 @ X256))) & (! [X257 : term,X258 : term] : (((sub @ X257 @ sh) != (sub @ X258 @ sh)) | (X257 = X258)) <=> shinj) & ((! [X259 : term,X260 : subst] : ((sub @ one @ (push @ X259 @ X260)) = X259) => (! [X261 : term,X262 : subst] : ((comp @ sh @ (push @ X261 @ X262)) = X262) => (! [X263 : term,X264 : term] : ((X263 = X264) | ((lam @ X263) != (lam @ X264))) => ! [X265 : subst > term > term,X266 : term,X267 : subst,X268 : subst > term > term] : (((lam @ (X265 @ sh @ one)) != (lam @ (X268 @ sh @ one))) | ((X265 @ X267 @ X266) = (X268 @ X267 @ X266)) | ~! [X269 : subst,X270 : term,X271 : subst] : ((X265 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)) = (sub @ (X265 @ X271 @ X270) @ X269)) | ~! [X272 : subst,X273 : term,X274 : subst] : ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)) = (sub @ (X268 @ X272 @ X273) @ X274)))))) <=> hoaslaminj_lthm) & (! [X275 : term > $o,X276 : subst,X277 : term] : ~! [X278 : term > $o] : ~! [X279 : term] : ((X275 @ (sub @ X279 @ (push @ X277 @ X276))) = (X278 @ X279)) <=> pushprop_lem0_lthm) & axapp & (hoasinduction_lem2v2 <=> ! [X280 : term,X281 : term > $o,X282 : term,X283 : subst > term > subst > $o] : (~! [X284 : term,X285 : term] : ((X283 @ id @ (ap @ (sub @ X285 @ id) @ X284) @ id) | ~(X283 @ id @ X284 @ id) | ~(X283 @ id @ X285 @ id)) | ~(X281 @ X282) | (X281 @ (ap @ X280 @ X282)) | ~! [X286 : subst,X287 : subst,X288 : term,X289 : subst] : (~(X283 @ (comp @ X286 @ X289) @ (sub @ X288 @ X289) @ X287) | (X283 @ X286 @ X288 @ (comp @ X289 @ X287))) | ~! [X290 : term,X291 : subst,X292 : subst,X293 : subst] : ((X283 @ (comp @ X291 @ X293) @ (sub @ X290 @ X293) @ X292) | ~(X283 @ X291 @ X290 @ (comp @ X293 @ X292))) | ~! [X294 : term] : ((X283 @ id @ X294 @ id) = (X281 @ X294)) | ~(X281 @ X280))) & ~(var @ (d2term @ d_one)) & hoasapinj1_gthm & ! [X295 : term] : ? [X296 : d_term] : ((d2term @ X296) = X295) & (hoasinduction_lem3v2a <=> ! [X297 : term > $o,X298 : term,X299 : subst > term > subst > $o] : (~! [X300 : subst > term > term] : (~! [X301 : term] : (~(X299 @ id @ X301 @ id) | (X299 @ id @ (X300 @ id @ X301) @ id)) | (X299 @ id @ (lam @ (X300 @ sh @ one)) @ id) | ~! [X302 : subst,X303 : term,X304 : subst] : ((X300 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302)) = (sub @ (X300 @ X304 @ X303) @ X302))) | (X297 @ (lam @ X298)) | ~! [X305 : term] : ((X297 @ X305) = (X299 @ id @ X305 @ id)) | ~! [X306 : term] : (~(X297 @ X306) | (X297 @ (sub @ X298 @ (push @ X306 @ id)))))) & hoasinduction_lem1v2_gthm & hoasinduction_lem3_gthm & ((! [X307 : subst > term > subst > $o] : ~! [X308 : term > $o] : ~! [X309 : term] : ((X308 @ X309) = (X307 @ id @ X309 @ id)) => (! [X310 : term > $o,X311 : term] : (~! [X312 : term] : (~(var @ X312) | (X310 @ X312)) | ~! [X313 : term,X314 : term] : (~(X310 @ X314) | ~(X310 @ X313) | (X310 @ (ap @ X313 @ X314))) | (X310 @ X311) | ~! [X315 : term] : (~! [X316 : term] : ((X310 @ (sub @ X315 @ (push @ X316 @ id))) | ~(X310 @ X316)) | (X310 @ (lam @ X315)))) => (! [X317 : term] : ((sub @ X317 @ id) = X317) => (! [X318 : term,X319 : term > $o,X320 : subst > term > subst > $o] : (~! [X321 : term] : ((X320 @ id @ X321 @ id) = (X319 @ X321)) | (X319 @ (lam @ X318)) | ~! [X322 : subst > term > term] : (~! [X323 : subst,X324 : subst,X325 : term] : ((sub @ (X322 @ X323 @ X325) @ X324) = (X322 @ (comp @ X323 @ X324) @ (sub @ X325 @ X324))) | (X320 @ id @ (lam @ (X322 @ sh @ one)) @ id) | ~! [X326 : term] : (~(X320 @ id @ X326 @ id) | (X320 @ id @ (X322 @ id @ X326) @ id))) | ~! [X327 : term] : ((X319 @ (sub @ X318 @ (push @ X327 @ id))) | ~(X319 @ X327))) => ! [X328 : subst > term > subst > $o,X329 : term] : (~! [X330 : term,X331 : term] : (~(X328 @ id @ X330 @ id) | ~(X328 @ id @ X331 @ id) | (X328 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id)) | (X328 @ id @ X329 @ id) | ~! [X332 : subst > term > term] : (~! [X333 : subst,X334 : subst,X335 : term] : ((sub @ (X332 @ X333 @ X335) @ X334) = (X332 @ (comp @ X333 @ X334) @ (sub @ X335 @ X334))) | ~! [X336 : term] : (~(X328 @ id @ X336 @ id) | (X328 @ id @ (X332 @ id @ X336) @ id)) | (X328 @ id @ (lam @ (X332 @ sh @ one)) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & ((! [X337 : term,X338 : subst] : ((sub @ one @ (push @ X337 @ X338)) = X337) => (! [X339 : subst,X340 : term] : ((comp @ sh @ (push @ X340 @ X339)) = X339) => ! [X341 : term > $o,X342 : term,X343 : subst,X344 : term,X345 : term > $o] : (~(X341 @ X344) | (X345 @ (sub @ X344 @ (push @ X342 @ X343)))))) <=> pushprop_lem1_lthm) & axassoc & (termmset <=> ! [X346 : term] : ((sub @ X346 @ id) = X346)) & hoasapnotvar_gthm & ulamvarsh & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X347 : term > $o,X348 : term,X349 : subst > term > subst > $o] : (~! [X350 : term] : (~(X347 @ X350) | (X347 @ (sub @ X348 @ (push @ X350 @ id)))) | ~! [X351 : subst > term > term] : (~! [X352 : term] : ((X349 @ id @ (X351 @ id @ X352) @ id) | ~(X349 @ id @ X352 @ id)) | (X349 @ id @ (lam @ (X351 @ sh @ one)) @ id) | ~! [X353 : subst,X354 : subst,X355 : term] : ((sub @ (X351 @ X353 @ X355) @ X354) = (X351 @ (comp @ X353 @ X354) @ (sub @ X355 @ X354)))) | ~! [X356 : subst,X357 : subst,X358 : subst,X359 : term] : ((X349 @ X356 @ X359 @ (comp @ X358 @ X357)) | ~(X349 @ (comp @ X356 @ X358) @ (sub @ X359 @ X358) @ X357)) | ~! [X360 : term] : ((X347 @ X360) = (X349 @ id @ X360 @ id)) | ~! [X361 : subst,X362 : subst,X363 : term,X364 : subst] : ((X349 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362) @ X364) | ~(X349 @ X361 @ X363 @ (comp @ X362 @ X364))) | (X347 @ (lam @ X348))) <=> hoasinduction_lem3v2) & ((! [X365 : term] : ((sub @ X365 @ id) = X365) => (! [X366 : term,X367 : subst > term > subst > $o] : (~! [X368 : subst > term > term] : (~! [X369 : term,X370 : subst,X371 : subst] : ((X368 @ (comp @ X371 @ X370) @ (sub @ X369 @ X370)) = (sub @ (X368 @ X371 @ X369) @ X370)) | ~! [X372 : term] : (~(X367 @ id @ X372 @ id) | (X367 @ id @ (X368 @ id @ X372) @ id)) | (X367 @ id @ (lam @ (X368 @ sh @ one)) @ id)) | (X367 @ id @ (lam @ (sub @ X366 @ (push @ one @ sh))) @ id) | ~! [X373 : term] : (~(X367 @ id @ X373 @ id) | (X367 @ id @ (sub @ X366 @ (push @ X373 @ id)) @ id))) => ! [X374 : subst > term > subst > $o,X375 : term] : ((X374 @ id @ (lam @ X375) @ id) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (~(X374 @ X378 @ X379 @ (comp @ X376 @ X377)) | (X374 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377)) | ~! [X380 : term] : ((X374 @ id @ (sub @ X375 @ (push @ X380 @ id)) @ id) | ~(X374 @ id @ X380 @ id)) | ~! [X381 : subst > term > term] : ((X374 @ id @ (lam @ (X381 @ sh @ one)) @ id) | ~! [X382 : term] : (~(X374 @ id @ X382 @ id) | (X374 @ id @ (X381 @ id @ X382) @ id)) | ~! [X383 : term,X384 : subst,X385 : subst] : ((sub @ (X381 @ X384 @ X383) @ X385) = (X381 @ (comp @ X384 @ X385) @ (sub @ X383 @ X385)))) | ~! [X386 : subst,X387 : subst,X388 : term,X389 : subst] : (~(X374 @ (comp @ X389 @ X386) @ (sub @ X388 @ X386) @ X387) | (X374 @ X389 @ X388 @ (comp @ X386 @ X387)))))) <=> hoasinduction_lem3_lthm) & ! [X390 : d_term] : (d_one = X390) & (! [X391 : term,X392 : subst > term > subst > $o] : ((X392 @ id @ (lam @ (sub @ X391 @ (push @ one @ sh))) @ id) | ~! [X393 : term] : (~(X392 @ id @ X393 @ id) | (X392 @ id @ (sub @ X391 @ (push @ X393 @ id)) @ id)) | ~! [X394 : subst > term > term] : ((X392 @ id @ (lam @ (X394 @ sh @ one)) @ id) | ~! [X395 : subst,X396 : term,X397 : subst] : ((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395)) = (sub @ (X394 @ X397 @ X396) @ X395)) | ~! [X398 : term] : ((X392 @ id @ (X394 @ id @ X398) @ id) | ~(X392 @ id @ X398 @ id)))) <=> hoasinduction_lem3aa) & (hoasinduction_lem0 <=> ! [X399 : subst > term > subst > $o] : ~! [X400 : term > $o] : ~! [X401 : term] : ((X399 @ id @ X401 @ id) = (X400 @ X401))) & (pushprop_lem1v2_lthm <=> (! [X402 : subst,X403 : term] : ((sub @ one @ (push @ X403 @ X402)) = X403) => ! [X404 : term > $o,X405 : subst,X406 : term > $o,X407 : term] : ((X406 @ one) | ~! [X408 : term] : ((X406 @ X408) = (X404 @ (sub @ X408 @ (push @ X407 @ X405)))) | ~(X404 @ X407)))) & ! [X409 : d_term,X410 : d_term] : (((d2term @ X409) = (d2term @ X410)) => (X409 = X410)) & (induction <=> ! [X411 : term,X412 : term > $o] : (~! [X413 : term] : (~(X412 @ X413) | (X412 @ (lam @ X413))) | (X412 @ X411) | ~! [X414 : term] : (~(var @ X414) | (X412 @ X414)) | ~! [X415 : term,X416 : term] : ((X412 @ (ap @ X416 @ X415)) | ~(X412 @ X416) | ~(X412 @ X415)))) & lamnotvar & (pushprop_p_and_p_prime = (^[X417 : term, X418 : subst, X419 : term > $o, X420 : term > $o] : (! [X421 : term] : ((X420 @ X421) = (X419 @ (sub @ X421 @ (push @ X417 @ X418))))))) & (hoaslaminj <=> ! [X422 : term,X423 : subst > term > term,X424 : subst > term > term,X425 : subst] : (((lam @ (X424 @ sh @ one)) != (lam @ (X423 @ sh @ one))) | ((X423 @ X425 @ X422) = (X424 @ X425 @ X422)) | ~! [X426 : subst,X427 : term,X428 : subst] : ((X424 @ (comp @ X426 @ X428) @ (sub @ X427 @ X428)) = (sub @ (X424 @ X426 @ X427) @ X428)) | ~! [X429 : subst,X430 : term,X431 : subst] : ((sub @ (X423 @ X431 @ X430) @ X429) = (X423 @ (comp @ X431 @ X429) @ (sub @ X430 @ X429))))) & pushprop_lem0_gthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & hoasinduction_lem2v2_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X432 : term] : ~! [X433 : subst > term > term] : ~! [X434 : term,X435 : subst] : ((X433 @ X435 @ X434) = (sub @ X432 @ (push @ X434 @ X435))) => (! [X436 : term] : ((sub @ X436 @ id) = X436) => ! [X437 : term,X438 : term > $o,X439 : subst > term > subst > $o] : ((X438 @ (lam @ X437)) | ~! [X440 : subst > term > term] : (~! [X441 : term] : (~(X439 @ id @ X441 @ id) | (X439 @ id @ (X440 @ id @ X441) @ id)) | ~! [X442 : subst,X443 : term,X444 : subst] : ((sub @ (X440 @ X444 @ X443) @ X442) = (X440 @ (comp @ X444 @ X442) @ (sub @ X443 @ X442))) | (X439 @ id @ (lam @ (X440 @ sh @ one)) @ id)) | ~! [X445 : term] : ((X439 @ id @ X445 @ id) = (X438 @ X445)) | ~! [X446 : term] : ((X438 @ (sub @ X437 @ (push @ X446 @ id))) | ~(X438 @ X446)))))) & hoaslamnotvar_gthm & (! [X447 : term,X448 : term] : (((lam @ X447) != (lam @ X448)) | (X447 = X448)) <=> laminj) & ulamvarind & (substmonoid <=> (! [X449 : subst] : ((comp @ X449 @ id) = X449) & ! [X450 : subst] : ((comp @ id @ X450) = X450))) & (hoasinduction <=> ! [X451 : subst > term > subst > $o,X452 : term] : (~! [X453 : term,X454 : term] : (~(X451 @ id @ X454 @ id) | (X451 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id) | ~(X451 @ id @ X453 @ id)) | ~! [X455 : term] : ((X451 @ id @ X455 @ id) | ~(var @ (sub @ X455 @ id))) | ~! [X456 : subst > term > term] : ((X451 @ id @ (lam @ (X456 @ sh @ one)) @ id) | ~! [X457 : term] : ((X451 @ id @ (X456 @ id @ X457) @ id) | ~(X451 @ id @ X457 @ id)) | ~! [X458 : subst,X459 : subst,X460 : term] : ((sub @ (X456 @ X459 @ X460) @ X458) = (X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | ~! [X461 : subst,X462 : subst,X463 : subst,X464 : term] : (~(X451 @ X461 @ X464 @ (comp @ X462 @ X463)) | (X451 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463)) | (X451 @ id @ X452 @ id) | ~! [X465 : term,X466 : subst,X467 : subst,X468 : subst] : ((X451 @ X467 @ X465 @ (comp @ X468 @ X466)) | ~(X451 @ (comp @ X467 @ X468) @ (sub @ X465 @ X468) @ X466)))) & ((^[X469 : subst > term > subst > $o, X470 : term > $o] : (! [X471 : term] : ((X470 @ X471) = (X469 @ id @ X471 @ id)))) = hoasinduction_p_and_p_prime) & hoasinduction_lem3v2_gthm & (hoasinduction_lthm_3 <=> (! [X472 : subst > term > subst > $o] : ~! [X473 : term > $o] : ~! [X474 : term] : ((X473 @ X474) = (X472 @ id @ X474 @ id)) => (! [X475 : term,X476 : term > $o] : (~! [X477 : term,X478 : term] : (~(X476 @ X477) | ~(X476 @ X478) | (X476 @ (ap @ X478 @ X477))) | ~! [X479 : term] : (~(var @ X479) | (X476 @ X479)) | ~! [X480 : term] : (~! [X481 : term] : ((X476 @ (sub @ X480 @ (push @ X481 @ id))) | ~(X476 @ X481)) | (X476 @ (lam @ X480))) | (X476 @ X475)) => (! [X482 : term] : ((sub @ X482 @ id) = X482) => (! [X483 : term > $o,X484 : subst > term > subst > $o,X485 : term] : ((X483 @ (lam @ X485)) | ~! [X486 : term] : ((X483 @ (sub @ X485 @ (push @ X486 @ id))) | ~(X483 @ X486)) | ~! [X487 : term] : ((X483 @ X487) = (X484 @ id @ X487 @ id)) | ~! [X488 : subst > term > term] : ((X484 @ id @ (lam @ (X488 @ sh @ one)) @ id) | ~! [X489 : term] : ((X484 @ id @ (X488 @ id @ X489) @ id) | ~(X484 @ id @ X489 @ id)) | ~! [X490 : term,X491 : subst,X492 : subst] : ((X488 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492)) = (sub @ (X488 @ X491 @ X490) @ X492)))) => ! [X493 : term,X494 : subst > term > subst > $o] : (~! [X495 : subst,X496 : subst,X497 : term,X498 : subst] : ((X494 @ X495 @ X497 @ (comp @ X498 @ X496)) | ~(X494 @ (comp @ X495 @ X498) @ (sub @ X497 @ X498) @ X496)) | ~! [X499 : subst,X500 : subst,X501 : term,X502 : subst] : ((X494 @ (comp @ X499 @ X502) @ (sub @ X501 @ X502) @ X500) | ~(X494 @ X499 @ X501 @ (comp @ X502 @ X500))) | (X494 @ id @ X493 @ id) | ~! [X503 : term,X504 : term] : (~(X494 @ id @ X504 @ id) | (X494 @ id @ (ap @ (sub @ X503 @ id) @ X504) @ id) | ~(X494 @ id @ X503 @ id)) | ~! [X505 : term] : ((X494 @ id @ X505 @ id) | ~(var @ (sub @ X505 @ id))) | ~! [X506 : subst > term > term] : ((X494 @ id @ (lam @ (X506 @ sh @ one)) @ id) | ~! [X507 : term,X508 : subst,X509 : subst] : ((X506 @ (comp @ X509 @ X508) @ (sub @ X507 @ X508)) = (sub @ (X506 @ X509 @ X507) @ X508)) | ~! [X510 : term] : (~(X494 @ id @ X510 @ id) | (X494 @ id @ (X506 @ id @ X510) @ id))))))))) & (! [X511 : term,X512 : subst > term > subst > $o] : (~! [X513 : subst > term > term] : (~! [X514 : subst,X515 : term,X516 : subst] : ((X513 @ (comp @ X516 @ X514) @ (sub @ X515 @ X514)) = (sub @ (X513 @ X516 @ X515) @ X514)) | ~! [X517 : term] : (~(X512 @ id @ X517 @ id) | (X512 @ id @ (X513 @ id @ X517) @ id)) | (X512 @ id @ (lam @ (X513 @ sh @ one)) @ id)) | (X512 @ id @ (lam @ (sub @ X511 @ (push @ one @ sh))) @ id) | ~! [X518 : term] : (~(X512 @ id @ X518 @ id) | (X512 @ id @ (sub @ X511 @ (push @ X518 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (! [X519 : term,X520 : term,X521 : subst > term > term] : (~! [X522 : subst,X523 : term,X524 : subst] : ((sub @ (X521 @ X522 @ X523) @ X524) = (X521 @ (comp @ X522 @ X524) @ (sub @ X523 @ X524))) | ((lam @ (X521 @ sh @ one)) != (ap @ (sub @ X520 @ id) @ X519))) <=> hoaslamnotap) & pushprop_lem2v2_gthm & axclos & (! [X525 : subst,X526 : term > $o,X527 : term] : (~! [X528 : term] : ((X526 @ (sub @ X528 @ X525)) | ~(var @ X528)) | ~! [X529 : term,X530 : term] : (~(X526 @ X529) | (X526 @ (ap @ X530 @ X529)) | ~(X526 @ X530)) | ~! [X531 : term] : (~! [X532 : term] : ((X526 @ (sub @ X531 @ (push @ X532 @ id))) | ~(X526 @ X532)) | (X526 @ (lam @ X531))) | (X526 @ (sub @ X527 @ X525))) <=> induction2lem) & (! [X533 : subst > term > subst > $o,X534 : term] : (~! [X535 : term] : (~(X533 @ id @ X535 @ id) | (X533 @ id @ (sub @ X534 @ (push @ X535 @ id)) @ id)) | ~! [X536 : subst,X537 : subst,X538 : subst,X539 : term] : (~(X533 @ X537 @ X539 @ (comp @ X536 @ X538)) | (X533 @ (comp @ X537 @ X536) @ (sub @ X539 @ X536) @ X538)) | (X533 @ id @ (lam @ X534) @ id) | ~! [X540 : subst > term > term] : (~! [X541 : subst,X542 : term,X543 : subst] : ((X540 @ (comp @ X541 @ X543) @ (sub @ X542 @ X543)) = (sub @ (X540 @ X541 @ X542) @ X543)) | (X533 @ id @ (lam @ (X540 @ sh @ one)) @ id) | ~! [X544 : term] : (~(X533 @ id @ X544 @ id) | (X533 @ id @ (X540 @ id @ X544) @ id))) | ~! [X545 : term,X546 : subst,X547 : subst,X548 : subst] : ((X533 @ X548 @ X545 @ (comp @ X546 @ X547)) | ~(X533 @ (comp @ X548 @ X546) @ (sub @ X545 @ X546) @ X547))) <=> hoasinduction_lem3) & (axidr <=> ! [X549 : subst] : ((comp @ X549 @ id) = X549)) & axvarshift),
% 42.64/7.44 inference(rectify,[status(thm)],[f1])).
% 42.64/7.44 thf(f1,axiom,(
% 42.64/7.44 termmset_gthm & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : subst > term > subst > $o,X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X14 : subst,X13 : term] : ((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] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id))))) <=> hoasinduction_lem3a_lthm) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f_lthm) & hoasapinj2_gthm & ! [X5 : d_subst] : (d_id = X5) & pushprop_lem1v2_gthm & hoasinduction_lem1v2 & (hoasinduction_lem2 <=> ! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : (~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id))) & hoaslamnotap_gthm & (hoasapinj1 <=> ! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) & hoasinduction_lem1 & ~lamnotap & pushprop_lthm_orig & hoaslaminj_gthm & (! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3a) & (hoasinduction_lem3b <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & ! [X7 : d_subst,X6 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & pushprop_lem3v2 & (one = (d2term @ d_one)) & (hoasinduction_lem3aaa <=> ! [X10 : subst > term > subst > $o,X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term,X35 : term] : (~! [X36 : subst,X37 : term,X38 : subst] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X39 : subst,X41 : subst,X40 : term] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))))) & (! [X13 : term,X26 : term > $o,X10 : term > $o,X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & (axidl <=> ! [X14 : subst] : ((comp @ id @ X14) = X14)) & (axshiftcons <=> ! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14)) & ((d2subst @ d_id) = sh) & hoasinduction_lem3b_gthm & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & hoaslamnotvar & (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X48 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,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))))) & hoasinduction_lem1_lthm & (! [X19 : term,X15 : term,X20 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20)) <=> hoasapinj2) & (pushprop_lem1v2 <=> ! [X10 : term > $o,X11 : term > $o,X14 : subst,X13 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | (X11 @ one) | ~(X10 @ X13))) & (induction2 <=> ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))) & hoasinduction_lem1_gthm & axmap & pushprop_lthm & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13))) & pushprop_gthm & pushprop_lem2v2 & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X10 : term > $o,X21 : term] : ((X10 @ X21) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13)))) => ! [X10 : term > $o,X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))))))))) & (! [X19 : term,X20 : term,X13 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) <=> apinj1) & hoaslamnotap_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)))) <=> substmonoid_lthm) & apnotvar & ((! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => (! [X10 : subst > term > subst > $o,X24 : term,X23 : term] : (~(X10 @ id @ X23 @ id) | ~! [X13 : term,X26 : subst,X25 : subst,X14 : 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 @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : subst > term > subst > $o,X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~! [X18 : subst > term > term] : ((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))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))))) <=> hoasinduction_lthm) & induction2lem_gthm & hoasinduction_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & pushprop & pushprop_lem1_gthm & induction2_gthm & hoasinduction_lem2_gthm & (pushprop_lem0 <=> ! [X14 : subst,X13 : term,X10 : term > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & hoaslamnotvar_lthm & (! [X10 : subst > term > subst > $o,X30 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ 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,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & (apinj2 <=> ! [X15 : term,X13 : term,X19 : term,X20 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20))) & pushprop_lem3v2_lthm & ~ulamvar1 & hoasapnotvar & ((^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one)) = hoaslam) & hoasapnotvar_lthm & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X13 : term,X20 : term,X19 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) => ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj1_lthm) & hoasinduction_lem3a_gthm & substmonoid_gthm & ((d2subst @ d_id) = id) & (induction2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : term > $o,X17 : subst,X16 : term] : (~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22))))) & (axscons <=> ! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & hoasinduction_lem2_lthm & axabs & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((! [X15 : term,X20 : term,X13 : term,X19 : term] : ((X19 = X20) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X15 : term,X19 : term,X13 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) <=> hoasapinj2_lthm) & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & (! [X13 : term,X15 : term] : (((sub @ X13 @ sh) != (sub @ X15 @ sh)) | (X13 = X15)) <=> shinj) & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X15 : term,X13 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15))) => ! [X18 : subst > term > term,X33 : term,X32 : subst,X31 : subst > term > term] : (((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) <=> hoaslaminj_lthm) & (! [X10 : term > $o,X14 : subst,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0_lthm) & axapp & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : term > $o,X45 : term,X10 : subst > term > subst > $o] : (~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~(X11 @ X44))) & ~(var @ (d2term @ d_one)) & hoasapinj1_gthm & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & (hoasinduction_lem3v2a <=> ! [X11 : term > $o,X29 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ 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)))) | (X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))))) & hoasinduction_lem1v2_gthm & hoasinduction_lem3_gthm & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ 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)) | (X11 @ (lam @ X29)) | ~! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X10 : subst > term > subst > $o,X30 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id) | ~! [X18 : subst > term > term] : (~! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X10 : term > $o,X15 : term,X14 : subst,X13 : term,X26 : term > $o] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & axassoc & (termmset <=> ! [X13 : term] : ((sub @ X13 @ id) = X13)) & hoasapnotvar_gthm & ulamvarsh & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X11 : term > $o,X48 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (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)))) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48))) <=> hoasinduction_lem3v2) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [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 @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : subst > term > subst > $o,X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~! [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)) | ~! [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)))) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) <=> hoasinduction_lem3_lthm) & ! [X1 : d_term] : (d_one = X1) & (! [X42 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : ((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))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) <=> hoasinduction_lem3aa) & (hoasinduction_lem0 <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X10 : term > $o,X14 : subst,X11 : term > $o,X13 : term] : ((X11 @ one) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | ~(X10 @ X13)))) & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & (induction <=> ! [X21 : term,X10 : term > $o] : (~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)))) & lamnotvar & (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))))))) & (hoaslaminj <=> ! [X33 : term,X18 : subst > term > term,X31 : subst > term > term,X32 : subst] : (((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) & pushprop_lem0_gthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & hoasinduction_lem2v2_gthm & (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] : ((X11 @ (lam @ X29)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))))) & hoaslamnotvar_gthm & (! [X15 : term,X13 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) <=> laminj) & ulamvarind & (substmonoid <=> (! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14))) & (hoasinduction <=> ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [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,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & ((^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) = hoasinduction_p_and_p_prime) & hoasinduction_lem3v2_gthm & (hoasinduction_lthm_3 <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : (~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ 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))))))))) & (! [X42 : term,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 @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (! [X47 : term,X46 : term,X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47))) <=> hoaslamnotap) & pushprop_lem2v2_gthm & axclos & (! [X17 : subst,X10 : term > $o,X16 : term] : (~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17))) <=> induction2lem) & (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ 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 @ (lam @ X27) @ id) | ~! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & (axidr <=> ! [X14 : subst] : ((comp @ X14 @ id) = X14)) & axvarshift),
% 42.64/7.44 file('/export/starexec/sandbox2/tmp/tmp.C6YnWq5B3d/DTF2THF_12223.p',alg444_1)).
% 42.64/7.44 thf(f1127,plain,(
% 42.64/7.44 ( ! [X152 : subst] : (((d2subst @ (sK531 @ X152)) = X152)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f3012,plain,(
% 42.64/7.44 (sK549 != (comp @ (d2subst @ d_id) @ (push @ sK550 @ sK549))) | spl591_279),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3010])).
% 42.64/7.44 thf(f3010,definition,(
% 42.64/7.44 spl591_279 <=> (sK549 = (comp @ (d2subst @ d_id) @ (push @ sK550 @ sK549)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_279])],[avatar_definition])).
% 42.64/7.44 thf(f6945,plain,(
% 42.64/7.44 ~spl591_196 | ~spl591_697),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f6944])).
% 42.64/7.44 thf(f6944,plain,(
% 42.64/7.44 $false | (~spl591_196 | ~spl591_697)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f1082,f6862])).
% 42.64/7.44 thf(f6862,plain,(
% 42.64/7.44 ( ! [X2 : term,X5 : subst > term > subst > $o] : (($true = (X5 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)))) ) | (~spl591_196 | ~spl591_697)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f6056,f6664])).
% 42.64/7.44 thf(f6056,plain,(
% 42.64/7.44 ( ! [X2 : term,X5 : subst > term > subst > $o] : (($true = (sK594 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X5 @ Y0 @ Y1 @ Y2))))))) @ X2)) | ($true = (X5 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)))) ) | ~spl591_196),
% 42.64/7.44 inference(not_proxy_clausification,[status(thm)],[f6055])).
% 42.64/7.44 thf(f6055,plain,(
% 42.64/7.44 ( ! [X2 : term,X5 : subst > term > subst > $o] : (((~ (X5 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id))) = $false) | ($true = (sK594 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X5 @ Y0 @ Y1 @ Y2))))))) @ X2))) ) | ~spl591_196),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f6041])).
% 42.64/7.44 thf(f6041,plain,(
% 42.64/7.44 ( ! [X2 : term,X5 : subst > term > subst > $o] : (($true = (sK594 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X5 @ Y0 @ Y1 @ Y2))))))) @ X2)) | ($false = ((^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X5 @ Y0 @ Y1 @ Y2))))))) @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)))) ) | ~spl591_196),
% 42.64/7.44 inference(primitive_instantiation,[status(thm)],[f2655])).
% 42.64/7.44 thf(f2655,plain,(
% 42.64/7.44 ( ! [X2 : term,X1 : subst > term > subst > $o] : (((X1 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) = $false) | ($true = (sK594 @ X1 @ X2))) ) | ~spl591_196),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2654])).
% 42.64/7.44 thf(f2654,definition,(
% 42.64/7.44 spl591_196 <=> ! [X2 : term,X1 : subst > term > subst > $o] : (((X1 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) = $false) | ($true = (sK594 @ X1 @ X2)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_196])],[avatar_definition])).
% 42.64/7.44 thf(f1082,plain,(
% 42.64/7.44 ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true)),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f6756,plain,(
% 42.64/7.44 ~spl591_341 | ~spl591_661),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f6755])).
% 42.64/7.44 thf(f6755,plain,(
% 42.64/7.44 $false | (~spl591_341 | ~spl591_661)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f3279,f6742])).
% 42.64/7.44 thf(f6742,plain,(
% 42.64/7.44 ( ! [X3 : term,X0 : term > $o,X4 : term] : (($true != (X0 @ X3)) | ($true != (X0 @ X4))) ) | ~spl591_661),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f6728])).
% 42.64/7.44 thf(f6728,plain,(
% 42.64/7.44 ( ! [X3 : term,X0 : term > $o,X4 : term] : (($true != (X0 @ X4)) | ($true = $false) | ($true != (X0 @ X3))) ) | ~spl591_661),
% 42.64/7.44 inference(backward_demodulation,[status(thm)],[f4949,f5250])).
% 42.64/7.44 thf(f5250,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($false = (X36 @ (d2term @ d_one)))) ) | ~spl591_661),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f5249])).
% 42.64/7.44 thf(f5249,definition,(
% 42.64/7.44 spl591_661 <=> ! [X36 : term > $o] : ($false = (X36 @ (d2term @ d_one)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_661])],[avatar_definition])).
% 42.64/7.44 thf(f4949,plain,(
% 42.64/7.44 ( ! [X3 : term,X0 : term > $o,X4 : term] : (($true != (X0 @ X4)) | ($true != (X0 @ X3)) | ($true = (X0 @ (d2term @ d_one)))) )),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f4845,f4896])).
% 42.64/7.44 thf(f4896,plain,(
% 42.64/7.44 ( ! [X0 : term > $o] : (($true = (X0 @ (d2term @ d_one))) | ($true = (sP40 @ X0))) )),
% 42.64/7.44 inference(backward_demodulation,[status(thm)],[f702,f4807])).
% 42.64/7.44 thf(f4807,plain,(
% 42.64/7.44 ( ! [X135 : term] : (((d2term @ d_one) = X135)) )),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f1145,f1155])).
% 42.64/7.44 thf(f1155,plain,(
% 42.64/7.44 ( ! [X114 : d_term] : ((d_one = X114)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f1145,plain,(
% 42.64/7.44 ( ! [X135 : term] : (((d2term @ (sK523 @ X135)) = X135)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f702,plain,(
% 42.64/7.44 ( ! [X0 : term > $o] : (((X0 @ (sK190 @ X0)) = $true) | ($true = (sP40 @ X0))) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f202])).
% 42.64/7.44 thf(f202,plain,(
% 42.64/7.44 ! [X0 : term > $o] : ((($true = (sP40 @ X0)) | (($true = (X0 @ (sK191 @ X0))) & ($true != (X0 @ (ap @ (sK190 @ X0) @ (sK191 @ X0)))) & ((X0 @ (sK190 @ X0)) = $true))) & (! [X3 : term,X4 : term] : (($true != (X0 @ X4)) | ($true = (X0 @ (ap @ X3 @ X4))) | ($true != (X0 @ X3))) | ($true != (sP40 @ X0))))),
% 42.64/7.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191])],[f200,f201])).
% 42.64/7.44 thf(f201,plain,(
% 42.64/7.44 ! [X0 : term > $o] : (? [X1 : term,X2 : term] : (($true = (X0 @ X2)) & ($true != (X0 @ (ap @ X1 @ X2))) & ($true = (X0 @ X1))) => (($true = (X0 @ (sK191 @ X0))) & ($true != (X0 @ (ap @ (sK190 @ X0) @ (sK191 @ X0)))) & ((X0 @ (sK190 @ X0)) = $true)))),
% 42.64/7.44 introduced(definition,[],[choice_axiom])).
% 42.64/7.44 thf(f200,plain,(
% 42.64/7.44 ! [X0 : term > $o] : ((($true = (sP40 @ X0)) | ? [X1 : term,X2 : term] : (($true = (X0 @ X2)) & ($true != (X0 @ (ap @ X1 @ X2))) & ($true = (X0 @ X1)))) & (! [X3 : term,X4 : term] : (($true != (X0 @ X4)) | ($true = (X0 @ (ap @ X3 @ X4))) | ($true != (X0 @ X3))) | ($true != (sP40 @ X0))))),
% 42.64/7.44 inference(rectify,[status(thm)],[f199])).
% 42.64/7.44 thf(f199,plain,(
% 42.64/7.44 ! [X308 : term > $o] : ((($true = (sP40 @ X308)) | ? [X311 : term,X312 : term] : (($true = (X308 @ X312)) & ($true != (X308 @ (ap @ X311 @ X312))) & ($true = (X308 @ X311)))) & (! [X311 : term,X312 : term] : (($true != (X308 @ X312)) | ($true = (X308 @ (ap @ X311 @ X312))) | ($true != (X308 @ X311))) | ($true != (sP40 @ X308))))),
% 42.64/7.44 inference(nnf_transformation,[status(thm)],[f54])).
% 42.64/7.44 thf(f4845,plain,(
% 42.64/7.44 ( ! [X3 : term,X0 : term > $o,X4 : term] : (($true != (sP40 @ X0)) | ($true = (X0 @ (d2term @ d_one))) | ($true != (X0 @ X4)) | ($true != (X0 @ X3))) )),
% 42.64/7.44 inference(backward_demodulation,[status(thm)],[f701,f4807])).
% 42.64/7.44 thf(f701,plain,(
% 42.64/7.44 ( ! [X3 : term,X0 : term > $o,X4 : term] : (($true != (X0 @ X3)) | ($true != (sP40 @ X0)) | ($true != (X0 @ X4)) | ($true = (X0 @ (ap @ X3 @ X4)))) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f202])).
% 42.64/7.44 thf(f3279,plain,(
% 42.64/7.44 ((sK551 @ sK554) = $true) | ~spl591_341),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3277])).
% 42.64/7.44 thf(f3277,definition,(
% 42.64/7.44 spl591_341 <=> ((sK551 @ sK554) = $true)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_341])],[avatar_definition])).
% 42.64/7.44 thf(f6665,plain,(
% 42.64/7.44 spl591_645 | spl591_697 | ~spl591_278),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f6264,f3007,f6663,f5046])).
% 42.64/7.44 thf(f5046,definition,(
% 42.64/7.44 spl591_645 <=> ! [X125 : term > $o] : ($true = (X125 @ (d2term @ d_one)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_645])],[avatar_definition])).
% 42.64/7.44 thf(f3007,definition,(
% 42.64/7.44 spl591_278 <=> ! [X189 : term,X188 : subst,X187 : term,X186 : term > $o,X190 : term > $o] : (($true != (X186 @ X189)) | ($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188)))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_278])],[avatar_definition])).
% 42.64/7.44 thf(f6264,plain,(
% 42.64/7.44 ( ! [X189 : term,X186 : term > $o,X190 : term > $o] : (((X190 @ (d2term @ d_one)) = $true) | ($true != (X186 @ X189))) ) | ~spl591_278),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f3008,f4807])).
% 42.64/7.44 thf(f3008,plain,(
% 42.64/7.44 ( ! [X188 : subst,X189 : term,X186 : term > $o,X187 : term,X190 : term > $o] : (($true != (X186 @ X189)) | ($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188))))) ) | ~spl591_278),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3007])).
% 42.64/7.44 thf(f6606,plain,(
% 42.64/7.44 spl591_645 | ~spl591_178 | ~spl591_660),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f6605,f5245,f2576,f5046])).
% 42.64/7.44 thf(f2576,definition,(
% 42.64/7.44 spl591_178 <=> ! [X36 : term > $o] : (($true = (sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id))) | ($true = (X36 @ (sK475 @ X36))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_178])],[avatar_definition])).
% 42.64/7.44 thf(f5245,definition,(
% 42.64/7.44 spl591_660 <=> ((sK474 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $false)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_660])],[avatar_definition])).
% 42.64/7.44 thf(f6605,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($true = (X36 @ (d2term @ d_one)))) ) | (~spl591_178 | ~spl591_660)),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f6604])).
% 42.64/7.44 thf(f6604,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($true = $false) | ($true = (X36 @ (d2term @ d_one)))) ) | (~spl591_178 | ~spl591_660)),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f6603,f5247])).
% 42.64/7.44 thf(f5247,plain,(
% 42.64/7.44 ((sK474 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $false) | ~spl591_660),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f5245])).
% 42.64/7.44 thf(f6603,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($true = (X36 @ (d2term @ d_one))) | ((sK474 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) ) | ~spl591_178),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f6602,f4807])).
% 42.64/7.44 thf(f6602,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($true = (sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id))) | ($true = (X36 @ (d2term @ d_one)))) ) | ~spl591_178),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f2577,f4807])).
% 42.64/7.44 thf(f2577,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($true = (X36 @ (sK475 @ X36))) | ($true = (sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id)))) ) | ~spl591_178),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2576])).
% 42.64/7.44 thf(f6458,plain,(
% 42.64/7.44 ~spl591_645),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f6457])).
% 42.64/7.44 thf(f6457,plain,(
% 42.64/7.44 $false | ~spl591_645),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f6456])).
% 42.64/7.44 thf(f6456,plain,(
% 42.64/7.44 ($true = $false) | ~spl591_645),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f6382])).
% 42.64/7.44 thf(f6382,plain,(
% 42.64/7.44 ($true = ((^[Y0 : term]: ($false)) @ (d2term @ d_one))) | ~spl591_645),
% 42.64/7.44 inference(primitive_instantiation,[status(thm)],[f5047])).
% 42.64/7.44 thf(f5047,plain,(
% 42.64/7.44 ( ! [X125 : term > $o] : (($true = (X125 @ (d2term @ d_one)))) ) | ~spl591_645),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f5046])).
% 42.64/7.44 thf(f6210,plain,(
% 42.64/7.44 spl591_220),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f6209])).
% 42.64/7.44 thf(f6209,plain,(
% 42.64/7.44 $false | spl591_220),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f6182,f6114])).
% 42.64/7.44 thf(f6114,plain,(
% 42.64/7.44 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 42.64/7.44 inference(superposition,[status(thm)],[f4807,f4807])).
% 42.64/7.44 thf(f6182,plain,(
% 42.64/7.44 ( ! [X0 : term] : ((sK583 != X0)) ) | spl591_220),
% 42.64/7.44 inference(superposition,[status(thm)],[f2760,f6114])).
% 42.64/7.44 thf(f2760,plain,(
% 42.64/7.44 (sK584 != sK583) | spl591_220),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2758])).
% 42.64/7.44 thf(f2758,definition,(
% 42.64/7.44 spl591_220 <=> (sK584 = sK583)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_220])],[avatar_definition])).
% 42.64/7.44 thf(f5958,plain,(
% 42.64/7.44 ~spl591_686 | ~spl591_687),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f5957])).
% 42.64/7.44 thf(f5957,plain,(
% 42.64/7.44 $false | (~spl591_686 | ~spl591_687)),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f5956])).
% 42.64/7.44 thf(f5956,plain,(
% 42.64/7.44 ($true = $false) | (~spl591_686 | ~spl591_687)),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f5907,f5885])).
% 42.64/7.44 thf(f5885,plain,(
% 42.64/7.44 ($false = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ~spl591_686),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f5883])).
% 42.64/7.44 thf(f5883,definition,(
% 42.64/7.44 spl591_686 <=> ($false = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_686])],[avatar_definition])).
% 42.64/7.44 thf(f5907,plain,(
% 42.64/7.44 ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ~spl591_687),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f5905])).
% 42.64/7.44 thf(f5905,definition,(
% 42.64/7.44 spl591_687 <=> ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_687])],[avatar_definition])).
% 42.64/7.44 thf(f5908,plain,(
% 42.64/7.44 spl591_687 | spl591_645 | ~spl591_197),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f5903,f2658,f5046,f5905])).
% 42.64/7.44 thf(f5903,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($true = (X1 @ (d2term @ d_one))) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) ) | ~spl591_197),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f5902,f4807])).
% 42.64/7.44 thf(f5902,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (X1 @ (sK593 @ X1)))) ) | ~spl591_197),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f2659,f4807])).
% 42.64/7.44 thf(f5886,plain,(
% 42.64/7.44 spl591_686 | spl591_661 | ~spl591_199),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f5881,f2666,f5249,f5883])).
% 42.64/7.44 thf(f2666,definition,(
% 42.64/7.44 spl591_199 <=> ! [X1 : term > $o] : (((sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)) = $false) | ((X1 @ (sK593 @ X1)) = $false))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_199])],[avatar_definition])).
% 42.64/7.44 thf(f5881,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($false = (X1 @ (d2term @ d_one))) | ($false = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) ) | ~spl591_199),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f5880,f4807])).
% 42.64/7.44 thf(f5880,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($false = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X1 @ (sK593 @ X1)) = $false)) ) | ~spl591_199),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f2667,f4807])).
% 42.64/7.44 thf(f2667,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (((sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)) = $false) | ((X1 @ (sK593 @ X1)) = $false)) ) | ~spl591_199),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2666])).
% 42.64/7.44 thf(f5707,plain,(
% 42.64/7.44 ~spl591_177 | ~spl591_198),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f5706])).
% 42.64/7.44 thf(f5706,plain,(
% 42.64/7.44 $false | (~spl591_177 | ~spl591_198)),
% 42.64/7.44 inference(trivial_inequality_removal,[status(thm)],[f5705])).
% 42.64/7.44 thf(f5705,plain,(
% 42.64/7.44 ($true = $false) | (~spl591_177 | ~spl591_198)),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f2574,f2663])).
% 42.64/7.44 thf(f2663,plain,(
% 42.64/7.44 (hoasinduction_lem0 = $false) | ~spl591_198),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2661])).
% 42.64/7.44 thf(f2661,definition,(
% 42.64/7.44 spl591_198 <=> (hoasinduction_lem0 = $false)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_198])],[avatar_definition])).
% 42.64/7.44 thf(f2574,plain,(
% 42.64/7.44 (hoasinduction_lem0 = $true) | ~spl591_177),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2572])).
% 42.64/7.44 thf(f2572,definition,(
% 42.64/7.44 spl591_177 <=> (hoasinduction_lem0 = $true)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_177])],[avatar_definition])).
% 42.64/7.44 thf(f5631,plain,(
% 42.64/7.44 spl591_277 | ~spl591_380),
% 42.64/7.44 inference(avatar_contradiction_clause,[status(thm)],[f5630])).
% 42.64/7.44 thf(f5630,plain,(
% 42.64/7.44 $false | (spl591_277 | ~spl591_380)),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f3005,f5616])).
% 42.64/7.44 thf(f5616,plain,(
% 42.64/7.44 ( ! [X259 : term,X258 : term] : ((X258 = X259)) ) | ~spl591_380),
% 42.64/7.44 inference(subsumption_resolution,[status(thm)],[f5615,f4807])).
% 42.64/7.44 thf(f5615,plain,(
% 42.64/7.44 ( ! [X259 : term,X258 : term] : (((d2term @ d_one) != (sub @ X258 @ (d2subst @ d_id))) | (X258 = X259)) ) | ~spl591_380),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f3449,f4807])).
% 42.64/7.44 thf(f3449,plain,(
% 42.64/7.44 ( ! [X259 : term,X258 : term] : (((sub @ X258 @ (d2subst @ d_id)) != (sub @ X259 @ (d2subst @ d_id))) | (X258 = X259)) ) | ~spl591_380),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3448])).
% 42.64/7.44 thf(f3448,definition,(
% 42.64/7.44 spl591_380 <=> ! [X259 : term,X258 : term] : ((X258 = X259) | ((sub @ X258 @ (d2subst @ d_id)) != (sub @ X259 @ (d2subst @ d_id))))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_380])],[avatar_definition])).
% 42.64/7.44 thf(f3005,plain,(
% 42.64/7.44 (sK547 != (sub @ (d2term @ d_one) @ (push @ sK547 @ sK548))) | spl591_277),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f3003])).
% 42.64/7.44 thf(f3003,definition,(
% 42.64/7.44 spl591_277 <=> (sK547 = (sub @ (d2term @ d_one) @ (push @ sK547 @ sK548)))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_277])],[avatar_definition])).
% 42.64/7.44 thf(f5251,plain,(
% 42.64/7.44 spl591_660 | spl591_661 | ~spl591_179),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f5243,f2580,f5249,f5245])).
% 42.64/7.44 thf(f2580,definition,(
% 42.64/7.44 spl591_179 <=> ! [X36 : term > $o] : (($false = (X36 @ (sK475 @ X36))) | ((sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id)) = $false))),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_179])],[avatar_definition])).
% 42.64/7.44 thf(f5243,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($false = (X36 @ (d2term @ d_one))) | ((sK474 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $false)) ) | ~spl591_179),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f5242,f4807])).
% 42.64/7.44 thf(f5242,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (((sK474 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $false) | ($false = (X36 @ (sK475 @ X36)))) ) | ~spl591_179),
% 42.64/7.44 inference(forward_demodulation,[status(thm)],[f2581,f4807])).
% 42.64/7.44 thf(f2581,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($false = (X36 @ (sK475 @ X36))) | ((sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id)) = $false)) ) | ~spl591_179),
% 42.64/7.44 inference(avatar_component_clause,[status(thm)],[f2580])).
% 42.64/7.44 thf(f3991,plain,(
% 42.64/7.44 spl591_504 | ~spl591_177),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1691,f2572,f3989])).
% 42.64/7.44 thf(f1691,plain,(
% 42.64/7.44 ( ! [X34 : term,X32 : subst > term > subst > $o] : (($true = (sK473 @ X32 @ X34)) | (hoasinduction_lem0 != $true) | ($false = (X32 @ (d2subst @ d_id) @ X34 @ (d2subst @ d_id)))) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1603])).
% 42.64/7.44 thf(f1603,plain,(
% 42.64/7.44 ( ! [X34 : term,X32 : subst > term > subst > $o] : ((hoasinduction_lem0 != $true) | ((sK473 @ X32 @ X34) = (X32 @ (d2subst @ d_id) @ X34 @ (d2subst @ d_id)))) )),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1215,f1092,f1092])).
% 42.64/7.44 thf(f1092,plain,(
% 42.64/7.44 ((d2subst @ d_id) = id)),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f1215,plain,(
% 42.64/7.44 ( ! [X34 : term,X32 : subst > term > subst > $o] : (((sK473 @ X32 @ X34) = (X32 @ id @ X34 @ id)) | (hoasinduction_lem0 != $true)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f3450,plain,(
% 42.64/7.44 spl591_380 | ~spl591_221),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1648,f2762,f3448])).
% 42.64/7.44 thf(f2762,definition,(
% 42.64/7.44 spl591_221 <=> (shinj = $true)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_221])],[avatar_definition])).
% 42.64/7.44 thf(f1648,plain,(
% 42.64/7.44 ( ! [X259 : term,X258 : term] : ((shinj != $true) | (X258 = X259) | ((sub @ X258 @ (d2subst @ d_id)) != (sub @ X259 @ (d2subst @ d_id)))) )),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1053,f1200,f1200])).
% 42.64/7.44 thf(f1200,plain,(
% 42.64/7.44 ((d2subst @ d_id) = sh)),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f1053,plain,(
% 42.64/7.44 ( ! [X259 : term,X258 : term] : (((sub @ X259 @ sh) != (sub @ X258 @ sh)) | (X258 = X259) | (shinj != $true)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f3280,plain,(
% 42.64/7.44 spl591_341 | spl591_115),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1099,f2305,f3277])).
% 42.64/7.44 thf(f2305,definition,(
% 42.64/7.44 spl591_115 <=> (pushprop_lem1_lthm = $true)),
% 42.64/7.44 introduced(definition,[new_symbols(naming,[spl591_115])],[avatar_definition])).
% 42.64/7.44 thf(f1099,plain,(
% 42.64/7.44 (pushprop_lem1_lthm = $true) | ((sK551 @ sK554) = $true)),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f3013,plain,(
% 42.64/7.44 ~spl591_115 | ~spl591_277 | spl591_278 | ~spl591_279),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1631,f3010,f3007,f3003,f2305])).
% 42.64/7.44 thf(f1631,plain,(
% 42.64/7.44 ( ! [X188 : subst,X189 : term,X186 : term > $o,X187 : term,X190 : term > $o] : ((sK547 != (sub @ (d2term @ d_one) @ (push @ sK547 @ sK548))) | ($true != (X186 @ X189)) | ($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188)))) | (pushprop_lem1_lthm != $true) | (sK549 != (comp @ (d2subst @ d_id) @ (push @ sK550 @ sK549)))) )),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1101,f1201,f1200])).
% 42.64/7.44 thf(f1201,plain,(
% 42.64/7.44 (one = (d2term @ d_one))),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f1101,plain,(
% 42.64/7.44 ( ! [X188 : subst,X189 : term,X186 : term > $o,X187 : term,X190 : term > $o] : (($true = (X190 @ (sub @ X189 @ (push @ X187 @ X188)))) | ($true != (X186 @ X189)) | (sK547 != (sub @ one @ (push @ sK547 @ sK548))) | (sK549 != (comp @ sh @ (push @ sK550 @ sK549))) | (pushprop_lem1_lthm != $true)) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f2765,plain,(
% 42.64/7.44 ~spl591_220 | spl591_221),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1051,f2762,f2758])).
% 42.64/7.44 thf(f1051,plain,(
% 42.64/7.44 (shinj = $true) | (sK584 != sK583)),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f2668,plain,(
% 42.64/7.44 spl591_199 | spl591_198),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1786,f2661,f2666])).
% 42.64/7.44 thf(f1786,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : ((hoasinduction_lem0 = $false) | ((sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)) = $false) | ((X1 @ (sK593 @ X1)) = $false)) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1784])).
% 42.64/7.44 thf(f1784,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (((sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)) != (X1 @ (sK593 @ X1))) | (hoasinduction_lem0 = $false)) )),
% 42.64/7.44 inference(equality_proxy_clausification,[status(thm)],[f1783])).
% 42.64/7.44 thf(f1783,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : ((hoasinduction_lem0 = $false) | (((X1 @ (sK593 @ X1)) = (sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id))) = $false)) )),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1782])).
% 42.64/7.44 thf(f1782,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : ((((^[Y0 : term]: ((X1 @ Y0) = (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))) @ (sK593 @ X1)) = $false) | (hoasinduction_lem0 = $false)) )),
% 42.64/7.44 inference(sigma_clausification,[status(thm)],[f1781])).
% 42.64/7.44 thf(f1781,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : ((hoasinduction_lem0 = $false) | ((!! @ term @ (^[Y0 : term]: ((X1 @ Y0) = (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) = $false)) )),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1780])).
% 42.64/7.44 thf(f1780,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : (($false = ((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)))))) @ X1)) | (hoasinduction_lem0 = $false)) )),
% 42.64/7.44 inference(pi_clausification,[status(thm)],[f1779])).
% 42.64/7.44 thf(f1779,plain,(
% 42.64/7.44 (hoasinduction_lem0 = $false) | ($false = (?? @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))))))),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1778])).
% 42.64/7.44 thf(f1778,plain,(
% 42.64/7.44 ($false = ((^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)))))))) @ sK592)) | (hoasinduction_lem0 = $false)),
% 42.64/7.44 inference(sigma_clausification,[status(thm)],[f1777])).
% 42.64/7.44 thf(f1777,plain,(
% 42.64/7.44 ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))))))) = $false) | (hoasinduction_lem0 = $false)),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1775])).
% 42.64/7.44 thf(f1775,plain,(
% 42.64/7.44 (hoasinduction_lem0 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))))))))),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1658])).
% 42.64/7.44 thf(f1658,plain,(
% 42.64/7.44 (hoasinduction_lem0 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: ((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (d2subst @ d_id) @ Y4 @ (d2subst @ d_id)))))))) @ Y0 @ Y1))))))),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1260,f1261])).
% 42.64/7.44 thf(f1261,plain,(
% 42.64/7.44 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)))))))))),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1119,f1092,f1092])).
% 42.64/7.44 thf(f1119,plain,(
% 42.64/7.44 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id))))))))),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f1260,plain,(
% 42.64/7.44 (hoasinduction_lem0 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1))))))),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f9])).
% 42.64/7.44 thf(f9,plain,(
% 42.64/7.44 (hoasinduction_lem0 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1))))))),
% 42.64/7.44 inference(flattening,[status(thm)],[f6])).
% 42.64/7.44 thf(f6,plain,(
% 42.64/7.44 ~(hoasinduction_lem0 = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1))))))),
% 42.64/7.44 inference(fool_elimination,[status(thm)],[f5])).
% 42.64/7.44 thf(f5,plain,(
% 42.64/7.44 ~(! [X0 : subst > term > subst > $o] : ? [X1 : term > $o] : (hoasinduction_p_and_p_prime @ X0 @ X1) = hoasinduction_lem0)),
% 42.64/7.44 inference(rectify,[status(thm)],[f3])).
% 42.64/7.44 thf(f3,negated_conjecture,(
% 42.64/7.44 ~(! [X10 : subst > term > subst > $o] : ? [X11 : term > $o] : (hoasinduction_p_and_p_prime @ X10 @ X11) = hoasinduction_lem0)),
% 42.64/7.44 inference(negated_conjecture,[status(cth)],[f2])).
% 42.64/7.44 thf(f2,conjecture,(
% 42.64/7.44 (! [X10 : subst > term > subst > $o] : ? [X11 : term > $o] : (hoasinduction_p_and_p_prime @ X10 @ X11) = hoasinduction_lem0)),
% 42.64/7.44 file('/export/starexec/sandbox2/tmp/tmp.C6YnWq5B3d/DTF2THF_12223.p',hoasinduction_lem0)).
% 42.64/7.44 thf(f2664,plain,(
% 42.64/7.44 spl591_197 | spl591_198),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1785,f2661,f2658])).
% 42.64/7.44 thf(f1785,plain,(
% 42.64/7.44 ( ! [X1 : term > $o] : ((hoasinduction_lem0 = $false) | ($true = (X1 @ (sK593 @ X1))) | ($true = (sK592 @ (d2subst @ d_id) @ (sK593 @ X1) @ (d2subst @ d_id)))) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1784])).
% 42.64/7.44 thf(f2656,plain,(
% 42.64/7.44 spl591_177 | spl591_196),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1795,f2654,f2572])).
% 42.64/7.44 thf(f1795,plain,(
% 42.64/7.44 ( ! [X2 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem0 = $true) | ((X1 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) = $false) | ($true = (sK594 @ X1 @ X2))) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1793])).
% 42.64/7.44 thf(f1793,plain,(
% 42.64/7.44 ( ! [X2 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem0 = $true) | ((X1 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) = (sK594 @ X1 @ X2))) )),
% 42.64/7.44 inference(equality_proxy_clausification,[status(thm)],[f1792])).
% 42.64/7.44 thf(f1792,plain,(
% 42.64/7.44 ( ! [X2 : term,X1 : subst > term > subst > $o] : (($true = ((sK594 @ X1 @ X2) = (X1 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)))) | (hoasinduction_lem0 = $true)) )),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1791])).
% 42.64/7.44 thf(f1791,plain,(
% 42.64/7.44 ( ! [X2 : term,X1 : subst > term > subst > $o] : ((hoasinduction_lem0 = $true) | (((^[Y0 : term]: ((sK594 @ X1 @ Y0) = (X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))) @ X2) = $true)) )),
% 42.64/7.44 inference(pi_clausification,[status(thm)],[f1790])).
% 42.64/7.44 thf(f1790,plain,(
% 42.64/7.44 ( ! [X1 : subst > term > subst > $o] : ((hoasinduction_lem0 = $true) | ((!! @ term @ (^[Y0 : term]: ((sK594 @ X1 @ Y0) = (X1 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) = $true)) )),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1789])).
% 42.64/7.44 thf(f1789,plain,(
% 42.64/7.44 ( ! [X1 : subst > term > subst > $o] : ((hoasinduction_lem0 = $true) | ($true = ((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)))))) @ (sK594 @ X1)))) )),
% 42.64/7.44 inference(sigma_clausification,[status(thm)],[f1788])).
% 42.64/7.44 thf(f1788,plain,(
% 42.64/7.44 ( ! [X1 : subst > term > subst > $o] : (($true = (?? @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (X1 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)))))))) | (hoasinduction_lem0 = $true)) )),
% 42.64/7.44 inference(beta_eta_normalization,[status(thm)],[f1787])).
% 42.64/7.44 thf(f1787,plain,(
% 42.64/7.44 ( ! [X1 : subst > term > subst > $o] : ((((^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)))))))) @ X1) = $true) | (hoasinduction_lem0 = $true)) )),
% 42.64/7.44 inference(pi_clausification,[status(thm)],[f1776])).
% 42.64/7.44 thf(f1776,plain,(
% 42.64/7.44 (hoasinduction_lem0 = $true) | ($true = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))))))))),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1775])).
% 42.64/7.44 thf(f2582,plain,(
% 42.64/7.44 spl591_179 | spl591_177),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1799,f2572,f2580])).
% 42.64/7.44 thf(f1799,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : (($false = (X36 @ (sK475 @ X36))) | (hoasinduction_lem0 = $true) | ((sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id)) = $false)) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1604])).
% 42.64/7.44 thf(f1604,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : ((hoasinduction_lem0 = $true) | ((sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id)) != (X36 @ (sK475 @ X36)))) )),
% 42.64/7.44 inference(definition_unfolding,[status(thm)],[f1214,f1092,f1092])).
% 42.64/7.44 thf(f1214,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : ((hoasinduction_lem0 = $true) | ((sK474 @ id @ (sK475 @ X36) @ id) != (X36 @ (sK475 @ X36)))) )),
% 42.64/7.44 inference(cnf_transformation,[status(thm)],[f545])).
% 42.64/7.44 thf(f2578,plain,(
% 42.64/7.44 spl591_177 | spl591_178),
% 42.64/7.44 inference(avatar_split_clause,[status(thm)],[f1798,f2576,f2572])).
% 42.64/7.44 thf(f1798,plain,(
% 42.64/7.44 ( ! [X36 : term > $o] : ((hoasinduction_lem0 = $true) | ($true = (sK474 @ (d2subst @ d_id) @ (sK475 @ X36) @ (d2subst @ d_id))) | ($true = (X36 @ (sK475 @ X36)))) )),
% 42.64/7.44 inference(binary_proxy_clausification,[status(thm)],[f1604])).
% 42.64/7.44 % SZS output end Proof for DTF2THF_12223
% 42.64/7.44 % (12633)------------------------------
% 42.64/7.44 % (12633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.64/7.44 % (12633)Termination reason: Refutation
% 42.64/7.44
% 42.64/7.44 % (12633)Memory used [KB]: 14583
% 42.64/7.44 % (12633)Time elapsed: 0.892 s
% 42.64/7.44 % (12633)Instructions burned: 1742 (million)
% 42.64/7.44 % (12633)------------------------------
% 42.64/7.44 % (12633)------------------------------
% 42.64/7.44 % (12425)Success in time 5.911 s
%------------------------------------------------------------------------------