%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 1.70s 1.50s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 195
% Syntax : Number of formulae : 231 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 11588 (5527 equ; 0 cnn)
% Maximal formula atoms : 530 ( 50 avg)
% Number of connectives : 26732 (3108 ~;2802 |;2445 &;17507 @)
% ( 563 <=>; 285 =>; 0 <=; 2 <~>)
% Maximal formula depth : 187 ( 15 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2194 (2194 >; 0 *; 0 +; 0 <<)
% Number of symbols : 786 ( 782 usr; 304 con; 0-4 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 5929 ( 184 ^;4357 !;1388 ?;5929 :)
% 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_141,type,
sP0: ( subst > term > subst > $o ) > $o ).
thf(func_def_143,type,
sP2: ( subst > term > subst > $o ) > $o ).
thf(func_def_144,type,
sP3: ( subst > term > subst > $o ) > $o ).
thf(func_def_147,type,
sP6: ( subst > term > subst > $o ) > $o ).
thf(func_def_148,type,
sP7: ( subst > term > subst > $o ) > $o ).
thf(func_def_149,type,
sP8: ( subst > term > subst > $o ) > $o ).
thf(func_def_150,type,
sP9: ( subst > term > subst > $o ) > $o ).
thf(func_def_151,type,
sP10: ( subst > term > subst > $o ) > $o ).
thf(func_def_152,type,
sP11: term > ( subst > term > subst > $o ) > $o ).
thf(func_def_153,type,
sP12: ( subst > term > subst > $o ) > $o ).
thf(func_def_154,type,
sP13: ( subst > term > subst > $o ) > $o ).
thf(func_def_155,type,
sP14: ( subst > term > subst > $o ) > $o ).
thf(func_def_156,type,
sP15: ( term > $o ) > $o ).
thf(func_def_157,type,
sP16: ( term > $o ) > $o ).
thf(func_def_158,type,
sP17: ( term > $o ) > $o ).
thf(func_def_163,type,
sP22: ( subst > term > subst > $o ) > $o ).
thf(func_def_164,type,
sP23: ( subst > term > subst > $o ) > $o ).
thf(func_def_165,type,
sP24: term > ( term > $o ) > $o ).
thf(func_def_167,type,
sP26: ( term > $o ) > $o ).
thf(func_def_168,type,
sP27: ( term > $o ) > $o ).
thf(func_def_170,type,
sP29: ( subst > term > subst > $o ) > $o ).
thf(func_def_171,type,
sP30: ( subst > term > subst > $o ) > $o ).
thf(func_def_172,type,
sP31: ( subst > term > subst > $o ) > $o ).
thf(func_def_173,type,
sP32: ( term > $o ) > $o ).
thf(func_def_174,type,
sP33: ( term > $o ) > $o ).
thf(func_def_175,type,
sP34: ( term > $o ) > $o ).
thf(func_def_176,type,
sP35: ( subst > term > subst > $o ) > $o ).
thf(func_def_177,type,
sP36: ( subst > term > subst > $o ) > $o ).
thf(func_def_178,type,
sP37: ( subst > term > subst > $o ) > $o ).
thf(func_def_179,type,
sP38: ( subst > term > subst > $o ) > $o ).
thf(func_def_183,type,
sP42: ( subst > term > subst > $o ) > $o ).
thf(func_def_184,type,
sP43: ( subst > term > subst > $o ) > $o ).
thf(func_def_185,type,
sP44: ( subst > term > subst > $o ) > $o ).
thf(func_def_186,type,
sP45: ( subst > term > subst > $o ) > $o ).
thf(func_def_189,type,
sP48: ( subst > term > subst > $o ) > $o ).
thf(func_def_190,type,
sP49: ( subst > term > subst > $o ) > $o ).
thf(func_def_192,type,
sP51: ( term > $o ) > $o ).
thf(func_def_193,type,
sP52: ( term > $o ) > $o ).
thf(func_def_194,type,
sP53: ( term > $o ) > $o ).
thf(func_def_195,type,
sP54: ( term > $o ) > $o ).
thf(func_def_200,type,
sP59: ( subst > term > subst > $o ) > $o ).
thf(func_def_202,type,
sP61: ( term > $o ) > $o ).
thf(func_def_203,type,
sP62: ( term > $o ) > $o ).
thf(func_def_204,type,
sP63: ( term > $o ) > $o ).
thf(func_def_205,type,
sP64: ( term > $o ) > $o ).
thf(func_def_208,type,
sP67: ( term > $o ) > $o ).
thf(func_def_209,type,
sP68: ( term > $o ) > $o ).
thf(func_def_211,type,
sP70: ( subst > term > subst > $o ) > $o ).
thf(func_def_212,type,
sP71: ( subst > term > subst > $o ) > $o ).
thf(func_def_213,type,
sP72: ( subst > term > subst > $o ) > $o ).
thf(func_def_214,type,
sP73: ( term > $o ) > $o ).
thf(func_def_215,type,
sP74: ( term > $o ) > $o ).
thf(func_def_219,type,
sP78: ( subst > term > subst > $o ) > $o ).
thf(func_def_220,type,
sP79: ( subst > term > subst > $o ) > $o ).
thf(func_def_221,type,
sP80: ( term > $o ) > term > $o ).
thf(func_def_223,type,
sP82: ( subst > term > subst > $o ) > $o ).
thf(func_def_224,type,
sP83: ( subst > term > subst > $o ) > $o ).
thf(func_def_228,type,
sP87: ( subst > term > subst > $o ) > $o ).
thf(func_def_230,type,
sP89: ( subst > term > subst > $o ) > $o ).
thf(func_def_232,type,
sP91: ( subst > term > subst > $o ) > $o ).
thf(func_def_233,type,
sP92: ( subst > term > subst > $o ) > $o ).
thf(func_def_234,type,
sP93: ( subst > term > subst > $o ) > $o ).
thf(func_def_237,type,
sP96: ( term > $o ) > $o ).
thf(func_def_238,type,
sP97: ( term > $o ) > $o ).
thf(func_def_242,type,
sP101: ( subst > term > subst > $o ) > $o ).
thf(func_def_244,type,
sP103: ( subst > term > subst > $o ) > $o ).
thf(func_def_246,type,
sP105: ( subst > term > subst > $o ) > $o ).
thf(func_def_247,type,
sP106: ( subst > term > subst > $o ) > $o ).
thf(func_def_248,type,
sP107: ( subst > term > subst > $o ) > $o ).
thf(func_def_249,type,
sP108: ( subst > term > subst > $o ) > $o ).
thf(func_def_251,type,
sK110: subst > term > term ).
thf(func_def_252,type,
sK111: subst > term > term ).
thf(func_def_253,type,
sK112: subst ).
thf(func_def_254,type,
sK113: term ).
thf(func_def_255,type,
sK114: ( subst > term > term ) > subst ).
thf(func_def_256,type,
sK115: ( subst > term > term ) > subst ).
thf(func_def_257,type,
sK116: ( subst > term > term ) > term ).
thf(func_def_258,type,
sK117: ( subst > term > term ) > subst ).
thf(func_def_259,type,
sK118: ( subst > term > term ) > subst ).
thf(func_def_260,type,
sK119: ( subst > term > term ) > term ).
thf(func_def_261,type,
sK120: term ).
thf(func_def_262,type,
sK121: subst > term > subst > $o ).
thf(func_def_263,type,
sK122: ( subst > term > subst > $o ) > term ).
thf(func_def_264,type,
sK123: ( subst > term > subst > $o ) > subst ).
thf(func_def_265,type,
sK124: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_267,type,
sK126: ( subst > term > subst > $o ) > term ).
thf(func_def_268,type,
sK127: ( subst > term > subst > $o ) > term ).
thf(func_def_269,type,
sK128: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK131: ( subst > term > subst > $o ) > term ).
thf(func_def_273,type,
sK132: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK133: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK134: ( subst > term > term ) > term ).
thf(func_def_276,type,
sK135: ( subst > term > term ) > subst ).
thf(func_def_277,type,
sK136: ( subst > term > term ) > subst ).
thf(func_def_278,type,
sK137: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_279,type,
sK138: term ).
thf(func_def_280,type,
sK139: subst > term > subst > $o ).
thf(func_def_281,type,
sK140: ( subst > term > subst > $o ) > term > term ).
thf(func_def_282,type,
sK141: ( subst > term > term ) > term > subst ).
thf(func_def_283,type,
sK142: ( subst > term > term ) > term > term ).
thf(func_def_284,type,
sK143: ( subst > term > term ) > term > subst ).
thf(func_def_285,type,
sK144: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_286,type,
sK145: ( subst > term > term ) > term > subst ).
thf(func_def_287,type,
sK146: ( subst > term > term ) > term > term ).
thf(func_def_288,type,
sK147: ( subst > term > term ) > term > subst ).
thf(func_def_289,type,
sK148: ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK149: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_291,type,
sK150: term ).
thf(func_def_292,type,
sK151: subst > term > subst > $o ).
thf(func_def_293,type,
sK152: term > $o ).
thf(func_def_294,type,
sK153: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_295,type,
sK154: ( term > $o ) > term > term ).
thf(func_def_296,type,
sK155: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_297,type,
sK156: ( subst > term > term ) > term ).
thf(func_def_298,type,
sK157: ( subst > term > term ) > subst ).
thf(func_def_299,type,
sK158: ( subst > term > term ) > subst ).
thf(func_def_300,type,
sK159: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_301,type,
sK160: term ).
thf(func_def_302,type,
sK161: term ).
thf(func_def_303,type,
sK162: term ).
thf(func_def_304,type,
sK163: term ).
thf(func_def_305,type,
sK164: term ).
thf(func_def_306,type,
sK165: term ).
thf(func_def_307,type,
sK166: term ).
thf(func_def_308,type,
sK167: term ).
thf(func_def_309,type,
sK168: term ).
thf(func_def_310,type,
sK169: subst ).
thf(func_def_311,type,
sK170: term ).
thf(func_def_312,type,
sK171: term > $o ).
thf(func_def_313,type,
sK172: ( term > $o ) > subst > term ).
thf(func_def_314,type,
sK173: ( term > $o ) > term ).
thf(func_def_315,type,
sK174: ( term > $o ) > term ).
thf(func_def_316,type,
sK175: term > ( term > $o ) > term ).
thf(func_def_317,type,
sK176: ( term > $o ) > term ).
thf(func_def_318,type,
sK177: subst ).
thf(func_def_319,type,
sK178: subst ).
thf(func_def_320,type,
sK179: subst ).
thf(func_def_321,type,
sK180: subst ).
thf(func_def_322,type,
sK181: subst > term > subst > $o ).
thf(func_def_323,type,
sK182: term ).
thf(func_def_324,type,
sK183: term > ( subst > term > subst > $o ) > term ).
thf(func_def_325,type,
sK184: ( subst > term > subst > $o ) > term ).
thf(func_def_326,type,
sK185: ( subst > term > subst > $o ) > subst ).
thf(func_def_327,type,
sK186: ( subst > term > subst > $o ) > subst ).
thf(func_def_328,type,
sK187: ( subst > term > subst > $o ) > subst ).
thf(func_def_329,type,
sK188: ( subst > term > subst > $o ) > term ).
thf(func_def_330,type,
sK189: ( subst > term > subst > $o ) > subst ).
thf(func_def_331,type,
sK190: ( subst > term > subst > $o ) > subst ).
thf(func_def_332,type,
sK191: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK192: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_334,type,
sK193: ( subst > term > term ) > term ).
thf(func_def_335,type,
sK194: ( subst > term > term ) > subst ).
thf(func_def_336,type,
sK195: ( subst > term > term ) > subst ).
thf(func_def_337,type,
sK196: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_338,type,
sK197: subst > term > subst > $o ).
thf(func_def_339,type,
sK198: term ).
thf(func_def_340,type,
sK199: term > ( subst > term > subst > $o ) > term ).
thf(func_def_341,type,
sK200: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_342,type,
sK201: ( subst > term > term ) > term ).
thf(func_def_343,type,
sK202: ( subst > term > term ) > subst ).
thf(func_def_344,type,
sK203: ( subst > term > term ) > subst ).
thf(func_def_345,type,
sK204: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_346,type,
sK205: term ).
thf(func_def_347,type,
sK206: subst > term > subst > $o ).
thf(func_def_348,type,
sK207: term > $o ).
thf(func_def_349,type,
sK208: ( term > $o ) > term > term ).
thf(func_def_350,type,
sK209: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_351,type,
sK210: ( subst > term > term ) > subst ).
thf(func_def_352,type,
sK211: ( subst > term > term ) > term ).
thf(func_def_353,type,
sK212: ( subst > term > term ) > subst ).
thf(func_def_354,type,
sK213: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_355,type,
sK214: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_356,type,
sK215: term ).
thf(func_def_357,type,
sK216: term ).
thf(func_def_358,type,
sK217: term ).
thf(func_def_359,type,
sK218: term ).
thf(func_def_360,type,
sK219: term ).
thf(func_def_361,type,
sK220: term ).
thf(func_def_362,type,
sK221: term ).
thf(func_def_363,type,
sK222: term ).
thf(func_def_364,type,
sK223: subst > term > subst > $o ).
thf(func_def_365,type,
sK224: term ).
thf(func_def_366,type,
sK225: term ).
thf(func_def_367,type,
sK226: term > $o ).
thf(func_def_368,type,
sK227: ( subst > term > subst > $o ) > term ).
thf(func_def_369,type,
sK228: ( subst > term > subst > $o ) > subst ).
thf(func_def_370,type,
sK229: ( subst > term > subst > $o ) > subst ).
thf(func_def_371,type,
sK230: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK231: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_373,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK233: ( subst > term > subst > $o ) > subst ).
thf(func_def_375,type,
sK234: ( subst > term > subst > $o ) > term ).
thf(func_def_376,type,
sK235: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK236: ( subst > term > subst > $o ) > term ).
thf(func_def_378,type,
sK237: ( subst > term > subst > $o ) > term ).
thf(func_def_379,type,
sK238: term > $o ).
thf(func_def_380,type,
sK239: term ).
thf(func_def_381,type,
sK240: subst > term > subst > $o ).
thf(func_def_382,type,
sK241: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_383,type,
sK242: ( subst > term > subst > $o ) > term ).
thf(func_def_384,type,
sK243: ( subst > term > subst > $o ) > subst ).
thf(func_def_385,type,
sK244: ( subst > term > subst > $o ) > subst ).
thf(func_def_386,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK246: ( term > $o ) > term > term ).
thf(func_def_388,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_389,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_390,type,
sK249: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK250: ( subst > term > subst > $o ) > term ).
thf(func_def_392,type,
sK251: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK252: ( subst > term > term ) > term ).
thf(func_def_394,type,
sK253: ( subst > term > term ) > subst ).
thf(func_def_395,type,
sK254: ( subst > term > term ) > subst ).
thf(func_def_396,type,
sK255: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_397,type,
sK256: ( term > $o ) > term ).
thf(func_def_398,type,
sK257: term ).
thf(func_def_399,type,
sK258: term > $o ).
thf(func_def_400,type,
sK259: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_401,type,
sK260: ( term > $o ) > term > term ).
thf(func_def_402,type,
sK261: subst > term > subst > $o ).
thf(func_def_403,type,
sK262: term ).
thf(func_def_404,type,
sK263: term > $o ).
thf(func_def_405,type,
sK264: term ).
thf(func_def_406,type,
sK265: subst > term > subst > $o ).
thf(func_def_407,type,
sK266: ( term > $o ) > term ).
thf(func_def_408,type,
sK267: term > ( term > $o ) > term ).
thf(func_def_409,type,
sK268: ( term > $o ) > term ).
thf(func_def_410,type,
sK269: ( term > $o ) > term ).
thf(func_def_411,type,
sK270: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_412,type,
sK271: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_413,type,
sK272: ( subst > term > term ) > subst ).
thf(func_def_414,type,
sK273: ( subst > term > term ) > term ).
thf(func_def_415,type,
sK274: ( subst > term > term ) > subst ).
thf(func_def_416,type,
sK275: ( subst > term > subst > $o ) > term ).
thf(func_def_417,type,
sK276: ( subst > term > subst > $o ) > term ).
thf(func_def_418,type,
sK277: ( subst > term > term ) > term ).
thf(func_def_419,type,
sK278: ( subst > term > term ) > subst ).
thf(func_def_420,type,
sK279: ( subst > term > term ) > subst ).
thf(func_def_421,type,
sK280: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_422,type,
sK281: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_423,type,
sK282: term ).
thf(func_def_424,type,
sK283: term > $o ).
thf(func_def_425,type,
sK284: ( term > $o ) > term ).
thf(func_def_426,type,
sK285: ( term > $o ) > term ).
thf(func_def_427,type,
sK286: ( term > $o ) > term ).
thf(func_def_428,type,
sK287: ( term > $o ) > term ).
thf(func_def_429,type,
sK288: ( term > $o ) > subst > term ).
thf(func_def_430,type,
sK289: term ).
thf(func_def_431,type,
sK290: subst ).
thf(func_def_432,type,
sK291: term > $o ).
thf(func_def_433,type,
sK292: term ).
thf(func_def_434,type,
sK293: term > $o ).
thf(func_def_435,type,
sK294: ( term > $o ) > term ).
thf(func_def_436,type,
sK295: ( term > $o ) > term ).
thf(func_def_437,type,
sK296: ( term > $o ) > term ).
thf(func_def_438,type,
sK297: term > ( term > $o ) > term ).
thf(func_def_439,type,
sK298: ( term > $o ) > term ).
thf(func_def_440,type,
sK299: ( term > $o ) > term ).
thf(func_def_441,type,
sK300: term > ( term > $o ) > term ).
thf(func_def_442,type,
sK301: ( term > $o ) > term ).
thf(func_def_443,type,
sK302: ( term > $o ) > term ).
thf(func_def_444,type,
sK303: subst > term > subst > $o ).
thf(func_def_445,type,
sK304: term ).
thf(func_def_446,type,
sK305: term > ( subst > term > subst > $o ) > term ).
thf(func_def_447,type,
sK306: ( subst > term > term ) > subst ).
thf(func_def_448,type,
sK307: ( subst > term > term ) > subst ).
thf(func_def_449,type,
sK308: ( subst > term > term ) > term ).
thf(func_def_450,type,
sK309: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_451,type,
sK310: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_452,type,
sK311: subst ).
thf(func_def_453,type,
sK312: term ).
thf(func_def_454,type,
sK313: term ).
thf(func_def_455,type,
sK314: term ).
thf(func_def_456,type,
sK315: term ).
thf(func_def_457,type,
sK316: subst ).
thf(func_def_458,type,
sK317: term ).
thf(func_def_459,type,
sK318: subst > term > term ).
thf(func_def_460,type,
sK319: subst ).
thf(func_def_461,type,
sK320: subst > term > term ).
thf(func_def_462,type,
sK321: ( subst > term > term ) > term ).
thf(func_def_463,type,
sK322: ( subst > term > term ) > subst ).
thf(func_def_464,type,
sK323: ( subst > term > term ) > subst ).
thf(func_def_465,type,
sK324: ( subst > term > term ) > subst ).
thf(func_def_466,type,
sK325: ( subst > term > term ) > subst ).
thf(func_def_467,type,
sK326: ( subst > term > term ) > term ).
thf(func_def_468,type,
sK327: ( term > $o ) > term ).
thf(func_def_469,type,
sK328: term ).
thf(func_def_470,type,
sK329: term > $o ).
thf(func_def_471,type,
sK330: subst ).
thf(func_def_472,type,
sK331: term ).
thf(func_def_473,type,
sK332: term > $o ).
thf(func_def_474,type,
sK333: ( term > $o ) > subst > term ).
thf(func_def_475,type,
sK334: ( term > $o ) > term ).
thf(func_def_476,type,
sK335: ( term > $o ) > term ).
thf(func_def_477,type,
sK336: ( term > $o ) > term ).
thf(func_def_478,type,
sK337: ( term > $o ) > term ).
thf(func_def_479,type,
sK338: ( term > $o ) > term ).
thf(func_def_480,type,
sK339: term > ( term > $o ) > term ).
thf(func_def_481,type,
sK340: ( term > $o ) > term ).
thf(func_def_482,type,
sK341: subst > term > subst > $o ).
thf(func_def_483,type,
sK342: term ).
thf(func_def_484,type,
sK343: term ).
thf(func_def_485,type,
sK344: ( subst > term > subst > $o ) > subst ).
thf(func_def_486,type,
sK345: ( subst > term > subst > $o ) > subst ).
thf(func_def_487,type,
sK346: ( subst > term > subst > $o ) > term ).
thf(func_def_488,type,
sK347: ( subst > term > subst > $o ) > subst ).
thf(func_def_489,type,
sK348: ( subst > term > subst > $o ) > subst ).
thf(func_def_490,type,
sK349: ( subst > term > subst > $o ) > term ).
thf(func_def_491,type,
sK350: ( subst > term > subst > $o ) > subst ).
thf(func_def_492,type,
sK351: ( subst > term > subst > $o ) > subst ).
thf(func_def_493,type,
sK352: ( subst > term > subst > $o ) > term ).
thf(func_def_494,type,
sK353: ( subst > term > subst > $o ) > term ).
thf(func_def_495,type,
sK354: term > ( subst > term > subst > $o ) > term ).
thf(func_def_496,type,
sK355: subst > term > subst > $o ).
thf(func_def_497,type,
sK356: term ).
thf(func_def_498,type,
sK357: subst > term > subst > $o ).
thf(func_def_499,type,
sK358: term ).
thf(func_def_500,type,
sK359: term > ( subst > term > subst > $o ) > term ).
thf(func_def_501,type,
sK360: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_502,type,
sK361: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_503,type,
sK362: ( subst > term > term ) > subst ).
thf(func_def_504,type,
sK363: ( subst > term > term ) > subst ).
thf(func_def_505,type,
sK364: ( subst > term > term ) > term ).
thf(func_def_506,type,
sK365: ( subst > term > subst > $o ) > subst ).
thf(func_def_507,type,
sK366: ( subst > term > subst > $o ) > subst ).
thf(func_def_508,type,
sK367: ( subst > term > subst > $o ) > term ).
thf(func_def_509,type,
sK368: ( subst > term > subst > $o ) > subst ).
thf(func_def_510,type,
sK369: ( subst > term > subst > $o ) > subst ).
thf(func_def_511,type,
sK370: ( subst > term > subst > $o ) > subst ).
thf(func_def_512,type,
sK371: ( subst > term > subst > $o ) > subst ).
thf(func_def_513,type,
sK372: ( subst > term > subst > $o ) > term ).
thf(func_def_514,type,
sK373: ( subst > term > term ) > term ).
thf(func_def_515,type,
sK374: ( subst > term > term ) > subst ).
thf(func_def_516,type,
sK375: ( subst > term > term ) > subst ).
thf(func_def_517,type,
sK376: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_518,type,
sK377: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_519,type,
sK378: term > $o ).
thf(func_def_520,type,
sK379: term ).
thf(func_def_521,type,
sK380: ( term > $o ) > term > term ).
thf(func_def_522,type,
sK381: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_523,type,
sK382: subst > term > subst > $o ).
thf(func_def_524,type,
sK383: term ).
thf(func_def_525,type,
sK384: term > $o ).
thf(func_def_526,type,
sK385: term ).
thf(func_def_527,type,
sK386: subst > term > subst > $o ).
thf(func_def_528,type,
sK387: ( subst > term > subst > $o ) > subst ).
thf(func_def_529,type,
sK388: ( subst > term > subst > $o ) > term ).
thf(func_def_530,type,
sK389: ( subst > term > subst > $o ) > subst ).
thf(func_def_531,type,
sK390: ( subst > term > subst > $o ) > subst ).
thf(func_def_532,type,
sK391: ( subst > term > subst > $o ) > term ).
thf(func_def_533,type,
sK392: ( subst > term > subst > $o ) > subst ).
thf(func_def_534,type,
sK393: ( subst > term > subst > $o ) > subst ).
thf(func_def_535,type,
sK394: ( subst > term > subst > $o ) > term ).
thf(func_def_536,type,
sK395: ( subst > term > subst > $o ) > subst ).
thf(func_def_537,type,
sK396: ( subst > term > subst > $o ) > term ).
thf(func_def_538,type,
sK397: ( subst > term > subst > $o ) > term ).
thf(func_def_539,type,
sK398: ( subst > term > term ) > term ).
thf(func_def_540,type,
sK399: ( subst > term > term ) > subst ).
thf(func_def_541,type,
sK400: ( subst > term > term ) > subst ).
thf(func_def_542,type,
sK401: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_543,type,
sK402: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_544,type,
sK403: ( term > $o ) > term ).
thf(func_def_545,type,
sK404: term > ( term > $o ) > term ).
thf(func_def_546,type,
sK405: ( term > $o ) > term ).
thf(func_def_547,type,
sK406: ( term > $o ) > term ).
thf(func_def_548,type,
sK407: ( term > $o ) > term ).
thf(func_def_549,type,
sK408: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_550,type,
sK409: ( subst > term > term ) > subst ).
thf(func_def_551,type,
sK410: ( subst > term > term ) > term ).
thf(func_def_552,type,
sK411: ( subst > term > term ) > subst ).
thf(func_def_553,type,
sK412: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_554,type,
sK413: ( subst > term > subst > $o ) > term ).
thf(func_def_555,type,
sK414: ( subst > term > subst > $o ) > term ).
thf(func_def_556,type,
sK415: ( subst > term > term ) > subst ).
thf(func_def_557,type,
sK416: ( subst > term > term ) > subst ).
thf(func_def_558,type,
sK417: ( subst > term > term ) > term ).
thf(func_def_559,type,
sK418: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_560,type,
sK419: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_561,type,
sK420: term > $o ).
thf(func_def_562,type,
sK421: term ).
thf(func_def_563,type,
sK422: ( term > $o ) > term ).
thf(func_def_564,type,
sK423: ( term > $o ) > term ).
thf(func_def_565,type,
sK424: ( term > $o ) > term ).
thf(func_def_566,type,
sK425: term > ( term > $o ) > term ).
thf(func_def_567,type,
sK426: ( term > $o ) > term ).
thf(func_def_568,type,
sK427: subst > term > subst > $o ).
thf(func_def_569,type,
sK428: term ).
thf(func_def_570,type,
sK429: term > $o ).
thf(func_def_571,type,
sK430: ( subst > term > subst > $o ) > subst ).
thf(func_def_572,type,
sK431: ( subst > term > subst > $o ) > term ).
thf(func_def_573,type,
sK432: ( subst > term > subst > $o ) > subst ).
thf(func_def_574,type,
sK433: ( subst > term > subst > $o ) > subst ).
thf(func_def_575,type,
sK434: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_576,type,
sK435: term > ( term > $o ) > term ).
thf(func_def_577,type,
sK436: ( subst > term > subst > $o ) > subst ).
thf(func_def_578,type,
sK437: ( subst > term > subst > $o ) > subst ).
thf(func_def_579,type,
sK438: ( subst > term > subst > $o ) > subst ).
thf(func_def_580,type,
sK439: ( subst > term > subst > $o ) > term ).
thf(func_def_581,type,
sK440: ( subst > term > term ) > subst ).
thf(func_def_582,type,
sK441: ( subst > term > term ) > subst ).
thf(func_def_583,type,
sK442: ( subst > term > term ) > term ).
thf(func_def_584,type,
sK443: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_585,type,
sK444: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_586,type,
sK445: term > $o ).
thf(func_def_587,type,
sK446: term ).
thf(func_def_588,type,
sK447: ( subst > term > subst > $o ) > subst ).
thf(func_def_589,type,
sK448: ( subst > term > subst > $o ) > subst ).
thf(func_def_590,type,
sK449: ( subst > term > subst > $o ) > term ).
thf(func_def_591,type,
sK450: ( subst > term > subst > $o ) > subst ).
thf(func_def_592,type,
sK451: term ).
thf(func_def_593,type,
sK452: subst > term > subst > $o ).
thf(func_def_594,type,
sK453: term ).
thf(func_def_595,type,
sK454: ( subst > term > subst > $o ) > subst ).
thf(func_def_596,type,
sK455: ( subst > term > subst > $o ) > term ).
thf(func_def_597,type,
sK456: ( subst > term > subst > $o ) > subst ).
thf(func_def_598,type,
sK457: ( subst > term > subst > $o ) > subst ).
thf(func_def_599,type,
sK458: subst > term > subst > $o ).
thf(func_def_600,type,
sK459: term ).
thf(func_def_601,type,
sK460: subst > term > subst > $o ).
thf(func_def_602,type,
sK461: term ).
thf(func_def_603,type,
sK462: ( subst > term > subst > $o ) > subst ).
thf(func_def_604,type,
sK463: ( subst > term > subst > $o ) > subst ).
thf(func_def_605,type,
sK464: ( subst > term > subst > $o ) > subst ).
thf(func_def_606,type,
sK465: ( subst > term > subst > $o ) > term ).
thf(func_def_607,type,
sK466: ( term > $o ) > term ).
thf(func_def_608,type,
sK467: term > ( term > $o ) > term ).
thf(func_def_609,type,
sK468: ( term > $o ) > term ).
thf(func_def_610,type,
sK469: ( term > $o ) > term ).
thf(func_def_611,type,
sK470: ( term > $o ) > term ).
thf(func_def_612,type,
sK471: ( subst > term > subst > $o ) > term ).
thf(func_def_613,type,
sK472: ( subst > term > subst > $o ) > subst ).
thf(func_def_614,type,
sK473: ( subst > term > subst > $o ) > subst ).
thf(func_def_615,type,
sK474: ( subst > term > subst > $o ) > subst ).
thf(func_def_616,type,
sK475: ( subst > term > subst > $o ) > term ).
thf(func_def_617,type,
sK476: ( subst > term > subst > $o ) > term ).
thf(func_def_618,type,
sK477: ( subst > term > subst > $o ) > subst ).
thf(func_def_619,type,
sK478: ( subst > term > subst > $o ) > term ).
thf(func_def_620,type,
sK479: ( subst > term > subst > $o ) > subst ).
thf(func_def_621,type,
sK480: ( subst > term > subst > $o ) > subst ).
thf(func_def_622,type,
sK481: term > ( subst > term > subst > $o ) > term ).
thf(func_def_623,type,
sK482: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_624,type,
sK483: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_625,type,
sK484: ( subst > term > term ) > subst ).
thf(func_def_626,type,
sK485: ( subst > term > term ) > term ).
thf(func_def_627,type,
sK486: ( subst > term > term ) > subst ).
thf(func_def_628,type,
sK487: ( subst > term > subst > $o ) > term ).
thf(func_def_629,type,
sK488: ( subst > term > subst > $o ) > subst ).
thf(func_def_630,type,
sK489: ( subst > term > subst > $o ) > subst ).
thf(func_def_631,type,
sK490: ( subst > term > subst > $o ) > subst ).
thf(func_def_632,type,
sK491: ( subst > term > subst > $o ) > term ).
thf(func_def_633,type,
sK492: ( subst > term > subst > $o ) > term ).
thf(func_def_634,type,
sK493: ( subst > term > subst > $o ) > term ).
thf(func_def_635,type,
sK494: ( subst > term > term ) > subst ).
thf(func_def_636,type,
sK495: ( subst > term > term ) > term ).
thf(func_def_637,type,
sK496: ( subst > term > term ) > subst ).
thf(func_def_638,type,
sK497: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_639,type,
sK498: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_640,type,
sK499: term > ( subst > term > subst > $o ) > term ).
thf(func_def_641,type,
sK500: subst > term > subst > $o ).
thf(func_def_642,type,
sK501: term ).
thf(func_def_643,type,
sK502: term ).
thf(func_def_644,type,
sK503: subst > term > subst > $o ).
thf(func_def_645,type,
sK504: ( subst > term > subst > $o ) > term > term ).
thf(func_def_646,type,
sK505: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_647,type,
sK506: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_648,type,
sK507: ( subst > term > term ) > term ).
thf(func_def_649,type,
sK508: ( subst > term > term ) > subst ).
thf(func_def_650,type,
sK509: ( subst > term > term ) > subst ).
thf(func_def_651,type,
sK510: ( subst > term > term ) > term ).
thf(func_def_652,type,
sK511: ( subst > term > term ) > subst ).
thf(func_def_653,type,
sK512: ( subst > term > term ) > subst ).
thf(func_def_654,type,
sK513: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_655,type,
sK514: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_656,type,
sK515: term ).
thf(func_def_657,type,
sK516: subst > term > subst > $o ).
thf(func_def_658,type,
sK517: ( subst > term > subst > $o ) > term > term ).
thf(func_def_659,type,
sK518: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_660,type,
sK519: ( subst > term > term ) > subst ).
thf(func_def_661,type,
sK520: ( subst > term > term ) > term ).
thf(func_def_662,type,
sK521: ( subst > term > term ) > subst ).
thf(func_def_663,type,
sK522: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_664,type,
sK523: term ).
thf(func_def_665,type,
sK524: term ).
thf(func_def_666,type,
sK525: term ).
thf(func_def_667,type,
sK526: term ).
thf(func_def_668,type,
sK527: term ).
thf(func_def_669,type,
sK528: term ).
thf(func_def_670,type,
sK529: term ).
thf(func_def_671,type,
sK530: term ).
thf(func_def_672,type,
sK531: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_673,type,
sK532: subst > term > subst > $o ).
thf(func_def_674,type,
sK533: ( term > $o ) > term ).
thf(func_def_675,type,
sK534: term ).
thf(func_def_676,type,
sK535: subst ).
thf(func_def_677,type,
sK536: term > $o ).
thf(func_def_678,type,
sK537: term > $o ).
thf(func_def_679,type,
sK538: term ).
thf(func_def_680,type,
sK539: term ).
thf(func_def_681,type,
sK540: term ).
thf(func_def_682,type,
sK541: ( subst > term > term ) > subst ).
thf(func_def_683,type,
sK542: ( subst > term > term ) > term ).
thf(func_def_684,type,
sK543: term > subst > term > term ).
thf(func_def_685,type,
sK544: term ).
thf(func_def_686,type,
sK545: subst ).
thf(func_def_687,type,
sK546: term ).
thf(func_def_688,type,
sK547: term ).
thf(func_def_689,type,
sK548: subst ).
thf(func_def_690,type,
sK549: term ).
thf(func_def_691,type,
sK550: term > $o ).
thf(func_def_692,type,
sK551: ( term > $o ) > term ).
thf(func_def_693,type,
sK552: ( term > $o ) > term > subst > term > $o ).
thf(func_def_694,type,
sK553: ( term > $o ) > term > ( term > $o ) > subst > term ).
thf(func_def_695,type,
sK554: term ).
thf(func_def_696,type,
sK555: subst ).
thf(func_def_697,type,
sK556: subst ).
thf(func_def_698,type,
sK557: term > $o ).
thf(func_def_699,type,
sK558: term ).
thf(func_def_700,type,
sK559: term > $o ).
thf(func_def_701,type,
sK560: term ).
thf(func_def_702,type,
sK561: subst > term > term ).
thf(func_def_703,type,
sK562: term ).
thf(func_def_704,type,
sK563: ( subst > term > term ) > subst ).
thf(func_def_705,type,
sK564: ( subst > term > term ) > term ).
thf(func_def_706,type,
sK565: ( subst > term > term ) > subst ).
thf(func_def_707,type,
sK566: term > subst > term > term ).
thf(func_def_708,type,
sK567: term ).
thf(func_def_709,type,
sK568: ( subst > term > term ) > term ).
thf(func_def_710,type,
sK569: ( subst > term > term ) > subst ).
thf(func_def_711,type,
sK570: subst ).
thf(func_def_712,type,
sK571: subst ).
thf(func_def_713,type,
sK572: subst > d_subst ).
thf(func_def_714,type,
sK573: term ).
thf(func_def_715,type,
sK574: term ).
thf(func_def_716,type,
sK575: term ).
thf(func_def_717,type,
sK576: term ).
thf(func_def_718,type,
sK577: term ).
thf(func_def_719,type,
sK578: term ).
thf(func_def_720,type,
sK579: term ).
thf(func_def_721,type,
sK580: term ).
thf(func_def_722,type,
sK581: subst ).
thf(func_def_723,type,
sK582: subst > ( term > $o ) > ( term > $o ) > term > term ).
thf(func_def_724,type,
sK583: term ).
thf(func_def_725,type,
sK584: term > $o ).
thf(func_def_726,type,
sK585: term > $o ).
thf(func_def_727,type,
sK586: subst ).
thf(func_def_728,type,
sK587: term ).
thf(func_def_729,type,
sK588: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_730,type,
sK589: term ).
thf(func_def_731,type,
sK590: subst > term > subst > $o ).
thf(func_def_732,type,
sK591: ( term > $o ) > term ).
thf(func_def_733,type,
sK592: term ).
thf(func_def_734,type,
sK593: term ).
thf(func_def_735,type,
sK594: term ).
thf(func_def_736,type,
sK595: term ).
thf(func_def_737,type,
sK596: term ).
thf(func_def_738,type,
sK597: term > subst > term > term ).
thf(func_def_739,type,
sK598: term ).
thf(func_def_740,type,
sK599: subst ).
thf(func_def_741,type,
sK600: subst ).
thf(func_def_742,type,
sK601: term ).
thf(func_def_743,type,
sK602: subst ).
thf(func_def_744,type,
sK603: term ).
thf(func_def_745,type,
sK604: term ).
thf(func_def_746,type,
sK605: term ).
thf(func_def_747,type,
sK606: subst > term > subst > $o ).
thf(func_def_748,type,
sK607: ( term > $o ) > term ).
thf(func_def_749,type,
sK608: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_750,type,
sK609: term ).
thf(func_def_751,type,
sK610: subst > term > term ).
thf(func_def_752,type,
sK611: subst > term > term ).
thf(func_def_753,type,
sK612: subst ).
thf(func_def_754,type,
sK613: term ).
thf(func_def_755,type,
sK614: ( subst > term > term ) > subst ).
thf(func_def_756,type,
sK615: ( subst > term > term ) > subst ).
thf(func_def_757,type,
sK616: ( subst > term > term ) > term ).
thf(func_def_758,type,
sK617: ( subst > term > term ) > subst ).
thf(func_def_759,type,
sK618: ( subst > term > term ) > term ).
thf(func_def_760,type,
sK619: ( subst > term > term ) > subst ).
thf(func_def_761,type,
sK620: term ).
thf(func_def_762,type,
sK621: term > $o ).
thf(func_def_763,type,
sK622: subst ).
thf(func_def_764,type,
sK623: ( term > $o ) > term ).
thf(func_def_765,type,
sK624: subst > ( term > $o ) > term > term > $o ).
thf(func_def_766,type,
sK625: term ).
thf(func_def_767,type,
sK626: subst > term > subst > $o ).
thf(func_def_768,type,
sK627: term > subst > term > term ).
thf(func_def_769,type,
sK628: term ).
thf(func_def_770,type,
sK629: ( subst > term > term ) > subst ).
thf(func_def_771,type,
sK630: ( subst > term > term ) > term ).
thf(func_def_772,type,
sK631: subst ).
thf(func_def_773,type,
sK632: term ).
thf(func_def_774,type,
sK633: subst ).
thf(func_def_775,type,
sK634: term ).
thf(func_def_776,type,
sK635: term ).
thf(func_def_777,type,
sK636: term > $o ).
thf(func_def_778,type,
sK637: term > $o ).
thf(func_def_779,type,
sK638: subst ).
thf(func_def_780,type,
sK639: term ).
thf(func_def_781,type,
sK640: term > d_term ).
thf(func_def_782,type,
sK641: subst ).
thf(func_def_783,type,
sK642: term ).
thf(func_def_784,type,
sK643: term ).
thf(func_def_785,type,
sK644: term > subst > term > term ).
thf(func_def_786,type,
sK645: term ).
thf(func_def_787,type,
sK646: subst ).
thf(func_def_788,type,
sK647: term ).
thf(func_def_789,type,
sK648: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_790,type,
sK649: subst > term > subst > $o ).
thf(func_def_791,type,
sK650: ( term > $o ) > term ).
thf(func_def_792,type,
sK651: subst ).
thf(func_def_795,type,
ph653:
!>[X0: $tType] : X0 ).
thf(f3848,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2495,f3148,f3840,f3844]) ).
thf(f3844,plain,
spl652_309,
inference(avatar_contradiction_clause,[status(thm)],[f3843]) ).
thf(f3843,plain,
( $false
| spl652_309 ),
inference(subsumption_resolution,[status(thm)],[f3842,f3829]) ).
thf(f3829,plain,
! [X240: term] :
( ( d2term @ d_one )
= X240 ),
inference(forward_demodulation,[status(thm)],[f1310,f1481]) ).
thf(f1481,plain,
! [X32: d_term] : ( d_one = X32 ),
inference(cnf_transformation,[status(thm)],[f753]) ).
thf(f753,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( X0 = X2 )
| ( ( ap @ ( sub @ X0 @ id ) @ X1 )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( sK525 != sK523 )
& ( ( ap @ ( sub @ sK523 @ id ) @ sK524 )
= ( ap @ ( sub @ sK525 @ id ) @ sK526 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
| ( sP109 != $true ) )
& ( ( sP109 = $true )
| ( hoasinduction != $true ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
| ( ( sK529 != sK527 )
& ( ( ap @ sK529 @ sK530 )
= ( ap @ sK527 @ sK528 ) ) ) )
& ( ! [X12: term,X13: term,X14: term,X15: term] :
( ( X12 = X14 )
| ( ( ap @ X12 @ X13 )
!= ( ap @ X14 @ X15 ) ) )
| ( apinj1 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X16: subst > term > subst > $o,X18: term] :
( ( sK531 @ X16 @ X18 )
= ( X16 @ id @ X18 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X20: term > $o] :
( ( X20 @ ( sK533 @ X20 ) )
!= ( sK532 @ id @ ( sK533 @ X20 ) @ id ) ) )
& ( ! [X22: term,X23: subst,X24: term > $o,X25: term > $o,X26: term] :
( ( $true
= ( X25 @ ( sub @ X26 @ ( push @ X22 @ X23 ) ) ) )
| ( $true
!= ( X24 @ X26 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ( ( $true
!= ( sK537 @ ( sub @ sK538 @ ( push @ sK534 @ sK535 ) ) ) )
& ( $true
= ( sK536 @ sK538 ) ) ) )
& ( ( sP104 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP104 != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X32: d_term] : ( d_one = X32 )
& ( ( ( sub @ sK539 @ id )
!= sK539 )
| ( sP102 = $true )
| ! [X35: subst > term > term] :
( ( sub @ sK540 @ ( push @ ( sK542 @ X35 ) @ ( sK541 @ X35 ) ) )
!= ( X35 @ ( sK541 @ X35 ) @ ( sK542 @ X35 ) ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ! [X38: term] :
( ( sub @ X38 @ id )
= X38 )
& ( sP102 != $true )
& ! [X39: term,X41: subst,X42: term] :
( ( sK543 @ X39 @ X41 @ X42 )
= ( sub @ X39 @ ( push @ X42 @ X41 ) ) ) ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( sP100 = $true )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( sP100 != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( $true = sP98 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP98 ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK544 @ sK545 ) )
!= sK545 ) )
& ( ! [X45: term,X46: subst] :
( ( comp @ sh @ ( push @ X45 @ X46 ) )
= X46 )
| ( axshiftcons != $true ) )
& ( ( shinj = $true )
| ( ( ( sub @ sK546 @ sh )
= ( sub @ sK547 @ sh ) )
& ( sK547 != sK546 ) ) )
& ( ! [X49: term,X50: term] :
( ( ( sub @ X50 @ sh )
!= ( sub @ X49 @ sh ) )
| ( X49 = X50 ) )
| ( shinj != $true ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP95 ) )
& ( ( $true = sP95 )
| ( substmonoid_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X54: term > $o] :
( ( sK550 @ ( sub @ ( sK551 @ X54 ) @ ( push @ sK549 @ sK548 ) ) )
!= ( X54 @ ( sK551 @ X54 ) ) ) )
& ( ! [X56: subst,X57: term,X58: term > $o,X60: term] :
( ( sK552 @ X58 @ X57 @ X56 @ X60 )
= ( X58 @ ( sub @ X60 @ ( push @ X57 @ X56 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( $true = sP94 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP94 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP90 ) )
& ( ( $true = sP90 )
| ( hoasinduction_lem3a != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X61: subst,X62: term > $o,X63: term,X64: term > $o] :
( ( ( X64 @ ( sub @ ( sK553 @ X64 @ X63 @ X62 @ X61 ) @ ( push @ X63 @ X61 ) ) )
!= ( X62 @ ( sK553 @ X64 @ X63 @ X62 @ X61 ) ) )
| ( ( X64 @ X63 )
!= $true )
| ( ( X62 @ one )
= $true ) )
| ( sK554
!= ( sub @ one @ ( push @ sK554 @ sK555 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X72: term] :
( ( sK557 @ X72 )
= ( sK559 @ ( sub @ X72 @ ( push @ sK558 @ sK556 ) ) ) )
& ( $true
= ( sK559 @ sK558 ) )
& ( ( sK557 @ one )
!= $true )
& ! [X73: term,X74: subst] :
( ( sub @ one @ ( push @ X73 @ X74 ) )
= X73 ) ) )
& ( ( hoaslamnotap = $true )
| ( ( ( ap @ ( sub @ sK562 @ id ) @ sK560 )
= ( lam @ ( sK561 @ sh @ one ) ) )
& ! [X78: subst,X79: term,X80: subst] :
( ( sub @ ( sK561 @ X78 @ X79 ) @ X80 )
= ( sK561 @ ( comp @ X78 @ X80 ) @ ( sub @ X79 @ X80 ) ) ) ) )
& ( ! [X81: term,X82: subst > term > term,X83: term] :
( ( ( lam @ ( X82 @ sh @ one ) )
!= ( ap @ ( sub @ X83 @ id ) @ X81 ) )
| ( ( sub @ ( X82 @ ( sK563 @ X82 ) @ ( sK564 @ X82 ) ) @ ( sK565 @ X82 ) )
!= ( X82 @ ( comp @ ( sK563 @ X82 ) @ ( sK565 @ X82 ) ) @ ( sub @ ( sK564 @ X82 ) @ ( sK565 @ X82 ) ) ) ) )
| ( hoaslamnotap != $true ) )
& ( axvarshift = $true )
& ( ! [X87: term,X89: term,X90: subst] :
( ( sK566 @ X87 @ X90 @ X89 )
= ( sub @ X87 @ ( push @ X89 @ X90 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X92: subst > term > term] :
( ( sub @ sK567 @ ( push @ ( sK568 @ X92 ) @ ( sK569 @ X92 ) ) )
!= ( X92 @ ( sK569 @ X92 ) @ ( sK568 @ X92 ) ) ) )
& ( ( substmonoid = $true )
| ( sK570
!= ( comp @ sK570 @ id ) )
| ( ( comp @ id @ sK571 )
!= sK571 ) )
& ( ( ! [X97: subst] :
( ( comp @ X97 @ id )
= X97 )
& ! [X98: subst] :
( ( comp @ id @ X98 )
= X98 ) )
| ( substmonoid != $true ) )
& ! [X99: d_term,X100: d_term] :
( ( X99 = X100 )
| ( ( d2term @ X99 )
!= ( d2term @ X100 ) ) )
& ! [X101: subst] :
( ( d2subst @ ( sK572 @ X101 ) )
= X101 )
& ( ! [X103: term,X104: term,X105: term,X106: term] :
( ( ( ap @ ( sub @ X104 @ id ) @ X103 )
!= ( ap @ ( sub @ X105 @ id ) @ X106 ) )
| ( X103 = X106 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( ( ap @ ( sub @ sK575 @ id ) @ sK576 )
= ( ap @ ( sub @ sK574 @ id ) @ sK573 ) )
& ( sK573 != sK576 ) ) )
& ( ( $true = sP88 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP88 ) )
& ( ( apinj2 = $true )
| ( ( sK577 != sK579 )
& ( ( ap @ sK580 @ sK577 )
= ( ap @ sK578 @ sK579 ) ) ) )
& ( ! [X115: term,X116: term,X117: term,X118: term] :
( ( X115 = X117 )
| ( ( ap @ X118 @ X115 )
!= ( ap @ X116 @ X117 ) ) )
| ( apinj2 != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP86 != $true ) )
& ( ( sP86 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP84 != $true ) )
& ( ( sP84 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP81 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP81 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X119: subst] :
( ( comp @ id @ X119 )
= X119 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ( sK581
!= ( comp @ id @ sK581 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X121: term,X122: term > $o,X123: term > $o,X124: subst] :
( ( ( X122 @ one )
= $true )
| ( $true
!= ( X123 @ X121 ) )
| ( ( X123 @ ( sub @ ( sK582 @ X124 @ X123 @ X122 @ X121 ) @ ( push @ X121 @ X124 ) ) )
!= ( X122 @ ( sK582 @ X124 @ X123 @ X122 @ X121 ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ( ( sK584 @ one )
!= $true )
& ( ( sK585 @ sK583 )
= $true )
& ! [X130: term] :
( ( sK584 @ X130 )
= ( sK585 @ ( sub @ X130 @ ( push @ sK583 @ sK586 ) ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ( sK587
!= ( sub @ sK587 @ id ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP77 != $true )
& ( $true != sP76 )
& ( sP75 != $true )
& ! [X133: term] :
( ( sub @ X133 @ id )
= X133 )
& ! [X134: subst > term > subst > $o,X136: term] :
( ( sK588 @ X134 @ X136 )
= ( X134 @ id @ X136 @ id ) ) ) )
& ( ( sP77 = $true )
| ( $true = sP76 )
| ( sP75 = $true )
| ( ( sub @ sK589 @ id )
!= sK589 )
| ! [X139: term > $o] :
( ( X139 @ ( sK591 @ X139 ) )
!= ( sK590 @ id @ ( sK591 @ X139 ) @ id ) )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( sP69 = $true )
| ( induction != $true ) )
& ( ( induction = $true )
| ( sP69 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP65 = $true )
| ( sK592
!= ( sub @ sK592 @ id ) )
| ( $true = sP66 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP65 != $true )
& ! [X142: term] :
( ( sub @ X142 @ id )
= X142 )
& ( $true != sP66 ) ) )
& ( ! [X143: term] :
( ( sub @ X143 @ id )
= X143 )
| ( sK593
!= ( sub @ sK593 @ id ) )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ( sK594
!= ( sub @ sK594 @ id ) )
& ! [X146: term] :
( ( sub @ X146 @ id )
= X146 ) ) )
& ( ( laminj = $true )
| ( ( sK595 != sK596 )
& ( ( lam @ sK595 )
= ( lam @ sK596 ) ) ) )
& ( ! [X149: term,X150: term] :
( ( X149 = X150 )
| ( ( lam @ X150 )
!= ( lam @ X149 ) ) )
| ( laminj != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP60 != $true ) )
& ( ( sP60 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoaslaminj_lthm != $true ) )
& ( ! [X151: term] :
( ( sub @ X151 @ ( push @ one @ sh ) )
= ( sK597 @ X151 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X154: subst > term > term] :
( ( X154 @ sh @ one )
!= ( sub @ sK598 @ ( push @ one @ sh ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( sP56 = $true )
| ( $true = sP55 )
| ( ( comp @ sK599 @ id )
!= sK599 )
| ( sK601
!= ( sub @ one @ ( push @ sK601 @ sK600 ) ) )
| ( sK602
!= ( comp @ sh @ ( push @ sK603 @ sK602 ) ) )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP56 != $true )
& ( $true != sP55 )
& ! [X160: subst] :
( ( comp @ X160 @ id )
= X160 )
& ! [X161: subst,X162: term] :
( ( sub @ one @ ( push @ X162 @ X161 ) )
= X162 )
& ! [X163: subst,X164: term] :
( ( comp @ sh @ ( push @ X164 @ X163 ) )
= X163 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( $true != sP47 )
& ! [X165: term] :
( ( sub @ X165 @ id )
= X165 )
& ( $true != sP46 ) ) )
& ( ( $true = sP47 )
| ( ( sub @ sK604 @ id )
!= sK604 )
| ( $true = sP46 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X167: d_subst] : ( d_id = X167 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( ( sub @ sK605 @ id )
!= sK605 )
| ( $true = sP39 )
| ( sP41 = $true )
| ! [X170: term > $o] :
( ( sK606 @ id @ ( sK607 @ X170 ) @ id )
!= ( X170 @ ( sK607 @ X170 ) ) )
| ( $true = sP40 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
& ( $true != sP39 )
& ( sP41 != $true )
& ! [X173: subst > term > subst > $o,X175: term] :
( ( X173 @ id @ X175 @ id )
= ( sK608 @ X173 @ X175 ) )
& ( $true != sP40 ) ) )
& ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ( ( sub @ sK609 @ id )
!= sK609 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
| ( ! [X182: subst,X183: subst,X184: term] :
( ( sK611 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) )
= ( sub @ ( sK611 @ X183 @ X184 ) @ X182 ) )
& ( ( sK610 @ sK612 @ sK613 )
!= ( sK611 @ sK612 @ sK613 ) )
& ! [X185: subst,X186: term,X187: subst] :
( ( sub @ ( sK610 @ X187 @ X186 ) @ X185 )
= ( sK610 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) ) )
& ( ( lam @ ( sK611 @ sh @ one ) )
= ( lam @ ( sK610 @ sh @ one ) ) ) ) )
& ( ! [X188: subst > term > term,X189: subst > term > term,X190: subst,X191: term] :
( ( ( sub @ ( X189 @ ( sK615 @ X189 ) @ ( sK616 @ X189 ) ) @ ( sK614 @ X189 ) )
!= ( X189 @ ( comp @ ( sK615 @ X189 ) @ ( sK614 @ X189 ) ) @ ( sub @ ( sK616 @ X189 ) @ ( sK614 @ X189 ) ) ) )
| ( ( X189 @ X190 @ X191 )
= ( X188 @ X190 @ X191 ) )
| ( ( X188 @ ( comp @ ( sK619 @ X188 ) @ ( sK617 @ X188 ) ) @ ( sub @ ( sK618 @ X188 ) @ ( sK617 @ X188 ) ) )
!= ( sub @ ( X188 @ ( sK619 @ X188 ) @ ( sK618 @ X188 ) ) @ ( sK617 @ X188 ) ) )
| ( ( lam @ ( X188 @ sh @ one ) )
!= ( lam @ ( X189 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ! [X201: term > $o] :
( ( sK621 @ ( sub @ ( sK623 @ X201 ) @ ( push @ sK620 @ sK622 ) ) )
!= ( X201 @ ( sK623 @ X201 ) ) ) )
& ( ! [X203: term,X204: term > $o,X205: subst,X207: term] :
( ( X204 @ ( sub @ X207 @ ( push @ X203 @ X205 ) ) )
= ( sK624 @ X205 @ X204 @ X203 @ X207 ) )
| ( pushprop_lem0 != $true ) )
& ! [X208: d_subst,X209: d_subst] :
( ( ( d2subst @ X209 )
!= ( d2subst @ X208 ) )
| ( X208 = X209 ) )
& ( termmset_gthm = $true )
& ( ! [X210: term,X211: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X211 ) )
| ( $true
= ( sP29 @ X211 ) )
| ( $true
= ( X211 @ id @ X210 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ( $true
!= ( sP30 @ sK626 ) )
& ( $true
!= ( sP29 @ sK626 ) )
& ( $true
!= ( sK626 @ id @ sK625 @ id ) ) ) )
& ( ! [X214: term,X216: subst,X217: term] :
( ( sK627 @ X214 @ X216 @ X217 )
= ( sub @ X214 @ ( push @ X217 @ X216 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X219: subst > term > term] :
( ( sub @ sK628 @ ( push @ ( sK630 @ X219 ) @ ( sK629 @ X219 ) ) )
!= ( X219 @ ( sK629 @ X219 ) @ ( sK630 @ X219 ) ) ) )
& ( ( induction2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP28 )
| ( induction2 != $true ) )
& ( ( sK632
!= ( sub @ one @ ( push @ sK632 @ sK631 ) ) )
| ! [X224: term,X225: term > $o,X226: term > $o,X227: subst,X228: term] :
( ( ( X225 @ X224 )
!= $true )
| ( ( X226 @ ( sub @ X224 @ ( push @ X228 @ X227 ) ) )
= $true ) )
| ( sK633
!= ( comp @ sh @ ( push @ sK634 @ sK633 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X231: subst,X232: term] :
( ( sub @ one @ ( push @ X232 @ X231 ) )
= X232 )
& ( $true
= ( sK636 @ sK635 ) )
& ( $true
!= ( sK637 @ ( sub @ sK635 @ ( push @ sK639 @ sK638 ) ) ) )
& ! [X238: subst,X239: term] :
( ( comp @ sh @ ( push @ X239 @ X238 ) )
= X238 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X240: term] :
( ( d2term @ ( sK640 @ X240 ) )
= X240 )
& ( axclos = $true )
& ( ( axvarcons = $true )
| ( ( sub @ one @ ( push @ sK642 @ sK641 ) )
!= sK642 ) )
& ( ! [X244: subst,X245: term] :
( ( sub @ one @ ( push @ X245 @ X244 ) )
= X245 )
| ( axvarcons != $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ( sP25 != $true )
& ! [X246: term] :
( ( sub @ X246 @ id )
= X246 ) ) )
& ( ( sP25 = $true )
| ( ( sub @ sK643 @ id )
!= sK643 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ! [X248: term] :
( ( sK644 @ X248 @ sh @ one )
= ( sub @ X248 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X251: subst > term > term] :
( ( sub @ sK645 @ ( push @ one @ sh ) )
!= ( X251 @ sh @ one ) ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
| ( sK646
!= ( push @ ( sub @ one @ sK646 ) @ ( comp @ sh @ sK646 ) ) ) )
& ( ! [X253: subst] :
( ( push @ ( sub @ one @ X253 ) @ ( comp @ sh @ X253 ) )
= X253 )
| ( axscons != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( $true != sP21 )
& ( $true != sP20 )
& ( sP19 != $true )
& ( sP18 != $true ) ) )
& ( ( $true = sP21 )
| ( $true = sP20 )
| ( sP19 = $true )
| ( sP18 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
& ( sP5 != $true )
& ( $true != sP4 ) ) )
& ( ( sK647
!= ( sub @ sK647 @ id ) )
| ( sP5 = $true )
| ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X256: subst > term > subst > $o,X258: term] :
( ( sK648 @ X256 @ X258 )
= ( X256 @ id @ X258 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ! [X260: term > $o] :
( ( sK649 @ id @ ( sK650 @ X260 ) @ id )
!= ( X260 @ ( sK650 @ X260 ) ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X262: subst] :
( ( comp @ X262 @ id )
= X262 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ( sK651
!= ( comp @ sK651 @ id ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[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,sK591,sK592,sK593,sK594,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,sK603,sK604,sK605,sK606,sK607,sK608,sK609,sK610,sK611,sK612,sK613,sK614,sK615,sK616,sK617,sK618,sK619,sK620,sK621,sK622,sK623,sK624,sK625,sK626,sK627,sK628,sK629,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,sK640,sK641,sK642,sK643,sK644,sK645,sK646,sK647,sK648,sK649,sK650,sK651])],[f677,f752,f751,f750,f749,f748,f747,f746,f745,f744,f743,f742,f741,f740,f739,f738,f737,f736,f735,f734,f733,f732,f731,f730,f729,f728,f727,f726,f725,f724,f723,f722,f721,f720,f719,f718,f717,f716,f715,f714,f713,f712,f711,f710,f709,f708,f707,f706,f705,f704,f703,f702,f701,f700,f699,f698,f697,f696,f695,f694,f693,f692,f691,f690,f689,f688,f687,f686,f685,f684,f683,f682,f681,f680,f679,f678]) ).
thf(f678,plain,
( ? [X4: term,X5: term,X6: term,X7: term] :
( ( X4 != X6 )
& ( ( ap @ ( sub @ X4 @ id ) @ X5 )
= ( ap @ ( sub @ X6 @ id ) @ X7 ) ) )
=> ( ( sK525 != sK523 )
& ( ( ap @ ( sub @ sK523 @ id ) @ sK524 )
= ( ap @ ( sub @ sK525 @ id ) @ sK526 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f679,plain,
( ? [X8: term,X9: term,X10: term,X11: term] :
( ( X8 != X10 )
& ( ( ap @ X8 @ X9 )
= ( ap @ X10 @ X11 ) ) )
=> ( ( sK529 != sK527 )
& ( ( ap @ sK529 @ sK530 )
= ( ap @ sK527 @ sK528 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f680,plain,
! [X16: subst > term > subst > $o] :
( ? [X17: term > $o] :
! [X18: term] :
( ( X17 @ X18 )
= ( X16 @ id @ X18 @ id ) )
=> ! [X18: term] :
( ( sK531 @ X16 @ X18 )
= ( X16 @ id @ X18 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f681,plain,
( ? [X19: subst > term > subst > $o] :
! [X20: term > $o] :
? [X21: term] :
( ( X19 @ id @ X21 @ id )
!= ( X20 @ X21 ) )
=> ! [X20: term > $o] :
? [X21: term] :
( ( sK532 @ id @ X21 @ id )
!= ( X20 @ X21 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f682,plain,
! [X20: term > $o] :
( ? [X21: term] :
( ( sK532 @ id @ X21 @ id )
!= ( X20 @ X21 ) )
=> ( ( X20 @ ( sK533 @ X20 ) )
!= ( sK532 @ id @ ( sK533 @ X20 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f683,plain,
( ? [X27: term,X28: subst,X29: term > $o,X30: term > $o,X31: term] :
( ( ( X30 @ ( sub @ X31 @ ( push @ X27 @ X28 ) ) )
!= $true )
& ( $true
= ( X29 @ X31 ) ) )
=> ( ( $true
!= ( sK537 @ ( sub @ sK538 @ ( push @ sK534 @ sK535 ) ) ) )
& ( $true
= ( sK536 @ sK538 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f684,plain,
( ? [X33: term] :
( ( sub @ X33 @ id )
!= X33 )
=> ( ( sub @ sK539 @ id )
!= sK539 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f685,plain,
( ? [X34: term] :
! [X35: subst > term > term] :
? [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
!= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
=> ! [X35: subst > term > term] :
? [X37: term,X36: subst] :
( ( sub @ sK540 @ ( push @ X37 @ X36 ) )
!= ( X35 @ X36 @ X37 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f686,plain,
! [X35: subst > term > term] :
( ? [X37: term,X36: subst] :
( ( sub @ sK540 @ ( push @ X37 @ X36 ) )
!= ( X35 @ X36 @ X37 ) )
=> ( ( sub @ sK540 @ ( push @ ( sK542 @ X35 ) @ ( sK541 @ X35 ) ) )
!= ( X35 @ ( sK541 @ X35 ) @ ( sK542 @ X35 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f687,plain,
! [X39: term] :
( ? [X40: subst > term > term] :
! [X41: subst,X42: term] :
( ( X40 @ X41 @ X42 )
= ( sub @ X39 @ ( push @ X42 @ X41 ) ) )
=> ! [X42: term,X41: subst] :
( ( sK543 @ X39 @ X41 @ X42 )
= ( sub @ X39 @ ( push @ X42 @ X41 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f688,plain,
( ? [X43: term,X44: subst] :
( ( comp @ sh @ ( push @ X43 @ X44 ) )
!= X44 )
=> ( ( comp @ sh @ ( push @ sK544 @ sK545 ) )
!= sK545 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f689,plain,
( ? [X47: term,X48: term] :
( ( ( sub @ X47 @ sh )
= ( sub @ X48 @ sh ) )
& ( X47 != X48 ) )
=> ( ( ( sub @ sK546 @ sh )
= ( sub @ sK547 @ sh ) )
& ( sK547 != sK546 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f690,plain,
( ? [X51: subst,X52: term,X53: term > $o] :
! [X54: term > $o] :
? [X55: term] :
( ( X54 @ X55 )
!= ( X53 @ ( sub @ X55 @ ( push @ X52 @ X51 ) ) ) )
=> ! [X54: term > $o] :
? [X55: term] :
( ( X54 @ X55 )
!= ( sK550 @ ( sub @ X55 @ ( push @ sK549 @ sK548 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f691,plain,
! [X54: term > $o] :
( ? [X55: term] :
( ( X54 @ X55 )
!= ( sK550 @ ( sub @ X55 @ ( push @ sK549 @ sK548 ) ) ) )
=> ( ( sK550 @ ( sub @ ( sK551 @ X54 ) @ ( push @ sK549 @ sK548 ) ) )
!= ( X54 @ ( sK551 @ X54 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f692,plain,
! [X56: subst,X57: term,X58: term > $o] :
( ? [X59: term > $o] :
! [X60: term] :
( ( X58 @ ( sub @ X60 @ ( push @ X57 @ X56 ) ) )
= ( X59 @ X60 ) )
=> ! [X60: term] :
( ( sK552 @ X58 @ X57 @ X56 @ X60 )
= ( X58 @ ( sub @ X60 @ ( push @ X57 @ X56 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f693,plain,
! [X61: subst,X62: term > $o,X63: term,X64: term > $o] :
( ? [X65: term] :
( ( X62 @ X65 )
!= ( X64 @ ( sub @ X65 @ ( push @ X63 @ X61 ) ) ) )
=> ( ( X64 @ ( sub @ ( sK553 @ X64 @ X63 @ X62 @ X61 ) @ ( push @ X63 @ X61 ) ) )
!= ( X62 @ ( sK553 @ X64 @ X63 @ X62 @ X61 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f694,plain,
( ? [X66: term,X67: subst] :
( ( sub @ one @ ( push @ X66 @ X67 ) )
!= X66 )
=> ( sK554
!= ( sub @ one @ ( push @ sK554 @ sK555 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f695,plain,
( ? [X68: subst,X69: term > $o,X70: term,X71: term > $o] :
( ! [X72: term] :
( ( X71 @ ( sub @ X72 @ ( push @ X70 @ X68 ) ) )
= ( X69 @ X72 ) )
& ( ( X71 @ X70 )
= $true )
& ( $true
!= ( X69 @ one ) ) )
=> ( ! [X72: term] :
( ( sK557 @ X72 )
= ( sK559 @ ( sub @ X72 @ ( push @ sK558 @ sK556 ) ) ) )
& ( $true
= ( sK559 @ sK558 ) )
& ( ( sK557 @ one )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f696,plain,
( ? [X75: term,X76: subst > term > term,X77: term] :
( ( ( ap @ ( sub @ X77 @ id ) @ X75 )
= ( lam @ ( X76 @ sh @ one ) ) )
& ! [X78: subst,X79: term,X80: subst] :
( ( X76 @ ( comp @ X78 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X76 @ X78 @ X79 ) @ X80 ) ) )
=> ( ( ( ap @ ( sub @ sK562 @ id ) @ sK560 )
= ( lam @ ( sK561 @ sh @ one ) ) )
& ! [X80: subst,X79: term,X78: subst] :
( ( sub @ ( sK561 @ X78 @ X79 ) @ X80 )
= ( sK561 @ ( comp @ X78 @ X80 ) @ ( sub @ X79 @ X80 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f697,plain,
! [X82: subst > term > term] :
( ? [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
!= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
=> ( ( sub @ ( X82 @ ( sK563 @ X82 ) @ ( sK564 @ X82 ) ) @ ( sK565 @ X82 ) )
!= ( X82 @ ( comp @ ( sK563 @ X82 ) @ ( sK565 @ X82 ) ) @ ( sub @ ( sK564 @ X82 ) @ ( sK565 @ X82 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f698,plain,
! [X87: term] :
( ? [X88: subst > term > term] :
! [X89: term,X90: subst] :
( ( sub @ X87 @ ( push @ X89 @ X90 ) )
= ( X88 @ X90 @ X89 ) )
=> ! [X90: subst,X89: term] :
( ( sK566 @ X87 @ X90 @ X89 )
= ( sub @ X87 @ ( push @ X89 @ X90 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f699,plain,
( ? [X91: term] :
! [X92: subst > term > term] :
? [X93: term,X94: subst] :
( ( sub @ X91 @ ( push @ X93 @ X94 ) )
!= ( X92 @ X94 @ X93 ) )
=> ! [X92: subst > term > term] :
? [X94: subst,X93: term] :
( ( sub @ sK567 @ ( push @ X93 @ X94 ) )
!= ( X92 @ X94 @ X93 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f700,plain,
! [X92: subst > term > term] :
( ? [X94: subst,X93: term] :
( ( sub @ sK567 @ ( push @ X93 @ X94 ) )
!= ( X92 @ X94 @ X93 ) )
=> ( ( sub @ sK567 @ ( push @ ( sK568 @ X92 ) @ ( sK569 @ X92 ) ) )
!= ( X92 @ ( sK569 @ X92 ) @ ( sK568 @ X92 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f701,plain,
( ? [X95: subst] :
( ( comp @ X95 @ id )
!= X95 )
=> ( sK570
!= ( comp @ sK570 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f702,plain,
( ? [X96: subst] :
( ( comp @ id @ X96 )
!= X96 )
=> ( ( comp @ id @ sK571 )
!= sK571 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f703,plain,
! [X101: subst] :
( ? [X102: d_subst] :
( ( d2subst @ X102 )
= X101 )
=> ( ( d2subst @ ( sK572 @ X101 ) )
= X101 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f704,plain,
( ? [X107: term,X108: term,X109: term,X110: term] :
( ( ( ap @ ( sub @ X109 @ id ) @ X110 )
= ( ap @ ( sub @ X108 @ id ) @ X107 ) )
& ( X107 != X110 ) )
=> ( ( ( ap @ ( sub @ sK575 @ id ) @ sK576 )
= ( ap @ ( sub @ sK574 @ id ) @ sK573 ) )
& ( sK573 != sK576 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f705,plain,
( ? [X111: term,X112: term,X113: term,X114: term] :
( ( X111 != X113 )
& ( ( ap @ X114 @ X111 )
= ( ap @ X112 @ X113 ) ) )
=> ( ( sK577 != sK579 )
& ( ( ap @ sK580 @ sK577 )
= ( ap @ sK578 @ sK579 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f706,plain,
( ? [X120: subst] :
( ( comp @ id @ X120 )
!= X120 )
=> ( sK581
!= ( comp @ id @ sK581 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f707,plain,
! [X121: term,X122: term > $o,X123: term > $o,X124: subst] :
( ? [X125: term] :
( ( X123 @ ( sub @ X125 @ ( push @ X121 @ X124 ) ) )
!= ( X122 @ X125 ) )
=> ( ( X123 @ ( sub @ ( sK582 @ X124 @ X123 @ X122 @ X121 ) @ ( push @ X121 @ X124 ) ) )
!= ( X122 @ ( sK582 @ X124 @ X123 @ X122 @ X121 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f708,plain,
( ? [X126: term,X127: term > $o,X128: term > $o,X129: subst] :
( ( $true
!= ( X127 @ one ) )
& ( $true
= ( X128 @ X126 ) )
& ! [X130: term] :
( ( X128 @ ( sub @ X130 @ ( push @ X126 @ X129 ) ) )
= ( X127 @ X130 ) ) )
=> ( ( ( sK584 @ one )
!= $true )
& ( ( sK585 @ sK583 )
= $true )
& ! [X130: term] :
( ( sK584 @ X130 )
= ( sK585 @ ( sub @ X130 @ ( push @ sK583 @ sK586 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f709,plain,
( ? [X132: term] :
( ( sub @ X132 @ id )
!= X132 )
=> ( sK587
!= ( sub @ sK587 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f710,plain,
! [X134: subst > term > subst > $o] :
( ? [X135: term > $o] :
! [X136: term] :
( ( X135 @ X136 )
= ( X134 @ id @ X136 @ id ) )
=> ! [X136: term] :
( ( sK588 @ X134 @ X136 )
= ( X134 @ id @ X136 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f711,plain,
( ? [X137: term] :
( ( sub @ X137 @ id )
!= X137 )
=> ( ( sub @ sK589 @ id )
!= sK589 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f712,plain,
( ? [X138: subst > term > subst > $o] :
! [X139: term > $o] :
? [X140: term] :
( ( X138 @ id @ X140 @ id )
!= ( X139 @ X140 ) )
=> ! [X139: term > $o] :
? [X140: term] :
( ( X139 @ X140 )
!= ( sK590 @ id @ X140 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f713,plain,
! [X139: term > $o] :
( ? [X140: term] :
( ( X139 @ X140 )
!= ( sK590 @ id @ X140 @ id ) )
=> ( ( X139 @ ( sK591 @ X139 ) )
!= ( sK590 @ id @ ( sK591 @ X139 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f714,plain,
( ? [X141: term] :
( ( sub @ X141 @ id )
!= X141 )
=> ( sK592
!= ( sub @ sK592 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f715,plain,
( ? [X144: term] :
( ( sub @ X144 @ id )
!= X144 )
=> ( sK593
!= ( sub @ sK593 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f716,plain,
( ? [X145: term] :
( ( sub @ X145 @ id )
!= X145 )
=> ( sK594
!= ( sub @ sK594 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f717,plain,
( ? [X147: term,X148: term] :
( ( X147 != X148 )
& ( ( lam @ X147 )
= ( lam @ X148 ) ) )
=> ( ( sK595 != sK596 )
& ( ( lam @ sK595 )
= ( lam @ sK596 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f718,plain,
! [X151: term] :
( ? [X152: subst > term > term] :
( ( sub @ X151 @ ( push @ one @ sh ) )
= ( X152 @ sh @ one ) )
=> ( ( sub @ X151 @ ( push @ one @ sh ) )
= ( sK597 @ X151 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f719,plain,
( ? [X153: term] :
! [X154: subst > term > term] :
( ( X154 @ sh @ one )
!= ( sub @ X153 @ ( push @ one @ sh ) ) )
=> ! [X154: subst > term > term] :
( ( X154 @ sh @ one )
!= ( sub @ sK598 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f720,plain,
( ? [X155: subst] :
( ( comp @ X155 @ id )
!= X155 )
=> ( ( comp @ sK599 @ id )
!= sK599 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f721,plain,
( ? [X156: subst,X157: term] :
( ( sub @ one @ ( push @ X157 @ X156 ) )
!= X157 )
=> ( sK601
!= ( sub @ one @ ( push @ sK601 @ sK600 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f722,plain,
( ? [X158: subst,X159: term] :
( ( comp @ sh @ ( push @ X159 @ X158 ) )
!= X158 )
=> ( sK602
!= ( comp @ sh @ ( push @ sK603 @ sK602 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f723,plain,
( ? [X166: term] :
( ( sub @ X166 @ id )
!= X166 )
=> ( ( sub @ sK604 @ id )
!= sK604 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f724,plain,
( ? [X168: term] :
( ( sub @ X168 @ id )
!= X168 )
=> ( ( sub @ sK605 @ id )
!= sK605 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f725,plain,
( ? [X169: subst > term > subst > $o] :
! [X170: term > $o] :
? [X171: term] :
( ( X169 @ id @ X171 @ id )
!= ( X170 @ X171 ) )
=> ! [X170: term > $o] :
? [X171: term] :
( ( sK606 @ id @ X171 @ id )
!= ( X170 @ X171 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f726,plain,
! [X170: term > $o] :
( ? [X171: term] :
( ( sK606 @ id @ X171 @ id )
!= ( X170 @ X171 ) )
=> ( ( sK606 @ id @ ( sK607 @ X170 ) @ id )
!= ( X170 @ ( sK607 @ X170 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f727,plain,
! [X173: subst > term > subst > $o] :
( ? [X174: term > $o] :
! [X175: term] :
( ( X173 @ id @ X175 @ id )
= ( X174 @ X175 ) )
=> ! [X175: term] :
( ( X173 @ id @ X175 @ id )
= ( sK608 @ X173 @ X175 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f728,plain,
( ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 )
=> ( ( sub @ sK609 @ id )
!= sK609 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f729,plain,
( ? [X178: subst > term > term,X179: subst > term > term,X180: subst,X181: term] :
( ! [X182: subst,X183: subst,X184: term] :
( ( X179 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) )
= ( sub @ ( X179 @ X183 @ X184 ) @ X182 ) )
& ( ( X179 @ X180 @ X181 )
!= ( X178 @ X180 @ X181 ) )
& ! [X185: subst,X186: term,X187: subst] :
( ( sub @ ( X178 @ X187 @ X186 ) @ X185 )
= ( X178 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) ) )
& ( ( lam @ ( X178 @ sh @ one ) )
= ( lam @ ( X179 @ sh @ one ) ) ) )
=> ( ! [X184: term,X183: subst,X182: subst] :
( ( sK611 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) )
= ( sub @ ( sK611 @ X183 @ X184 ) @ X182 ) )
& ( ( sK610 @ sK612 @ sK613 )
!= ( sK611 @ sK612 @ sK613 ) )
& ! [X187: subst,X186: term,X185: subst] :
( ( sub @ ( sK610 @ X187 @ X186 ) @ X185 )
= ( sK610 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) ) )
& ( ( lam @ ( sK611 @ sh @ one ) )
= ( lam @ ( sK610 @ sh @ one ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f730,plain,
! [X189: subst > term > term] :
( ? [X192: subst,X193: subst,X194: term] :
( ( sub @ ( X189 @ X193 @ X194 ) @ X192 )
!= ( X189 @ ( comp @ X193 @ X192 ) @ ( sub @ X194 @ X192 ) ) )
=> ( ( sub @ ( X189 @ ( sK615 @ X189 ) @ ( sK616 @ X189 ) ) @ ( sK614 @ X189 ) )
!= ( X189 @ ( comp @ ( sK615 @ X189 ) @ ( sK614 @ X189 ) ) @ ( sub @ ( sK616 @ X189 ) @ ( sK614 @ X189 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f731,plain,
! [X188: subst > term > term] :
( ? [X195: subst,X196: term,X197: subst] :
( ( sub @ ( X188 @ X197 @ X196 ) @ X195 )
!= ( X188 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) ) )
=> ( ( X188 @ ( comp @ ( sK619 @ X188 ) @ ( sK617 @ X188 ) ) @ ( sub @ ( sK618 @ X188 ) @ ( sK617 @ X188 ) ) )
!= ( sub @ ( X188 @ ( sK619 @ X188 ) @ ( sK618 @ X188 ) ) @ ( sK617 @ X188 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f732,plain,
( ? [X198: term,X199: term > $o,X200: subst] :
! [X201: term > $o] :
? [X202: term] :
( ( X199 @ ( sub @ X202 @ ( push @ X198 @ X200 ) ) )
!= ( X201 @ X202 ) )
=> ! [X201: term > $o] :
? [X202: term] :
( ( sK621 @ ( sub @ X202 @ ( push @ sK620 @ sK622 ) ) )
!= ( X201 @ X202 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f733,plain,
! [X201: term > $o] :
( ? [X202: term] :
( ( sK621 @ ( sub @ X202 @ ( push @ sK620 @ sK622 ) ) )
!= ( X201 @ X202 ) )
=> ( ( sK621 @ ( sub @ ( sK623 @ X201 ) @ ( push @ sK620 @ sK622 ) ) )
!= ( X201 @ ( sK623 @ X201 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f734,plain,
! [X203: term,X204: term > $o,X205: subst] :
( ? [X206: term > $o] :
! [X207: term] :
( ( X204 @ ( sub @ X207 @ ( push @ X203 @ X205 ) ) )
= ( X206 @ X207 ) )
=> ! [X207: term] :
( ( X204 @ ( sub @ X207 @ ( push @ X203 @ X205 ) ) )
= ( sK624 @ X205 @ X204 @ X203 @ X207 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f735,plain,
( ? [X212: term,X213: subst > term > subst > $o] :
( ( ( sP30 @ X213 )
!= $true )
& ( ( sP29 @ X213 )
!= $true )
& ( ( X213 @ id @ X212 @ id )
!= $true ) )
=> ( ( $true
!= ( sP30 @ sK626 ) )
& ( $true
!= ( sP29 @ sK626 ) )
& ( $true
!= ( sK626 @ id @ sK625 @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f736,plain,
! [X214: term] :
( ? [X215: subst > term > term] :
! [X216: subst,X217: term] :
( ( X215 @ X216 @ X217 )
= ( sub @ X214 @ ( push @ X217 @ X216 ) ) )
=> ! [X217: term,X216: subst] :
( ( sK627 @ X214 @ X216 @ X217 )
= ( sub @ X214 @ ( push @ X217 @ X216 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f737,plain,
( ? [X218: term] :
! [X219: subst > term > term] :
? [X220: subst,X221: term] :
( ( X219 @ X220 @ X221 )
!= ( sub @ X218 @ ( push @ X221 @ X220 ) ) )
=> ! [X219: subst > term > term] :
? [X221: term,X220: subst] :
( ( X219 @ X220 @ X221 )
!= ( sub @ sK628 @ ( push @ X221 @ X220 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f738,plain,
! [X219: subst > term > term] :
( ? [X221: term,X220: subst] :
( ( X219 @ X220 @ X221 )
!= ( sub @ sK628 @ ( push @ X221 @ X220 ) ) )
=> ( ( sub @ sK628 @ ( push @ ( sK630 @ X219 ) @ ( sK629 @ X219 ) ) )
!= ( X219 @ ( sK629 @ X219 ) @ ( sK630 @ X219 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f739,plain,
( ? [X222: subst,X223: term] :
( ( sub @ one @ ( push @ X223 @ X222 ) )
!= X223 )
=> ( sK632
!= ( sub @ one @ ( push @ sK632 @ sK631 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f740,plain,
( ? [X229: subst,X230: term] :
( ( comp @ sh @ ( push @ X230 @ X229 ) )
!= X229 )
=> ( sK633
!= ( comp @ sh @ ( push @ sK634 @ sK633 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f741,plain,
( ? [X233: term,X234: term > $o,X235: term > $o,X236: subst,X237: term] :
( ( ( X234 @ X233 )
= $true )
& ( ( X235 @ ( sub @ X233 @ ( push @ X237 @ X236 ) ) )
!= $true ) )
=> ( ( $true
= ( sK636 @ sK635 ) )
& ( $true
!= ( sK637 @ ( sub @ sK635 @ ( push @ sK639 @ sK638 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f742,plain,
! [X240: term] :
( ? [X241: d_term] :
( ( d2term @ X241 )
= X240 )
=> ( ( d2term @ ( sK640 @ X240 ) )
= X240 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f743,plain,
( ? [X242: subst,X243: term] :
( ( sub @ one @ ( push @ X243 @ X242 ) )
!= X243 )
=> ( ( sub @ one @ ( push @ sK642 @ sK641 ) )
!= sK642 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f744,plain,
( ? [X247: term] :
( ( sub @ X247 @ id )
!= X247 )
=> ( ( sub @ sK643 @ id )
!= sK643 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f745,plain,
! [X248: term] :
( ? [X249: subst > term > term] :
( ( sub @ X248 @ ( push @ one @ sh ) )
= ( X249 @ sh @ one ) )
=> ( ( sK644 @ X248 @ sh @ one )
= ( sub @ X248 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f746,plain,
( ? [X250: term] :
! [X251: subst > term > term] :
( ( X251 @ sh @ one )
!= ( sub @ X250 @ ( push @ one @ sh ) ) )
=> ! [X251: subst > term > term] :
( ( sub @ sK645 @ ( push @ one @ sh ) )
!= ( X251 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f747,plain,
( ? [X252: subst] :
( ( push @ ( sub @ one @ X252 ) @ ( comp @ sh @ X252 ) )
!= X252 )
=> ( sK646
!= ( push @ ( sub @ one @ sK646 ) @ ( comp @ sh @ sK646 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f748,plain,
( ? [X255: term] :
( ( sub @ X255 @ id )
!= X255 )
=> ( sK647
!= ( sub @ sK647 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f749,plain,
! [X256: subst > term > subst > $o] :
( ? [X257: term > $o] :
! [X258: term] :
( ( X256 @ id @ X258 @ id )
= ( X257 @ X258 ) )
=> ! [X258: term] :
( ( sK648 @ X256 @ X258 )
= ( X256 @ id @ X258 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f750,plain,
( ? [X259: subst > term > subst > $o] :
! [X260: term > $o] :
? [X261: term] :
( ( X259 @ id @ X261 @ id )
!= ( X260 @ X261 ) )
=> ! [X260: term > $o] :
? [X261: term] :
( ( sK649 @ id @ X261 @ id )
!= ( X260 @ X261 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f751,plain,
! [X260: term > $o] :
( ? [X261: term] :
( ( sK649 @ id @ X261 @ id )
!= ( X260 @ X261 ) )
=> ( ( sK649 @ id @ ( sK650 @ X260 ) @ id )
!= ( X260 @ ( sK650 @ X260 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f752,plain,
( ? [X263: subst] :
( ( comp @ X263 @ id )
!= X263 )
=> ( sK651
!= ( comp @ sK651 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f677,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( X0 = X2 )
| ( ( ap @ ( sub @ X0 @ id ) @ X1 )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X4: term,X5: term,X6: term,X7: term] :
( ( X4 != X6 )
& ( ( ap @ ( sub @ X4 @ id ) @ X5 )
= ( ap @ ( sub @ X6 @ id ) @ X7 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
| ( sP109 != $true ) )
& ( ( sP109 = $true )
| ( hoasinduction != $true ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
| ? [X8: term,X9: term,X10: term,X11: term] :
( ( X8 != X10 )
& ( ( ap @ X8 @ X9 )
= ( ap @ X10 @ X11 ) ) ) )
& ( ! [X12: term,X13: term,X14: term,X15: term] :
( ( X12 = X14 )
| ( ( ap @ X12 @ X13 )
!= ( ap @ X14 @ X15 ) ) )
| ( apinj1 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X16: subst > term > subst > $o] :
? [X17: term > $o] :
! [X18: term] :
( ( X17 @ X18 )
= ( X16 @ id @ X18 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X19: subst > term > subst > $o] :
! [X20: term > $o] :
? [X21: term] :
( ( X19 @ id @ X21 @ id )
!= ( X20 @ X21 ) ) )
& ( ! [X22: term,X23: subst,X24: term > $o,X25: term > $o,X26: term] :
( ( $true
= ( X25 @ ( sub @ X26 @ ( push @ X22 @ X23 ) ) ) )
| ( $true
!= ( X24 @ X26 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X27: term,X28: subst,X29: term > $o,X30: term > $o,X31: term] :
( ( ( X30 @ ( sub @ X31 @ ( push @ X27 @ X28 ) ) )
!= $true )
& ( $true
= ( X29 @ X31 ) ) ) )
& ( ( sP104 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP104 != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X32: d_term] : ( d_one = X32 )
& ( ? [X33: term] :
( ( sub @ X33 @ id )
!= X33 )
| ( sP102 = $true )
| ? [X34: term] :
! [X35: subst > term > term] :
? [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
!= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ! [X38: term] :
( ( sub @ X38 @ id )
= X38 )
& ( sP102 != $true )
& ! [X39: term] :
? [X40: subst > term > term] :
! [X41: subst,X42: term] :
( ( X40 @ X41 @ X42 )
= ( sub @ X39 @ ( push @ X42 @ X41 ) ) ) ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( sP100 = $true )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( sP100 != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( $true = sP98 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP98 ) )
& ( ( axshiftcons = $true )
| ? [X43: term,X44: subst] :
( ( comp @ sh @ ( push @ X43 @ X44 ) )
!= X44 ) )
& ( ! [X45: term,X46: subst] :
( ( comp @ sh @ ( push @ X45 @ X46 ) )
= X46 )
| ( axshiftcons != $true ) )
& ( ( shinj = $true )
| ? [X47: term,X48: term] :
( ( ( sub @ X47 @ sh )
= ( sub @ X48 @ sh ) )
& ( X47 != X48 ) ) )
& ( ! [X49: term,X50: term] :
( ( ( sub @ X50 @ sh )
!= ( sub @ X49 @ sh ) )
| ( X49 = X50 ) )
| ( shinj != $true ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP95 ) )
& ( ( $true = sP95 )
| ( substmonoid_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X51: subst,X52: term,X53: term > $o] :
! [X54: term > $o] :
? [X55: term] :
( ( X54 @ X55 )
!= ( X53 @ ( sub @ X55 @ ( push @ X52 @ X51 ) ) ) ) )
& ( ! [X56: subst,X57: term,X58: term > $o] :
? [X59: term > $o] :
! [X60: term] :
( ( X58 @ ( sub @ X60 @ ( push @ X57 @ X56 ) ) )
= ( X59 @ X60 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( $true = sP94 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP94 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP90 ) )
& ( ( $true = sP90 )
| ( hoasinduction_lem3a != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X61: subst,X62: term > $o,X63: term,X64: term > $o] :
( ? [X65: term] :
( ( X62 @ X65 )
!= ( X64 @ ( sub @ X65 @ ( push @ X63 @ X61 ) ) ) )
| ( ( X64 @ X63 )
!= $true )
| ( ( X62 @ one )
= $true ) )
| ? [X66: term,X67: subst] :
( ( sub @ one @ ( push @ X66 @ X67 ) )
!= X66 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X68: subst,X69: term > $o,X70: term,X71: term > $o] :
( ! [X72: term] :
( ( X71 @ ( sub @ X72 @ ( push @ X70 @ X68 ) ) )
= ( X69 @ X72 ) )
& ( ( X71 @ X70 )
= $true )
& ( $true
!= ( X69 @ one ) ) )
& ! [X73: term,X74: subst] :
( ( sub @ one @ ( push @ X73 @ X74 ) )
= X73 ) ) )
& ( ( hoaslamnotap = $true )
| ? [X75: term,X76: subst > term > term,X77: term] :
( ( ( ap @ ( sub @ X77 @ id ) @ X75 )
= ( lam @ ( X76 @ sh @ one ) ) )
& ! [X78: subst,X79: term,X80: subst] :
( ( X76 @ ( comp @ X78 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X76 @ X78 @ X79 ) @ X80 ) ) ) )
& ( ! [X81: term,X82: subst > term > term,X83: term] :
( ( ( lam @ ( X82 @ sh @ one ) )
!= ( ap @ ( sub @ X83 @ id ) @ X81 ) )
| ? [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
!= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( axvarshift = $true )
& ( ! [X87: term] :
? [X88: subst > term > term] :
! [X89: term,X90: subst] :
( ( sub @ X87 @ ( push @ X89 @ X90 ) )
= ( X88 @ X90 @ X89 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X91: term] :
! [X92: subst > term > term] :
? [X93: term,X94: subst] :
( ( sub @ X91 @ ( push @ X93 @ X94 ) )
!= ( X92 @ X94 @ X93 ) ) )
& ( ( substmonoid = $true )
| ? [X95: subst] :
( ( comp @ X95 @ id )
!= X95 )
| ? [X96: subst] :
( ( comp @ id @ X96 )
!= X96 ) )
& ( ( ! [X97: subst] :
( ( comp @ X97 @ id )
= X97 )
& ! [X98: subst] :
( ( comp @ id @ X98 )
= X98 ) )
| ( substmonoid != $true ) )
& ! [X99: d_term,X100: d_term] :
( ( X99 = X100 )
| ( ( d2term @ X99 )
!= ( d2term @ X100 ) ) )
& ! [X101: subst] :
? [X102: d_subst] :
( ( d2subst @ X102 )
= X101 )
& ( ! [X103: term,X104: term,X105: term,X106: term] :
( ( ( ap @ ( sub @ X104 @ id ) @ X103 )
!= ( ap @ ( sub @ X105 @ id ) @ X106 ) )
| ( X103 = X106 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X107: term,X108: term,X109: term,X110: term] :
( ( ( ap @ ( sub @ X109 @ id ) @ X110 )
= ( ap @ ( sub @ X108 @ id ) @ X107 ) )
& ( X107 != X110 ) ) )
& ( ( $true = sP88 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP88 ) )
& ( ( apinj2 = $true )
| ? [X111: term,X112: term,X113: term,X114: term] :
( ( X111 != X113 )
& ( ( ap @ X114 @ X111 )
= ( ap @ X112 @ X113 ) ) ) )
& ( ! [X115: term,X116: term,X117: term,X118: term] :
( ( X115 = X117 )
| ( ( ap @ X118 @ X115 )
!= ( ap @ X116 @ X117 ) ) )
| ( apinj2 != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP86 != $true ) )
& ( ( sP86 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP84 != $true ) )
& ( ( sP84 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP81 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP81 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X119: subst] :
( ( comp @ id @ X119 )
= X119 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X120: subst] :
( ( comp @ id @ X120 )
!= X120 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X121: term,X122: term > $o,X123: term > $o,X124: subst] :
( ( ( X122 @ one )
= $true )
| ( $true
!= ( X123 @ X121 ) )
| ? [X125: term] :
( ( X123 @ ( sub @ X125 @ ( push @ X121 @ X124 ) ) )
!= ( X122 @ X125 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X126: term,X127: term > $o,X128: term > $o,X129: subst] :
( ( $true
!= ( X127 @ one ) )
& ( $true
= ( X128 @ X126 ) )
& ! [X130: term] :
( ( X128 @ ( sub @ X130 @ ( push @ X126 @ X129 ) ) )
= ( X127 @ X130 ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X132: term] :
( ( sub @ X132 @ id )
!= X132 ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP77 != $true )
& ( $true != sP76 )
& ( sP75 != $true )
& ! [X133: term] :
( ( sub @ X133 @ id )
= X133 )
& ! [X134: subst > term > subst > $o] :
? [X135: term > $o] :
! [X136: term] :
( ( X135 @ X136 )
= ( X134 @ id @ X136 @ id ) ) ) )
& ( ( sP77 = $true )
| ( $true = sP76 )
| ( sP75 = $true )
| ? [X137: term] :
( ( sub @ X137 @ id )
!= X137 )
| ? [X138: subst > term > subst > $o] :
! [X139: term > $o] :
? [X140: term] :
( ( X138 @ id @ X140 @ id )
!= ( X139 @ X140 ) )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( sP69 = $true )
| ( induction != $true ) )
& ( ( induction = $true )
| ( sP69 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP65 = $true )
| ? [X141: term] :
( ( sub @ X141 @ id )
!= X141 )
| ( $true = sP66 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP65 != $true )
& ! [X142: term] :
( ( sub @ X142 @ id )
= X142 )
& ( $true != sP66 ) ) )
& ( ! [X143: term] :
( ( sub @ X143 @ id )
= X143 )
| ? [X144: term] :
( ( sub @ X144 @ id )
!= X144 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X145: term] :
( ( sub @ X145 @ id )
!= X145 )
& ! [X146: term] :
( ( sub @ X146 @ id )
= X146 ) ) )
& ( ( laminj = $true )
| ? [X147: term,X148: term] :
( ( X147 != X148 )
& ( ( lam @ X147 )
= ( lam @ X148 ) ) ) )
& ( ! [X149: term,X150: term] :
( ( X149 = X150 )
| ( ( lam @ X150 )
!= ( lam @ X149 ) ) )
| ( laminj != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP60 != $true ) )
& ( ( sP60 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoaslaminj_lthm != $true ) )
& ( ! [X151: term] :
? [X152: subst > term > term] :
( ( sub @ X151 @ ( push @ one @ sh ) )
= ( X152 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X153: term] :
! [X154: subst > term > term] :
( ( X154 @ sh @ one )
!= ( sub @ X153 @ ( push @ one @ sh ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( sP56 = $true )
| ( $true = sP55 )
| ? [X155: subst] :
( ( comp @ X155 @ id )
!= X155 )
| ? [X156: subst,X157: term] :
( ( sub @ one @ ( push @ X157 @ X156 ) )
!= X157 )
| ? [X158: subst,X159: term] :
( ( comp @ sh @ ( push @ X159 @ X158 ) )
!= X158 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP56 != $true )
& ( $true != sP55 )
& ! [X160: subst] :
( ( comp @ X160 @ id )
= X160 )
& ! [X161: subst,X162: term] :
( ( sub @ one @ ( push @ X162 @ X161 ) )
= X162 )
& ! [X163: subst,X164: term] :
( ( comp @ sh @ ( push @ X164 @ X163 ) )
= X163 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( $true != sP47 )
& ! [X165: term] :
( ( sub @ X165 @ id )
= X165 )
& ( $true != sP46 ) ) )
& ( ( $true = sP47 )
| ? [X166: term] :
( ( sub @ X166 @ id )
!= X166 )
| ( $true = sP46 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X167: d_subst] : ( d_id = X167 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ? [X168: term] :
( ( sub @ X168 @ id )
!= X168 )
| ( $true = sP39 )
| ( sP41 = $true )
| ? [X169: subst > term > subst > $o] :
! [X170: term > $o] :
? [X171: term] :
( ( X169 @ id @ X171 @ id )
!= ( X170 @ X171 ) )
| ( $true = sP40 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
& ( $true != sP39 )
& ( sP41 != $true )
& ! [X173: subst > term > subst > $o] :
? [X174: term > $o] :
! [X175: term] :
( ( X173 @ id @ X175 @ id )
= ( X174 @ X175 ) )
& ( $true != sP40 ) ) )
& ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X178: subst > term > term,X179: subst > term > term,X180: subst,X181: term] :
( ! [X182: subst,X183: subst,X184: term] :
( ( X179 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) )
= ( sub @ ( X179 @ X183 @ X184 ) @ X182 ) )
& ( ( X179 @ X180 @ X181 )
!= ( X178 @ X180 @ X181 ) )
& ! [X185: subst,X186: term,X187: subst] :
( ( sub @ ( X178 @ X187 @ X186 ) @ X185 )
= ( X178 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) ) )
& ( ( lam @ ( X178 @ sh @ one ) )
= ( lam @ ( X179 @ sh @ one ) ) ) ) )
& ( ! [X188: subst > term > term,X189: subst > term > term,X190: subst,X191: term] :
( ? [X192: subst,X193: subst,X194: term] :
( ( sub @ ( X189 @ X193 @ X194 ) @ X192 )
!= ( X189 @ ( comp @ X193 @ X192 ) @ ( sub @ X194 @ X192 ) ) )
| ( ( X189 @ X190 @ X191 )
= ( X188 @ X190 @ X191 ) )
| ? [X195: subst,X196: term,X197: subst] :
( ( sub @ ( X188 @ X197 @ X196 ) @ X195 )
!= ( X188 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) ) )
| ( ( lam @ ( X188 @ sh @ one ) )
!= ( lam @ ( X189 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X198: term,X199: term > $o,X200: subst] :
! [X201: term > $o] :
? [X202: term] :
( ( X199 @ ( sub @ X202 @ ( push @ X198 @ X200 ) ) )
!= ( X201 @ X202 ) ) )
& ( ! [X203: term,X204: term > $o,X205: subst] :
? [X206: term > $o] :
! [X207: term] :
( ( X204 @ ( sub @ X207 @ ( push @ X203 @ X205 ) ) )
= ( X206 @ X207 ) )
| ( pushprop_lem0 != $true ) )
& ! [X208: d_subst,X209: d_subst] :
( ( ( d2subst @ X209 )
!= ( d2subst @ X208 ) )
| ( X208 = X209 ) )
& ( termmset_gthm = $true )
& ( ! [X210: term,X211: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X211 ) )
| ( $true
= ( sP29 @ X211 ) )
| ( $true
= ( X211 @ id @ X210 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X212: term,X213: subst > term > subst > $o] :
( ( ( sP30 @ X213 )
!= $true )
& ( ( sP29 @ X213 )
!= $true )
& ( ( X213 @ id @ X212 @ id )
!= $true ) ) )
& ( ! [X214: term] :
? [X215: subst > term > term] :
! [X216: subst,X217: term] :
( ( X215 @ X216 @ X217 )
= ( sub @ X214 @ ( push @ X217 @ X216 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X218: term] :
! [X219: subst > term > term] :
? [X220: subst,X221: term] :
( ( X219 @ X220 @ X221 )
!= ( sub @ X218 @ ( push @ X221 @ X220 ) ) ) )
& ( ( induction2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP28 )
| ( induction2 != $true ) )
& ( ? [X222: subst,X223: term] :
( ( sub @ one @ ( push @ X223 @ X222 ) )
!= X223 )
| ! [X224: term,X225: term > $o,X226: term > $o,X227: subst,X228: term] :
( ( ( X225 @ X224 )
!= $true )
| ( ( X226 @ ( sub @ X224 @ ( push @ X228 @ X227 ) ) )
= $true ) )
| ? [X229: subst,X230: term] :
( ( comp @ sh @ ( push @ X230 @ X229 ) )
!= X229 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X231: subst,X232: term] :
( ( sub @ one @ ( push @ X232 @ X231 ) )
= X232 )
& ? [X233: term,X234: term > $o,X235: term > $o,X236: subst,X237: term] :
( ( ( X234 @ X233 )
= $true )
& ( ( X235 @ ( sub @ X233 @ ( push @ X237 @ X236 ) ) )
!= $true ) )
& ! [X238: subst,X239: term] :
( ( comp @ sh @ ( push @ X239 @ X238 ) )
= X238 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X240: term] :
? [X241: d_term] :
( ( d2term @ X241 )
= X240 )
& ( axclos = $true )
& ( ( axvarcons = $true )
| ? [X242: subst,X243: term] :
( ( sub @ one @ ( push @ X243 @ X242 ) )
!= X243 ) )
& ( ! [X244: subst,X245: term] :
( ( sub @ one @ ( push @ X245 @ X244 ) )
= X245 )
| ( axvarcons != $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ( sP25 != $true )
& ! [X246: term] :
( ( sub @ X246 @ id )
= X246 ) ) )
& ( ( sP25 = $true )
| ? [X247: term] :
( ( sub @ X247 @ id )
!= X247 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ! [X248: term] :
? [X249: subst > term > term] :
( ( sub @ X248 @ ( push @ one @ sh ) )
= ( X249 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X250: term] :
! [X251: subst > term > term] :
( ( X251 @ sh @ one )
!= ( sub @ X250 @ ( push @ one @ sh ) ) ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
| ? [X252: subst] :
( ( push @ ( sub @ one @ X252 ) @ ( comp @ sh @ X252 ) )
!= X252 ) )
& ( ! [X253: subst] :
( ( push @ ( sub @ one @ X253 ) @ ( comp @ sh @ X253 ) )
= X253 )
| ( axscons != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( $true != sP21 )
& ( $true != sP20 )
& ( sP19 != $true )
& ( sP18 != $true ) ) )
& ( ( $true = sP21 )
| ( $true = sP20 )
| ( sP19 = $true )
| ( sP18 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
& ( sP5 != $true )
& ( $true != sP4 ) ) )
& ( ? [X255: term] :
( ( sub @ X255 @ id )
!= X255 )
| ( sP5 = $true )
| ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X256: subst > term > subst > $o] :
? [X257: term > $o] :
! [X258: term] :
( ( X256 @ id @ X258 @ id )
= ( X257 @ X258 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X259: subst > term > subst > $o] :
! [X260: term > $o] :
? [X261: term] :
( ( X259 @ id @ X261 @ id )
!= ( X260 @ X261 ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X262: subst] :
( ( comp @ X262 @ id )
= X262 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X263: subst] :
( ( comp @ X263 @ id )
!= X263 ) ) ),
inference(rectify,[status(thm)],[f676]) ).
thf(f676,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X386: term,X387: term,X388: term,X389: term] :
( ( X386 != X388 )
& ( ( ap @ ( sub @ X388 @ id ) @ X389 )
= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
| ( sP109 != $true ) )
& ( ( sP109 = $true )
| ( hoasinduction != $true ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
| ? [X315: term,X316: term,X317: term,X318: term] :
( ( X315 != X317 )
& ( ( ap @ X317 @ X318 )
= ( ap @ X315 @ X316 ) ) ) )
& ( ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) )
| ( apinj1 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X65: subst > term > subst > $o] :
? [X66: term > $o] :
! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X65: subst > term > subst > $o] :
! [X66: term > $o] :
? [X67: term] :
( ( X65 @ id @ X67 @ id )
!= ( X66 @ X67 ) ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
!= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
& ( $true
= ( X79 @ X81 ) ) ) )
& ( ( sP104 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP104 != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X381: d_term] : ( d_one = X381 )
& ( ? [X261: term] :
( ( sub @ X261 @ id )
!= X261 )
| ( sP102 = $true )
| ? [X257: term] :
! [X258: subst > term > term] :
? [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
!= ( X258 @ X259 @ X260 ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ! [X261: term] :
( ( sub @ X261 @ id )
= X261 )
& ( sP102 != $true )
& ! [X257: term] :
? [X258: subst > term > term] :
! [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
= ( X258 @ X259 @ X260 ) ) ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( sP100 = $true )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( sP100 != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( $true = sP98 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP98 ) )
& ( ( axshiftcons = $true )
| ? [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
!= X181 ) )
& ( ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 )
| ( axshiftcons != $true ) )
& ( ( shinj = $true )
| ? [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
= ( sub @ X231 @ sh ) )
& ( X230 != X231 ) ) )
& ( ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) )
| ( shinj != $true ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP95 ) )
& ( ( $true = sP95 )
| ( substmonoid_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X272: subst,X273: term,X274: term > $o] :
! [X275: term > $o] :
? [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
!= ( X275 @ X276 ) ) )
& ( ! [X272: subst,X273: term,X274: term > $o] :
? [X275: term > $o] :
! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( $true = sP94 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP94 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP90 ) )
& ( ( $true = sP90 )
| ( hoasinduction_lem3a != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ? [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
!= ( X85 @ X88 ) )
| ( ( X87 @ X86 )
!= $true )
| ( $true
= ( X85 @ one ) ) )
| ? [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
!= X82 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) )
& ( ( X87 @ X86 )
= $true )
& ( $true
!= ( X85 @ one ) ) )
& ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 ) ) )
& ( ( hoaslamnotap = $true )
| ? [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
= ( lam @ ( X516 @ sh @ one ) ) )
& ! [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) ) )
& ( ! [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) )
| ? [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
!= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) )
| ( hoaslamnotap != $true ) )
& ( axvarshift = $true )
& ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X0: term] :
! [X1: subst > term > term] :
? [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
!= ( X1 @ X3 @ X2 ) ) )
& ( ( substmonoid = $true )
| ? [X385: subst] :
( ( comp @ X385 @ id )
!= X385 )
| ? [X384: subst] :
( ( comp @ id @ X384 )
!= X384 ) )
& ( ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) )
| ( substmonoid != $true ) )
& ! [X382: d_term,X383: d_term] :
( ( X382 = X383 )
| ( ( d2term @ X383 )
!= ( d2term @ X382 ) ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
& ( X182 != X185 ) ) )
& ( ( $true = sP88 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP88 ) )
& ( ( apinj2 = $true )
| ? [X89: term,X90: term,X91: term,X92: term] :
( ( X89 != X91 )
& ( ( ap @ X92 @ X89 )
= ( ap @ X90 @ X91 ) ) ) )
& ( ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) )
| ( apinj2 != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP86 != $true ) )
& ( ( sP86 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP84 != $true ) )
& ( ( sP84 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP81 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP81 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X22: subst] :
( ( comp @ id @ X22 )
!= X22 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
= ( X151 @ one ) )
| ( $true
!= ( X152 @ X150 ) )
| ? [X154: term] :
( ( X151 @ X154 )
!= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
!= ( X151 @ one ) )
& ( $true
= ( X152 @ X150 ) )
& ! [X154: term] :
( ( X151 @ X154 )
= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X314: term] :
( ( sub @ X314 @ id )
!= X314 ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP77 != $true )
& ( $true != sP76 )
& ( sP75 != $true )
& ! [X329: term] :
( ( sub @ X329 @ id )
= X329 )
& ! [X319: subst > term > subst > $o] :
? [X320: term > $o] :
! [X321: term] :
( ( X319 @ id @ X321 @ id )
= ( X320 @ X321 ) ) ) )
& ( ( sP77 = $true )
| ( $true = sP76 )
| ( sP75 = $true )
| ? [X329: term] :
( ( sub @ X329 @ id )
!= X329 )
| ? [X319: subst > term > subst > $o] :
! [X320: term > $o] :
? [X321: term] :
( ( X319 @ id @ X321 @ id )
!= ( X320 @ X321 ) )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( sP69 = $true )
| ( induction != $true ) )
& ( ( induction = $true )
| ( sP69 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP65 = $true )
| ? [X93: term] :
( ( sub @ X93 @ id )
!= X93 )
| ( $true = sP66 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP65 != $true )
& ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
& ( $true != sP66 ) ) )
& ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X21: term] :
( ( sub @ X21 @ id )
!= X21 )
& ! [X20: term] :
( ( sub @ X20 @ id )
= X20 ) ) )
& ( ( laminj = $true )
| ? [X109: term,X110: term] :
( ( X109 != X110 )
& ( ( lam @ X110 )
= ( lam @ X109 ) ) ) )
& ( ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) )
| ( laminj != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP60 != $true ) )
& ( ( sP60 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoaslaminj_lthm != $true ) )
& ( ! [X408: term] :
? [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
= ( X409 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X408: term] :
! [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
!= ( X409 @ sh @ one ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( sP56 = $true )
| ( $true = sP55 )
| ? [X50: subst] :
( ( comp @ X50 @ id )
!= X50 )
| ? [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
!= X47 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP56 != $true )
& ( $true != sP55 )
& ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
& ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
& ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( $true != sP47 )
& ! [X155: term] :
( ( sub @ X155 @ id )
= X155 )
& ( $true != sP46 ) ) )
& ( ( $true = sP47 )
| ? [X155: term] :
( ( sub @ X155 @ id )
!= X155 )
| ( $true = sP46 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ? [X420: term] :
( ( sub @ X420 @ id )
!= X420 )
| ( $true = sP39 )
| ( sP41 = $true )
| ? [X410: subst > term > subst > $o] :
! [X411: term > $o] :
? [X412: term] :
( ( X410 @ id @ X412 @ id )
!= ( X411 @ X412 ) )
| ( $true = sP40 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ! [X420: term] :
( ( sub @ X420 @ id )
= X420 )
& ( $true != sP39 )
& ( sP41 != $true )
& ! [X410: subst > term > subst > $o] :
? [X411: term > $o] :
! [X412: term] :
( ( X410 @ id @ X412 @ id )
= ( X411 @ X412 ) )
& ( $true != sP40 ) ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X297: term] :
( ( sub @ X297 @ id )
!= X297 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
& ( ( X36 @ X38 @ X39 )
!= ( X37 @ X38 @ X39 ) )
& ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
& ( ( lam @ ( X36 @ sh @ one ) )
= ( lam @ ( X37 @ sh @ one ) ) ) ) )
& ( ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ? [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
!= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ? [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
!= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X186: term,X187: term > $o,X188: subst] :
! [X189: term > $o] :
? [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
!= ( X189 @ X190 ) ) )
& ( ! [X186: term,X187: term > $o,X188: subst] :
? [X189: term > $o] :
! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) )
| ( pushprop_lem0 != $true ) )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
!= ( d2subst @ X253 ) )
| ( X253 = X254 ) )
& ( termmset_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X123 ) )
| ( ( sP29 @ X123 )
= $true )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X122: term,X123: subst > term > subst > $o] :
( ( $true
!= ( sP30 @ X123 ) )
& ( ( sP29 @ X123 )
!= $true )
& ( ( X123 @ id @ X122 @ id )
!= $true ) ) )
& ( ! [X23: term] :
? [X24: subst > term > term] :
! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X23: term] :
! [X24: subst > term > term] :
? [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
!= ( sub @ X23 @ ( push @ X26 @ X25 ) ) ) )
& ( ( induction2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP28 )
| ( induction2 != $true ) )
& ( ? [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
!= X532 )
| ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) )
| ? [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
!= X533 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
= X532 )
& ? [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
= ( X536 @ X535 ) )
& ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
!= $true ) )
& ! [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
= X533 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( axclos = $true )
& ( ( axvarcons = $true )
| ? [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
!= X121 ) )
& ( ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 )
| ( axvarcons != $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ( sP25 != $true )
& ! [X131: term] :
( ( sub @ X131 @ id )
= X131 ) ) )
& ( ( sP25 = $true )
| ? [X131: term] :
( ( sub @ X131 @ id )
!= X131 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ! [X255: term] :
? [X256: subst > term > term] :
( ( X256 @ sh @ one )
= ( sub @ X255 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X255: term] :
! [X256: subst > term > term] :
( ( X256 @ sh @ one )
!= ( sub @ X255 @ ( push @ one @ sh ) ) ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
| ? [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
!= X298 ) )
& ( ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 )
| ( axscons != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( $true != sP21 )
& ( $true != sP20 )
& ( sP19 != $true )
& ( sP18 != $true ) ) )
& ( ( $true = sP21 )
| ( $true = sP20 )
| ( sP19 = $true )
| ( sP18 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ! [X349: term] :
( ( sub @ X349 @ id )
= X349 )
& ( sP5 != $true )
& ( $true != sP4 ) ) )
& ( ? [X349: term] :
( ( sub @ X349 @ id )
!= X349 )
| ( sP5 = $true )
| ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X232: subst > term > subst > $o] :
? [X233: term > $o] :
! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X232: subst > term > subst > $o] :
! [X233: term > $o] :
? [X234: term] :
( ( X232 @ id @ X234 @ id )
!= ( X233 @ X234 ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X119: subst] :
( ( comp @ X119 @ id )
!= X119 ) ) ),
inference(flattening,[status(thm)],[f675]) ).
thf(f675,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X386: term,X387: term,X388: term,X389: term] :
( ( X386 != X388 )
& ( ( ap @ ( sub @ X388 @ id ) @ X389 )
= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
| ( sP109 != $true ) )
& ( ( sP109 = $true )
| ( hoasinduction != $true ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
| ? [X315: term,X316: term,X317: term,X318: term] :
( ( X315 != X317 )
& ( ( ap @ X317 @ X318 )
= ( ap @ X315 @ X316 ) ) ) )
& ( ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) )
| ( apinj1 != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X65: subst > term > subst > $o] :
? [X66: term > $o] :
! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X65: subst > term > subst > $o] :
! [X66: term > $o] :
? [X67: term] :
( ( X65 @ id @ X67 @ id )
!= ( X66 @ X67 ) ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
!= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
& ( $true
= ( X79 @ X81 ) ) ) )
& ( ( sP104 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP104 != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X381: d_term] : ( d_one = X381 )
& ( ? [X261: term] :
( ( sub @ X261 @ id )
!= X261 )
| ( sP102 = $true )
| ? [X257: term] :
! [X258: subst > term > term] :
? [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
!= ( X258 @ X259 @ X260 ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ! [X261: term] :
( ( sub @ X261 @ id )
= X261 )
& ( sP102 != $true )
& ! [X257: term] :
? [X258: subst > term > term] :
! [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
= ( X258 @ X259 @ X260 ) ) ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( sP100 = $true )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( sP100 != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( $true = sP98 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP98 ) )
& ( ( axshiftcons = $true )
| ? [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
!= X181 ) )
& ( ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 )
| ( axshiftcons != $true ) )
& ( ( shinj = $true )
| ? [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
= ( sub @ X231 @ sh ) )
& ( X230 != X231 ) ) )
& ( ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) )
| ( shinj != $true ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP95 ) )
& ( ( $true = sP95 )
| ( substmonoid_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X272: subst,X273: term,X274: term > $o] :
! [X275: term > $o] :
? [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
!= ( X275 @ X276 ) ) )
& ( ! [X272: subst,X273: term,X274: term > $o] :
? [X275: term > $o] :
! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( $true = sP94 )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP94 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP90 ) )
& ( ( $true = sP90 )
| ( hoasinduction_lem3a != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ? [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
!= ( X85 @ X88 ) )
| ( ( X87 @ X86 )
!= $true )
| ( $true
= ( X85 @ one ) ) )
| ? [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
!= X82 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) )
& ( ( X87 @ X86 )
= $true )
& ( $true
!= ( X85 @ one ) ) )
& ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 ) ) )
& ( ( hoaslamnotap = $true )
| ? [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
= ( lam @ ( X516 @ sh @ one ) ) )
& ! [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) ) )
& ( ! [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) )
| ? [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
!= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) )
| ( hoaslamnotap != $true ) )
& ( axvarshift = $true )
& ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X0: term] :
! [X1: subst > term > term] :
? [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
!= ( X1 @ X3 @ X2 ) ) )
& ( ( substmonoid = $true )
| ? [X385: subst] :
( ( comp @ X385 @ id )
!= X385 )
| ? [X384: subst] :
( ( comp @ id @ X384 )
!= X384 ) )
& ( ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) )
| ( substmonoid != $true ) )
& ! [X382: d_term,X383: d_term] :
( ( X382 = X383 )
| ( ( d2term @ X383 )
!= ( d2term @ X382 ) ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
& ( X182 != X185 ) ) )
& ( ( $true = sP88 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP88 ) )
& ( ( apinj2 = $true )
| ? [X89: term,X90: term,X91: term,X92: term] :
( ( X89 != X91 )
& ( ( ap @ X92 @ X89 )
= ( ap @ X90 @ X91 ) ) ) )
& ( ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) )
| ( apinj2 != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP86 != $true ) )
& ( ( sP86 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP84 != $true ) )
& ( ( sP84 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP81 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP81 ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X22: subst] :
( ( comp @ id @ X22 )
!= X22 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
= ( X151 @ one ) )
| ( $true
!= ( X152 @ X150 ) )
| ? [X154: term] :
( ( X151 @ X154 )
!= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
!= ( X151 @ one ) )
& ( $true
= ( X152 @ X150 ) )
& ! [X154: term] :
( ( X151 @ X154 )
= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X314: term] :
( ( sub @ X314 @ id )
!= X314 ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP77 != $true )
& ( $true != sP76 )
& ( sP75 != $true )
& ! [X329: term] :
( ( sub @ X329 @ id )
= X329 )
& ! [X319: subst > term > subst > $o] :
? [X320: term > $o] :
! [X321: term] :
( ( X319 @ id @ X321 @ id )
= ( X320 @ X321 ) ) ) )
& ( ( sP77 = $true )
| ( $true = sP76 )
| ( sP75 = $true )
| ? [X329: term] :
( ( sub @ X329 @ id )
!= X329 )
| ? [X319: subst > term > subst > $o] :
! [X320: term > $o] :
? [X321: term] :
( ( X319 @ id @ X321 @ id )
!= ( X320 @ X321 ) )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( sP69 = $true )
| ( induction != $true ) )
& ( ( induction = $true )
| ( sP69 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP65 = $true )
| ? [X93: term] :
( ( sub @ X93 @ id )
!= X93 )
| ( $true = sP66 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP65 != $true )
& ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
& ( $true != sP66 ) ) )
& ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X21: term] :
( ( sub @ X21 @ id )
!= X21 )
& ! [X20: term] :
( ( sub @ X20 @ id )
= X20 ) ) )
& ( ( laminj = $true )
| ? [X109: term,X110: term] :
( ( X109 != X110 )
& ( ( lam @ X110 )
= ( lam @ X109 ) ) ) )
& ( ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) )
| ( laminj != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP60 != $true ) )
& ( ( sP60 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP58 ) )
& ( ( $true = sP58 )
| ( hoaslaminj_lthm != $true ) )
& ( ! [X408: term] :
? [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
= ( X409 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X408: term] :
! [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
!= ( X409 @ sh @ one ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( sP56 = $true )
| ( $true = sP55 )
| ? [X50: subst] :
( ( comp @ X50 @ id )
!= X50 )
| ? [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
!= X47 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP56 != $true )
& ( $true != sP55 )
& ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
& ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
& ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
| ( sP50 != $true ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( $true != sP47 )
& ! [X155: term] :
( ( sub @ X155 @ id )
= X155 )
& ( $true != sP46 ) ) )
& ( ( $true = sP47 )
| ? [X155: term] :
( ( sub @ X155 @ id )
!= X155 )
| ( $true = sP46 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ? [X420: term] :
( ( sub @ X420 @ id )
!= X420 )
| ( $true = sP39 )
| ( sP41 = $true )
| ? [X410: subst > term > subst > $o] :
! [X411: term > $o] :
? [X412: term] :
( ( X410 @ id @ X412 @ id )
!= ( X411 @ X412 ) )
| ( $true = sP40 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ! [X420: term] :
( ( sub @ X420 @ id )
= X420 )
& ( $true != sP39 )
& ( sP41 != $true )
& ! [X410: subst > term > subst > $o] :
? [X411: term > $o] :
! [X412: term] :
( ( X410 @ id @ X412 @ id )
= ( X411 @ X412 ) )
& ( $true != sP40 ) ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X297: term] :
( ( sub @ X297 @ id )
!= X297 ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
& ( ( X36 @ X38 @ X39 )
!= ( X37 @ X38 @ X39 ) )
& ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
& ( ( lam @ ( X36 @ sh @ one ) )
= ( lam @ ( X37 @ sh @ one ) ) ) ) )
& ( ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ? [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
!= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ? [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
!= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X186: term,X187: term > $o,X188: subst] :
! [X189: term > $o] :
? [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
!= ( X189 @ X190 ) ) )
& ( ! [X186: term,X187: term > $o,X188: subst] :
? [X189: term > $o] :
! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) )
| ( pushprop_lem0 != $true ) )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
!= ( d2subst @ X253 ) )
| ( X253 = X254 ) )
& ( termmset_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X123 ) )
| ( ( sP29 @ X123 )
= $true )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X122: term,X123: subst > term > subst > $o] :
( ( $true
!= ( sP30 @ X123 ) )
& ( ( sP29 @ X123 )
!= $true )
& ( ( X123 @ id @ X122 @ id )
!= $true ) ) )
& ( ! [X23: term] :
? [X24: subst > term > term] :
! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X23: term] :
! [X24: subst > term > term] :
? [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
!= ( sub @ X23 @ ( push @ X26 @ X25 ) ) ) )
& ( ( induction2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP28 )
| ( induction2 != $true ) )
& ( ? [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
!= X532 )
| ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) )
| ? [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
!= X533 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
= X532 )
& ? [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
= ( X536 @ X535 ) )
& ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
!= $true ) )
& ! [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
= X533 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( axclos = $true )
& ( ( axvarcons = $true )
| ? [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
!= X121 ) )
& ( ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 )
| ( axvarcons != $true ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ( sP25 != $true )
& ! [X131: term] :
( ( sub @ X131 @ id )
= X131 ) ) )
& ( ( sP25 = $true )
| ? [X131: term] :
( ( sub @ X131 @ id )
!= X131 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ! [X255: term] :
? [X256: subst > term > term] :
( ( X256 @ sh @ one )
= ( sub @ X255 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X255: term] :
! [X256: subst > term > term] :
( ( X256 @ sh @ one )
!= ( sub @ X255 @ ( push @ one @ sh ) ) ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
| ? [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
!= X298 ) )
& ( ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 )
| ( axscons != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( $true != sP21 )
& ( $true != sP20 )
& ( sP19 != $true )
& ( sP18 != $true ) ) )
& ( ( $true = sP21 )
| ( $true = sP20 )
| ( sP19 = $true )
| ( sP18 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ! [X349: term] :
( ( sub @ X349 @ id )
= X349 )
& ( sP5 != $true )
& ( $true != sP4 ) ) )
& ( ? [X349: term] :
( ( sub @ X349 @ id )
!= X349 )
| ( sP5 = $true )
| ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X232: subst > term > subst > $o] :
? [X233: term > $o] :
! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X232: subst > term > subst > $o] :
! [X233: term > $o] :
? [X234: term] :
( ( X232 @ id @ X234 @ id )
!= ( X233 @ X234 ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X119: subst] :
( ( comp @ X119 @ id )
!= X119 ) ) ),
inference(nnf_transformation,[status(thm)],[f126]) ).
thf(f126,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
<=> ( sP109 = $true ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X65: subst > term > subst > $o] :
? [X66: term > $o] :
! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( sP104 = $true )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X381: d_term] : ( d_one = X381 )
& ( ( ? [X261: term] :
( ( sub @ X261 @ id )
!= X261 )
| ( sP102 = $true )
| ? [X257: term] :
! [X258: subst > term > term] :
? [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
!= ( X258 @ X259 @ X260 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( sP100 = $true )
<=> ( hoasapinj1_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( $true = sP98 )
<=> ( induction2lem = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 ) )
& ( ( shinj = $true )
<=> ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
<=> ( $true = sP95 ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X272: subst,X273: term,X274: term > $o] :
? [X275: term > $o] :
! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( $true = sP94 )
<=> ( hoasinduction_lem3 = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ( $true = sP90 ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ? [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
!= ( X85 @ X88 ) )
| ( ( X87 @ X86 )
!= $true )
| ( $true
= ( X85 @ one ) ) )
| ? [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
!= X82 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) )
| ? [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
!= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) ) )
& ( axvarshift = $true )
& ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( substmonoid = $true )
<=> ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) ) )
& ! [X382: d_term,X383: d_term] :
( ( X382 = X383 )
| ( ( d2term @ X383 )
!= ( d2term @ X382 ) ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( $true = sP88 )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( sP86 = $true ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ( sP84 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP81 )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
= ( X151 @ one ) )
| ( $true
!= ( X152 @ X150 ) )
| ? [X154: term] :
( ( X151 @ X154 )
!= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ( sP77 = $true )
| ( $true = sP76 )
| ( sP75 = $true )
| ? [X329: term] :
( ( sub @ X329 @ id )
!= X329 )
| ? [X319: subst > term > subst > $o] :
! [X320: term > $o] :
? [X321: term] :
( ( X319 @ id @ X321 @ id )
!= ( X320 @ X321 ) ) ) )
& ( ( sP69 = $true )
<=> ( induction = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ( sP65 = $true )
| ? [X93: term] :
( ( sub @ X93 @ id )
!= X93 )
| ( $true = sP66 ) )
<=> ( induction2_lthm = $true ) )
& ( ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 ) )
<=> ( termmset_lthm = $true ) )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ( sP60 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( $true = sP58 ) )
& ( ! [X408: term] :
? [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
= ( X409 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( ( sP56 = $true )
| ( $true = sP55 )
| ? [X50: subst] :
( ( comp @ X50 @ id )
!= X50 )
| ? [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
!= X47 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ( sP50 = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ( $true = sP47 )
| ? [X155: term] :
( ( sub @ X155 @ id )
!= X155 )
| ( $true = sP46 ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( ? [X420: term] :
( ( sub @ X420 @ id )
!= X420 )
| ( $true = sP39 )
| ( sP41 = $true )
| ? [X410: subst > term > subst > $o] :
! [X411: term > $o] :
? [X412: term] :
( ( X410 @ id @ X412 @ id )
!= ( X411 @ X412 ) )
| ( $true = sP40 ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
<=> ( termmset = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ? [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
!= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ? [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
!= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X186: term,X187: term > $o,X188: subst] :
? [X189: term > $o] :
! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) ) )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
!= ( d2subst @ X253 ) )
| ( X253 = X254 ) )
& ( termmset_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X123 ) )
| ( ( sP29 @ X123 )
= $true )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X23: term] :
? [X24: subst > term > term] :
! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( induction2 = $true )
<=> ( $true = sP28 ) )
& ( ( ? [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
!= X532 )
| ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) )
| ? [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
!= X533 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( axclos = $true )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ( sP25 = $true )
| ? [X131: term] :
( ( sub @ X131 @ id )
!= X131 ) ) )
& ( ! [X255: term] :
? [X256: subst > term > term] :
( ( X256 @ sh @ one )
= ( sub @ X255 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
<=> ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ( $true = sP21 )
| ( $true = sP20 )
| ( sP19 = $true )
| ( sP18 = $true ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ? [X349: term] :
( ( sub @ X349 @ id )
!= X349 )
| ( sP5 = $true )
| ( $true = sP4 ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ( sP1 = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X232: subst > term > subst > $o] :
? [X233: term > $o] :
! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) ) ),
inference(definition_folding,[status(thm)],[f13,f125,f124,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,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]) ).
thf(f16,plain,
! [X223: subst > term > subst > $o] :
( ( $true
= ( sP0 @ X223 ) )
<=> ? [X225: subst > term > term] :
( ! [X229: term] :
( ( $true
= ( X223 @ id @ ( X225 @ id @ X229 ) @ id ) )
| ( $true
!= ( X223 @ id @ X229 @ id ) ) )
& ! [X226: subst,X227: term,X228: subst] :
( ( X225 @ ( comp @ X228 @ X226 ) @ ( sub @ X227 @ X226 ) )
= ( sub @ ( X225 @ X228 @ X227 ) @ X226 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( sP1 = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ( $true
= ( sP0 @ X223 ) )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
! [X359: subst > term > subst > $o] :
( ( ( sP2 @ X359 )
= $true )
<=> ? [X360: subst > term > term] :
( ! [X361: term,X362: subst,X363: subst] :
( ( sub @ ( X360 @ X362 @ X361 ) @ X363 )
= ( X360 @ ( comp @ X362 @ X363 ) @ ( sub @ X361 @ X363 ) ) )
& ! [X364: term] :
( ( ( X359 @ id @ ( X360 @ id @ X364 ) @ id )
= $true )
| ( ( X359 @ id @ X364 @ id )
!= $true ) )
& ( ( X359 @ id @ ( lam @ ( X360 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X350: subst > term > subst > $o] :
( ( ( sP3 @ X350 )
= $true )
<=> ! [X352: subst > term > term] :
( ? [X356: term] :
( ( ( X350 @ id @ ( X352 @ id @ X356 ) @ id )
!= $true )
& ( ( X350 @ id @ X356 @ id )
= $true ) )
| ? [X353: term,X354: subst,X355: subst] :
( ( X352 @ ( comp @ X355 @ X354 ) @ ( sub @ X353 @ X354 ) )
!= ( sub @ ( X352 @ X355 @ X353 ) @ X354 ) )
| ( $true
= ( X350 @ id @ ( lam @ ( X352 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
( ( $true = sP4 )
<=> ! [X358: term,X359: subst > term > subst > $o] :
( ( ( sP2 @ X359 )
= $true )
| ( $true
= ( X359 @ id @ ( lam @ X358 ) @ id ) )
| ? [X365: term] :
( ( $true
!= ( X359 @ id @ ( sub @ X358 @ ( push @ X365 @ id ) ) @ id ) )
& ( $true
= ( X359 @ id @ X365 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
( ( sP5 = $true )
<=> ? [X350: subst > term > subst > $o,X351: term] :
( ( $true
!= ( X350 @ id @ ( lam @ ( sub @ X351 @ ( push @ one @ sh ) ) ) @ id ) )
& ( ( sP3 @ X350 )
= $true )
& ! [X357: term] :
( ( $true
!= ( X350 @ id @ X357 @ id ) )
| ( ( X350 @ id @ ( sub @ X351 @ ( push @ X357 @ id ) ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X497: subst > term > subst > $o] :
( ( $true
= ( sP6 @ X497 ) )
<=> ? [X510: subst > term > term] :
( ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X510 @ X512 @ X513 ) @ X514 )
= ( X510 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
& ( $true
!= ( X497 @ id @ ( lam @ ( X510 @ sh @ one ) ) @ id ) )
& ! [X511: term] :
( ( ( X497 @ id @ ( X510 @ id @ X511 ) @ id )
= $true )
| ( $true
!= ( X497 @ id @ X511 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
! [X497: subst > term > subst > $o] :
( ( $true
= ( sP7 @ X497 ) )
<=> ? [X508: term,X509: term] :
( ( $true
!= ( X497 @ id @ ( ap @ ( sub @ X509 @ id ) @ X508 ) @ id ) )
& ( ( X497 @ id @ X509 @ id )
= $true )
& ( ( X497 @ id @ X508 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
! [X497: subst > term > subst > $o] :
( ( ( sP8 @ X497 )
= $true )
<=> ? [X499: subst,X500: subst,X501: subst,X502: term] :
( ( ( X497 @ ( comp @ X501 @ X500 ) @ ( sub @ X502 @ X500 ) @ X499 )
= $true )
& ( $true
!= ( X497 @ X501 @ X502 @ ( comp @ X500 @ X499 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
! [X497: subst > term > subst > $o] :
( ( ( sP9 @ X497 )
= $true )
<=> ? [X507: term] :
( ( $true
= ( var @ ( sub @ X507 @ id ) ) )
& ( ( X497 @ id @ X507 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
! [X481: subst > term > subst > $o] :
( ( ( sP10 @ X481 )
= $true )
<=> ! [X483: subst > term > term] :
( ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) )
| ? [X484: term] :
( ( $true
= ( X481 @ id @ X484 @ id ) )
& ( $true
!= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) ) )
| ? [X485: subst,X486: term,X487: subst] :
( ( sub @ ( X483 @ X485 @ X486 ) @ X487 )
!= ( X483 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
! [X481: subst > term > subst > $o,X482: term] :
( ( ( sP11 @ X482 @ X481 )
= $true )
<=> ! [X488: term] :
( ( ( X481 @ id @ X488 @ id )
!= $true )
| ( $true
= ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X481: subst > term > subst > $o] :
( ( ( sP12 @ X481 )
= $true )
<=> ! [X493: subst,X494: term,X495: subst,X496: subst] :
( ( $true
!= ( X481 @ ( comp @ X493 @ X496 ) @ ( sub @ X494 @ X496 ) @ X495 ) )
| ( $true
= ( X481 @ X493 @ X494 @ ( comp @ X496 @ X495 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
! [X469: subst > term > subst > $o] :
( ( $true
= ( sP13 @ X469 ) )
<=> ! [X479: term,X480: term] :
( ( $true
!= ( X469 @ id @ X479 @ id ) )
| ( $true
= ( X469 @ id @ ( ap @ ( sub @ X480 @ id ) @ X479 ) @ id ) )
| ( $true
!= ( X469 @ id @ X480 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
! [X469: subst > term > subst > $o] :
( ( ( sP14 @ X469 )
= $true )
<=> ! [X471: term,X472: subst,X473: subst,X474: subst] :
( ( ( X469 @ X473 @ X471 @ ( comp @ X474 @ X472 ) )
!= $true )
| ( ( X469 @ ( comp @ X473 @ X474 ) @ ( sub @ X471 @ X474 ) @ X472 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
! [X461: term > $o] :
( ( $true
= ( sP15 @ X461 ) )
<=> ! [X465: term,X466: term] :
( ( $true
!= ( X461 @ X466 ) )
| ( ( X461 @ ( ap @ X466 @ X465 ) )
= $true )
| ( ( X461 @ X465 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
! [X461: term > $o] :
( ( ( sP16 @ X461 )
= $true )
<=> ! [X467: term] :
( ( $true
!= ( var @ X467 ) )
| ( $true
= ( X461 @ X467 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
! [X461: term > $o] :
( ( ( sP17 @ X461 )
= $true )
<=> ! [X463: term] :
( ? [X464: term] :
( ( $true
!= ( X461 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) )
& ( $true
= ( X461 @ X464 ) ) )
| ( $true
= ( X461 @ ( lam @ X463 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
( ( sP18 = $true )
<=> ! [X497: subst > term > subst > $o,X498: term] :
( ? [X503: subst,X504: subst,X505: subst,X506: term] :
( ( ( X497 @ X503 @ X506 @ ( comp @ X505 @ X504 ) )
= $true )
& ( ( X497 @ ( comp @ X503 @ X505 ) @ ( sub @ X506 @ X505 ) @ X504 )
!= $true ) )
| ( $true
= ( X497 @ id @ X498 @ id ) )
| ( ( sP9 @ X497 )
= $true )
| ( ( sP8 @ X497 )
= $true )
| ( $true
= ( sP6 @ X497 ) )
| ( $true
= ( sP7 @ X497 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
( ( sP19 = $true )
<=> ? [X481: subst > term > subst > $o,X482: term] :
( ( ( X481 @ id @ ( lam @ X482 ) @ id )
!= $true )
& ! [X489: subst,X490: term,X491: subst,X492: subst] :
( ( $true
!= ( X481 @ X491 @ X490 @ ( comp @ X492 @ X489 ) ) )
| ( $true
= ( X481 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) @ X489 ) ) )
& ( ( sP10 @ X481 )
= $true )
& ( ( sP12 @ X481 )
= $true )
& ( ( sP11 @ X482 @ X481 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( $true = sP20 )
<=> ? [X468: term,X469: subst > term > subst > $o,X470: term] :
( ( $true
= ( sP13 @ X469 ) )
& ! [X475: subst,X476: subst,X477: term,X478: subst] :
( ( ( X469 @ ( comp @ X476 @ X478 ) @ ( sub @ X477 @ X478 ) @ X475 )
!= $true )
| ( $true
= ( X469 @ X476 @ X477 @ ( comp @ X478 @ X475 ) ) ) )
& ( $true
!= ( X469 @ id @ ( ap @ X468 @ X470 ) @ id ) )
& ( $true
= ( X469 @ id @ X468 @ id ) )
& ( ( X469 @ id @ X470 @ id )
= $true )
& ( ( sP14 @ X469 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
( ( $true = sP21 )
<=> ? [X461: term > $o,X462: term] :
( ( $true
= ( sP15 @ X461 ) )
& ( ( sP17 @ X461 )
= $true )
& ( ( sP16 @ X461 )
= $true )
& ( $true
!= ( X461 @ X462 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
! [X132: subst > term > subst > $o] :
( ( ( sP22 @ X132 )
= $true )
<=> ? [X135: subst > term > term] :
( ( $true
!= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
& ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
& ! [X139: term] :
( ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) )
| ( $true
!= ( X132 @ id @ X139 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
! [X132: subst > term > subst > $o] :
( ( $true
= ( sP23 @ X132 ) )
<=> ? [X141: subst,X142: subst,X143: subst,X144: term] :
( ( $true
!= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) )
& ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
! [X134: term > $o,X133: term] :
( ( ( sP24 @ X133 @ X134 )
= $true )
<=> ? [X149: term] :
( ( $true
= ( X134 @ X149 ) )
& ( $true
!= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
( ( sP25 = $true )
<=> ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ? [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
!= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) )
& ( $true
= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) ) )
| ? [X140: term] :
( ( X132 @ id @ X140 @ id )
!= ( X134 @ X140 ) )
| ( ( sP24 @ X133 @ X134 )
= $true )
| ( ( sP22 @ X132 )
= $true )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ( $true
= ( sP23 @ X132 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
! [X191: term > $o] :
( ( ( sP26 @ X191 )
= $true )
<=> ? [X195: term] :
( ! [X196: term] :
( ( ( X191 @ X196 )
!= $true )
| ( $true
= ( X191 @ ( sub @ X195 @ ( push @ X196 @ id ) ) ) ) )
& ( ( X191 @ ( lam @ X195 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
! [X191: term > $o] :
( ( $true
= ( sP27 @ X191 ) )
<=> ? [X193: term,X194: term] :
( ( ( X191 @ ( ap @ X194 @ X193 ) )
!= $true )
& ( ( X191 @ X193 )
= $true )
& ( $true
= ( X191 @ X194 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( $true = sP28 )
<=> ! [X191: term > $o,X192: term] :
( ( $true
= ( sP27 @ X191 ) )
| ? [X197: term] :
( ( $true
= ( var @ X197 ) )
& ( $true
!= ( X191 @ X197 ) ) )
| ( $true
= ( X191 @ X192 ) )
| ( ( sP26 @ X191 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
! [X123: subst > term > subst > $o] :
( ( ( sP29 @ X123 )
= $true )
<=> ? [X124: subst > term > term] :
( ( $true
!= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) )
& ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
& ! [X128: term] :
( ( ( X123 @ id @ X128 @ id )
!= $true )
| ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
! [X123: subst > term > subst > $o] :
( ( $true
= ( sP30 @ X123 ) )
<=> ? [X129: term,X130: term] :
( ( $true
!= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) )
& ( ( X123 @ id @ X130 @ id )
= $true )
& ( $true
= ( X123 @ id @ X129 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
! [X421: subst > term > subst > $o] :
( ( $true
= ( sP31 @ X421 ) )
<=> ! [X426: subst > term > term] :
( ? [X427: subst,X428: term,X429: subst] :
( ( X426 @ ( comp @ X427 @ X429 ) @ ( sub @ X428 @ X429 ) )
!= ( sub @ ( X426 @ X427 @ X428 ) @ X429 ) )
| ? [X430: term] :
( ( $true
!= ( X421 @ id @ ( X426 @ id @ X430 ) @ id ) )
& ( ( X421 @ id @ X430 @ id )
= $true ) )
| ( ( X421 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
! [X413: term > $o] :
( ( $true
= ( sP32 @ X413 ) )
<=> ! [X417: term,X418: term] :
( ( $true
= ( X413 @ ( ap @ X417 @ X418 ) ) )
| ( $true
!= ( X413 @ X417 ) )
| ( $true
!= ( X413 @ X418 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
! [X413: term > $o] :
( ( $true
= ( sP33 @ X413 ) )
<=> ! [X419: term] :
( ( ( var @ X419 )
!= $true )
| ( ( X413 @ X419 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
! [X413: term > $o] :
( ( $true
= ( sP34 @ X413 ) )
<=> ! [X415: term] :
( ( $true
= ( X413 @ ( lam @ X415 ) ) )
| ? [X416: term] :
( ( ( X413 @ X416 )
= $true )
& ( $true
!= ( X413 @ ( sub @ X415 @ ( push @ X416 @ id ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
! [X432: subst > term > subst > $o] :
( ( $true
= ( sP35 @ X432 ) )
<=> ? [X444: subst > term > term] :
( ! [X445: term,X446: subst,X447: subst] :
( ( X444 @ ( comp @ X446 @ X447 ) @ ( sub @ X445 @ X447 ) )
= ( sub @ ( X444 @ X446 @ X445 ) @ X447 ) )
& ! [X448: term] :
( ( $true
!= ( X432 @ id @ X448 @ id ) )
| ( ( X432 @ id @ ( X444 @ id @ X448 ) @ id )
= $true ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
! [X432: subst > term > subst > $o] :
( ( $true
= ( sP36 @ X432 ) )
<=> ? [X433: term,X434: term] :
( ( ( X432 @ id @ ( ap @ ( sub @ X433 @ id ) @ X434 ) @ id )
!= $true )
& ( $true
= ( X432 @ id @ X433 @ id ) )
& ( $true
= ( X432 @ id @ X434 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
! [X432: subst > term > subst > $o] :
( ( ( sP37 @ X432 )
= $true )
<=> ? [X435: subst,X436: subst,X437: term,X438: subst] :
( ( ( X432 @ X436 @ X437 @ ( comp @ X435 @ X438 ) )
!= $true )
& ( ( X432 @ ( comp @ X436 @ X435 ) @ ( sub @ X437 @ X435 ) @ X438 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X432: subst > term > subst > $o] :
( ( ( sP38 @ X432 )
= $true )
<=> ? [X439: term] :
( ( ( var @ ( sub @ X439 @ id ) )
= $true )
& ( ( X432 @ id @ X439 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( $true = sP39 )
<=> ! [X431: term,X432: subst > term > subst > $o] :
( ( $true
= ( X432 @ id @ X431 @ id ) )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X432 @ ( comp @ X442 @ X443 ) @ ( sub @ X441 @ X443 ) @ X440 )
!= $true )
& ( $true
= ( X432 @ X442 @ X441 @ ( comp @ X443 @ X440 ) ) ) )
| ( ( sP38 @ X432 )
= $true )
| ( $true
= ( sP35 @ X432 ) )
| ( $true
= ( sP36 @ X432 ) )
| ( ( sP37 @ X432 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
( ( $true = sP40 )
<=> ? [X421: subst > term > subst > $o,X422: term,X423: term > $o] :
( ! [X424: term] :
( ( $true
!= ( X423 @ X424 ) )
| ( ( X423 @ ( sub @ X422 @ ( push @ X424 @ id ) ) )
= $true ) )
& ( $true
= ( sP31 @ X421 ) )
& ( ( X423 @ ( lam @ X422 ) )
!= $true )
& ! [X425: term] :
( ( X423 @ X425 )
= ( X421 @ id @ X425 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
( ( sP41 = $true )
<=> ? [X413: term > $o,X414: term] :
( ( ( X413 @ X414 )
!= $true )
& ( $true
= ( sP32 @ X413 ) )
& ( $true
= ( sP34 @ X413 ) )
& ( $true
= ( sP33 @ X413 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
! [X164: subst > term > subst > $o] :
( ( ( sP42 @ X164 )
= $true )
<=> ? [X167: subst > term > term] :
( ! [X168: term,X169: subst,X170: subst] :
( ( sub @ ( X167 @ X169 @ X168 ) @ X170 )
= ( X167 @ ( comp @ X169 @ X170 ) @ ( sub @ X168 @ X170 ) ) )
& ! [X171: term] :
( ( ( X164 @ id @ X171 @ id )
!= $true )
| ( $true
= ( X164 @ id @ ( X167 @ id @ X171 ) @ id ) ) )
& ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
! [X164: subst > term > subst > $o] :
( ( $true
= ( sP43 @ X164 ) )
<=> ? [X172: subst,X173: subst,X174: subst,X175: term] :
( ( ( X164 @ X173 @ X175 @ ( comp @ X174 @ X172 ) )
!= $true )
& ( $true
= ( X164 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) @ X172 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
! [X164: subst > term > subst > $o] :
( ( ( sP44 @ X164 )
= $true )
<=> ? [X176: subst,X177: subst,X178: term,X179: subst] :
( ( ( X164 @ X177 @ X178 @ ( comp @ X179 @ X176 ) )
= $true )
& ( $true
!= ( X164 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) @ X176 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
! [X156: subst > term > subst > $o] :
( ( ( sP45 @ X156 )
= $true )
<=> ! [X159: subst > term > term] :
( ? [X160: term] :
( ( ( X156 @ id @ X160 @ id )
= $true )
& ( ( X156 @ id @ ( X159 @ id @ X160 ) @ id )
!= $true ) )
| ( $true
= ( X156 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id ) )
| ? [X161: subst,X162: subst,X163: term] :
( ( X159 @ ( comp @ X161 @ X162 ) @ ( sub @ X163 @ X162 ) )
!= ( sub @ ( X159 @ X161 @ X163 ) @ X162 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
( ( $true = sP46 )
<=> ! [X164: subst > term > subst > $o,X165: term] :
( ( ( X164 @ id @ ( lam @ X165 ) @ id )
= $true )
| ? [X166: term] :
( ( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
!= $true )
& ( $true
= ( X164 @ id @ X166 @ id ) ) )
| ( ( sP44 @ X164 )
= $true )
| ( $true
= ( sP43 @ X164 ) )
| ( ( sP42 @ X164 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
( ( $true = sP47 )
<=> ? [X156: subst > term > subst > $o,X157: term] :
( ( ( X156 @ id @ ( lam @ ( sub @ X157 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ( ( sP45 @ X156 )
= $true )
& ! [X158: term] :
( ( ( X156 @ id @ ( sub @ X157 @ ( push @ X158 @ id ) ) @ id )
= $true )
| ( ( X156 @ id @ X158 @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
! [X301: subst > term > subst > $o] :
( ( ( sP48 @ X301 )
= $true )
<=> ? [X304: term,X305: term] :
( ( $true
= ( X301 @ id @ X304 @ id ) )
& ( $true
!= ( X301 @ id @ ( ap @ ( sub @ X305 @ id ) @ X304 ) @ id ) )
& ( ( X301 @ id @ X305 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
! [X301: subst > term > subst > $o] :
( ( $true
= ( sP49 @ X301 ) )
<=> ? [X310: subst,X311: term,X312: subst,X313: subst] :
( ( ( X301 @ ( comp @ X312 @ X313 ) @ ( sub @ X311 @ X313 ) @ X310 )
!= $true )
& ( $true
= ( X301 @ X312 @ X311 @ ( comp @ X313 @ X310 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( sP50 = $true )
<=> ! [X301: subst > term > subst > $o,X302: term,X303: term] :
( ( ( sP48 @ X301 )
= $true )
| ( ( X301 @ id @ X302 @ id )
!= $true )
| ( $true
= ( X301 @ id @ ( ap @ X302 @ X303 ) @ id ) )
| ? [X306: subst,X307: subst,X308: term,X309: subst] :
( ( $true
= ( X301 @ ( comp @ X307 @ X309 ) @ ( sub @ X308 @ X309 ) @ X306 ) )
& ( $true
!= ( X301 @ X307 @ X308 @ ( comp @ X309 @ X306 ) ) ) )
| ( ( X301 @ id @ X303 @ id )
!= $true )
| ( $true
= ( sP49 @ X301 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
! [X59: term > $o] :
( ( $true
= ( sP51 @ X59 ) )
<=> ? [X60: term] :
( ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) )
& ( ( X59 @ ( lam @ X60 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X59: term > $o] :
( ( ( sP52 @ X59 )
= $true )
<=> ? [X62: term,X63: term] :
( ( ( X59 @ X63 )
= $true )
& ( $true
= ( X59 @ X62 ) )
& ( $true
!= ( X59 @ ( ap @ X62 @ X63 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
! [X52: term > $o] :
( ( ( sP53 @ X52 )
= $true )
<=> ! [X55: term,X56: term] :
( ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) )
| ( $true
!= ( X52 @ X55 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
! [X52: term > $o] :
( ( $true
= ( sP54 @ X52 ) )
<=> ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
( ( $true = sP55 )
<=> ! [X57: subst,X58: term,X59: term > $o] :
( ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true )
| ( $true
= ( sP51 @ X59 ) )
| ( ( sP52 @ X59 )
= $true )
| ? [X64: term] :
( ( ( var @ X64 )
= $true )
& ( ( X59 @ ( sub @ X64 @ X57 ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( sP56 = $true )
<=> ? [X51: term,X52: term > $o] :
( ( ( sP53 @ X52 )
= $true )
& ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
& ( $true
!= ( X52 @ X51 ) )
& ( $true
= ( sP54 @ X52 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f73,plain,
( ( sP57 = $true )
<=> ! [X283: term,X284: subst > term > term,X285: subst,X286: subst > term > term] :
( ? [X287: term,X288: subst,X289: subst] :
( ( sub @ ( X284 @ X288 @ X287 ) @ X289 )
!= ( X284 @ ( comp @ X288 @ X289 ) @ ( sub @ X287 @ X289 ) ) )
| ( ( X286 @ X285 @ X283 )
= ( X284 @ X285 @ X283 ) )
| ? [X290: subst,X291: subst,X292: term] :
( ( X286 @ ( comp @ X291 @ X290 ) @ ( sub @ X292 @ X290 ) )
!= ( sub @ ( X286 @ X291 @ X292 ) @ X290 ) )
| ( ( lam @ ( X284 @ sh @ one ) )
!= ( lam @ ( X286 @ sh @ one ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f74,plain,
( ( $true = sP58 )
<=> ( ( sP57 = $true )
| ? [X277: subst,X278: term] :
( ( sub @ one @ ( push @ X278 @ X277 ) )
!= X278 )
| ? [X281: term,X282: term] :
( ( X281 != X282 )
& ( ( lam @ X281 )
= ( lam @ X282 ) ) )
| ? [X279: term,X280: subst] :
( ( comp @ sh @ ( push @ X279 @ X280 ) )
!= X280 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f75,plain,
! [X111: subst > term > subst > $o] :
( ( $true
= ( sP59 @ X111 ) )
<=> ? [X114: subst > term > term] :
( ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
& ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
!= $true )
& ! [X118: term] :
( ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) )
| ( ( X111 @ id @ X118 @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f76,plain,
( ( sP60 = $true )
<=> ! [X111: subst > term > subst > $o,X112: term] :
( ? [X113: term] :
( ( $true
= ( X111 @ id @ X113 @ id ) )
& ( $true
!= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) ) )
| ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( $true
= ( sP59 @ X111 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f77,plain,
! [X96: term > $o] :
( ( $true
= ( sP61 @ X96 ) )
<=> ! [X99: term,X100: term] :
( ( ( X96 @ X100 )
!= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f78,plain,
! [X96: term > $o] :
( ( $true
= ( sP62 @ X96 ) )
<=> ! [X97: term] :
( ( $true
= ( X96 @ ( lam @ X97 ) ) )
| ? [X98: term] :
( ( ( X96 @ X98 )
= $true )
& ( $true
!= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f79,plain,
! [X103: term > $o] :
( ( ( sP63 @ X103 )
= $true )
<=> ? [X104: term] :
( ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) )
& ( $true
!= ( X103 @ ( lam @ X104 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f80,plain,
! [X103: term > $o] :
( ( $true
= ( sP64 @ X103 ) )
<=> ? [X107: term,X108: term] :
( ( ( X103 @ X107 )
= $true )
& ( $true
!= ( X103 @ ( ap @ X108 @ X107 ) ) )
& ( ( X103 @ X108 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f81,plain,
( ( sP65 = $true )
<=> ! [X102: term,X103: term > $o] :
( ? [X106: term] :
( ( ( var @ X106 )
= $true )
& ( $true
!= ( X103 @ X106 ) ) )
| ( ( X103 @ X102 )
= $true )
| ( $true
= ( sP64 @ X103 ) )
| ( ( sP63 @ X103 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f82,plain,
( ( $true = sP66 )
<=> ? [X94: term,X95: subst,X96: term > $o] :
( ! [X101: term] :
( ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true )
| ( ( var @ X101 )
!= $true ) )
& ( ( X96 @ ( sub @ X94 @ X95 ) )
!= $true )
& ( $true
= ( sP62 @ X96 ) )
& ( $true
= ( sP61 @ X96 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f83,plain,
! [X217: term > $o] :
( ( $true
= ( sP67 @ X217 ) )
<=> ? [X219: term,X220: term] :
( ( ( X217 @ ( ap @ X219 @ X220 ) )
!= $true )
& ( $true
= ( X217 @ X219 ) )
& ( ( X217 @ X220 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f84,plain,
! [X217: term > $o] :
( ( $true
= ( sP68 @ X217 ) )
<=> ? [X221: term] :
( ( ( X217 @ X221 )
= $true )
& ( $true
!= ( X217 @ ( lam @ X221 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f85,plain,
( ( sP69 = $true )
<=> ! [X216: term,X217: term > $o] :
( ? [X218: term] :
( ( ( var @ X218 )
= $true )
& ( $true
!= ( X217 @ X218 ) ) )
| ( $true
= ( sP67 @ X217 ) )
| ( $true
= ( sP68 @ X217 ) )
| ( $true
= ( X217 @ X216 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f86,plain,
! [X341: subst > term > subst > $o] :
( ( ( sP70 @ X341 )
= $true )
<=> ? [X344: subst > term > term] :
( ! [X345: term,X346: subst,X347: subst] :
( ( sub @ ( X344 @ X346 @ X345 ) @ X347 )
= ( X344 @ ( comp @ X346 @ X347 ) @ ( sub @ X345 @ X347 ) ) )
& ! [X348: term] :
( ( $true
!= ( X341 @ id @ X348 @ id ) )
| ( ( X341 @ id @ ( X344 @ id @ X348 ) @ id )
= $true ) )
& ( ( X341 @ id @ ( lam @ ( X344 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f87,plain,
! [X341: subst > term > subst > $o] :
( ( $true
= ( sP71 @ X341 ) )
<=> ? [X342: term,X343: term] :
( ( ( X341 @ id @ X342 @ id )
= $true )
& ( ( X341 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
!= $true )
& ( ( X341 @ id @ X343 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f88,plain,
! [X330: subst > term > subst > $o] :
( ( ( sP72 @ X330 )
= $true )
<=> ! [X333: subst > term > term] :
( ? [X334: term] :
( ( $true
= ( X330 @ id @ X334 @ id ) )
& ( $true
!= ( X330 @ id @ ( X333 @ id @ X334 ) @ id ) ) )
| ? [X335: subst,X336: term,X337: subst] :
( ( X333 @ ( comp @ X337 @ X335 ) @ ( sub @ X336 @ X335 ) )
!= ( sub @ ( X333 @ X337 @ X336 ) @ X335 ) )
| ( ( X330 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f89,plain,
! [X323: term > $o] :
( ( $true
= ( sP73 @ X323 ) )
<=> ! [X327: term,X328: term] :
( ( ( X323 @ X328 )
!= $true )
| ( $true
= ( X323 @ ( ap @ X327 @ X328 ) ) )
| ( $true
!= ( X323 @ X327 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f90,plain,
! [X323: term > $o] :
( ( $true
= ( sP74 @ X323 ) )
<=> ! [X325: term] :
( ( $true
= ( X323 @ ( lam @ X325 ) ) )
| ? [X326: term] :
( ( $true
= ( X323 @ X326 ) )
& ( ( X323 @ ( sub @ X325 @ ( push @ X326 @ id ) ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f91,plain,
( ( sP75 = $true )
<=> ! [X340: term,X341: subst > term > subst > $o] :
( ( ( sP70 @ X341 )
= $true )
| ( ( X341 @ id @ X340 @ id )
= $true )
| ( $true
= ( sP71 @ X341 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f92,plain,
( ( $true = sP76 )
<=> ? [X330: subst > term > subst > $o,X331: term,X332: term > $o] :
( ( ( sP72 @ X330 )
= $true )
& ! [X338: term] :
( ( X330 @ id @ X338 @ id )
= ( X332 @ X338 ) )
& ( ( X332 @ ( lam @ X331 ) )
!= $true )
& ! [X339: term] :
( ( ( X332 @ X339 )
!= $true )
| ( ( X332 @ ( sub @ X331 @ ( push @ X339 @ id ) ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f93,plain,
( ( sP77 = $true )
<=> ? [X322: term,X323: term > $o] :
( ( $true
!= ( X323 @ X322 ) )
& ( $true
= ( sP73 @ X323 ) )
& ! [X324: term] :
( ( ( var @ X324 )
!= $true )
| ( ( X323 @ X324 )
= $true ) )
& ( $true
= ( sP74 @ X323 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f94,plain,
! [X200: subst > term > subst > $o] :
( ( ( sP78 @ X200 )
= $true )
<=> ? [X211: subst > term > term] :
( ! [X212: term] :
( ( $true
!= ( X200 @ id @ X212 @ id ) )
| ( $true
= ( X200 @ id @ ( X211 @ id @ X212 ) @ id ) ) )
& ( $true
!= ( X200 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) )
& ! [X213: term,X214: subst,X215: subst] :
( ( X211 @ ( comp @ X214 @ X215 ) @ ( sub @ X213 @ X215 ) )
= ( sub @ ( X211 @ X214 @ X213 ) @ X215 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f95,plain,
! [X200: subst > term > subst > $o] :
( ( ( sP79 @ X200 )
= $true )
<=> ? [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X200 @ X206 @ X209 @ ( comp @ X208 @ X207 ) )
!= $true )
& ( ( X200 @ ( comp @ X206 @ X208 ) @ ( sub @ X209 @ X208 ) @ X207 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f96,plain,
! [X199: term,X198: term > $o] :
( ( ( sP80 @ X198 @ X199 )
= $true )
<=> ? [X205: term] :
( ( $true
!= ( X198 @ ( sub @ X199 @ ( push @ X205 @ id ) ) ) )
& ( $true
= ( X198 @ X205 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f97,plain,
( ( $true = sP81 )
<=> ! [X198: term > $o,X199: term,X200: subst > term > subst > $o] :
( ? [X210: term] :
( ( X200 @ id @ X210 @ id )
!= ( X198 @ X210 ) )
| ( ( sP78 @ X200 )
= $true )
| ? [X201: term,X202: subst,X203: subst,X204: subst] :
( ( $true
!= ( X200 @ ( comp @ X202 @ X204 ) @ ( sub @ X201 @ X204 ) @ X203 ) )
& ( $true
= ( X200 @ X202 @ X201 @ ( comp @ X204 @ X203 ) ) ) )
| ( ( sP80 @ X198 @ X199 )
= $true )
| ( ( sP79 @ X200 )
= $true )
| ( ( X198 @ ( lam @ X199 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f98,plain,
! [X366: subst > term > subst > $o] :
( ( $true
= ( sP82 @ X366 ) )
<=> ? [X371: term,X372: term] :
( ( $true
= ( X366 @ id @ X371 @ id ) )
& ( $true
= ( X366 @ id @ X372 @ id ) )
& ( ( X366 @ id @ ( ap @ ( sub @ X371 @ id ) @ X372 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f99,plain,
! [X366: subst > term > subst > $o] :
( ( ( sP83 @ X366 )
= $true )
<=> ? [X373: subst,X374: subst,X375: term,X376: subst] :
( ( ( X366 @ X376 @ X375 @ ( comp @ X373 @ X374 ) )
!= $true )
& ( $true
= ( X366 @ ( comp @ X376 @ X373 ) @ ( sub @ X375 @ X373 ) @ X374 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f100,plain,
( ( sP84 = $true )
<=> ! [X366: subst > term > subst > $o,X367: term,X368: term,X369: term > $o] :
( ? [X377: term,X378: subst,X379: subst,X380: subst] :
( ( ( X366 @ X379 @ X377 @ ( comp @ X380 @ X378 ) )
= $true )
& ( $true
!= ( X366 @ ( comp @ X379 @ X380 ) @ ( sub @ X377 @ X380 ) @ X378 ) ) )
| ( ( sP83 @ X366 )
= $true )
| ( $true
= ( sP82 @ X366 ) )
| ? [X370: term] :
( ( X366 @ id @ X370 @ id )
!= ( X369 @ X370 ) )
| ( $true
= ( X369 @ ( ap @ X367 @ X368 ) ) )
| ( $true
!= ( X369 @ X367 ) )
| ( ( X369 @ X368 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f101,plain,
( ( $true = sP85 )
<=> ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f102,plain,
( ( sP86 = $true )
<=> ( ? [X28: term,X29: term,X30: term,X31: term] :
( ( X30 != X31 )
& ( ( ap @ X28 @ X30 )
= ( ap @ X29 @ X31 ) ) )
| ( $true = sP85 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f103,plain,
! [X236: subst > term > subst > $o] :
( ( $true
= ( sP87 @ X236 ) )
<=> ? [X240: subst > term > term] :
( ! [X242: subst,X243: term,X244: subst] :
( ( sub @ ( X240 @ X242 @ X243 ) @ X244 )
= ( X240 @ ( comp @ X242 @ X244 ) @ ( sub @ X243 @ X244 ) ) )
& ! [X241: term] :
( ( ( X236 @ id @ X241 @ id )
!= $true )
| ( ( X236 @ id @ ( X240 @ id @ X241 ) @ id )
= $true ) )
& ( ( X236 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f104,plain,
( ( $true = sP88 )
<=> ! [X235: term,X236: subst > term > subst > $o,X237: term > $o] :
( ? [X239: term] :
( ( $true
!= ( X237 @ ( sub @ X235 @ ( push @ X239 @ id ) ) ) )
& ( ( X237 @ X239 )
= $true ) )
| ( $true
= ( sP87 @ X236 ) )
| ? [X238: term] :
( ( X236 @ id @ X238 @ id )
!= ( X237 @ X238 ) )
| ( $true
= ( X237 @ ( lam @ X235 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f105,plain,
! [X521: subst > term > subst > $o] :
( ( ( sP89 @ X521 )
= $true )
<=> ? [X523: subst > term > term] :
( ! [X527: term] :
( ( ( X521 @ id @ X527 @ id )
!= $true )
| ( $true
= ( X521 @ id @ ( X523 @ id @ X527 ) @ id ) ) )
& ! [X524: term,X525: subst,X526: subst] :
( ( X523 @ ( comp @ X526 @ X525 ) @ ( sub @ X524 @ X525 ) )
= ( sub @ ( X523 @ X526 @ X524 ) @ X525 ) )
& ( $true
!= ( X521 @ id @ ( lam @ ( X523 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f106,plain,
( ( $true = sP90 )
<=> ! [X521: subst > term > subst > $o,X522: term] :
( ? [X528: term] :
( ( ( X521 @ id @ ( sub @ X522 @ ( push @ X528 @ id ) ) @ id )
!= $true )
& ( ( X521 @ id @ X528 @ id )
= $true ) )
| ( ( X521 @ id @ ( lam @ X522 ) @ id )
= $true )
| ( ( sP89 @ X521 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f107,plain,
! [X4: subst > term > subst > $o] :
( ( $true
= ( sP91 @ X4 ) )
<=> ? [X10: subst > term > term] :
( ! [X11: term] :
( ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) )
| ( $true
!= ( X4 @ id @ X11 @ id ) ) )
& ( $true
!= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
& ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f108,plain,
! [X4: subst > term > subst > $o] :
( ( ( sP92 @ X4 )
= $true )
<=> ? [X6: term,X7: subst,X8: subst,X9: subst] :
( ( $true
= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) )
& ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f109,plain,
! [X4: subst > term > subst > $o] :
( ( ( sP93 @ X4 )
= $true )
<=> ? [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
!= $true )
& ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f110,plain,
( ( $true = sP94 )
<=> ! [X4: subst > term > subst > $o,X5: term] :
( ? [X19: term] :
( ( ( X4 @ id @ X19 @ id )
= $true )
& ( $true
!= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) ) )
| ( ( sP93 @ X4 )
= $true )
| ( ( sP92 @ X4 )
= $true )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) )
| ( $true
= ( sP91 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f111,plain,
( ( $true = sP95 )
<=> ( ( ! [X296: subst] :
( ( comp @ id @ X296 )
= X296 )
& ! [X295: subst] :
( ( comp @ X295 @ id )
= X295 ) )
| ? [X293: subst] :
( ( comp @ id @ X293 )
!= X293 )
| ? [X294: subst] :
( ( comp @ X294 @ id )
!= X294 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f112,plain,
! [X247: term > $o] :
( ( $true
= ( sP96 @ X247 ) )
<=> ? [X250: term] :
( ! [X251: term] :
( ( $true
= ( X247 @ ( sub @ X250 @ ( push @ X251 @ id ) ) ) )
| ( ( X247 @ X251 )
!= $true ) )
& ( ( X247 @ ( lam @ X250 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f113,plain,
! [X247: term > $o] :
( ( $true
= ( sP97 @ X247 ) )
<=> ? [X248: term,X249: term] :
( ( $true
!= ( X247 @ ( ap @ X249 @ X248 ) ) )
& ( $true
= ( X247 @ X249 ) )
& ( ( X247 @ X248 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f114,plain,
( ( $true = sP98 )
<=> ! [X245: subst,X246: term,X247: term > $o] :
( ( $true
= ( sP97 @ X247 ) )
| ( ( X247 @ ( sub @ X246 @ X245 ) )
= $true )
| ? [X252: term] :
( ( $true
!= ( X247 @ ( sub @ X252 @ X245 ) ) )
& ( $true
= ( var @ X252 ) ) )
| ( $true
= ( sP96 @ X247 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f115,plain,
( ( $true = sP99 )
<=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f116,plain,
( ( sP100 = $true )
<=> ( ( $true = sP99 )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( X69 != X70 )
& ( ( ap @ X70 @ X72 )
= ( ap @ X69 @ X71 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f117,plain,
! [X263: subst > term > subst > $o] :
( ( ( sP101 @ X263 )
= $true )
<=> ? [X266: subst > term > term] :
( ! [X270: term] :
( ( ( X263 @ id @ X270 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X266 @ id @ X270 ) @ id ) ) )
& ( ( X263 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
!= $true )
& ! [X267: term,X268: subst,X269: subst] :
( ( X266 @ ( comp @ X269 @ X268 ) @ ( sub @ X267 @ X268 ) )
= ( sub @ ( X266 @ X269 @ X267 ) @ X268 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f118,plain,
( ( sP102 = $true )
<=> ! [X262: term,X263: subst > term > subst > $o,X264: term > $o] :
( ( $true
= ( X264 @ ( lam @ X262 ) ) )
| ? [X271: term] :
( ( X264 @ X271 )
!= ( X263 @ id @ X271 @ id ) )
| ( ( sP101 @ X263 )
= $true )
| ? [X265: term] :
( ( $true
= ( X264 @ X265 ) )
& ( $true
!= ( X264 @ ( sub @ X262 @ ( push @ X265 @ id ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f119,plain,
! [X450: subst > term > subst > $o] :
( ( $true
= ( sP103 @ X450 ) )
<=> ? [X451: term,X452: subst > term > term] :
( ( $true
!= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) )
& ! [X453: subst,X454: term,X455: subst] :
( ( X452 @ ( comp @ X453 @ X455 ) @ ( sub @ X454 @ X455 ) )
= ( sub @ X451 @ ( push @ ( sub @ X454 @ X455 ) @ ( comp @ X453 @ X455 ) ) ) )
& ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( $true
!= ( X450 @ id @ X456 @ id ) ) )
& ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( sub @ X451 @ ( push @ X458 @ X457 ) ) @ X459 )
= ( sub @ ( X452 @ X457 @ X458 ) @ X459 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f120,plain,
( ( sP104 = $true )
<=> ! [X449: term,X450: subst > term > subst > $o] :
( ( $true
= ( X450 @ id @ ( lam @ ( sub @ X449 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X460: term] :
( ( $true
= ( X450 @ id @ X460 @ id ) )
& ( ( X450 @ id @ ( sub @ X449 @ ( push @ X460 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( sP103 @ X450 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f121,plain,
! [X391: subst > term > subst > $o] :
( ( $true
= ( sP105 @ X391 ) )
<=> ? [X403: subst > term > term] :
( ! [X407: term] :
( ( ( X391 @ id @ X407 @ id )
!= $true )
| ( ( X391 @ id @ ( X403 @ id @ X407 ) @ id )
= $true ) )
& ! [X404: term,X405: subst,X406: subst] :
( ( sub @ ( X403 @ X406 @ X404 ) @ X405 )
= ( X403 @ ( comp @ X406 @ X405 ) @ ( sub @ X404 @ X405 ) ) )
& ( ( X391 @ id @ ( lam @ ( X403 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f122,plain,
! [X391: subst > term > subst > $o] :
( ( $true
= ( sP106 @ X391 ) )
<=> ? [X392: term,X393: term] :
( ( ( X391 @ id @ X393 @ id )
= $true )
& ( ( X391 @ id @ ( ap @ ( sub @ X392 @ id ) @ X393 ) @ id )
!= $true )
& ( $true
= ( X391 @ id @ X392 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f123,plain,
! [X391: subst > term > subst > $o] :
( ( $true
= ( sP107 @ X391 ) )
<=> ? [X395: term,X396: subst,X397: subst,X398: subst] :
( ( ( X391 @ ( comp @ X397 @ X398 ) @ ( sub @ X395 @ X398 ) @ X396 )
!= $true )
& ( $true
= ( X391 @ X397 @ X395 @ ( comp @ X398 @ X396 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f124,plain,
! [X391: subst > term > subst > $o] :
( ( ( sP108 @ X391 )
= $true )
<=> ? [X394: term] :
( ( ( var @ ( sub @ X394 @ id ) )
= $true )
& ( ( X391 @ id @ X394 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f125,plain,
( ( sP109 = $true )
<=> ! [X390: term,X391: subst > term > subst > $o] :
( ( $true
= ( sP106 @ X391 ) )
| ( $true
= ( X391 @ id @ X390 @ id ) )
| ? [X399: term,X400: subst,X401: subst,X402: subst] :
( ( ( X391 @ ( comp @ X402 @ X401 ) @ ( sub @ X399 @ X401 ) @ X400 )
= $true )
& ( $true
!= ( X391 @ X402 @ X399 @ ( comp @ X401 @ X400 ) ) ) )
| ( ( sP108 @ X391 )
= $true )
| ( $true
= ( sP105 @ X391 ) )
| ( $true
= ( sP107 @ X391 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( hoaslamnotvar_lthm = $true )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( hoasapnotvar = $true )
& ( ( hoasinduction = $true )
<=> ! [X390: term,X391: subst > term > subst > $o] :
( ? [X392: term,X393: term] :
( ( ( X391 @ id @ X393 @ id )
= $true )
& ( ( X391 @ id @ ( ap @ ( sub @ X392 @ id ) @ X393 ) @ id )
!= $true )
& ( $true
= ( X391 @ id @ X392 @ id ) ) )
| ( $true
= ( X391 @ id @ X390 @ id ) )
| ? [X399: term,X400: subst,X401: subst,X402: subst] :
( ( ( X391 @ ( comp @ X402 @ X401 ) @ ( sub @ X399 @ X401 ) @ X400 )
= $true )
& ( $true
!= ( X391 @ X402 @ X399 @ ( comp @ X401 @ X400 ) ) ) )
| ? [X394: term] :
( ( ( var @ ( sub @ X394 @ id ) )
= $true )
& ( ( X391 @ id @ X394 @ id )
!= $true ) )
| ? [X403: subst > term > term] :
( ! [X407: term] :
( ( ( X391 @ id @ X407 @ id )
!= $true )
| ( ( X391 @ id @ ( X403 @ id @ X407 ) @ id )
= $true ) )
& ! [X404: term,X405: subst,X406: subst] :
( ( sub @ ( X403 @ X406 @ X404 ) @ X405 )
= ( X403 @ ( comp @ X406 @ X405 ) @ ( sub @ X404 @ X405 ) ) )
& ( ( X391 @ id @ ( lam @ ( X403 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X395: term,X396: subst,X397: subst,X398: subst] :
( ( ( X391 @ ( comp @ X397 @ X398 ) @ ( sub @ X395 @ X398 ) @ X396 )
!= $true )
& ( $true
= ( X391 @ X397 @ X395 @ ( comp @ X398 @ X396 ) ) ) ) ) )
& ( substmonoid_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X65: subst > term > subst > $o] :
? [X66: term > $o] :
! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ! [X449: term,X450: subst > term > subst > $o] :
( ( $true
= ( X450 @ id @ ( lam @ ( sub @ X449 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X460: term] :
( ( $true
= ( X450 @ id @ X460 @ id ) )
& ( ( X450 @ id @ ( sub @ X449 @ ( push @ X460 @ id ) ) @ id )
!= $true ) )
| ? [X451: term,X452: subst > term > term] :
( ( $true
!= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) )
& ! [X453: subst,X454: term,X455: subst] :
( ( X452 @ ( comp @ X453 @ X455 ) @ ( sub @ X454 @ X455 ) )
= ( sub @ X451 @ ( push @ ( sub @ X454 @ X455 ) @ ( comp @ X453 @ X455 ) ) ) )
& ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( $true
!= ( X450 @ id @ X456 @ id ) ) )
& ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( sub @ X451 @ ( push @ X458 @ X457 ) ) @ X459 )
= ( sub @ ( X452 @ X457 @ X458 ) @ X459 ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ! [X381: d_term] : ( d_one = X381 )
& ( ( ? [X261: term] :
( ( sub @ X261 @ id )
!= X261 )
| ! [X262: term,X263: subst > term > subst > $o,X264: term > $o] :
( ( $true
= ( X264 @ ( lam @ X262 ) ) )
| ? [X271: term] :
( ( X264 @ X271 )
!= ( X263 @ id @ X271 @ id ) )
| ? [X266: subst > term > term] :
( ! [X270: term] :
( ( ( X263 @ id @ X270 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X266 @ id @ X270 ) @ id ) ) )
& ( ( X263 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
!= $true )
& ! [X267: term,X268: subst,X269: subst] :
( ( X266 @ ( comp @ X269 @ X268 ) @ ( sub @ X267 @ X268 ) )
= ( sub @ ( X266 @ X269 @ X267 ) @ X268 ) ) )
| ? [X265: term] :
( ( $true
= ( X264 @ X265 ) )
& ( $true
!= ( X264 @ ( sub @ X262 @ ( push @ X265 @ id ) ) ) ) ) )
| ? [X257: term] :
! [X258: subst > term > term] :
? [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
!= ( X258 @ X259 @ X260 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( lamnotvar = $true )
& ( ( ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( X69 != X70 )
& ( ( ap @ X70 @ X72 )
= ( ap @ X69 @ X71 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X245: subst,X246: term,X247: term > $o] :
( ? [X248: term,X249: term] :
( ( $true
!= ( X247 @ ( ap @ X249 @ X248 ) ) )
& ( $true
= ( X247 @ X249 ) )
& ( ( X247 @ X248 )
= $true ) )
| ( ( X247 @ ( sub @ X246 @ X245 ) )
= $true )
| ? [X252: term] :
( ( $true
!= ( X247 @ ( sub @ X252 @ X245 ) ) )
& ( $true
= ( var @ X252 ) ) )
| ? [X250: term] :
( ! [X251: term] :
( ( $true
= ( X247 @ ( sub @ X250 @ ( push @ X251 @ id ) ) ) )
| ( ( X247 @ X251 )
!= $true ) )
& ( ( X247 @ ( lam @ X250 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 ) )
& ( ( shinj = $true )
<=> ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) ) )
& ( apnotvar = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ( ! [X296: subst] :
( ( comp @ id @ X296 )
= X296 )
& ! [X295: subst] :
( ( comp @ X295 @ id )
= X295 ) )
| ? [X293: subst] :
( ( comp @ id @ X293 )
!= X293 )
| ? [X294: subst] :
( ( comp @ X294 @ id )
!= X294 ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X272: subst,X273: term,X274: term > $o] :
? [X275: term > $o] :
! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X4: subst > term > subst > $o,X5: term] :
( ? [X19: term] :
( ( ( X4 @ id @ X19 @ id )
= $true )
& ( $true
!= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) ) )
| ? [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
!= $true )
& ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
= $true ) )
| ? [X6: term,X7: subst,X8: subst,X9: subst] :
( ( $true
= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) )
& ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
!= $true ) )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) )
| ? [X10: subst > term > term] :
( ! [X11: term] :
( ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) )
| ( $true
!= ( X4 @ id @ X11 @ id ) ) )
& ( $true
!= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
& ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X521: subst > term > subst > $o,X522: term] :
( ? [X528: term] :
( ( ( X521 @ id @ ( sub @ X522 @ ( push @ X528 @ id ) ) @ id )
!= $true )
& ( ( X521 @ id @ X528 @ id )
= $true ) )
| ( ( X521 @ id @ ( lam @ X522 ) @ id )
= $true )
| ? [X523: subst > term > term] :
( ! [X527: term] :
( ( ( X521 @ id @ X527 @ id )
!= $true )
| ( $true
= ( X521 @ id @ ( X523 @ id @ X527 ) @ id ) ) )
& ! [X524: term,X525: subst,X526: subst] :
( ( X523 @ ( comp @ X526 @ X525 ) @ ( sub @ X524 @ X525 ) )
= ( sub @ ( X523 @ X526 @ X524 ) @ X525 ) )
& ( $true
!= ( X521 @ id @ ( lam @ ( X523 @ sh @ one ) ) @ id ) ) ) ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ? [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
!= ( X85 @ X88 ) )
| ( ( X87 @ X86 )
!= $true )
| ( $true
= ( X85 @ one ) ) )
| ? [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
!= X82 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) )
| ? [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
!= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) ) )
& ( axvarshift = $true )
& ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( substmonoid = $true )
<=> ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) ) )
& ! [X382: d_term,X383: d_term] :
( ( X382 = X383 )
| ( ( d2term @ X383 )
!= ( d2term @ X382 ) ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
<=> ( hoasapinj2 = $true ) )
& ( ! [X235: term,X236: subst > term > subst > $o,X237: term > $o] :
( ? [X239: term] :
( ( $true
!= ( X237 @ ( sub @ X235 @ ( push @ X239 @ id ) ) ) )
& ( ( X237 @ X239 )
= $true ) )
| ? [X240: subst > term > term] :
( ! [X242: subst,X243: term,X244: subst] :
( ( sub @ ( X240 @ X242 @ X243 ) @ X244 )
= ( X240 @ ( comp @ X242 @ X244 ) @ ( sub @ X243 @ X244 ) ) )
& ! [X241: term] :
( ( ( X236 @ id @ X241 @ id )
!= $true )
| ( ( X236 @ id @ ( X240 @ id @ X241 ) @ id )
= $true ) )
& ( ( X236 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X238: term] :
( ( X236 @ id @ X238 @ id )
!= ( X237 @ X238 ) )
| ( $true
= ( X237 @ ( lam @ X235 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X28: term,X29: term,X30: term,X31: term] :
( ( X30 != X31 )
& ( ( ap @ X28 @ X30 )
= ( ap @ X29 @ X31 ) ) )
| ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) ) )
& ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X366: subst > term > subst > $o,X367: term,X368: term,X369: term > $o] :
( ? [X377: term,X378: subst,X379: subst,X380: subst] :
( ( ( X366 @ X379 @ X377 @ ( comp @ X380 @ X378 ) )
= $true )
& ( $true
!= ( X366 @ ( comp @ X379 @ X380 ) @ ( sub @ X377 @ X380 ) @ X378 ) ) )
| ? [X373: subst,X374: subst,X375: term,X376: subst] :
( ( ( X366 @ X376 @ X375 @ ( comp @ X373 @ X374 ) )
!= $true )
& ( $true
= ( X366 @ ( comp @ X376 @ X373 ) @ ( sub @ X375 @ X373 ) @ X374 ) ) )
| ? [X371: term,X372: term] :
( ( $true
= ( X366 @ id @ X371 @ id ) )
& ( $true
= ( X366 @ id @ X372 @ id ) )
& ( ( X366 @ id @ ( ap @ ( sub @ X371 @ id ) @ X372 ) @ id )
!= $true ) )
| ? [X370: term] :
( ( X366 @ id @ X370 @ id )
!= ( X369 @ X370 ) )
| ( $true
= ( X369 @ ( ap @ X367 @ X368 ) ) )
| ( $true
!= ( X369 @ X367 ) )
| ( ( X369 @ X368 )
!= $true ) ) )
& ( hoasapnotvar_lthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X198: term > $o,X199: term,X200: subst > term > subst > $o] :
( ? [X210: term] :
( ( X200 @ id @ X210 @ id )
!= ( X198 @ X210 ) )
| ? [X211: subst > term > term] :
( ! [X212: term] :
( ( $true
!= ( X200 @ id @ X212 @ id ) )
| ( $true
= ( X200 @ id @ ( X211 @ id @ X212 ) @ id ) ) )
& ( $true
!= ( X200 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) )
& ! [X213: term,X214: subst,X215: subst] :
( ( X211 @ ( comp @ X214 @ X215 ) @ ( sub @ X213 @ X215 ) )
= ( sub @ ( X211 @ X214 @ X213 ) @ X215 ) ) )
| ? [X201: term,X202: subst,X203: subst,X204: subst] :
( ( $true
!= ( X200 @ ( comp @ X202 @ X204 ) @ ( sub @ X201 @ X204 ) @ X203 ) )
& ( $true
= ( X200 @ X202 @ X201 @ ( comp @ X204 @ X203 ) ) ) )
| ? [X205: term] :
( ( $true
!= ( X198 @ ( sub @ X199 @ ( push @ X205 @ id ) ) ) )
& ( $true
= ( X198 @ X205 ) ) )
| ? [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X200 @ X206 @ X209 @ ( comp @ X208 @ X207 ) )
!= $true )
& ( ( X200 @ ( comp @ X206 @ X208 ) @ ( sub @ X209 @ X208 ) @ X207 )
= $true ) )
| ( ( X198 @ ( lam @ X199 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
= ( X151 @ one ) )
| ( $true
!= ( X152 @ X150 ) )
| ? [X154: term] :
( ( X151 @ X154 )
!= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ? [X322: term,X323: term > $o] :
( ( $true
!= ( X323 @ X322 ) )
& ! [X327: term,X328: term] :
( ( ( X323 @ X328 )
!= $true )
| ( $true
= ( X323 @ ( ap @ X327 @ X328 ) ) )
| ( $true
!= ( X323 @ X327 ) ) )
& ! [X324: term] :
( ( ( var @ X324 )
!= $true )
| ( ( X323 @ X324 )
= $true ) )
& ! [X325: term] :
( ( $true
= ( X323 @ ( lam @ X325 ) ) )
| ? [X326: term] :
( ( $true
= ( X323 @ X326 ) )
& ( ( X323 @ ( sub @ X325 @ ( push @ X326 @ id ) ) )
!= $true ) ) ) )
| ? [X330: subst > term > subst > $o,X331: term,X332: term > $o] :
( ! [X333: subst > term > term] :
( ? [X334: term] :
( ( $true
= ( X330 @ id @ X334 @ id ) )
& ( $true
!= ( X330 @ id @ ( X333 @ id @ X334 ) @ id ) ) )
| ? [X335: subst,X336: term,X337: subst] :
( ( X333 @ ( comp @ X337 @ X335 ) @ ( sub @ X336 @ X335 ) )
!= ( sub @ ( X333 @ X337 @ X336 ) @ X335 ) )
| ( ( X330 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) )
& ! [X338: term] :
( ( X330 @ id @ X338 @ id )
= ( X332 @ X338 ) )
& ( ( X332 @ ( lam @ X331 ) )
!= $true )
& ! [X339: term] :
( ( ( X332 @ X339 )
!= $true )
| ( ( X332 @ ( sub @ X331 @ ( push @ X339 @ id ) ) )
= $true ) ) )
| ! [X340: term,X341: subst > term > subst > $o] :
( ? [X344: subst > term > term] :
( ! [X345: term,X346: subst,X347: subst] :
( ( sub @ ( X344 @ X346 @ X345 ) @ X347 )
= ( X344 @ ( comp @ X346 @ X347 ) @ ( sub @ X345 @ X347 ) ) )
& ! [X348: term] :
( ( $true
!= ( X341 @ id @ X348 @ id ) )
| ( ( X341 @ id @ ( X344 @ id @ X348 ) @ id )
= $true ) )
& ( ( X341 @ id @ ( lam @ ( X344 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X341 @ id @ X340 @ id )
= $true )
| ? [X342: term,X343: term] :
( ( ( X341 @ id @ X342 @ id )
= $true )
& ( ( X341 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
!= $true )
& ( ( X341 @ id @ X343 @ id )
= $true ) ) )
| ? [X329: term] :
( ( sub @ X329 @ id )
!= X329 )
| ? [X319: subst > term > subst > $o] :
! [X320: term > $o] :
? [X321: term] :
( ( X319 @ id @ X321 @ id )
!= ( X320 @ X321 ) ) ) )
& ( ! [X216: term,X217: term > $o] :
( ? [X218: term] :
( ( ( var @ X218 )
= $true )
& ( $true
!= ( X217 @ X218 ) ) )
| ? [X219: term,X220: term] :
( ( ( X217 @ ( ap @ X219 @ X220 ) )
!= $true )
& ( $true
= ( X217 @ X219 ) )
& ( ( X217 @ X220 )
= $true ) )
| ? [X221: term] :
( ( ( X217 @ X221 )
= $true )
& ( $true
!= ( X217 @ ( lam @ X221 ) ) ) )
| ( $true
= ( X217 @ X216 ) ) )
<=> ( induction = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ! [X102: term,X103: term > $o] :
( ? [X106: term] :
( ( ( var @ X106 )
= $true )
& ( $true
!= ( X103 @ X106 ) ) )
| ( ( X103 @ X102 )
= $true )
| ? [X107: term,X108: term] :
( ( ( X103 @ X107 )
= $true )
& ( $true
!= ( X103 @ ( ap @ X108 @ X107 ) ) )
& ( ( X103 @ X108 )
= $true ) )
| ? [X104: term] :
( ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) )
& ( $true
!= ( X103 @ ( lam @ X104 ) ) ) ) )
| ? [X93: term] :
( ( sub @ X93 @ id )
!= X93 )
| ? [X94: term,X95: subst,X96: term > $o] :
( ! [X101: term] :
( ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true )
| ( ( var @ X101 )
!= $true ) )
& ( ( X96 @ ( sub @ X94 @ X95 ) )
!= $true )
& ! [X97: term] :
( ( $true
= ( X96 @ ( lam @ X97 ) ) )
| ? [X98: term] :
( ( ( X96 @ X98 )
= $true )
& ( $true
!= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) ) ) )
& ! [X99: term,X100: term] :
( ( ( X96 @ X100 )
!= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 ) )
<=> ( termmset_lthm = $true ) )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X111: subst > term > subst > $o,X112: term] :
( ? [X113: term] :
( ( $true
= ( X111 @ id @ X113 @ id ) )
& ( $true
!= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) ) )
| ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X114: subst > term > term] :
( ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
& ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
!= $true )
& ! [X118: term] :
( ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) )
| ( ( X111 @ id @ X118 @ id )
!= $true ) ) ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X283: term,X284: subst > term > term,X285: subst,X286: subst > term > term] :
( ? [X287: term,X288: subst,X289: subst] :
( ( sub @ ( X284 @ X288 @ X287 ) @ X289 )
!= ( X284 @ ( comp @ X288 @ X289 ) @ ( sub @ X287 @ X289 ) ) )
| ( ( X286 @ X285 @ X283 )
= ( X284 @ X285 @ X283 ) )
| ? [X290: subst,X291: subst,X292: term] :
( ( X286 @ ( comp @ X291 @ X290 ) @ ( sub @ X292 @ X290 ) )
!= ( sub @ ( X286 @ X291 @ X292 ) @ X290 ) )
| ( ( lam @ ( X284 @ sh @ one ) )
!= ( lam @ ( X286 @ sh @ one ) ) ) )
| ? [X277: subst,X278: term] :
( ( sub @ one @ ( push @ X278 @ X277 ) )
!= X278 )
| ? [X281: term,X282: term] :
( ( X281 != X282 )
& ( ( lam @ X281 )
= ( lam @ X282 ) ) )
| ? [X279: term,X280: subst] :
( ( comp @ sh @ ( push @ X279 @ X280 ) )
!= X280 ) ) )
& ( ! [X408: term] :
? [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
= ( X409 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( ? [X51: term,X52: term > $o] :
( ! [X55: term,X56: term] :
( ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) )
| ( $true
!= ( X52 @ X55 ) ) )
& ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
& ( $true
!= ( X52 @ X51 ) )
& ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) ) )
| ! [X57: subst,X58: term,X59: term > $o] :
( ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true )
| ? [X60: term] :
( ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) )
& ( ( X59 @ ( lam @ X60 ) )
!= $true ) )
| ? [X62: term,X63: term] :
( ( ( X59 @ X63 )
= $true )
& ( $true
= ( X59 @ X62 ) )
& ( $true
!= ( X59 @ ( ap @ X62 @ X63 ) ) ) )
| ? [X64: term] :
( ( ( var @ X64 )
= $true )
& ( ( X59 @ ( sub @ X64 @ X57 ) )
!= $true ) ) )
| ? [X50: subst] :
( ( comp @ X50 @ id )
!= X50 )
| ? [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
!= X47 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X301: subst > term > subst > $o,X302: term,X303: term] :
( ? [X304: term,X305: term] :
( ( $true
= ( X301 @ id @ X304 @ id ) )
& ( $true
!= ( X301 @ id @ ( ap @ ( sub @ X305 @ id ) @ X304 ) @ id ) )
& ( ( X301 @ id @ X305 @ id )
= $true ) )
| ( ( X301 @ id @ X302 @ id )
!= $true )
| ( $true
= ( X301 @ id @ ( ap @ X302 @ X303 ) @ id ) )
| ? [X306: subst,X307: subst,X308: term,X309: subst] :
( ( $true
= ( X301 @ ( comp @ X307 @ X309 ) @ ( sub @ X308 @ X309 ) @ X306 ) )
& ( $true
!= ( X301 @ X307 @ X308 @ ( comp @ X309 @ X306 ) ) ) )
| ( ( X301 @ id @ X303 @ id )
!= $true )
| ? [X310: subst,X311: term,X312: subst,X313: subst] :
( ( ( X301 @ ( comp @ X312 @ X313 ) @ ( sub @ X311 @ X313 ) @ X310 )
!= $true )
& ( $true
= ( X301 @ X312 @ X311 @ ( comp @ X313 @ X310 ) ) ) ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ? [X156: subst > term > subst > $o,X157: term] :
( ( ( X156 @ id @ ( lam @ ( sub @ X157 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X159: subst > term > term] :
( ? [X160: term] :
( ( ( X156 @ id @ X160 @ id )
= $true )
& ( ( X156 @ id @ ( X159 @ id @ X160 ) @ id )
!= $true ) )
| ( $true
= ( X156 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id ) )
| ? [X161: subst,X162: subst,X163: term] :
( ( X159 @ ( comp @ X161 @ X162 ) @ ( sub @ X163 @ X162 ) )
!= ( sub @ ( X159 @ X161 @ X163 ) @ X162 ) ) )
& ! [X158: term] :
( ( ( X156 @ id @ ( sub @ X157 @ ( push @ X158 @ id ) ) @ id )
= $true )
| ( ( X156 @ id @ X158 @ id )
!= $true ) ) )
| ? [X155: term] :
( ( sub @ X155 @ id )
!= X155 )
| ! [X164: subst > term > subst > $o,X165: term] :
( ( ( X164 @ id @ ( lam @ X165 ) @ id )
= $true )
| ? [X166: term] :
( ( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
!= $true )
& ( $true
= ( X164 @ id @ X166 @ id ) ) )
| ? [X176: subst,X177: subst,X178: term,X179: subst] :
( ( ( X164 @ X177 @ X178 @ ( comp @ X179 @ X176 ) )
= $true )
& ( $true
!= ( X164 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) @ X176 ) ) )
| ? [X172: subst,X173: subst,X174: subst,X175: term] :
( ( ( X164 @ X173 @ X175 @ ( comp @ X174 @ X172 ) )
!= $true )
& ( $true
= ( X164 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) @ X172 ) ) )
| ? [X167: subst > term > term] :
( ! [X168: term,X169: subst,X170: subst] :
( ( sub @ ( X167 @ X169 @ X168 ) @ X170 )
= ( X167 @ ( comp @ X169 @ X170 ) @ ( sub @ X168 @ X170 ) ) )
& ! [X171: term] :
( ( ( X164 @ id @ X171 @ id )
!= $true )
| ( $true
= ( X164 @ id @ ( X167 @ id @ X171 ) @ id ) ) )
& ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
!= $true ) ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( pushprop_lthm = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lthm_orig = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( ? [X420: term] :
( ( sub @ X420 @ id )
!= X420 )
| ! [X431: term,X432: subst > term > subst > $o] :
( ( $true
= ( X432 @ id @ X431 @ id ) )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X432 @ ( comp @ X442 @ X443 ) @ ( sub @ X441 @ X443 ) @ X440 )
!= $true )
& ( $true
= ( X432 @ X442 @ X441 @ ( comp @ X443 @ X440 ) ) ) )
| ? [X439: term] :
( ( ( var @ ( sub @ X439 @ id ) )
= $true )
& ( ( X432 @ id @ X439 @ id )
!= $true ) )
| ? [X444: subst > term > term] :
( ! [X445: term,X446: subst,X447: subst] :
( ( X444 @ ( comp @ X446 @ X447 ) @ ( sub @ X445 @ X447 ) )
= ( sub @ ( X444 @ X446 @ X445 ) @ X447 ) )
& ! [X448: term] :
( ( $true
!= ( X432 @ id @ X448 @ id ) )
| ( ( X432 @ id @ ( X444 @ id @ X448 ) @ id )
= $true ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id ) ) )
| ? [X433: term,X434: term] :
( ( ( X432 @ id @ ( ap @ ( sub @ X433 @ id ) @ X434 ) @ id )
!= $true )
& ( $true
= ( X432 @ id @ X433 @ id ) )
& ( $true
= ( X432 @ id @ X434 @ id ) ) )
| ? [X435: subst,X436: subst,X437: term,X438: subst] :
( ( ( X432 @ X436 @ X437 @ ( comp @ X435 @ X438 ) )
!= $true )
& ( ( X432 @ ( comp @ X436 @ X435 ) @ ( sub @ X437 @ X435 ) @ X438 )
= $true ) ) )
| ? [X413: term > $o,X414: term] :
( ( ( X413 @ X414 )
!= $true )
& ! [X417: term,X418: term] :
( ( $true
= ( X413 @ ( ap @ X417 @ X418 ) ) )
| ( $true
!= ( X413 @ X417 ) )
| ( $true
!= ( X413 @ X418 ) ) )
& ! [X415: term] :
( ( $true
= ( X413 @ ( lam @ X415 ) ) )
| ? [X416: term] :
( ( ( X413 @ X416 )
= $true )
& ( $true
!= ( X413 @ ( sub @ X415 @ ( push @ X416 @ id ) ) ) ) ) )
& ! [X419: term] :
( ( ( var @ X419 )
!= $true )
| ( ( X413 @ X419 )
= $true ) ) )
| ? [X410: subst > term > subst > $o] :
! [X411: term > $o] :
? [X412: term] :
( ( X410 @ id @ X412 @ id )
!= ( X411 @ X412 ) )
| ? [X421: subst > term > subst > $o,X422: term,X423: term > $o] :
( ! [X424: term] :
( ( $true
!= ( X423 @ X424 ) )
| ( ( X423 @ ( sub @ X422 @ ( push @ X424 @ id ) ) )
= $true ) )
& ! [X426: subst > term > term] :
( ? [X427: subst,X428: term,X429: subst] :
( ( X426 @ ( comp @ X427 @ X429 ) @ ( sub @ X428 @ X429 ) )
!= ( sub @ ( X426 @ X427 @ X428 ) @ X429 ) )
| ? [X430: term] :
( ( $true
!= ( X421 @ id @ ( X426 @ id @ X430 ) @ id ) )
& ( ( X421 @ id @ X430 @ id )
= $true ) )
| ( ( X421 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X423 @ ( lam @ X422 ) )
!= $true )
& ! [X425: term] :
( ( X423 @ X425 )
= ( X421 @ id @ X425 @ id ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
<=> ( termmset = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3_gthm = $true )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ? [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
!= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ? [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
!= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X186: term,X187: term > $o,X188: subst] :
? [X189: term > $o] :
! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) ) )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
!= ( d2subst @ X253 ) )
| ( X253 = X254 ) )
& ( termmset_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ? [X129: term,X130: term] :
( ( $true
!= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) )
& ( ( X123 @ id @ X130 @ id )
= $true )
& ( $true
= ( X123 @ id @ X129 @ id ) ) )
| ? [X124: subst > term > term] :
( ( $true
!= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) )
& ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
& ! [X128: term] :
( ( ( X123 @ id @ X128 @ id )
!= $true )
| ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) ) ) )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X23: term] :
? [X24: subst > term > term] :
! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( induction2 = $true )
<=> ! [X191: term > $o,X192: term] :
( ? [X193: term,X194: term] :
( ( ( X191 @ ( ap @ X194 @ X193 ) )
!= $true )
& ( ( X191 @ X193 )
= $true )
& ( $true
= ( X191 @ X194 ) ) )
| ? [X197: term] :
( ( $true
= ( var @ X197 ) )
& ( $true
!= ( X191 @ X197 ) ) )
| ( $true
= ( X191 @ X192 ) )
| ? [X195: term] :
( ! [X196: term] :
( ( ( X191 @ X196 )
!= $true )
| ( $true
= ( X191 @ ( sub @ X195 @ ( push @ X196 @ id ) ) ) ) )
& ( ( X191 @ ( lam @ X195 ) )
!= $true ) ) ) )
& ( ( ? [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
!= X532 )
| ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) )
| ? [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
!= X533 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( lamnotap != $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( axclos = $true )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( hoasapinj2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ? [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
!= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) )
& ( $true
= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) ) )
| ? [X140: term] :
( ( X132 @ id @ X140 @ id )
!= ( X134 @ X140 ) )
| ? [X149: term] :
( ( $true
= ( X134 @ X149 ) )
& ( $true
!= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) )
| ? [X135: subst > term > term] :
( ( $true
!= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
& ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
& ! [X139: term] :
( ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) )
| ( $true
!= ( X132 @ id @ X139 @ id ) ) ) )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ? [X141: subst,X142: subst,X143: subst,X144: term] :
( ( $true
!= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) )
& ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
= $true ) ) )
| ? [X131: term] :
( ( sub @ X131 @ id )
!= X131 ) ) )
& ( ! [X255: term] :
? [X256: subst > term > term] :
( ( X256 @ sh @ one )
= ( sub @ X255 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( axassoc = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( axscons = $true )
<=> ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ? [X461: term > $o,X462: term] :
( ! [X465: term,X466: term] :
( ( $true
!= ( X461 @ X466 ) )
| ( ( X461 @ ( ap @ X466 @ X465 ) )
= $true )
| ( ( X461 @ X465 )
!= $true ) )
& ! [X463: term] :
( ? [X464: term] :
( ( $true
!= ( X461 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) )
& ( $true
= ( X461 @ X464 ) ) )
| ( $true
= ( X461 @ ( lam @ X463 ) ) ) )
& ! [X467: term] :
( ( $true
!= ( var @ X467 ) )
| ( $true
= ( X461 @ X467 ) ) )
& ( $true
!= ( X461 @ X462 ) ) )
| ? [X468: term,X469: subst > term > subst > $o,X470: term] :
( ! [X479: term,X480: term] :
( ( $true
!= ( X469 @ id @ X479 @ id ) )
| ( $true
= ( X469 @ id @ ( ap @ ( sub @ X480 @ id ) @ X479 ) @ id ) )
| ( $true
!= ( X469 @ id @ X480 @ id ) ) )
& ! [X475: subst,X476: subst,X477: term,X478: subst] :
( ( ( X469 @ ( comp @ X476 @ X478 ) @ ( sub @ X477 @ X478 ) @ X475 )
!= $true )
| ( $true
= ( X469 @ X476 @ X477 @ ( comp @ X478 @ X475 ) ) ) )
& ( $true
!= ( X469 @ id @ ( ap @ X468 @ X470 ) @ id ) )
& ( $true
= ( X469 @ id @ X468 @ id ) )
& ( ( X469 @ id @ X470 @ id )
= $true )
& ! [X471: term,X472: subst,X473: subst,X474: subst] :
( ( ( X469 @ X473 @ X471 @ ( comp @ X474 @ X472 ) )
!= $true )
| ( ( X469 @ ( comp @ X473 @ X474 ) @ ( sub @ X471 @ X474 ) @ X472 )
= $true ) ) )
| ? [X481: subst > term > subst > $o,X482: term] :
( ( ( X481 @ id @ ( lam @ X482 ) @ id )
!= $true )
& ! [X489: subst,X490: term,X491: subst,X492: subst] :
( ( $true
!= ( X481 @ X491 @ X490 @ ( comp @ X492 @ X489 ) ) )
| ( $true
= ( X481 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) @ X489 ) ) )
& ! [X483: subst > term > term] :
( ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) )
| ? [X484: term] :
( ( $true
= ( X481 @ id @ X484 @ id ) )
& ( $true
!= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) ) )
| ? [X485: subst,X486: term,X487: subst] :
( ( sub @ ( X483 @ X485 @ X486 ) @ X487 )
!= ( X483 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) ) ) )
& ! [X493: subst,X494: term,X495: subst,X496: subst] :
( ( $true
!= ( X481 @ ( comp @ X493 @ X496 ) @ ( sub @ X494 @ X496 ) @ X495 ) )
| ( $true
= ( X481 @ X493 @ X494 @ ( comp @ X496 @ X495 ) ) ) )
& ! [X488: term] :
( ( ( X481 @ id @ X488 @ id )
!= $true )
| ( $true
= ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id ) ) ) )
| ! [X497: subst > term > subst > $o,X498: term] :
( ? [X503: subst,X504: subst,X505: subst,X506: term] :
( ( ( X497 @ X503 @ X506 @ ( comp @ X505 @ X504 ) )
= $true )
& ( ( X497 @ ( comp @ X503 @ X505 ) @ ( sub @ X506 @ X505 ) @ X504 )
!= $true ) )
| ( $true
= ( X497 @ id @ X498 @ id ) )
| ? [X507: term] :
( ( $true
= ( var @ ( sub @ X507 @ id ) ) )
& ( ( X497 @ id @ X507 @ id )
!= $true ) )
| ? [X499: subst,X500: subst,X501: subst,X502: term] :
( ( ( X497 @ ( comp @ X501 @ X500 ) @ ( sub @ X502 @ X500 ) @ X499 )
= $true )
& ( $true
!= ( X497 @ X501 @ X502 @ ( comp @ X500 @ X499 ) ) ) )
| ? [X510: subst > term > term] :
( ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X510 @ X512 @ X513 ) @ X514 )
= ( X510 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
& ( $true
!= ( X497 @ id @ ( lam @ ( X510 @ sh @ one ) ) @ id ) )
& ! [X511: term] :
( ( ( X497 @ id @ ( X510 @ id @ X511 ) @ id )
= $true )
| ( $true
!= ( X497 @ id @ X511 @ id ) ) ) )
| ? [X508: term,X509: term] :
( ( $true
!= ( X497 @ id @ ( ap @ ( sub @ X509 @ id ) @ X508 ) @ id ) )
& ( ( X497 @ id @ X509 @ id )
= $true )
& ( ( X497 @ id @ X508 @ id )
= $true ) ) ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ? [X349: term] :
( ( sub @ X349 @ id )
!= X349 )
| ? [X350: subst > term > subst > $o,X351: term] :
( ( $true
!= ( X350 @ id @ ( lam @ ( sub @ X351 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X352: subst > term > term] :
( ? [X356: term] :
( ( ( X350 @ id @ ( X352 @ id @ X356 ) @ id )
!= $true )
& ( ( X350 @ id @ X356 @ id )
= $true ) )
| ? [X353: term,X354: subst,X355: subst] :
( ( X352 @ ( comp @ X355 @ X354 ) @ ( sub @ X353 @ X354 ) )
!= ( sub @ ( X352 @ X355 @ X353 ) @ X354 ) )
| ( $true
= ( X350 @ id @ ( lam @ ( X352 @ sh @ one ) ) @ id ) ) )
& ! [X357: term] :
( ( $true
!= ( X350 @ id @ X357 @ id ) )
| ( ( X350 @ id @ ( sub @ X351 @ ( push @ X357 @ id ) ) @ id )
= $true ) ) )
| ! [X358: term,X359: subst > term > subst > $o] :
( ? [X360: subst > term > term] :
( ! [X361: term,X362: subst,X363: subst] :
( ( sub @ ( X360 @ X362 @ X361 ) @ X363 )
= ( X360 @ ( comp @ X362 @ X363 ) @ ( sub @ X361 @ X363 ) ) )
& ! [X364: term] :
( ( ( X359 @ id @ ( X360 @ id @ X364 ) @ id )
= $true )
| ( ( X359 @ id @ X364 @ id )
!= $true ) )
& ( ( X359 @ id @ ( lam @ ( X360 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X359 @ id @ ( lam @ X358 ) @ id ) )
| ? [X365: term] :
( ( $true
!= ( X359 @ id @ ( sub @ X358 @ ( push @ X365 @ id ) ) @ id ) )
& ( $true
= ( X359 @ id @ X365 @ id ) ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ? [X225: subst > term > term] :
( ! [X229: term] :
( ( $true
= ( X223 @ id @ ( X225 @ id @ X229 ) @ id ) )
| ( $true
!= ( X223 @ id @ X229 @ id ) ) )
& ! [X226: subst,X227: term,X228: subst] :
( ( X225 @ ( comp @ X228 @ X226 ) @ ( sub @ X227 @ X226 ) )
= ( sub @ ( X225 @ X228 @ X227 ) @ X226 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) ) )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X232: subst > term > subst > $o] :
? [X233: term > $o] :
! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
= ( X151 @ one ) )
| ( $true
!= ( X152 @ X150 ) )
| ? [X154: term] :
( ( X151 @ X154 )
!= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ? [X225: subst > term > term] :
( ! [X229: term] :
( ( $true
= ( X223 @ id @ ( X225 @ id @ X229 ) @ id ) )
| ( $true
!= ( X223 @ id @ X229 @ id ) ) )
& ! [X226: subst,X227: term,X228: subst] :
( ( X225 @ ( comp @ X228 @ X226 ) @ ( sub @ X227 @ X226 ) )
= ( sub @ ( X225 @ X228 @ X227 ) @ X226 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) ) )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem3v2 = $true )
& ( axmap = $true )
& ( axabs = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X111: subst > term > subst > $o,X112: term] :
( ? [X113: term] :
( ( $true
= ( X111 @ id @ X113 @ id ) )
& ( $true
!= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) ) )
| ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X114: subst > term > term] :
( ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
& ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
!= $true )
& ! [X118: term] :
( ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) )
| ( ( X111 @ id @ X118 @ id )
!= $true ) ) ) ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ( apinj1 = $true )
<=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ( ! [X283: term,X284: subst > term > term,X285: subst,X286: subst > term > term] :
( ? [X287: term,X288: subst,X289: subst] :
( ( sub @ ( X284 @ X288 @ X287 ) @ X289 )
!= ( X284 @ ( comp @ X288 @ X289 ) @ ( sub @ X287 @ X289 ) ) )
| ( ( X286 @ X285 @ X283 )
= ( X284 @ X285 @ X283 ) )
| ? [X290: subst,X291: subst,X292: term] :
( ( X286 @ ( comp @ X291 @ X290 ) @ ( sub @ X292 @ X290 ) )
!= ( sub @ ( X286 @ X291 @ X292 ) @ X290 ) )
| ( ( lam @ ( X284 @ sh @ one ) )
!= ( lam @ ( X286 @ sh @ one ) ) ) )
| ? [X281: term,X282: term] :
( ( X281 != X282 )
& ( ( lam @ X281 )
= ( lam @ X282 ) ) )
| ? [X279: term,X280: subst] :
( ( comp @ sh @ ( push @ X279 @ X280 ) )
!= X280 )
| ? [X277: subst,X278: term] :
( ( sub @ one @ ( push @ X278 @ X277 ) )
!= X278 ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoaslaminj = $true )
<=> ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ? [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
!= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ? [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
!= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X301: subst > term > subst > $o,X302: term,X303: term] :
( ? [X304: term,X305: term] :
( ( $true
= ( X301 @ id @ X304 @ id ) )
& ( $true
!= ( X301 @ id @ ( ap @ ( sub @ X305 @ id ) @ X304 ) @ id ) )
& ( ( X301 @ id @ X305 @ id )
= $true ) )
| ( ( X301 @ id @ X302 @ id )
!= $true )
| ( $true
= ( X301 @ id @ ( ap @ X302 @ X303 ) @ id ) )
| ? [X306: subst,X307: subst,X308: term,X309: subst] :
( ( $true
= ( X301 @ ( comp @ X307 @ X309 ) @ ( sub @ X308 @ X309 ) @ X306 ) )
& ( $true
!= ( X301 @ X307 @ X308 @ ( comp @ X309 @ X306 ) ) ) )
| ( ( X301 @ id @ X303 @ id )
!= $true )
| ? [X310: subst,X311: term,X312: subst,X313: subst] :
( ( ( X301 @ ( comp @ X312 @ X313 ) @ ( sub @ X311 @ X313 ) @ X310 )
!= $true )
& ( $true
= ( X301 @ X312 @ X311 @ ( comp @ X313 @ X310 ) ) ) ) ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axassoc = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X497: subst > term > subst > $o,X498: term] :
( ? [X503: subst,X504: subst,X505: subst,X506: term] :
( ( ( X497 @ X503 @ X506 @ ( comp @ X505 @ X504 ) )
= $true )
& ( ( X497 @ ( comp @ X503 @ X505 ) @ ( sub @ X506 @ X505 ) @ X504 )
!= $true ) )
| ( $true
= ( X497 @ id @ X498 @ id ) )
| ? [X507: term] :
( ( $true
= ( var @ ( sub @ X507 @ id ) ) )
& ( ( X497 @ id @ X507 @ id )
!= $true ) )
| ? [X499: subst,X500: subst,X501: subst,X502: term] :
( ( ( X497 @ ( comp @ X501 @ X500 ) @ ( sub @ X502 @ X500 ) @ X499 )
= $true )
& ( $true
!= ( X497 @ X501 @ X502 @ ( comp @ X500 @ X499 ) ) ) )
| ? [X510: subst > term > term] :
( ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X510 @ X512 @ X513 ) @ X514 )
= ( X510 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
& ( $true
!= ( X497 @ id @ ( lam @ ( X510 @ sh @ one ) ) @ id ) )
& ! [X511: term] :
( ( ( X497 @ id @ ( X510 @ id @ X511 ) @ id )
= $true )
| ( $true
!= ( X497 @ id @ X511 @ id ) ) ) )
| ? [X508: term,X509: term] :
( ( $true
!= ( X497 @ id @ ( ap @ ( sub @ X509 @ id ) @ X508 ) @ id ) )
& ( ( X497 @ id @ X509 @ id )
= $true )
& ( ( X497 @ id @ X508 @ id )
= $true ) ) )
| ? [X481: subst > term > subst > $o,X482: term] :
( ( ( X481 @ id @ ( lam @ X482 ) @ id )
!= $true )
& ! [X489: subst,X490: term,X491: subst,X492: subst] :
( ( $true
!= ( X481 @ X491 @ X490 @ ( comp @ X492 @ X489 ) ) )
| ( $true
= ( X481 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) @ X489 ) ) )
& ! [X483: subst > term > term] :
( ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) )
| ? [X484: term] :
( ( $true
= ( X481 @ id @ X484 @ id ) )
& ( $true
!= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) ) )
| ? [X485: subst,X486: term,X487: subst] :
( ( sub @ ( X483 @ X485 @ X486 ) @ X487 )
!= ( X483 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) ) ) )
& ! [X493: subst,X494: term,X495: subst,X496: subst] :
( ( $true
!= ( X481 @ ( comp @ X493 @ X496 ) @ ( sub @ X494 @ X496 ) @ X495 ) )
| ( $true
= ( X481 @ X493 @ X494 @ ( comp @ X496 @ X495 ) ) ) )
& ! [X488: term] :
( ( ( X481 @ id @ X488 @ id )
!= $true )
| ( $true
= ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id ) ) ) )
| ? [X468: term,X469: subst > term > subst > $o,X470: term] :
( ! [X479: term,X480: term] :
( ( $true
!= ( X469 @ id @ X479 @ id ) )
| ( $true
= ( X469 @ id @ ( ap @ ( sub @ X480 @ id ) @ X479 ) @ id ) )
| ( $true
!= ( X469 @ id @ X480 @ id ) ) )
& ! [X475: subst,X476: subst,X477: term,X478: subst] :
( ( ( X469 @ ( comp @ X476 @ X478 ) @ ( sub @ X477 @ X478 ) @ X475 )
!= $true )
| ( $true
= ( X469 @ X476 @ X477 @ ( comp @ X478 @ X475 ) ) ) )
& ( $true
!= ( X469 @ id @ ( ap @ X468 @ X470 ) @ id ) )
& ( $true
= ( X469 @ id @ X468 @ id ) )
& ( ( X469 @ id @ X470 @ id )
= $true )
& ! [X471: term,X472: subst,X473: subst,X474: subst] :
( ( ( X469 @ X473 @ X471 @ ( comp @ X474 @ X472 ) )
!= $true )
| ( ( X469 @ ( comp @ X473 @ X474 ) @ ( sub @ X471 @ X474 ) @ X472 )
= $true ) ) )
| ? [X461: term > $o,X462: term] :
( ! [X465: term,X466: term] :
( ( $true
!= ( X461 @ X466 ) )
| ( ( X461 @ ( ap @ X466 @ X465 ) )
= $true )
| ( ( X461 @ X465 )
!= $true ) )
& ! [X463: term] :
( ? [X464: term] :
( ( $true
!= ( X461 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) )
& ( $true
= ( X461 @ X464 ) ) )
| ( $true
= ( X461 @ ( lam @ X463 ) ) ) )
& ! [X467: term] :
( ( $true
!= ( var @ X467 ) )
| ( $true
= ( X461 @ X467 ) ) )
& ( $true
!= ( X461 @ X462 ) ) ) ) )
& ( ! [X4: subst > term > subst > $o,X5: term] :
( ? [X19: term] :
( ( ( X4 @ id @ X19 @ id )
= $true )
& ( $true
!= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) ) )
| ? [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
!= $true )
& ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
= $true ) )
| ? [X6: term,X7: subst,X8: subst,X9: subst] :
( ( $true
= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) )
& ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
!= $true ) )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) )
| ? [X10: subst > term > term] :
( ! [X11: term] :
( ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) )
| ( $true
!= ( X4 @ id @ X11 @ id ) ) )
& ( $true
!= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
& ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X272: subst,X273: term,X274: term > $o] :
? [X275: term > $o] :
! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
<=> ( axvarid = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ulamvar1 != $true )
& ( axvarshift = $true )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( shinj = $true )
<=> ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) ) )
& ( ! [X216: term,X217: term > $o] :
( ? [X218: term] :
( ( ( var @ X218 )
= $true )
& ( $true
!= ( X217 @ X218 ) ) )
| ? [X219: term,X220: term] :
( ( ( X217 @ ( ap @ X219 @ X220 ) )
!= $true )
& ( $true
= ( X217 @ X219 ) )
& ( ( X217 @ X220 )
= $true ) )
| ? [X221: term] :
( ( ( X217 @ X221 )
= $true )
& ( $true
!= ( X217 @ ( lam @ X221 ) ) ) )
| ( $true
= ( X217 @ X216 ) ) )
<=> ( induction = $true ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) )
| ? [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
!= X533 )
| ? [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
!= X532 ) ) )
& ( hoasapinj1_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ? [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
!= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) )
& ( $true
= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) ) )
| ? [X140: term] :
( ( X132 @ id @ X140 @ id )
!= ( X134 @ X140 ) )
| ? [X149: term] :
( ( $true
= ( X134 @ X149 ) )
& ( $true
!= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) )
| ? [X135: subst > term > term] :
( ( $true
!= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
& ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
& ! [X139: term] :
( ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) )
| ( $true
!= ( X132 @ id @ X139 @ id ) ) ) )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ? [X141: subst,X142: subst,X143: subst,X144: term] :
( ( $true
!= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) )
& ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
= $true ) ) )
| ? [X131: term] :
( ( sub @ X131 @ id )
!= X131 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2_gthm = $true )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
<=> ( hoasapinj2 = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X23: term] :
? [X24: subst > term > term] :
! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X186: term,X187: term > $o,X188: subst] :
? [X189: term > $o] :
! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) ) )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( X69 != X70 )
& ( ( ap @ X70 @ X72 )
= ( ap @ X69 @ X71 ) ) )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ? [X129: term,X130: term] :
( ( $true
!= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) )
& ( ( X123 @ id @ X130 @ id )
= $true )
& ( $true
= ( X123 @ id @ X129 @ id ) ) )
| ? [X124: subst > term > term] :
( ( $true
!= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) )
& ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
& ! [X128: term] :
( ( ( X123 @ id @ X128 @ id )
!= $true )
| ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) ) ) )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X232: subst > term > subst > $o] :
? [X233: term > $o] :
! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X449: term,X450: subst > term > subst > $o] :
( ( $true
= ( X450 @ id @ ( lam @ ( sub @ X449 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X460: term] :
( ( $true
= ( X450 @ id @ X460 @ id ) )
& ( ( X450 @ id @ ( sub @ X449 @ ( push @ X460 @ id ) ) @ id )
!= $true ) )
| ? [X451: term,X452: subst > term > term] :
( ( $true
!= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) )
& ! [X453: subst,X454: term,X455: subst] :
( ( X452 @ ( comp @ X453 @ X455 ) @ ( sub @ X454 @ X455 ) )
= ( sub @ X451 @ ( push @ ( sub @ X454 @ X455 ) @ ( comp @ X453 @ X455 ) ) ) )
& ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( $true
!= ( X450 @ id @ X456 @ id ) ) )
& ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( sub @ X451 @ ( push @ X458 @ X457 ) ) @ X459 )
= ( sub @ ( X452 @ X457 @ X458 ) @ X459 ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( axapp = $true )
& ( ( ! [X340: term,X341: subst > term > subst > $o] :
( ? [X344: subst > term > term] :
( ! [X345: term,X346: subst,X347: subst] :
( ( sub @ ( X344 @ X346 @ X345 ) @ X347 )
= ( X344 @ ( comp @ X346 @ X347 ) @ ( sub @ X345 @ X347 ) ) )
& ! [X348: term] :
( ( $true
!= ( X341 @ id @ X348 @ id ) )
| ( ( X341 @ id @ ( X344 @ id @ X348 ) @ id )
= $true ) )
& ( ( X341 @ id @ ( lam @ ( X344 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X341 @ id @ X340 @ id )
= $true )
| ? [X342: term,X343: term] :
( ( ( X341 @ id @ X342 @ id )
= $true )
& ( ( X341 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
!= $true )
& ( ( X341 @ id @ X343 @ id )
= $true ) ) )
| ? [X330: subst > term > subst > $o,X331: term,X332: term > $o] :
( ! [X333: subst > term > term] :
( ? [X334: term] :
( ( $true
= ( X330 @ id @ X334 @ id ) )
& ( $true
!= ( X330 @ id @ ( X333 @ id @ X334 ) @ id ) ) )
| ? [X335: subst,X336: term,X337: subst] :
( ( X333 @ ( comp @ X337 @ X335 ) @ ( sub @ X336 @ X335 ) )
!= ( sub @ ( X333 @ X337 @ X336 ) @ X335 ) )
| ( ( X330 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) )
& ! [X338: term] :
( ( X330 @ id @ X338 @ id )
= ( X332 @ X338 ) )
& ( ( X332 @ ( lam @ X331 ) )
!= $true )
& ! [X339: term] :
( ( ( X332 @ X339 )
!= $true )
| ( ( X332 @ ( sub @ X331 @ ( push @ X339 @ id ) ) )
= $true ) ) )
| ? [X329: term] :
( ( sub @ X329 @ id )
!= X329 )
| ? [X322: term,X323: term > $o] :
( ( $true
!= ( X323 @ X322 ) )
& ! [X327: term,X328: term] :
( ( ( X323 @ X328 )
!= $true )
| ( $true
= ( X323 @ ( ap @ X327 @ X328 ) ) )
| ( $true
!= ( X323 @ X327 ) ) )
& ! [X324: term] :
( ( ( var @ X324 )
!= $true )
| ( ( X323 @ X324 )
= $true ) )
& ! [X325: term] :
( ( $true
= ( X323 @ ( lam @ X325 ) ) )
| ? [X326: term] :
( ( $true
= ( X323 @ X326 ) )
& ( ( X323 @ ( sub @ X325 @ ( push @ X326 @ id ) ) )
!= $true ) ) ) )
| ? [X319: subst > term > subst > $o] :
! [X320: term > $o] :
? [X321: term] :
( ( X319 @ id @ X321 @ id )
!= ( X320 @ X321 ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X164: subst > term > subst > $o,X165: term] :
( ( ( X164 @ id @ ( lam @ X165 ) @ id )
= $true )
| ? [X166: term] :
( ( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
!= $true )
& ( $true
= ( X164 @ id @ X166 @ id ) ) )
| ? [X176: subst,X177: subst,X178: term,X179: subst] :
( ( ( X164 @ X177 @ X178 @ ( comp @ X179 @ X176 ) )
= $true )
& ( $true
!= ( X164 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) @ X176 ) ) )
| ? [X172: subst,X173: subst,X174: subst,X175: term] :
( ( ( X164 @ X173 @ X175 @ ( comp @ X174 @ X172 ) )
!= $true )
& ( $true
= ( X164 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) @ X172 ) ) )
| ? [X167: subst > term > term] :
( ! [X168: term,X169: subst,X170: subst] :
( ( sub @ ( X167 @ X169 @ X168 ) @ X170 )
= ( X167 @ ( comp @ X169 @ X170 ) @ ( sub @ X168 @ X170 ) ) )
& ! [X171: term] :
( ( ( X164 @ id @ X171 @ id )
!= $true )
| ( $true
= ( X164 @ id @ ( X167 @ id @ X171 ) @ id ) ) )
& ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X156: subst > term > subst > $o,X157: term] :
( ( ( X156 @ id @ ( lam @ ( sub @ X157 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X159: subst > term > term] :
( ? [X160: term] :
( ( ( X156 @ id @ X160 @ id )
= $true )
& ( ( X156 @ id @ ( X159 @ id @ X160 ) @ id )
!= $true ) )
| ( $true
= ( X156 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id ) )
| ? [X161: subst,X162: subst,X163: term] :
( ( X159 @ ( comp @ X161 @ X162 ) @ ( sub @ X163 @ X162 ) )
!= ( sub @ ( X159 @ X161 @ X163 ) @ X162 ) ) )
& ! [X158: term] :
( ( ( X156 @ id @ ( sub @ X157 @ ( push @ X158 @ id ) ) @ id )
= $true )
| ( ( X156 @ id @ X158 @ id )
!= $true ) ) )
| ? [X155: term] :
( ( sub @ X155 @ id )
!= X155 ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( pushprop = $true )
& ( ulamvarsh = $true )
& ( ( hoasinduction = $true )
<=> ! [X390: term,X391: subst > term > subst > $o] :
( ? [X392: term,X393: term] :
( ( ( X391 @ id @ X393 @ id )
= $true )
& ( ( X391 @ id @ ( ap @ ( sub @ X392 @ id ) @ X393 ) @ id )
!= $true )
& ( $true
= ( X391 @ id @ X392 @ id ) ) )
| ( $true
= ( X391 @ id @ X390 @ id ) )
| ? [X399: term,X400: subst,X401: subst,X402: subst] :
( ( ( X391 @ ( comp @ X402 @ X401 ) @ ( sub @ X399 @ X401 ) @ X400 )
= $true )
& ( $true
!= ( X391 @ X402 @ X399 @ ( comp @ X401 @ X400 ) ) ) )
| ? [X394: term] :
( ( ( var @ ( sub @ X394 @ id ) )
= $true )
& ( ( X391 @ id @ X394 @ id )
!= $true ) )
| ? [X403: subst > term > term] :
( ! [X407: term] :
( ( ( X391 @ id @ X407 @ id )
!= $true )
| ( ( X391 @ id @ ( X403 @ id @ X407 ) @ id )
= $true ) )
& ! [X404: term,X405: subst,X406: subst] :
( ( sub @ ( X403 @ X406 @ X404 ) @ X405 )
= ( X403 @ ( comp @ X406 @ X405 ) @ ( sub @ X404 @ X405 ) ) )
& ( ( X391 @ id @ ( lam @ ( X403 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X395: term,X396: subst,X397: subst,X398: subst] :
( ( ( X391 @ ( comp @ X397 @ X398 ) @ ( sub @ X395 @ X398 ) @ X396 )
!= $true )
& ( $true
= ( X391 @ X397 @ X395 @ ( comp @ X398 @ X396 ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X28: term,X29: term,X30: term,X31: term] :
( ( X30 != X31 )
& ( ( ap @ X28 @ X30 )
= ( ap @ X29 @ X31 ) ) )
| ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop_gthm = $true )
& ( ! [X408: term] :
? [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
= ( X409 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X381: d_term] : ( d_one = X381 )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ? [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
!= ( X85 @ X88 ) )
| ( ( X87 @ X86 )
!= $true )
| ( $true
= ( X85 @ one ) ) )
| ? [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
!= X82 ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( substmonoid = $true )
<=> ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) ) )
& ( ( ! [X431: term,X432: subst > term > subst > $o] :
( ( $true
= ( X432 @ id @ X431 @ id ) )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X432 @ ( comp @ X442 @ X443 ) @ ( sub @ X441 @ X443 ) @ X440 )
!= $true )
& ( $true
= ( X432 @ X442 @ X441 @ ( comp @ X443 @ X440 ) ) ) )
| ? [X439: term] :
( ( ( var @ ( sub @ X439 @ id ) )
= $true )
& ( ( X432 @ id @ X439 @ id )
!= $true ) )
| ? [X444: subst > term > term] :
( ! [X445: term,X446: subst,X447: subst] :
( ( X444 @ ( comp @ X446 @ X447 ) @ ( sub @ X445 @ X447 ) )
= ( sub @ ( X444 @ X446 @ X445 ) @ X447 ) )
& ! [X448: term] :
( ( $true
!= ( X432 @ id @ X448 @ id ) )
| ( ( X432 @ id @ ( X444 @ id @ X448 ) @ id )
= $true ) )
& ( $true
!= ( X432 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id ) ) )
| ? [X433: term,X434: term] :
( ( ( X432 @ id @ ( ap @ ( sub @ X433 @ id ) @ X434 ) @ id )
!= $true )
& ( $true
= ( X432 @ id @ X433 @ id ) )
& ( $true
= ( X432 @ id @ X434 @ id ) ) )
| ? [X435: subst,X436: subst,X437: term,X438: subst] :
( ( ( X432 @ X436 @ X437 @ ( comp @ X435 @ X438 ) )
!= $true )
& ( ( X432 @ ( comp @ X436 @ X435 ) @ ( sub @ X437 @ X435 ) @ X438 )
= $true ) ) )
| ? [X421: subst > term > subst > $o,X422: term,X423: term > $o] :
( ! [X424: term] :
( ( $true
!= ( X423 @ X424 ) )
| ( ( X423 @ ( sub @ X422 @ ( push @ X424 @ id ) ) )
= $true ) )
& ! [X426: subst > term > term] :
( ? [X427: subst,X428: term,X429: subst] :
( ( X426 @ ( comp @ X427 @ X429 ) @ ( sub @ X428 @ X429 ) )
!= ( sub @ ( X426 @ X427 @ X428 ) @ X429 ) )
| ? [X430: term] :
( ( $true
!= ( X421 @ id @ ( X426 @ id @ X430 ) @ id ) )
& ( ( X421 @ id @ X430 @ id )
= $true ) )
| ( ( X421 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X423 @ ( lam @ X422 ) )
!= $true )
& ! [X425: term] :
( ( X423 @ X425 )
= ( X421 @ id @ X425 @ id ) ) )
| ? [X420: term] :
( ( sub @ X420 @ id )
!= X420 )
| ? [X413: term > $o,X414: term] :
( ( ( X413 @ X414 )
!= $true )
& ! [X417: term,X418: term] :
( ( $true
= ( X413 @ ( ap @ X417 @ X418 ) ) )
| ( $true
!= ( X413 @ X417 ) )
| ( $true
!= ( X413 @ X418 ) ) )
& ! [X415: term] :
( ( $true
= ( X413 @ ( lam @ X415 ) ) )
| ? [X416: term] :
( ( ( X413 @ X416 )
= $true )
& ( $true
!= ( X413 @ ( sub @ X415 @ ( push @ X416 @ id ) ) ) ) ) )
& ! [X419: term] :
( ( ( var @ X419 )
!= $true )
| ( ( X413 @ X419 )
= $true ) ) )
| ? [X410: subst > term > subst > $o] :
! [X411: term > $o] :
? [X412: term] :
( ( X410 @ id @ X412 @ id )
!= ( X411 @ X412 ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ! [X255: term] :
? [X256: subst > term > term] :
( ( X256 @ sh @ one )
= ( sub @ X255 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X57: subst,X58: term,X59: term > $o] :
( ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true )
| ? [X60: term] :
( ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) )
& ( ( X59 @ ( lam @ X60 ) )
!= $true ) )
| ? [X62: term,X63: term] :
( ( ( X59 @ X63 )
= $true )
& ( $true
= ( X59 @ X62 ) )
& ( $true
!= ( X59 @ ( ap @ X62 @ X63 ) ) ) )
| ? [X64: term] :
( ( ( var @ X64 )
= $true )
& ( ( X59 @ ( sub @ X64 @ X57 ) )
!= $true ) ) )
| ? [X51: term,X52: term > $o] :
( ! [X55: term,X56: term] :
( ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) )
| ( $true
!= ( X52 @ X55 ) ) )
& ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
& ( $true
!= ( X52 @ X51 ) )
& ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) ) )
| ? [X50: subst] :
( ( comp @ X50 @ id )
!= X50 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 )
| ? [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
!= X47 ) ) )
& ( ( ! [X358: term,X359: subst > term > subst > $o] :
( ? [X360: subst > term > term] :
( ! [X361: term,X362: subst,X363: subst] :
( ( sub @ ( X360 @ X362 @ X361 ) @ X363 )
= ( X360 @ ( comp @ X362 @ X363 ) @ ( sub @ X361 @ X363 ) ) )
& ! [X364: term] :
( ( ( X359 @ id @ ( X360 @ id @ X364 ) @ id )
= $true )
| ( ( X359 @ id @ X364 @ id )
!= $true ) )
& ( ( X359 @ id @ ( lam @ ( X360 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X359 @ id @ ( lam @ X358 ) @ id ) )
| ? [X365: term] :
( ( $true
!= ( X359 @ id @ ( sub @ X358 @ ( push @ X365 @ id ) ) @ id ) )
& ( $true
= ( X359 @ id @ X365 @ id ) ) ) )
| ? [X350: subst > term > subst > $o,X351: term] :
( ( $true
!= ( X350 @ id @ ( lam @ ( sub @ X351 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X352: subst > term > term] :
( ? [X356: term] :
( ( ( X350 @ id @ ( X352 @ id @ X356 ) @ id )
!= $true )
& ( ( X350 @ id @ X356 @ id )
= $true ) )
| ? [X353: term,X354: subst,X355: subst] :
( ( X352 @ ( comp @ X355 @ X354 ) @ ( sub @ X353 @ X354 ) )
!= ( sub @ ( X352 @ X355 @ X353 ) @ X354 ) )
| ( $true
= ( X350 @ id @ ( lam @ ( X352 @ sh @ one ) ) @ id ) ) )
& ! [X357: term] :
( ( $true
!= ( X350 @ id @ X357 @ id ) )
| ( ( X350 @ id @ ( sub @ X351 @ ( push @ X357 @ id ) ) @ id )
= $true ) ) )
| ? [X349: term] :
( ( sub @ X349 @ id )
!= X349 ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( lamnotvar = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X366: subst > term > subst > $o,X367: term,X368: term,X369: term > $o] :
( ? [X377: term,X378: subst,X379: subst,X380: subst] :
( ( ( X366 @ X379 @ X377 @ ( comp @ X380 @ X378 ) )
= $true )
& ( $true
!= ( X366 @ ( comp @ X379 @ X380 ) @ ( sub @ X377 @ X380 ) @ X378 ) ) )
| ? [X373: subst,X374: subst,X375: term,X376: subst] :
( ( ( X366 @ X376 @ X375 @ ( comp @ X373 @ X374 ) )
!= $true )
& ( $true
= ( X366 @ ( comp @ X376 @ X373 ) @ ( sub @ X375 @ X373 ) @ X374 ) ) )
| ? [X371: term,X372: term] :
( ( $true
= ( X366 @ id @ X371 @ id ) )
& ( $true
= ( X366 @ id @ X372 @ id ) )
& ( ( X366 @ id @ ( ap @ ( sub @ X371 @ id ) @ X372 ) @ id )
!= $true ) )
| ? [X370: term] :
( ( X366 @ id @ X370 @ id )
!= ( X369 @ X370 ) )
| ( $true
= ( X369 @ ( ap @ X367 @ X368 ) ) )
| ( $true
!= ( X369 @ X367 ) )
| ( ( X369 @ X368 )
!= $true ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( ! [X262: term,X263: subst > term > subst > $o,X264: term > $o] :
( ( $true
= ( X264 @ ( lam @ X262 ) ) )
| ? [X271: term] :
( ( X264 @ X271 )
!= ( X263 @ id @ X271 @ id ) )
| ? [X266: subst > term > term] :
( ! [X270: term] :
( ( ( X263 @ id @ X270 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X266 @ id @ X270 ) @ id ) ) )
& ( ( X263 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
!= $true )
& ! [X267: term,X268: subst,X269: subst] :
( ( X266 @ ( comp @ X269 @ X268 ) @ ( sub @ X267 @ X268 ) )
= ( sub @ ( X266 @ X269 @ X267 ) @ X268 ) ) )
| ? [X265: term] :
( ( $true
= ( X264 @ X265 ) )
& ( $true
!= ( X264 @ ( sub @ X262 @ ( push @ X265 @ id ) ) ) ) ) )
| ? [X261: term] :
( ( sub @ X261 @ id )
!= X261 )
| ? [X257: term] :
! [X258: subst > term > term] :
? [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
!= ( X258 @ X259 @ X260 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( lamnotap != $true )
& ( ( ! [X21: term] :
( ( sub @ X21 @ id )
= X21 )
| ? [X20: term] :
( ( sub @ X20 @ id )
!= X20 ) )
<=> ( termmset_lthm = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( pushprop_lthm_orig = $true )
& ! [X382: d_term,X383: d_term] :
( ( X382 = X383 )
| ( ( d2term @ X383 )
!= ( d2term @ X382 ) ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 ) )
& ( termmset_gthm = $true )
& ( axclos = $true )
& ( ! [X65: subst > term > subst > $o] :
? [X66: term > $o] :
! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X102: term,X103: term > $o] :
( ? [X106: term] :
( ( ( var @ X106 )
= $true )
& ( $true
!= ( X103 @ X106 ) ) )
| ( ( X103 @ X102 )
= $true )
| ? [X107: term,X108: term] :
( ( ( X103 @ X107 )
= $true )
& ( $true
!= ( X103 @ ( ap @ X108 @ X107 ) ) )
& ( ( X103 @ X108 )
= $true ) )
| ? [X104: term] :
( ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) )
& ( $true
!= ( X103 @ ( lam @ X104 ) ) ) ) )
| ? [X94: term,X95: subst,X96: term > $o] :
( ! [X101: term] :
( ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true )
| ( ( var @ X101 )
!= $true ) )
& ( ( X96 @ ( sub @ X94 @ X95 ) )
!= $true )
& ! [X97: term] :
( ( $true
= ( X96 @ ( lam @ X97 ) ) )
| ? [X98: term] :
( ( ( X96 @ X98 )
= $true )
& ( $true
!= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) ) ) )
& ! [X99: term,X100: term] :
( ( ( X96 @ X100 )
!= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true ) ) )
| ? [X93: term] :
( ( sub @ X93 @ id )
!= X93 ) ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X521: subst > term > subst > $o,X522: term] :
( ? [X528: term] :
( ( ( X521 @ id @ ( sub @ X522 @ ( push @ X528 @ id ) ) @ id )
!= $true )
& ( ( X521 @ id @ X528 @ id )
= $true ) )
| ( ( X521 @ id @ ( lam @ X522 ) @ id )
= $true )
| ? [X523: subst > term > term] :
( ! [X527: term] :
( ( ( X521 @ id @ X527 @ id )
!= $true )
| ( $true
= ( X521 @ id @ ( X523 @ id @ X527 ) @ id ) ) )
& ! [X524: term,X525: subst,X526: subst] :
( ( X523 @ ( comp @ X526 @ X525 ) @ ( sub @ X524 @ X525 ) )
= ( sub @ ( X523 @ X526 @ X524 ) @ X525 ) )
& ( $true
!= ( X521 @ id @ ( lam @ ( X523 @ sh @ one ) ) @ id ) ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( hoasinduction_lem1 = $true )
& ( ( ( ! [X296: subst] :
( ( comp @ id @ X296 )
= X296 )
& ! [X295: subst] :
( ( comp @ X295 @ id )
= X295 ) )
| ? [X294: subst] :
( ( comp @ X294 @ id )
!= X294 )
| ? [X293: subst] :
( ( comp @ id @ X293 )
!= X293 ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X245: subst,X246: term,X247: term > $o] :
( ? [X248: term,X249: term] :
( ( $true
!= ( X247 @ ( ap @ X249 @ X248 ) ) )
& ( $true
= ( X247 @ X249 ) )
& ( ( X247 @ X248 )
= $true ) )
| ( ( X247 @ ( sub @ X246 @ X245 ) )
= $true )
| ? [X252: term] :
( ( $true
!= ( X247 @ ( sub @ X252 @ X245 ) ) )
& ( $true
= ( var @ X252 ) ) )
| ? [X250: term] :
( ! [X251: term] :
( ( $true
= ( X247 @ ( sub @ X250 @ ( push @ X251 @ id ) ) ) )
| ( ( X247 @ X251 )
!= $true ) )
& ( ( X247 @ ( lam @ X250 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( induction2 = $true )
<=> ! [X191: term > $o,X192: term] :
( ? [X193: term,X194: term] :
( ( ( X191 @ ( ap @ X194 @ X193 ) )
!= $true )
& ( ( X191 @ X193 )
= $true )
& ( $true
= ( X191 @ X194 ) ) )
| ? [X197: term] :
( ( $true
= ( var @ X197 ) )
& ( $true
!= ( X191 @ X197 ) ) )
| ( $true
= ( X191 @ X192 ) )
| ? [X195: term] :
( ! [X196: term] :
( ( ( X191 @ X196 )
!= $true )
| ( $true
= ( X191 @ ( sub @ X195 @ ( push @ X196 @ id ) ) ) ) )
& ( ( X191 @ ( lam @ X195 ) )
!= $true ) ) ) )
& ( ! [X235: term,X236: subst > term > subst > $o,X237: term > $o] :
( ? [X239: term] :
( ( $true
!= ( X237 @ ( sub @ X235 @ ( push @ X239 @ id ) ) ) )
& ( ( X237 @ X239 )
= $true ) )
| ? [X240: subst > term > term] :
( ! [X242: subst,X243: term,X244: subst] :
( ( sub @ ( X240 @ X242 @ X243 ) @ X244 )
= ( X240 @ ( comp @ X242 @ X244 ) @ ( sub @ X243 @ X244 ) ) )
& ! [X241: term] :
( ( ( X236 @ id @ X241 @ id )
!= $true )
| ( ( X236 @ id @ ( X240 @ id @ X241 ) @ id )
= $true ) )
& ( ( X236 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X238: term] :
( ( X236 @ id @ X238 @ id )
!= ( X237 @ X238 ) )
| ( $true
= ( X237 @ ( lam @ X235 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( induction2lem_gthm = $true )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
!= ( d2subst @ X253 ) )
| ( X253 = X254 ) )
& ( substmonoid_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X515: term,X516: subst > term > term,X517: term] :
( ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) )
| ? [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
!= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) ) ) )
& ( ! [X198: term > $o,X199: term,X200: subst > term > subst > $o] :
( ? [X210: term] :
( ( X200 @ id @ X210 @ id )
!= ( X198 @ X210 ) )
| ? [X211: subst > term > term] :
( ! [X212: term] :
( ( $true
!= ( X200 @ id @ X212 @ id ) )
| ( $true
= ( X200 @ id @ ( X211 @ id @ X212 ) @ id ) ) )
& ( $true
!= ( X200 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) )
& ! [X213: term,X214: subst,X215: subst] :
( ( X211 @ ( comp @ X214 @ X215 ) @ ( sub @ X213 @ X215 ) )
= ( sub @ ( X211 @ X214 @ X213 ) @ X215 ) ) )
| ? [X201: term,X202: subst,X203: subst,X204: subst] :
( ( $true
!= ( X200 @ ( comp @ X202 @ X204 ) @ ( sub @ X201 @ X204 ) @ X203 ) )
& ( $true
= ( X200 @ X202 @ X201 @ ( comp @ X204 @ X203 ) ) ) )
| ? [X205: term] :
( ( $true
!= ( X198 @ ( sub @ X199 @ ( push @ X205 @ id ) ) ) )
& ( $true
= ( X198 @ X205 ) ) )
| ? [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X200 @ X206 @ X209 @ ( comp @ X208 @ X207 ) )
!= $true )
& ( ( X200 @ ( comp @ X206 @ X208 ) @ ( sub @ X209 @ X208 ) @ X207 )
= $true ) )
| ( ( X198 @ ( lam @ X199 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
<=> ( termmset = $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
!= ( X152 @ X150 ) )
| ~ ! [X154: term] :
( ( X151 @ X154 )
= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) )
| ( $true
= ( X151 @ one ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ~ ! [X225: subst > term > term] :
( ~ ! [X229: term] :
( ( $true
= ( X223 @ id @ ( X225 @ id @ X229 ) @ id ) )
| ( $true
!= ( X223 @ id @ X229 @ id ) ) )
| ~ ! [X226: subst,X227: term,X228: subst] :
( ( X225 @ ( comp @ X228 @ X226 ) @ ( sub @ X227 @ X226 ) )
= ( sub @ ( X225 @ X228 @ X227 ) @ X226 ) )
| ( $true
= ( X223 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X224: term] :
( ( $true
= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) )
| ( ( X223 @ id @ X224 @ id )
!= $true ) ) ) )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem3v2 = $true )
& ( axmap = $true )
& ( axabs = $true )
& ( ! [X111: subst > term > subst > $o,X112: term] :
( ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X113: term] :
( ( $true
= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) )
| ( $true
!= ( X111 @ id @ X113 @ id ) ) )
| ~ ! [X114: subst > term > term] :
( ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X118: term] :
( ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) )
| ( ( X111 @ id @ X118 @ id )
!= $true ) )
| ~ ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( ( apinj1 = $true )
<=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ( ! [X277: subst,X278: term] :
( ( sub @ one @ ( push @ X278 @ X277 ) )
= X278 )
=> ( ! [X279: term,X280: subst] :
( ( comp @ sh @ ( push @ X279 @ X280 ) )
= X280 )
=> ( ! [X281: term,X282: term] :
( ( X281 = X282 )
| ( ( lam @ X281 )
!= ( lam @ X282 ) ) )
=> ! [X283: term,X284: subst > term > term,X285: subst,X286: subst > term > term] :
( ~ ! [X287: term,X288: subst,X289: subst] :
( ( sub @ ( X284 @ X288 @ X287 ) @ X289 )
= ( X284 @ ( comp @ X288 @ X289 ) @ ( sub @ X287 @ X289 ) ) )
| ~ ! [X290: subst,X291: subst,X292: term] :
( ( X286 @ ( comp @ X291 @ X290 ) @ ( sub @ X292 @ X290 ) )
= ( sub @ ( X286 @ X291 @ X292 ) @ X290 ) )
| ( ( lam @ ( X284 @ sh @ one ) )
!= ( lam @ ( X286 @ sh @ one ) ) )
| ( ( X286 @ X285 @ X283 )
= ( X284 @ X285 @ X283 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ~ ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) )
| ~ ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) ) )
<=> ( hoaslaminj = $true ) )
& ( ! [X301: subst > term > subst > $o,X302: term,X303: term] :
( ~ ! [X304: term,X305: term] :
( ( $true
!= ( X301 @ id @ X304 @ id ) )
| ( $true
= ( X301 @ id @ ( ap @ ( sub @ X305 @ id ) @ X304 ) @ id ) )
| ( ( X301 @ id @ X305 @ id )
!= $true ) )
| ~ ! [X310: subst,X311: term,X312: subst,X313: subst] :
( ( ( X301 @ ( comp @ X312 @ X313 ) @ ( sub @ X311 @ X313 ) @ X310 )
= $true )
| ( $true
!= ( X301 @ X312 @ X311 @ ( comp @ X313 @ X310 ) ) ) )
| ~ ! [X306: subst,X307: subst,X308: term,X309: subst] :
( ( $true
!= ( X301 @ ( comp @ X307 @ X309 ) @ ( sub @ X308 @ X309 ) @ X306 ) )
| ( $true
= ( X301 @ X307 @ X308 @ ( comp @ X309 @ X306 ) ) ) )
| ( $true
= ( X301 @ id @ ( ap @ X302 @ X303 ) @ id ) )
| ( ( X301 @ id @ X302 @ id )
!= $true )
| ( ( X301 @ id @ X303 @ id )
!= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axassoc = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X461: term > $o,X462: term] :
( ~ ! [X463: term] :
( ~ ! [X464: term] :
( ( $true
= ( X461 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) )
| ( $true
!= ( X461 @ X464 ) ) )
| ( $true
= ( X461 @ ( lam @ X463 ) ) ) )
| ~ ! [X465: term,X466: term] :
( ( $true
!= ( X461 @ X466 ) )
| ( ( X461 @ ( ap @ X466 @ X465 ) )
= $true )
| ( ( X461 @ X465 )
!= $true ) )
| ( $true
= ( X461 @ X462 ) )
| ~ ! [X467: term] :
( ( $true
!= ( var @ X467 ) )
| ( $true
= ( X461 @ X467 ) ) ) )
=> ( ! [X468: term,X469: subst > term > subst > $o,X470: term] :
( ~ ! [X471: term,X472: subst,X473: subst,X474: subst] :
( ( ( X469 @ X473 @ X471 @ ( comp @ X474 @ X472 ) )
!= $true )
| ( ( X469 @ ( comp @ X473 @ X474 ) @ ( sub @ X471 @ X474 ) @ X472 )
= $true ) )
| ( $true
!= ( X469 @ id @ X468 @ id ) )
| ( $true
= ( X469 @ id @ ( ap @ X468 @ X470 ) @ id ) )
| ( ( X469 @ id @ X470 @ id )
!= $true )
| ~ ! [X475: subst,X476: subst,X477: term,X478: subst] :
( ( ( X469 @ ( comp @ X476 @ X478 ) @ ( sub @ X477 @ X478 ) @ X475 )
!= $true )
| ( $true
= ( X469 @ X476 @ X477 @ ( comp @ X478 @ X475 ) ) ) )
| ~ ! [X479: term,X480: term] :
( ( $true
!= ( X469 @ id @ X479 @ id ) )
| ( $true
= ( X469 @ id @ ( ap @ ( sub @ X480 @ id ) @ X479 ) @ id ) )
| ( $true
!= ( X469 @ id @ X480 @ id ) ) ) )
=> ( ! [X481: subst > term > subst > $o,X482: term] :
( ~ ! [X493: subst,X494: term,X495: subst,X496: subst] :
( ( $true
!= ( X481 @ ( comp @ X493 @ X496 ) @ ( sub @ X494 @ X496 ) @ X495 ) )
| ( $true
= ( X481 @ X493 @ X494 @ ( comp @ X496 @ X495 ) ) ) )
| ( ( X481 @ id @ ( lam @ X482 ) @ id )
= $true )
| ~ ! [X488: term] :
( ( ( X481 @ id @ X488 @ id )
!= $true )
| ( $true
= ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id ) ) )
| ~ ! [X483: subst > term > term] :
( ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) )
| ~ ! [X485: subst,X486: term,X487: subst] :
( ( sub @ ( X483 @ X485 @ X486 ) @ X487 )
= ( X483 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) ) )
| ~ ! [X484: term] :
( ( $true
= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) )
| ( $true
!= ( X481 @ id @ X484 @ id ) ) ) )
| ~ ! [X489: subst,X490: term,X491: subst,X492: subst] :
( ( $true
!= ( X481 @ X491 @ X490 @ ( comp @ X492 @ X489 ) ) )
| ( $true
= ( X481 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) @ X489 ) ) ) )
=> ! [X497: subst > term > subst > $o,X498: term] :
( ( $true
= ( X497 @ id @ X498 @ id ) )
| ~ ! [X503: subst,X504: subst,X505: subst,X506: term] :
( ( ( X497 @ ( comp @ X503 @ X505 ) @ ( sub @ X506 @ X505 ) @ X504 )
= $true )
| ( ( X497 @ X503 @ X506 @ ( comp @ X505 @ X504 ) )
!= $true ) )
| ~ ! [X499: subst,X500: subst,X501: subst,X502: term] :
( ( ( X497 @ ( comp @ X501 @ X500 ) @ ( sub @ X502 @ X500 ) @ X499 )
!= $true )
| ( $true
= ( X497 @ X501 @ X502 @ ( comp @ X500 @ X499 ) ) ) )
| ~ ! [X508: term,X509: term] :
( ( $true
= ( X497 @ id @ ( ap @ ( sub @ X509 @ id ) @ X508 ) @ id ) )
| ( ( X497 @ id @ X509 @ id )
!= $true )
| ( ( X497 @ id @ X508 @ id )
!= $true ) )
| ~ ! [X510: subst > term > term] :
( ~ ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X510 @ X512 @ X513 ) @ X514 )
= ( X510 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
| ( $true
= ( X497 @ id @ ( lam @ ( X510 @ sh @ one ) ) @ id ) )
| ~ ! [X511: term] :
( ( ( X497 @ id @ ( X510 @ id @ X511 ) @ id )
= $true )
| ( $true
!= ( X497 @ id @ X511 @ id ) ) ) )
| ~ ! [X507: term] :
( ( $true
!= ( var @ ( sub @ X507 @ id ) ) )
| ( ( X497 @ id @ X507 @ id )
= $true ) ) ) ) ) ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X4: subst > term > subst > $o,X5: term] :
( ~ ! [X19: term] :
( ( ( X4 @ id @ X19 @ id )
!= $true )
| ( $true
= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) ) )
| ~ ! [X6: term,X7: subst,X8: subst,X9: subst] :
( ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
= $true )
| ( $true
!= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) ) )
| ~ ! [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
= $true )
| ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
!= $true ) )
| ~ ! [X10: subst > term > term] :
( ( $true
= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
| ~ ! [X11: term] :
( ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) )
| ( $true
!= ( X4 @ id @ X11 @ id ) ) )
| ~ ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X272: subst,X273: term,X274: term > $o] :
~ ! [X275: term > $o] :
~ ! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) ) )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
<=> ( axvarid = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ulamvar1 != $true )
& ( axvarshift = $true )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( shinj = $true )
<=> ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) ) )
& ( ! [X216: term,X217: term > $o] :
( ( $true
= ( X217 @ X216 ) )
| ~ ! [X221: term] :
( ( ( X217 @ X221 )
!= $true )
| ( $true
= ( X217 @ ( lam @ X221 ) ) ) )
| ~ ! [X219: term,X220: term] :
( ( $true
!= ( X217 @ X219 ) )
| ( ( X217 @ X220 )
!= $true )
| ( ( X217 @ ( ap @ X219 @ X220 ) )
= $true ) )
| ~ ! [X218: term] :
( ( ( var @ X218 )
!= $true )
| ( $true
= ( X217 @ X218 ) ) ) )
<=> ( induction = $true ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
= X532 )
=> ( ! [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
= X533 )
=> ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ~ ! [X140: term] :
( ( X132 @ id @ X140 @ id )
= ( X134 @ X140 ) )
| ~ ! [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
!= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) )
| ( $true
= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) ) )
| ~ ! [X149: term] :
( ( $true
= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) )
| ( $true
!= ( X134 @ X149 ) ) )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ~ ! [X135: subst > term > term] :
( ( $true
= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
| ~ ! [X139: term] :
( ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) )
| ( $true
!= ( X132 @ id @ X139 @ id ) ) )
| ~ ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) ) )
| ~ ! [X141: subst,X142: subst,X143: subst,X144: term] :
( ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
!= $true )
| ( $true
= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2_gthm = $true )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
<=> ( hoasapinj2 = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X23: term] :
~ ! [X24: subst > term > term] :
~ ! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X186: term,X187: term > $o,X188: subst] :
~ ! [X189: term > $o] :
~ ! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) ) )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X70 @ X72 )
!= ( ap @ X69 @ X71 ) )
| ( X69 = X70 ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ~ ! [X129: term,X130: term] :
( ( $true
= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) )
| ( ( X123 @ id @ X130 @ id )
!= $true )
| ( $true
!= ( X123 @ id @ X129 @ id ) ) )
| ~ ! [X124: subst > term > term] :
( ~ ! [X128: term] :
( ( ( X123 @ id @ X128 @ id )
!= $true )
| ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) ) )
| ( $true
= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) )
| ~ ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) ) )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X232: subst > term > subst > $o] :
~ ! [X233: term > $o] :
~ ! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X449: term,X450: subst > term > subst > $o] :
( ~ ! [X451: term,X452: subst > term > term] :
( ~ ! [X453: subst,X454: term,X455: subst] :
( ( X452 @ ( comp @ X453 @ X455 ) @ ( sub @ X454 @ X455 ) )
= ( sub @ X451 @ ( push @ ( sub @ X454 @ X455 ) @ ( comp @ X453 @ X455 ) ) ) )
| ~ ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( sub @ X451 @ ( push @ X458 @ X457 ) ) @ X459 )
= ( sub @ ( X452 @ X457 @ X458 ) @ X459 ) )
| ~ ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( $true
!= ( X450 @ id @ X456 @ id ) ) )
| ( $true
= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X450 @ id @ ( lam @ ( sub @ X449 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X460: term] :
( ( ( X450 @ id @ ( sub @ X449 @ ( push @ X460 @ id ) ) @ id )
= $true )
| ( $true
!= ( X450 @ id @ X460 @ id ) ) ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( axapp = $true )
& ( ( ! [X319: subst > term > subst > $o] :
~ ! [X320: term > $o] :
~ ! [X321: term] :
( ( X319 @ id @ X321 @ id )
= ( X320 @ X321 ) )
=> ( ! [X322: term,X323: term > $o] :
( ~ ! [X325: term] :
( ( $true
= ( X323 @ ( lam @ X325 ) ) )
| ~ ! [X326: term] :
( ( $true
!= ( X323 @ X326 ) )
| ( ( X323 @ ( sub @ X325 @ ( push @ X326 @ id ) ) )
= $true ) ) )
| ~ ! [X327: term,X328: term] :
( ( ( X323 @ X328 )
!= $true )
| ( $true
= ( X323 @ ( ap @ X327 @ X328 ) ) )
| ( $true
!= ( X323 @ X327 ) ) )
| ( $true
= ( X323 @ X322 ) )
| ~ ! [X324: term] :
( ( ( var @ X324 )
!= $true )
| ( ( X323 @ X324 )
= $true ) ) )
=> ( ! [X329: term] :
( ( sub @ X329 @ id )
= X329 )
=> ( ! [X330: subst > term > subst > $o,X331: term,X332: term > $o] :
( ~ ! [X339: term] :
( ( ( X332 @ X339 )
!= $true )
| ( ( X332 @ ( sub @ X331 @ ( push @ X339 @ id ) ) )
= $true ) )
| ~ ! [X338: term] :
( ( X330 @ id @ X338 @ id )
= ( X332 @ X338 ) )
| ~ ! [X333: subst > term > term] :
( ~ ! [X334: term] :
( ( $true
= ( X330 @ id @ ( X333 @ id @ X334 ) @ id ) )
| ( $true
!= ( X330 @ id @ X334 @ id ) ) )
| ~ ! [X335: subst,X336: term,X337: subst] :
( ( X333 @ ( comp @ X337 @ X335 ) @ ( sub @ X336 @ X335 ) )
= ( sub @ ( X333 @ X337 @ X336 ) @ X335 ) )
| ( ( X330 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X332 @ ( lam @ X331 ) )
= $true ) )
=> ! [X340: term,X341: subst > term > subst > $o] :
( ( ( X341 @ id @ X340 @ id )
= $true )
| ~ ! [X342: term,X343: term] :
( ( ( X341 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
= $true )
| ( ( X341 @ id @ X343 @ id )
!= $true )
| ( ( X341 @ id @ X342 @ id )
!= $true ) )
| ~ ! [X344: subst > term > term] :
( ~ ! [X348: term] :
( ( $true
!= ( X341 @ id @ X348 @ id ) )
| ( ( X341 @ id @ ( X344 @ id @ X348 ) @ id )
= $true ) )
| ( ( X341 @ id @ ( lam @ ( X344 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X345: term,X346: subst,X347: subst] :
( ( sub @ ( X344 @ X346 @ X345 ) @ X347 )
= ( X344 @ ( comp @ X346 @ X347 ) @ ( sub @ X345 @ X347 ) ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X155: term] :
( ( sub @ X155 @ id )
= X155 )
=> ( ! [X156: subst > term > subst > $o,X157: term] :
( ( ( X156 @ id @ ( lam @ ( sub @ X157 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X158: term] :
( ( ( X156 @ id @ ( sub @ X157 @ ( push @ X158 @ id ) ) @ id )
= $true )
| ( ( X156 @ id @ X158 @ id )
!= $true ) )
| ~ ! [X159: subst > term > term] :
( ~ ! [X161: subst,X162: subst,X163: term] :
( ( X159 @ ( comp @ X161 @ X162 ) @ ( sub @ X163 @ X162 ) )
= ( sub @ ( X159 @ X161 @ X163 ) @ X162 ) )
| ~ ! [X160: term] :
( ( ( X156 @ id @ X160 @ id )
!= $true )
| ( ( X156 @ id @ ( X159 @ id @ X160 ) @ id )
= $true ) )
| ( $true
= ( X156 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id ) ) ) )
=> ! [X164: subst > term > subst > $o,X165: term] :
( ~ ! [X176: subst,X177: subst,X178: term,X179: subst] :
( ( $true
= ( X164 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) @ X176 ) )
| ( ( X164 @ X177 @ X178 @ ( comp @ X179 @ X176 ) )
!= $true ) )
| ~ ! [X167: subst > term > term] :
( ~ ! [X171: term] :
( ( ( X164 @ id @ X171 @ id )
!= $true )
| ( $true
= ( X164 @ id @ ( X167 @ id @ X171 ) @ id ) ) )
| ~ ! [X168: term,X169: subst,X170: subst] :
( ( sub @ ( X167 @ X169 @ X168 ) @ X170 )
= ( X167 @ ( comp @ X169 @ X170 ) @ ( sub @ X168 @ X170 ) ) )
| ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X164 @ id @ ( lam @ X165 ) @ id )
= $true )
| ~ ! [X166: term] :
( ( $true
!= ( X164 @ id @ X166 @ id ) )
| ( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
= $true ) )
| ~ ! [X172: subst,X173: subst,X174: subst,X175: term] :
( ( $true
!= ( X164 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) @ X172 ) )
| ( ( X164 @ X173 @ X175 @ ( comp @ X174 @ X172 ) )
= $true ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( pushprop = $true )
& ( ulamvarsh = $true )
& ( ! [X390: term,X391: subst > term > subst > $o] :
( ~ ! [X395: term,X396: subst,X397: subst,X398: subst] :
( ( $true
!= ( X391 @ X397 @ X395 @ ( comp @ X398 @ X396 ) ) )
| ( ( X391 @ ( comp @ X397 @ X398 ) @ ( sub @ X395 @ X398 ) @ X396 )
= $true ) )
| ~ ! [X392: term,X393: term] :
( ( ( X391 @ id @ ( ap @ ( sub @ X392 @ id ) @ X393 ) @ id )
= $true )
| ( ( X391 @ id @ X393 @ id )
!= $true )
| ( $true
!= ( X391 @ id @ X392 @ id ) ) )
| ~ ! [X394: term] :
( ( ( X391 @ id @ X394 @ id )
= $true )
| ( ( var @ ( sub @ X394 @ id ) )
!= $true ) )
| ( $true
= ( X391 @ id @ X390 @ id ) )
| ~ ! [X399: term,X400: subst,X401: subst,X402: subst] :
( ( $true
= ( X391 @ X402 @ X399 @ ( comp @ X401 @ X400 ) ) )
| ( ( X391 @ ( comp @ X402 @ X401 ) @ ( sub @ X399 @ X401 ) @ X400 )
!= $true ) )
| ~ ! [X403: subst > term > term] :
( ( ( X391 @ id @ ( lam @ ( X403 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X404: term,X405: subst,X406: subst] :
( ( sub @ ( X403 @ X406 @ X404 ) @ X405 )
= ( X403 @ ( comp @ X406 @ X405 ) @ ( sub @ X404 @ X405 ) ) )
| ~ ! [X407: term] :
( ( ( X391 @ id @ X407 @ id )
!= $true )
| ( ( X391 @ id @ ( X403 @ id @ X407 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ X28 @ X30 )
!= ( ap @ X29 @ X31 ) )
| ( X30 = X31 ) )
=> ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop_gthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X408: term] :
~ ! [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
!= ( X409 @ sh @ one ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ! [X381: d_term] : ( d_one = X381 )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 )
=> ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ( $true
= ( X85 @ one ) )
| ( ( X87 @ X86 )
!= $true )
| ~ ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ! [X0: term] :
~ ! [X1: subst > term > term] :
~ ! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( substmonoid = $true )
<=> ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) ) )
& ( ( ! [X410: subst > term > subst > $o] :
~ ! [X411: term > $o] :
~ ! [X412: term] :
( ( X410 @ id @ X412 @ id )
= ( X411 @ X412 ) )
=> ( ! [X413: term > $o,X414: term] :
( ~ ! [X415: term] :
( ( $true
= ( X413 @ ( lam @ X415 ) ) )
| ~ ! [X416: term] :
( ( ( X413 @ X416 )
!= $true )
| ( $true
= ( X413 @ ( sub @ X415 @ ( push @ X416 @ id ) ) ) ) ) )
| ~ ! [X417: term,X418: term] :
( ( $true
= ( X413 @ ( ap @ X417 @ X418 ) ) )
| ( $true
!= ( X413 @ X417 ) )
| ( $true
!= ( X413 @ X418 ) ) )
| ( ( X413 @ X414 )
= $true )
| ~ ! [X419: term] :
( ( ( var @ X419 )
!= $true )
| ( ( X413 @ X419 )
= $true ) ) )
=> ( ! [X420: term] :
( ( sub @ X420 @ id )
= X420 )
=> ( ! [X421: subst > term > subst > $o,X422: term,X423: term > $o] :
( ~ ! [X425: term] :
( ( X423 @ X425 )
= ( X421 @ id @ X425 @ id ) )
| ~ ! [X426: subst > term > term] :
( ( ( X421 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X430: term] :
( ( ( X421 @ id @ X430 @ id )
!= $true )
| ( $true
= ( X421 @ id @ ( X426 @ id @ X430 ) @ id ) ) )
| ~ ! [X427: subst,X428: term,X429: subst] :
( ( X426 @ ( comp @ X427 @ X429 ) @ ( sub @ X428 @ X429 ) )
= ( sub @ ( X426 @ X427 @ X428 ) @ X429 ) ) )
| ~ ! [X424: term] :
( ( $true
!= ( X423 @ X424 ) )
| ( ( X423 @ ( sub @ X422 @ ( push @ X424 @ id ) ) )
= $true ) )
| ( ( X423 @ ( lam @ X422 ) )
= $true ) )
=> ! [X431: term,X432: subst > term > subst > $o] :
( ~ ! [X444: subst > term > term] :
( ( $true
= ( X432 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id ) )
| ~ ! [X445: term,X446: subst,X447: subst] :
( ( X444 @ ( comp @ X446 @ X447 ) @ ( sub @ X445 @ X447 ) )
= ( sub @ ( X444 @ X446 @ X445 ) @ X447 ) )
| ~ ! [X448: term] :
( ( $true
!= ( X432 @ id @ X448 @ id ) )
| ( ( X432 @ id @ ( X444 @ id @ X448 ) @ id )
= $true ) ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X432 @ ( comp @ X442 @ X443 ) @ ( sub @ X441 @ X443 ) @ X440 )
= $true )
| ( $true
!= ( X432 @ X442 @ X441 @ ( comp @ X443 @ X440 ) ) ) )
| ~ ! [X433: term,X434: term] :
( ( $true
!= ( X432 @ id @ X433 @ id ) )
| ( $true
!= ( X432 @ id @ X434 @ id ) )
| ( ( X432 @ id @ ( ap @ ( sub @ X433 @ id ) @ X434 ) @ id )
= $true ) )
| ~ ! [X439: term] :
( ( ( X432 @ id @ X439 @ id )
= $true )
| ( ( var @ ( sub @ X439 @ id ) )
!= $true ) )
| ~ ! [X435: subst,X436: subst,X437: term,X438: subst] :
( ( ( X432 @ X436 @ X437 @ ( comp @ X435 @ X438 ) )
= $true )
| ( ( X432 @ ( comp @ X436 @ X435 ) @ ( sub @ X437 @ X435 ) @ X438 )
!= $true ) )
| ( $true
= ( X432 @ id @ X431 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ! [X255: term] :
~ ! [X256: subst > term > term] :
( ( X256 @ sh @ one )
!= ( sub @ X255 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
=> ( ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 )
=> ( ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
=> ( ! [X51: term,X52: term > $o] :
( ~ ! [X55: term,X56: term] :
( ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) )
| ( $true
!= ( X52 @ X55 ) ) )
| ~ ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) )
| ~ ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
| ( $true
= ( X52 @ X51 ) ) )
=> ! [X57: subst,X58: term,X59: term > $o] :
( ~ ! [X60: term] :
( ~ ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) )
| ( ( X59 @ ( lam @ X60 ) )
= $true ) )
| ~ ! [X64: term] :
( ( ( var @ X64 )
!= $true )
| ( ( X59 @ ( sub @ X64 @ X57 ) )
= $true ) )
| ~ ! [X62: term,X63: term] :
( ( $true
= ( X59 @ ( ap @ X62 @ X63 ) ) )
| ( ( X59 @ X63 )
!= $true )
| ( $true
!= ( X59 @ X62 ) ) )
| ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true ) ) ) ) ) ) )
& ( ( ! [X349: term] :
( ( sub @ X349 @ id )
= X349 )
=> ( ! [X350: subst > term > subst > $o,X351: term] :
( ( $true
= ( X350 @ id @ ( lam @ ( sub @ X351 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X357: term] :
( ( $true
!= ( X350 @ id @ X357 @ id ) )
| ( ( X350 @ id @ ( sub @ X351 @ ( push @ X357 @ id ) ) @ id )
= $true ) )
| ~ ! [X352: subst > term > term] :
( ~ ! [X353: term,X354: subst,X355: subst] :
( ( X352 @ ( comp @ X355 @ X354 ) @ ( sub @ X353 @ X354 ) )
= ( sub @ ( X352 @ X355 @ X353 ) @ X354 ) )
| ~ ! [X356: term] :
( ( ( X350 @ id @ X356 @ id )
!= $true )
| ( ( X350 @ id @ ( X352 @ id @ X356 ) @ id )
= $true ) )
| ( $true
= ( X350 @ id @ ( lam @ ( X352 @ sh @ one ) ) @ id ) ) ) )
=> ! [X358: term,X359: subst > term > subst > $o] :
( ~ ! [X360: subst > term > term] :
( ( ( X359 @ id @ ( lam @ ( X360 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X364: term] :
( ( ( X359 @ id @ ( X360 @ id @ X364 ) @ id )
= $true )
| ( ( X359 @ id @ X364 @ id )
!= $true ) )
| ~ ! [X361: term,X362: subst,X363: subst] :
( ( sub @ ( X360 @ X362 @ X361 ) @ X363 )
= ( X360 @ ( comp @ X362 @ X363 ) @ ( sub @ X361 @ X363 ) ) ) )
| ( $true
= ( X359 @ id @ ( lam @ X358 ) @ id ) )
| ~ ! [X365: term] :
( ( $true
!= ( X359 @ id @ X365 @ id ) )
| ( $true
= ( X359 @ id @ ( sub @ X358 @ ( push @ X365 @ id ) ) @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( lamnotvar = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X366: subst > term > subst > $o,X367: term,X368: term,X369: term > $o] :
( ( ( X369 @ X368 )
!= $true )
| ~ ! [X370: term] :
( ( X366 @ id @ X370 @ id )
= ( X369 @ X370 ) )
| ( $true
!= ( X369 @ X367 ) )
| ~ ! [X371: term,X372: term] :
( ( ( X366 @ id @ ( ap @ ( sub @ X371 @ id ) @ X372 ) @ id )
= $true )
| ( $true
!= ( X366 @ id @ X372 @ id ) )
| ( $true
!= ( X366 @ id @ X371 @ id ) ) )
| ~ ! [X373: subst,X374: subst,X375: term,X376: subst] :
( ( ( X366 @ X376 @ X375 @ ( comp @ X373 @ X374 ) )
= $true )
| ( $true
!= ( X366 @ ( comp @ X376 @ X373 ) @ ( sub @ X375 @ X373 ) @ X374 ) ) )
| ( $true
= ( X369 @ ( ap @ X367 @ X368 ) ) )
| ~ ! [X377: term,X378: subst,X379: subst,X380: subst] :
( ( $true
= ( X366 @ ( comp @ X379 @ X380 ) @ ( sub @ X377 @ X380 ) @ X378 ) )
| ( ( X366 @ X379 @ X377 @ ( comp @ X380 @ X378 ) )
!= $true ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( ! [X257: term] :
~ ! [X258: subst > term > term] :
~ ! [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
= ( X258 @ X259 @ X260 ) )
=> ( ! [X261: term] :
( ( sub @ X261 @ id )
= X261 )
=> ! [X262: term,X263: subst > term > subst > $o,X264: term > $o] :
( ~ ! [X265: term] :
( ( $true
= ( X264 @ ( sub @ X262 @ ( push @ X265 @ id ) ) ) )
| ( $true
!= ( X264 @ X265 ) ) )
| ~ ! [X266: subst > term > term] :
( ( ( X263 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X267: term,X268: subst,X269: subst] :
( ( X266 @ ( comp @ X269 @ X268 ) @ ( sub @ X267 @ X268 ) )
= ( sub @ ( X266 @ X269 @ X267 ) @ X268 ) )
| ~ ! [X270: term] :
( ( ( X263 @ id @ X270 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X266 @ id @ X270 ) @ id ) ) ) )
| ( $true
= ( X264 @ ( lam @ X262 ) ) )
| ~ ! [X271: term] :
( ( X264 @ X271 )
= ( X263 @ id @ X271 @ id ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( lamnotap != $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X20: term] :
( ( sub @ X20 @ id )
= X20 )
=> ! [X21: term] :
( ( sub @ X21 @ id )
= X21 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( pushprop_lthm_orig = $true )
& ! [X382: d_term,X383: d_term] :
( ( ( d2term @ X383 )
= ( d2term @ X382 ) )
=> ( X382 = X383 ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 ) )
& ( termmset_gthm = $true )
& ( axclos = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X65: subst > term > subst > $o] :
~ ! [X66: term > $o] :
~ ! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) ) )
& ( hoasinduction_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
=> ( ! [X94: term,X95: subst,X96: term > $o] :
( ~ ! [X97: term] :
( ( $true
= ( X96 @ ( lam @ X97 ) ) )
| ~ ! [X98: term] :
( ( $true
= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) )
| ( ( X96 @ X98 )
!= $true ) ) )
| ~ ! [X101: term] :
( ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true )
| ( ( var @ X101 )
!= $true ) )
| ( ( X96 @ ( sub @ X94 @ X95 ) )
= $true )
| ~ ! [X99: term,X100: term] :
( ( ( X96 @ X100 )
!= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true ) ) )
=> ! [X102: term,X103: term > $o] :
( ( ( X103 @ X102 )
= $true )
| ~ ! [X107: term,X108: term] :
( ( ( X103 @ X107 )
!= $true )
| ( ( X103 @ X108 )
!= $true )
| ( $true
= ( X103 @ ( ap @ X108 @ X107 ) ) ) )
| ~ ! [X106: term] :
( ( ( var @ X106 )
!= $true )
| ( $true
= ( X103 @ X106 ) ) )
| ~ ! [X104: term] :
( ~ ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) )
| ( $true
= ( X103 @ ( lam @ X104 ) ) ) ) ) ) ) )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
| ( $true
!= ( X79 @ X81 ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X521: subst > term > subst > $o,X522: term] :
( ~ ! [X528: term] :
( ( ( X521 @ id @ ( sub @ X522 @ ( push @ X528 @ id ) ) @ id )
= $true )
| ( ( X521 @ id @ X528 @ id )
!= $true ) )
| ~ ! [X523: subst > term > term] :
( ( $true
= ( X521 @ id @ ( lam @ ( X523 @ sh @ one ) ) @ id ) )
| ~ ! [X527: term] :
( ( ( X521 @ id @ X527 @ id )
!= $true )
| ( $true
= ( X521 @ id @ ( X523 @ id @ X527 ) @ id ) ) )
| ~ ! [X524: term,X525: subst,X526: subst] :
( ( X523 @ ( comp @ X526 @ X525 ) @ ( sub @ X524 @ X525 ) )
= ( sub @ ( X523 @ X526 @ X524 ) @ X525 ) ) )
| ( ( X521 @ id @ ( lam @ X522 ) @ id )
= $true ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( hoasinduction_lem1 = $true )
& ( ( ! [X293: subst] :
( ( comp @ id @ X293 )
= X293 )
=> ( ! [X294: subst] :
( ( comp @ X294 @ id )
= X294 )
=> ( ! [X296: subst] :
( ( comp @ id @ X296 )
= X296 )
& ! [X295: subst] :
( ( comp @ X295 @ id )
= X295 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X245: subst,X246: term,X247: term > $o] :
( ~ ! [X250: term] :
( ( ( X247 @ ( lam @ X250 ) )
= $true )
| ~ ! [X251: term] :
( ( $true
= ( X247 @ ( sub @ X250 @ ( push @ X251 @ id ) ) ) )
| ( ( X247 @ X251 )
!= $true ) ) )
| ( ( X247 @ ( sub @ X246 @ X245 ) )
= $true )
| ~ ! [X252: term] :
( ( $true
= ( X247 @ ( sub @ X252 @ X245 ) ) )
| ( $true
!= ( var @ X252 ) ) )
| ~ ! [X248: term,X249: term] :
( ( $true
= ( X247 @ ( ap @ X249 @ X248 ) ) )
| ( $true
!= ( X247 @ X249 ) )
| ( ( X247 @ X248 )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ! [X191: term > $o,X192: term] :
( ~ ! [X195: term] :
( ( ( X191 @ ( lam @ X195 ) )
= $true )
| ~ ! [X196: term] :
( ( ( X191 @ X196 )
!= $true )
| ( $true
= ( X191 @ ( sub @ X195 @ ( push @ X196 @ id ) ) ) ) ) )
| ~ ! [X193: term,X194: term] :
( ( ( X191 @ ( ap @ X194 @ X193 ) )
= $true )
| ( ( X191 @ X193 )
!= $true )
| ( $true
!= ( X191 @ X194 ) ) )
| ( $true
= ( X191 @ X192 ) )
| ~ ! [X197: term] :
( ( $true
!= ( var @ X197 ) )
| ( $true
= ( X191 @ X197 ) ) ) )
<=> ( induction2 = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X235: term,X236: subst > term > subst > $o,X237: term > $o] :
( ~ ! [X239: term] :
( ( $true
= ( X237 @ ( sub @ X235 @ ( push @ X239 @ id ) ) ) )
| ( ( X237 @ X239 )
!= $true ) )
| ( $true
= ( X237 @ ( lam @ X235 ) ) )
| ~ ! [X238: term] :
( ( X236 @ id @ X238 @ id )
= ( X237 @ X238 ) )
| ~ ! [X240: subst > term > term] :
( ~ ! [X242: subst,X243: term,X244: subst] :
( ( sub @ ( X240 @ X242 @ X243 ) @ X244 )
= ( X240 @ ( comp @ X242 @ X244 ) @ ( sub @ X243 @ X244 ) ) )
| ~ ! [X241: term] :
( ( ( X236 @ id @ X241 @ id )
!= $true )
| ( ( X236 @ id @ ( X240 @ id @ X241 ) @ id )
= $true ) )
| ( ( X236 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( induction2lem_gthm = $true )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
= ( d2subst @ X253 ) )
=> ( X253 = X254 ) )
& ( substmonoid_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X515: term,X516: subst > term > term,X517: term] :
( ~ ! [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) )
| ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) ) ) )
& ( ! [X198: term > $o,X199: term,X200: subst > term > subst > $o] :
( ~ ! [X201: term,X202: subst,X203: subst,X204: subst] :
( ( $true
!= ( X200 @ X202 @ X201 @ ( comp @ X204 @ X203 ) ) )
| ( $true
= ( X200 @ ( comp @ X202 @ X204 ) @ ( sub @ X201 @ X204 ) @ X203 ) ) )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: term] :
( ( $true
!= ( X200 @ id @ X212 @ id ) )
| ( $true
= ( X200 @ id @ ( X211 @ id @ X212 ) @ id ) ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) )
| ~ ! [X213: term,X214: subst,X215: subst] :
( ( X211 @ ( comp @ X214 @ X215 ) @ ( sub @ X213 @ X215 ) )
= ( sub @ ( X211 @ X214 @ X213 ) @ X215 ) ) )
| ~ ! [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X200 @ ( comp @ X206 @ X208 ) @ ( sub @ X209 @ X208 ) @ X207 )
!= $true )
| ( ( X200 @ X206 @ X209 @ ( comp @ X208 @ X207 ) )
= $true ) )
| ~ ! [X210: term] :
( ( X200 @ id @ X210 @ id )
= ( X198 @ X210 ) )
| ~ ! [X205: term] :
( ( $true
!= ( X198 @ X205 ) )
| ( $true
= ( X198 @ ( sub @ X199 @ ( push @ X205 @ id ) ) ) ) )
| ( ( X198 @ ( lam @ X199 ) )
= $true ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
<=> ( termmset = $true ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( hoasinduction_lem2_gthm = $true )
& ( ! [X0: term] :
~ ! [X1: subst > term > term] :
~ ! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( apnotvar = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X4: subst > term > subst > $o,X5: term] :
( ~ ! [X6: term,X7: subst,X8: subst,X9: subst] :
( ( $true
!= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) )
| ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
= $true ) )
| ~ ! [X10: subst > term > term] :
( ~ ! [X11: term] :
( ( $true
!= ( X4 @ id @ X11 @ id ) )
| ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
| ( $true
= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
| ~ ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) )
| ~ ! [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
!= $true )
| ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
= $true ) )
| ~ ! [X19: term] :
( ( $true
= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) )
| ( ( X4 @ id @ X19 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( termmset_lthm = $true )
<=> ( ! [X20: term] :
( ( sub @ X20 @ id )
= X20 )
=> ! [X21: term] :
( ( sub @ X21 @ id )
= X21 ) ) )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( ! [X23: term] :
~ ! [X24: subst > term > term] :
~ ! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( hoasapnotvar_lthm = $true )
& ( ( ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ X28 @ X30 )
!= ( ap @ X29 @ X31 ) )
| ( X30 = X31 ) )
=> ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ~ ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) )
| ~ ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) ) )
<=> ( hoaslaminj = $true ) )
& ( lamnotap != $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
=> ( ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 )
=> ( ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
=> ( ! [X51: term,X52: term > $o] :
( ( $true
= ( X52 @ X51 ) )
| ~ ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) )
| ~ ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
| ~ ! [X55: term,X56: term] :
( ( $true
!= ( X52 @ X55 ) )
| ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) ) ) )
=> ! [X57: subst,X58: term,X59: term > $o] :
( ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true )
| ~ ! [X60: term] :
( ( ( X59 @ ( lam @ X60 ) )
= $true )
| ~ ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) ) )
| ~ ! [X62: term,X63: term] :
( ( $true
= ( X59 @ ( ap @ X62 @ X63 ) ) )
| ( $true
!= ( X59 @ X62 ) )
| ( ( X59 @ X63 )
!= $true ) )
| ~ ! [X64: term] :
( ( ( var @ X64 )
!= $true )
| ( ( X59 @ ( sub @ X64 @ X57 ) )
= $true ) ) ) ) ) ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X65: subst > term > subst > $o] :
~ ! [X66: term > $o] :
~ ! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X70 @ X72 )
!= ( ap @ X69 @ X71 ) )
| ( X69 = X70 ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
!= ( X79 @ X81 ) )
| ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 )
=> ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ~ ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) )
| ( $true
= ( X85 @ one ) )
| ( ( X87 @ X86 )
!= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( axabs = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lthm_orig = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
=> ( ! [X94: term,X95: subst,X96: term > $o] :
( ~ ! [X97: term] :
( ~ ! [X98: term] :
( ( $true
= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) )
| ( ( X96 @ X98 )
!= $true ) )
| ( $true
= ( X96 @ ( lam @ X97 ) ) ) )
| ( ( X96 @ ( sub @ X94 @ X95 ) )
= $true )
| ~ ! [X99: term,X100: term] :
( ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ X100 )
!= $true ) )
| ~ ! [X101: term] :
( ( ( var @ X101 )
!= $true )
| ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true ) ) )
=> ! [X102: term,X103: term > $o] :
( ( ( X103 @ X102 )
= $true )
| ~ ! [X104: term] :
( ( $true
= ( X103 @ ( lam @ X104 ) ) )
| ~ ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) ) )
| ~ ! [X106: term] :
( ( $true
= ( X103 @ X106 ) )
| ( ( var @ X106 )
!= $true ) )
| ~ ! [X107: term,X108: term] :
( ( ( X103 @ X108 )
!= $true )
| ( ( X103 @ X107 )
!= $true )
| ( $true
= ( X103 @ ( ap @ X108 @ X107 ) ) ) ) ) ) ) )
& ( pushprop_gthm = $true )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ! [X111: subst > term > subst > $o,X112: term] :
( ~ ! [X113: term] :
( ( $true
!= ( X111 @ id @ X113 @ id ) )
| ( $true
= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) ) )
| ~ ! [X114: subst > term > term] :
( ~ ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
| ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X118: term] :
( ( ( X111 @ id @ X118 @ id )
!= $true )
| ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) ) ) )
| ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ~ ! [X124: subst > term > term] :
( ~ ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
| ~ ! [X128: term] :
( ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) )
| ( ( X123 @ id @ X128 @ id )
!= $true ) )
| ( $true
= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) ) )
| ~ ! [X129: term,X130: term] :
( ( ( X123 @ id @ X130 @ id )
!= $true )
| ( $true
!= ( X123 @ id @ X129 @ id ) )
| ( $true
= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) ) )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ~ ! [X135: subst > term > term] :
( ( $true
= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
| ~ ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
| ~ ! [X139: term] :
( ( $true
!= ( X132 @ id @ X139 @ id ) )
| ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) ) ) )
| ~ ! [X140: term] :
( ( X132 @ id @ X140 @ id )
= ( X134 @ X140 ) )
| ~ ! [X141: subst,X142: subst,X143: subst,X144: term] :
( ( $true
= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) )
| ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
!= $true ) )
| ~ ! [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) )
| ( $true
!= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) ) )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ~ ! [X149: term] :
( ( $true
!= ( X134 @ X149 ) )
| ( $true
= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X150: term,X151: term > $o,X152: term > $o,X153: subst] :
( ( $true
!= ( X152 @ X150 ) )
| ( $true
= ( X151 @ one ) )
| ~ ! [X154: term] :
( ( X151 @ X154 )
= ( X152 @ ( sub @ X154 @ ( push @ X150 @ X153 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( ! [X155: term] :
( ( sub @ X155 @ id )
= X155 )
=> ( ! [X156: subst > term > subst > $o,X157: term] :
( ~ ! [X158: term] :
( ( ( X156 @ id @ ( sub @ X157 @ ( push @ X158 @ id ) ) @ id )
= $true )
| ( ( X156 @ id @ X158 @ id )
!= $true ) )
| ~ ! [X159: subst > term > term] :
( ~ ! [X160: term] :
( ( ( X156 @ id @ ( X159 @ id @ X160 ) @ id )
= $true )
| ( ( X156 @ id @ X160 @ id )
!= $true ) )
| ~ ! [X161: subst,X162: subst,X163: term] :
( ( X159 @ ( comp @ X161 @ X162 ) @ ( sub @ X163 @ X162 ) )
= ( sub @ ( X159 @ X161 @ X163 ) @ X162 ) )
| ( $true
= ( X156 @ id @ ( lam @ ( X159 @ sh @ one ) ) @ id ) ) )
| ( ( X156 @ id @ ( lam @ ( sub @ X157 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X164: subst > term > subst > $o,X165: term] :
( ~ ! [X166: term] :
( ( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
= $true )
| ( $true
!= ( X164 @ id @ X166 @ id ) ) )
| ~ ! [X167: subst > term > term] :
( ~ ! [X168: term,X169: subst,X170: subst] :
( ( sub @ ( X167 @ X169 @ X168 ) @ X170 )
= ( X167 @ ( comp @ X169 @ X170 ) @ ( sub @ X168 @ X170 ) ) )
| ~ ! [X171: term] :
( ( $true
= ( X164 @ id @ ( X167 @ id @ X171 ) @ id ) )
| ( ( X164 @ id @ X171 @ id )
!= $true ) )
| ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X172: subst,X173: subst,X174: subst,X175: term] :
( ( $true
!= ( X164 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) @ X172 ) )
| ( ( X164 @ X173 @ X175 @ ( comp @ X174 @ X172 ) )
= $true ) )
| ~ ! [X176: subst,X177: subst,X178: term,X179: subst] :
( ( $true
= ( X164 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) @ X176 ) )
| ( ( X164 @ X177 @ X178 @ ( comp @ X179 @ X176 ) )
!= $true ) )
| ( ( X164 @ id @ ( lam @ X165 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X180: term,X181: subst] :
( ( comp @ sh @ ( push @ X180 @ X181 ) )
= X181 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X182: term,X183: term,X184: term,X185: term] :
( ( ( ap @ ( sub @ X184 @ id ) @ X185 )
!= ( ap @ ( sub @ X183 @ id ) @ X182 ) )
| ( X182 = X185 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X186: term,X187: term > $o,X188: subst] :
~ ! [X189: term > $o] :
~ ! [X190: term] :
( ( X187 @ ( sub @ X190 @ ( push @ X186 @ X188 ) ) )
= ( X189 @ X190 ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X191: term > $o,X192: term] :
( ~ ! [X193: term,X194: term] :
( ( $true
!= ( X191 @ X194 ) )
| ( ( X191 @ ( ap @ X194 @ X193 ) )
= $true )
| ( ( X191 @ X193 )
!= $true ) )
| ~ ! [X195: term] :
( ~ ! [X196: term] :
( ( $true
= ( X191 @ ( sub @ X195 @ ( push @ X196 @ id ) ) ) )
| ( ( X191 @ X196 )
!= $true ) )
| ( ( X191 @ ( lam @ X195 ) )
= $true ) )
| ( $true
= ( X191 @ X192 ) )
| ~ ! [X197: term] :
( ( $true
!= ( var @ X197 ) )
| ( $true
= ( X191 @ X197 ) ) ) )
<=> ( induction2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ! [X198: term > $o,X199: term,X200: subst > term > subst > $o] :
( ( ( X198 @ ( lam @ X199 ) )
= $true )
| ~ ! [X201: term,X202: subst,X203: subst,X204: subst] :
( ( $true
= ( X200 @ ( comp @ X202 @ X204 ) @ ( sub @ X201 @ X204 ) @ X203 ) )
| ( $true
!= ( X200 @ X202 @ X201 @ ( comp @ X204 @ X203 ) ) ) )
| ~ ! [X205: term] :
( ( $true
= ( X198 @ ( sub @ X199 @ ( push @ X205 @ id ) ) ) )
| ( $true
!= ( X198 @ X205 ) ) )
| ~ ! [X206: subst,X207: subst,X208: subst,X209: term] :
( ( ( X200 @ ( comp @ X206 @ X208 ) @ ( sub @ X209 @ X208 ) @ X207 )
!= $true )
| ( ( X200 @ X206 @ X209 @ ( comp @ X208 @ X207 ) )
= $true ) )
| ~ ! [X210: term] :
( ( X200 @ id @ X210 @ id )
= ( X198 @ X210 ) )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: term] :
( ( $true
!= ( X200 @ id @ X212 @ id ) )
| ( $true
= ( X200 @ id @ ( X211 @ id @ X212 ) @ id ) ) )
| ( $true
= ( X200 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) )
| ~ ! [X213: term,X214: subst,X215: subst] :
( ( X211 @ ( comp @ X214 @ X215 ) @ ( sub @ X213 @ X215 ) )
= ( sub @ ( X211 @ X214 @ X213 ) @ X215 ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( pushprop = $true )
& ( ( induction = $true )
<=> ! [X216: term,X217: term > $o] :
( ~ ! [X218: term] :
( ( $true
= ( X217 @ X218 ) )
| ( ( var @ X218 )
!= $true ) )
| ~ ! [X219: term,X220: term] :
( ( $true
!= ( X217 @ X219 ) )
| ( ( X217 @ X220 )
!= $true )
| ( ( X217 @ ( ap @ X219 @ X220 ) )
= $true ) )
| ~ ! [X221: term] :
( ( ( X217 @ X221 )
!= $true )
| ( $true
= ( X217 @ ( lam @ X221 ) ) ) )
| ( $true
= ( X217 @ X216 ) ) ) )
& ( ! [X222: term,X223: subst > term > subst > $o] :
( ~ ! [X224: term] :
( ( ( X223 @ id @ X224 @ id )
!= $true )
| ( $true
= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ~ ! [X225: subst > term > term] :
( ~ ! [X226: subst,X227: term,X228: subst] :
( ( X225 @ ( comp @ X228 @ X226 ) @ ( sub @ X227 @ X226 ) )
= ( sub @ ( X225 @ X228 @ X227 ) @ X226 ) )
| ( $true
= ( X223 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) )
| ~ ! [X229: term] :
( ( $true
!= ( X223 @ id @ X229 @ id ) )
| ( $true
= ( X223 @ id @ ( X225 @ id @ X229 ) @ id ) ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( shinj = $true )
<=> ! [X230: term,X231: term] :
( ( ( sub @ X230 @ sh )
!= ( sub @ X231 @ sh ) )
| ( X230 = X231 ) ) )
& ( pushprop_lem2v2 = $true )
& ( axassoc = $true )
& ( termmset_gthm = $true )
& ( axvarshift = $true )
& ( ! [X232: subst > term > subst > $o] :
~ ! [X233: term > $o] :
~ ! [X234: term] :
( ( X232 @ id @ X234 @ id )
= ( X233 @ X234 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ! [X235: term,X236: subst > term > subst > $o,X237: term > $o] :
( ( $true
= ( X237 @ ( lam @ X235 ) ) )
| ~ ! [X238: term] :
( ( X236 @ id @ X238 @ id )
= ( X237 @ X238 ) )
| ~ ! [X239: term] :
( ( ( X237 @ X239 )
!= $true )
| ( $true
= ( X237 @ ( sub @ X235 @ ( push @ X239 @ id ) ) ) ) )
| ~ ! [X240: subst > term > term] :
( ~ ! [X241: term] :
( ( ( X236 @ id @ X241 @ id )
!= $true )
| ( ( X236 @ id @ ( X240 @ id @ X241 ) @ id )
= $true ) )
| ( ( X236 @ id @ ( lam @ ( X240 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X242: subst,X243: term,X244: subst] :
( ( sub @ ( X240 @ X242 @ X243 ) @ X244 )
= ( X240 @ ( comp @ X242 @ X244 ) @ ( sub @ X243 @ X244 ) ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X245: subst,X246: term,X247: term > $o] :
( ~ ! [X248: term,X249: term] :
( ( $true
!= ( X247 @ X249 ) )
| ( ( X247 @ X248 )
!= $true )
| ( $true
= ( X247 @ ( ap @ X249 @ X248 ) ) ) )
| ~ ! [X250: term] :
( ( ( X247 @ ( lam @ X250 ) )
= $true )
| ~ ! [X251: term] :
( ( $true
= ( X247 @ ( sub @ X250 @ ( push @ X251 @ id ) ) ) )
| ( ( X247 @ X251 )
!= $true ) ) )
| ( ( X247 @ ( sub @ X246 @ X245 ) )
= $true )
| ~ ! [X252: term] :
( ( $true
= ( X247 @ ( sub @ X252 @ X245 ) ) )
| ( $true
!= ( var @ X252 ) ) ) )
<=> ( induction2lem = $true ) )
& ( pushprop_lem3v2 = $true )
& ( axapp = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X253: d_subst,X254: d_subst] :
( ( ( d2subst @ X254 )
= ( d2subst @ X253 ) )
=> ( X253 = X254 ) )
& ( ! [X255: term] :
~ ! [X256: subst > term > term] :
( ( X256 @ sh @ one )
!= ( sub @ X255 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X257: term] :
~ ! [X258: subst > term > term] :
~ ! [X259: subst,X260: term] :
( ( sub @ X257 @ ( push @ X260 @ X259 ) )
= ( X258 @ X259 @ X260 ) )
=> ( ! [X261: term] :
( ( sub @ X261 @ id )
= X261 )
=> ! [X262: term,X263: subst > term > subst > $o,X264: term > $o] :
( ~ ! [X265: term] :
( ( $true
= ( X264 @ ( sub @ X262 @ ( push @ X265 @ id ) ) ) )
| ( $true
!= ( X264 @ X265 ) ) )
| ( $true
= ( X264 @ ( lam @ X262 ) ) )
| ~ ! [X266: subst > term > term] :
( ~ ! [X267: term,X268: subst,X269: subst] :
( ( X266 @ ( comp @ X269 @ X268 ) @ ( sub @ X267 @ X268 ) )
= ( sub @ ( X266 @ X269 @ X267 ) @ X268 ) )
| ~ ! [X270: term] :
( ( ( X263 @ id @ X270 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X266 @ id @ X270 ) @ id ) ) )
| ( ( X263 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X271: term] :
( ( X264 @ X271 )
= ( X263 @ id @ X271 @ id ) ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X272: subst,X273: term,X274: term > $o] :
~ ! [X275: term > $o] :
~ ! [X276: term] :
( ( X274 @ ( sub @ X276 @ ( push @ X273 @ X272 ) ) )
= ( X275 @ X276 ) ) )
& ( hoasinduction_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( ! [X277: subst,X278: term] :
( ( sub @ one @ ( push @ X278 @ X277 ) )
= X278 )
=> ( ! [X279: term,X280: subst] :
( ( comp @ sh @ ( push @ X279 @ X280 ) )
= X280 )
=> ( ! [X281: term,X282: term] :
( ( X281 = X282 )
| ( ( lam @ X281 )
!= ( lam @ X282 ) ) )
=> ! [X283: term,X284: subst > term > term,X285: subst,X286: subst > term > term] :
( ~ ! [X287: term,X288: subst,X289: subst] :
( ( sub @ ( X284 @ X288 @ X287 ) @ X289 )
= ( X284 @ ( comp @ X288 @ X289 ) @ ( sub @ X287 @ X289 ) ) )
| ~ ! [X290: subst,X291: subst,X292: term] :
( ( X286 @ ( comp @ X291 @ X290 ) @ ( sub @ X292 @ X290 ) )
= ( sub @ ( X286 @ X291 @ X292 ) @ X290 ) )
| ( ( lam @ ( X284 @ sh @ one ) )
!= ( lam @ ( X286 @ sh @ one ) ) )
| ( ( X286 @ X285 @ X283 )
= ( X284 @ X285 @ X283 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( ! [X293: subst] :
( ( comp @ id @ X293 )
= X293 )
=> ( ! [X294: subst] :
( ( comp @ X294 @ id )
= X294 )
=> ( ! [X296: subst] :
( ( comp @ id @ X296 )
= X296 )
& ! [X295: subst] :
( ( comp @ X295 @ id )
= X295 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X297: term] :
( ( sub @ X297 @ id )
= X297 )
<=> ( termmset = $true ) )
& ( axmap = $true )
& ( ( axscons = $true )
<=> ! [X298: subst] :
( ( push @ ( sub @ one @ X298 ) @ ( comp @ sh @ X298 ) )
= X298 ) )
& ! [X299: subst] :
? [X300: d_subst] :
( ( d2subst @ X300 )
= X299 )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X301: subst > term > subst > $o,X302: term,X303: term] :
( ~ ! [X304: term,X305: term] :
( ( ( X301 @ id @ X305 @ id )
!= $true )
| ( $true
= ( X301 @ id @ ( ap @ ( sub @ X305 @ id ) @ X304 ) @ id ) )
| ( $true
!= ( X301 @ id @ X304 @ id ) ) )
| ( $true
= ( X301 @ id @ ( ap @ X302 @ X303 ) @ id ) )
| ~ ! [X306: subst,X307: subst,X308: term,X309: subst] :
( ( $true
!= ( X301 @ ( comp @ X307 @ X309 ) @ ( sub @ X308 @ X309 ) @ X306 ) )
| ( $true
= ( X301 @ X307 @ X308 @ ( comp @ X309 @ X306 ) ) ) )
| ~ ! [X310: subst,X311: term,X312: subst,X313: subst] :
( ( $true
!= ( X301 @ X312 @ X311 @ ( comp @ X313 @ X310 ) ) )
| ( ( X301 @ ( comp @ X312 @ X313 ) @ ( sub @ X311 @ X313 ) @ X310 )
= $true ) )
| ( ( X301 @ id @ X302 @ id )
!= $true )
| ( ( X301 @ id @ X303 @ id )
!= $true ) ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X314: term] :
( ( sub @ X314 @ id )
= X314 )
<=> ( axvarid = $true ) )
& ( ( apinj1 = $true )
<=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X315 = X317 )
| ( ( ap @ X317 @ X318 )
!= ( ap @ X315 @ X316 ) ) ) )
& ( ( ! [X319: subst > term > subst > $o] :
~ ! [X320: term > $o] :
~ ! [X321: term] :
( ( X319 @ id @ X321 @ id )
= ( X320 @ X321 ) )
=> ( ! [X322: term,X323: term > $o] :
( ~ ! [X324: term] :
( ( ( X323 @ X324 )
= $true )
| ( ( var @ X324 )
!= $true ) )
| ~ ! [X325: term] :
( ( $true
= ( X323 @ ( lam @ X325 ) ) )
| ~ ! [X326: term] :
( ( $true
!= ( X323 @ X326 ) )
| ( ( X323 @ ( sub @ X325 @ ( push @ X326 @ id ) ) )
= $true ) ) )
| ~ ! [X327: term,X328: term] :
( ( ( X323 @ X328 )
!= $true )
| ( $true
!= ( X323 @ X327 ) )
| ( $true
= ( X323 @ ( ap @ X327 @ X328 ) ) ) )
| ( $true
= ( X323 @ X322 ) ) )
=> ( ! [X329: term] :
( ( sub @ X329 @ id )
= X329 )
=> ( ! [X330: subst > term > subst > $o,X331: term,X332: term > $o] :
( ~ ! [X333: subst > term > term] :
( ~ ! [X334: term] :
( ( $true
= ( X330 @ id @ ( X333 @ id @ X334 ) @ id ) )
| ( $true
!= ( X330 @ id @ X334 @ id ) ) )
| ( ( X330 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X335: subst,X336: term,X337: subst] :
( ( X333 @ ( comp @ X337 @ X335 ) @ ( sub @ X336 @ X335 ) )
= ( sub @ ( X333 @ X337 @ X336 ) @ X335 ) ) )
| ~ ! [X338: term] :
( ( X330 @ id @ X338 @ id )
= ( X332 @ X338 ) )
| ( ( X332 @ ( lam @ X331 ) )
= $true )
| ~ ! [X339: term] :
( ( ( X332 @ X339 )
!= $true )
| ( ( X332 @ ( sub @ X331 @ ( push @ X339 @ id ) ) )
= $true ) ) )
=> ! [X340: term,X341: subst > term > subst > $o] :
( ~ ! [X342: term,X343: term] :
( ( ( X341 @ id @ X343 @ id )
!= $true )
| ( ( X341 @ id @ X342 @ id )
!= $true )
| ( ( X341 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
= $true ) )
| ( ( X341 @ id @ X340 @ id )
= $true )
| ~ ! [X344: subst > term > term] :
( ~ ! [X345: term,X346: subst,X347: subst] :
( ( sub @ ( X344 @ X346 @ X345 ) @ X347 )
= ( X344 @ ( comp @ X346 @ X347 ) @ ( sub @ X345 @ X347 ) ) )
| ~ ! [X348: term] :
( ( $true
!= ( X341 @ id @ X348 @ id ) )
| ( ( X341 @ id @ ( X344 @ id @ X348 ) @ id )
= $true ) )
| ( ( X341 @ id @ ( lam @ ( X344 @ sh @ one ) ) @ id )
= $true ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X349: term] :
( ( sub @ X349 @ id )
= X349 )
=> ( ! [X350: subst > term > subst > $o,X351: term] :
( ( $true
= ( X350 @ id @ ( lam @ ( sub @ X351 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X352: subst > term > term] :
( ~ ! [X353: term,X354: subst,X355: subst] :
( ( X352 @ ( comp @ X355 @ X354 ) @ ( sub @ X353 @ X354 ) )
= ( sub @ ( X352 @ X355 @ X353 ) @ X354 ) )
| ~ ! [X356: term] :
( ( ( X350 @ id @ X356 @ id )
!= $true )
| ( ( X350 @ id @ ( X352 @ id @ X356 ) @ id )
= $true ) )
| ( $true
= ( X350 @ id @ ( lam @ ( X352 @ sh @ one ) ) @ id ) ) )
| ~ ! [X357: term] :
( ( ( X350 @ id @ ( sub @ X351 @ ( push @ X357 @ id ) ) @ id )
= $true )
| ( $true
!= ( X350 @ id @ X357 @ id ) ) ) )
=> ! [X358: term,X359: subst > term > subst > $o] :
( ( $true
= ( X359 @ id @ ( lam @ X358 ) @ id ) )
| ~ ! [X360: subst > term > term] :
( ~ ! [X361: term,X362: subst,X363: subst] :
( ( sub @ ( X360 @ X362 @ X361 ) @ X363 )
= ( X360 @ ( comp @ X362 @ X363 ) @ ( sub @ X361 @ X363 ) ) )
| ~ ! [X364: term] :
( ( ( X359 @ id @ X364 @ id )
!= $true )
| ( ( X359 @ id @ ( X360 @ id @ X364 ) @ id )
= $true ) )
| ( ( X359 @ id @ ( lam @ ( X360 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X365: term] :
( ( $true
= ( X359 @ id @ ( sub @ X358 @ ( push @ X365 @ id ) ) @ id ) )
| ( $true
!= ( X359 @ id @ X365 @ id ) ) ) ) ) ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X366: subst > term > subst > $o,X367: term,X368: term,X369: term > $o] :
( ( $true
= ( X369 @ ( ap @ X367 @ X368 ) ) )
| ~ ! [X370: term] :
( ( X366 @ id @ X370 @ id )
= ( X369 @ X370 ) )
| ~ ! [X371: term,X372: term] :
( ( $true
!= ( X366 @ id @ X372 @ id ) )
| ( $true
!= ( X366 @ id @ X371 @ id ) )
| ( ( X366 @ id @ ( ap @ ( sub @ X371 @ id ) @ X372 ) @ id )
= $true ) )
| ( ( X369 @ X368 )
!= $true )
| ( $true
!= ( X369 @ X367 ) )
| ~ ! [X373: subst,X374: subst,X375: term,X376: subst] :
( ( ( X366 @ X376 @ X375 @ ( comp @ X373 @ X374 ) )
= $true )
| ( $true
!= ( X366 @ ( comp @ X376 @ X373 ) @ ( sub @ X375 @ X373 ) @ X374 ) ) )
| ~ ! [X377: term,X378: subst,X379: subst,X380: subst] :
( ( ( X366 @ X379 @ X377 @ ( comp @ X380 @ X378 ) )
!= $true )
| ( $true
= ( X366 @ ( comp @ X379 @ X380 ) @ ( sub @ X377 @ X380 ) @ X378 ) ) ) ) )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X381: d_term] : ( d_one = X381 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ! [X382: d_term,X383: d_term] :
( ( ( d2term @ X383 )
= ( d2term @ X382 ) )
=> ( X382 = X383 ) )
& ( ( d2subst @ d_id )
= id )
& ( lamnotvar = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X385: subst] :
( ( comp @ X385 @ id )
= X385 )
& ! [X384: subst] :
( ( comp @ id @ X384 )
= X384 ) ) )
& ( ! [X386: term,X387: term,X388: term,X389: term] :
( ( X386 = X388 )
| ( ( ap @ ( sub @ X388 @ id ) @ X389 )
!= ( ap @ ( sub @ X386 @ id ) @ X387 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction = $true )
<=> ! [X390: term,X391: subst > term > subst > $o] :
( ~ ! [X392: term,X393: term] :
( ( $true
!= ( X391 @ id @ X392 @ id ) )
| ( ( X391 @ id @ ( ap @ ( sub @ X392 @ id ) @ X393 ) @ id )
= $true )
| ( ( X391 @ id @ X393 @ id )
!= $true ) )
| ~ ! [X394: term] :
( ( ( var @ ( sub @ X394 @ id ) )
!= $true )
| ( ( X391 @ id @ X394 @ id )
= $true ) )
| ~ ! [X395: term,X396: subst,X397: subst,X398: subst] :
( ( ( X391 @ ( comp @ X397 @ X398 ) @ ( sub @ X395 @ X398 ) @ X396 )
= $true )
| ( $true
!= ( X391 @ X397 @ X395 @ ( comp @ X398 @ X396 ) ) ) )
| ~ ! [X399: term,X400: subst,X401: subst,X402: subst] :
( ( $true
= ( X391 @ X402 @ X399 @ ( comp @ X401 @ X400 ) ) )
| ( ( X391 @ ( comp @ X402 @ X401 ) @ ( sub @ X399 @ X401 ) @ X400 )
!= $true ) )
| ( $true
= ( X391 @ id @ X390 @ id ) )
| ~ ! [X403: subst > term > term] :
( ~ ! [X404: term,X405: subst,X406: subst] :
( ( sub @ ( X403 @ X406 @ X404 ) @ X405 )
= ( X403 @ ( comp @ X406 @ X405 ) @ ( sub @ X404 @ X405 ) ) )
| ~ ! [X407: term] :
( ( ( X391 @ id @ X407 @ id )
!= $true )
| ( ( X391 @ id @ ( X403 @ id @ X407 ) @ id )
= $true ) )
| ( ( X391 @ id @ ( lam @ ( X403 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X408: term] :
~ ! [X409: subst > term > term] :
( ( sub @ X408 @ ( push @ one @ sh ) )
!= ( X409 @ sh @ one ) ) )
& ( induction2_gthm = $true )
& ( pushprop_lthm = $true )
& ( axclos = $true )
& ( ( ! [X410: subst > term > subst > $o] :
~ ! [X411: term > $o] :
~ ! [X412: term] :
( ( X410 @ id @ X412 @ id )
= ( X411 @ X412 ) )
=> ( ! [X413: term > $o,X414: term] :
( ~ ! [X415: term] :
( ( $true
= ( X413 @ ( lam @ X415 ) ) )
| ~ ! [X416: term] :
( ( ( X413 @ X416 )
!= $true )
| ( $true
= ( X413 @ ( sub @ X415 @ ( push @ X416 @ id ) ) ) ) ) )
| ~ ! [X417: term,X418: term] :
( ( $true
!= ( X413 @ X418 ) )
| ( $true
!= ( X413 @ X417 ) )
| ( $true
= ( X413 @ ( ap @ X417 @ X418 ) ) ) )
| ( ( X413 @ X414 )
= $true )
| ~ ! [X419: term] :
( ( ( var @ X419 )
!= $true )
| ( ( X413 @ X419 )
= $true ) ) )
=> ( ! [X420: term] :
( ( sub @ X420 @ id )
= X420 )
=> ( ! [X421: subst > term > subst > $o,X422: term,X423: term > $o] :
( ~ ! [X424: term] :
( ( ( X423 @ ( sub @ X422 @ ( push @ X424 @ id ) ) )
= $true )
| ( $true
!= ( X423 @ X424 ) ) )
| ( ( X423 @ ( lam @ X422 ) )
= $true )
| ~ ! [X425: term] :
( ( X423 @ X425 )
= ( X421 @ id @ X425 @ id ) )
| ~ ! [X426: subst > term > term] :
( ( ( X421 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X427: subst,X428: term,X429: subst] :
( ( X426 @ ( comp @ X427 @ X429 ) @ ( sub @ X428 @ X429 ) )
= ( sub @ ( X426 @ X427 @ X428 ) @ X429 ) )
| ~ ! [X430: term] :
( ( $true
= ( X421 @ id @ ( X426 @ id @ X430 ) @ id ) )
| ( ( X421 @ id @ X430 @ id )
!= $true ) ) ) )
=> ! [X431: term,X432: subst > term > subst > $o] :
( ~ ! [X433: term,X434: term] :
( ( $true
!= ( X432 @ id @ X433 @ id ) )
| ( ( X432 @ id @ ( ap @ ( sub @ X433 @ id ) @ X434 ) @ id )
= $true )
| ( $true
!= ( X432 @ id @ X434 @ id ) ) )
| ( $true
= ( X432 @ id @ X431 @ id ) )
| ~ ! [X435: subst,X436: subst,X437: term,X438: subst] :
( ( ( X432 @ ( comp @ X436 @ X435 ) @ ( sub @ X437 @ X435 ) @ X438 )
!= $true )
| ( ( X432 @ X436 @ X437 @ ( comp @ X435 @ X438 ) )
= $true ) )
| ~ ! [X439: term] :
( ( ( X432 @ id @ X439 @ id )
= $true )
| ( ( var @ ( sub @ X439 @ id ) )
!= $true ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ( $true
!= ( X432 @ X442 @ X441 @ ( comp @ X443 @ X440 ) ) )
| ( ( X432 @ ( comp @ X442 @ X443 ) @ ( sub @ X441 @ X443 ) @ X440 )
= $true ) )
| ~ ! [X444: subst > term > term] :
( ~ ! [X445: term,X446: subst,X447: subst] :
( ( X444 @ ( comp @ X446 @ X447 ) @ ( sub @ X445 @ X447 ) )
= ( sub @ ( X444 @ X446 @ X445 ) @ X447 ) )
| ~ ! [X448: term] :
( ( $true
!= ( X432 @ id @ X448 @ id ) )
| ( ( X432 @ id @ ( X444 @ id @ X448 ) @ id )
= $true ) )
| ( $true
= ( X432 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X449: term,X450: subst > term > subst > $o] :
( ~ ! [X451: term,X452: subst > term > term] :
( ~ ! [X453: subst,X454: term,X455: subst] :
( ( X452 @ ( comp @ X453 @ X455 ) @ ( sub @ X454 @ X455 ) )
= ( sub @ X451 @ ( push @ ( sub @ X454 @ X455 ) @ ( comp @ X453 @ X455 ) ) ) )
| ~ ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( $true
!= ( X450 @ id @ X456 @ id ) ) )
| ~ ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( sub @ X451 @ ( push @ X458 @ X457 ) ) @ X459 )
= ( sub @ ( X452 @ X457 @ X458 ) @ X459 ) )
| ( $true
= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) ) )
| ~ ! [X460: term] :
( ( $true
!= ( X450 @ id @ X460 @ id ) )
| ( ( X450 @ id @ ( sub @ X449 @ ( push @ X460 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X450 @ id @ ( lam @ ( sub @ X449 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X461: term > $o,X462: term] :
( ( $true
= ( X461 @ X462 ) )
| ~ ! [X463: term] :
( ~ ! [X464: term] :
( ( $true
!= ( X461 @ X464 ) )
| ( $true
= ( X461 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) ) )
| ( $true
= ( X461 @ ( lam @ X463 ) ) ) )
| ~ ! [X465: term,X466: term] :
( ( ( X461 @ ( ap @ X466 @ X465 ) )
= $true )
| ( $true
!= ( X461 @ X466 ) )
| ( ( X461 @ X465 )
!= $true ) )
| ~ ! [X467: term] :
( ( $true
= ( X461 @ X467 ) )
| ( $true
!= ( var @ X467 ) ) ) )
=> ( ! [X468: term,X469: subst > term > subst > $o,X470: term] :
( ( $true
= ( X469 @ id @ ( ap @ X468 @ X470 ) @ id ) )
| ~ ! [X471: term,X472: subst,X473: subst,X474: subst] :
( ( ( X469 @ ( comp @ X473 @ X474 ) @ ( sub @ X471 @ X474 ) @ X472 )
= $true )
| ( ( X469 @ X473 @ X471 @ ( comp @ X474 @ X472 ) )
!= $true ) )
| ( $true
!= ( X469 @ id @ X468 @ id ) )
| ( ( X469 @ id @ X470 @ id )
!= $true )
| ~ ! [X475: subst,X476: subst,X477: term,X478: subst] :
( ( $true
= ( X469 @ X476 @ X477 @ ( comp @ X478 @ X475 ) ) )
| ( ( X469 @ ( comp @ X476 @ X478 ) @ ( sub @ X477 @ X478 ) @ X475 )
!= $true ) )
| ~ ! [X479: term,X480: term] :
( ( $true
= ( X469 @ id @ ( ap @ ( sub @ X480 @ id ) @ X479 ) @ id ) )
| ( $true
!= ( X469 @ id @ X480 @ id ) )
| ( $true
!= ( X469 @ id @ X479 @ id ) ) ) )
=> ( ! [X481: subst > term > subst > $o,X482: term] :
( ~ ! [X483: subst > term > term] :
( ~ ! [X484: term] :
( ( $true
= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) )
| ( $true
!= ( X481 @ id @ X484 @ id ) ) )
| ~ ! [X485: subst,X486: term,X487: subst] :
( ( sub @ ( X483 @ X485 @ X486 ) @ X487 )
= ( X483 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) ) )
| ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) ) )
| ( ( X481 @ id @ ( lam @ X482 ) @ id )
= $true )
| ~ ! [X488: term] :
( ( $true
= ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id ) )
| ( ( X481 @ id @ X488 @ id )
!= $true ) )
| ~ ! [X489: subst,X490: term,X491: subst,X492: subst] :
( ( $true
!= ( X481 @ X491 @ X490 @ ( comp @ X492 @ X489 ) ) )
| ( $true
= ( X481 @ ( comp @ X491 @ X492 ) @ ( sub @ X490 @ X492 ) @ X489 ) ) )
| ~ ! [X493: subst,X494: term,X495: subst,X496: subst] :
( ( $true
!= ( X481 @ ( comp @ X493 @ X496 ) @ ( sub @ X494 @ X496 ) @ X495 ) )
| ( $true
= ( X481 @ X493 @ X494 @ ( comp @ X496 @ X495 ) ) ) ) )
=> ! [X497: subst > term > subst > $o,X498: term] :
( ( $true
= ( X497 @ id @ X498 @ id ) )
| ~ ! [X499: subst,X500: subst,X501: subst,X502: term] :
( ( $true
= ( X497 @ X501 @ X502 @ ( comp @ X500 @ X499 ) ) )
| ( ( X497 @ ( comp @ X501 @ X500 ) @ ( sub @ X502 @ X500 ) @ X499 )
!= $true ) )
| ~ ! [X503: subst,X504: subst,X505: subst,X506: term] :
( ( ( X497 @ ( comp @ X503 @ X505 ) @ ( sub @ X506 @ X505 ) @ X504 )
= $true )
| ( ( X497 @ X503 @ X506 @ ( comp @ X505 @ X504 ) )
!= $true ) )
| ~ ! [X507: term] :
( ( $true
!= ( var @ ( sub @ X507 @ id ) ) )
| ( ( X497 @ id @ X507 @ id )
= $true ) )
| ~ ! [X508: term,X509: term] :
( ( ( X497 @ id @ X509 @ id )
!= $true )
| ( $true
= ( X497 @ id @ ( ap @ ( sub @ X509 @ id ) @ X508 ) @ id ) )
| ( ( X497 @ id @ X508 @ id )
!= $true ) )
| ~ ! [X510: subst > term > term] :
( ~ ! [X511: term] :
( ( ( X497 @ id @ ( X510 @ id @ X511 ) @ id )
= $true )
| ( $true
!= ( X497 @ id @ X511 @ id ) ) )
| ~ ! [X512: subst,X513: term,X514: subst] :
( ( sub @ ( X510 @ X512 @ X513 ) @ X514 )
= ( X510 @ ( comp @ X512 @ X514 ) @ ( sub @ X513 @ X514 ) ) )
| ( $true
= ( X497 @ id @ ( lam @ ( X510 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X515: term,X516: subst > term > term,X517: term] :
( ~ ! [X518: subst,X519: term,X520: subst] :
( ( X516 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) )
= ( sub @ ( X516 @ X518 @ X519 ) @ X520 ) )
| ( ( ap @ ( sub @ X517 @ id ) @ X515 )
!= ( lam @ ( X516 @ sh @ one ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X521: subst > term > subst > $o,X522: term] :
( ~ ! [X523: subst > term > term] :
( ( $true
= ( X521 @ id @ ( lam @ ( X523 @ sh @ one ) ) @ id ) )
| ~ ! [X524: term,X525: subst,X526: subst] :
( ( X523 @ ( comp @ X526 @ X525 ) @ ( sub @ X524 @ X525 ) )
= ( sub @ ( X523 @ X526 @ X524 ) @ X525 ) )
| ~ ! [X527: term] :
( ( $true
= ( X521 @ id @ ( X523 @ id @ X527 ) @ id ) )
| ( ( X521 @ id @ X527 @ id )
!= $true ) ) )
| ( ( X521 @ id @ ( lam @ X522 ) @ id )
= $true )
| ~ ! [X528: term] :
( ( ( X521 @ id @ ( sub @ X522 @ ( push @ X528 @ id ) ) @ id )
= $true )
| ( ( X521 @ id @ X528 @ id )
!= $true ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X529: term] :
? [X530: d_term] :
( ( d2term @ X530 )
= X529 )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X531: subst,X532: term] :
( ( sub @ one @ ( push @ X532 @ X531 ) )
= X532 )
=> ( ! [X533: subst,X534: term] :
( ( comp @ sh @ ( push @ X534 @ X533 ) )
= X533 )
=> ! [X535: term,X536: term > $o,X537: term > $o,X538: subst,X539: term] :
( ( $true
!= ( X536 @ X535 ) )
| ( ( X537 @ ( sub @ X535 @ ( push @ X539 @ X538 ) ) )
= $true ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( hoasinduction_lem2_gthm = $true )
& ( ! [X0: term] :
~ ! [X1: subst > term > term] :
~ ! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( apnotvar = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X4: subst > term > subst > $o,X5: term] :
( ~ ! [X6: term,X7: subst,X8: subst,X9: subst] :
( ( $true
!= ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) ) )
| ( ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 )
= $true ) )
| ~ ! [X10: subst > term > term] :
( ~ ! [X11: term] :
( ( $true
!= ( X4 @ id @ X11 @ id ) )
| ( $true
= ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
| ( $true
= ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) )
| ~ ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) )
| ( $true
= ( X4 @ id @ ( lam @ X5 ) @ id ) )
| ~ ! [X15: term,X16: subst,X17: subst,X18: subst] :
( ( ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
!= $true )
| ( ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) )
= $true ) )
| ~ ! [X19: term] :
( ( $true
= ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id ) )
| ( ( X4 @ id @ X19 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( termmset_lthm = $true )
<=> ( ! [X20: term] :
( ( sub @ X20 @ id )
= X20 )
=> ! [X21: term] :
( ( sub @ X21 @ id )
= X21 ) ) )
& ( ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 )
<=> ( axidl = $true ) )
& ( ! [X23: term] :
~ ! [X24: subst > term > term] :
~ ! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( hoasapnotvar_lthm = $true )
& ( ( ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ X28 @ X30 )
!= ( ap @ X29 @ X31 ) )
| ( X30 = X31 ) )
=> ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ~ ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) )
| ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) )
| ~ ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) ) )
<=> ( hoaslaminj = $true ) )
& ( lamnotap != $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
=> ( ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 )
=> ( ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
=> ( ! [X51: term,X52: term > $o] :
( ( $true
= ( X52 @ X51 ) )
| ~ ! [X53: term] :
( ( $true
!= ( X52 @ X53 ) )
| ( $true
= ( X52 @ ( lam @ X53 ) ) ) )
| ~ ! [X54: term] :
( ( ( var @ X54 )
!= $true )
| ( ( X52 @ X54 )
= $true ) )
| ~ ! [X55: term,X56: term] :
( ( $true
!= ( X52 @ X55 ) )
| ( ( X52 @ X56 )
!= $true )
| ( $true
= ( X52 @ ( ap @ X56 @ X55 ) ) ) ) )
=> ! [X57: subst,X58: term,X59: term > $o] :
( ( ( X59 @ ( sub @ X58 @ X57 ) )
= $true )
| ~ ! [X60: term] :
( ( ( X59 @ ( lam @ X60 ) )
= $true )
| ~ ! [X61: term] :
( ( $true
= ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) ) )
| ( ( X59 @ X61 )
!= $true ) ) )
| ~ ! [X62: term,X63: term] :
( ( $true
= ( X59 @ ( ap @ X62 @ X63 ) ) )
| ( $true
!= ( X59 @ X62 ) )
| ( ( X59 @ X63 )
!= $true ) )
| ~ ! [X64: term] :
( ( ( var @ X64 )
!= $true )
| ( ( X59 @ ( sub @ X64 @ X57 ) )
= $true ) ) ) ) ) ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X65: subst > term > subst > $o] :
~ ! [X66: term > $o] :
~ ! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X70 @ X72 )
!= ( ap @ X69 @ X71 ) )
| ( X69 = X70 ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ( $true
!= ( X79 @ X81 ) )
| ( $true
= ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 )
=> ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ~ ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) )
| ( $true
= ( X85 @ one ) )
| ( ( X87 @ X86 )
!= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ( apinj2 = $true )
<=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( X89 = X91 )
| ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) ) ) )
& ( axabs = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lthm_orig = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
=> ( ! [X94: term,X95: subst,X96: term > $o] :
( ~ ! [X97: term] :
( ~ ! [X98: term] :
( ( $true
= ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) ) )
| ( ( X96 @ X98 )
!= $true ) )
| ( $true
= ( X96 @ ( lam @ X97 ) ) ) )
| ( ( X96 @ ( sub @ X94 @ X95 ) )
= $true )
| ~ ! [X99: term,X100: term] :
( ( ( X96 @ ( ap @ X99 @ X100 ) )
= $true )
| ( $true
!= ( X96 @ X99 ) )
| ( ( X96 @ X100 )
!= $true ) )
| ~ ! [X101: term] :
( ( ( var @ X101 )
!= $true )
| ( ( X96 @ ( sub @ X101 @ X95 ) )
= $true ) ) )
=> ! [X102: term,X103: term > $o] :
( ( ( X103 @ X102 )
= $true )
| ~ ! [X104: term] :
( ( $true
= ( X103 @ ( lam @ X104 ) ) )
| ~ ! [X105: term] :
( ( $true
!= ( X103 @ X105 ) )
| ( ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) ) )
| ~ ! [X106: term] :
( ( $true
= ( X103 @ X106 ) )
| ( ( var @ X106 )
!= $true ) )
| ~ ! [X107: term,X108: term] :
( ( ( X103 @ X108 )
!= $true )
| ( ( X103 @ X107 )
!= $true )
| ( $true
= ( X103 @ ( ap @ X108 @ X107 ) ) ) ) ) ) ) )
& ( pushprop_gthm = $true )
& ( ( laminj = $true )
<=> ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) ) )
& ( ! [X111: subst > term > subst > $o,X112: term] :
( ~ ! [X113: term] :
( ( $true
!= ( X111 @ id @ X113 @ id ) )
| ( $true
= ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) ) )
| ~ ! [X114: subst > term > term] :
( ~ ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
| ( ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X118: term] :
( ( ( X111 @ id @ X118 @ id )
!= $true )
| ( $true
= ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) ) ) )
| ( ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 )
<=> ( axidr = $true ) )
& ( ( axvarcons = $true )
<=> ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 ) )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ~ ! [X124: subst > term > term] :
( ~ ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
| ~ ! [X128: term] :
( ( $true
= ( X123 @ id @ ( X124 @ id @ X128 ) @ id ) )
| ( ( X123 @ id @ X128 @ id )
!= $true ) )
| ( $true
= ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) ) )
| ~ ! [X129: term,X130: term] :
( ( ( X123 @ id @ X130 @ id )
!= $true )
| ( $true
!= ( X123 @ id @ X129 @ id ) )
| ( $true
= ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) ) )
| ( ( X123 @ id @ X122 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ~ ! [X135: subst > term > term] :
( ( $true
= ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id ) )
| ~ ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
| ~ ! [X139: term] :
( ( $true
!= ( X132 @ id @ X139 @ id ) )
| ( $true
= ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) ) ) )
| ~ ! [X140: term] :
( ( X132 @ id @ X140 @ id )
= ( X134 @ X140 ) )
| ~ ! [X141: subst,X142: subst,X143: subst,X144: term] :
( ( $true
= ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) ) )
| ( ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 )
!= $true ) )
| ~ ! [X145: subst,X146: term,X147: subst,X148: subst] :
( ( $true
= ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 ) )
| ( $true
!= ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) ) )
| ( $true
= ( X134 @ ( lam @ X133 ) ) )
| ~ ! [X149: term] :
( ( $true
!= ( X134 @ X149 ) )
| ( $true
= ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X153: term,X154: term > $o,X155: term > $o,X156: subst] :
( ( ( X155 @ X153 )
!= $true )
| ( $true
= ( X154 @ one ) )
| ~ ! [X157: term] :
( ( X155 @ ( sub @ X157 @ ( push @ X153 @ X156 ) ) )
= ( X154 @ X157 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( ! [X158: term] :
( ( sub @ X158 @ id )
= X158 )
=> ( ! [X159: subst > term > subst > $o,X160: term] :
( ~ ! [X161: term] :
( ( $true
= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) )
| ( $true
!= ( X159 @ id @ X161 @ id ) ) )
| ~ ! [X162: subst > term > term] :
( ~ ! [X163: term] :
( ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) )
| ( ( X159 @ id @ X163 @ id )
!= $true ) )
| ~ ! [X164: subst,X165: subst,X166: term] :
( ( sub @ ( X162 @ X164 @ X166 ) @ X165 )
= ( X162 @ ( comp @ X164 @ X165 ) @ ( sub @ X166 @ X165 ) ) )
| ( $true
= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X167: subst > term > subst > $o,X168: term] :
( ~ ! [X169: term] :
( ( $true
= ( X167 @ id @ ( sub @ X168 @ ( push @ X169 @ id ) ) @ id ) )
| ( $true
!= ( X167 @ id @ X169 @ id ) ) )
| ~ ! [X170: subst > term > term] :
( ~ ! [X171: term,X172: subst,X173: subst] :
( ( sub @ ( X170 @ X172 @ X171 ) @ X173 )
= ( X170 @ ( comp @ X172 @ X173 ) @ ( sub @ X171 @ X173 ) ) )
| ~ ! [X174: term] :
( ( $true
= ( X167 @ id @ ( X170 @ id @ X174 ) @ id ) )
| ( $true
!= ( X167 @ id @ X174 @ id ) ) )
| ( $true
= ( X167 @ id @ ( lam @ ( X170 @ sh @ one ) ) @ id ) ) )
| ~ ! [X175: subst,X176: subst,X177: subst,X178: term] :
( ( $true
!= ( X167 @ ( comp @ X176 @ X177 ) @ ( sub @ X178 @ X177 ) @ X175 ) )
| ( $true
= ( X167 @ X176 @ X178 @ ( comp @ X177 @ X175 ) ) ) )
| ~ ! [X179: subst,X180: subst,X181: term,X182: subst] :
( ( ( X167 @ ( comp @ X180 @ X182 ) @ ( sub @ X181 @ X182 ) @ X179 )
= $true )
| ( ( X167 @ X180 @ X181 @ ( comp @ X182 @ X179 ) )
!= $true ) )
| ( $true
= ( X167 @ id @ ( lam @ X168 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X183: term,X184: subst] :
( ( comp @ sh @ ( push @ X183 @ X184 ) )
= X184 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X185: term,X186: term,X187: term,X188: term] :
( ( ( ap @ ( sub @ X187 @ id ) @ X188 )
!= ( ap @ ( sub @ X186 @ id ) @ X185 ) )
| ( X185 = X188 ) ) )
& ( ! [X189: term,X190: term > $o,X191: subst] :
~ ! [X192: term > $o] :
~ ! [X193: term] :
( ( X192 @ X193 )
= ( X190 @ ( sub @ X193 @ ( push @ X189 @ X191 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X194: term > $o,X195: term] :
( ~ ! [X196: term,X197: term] :
( ( $true
!= ( X194 @ X197 ) )
| ( ( X194 @ ( ap @ X197 @ X196 ) )
= $true )
| ( $true
!= ( X194 @ X196 ) ) )
| ~ ! [X198: term] :
( ~ ! [X199: term] :
( ( $true
= ( X194 @ ( sub @ X198 @ ( push @ X199 @ id ) ) ) )
| ( $true
!= ( X194 @ X199 ) ) )
| ( $true
= ( X194 @ ( lam @ X198 ) ) ) )
| ( ( X194 @ X195 )
= $true )
| ~ ! [X200: term] :
( ( $true
!= ( var @ X200 ) )
| ( $true
= ( X194 @ X200 ) ) ) )
<=> ( induction2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ! [X206: term > $o,X207: term,X208: subst > term > subst > $o] :
( ( ( X206 @ ( lam @ X207 ) )
= $true )
| ~ ! [X209: term,X210: subst,X211: subst,X212: subst] :
( ( $true
= ( X208 @ ( comp @ X210 @ X212 ) @ ( sub @ X209 @ X212 ) @ X211 ) )
| ( ( X208 @ X210 @ X209 @ ( comp @ X212 @ X211 ) )
!= $true ) )
| ~ ! [X213: term] :
( ( $true
= ( X206 @ ( sub @ X207 @ ( push @ X213 @ id ) ) ) )
| ( $true
!= ( X206 @ X213 ) ) )
| ~ ! [X214: subst,X215: subst,X216: subst,X217: term] :
( ( $true
!= ( X208 @ ( comp @ X214 @ X216 ) @ ( sub @ X217 @ X216 ) @ X215 ) )
| ( $true
= ( X208 @ X214 @ X217 @ ( comp @ X216 @ X215 ) ) ) )
| ~ ! [X218: term] :
( ( X206 @ X218 )
= ( X208 @ id @ X218 @ id ) )
| ~ ! [X219: subst > term > term] :
( ~ ! [X220: term] :
( ( $true
!= ( X208 @ id @ X220 @ id ) )
| ( $true
= ( X208 @ id @ ( X219 @ id @ X220 ) @ id ) ) )
| ( ( X208 @ id @ ( lam @ ( X219 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( pushprop = $true )
& ( ( induction = $true )
<=> ! [X224: term,X225: term > $o] :
( ~ ! [X226: term] :
( ( $true
= ( X225 @ X226 ) )
| ( $true
!= ( var @ X226 ) ) )
| ~ ! [X227: term,X228: term] :
( ( ( X225 @ X227 )
!= $true )
| ( ( X225 @ X228 )
!= $true )
| ( ( X225 @ ( ap @ X227 @ X228 ) )
= $true ) )
| ~ ! [X229: term] :
( ( ( X225 @ X229 )
!= $true )
| ( ( X225 @ ( lam @ X229 ) )
= $true ) )
| ( ( X225 @ X224 )
= $true ) ) )
& ( ! [X230: term,X231: subst > term > subst > $o] :
( ~ ! [X232: term] :
( ( $true
!= ( X231 @ id @ X232 @ id ) )
| ( $true
= ( X231 @ id @ ( sub @ X230 @ ( push @ X232 @ id ) ) @ id ) ) )
| ~ ! [X233: subst > term > term] :
( ~ ! [X234: subst,X235: term,X236: subst] :
( ( sub @ ( X233 @ X236 @ X235 ) @ X234 )
= ( X233 @ ( comp @ X236 @ X234 ) @ ( sub @ X235 @ X234 ) ) )
| ( $true
= ( X231 @ id @ ( lam @ ( X233 @ sh @ one ) ) @ id ) )
| ~ ! [X237: term] :
( ( $true
!= ( X231 @ id @ X237 @ id ) )
| ( ( X231 @ id @ ( X233 @ id @ X237 ) @ id )
= $true ) ) )
| ( $true
= ( X231 @ id @ ( lam @ ( sub @ X230 @ ( push @ one @ sh ) ) ) @ id ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ! [X238: term,X239: term] :
( ( ( sub @ X239 @ sh )
!= ( sub @ X238 @ sh ) )
| ( X238 = X239 ) )
<=> ( shinj = $true ) )
& ( pushprop_lem2v2 = $true )
& ( axassoc = $true )
& ( termmset_gthm = $true )
& ( axvarshift = $true )
& ( ! [X240: subst > term > subst > $o] :
~ ! [X241: term > $o] :
~ ! [X242: term] :
( ( X241 @ X242 )
= ( X240 @ id @ X242 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ! [X243: term,X244: subst > term > subst > $o,X245: term > $o] :
( ( $true
= ( X245 @ ( lam @ X243 ) ) )
| ~ ! [X246: term] :
( ( X245 @ X246 )
= ( X244 @ id @ X246 @ id ) )
| ~ ! [X247: term] :
( ( ( X245 @ X247 )
!= $true )
| ( $true
= ( X245 @ ( sub @ X243 @ ( push @ X247 @ id ) ) ) ) )
| ~ ! [X248: subst > term > term] :
( ~ ! [X249: term] :
( ( ( X244 @ id @ X249 @ id )
!= $true )
| ( $true
= ( X244 @ id @ ( X248 @ id @ X249 ) @ id ) ) )
| ( $true
= ( X244 @ id @ ( lam @ ( X248 @ sh @ one ) ) @ id ) )
| ~ ! [X250: subst,X251: term,X252: subst] :
( ( sub @ ( X248 @ X250 @ X251 ) @ X252 )
= ( X248 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X255: subst,X256: term,X257: term > $o] :
( ~ ! [X258: term,X259: term] :
( ( $true
!= ( X257 @ X259 ) )
| ( $true
!= ( X257 @ X258 ) )
| ( $true
= ( X257 @ ( ap @ X259 @ X258 ) ) ) )
| ~ ! [X260: term] :
( ( ( X257 @ ( lam @ X260 ) )
= $true )
| ~ ! [X261: term] :
( ( ( X257 @ ( sub @ X260 @ ( push @ X261 @ id ) ) )
= $true )
| ( $true
!= ( X257 @ X261 ) ) ) )
| ( ( X257 @ ( sub @ X256 @ X255 ) )
= $true )
| ~ ! [X262: term] :
( ( $true
= ( X257 @ ( sub @ X262 @ X255 ) ) )
| ( $true
!= ( var @ X262 ) ) ) )
<=> ( induction2lem = $true ) )
& ( pushprop_lem3v2 = $true )
& ( axapp = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X263: d_subst,X264: d_subst] :
( ( ( d2subst @ X263 )
= ( d2subst @ X264 ) )
=> ( X263 = X264 ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X265: term] :
~ ! [X266: subst > term > term] :
( ( X266 @ sh @ one )
!= ( sub @ X265 @ ( push @ one @ sh ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X267: term] :
~ ! [X268: subst > term > term] :
~ ! [X269: subst,X270: term] :
( ( sub @ X267 @ ( push @ X270 @ X269 ) )
= ( X268 @ X269 @ X270 ) )
=> ( ! [X271: term] :
( ( sub @ X271 @ id )
= X271 )
=> ! [X272: term,X273: subst > term > subst > $o,X274: term > $o] :
( ~ ! [X275: term] :
( ( ( X274 @ ( sub @ X272 @ ( push @ X275 @ id ) ) )
= $true )
| ( $true
!= ( X274 @ X275 ) ) )
| ( $true
= ( X274 @ ( lam @ X272 ) ) )
| ~ ! [X276: subst > term > term] :
( ~ ! [X277: term,X278: subst,X279: subst] :
( ( X276 @ ( comp @ X279 @ X278 ) @ ( sub @ X277 @ X278 ) )
= ( sub @ ( X276 @ X279 @ X277 ) @ X278 ) )
| ~ ! [X280: term] :
( ( $true
!= ( X273 @ id @ X280 @ id ) )
| ( $true
= ( X273 @ id @ ( X276 @ id @ X280 ) @ id ) ) )
| ( $true
= ( X273 @ id @ ( lam @ ( X276 @ sh @ one ) ) @ id ) ) )
| ~ ! [X281: term] :
( ( X274 @ X281 )
= ( X273 @ id @ X281 @ id ) ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X282: subst,X283: term,X284: term > $o] :
~ ! [X285: term > $o] :
~ ! [X286: term] :
( ( X285 @ X286 )
= ( X284 @ ( sub @ X286 @ ( push @ X283 @ X282 ) ) ) ) )
& ( hoasinduction_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X287: subst,X288: term] :
( ( sub @ one @ ( push @ X288 @ X287 ) )
= X288 )
=> ( ! [X289: term,X290: subst] :
( ( comp @ sh @ ( push @ X289 @ X290 ) )
= X290 )
=> ( ! [X291: term,X292: term] :
( ( X291 = X292 )
| ( ( lam @ X291 )
!= ( lam @ X292 ) ) )
=> ! [X293: term,X294: subst > term > term,X295: subst,X296: subst > term > term] :
( ~ ! [X297: term,X298: subst,X299: subst] :
( ( X294 @ ( comp @ X298 @ X299 ) @ ( sub @ X297 @ X299 ) )
= ( sub @ ( X294 @ X298 @ X297 ) @ X299 ) )
| ( ( lam @ ( X296 @ sh @ one ) )
!= ( lam @ ( X294 @ sh @ one ) ) )
| ( ( X296 @ X295 @ X293 )
= ( X294 @ X295 @ X293 ) )
| ~ ! [X300: subst,X301: subst,X302: term] :
( ( sub @ ( X296 @ X301 @ X302 ) @ X300 )
= ( X296 @ ( comp @ X301 @ X300 ) @ ( sub @ X302 @ X300 ) ) ) ) ) ) ) )
& ( ( ! [X303: subst] :
( ( comp @ id @ X303 )
= X303 )
=> ( ! [X304: subst] :
( ( comp @ X304 @ id )
= X304 )
=> ( ! [X305: subst] :
( ( comp @ X305 @ id )
= X305 )
& ! [X306: subst] :
( ( comp @ id @ X306 )
= X306 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X307: term] :
( ( sub @ X307 @ id )
= X307 )
<=> ( termmset = $true ) )
& ( axmap = $true )
& ( ( axscons = $true )
<=> ! [X308: subst] :
( ( push @ ( sub @ one @ X308 ) @ ( comp @ sh @ X308 ) )
= X308 ) )
& ! [X309: subst] :
? [X310: d_subst] :
( ( d2subst @ X310 )
= X309 )
& ( induction2lem_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X311: subst > term > subst > $o,X312: term,X313: term] :
( ~ ! [X314: term,X315: term] :
( ( $true
!= ( X311 @ id @ X315 @ id ) )
| ( ( X311 @ id @ ( ap @ ( sub @ X315 @ id ) @ X314 ) @ id )
= $true )
| ( ( X311 @ id @ X314 @ id )
!= $true ) )
| ( ( X311 @ id @ ( ap @ X312 @ X313 ) @ id )
= $true )
| ~ ! [X316: subst,X317: subst,X318: term,X319: subst] :
( ( ( X311 @ ( comp @ X317 @ X319 ) @ ( sub @ X318 @ X319 ) @ X316 )
!= $true )
| ( ( X311 @ X317 @ X318 @ ( comp @ X319 @ X316 ) )
= $true ) )
| ~ ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X311 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) )
| ( $true
= ( X311 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) ) )
| ( $true
!= ( X311 @ id @ X312 @ id ) )
| ( $true
!= ( X311 @ id @ X313 @ id ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X324: term] :
( ( sub @ X324 @ id )
= X324 )
<=> ( axvarid = $true ) )
& ( ! [X325: term,X326: term,X327: term,X328: term] :
( ( X325 = X327 )
| ( ( ap @ X325 @ X326 )
!= ( ap @ X327 @ X328 ) ) )
<=> ( apinj1 = $true ) )
& ( ( ! [X329: subst > term > subst > $o] :
~ ! [X330: term > $o] :
~ ! [X331: term] :
( ( X329 @ id @ X331 @ id )
= ( X330 @ X331 ) )
=> ( ! [X332: term,X333: term > $o] :
( ~ ! [X334: term] :
( ( $true
= ( X333 @ X334 ) )
| ( ( var @ X334 )
!= $true ) )
| ~ ! [X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ~ ! [X336: term] :
( ( ( X333 @ X336 )
!= $true )
| ( $true
= ( X333 @ ( sub @ X335 @ ( push @ X336 @ id ) ) ) ) ) )
| ~ ! [X337: term,X338: term] :
( ( ( X333 @ X338 )
!= $true )
| ( $true
!= ( X333 @ X337 ) )
| ( ( X333 @ ( ap @ X337 @ X338 ) )
= $true ) )
| ( ( X333 @ X332 )
= $true ) )
=> ( ! [X339: term] :
( ( sub @ X339 @ id )
= X339 )
=> ( ! [X340: subst > term > subst > $o,X341: term,X342: term > $o] :
( ~ ! [X343: subst > term > term] :
( ~ ! [X344: term] :
( ( ( X340 @ id @ ( X343 @ id @ X344 ) @ id )
= $true )
| ( $true
!= ( X340 @ id @ X344 @ id ) ) )
| ( ( X340 @ id @ ( lam @ ( X343 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X345: subst,X346: term,X347: subst] :
( ( sub @ ( X343 @ X347 @ X346 ) @ X345 )
= ( X343 @ ( comp @ X347 @ X345 ) @ ( sub @ X346 @ X345 ) ) ) )
| ~ ! [X348: term] :
( ( X340 @ id @ X348 @ id )
= ( X342 @ X348 ) )
| ( $true
= ( X342 @ ( lam @ X341 ) ) )
| ~ ! [X349: term] :
( ( ( X342 @ X349 )
!= $true )
| ( ( X342 @ ( sub @ X341 @ ( push @ X349 @ id ) ) )
= $true ) ) )
=> ! [X350: term,X351: subst > term > subst > $o] :
( ~ ! [X352: term,X353: term] :
( ( $true
!= ( X351 @ id @ X353 @ id ) )
| ( $true
!= ( X351 @ id @ X352 @ id ) )
| ( $true
= ( X351 @ id @ ( ap @ ( sub @ X352 @ id ) @ X353 ) @ id ) ) )
| ( ( X351 @ id @ X350 @ id )
= $true )
| ~ ! [X354: subst > term > term] :
( ~ ! [X355: term,X356: subst,X357: subst] :
( ( sub @ ( X354 @ X356 @ X355 ) @ X357 )
= ( X354 @ ( comp @ X356 @ X357 ) @ ( sub @ X355 @ X357 ) ) )
| ~ ! [X358: term] :
( ( $true
!= ( X351 @ id @ X358 @ id ) )
| ( $true
= ( X351 @ id @ ( X354 @ id @ X358 ) @ id ) ) )
| ( ( X351 @ id @ ( lam @ ( X354 @ sh @ one ) ) @ id )
= $true ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X359: term] :
( ( sub @ X359 @ id )
= X359 )
=> ( ! [X360: subst > term > subst > $o,X361: term] :
( ( $true
= ( X360 @ id @ ( lam @ ( sub @ X361 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X362: subst > term > term] :
( ~ ! [X363: term,X364: subst,X365: subst] :
( ( X362 @ ( comp @ X365 @ X364 ) @ ( sub @ X363 @ X364 ) )
= ( sub @ ( X362 @ X365 @ X363 ) @ X364 ) )
| ~ ! [X366: term] :
( ( $true
!= ( X360 @ id @ X366 @ id ) )
| ( $true
= ( X360 @ id @ ( X362 @ id @ X366 ) @ id ) ) )
| ( ( X360 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X367: term] :
( ( $true
= ( X360 @ id @ ( sub @ X361 @ ( push @ X367 @ id ) ) @ id ) )
| ( $true
!= ( X360 @ id @ X367 @ id ) ) ) )
=> ! [X368: term,X369: subst > term > subst > $o] :
( ( $true
= ( X369 @ id @ ( lam @ X368 ) @ id ) )
| ~ ! [X370: subst > term > term] :
( ~ ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X370 @ X372 @ X371 ) @ X373 )
= ( X370 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) ) )
| ~ ! [X374: term] :
( ( ( X369 @ id @ X374 @ id )
!= $true )
| ( $true
= ( X369 @ id @ ( X370 @ id @ X374 ) @ id ) ) )
| ( $true
= ( X369 @ id @ ( lam @ ( X370 @ sh @ one ) ) @ id ) ) )
| ~ ! [X375: term] :
( ( $true
= ( X369 @ id @ ( sub @ X368 @ ( push @ X375 @ id ) ) @ id ) )
| ( $true
!= ( X369 @ id @ X375 @ id ) ) ) ) ) ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X376: subst > term > subst > $o,X377: term,X378: term,X379: term > $o] :
( ( $true
= ( X379 @ ( ap @ X377 @ X378 ) ) )
| ~ ! [X380: term] :
( ( X376 @ id @ X380 @ id )
= ( X379 @ X380 ) )
| ~ ! [X381: term,X382: term] :
( ( $true
!= ( X376 @ id @ X382 @ id ) )
| ( $true
!= ( X376 @ id @ X381 @ id ) )
| ( $true
= ( X376 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) ) )
| ( $true
!= ( X379 @ X378 ) )
| ( $true
!= ( X379 @ X377 ) )
| ~ ! [X383: subst,X384: subst,X385: term,X386: subst] :
( ( ( X376 @ X386 @ X385 @ ( comp @ X383 @ X384 ) )
= $true )
| ( $true
!= ( X376 @ ( comp @ X386 @ X383 ) @ ( sub @ X385 @ X383 ) @ X384 ) ) )
| ~ ! [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
!= ( X376 @ X389 @ X387 @ ( comp @ X390 @ X388 ) ) )
| ( $true
= ( X376 @ ( comp @ X389 @ X390 ) @ ( sub @ X387 @ X390 ) @ X388 ) ) ) ) )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X391: d_term] : ( d_one = X391 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ! [X392: d_term,X393: d_term] :
( ( ( d2term @ X392 )
= ( d2term @ X393 ) )
=> ( X392 = X393 ) )
& ( ( d2subst @ d_id )
= id )
& ( lamnotvar = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( ! [X394: subst] :
( ( comp @ id @ X394 )
= X394 )
& ! [X395: subst] :
( ( comp @ X395 @ id )
= X395 ) )
<=> ( substmonoid = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X396: term,X397: term,X398: term,X399: term] :
( ( X396 = X398 )
| ( ( ap @ ( sub @ X396 @ id ) @ X397 )
!= ( ap @ ( sub @ X398 @ id ) @ X399 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction = $true )
<=> ! [X400: term,X401: subst > term > subst > $o] :
( ~ ! [X402: term,X403: term] :
( ( $true
!= ( X401 @ id @ X402 @ id ) )
| ( $true
= ( X401 @ id @ ( ap @ ( sub @ X402 @ id ) @ X403 ) @ id ) )
| ( $true
!= ( X401 @ id @ X403 @ id ) ) )
| ~ ! [X404: term] :
( ( $true
!= ( var @ ( sub @ X404 @ id ) ) )
| ( $true
= ( X401 @ id @ X404 @ id ) ) )
| ~ ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X401 @ ( comp @ X407 @ X408 ) @ ( sub @ X405 @ X408 ) @ X406 ) )
| ( ( X401 @ X407 @ X405 @ ( comp @ X408 @ X406 ) )
!= $true ) )
| ~ ! [X409: term,X410: subst,X411: subst,X412: subst] :
( ( ( X401 @ X412 @ X409 @ ( comp @ X411 @ X410 ) )
= $true )
| ( $true
!= ( X401 @ ( comp @ X412 @ X411 ) @ ( sub @ X409 @ X411 ) @ X410 ) ) )
| ( $true
= ( X401 @ id @ X400 @ id ) )
| ~ ! [X413: subst > term > term] :
( ~ ! [X414: term,X415: subst,X416: subst] :
( ( X413 @ ( comp @ X416 @ X415 ) @ ( sub @ X414 @ X415 ) )
= ( sub @ ( X413 @ X416 @ X414 ) @ X415 ) )
| ~ ! [X417: term] :
( ( $true
!= ( X401 @ id @ X417 @ id ) )
| ( ( X401 @ id @ ( X413 @ id @ X417 ) @ id )
= $true ) )
| ( $true
= ( X401 @ id @ ( lam @ ( X413 @ sh @ one ) ) @ id ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ! [X418: term] :
~ ! [X419: subst > term > term] :
( ( sub @ X418 @ ( push @ one @ sh ) )
!= ( X419 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( induction2_gthm = $true )
& ( pushprop_lthm = $true )
& ( axclos = $true )
& ( ( ! [X420: subst > term > subst > $o] :
~ ! [X421: term > $o] :
~ ! [X422: term] :
( ( X420 @ id @ X422 @ id )
= ( X421 @ X422 ) )
=> ( ! [X423: term > $o,X424: term] :
( ~ ! [X425: term] :
( ( $true
= ( X423 @ ( lam @ X425 ) ) )
| ~ ! [X426: term] :
( ( $true
!= ( X423 @ X426 ) )
| ( ( X423 @ ( sub @ X425 @ ( push @ X426 @ id ) ) )
= $true ) ) )
| ~ ! [X427: term,X428: term] :
( ( $true
!= ( X423 @ X428 ) )
| ( $true
!= ( X423 @ X427 ) )
| ( $true
= ( X423 @ ( ap @ X427 @ X428 ) ) ) )
| ( $true
= ( X423 @ X424 ) )
| ~ ! [X429: term] :
( ( ( var @ X429 )
!= $true )
| ( ( X423 @ X429 )
= $true ) ) )
=> ( ! [X430: term] :
( ( sub @ X430 @ id )
= X430 )
=> ( ! [X431: subst > term > subst > $o,X432: term,X433: term > $o] :
( ~ ! [X434: term] :
( ( $true
= ( X433 @ ( sub @ X432 @ ( push @ X434 @ id ) ) ) )
| ( $true
!= ( X433 @ X434 ) ) )
| ( ( X433 @ ( lam @ X432 ) )
= $true )
| ~ ! [X435: term] :
( ( X431 @ id @ X435 @ id )
= ( X433 @ X435 ) )
| ~ ! [X436: subst > term > term] :
( ( ( X431 @ id @ ( lam @ ( X436 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X437: subst,X438: term,X439: subst] :
( ( sub @ ( X436 @ X437 @ X438 ) @ X439 )
= ( X436 @ ( comp @ X437 @ X439 ) @ ( sub @ X438 @ X439 ) ) )
| ~ ! [X440: term] :
( ( $true
= ( X431 @ id @ ( X436 @ id @ X440 ) @ id ) )
| ( $true
!= ( X431 @ id @ X440 @ id ) ) ) ) )
=> ! [X441: term,X442: subst > term > subst > $o] :
( ~ ! [X443: term,X444: term] :
( ( $true
!= ( X442 @ id @ X443 @ id ) )
| ( ( X442 @ id @ ( ap @ ( sub @ X443 @ id ) @ X444 ) @ id )
= $true )
| ( ( X442 @ id @ X444 @ id )
!= $true ) )
| ( ( X442 @ id @ X441 @ id )
= $true )
| ~ ! [X445: subst,X446: subst,X447: term,X448: subst] :
( ( $true
!= ( X442 @ ( comp @ X446 @ X445 ) @ ( sub @ X447 @ X445 ) @ X448 ) )
| ( ( X442 @ X446 @ X447 @ ( comp @ X445 @ X448 ) )
= $true ) )
| ~ ! [X449: term] :
( ( ( X442 @ id @ X449 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X449 @ id ) ) ) )
| ~ ! [X450: subst,X451: term,X452: subst,X453: subst] :
( ( $true
!= ( X442 @ X452 @ X451 @ ( comp @ X453 @ X450 ) ) )
| ( ( X442 @ ( comp @ X452 @ X453 ) @ ( sub @ X451 @ X453 ) @ X450 )
= $true ) )
| ~ ! [X454: subst > term > term] :
( ~ ! [X455: term,X456: subst,X457: subst] :
( ( X454 @ ( comp @ X456 @ X457 ) @ ( sub @ X455 @ X457 ) )
= ( sub @ ( X454 @ X456 @ X455 ) @ X457 ) )
| ~ ! [X458: term] :
( ( $true
!= ( X442 @ id @ X458 @ id ) )
| ( ( X442 @ id @ ( X454 @ id @ X458 ) @ id )
= $true ) )
| ( $true
= ( X442 @ id @ ( lam @ ( X454 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X459: term,X460: subst > term > subst > $o] :
( ~ ! [X461: term,X462: subst > term > term] :
( ~ ! [X463: subst,X464: term,X465: subst] :
( ( sub @ X461 @ ( push @ ( sub @ X464 @ X465 ) @ ( comp @ X463 @ X465 ) ) )
= ( X462 @ ( comp @ X463 @ X465 ) @ ( sub @ X464 @ X465 ) ) )
| ~ ! [X466: term] :
( ( ( X460 @ id @ ( X462 @ id @ X466 ) @ id )
= $true )
| ( $true
!= ( X460 @ id @ X466 @ id ) ) )
| ~ ! [X467: subst,X468: term,X469: subst] :
( ( sub @ ( X462 @ X467 @ X468 ) @ X469 )
= ( sub @ ( sub @ X461 @ ( push @ X468 @ X467 ) ) @ X469 ) )
| ( $true
= ( X460 @ id @ ( lam @ ( X462 @ sh @ one ) ) @ id ) ) )
| ~ ! [X470: term] :
( ( $true
!= ( X460 @ id @ X470 @ id ) )
| ( $true
= ( X460 @ id @ ( sub @ X459 @ ( push @ X470 @ id ) ) @ id ) ) )
| ( ( X460 @ id @ ( lam @ ( sub @ X459 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X471: term > $o,X472: term] :
( ( ( X471 @ X472 )
= $true )
| ~ ! [X473: term] :
( ~ ! [X474: term] :
( ( ( X471 @ X474 )
!= $true )
| ( $true
= ( X471 @ ( sub @ X473 @ ( push @ X474 @ id ) ) ) ) )
| ( $true
= ( X471 @ ( lam @ X473 ) ) ) )
| ~ ! [X475: term,X476: term] :
( ( ( X471 @ ( ap @ X476 @ X475 ) )
= $true )
| ( $true
!= ( X471 @ X476 ) )
| ( $true
!= ( X471 @ X475 ) ) )
| ~ ! [X477: term] :
( ( ( X471 @ X477 )
= $true )
| ( $true
!= ( var @ X477 ) ) ) )
=> ( ! [X478: term,X479: subst > term > subst > $o,X480: term] :
( ( ( X479 @ id @ ( ap @ X478 @ X480 ) @ id )
= $true )
| ~ ! [X481: term,X482: subst,X483: subst,X484: subst] :
( ( $true
= ( X479 @ ( comp @ X483 @ X484 ) @ ( sub @ X481 @ X484 ) @ X482 ) )
| ( ( X479 @ X483 @ X481 @ ( comp @ X484 @ X482 ) )
!= $true ) )
| ( $true
!= ( X479 @ id @ X478 @ id ) )
| ( $true
!= ( X479 @ id @ X480 @ id ) )
| ~ ! [X485: subst,X486: subst,X487: term,X488: subst] :
( ( ( X479 @ X486 @ X487 @ ( comp @ X488 @ X485 ) )
= $true )
| ( $true
!= ( X479 @ ( comp @ X486 @ X488 ) @ ( sub @ X487 @ X488 ) @ X485 ) ) )
| ~ ! [X489: term,X490: term] :
( ( ( X479 @ id @ ( ap @ ( sub @ X490 @ id ) @ X489 ) @ id )
= $true )
| ( $true
!= ( X479 @ id @ X490 @ id ) )
| ( $true
!= ( X479 @ id @ X489 @ id ) ) ) )
=> ( ! [X491: subst > term > subst > $o,X492: term] :
( ~ ! [X493: subst > term > term] :
( ~ ! [X494: term] :
( ( ( X491 @ id @ ( X493 @ id @ X494 ) @ id )
= $true )
| ( $true
!= ( X491 @ id @ X494 @ id ) ) )
| ~ ! [X495: subst,X496: term,X497: subst] :
( ( X493 @ ( comp @ X495 @ X497 ) @ ( sub @ X496 @ X497 ) )
= ( sub @ ( X493 @ X495 @ X496 ) @ X497 ) )
| ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X491 @ id @ ( lam @ X492 ) @ id )
= $true )
| ~ ! [X498: term] :
( ( ( X491 @ id @ ( sub @ X492 @ ( push @ X498 @ id ) ) @ id )
= $true )
| ( $true
!= ( X491 @ id @ X498 @ id ) ) )
| ~ ! [X499: subst,X500: term,X501: subst,X502: subst] :
( ( ( X491 @ X501 @ X500 @ ( comp @ X502 @ X499 ) )
!= $true )
| ( ( X491 @ ( comp @ X501 @ X502 ) @ ( sub @ X500 @ X502 ) @ X499 )
= $true ) )
| ~ ! [X503: subst,X504: term,X505: subst,X506: subst] :
( ( $true
!= ( X491 @ ( comp @ X503 @ X506 ) @ ( sub @ X504 @ X506 ) @ X505 ) )
| ( ( X491 @ X503 @ X504 @ ( comp @ X506 @ X505 ) )
= $true ) ) )
=> ! [X507: subst > term > subst > $o,X508: term] :
( ( $true
= ( X507 @ id @ X508 @ id ) )
| ~ ! [X509: subst,X510: subst,X511: subst,X512: term] :
( ( $true
= ( X507 @ X511 @ X512 @ ( comp @ X510 @ X509 ) ) )
| ( $true
!= ( X507 @ ( comp @ X511 @ X510 ) @ ( sub @ X512 @ X510 ) @ X509 ) ) )
| ~ ! [X513: subst,X514: subst,X515: subst,X516: term] :
( ( $true
= ( X507 @ ( comp @ X513 @ X515 ) @ ( sub @ X516 @ X515 ) @ X514 ) )
| ( ( X507 @ X513 @ X516 @ ( comp @ X515 @ X514 ) )
!= $true ) )
| ~ ! [X517: term] :
( ( ( var @ ( sub @ X517 @ id ) )
!= $true )
| ( $true
= ( X507 @ id @ X517 @ id ) ) )
| ~ ! [X518: term,X519: term] :
( ( ( X507 @ id @ X519 @ id )
!= $true )
| ( ( X507 @ id @ ( ap @ ( sub @ X519 @ id ) @ X518 ) @ id )
= $true )
| ( ( X507 @ id @ X518 @ id )
!= $true ) )
| ~ ! [X520: subst > term > term] :
( ~ ! [X521: term] :
( ( ( X507 @ id @ ( X520 @ id @ X521 ) @ id )
= $true )
| ( $true
!= ( X507 @ id @ X521 @ id ) ) )
| ~ ! [X522: subst,X523: term,X524: subst] :
( ( X520 @ ( comp @ X522 @ X524 ) @ ( sub @ X523 @ X524 ) )
= ( sub @ ( X520 @ X522 @ X523 ) @ X524 ) )
| ( $true
= ( X507 @ id @ ( lam @ ( X520 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X525: term,X526: subst > term > term,X527: term] :
( ~ ! [X528: subst,X529: term,X530: subst] :
( ( sub @ ( X526 @ X528 @ X529 ) @ X530 )
= ( X526 @ ( comp @ X528 @ X530 ) @ ( sub @ X529 @ X530 ) ) )
| ( ( ap @ ( sub @ X527 @ id ) @ X525 )
!= ( lam @ ( X526 @ sh @ one ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X531: subst > term > subst > $o,X532: term] :
( ~ ! [X533: subst > term > term] :
( ( ( X531 @ id @ ( lam @ ( X533 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X534: term,X535: subst,X536: subst] :
( ( sub @ ( X533 @ X536 @ X534 ) @ X535 )
= ( X533 @ ( comp @ X536 @ X535 ) @ ( sub @ X534 @ X535 ) ) )
| ~ ! [X537: term] :
( ( $true
= ( X531 @ id @ ( X533 @ id @ X537 ) @ id ) )
| ( $true
!= ( X531 @ id @ X537 @ id ) ) ) )
| ( ( X531 @ id @ ( lam @ X532 ) @ id )
= $true )
| ~ ! [X538: term] :
( ( $true
= ( X531 @ id @ ( sub @ X532 @ ( push @ X538 @ id ) ) @ id ) )
| ( ( X531 @ id @ X538 @ id )
!= $true ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X539: term] :
? [X540: d_term] :
( ( d2term @ X540 )
= X539 )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X541: subst,X542: term] :
( ( sub @ one @ ( push @ X542 @ X541 ) )
= X542 )
=> ( ! [X543: subst,X544: term] :
( ( comp @ sh @ ( push @ X544 @ X543 ) )
= X543 )
=> ! [X545: term,X546: term > $o,X547: term > $o,X548: subst,X549: term] :
( ( ( X546 @ X545 )
!= $true )
| ( ( X547 @ ( sub @ X545 @ ( push @ X549 @ X548 ) ) )
= $true ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( hoasinduction_lem2_gthm
& ( ! [X0: term] :
~ ! [X1: subst > term > term] :
~ ! [X2: term,X3: subst] :
( ( sub @ X0 @ ( push @ X2 @ X3 ) )
= ( X1 @ X3 @ X2 ) )
<=> hoasinduction_lem3v2_f )
& apnotvar
& hoaslamnotvar_lthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X4: subst > term > subst > $o,X5: term] :
( ~ ! [X6: term,X7: subst,X8: subst,X9: subst] :
( ~ ( X4 @ X8 @ X6 @ ( comp @ X9 @ X7 ) )
| ( X4 @ ( comp @ X8 @ X9 ) @ ( sub @ X6 @ X9 ) @ X7 ) )
| ~ ! [X10: subst > term > term] :
( ~ ! [X11: term] :
( ~ ( X4 @ id @ X11 @ id )
| ( X4 @ id @ ( X10 @ id @ X11 ) @ id ) )
| ( X4 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
| ~ ! [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) ) )
| ( X4 @ id @ ( lam @ X5 ) @ id )
| ~ ! [X15: term,X16: subst,X17: subst,X18: subst] :
( ~ ( X4 @ ( comp @ X17 @ X16 ) @ ( sub @ X15 @ X16 ) @ X18 )
| ( X4 @ X17 @ X15 @ ( comp @ X16 @ X18 ) ) )
| ~ ! [X19: term] :
( ( X4 @ id @ ( sub @ X5 @ ( push @ X19 @ id ) ) @ id )
| ~ ( X4 @ id @ X19 @ id ) ) )
<=> hoasinduction_lem3 )
& ( termmset_lthm
<=> ( ! [X20: term] :
( ( sub @ X20 @ id )
= X20 )
=> ! [X21: term] :
( ( sub @ X21 @ id )
= X21 ) ) )
& ( axidl
<=> ! [X22: subst] :
( ( comp @ id @ X22 )
= X22 ) )
& ( ! [X23: term] :
~ ! [X24: subst > term > term] :
~ ! [X25: subst,X26: term] :
( ( X24 @ X25 @ X26 )
= ( sub @ X23 @ ( push @ X26 @ X25 ) ) )
<=> hoasinduction_lem3v2_f_lthm )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X27: d_subst] : ( d_id = X27 )
& hoasapnotvar_lthm
& ( hoasapinj2_lthm
<=> ( ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ X28 @ X30 )
!= ( ap @ X29 @ X31 ) )
| ( X30 = X31 ) )
=> ! [X32: term,X33: term,X34: term,X35: term] :
( ( ( ap @ ( sub @ X33 @ id ) @ X34 )
!= ( ap @ ( sub @ X32 @ id ) @ X35 ) )
| ( X34 = X35 ) ) ) )
& ( hoaslaminj
<=> ! [X36: subst > term > term,X37: subst > term > term,X38: subst,X39: term] :
( ( ( lam @ ( X36 @ sh @ one ) )
!= ( lam @ ( X37 @ sh @ one ) ) )
| ~ ! [X40: subst,X41: term,X42: subst] :
( ( sub @ ( X36 @ X42 @ X41 ) @ X40 )
= ( X36 @ ( comp @ X42 @ X40 ) @ ( sub @ X41 @ X40 ) ) )
| ( ( X36 @ X38 @ X39 )
= ( X37 @ X38 @ X39 ) )
| ~ ! [X43: subst,X44: subst,X45: term] :
( ( X37 @ ( comp @ X44 @ X43 ) @ ( sub @ X45 @ X43 ) )
= ( sub @ ( X37 @ X44 @ X45 ) @ X43 ) ) ) )
& ~ lamnotap
& ( induction2lem_lthm
<=> ( ! [X46: subst,X47: term] :
( ( sub @ one @ ( push @ X47 @ X46 ) )
= X47 )
=> ( ! [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
= X48 )
=> ( ! [X50: subst] :
( ( comp @ X50 @ id )
= X50 )
=> ( ! [X51: term,X52: term > $o] :
( ( X52 @ X51 )
| ~ ! [X53: term] :
( ~ ( X52 @ X53 )
| ( X52 @ ( lam @ X53 ) ) )
| ~ ! [X54: term] :
( ~ ( var @ X54 )
| ( X52 @ X54 ) )
| ~ ! [X55: term,X56: term] :
( ~ ( X52 @ X55 )
| ~ ( X52 @ X56 )
| ( X52 @ ( ap @ X56 @ X55 ) ) ) )
=> ! [X57: subst,X58: term,X59: term > $o] :
( ( X59 @ ( sub @ X58 @ X57 ) )
| ~ ! [X60: term] :
( ( X59 @ ( lam @ X60 ) )
| ~ ! [X61: term] :
( ( X59 @ ( sub @ X60 @ ( push @ X61 @ id ) ) )
| ~ ( X59 @ X61 ) ) )
| ~ ! [X62: term,X63: term] :
( ( X59 @ ( ap @ X62 @ X63 ) )
| ~ ( X59 @ X62 )
| ~ ( X59 @ X63 ) )
| ~ ! [X64: term] :
( ~ ( var @ X64 )
| ( X59 @ ( sub @ X64 @ X57 ) ) ) ) ) ) ) ) )
& ( hoasinduction_lem0_lthm
<=> ! [X65: subst > term > subst > $o] :
~ ! [X66: term > $o] :
~ ! [X67: term] :
( ( X65 @ id @ X67 @ id )
= ( X66 @ X67 ) ) )
& ( hoasapinj1_lthm
<=> ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X70 @ X72 )
!= ( ap @ X69 @ X71 ) )
| ( X69 = X70 ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X76 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) ) ) ) )
& hoasinduction_lem3a_gthm
& pushprop_lem1v2_gthm
& ( ! [X77: term,X78: subst,X79: term > $o,X80: term > $o,X81: term] :
( ~ ( X79 @ X81 )
| ( X80 @ ( sub @ X81 @ ( push @ X77 @ X78 ) ) ) )
<=> pushprop_lem1 )
& pushprop_lem2v2_lthm
& hoasinduction_lem1
& ( ( ! [X82: term,X83: subst] :
( ( sub @ one @ ( push @ X82 @ X83 ) )
= X82 )
=> ! [X84: subst,X85: term > $o,X86: term,X87: term > $o] :
( ~ ! [X88: term] :
( ( X87 @ ( sub @ X88 @ ( push @ X86 @ X84 ) ) )
= ( X85 @ X88 ) )
| ( X85 @ one )
| ~ ( X87 @ X86 ) ) )
<=> pushprop_lem1v2_lthm )
& ( ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ X92 @ X89 )
!= ( ap @ X90 @ X91 ) )
| ( X89 = X91 ) )
<=> apinj2 )
& axabs
& ( one
= ( d2term @ d_one ) )
& pushprop_lthm_orig
& ( induction2_lthm
<=> ( ! [X93: term] :
( ( sub @ X93 @ id )
= X93 )
=> ( ! [X94: term,X95: subst,X96: term > $o] :
( ~ ! [X97: term] :
( ~ ! [X98: term] :
( ( X96 @ ( sub @ X97 @ ( push @ X98 @ id ) ) )
| ~ ( X96 @ X98 ) )
| ( X96 @ ( lam @ X97 ) ) )
| ( X96 @ ( sub @ X94 @ X95 ) )
| ~ ! [X99: term,X100: term] :
( ( X96 @ ( ap @ X99 @ X100 ) )
| ~ ( X96 @ X99 )
| ~ ( X96 @ X100 ) )
| ~ ! [X101: term] :
( ~ ( var @ X101 )
| ( X96 @ ( sub @ X101 @ X95 ) ) ) )
=> ! [X102: term,X103: term > $o] :
( ( X103 @ X102 )
| ~ ! [X104: term] :
( ( X103 @ ( lam @ X104 ) )
| ~ ! [X105: term] :
( ~ ( X103 @ X105 )
| ( X103 @ ( sub @ X104 @ ( push @ X105 @ id ) ) ) ) )
| ~ ! [X106: term] :
( ( X103 @ X106 )
| ~ ( var @ X106 ) )
| ~ ! [X107: term,X108: term] :
( ~ ( X103 @ X108 )
| ~ ( X103 @ X107 )
| ( X103 @ ( ap @ X108 @ X107 ) ) ) ) ) ) )
& pushprop_gthm
& ( ! [X109: term,X110: term] :
( ( X109 = X110 )
| ( ( lam @ X110 )
!= ( lam @ X109 ) ) )
<=> laminj )
& ( ! [X111: subst > term > subst > $o,X112: term] :
( ~ ! [X113: term] :
( ~ ( X111 @ id @ X113 @ id )
| ( X111 @ id @ ( sub @ X112 @ ( push @ X113 @ id ) ) @ id ) )
| ~ ! [X114: subst > term > term] :
( ~ ! [X115: subst,X116: subst,X117: term] :
( ( sub @ ( X114 @ X115 @ X117 ) @ X116 )
= ( X114 @ ( comp @ X115 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
| ( X111 @ id @ ( lam @ ( X114 @ sh @ one ) ) @ id )
| ~ ! [X118: term] :
( ~ ( X111 @ id @ X118 @ id )
| ( X111 @ id @ ( X114 @ id @ X118 ) @ id ) ) )
| ( X111 @ id @ ( lam @ ( sub @ X112 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa_lthm )
& ( axidr
<=> ! [X119: subst] :
( ( comp @ X119 @ id )
= X119 ) )
& ( ! [X120: subst,X121: term] :
( ( sub @ one @ ( push @ X121 @ X120 ) )
= X121 )
<=> axvarcons )
& ( ! [X122: term,X123: subst > term > subst > $o] :
( ~ ! [X124: subst > term > term] :
( ~ ! [X125: subst,X126: subst,X127: term] :
( ( X124 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X124 @ X125 @ X127 ) @ X126 ) )
| ~ ! [X128: term] :
( ( X123 @ id @ ( X124 @ id @ X128 ) @ id )
| ~ ( X123 @ id @ X128 @ id ) )
| ( X123 @ id @ ( lam @ ( X124 @ sh @ one ) ) @ id ) )
| ~ ! [X129: term,X130: term] :
( ~ ( X123 @ id @ X130 @ id )
| ~ ( X123 @ id @ X129 @ id )
| ( X123 @ id @ ( ap @ ( sub @ X130 @ id ) @ X129 ) @ id ) )
| ( X123 @ id @ X122 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ! [X132: subst > term > subst > $o,X133: term,X134: term > $o] :
( ~ ! [X135: subst > term > term] :
( ( X132 @ id @ ( lam @ ( X135 @ sh @ one ) ) @ id )
| ~ ! [X136: subst,X137: subst,X138: term] :
( ( X135 @ ( comp @ X136 @ X137 ) @ ( sub @ X138 @ X137 ) )
= ( sub @ ( X135 @ X136 @ X138 ) @ X137 ) )
| ~ ! [X139: term] :
( ~ ( X132 @ id @ X139 @ id )
| ( X132 @ id @ ( X135 @ id @ X139 ) @ id ) ) )
| ~ ! [X140: term] :
( ( X132 @ id @ X140 @ id )
= ( X134 @ X140 ) )
| ~ ! [X141: subst,X142: subst,X143: subst,X144: term] :
( ( X132 @ X143 @ X144 @ ( comp @ X141 @ X142 ) )
| ~ ( X132 @ ( comp @ X143 @ X141 ) @ ( sub @ X144 @ X141 ) @ X142 ) )
| ~ ! [X145: subst,X146: term,X147: subst,X148: subst] :
( ( X132 @ ( comp @ X147 @ X145 ) @ ( sub @ X146 @ X145 ) @ X148 )
| ~ ( X132 @ X147 @ X146 @ ( comp @ X145 @ X148 ) ) )
| ( X134 @ ( lam @ X133 ) )
| ~ ! [X149: term] :
( ~ ( X134 @ X149 )
| ( X134 @ ( sub @ X133 @ ( push @ X149 @ id ) ) ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& hoaslaminj_gthm
& ( hoasinduction_p_and_p_prime
= ( ^ [X150: subst > term > subst > $o,X151: term > $o] :
! [X152: term] :
( ( X151 @ X152 )
= ( X150 @ id @ X152 @ id ) ) ) )
& ( ! [X153: term,X154: term > $o,X155: term > $o,X156: subst] :
( ~ ( X155 @ X153 )
| ( X154 @ one )
| ~ ! [X157: term] :
( ( X155 @ ( sub @ X157 @ ( push @ X153 @ X156 ) ) )
= ( X154 @ X157 ) ) )
<=> pushprop_lem1v2 )
& ( ( ! [X158: term] :
( ( sub @ X158 @ id )
= X158 )
=> ( ! [X159: subst > term > subst > $o,X160: term] :
( ~ ! [X161: term] :
( ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id )
| ~ ( X159 @ id @ X161 @ id ) )
| ~ ! [X162: subst > term > term] :
( ~ ! [X163: term] :
( ( X159 @ id @ ( X162 @ id @ X163 ) @ id )
| ~ ( X159 @ id @ X163 @ id ) )
| ~ ! [X164: subst,X165: subst,X166: term] :
( ( sub @ ( X162 @ X164 @ X166 ) @ X165 )
= ( X162 @ ( comp @ X164 @ X165 ) @ ( sub @ X166 @ X165 ) ) )
| ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
| ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X167: subst > term > subst > $o,X168: term] :
( ~ ! [X169: term] :
( ( X167 @ id @ ( sub @ X168 @ ( push @ X169 @ id ) ) @ id )
| ~ ( X167 @ id @ X169 @ id ) )
| ~ ! [X170: subst > term > term] :
( ~ ! [X171: term,X172: subst,X173: subst] :
( ( sub @ ( X170 @ X172 @ X171 ) @ X173 )
= ( X170 @ ( comp @ X172 @ X173 ) @ ( sub @ X171 @ X173 ) ) )
| ~ ! [X174: term] :
( ( X167 @ id @ ( X170 @ id @ X174 ) @ id )
| ~ ( X167 @ id @ X174 @ id ) )
| ( X167 @ id @ ( lam @ ( X170 @ sh @ one ) ) @ id ) )
| ~ ! [X175: subst,X176: subst,X177: subst,X178: term] :
( ~ ( X167 @ ( comp @ X176 @ X177 ) @ ( sub @ X178 @ X177 ) @ X175 )
| ( X167 @ X176 @ X178 @ ( comp @ X177 @ X175 ) ) )
| ~ ! [X179: subst,X180: subst,X181: term,X182: subst] :
( ( X167 @ ( comp @ X180 @ X182 ) @ ( sub @ X181 @ X182 ) @ X179 )
| ~ ( X167 @ X180 @ X181 @ ( comp @ X182 @ X179 ) ) )
| ( X167 @ id @ ( lam @ X168 ) @ id ) ) ) )
<=> hoasinduction_lem3_lthm )
& substmonoid_gthm
& ( axshiftcons
<=> ! [X183: term,X184: subst] :
( ( comp @ sh @ ( push @ X183 @ X184 ) )
= X184 ) )
& hoasinduction_lem1v2_gthm
& ( hoasapinj2
<=> ! [X185: term,X186: term,X187: term,X188: term] :
( ( ( ap @ ( sub @ X187 @ id ) @ X188 )
!= ( ap @ ( sub @ X186 @ id ) @ X185 ) )
| ( X185 = X188 ) ) )
& ( ! [X189: term,X190: term > $o,X191: subst] :
~ ! [X192: term > $o] :
~ ! [X193: term] :
( ( X192 @ X193 )
= ( X190 @ ( sub @ X193 @ ( push @ X189 @ X191 ) ) ) )
<=> pushprop_lem0 )
& hoasinduction_lem3b_gthm
& ( ! [X194: term > $o,X195: term] :
( ~ ! [X196: term,X197: term] :
( ~ ( X194 @ X197 )
| ( X194 @ ( ap @ X197 @ X196 ) )
| ~ ( X194 @ X196 ) )
| ~ ! [X198: term] :
( ~ ! [X199: term] :
( ( X194 @ ( sub @ X198 @ ( push @ X199 @ id ) ) )
| ~ ( X194 @ X199 ) )
| ( X194 @ ( lam @ X198 ) ) )
| ( X194 @ X195 )
| ~ ! [X200: term] :
( ~ ( var @ X200 )
| ( X194 @ X200 ) ) )
<=> induction2 )
& ( ( ^ [X201: term,X202: subst,X203: term > $o,X204: term > $o] :
! [X205: term] :
( ( X203 @ ( sub @ X205 @ ( push @ X201 @ X202 ) ) )
= ( X204 @ X205 ) ) )
= pushprop_p_and_p_prime )
& ( ! [X206: term > $o,X207: term,X208: subst > term > subst > $o] :
( ( X206 @ ( lam @ X207 ) )
| ~ ! [X209: term,X210: subst,X211: subst,X212: subst] :
( ( X208 @ ( comp @ X210 @ X212 ) @ ( sub @ X209 @ X212 ) @ X211 )
| ~ ( X208 @ X210 @ X209 @ ( comp @ X212 @ X211 ) ) )
| ~ ! [X213: term] :
( ( X206 @ ( sub @ X207 @ ( push @ X213 @ id ) ) )
| ~ ( X206 @ X213 ) )
| ~ ! [X214: subst,X215: subst,X216: subst,X217: term] :
( ~ ( X208 @ ( comp @ X214 @ X216 ) @ ( sub @ X217 @ X216 ) @ X215 )
| ( X208 @ X214 @ X217 @ ( comp @ X216 @ X215 ) ) )
| ~ ! [X218: term] :
( ( X206 @ X218 )
= ( X208 @ id @ X218 @ id ) )
| ~ ! [X219: subst > term > term] :
( ~ ! [X220: term] :
( ~ ( X208 @ id @ X220 @ id )
| ( X208 @ id @ ( X219 @ id @ X220 ) @ id ) )
| ( X208 @ id @ ( lam @ ( X219 @ sh @ one ) ) @ id )
| ~ ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) ) ) )
<=> hoasinduction_lem3v2 )
& pushprop
& ( induction
<=> ! [X224: term,X225: term > $o] :
( ~ ! [X226: term] :
( ( X225 @ X226 )
| ~ ( var @ X226 ) )
| ~ ! [X227: term,X228: term] :
( ~ ( X225 @ X227 )
| ~ ( X225 @ X228 )
| ( X225 @ ( ap @ X227 @ X228 ) ) )
| ~ ! [X229: term] :
( ~ ( X225 @ X229 )
| ( X225 @ ( lam @ X229 ) ) )
| ( X225 @ X224 ) ) )
& ( ! [X230: term,X231: subst > term > subst > $o] :
( ~ ! [X232: term] :
( ~ ( X231 @ id @ X232 @ id )
| ( X231 @ id @ ( sub @ X230 @ ( push @ X232 @ id ) ) @ id ) )
| ~ ! [X233: subst > term > term] :
( ~ ! [X234: subst,X235: term,X236: subst] :
( ( sub @ ( X233 @ X236 @ X235 ) @ X234 )
= ( X233 @ ( comp @ X236 @ X234 ) @ ( sub @ X235 @ X234 ) ) )
| ( X231 @ id @ ( lam @ ( X233 @ sh @ one ) ) @ id )
| ~ ! [X237: term] :
( ~ ( X231 @ id @ X237 @ id )
| ( X231 @ id @ ( X233 @ id @ X237 ) @ id ) ) )
| ( X231 @ id @ ( lam @ ( sub @ X230 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa )
& ( ! [X238: term,X239: term] :
( ( ( sub @ X239 @ sh )
!= ( sub @ X238 @ sh ) )
| ( X238 = X239 ) )
<=> shinj )
& pushprop_lem2v2
& axassoc
& termmset_gthm
& axvarshift
& ( ! [X240: subst > term > subst > $o] :
~ ! [X241: term > $o] :
~ ! [X242: term] :
( ( X241 @ X242 )
= ( X240 @ id @ X242 @ id ) )
<=> hoasinduction_lem0 )
& pushprop_lem0_gthm
& ( ! [X243: term,X244: subst > term > subst > $o,X245: term > $o] :
( ( X245 @ ( lam @ X243 ) )
| ~ ! [X246: term] :
( ( X245 @ X246 )
= ( X244 @ id @ X246 @ id ) )
| ~ ! [X247: term] :
( ~ ( X245 @ X247 )
| ( X245 @ ( sub @ X243 @ ( push @ X247 @ id ) ) ) )
| ~ ! [X248: subst > term > term] :
( ~ ! [X249: term] :
( ~ ( X244 @ id @ X249 @ id )
| ( X244 @ id @ ( X248 @ id @ X249 ) @ id ) )
| ( X244 @ id @ ( lam @ ( X248 @ sh @ one ) ) @ id )
| ~ ! [X250: subst,X251: term,X252: subst] :
( ( sub @ ( X248 @ X250 @ X251 ) @ X252 )
= ( X248 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) ) ) ) )
<=> hoasinduction_lem3v2a )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ^ [X253: subst,X254: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& pushprop_lem3v2_lthm
& ( ! [X255: subst,X256: term,X257: term > $o] :
( ~ ! [X258: term,X259: term] :
( ~ ( X257 @ X259 )
| ~ ( X257 @ X258 )
| ( X257 @ ( ap @ X259 @ X258 ) ) )
| ~ ! [X260: term] :
( ( X257 @ ( lam @ X260 ) )
| ~ ! [X261: term] :
( ( X257 @ ( sub @ X260 @ ( push @ X261 @ id ) ) )
| ~ ( X257 @ X261 ) ) )
| ( X257 @ ( sub @ X256 @ X255 ) )
| ~ ! [X262: term] :
( ( X257 @ ( sub @ X262 @ X255 ) )
| ~ ( var @ X262 ) ) )
<=> induction2lem )
& pushprop_lem3v2
& axapp
& pushprop_lem2v2_gthm
& ! [X263: d_subst,X264: d_subst] :
( ( ( d2subst @ X263 )
= ( d2subst @ X264 ) )
=> ( X263 = X264 ) )
& ( hoasinduction_lem3b_lthm
<=> ! [X265: term] :
~ ! [X266: subst > term > term] :
( ( X266 @ sh @ one )
!= ( sub @ X265 @ ( push @ one @ sh ) ) ) )
& hoasinduction_lem1v2
& hoasinduction_lem2v2_gthm
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X267: term] :
~ ! [X268: subst > term > term] :
~ ! [X269: subst,X270: term] :
( ( sub @ X267 @ ( push @ X270 @ X269 ) )
= ( X268 @ X269 @ X270 ) )
=> ( ! [X271: term] :
( ( sub @ X271 @ id )
= X271 )
=> ! [X272: term,X273: subst > term > subst > $o,X274: term > $o] :
( ~ ! [X275: term] :
( ( X274 @ ( sub @ X272 @ ( push @ X275 @ id ) ) )
| ~ ( X274 @ X275 ) )
| ( X274 @ ( lam @ X272 ) )
| ~ ! [X276: subst > term > term] :
( ~ ! [X277: term,X278: subst,X279: subst] :
( ( X276 @ ( comp @ X279 @ X278 ) @ ( sub @ X277 @ X278 ) )
= ( sub @ ( X276 @ X279 @ X277 ) @ X278 ) )
| ~ ! [X280: term] :
( ~ ( X273 @ id @ X280 @ id )
| ( X273 @ id @ ( X276 @ id @ X280 ) @ id ) )
| ( X273 @ id @ ( lam @ ( X276 @ sh @ one ) ) @ id ) )
| ~ ! [X281: term] :
( ( X274 @ X281 )
= ( X273 @ id @ X281 @ id ) ) ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X282: subst,X283: term,X284: term > $o] :
~ ! [X285: term > $o] :
~ ! [X286: term] :
( ( X285 @ X286 )
= ( X284 @ ( sub @ X286 @ ( push @ X283 @ X282 ) ) ) ) )
& hoasinduction_gthm
& hoaslamnotvar
& ( hoaslaminj_lthm
<=> ( ! [X287: subst,X288: term] :
( ( sub @ one @ ( push @ X288 @ X287 ) )
= X288 )
=> ( ! [X289: term,X290: subst] :
( ( comp @ sh @ ( push @ X289 @ X290 ) )
= X290 )
=> ( ! [X291: term,X292: term] :
( ( X291 = X292 )
| ( ( lam @ X291 )
!= ( lam @ X292 ) ) )
=> ! [X293: term,X294: subst > term > term,X295: subst,X296: subst > term > term] :
( ~ ! [X297: term,X298: subst,X299: subst] :
( ( X294 @ ( comp @ X298 @ X299 ) @ ( sub @ X297 @ X299 ) )
= ( sub @ ( X294 @ X298 @ X297 ) @ X299 ) )
| ( ( lam @ ( X296 @ sh @ one ) )
!= ( lam @ ( X294 @ sh @ one ) ) )
| ( ( X296 @ X295 @ X293 )
= ( X294 @ X295 @ X293 ) )
| ~ ! [X300: subst,X301: subst,X302: term] :
( ( sub @ ( X296 @ X301 @ X302 ) @ X300 )
= ( X296 @ ( comp @ X301 @ X300 ) @ ( sub @ X302 @ X300 ) ) ) ) ) ) ) )
& ( ( ! [X303: subst] :
( ( comp @ id @ X303 )
= X303 )
=> ( ! [X304: subst] :
( ( comp @ X304 @ id )
= X304 )
=> ( ! [X305: subst] :
( ( comp @ X305 @ id )
= X305 )
& ! [X306: subst] :
( ( comp @ id @ X306 )
= X306 ) ) ) )
<=> substmonoid_lthm )
& hoaslamnotap_gthm
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& hoaslamnotvar_gthm
& ( ! [X307: term] :
( ( sub @ X307 @ id )
= X307 )
<=> termmset )
& axmap
& ( axscons
<=> ! [X308: subst] :
( ( push @ ( sub @ one @ X308 ) @ ( comp @ sh @ X308 ) )
= X308 ) )
& ! [X309: subst] :
? [X310: d_subst] :
( ( d2subst @ X310 )
= X309 )
& induction2lem_gthm
& hoasapinj1_gthm
& ( hoasinduction_lem2
<=> ! [X311: subst > term > subst > $o,X312: term,X313: term] :
( ~ ! [X314: term,X315: term] :
( ~ ( X311 @ id @ X315 @ id )
| ( X311 @ id @ ( ap @ ( sub @ X315 @ id ) @ X314 ) @ id )
| ~ ( X311 @ id @ X314 @ id ) )
| ( X311 @ id @ ( ap @ X312 @ X313 ) @ id )
| ~ ! [X316: subst,X317: subst,X318: term,X319: subst] :
( ~ ( X311 @ ( comp @ X317 @ X319 ) @ ( sub @ X318 @ X319 ) @ X316 )
| ( X311 @ X317 @ X318 @ ( comp @ X319 @ X316 ) ) )
| ~ ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ~ ( X311 @ X322 @ X321 @ ( comp @ X323 @ X320 ) )
| ( X311 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ~ ( X311 @ id @ X312 @ id )
| ~ ( X311 @ id @ X313 @ id ) ) )
& hoasapnotvar
& hoasinduction_lem1_gthm
& ~ ( var @ ( d2term @ d_one ) )
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ! [X324: term] :
( ( sub @ X324 @ id )
= X324 )
<=> axvarid )
& ( ! [X325: term,X326: term,X327: term,X328: term] :
( ( X325 = X327 )
| ( ( ap @ X325 @ X326 )
!= ( ap @ X327 @ X328 ) ) )
<=> apinj1 )
& ( ( ! [X329: subst > term > subst > $o] :
~ ! [X330: term > $o] :
~ ! [X331: term] :
( ( X329 @ id @ X331 @ id )
= ( X330 @ X331 ) )
=> ( ! [X332: term,X333: term > $o] :
( ~ ! [X334: term] :
( ( X333 @ X334 )
| ~ ( var @ X334 ) )
| ~ ! [X335: term] :
( ( X333 @ ( lam @ X335 ) )
| ~ ! [X336: term] :
( ~ ( X333 @ X336 )
| ( X333 @ ( sub @ X335 @ ( push @ X336 @ id ) ) ) ) )
| ~ ! [X337: term,X338: term] :
( ~ ( X333 @ X338 )
| ~ ( X333 @ X337 )
| ( X333 @ ( ap @ X337 @ X338 ) ) )
| ( X333 @ X332 ) )
=> ( ! [X339: term] :
( ( sub @ X339 @ id )
= X339 )
=> ( ! [X340: subst > term > subst > $o,X341: term,X342: term > $o] :
( ~ ! [X343: subst > term > term] :
( ~ ! [X344: term] :
( ( X340 @ id @ ( X343 @ id @ X344 ) @ id )
| ~ ( X340 @ id @ X344 @ id ) )
| ( X340 @ id @ ( lam @ ( X343 @ sh @ one ) ) @ id )
| ~ ! [X345: subst,X346: term,X347: subst] :
( ( sub @ ( X343 @ X347 @ X346 ) @ X345 )
= ( X343 @ ( comp @ X347 @ X345 ) @ ( sub @ X346 @ X345 ) ) ) )
| ~ ! [X348: term] :
( ( X340 @ id @ X348 @ id )
= ( X342 @ X348 ) )
| ( X342 @ ( lam @ X341 ) )
| ~ ! [X349: term] :
( ~ ( X342 @ X349 )
| ( X342 @ ( sub @ X341 @ ( push @ X349 @ id ) ) ) ) )
=> ! [X350: term,X351: subst > term > subst > $o] :
( ~ ! [X352: term,X353: term] :
( ~ ( X351 @ id @ X353 @ id )
| ~ ( X351 @ id @ X352 @ id )
| ( X351 @ id @ ( ap @ ( sub @ X352 @ id ) @ X353 ) @ id ) )
| ( X351 @ id @ X350 @ id )
| ~ ! [X354: subst > term > term] :
( ~ ! [X355: term,X356: subst,X357: subst] :
( ( sub @ ( X354 @ X356 @ X355 ) @ X357 )
= ( X354 @ ( comp @ X356 @ X357 ) @ ( sub @ X355 @ X357 ) ) )
| ~ ! [X358: term] :
( ~ ( X351 @ id @ X358 @ id )
| ( X351 @ id @ ( X354 @ id @ X358 ) @ id ) )
| ( X351 @ id @ ( lam @ ( X354 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X359: term] :
( ( sub @ X359 @ id )
= X359 )
=> ( ! [X360: subst > term > subst > $o,X361: term] :
( ( X360 @ id @ ( lam @ ( sub @ X361 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X362: subst > term > term] :
( ~ ! [X363: term,X364: subst,X365: subst] :
( ( X362 @ ( comp @ X365 @ X364 ) @ ( sub @ X363 @ X364 ) )
= ( sub @ ( X362 @ X365 @ X363 ) @ X364 ) )
| ~ ! [X366: term] :
( ~ ( X360 @ id @ X366 @ id )
| ( X360 @ id @ ( X362 @ id @ X366 ) @ id ) )
| ( X360 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) )
| ~ ! [X367: term] :
( ( X360 @ id @ ( sub @ X361 @ ( push @ X367 @ id ) ) @ id )
| ~ ( X360 @ id @ X367 @ id ) ) )
=> ! [X368: term,X369: subst > term > subst > $o] :
( ( X369 @ id @ ( lam @ X368 ) @ id )
| ~ ! [X370: subst > term > term] :
( ~ ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X370 @ X372 @ X371 ) @ X373 )
= ( X370 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) ) )
| ~ ! [X374: term] :
( ~ ( X369 @ id @ X374 @ id )
| ( X369 @ id @ ( X370 @ id @ X374 ) @ id ) )
| ( X369 @ id @ ( lam @ ( X370 @ sh @ one ) ) @ id ) )
| ~ ! [X375: term] :
( ( X369 @ id @ ( sub @ X368 @ ( push @ X375 @ id ) ) @ id )
| ~ ( X369 @ id @ X375 @ id ) ) ) ) ) )
& ulamvarind
& hoasinduction_lem2_lthm
& ( hoasinduction_lem2v2
<=> ! [X376: subst > term > subst > $o,X377: term,X378: term,X379: term > $o] :
( ( X379 @ ( ap @ X377 @ X378 ) )
| ~ ! [X380: term] :
( ( X376 @ id @ X380 @ id )
= ( X379 @ X380 ) )
| ~ ! [X381: term,X382: term] :
( ~ ( X376 @ id @ X382 @ id )
| ~ ( X376 @ id @ X381 @ id )
| ( X376 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) )
| ~ ( X379 @ X378 )
| ~ ( X379 @ X377 )
| ~ ! [X383: subst,X384: subst,X385: term,X386: subst] :
( ( X376 @ X386 @ X385 @ ( comp @ X383 @ X384 ) )
| ~ ( X376 @ ( comp @ X386 @ X383 ) @ ( sub @ X385 @ X383 ) @ X384 ) )
| ~ ! [X387: term,X388: subst,X389: subst,X390: subst] :
( ~ ( X376 @ X389 @ X387 @ ( comp @ X390 @ X388 ) )
| ( X376 @ ( comp @ X389 @ X390 ) @ ( sub @ X387 @ X390 ) @ X388 ) ) ) )
& ~ ulamvar1
& hoasinduction_lem3_gthm
& ! [X391: d_term] : ( d_one = X391 )
& ulamvarsh
& hoasapinj2_gthm
& ! [X392: d_term,X393: d_term] :
( ( ( d2term @ X392 )
= ( d2term @ X393 ) )
=> ( X392 = X393 ) )
& ( ( d2subst @ d_id )
= id )
& lamnotvar
& hoasinduction_lem3v2_gthm
& hoasinduction_lem1_lthm
& ( ( ! [X394: subst] :
( ( comp @ id @ X394 )
= X394 )
& ! [X395: subst] :
( ( comp @ X395 @ id )
= X395 ) )
<=> substmonoid )
& ( hoasapinj1
<=> ! [X396: term,X397: term,X398: term,X399: term] :
( ( X396 = X398 )
| ( ( ap @ ( sub @ X396 @ id ) @ X397 )
!= ( ap @ ( sub @ X398 @ id ) @ X399 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction
<=> ! [X400: term,X401: subst > term > subst > $o] :
( ~ ! [X402: term,X403: term] :
( ~ ( X401 @ id @ X402 @ id )
| ( X401 @ id @ ( ap @ ( sub @ X402 @ id ) @ X403 ) @ id )
| ~ ( X401 @ id @ X403 @ id ) )
| ~ ! [X404: term] :
( ~ ( var @ ( sub @ X404 @ id ) )
| ( X401 @ id @ X404 @ id ) )
| ~ ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( X401 @ ( comp @ X407 @ X408 ) @ ( sub @ X405 @ X408 ) @ X406 )
| ~ ( X401 @ X407 @ X405 @ ( comp @ X408 @ X406 ) ) )
| ~ ! [X409: term,X410: subst,X411: subst,X412: subst] :
( ( X401 @ X412 @ X409 @ ( comp @ X411 @ X410 ) )
| ~ ( X401 @ ( comp @ X412 @ X411 ) @ ( sub @ X409 @ X411 ) @ X410 ) )
| ( X401 @ id @ X400 @ id )
| ~ ! [X413: subst > term > term] :
( ~ ! [X414: term,X415: subst,X416: subst] :
( ( X413 @ ( comp @ X416 @ X415 ) @ ( sub @ X414 @ X415 ) )
= ( sub @ ( X413 @ X416 @ X414 ) @ X415 ) )
| ~ ! [X417: term] :
( ~ ( X401 @ id @ X417 @ id )
| ( X401 @ id @ ( X413 @ id @ X417 ) @ id ) )
| ( X401 @ id @ ( lam @ ( X413 @ sh @ one ) ) @ id ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoaslamnotap_lthm
& ( ! [X418: term] :
~ ! [X419: subst > term > term] :
( ( sub @ X418 @ ( push @ one @ sh ) )
!= ( X419 @ sh @ one ) )
<=> hoasinduction_lem3b )
& induction2_gthm
& pushprop_lthm
& axclos
& ( ( ! [X420: subst > term > subst > $o] :
~ ! [X421: term > $o] :
~ ! [X422: term] :
( ( X420 @ id @ X422 @ id )
= ( X421 @ X422 ) )
=> ( ! [X423: term > $o,X424: term] :
( ~ ! [X425: term] :
( ( X423 @ ( lam @ X425 ) )
| ~ ! [X426: term] :
( ~ ( X423 @ X426 )
| ( X423 @ ( sub @ X425 @ ( push @ X426 @ id ) ) ) ) )
| ~ ! [X427: term,X428: term] :
( ~ ( X423 @ X428 )
| ~ ( X423 @ X427 )
| ( X423 @ ( ap @ X427 @ X428 ) ) )
| ( X423 @ X424 )
| ~ ! [X429: term] :
( ~ ( var @ X429 )
| ( X423 @ X429 ) ) )
=> ( ! [X430: term] :
( ( sub @ X430 @ id )
= X430 )
=> ( ! [X431: subst > term > subst > $o,X432: term,X433: term > $o] :
( ~ ! [X434: term] :
( ( X433 @ ( sub @ X432 @ ( push @ X434 @ id ) ) )
| ~ ( X433 @ X434 ) )
| ( X433 @ ( lam @ X432 ) )
| ~ ! [X435: term] :
( ( X431 @ id @ X435 @ id )
= ( X433 @ X435 ) )
| ~ ! [X436: subst > term > term] :
( ( X431 @ id @ ( lam @ ( X436 @ sh @ one ) ) @ id )
| ~ ! [X437: subst,X438: term,X439: subst] :
( ( sub @ ( X436 @ X437 @ X438 ) @ X439 )
= ( X436 @ ( comp @ X437 @ X439 ) @ ( sub @ X438 @ X439 ) ) )
| ~ ! [X440: term] :
( ( X431 @ id @ ( X436 @ id @ X440 ) @ id )
| ~ ( X431 @ id @ X440 @ id ) ) ) )
=> ! [X441: term,X442: subst > term > subst > $o] :
( ~ ! [X443: term,X444: term] :
( ~ ( X442 @ id @ X443 @ id )
| ( X442 @ id @ ( ap @ ( sub @ X443 @ id ) @ X444 ) @ id )
| ~ ( X442 @ id @ X444 @ id ) )
| ( X442 @ id @ X441 @ id )
| ~ ! [X445: subst,X446: subst,X447: term,X448: subst] :
( ~ ( X442 @ ( comp @ X446 @ X445 ) @ ( sub @ X447 @ X445 ) @ X448 )
| ( X442 @ X446 @ X447 @ ( comp @ X445 @ X448 ) ) )
| ~ ! [X449: term] :
( ( X442 @ id @ X449 @ id )
| ~ ( var @ ( sub @ X449 @ id ) ) )
| ~ ! [X450: subst,X451: term,X452: subst,X453: subst] :
( ~ ( X442 @ X452 @ X451 @ ( comp @ X453 @ X450 ) )
| ( X442 @ ( comp @ X452 @ X453 ) @ ( sub @ X451 @ X453 ) @ X450 ) )
| ~ ! [X454: subst > term > term] :
( ~ ! [X455: term,X456: subst,X457: subst] :
( ( X454 @ ( comp @ X456 @ X457 ) @ ( sub @ X455 @ X457 ) )
= ( sub @ ( X454 @ X456 @ X455 ) @ X457 ) )
| ~ ! [X458: term] :
( ~ ( X442 @ id @ X458 @ id )
| ( X442 @ id @ ( X454 @ id @ X458 ) @ id ) )
| ( X442 @ id @ ( lam @ ( X454 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_lthm_3 )
& ( hoasinduction_lem3aaa
<=> ! [X459: term,X460: subst > term > subst > $o] :
( ~ ! [X461: term,X462: subst > term > term] :
( ~ ! [X463: subst,X464: term,X465: subst] :
( ( sub @ X461 @ ( push @ ( sub @ X464 @ X465 ) @ ( comp @ X463 @ X465 ) ) )
= ( X462 @ ( comp @ X463 @ X465 ) @ ( sub @ X464 @ X465 ) ) )
| ~ ! [X466: term] :
( ( X460 @ id @ ( X462 @ id @ X466 ) @ id )
| ~ ( X460 @ id @ X466 @ id ) )
| ~ ! [X467: subst,X468: term,X469: subst] :
( ( sub @ ( X462 @ X467 @ X468 ) @ X469 )
= ( sub @ ( sub @ X461 @ ( push @ X468 @ X467 ) ) @ X469 ) )
| ( X460 @ id @ ( lam @ ( X462 @ sh @ one ) ) @ id ) )
| ~ ! [X470: term] :
( ~ ( X460 @ id @ X470 @ id )
| ( X460 @ id @ ( sub @ X459 @ ( push @ X470 @ id ) ) @ id ) )
| ( X460 @ id @ ( lam @ ( sub @ X459 @ ( push @ one @ sh ) ) ) @ id ) ) )
& ( hoasinduction_lthm
<=> ( ! [X471: term > $o,X472: term] :
( ( X471 @ X472 )
| ~ ! [X473: term] :
( ~ ! [X474: term] :
( ~ ( X471 @ X474 )
| ( X471 @ ( sub @ X473 @ ( push @ X474 @ id ) ) ) )
| ( X471 @ ( lam @ X473 ) ) )
| ~ ! [X475: term,X476: term] :
( ( X471 @ ( ap @ X476 @ X475 ) )
| ~ ( X471 @ X476 )
| ~ ( X471 @ X475 ) )
| ~ ! [X477: term] :
( ( X471 @ X477 )
| ~ ( var @ X477 ) ) )
=> ( ! [X478: term,X479: subst > term > subst > $o,X480: term] :
( ( X479 @ id @ ( ap @ X478 @ X480 ) @ id )
| ~ ! [X481: term,X482: subst,X483: subst,X484: subst] :
( ( X479 @ ( comp @ X483 @ X484 ) @ ( sub @ X481 @ X484 ) @ X482 )
| ~ ( X479 @ X483 @ X481 @ ( comp @ X484 @ X482 ) ) )
| ~ ( X479 @ id @ X478 @ id )
| ~ ( X479 @ id @ X480 @ id )
| ~ ! [X485: subst,X486: subst,X487: term,X488: subst] :
( ( X479 @ X486 @ X487 @ ( comp @ X488 @ X485 ) )
| ~ ( X479 @ ( comp @ X486 @ X488 ) @ ( sub @ X487 @ X488 ) @ X485 ) )
| ~ ! [X489: term,X490: term] :
( ( X479 @ id @ ( ap @ ( sub @ X490 @ id ) @ X489 ) @ id )
| ~ ( X479 @ id @ X490 @ id )
| ~ ( X479 @ id @ X489 @ id ) ) )
=> ( ! [X491: subst > term > subst > $o,X492: term] :
( ~ ! [X493: subst > term > term] :
( ~ ! [X494: term] :
( ( X491 @ id @ ( X493 @ id @ X494 ) @ id )
| ~ ( X491 @ id @ X494 @ id ) )
| ~ ! [X495: subst,X496: term,X497: subst] :
( ( X493 @ ( comp @ X495 @ X497 ) @ ( sub @ X496 @ X497 ) )
= ( sub @ ( X493 @ X495 @ X496 ) @ X497 ) )
| ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id ) )
| ( X491 @ id @ ( lam @ X492 ) @ id )
| ~ ! [X498: term] :
( ( X491 @ id @ ( sub @ X492 @ ( push @ X498 @ id ) ) @ id )
| ~ ( X491 @ id @ X498 @ id ) )
| ~ ! [X499: subst,X500: term,X501: subst,X502: subst] :
( ~ ( X491 @ X501 @ X500 @ ( comp @ X502 @ X499 ) )
| ( X491 @ ( comp @ X501 @ X502 ) @ ( sub @ X500 @ X502 ) @ X499 ) )
| ~ ! [X503: subst,X504: term,X505: subst,X506: subst] :
( ~ ( X491 @ ( comp @ X503 @ X506 ) @ ( sub @ X504 @ X506 ) @ X505 )
| ( X491 @ X503 @ X504 @ ( comp @ X506 @ X505 ) ) ) )
=> ! [X507: subst > term > subst > $o,X508: term] :
( ( X507 @ id @ X508 @ id )
| ~ ! [X509: subst,X510: subst,X511: subst,X512: term] :
( ( X507 @ X511 @ X512 @ ( comp @ X510 @ X509 ) )
| ~ ( X507 @ ( comp @ X511 @ X510 ) @ ( sub @ X512 @ X510 ) @ X509 ) )
| ~ ! [X513: subst,X514: subst,X515: subst,X516: term] :
( ( X507 @ ( comp @ X513 @ X515 ) @ ( sub @ X516 @ X515 ) @ X514 )
| ~ ( X507 @ X513 @ X516 @ ( comp @ X515 @ X514 ) ) )
| ~ ! [X517: term] :
( ~ ( var @ ( sub @ X517 @ id ) )
| ( X507 @ id @ X517 @ id ) )
| ~ ! [X518: term,X519: term] :
( ~ ( X507 @ id @ X519 @ id )
| ( X507 @ id @ ( ap @ ( sub @ X519 @ id ) @ X518 ) @ id )
| ~ ( X507 @ id @ X518 @ id ) )
| ~ ! [X520: subst > term > term] :
( ~ ! [X521: term] :
( ( X507 @ id @ ( X520 @ id @ X521 ) @ id )
| ~ ( X507 @ id @ X521 @ id ) )
| ~ ! [X522: subst,X523: term,X524: subst] :
( ( X520 @ ( comp @ X522 @ X524 ) @ ( sub @ X523 @ X524 ) )
= ( sub @ ( X520 @ X522 @ X523 ) @ X524 ) )
| ( X507 @ id @ ( lam @ ( X520 @ sh @ one ) ) @ id ) ) ) ) ) ) )
& hoasapnotvar_gthm
& ( hoaslamnotap
<=> ! [X525: term,X526: subst > term > term,X527: term] :
( ~ ! [X528: subst,X529: term,X530: subst] :
( ( sub @ ( X526 @ X528 @ X529 ) @ X530 )
= ( X526 @ ( comp @ X528 @ X530 ) @ ( sub @ X529 @ X530 ) ) )
| ( ( ap @ ( sub @ X527 @ id ) @ X525 )
!= ( lam @ ( X526 @ sh @ one ) ) ) ) )
& ( hoasinduction_lem3a
<=> ! [X531: subst > term > subst > $o,X532: term] :
( ~ ! [X533: subst > term > term] :
( ( X531 @ id @ ( lam @ ( X533 @ sh @ one ) ) @ id )
| ~ ! [X534: term,X535: subst,X536: subst] :
( ( sub @ ( X533 @ X536 @ X534 ) @ X535 )
= ( X533 @ ( comp @ X536 @ X535 ) @ ( sub @ X534 @ X535 ) ) )
| ~ ! [X537: term] :
( ( X531 @ id @ ( X533 @ id @ X537 ) @ id )
| ~ ( X531 @ id @ X537 @ id ) ) )
| ( X531 @ id @ ( lam @ X532 ) @ id )
| ~ ! [X538: term] :
( ( X531 @ id @ ( sub @ X532 @ ( push @ X538 @ id ) ) @ id )
| ~ ( X531 @ id @ X538 @ id ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X539: term] :
? [X540: d_term] :
( ( d2term @ X540 )
= X539 )
& pushprop_lem1_gthm
& ( ( ! [X541: subst,X542: term] :
( ( sub @ one @ ( push @ X542 @ X541 ) )
= X542 )
=> ( ! [X543: subst,X544: term] :
( ( comp @ sh @ ( push @ X544 @ X543 ) )
= X543 )
=> ! [X545: term,X546: term > $o,X547: term > $o,X548: subst,X549: term] :
( ~ ( X546 @ X545 )
| ( X547 @ ( sub @ X545 @ ( push @ X549 @ X548 ) ) ) ) ) )
<=> pushprop_lem1_lthm ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( hoasinduction_lem2_gthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& apnotvar
& hoaslamnotvar_lthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_lem3 )
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& ( axidl
<=> ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f_lthm )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X5: d_subst] : ( d_id = X5 )
& hoasapnotvar_lthm
& ( hoasapinj2_lthm
<=> ( ! [X15: term,X13: term,X20: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
=> ! [X15: term,X13: term,X19: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) ) )
& ( hoaslaminj
<=> ! [X18: subst > term > term,X31: subst > term > term,X32: subst,X33: term] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
& ~ lamnotap
& ( 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 )
=> ( ! [X21: term,X10: term > $o] :
( ( X10 @ X21 )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) ) )
=> ! [X17: subst,X16: term,X10: term > $o] :
( ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) ) ) ) ) ) ) )
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( hoasapinj1_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X15: term,X13: term,X20: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
=> ! [X15: term,X19: term,X13: term,X20: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) ) ) )
& hoasinduction_lem3a_gthm
& pushprop_lem1v2_gthm
& ( ! [X15: term,X14: subst,X10: term > $o,X26: term > $o,X13: term] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) )
<=> pushprop_lem1 )
& pushprop_lem2v2_lthm
& hoasinduction_lem1
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X14: subst,X11: term > $o,X13: term,X10: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ( X11 @ one )
| ~ ( X10 @ X13 ) ) )
<=> pushprop_lem1v2_lthm )
& ( ! [X19: term,X15: term,X20: term,X13: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
<=> apinj2 )
& axabs
& ( one
= ( d2term @ d_one ) )
& pushprop_lthm_orig
& ( induction2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X16: term,X17: subst,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) ) )
=> ! [X22: term,X10: term > $o] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) ) ) ) ) )
& pushprop_gthm
& ( ! [X13: term,X15: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) )
<=> laminj )
& ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ 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 ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa_lthm )
& ( axidr
<=> ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
& ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& ( ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [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 @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ( X10 @ id @ X30 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X48: term,X11: term > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& hoaslaminj_gthm
& ( hoasinduction_p_and_p_prime
= ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) )
& ( ! [X13: term,X11: term > $o,X10: term > $o,X14: subst] :
( ~ ( X10 @ X13 )
| ( X11 @ one )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
<=> pushprop_lem1v2 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [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 ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ id ) ) ) )
<=> hoasinduction_lem3_lthm )
& substmonoid_gthm
& ( axshiftcons
<=> ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 ) )
& hoasinduction_lem1v2_gthm
& ( hoasapinj2
<=> ! [X19: term,X13: term,X15: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
& ( ! [X13: term,X10: term > $o,X14: subst] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0 )
& hoasinduction_lem3b_gthm
& ( ! [X10: term > $o,X22: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) )
<=> induction2 )
& ( ( ^ [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
= pushprop_p_and_p_prime )
& ( ! [X11: term > $o,X48: term,X10: subst > term > subst > $o] :
( ( X11 @ ( lam @ X48 ) )
| ~ ! [X13: term,X14: subst,X25: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
<=> hoasinduction_lem3v2 )
& pushprop
& ( induction
<=> ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X21 ) ) )
& ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [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 )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa )
& ( ! [X13: term,X15: term] :
( ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) )
| ( X13 = X15 ) )
<=> shinj )
& pushprop_lem2v2
& axassoc
& termmset_gthm
& axvarshift
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0 )
& pushprop_lem0_gthm
& ( ! [X29: term,X10: subst > term > subst > $o,X11: term > $o] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
<=> hoasinduction_lem3v2a )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& pushprop_lem3v2_lthm
& ( ! [X17: subst,X16: term,X10: term > $o] :
( ~ ! [X15: term,X13: 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 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) ) )
<=> induction2lem )
& pushprop_lem3v2
& axapp
& pushprop_lem2v2_gthm
& ! [X7: d_subst,X6: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( hoasinduction_lem3b_lthm
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& hoasinduction_lem1v2
& hoasinduction_lem2v2_gthm
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X29: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [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 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X14: subst,X13: term,X10: term > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& hoasinduction_gthm
& hoaslamnotvar
& ( hoaslaminj_lthm
<=> ( ! [X14: subst,X13: term] :
( ( 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 ) ) )
=> ! [X33: term,X18: subst > term > term,X32: subst,X31: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) )
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) ) ) )
<=> substmonoid_lthm )
& hoaslamnotap_gthm
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& hoaslamnotvar_gthm
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& axmap
& ( axscons
<=> ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 ) )
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& induction2lem_gthm
& hoasapinj1_gthm
& ( hoasinduction_lem2
<=> ! [X10: subst > term > subst > $o,X23: term,X24: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ( X10 @ id @ X24 @ id ) ) )
& hoasapnotvar
& hoasinduction_lem1_gthm
& ~ ( var @ ( d2term @ d_one ) )
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& ( ! [X13: term,X19: term,X15: term,X20: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
<=> apinj1 )
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) )
=> ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: 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] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [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 ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
=> ! [X43: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) ) ) )
& ulamvarind
& hoasinduction_lem2_lthm
& ( hoasinduction_lem2v2
<=> ! [X10: subst > term > subst > $o,X44: term,X45: term,X11: term > $o] :
( ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ( X11 @ X45 )
| ~ ( X11 @ X44 )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) )
& ~ ulamvar1
& hoasinduction_lem3_gthm
& ! [X1: d_term] : ( d_one = X1 )
& ulamvarsh
& hoasapinj2_gthm
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& ( ( d2subst @ d_id )
= id )
& lamnotvar
& hoasinduction_lem3v2_gthm
& hoasinduction_lem1_lthm
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
<=> substmonoid )
& ( hoasapinj1
<=> ! [X13: term,X19: term,X15: term,X20: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction
<=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X25: subst,X26: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [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 ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoaslamnotap_lthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b )
& induction2_gthm
& pushprop_lthm
& axclos
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) ) )
<=> hoasinduction_lthm_3 )
& ( hoasinduction_lem3aaa
<=> ! [X34: term,X10: subst > term > subst > $o] :
( ~ ! [X35: term,X18: subst > term > term] :
( ~ ! [X39: subst,X40: term,X41: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [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 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id ) ) )
& ( hoasinduction_lthm
<=> ( ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) ) )
=> ( ! [X23: term,X10: subst > term > subst > $o,X24: term] :
( ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X25: subst,X14: subst,X13: term,X26: 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: subst > term > subst > $o,X27: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X14: subst,X13: term,X25: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ( X10 @ id @ X28 @ id )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) ) )
& hoasapnotvar_gthm
& ( hoaslamnotap
<=> ! [X47: term,X18: subst > term > term,X46: 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 ) ) ) )
& ( hoasinduction_lem3a
<=> ! [X10: subst > term > subst > $o,X43: term] :
( ~ ! [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 @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& pushprop_lem1_gthm
& ( ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X13: term,X10: term > $o,X26: term > $o,X14: subst,X15: term] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) ) )
<=> pushprop_lem1_lthm ) ),
file('/export/starexec/sandbox/tmp/tmp.tVjixEyHtK/DTF2THF_10797.p',alg444_1) ).
thf(f1310,plain,
! [X240: term] :
( ( d2term @ ( sK640 @ X240 ) )
= X240 ),
inference(cnf_transformation,[status(thm)],[f753]) ).
thf(f3842,plain,
( ( ( d2term @ d_one )
!= ( sK610 @ sK612 @ sK613 ) )
| spl652_309 ),
inference(forward_demodulation,[status(thm)],[f3147,f3829]) ).
thf(f3147,plain,
( ( ( sK610 @ sK612 @ sK613 )
!= ( sK611 @ sK612 @ sK613 ) )
| spl652_309 ),
inference(avatar_component_clause,[status(thm)],[f3146]) ).
thf(f3146,definition,
( spl652_309
<=> ( ( sK610 @ sK612 @ sK613 )
= ( sK611 @ sK612 @ sK613 ) ) ),
introduced(definition,[new_symbols(naming,[spl652_309])],[avatar_definition]) ).
thf(f3840,plain,
spl652_154,
inference(avatar_contradiction_clause,[status(thm)],[f3839]) ).
thf(f3839,plain,
( $false
| spl652_154 ),
inference(subsumption_resolution,[status(thm)],[f3832,f3829]) ).
thf(f3832,plain,
( ( ( d2term @ d_one )
!= ( sK111 @ sK112 @ sK113 ) )
| spl652_154 ),
inference(backward_demodulation,[status(thm)],[f2494,f3829]) ).
thf(f2494,plain,
( ( ( sK111 @ sK112 @ sK113 )
!= ( sK110 @ sK112 @ sK113 ) )
| spl652_154 ),
inference(avatar_component_clause,[status(thm)],[f2493]) ).
thf(f2493,definition,
( spl652_154
<=> ( ( sK111 @ sK112 @ sK113 )
= ( sK110 @ sK112 @ sK113 ) ) ),
introduced(definition,[new_symbols(naming,[spl652_154])],[avatar_definition]) ).
thf(f3148,plain,
( ~ spl652_309
| spl652_3 ),
inference(avatar_split_clause,[status(thm)],[f1336,f1914,f3146]) ).
thf(f1914,definition,
( spl652_3
<=> ( hoaslaminj = $true ) ),
introduced(definition,[new_symbols(naming,[spl652_3])],[avatar_definition]) ).
thf(f1336,plain,
( ( hoaslaminj = $true )
| ( ( sK610 @ sK612 @ sK613 )
!= ( sK611 @ sK612 @ sK613 ) ) ),
inference(cnf_transformation,[status(thm)],[f753]) ).
thf(f2495,plain,
( ~ spl652_3
| ~ spl652_154 ),
inference(avatar_split_clause,[status(thm)],[f756,f2493,f1914]) ).
thf(f756,plain,
( ( ( sK111 @ sK112 @ sK113 )
!= ( sK110 @ sK112 @ sK113 ) )
| ( hoaslaminj != $true ) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( hoaslaminj != $true )
| ( ! [X1: subst,X2: subst,X3: term] :
( ( sK110 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( sK110 @ X2 @ X3 ) @ X1 ) )
& ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK110 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK111 @ Y0 @ Y1 ) ) )
& ( ( sK111 @ sK112 @ sK113 )
!= ( sK110 @ sK112 @ sK113 ) )
& ! [X7: subst,X8: subst,X9: term] :
( ( sub @ ( sK111 @ X8 @ X9 ) @ X7 )
= ( sK111 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) ) )
& ( ( hoaslaminj = $true )
| ! [X10: subst > term > term] :
( ( ( X10 @ ( comp @ ( sK115 @ X10 ) @ ( sK114 @ X10 ) ) @ ( sub @ ( sK116 @ X10 ) @ ( sK114 @ X10 ) ) )
!= ( sub @ ( X10 @ ( sK115 @ X10 ) @ ( sK116 @ X10 ) ) @ ( sK114 @ X10 ) ) )
| ! [X14: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X10 @ Y0 @ Y1 ) )
!= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X14 @ Y0 @ Y1 ) ) )
| ! [X15: subst,X16: term] :
( ( X10 @ X15 @ X16 )
= ( X14 @ X15 @ X16 ) )
| ( ( sub @ ( X14 @ ( sK118 @ X14 ) @ ( sK119 @ X14 ) ) @ ( sK117 @ X14 ) )
!= ( X14 @ ( comp @ ( sK118 @ X14 ) @ ( sK117 @ X14 ) ) @ ( sub @ ( sK119 @ X14 ) @ ( sK117 @ X14 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111,sK112,sK113,sK114,sK115,sK116,sK117,sK118,sK119])],[f128,f133,f132,f131,f130,f129]) ).
thf(f129,plain,
( ? [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
& ? [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
& ? [X5: subst,X6: term] :
( ( X0 @ X5 @ X6 )
!= ( X4 @ X5 @ X6 ) )
& ! [X7: subst,X8: subst,X9: term] :
( ( sub @ ( X4 @ X8 @ X9 ) @ X7 )
= ( X4 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) ) )
=> ( ! [X3: term,X2: subst,X1: subst] :
( ( sK110 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( sK110 @ X2 @ X3 ) @ X1 ) )
& ? [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK110 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
& ? [X6: term,X5: subst] :
( ( sK110 @ X5 @ X6 )
!= ( X4 @ X5 @ X6 ) )
& ! [X7: subst,X8: subst,X9: term] :
( ( sub @ ( X4 @ X8 @ X9 ) @ X7 )
= ( X4 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f130,plain,
( ? [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK110 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
& ? [X6: term,X5: subst] :
( ( sK110 @ X5 @ X6 )
!= ( X4 @ X5 @ X6 ) )
& ! [X7: subst,X8: subst,X9: term] :
( ( sub @ ( X4 @ X8 @ X9 ) @ X7 )
= ( X4 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK110 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK111 @ Y0 @ Y1 ) ) )
& ? [X6: term,X5: subst] :
( ( sK111 @ X5 @ X6 )
!= ( sK110 @ X5 @ X6 ) )
& ! [X9: term,X8: subst,X7: subst] :
( ( sub @ ( sK111 @ X8 @ X9 ) @ X7 )
= ( sK111 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f131,plain,
( ? [X6: term,X5: subst] :
( ( sK111 @ X5 @ X6 )
!= ( sK110 @ X5 @ X6 ) )
=> ( ( sK111 @ sK112 @ sK113 )
!= ( sK110 @ sK112 @ sK113 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f132,plain,
! [X10: subst > term > term] :
( ? [X11: subst,X12: subst,X13: term] :
( ( X10 @ ( comp @ X12 @ X11 ) @ ( sub @ X13 @ X11 ) )
!= ( sub @ ( X10 @ X12 @ X13 ) @ X11 ) )
=> ( ( X10 @ ( comp @ ( sK115 @ X10 ) @ ( sK114 @ X10 ) ) @ ( sub @ ( sK116 @ X10 ) @ ( sK114 @ X10 ) ) )
!= ( sub @ ( X10 @ ( sK115 @ X10 ) @ ( sK116 @ X10 ) ) @ ( sK114 @ X10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f133,plain,
! [X14: subst > term > term] :
( ? [X17: subst,X18: subst,X19: term] :
( ( sub @ ( X14 @ X18 @ X19 ) @ X17 )
!= ( X14 @ ( comp @ X18 @ X17 ) @ ( sub @ X19 @ X17 ) ) )
=> ( ( sub @ ( X14 @ ( sK118 @ X14 ) @ ( sK119 @ X14 ) ) @ ( sK117 @ X14 ) )
!= ( X14 @ ( comp @ ( sK118 @ X14 ) @ ( sK117 @ X14 ) ) @ ( sub @ ( sK119 @ X14 ) @ ( sK117 @ X14 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f128,plain,
( ( ( hoaslaminj != $true )
| ? [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
& ? [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
& ? [X5: subst,X6: term] :
( ( X0 @ X5 @ X6 )
!= ( X4 @ X5 @ X6 ) )
& ! [X7: subst,X8: subst,X9: term] :
( ( sub @ ( X4 @ X8 @ X9 ) @ X7 )
= ( X4 @ ( comp @ X8 @ X7 ) @ ( sub @ X9 @ X7 ) ) ) ) ) )
& ( ( hoaslaminj = $true )
| ! [X10: subst > term > term] :
( ? [X11: subst,X12: subst,X13: term] :
( ( X10 @ ( comp @ X12 @ X11 ) @ ( sub @ X13 @ X11 ) )
!= ( sub @ ( X10 @ X12 @ X13 ) @ X11 ) )
| ! [X14: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X10 @ Y0 @ Y1 ) )
!= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X14 @ Y0 @ Y1 ) ) )
| ! [X15: subst,X16: term] :
( ( X10 @ X15 @ X16 )
= ( X14 @ X15 @ X16 ) )
| ? [X17: subst,X18: subst,X19: term] :
( ( sub @ ( X14 @ X18 @ X19 ) @ X17 )
!= ( X14 @ ( comp @ X18 @ X17 ) @ ( sub @ X19 @ X17 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( hoaslaminj != $true )
| ? [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
& ? [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
& ? [X8: subst,X9: term] :
( ( X0 @ X8 @ X9 )
!= ( X4 @ X8 @ X9 ) )
& ! [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) ) ) ) )
& ( ( hoaslaminj = $true )
| ! [X0: subst > term > term] :
( ? [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
!= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
| ! [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
!= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
| ! [X8: subst,X9: term] :
( ( X0 @ X8 @ X9 )
= ( X4 @ X8 @ X9 ) )
| ? [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
!= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: subst > term > term] :
( ? [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
!= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
| ! [X4: subst > term > term] :
( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
!= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
| ! [X8: subst,X9: term] :
( ( X0 @ X8 @ X9 )
= ( X4 @ X8 @ X9 ) )
| ? [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
!= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) ) ) )
<~> ( hoaslaminj = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: subst > term > term] :
( ! [X4: subst > term > term] :
( ! [X8: subst,X9: term] :
( ( X0 @ X8 @ X9 )
= ( X4 @ X8 @ X9 ) )
| ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
!= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
| ? [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
!= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) ) )
| ? [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
!= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) ) )
<~> ( hoaslaminj = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
=> ! [X8: subst,X9: term] :
( ( X0 @ X8 @ X9 )
= ( X4 @ X8 @ X9 ) ) ) ) )
<=> ( hoaslaminj = $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X0 @ Y0 @ Y1 ) )
= ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X4 @ Y0 @ Y1 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) )
<=> ( hoaslaminj = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: subst > term > term] :
( ( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X6 @ X7 ) @ X5 )
= ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X4 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X0 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X18: subst > term > term] :
( ( ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ! [X49: subst > term > term] :
( ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X49 @ X14 @ X13 ) @ X25 )
= ( X49 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X49 @ X14 @ X13 ) )
= ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) ) )
=> ! [X14: subst,X13: term] :
( ( X18 @ X14 @ X13 )
= ( X49 @ X14 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X18: subst > term > term] :
( ( ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ! [X49: subst > term > term] :
( ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X49 @ X14 @ X13 ) @ X25 )
= ( X49 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X49 @ X14 @ X13 ) )
= ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) ) )
=> ! [X14: subst,X13: term] :
( ( X18 @ X14 @ X13 )
= ( X49 @ X14 @ X13 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox/tmp/tmp.tVjixEyHtK/DTF2THF_10797.p',hoaslaminj) ).
%------------------------------------------------------------------------------
%----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/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 09:01:30 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.07/0.31 % Domain : Software Verification
% 0.07/0.31 % Problem : Benchmark: ALG444^1, Active target: hoaslaminj
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Kon26]
% 0.07/0.31 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : ? v9.3.0
% 0.07/0.31 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.07/0.31 % Number of atoms : 258 ( 132 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 248 ( 129 avg)
% 0.07/0.31 % Number of connectives : 2604 ( 333 ~; 306 |; 129 &;1739 @)
% 0.07/0.31 % ( 56 <=>; 41 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 151 ( 76 avg)
% 0.07/0.31 % Number of types : 5 ( 4 usr)
% 0.07/0.31 % Number of type conns : 226 ( 226 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.07/0.31 % Number of variables : 564 ( 12 ^; 550 !; 2 ?; 564 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments :
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(term_type,type,
% 0.07/0.31 term: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(subst_type,type,
% 0.07/0.31 subst: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(one_decl,type,
% 0.07/0.31 one: term ).
% 0.07/0.31
% 0.07/0.31 thf(ap_decl,type,
% 0.07/0.31 ap: term > term > term ).
% 0.07/0.31
% 0.07/0.31 thf(lam_decl,type,
% 0.07/0.31 lam: term > term ).
% 0.07/0.31
% 0.07/0.31 thf(sub_decl,type,
% 0.07/0.31 sub: term > subst > term ).
% 0.07/0.31
% 0.07/0.31 thf(id_decl,type,
% 0.07/0.31 id: subst ).
% 0.07/0.31
% 0.07/0.31 thf(sh_decl,type,
% 0.07/0.31 sh: subst ).
% 0.07/0.31
% 0.07/0.31 thf(push_decl,type,
% 0.07/0.31 push: term > subst > subst ).
% 0.07/0.31
% 0.07/0.31 thf(comp_decl,type,
% 0.07/0.31 comp: subst > subst > subst ).
% 0.07/0.31
% 0.07/0.31 thf(var_decl,type,
% 0.07/0.31 var: term > $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1v2_decl,type,
% 0.07/0.31 pushprop_lem1v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1_gthm_decl,type,
% 0.07/0.31 pushprop_lem1_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axmap_decl,type,
% 0.07/0.31 axmap: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem0_gthm_decl,type,
% 0.07/0.31 pushprop_lem0_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(shinj_decl,type,
% 0.07/0.31 shinj: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem1v2_decl,type,
% 0.07/0.31 hoasinduction_lem1v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem1v2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasap_decl,type,
% 0.07/0.31 hoasap: subst > term > subst > term > term ).
% 0.07/0.31
% 0.07/0.31 thf(induction2lem_decl,type,
% 0.07/0.31 induction2lem: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2_f_decl,type,
% 0.07/0.31 hoasinduction_lem3v2_f: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axvarshift_decl,type,
% 0.07/0.31 axvarshift: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj2_decl,type,
% 0.07/0.31 hoasapinj2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapnotvar_gthm_decl,type,
% 0.07/0.31 hoasapnotvar_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj1_decl,type,
% 0.07/0.31 hoasapinj1: $o ).
% 0.07/0.31
% 0.07/0.31 thf(ulamvar1_decl,type,
% 0.07/0.31 ulamvar1: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction2lem_lthm_decl,type,
% 0.07/0.31 induction2lem_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem3v2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(apnotvar_decl,type,
% 0.07/0.31 apnotvar: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lthm_orig_decl,type,
% 0.07/0.31 pushprop_lthm_orig: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3v2_f_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lthm_decl,type,
% 0.07/0.31 hoasinduction_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.07/0.31 hoasinduction_no_psi_cond_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslaminj_decl,type,
% 0.07/0.31 hoaslaminj: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3aaa_decl,type,
% 0.07/0.31 hoasinduction_lem3aaa: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction2lem_gthm_decl,type,
% 0.07/0.31 induction2lem_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3aa_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3_decl,type,
% 0.07/0.31 hoasinduction_lem3: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem2_decl,type,
% 0.07/0.31 hoasinduction_lem2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(termmset_lthm_decl,type,
% 0.07/0.31 termmset_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem1_decl,type,
% 0.07/0.31 hoasinduction_lem1: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotap_lthm_decl,type,
% 0.07/0.31 hoaslamnotap_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1v2_lthm_decl,type,
% 0.07/0.31 pushprop_lem1v2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapnotvar_decl,type,
% 0.07/0.31 hoasapnotvar: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem0_decl,type,
% 0.07/0.31 hoasinduction_lem0: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_decl,type,
% 0.07/0.31 hoasinduction: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_gthm_decl,type,
% 0.07/0.31 hoasinduction_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axapp_decl,type,
% 0.07/0.31 axapp: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotvar_lthm_decl,type,
% 0.07/0.31 hoaslamnotvar_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem3v2_lthm_decl,type,
% 0.07/0.31 pushprop_lem3v2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3b_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(ulamvarind_decl,type,
% 0.07/0.31 ulamvarind: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction_decl,type,
% 0.07/0.31 induction: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3a_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(termmset_gthm_decl,type,
% 0.07/0.31 termmset_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3aa_decl,type,
% 0.07/0.31 hoasinduction_lem3aa: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1v2_gthm_decl,type,
% 0.07/0.31 pushprop_lem1v2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotap_gthm_decl,type,
% 0.07/0.31 hoaslamnotap_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotvar_gthm_decl,type,
% 0.07/0.31 hoaslamnotvar_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem3b_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem2v2_decl,type,
% 0.07/0.31 pushprop_lem2v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem3a_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axclos_decl,type,
% 0.07/0.31 axclos: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axassoc_decl,type,
% 0.07/0.31 axassoc: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem2v2_decl,type,
% 0.07/0.31 hoasinduction_lem2v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lthm_decl,type,
% 0.07/0.31 pushprop_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(apinj2_decl,type,
% 0.07/0.31 apinj2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(apinj1_decl,type,
% 0.07/0.31 apinj1: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj2_lthm_decl,type,
% 0.07/0.31 hoasapinj2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2a_decl,type,
% 0.07/0.31 hoasinduction_lem3v2a: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj1_lthm_decl,type,
% 0.07/0.31 hoasapinj1_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslaminj_lthm_decl,type,
% 0.07/0.31 hoaslaminj_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axvarcons_decl,type,
% 0.07/0.31 axvarcons: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslam_decl,type,
% 0.07/0.31 hoaslam: subst > ( subst > term > term ) > term ).
% 0.07/0.31
% 0.07/0.31 thf(axscons_decl,type,
% 0.07/0.31 axscons: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem2v2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axidr_decl,type,
% 0.07/0.31 axidr: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1_decl,type,
% 0.07/0.31 pushprop_lem1: $o ).
% 0.07/0.31
% 0.07/0.31 thf(laminj_decl,type,
% 0.07/0.31 laminj: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem0_decl,type,
% 0.07/0.31 pushprop_lem0: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_gthm_decl,type,
% 0.07/0.31 pushprop_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axabs_decl,type,
% 0.07/0.31 axabs: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3v2a_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem2_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj2_gthm_decl,type,
% 0.07/0.31 hoasapinj2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.07/0.31 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem1_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem1_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(lamnotap_decl,type,
% 0.07/0.31 lamnotap: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapinj1_gthm_decl,type,
% 0.07/0.31 hoasapinj1_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotvar_decl,type,
% 0.07/0.31 hoaslamnotvar: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axidl_decl,type,
% 0.07/0.31 axidl: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslaminj_gthm_decl,type,
% 0.07/0.31 hoaslaminj_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction2_lthm_decl,type,
% 0.07/0.31 induction2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem0_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem0_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(substmonoid_lthm_decl,type,
% 0.07/0.31 substmonoid_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_decl,type,
% 0.07/0.31 pushprop: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem3_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem2_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3b_decl,type,
% 0.07/0.31 hoasinduction_lem3b: $o ).
% 0.07/0.31
% 0.07/0.31 thf(substmonoid_decl,type,
% 0.07/0.31 substmonoid: $o ).
% 0.07/0.31
% 0.07/0.31 thf(lamnotvar_decl,type,
% 0.07/0.31 lamnotvar: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3a_decl,type,
% 0.07/0.31 hoasinduction_lem3a: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem1_gthm_decl,type,
% 0.07/0.31 hoasinduction_lem1_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_no_psi_cond_decl,type,
% 0.07/0.31 hoasinduction_no_psi_cond: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction2_gthm_decl,type,
% 0.07/0.31 induction2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem2v2_lthm_decl,type,
% 0.07/0.31 pushprop_lem2v2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasvar_decl,type,
% 0.07/0.31 hoasvar: subst > term > subst > $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslamnotap_decl,type,
% 0.07/0.31 hoaslamnotap: $o ).
% 0.07/0.31
% 0.07/0.31 thf(substmonoid_gthm_decl,type,
% 0.07/0.31 substmonoid_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(ulamvarsh_decl,type,
% 0.07/0.31 ulamvarsh: $o ).
% 0.07/0.31
% 0.07/0.31 thf(induction2_decl,type,
% 0.07/0.31 induction2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem3v2_decl,type,
% 0.07/0.31 pushprop_lem3v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem2v2_gthm_decl,type,
% 0.07/0.31 pushprop_lem2v2_gthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem1_lthm_decl,type,
% 0.07/0.31 pushprop_lem1_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2_decl,type,
% 0.07/0.31 hoasinduction_lem3v2: $o ).
% 0.07/0.31
% 0.07/0.31 thf(axshiftcons_decl,type,
% 0.07/0.31 axshiftcons: $o ).
% 0.07/0.31
% 0.07/0.31 thf(termmset_decl,type,
% 0.07/0.31 termmset: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_lem0_lthm_decl,type,
% 0.07/0.31 pushprop_lem0_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasapnotvar_lthm_decl,type,
% 0.07/0.31 hoasapnotvar_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.07/0.31 hoasinduction_lem3v2_lthm: $o ).
% 0.07/0.31
% 0.07/0.31 thf(pushprop_p_and_p_prime_decl,type,
% 0.07/0.31 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.07/0.31
% 0.07/0.31 thf(axvarid_decl,type,
% 0.07/0.31 axvarid: $o ).
% 0.07/0.31
% 0.07/0.31 thf(hoasinduction_lthm_3_decl,type,
% 0.07/0.31 hoasinduction_lthm_3: $o ).
% 0.07/0.31
% 0.07/0.31 %----Types of the domains
% 0.07/0.31 thf(d_term_type,type,
% 0.07/0.31 d_term: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(d_subst_type,type,
% 0.07/0.31 d_subst: $tType ).
% 0.07/0.31
% 0.07/0.31 %----Types of the promotion functions
% 0.07/0.31 thf(d2term_decl,type,
% 0.07/0.31 d2term: d_term > term ).
% 0.07/0.31
% 0.07/0.31 thf(d2subst_decl,type,
% 0.07/0.31 d2subst: d_subst > subst ).
% 0.07/0.31
% 0.07/0.31 %----Types of the domain elements
% 0.07/0.31 thf(d_one_decl,type,
% 0.07/0.31 d_one: d_term ).
% 0.07/0.31
% 0.07/0.31 thf(d_id_decl,type,
% 0.07/0.31 d_id: d_subst ).
% 0.07/0.31
% 0.07/0.31 thf(alg444_1,axiom,
% 0.07/0.31 ( ! [T: term] :
% 0.07/0.31 ? [DT: d_term] :
% 0.07/0.31 ( T
% 0.07/0.31 = ( d2term @ DT ) )
% 0.07/0.31 & ! [DT: d_term] : ( DT = d_one )
% 0.07/0.31 & ! [DT1: d_term,DT2: d_term] :
% 0.07/0.31 ( ( ( d2term @ DT1 )
% 0.07/0.31 = ( d2term @ DT2 ) )
% 0.07/0.31 => ( DT1 = DT2 ) )
% 0.07/0.31 & ! [S: subst] :
% 0.07/0.31 ? [DS: d_subst] :
% 0.07/0.31 ( S
% 0.07/0.31 = ( d2subst @ DS ) )
% 0.07/0.31 & ! [DS: d_subst] : ( DS = d_id )
% 0.07/0.31 & ! [DS1: d_subst,DS2: d_subst] :
% 0.07/0.31 ( ( ( d2subst @ DS1 )
% 0.07/0.31 = ( d2subst @ DS2 ) )
% 0.07/0.31 => ( DS1 = DS2 ) )
% 0.07/0.31 & ( one
% 0.07/0.31 = ( d2term @ d_one ) )
% 0.07/0.31 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.07/0.31 = ( d2term @ d_one ) )
% 0.07/0.31 & ( ( lam @ ( d2term @ d_one ) )
% 0.07/0.31 = ( d2term @ d_one ) )
% 0.07/0.31 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.07/0.31 = ( d2term @ d_one ) )
% 0.07/0.31 & ( id
% 0.07/0.31 = ( d2subst @ d_id ) )
% 0.07/0.31 & ( sh
% 0.07/0.31 = ( d2subst @ d_id ) )
% 0.07/0.31 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.07/0.31 = ( d2subst @ d_id ) )
% 0.07/0.31 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.07/0.31 = ( d2subst @ d_id ) )
% 0.07/0.31 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.07/0.31 = ( d2term @ d_one ) )
% 0.07/0.31 & ( hoaslam
% 0.07/0.31 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.07/0.31 & ( hoasinduction_p_and_p_prime
% 0.07/0.31 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.07/0.31 ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) ) ) )
% 0.07/0.31 & ( pushprop_p_and_p_prime
% 0.07/0.31 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.07/0.31 ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.07/0.31 & ~ ( var @ ( d2term @ d_one ) )
% 0.07/0.31 & ( pushprop_lem1v2
% 0.07/0.31 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.07/0.31 | ( Q @ one ) ) )
% 0.07/0.31 & pushprop_lem1_gthm
% 0.07/0.31 & axmap
% 0.07/0.31 & pushprop_lem0_gthm
% 0.07/0.31 & ( shinj
% 0.07/0.31 <=> ! [A: term,B: term] :
% 0.07/0.31 ( ( ( sub @ A @ sh )
% 0.07/0.31 != ( sub @ B @ sh ) )
% 0.07/0.31 | ( A = B ) ) )
% 0.07/0.31 & hoasinduction_lem1v2
% 0.07/0.31 & hoasinduction_lem1v2_gthm
% 0.07/0.31 & ( induction2lem
% 0.07/0.31 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.07/0.31 ( ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( var @ B )
% 0.07/0.31 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.07/0.31 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.07/0.31 & ( hoasinduction_lem3v2_f
% 0.07/0.31 <=> ! [B: term] :
% 0.07/0.31 ~ ! [F: subst > term > term] :
% 0.07/0.31 ~ ! [A: term,M: subst] :
% 0.07/0.31 ( ( sub @ B @ ( push @ A @ M ) )
% 0.07/0.31 = ( F @ M @ A ) ) )
% 0.07/0.31 & axvarshift
% 0.07/0.31 & ( hoasapinj2
% 0.07/0.31 <=> ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.07/0.31 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.07/0.31 | ( C = D ) ) )
% 0.07/0.31 & hoasapnotvar_gthm
% 0.07/0.31 & ( hoasapinj1
% 0.07/0.31 <=> ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.07/0.31 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.07/0.31 | ( A = B ) ) )
% 0.07/0.31 & ~ ulamvar1
% 0.07/0.31 & ( induction2lem_lthm
% 0.07/0.31 <=> ( ! [A: term,M: subst] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.07/0.31 => ( ! [A: term,M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.07/0.31 => ( ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ M @ id ) )
% 0.07/0.31 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2140 ) )
% 0.07/0.31 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.07/0.31 ( ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( var @ B )
% 0.07/0.31 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.07/0.31 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.07/0.31 & hoasinduction_lem3v2_gthm
% 0.07/0.31 & apnotvar
% 0.07/0.31 & pushprop_lthm_orig
% 0.07/0.31 & ( hoasinduction_lem3v2_f_lthm
% 0.07/0.31 <=> ! [B: term] :
% 0.07/0.31 ~ ! [F: subst > term > term] :
% 0.07/0.31 ~ ! [A: term,M: subst] :
% 0.07/0.31 ( ( sub @ B @ ( push @ A @ M ) )
% 0.07/0.31 = ( F @ M @ A ) ) )
% 0.07/0.31 & ( hoasinduction_lthm
% 0.07/0.31 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2367 ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.07/0.31 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ ( sub @ A @ id ) )
% 0.07/0.31 | ( P @ id @ A @ id ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.07/0.31 & ( hoasinduction_no_psi_cond_lthm
% 0.07/0.31 <=> ( ! [P: subst > term > subst > $o] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2367 ) )
% 0.07/0.31 => ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.07/0.31 ( ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.07/0.31 & ( hoaslaminj
% 0.07/0.31 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.07/0.31 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ( ( lam @ ( F @ sh @ one ) )
% 0.07/0.31 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.07/0.31 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.07/0.31 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.07/0.31 & ( hoasinduction_lem3aaa
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.07/0.31 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.07/0.31 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.07/0.31 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.07/0.31 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.07/0.31 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.07/0.31 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.07/0.31 & induction2lem_gthm
% 0.07/0.31 & ( hoasinduction_lem3aa_lthm
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.07/0.31 & ( hoasinduction_lem3
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.07/0.31 & ( hoasinduction_lem2
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.07/0.31 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.07/0.31 & ( termmset_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) ) ) )
% 0.07/0.31 & hoasinduction_lem1
% 0.07/0.31 & hoaslamnotap_lthm
% 0.07/0.31 & ( pushprop_lem1v2_lthm
% 0.07/0.31 <=> ( ! [A: term,M: subst] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.07/0.31 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.07/0.31 | ( Q @ one ) ) ) )
% 0.07/0.31 & hoasapnotvar
% 0.07/0.31 & ( hoasinduction_lem0
% 0.07/0.31 <=> ! [P: subst > term > subst > $o] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) ) )
% 0.07/0.31 & ( hoasinduction
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ ( sub @ A @ id ) )
% 0.07/0.31 | ( P @ id @ A @ id ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.07/0.31 & hoasinduction_gthm
% 0.07/0.31 & axapp
% 0.07/0.31 & hoaslamnotvar_lthm
% 0.07/0.31 & pushprop_lem3v2_lthm
% 0.07/0.31 & ( hoasinduction_lem3b_lthm
% 0.07/0.31 <=> ! [B: term] :
% 0.07/0.31 ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ( F @ sh @ one )
% 0.07/0.31 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.07/0.31 & ulamvarind
% 0.07/0.31 & ( induction
% 0.07/0.31 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2140 ) ) )
% 0.07/0.31 & ( hoasinduction_lem3a_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.07/0.31 & termmset_gthm
% 0.07/0.31 & ( hoasinduction_lem3aa
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.07/0.31 & pushprop_lem1v2_gthm
% 0.07/0.31 & hoaslamnotap_gthm
% 0.07/0.31 & hoaslamnotvar_gthm
% 0.07/0.31 & hoasinduction_lem3b_gthm
% 0.07/0.31 & pushprop_lem2v2
% 0.07/0.31 & hoasinduction_lem3a_gthm
% 0.07/0.31 & axclos
% 0.07/0.31 & axassoc
% 0.07/0.31 & ( hoasinduction_lem2v2
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ( Q @ Bound_variable_2820 )
% 0.07/0.31 | ~ ( Q @ Bound_variable_2822 )
% 0.07/0.31 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.07/0.31 & pushprop_lthm
% 0.07/0.31 & ( apinj2
% 0.07/0.31 <=> ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ A @ C )
% 0.07/0.31 != ( ap @ B @ D ) )
% 0.07/0.31 | ( C = D ) ) )
% 0.07/0.31 & ( apinj1
% 0.07/0.31 <=> ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ A @ C )
% 0.07/0.31 != ( ap @ B @ D ) )
% 0.07/0.31 | ( A = B ) ) )
% 0.07/0.31 & ( hoasapinj2_lthm
% 0.07/0.31 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ A @ C )
% 0.07/0.31 != ( ap @ B @ D ) )
% 0.07/0.31 | ( C = D ) )
% 0.07/0.31 => ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.07/0.31 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.07/0.31 | ( C = D ) ) ) )
% 0.07/0.31 & ( hoasinduction_lem3v2a
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.07/0.31 & ( hoasapinj1_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ A @ C )
% 0.07/0.31 != ( ap @ B @ D ) )
% 0.07/0.31 | ( A = B ) )
% 0.07/0.31 => ! [A: term,B: term,C: term,D: term] :
% 0.07/0.31 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.07/0.31 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.07/0.31 | ( A = B ) ) ) ) )
% 0.07/0.31 & ( hoaslaminj_lthm
% 0.07/0.31 <=> ( ! [A: term,M: subst] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.07/0.31 => ( ! [A: term,M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.07/0.31 => ( ! [A: term,B: term] :
% 0.07/0.31 ( ( ( lam @ A )
% 0.07/0.31 != ( lam @ B ) )
% 0.07/0.31 | ( A = B ) )
% 0.07/0.31 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.07/0.31 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ( ( lam @ ( F @ sh @ one ) )
% 0.07/0.31 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.07/0.31 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.07/0.31 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.07/0.31 & ( axvarcons
% 0.07/0.31 <=> ! [A: term,M: subst] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.07/0.31 & ( axscons
% 0.07/0.31 <=> ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.07/0.31 & hoasinduction_lem2v2_gthm
% 0.07/0.31 & ( axidr
% 0.07/0.31 <=> ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ M @ id ) ) )
% 0.07/0.31 & ( pushprop_lem1
% 0.07/0.31 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.07/0.31 & ( laminj
% 0.07/0.31 <=> ! [A: term,B: term] :
% 0.07/0.31 ( ( ( lam @ A )
% 0.07/0.31 != ( lam @ B ) )
% 0.07/0.31 | ( A = B ) ) )
% 0.07/0.31 & ( hoasinduction_lem3_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.07/0.31 & ( pushprop_lem0
% 0.07/0.31 <=> ! [P: term > $o,A: term,M: subst] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.07/0.31 & pushprop_gthm
% 0.07/0.31 & axabs
% 0.07/0.31 & ( hoasinduction_lem3v2a_lthm
% 0.07/0.31 <=> ( ! [B: term] :
% 0.07/0.31 ~ ! [F: subst > term > term] :
% 0.07/0.31 ~ ! [A: term,M: subst] :
% 0.07/0.31 ( ( sub @ B @ ( push @ A @ M ) )
% 0.07/0.31 = ( F @ M @ A ) )
% 0.07/0.31 => ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.07/0.31 & hoasinduction_lem2_lthm
% 0.07/0.31 & hoasapinj2_gthm
% 0.07/0.31 & hoasinduction_lem1_lthm
% 0.07/0.31 & ~ lamnotap
% 0.07/0.31 & hoasapinj1_gthm
% 0.07/0.31 & hoaslamnotvar
% 0.07/0.31 & ( axidl
% 0.07/0.31 <=> ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ id @ M ) ) )
% 0.07/0.31 & hoaslaminj_gthm
% 0.07/0.31 & ( induction2_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.07/0.31 ( ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( var @ B )
% 0.07/0.31 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.07/0.31 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.07/0.31 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.07/0.31 & ( hoasinduction_lem0_lthm
% 0.07/0.31 <=> ! [P: subst > term > subst > $o] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) ) )
% 0.07/0.31 & ( substmonoid_lthm
% 0.07/0.31 <=> ( ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ id @ M ) )
% 0.07/0.31 => ( ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ M @ id ) )
% 0.07/0.31 => ( ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ id @ M ) )
% 0.07/0.31 & ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ M @ id ) ) ) ) ) )
% 0.07/0.31 & pushprop
% 0.07/0.31 & hoasinduction_lem3_gthm
% 0.07/0.31 & hoasinduction_lem2_gthm
% 0.07/0.31 & ( hoasinduction_lem3b
% 0.07/0.31 <=> ! [B: term] :
% 0.07/0.31 ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ( F @ sh @ one )
% 0.07/0.31 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.07/0.31 & ( substmonoid
% 0.07/0.31 <=> ( ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ id @ M ) )
% 0.07/0.31 & ! [M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ M @ id ) ) ) )
% 0.07/0.31 & lamnotvar
% 0.07/0.31 & ( hoasinduction_lem3a
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.07/0.31 & hoasinduction_lem1_gthm
% 0.07/0.31 & ( hoasinduction_no_psi_cond
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.07/0.31 ( ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.07/0.31 & induction2_gthm
% 0.07/0.31 & pushprop_lem2v2_lthm
% 0.07/0.31 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.07/0.31 & ( hoaslamnotap
% 0.07/0.31 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ( ( lam @ ( F @ sh @ one ) )
% 0.07/0.31 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.07/0.31 & substmonoid_gthm
% 0.07/0.31 & ulamvarsh
% 0.07/0.31 & ( induction2
% 0.07/0.31 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2367 ) ) )
% 0.07/0.31 & pushprop_lem3v2
% 0.07/0.31 & pushprop_lem2v2_gthm
% 0.07/0.31 & ( pushprop_lem1_lthm
% 0.07/0.31 <=> ( ! [A: term,M: subst] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.07/0.31 => ( ! [A: term,M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.07/0.31 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.07/0.31 & ( hoasinduction_lem3v2
% 0.07/0.31 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.07/0.31 & ( axshiftcons
% 0.07/0.31 <=> ! [A: term,M: subst] :
% 0.07/0.31 ( M
% 0.07/0.31 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.07/0.31 & ( termmset
% 0.07/0.31 <=> ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) ) )
% 0.07/0.31 & ( pushprop_lem0_lthm
% 0.07/0.31 <=> ! [P: term > $o,A: term,M: subst] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.07/0.31 & hoasapnotvar_lthm
% 0.07/0.31 & ( hoasinduction_lem3v2_lthm
% 0.07/0.31 <=> ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.07/0.31 & ( axvarid
% 0.07/0.31 <=> ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) ) )
% 0.07/0.31 & ( hoasinduction_lthm_3
% 0.07/0.31 <=> ( ! [P: subst > term > subst > $o] :
% 0.07/0.31 ~ ! [Q: term > $o] :
% 0.07/0.31 ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.07/0.31 ( ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ A )
% 0.07/0.31 | ( P @ A ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ A )
% 0.07/0.31 | ~ ( P @ B )
% 0.07/0.31 | ( P @ ( ap @ A @ B ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ! [B: term] :
% 0.07/0.31 ( ~ ( P @ B )
% 0.07/0.31 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( P @ ( lam @ A ) ) )
% 0.07/0.31 | ( P @ Bound_variable_2367 ) )
% 0.07/0.31 => ( ! [A: term] :
% 0.07/0.31 ( A
% 0.07/0.31 = ( sub @ A @ id ) )
% 0.07/0.31 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.07/0.31 ( ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ~ ! [X: term] :
% 0.07/0.31 ( ( Q @ X )
% 0.07/0.31 = ( P @ id @ X @ id ) )
% 0.07/0.31 | ~ ! [B: term] :
% 0.07/0.31 ( ~ ( Q @ B )
% 0.07/0.31 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.07/0.31 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.07/0.31 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.07/0.31 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.07/0.31 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.07/0.31 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.07/0.31 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( var @ ( sub @ A @ id ) )
% 0.07/0.31 | ( P @ id @ A @ id ) )
% 0.07/0.31 | ~ ! [A: term,B: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ~ ( P @ id @ B @ id )
% 0.07/0.31 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.07/0.31 | ~ ! [F: subst > term > term] :
% 0.07/0.31 ( ~ ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 | ~ ! [A: term] :
% 0.07/0.31 ( ~ ( P @ id @ A @ id )
% 0.07/0.31 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.07/0.31 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.07/0.31 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf(hoaslaminj,conjecture,
% 0.07/0.31 ( hoaslaminj
% 0.07/0.31 = ( ! [F: subst > term > term] :
% 0.07/0.31 ( ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( F @ M @ A ) @ N )
% 0.07/0.31 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 => ! [G: subst > term > term] :
% 0.07/0.31 ( ! [M: subst,A: term,N: subst] :
% 0.07/0.31 ( ( sub @ ( G @ M @ A ) @ N )
% 0.07/0.31 = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.07/0.31 => ( ( ( hoaslam @ id
% 0.07/0.31 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.07/0.31 = ( hoaslam @ id
% 0.07/0.31 @ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
% 0.07/0.31 => ! [M: subst,A: term] :
% 0.07/0.31 ( ( F @ M @ A )
% 0.07/0.31 = ( G @ M @ A ) ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 1.60/1.05 ---- Embedded in THF ---
% 1.60/1.05 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.05 %%% Generated on Tue May 05 09:01:31 EDT 2026
% 1.60/1.05 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.05 %%% Logic specification used:
% 1.60/1.05 %%% thf(spec, logic, $$dhol).
% 1.60/1.05
% 1.60/1.05 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tVjixEyHtK/DTF2DTF10797.p
% See solution above
% 1.60/1.05 ------------------------
% 1.60/1.07 ---- Cleaned THF ---
% 1.60/1.07 thf(term_type,type,
% 1.60/1.07 term: $tType ).
% 1.60/1.07
% 1.60/1.07 thf(subst_type,type,
% 1.60/1.07 subst: $tType ).
% 1.60/1.07
% 1.60/1.07 thf(one_decl,type,
% 1.60/1.07 one: term ).
% 1.60/1.07
% 1.60/1.07 thf(ap_decl,type,
% 1.60/1.07 ap: term > term > term ).
% 1.60/1.07
% 1.60/1.07 thf(lam_decl,type,
% 1.60/1.07 lam: term > term ).
% 1.60/1.07
% 1.60/1.07 thf(sub_decl,type,
% 1.60/1.07 sub: term > subst > term ).
% 1.60/1.07
% 1.60/1.07 thf(id_decl,type,
% 1.60/1.07 id: subst ).
% 1.60/1.07
% 1.60/1.07 thf(sh_decl,type,
% 1.60/1.07 sh: subst ).
% 1.60/1.07
% 1.60/1.07 thf(push_decl,type,
% 1.60/1.07 push: term > subst > subst ).
% 1.60/1.07
% 1.60/1.07 thf(comp_decl,type,
% 1.60/1.07 comp: subst > subst > subst ).
% 1.60/1.07
% 1.60/1.07 thf(var_decl,type,
% 1.60/1.07 var: term > $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1v2_decl,type,
% 1.60/1.07 pushprop_lem1v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1_gthm_decl,type,
% 1.60/1.07 pushprop_lem1_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axmap_decl,type,
% 1.60/1.07 axmap: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem0_gthm_decl,type,
% 1.60/1.07 pushprop_lem0_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(shinj_decl,type,
% 1.60/1.07 shinj: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem1v2_decl,type,
% 1.60/1.07 hoasinduction_lem1v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem1v2_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem1v2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasap_decl,type,
% 1.60/1.07 hoasap: subst > term > subst > term > term ).
% 1.60/1.07
% 1.60/1.07 thf(induction2lem_decl,type,
% 1.60/1.07 induction2lem: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2_f_decl,type,
% 1.60/1.07 hoasinduction_lem3v2_f: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axvarshift_decl,type,
% 1.60/1.07 axvarshift: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj2_decl,type,
% 1.60/1.07 hoasapinj2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapnotvar_gthm_decl,type,
% 1.60/1.07 hoasapnotvar_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj1_decl,type,
% 1.60/1.07 hoasapinj1: $o ).
% 1.60/1.07
% 1.60/1.07 thf(ulamvar1_decl,type,
% 1.60/1.07 ulamvar1: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction2lem_lthm_decl,type,
% 1.60/1.07 induction2lem_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem3v2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(apnotvar_decl,type,
% 1.60/1.07 apnotvar: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lthm_orig_decl,type,
% 1.60/1.07 pushprop_lthm_orig: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3v2_f_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lthm_decl,type,
% 1.60/1.07 hoasinduction_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 1.60/1.07 hoasinduction_no_psi_cond_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslaminj_decl,type,
% 1.60/1.07 hoaslaminj: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3aaa_decl,type,
% 1.60/1.07 hoasinduction_lem3aaa: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction2lem_gthm_decl,type,
% 1.60/1.07 induction2lem_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3aa_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3aa_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3_decl,type,
% 1.60/1.07 hoasinduction_lem3: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem2_decl,type,
% 1.60/1.07 hoasinduction_lem2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(termmset_lthm_decl,type,
% 1.60/1.07 termmset_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem1_decl,type,
% 1.60/1.07 hoasinduction_lem1: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotap_lthm_decl,type,
% 1.60/1.07 hoaslamnotap_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1v2_lthm_decl,type,
% 1.60/1.07 pushprop_lem1v2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapnotvar_decl,type,
% 1.60/1.07 hoasapnotvar: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem0_decl,type,
% 1.60/1.07 hoasinduction_lem0: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_decl,type,
% 1.60/1.07 hoasinduction: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_gthm_decl,type,
% 1.60/1.07 hoasinduction_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axapp_decl,type,
% 1.60/1.07 axapp: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotvar_lthm_decl,type,
% 1.60/1.07 hoaslamnotvar_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem3v2_lthm_decl,type,
% 1.60/1.07 pushprop_lem3v2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3b_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3b_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(ulamvarind_decl,type,
% 1.60/1.07 ulamvarind: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction_decl,type,
% 1.60/1.07 induction: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3a_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3a_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(termmset_gthm_decl,type,
% 1.60/1.07 termmset_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3aa_decl,type,
% 1.60/1.07 hoasinduction_lem3aa: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1v2_gthm_decl,type,
% 1.60/1.07 pushprop_lem1v2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotap_gthm_decl,type,
% 1.60/1.07 hoaslamnotap_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotvar_gthm_decl,type,
% 1.60/1.07 hoaslamnotvar_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3b_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem3b_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem2v2_decl,type,
% 1.60/1.07 pushprop_lem2v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3a_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem3a_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axclos_decl,type,
% 1.60/1.07 axclos: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axassoc_decl,type,
% 1.60/1.07 axassoc: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem2v2_decl,type,
% 1.60/1.07 hoasinduction_lem2v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lthm_decl,type,
% 1.60/1.07 pushprop_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(apinj2_decl,type,
% 1.60/1.07 apinj2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(apinj1_decl,type,
% 1.60/1.07 apinj1: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj2_lthm_decl,type,
% 1.60/1.07 hoasapinj2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2a_decl,type,
% 1.60/1.07 hoasinduction_lem3v2a: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj1_lthm_decl,type,
% 1.60/1.07 hoasapinj1_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslaminj_lthm_decl,type,
% 1.60/1.07 hoaslaminj_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axvarcons_decl,type,
% 1.60/1.07 axvarcons: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslam_decl,type,
% 1.60/1.07 hoaslam: subst > ( subst > term > term ) > term ).
% 1.60/1.07
% 1.60/1.07 thf(axscons_decl,type,
% 1.60/1.07 axscons: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem2v2_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem2v2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axidr_decl,type,
% 1.60/1.07 axidr: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1_decl,type,
% 1.60/1.07 pushprop_lem1: $o ).
% 1.60/1.07
% 1.60/1.07 thf(laminj_decl,type,
% 1.60/1.07 laminj: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem0_decl,type,
% 1.60/1.07 pushprop_lem0: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_gthm_decl,type,
% 1.60/1.07 pushprop_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axabs_decl,type,
% 1.60/1.07 axabs: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3v2a_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem2_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj2_gthm_decl,type,
% 1.60/1.07 hoasapinj2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_p_and_p_prime_decl,type,
% 1.60/1.07 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem1_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem1_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(lamnotap_decl,type,
% 1.60/1.07 lamnotap: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapinj1_gthm_decl,type,
% 1.60/1.07 hoasapinj1_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotvar_decl,type,
% 1.60/1.07 hoaslamnotvar: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axidl_decl,type,
% 1.60/1.07 axidl: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslaminj_gthm_decl,type,
% 1.60/1.07 hoaslaminj_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction2_lthm_decl,type,
% 1.60/1.07 induction2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem0_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem0_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(substmonoid_lthm_decl,type,
% 1.60/1.07 substmonoid_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_decl,type,
% 1.60/1.07 pushprop: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem3_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem2_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3b_decl,type,
% 1.60/1.07 hoasinduction_lem3b: $o ).
% 1.60/1.07
% 1.60/1.07 thf(substmonoid_decl,type,
% 1.60/1.07 substmonoid: $o ).
% 1.60/1.07
% 1.60/1.07 thf(lamnotvar_decl,type,
% 1.60/1.07 lamnotvar: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3a_decl,type,
% 1.60/1.07 hoasinduction_lem3a: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem1_gthm_decl,type,
% 1.60/1.07 hoasinduction_lem1_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_no_psi_cond_decl,type,
% 1.60/1.07 hoasinduction_no_psi_cond: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction2_gthm_decl,type,
% 1.60/1.07 induction2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem2v2_lthm_decl,type,
% 1.60/1.07 pushprop_lem2v2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasvar_decl,type,
% 1.60/1.07 hoasvar: subst > term > subst > $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslamnotap_decl,type,
% 1.60/1.07 hoaslamnotap: $o ).
% 1.60/1.07
% 1.60/1.07 thf(substmonoid_gthm_decl,type,
% 1.60/1.07 substmonoid_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(ulamvarsh_decl,type,
% 1.60/1.07 ulamvarsh: $o ).
% 1.60/1.07
% 1.60/1.07 thf(induction2_decl,type,
% 1.60/1.07 induction2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem3v2_decl,type,
% 1.60/1.07 pushprop_lem3v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem2v2_gthm_decl,type,
% 1.60/1.07 pushprop_lem2v2_gthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem1_lthm_decl,type,
% 1.60/1.07 pushprop_lem1_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2_decl,type,
% 1.60/1.07 hoasinduction_lem3v2: $o ).
% 1.60/1.07
% 1.60/1.07 thf(axshiftcons_decl,type,
% 1.60/1.07 axshiftcons: $o ).
% 1.60/1.07
% 1.60/1.07 thf(termmset_decl,type,
% 1.60/1.07 termmset: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_lem0_lthm_decl,type,
% 1.60/1.07 pushprop_lem0_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasapnotvar_lthm_decl,type,
% 1.60/1.07 hoasapnotvar_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lem3v2_lthm_decl,type,
% 1.60/1.07 hoasinduction_lem3v2_lthm: $o ).
% 1.60/1.07
% 1.60/1.07 thf(pushprop_p_and_p_prime_decl,type,
% 1.60/1.07 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 1.60/1.07
% 1.60/1.07 thf(axvarid_decl,type,
% 1.60/1.07 axvarid: $o ).
% 1.60/1.07
% 1.60/1.07 thf(hoasinduction_lthm_3_decl,type,
% 1.60/1.07 hoasinduction_lthm_3: $o ).
% 1.60/1.07
% 1.60/1.07 thf(d_term_type,type,
% 1.60/1.07 d_term: $tType ).
% 1.60/1.07
% 1.60/1.07 thf(d_subst_type,type,
% 1.60/1.07 d_subst: $tType ).
% 1.60/1.07
% 1.60/1.07 thf(d2term_decl,type,
% 1.60/1.07 d2term: d_term > term ).
% 1.60/1.07
% 1.60/1.07 thf(d2subst_decl,type,
% 1.60/1.07 d2subst: d_subst > subst ).
% 1.60/1.07
% 1.60/1.07 thf(d_one_decl,type,
% 1.60/1.07 d_one: d_term ).
% 1.60/1.07
% 1.60/1.07 thf(d_id_decl,type,
% 1.60/1.07 d_id: d_subst ).
% 1.60/1.07
% 1.60/1.07 thf(alg444_1,axiom,
% 1.60/1.07 ( ! [T: term] :
% 1.60/1.07 ? [DT: d_term] :
% 1.60/1.07 ( T
% 1.60/1.07 = ( d2term @ DT ) )
% 1.60/1.07 & ! [DT: d_term] : ( DT = d_one )
% 1.60/1.07 & ! [DT1: d_term,DT2: d_term] :
% 1.60/1.07 ( ( ( d2term @ DT1 )
% 1.60/1.07 = ( d2term @ DT2 ) )
% 1.60/1.07 => ( DT1 = DT2 ) )
% 1.60/1.07 & ! [S: subst] :
% 1.60/1.07 ? [DS: d_subst] :
% 1.60/1.07 ( S
% 1.60/1.07 = ( d2subst @ DS ) )
% 1.60/1.07 & ! [DS: d_subst] : ( DS = d_id )
% 1.60/1.07 & ! [DS1: d_subst,DS2: d_subst] :
% 1.60/1.07 ( ( ( d2subst @ DS1 )
% 1.60/1.07 = ( d2subst @ DS2 ) )
% 1.60/1.07 => ( DS1 = DS2 ) )
% 1.60/1.07 & ( one
% 1.60/1.07 = ( d2term @ d_one ) )
% 1.60/1.07 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 1.60/1.07 = ( d2term @ d_one ) )
% 1.60/1.07 & ( ( lam @ ( d2term @ d_one ) )
% 1.60/1.07 = ( d2term @ d_one ) )
% 1.60/1.07 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 1.60/1.07 = ( d2term @ d_one ) )
% 1.60/1.07 & ( id
% 1.60/1.07 = ( d2subst @ d_id ) )
% 1.60/1.07 & ( sh
% 1.60/1.07 = ( d2subst @ d_id ) )
% 1.60/1.07 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 1.60/1.07 = ( d2subst @ d_id ) )
% 1.60/1.07 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 1.60/1.07 = ( d2subst @ d_id ) )
% 1.60/1.07 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 1.60/1.07 = ( d2term @ d_one ) )
% 1.60/1.07 & ( hoaslam
% 1.60/1.07 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 1.60/1.07 & ( hoasinduction_p_and_p_prime
% 1.60/1.07 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 1.60/1.07 ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) ) ) )
% 1.60/1.07 & ( pushprop_p_and_p_prime
% 1.60/1.07 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 1.60/1.07 ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 1.60/1.07 & ~ ( var @ ( d2term @ d_one ) )
% 1.60/1.07 & ( pushprop_lem1v2
% 1.60/1.07 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 1.60/1.07 | ( Q @ one ) ) )
% 1.60/1.07 & pushprop_lem1_gthm
% 1.60/1.07 & axmap
% 1.60/1.07 & pushprop_lem0_gthm
% 1.60/1.07 & ( shinj
% 1.60/1.07 <=> ! [A: term,B: term] :
% 1.60/1.07 ( ( ( sub @ A @ sh )
% 1.60/1.07 != ( sub @ B @ sh ) )
% 1.60/1.07 | ( A = B ) ) )
% 1.60/1.07 & hoasinduction_lem1v2
% 1.60/1.07 & hoasinduction_lem1v2_gthm
% 1.60/1.07 & ( induction2lem
% 1.60/1.07 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 1.60/1.07 ( ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( var @ B )
% 1.60/1.07 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 1.60/1.07 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 1.60/1.07 & ( hoasinduction_lem3v2_f
% 1.60/1.07 <=> ! [B: term] :
% 1.60/1.07 ~ ! [F: subst > term > term] :
% 1.60/1.07 ~ ! [A: term,M: subst] :
% 1.60/1.07 ( ( sub @ B @ ( push @ A @ M ) )
% 1.60/1.07 = ( F @ M @ A ) ) )
% 1.60/1.07 & axvarshift
% 1.60/1.07 & ( hoasapinj2
% 1.60/1.07 <=> ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 1.60/1.07 != ( ap @ ( sub @ B @ id ) @ D ) )
% 1.60/1.07 | ( C = D ) ) )
% 1.60/1.07 & hoasapnotvar_gthm
% 1.60/1.07 & ( hoasapinj1
% 1.60/1.07 <=> ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 1.60/1.07 != ( ap @ ( sub @ B @ id ) @ D ) )
% 1.60/1.07 | ( A = B ) ) )
% 1.60/1.07 & ~ ulamvar1
% 1.60/1.07 & ( induction2lem_lthm
% 1.60/1.07 <=> ( ! [A: term,M: subst] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ one @ ( push @ A @ M ) ) )
% 1.60/1.07 => ( ! [A: term,M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ sh @ ( push @ A @ M ) ) )
% 1.60/1.07 => ( ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ M @ id ) )
% 1.60/1.07 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2140 ) )
% 1.60/1.07 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 1.60/1.07 ( ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( var @ B )
% 1.60/1.07 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 1.60/1.07 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 1.60/1.07 & hoasinduction_lem3v2_gthm
% 1.60/1.07 & apnotvar
% 1.60/1.07 & pushprop_lthm_orig
% 1.60/1.07 & ( hoasinduction_lem3v2_f_lthm
% 1.60/1.07 <=> ! [B: term] :
% 1.60/1.07 ~ ! [F: subst > term > term] :
% 1.60/1.07 ~ ! [A: term,M: subst] :
% 1.60/1.07 ( ( sub @ B @ ( push @ A @ M ) )
% 1.60/1.07 = ( F @ M @ A ) ) )
% 1.60/1.07 & ( hoasinduction_lthm
% 1.60/1.07 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2367 ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 1.60/1.07 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ ( sub @ A @ id ) )
% 1.60/1.07 | ( P @ id @ A @ id ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 1.60/1.07 & ( hoasinduction_no_psi_cond_lthm
% 1.60/1.07 <=> ( ! [P: subst > term > subst > $o] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2367 ) )
% 1.60/1.07 => ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 1.60/1.07 ( ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 1.60/1.07 & ( hoaslaminj
% 1.60/1.07 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 1.60/1.07 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ( ( lam @ ( F @ sh @ one ) )
% 1.60/1.07 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 1.60/1.07 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 1.60/1.07 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 1.60/1.07 & ( hoasinduction_lem3aaa
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 1.60/1.07 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 1.60/1.07 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 1.60/1.07 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 1.60/1.07 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 1.60/1.07 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 1.60/1.07 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 1.60/1.07 & induction2lem_gthm
% 1.60/1.07 & ( hoasinduction_lem3aa_lthm
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 1.60/1.07 & ( hoasinduction_lem3
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 1.60/1.07 & ( hoasinduction_lem2
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 1.60/1.07 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 1.60/1.07 & ( termmset_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) ) ) )
% 1.60/1.07 & hoasinduction_lem1
% 1.60/1.07 & hoaslamnotap_lthm
% 1.60/1.07 & ( pushprop_lem1v2_lthm
% 1.60/1.07 <=> ( ! [A: term,M: subst] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ one @ ( push @ A @ M ) ) )
% 1.60/1.07 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 1.60/1.07 | ( Q @ one ) ) ) )
% 1.60/1.07 & hoasapnotvar
% 1.60/1.07 & ( hoasinduction_lem0
% 1.60/1.07 <=> ! [P: subst > term > subst > $o] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) ) )
% 1.60/1.07 & ( hoasinduction
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ ( sub @ A @ id ) )
% 1.60/1.07 | ( P @ id @ A @ id ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 1.60/1.07 & hoasinduction_gthm
% 1.60/1.07 & axapp
% 1.60/1.07 & hoaslamnotvar_lthm
% 1.60/1.07 & pushprop_lem3v2_lthm
% 1.60/1.07 & ( hoasinduction_lem3b_lthm
% 1.60/1.07 <=> ! [B: term] :
% 1.60/1.07 ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ( F @ sh @ one )
% 1.60/1.07 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 1.60/1.07 & ulamvarind
% 1.60/1.07 & ( induction
% 1.60/1.07 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2140 ) ) )
% 1.60/1.07 & ( hoasinduction_lem3a_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 1.60/1.07 & termmset_gthm
% 1.60/1.07 & ( hoasinduction_lem3aa
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 1.60/1.07 & pushprop_lem1v2_gthm
% 1.60/1.07 & hoaslamnotap_gthm
% 1.60/1.07 & hoaslamnotvar_gthm
% 1.60/1.07 & hoasinduction_lem3b_gthm
% 1.60/1.07 & pushprop_lem2v2
% 1.60/1.07 & hoasinduction_lem3a_gthm
% 1.60/1.07 & axclos
% 1.60/1.07 & axassoc
% 1.60/1.07 & ( hoasinduction_lem2v2
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ( Q @ Bound_variable_2820 )
% 1.60/1.07 | ~ ( Q @ Bound_variable_2822 )
% 1.60/1.07 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 1.60/1.07 & pushprop_lthm
% 1.60/1.07 & ( apinj2
% 1.60/1.07 <=> ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ A @ C )
% 1.60/1.07 != ( ap @ B @ D ) )
% 1.60/1.07 | ( C = D ) ) )
% 1.60/1.07 & ( apinj1
% 1.60/1.07 <=> ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ A @ C )
% 1.60/1.07 != ( ap @ B @ D ) )
% 1.60/1.07 | ( A = B ) ) )
% 1.60/1.07 & ( hoasapinj2_lthm
% 1.60/1.07 <=> ( ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ A @ C )
% 1.60/1.07 != ( ap @ B @ D ) )
% 1.60/1.07 | ( C = D ) )
% 1.60/1.07 => ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 1.60/1.07 != ( ap @ ( sub @ B @ id ) @ D ) )
% 1.60/1.07 | ( C = D ) ) ) )
% 1.60/1.07 & ( hoasinduction_lem3v2a
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 1.60/1.07 & ( hoasapinj1_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ A @ C )
% 1.60/1.07 != ( ap @ B @ D ) )
% 1.60/1.07 | ( A = B ) )
% 1.60/1.07 => ! [A: term,B: term,C: term,D: term] :
% 1.60/1.07 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 1.60/1.07 != ( ap @ ( sub @ B @ id ) @ D ) )
% 1.60/1.07 | ( A = B ) ) ) ) )
% 1.60/1.07 & ( hoaslaminj_lthm
% 1.60/1.07 <=> ( ! [A: term,M: subst] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ one @ ( push @ A @ M ) ) )
% 1.60/1.07 => ( ! [A: term,M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ sh @ ( push @ A @ M ) ) )
% 1.60/1.07 => ( ! [A: term,B: term] :
% 1.60/1.07 ( ( ( lam @ A )
% 1.60/1.07 != ( lam @ B ) )
% 1.60/1.07 | ( A = B ) )
% 1.60/1.07 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 1.60/1.07 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ( ( lam @ ( F @ sh @ one ) )
% 1.60/1.07 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 1.60/1.07 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 1.60/1.07 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 1.60/1.07 & ( axvarcons
% 1.60/1.07 <=> ! [A: term,M: subst] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 1.60/1.07 & ( axscons
% 1.60/1.07 <=> ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 1.60/1.07 & hoasinduction_lem2v2_gthm
% 1.60/1.07 & ( axidr
% 1.60/1.07 <=> ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ M @ id ) ) )
% 1.60/1.07 & ( pushprop_lem1
% 1.60/1.07 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 1.60/1.07 & ( laminj
% 1.60/1.07 <=> ! [A: term,B: term] :
% 1.60/1.07 ( ( ( lam @ A )
% 1.60/1.07 != ( lam @ B ) )
% 1.60/1.07 | ( A = B ) ) )
% 1.60/1.07 & ( hoasinduction_lem3_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 1.60/1.07 & ( pushprop_lem0
% 1.60/1.07 <=> ! [P: term > $o,A: term,M: subst] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 1.60/1.07 & pushprop_gthm
% 1.60/1.07 & axabs
% 1.60/1.07 & ( hoasinduction_lem3v2a_lthm
% 1.60/1.07 <=> ( ! [B: term] :
% 1.60/1.07 ~ ! [F: subst > term > term] :
% 1.60/1.07 ~ ! [A: term,M: subst] :
% 1.60/1.07 ( ( sub @ B @ ( push @ A @ M ) )
% 1.60/1.07 = ( F @ M @ A ) )
% 1.60/1.07 => ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 1.60/1.07 & hoasinduction_lem2_lthm
% 1.60/1.07 & hoasapinj2_gthm
% 1.60/1.07 & hoasinduction_lem1_lthm
% 1.60/1.07 & ~ lamnotap
% 1.60/1.07 & hoasapinj1_gthm
% 1.60/1.07 & hoaslamnotvar
% 1.60/1.07 & ( axidl
% 1.60/1.07 <=> ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ id @ M ) ) )
% 1.60/1.07 & hoaslaminj_gthm
% 1.60/1.07 & ( induction2_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 1.60/1.07 ( ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( var @ B )
% 1.60/1.07 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 1.60/1.07 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 1.60/1.07 => ! [P: term > $o,Bound_variable_2367: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2367 ) ) ) ) )
% 1.60/1.07 & ( hoasinduction_lem0_lthm
% 1.60/1.07 <=> ! [P: subst > term > subst > $o] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) ) )
% 1.60/1.07 & ( substmonoid_lthm
% 1.60/1.07 <=> ( ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ id @ M ) )
% 1.60/1.07 => ( ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ M @ id ) )
% 1.60/1.07 => ( ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ id @ M ) )
% 1.60/1.07 & ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ M @ id ) ) ) ) ) )
% 1.60/1.07 & pushprop
% 1.60/1.07 & hoasinduction_lem3_gthm
% 1.60/1.07 & hoasinduction_lem2_gthm
% 1.60/1.07 & ( hoasinduction_lem3b
% 1.60/1.07 <=> ! [B: term] :
% 1.60/1.07 ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ( F @ sh @ one )
% 1.60/1.07 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 1.60/1.07 & ( substmonoid
% 1.60/1.07 <=> ( ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ id @ M ) )
% 1.60/1.07 & ! [M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ M @ id ) ) ) )
% 1.60/1.07 & lamnotvar
% 1.60/1.07 & ( hoasinduction_lem3a
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 1.60/1.07 & hoasinduction_lem1_gthm
% 1.60/1.07 & ( hoasinduction_no_psi_cond
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 1.60/1.07 ( ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 1.60/1.07 & induction2_gthm
% 1.60/1.07 & pushprop_lem2v2_lthm
% 1.60/1.07 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 1.60/1.07 & ( hoaslamnotap
% 1.60/1.07 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ( ( lam @ ( F @ sh @ one ) )
% 1.60/1.07 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 1.60/1.07 & substmonoid_gthm
% 1.60/1.07 & ulamvarsh
% 1.60/1.07 & ( induction2
% 1.60/1.07 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2367 ) ) )
% 1.60/1.07 & pushprop_lem3v2
% 1.60/1.07 & pushprop_lem2v2_gthm
% 1.60/1.07 & ( pushprop_lem1_lthm
% 1.60/1.07 <=> ( ! [A: term,M: subst] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ one @ ( push @ A @ M ) ) )
% 1.60/1.07 => ( ! [A: term,M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ sh @ ( push @ A @ M ) ) )
% 1.60/1.07 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 1.60/1.07 & ( hoasinduction_lem3v2
% 1.60/1.07 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 1.60/1.07 & ( axshiftcons
% 1.60/1.07 <=> ! [A: term,M: subst] :
% 1.60/1.07 ( M
% 1.60/1.07 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 1.60/1.07 & ( termmset
% 1.60/1.07 <=> ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) ) )
% 1.60/1.07 & ( pushprop_lem0_lthm
% 1.60/1.07 <=> ! [P: term > $o,A: term,M: subst] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 1.60/1.07 & hoasapnotvar_lthm
% 1.60/1.07 & ( hoasinduction_lem3v2_lthm
% 1.60/1.07 <=> ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 1.60/1.07 & ( axvarid
% 1.60/1.07 <=> ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) ) )
% 1.60/1.07 & ( hoasinduction_lthm_3
% 1.60/1.07 <=> ( ! [P: subst > term > subst > $o] :
% 1.60/1.07 ~ ! [Q: term > $o] :
% 1.60/1.07 ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 1.60/1.07 ( ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ A )
% 1.60/1.07 | ( P @ A ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ A )
% 1.60/1.07 | ~ ( P @ B )
% 1.60/1.07 | ( P @ ( ap @ A @ B ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ! [B: term] :
% 1.60/1.07 ( ~ ( P @ B )
% 1.60/1.07 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( P @ ( lam @ A ) ) )
% 1.60/1.07 | ( P @ Bound_variable_2367 ) )
% 1.60/1.07 => ( ! [A: term] :
% 1.60/1.07 ( A
% 1.60/1.07 = ( sub @ A @ id ) )
% 1.60/1.07 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 1.60/1.07 ( ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ~ ! [X: term] :
% 1.60/1.07 ( ( Q @ X )
% 1.60/1.07 = ( P @ id @ X @ id ) )
% 1.60/1.07 | ~ ! [B: term] :
% 1.60/1.07 ( ~ ( Q @ B )
% 1.60/1.07 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 1.60/1.07 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 1.60/1.07 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 1.60/1.07 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 1.60/1.07 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 1.60/1.07 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 1.60/1.07 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( var @ ( sub @ A @ id ) )
% 1.60/1.07 | ( P @ id @ A @ id ) )
% 1.60/1.07 | ~ ! [A: term,B: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ~ ( P @ id @ B @ id )
% 1.60/1.07 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 1.60/1.07 | ~ ! [F: subst > term > term] :
% 1.60/1.07 ( ~ ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 | ~ ! [A: term] :
% 1.60/1.07 ( ~ ( P @ id @ A @ id )
% 1.60/1.07 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 1.60/1.07 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 1.60/1.07 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 1.60/1.07
% 1.60/1.07 thf(hoaslaminj,conjecture,
% 1.60/1.07 ( hoaslaminj
% 1.60/1.07 = ( ! [F: subst > term > term] :
% 1.60/1.07 ( ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( F @ M @ A ) @ N )
% 1.60/1.07 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 => ! [G: subst > term > term] :
% 1.60/1.07 ( ! [M: subst,A: term,N: subst] :
% 1.60/1.07 ( ( sub @ ( G @ M @ A ) @ N )
% 1.60/1.07 = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 1.60/1.07 => ( ( ( hoaslam @ id
% 1.60/1.07 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 1.60/1.07 = ( hoaslam @ id
% 1.60/1.07 @ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
% 1.60/1.07 => ! [M: subst,A: term] :
% 1.60/1.07 ( ( F @ M @ A )
% 1.60/1.07 = ( G @ M @ A ) ) ) ) ) ) ) ).
% 1.60/1.07 ------------------------
% 1.60/1.09 % (10896)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/183Mi)
% 1.60/1.09 % (10900)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_10797 for (2999ds/2Mi)
% 1.60/1.09 % (10899)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/2Mi)
% 1.60/1.09 % (10901)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_10797 for (2999ds/275Mi)
% 1.60/1.09 % (10898)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_10797 for (2999ds/27Mi)
% 1.60/1.09 % (10897)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_10797 for (2999ds/4Mi)
% 1.60/1.09 % (10902)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/18Mi)
% 1.60/1.09 % (10899)Instruction limit reached!
% 1.60/1.09 % (10899)------------------------------
% 1.60/1.09 % (10899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.09 % (10899)Termination reason: Unknown
% 1.60/1.09 % (10899)Termination phase: shuffling
% 1.60/1.09
% 1.60/1.09 % (10899)Memory used [KB]: 1151
% 1.60/1.09 % (10899)Time elapsed: 0.002 s
% 1.60/1.09 % (10899)Instructions burned: 2 (million)
% 1.60/1.09 % (10899)------------------------------
% 1.60/1.09 % (10899)------------------------------
% 1.60/1.09 % (10900)Instruction limit reached!
% 1.60/1.09 % (10900)------------------------------
% 1.60/1.09 % (10900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.09 % (10900)Termination reason: Unknown
% 1.60/1.09 % (10900)Termination phase: shuffling
% 1.60/1.09
% 1.60/1.09 % (10900)Memory used [KB]: 1151
% 1.60/1.09 % (10900)Time elapsed: 0.002 s
% 1.60/1.09 % (10900)Instructions burned: 2 (million)
% 1.60/1.09 % (10900)------------------------------
% 1.60/1.09 % (10900)------------------------------
% 1.60/1.09 % (10897)Instruction limit reached!
% 1.60/1.09 % (10897)------------------------------
% 1.60/1.09 % (10897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.09 % (10897)Termination reason: Unknown
% 1.60/1.09 % (10897)Termination phase: shuffling
% 1.60/1.09
% 1.60/1.09 % (10897)Memory used [KB]: 1279
% 1.60/1.09 % (10897)Time elapsed: 0.003 s
% 1.60/1.09 % (10897)Instructions burned: 5 (million)
% 1.60/1.09 % (10897)------------------------------
% 1.60/1.09 % (10897)------------------------------
% 1.60/1.09 % (10902)Instruction limit reached!
% 1.60/1.09 % (10902)------------------------------
% 1.60/1.09 % (10902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.09 % (10902)Termination reason: Unknown
% 1.60/1.09 % (10902)Termination phase: shuffling
% 1.60/1.09
% 1.60/1.09 % (10902)Memory used [KB]: 2046
% 1.60/1.09 % (10902)Time elapsed: 0.007 s
% 1.60/1.09 % (10902)Instructions burned: 18 (million)
% 1.60/1.09 % (10902)------------------------------
% 1.60/1.09 % (10902)------------------------------
% 1.60/1.10 % (10898)Instruction limit reached!
% 1.60/1.10 % (10898)------------------------------
% 1.60/1.10 % (10898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.10 % (10898)Termination reason: Unknown
% 1.60/1.10 % (10898)Termination phase: Property scanning
% 1.60/1.10
% 1.60/1.10 % (10898)Memory used [KB]: 2174
% 1.60/1.10 % (10898)Time elapsed: 0.010 s
% 1.60/1.10 % (10898)Instructions burned: 27 (million)
% 1.60/1.10 % (10898)------------------------------
% 1.60/1.10 % (10898)------------------------------
% 1.60/1.10 % (10903)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/3Mi)
% 1.60/1.10 % (10905)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_10797 for (2999ds/15Mi)
% 1.60/1.10 % (10903)Instruction limit reached!
% 1.60/1.10 % (10903)------------------------------
% 1.60/1.10 % (10903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.10 % (10903)Termination reason: Unknown
% 1.60/1.10 % (10903)Termination phase: shuffling
% 1.60/1.10
% 1.60/1.10 % (10903)Memory used [KB]: 1279
% 1.60/1.10 % (10903)Time elapsed: 0.002 s
% 1.60/1.10 % (10903)Instructions burned: 4 (million)
% 1.60/1.10 % (10903)------------------------------
% 1.60/1.10 % (10903)------------------------------
% 1.60/1.10 % (10901)Refutation not found, incomplete strategy
% 1.60/1.10 % (10901)------------------------------
% 1.60/1.10 % (10901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.10 % (10901)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.10
% 1.60/1.10
% 1.60/1.10 % (10901)Memory used [KB]: 6652
% 1.60/1.10 % (10901)Time elapsed: 0.013 s
% 1.60/1.10 % (10901)Instructions burned: 39 (million)
% 1.60/1.10 % (10901)------------------------------
% 1.60/1.10 % (10901)------------------------------
% 1.60/1.10 % (10906)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_10797 for (2999ds/3Mi)
% 1.60/1.10 % (10905)Instruction limit reached!
% 1.60/1.10 % (10905)------------------------------
% 1.60/1.10 % (10905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.10 % (10905)Termination reason: Unknown
% 1.60/1.10 % (10905)Termination phase: shuffling
% 1.60/1.10
% 1.60/1.10 % (10905)Memory used [KB]: 1918
% 1.60/1.10 % (10905)Time elapsed: 0.006 s
% 1.60/1.10 % (10905)Instructions burned: 17 (million)
% 1.60/1.10 % (10905)------------------------------
% 1.60/1.10 % (10905)------------------------------
% 1.60/1.11 % (10906)Instruction limit reached!
% 1.60/1.11 % (10906)------------------------------
% 1.60/1.11 % (10906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.11 % (10906)Termination reason: Unknown
% 1.60/1.11 % (10906)Termination phase: shuffling
% 1.60/1.11
% 1.60/1.11 % (10906)Memory used [KB]: 1279
% 1.60/1.11 % (10906)Time elapsed: 0.002 s
% 1.60/1.11 % (10906)Instructions burned: 4 (million)
% 1.60/1.11 % (10906)------------------------------
% 1.60/1.11 % (10906)------------------------------
% 1.60/1.11 % (10904)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_10797 for (2999ds/37Mi)
% 1.60/1.11 % (10907)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_10797 for (2999ds/1041Mi)
% 1.60/1.11 % (10908)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/7Mi)
% 1.60/1.11 % (10909)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/16Mi)
% 1.60/1.11 % (10908)Instruction limit reached!
% 1.60/1.11 % (10908)------------------------------
% 1.60/1.11 % (10908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.11 % (10908)Termination reason: Unknown
% 1.60/1.11 % (10908)Termination phase: shuffling
% 1.60/1.11
% 1.60/1.11 % (10908)Memory used [KB]: 1407
% 1.60/1.11 % (10908)Time elapsed: 0.003 s
% 1.60/1.11 % (10908)Instructions burned: 8 (million)
% 1.60/1.11 % (10908)------------------------------
% 1.60/1.11 % (10908)------------------------------
% 1.70/1.11 % (10910)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_10797 for (2999ds/3Mi)
% 1.70/1.11 % (10911)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_10797 for (2999ds/3Mi)
% 1.70/1.12 % (10910)Instruction limit reached!
% 1.70/1.12 % (10910)------------------------------
% 1.70/1.12 % (10910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.12 % (10910)Termination reason: Unknown
% 1.70/1.12 % (10910)Termination phase: shuffling
% 1.70/1.12
% 1.70/1.12 % (10910)Memory used [KB]: 1279
% 1.70/1.12 % (10910)Time elapsed: 0.002 s
% 1.70/1.12 % (10910)Instructions burned: 4 (million)
% 1.70/1.12 % (10910)------------------------------
% 1.70/1.12 % (10910)------------------------------
% 1.70/1.12 % (10911)Instruction limit reached!
% 1.70/1.12 % (10911)------------------------------
% 1.70/1.12 % (10911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.12 % (10911)Termination reason: Unknown
% 1.70/1.12 % (10911)Termination phase: shuffling
% 1.70/1.12
% 1.70/1.12 % (10911)Memory used [KB]: 1279
% 1.70/1.12 % (10911)Time elapsed: 0.002 s
% 1.70/1.12 % (10911)Instructions burned: 4 (million)
% 1.70/1.12 % (10911)------------------------------
% 1.70/1.12 % (10911)------------------------------
% 1.70/1.12 % (10909)Instruction limit reached!
% 1.70/1.12 % (10909)------------------------------
% 1.70/1.12 % (10909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.12 % (10909)Termination reason: Unknown
% 1.70/1.12 % (10909)Termination phase: shuffling
% 1.70/1.12
% 1.70/1.12 % (10909)Memory used [KB]: 2046
% 1.70/1.12 % (10909)Time elapsed: 0.007 s
% 1.70/1.12 % (10909)Instructions burned: 18 (million)
% 1.70/1.12 % (10909)------------------------------
% 1.70/1.12 % (10909)------------------------------
% 1.70/1.12 % (10912)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/7Mi)
% 1.70/1.12 % (10904)Instruction limit reached!
% 1.70/1.12 % (10904)------------------------------
% 1.70/1.12 % (10904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.12 % (10904)Termination reason: Unknown
% 1.70/1.12 % (10904)Termination phase: shuffling
% 1.70/1.12
% 1.70/1.12 % (10904)Memory used [KB]: 1918
% 1.70/1.12 % (10904)Time elapsed: 0.018 s
% 1.70/1.12 % (10904)Instructions burned: 37 (million)
% 1.70/1.12 % (10904)------------------------------
% 1.70/1.12 % (10904)------------------------------
% 1.70/1.12 % (10912)Instruction limit reached!
% 1.70/1.12 % (10912)------------------------------
% 1.70/1.12 % (10912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.12 % (10912)Termination reason: Unknown
% 1.70/1.12 % (10912)Termination phase: shuffling
% 1.70/1.12
% 1.70/1.12 % (10912)Memory used [KB]: 1407
% 1.70/1.12 % (10912)Time elapsed: 0.003 s
% 1.70/1.12 % (10912)Instructions burned: 8 (million)
% 1.70/1.12 % (10912)------------------------------
% 1.70/1.12 % (10912)------------------------------
% 1.70/1.12 % (10913)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/3Mi)
% 1.70/1.12 % (10914)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/4Mi)
% 1.70/1.13 % (10913)Instruction limit reached!
% 1.70/1.13 % (10913)------------------------------
% 1.70/1.13 % (10913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.13 % (10913)Termination reason: Unknown
% 1.70/1.13 % (10913)Termination phase: shuffling
% 1.70/1.13
% 1.70/1.13 % (10913)Memory used [KB]: 1279
% 1.70/1.13 % (10913)Time elapsed: 0.002 s
% 1.70/1.13 % (10913)Instructions burned: 4 (million)
% 1.70/1.13 % (10913)------------------------------
% 1.70/1.13 % (10913)------------------------------
% 1.70/1.13 % (10914)Instruction limit reached!
% 1.70/1.13 % (10914)------------------------------
% 1.70/1.13 % (10914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.13 % (10914)Termination reason: Unknown
% 1.70/1.13 % (10914)Termination phase: shuffling
% 1.70/1.13
% 1.70/1.13 % (10914)Memory used [KB]: 1279
% 1.70/1.13 % (10914)Time elapsed: 0.002 s
% 1.70/1.13 % (10914)Instructions burned: 4 (million)
% 1.70/1.13 % (10914)------------------------------
% 1.70/1.13 % (10914)------------------------------
% 1.70/1.13 % (10915)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/18Mi)
% 1.70/1.13 % (10916)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/710Mi)
% 1.70/1.13 % (10917)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/6Mi)
% 1.70/1.13 % (10915)Instruction limit reached!
% 1.70/1.13 % (10915)------------------------------
% 1.70/1.13 % (10915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.13 % (10915)Termination reason: Unknown
% 1.70/1.13 % (10915)Termination phase: shuffling
% 1.70/1.13
% 1.70/1.13 % (10915)Memory used [KB]: 2046
% 1.70/1.13 % (10915)Time elapsed: 0.007 s
% 1.70/1.13 % (10915)Instructions burned: 20 (million)
% 1.70/1.13 % (10915)------------------------------
% 1.70/1.13 % (10915)------------------------------
% 1.70/1.13 % (10917)Instruction limit reached!
% 1.70/1.13 % (10917)------------------------------
% 1.70/1.13 % (10917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.13 % (10917)Termination reason: Unknown
% 1.70/1.13 % (10917)Termination phase: shuffling
% 1.70/1.13
% 1.70/1.13 % (10917)Memory used [KB]: 1407
% 1.70/1.13 % (10917)Time elapsed: 0.003 s
% 1.70/1.13 % (10917)Instructions burned: 7 (million)
% 1.70/1.13 % (10917)------------------------------
% 1.70/1.13 % (10917)------------------------------
% 1.70/1.13 % (10918)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_10797 for (2999ds/902Mi)
% 1.70/1.14 % (10919)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_10797 for (2999ds/21Mi)
% 1.70/1.14 % (10896)Instruction limit reached!
% 1.70/1.14 % (10896)------------------------------
% 1.70/1.14 % (10896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.14 % (10896)Termination reason: Unknown
% 1.70/1.14 % (10896)Termination phase: Property scanning
% 1.70/1.14
% 1.70/1.14 % (10896)Memory used [KB]: 4477
% 1.70/1.14 % (10896)Time elapsed: 0.050 s
% 1.70/1.14 % (10896)Instructions burned: 184 (million)
% 1.70/1.14 % (10896)------------------------------
% 1.70/1.14 % (10896)------------------------------
% 1.70/1.14 % (10920)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/5Mi)
% 1.70/1.14 % (10919)Instruction limit reached!
% 1.70/1.14 % (10919)------------------------------
% 1.70/1.14 % (10919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.14 % (10919)Termination reason: Unknown
% 1.70/1.14 % (10919)Termination phase: shuffling
% 1.70/1.14
% 1.70/1.14 % (10919)Memory used [KB]: 2174
% 1.70/1.14 % (10919)Time elapsed: 0.008 s
% 1.70/1.14 % (10919)Instructions burned: 23 (million)
% 1.70/1.14 % (10919)------------------------------
% 1.70/1.14 % (10919)------------------------------
% 1.70/1.14 % (10921)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_10797 for (2999ds/6Mi)
% 1.70/1.14 % (10920)Instruction limit reached!
% 1.70/1.14 % (10920)------------------------------
% 1.70/1.14 % (10920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.14 % (10920)Termination reason: Unknown
% 1.70/1.14 % (10920)Termination phase: shuffling
% 1.70/1.14
% 1.70/1.14 % (10920)Memory used [KB]: 1407
% 1.70/1.14 % (10920)Time elapsed: 0.003 s
% 1.70/1.14 % (10920)Instructions burned: 8 (million)
% 1.70/1.14 % (10920)------------------------------
% 1.70/1.14 % (10920)------------------------------
% 1.70/1.15 % (10921)Instruction limit reached!
% 1.70/1.15 % (10921)------------------------------
% 1.70/1.15 % (10921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.15 % (10921)Termination reason: Unknown
% 1.70/1.15 % (10921)Termination phase: shuffling
% 1.70/1.15
% 1.70/1.15 % (10921)Memory used [KB]: 1407
% 1.70/1.15 % (10921)Time elapsed: 0.003 s
% 1.70/1.15 % (10921)Instructions burned: 7 (million)
% 1.70/1.15 % (10921)------------------------------
% 1.70/1.15 % (10921)------------------------------
% 1.70/1.15 % (10922)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/377Mi)
% 1.70/1.15 % (10923)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_10797 for (2999ds/779Mi)
% 1.70/1.15 % (10924)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_10797 for (2999ds/19Mi)
% 1.70/1.16 % (10925)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/879Mi)
% 1.70/1.16 % (10924)Instruction limit reached!
% 1.70/1.16 % (10924)------------------------------
% 1.70/1.16 % (10924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.16 % (10924)Termination reason: Unknown
% 1.70/1.16 % (10924)Termination phase: shuffling
% 1.70/1.16
% 1.70/1.16 % (10924)Memory used [KB]: 1663
% 1.70/1.16 % (10924)Time elapsed: 0.006 s
% 1.70/1.16 % (10924)Instructions burned: 19 (million)
% 1.70/1.16 % (10924)------------------------------
% 1.70/1.16 % (10924)------------------------------
% 1.70/1.17 % (10926)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10797 for (2999ds/17Mi)
% 1.70/1.17 % (10926)Instruction limit reached!
% 1.70/1.17 % (10926)------------------------------
% 1.70/1.17 % (10926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.17 % (10926)Termination reason: Unknown
% 1.70/1.17 % (10926)Termination phase: shuffling
% 1.70/1.17
% 1.70/1.17 % (10926)Memory used [KB]: 2046
% 1.70/1.17 % (10926)Time elapsed: 0.007 s
% 1.70/1.17 % (10926)Instructions burned: 19 (million)
% 1.70/1.17 % (10926)------------------------------
% 1.70/1.17 % (10926)------------------------------
% 1.70/1.18 % (10927)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10797 for (2998ds/3Mi)
% 1.70/1.18 % (10927)Instruction limit reached!
% 1.70/1.18 % (10927)------------------------------
% 1.70/1.18 % (10927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.18 % (10927)Termination reason: Unknown
% 1.70/1.18 % (10927)Termination phase: shuffling
% 1.70/1.18
% 1.70/1.18 % (10927)Memory used [KB]: 1279
% 1.70/1.18 % (10927)Time elapsed: 0.002 s
% 1.70/1.18 % (10927)Instructions burned: 3 (million)
% 1.70/1.18 % (10927)------------------------------
% 1.70/1.18 % (10927)------------------------------
% 1.70/1.19 % (10928)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10797 for (2998ds/30Mi)
% 1.70/1.20 % (10928)Instruction limit reached!
% 1.70/1.20 % (10928)------------------------------
% 1.70/1.20 % (10928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.20 % (10928)Termination reason: Unknown
% 1.70/1.20 % (10928)Termination phase: Property scanning
% 1.70/1.20
% 1.70/1.20 % (10928)Memory used [KB]: 2174
% 1.70/1.20 % (10928)Time elapsed: 0.011 s
% 1.70/1.20 % (10928)Instructions burned: 32 (million)
% 1.70/1.20 % (10928)------------------------------
% 1.70/1.20 % (10928)------------------------------
% 1.70/1.21 % (10929)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10797 for (2998ds/127Mi)
% 1.70/1.25 % (10929)Instruction limit reached!
% 1.70/1.25 % (10929)------------------------------
% 1.70/1.25 % (10929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.25 % (10929)Termination reason: Unknown
% 1.70/1.25 % (10929)Termination phase: Property scanning
% 1.70/1.25
% 1.70/1.25 % (10929)Memory used [KB]: 4349
% 1.70/1.25 % (10929)Time elapsed: 0.037 s
% 1.70/1.25 % (10929)Instructions burned: 128 (million)
% 1.70/1.25 % (10929)------------------------------
% 1.70/1.25 % (10929)------------------------------
% 1.70/1.26 % (10922)Instruction limit reached!
% 1.70/1.26 % (10922)------------------------------
% 1.70/1.26 % (10922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.26 % (10922)Termination reason: Unknown
% 1.70/1.26 % (10922)Termination phase: Saturation
% 1.70/1.26
% 1.70/1.26 % (10922)Memory used [KB]: 10362
% 1.70/1.26 % (10922)Time elapsed: 0.109 s
% 1.70/1.26 % (10922)Instructions burned: 378 (million)
% 1.70/1.26 % (10922)------------------------------
% 1.70/1.26 % (10922)------------------------------
% 1.70/1.26 % (10930)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10797 for (2998ds/100Mi)
% 1.70/1.27 % (10931)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_10797 for (2998ds/3Mi)
% 1.70/1.27 % (10931)Instruction limit reached!
% 1.70/1.27 % (10931)------------------------------
% 1.70/1.27 % (10931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.27 % (10931)Termination reason: Unknown
% 1.70/1.27 % (10931)Termination phase: shuffling
% 1.70/1.27
% 1.70/1.27 % (10931)Memory used [KB]: 1279
% 1.70/1.27 % (10931)Time elapsed: 0.002 s
% 1.70/1.27 % (10931)Instructions burned: 3 (million)
% 1.70/1.27 % (10931)------------------------------
% 1.70/1.27 % (10931)------------------------------
% 1.70/1.28 % (10932)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_10797 for (2998ds/20Mi)
% 1.70/1.28 % (10932)Instruction limit reached!
% 1.70/1.28 % (10932)------------------------------
% 1.70/1.28 % (10932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.28 % (10932)Termination reason: Unknown
% 1.70/1.28 % (10932)Termination phase: shuffling
% 1.70/1.28
% 1.70/1.28 % (10932)Memory used [KB]: 2174
% 1.70/1.28 % (10932)Time elapsed: 0.008 s
% 1.70/1.28 % (10932)Instructions burned: 22 (million)
% 1.70/1.28 % (10932)------------------------------
% 1.70/1.28 % (10932)------------------------------
% 1.70/1.28 % (10930)Instruction limit reached!
% 1.70/1.28 % (10930)------------------------------
% 1.70/1.28 % (10930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.28 % (10930)Termination reason: Unknown
% 1.70/1.28 % (10930)Termination phase: Saturation
% 1.70/1.28
% 1.70/1.28 % (10930)Memory used [KB]: 6524
% 1.70/1.28 % (10930)Time elapsed: 0.027 s
% 1.70/1.28 % (10930)Instructions burned: 103 (million)
% 1.70/1.28 % (10930)------------------------------
% 1.70/1.28 % (10930)------------------------------
% 1.70/1.29 % (10933)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_10797 for (2997ds/86Mi)
% 1.70/1.29 % (10934)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_10797 for (2997ds/107Mi)
% 1.70/1.32 % (10933)Instruction limit reached!
% 1.70/1.32 % (10933)------------------------------
% 1.70/1.32 % (10933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (10933)Termination reason: Unknown
% 1.70/1.32 % (10933)Termination phase: Preprocessing 3
% 1.70/1.32
% 1.70/1.32 % (10933)Memory used [KB]: 4093
% 1.70/1.32 % (10933)Time elapsed: 0.026 s
% 1.70/1.32 % (10933)Instructions burned: 87 (million)
% 1.70/1.32 % (10933)------------------------------
% 1.70/1.32 % (10933)------------------------------
% 1.70/1.33 % (10934)Instruction limit reached!
% 1.70/1.33 % (10934)------------------------------
% 1.70/1.33 % (10934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (10934)Termination reason: Unknown
% 1.70/1.33 % (10934)Termination phase: Property scanning
% 1.70/1.33
% 1.70/1.33 % (10934)Memory used [KB]: 4477
% 1.70/1.33 % (10934)Time elapsed: 0.033 s
% 1.70/1.33 % (10934)Instructions burned: 109 (million)
% 1.70/1.33 % (10934)------------------------------
% 1.70/1.33 % (10934)------------------------------
% 1.70/1.33 % (10935)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_10797 for (2997ds/39Mi)
% 1.70/1.34 % (10936)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_10797 for (2997ds/448Mi)
% 1.70/1.34 % (10935)Instruction limit reached!
% 1.70/1.34 % (10935)------------------------------
% 1.70/1.34 % (10935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (10923)Instruction limit reached!
% 1.70/1.34 % (10923)------------------------------
% 1.70/1.34 % (10923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (10923)Termination reason: Unknown
% 1.70/1.34 % (10923)Termination phase: Saturation
% 1.70/1.34
% 1.70/1.34 % (10923)Memory used [KB]: 6780
% 1.70/1.34 % (10923)Time elapsed: 0.187 s
% 1.70/1.34 % (10923)Instructions burned: 782 (million)
% 1.70/1.34 % (10923)------------------------------
% 1.70/1.34 % (10923)------------------------------
% 1.70/1.34 % (10935)Termination reason: Unknown
% 1.70/1.34 % (10935)Termination phase: Property scanning
% 1.70/1.34
% 1.70/1.34 % (10935)Memory used [KB]: 1918
% 1.70/1.34 % (10935)Time elapsed: 0.012 s
% 1.70/1.34 % (10935)Instructions burned: 41 (million)
% 1.70/1.34 % (10935)------------------------------
% 1.70/1.34 % (10935)------------------------------
% 1.70/1.35 % (10937)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_10797 for (2997ds/46Mi)
% 1.70/1.35 % (10938)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_10797 for (2997ds/98Mi)
% 1.70/1.35 % (10916)Instruction limit reached!
% 1.70/1.35 % (10916)------------------------------
% 1.70/1.35 % (10916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (10916)Termination reason: Unknown
% 1.70/1.35 % (10916)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (10916)Memory used [KB]: 11513
% 1.70/1.35 % (10916)Time elapsed: 0.218 s
% 1.70/1.35 % (10916)Instructions burned: 712 (million)
% 1.70/1.35 % (10916)------------------------------
% 1.70/1.35 % (10916)------------------------------
% 1.70/1.36 % (10907)Instruction limit reached!
% 1.70/1.36 % (10907)------------------------------
% 1.70/1.36 % (10907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (10907)Termination reason: Unknown
% 1.70/1.36 % (10907)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (10907)Memory used [KB]: 7675
% 1.70/1.36 % (10907)Time elapsed: 0.253 s
% 1.70/1.36 % (10907)Instructions burned: 1041 (million)
% 1.70/1.36 % (10907)------------------------------
% 1.70/1.36 % (10907)------------------------------
% 1.70/1.36 % (10939)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_10797 for (2997ds/507Mi)
% 1.70/1.36 % (10937)Instruction limit reached!
% 1.70/1.36 % (10937)------------------------------
% 1.70/1.36 % (10937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (10937)Termination reason: Unknown
% 1.70/1.36 % (10937)Termination phase: Preprocessing 2
% 1.70/1.36
% 1.70/1.36 % (10937)Memory used [KB]: 2558
% 1.70/1.36 % (10937)Time elapsed: 0.015 s
% 1.70/1.36 % (10937)Instructions burned: 48 (million)
% 1.70/1.36 % (10937)------------------------------
% 1.70/1.36 % (10937)------------------------------
% 1.70/1.37 % (10940)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_10797 for (2997ds/149Mi)
% 1.70/1.37 % (10941)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10797 for (2997ds/39Mi)
% 1.70/1.37 % (10938)Instruction limit reached!
% 1.70/1.37 % (10938)------------------------------
% 1.70/1.37 % (10938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (10938)Termination reason: Unknown
% 1.70/1.37 % (10938)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (10938)Memory used [KB]: 2046
% 1.70/1.37 % (10938)Time elapsed: 0.026 s
% 1.70/1.37 % (10938)Instructions burned: 100 (million)
% 1.70/1.37 % (10938)------------------------------
% 1.70/1.37 % (10938)------------------------------
% 1.70/1.38 % (10942)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_10797 for (2997ds/6Mi)
% 1.70/1.38 % (10941)Instruction limit reached!
% 1.70/1.38 % (10941)------------------------------
% 1.70/1.38 % (10941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (10941)Termination reason: Unknown
% 1.70/1.38 % (10941)Termination phase: Preprocessing 1
% 1.70/1.38
% 1.70/1.38 % (10941)Memory used [KB]: 2302
% 1.70/1.38 % (10941)Time elapsed: 0.013 s
% 1.70/1.38 % (10941)Instructions burned: 41 (million)
% 1.70/1.38 % (10941)------------------------------
% 1.70/1.38 % (10941)------------------------------
% 1.70/1.38 % (10942)Instruction limit reached!
% 1.70/1.38 % (10942)------------------------------
% 1.70/1.38 % (10942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (10942)Termination reason: Unknown
% 1.70/1.38 % (10942)Termination phase: shuffling
% 1.70/1.38
% 1.70/1.38 % (10942)Memory used [KB]: 1407
% 1.70/1.38 % (10942)Time elapsed: 0.003 s
% 1.70/1.38 % (10942)Instructions burned: 7 (million)
% 1.70/1.38 % (10942)------------------------------
% 1.70/1.38 % (10942)------------------------------
% 1.70/1.39 % (10943)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_10797 for (2996ds/1087Mi)
% 1.70/1.39 % (10944)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/47Mi)
% 1.70/1.40 % (10918)Instruction limit reached!
% 1.70/1.40 % (10918)------------------------------
% 1.70/1.40 % (10918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (10918)Termination reason: Unknown
% 1.70/1.40 % (10918)Termination phase: Saturation
% 1.70/1.40
% 1.70/1.40 % (10918)Memory used [KB]: 12537
% 1.70/1.40 % (10918)Time elapsed: 0.266 s
% 1.70/1.40 % (10918)Instructions burned: 904 (million)
% 1.70/1.40 % (10918)------------------------------
% 1.70/1.40 % (10918)------------------------------
% 1.70/1.41 % (10944)Instruction limit reached!
% 1.70/1.41 % (10944)------------------------------
% 1.70/1.41 % (10944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.41 % (10944)Termination reason: Unknown
% 1.70/1.41 % (10944)Termination phase: Naming
% 1.70/1.41
% 1.70/1.41 % (10944)Memory used [KB]: 2686
% 1.70/1.41 % (10944)Time elapsed: 0.015 s
% 1.70/1.41 % (10944)Instructions burned: 48 (million)
% 1.70/1.41 % (10944)------------------------------
% 1.70/1.41 % (10944)------------------------------
% 1.70/1.41 % (10945)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_10797 for (2996ds/44Mi)
% 1.70/1.41 % (10940)Instruction limit reached!
% 1.70/1.41 % (10940)------------------------------
% 1.70/1.41 % (10940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.41 % (10940)Termination reason: Unknown
% 1.70/1.41 % (10940)Termination phase: Property scanning
% 1.70/1.41
% 1.70/1.41 % (10940)Memory used [KB]: 7803
% 1.70/1.41 % (10940)Time elapsed: 0.043 s
% 1.70/1.41 % (10940)Instructions burned: 152 (million)
% 1.70/1.41 % (10940)------------------------------
% 1.70/1.41 % (10940)------------------------------
% 1.70/1.42 % (10946)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_10797 for (2996ds/432Mi)
% 1.70/1.42 % (10947)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/62Mi)
% 1.70/1.42 % (10945)Instruction limit reached!
% 1.70/1.42 % (10945)------------------------------
% 1.70/1.42 % (10945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (10945)Termination reason: Unknown
% 1.70/1.42 % (10945)Termination phase: Property scanning
% 1.70/1.42
% 1.70/1.42 % (10945)Memory used [KB]: 1918
% 1.70/1.42 % (10945)Time elapsed: 0.013 s
% 1.70/1.42 % (10945)Instructions burned: 46 (million)
% 1.70/1.42 % (10945)------------------------------
% 1.70/1.42 % (10945)------------------------------
% 1.70/1.43 % (10925)Instruction limit reached!
% 1.70/1.43 % (10925)------------------------------
% 1.70/1.43 % (10925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.43 % (10925)Termination reason: Unknown
% 1.70/1.43 % (10925)Termination phase: Saturation
% 1.70/1.43
% 1.70/1.43 % (10925)Memory used [KB]: 12025
% 1.70/1.43 % (10925)Time elapsed: 0.272 s
% 1.70/1.43 % (10925)Instructions burned: 880 (million)
% 1.70/1.43 % (10925)------------------------------
% 1.70/1.43 % (10925)------------------------------
% 1.70/1.43 % (10948)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_10797 for (2996ds/31Mi)
% 1.70/1.44 % (10949)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/96Mi)
% 1.70/1.44 % (10947)Instruction limit reached!
% 1.70/1.44 % (10947)------------------------------
% 1.70/1.44 % (10947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (10947)Termination reason: Unknown
% 1.70/1.44 % (10947)Termination phase: Property scanning
% 1.70/1.44
% 1.70/1.44 % (10947)Memory used [KB]: 1918
% 1.70/1.44 % (10947)Time elapsed: 0.017 s
% 1.70/1.44 % (10947)Instructions burned: 63 (million)
% 1.70/1.44 % (10947)------------------------------
% 1.70/1.44 % (10947)------------------------------
% 1.70/1.44 % (10939)Refutation not found, incomplete strategy
% 1.70/1.44 % (10939)------------------------------
% 1.70/1.44 % (10939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (10939)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.44
% 1.70/1.44
% 1.70/1.44 % (10939)Memory used [KB]: 9850
% 1.70/1.44 % (10939)Time elapsed: 0.078 s
% 1.70/1.44 % (10939)Instructions burned: 279 (million)
% 1.70/1.44 % (10939)------------------------------
% 1.70/1.44 % (10939)------------------------------
% 1.70/1.44 % (10948)Instruction limit reached!
% 1.70/1.44 % (10948)------------------------------
% 1.70/1.44 % (10948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (10948)Termination reason: Unknown
% 1.70/1.44 % (10948)Termination phase: Property scanning
% 1.70/1.44
% 1.70/1.44 % (10948)Memory used [KB]: 2174
% 1.70/1.44 % (10948)Time elapsed: 0.011 s
% 1.70/1.44 % (10948)Instructions burned: 34 (million)
% 1.70/1.44 % (10948)------------------------------
% 1.70/1.44 % (10948)------------------------------
% 1.70/1.45 % (10950)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_10797 for (2996ds/453Mi)
% 1.70/1.45 % (10951)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_10797 for (2996ds/71Mi)
% 1.70/1.45 % (10952)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/83Mi)
% 1.70/1.46 % (10936)Instruction limit reached!
% 1.70/1.46 % (10936)------------------------------
% 1.70/1.46 % (10936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (10936)Termination reason: Unknown
% 1.70/1.46 % (10936)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (10936)Memory used [KB]: 8059
% 1.70/1.46 % (10936)Time elapsed: 0.122 s
% 1.70/1.46 % (10936)Instructions burned: 449 (million)
% 1.70/1.46 % (10936)------------------------------
% 1.70/1.46 % (10936)------------------------------
% 1.70/1.46 % (10949)Instruction limit reached!
% 1.70/1.46 % (10949)------------------------------
% 1.70/1.46 % (10949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (10949)Termination reason: Unknown
% 1.70/1.46 % (10949)Termination phase: Property scanning
% 1.70/1.46
% 1.70/1.46 % (10949)Memory used [KB]: 4221
% 1.70/1.46 % (10949)Time elapsed: 0.029 s
% 1.70/1.46 % (10949)Instructions burned: 97 (million)
% 1.70/1.46 % (10949)------------------------------
% 1.70/1.46 % (10949)------------------------------
% 1.70/1.47 % (10953)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/11Mi)
% 1.70/1.47 % (10951)Instruction limit reached!
% 1.70/1.47 % (10951)------------------------------
% 1.70/1.47 % (10951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10951)Termination reason: Unknown
% 1.70/1.47 % (10951)Termination phase: Preprocessing 3
% 1.70/1.47 % (10943)First to succeed.
% 1.70/1.47
% 1.70/1.47 % (10951)Memory used [KB]: 3454
% 1.70/1.47 % (10951)Time elapsed: 0.022 s
% 1.70/1.47 % (10951)Instructions burned: 73 (million)
% 1.70/1.47 % (10951)------------------------------
% 1.70/1.47 % (10951)------------------------------
% 1.70/1.47 % (10953)Instruction limit reached!
% 1.70/1.47 % (10953)------------------------------
% 1.70/1.47 % (10953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10953)Termination reason: Unknown
% 1.70/1.47 % (10953)Termination phase: shuffling
% 1.70/1.47
% 1.70/1.47 % (10953)Memory used [KB]: 1535
% 1.70/1.47 % (10953)Time elapsed: 0.005 s
% 1.70/1.47 % (10953)Instructions burned: 14 (million)
% 1.70/1.47 % (10953)------------------------------
% 1.70/1.47 % (10953)------------------------------
% 1.70/1.47 % (10954)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_10797 for (2996ds/41Mi)
% 1.70/1.47 % (10952)Instruction limit reached!
% 1.70/1.47 % (10952)------------------------------
% 1.70/1.47 % (10952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10952)Termination reason: Unknown
% 1.70/1.47 % (10952)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (10952)Memory used [KB]: 7036
% 1.70/1.47 % (10952)Time elapsed: 0.025 s
% 1.70/1.47 % (10952)Instructions burned: 84 (million)
% 1.70/1.47 % (10952)------------------------------
% 1.70/1.47 % (10952)------------------------------
% 1.70/1.48 % (10955)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/6Mi)
% 1.70/1.48 % (10955)Instruction limit reached!
% 1.70/1.48 % (10955)------------------------------
% 1.70/1.48 % (10955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (10955)Termination reason: Unknown
% 1.70/1.48 % (10955)Termination phase: shuffling
% 1.70/1.48
% 1.70/1.48 % (10955)Memory used [KB]: 1407
% 1.70/1.48 % (10955)Time elapsed: 0.003 s
% 1.70/1.48 % (10955)Instructions burned: 7 (million)
% 1.70/1.48 % (10955)------------------------------
% 1.70/1.48 % (10955)------------------------------
% 1.70/1.48 % (10956)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/150Mi)
% 1.70/1.48 % (10957)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10797 for (2996ds/343Mi)
% 1.70/1.48 % (10954)Instruction limit reached!
% 1.70/1.48 % (10954)------------------------------
% 1.70/1.48 % (10954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (10954)Termination reason: Unknown
% 1.70/1.48 % (10954)Termination phase: Property scanning
% 1.70/1.48
% 1.70/1.48 % (10954)Memory used [KB]: 1918
% 1.70/1.48 % (10954)Time elapsed: 0.012 s
% 1.70/1.48 % (10954)Instructions burned: 43 (million)
% 1.70/1.48 % (10954)------------------------------
% 1.70/1.48 % (10954)------------------------------
% 1.70/1.49 % (10958)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_10797 for (2996ds/109Mi)
% 1.70/1.49 % (10959)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_10797 for (2996ds/253Mi)
% 1.70/1.50 % (10957)Refutation not found, incomplete strategy
% 1.70/1.50 % (10957)------------------------------
% 1.70/1.50 % (10957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.50 % (10957)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.50
% 1.70/1.50
% 1.70/1.50 % (10957)Memory used [KB]: 6780
% 1.70/1.50 % (10957)Time elapsed: 0.015 s
% 1.70/1.50 % (10957)Instructions burned: 49 (million)
% 1.70/1.50 % (10957)------------------------------
% 1.70/1.50 % (10957)------------------------------
% 1.70/1.50 % (10943)Refutation found. Thanks to Tanya!
% 1.70/1.50 % SZS status Theorem for DTF2THF_10797
% 1.70/1.50 % SZS output start Proof for DTF2THF_10797
% 1.70/1.50 thf(type_def_5, type, term: $tType).
% 1.70/1.50 thf(type_def_7, type, subst: $tType).
% 1.70/1.50 thf(type_def_8, type, d_term: $tType).
% 1.70/1.50 thf(type_def_9, type, d_subst: $tType).
% 1.70/1.50 thf(func_def_0, type, term: $tType).
% 1.70/1.50 thf(func_def_1, type, subst: $tType).
% 1.70/1.50 thf(func_def_2, type, one: term).
% 1.70/1.50 thf(func_def_3, type, ap: term > term > term).
% 1.70/1.50 thf(func_def_4, type, lam: term > term).
% 1.70/1.50 thf(func_def_5, type, sub: term > subst > term).
% 1.70/1.50 thf(func_def_6, type, id: subst).
% 1.70/1.50 thf(func_def_7, type, sh: subst).
% 1.70/1.50 thf(func_def_8, type, push: term > subst > subst).
% 1.70/1.50 thf(func_def_9, type, comp: subst > subst > subst).
% 1.70/1.50 thf(func_def_10, type, var: term > $o).
% 1.70/1.50 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 1.70/1.50 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 1.70/1.50 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 1.70/1.50 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 1.70/1.50 thf(func_def_124, type, d_term: $tType).
% 1.70/1.50 thf(func_def_125, type, d_subst: $tType).
% 1.70/1.50 thf(func_def_126, type, d2term: d_term > term).
% 1.70/1.50 thf(func_def_127, type, d2subst: d_subst > subst).
% 1.70/1.50 thf(func_def_128, type, d_one: d_term).
% 1.70/1.50 thf(func_def_129, type, d_id: d_subst).
% 1.70/1.50 thf(func_def_141, type, sP0: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_143, type, sP2: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_144, type, sP3: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_147, type, sP6: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_148, type, sP7: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_149, type, sP8: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_150, type, sP9: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_151, type, sP10: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_152, type, sP11: term > (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_153, type, sP12: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_154, type, sP13: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_155, type, sP14: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_156, type, sP15: (term > $o) > $o).
% 1.70/1.50 thf(func_def_157, type, sP16: (term > $o) > $o).
% 1.70/1.50 thf(func_def_158, type, sP17: (term > $o) > $o).
% 1.70/1.50 thf(func_def_163, type, sP22: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_164, type, sP23: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_165, type, sP24: term > (term > $o) > $o).
% 1.70/1.50 thf(func_def_167, type, sP26: (term > $o) > $o).
% 1.70/1.50 thf(func_def_168, type, sP27: (term > $o) > $o).
% 1.70/1.50 thf(func_def_170, type, sP29: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_171, type, sP30: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_172, type, sP31: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_173, type, sP32: (term > $o) > $o).
% 1.70/1.50 thf(func_def_174, type, sP33: (term > $o) > $o).
% 1.70/1.50 thf(func_def_175, type, sP34: (term > $o) > $o).
% 1.70/1.50 thf(func_def_176, type, sP35: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_177, type, sP36: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_178, type, sP37: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_179, type, sP38: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_183, type, sP42: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_184, type, sP43: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_185, type, sP44: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_186, type, sP45: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_189, type, sP48: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_190, type, sP49: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_192, type, sP51: (term > $o) > $o).
% 1.70/1.50 thf(func_def_193, type, sP52: (term > $o) > $o).
% 1.70/1.50 thf(func_def_194, type, sP53: (term > $o) > $o).
% 1.70/1.50 thf(func_def_195, type, sP54: (term > $o) > $o).
% 1.70/1.50 thf(func_def_200, type, sP59: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_202, type, sP61: (term > $o) > $o).
% 1.70/1.50 thf(func_def_203, type, sP62: (term > $o) > $o).
% 1.70/1.50 thf(func_def_204, type, sP63: (term > $o) > $o).
% 1.70/1.50 thf(func_def_205, type, sP64: (term > $o) > $o).
% 1.70/1.50 thf(func_def_208, type, sP67: (term > $o) > $o).
% 1.70/1.50 thf(func_def_209, type, sP68: (term > $o) > $o).
% 1.70/1.50 thf(func_def_211, type, sP70: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_212, type, sP71: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_213, type, sP72: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_214, type, sP73: (term > $o) > $o).
% 1.70/1.50 thf(func_def_215, type, sP74: (term > $o) > $o).
% 1.70/1.50 thf(func_def_219, type, sP78: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_220, type, sP79: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_221, type, sP80: (term > $o) > term > $o).
% 1.70/1.50 thf(func_def_223, type, sP82: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_224, type, sP83: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_228, type, sP87: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_230, type, sP89: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_232, type, sP91: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_233, type, sP92: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_234, type, sP93: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_237, type, sP96: (term > $o) > $o).
% 1.70/1.50 thf(func_def_238, type, sP97: (term > $o) > $o).
% 1.70/1.50 thf(func_def_242, type, sP101: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_244, type, sP103: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_246, type, sP105: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_247, type, sP106: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_248, type, sP107: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_249, type, sP108: (subst > term > subst > $o) > $o).
% 1.70/1.50 thf(func_def_251, type, sK110: subst > term > term).
% 1.70/1.50 thf(func_def_252, type, sK111: subst > term > term).
% 1.70/1.50 thf(func_def_253, type, sK112: subst).
% 1.70/1.50 thf(func_def_254, type, sK113: term).
% 1.70/1.50 thf(func_def_255, type, sK114: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_256, type, sK115: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_257, type, sK116: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_258, type, sK117: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_259, type, sK118: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_260, type, sK119: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_261, type, sK120: term).
% 1.70/1.50 thf(func_def_262, type, sK121: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_263, type, sK122: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_264, type, sK123: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_265, type, sK124: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_266, type, sK125: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_267, type, sK126: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_268, type, sK127: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_269, type, sK128: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_270, type, sK129: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_271, type, sK130: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_272, type, sK131: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_273, type, sK132: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_274, type, sK133: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_275, type, sK134: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_276, type, sK135: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_277, type, sK136: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_278, type, sK137: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_279, type, sK138: term).
% 1.70/1.50 thf(func_def_280, type, sK139: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_281, type, sK140: (subst > term > subst > $o) > term > term).
% 1.70/1.50 thf(func_def_282, type, sK141: (subst > term > term) > term > subst).
% 1.70/1.50 thf(func_def_283, type, sK142: (subst > term > term) > term > term).
% 1.70/1.50 thf(func_def_284, type, sK143: (subst > term > term) > term > subst).
% 1.70/1.50 thf(func_def_285, type, sK144: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_286, type, sK145: (subst > term > term) > term > subst).
% 1.70/1.50 thf(func_def_287, type, sK146: (subst > term > term) > term > term).
% 1.70/1.50 thf(func_def_288, type, sK147: (subst > term > term) > term > subst).
% 1.70/1.50 thf(func_def_289, type, sK148: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_290, type, sK149: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_291, type, sK150: term).
% 1.70/1.50 thf(func_def_292, type, sK151: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_293, type, sK152: term > $o).
% 1.70/1.50 thf(func_def_294, type, sK153: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_295, type, sK154: (term > $o) > term > term).
% 1.70/1.50 thf(func_def_296, type, sK155: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_297, type, sK156: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_298, type, sK157: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_299, type, sK158: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_300, type, sK159: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_301, type, sK160: term).
% 1.70/1.50 thf(func_def_302, type, sK161: term).
% 1.70/1.50 thf(func_def_303, type, sK162: term).
% 1.70/1.50 thf(func_def_304, type, sK163: term).
% 1.70/1.50 thf(func_def_305, type, sK164: term).
% 1.70/1.50 thf(func_def_306, type, sK165: term).
% 1.70/1.50 thf(func_def_307, type, sK166: term).
% 1.70/1.50 thf(func_def_308, type, sK167: term).
% 1.70/1.50 thf(func_def_309, type, sK168: term).
% 1.70/1.50 thf(func_def_310, type, sK169: subst).
% 1.70/1.50 thf(func_def_311, type, sK170: term).
% 1.70/1.50 thf(func_def_312, type, sK171: term > $o).
% 1.70/1.50 thf(func_def_313, type, sK172: (term > $o) > subst > term).
% 1.70/1.50 thf(func_def_314, type, sK173: (term > $o) > term).
% 1.70/1.50 thf(func_def_315, type, sK174: (term > $o) > term).
% 1.70/1.50 thf(func_def_316, type, sK175: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_317, type, sK176: (term > $o) > term).
% 1.70/1.50 thf(func_def_318, type, sK177: subst).
% 1.70/1.50 thf(func_def_319, type, sK178: subst).
% 1.70/1.50 thf(func_def_320, type, sK179: subst).
% 1.70/1.50 thf(func_def_321, type, sK180: subst).
% 1.70/1.50 thf(func_def_322, type, sK181: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_323, type, sK182: term).
% 1.70/1.50 thf(func_def_324, type, sK183: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_325, type, sK184: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_326, type, sK185: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_327, type, sK186: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_328, type, sK187: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_329, type, sK188: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_330, type, sK189: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_331, type, sK190: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_332, type, sK191: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_333, type, sK192: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_334, type, sK193: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_335, type, sK194: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_336, type, sK195: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_337, type, sK196: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_338, type, sK197: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_339, type, sK198: term).
% 1.70/1.50 thf(func_def_340, type, sK199: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_341, type, sK200: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_342, type, sK201: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_343, type, sK202: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_344, type, sK203: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_345, type, sK204: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_346, type, sK205: term).
% 1.70/1.50 thf(func_def_347, type, sK206: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_348, type, sK207: term > $o).
% 1.70/1.50 thf(func_def_349, type, sK208: (term > $o) > term > term).
% 1.70/1.50 thf(func_def_350, type, sK209: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_351, type, sK210: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_352, type, sK211: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_353, type, sK212: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_354, type, sK213: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_355, type, sK214: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_356, type, sK215: term).
% 1.70/1.50 thf(func_def_357, type, sK216: term).
% 1.70/1.50 thf(func_def_358, type, sK217: term).
% 1.70/1.50 thf(func_def_359, type, sK218: term).
% 1.70/1.50 thf(func_def_360, type, sK219: term).
% 1.70/1.50 thf(func_def_361, type, sK220: term).
% 1.70/1.50 thf(func_def_362, type, sK221: term).
% 1.70/1.50 thf(func_def_363, type, sK222: term).
% 1.70/1.50 thf(func_def_364, type, sK223: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_365, type, sK224: term).
% 1.70/1.50 thf(func_def_366, type, sK225: term).
% 1.70/1.50 thf(func_def_367, type, sK226: term > $o).
% 1.70/1.50 thf(func_def_368, type, sK227: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_369, type, sK228: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_370, type, sK229: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_371, type, sK230: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_372, type, sK231: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_373, type, sK232: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_374, type, sK233: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_375, type, sK234: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_376, type, sK235: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_377, type, sK236: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_378, type, sK237: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_379, type, sK238: term > $o).
% 1.70/1.50 thf(func_def_380, type, sK239: term).
% 1.70/1.50 thf(func_def_381, type, sK240: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_382, type, sK241: (subst > term > subst > $o) > (term > $o) > term).
% 1.70/1.50 thf(func_def_383, type, sK242: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_384, type, sK243: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_385, type, sK244: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_386, type, sK245: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_387, type, sK246: (term > $o) > term > term).
% 1.70/1.50 thf(func_def_388, type, sK247: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_389, type, sK248: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_390, type, sK249: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_391, type, sK250: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_392, type, sK251: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_393, type, sK252: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_394, type, sK253: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_395, type, sK254: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_396, type, sK255: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_397, type, sK256: (term > $o) > term).
% 1.70/1.50 thf(func_def_398, type, sK257: term).
% 1.70/1.50 thf(func_def_399, type, sK258: term > $o).
% 1.70/1.50 thf(func_def_400, type, sK259: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_401, type, sK260: (term > $o) > term > term).
% 1.70/1.50 thf(func_def_402, type, sK261: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_403, type, sK262: term).
% 1.70/1.50 thf(func_def_404, type, sK263: term > $o).
% 1.70/1.50 thf(func_def_405, type, sK264: term).
% 1.70/1.50 thf(func_def_406, type, sK265: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_407, type, sK266: (term > $o) > term).
% 1.70/1.50 thf(func_def_408, type, sK267: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_409, type, sK268: (term > $o) > term).
% 1.70/1.50 thf(func_def_410, type, sK269: (term > $o) > term).
% 1.70/1.50 thf(func_def_411, type, sK270: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_412, type, sK271: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_413, type, sK272: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_414, type, sK273: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_415, type, sK274: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_416, type, sK275: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_417, type, sK276: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_418, type, sK277: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_419, type, sK278: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_420, type, sK279: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_421, type, sK280: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_422, type, sK281: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_423, type, sK282: term).
% 1.70/1.50 thf(func_def_424, type, sK283: term > $o).
% 1.70/1.50 thf(func_def_425, type, sK284: (term > $o) > term).
% 1.70/1.50 thf(func_def_426, type, sK285: (term > $o) > term).
% 1.70/1.50 thf(func_def_427, type, sK286: (term > $o) > term).
% 1.70/1.50 thf(func_def_428, type, sK287: (term > $o) > term).
% 1.70/1.50 thf(func_def_429, type, sK288: (term > $o) > subst > term).
% 1.70/1.50 thf(func_def_430, type, sK289: term).
% 1.70/1.50 thf(func_def_431, type, sK290: subst).
% 1.70/1.50 thf(func_def_432, type, sK291: term > $o).
% 1.70/1.50 thf(func_def_433, type, sK292: term).
% 1.70/1.50 thf(func_def_434, type, sK293: term > $o).
% 1.70/1.50 thf(func_def_435, type, sK294: (term > $o) > term).
% 1.70/1.50 thf(func_def_436, type, sK295: (term > $o) > term).
% 1.70/1.50 thf(func_def_437, type, sK296: (term > $o) > term).
% 1.70/1.50 thf(func_def_438, type, sK297: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_439, type, sK298: (term > $o) > term).
% 1.70/1.50 thf(func_def_440, type, sK299: (term > $o) > term).
% 1.70/1.50 thf(func_def_441, type, sK300: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_442, type, sK301: (term > $o) > term).
% 1.70/1.50 thf(func_def_443, type, sK302: (term > $o) > term).
% 1.70/1.50 thf(func_def_444, type, sK303: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_445, type, sK304: term).
% 1.70/1.50 thf(func_def_446, type, sK305: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_447, type, sK306: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_448, type, sK307: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_449, type, sK308: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_450, type, sK309: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_451, type, sK310: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_452, type, sK311: subst).
% 1.70/1.50 thf(func_def_453, type, sK312: term).
% 1.70/1.50 thf(func_def_454, type, sK313: term).
% 1.70/1.50 thf(func_def_455, type, sK314: term).
% 1.70/1.50 thf(func_def_456, type, sK315: term).
% 1.70/1.50 thf(func_def_457, type, sK316: subst).
% 1.70/1.50 thf(func_def_458, type, sK317: term).
% 1.70/1.50 thf(func_def_459, type, sK318: subst > term > term).
% 1.70/1.50 thf(func_def_460, type, sK319: subst).
% 1.70/1.50 thf(func_def_461, type, sK320: subst > term > term).
% 1.70/1.50 thf(func_def_462, type, sK321: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_463, type, sK322: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_464, type, sK323: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_465, type, sK324: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_466, type, sK325: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_467, type, sK326: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_468, type, sK327: (term > $o) > term).
% 1.70/1.50 thf(func_def_469, type, sK328: term).
% 1.70/1.50 thf(func_def_470, type, sK329: term > $o).
% 1.70/1.50 thf(func_def_471, type, sK330: subst).
% 1.70/1.50 thf(func_def_472, type, sK331: term).
% 1.70/1.50 thf(func_def_473, type, sK332: term > $o).
% 1.70/1.50 thf(func_def_474, type, sK333: (term > $o) > subst > term).
% 1.70/1.50 thf(func_def_475, type, sK334: (term > $o) > term).
% 1.70/1.50 thf(func_def_476, type, sK335: (term > $o) > term).
% 1.70/1.50 thf(func_def_477, type, sK336: (term > $o) > term).
% 1.70/1.50 thf(func_def_478, type, sK337: (term > $o) > term).
% 1.70/1.50 thf(func_def_479, type, sK338: (term > $o) > term).
% 1.70/1.50 thf(func_def_480, type, sK339: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_481, type, sK340: (term > $o) > term).
% 1.70/1.50 thf(func_def_482, type, sK341: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_483, type, sK342: term).
% 1.70/1.50 thf(func_def_484, type, sK343: term).
% 1.70/1.50 thf(func_def_485, type, sK344: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_486, type, sK345: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_487, type, sK346: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_488, type, sK347: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_489, type, sK348: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_490, type, sK349: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_491, type, sK350: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_492, type, sK351: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_493, type, sK352: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_494, type, sK353: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_495, type, sK354: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_496, type, sK355: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_497, type, sK356: term).
% 1.70/1.50 thf(func_def_498, type, sK357: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_499, type, sK358: term).
% 1.70/1.50 thf(func_def_500, type, sK359: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_501, type, sK360: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_502, type, sK361: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_503, type, sK362: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_504, type, sK363: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_505, type, sK364: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_506, type, sK365: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_507, type, sK366: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_508, type, sK367: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_509, type, sK368: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_510, type, sK369: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_511, type, sK370: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_512, type, sK371: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_513, type, sK372: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_514, type, sK373: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_515, type, sK374: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_516, type, sK375: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_517, type, sK376: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_518, type, sK377: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_519, type, sK378: term > $o).
% 1.70/1.50 thf(func_def_520, type, sK379: term).
% 1.70/1.50 thf(func_def_521, type, sK380: (term > $o) > term > term).
% 1.70/1.50 thf(func_def_522, type, sK381: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_523, type, sK382: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_524, type, sK383: term).
% 1.70/1.50 thf(func_def_525, type, sK384: term > $o).
% 1.70/1.50 thf(func_def_526, type, sK385: term).
% 1.70/1.50 thf(func_def_527, type, sK386: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_528, type, sK387: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_529, type, sK388: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_530, type, sK389: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_531, type, sK390: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_532, type, sK391: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_533, type, sK392: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_534, type, sK393: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_535, type, sK394: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_536, type, sK395: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_537, type, sK396: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_538, type, sK397: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_539, type, sK398: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_540, type, sK399: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_541, type, sK400: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_542, type, sK401: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_543, type, sK402: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_544, type, sK403: (term > $o) > term).
% 1.70/1.50 thf(func_def_545, type, sK404: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_546, type, sK405: (term > $o) > term).
% 1.70/1.50 thf(func_def_547, type, sK406: (term > $o) > term).
% 1.70/1.50 thf(func_def_548, type, sK407: (term > $o) > term).
% 1.70/1.50 thf(func_def_549, type, sK408: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_550, type, sK409: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_551, type, sK410: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_552, type, sK411: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_553, type, sK412: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_554, type, sK413: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_555, type, sK414: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_556, type, sK415: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_557, type, sK416: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_558, type, sK417: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_559, type, sK418: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_560, type, sK419: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_561, type, sK420: term > $o).
% 1.70/1.50 thf(func_def_562, type, sK421: term).
% 1.70/1.50 thf(func_def_563, type, sK422: (term > $o) > term).
% 1.70/1.50 thf(func_def_564, type, sK423: (term > $o) > term).
% 1.70/1.50 thf(func_def_565, type, sK424: (term > $o) > term).
% 1.70/1.50 thf(func_def_566, type, sK425: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_567, type, sK426: (term > $o) > term).
% 1.70/1.50 thf(func_def_568, type, sK427: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_569, type, sK428: term).
% 1.70/1.50 thf(func_def_570, type, sK429: term > $o).
% 1.70/1.50 thf(func_def_571, type, sK430: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_572, type, sK431: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_573, type, sK432: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_574, type, sK433: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_575, type, sK434: (term > $o) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_576, type, sK435: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_577, type, sK436: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_578, type, sK437: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_579, type, sK438: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_580, type, sK439: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_581, type, sK440: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_582, type, sK441: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_583, type, sK442: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_584, type, sK443: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_585, type, sK444: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_586, type, sK445: term > $o).
% 1.70/1.50 thf(func_def_587, type, sK446: term).
% 1.70/1.50 thf(func_def_588, type, sK447: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_589, type, sK448: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_590, type, sK449: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_591, type, sK450: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_592, type, sK451: term).
% 1.70/1.50 thf(func_def_593, type, sK452: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_594, type, sK453: term).
% 1.70/1.50 thf(func_def_595, type, sK454: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_596, type, sK455: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_597, type, sK456: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_598, type, sK457: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_599, type, sK458: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_600, type, sK459: term).
% 1.70/1.50 thf(func_def_601, type, sK460: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_602, type, sK461: term).
% 1.70/1.50 thf(func_def_603, type, sK462: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_604, type, sK463: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_605, type, sK464: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_606, type, sK465: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_607, type, sK466: (term > $o) > term).
% 1.70/1.50 thf(func_def_608, type, sK467: term > (term > $o) > term).
% 1.70/1.50 thf(func_def_609, type, sK468: (term > $o) > term).
% 1.70/1.50 thf(func_def_610, type, sK469: (term > $o) > term).
% 1.70/1.50 thf(func_def_611, type, sK470: (term > $o) > term).
% 1.70/1.50 thf(func_def_612, type, sK471: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_613, type, sK472: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_614, type, sK473: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_615, type, sK474: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_616, type, sK475: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_617, type, sK476: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_618, type, sK477: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_619, type, sK478: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_620, type, sK479: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_621, type, sK480: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_622, type, sK481: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_623, type, sK482: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_624, type, sK483: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_625, type, sK484: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_626, type, sK485: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_627, type, sK486: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_628, type, sK487: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_629, type, sK488: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_630, type, sK489: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_631, type, sK490: (subst > term > subst > $o) > subst).
% 1.70/1.50 thf(func_def_632, type, sK491: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_633, type, sK492: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_634, type, sK493: (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_635, type, sK494: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_636, type, sK495: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_637, type, sK496: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_638, type, sK497: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_639, type, sK498: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_640, type, sK499: term > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_641, type, sK500: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_642, type, sK501: term).
% 1.70/1.50 thf(func_def_643, type, sK502: term).
% 1.70/1.50 thf(func_def_644, type, sK503: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_645, type, sK504: (subst > term > subst > $o) > term > term).
% 1.70/1.50 thf(func_def_646, type, sK505: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_647, type, sK506: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_648, type, sK507: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_649, type, sK508: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_650, type, sK509: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_651, type, sK510: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_652, type, sK511: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_653, type, sK512: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_654, type, sK513: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_655, type, sK514: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_656, type, sK515: term).
% 1.70/1.50 thf(func_def_657, type, sK516: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_658, type, sK517: (subst > term > subst > $o) > term > term).
% 1.70/1.50 thf(func_def_659, type, sK518: (subst > term > term) > (subst > term > subst > $o) > term).
% 1.70/1.50 thf(func_def_660, type, sK519: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_661, type, sK520: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_662, type, sK521: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_663, type, sK522: (subst > term > subst > $o) > subst > term > term).
% 1.70/1.50 thf(func_def_664, type, sK523: term).
% 1.70/1.50 thf(func_def_665, type, sK524: term).
% 1.70/1.50 thf(func_def_666, type, sK525: term).
% 1.70/1.50 thf(func_def_667, type, sK526: term).
% 1.70/1.50 thf(func_def_668, type, sK527: term).
% 1.70/1.50 thf(func_def_669, type, sK528: term).
% 1.70/1.50 thf(func_def_670, type, sK529: term).
% 1.70/1.50 thf(func_def_671, type, sK530: term).
% 1.70/1.50 thf(func_def_672, type, sK531: (subst > term > subst > $o) > term > $o).
% 1.70/1.50 thf(func_def_673, type, sK532: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_674, type, sK533: (term > $o) > term).
% 1.70/1.50 thf(func_def_675, type, sK534: term).
% 1.70/1.50 thf(func_def_676, type, sK535: subst).
% 1.70/1.50 thf(func_def_677, type, sK536: term > $o).
% 1.70/1.50 thf(func_def_678, type, sK537: term > $o).
% 1.70/1.50 thf(func_def_679, type, sK538: term).
% 1.70/1.50 thf(func_def_680, type, sK539: term).
% 1.70/1.50 thf(func_def_681, type, sK540: term).
% 1.70/1.50 thf(func_def_682, type, sK541: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_683, type, sK542: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_684, type, sK543: term > subst > term > term).
% 1.70/1.50 thf(func_def_685, type, sK544: term).
% 1.70/1.50 thf(func_def_686, type, sK545: subst).
% 1.70/1.50 thf(func_def_687, type, sK546: term).
% 1.70/1.50 thf(func_def_688, type, sK547: term).
% 1.70/1.50 thf(func_def_689, type, sK548: subst).
% 1.70/1.50 thf(func_def_690, type, sK549: term).
% 1.70/1.50 thf(func_def_691, type, sK550: term > $o).
% 1.70/1.50 thf(func_def_692, type, sK551: (term > $o) > term).
% 1.70/1.50 thf(func_def_693, type, sK552: (term > $o) > term > subst > term > $o).
% 1.70/1.50 thf(func_def_694, type, sK553: (term > $o) > term > (term > $o) > subst > term).
% 1.70/1.50 thf(func_def_695, type, sK554: term).
% 1.70/1.50 thf(func_def_696, type, sK555: subst).
% 1.70/1.50 thf(func_def_697, type, sK556: subst).
% 1.70/1.50 thf(func_def_698, type, sK557: term > $o).
% 1.70/1.50 thf(func_def_699, type, sK558: term).
% 1.70/1.50 thf(func_def_700, type, sK559: term > $o).
% 1.70/1.50 thf(func_def_701, type, sK560: term).
% 1.70/1.50 thf(func_def_702, type, sK561: subst > term > term).
% 1.70/1.50 thf(func_def_703, type, sK562: term).
% 1.70/1.50 thf(func_def_704, type, sK563: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_705, type, sK564: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_706, type, sK565: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_707, type, sK566: term > subst > term > term).
% 1.70/1.50 thf(func_def_708, type, sK567: term).
% 1.70/1.50 thf(func_def_709, type, sK568: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_710, type, sK569: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_711, type, sK570: subst).
% 1.70/1.50 thf(func_def_712, type, sK571: subst).
% 1.70/1.50 thf(func_def_713, type, sK572: subst > d_subst).
% 1.70/1.50 thf(func_def_714, type, sK573: term).
% 1.70/1.50 thf(func_def_715, type, sK574: term).
% 1.70/1.50 thf(func_def_716, type, sK575: term).
% 1.70/1.50 thf(func_def_717, type, sK576: term).
% 1.70/1.50 thf(func_def_718, type, sK577: term).
% 1.70/1.50 thf(func_def_719, type, sK578: term).
% 1.70/1.50 thf(func_def_720, type, sK579: term).
% 1.70/1.50 thf(func_def_721, type, sK580: term).
% 1.70/1.50 thf(func_def_722, type, sK581: subst).
% 1.70/1.50 thf(func_def_723, type, sK582: subst > (term > $o) > (term > $o) > term > term).
% 1.70/1.50 thf(func_def_724, type, sK583: term).
% 1.70/1.50 thf(func_def_725, type, sK584: term > $o).
% 1.70/1.50 thf(func_def_726, type, sK585: term > $o).
% 1.70/1.50 thf(func_def_727, type, sK586: subst).
% 1.70/1.50 thf(func_def_728, type, sK587: term).
% 1.70/1.50 thf(func_def_729, type, sK588: (subst > term > subst > $o) > term > $o).
% 1.70/1.50 thf(func_def_730, type, sK589: term).
% 1.70/1.50 thf(func_def_731, type, sK590: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_732, type, sK591: (term > $o) > term).
% 1.70/1.50 thf(func_def_733, type, sK592: term).
% 1.70/1.50 thf(func_def_734, type, sK593: term).
% 1.70/1.50 thf(func_def_735, type, sK594: term).
% 1.70/1.50 thf(func_def_736, type, sK595: term).
% 1.70/1.50 thf(func_def_737, type, sK596: term).
% 1.70/1.50 thf(func_def_738, type, sK597: term > subst > term > term).
% 1.70/1.50 thf(func_def_739, type, sK598: term).
% 1.70/1.50 thf(func_def_740, type, sK599: subst).
% 1.70/1.50 thf(func_def_741, type, sK600: subst).
% 1.70/1.50 thf(func_def_742, type, sK601: term).
% 1.70/1.50 thf(func_def_743, type, sK602: subst).
% 1.70/1.50 thf(func_def_744, type, sK603: term).
% 1.70/1.50 thf(func_def_745, type, sK604: term).
% 1.70/1.50 thf(func_def_746, type, sK605: term).
% 1.70/1.50 thf(func_def_747, type, sK606: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_748, type, sK607: (term > $o) > term).
% 1.70/1.50 thf(func_def_749, type, sK608: (subst > term > subst > $o) > term > $o).
% 1.70/1.50 thf(func_def_750, type, sK609: term).
% 1.70/1.50 thf(func_def_751, type, sK610: subst > term > term).
% 1.70/1.50 thf(func_def_752, type, sK611: subst > term > term).
% 1.70/1.50 thf(func_def_753, type, sK612: subst).
% 1.70/1.50 thf(func_def_754, type, sK613: term).
% 1.70/1.50 thf(func_def_755, type, sK614: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_756, type, sK615: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_757, type, sK616: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_758, type, sK617: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_759, type, sK618: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_760, type, sK619: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_761, type, sK620: term).
% 1.70/1.50 thf(func_def_762, type, sK621: term > $o).
% 1.70/1.50 thf(func_def_763, type, sK622: subst).
% 1.70/1.50 thf(func_def_764, type, sK623: (term > $o) > term).
% 1.70/1.50 thf(func_def_765, type, sK624: subst > (term > $o) > term > term > $o).
% 1.70/1.50 thf(func_def_766, type, sK625: term).
% 1.70/1.50 thf(func_def_767, type, sK626: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_768, type, sK627: term > subst > term > term).
% 1.70/1.50 thf(func_def_769, type, sK628: term).
% 1.70/1.50 thf(func_def_770, type, sK629: (subst > term > term) > subst).
% 1.70/1.50 thf(func_def_771, type, sK630: (subst > term > term) > term).
% 1.70/1.50 thf(func_def_772, type, sK631: subst).
% 1.70/1.50 thf(func_def_773, type, sK632: term).
% 1.70/1.50 thf(func_def_774, type, sK633: subst).
% 1.70/1.50 thf(func_def_775, type, sK634: term).
% 1.70/1.50 thf(func_def_776, type, sK635: term).
% 1.70/1.50 thf(func_def_777, type, sK636: term > $o).
% 1.70/1.50 thf(func_def_778, type, sK637: term > $o).
% 1.70/1.50 thf(func_def_779, type, sK638: subst).
% 1.70/1.50 thf(func_def_780, type, sK639: term).
% 1.70/1.50 thf(func_def_781, type, sK640: term > d_term).
% 1.70/1.50 thf(func_def_782, type, sK641: subst).
% 1.70/1.50 thf(func_def_783, type, sK642: term).
% 1.70/1.50 thf(func_def_784, type, sK643: term).
% 1.70/1.50 thf(func_def_785, type, sK644: term > subst > term > term).
% 1.70/1.50 thf(func_def_786, type, sK645: term).
% 1.70/1.50 thf(func_def_787, type, sK646: subst).
% 1.70/1.50 thf(func_def_788, type, sK647: term).
% 1.70/1.50 thf(func_def_789, type, sK648: (subst > term > subst > $o) > term > $o).
% 1.70/1.50 thf(func_def_790, type, sK649: subst > term > subst > $o).
% 1.70/1.50 thf(func_def_791, type, sK650: (term > $o) > term).
% 1.70/1.50 thf(func_def_792, type, sK651: subst).
% 1.70/1.50 thf(func_def_795, type, ph653: !>[X0: $tType]:(X0)).
% 1.70/1.50 thf(f3848,plain,(
% 1.70/1.50 $false),
% 1.70/1.50 inference(avatar_sat_refutation,[status(thm)],[f2495,f3148,f3840,f3844])).
% 1.70/1.50 thf(f3844,plain,(
% 1.70/1.50 spl652_309),
% 1.70/1.50 inference(avatar_contradiction_clause,[status(thm)],[f3843])).
% 1.70/1.50 thf(f3843,plain,(
% 1.70/1.50 $false | spl652_309),
% 1.70/1.50 inference(subsumption_resolution,[status(thm)],[f3842,f3829])).
% 1.70/1.50 thf(f3829,plain,(
% 1.70/1.50 ( ! [X240 : term] : (((d2term @ d_one) = X240)) )),
% 1.70/1.50 inference(forward_demodulation,[status(thm)],[f1310,f1481])).
% 1.70/1.50 thf(f1481,plain,(
% 1.70/1.50 ( ! [X32 : d_term] : ((d_one = X32)) )),
% 1.70/1.50 inference(cnf_transformation,[status(thm)],[f753])).
% 1.70/1.50 thf(f753,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & (! [X0 : term,X1 : term,X2 : term,X3 : term] : ((X0 = X2) | ((ap @ (sub @ X0 @ id) @ X1) != (ap @ (sub @ X2 @ id) @ X3))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((sK525 != sK523) & ((ap @ (sub @ sK523 @ id) @ sK524) = (ap @ (sub @ sK525 @ id) @ sK526)))) & (hoasapnotvar = $true) & ((hoasinduction = $true) | (sP109 != $true)) & ((sP109 = $true) | (hoasinduction != $true)) & (substmonoid_gthm = $true) & ((apinj1 = $true) | ((sK529 != sK527) & ((ap @ sK529 @ sK530) = (ap @ sK527 @ sK528)))) & (! [X12 : term,X13 : term,X14 : term,X15 : term] : ((X12 = X14) | ((ap @ X12 @ X13) != (ap @ X14 @ X15))) | (apinj1 != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X16 : subst > term > subst > $o] : ! [X18 : term] : ((sK531 @ X16 @ X18) = (X16 @ id @ X18 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X20 : term > $o] : ((X20 @ (sK533 @ X20)) != (sK532 @ id @ (sK533 @ X20) @ id))) & (! [X22 : term,X23 : subst,X24 : term > $o,X25 : term > $o,X26 : term] : (($true = (X25 @ (sub @ X26 @ (push @ X22 @ X23)))) | ($true != (X24 @ X26))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true != (sK537 @ (sub @ sK538 @ (push @ sK534 @ sK535)))) & ($true = (sK536 @ sK538)))) & ((sP104 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP104 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X32 : d_term] : (d_one = X32) & (((sub @ sK539 @ id) != sK539) | (sP102 = $true) | ! [X35 : subst > term > term] : ((sub @ sK540 @ (push @ (sK542 @ X35) @ (sK541 @ X35))) != (X35 @ (sK541 @ X35) @ (sK542 @ X35))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X38 : term] : ((sub @ X38 @ id) = X38) & (sP102 != $true) & ! [X39 : term] : ! [X41 : subst,X42 : term] : ((sK543 @ X39 @ X41 @ X42) = (sub @ X39 @ (push @ X42 @ X41))))) & (pushprop_gthm = $true) & (lamnotvar = $true) & ((sP100 = $true) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (sP100 != $true)) & (hoasinduction_lem1_lthm = $true) & (($true = sP98) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP98)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK544 @ sK545)) != sK545)) & (! [X45 : term,X46 : subst] : ((comp @ sh @ (push @ X45 @ X46)) = X46) | (axshiftcons != $true)) & ((shinj = $true) | (((sub @ sK546 @ sh) = (sub @ sK547 @ sh)) & (sK547 != sK546))) & (! [X49 : term,X50 : term] : (((sub @ X50 @ sh) != (sub @ X49 @ sh)) | (X49 = X50)) | (shinj != $true)) & (apnotvar = $true) & ((substmonoid_lthm = $true) | ($true != sP95)) & (($true = sP95) | (substmonoid_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X54 : term > $o] : ((sK550 @ (sub @ (sK551 @ X54) @ (push @ sK549 @ sK548))) != (X54 @ (sK551 @ X54)))) & (! [X56 : subst,X57 : term,X58 : term > $o] : ! [X60 : term] : ((sK552 @ X58 @ X57 @ X56 @ X60) = (X58 @ (sub @ X60 @ (push @ X57 @ X56)))) | (pushprop_lem0_lthm != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (($true = sP94) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP94)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3a != $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X61 : subst,X62 : term > $o,X63 : term,X64 : term > $o] : (((X64 @ (sub @ (sK553 @ X64 @ X63 @ X62 @ X61) @ (push @ X63 @ X61))) != (X62 @ (sK553 @ X64 @ X63 @ X62 @ X61))) | ((X64 @ X63) != $true) | ((X62 @ one) = $true)) | (sK554 != (sub @ one @ (push @ sK554 @ sK555))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((! [X72 : term] : ((sK557 @ X72) = (sK559 @ (sub @ X72 @ (push @ sK558 @ sK556)))) & ($true = (sK559 @ sK558)) & ((sK557 @ one) != $true)) & ! [X73 : term,X74 : subst] : ((sub @ one @ (push @ X73 @ X74)) = X73))) & ((hoaslamnotap = $true) | (((ap @ (sub @ sK562 @ id) @ sK560) = (lam @ (sK561 @ sh @ one))) & ! [X78 : subst,X79 : term,X80 : subst] : ((sub @ (sK561 @ X78 @ X79) @ X80) = (sK561 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))))) & (! [X81 : term,X82 : subst > term > term,X83 : term] : (((lam @ (X82 @ sh @ one)) != (ap @ (sub @ X83 @ id) @ X81)) | ((sub @ (X82 @ (sK563 @ X82) @ (sK564 @ X82)) @ (sK565 @ X82)) != (X82 @ (comp @ (sK563 @ X82) @ (sK565 @ X82)) @ (sub @ (sK564 @ X82) @ (sK565 @ X82))))) | (hoaslamnotap != $true)) & (axvarshift = $true) & (! [X87 : term] : ! [X89 : term,X90 : subst] : ((sK566 @ X87 @ X90 @ X89) = (sub @ X87 @ (push @ X89 @ X90))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X92 : subst > term > term] : ((sub @ sK567 @ (push @ (sK568 @ X92) @ (sK569 @ X92))) != (X92 @ (sK569 @ X92) @ (sK568 @ X92)))) & ((substmonoid = $true) | (sK570 != (comp @ sK570 @ id)) | ((comp @ id @ sK571) != sK571)) & ((! [X97 : subst] : ((comp @ X97 @ id) = X97) & ! [X98 : subst] : ((comp @ id @ X98) = X98)) | (substmonoid != $true)) & ! [X99 : d_term,X100 : d_term] : ((X99 = X100) | ((d2term @ X99) != (d2term @ X100))) & ! [X101 : subst] : ((d2subst @ (sK572 @ X101)) = X101) & (! [X103 : term,X104 : term,X105 : term,X106 : term] : (((ap @ (sub @ X104 @ id) @ X103) != (ap @ (sub @ X105 @ id) @ X106)) | (X103 = X106)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | (((ap @ (sub @ sK575 @ id) @ sK576) = (ap @ (sub @ sK574 @ id) @ sK573)) & (sK573 != sK576))) & (($true = sP88) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP88)) & ((apinj2 = $true) | ((sK577 != sK579) & ((ap @ sK580 @ sK577) = (ap @ sK578 @ sK579)))) & (! [X115 : term,X116 : term,X117 : term,X118 : term] : ((X115 = X117) | ((ap @ X118 @ X115) != (ap @ X116 @ X117))) | (apinj2 != $true)) & ((hoasapinj2_lthm = $true) | (sP86 != $true)) & ((sP86 = $true) | (hoasapinj2_lthm != $true)) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | (sP84 != $true)) & ((sP84 = $true) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP81) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP81)) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (! [X119 : subst] : ((comp @ id @ X119) = X119) | (axidl != $true)) & ((axidl = $true) | (sK581 != (comp @ id @ sK581))) & (hoasinduction_lem1v2 = $true) & (! [X121 : term,X122 : term > $o,X123 : term > $o,X124 : subst] : (((X122 @ one) = $true) | ($true != (X123 @ X121)) | ((X123 @ (sub @ (sK582 @ X124 @ X123 @ X122 @ X121) @ (push @ X121 @ X124))) != (X122 @ (sK582 @ X124 @ X123 @ X122 @ X121)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (((sK584 @ one) != $true) & ((sK585 @ sK583) = $true) & ! [X130 : term] : ((sK584 @ X130) = (sK585 @ (sub @ X130 @ (push @ sK583 @ sK586)))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X131 : term] : ((sub @ X131 @ id) = X131) | (axvarid != $true)) & ((axvarid = $true) | (sK587 != (sub @ sK587 @ id))) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP77 != $true) & ($true != sP76) & (sP75 != $true) & ! [X133 : term] : ((sub @ X133 @ id) = X133) & ! [X134 : subst > term > subst > $o] : ! [X136 : term] : ((sK588 @ X134 @ X136) = (X134 @ id @ X136 @ id)))) & ((sP77 = $true) | ($true = sP76) | (sP75 = $true) | ((sub @ sK589 @ id) != sK589) | ! [X139 : term > $o] : ((X139 @ (sK591 @ X139)) != (sK590 @ id @ (sK591 @ X139) @ id)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((sP69 = $true) | (induction != $true)) & ((induction = $true) | (sP69 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP65 = $true) | (sK592 != (sub @ sK592 @ id)) | ($true = sP66) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP65 != $true) & ! [X142 : term] : ((sub @ X142 @ id) = X142) & ($true != sP66))) & (! [X143 : term] : ((sub @ X143 @ id) = X143) | (sK593 != (sub @ sK593 @ id)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((sK594 != (sub @ sK594 @ id)) & ! [X146 : term] : ((sub @ X146 @ id) = X146))) & ((laminj = $true) | ((sK595 != sK596) & ((lam @ sK595) = (lam @ sK596)))) & (! [X149 : term,X150 : term] : ((X149 = X150) | ((lam @ X150) != (lam @ X149))) | (laminj != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP60 != $true)) & ((sP60 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (($true = sP58) | (hoaslaminj_lthm != $true)) & (! [X151 : term] : ((sub @ X151 @ (push @ one @ sh)) = (sK597 @ X151 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X154 : subst > term > term] : ((X154 @ sh @ one) != (sub @ sK598 @ (push @ one @ sh)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((sP56 = $true) | ($true = sP55) | ((comp @ sK599 @ id) != sK599) | (sK601 != (sub @ one @ (push @ sK601 @ sK600))) | (sK602 != (comp @ sh @ (push @ sK603 @ sK602))) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP56 != $true) & ($true != sP55) & ! [X160 : subst] : ((comp @ X160 @ id) = X160) & ! [X161 : subst,X162 : term] : ((sub @ one @ (push @ X162 @ X161)) = X162) & ! [X163 : subst,X164 : term] : ((comp @ sh @ (push @ X164 @ X163)) = X163))) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & ((hoasinduction_lem2 = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP47) & ! [X165 : term] : ((sub @ X165 @ id) = X165) & ($true != sP46))) & (($true = sP47) | ((sub @ sK604 @ id) != sK604) | ($true = sP46) | (hoasinduction_lem3_lthm != $true)) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X167 : d_subst] : (d_id = X167) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (((sub @ sK605 @ id) != sK605) | ($true = sP39) | (sP41 = $true) | ! [X170 : term > $o] : ((sK606 @ id @ (sK607 @ X170) @ id) != (X170 @ (sK607 @ X170))) | ($true = sP40) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X172 : term] : ((sub @ X172 @ id) = X172) & ($true != sP39) & (sP41 != $true) & ! [X173 : subst > term > subst > $o] : ! [X175 : term] : ((X173 @ id @ X175 @ id) = (sK608 @ X173 @ X175)) & ($true != sP40))) & (! [X176 : term] : ((sub @ X176 @ id) = X176) | (termmset != $true)) & ((termmset = $true) | ((sub @ sK609 @ id) != sK609)) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoaslaminj = $true) | (! [X182 : subst,X183 : subst,X184 : term] : ((sK611 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182)) = (sub @ (sK611 @ X183 @ X184) @ X182)) & ((sK610 @ sK612 @ sK613) != (sK611 @ sK612 @ sK613)) & ! [X185 : subst,X186 : term,X187 : subst] : ((sub @ (sK610 @ X187 @ X186) @ X185) = (sK610 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185))) & ((lam @ (sK611 @ sh @ one)) = (lam @ (sK610 @ sh @ one))))) & (! [X188 : subst > term > term,X189 : subst > term > term,X190 : subst,X191 : term] : (((sub @ (X189 @ (sK615 @ X189) @ (sK616 @ X189)) @ (sK614 @ X189)) != (X189 @ (comp @ (sK615 @ X189) @ (sK614 @ X189)) @ (sub @ (sK616 @ X189) @ (sK614 @ X189)))) | ((X189 @ X190 @ X191) = (X188 @ X190 @ X191)) | ((X188 @ (comp @ (sK619 @ X188) @ (sK617 @ X188)) @ (sub @ (sK618 @ X188) @ (sK617 @ X188))) != (sub @ (X188 @ (sK619 @ X188) @ (sK618 @ X188)) @ (sK617 @ X188))) | ((lam @ (X188 @ sh @ one)) != (lam @ (X189 @ sh @ one)))) | (hoaslaminj != $true)) & (hoaslamnotvar = $true) & ((pushprop_lem0 = $true) | ! [X201 : term > $o] : ((sK621 @ (sub @ (sK623 @ X201) @ (push @ sK620 @ sK622))) != (X201 @ (sK623 @ X201)))) & (! [X203 : term,X204 : term > $o,X205 : subst] : ! [X207 : term] : ((X204 @ (sub @ X207 @ (push @ X203 @ X205))) = (sK624 @ X205 @ X204 @ X203 @ X207)) | (pushprop_lem0 != $true)) & ! [X208 : d_subst,X209 : d_subst] : (((d2subst @ X209) != (d2subst @ X208)) | (X208 = X209)) & (termmset_gthm = $true) & (! [X210 : term,X211 : subst > term > subst > $o] : (($true = (sP30 @ X211)) | ($true = (sP29 @ X211)) | ($true = (X211 @ id @ X210 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (($true != (sP30 @ sK626)) & ($true != (sP29 @ sK626)) & ($true != (sK626 @ id @ sK625 @ id)))) & (! [X214 : term] : ! [X216 : subst,X217 : term] : ((sK627 @ X214 @ X216 @ X217) = (sub @ X214 @ (push @ X217 @ X216))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X219 : subst > term > term] : ((sub @ sK628 @ (push @ (sK630 @ X219) @ (sK629 @ X219))) != (X219 @ (sK629 @ X219) @ (sK630 @ X219)))) & ((induction2 = $true) | ($true != sP28)) & (($true = sP28) | (induction2 != $true)) & ((sK632 != (sub @ one @ (push @ sK632 @ sK631))) | ! [X224 : term,X225 : term > $o,X226 : term > $o,X227 : subst,X228 : term] : (((X225 @ X224) != $true) | ((X226 @ (sub @ X224 @ (push @ X228 @ X227))) = $true)) | (sK633 != (comp @ sh @ (push @ sK634 @ sK633))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X231 : subst,X232 : term] : ((sub @ one @ (push @ X232 @ X231)) = X232) & (($true = (sK636 @ sK635)) & ($true != (sK637 @ (sub @ sK635 @ (push @ sK639 @ sK638))))) & ! [X238 : subst,X239 : term] : ((comp @ sh @ (push @ X239 @ X238)) = X238))) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X240 : term] : ((d2term @ (sK640 @ X240)) = X240) & (axclos = $true) & ((axvarcons = $true) | ((sub @ one @ (push @ sK642 @ sK641)) != sK642)) & (! [X244 : subst,X245 : term] : ((sub @ one @ (push @ X245 @ X244)) = X245) | (axvarcons != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) | ((sP25 != $true) & ! [X246 : term] : ((sub @ X246 @ id) = X246))) & ((sP25 = $true) | ((sub @ sK643 @ id) != sK643) | (hoasinduction_lem3v2_lthm != $true)) & (! [X248 : term] : ((sK644 @ X248 @ sh @ one) = (sub @ X248 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X251 : subst > term > term] : ((sub @ sK645 @ (push @ one @ sh)) != (X251 @ sh @ one))) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & ((axscons = $true) | (sK646 != (push @ (sub @ one @ sK646) @ (comp @ sh @ sK646)))) & (! [X253 : subst] : ((push @ (sub @ one @ X253) @ (comp @ sh @ X253)) = X253) | (axscons != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP20) & (sP19 != $true) & (sP18 != $true))) & (($true = sP21) | ($true = sP20) | (sP19 = $true) | (sP18 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X254 : term] : ((sub @ X254 @ id) = X254) & (sP5 != $true) & ($true != sP4))) & ((sK647 != (sub @ sK647 @ id)) | (sP5 = $true) | ($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X256 : subst > term > subst > $o] : ! [X258 : term] : ((sK648 @ X256 @ X258) = (X256 @ id @ X258 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X260 : term > $o] : ((sK649 @ id @ (sK650 @ X260) @ id) != (X260 @ (sK650 @ X260)))) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X262 : subst] : ((comp @ X262 @ id) = X262) | (axidr != $true)) & ((axidr = $true) | (sK651 != (comp @ sK651 @ id)))),
% 1.70/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[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,sK591,sK592,sK593,sK594,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,sK603,sK604,sK605,sK606,sK607,sK608,sK609,sK610,sK611,sK612,sK613,sK614,sK615,sK616,sK617,sK618,sK619,sK620,sK621,sK622,sK623,sK624,sK625,sK626,sK627,sK628,sK629,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,sK640,sK641,sK642,sK643,sK644,sK645,sK646,sK647,sK648,sK649,sK650,sK651])],[f677,f752,f751,f750,f749,f748,f747,f746,f745,f744,f743,f742,f741,f740,f739,f738,f737,f736,f735,f734,f733,f732,f731,f730,f729,f728,f727,f726,f725,f724,f723,f722,f721,f720,f719,f718,f717,f716,f715,f714,f713,f712,f711,f710,f709,f708,f707,f706,f705,f704,f703,f702,f701,f700,f699,f698,f697,f696,f695,f694,f693,f692,f691,f690,f689,f688,f687,f686,f685,f684,f683,f682,f681,f680,f679,f678])).
% 1.70/1.50 thf(f678,plain,(
% 1.70/1.50 ? [X4 : term,X5 : term,X6 : term,X7 : term] : ((X4 != X6) & ((ap @ (sub @ X4 @ id) @ X5) = (ap @ (sub @ X6 @ id) @ X7))) => ((sK525 != sK523) & ((ap @ (sub @ sK523 @ id) @ sK524) = (ap @ (sub @ sK525 @ id) @ sK526)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f679,plain,(
% 1.70/1.50 ? [X8 : term,X9 : term,X10 : term,X11 : term] : ((X8 != X10) & ((ap @ X8 @ X9) = (ap @ X10 @ X11))) => ((sK529 != sK527) & ((ap @ sK529 @ sK530) = (ap @ sK527 @ sK528)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f680,plain,(
% 1.70/1.50 ! [X16 : subst > term > subst > $o] : (? [X17 : term > $o] : ! [X18 : term] : ((X17 @ X18) = (X16 @ id @ X18 @ id)) => ! [X18 : term] : ((sK531 @ X16 @ X18) = (X16 @ id @ X18 @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f681,plain,(
% 1.70/1.50 ? [X19 : subst > term > subst > $o] : ! [X20 : term > $o] : ? [X21 : term] : ((X19 @ id @ X21 @ id) != (X20 @ X21)) => ! [X20 : term > $o] : ? [X21 : term] : ((sK532 @ id @ X21 @ id) != (X20 @ X21))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f682,plain,(
% 1.70/1.50 ! [X20 : term > $o] : (? [X21 : term] : ((sK532 @ id @ X21 @ id) != (X20 @ X21)) => ((X20 @ (sK533 @ X20)) != (sK532 @ id @ (sK533 @ X20) @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f683,plain,(
% 1.70/1.50 ? [X27 : term,X28 : subst,X29 : term > $o,X30 : term > $o,X31 : term] : (((X30 @ (sub @ X31 @ (push @ X27 @ X28))) != $true) & ($true = (X29 @ X31))) => (($true != (sK537 @ (sub @ sK538 @ (push @ sK534 @ sK535)))) & ($true = (sK536 @ sK538)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f684,plain,(
% 1.70/1.50 ? [X33 : term] : ((sub @ X33 @ id) != X33) => ((sub @ sK539 @ id) != sK539)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f685,plain,(
% 1.70/1.50 ? [X34 : term] : ! [X35 : subst > term > term] : ? [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) != (sub @ X34 @ (push @ X37 @ X36))) => ! [X35 : subst > term > term] : ? [X37 : term,X36 : subst] : ((sub @ sK540 @ (push @ X37 @ X36)) != (X35 @ X36 @ X37))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f686,plain,(
% 1.70/1.50 ! [X35 : subst > term > term] : (? [X37 : term,X36 : subst] : ((sub @ sK540 @ (push @ X37 @ X36)) != (X35 @ X36 @ X37)) => ((sub @ sK540 @ (push @ (sK542 @ X35) @ (sK541 @ X35))) != (X35 @ (sK541 @ X35) @ (sK542 @ X35))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f687,plain,(
% 1.70/1.50 ! [X39 : term] : (? [X40 : subst > term > term] : ! [X41 : subst,X42 : term] : ((X40 @ X41 @ X42) = (sub @ X39 @ (push @ X42 @ X41))) => ! [X42 : term,X41 : subst] : ((sK543 @ X39 @ X41 @ X42) = (sub @ X39 @ (push @ X42 @ X41))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f688,plain,(
% 1.70/1.50 ? [X43 : term,X44 : subst] : ((comp @ sh @ (push @ X43 @ X44)) != X44) => ((comp @ sh @ (push @ sK544 @ sK545)) != sK545)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f689,plain,(
% 1.70/1.50 ? [X47 : term,X48 : term] : (((sub @ X47 @ sh) = (sub @ X48 @ sh)) & (X47 != X48)) => (((sub @ sK546 @ sh) = (sub @ sK547 @ sh)) & (sK547 != sK546))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f690,plain,(
% 1.70/1.50 ? [X51 : subst,X52 : term,X53 : term > $o] : ! [X54 : term > $o] : ? [X55 : term] : ((X54 @ X55) != (X53 @ (sub @ X55 @ (push @ X52 @ X51)))) => ! [X54 : term > $o] : ? [X55 : term] : ((X54 @ X55) != (sK550 @ (sub @ X55 @ (push @ sK549 @ sK548))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f691,plain,(
% 1.70/1.50 ! [X54 : term > $o] : (? [X55 : term] : ((X54 @ X55) != (sK550 @ (sub @ X55 @ (push @ sK549 @ sK548)))) => ((sK550 @ (sub @ (sK551 @ X54) @ (push @ sK549 @ sK548))) != (X54 @ (sK551 @ X54))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f692,plain,(
% 1.70/1.50 ! [X56 : subst,X57 : term,X58 : term > $o] : (? [X59 : term > $o] : ! [X60 : term] : ((X58 @ (sub @ X60 @ (push @ X57 @ X56))) = (X59 @ X60)) => ! [X60 : term] : ((sK552 @ X58 @ X57 @ X56 @ X60) = (X58 @ (sub @ X60 @ (push @ X57 @ X56)))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f693,plain,(
% 1.70/1.50 ! [X61 : subst,X62 : term > $o,X63 : term,X64 : term > $o] : (? [X65 : term] : ((X62 @ X65) != (X64 @ (sub @ X65 @ (push @ X63 @ X61)))) => ((X64 @ (sub @ (sK553 @ X64 @ X63 @ X62 @ X61) @ (push @ X63 @ X61))) != (X62 @ (sK553 @ X64 @ X63 @ X62 @ X61))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f694,plain,(
% 1.70/1.50 ? [X66 : term,X67 : subst] : ((sub @ one @ (push @ X66 @ X67)) != X66) => (sK554 != (sub @ one @ (push @ sK554 @ sK555)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f695,plain,(
% 1.70/1.50 ? [X68 : subst,X69 : term > $o,X70 : term,X71 : term > $o] : (! [X72 : term] : ((X71 @ (sub @ X72 @ (push @ X70 @ X68))) = (X69 @ X72)) & ((X71 @ X70) = $true) & ($true != (X69 @ one))) => (! [X72 : term] : ((sK557 @ X72) = (sK559 @ (sub @ X72 @ (push @ sK558 @ sK556)))) & ($true = (sK559 @ sK558)) & ((sK557 @ one) != $true))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f696,plain,(
% 1.70/1.50 ? [X75 : term,X76 : subst > term > term,X77 : term] : (((ap @ (sub @ X77 @ id) @ X75) = (lam @ (X76 @ sh @ one))) & ! [X78 : subst,X79 : term,X80 : subst] : ((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X76 @ X78 @ X79) @ X80))) => (((ap @ (sub @ sK562 @ id) @ sK560) = (lam @ (sK561 @ sh @ one))) & ! [X80 : subst,X79 : term,X78 : subst] : ((sub @ (sK561 @ X78 @ X79) @ X80) = (sK561 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f697,plain,(
% 1.70/1.50 ! [X82 : subst > term > term] : (? [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) != (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86))) => ((sub @ (X82 @ (sK563 @ X82) @ (sK564 @ X82)) @ (sK565 @ X82)) != (X82 @ (comp @ (sK563 @ X82) @ (sK565 @ X82)) @ (sub @ (sK564 @ X82) @ (sK565 @ X82)))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f698,plain,(
% 1.70/1.50 ! [X87 : term] : (? [X88 : subst > term > term] : ! [X89 : term,X90 : subst] : ((sub @ X87 @ (push @ X89 @ X90)) = (X88 @ X90 @ X89)) => ! [X90 : subst,X89 : term] : ((sK566 @ X87 @ X90 @ X89) = (sub @ X87 @ (push @ X89 @ X90))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f699,plain,(
% 1.70/1.50 ? [X91 : term] : ! [X92 : subst > term > term] : ? [X93 : term,X94 : subst] : ((sub @ X91 @ (push @ X93 @ X94)) != (X92 @ X94 @ X93)) => ! [X92 : subst > term > term] : ? [X94 : subst,X93 : term] : ((sub @ sK567 @ (push @ X93 @ X94)) != (X92 @ X94 @ X93))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f700,plain,(
% 1.70/1.50 ! [X92 : subst > term > term] : (? [X94 : subst,X93 : term] : ((sub @ sK567 @ (push @ X93 @ X94)) != (X92 @ X94 @ X93)) => ((sub @ sK567 @ (push @ (sK568 @ X92) @ (sK569 @ X92))) != (X92 @ (sK569 @ X92) @ (sK568 @ X92))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X95 : subst] : ((comp @ X95 @ id) != X95) => (sK570 != (comp @ sK570 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f702,plain,(
% 1.70/1.50 ? [X96 : subst] : ((comp @ id @ X96) != X96) => ((comp @ id @ sK571) != sK571)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f703,plain,(
% 1.70/1.50 ! [X101 : subst] : (? [X102 : d_subst] : ((d2subst @ X102) = X101) => ((d2subst @ (sK572 @ X101)) = X101))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f704,plain,(
% 1.70/1.50 ? [X107 : term,X108 : term,X109 : term,X110 : term] : (((ap @ (sub @ X109 @ id) @ X110) = (ap @ (sub @ X108 @ id) @ X107)) & (X107 != X110)) => (((ap @ (sub @ sK575 @ id) @ sK576) = (ap @ (sub @ sK574 @ id) @ sK573)) & (sK573 != sK576))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f705,plain,(
% 1.70/1.50 ? [X111 : term,X112 : term,X113 : term,X114 : term] : ((X111 != X113) & ((ap @ X114 @ X111) = (ap @ X112 @ X113))) => ((sK577 != sK579) & ((ap @ sK580 @ sK577) = (ap @ sK578 @ sK579)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f706,plain,(
% 1.70/1.50 ? [X120 : subst] : ((comp @ id @ X120) != X120) => (sK581 != (comp @ id @ sK581))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f707,plain,(
% 1.70/1.50 ! [X121 : term,X122 : term > $o,X123 : term > $o,X124 : subst] : (? [X125 : term] : ((X123 @ (sub @ X125 @ (push @ X121 @ X124))) != (X122 @ X125)) => ((X123 @ (sub @ (sK582 @ X124 @ X123 @ X122 @ X121) @ (push @ X121 @ X124))) != (X122 @ (sK582 @ X124 @ X123 @ X122 @ X121))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f708,plain,(
% 1.70/1.50 ? [X126 : term,X127 : term > $o,X128 : term > $o,X129 : subst] : (($true != (X127 @ one)) & ($true = (X128 @ X126)) & ! [X130 : term] : ((X128 @ (sub @ X130 @ (push @ X126 @ X129))) = (X127 @ X130))) => (((sK584 @ one) != $true) & ((sK585 @ sK583) = $true) & ! [X130 : term] : ((sK584 @ X130) = (sK585 @ (sub @ X130 @ (push @ sK583 @ sK586)))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f709,plain,(
% 1.70/1.50 ? [X132 : term] : ((sub @ X132 @ id) != X132) => (sK587 != (sub @ sK587 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f710,plain,(
% 1.70/1.50 ! [X134 : subst > term > subst > $o] : (? [X135 : term > $o] : ! [X136 : term] : ((X135 @ X136) = (X134 @ id @ X136 @ id)) => ! [X136 : term] : ((sK588 @ X134 @ X136) = (X134 @ id @ X136 @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f711,plain,(
% 1.70/1.50 ? [X137 : term] : ((sub @ X137 @ id) != X137) => ((sub @ sK589 @ id) != sK589)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X138 : subst > term > subst > $o] : ! [X139 : term > $o] : ? [X140 : term] : ((X138 @ id @ X140 @ id) != (X139 @ X140)) => ! [X139 : term > $o] : ? [X140 : term] : ((X139 @ X140) != (sK590 @ id @ X140 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ! [X139 : term > $o] : (? [X140 : term] : ((X139 @ X140) != (sK590 @ id @ X140 @ id)) => ((X139 @ (sK591 @ X139)) != (sK590 @ id @ (sK591 @ X139) @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X141 : term] : ((sub @ X141 @ id) != X141) => (sK592 != (sub @ sK592 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X144 : term] : ((sub @ X144 @ id) != X144) => (sK593 != (sub @ sK593 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X145 : term] : ((sub @ X145 @ id) != X145) => (sK594 != (sub @ sK594 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f717,plain,(
% 1.70/1.50 ? [X147 : term,X148 : term] : ((X147 != X148) & ((lam @ X147) = (lam @ X148))) => ((sK595 != sK596) & ((lam @ sK595) = (lam @ sK596)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f718,plain,(
% 1.70/1.50 ! [X151 : term] : (? [X152 : subst > term > term] : ((sub @ X151 @ (push @ one @ sh)) = (X152 @ sh @ one)) => ((sub @ X151 @ (push @ one @ sh)) = (sK597 @ X151 @ sh @ one)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f719,plain,(
% 1.70/1.50 ? [X153 : term] : ! [X154 : subst > term > term] : ((X154 @ sh @ one) != (sub @ X153 @ (push @ one @ sh))) => ! [X154 : subst > term > term] : ((X154 @ sh @ one) != (sub @ sK598 @ (push @ one @ sh)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f720,plain,(
% 1.70/1.50 ? [X155 : subst] : ((comp @ X155 @ id) != X155) => ((comp @ sK599 @ id) != sK599)),
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% 1.70/1.50 ? [X156 : subst,X157 : term] : ((sub @ one @ (push @ X157 @ X156)) != X157) => (sK601 != (sub @ one @ (push @ sK601 @ sK600)))),
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% 1.70/1.50 ? [X158 : subst,X159 : term] : ((comp @ sh @ (push @ X159 @ X158)) != X158) => (sK602 != (comp @ sh @ (push @ sK603 @ sK602)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f723,plain,(
% 1.70/1.50 ? [X166 : term] : ((sub @ X166 @ id) != X166) => ((sub @ sK604 @ id) != sK604)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f724,plain,(
% 1.70/1.50 ? [X168 : term] : ((sub @ X168 @ id) != X168) => ((sub @ sK605 @ id) != sK605)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X169 : subst > term > subst > $o] : ! [X170 : term > $o] : ? [X171 : term] : ((X169 @ id @ X171 @ id) != (X170 @ X171)) => ! [X170 : term > $o] : ? [X171 : term] : ((sK606 @ id @ X171 @ id) != (X170 @ X171))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f726,plain,(
% 1.70/1.50 ! [X170 : term > $o] : (? [X171 : term] : ((sK606 @ id @ X171 @ id) != (X170 @ X171)) => ((sK606 @ id @ (sK607 @ X170) @ id) != (X170 @ (sK607 @ X170))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f727,plain,(
% 1.70/1.50 ! [X173 : subst > term > subst > $o] : (? [X174 : term > $o] : ! [X175 : term] : ((X173 @ id @ X175 @ id) = (X174 @ X175)) => ! [X175 : term] : ((X173 @ id @ X175 @ id) = (sK608 @ X173 @ X175)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f728,plain,(
% 1.70/1.50 ? [X177 : term] : ((sub @ X177 @ id) != X177) => ((sub @ sK609 @ id) != sK609)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f729,plain,(
% 1.70/1.50 ? [X178 : subst > term > term,X179 : subst > term > term,X180 : subst,X181 : term] : (! [X182 : subst,X183 : subst,X184 : term] : ((X179 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182)) = (sub @ (X179 @ X183 @ X184) @ X182)) & ((X179 @ X180 @ X181) != (X178 @ X180 @ X181)) & ! [X185 : subst,X186 : term,X187 : subst] : ((sub @ (X178 @ X187 @ X186) @ X185) = (X178 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185))) & ((lam @ (X178 @ sh @ one)) = (lam @ (X179 @ sh @ one)))) => (! [X184 : term,X183 : subst,X182 : subst] : ((sK611 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182)) = (sub @ (sK611 @ X183 @ X184) @ X182)) & ((sK610 @ sK612 @ sK613) != (sK611 @ sK612 @ sK613)) & ! [X187 : subst,X186 : term,X185 : subst] : ((sub @ (sK610 @ X187 @ X186) @ X185) = (sK610 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185))) & ((lam @ (sK611 @ sh @ one)) = (lam @ (sK610 @ sh @ one))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f730,plain,(
% 1.70/1.50 ! [X189 : subst > term > term] : (? [X192 : subst,X193 : subst,X194 : term] : ((sub @ (X189 @ X193 @ X194) @ X192) != (X189 @ (comp @ X193 @ X192) @ (sub @ X194 @ X192))) => ((sub @ (X189 @ (sK615 @ X189) @ (sK616 @ X189)) @ (sK614 @ X189)) != (X189 @ (comp @ (sK615 @ X189) @ (sK614 @ X189)) @ (sub @ (sK616 @ X189) @ (sK614 @ X189)))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f731,plain,(
% 1.70/1.50 ! [X188 : subst > term > term] : (? [X195 : subst,X196 : term,X197 : subst] : ((sub @ (X188 @ X197 @ X196) @ X195) != (X188 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195))) => ((X188 @ (comp @ (sK619 @ X188) @ (sK617 @ X188)) @ (sub @ (sK618 @ X188) @ (sK617 @ X188))) != (sub @ (X188 @ (sK619 @ X188) @ (sK618 @ X188)) @ (sK617 @ X188))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ! [X201 : term > $o] : (? [X202 : term] : ((sK621 @ (sub @ X202 @ (push @ sK620 @ sK622))) != (X201 @ X202)) => ((sK621 @ (sub @ (sK623 @ X201) @ (push @ sK620 @ sK622))) != (X201 @ (sK623 @ X201))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f734,plain,(
% 1.70/1.50 ! [X203 : term,X204 : term > $o,X205 : subst] : (? [X206 : term > $o] : ! [X207 : term] : ((X204 @ (sub @ X207 @ (push @ X203 @ X205))) = (X206 @ X207)) => ! [X207 : term] : ((X204 @ (sub @ X207 @ (push @ X203 @ X205))) = (sK624 @ X205 @ X204 @ X203 @ X207)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X212 : term,X213 : subst > term > subst > $o] : (((sP30 @ X213) != $true) & ((sP29 @ X213) != $true) & ((X213 @ id @ X212 @ id) != $true)) => (($true != (sP30 @ sK626)) & ($true != (sP29 @ sK626)) & ($true != (sK626 @ id @ sK625 @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f736,plain,(
% 1.70/1.50 ! [X214 : term] : (? [X215 : subst > term > term] : ! [X216 : subst,X217 : term] : ((X215 @ X216 @ X217) = (sub @ X214 @ (push @ X217 @ X216))) => ! [X217 : term,X216 : subst] : ((sK627 @ X214 @ X216 @ X217) = (sub @ X214 @ (push @ X217 @ X216))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X218 : term] : ! [X219 : subst > term > term] : ? [X220 : subst,X221 : term] : ((X219 @ X220 @ X221) != (sub @ X218 @ (push @ X221 @ X220))) => ! [X219 : subst > term > term] : ? [X221 : term,X220 : subst] : ((X219 @ X220 @ X221) != (sub @ sK628 @ (push @ X221 @ X220)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f738,plain,(
% 1.70/1.50 ! [X219 : subst > term > term] : (? [X221 : term,X220 : subst] : ((X219 @ X220 @ X221) != (sub @ sK628 @ (push @ X221 @ X220))) => ((sub @ sK628 @ (push @ (sK630 @ X219) @ (sK629 @ X219))) != (X219 @ (sK629 @ X219) @ (sK630 @ X219))))),
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% 1.70/1.50 ? [X222 : subst,X223 : term] : ((sub @ one @ (push @ X223 @ X222)) != X223) => (sK632 != (sub @ one @ (push @ sK632 @ sK631)))),
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% 1.70/1.50 ? [X229 : subst,X230 : term] : ((comp @ sh @ (push @ X230 @ X229)) != X229) => (sK633 != (comp @ sh @ (push @ sK634 @ sK633)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
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% 1.70/1.50 ? [X233 : term,X234 : term > $o,X235 : term > $o,X236 : subst,X237 : term] : (((X234 @ X233) = $true) & ((X235 @ (sub @ X233 @ (push @ X237 @ X236))) != $true)) => (($true = (sK636 @ sK635)) & ($true != (sK637 @ (sub @ sK635 @ (push @ sK639 @ sK638)))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f742,plain,(
% 1.70/1.50 ! [X240 : term] : (? [X241 : d_term] : ((d2term @ X241) = X240) => ((d2term @ (sK640 @ X240)) = X240))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f743,plain,(
% 1.70/1.50 ? [X242 : subst,X243 : term] : ((sub @ one @ (push @ X243 @ X242)) != X243) => ((sub @ one @ (push @ sK642 @ sK641)) != sK642)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f744,plain,(
% 1.70/1.50 ? [X247 : term] : ((sub @ X247 @ id) != X247) => ((sub @ sK643 @ id) != sK643)),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f745,plain,(
% 1.70/1.50 ! [X248 : term] : (? [X249 : subst > term > term] : ((sub @ X248 @ (push @ one @ sh)) = (X249 @ sh @ one)) => ((sK644 @ X248 @ sh @ one) = (sub @ X248 @ (push @ one @ sh))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f746,plain,(
% 1.70/1.50 ? [X250 : term] : ! [X251 : subst > term > term] : ((X251 @ sh @ one) != (sub @ X250 @ (push @ one @ sh))) => ! [X251 : subst > term > term] : ((sub @ sK645 @ (push @ one @ sh)) != (X251 @ sh @ one))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f747,plain,(
% 1.70/1.50 ? [X252 : subst] : ((push @ (sub @ one @ X252) @ (comp @ sh @ X252)) != X252) => (sK646 != (push @ (sub @ one @ sK646) @ (comp @ sh @ sK646)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f748,plain,(
% 1.70/1.50 ? [X255 : term] : ((sub @ X255 @ id) != X255) => (sK647 != (sub @ sK647 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f749,plain,(
% 1.70/1.50 ! [X256 : subst > term > subst > $o] : (? [X257 : term > $o] : ! [X258 : term] : ((X256 @ id @ X258 @ id) = (X257 @ X258)) => ! [X258 : term] : ((sK648 @ X256 @ X258) = (X256 @ id @ X258 @ id)))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f750,plain,(
% 1.70/1.50 ? [X259 : subst > term > subst > $o] : ! [X260 : term > $o] : ? [X261 : term] : ((X259 @ id @ X261 @ id) != (X260 @ X261)) => ! [X260 : term > $o] : ? [X261 : term] : ((sK649 @ id @ X261 @ id) != (X260 @ X261))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f751,plain,(
% 1.70/1.50 ! [X260 : term > $o] : (? [X261 : term] : ((sK649 @ id @ X261 @ id) != (X260 @ X261)) => ((sK649 @ id @ (sK650 @ X260) @ id) != (X260 @ (sK650 @ X260))))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f752,plain,(
% 1.70/1.50 ? [X263 : subst] : ((comp @ X263 @ id) != X263) => (sK651 != (comp @ sK651 @ id))),
% 1.70/1.50 introduced(definition,[],[choice_axiom])).
% 1.70/1.50 thf(f677,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & (! [X0 : term,X1 : term,X2 : term,X3 : term] : ((X0 = X2) | ((ap @ (sub @ X0 @ id) @ X1) != (ap @ (sub @ X2 @ id) @ X3))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X4 : term,X5 : term,X6 : term,X7 : term] : ((X4 != X6) & ((ap @ (sub @ X4 @ id) @ X5) = (ap @ (sub @ X6 @ id) @ X7)))) & (hoasapnotvar = $true) & ((hoasinduction = $true) | (sP109 != $true)) & ((sP109 = $true) | (hoasinduction != $true)) & (substmonoid_gthm = $true) & ((apinj1 = $true) | ? [X8 : term,X9 : term,X10 : term,X11 : term] : ((X8 != X10) & ((ap @ X8 @ X9) = (ap @ X10 @ X11)))) & (! [X12 : term,X13 : term,X14 : term,X15 : term] : ((X12 = X14) | ((ap @ X12 @ X13) != (ap @ X14 @ X15))) | (apinj1 != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X16 : subst > term > subst > $o] : ? [X17 : term > $o] : ! [X18 : term] : ((X17 @ X18) = (X16 @ id @ X18 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X19 : subst > term > subst > $o] : ! [X20 : term > $o] : ? [X21 : term] : ((X19 @ id @ X21 @ id) != (X20 @ X21))) & (! [X22 : term,X23 : subst,X24 : term > $o,X25 : term > $o,X26 : term] : (($true = (X25 @ (sub @ X26 @ (push @ X22 @ X23)))) | ($true != (X24 @ X26))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X27 : term,X28 : subst,X29 : term > $o,X30 : term > $o,X31 : term] : (((X30 @ (sub @ X31 @ (push @ X27 @ X28))) != $true) & ($true = (X29 @ X31)))) & ((sP104 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP104 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X32 : d_term] : (d_one = X32) & (? [X33 : term] : ((sub @ X33 @ id) != X33) | (sP102 = $true) | ? [X34 : term] : ! [X35 : subst > term > term] : ? [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) != (sub @ X34 @ (push @ X37 @ X36))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X38 : term] : ((sub @ X38 @ id) = X38) & (sP102 != $true) & ! [X39 : term] : ? [X40 : subst > term > term] : ! [X41 : subst,X42 : term] : ((X40 @ X41 @ X42) = (sub @ X39 @ (push @ X42 @ X41))))) & (pushprop_gthm = $true) & (lamnotvar = $true) & ((sP100 = $true) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (sP100 != $true)) & (hoasinduction_lem1_lthm = $true) & (($true = sP98) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP98)) & ((axshiftcons = $true) | ? [X43 : term,X44 : subst] : ((comp @ sh @ (push @ X43 @ X44)) != X44)) & (! [X45 : term,X46 : subst] : ((comp @ sh @ (push @ X45 @ X46)) = X46) | (axshiftcons != $true)) & ((shinj = $true) | ? [X47 : term,X48 : term] : (((sub @ X47 @ sh) = (sub @ X48 @ sh)) & (X47 != X48))) & (! [X49 : term,X50 : term] : (((sub @ X50 @ sh) != (sub @ X49 @ sh)) | (X49 = X50)) | (shinj != $true)) & (apnotvar = $true) & ((substmonoid_lthm = $true) | ($true != sP95)) & (($true = sP95) | (substmonoid_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X51 : subst,X52 : term,X53 : term > $o] : ! [X54 : term > $o] : ? [X55 : term] : ((X54 @ X55) != (X53 @ (sub @ X55 @ (push @ X52 @ X51))))) & (! [X56 : subst,X57 : term,X58 : term > $o] : ? [X59 : term > $o] : ! [X60 : term] : ((X58 @ (sub @ X60 @ (push @ X57 @ X56))) = (X59 @ X60)) | (pushprop_lem0_lthm != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (($true = sP94) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP94)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3a != $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X61 : subst,X62 : term > $o,X63 : term,X64 : term > $o] : (? [X65 : term] : ((X62 @ X65) != (X64 @ (sub @ X65 @ (push @ X63 @ X61)))) | ((X64 @ X63) != $true) | ((X62 @ one) = $true)) | ? [X66 : term,X67 : subst] : ((sub @ one @ (push @ X66 @ X67)) != X66) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X68 : subst,X69 : term > $o,X70 : term,X71 : term > $o] : (! [X72 : term] : ((X71 @ (sub @ X72 @ (push @ X70 @ X68))) = (X69 @ X72)) & ((X71 @ X70) = $true) & ($true != (X69 @ one))) & ! [X73 : term,X74 : subst] : ((sub @ one @ (push @ X73 @ X74)) = X73))) & ((hoaslamnotap = $true) | ? [X75 : term,X76 : subst > term > term,X77 : term] : (((ap @ (sub @ X77 @ id) @ X75) = (lam @ (X76 @ sh @ one))) & ! [X78 : subst,X79 : term,X80 : subst] : ((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X76 @ X78 @ X79) @ X80)))) & (! [X81 : term,X82 : subst > term > term,X83 : term] : (((lam @ (X82 @ sh @ one)) != (ap @ (sub @ X83 @ id) @ X81)) | ? [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) != (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | (hoaslamnotap != $true)) & (axvarshift = $true) & (! [X87 : term] : ? [X88 : subst > term > term] : ! [X89 : term,X90 : subst] : ((sub @ X87 @ (push @ X89 @ X90)) = (X88 @ X90 @ X89)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X91 : term] : ! [X92 : subst > term > term] : ? [X93 : term,X94 : subst] : ((sub @ X91 @ (push @ X93 @ X94)) != (X92 @ X94 @ X93))) & ((substmonoid = $true) | ? [X95 : subst] : ((comp @ X95 @ id) != X95) | ? [X96 : subst] : ((comp @ id @ X96) != X96)) & ((! [X97 : subst] : ((comp @ X97 @ id) = X97) & ! [X98 : subst] : ((comp @ id @ X98) = X98)) | (substmonoid != $true)) & ! [X99 : d_term,X100 : d_term] : ((X99 = X100) | ((d2term @ X99) != (d2term @ X100))) & ! [X101 : subst] : ? [X102 : d_subst] : ((d2subst @ X102) = X101) & (! [X103 : term,X104 : term,X105 : term,X106 : term] : (((ap @ (sub @ X104 @ id) @ X103) != (ap @ (sub @ X105 @ id) @ X106)) | (X103 = X106)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X107 : term,X108 : term,X109 : term,X110 : term] : (((ap @ (sub @ X109 @ id) @ X110) = (ap @ (sub @ X108 @ id) @ X107)) & (X107 != X110))) & (($true = sP88) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP88)) & ((apinj2 = $true) | ? [X111 : term,X112 : term,X113 : term,X114 : term] : ((X111 != X113) & ((ap @ X114 @ X111) = (ap @ X112 @ X113)))) & (! [X115 : term,X116 : term,X117 : term,X118 : term] : ((X115 = X117) | ((ap @ X118 @ X115) != (ap @ X116 @ X117))) | (apinj2 != $true)) & ((hoasapinj2_lthm = $true) | (sP86 != $true)) & ((sP86 = $true) | (hoasapinj2_lthm != $true)) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | (sP84 != $true)) & ((sP84 = $true) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP81) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP81)) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (! [X119 : subst] : ((comp @ id @ X119) = X119) | (axidl != $true)) & ((axidl = $true) | ? [X120 : subst] : ((comp @ id @ X120) != X120)) & (hoasinduction_lem1v2 = $true) & (! [X121 : term,X122 : term > $o,X123 : term > $o,X124 : subst] : (((X122 @ one) = $true) | ($true != (X123 @ X121)) | ? [X125 : term] : ((X123 @ (sub @ X125 @ (push @ X121 @ X124))) != (X122 @ X125))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X126 : term,X127 : term > $o,X128 : term > $o,X129 : subst] : (($true != (X127 @ one)) & ($true = (X128 @ X126)) & ! [X130 : term] : ((X128 @ (sub @ X130 @ (push @ X126 @ X129))) = (X127 @ X130)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X131 : term] : ((sub @ X131 @ id) = X131) | (axvarid != $true)) & ((axvarid = $true) | ? [X132 : term] : ((sub @ X132 @ id) != X132)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP77 != $true) & ($true != sP76) & (sP75 != $true) & ! [X133 : term] : ((sub @ X133 @ id) = X133) & ! [X134 : subst > term > subst > $o] : ? [X135 : term > $o] : ! [X136 : term] : ((X135 @ X136) = (X134 @ id @ X136 @ id)))) & ((sP77 = $true) | ($true = sP76) | (sP75 = $true) | ? [X137 : term] : ((sub @ X137 @ id) != X137) | ? [X138 : subst > term > subst > $o] : ! [X139 : term > $o] : ? [X140 : term] : ((X138 @ id @ X140 @ id) != (X139 @ X140)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((sP69 = $true) | (induction != $true)) & ((induction = $true) | (sP69 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP65 = $true) | ? [X141 : term] : ((sub @ X141 @ id) != X141) | ($true = sP66) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP65 != $true) & ! [X142 : term] : ((sub @ X142 @ id) = X142) & ($true != sP66))) & (! [X143 : term] : ((sub @ X143 @ id) = X143) | ? [X144 : term] : ((sub @ X144 @ id) != X144) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X145 : term] : ((sub @ X145 @ id) != X145) & ! [X146 : term] : ((sub @ X146 @ id) = X146))) & ((laminj = $true) | ? [X147 : term,X148 : term] : ((X147 != X148) & ((lam @ X147) = (lam @ X148)))) & (! [X149 : term,X150 : term] : ((X149 = X150) | ((lam @ X150) != (lam @ X149))) | (laminj != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP60 != $true)) & ((sP60 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (($true = sP58) | (hoaslaminj_lthm != $true)) & (! [X151 : term] : ? [X152 : subst > term > term] : ((sub @ X151 @ (push @ one @ sh)) = (X152 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X153 : term] : ! [X154 : subst > term > term] : ((X154 @ sh @ one) != (sub @ X153 @ (push @ one @ sh)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((sP56 = $true) | ($true = sP55) | ? [X155 : subst] : ((comp @ X155 @ id) != X155) | ? [X156 : subst,X157 : term] : ((sub @ one @ (push @ X157 @ X156)) != X157) | ? [X158 : subst,X159 : term] : ((comp @ sh @ (push @ X159 @ X158)) != X158) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP56 != $true) & ($true != sP55) & ! [X160 : subst] : ((comp @ X160 @ id) = X160) & ! [X161 : subst,X162 : term] : ((sub @ one @ (push @ X162 @ X161)) = X162) & ! [X163 : subst,X164 : term] : ((comp @ sh @ (push @ X164 @ X163)) = X163))) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & ((hoasinduction_lem2 = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP47) & ! [X165 : term] : ((sub @ X165 @ id) = X165) & ($true != sP46))) & (($true = sP47) | ? [X166 : term] : ((sub @ X166 @ id) != X166) | ($true = sP46) | (hoasinduction_lem3_lthm != $true)) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X167 : d_subst] : (d_id = X167) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (? [X168 : term] : ((sub @ X168 @ id) != X168) | ($true = sP39) | (sP41 = $true) | ? [X169 : subst > term > subst > $o] : ! [X170 : term > $o] : ? [X171 : term] : ((X169 @ id @ X171 @ id) != (X170 @ X171)) | ($true = sP40) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X172 : term] : ((sub @ X172 @ id) = X172) & ($true != sP39) & (sP41 != $true) & ! [X173 : subst > term > subst > $o] : ? [X174 : term > $o] : ! [X175 : term] : ((X173 @ id @ X175 @ id) = (X174 @ X175)) & ($true != sP40))) & (! [X176 : term] : ((sub @ X176 @ id) = X176) | (termmset != $true)) & ((termmset = $true) | ? [X177 : term] : ((sub @ X177 @ id) != X177)) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoaslaminj = $true) | ? [X178 : subst > term > term,X179 : subst > term > term,X180 : subst,X181 : term] : (! [X182 : subst,X183 : subst,X184 : term] : ((X179 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182)) = (sub @ (X179 @ X183 @ X184) @ X182)) & ((X179 @ X180 @ X181) != (X178 @ X180 @ X181)) & ! [X185 : subst,X186 : term,X187 : subst] : ((sub @ (X178 @ X187 @ X186) @ X185) = (X178 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185))) & ((lam @ (X178 @ sh @ one)) = (lam @ (X179 @ sh @ one))))) & (! [X188 : subst > term > term,X189 : subst > term > term,X190 : subst,X191 : term] : (? [X192 : subst,X193 : subst,X194 : term] : ((sub @ (X189 @ X193 @ X194) @ X192) != (X189 @ (comp @ X193 @ X192) @ (sub @ X194 @ X192))) | ((X189 @ X190 @ X191) = (X188 @ X190 @ X191)) | ? [X195 : subst,X196 : term,X197 : subst] : ((sub @ (X188 @ X197 @ X196) @ X195) != (X188 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195))) | ((lam @ (X188 @ sh @ one)) != (lam @ (X189 @ sh @ one)))) | (hoaslaminj != $true)) & (hoaslamnotvar = $true) & ((pushprop_lem0 = $true) | ? [X198 : term,X199 : term > $o,X200 : subst] : ! [X201 : term > $o] : ? [X202 : term] : ((X199 @ (sub @ X202 @ (push @ X198 @ X200))) != (X201 @ X202))) & (! [X203 : term,X204 : term > $o,X205 : subst] : ? [X206 : term > $o] : ! [X207 : term] : ((X204 @ (sub @ X207 @ (push @ X203 @ X205))) = (X206 @ X207)) | (pushprop_lem0 != $true)) & ! [X208 : d_subst,X209 : d_subst] : (((d2subst @ X209) != (d2subst @ X208)) | (X208 = X209)) & (termmset_gthm = $true) & (! [X210 : term,X211 : subst > term > subst > $o] : (($true = (sP30 @ X211)) | ($true = (sP29 @ X211)) | ($true = (X211 @ id @ X210 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X212 : term,X213 : subst > term > subst > $o] : (((sP30 @ X213) != $true) & ((sP29 @ X213) != $true) & ((X213 @ id @ X212 @ id) != $true))) & (! [X214 : term] : ? [X215 : subst > term > term] : ! [X216 : subst,X217 : term] : ((X215 @ X216 @ X217) = (sub @ X214 @ (push @ X217 @ X216))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X218 : term] : ! [X219 : subst > term > term] : ? [X220 : subst,X221 : term] : ((X219 @ X220 @ X221) != (sub @ X218 @ (push @ X221 @ X220)))) & ((induction2 = $true) | ($true != sP28)) & (($true = sP28) | (induction2 != $true)) & (? [X222 : subst,X223 : term] : ((sub @ one @ (push @ X223 @ X222)) != X223) | ! [X224 : term,X225 : term > $o,X226 : term > $o,X227 : subst,X228 : term] : (((X225 @ X224) != $true) | ((X226 @ (sub @ X224 @ (push @ X228 @ X227))) = $true)) | ? [X229 : subst,X230 : term] : ((comp @ sh @ (push @ X230 @ X229)) != X229) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X231 : subst,X232 : term] : ((sub @ one @ (push @ X232 @ X231)) = X232) & ? [X233 : term,X234 : term > $o,X235 : term > $o,X236 : subst,X237 : term] : (((X234 @ X233) = $true) & ((X235 @ (sub @ X233 @ (push @ X237 @ X236))) != $true)) & ! [X238 : subst,X239 : term] : ((comp @ sh @ (push @ X239 @ X238)) = X238))) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X240 : term] : ? [X241 : d_term] : ((d2term @ X241) = X240) & (axclos = $true) & ((axvarcons = $true) | ? [X242 : subst,X243 : term] : ((sub @ one @ (push @ X243 @ X242)) != X243)) & (! [X244 : subst,X245 : term] : ((sub @ one @ (push @ X245 @ X244)) = X245) | (axvarcons != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) | ((sP25 != $true) & ! [X246 : term] : ((sub @ X246 @ id) = X246))) & ((sP25 = $true) | ? [X247 : term] : ((sub @ X247 @ id) != X247) | (hoasinduction_lem3v2_lthm != $true)) & (! [X248 : term] : ? [X249 : subst > term > term] : ((sub @ X248 @ (push @ one @ sh)) = (X249 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X250 : term] : ! [X251 : subst > term > term] : ((X251 @ sh @ one) != (sub @ X250 @ (push @ one @ sh)))) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & ((axscons = $true) | ? [X252 : subst] : ((push @ (sub @ one @ X252) @ (comp @ sh @ X252)) != X252)) & (! [X253 : subst] : ((push @ (sub @ one @ X253) @ (comp @ sh @ X253)) = X253) | (axscons != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP20) & (sP19 != $true) & (sP18 != $true))) & (($true = sP21) | ($true = sP20) | (sP19 = $true) | (sP18 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X254 : term] : ((sub @ X254 @ id) = X254) & (sP5 != $true) & ($true != sP4))) & (? [X255 : term] : ((sub @ X255 @ id) != X255) | (sP5 = $true) | ($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X256 : subst > term > subst > $o] : ? [X257 : term > $o] : ! [X258 : term] : ((X256 @ id @ X258 @ id) = (X257 @ X258)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X259 : subst > term > subst > $o] : ! [X260 : term > $o] : ? [X261 : term] : ((X259 @ id @ X261 @ id) != (X260 @ X261))) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X262 : subst] : ((comp @ X262 @ id) = X262) | (axidr != $true)) & ((axidr = $true) | ? [X263 : subst] : ((comp @ X263 @ id) != X263))),
% 1.70/1.50 inference(rectify,[status(thm)],[f676])).
% 1.70/1.50 thf(f676,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 != X388) & ((ap @ (sub @ X388 @ id) @ X389) = (ap @ (sub @ X386 @ id) @ X387)))) & (hoasapnotvar = $true) & ((hoasinduction = $true) | (sP109 != $true)) & ((sP109 = $true) | (hoasinduction != $true)) & (substmonoid_gthm = $true) & ((apinj1 = $true) | ? [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 != X317) & ((ap @ X317 @ X318) = (ap @ X315 @ X316)))) & (! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316))) | (apinj1 != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X65 : subst > term > subst > $o] : ? [X66 : term > $o] : ! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X65 : subst > term > subst > $o] : ! [X66 : term > $o] : ? [X67 : term] : ((X65 @ id @ X67 @ id) != (X66 @ X67))) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true != (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) & ($true = (X79 @ X81)))) & ((sP104 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP104 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X381 : d_term] : (d_one = X381) & (? [X261 : term] : ((sub @ X261 @ id) != X261) | (sP102 = $true) | ? [X257 : term] : ! [X258 : subst > term > term] : ? [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) != (X258 @ X259 @ X260)) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X261 : term] : ((sub @ X261 @ id) = X261) & (sP102 != $true) & ! [X257 : term] : ? [X258 : subst > term > term] : ! [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) = (X258 @ X259 @ X260)))) & (pushprop_gthm = $true) & (lamnotvar = $true) & ((sP100 = $true) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (sP100 != $true)) & (hoasinduction_lem1_lthm = $true) & (($true = sP98) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP98)) & ((axshiftcons = $true) | ? [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) != X181)) & (! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181) | (axshiftcons != $true)) & ((shinj = $true) | ? [X230 : term,X231 : term] : (((sub @ X230 @ sh) = (sub @ X231 @ sh)) & (X230 != X231))) & (! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231)) | (shinj != $true)) & (apnotvar = $true) & ((substmonoid_lthm = $true) | ($true != sP95)) & (($true = sP95) | (substmonoid_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X272 : subst,X273 : term,X274 : term > $o] : ! [X275 : term > $o] : ? [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) != (X275 @ X276))) & (! [X272 : subst,X273 : term,X274 : term > $o] : ? [X275 : term > $o] : ! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276)) | (pushprop_lem0_lthm != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (($true = sP94) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP94)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3a != $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (? [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) != (X85 @ X88)) | ((X87 @ X86) != $true) | ($true = (X85 @ one))) | ? [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) != X82) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88)) & ((X87 @ X86) = $true) & ($true != (X85 @ one))) & ! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82))) & ((hoaslamnotap = $true) | ? [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) = (lam @ (X516 @ sh @ one))) & ! [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) = (sub @ (X516 @ X518 @ X519) @ X520)))) & (! [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))) | ? [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) != (sub @ (X516 @ X518 @ X519) @ X520))) | (hoaslamnotap != $true)) & (axvarshift = $true) & (! [X0 : term] : ? [X1 : subst > term > term] : ! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X0 : term] : ! [X1 : subst > term > term] : ? [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) != (X1 @ X3 @ X2))) & ((substmonoid = $true) | ? [X385 : subst] : ((comp @ X385 @ id) != X385) | ? [X384 : subst] : ((comp @ id @ X384) != X384)) & ((! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384)) | (substmonoid != $true)) & ! [X382 : d_term,X383 : d_term] : ((X382 = X383) | ((d2term @ X383) != (d2term @ X382))) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) = (ap @ (sub @ X183 @ id) @ X182)) & (X182 != X185))) & (($true = sP88) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP88)) & ((apinj2 = $true) | ? [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 != X91) & ((ap @ X92 @ X89) = (ap @ X90 @ X91)))) & (! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91))) | (apinj2 != $true)) & ((hoasapinj2_lthm = $true) | (sP86 != $true)) & ((sP86 = $true) | (hoasapinj2_lthm != $true)) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | (sP84 != $true)) & ((sP84 = $true) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP81) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP81)) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (! [X22 : subst] : ((comp @ id @ X22) = X22) | (axidl != $true)) & ((axidl = $true) | ? [X22 : subst] : ((comp @ id @ X22) != X22)) & (hoasinduction_lem1v2 = $true) & (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true = (X151 @ one)) | ($true != (X152 @ X150)) | ? [X154 : term] : ((X151 @ X154) != (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true != (X151 @ one)) & ($true = (X152 @ X150)) & ! [X154 : term] : ((X151 @ X154) = (X152 @ (sub @ X154 @ (push @ X150 @ X153)))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X314 : term] : ((sub @ X314 @ id) = X314) | (axvarid != $true)) & ((axvarid = $true) | ? [X314 : term] : ((sub @ X314 @ id) != X314)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP77 != $true) & ($true != sP76) & (sP75 != $true) & ! [X329 : term] : ((sub @ X329 @ id) = X329) & ! [X319 : subst > term > subst > $o] : ? [X320 : term > $o] : ! [X321 : term] : ((X319 @ id @ X321 @ id) = (X320 @ X321)))) & ((sP77 = $true) | ($true = sP76) | (sP75 = $true) | ? [X329 : term] : ((sub @ X329 @ id) != X329) | ? [X319 : subst > term > subst > $o] : ! [X320 : term > $o] : ? [X321 : term] : ((X319 @ id @ X321 @ id) != (X320 @ X321)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((sP69 = $true) | (induction != $true)) & ((induction = $true) | (sP69 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP65 = $true) | ? [X93 : term] : ((sub @ X93 @ id) != X93) | ($true = sP66) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP65 != $true) & ! [X93 : term] : ((sub @ X93 @ id) = X93) & ($true != sP66))) & (! [X21 : term] : ((sub @ X21 @ id) = X21) | ? [X20 : term] : ((sub @ X20 @ id) != X20) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X21 : term] : ((sub @ X21 @ id) != X21) & ! [X20 : term] : ((sub @ X20 @ id) = X20))) & ((laminj = $true) | ? [X109 : term,X110 : term] : ((X109 != X110) & ((lam @ X110) = (lam @ X109)))) & (! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109))) | (laminj != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP60 != $true)) & ((sP60 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (($true = sP58) | (hoaslaminj_lthm != $true)) & (! [X408 : term] : ? [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) = (X409 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X408 : term] : ! [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) != (X409 @ sh @ one))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((sP56 = $true) | ($true = sP55) | ? [X50 : subst] : ((comp @ X50 @ id) != X50) | ? [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) != X47) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP56 != $true) & ($true != sP55) & ! [X50 : subst] : ((comp @ X50 @ id) = X50) & ! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) & ! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48))) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & ((hoasinduction_lem2 = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP47) & ! [X155 : term] : ((sub @ X155 @ id) = X155) & ($true != sP46))) & (($true = sP47) | ? [X155 : term] : ((sub @ X155 @ id) != X155) | ($true = sP46) | (hoasinduction_lem3_lthm != $true)) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X27 : d_subst] : (d_id = X27) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (? [X420 : term] : ((sub @ X420 @ id) != X420) | ($true = sP39) | (sP41 = $true) | ? [X410 : subst > term > subst > $o] : ! [X411 : term > $o] : ? [X412 : term] : ((X410 @ id @ X412 @ id) != (X411 @ X412)) | ($true = sP40) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X420 : term] : ((sub @ X420 @ id) = X420) & ($true != sP39) & (sP41 != $true) & ! [X410 : subst > term > subst > $o] : ? [X411 : term > $o] : ! [X412 : term] : ((X410 @ id @ X412 @ id) = (X411 @ X412)) & ($true != sP40))) & (! [X297 : term] : ((sub @ X297 @ id) = X297) | (termmset != $true)) & ((termmset = $true) | ? [X297 : term] : ((sub @ X297 @ id) != X297)) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoaslaminj = $true) | ? [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)) & ((X36 @ X38 @ X39) != (X37 @ X38 @ X39)) & ! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) & ((lam @ (X36 @ sh @ one)) = (lam @ (X37 @ sh @ one))))) & (! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (? [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) != (sub @ (X37 @ X44 @ X45) @ X43)) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ? [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) != (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one)))) | (hoaslaminj != $true)) & (hoaslamnotvar = $true) & ((pushprop_lem0 = $true) | ? [X186 : term,X187 : term > $o,X188 : subst] : ! [X189 : term > $o] : ? [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) != (X189 @ X190))) & (! [X186 : term,X187 : term > $o,X188 : subst] : ? [X189 : term > $o] : ! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190)) | (pushprop_lem0 != $true)) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) != (d2subst @ X253)) | (X253 = X254)) & (termmset_gthm = $true) & (! [X122 : term,X123 : subst > term > subst > $o] : (($true = (sP30 @ X123)) | ((sP29 @ X123) = $true) | ((X123 @ id @ X122 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X122 : term,X123 : subst > term > subst > $o] : (($true != (sP30 @ X123)) & ((sP29 @ X123) != $true) & ((X123 @ id @ X122 @ id) != $true))) & (! [X23 : term] : ? [X24 : subst > term > term] : ! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X23 : term] : ! [X24 : subst > term > term] : ? [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) != (sub @ X23 @ (push @ X26 @ X25)))) & ((induction2 = $true) | ($true != sP28)) & (($true = sP28) | (induction2 != $true)) & (? [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) != X532) | ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)) | ? [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) != X533) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) = X532) & ? [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true = (X536 @ X535)) & ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) != $true)) & ! [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) = X533))) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (axclos = $true) & ((axvarcons = $true) | ? [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) != X121)) & (! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121) | (axvarcons != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) | ((sP25 != $true) & ! [X131 : term] : ((sub @ X131 @ id) = X131))) & ((sP25 = $true) | ? [X131 : term] : ((sub @ X131 @ id) != X131) | (hoasinduction_lem3v2_lthm != $true)) & (! [X255 : term] : ? [X256 : subst > term > term] : ((X256 @ sh @ one) = (sub @ X255 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X255 : term] : ! [X256 : subst > term > term] : ((X256 @ sh @ one) != (sub @ X255 @ (push @ one @ sh)))) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & ((axscons = $true) | ? [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) != X298)) & (! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298) | (axscons != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP20) & (sP19 != $true) & (sP18 != $true))) & (($true = sP21) | ($true = sP20) | (sP19 = $true) | (sP18 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X349 : term] : ((sub @ X349 @ id) = X349) & (sP5 != $true) & ($true != sP4))) & (? [X349 : term] : ((sub @ X349 @ id) != X349) | (sP5 = $true) | ($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X232 : subst > term > subst > $o] : ? [X233 : term > $o] : ! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X232 : subst > term > subst > $o] : ! [X233 : term > $o] : ? [X234 : term] : ((X232 @ id @ X234 @ id) != (X233 @ X234))) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) | (axidr != $true)) & ((axidr = $true) | ? [X119 : subst] : ((comp @ X119 @ id) != X119))),
% 1.70/1.50 inference(flattening,[status(thm)],[f675])).
% 1.70/1.50 thf(f675,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & ((! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 != X388) & ((ap @ (sub @ X388 @ id) @ X389) = (ap @ (sub @ X386 @ id) @ X387))))) & (hoasapnotvar = $true) & (((hoasinduction = $true) | (sP109 != $true)) & ((sP109 = $true) | (hoasinduction != $true))) & (substmonoid_gthm = $true) & (((apinj1 = $true) | ? [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 != X317) & ((ap @ X317 @ X318) = (ap @ X315 @ X316)))) & (! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316))) | (apinj1 != $true))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((! [X65 : subst > term > subst > $o] : ? [X66 : term > $o] : ! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X65 : subst > term > subst > $o] : ! [X66 : term > $o] : ? [X67 : term] : ((X65 @ id @ X67 @ id) != (X66 @ X67)))) & ((! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true != (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) & ($true = (X79 @ X81))))) & (((sP104 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP104 != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X381 : d_term] : (d_one = X381) & (((? [X261 : term] : ((sub @ X261 @ id) != X261) | (sP102 = $true) | ? [X257 : term] : ! [X258 : subst > term > term] : ? [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) != (X258 @ X259 @ X260))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X261 : term] : ((sub @ X261 @ id) = X261) & (sP102 != $true) & ! [X257 : term] : ? [X258 : subst > term > term] : ! [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) = (X258 @ X259 @ X260))))) & (pushprop_gthm = $true) & (lamnotvar = $true) & (((sP100 = $true) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (sP100 != $true))) & (hoasinduction_lem1_lthm = $true) & ((($true = sP98) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP98))) & (((axshiftcons = $true) | ? [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) != X181)) & (! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181) | (axshiftcons != $true))) & (((shinj = $true) | ? [X230 : term,X231 : term] : (((sub @ X230 @ sh) = (sub @ X231 @ sh)) & (X230 != X231))) & (! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231)) | (shinj != $true))) & (apnotvar = $true) & (((substmonoid_lthm = $true) | ($true != sP95)) & (($true = sP95) | (substmonoid_lthm != $true))) & (((pushprop_lem0_lthm = $true) | ? [X272 : subst,X273 : term,X274 : term > $o] : ! [X275 : term > $o] : ? [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) != (X275 @ X276))) & (! [X272 : subst,X273 : term,X274 : term > $o] : ? [X275 : term > $o] : ! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276)) | (pushprop_lem0_lthm != $true))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((($true = sP94) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP94))) & (hoasinduction_lem3b_gthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3a != $true))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (((! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (? [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) != (X85 @ X88)) | ((X87 @ X86) != $true) | ($true = (X85 @ one))) | ? [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) != X82)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88)) & ((X87 @ X86) = $true) & ($true != (X85 @ one))) & ! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82)))) & (((hoaslamnotap = $true) | ? [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) = (lam @ (X516 @ sh @ one))) & ! [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) = (sub @ (X516 @ X518 @ X519) @ X520)))) & (! [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))) | ? [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) != (sub @ (X516 @ X518 @ X519) @ X520))) | (hoaslamnotap != $true))) & (axvarshift = $true) & ((! [X0 : term] : ? [X1 : subst > term > term] : ! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X0 : term] : ! [X1 : subst > term > term] : ? [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) != (X1 @ X3 @ X2)))) & (((substmonoid = $true) | (? [X385 : subst] : ((comp @ X385 @ id) != X385) | ? [X384 : subst] : ((comp @ id @ X384) != X384))) & ((! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384)) | (substmonoid != $true))) & ! [X382 : d_term,X383 : d_term] : ((X382 = X383) | ((d2term @ X383) != (d2term @ X382))) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & ((! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) = (ap @ (sub @ X183 @ id) @ X182)) & (X182 != X185)))) & ((($true = sP88) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP88))) & (((apinj2 = $true) | ? [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 != X91) & ((ap @ X92 @ X89) = (ap @ X90 @ X91)))) & (! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91))) | (apinj2 != $true))) & (((hoasapinj2_lthm = $true) | (sP86 != $true)) & ((sP86 = $true) | (hoasapinj2_lthm != $true))) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & (((hoasinduction_lem2v2 = $true) | (sP84 != $true)) & ((sP84 = $true) | (hoasinduction_lem2v2 != $true))) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & ((($true = sP81) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP81))) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & ((! [X22 : subst] : ((comp @ id @ X22) = X22) | (axidl != $true)) & ((axidl = $true) | ? [X22 : subst] : ((comp @ id @ X22) != X22))) & (hoasinduction_lem1v2 = $true) & ((! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true = (X151 @ one)) | ($true != (X152 @ X150)) | ? [X154 : term] : ((X151 @ X154) != (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true != (X151 @ one)) & ($true = (X152 @ X150)) & ! [X154 : term] : ((X151 @ X154) = (X152 @ (sub @ X154 @ (push @ X150 @ X153))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X314 : term] : ((sub @ X314 @ id) = X314) | (axvarid != $true)) & ((axvarid = $true) | ? [X314 : term] : ((sub @ X314 @ id) != X314))) & (((hoasinduction_no_psi_cond_lthm = $true) | ((sP77 != $true) & ($true != sP76) & (sP75 != $true) & ! [X329 : term] : ((sub @ X329 @ id) = X329) & ! [X319 : subst > term > subst > $o] : ? [X320 : term > $o] : ! [X321 : term] : ((X319 @ id @ X321 @ id) = (X320 @ X321)))) & (((sP77 = $true) | ($true = sP76) | (sP75 = $true) | ? [X329 : term] : ((sub @ X329 @ id) != X329) | ? [X319 : subst > term > subst > $o] : ! [X320 : term > $o] : ? [X321 : term] : ((X319 @ id @ X321 @ id) != (X320 @ X321))) | (hoasinduction_no_psi_cond_lthm != $true))) & (((sP69 = $true) | (induction != $true)) & ((induction = $true) | (sP69 != $true))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((((sP65 = $true) | ? [X93 : term] : ((sub @ X93 @ id) != X93) | ($true = sP66)) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP65 != $true) & ! [X93 : term] : ((sub @ X93 @ id) = X93) & ($true != sP66)))) & (((! [X21 : term] : ((sub @ X21 @ id) = X21) | ? [X20 : term] : ((sub @ X20 @ id) != X20)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X21 : term] : ((sub @ X21 @ id) != X21) & ! [X20 : term] : ((sub @ X20 @ id) = X20)))) & (((laminj = $true) | ? [X109 : term,X110 : term] : ((X109 != X110) & ((lam @ X110) = (lam @ X109)))) & (! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109))) | (laminj != $true))) & (((hoasinduction_lem3aa_lthm = $true) | (sP60 != $true)) & ((sP60 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (hoasinduction_lem2v2_gthm = $true) & (((hoaslaminj_lthm = $true) | ($true != sP58)) & (($true = sP58) | (hoaslaminj_lthm != $true))) & ((! [X408 : term] : ? [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) = (X409 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X408 : term] : ! [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) != (X409 @ sh @ one)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((((sP56 = $true) | ($true = sP55) | ? [X50 : subst] : ((comp @ X50 @ id) != X50) | ? [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) != X47) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48)) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP56 != $true) & ($true != sP55) & ! [X50 : subst] : ((comp @ X50 @ id) = X50) & ! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) & ! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48)))) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & (((hoasinduction_lem2 = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem2 != $true))) & (((hoasinduction_lem3_lthm = $true) | (($true != sP47) & ! [X155 : term] : ((sub @ X155 @ id) = X155) & ($true != sP46))) & ((($true = sP47) | ? [X155 : term] : ((sub @ X155 @ id) != X155) | ($true = sP46)) | (hoasinduction_lem3_lthm != $true))) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X27 : d_subst] : (d_id = X27) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (((? [X420 : term] : ((sub @ X420 @ id) != X420) | ($true = sP39) | (sP41 = $true) | ? [X410 : subst > term > subst > $o] : ! [X411 : term > $o] : ? [X412 : term] : ((X410 @ id @ X412 @ id) != (X411 @ X412)) | ($true = sP40)) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X420 : term] : ((sub @ X420 @ id) = X420) & ($true != sP39) & (sP41 != $true) & ! [X410 : subst > term > subst > $o] : ? [X411 : term > $o] : ! [X412 : term] : ((X410 @ id @ X412 @ id) = (X411 @ X412)) & ($true != sP40)))) & ((! [X297 : term] : ((sub @ X297 @ id) = X297) | (termmset != $true)) & ((termmset = $true) | ? [X297 : term] : ((sub @ X297 @ id) != X297))) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & (((hoaslaminj = $true) | ? [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)) & ((X36 @ X38 @ X39) != (X37 @ X38 @ X39)) & ! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) & ((lam @ (X36 @ sh @ one)) = (lam @ (X37 @ sh @ one))))) & (! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (? [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) != (sub @ (X37 @ X44 @ X45) @ X43)) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ? [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) != (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one)))) | (hoaslaminj != $true))) & (hoaslamnotvar = $true) & (((pushprop_lem0 = $true) | ? [X186 : term,X187 : term > $o,X188 : subst] : ! [X189 : term > $o] : ? [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) != (X189 @ X190))) & (! [X186 : term,X187 : term > $o,X188 : subst] : ? [X189 : term > $o] : ! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190)) | (pushprop_lem0 != $true))) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) != (d2subst @ X253)) | (X253 = X254)) & (termmset_gthm = $true) & ((! [X122 : term,X123 : subst > term > subst > $o] : (($true = (sP30 @ X123)) | ((sP29 @ X123) = $true) | ((X123 @ id @ X122 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X122 : term,X123 : subst > term > subst > $o] : (($true != (sP30 @ X123)) & ((sP29 @ X123) != $true) & ((X123 @ id @ X122 @ id) != $true)))) & ((! [X23 : term] : ? [X24 : subst > term > term] : ! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X23 : term] : ! [X24 : subst > term > term] : ? [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) != (sub @ X23 @ (push @ X26 @ X25))))) & (((induction2 = $true) | ($true != sP28)) & (($true = sP28) | (induction2 != $true))) & (((? [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) != X532) | ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)) | ? [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) != X533)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) = X532) & ? [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true = (X536 @ X535)) & ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) != $true)) & ! [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) = X533)))) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (axclos = $true) & (((axvarcons = $true) | ? [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) != X121)) & (! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121) | (axvarcons != $true))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & (((hoasinduction_lem3v2_lthm = $true) | ((sP25 != $true) & ! [X131 : term] : ((sub @ X131 @ id) = X131))) & (((sP25 = $true) | ? [X131 : term] : ((sub @ X131 @ id) != X131)) | (hoasinduction_lem3v2_lthm != $true))) & ((! [X255 : term] : ? [X256 : subst > term > term] : ((X256 @ sh @ one) = (sub @ X255 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X255 : term] : ! [X256 : subst > term > term] : ((X256 @ sh @ one) != (sub @ X255 @ (push @ one @ sh))))) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & (((axscons = $true) | ? [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) != X298)) & (! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298) | (axscons != $true))) & (((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP20) & (sP19 != $true) & (sP18 != $true))) & ((($true = sP21) | ($true = sP20) | (sP19 = $true) | (sP18 = $true)) | (hoasinduction_lthm != $true))) & (((hoasinduction_lem3a_lthm = $true) | (! [X349 : term] : ((sub @ X349 @ id) = X349) & (sP5 != $true) & ($true != sP4))) & ((? [X349 : term] : ((sub @ X349 @ id) != X349) | (sP5 = $true) | ($true = sP4)) | (hoasinduction_lem3a_lthm != $true))) & (((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X232 : subst > term > subst > $o] : ? [X233 : term > $o] : ! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X232 : subst > term > subst > $o] : ! [X233 : term > $o] : ? [X234 : term] : ((X232 @ id @ X234 @ id) != (X233 @ X234)))) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((! [X119 : subst] : ((comp @ X119 @ id) = X119) | (axidr != $true)) & ((axidr = $true) | ? [X119 : subst] : ((comp @ X119 @ id) != X119)))),
% 1.70/1.50 inference(nnf_transformation,[status(thm)],[f126])).
% 1.70/1.50 thf(f126,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) <=> (hoasapinj1 = $true)) & (hoasapnotvar = $true) & ((hoasinduction = $true) <=> (sP109 = $true)) & (substmonoid_gthm = $true) & ((apinj1 = $true) <=> ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316)))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X65 : subst > term > subst > $o] : ? [X66 : term > $o] : ! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67)) <=> (hoasinduction_lem0_lthm = $true)) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) <=> (pushprop_lem1 = $true)) & ((sP104 = $true) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X381 : d_term] : (d_one = X381) & ((? [X261 : term] : ((sub @ X261 @ id) != X261) | (sP102 = $true) | ? [X257 : term] : ! [X258 : subst > term > term] : ? [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) != (X258 @ X259 @ X260))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_gthm = $true) & (lamnotvar = $true) & ((sP100 = $true) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (($true = sP98) <=> (induction2lem = $true)) & ((axshiftcons = $true) <=> ! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181)) & ((shinj = $true) <=> ! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231))) & (apnotvar = $true) & ((substmonoid_lthm = $true) <=> ($true = sP95)) & ((pushprop_lem0_lthm = $true) <=> ! [X272 : subst,X273 : term,X274 : term > $o] : ? [X275 : term > $o] : ! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (($true = sP94) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP90)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (? [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) != (X85 @ X88)) | ((X87 @ X86) != $true) | ($true = (X85 @ one))) | ? [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) != X82)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))) | ? [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) != (sub @ (X516 @ X518 @ X519) @ X520)))) & (axvarshift = $true) & (! [X0 : term] : ? [X1 : subst > term > term] : ! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & ((substmonoid = $true) <=> (! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384))) & ! [X382 : d_term,X383 : d_term] : ((X382 = X383) | ((d2term @ X383) != (d2term @ X382))) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) <=> (hoasapinj2 = $true)) & (($true = sP88) <=> (hoasinduction_lem3v2a = $true)) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & ((hoasapinj2_lthm = $true) <=> (sP86 = $true)) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> (sP84 = $true)) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP81) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true = (X151 @ one)) | ($true != (X152 @ X150)) | ? [X154 : term] : ((X151 @ X154) != (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) <=> (pushprop_lem1v2 = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X314 : term] : ((sub @ X314 @ id) = X314) <=> (axvarid = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((sP77 = $true) | ($true = sP76) | (sP75 = $true) | ? [X329 : term] : ((sub @ X329 @ id) != X329) | ? [X319 : subst > term > subst > $o] : ! [X320 : term > $o] : ? [X321 : term] : ((X319 @ id @ X321 @ id) != (X320 @ X321)))) & ((sP69 = $true) <=> (induction = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((sP65 = $true) | ? [X93 : term] : ((sub @ X93 @ id) != X93) | ($true = sP66)) <=> (induction2_lthm = $true)) & ((! [X21 : term] : ((sub @ X21 @ id) = X21) | ? [X20 : term] : ((sub @ X20 @ id) != X20)) <=> (termmset_lthm = $true)) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP60 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> ($true = sP58)) & (! [X408 : term] : ? [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) = (X409 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((sP56 = $true) | ($true = sP55) | ? [X50 : subst] : ((comp @ X50 @ id) != X50) | ? [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) != X47) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48)) <=> (induction2lem_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & ((hoasinduction_lem2 = $true) <=> (sP50 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (($true = sP47) | ? [X155 : term] : ((sub @ X155 @ id) != X155) | ($true = sP46))) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X27 : d_subst] : (d_id = X27) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((? [X420 : term] : ((sub @ X420 @ id) != X420) | ($true = sP39) | (sP41 = $true) | ? [X410 : subst > term > subst > $o] : ! [X411 : term > $o] : ? [X412 : term] : ((X410 @ id @ X412 @ id) != (X411 @ X412)) | ($true = sP40)) <=> (hoasinduction_lthm_3 = $true)) & (! [X297 : term] : ((sub @ X297 @ id) = X297) <=> (termmset = $true)) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (? [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) != (sub @ (X37 @ X44 @ X45) @ X43)) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ? [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) != (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))))) & (hoaslamnotvar = $true) & ((pushprop_lem0 = $true) <=> ! [X186 : term,X187 : term > $o,X188 : subst] : ? [X189 : term > $o] : ! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190))) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) != (d2subst @ X253)) | (X253 = X254)) & (termmset_gthm = $true) & (! [X122 : term,X123 : subst > term > subst > $o] : (($true = (sP30 @ X123)) | ((sP29 @ X123) = $true) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X23 : term] : ? [X24 : subst > term > term] : ! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((induction2 = $true) <=> ($true = sP28)) & ((? [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) != X532) | ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)) | ? [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) != X533)) <=> (pushprop_lem1_lthm = $true)) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (axclos = $true) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> ((sP25 = $true) | ? [X131 : term] : ((sub @ X131 @ id) != X131))) & (! [X255 : term] : ? [X256 : subst > term > term] : ((X256 @ sh @ one) = (sub @ X255 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & ((axscons = $true) <=> ! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298)) & ((hoasinduction_lthm = $true) <=> (($true = sP21) | ($true = sP20) | (sP19 = $true) | (sP18 = $true))) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X349 : term] : ((sub @ X349 @ id) != X349) | (sP5 = $true) | ($true = sP4))) & ((hoasinduction_lem3aa = $true) <=> (sP1 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X232 : subst > term > subst > $o] : ? [X233 : term > $o] : ! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) <=> (hoasinduction_lem0 = $true)) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true))),
% 1.70/1.50 inference(definition_folding,[status(thm)],[f13,f125,f124,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,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])).
% 1.70/1.50 thf(f16,plain,(
% 1.70/1.50 ! [X223 : subst > term > subst > $o] : (($true = (sP0 @ X223)) <=> ? [X225 : subst > term > term] : (! [X229 : term] : (($true = (X223 @ id @ (X225 @ id @ X229) @ id)) | ($true != (X223 @ id @ X229 @ id))) & ! [X226 : subst,X227 : term,X228 : subst] : ((X225 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226)) = (sub @ (X225 @ X228 @ X227) @ X226)) & ($true != (X223 @ id @ (lam @ (X225 @ sh @ one)) @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f17,plain,(
% 1.70/1.50 (sP1 = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (($true = (sP0 @ X223)) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f18,plain,(
% 1.70/1.50 ! [X359 : subst > term > subst > $o] : (((sP2 @ X359) = $true) <=> ? [X360 : subst > term > term] : (! [X361 : term,X362 : subst,X363 : subst] : ((sub @ (X360 @ X362 @ X361) @ X363) = (X360 @ (comp @ X362 @ X363) @ (sub @ X361 @ X363))) & ! [X364 : term] : (((X359 @ id @ (X360 @ id @ X364) @ id) = $true) | ((X359 @ id @ X364 @ id) != $true)) & ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f19,plain,(
% 1.70/1.50 ! [X350 : subst > term > subst > $o] : (((sP3 @ X350) = $true) <=> ! [X352 : subst > term > term] : (? [X356 : term] : (((X350 @ id @ (X352 @ id @ X356) @ id) != $true) & ((X350 @ id @ X356 @ id) = $true)) | ? [X353 : term,X354 : subst,X355 : subst] : ((X352 @ (comp @ X355 @ X354) @ (sub @ X353 @ X354)) != (sub @ (X352 @ X355 @ X353) @ X354)) | ($true = (X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f20,plain,(
% 1.70/1.50 ($true = sP4) <=> ! [X358 : term,X359 : subst > term > subst > $o] : (((sP2 @ X359) = $true) | ($true = (X359 @ id @ (lam @ X358) @ id)) | ? [X365 : term] : (($true != (X359 @ id @ (sub @ X358 @ (push @ X365 @ id)) @ id)) & ($true = (X359 @ id @ X365 @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f21,plain,(
% 1.70/1.50 (sP5 = $true) <=> ? [X350 : subst > term > subst > $o,X351 : term] : (($true != (X350 @ id @ (lam @ (sub @ X351 @ (push @ one @ sh))) @ id)) & ((sP3 @ X350) = $true) & ! [X357 : term] : (($true != (X350 @ id @ X357 @ id)) | ((X350 @ id @ (sub @ X351 @ (push @ X357 @ id)) @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f22,plain,(
% 1.70/1.50 ! [X497 : subst > term > subst > $o] : (($true = (sP6 @ X497)) <=> ? [X510 : subst > term > term] : (! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X510 @ X512 @ X513) @ X514) = (X510 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) & ($true != (X497 @ id @ (lam @ (X510 @ sh @ one)) @ id)) & ! [X511 : term] : (((X497 @ id @ (X510 @ id @ X511) @ id) = $true) | ($true != (X497 @ id @ X511 @ id)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f23,plain,(
% 1.70/1.50 ! [X497 : subst > term > subst > $o] : (($true = (sP7 @ X497)) <=> ? [X508 : term,X509 : term] : (($true != (X497 @ id @ (ap @ (sub @ X509 @ id) @ X508) @ id)) & ((X497 @ id @ X509 @ id) = $true) & ((X497 @ id @ X508 @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f24,plain,(
% 1.70/1.50 ! [X497 : subst > term > subst > $o] : (((sP8 @ X497) = $true) <=> ? [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (((X497 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499) = $true) & ($true != (X497 @ X501 @ X502 @ (comp @ X500 @ X499)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f25,plain,(
% 1.70/1.50 ! [X497 : subst > term > subst > $o] : (((sP9 @ X497) = $true) <=> ? [X507 : term] : (($true = (var @ (sub @ X507 @ id))) & ((X497 @ id @ X507 @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f26,plain,(
% 1.70/1.50 ! [X481 : subst > term > subst > $o] : (((sP10 @ X481) = $true) <=> ! [X483 : subst > term > term] : (($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id)) | ? [X484 : term] : (($true = (X481 @ id @ X484 @ id)) & ($true != (X481 @ id @ (X483 @ id @ X484) @ id))) | ? [X485 : subst,X486 : term,X487 : subst] : ((sub @ (X483 @ X485 @ X486) @ X487) != (X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f27,plain,(
% 1.70/1.50 ! [X481 : subst > term > subst > $o,X482 : term] : (((sP11 @ X482 @ X481) = $true) <=> ! [X488 : term] : (((X481 @ id @ X488 @ id) != $true) | ($true = (X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f28,plain,(
% 1.70/1.50 ! [X481 : subst > term > subst > $o] : (((sP12 @ X481) = $true) <=> ! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (($true != (X481 @ (comp @ X493 @ X496) @ (sub @ X494 @ X496) @ X495)) | ($true = (X481 @ X493 @ X494 @ (comp @ X496 @ X495)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f29,plain,(
% 1.70/1.50 ! [X469 : subst > term > subst > $o] : (($true = (sP13 @ X469)) <=> ! [X479 : term,X480 : term] : (($true != (X469 @ id @ X479 @ id)) | ($true = (X469 @ id @ (ap @ (sub @ X480 @ id) @ X479) @ id)) | ($true != (X469 @ id @ X480 @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f30,plain,(
% 1.70/1.50 ! [X469 : subst > term > subst > $o] : (((sP14 @ X469) = $true) <=> ! [X471 : term,X472 : subst,X473 : subst,X474 : subst] : (((X469 @ X473 @ X471 @ (comp @ X474 @ X472)) != $true) | ((X469 @ (comp @ X473 @ X474) @ (sub @ X471 @ X474) @ X472) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f31,plain,(
% 1.70/1.50 ! [X461 : term > $o] : (($true = (sP15 @ X461)) <=> ! [X465 : term,X466 : term] : (($true != (X461 @ X466)) | ((X461 @ (ap @ X466 @ X465)) = $true) | ((X461 @ X465) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f32,plain,(
% 1.70/1.50 ! [X461 : term > $o] : (((sP16 @ X461) = $true) <=> ! [X467 : term] : (($true != (var @ X467)) | ($true = (X461 @ X467))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f33,plain,(
% 1.70/1.50 ! [X461 : term > $o] : (((sP17 @ X461) = $true) <=> ! [X463 : term] : (? [X464 : term] : (($true != (X461 @ (sub @ X463 @ (push @ X464 @ id)))) & ($true = (X461 @ X464))) | ($true = (X461 @ (lam @ X463)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f34,plain,(
% 1.70/1.50 (sP18 = $true) <=> ! [X497 : subst > term > subst > $o,X498 : term] : (? [X503 : subst,X504 : subst,X505 : subst,X506 : term] : (((X497 @ X503 @ X506 @ (comp @ X505 @ X504)) = $true) & ((X497 @ (comp @ X503 @ X505) @ (sub @ X506 @ X505) @ X504) != $true)) | ($true = (X497 @ id @ X498 @ id)) | ((sP9 @ X497) = $true) | ((sP8 @ X497) = $true) | ($true = (sP6 @ X497)) | ($true = (sP7 @ X497)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f35,plain,(
% 1.70/1.50 (sP19 = $true) <=> ? [X481 : subst > term > subst > $o,X482 : term] : (((X481 @ id @ (lam @ X482) @ id) != $true) & ! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (($true != (X481 @ X491 @ X490 @ (comp @ X492 @ X489))) | ($true = (X481 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492) @ X489))) & ((sP10 @ X481) = $true) & ((sP12 @ X481) = $true) & ((sP11 @ X482 @ X481) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f36,plain,(
% 1.70/1.50 ($true = sP20) <=> ? [X468 : term,X469 : subst > term > subst > $o,X470 : term] : (($true = (sP13 @ X469)) & ! [X475 : subst,X476 : subst,X477 : term,X478 : subst] : (((X469 @ (comp @ X476 @ X478) @ (sub @ X477 @ X478) @ X475) != $true) | ($true = (X469 @ X476 @ X477 @ (comp @ X478 @ X475)))) & ($true != (X469 @ id @ (ap @ X468 @ X470) @ id)) & ($true = (X469 @ id @ X468 @ id)) & ((X469 @ id @ X470 @ id) = $true) & ((sP14 @ X469) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f37,plain,(
% 1.70/1.50 ($true = sP21) <=> ? [X461 : term > $o,X462 : term] : (($true = (sP15 @ X461)) & ((sP17 @ X461) = $true) & ((sP16 @ X461) = $true) & ($true != (X461 @ X462)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f38,plain,(
% 1.70/1.50 ! [X132 : subst > term > subst > $o] : (((sP22 @ X132) = $true) <=> ? [X135 : subst > term > term] : (($true != (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) & ! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) & ! [X139 : term] : (($true = (X132 @ id @ (X135 @ id @ X139) @ id)) | ($true != (X132 @ id @ X139 @ id)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f39,plain,(
% 1.70/1.50 ! [X132 : subst > term > subst > $o] : (($true = (sP23 @ X132)) <=> ? [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (($true != (X132 @ X143 @ X144 @ (comp @ X141 @ X142))) & ((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f40,plain,(
% 1.70/1.50 ! [X134 : term > $o,X133 : term] : (((sP24 @ X133 @ X134) = $true) <=> ? [X149 : term] : (($true = (X134 @ X149)) & ($true != (X134 @ (sub @ X133 @ (push @ X149 @ id))))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f41,plain,(
% 1.70/1.50 (sP25 = $true) <=> ! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (? [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true != (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148)) & ($true = (X132 @ X147 @ X146 @ (comp @ X145 @ X148)))) | ? [X140 : term] : ((X132 @ id @ X140 @ id) != (X134 @ X140)) | ((sP24 @ X133 @ X134) = $true) | ((sP22 @ X132) = $true) | ($true = (X134 @ (lam @ X133))) | ($true = (sP23 @ X132)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f42,plain,(
% 1.70/1.50 ! [X191 : term > $o] : (((sP26 @ X191) = $true) <=> ? [X195 : term] : (! [X196 : term] : (((X191 @ X196) != $true) | ($true = (X191 @ (sub @ X195 @ (push @ X196 @ id))))) & ((X191 @ (lam @ X195)) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f43,plain,(
% 1.70/1.50 ! [X191 : term > $o] : (($true = (sP27 @ X191)) <=> ? [X193 : term,X194 : term] : (((X191 @ (ap @ X194 @ X193)) != $true) & ((X191 @ X193) = $true) & ($true = (X191 @ X194))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f44,plain,(
% 1.70/1.50 ($true = sP28) <=> ! [X191 : term > $o,X192 : term] : (($true = (sP27 @ X191)) | ? [X197 : term] : (($true = (var @ X197)) & ($true != (X191 @ X197))) | ($true = (X191 @ X192)) | ((sP26 @ X191) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f45,plain,(
% 1.70/1.50 ! [X123 : subst > term > subst > $o] : (((sP29 @ X123) = $true) <=> ? [X124 : subst > term > term] : (($true != (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id)) & ! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) & ! [X128 : term] : (((X123 @ id @ X128 @ id) != $true) | ($true = (X123 @ id @ (X124 @ id @ X128) @ id)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f46,plain,(
% 1.70/1.50 ! [X123 : subst > term > subst > $o] : (($true = (sP30 @ X123)) <=> ? [X129 : term,X130 : term] : (($true != (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) & ((X123 @ id @ X130 @ id) = $true) & ($true = (X123 @ id @ X129 @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f47,plain,(
% 1.70/1.50 ! [X421 : subst > term > subst > $o] : (($true = (sP31 @ X421)) <=> ! [X426 : subst > term > term] : (? [X427 : subst,X428 : term,X429 : subst] : ((X426 @ (comp @ X427 @ X429) @ (sub @ X428 @ X429)) != (sub @ (X426 @ X427 @ X428) @ X429)) | ? [X430 : term] : (($true != (X421 @ id @ (X426 @ id @ X430) @ id)) & ((X421 @ id @ X430 @ id) = $true)) | ((X421 @ id @ (lam @ (X426 @ sh @ one)) @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f48,plain,(
% 1.70/1.50 ! [X413 : term > $o] : (($true = (sP32 @ X413)) <=> ! [X417 : term,X418 : term] : (($true = (X413 @ (ap @ X417 @ X418))) | ($true != (X413 @ X417)) | ($true != (X413 @ X418))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f49,plain,(
% 1.70/1.50 ! [X413 : term > $o] : (($true = (sP33 @ X413)) <=> ! [X419 : term] : (((var @ X419) != $true) | ((X413 @ X419) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f50,plain,(
% 1.70/1.50 ! [X413 : term > $o] : (($true = (sP34 @ X413)) <=> ! [X415 : term] : (($true = (X413 @ (lam @ X415))) | ? [X416 : term] : (((X413 @ X416) = $true) & ($true != (X413 @ (sub @ X415 @ (push @ X416 @ id)))))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f51,plain,(
% 1.70/1.50 ! [X432 : subst > term > subst > $o] : (($true = (sP35 @ X432)) <=> ? [X444 : subst > term > term] : (! [X445 : term,X446 : subst,X447 : subst] : ((X444 @ (comp @ X446 @ X447) @ (sub @ X445 @ X447)) = (sub @ (X444 @ X446 @ X445) @ X447)) & ! [X448 : term] : (($true != (X432 @ id @ X448 @ id)) | ((X432 @ id @ (X444 @ id @ X448) @ id) = $true)) & ($true != (X432 @ id @ (lam @ (X444 @ sh @ one)) @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f52,plain,(
% 1.70/1.50 ! [X432 : subst > term > subst > $o] : (($true = (sP36 @ X432)) <=> ? [X433 : term,X434 : term] : (((X432 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) != $true) & ($true = (X432 @ id @ X433 @ id)) & ($true = (X432 @ id @ X434 @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f53,plain,(
% 1.70/1.50 ! [X432 : subst > term > subst > $o] : (((sP37 @ X432) = $true) <=> ? [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (((X432 @ X436 @ X437 @ (comp @ X435 @ X438)) != $true) & ((X432 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435) @ X438) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f54,plain,(
% 1.70/1.50 ! [X432 : subst > term > subst > $o] : (((sP38 @ X432) = $true) <=> ? [X439 : term] : (((var @ (sub @ X439 @ id)) = $true) & ((X432 @ id @ X439 @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f55,plain,(
% 1.70/1.50 ($true = sP39) <=> ! [X431 : term,X432 : subst > term > subst > $o] : (($true = (X432 @ id @ X431 @ id)) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X432 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443) @ X440) != $true) & ($true = (X432 @ X442 @ X441 @ (comp @ X443 @ X440)))) | ((sP38 @ X432) = $true) | ($true = (sP35 @ X432)) | ($true = (sP36 @ X432)) | ((sP37 @ X432) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f56,plain,(
% 1.70/1.50 ($true = sP40) <=> ? [X421 : subst > term > subst > $o,X422 : term,X423 : term > $o] : (! [X424 : term] : (($true != (X423 @ X424)) | ((X423 @ (sub @ X422 @ (push @ X424 @ id))) = $true)) & ($true = (sP31 @ X421)) & ((X423 @ (lam @ X422)) != $true) & ! [X425 : term] : ((X423 @ X425) = (X421 @ id @ X425 @ id)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f57,plain,(
% 1.70/1.50 (sP41 = $true) <=> ? [X413 : term > $o,X414 : term] : (((X413 @ X414) != $true) & ($true = (sP32 @ X413)) & ($true = (sP34 @ X413)) & ($true = (sP33 @ X413)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f58,plain,(
% 1.70/1.50 ! [X164 : subst > term > subst > $o] : (((sP42 @ X164) = $true) <=> ? [X167 : subst > term > term] : (! [X168 : term,X169 : subst,X170 : subst] : ((sub @ (X167 @ X169 @ X168) @ X170) = (X167 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) & ! [X171 : term] : (((X164 @ id @ X171 @ id) != $true) | ($true = (X164 @ id @ (X167 @ id @ X171) @ id))) & ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f59,plain,(
% 1.70/1.50 ! [X164 : subst > term > subst > $o] : (($true = (sP43 @ X164)) <=> ? [X172 : subst,X173 : subst,X174 : subst,X175 : term] : (((X164 @ X173 @ X175 @ (comp @ X174 @ X172)) != $true) & ($true = (X164 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174) @ X172))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f60,plain,(
% 1.70/1.50 ! [X164 : subst > term > subst > $o] : (((sP44 @ X164) = $true) <=> ? [X176 : subst,X177 : subst,X178 : term,X179 : subst] : (((X164 @ X177 @ X178 @ (comp @ X179 @ X176)) = $true) & ($true != (X164 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179) @ X176))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f61,plain,(
% 1.70/1.50 ! [X156 : subst > term > subst > $o] : (((sP45 @ X156) = $true) <=> ! [X159 : subst > term > term] : (? [X160 : term] : (((X156 @ id @ X160 @ id) = $true) & ((X156 @ id @ (X159 @ id @ X160) @ id) != $true)) | ($true = (X156 @ id @ (lam @ (X159 @ sh @ one)) @ id)) | ? [X161 : subst,X162 : subst,X163 : term] : ((X159 @ (comp @ X161 @ X162) @ (sub @ X163 @ X162)) != (sub @ (X159 @ X161 @ X163) @ X162))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f62,plain,(
% 1.70/1.50 ($true = sP46) <=> ! [X164 : subst > term > subst > $o,X165 : term] : (((X164 @ id @ (lam @ X165) @ id) = $true) | ? [X166 : term] : (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) != $true) & ($true = (X164 @ id @ X166 @ id))) | ((sP44 @ X164) = $true) | ($true = (sP43 @ X164)) | ((sP42 @ X164) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f63,plain,(
% 1.70/1.50 ($true = sP47) <=> ? [X156 : subst > term > subst > $o,X157 : term] : (((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id) != $true) & ((sP45 @ X156) = $true) & ! [X158 : term] : (((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id) = $true) | ((X156 @ id @ X158 @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f64,plain,(
% 1.70/1.50 ! [X301 : subst > term > subst > $o] : (((sP48 @ X301) = $true) <=> ? [X304 : term,X305 : term] : (($true = (X301 @ id @ X304 @ id)) & ($true != (X301 @ id @ (ap @ (sub @ X305 @ id) @ X304) @ id)) & ((X301 @ id @ X305 @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f65,plain,(
% 1.70/1.50 ! [X301 : subst > term > subst > $o] : (($true = (sP49 @ X301)) <=> ? [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (((X301 @ (comp @ X312 @ X313) @ (sub @ X311 @ X313) @ X310) != $true) & ($true = (X301 @ X312 @ X311 @ (comp @ X313 @ X310)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f66,plain,(
% 1.70/1.50 (sP50 = $true) <=> ! [X301 : subst > term > subst > $o,X302 : term,X303 : term] : (((sP48 @ X301) = $true) | ((X301 @ id @ X302 @ id) != $true) | ($true = (X301 @ id @ (ap @ X302 @ X303) @ id)) | ? [X306 : subst,X307 : subst,X308 : term,X309 : subst] : (($true = (X301 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309) @ X306)) & ($true != (X301 @ X307 @ X308 @ (comp @ X309 @ X306)))) | ((X301 @ id @ X303 @ id) != $true) | ($true = (sP49 @ X301)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f67,plain,(
% 1.70/1.50 ! [X59 : term > $o] : (($true = (sP51 @ X59)) <=> ? [X60 : term] : (! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ((X59 @ X61) != $true)) & ((X59 @ (lam @ X60)) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f68,plain,(
% 1.70/1.50 ! [X59 : term > $o] : (((sP52 @ X59) = $true) <=> ? [X62 : term,X63 : term] : (((X59 @ X63) = $true) & ($true = (X59 @ X62)) & ($true != (X59 @ (ap @ X62 @ X63)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f69,plain,(
% 1.70/1.50 ! [X52 : term > $o] : (((sP53 @ X52) = $true) <=> ! [X55 : term,X56 : term] : (((X52 @ X56) != $true) | ($true = (X52 @ (ap @ X56 @ X55))) | ($true != (X52 @ X55))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f70,plain,(
% 1.70/1.50 ! [X52 : term > $o] : (($true = (sP54 @ X52)) <=> ! [X53 : term] : (($true != (X52 @ X53)) | ($true = (X52 @ (lam @ X53)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f71,plain,(
% 1.70/1.50 ($true = sP55) <=> ! [X57 : subst,X58 : term,X59 : term > $o] : (((X59 @ (sub @ X58 @ X57)) = $true) | ($true = (sP51 @ X59)) | ((sP52 @ X59) = $true) | ? [X64 : term] : (((var @ X64) = $true) & ((X59 @ (sub @ X64 @ X57)) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f72,plain,(
% 1.70/1.50 (sP56 = $true) <=> ? [X51 : term,X52 : term > $o] : (((sP53 @ X52) = $true) & ! [X54 : term] : (((var @ X54) != $true) | ((X52 @ X54) = $true)) & ($true != (X52 @ X51)) & ($true = (sP54 @ X52)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f73,plain,(
% 1.70/1.50 (sP57 = $true) <=> ! [X283 : term,X284 : subst > term > term,X285 : subst,X286 : subst > term > term] : (? [X287 : term,X288 : subst,X289 : subst] : ((sub @ (X284 @ X288 @ X287) @ X289) != (X284 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) | ((X286 @ X285 @ X283) = (X284 @ X285 @ X283)) | ? [X290 : subst,X291 : subst,X292 : term] : ((X286 @ (comp @ X291 @ X290) @ (sub @ X292 @ X290)) != (sub @ (X286 @ X291 @ X292) @ X290)) | ((lam @ (X284 @ sh @ one)) != (lam @ (X286 @ sh @ one))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f74,plain,(
% 1.70/1.50 ($true = sP58) <=> ((sP57 = $true) | ? [X277 : subst,X278 : term] : ((sub @ one @ (push @ X278 @ X277)) != X278) | ? [X281 : term,X282 : term] : ((X281 != X282) & ((lam @ X281) = (lam @ X282))) | ? [X279 : term,X280 : subst] : ((comp @ sh @ (push @ X279 @ X280)) != X280))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f75,plain,(
% 1.70/1.50 ! [X111 : subst > term > subst > $o] : (($true = (sP59 @ X111)) <=> ? [X114 : subst > term > term] : (! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) & ((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) != $true) & ! [X118 : term] : (($true = (X111 @ id @ (X114 @ id @ X118) @ id)) | ((X111 @ id @ X118 @ id) != $true))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f76,plain,(
% 1.70/1.50 (sP60 = $true) <=> ! [X111 : subst > term > subst > $o,X112 : term] : (? [X113 : term] : (($true = (X111 @ id @ X113 @ id)) & ($true != (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id))) | ((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true) | ($true = (sP59 @ X111)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f77,plain,(
% 1.70/1.50 ! [X96 : term > $o] : (($true = (sP61 @ X96)) <=> ! [X99 : term,X100 : term] : (((X96 @ X100) != $true) | ($true != (X96 @ X99)) | ((X96 @ (ap @ X99 @ X100)) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f78,plain,(
% 1.70/1.50 ! [X96 : term > $o] : (($true = (sP62 @ X96)) <=> ! [X97 : term] : (($true = (X96 @ (lam @ X97))) | ? [X98 : term] : (((X96 @ X98) = $true) & ($true != (X96 @ (sub @ X97 @ (push @ X98 @ id)))))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f79,plain,(
% 1.70/1.50 ! [X103 : term > $o] : (((sP63 @ X103) = $true) <=> ? [X104 : term] : (! [X105 : term] : (($true != (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true)) & ($true != (X103 @ (lam @ X104)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f80,plain,(
% 1.70/1.50 ! [X103 : term > $o] : (($true = (sP64 @ X103)) <=> ? [X107 : term,X108 : term] : (((X103 @ X107) = $true) & ($true != (X103 @ (ap @ X108 @ X107))) & ((X103 @ X108) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f81,plain,(
% 1.70/1.50 (sP65 = $true) <=> ! [X102 : term,X103 : term > $o] : (? [X106 : term] : (((var @ X106) = $true) & ($true != (X103 @ X106))) | ((X103 @ X102) = $true) | ($true = (sP64 @ X103)) | ((sP63 @ X103) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f82,plain,(
% 1.70/1.50 ($true = sP66) <=> ? [X94 : term,X95 : subst,X96 : term > $o] : (! [X101 : term] : (((X96 @ (sub @ X101 @ X95)) = $true) | ((var @ X101) != $true)) & ((X96 @ (sub @ X94 @ X95)) != $true) & ($true = (sP62 @ X96)) & ($true = (sP61 @ X96)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f83,plain,(
% 1.70/1.50 ! [X217 : term > $o] : (($true = (sP67 @ X217)) <=> ? [X219 : term,X220 : term] : (((X217 @ (ap @ X219 @ X220)) != $true) & ($true = (X217 @ X219)) & ((X217 @ X220) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f84,plain,(
% 1.70/1.50 ! [X217 : term > $o] : (($true = (sP68 @ X217)) <=> ? [X221 : term] : (((X217 @ X221) = $true) & ($true != (X217 @ (lam @ X221)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f85,plain,(
% 1.70/1.50 (sP69 = $true) <=> ! [X216 : term,X217 : term > $o] : (? [X218 : term] : (((var @ X218) = $true) & ($true != (X217 @ X218))) | ($true = (sP67 @ X217)) | ($true = (sP68 @ X217)) | ($true = (X217 @ X216)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f86,plain,(
% 1.70/1.50 ! [X341 : subst > term > subst > $o] : (((sP70 @ X341) = $true) <=> ? [X344 : subst > term > term] : (! [X345 : term,X346 : subst,X347 : subst] : ((sub @ (X344 @ X346 @ X345) @ X347) = (X344 @ (comp @ X346 @ X347) @ (sub @ X345 @ X347))) & ! [X348 : term] : (($true != (X341 @ id @ X348 @ id)) | ((X341 @ id @ (X344 @ id @ X348) @ id) = $true)) & ((X341 @ id @ (lam @ (X344 @ sh @ one)) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f87,plain,(
% 1.70/1.50 ! [X341 : subst > term > subst > $o] : (($true = (sP71 @ X341)) <=> ? [X342 : term,X343 : term] : (((X341 @ id @ X342 @ id) = $true) & ((X341 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) != $true) & ((X341 @ id @ X343 @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f88,plain,(
% 1.70/1.50 ! [X330 : subst > term > subst > $o] : (((sP72 @ X330) = $true) <=> ! [X333 : subst > term > term] : (? [X334 : term] : (($true = (X330 @ id @ X334 @ id)) & ($true != (X330 @ id @ (X333 @ id @ X334) @ id))) | ? [X335 : subst,X336 : term,X337 : subst] : ((X333 @ (comp @ X337 @ X335) @ (sub @ X336 @ X335)) != (sub @ (X333 @ X337 @ X336) @ X335)) | ((X330 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f89,plain,(
% 1.70/1.50 ! [X323 : term > $o] : (($true = (sP73 @ X323)) <=> ! [X327 : term,X328 : term] : (((X323 @ X328) != $true) | ($true = (X323 @ (ap @ X327 @ X328))) | ($true != (X323 @ X327))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f90,plain,(
% 1.70/1.50 ! [X323 : term > $o] : (($true = (sP74 @ X323)) <=> ! [X325 : term] : (($true = (X323 @ (lam @ X325))) | ? [X326 : term] : (($true = (X323 @ X326)) & ((X323 @ (sub @ X325 @ (push @ X326 @ id))) != $true))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f91,plain,(
% 1.70/1.50 (sP75 = $true) <=> ! [X340 : term,X341 : subst > term > subst > $o] : (((sP70 @ X341) = $true) | ((X341 @ id @ X340 @ id) = $true) | ($true = (sP71 @ X341)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f92,plain,(
% 1.70/1.50 ($true = sP76) <=> ? [X330 : subst > term > subst > $o,X331 : term,X332 : term > $o] : (((sP72 @ X330) = $true) & ! [X338 : term] : ((X330 @ id @ X338 @ id) = (X332 @ X338)) & ((X332 @ (lam @ X331)) != $true) & ! [X339 : term] : (((X332 @ X339) != $true) | ((X332 @ (sub @ X331 @ (push @ X339 @ id))) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f93,plain,(
% 1.70/1.50 (sP77 = $true) <=> ? [X322 : term,X323 : term > $o] : (($true != (X323 @ X322)) & ($true = (sP73 @ X323)) & ! [X324 : term] : (((var @ X324) != $true) | ((X323 @ X324) = $true)) & ($true = (sP74 @ X323)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f94,plain,(
% 1.70/1.50 ! [X200 : subst > term > subst > $o] : (((sP78 @ X200) = $true) <=> ? [X211 : subst > term > term] : (! [X212 : term] : (($true != (X200 @ id @ X212 @ id)) | ($true = (X200 @ id @ (X211 @ id @ X212) @ id))) & ($true != (X200 @ id @ (lam @ (X211 @ sh @ one)) @ id)) & ! [X213 : term,X214 : subst,X215 : subst] : ((X211 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)) = (sub @ (X211 @ X214 @ X213) @ X215))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f95,plain,(
% 1.70/1.50 ! [X200 : subst > term > subst > $o] : (((sP79 @ X200) = $true) <=> ? [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (((X200 @ X206 @ X209 @ (comp @ X208 @ X207)) != $true) & ((X200 @ (comp @ X206 @ X208) @ (sub @ X209 @ X208) @ X207) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f96,plain,(
% 1.70/1.50 ! [X199 : term,X198 : term > $o] : (((sP80 @ X198 @ X199) = $true) <=> ? [X205 : term] : (($true != (X198 @ (sub @ X199 @ (push @ X205 @ id)))) & ($true = (X198 @ X205))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f97,plain,(
% 1.70/1.50 ($true = sP81) <=> ! [X198 : term > $o,X199 : term,X200 : subst > term > subst > $o] : (? [X210 : term] : ((X200 @ id @ X210 @ id) != (X198 @ X210)) | ((sP78 @ X200) = $true) | ? [X201 : term,X202 : subst,X203 : subst,X204 : subst] : (($true != (X200 @ (comp @ X202 @ X204) @ (sub @ X201 @ X204) @ X203)) & ($true = (X200 @ X202 @ X201 @ (comp @ X204 @ X203)))) | ((sP80 @ X198 @ X199) = $true) | ((sP79 @ X200) = $true) | ((X198 @ (lam @ X199)) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f98,plain,(
% 1.70/1.50 ! [X366 : subst > term > subst > $o] : (($true = (sP82 @ X366)) <=> ? [X371 : term,X372 : term] : (($true = (X366 @ id @ X371 @ id)) & ($true = (X366 @ id @ X372 @ id)) & ((X366 @ id @ (ap @ (sub @ X371 @ id) @ X372) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f99,plain,(
% 1.70/1.50 ! [X366 : subst > term > subst > $o] : (((sP83 @ X366) = $true) <=> ? [X373 : subst,X374 : subst,X375 : term,X376 : subst] : (((X366 @ X376 @ X375 @ (comp @ X373 @ X374)) != $true) & ($true = (X366 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f100,plain,(
% 1.70/1.50 (sP84 = $true) <=> ! [X366 : subst > term > subst > $o,X367 : term,X368 : term,X369 : term > $o] : (? [X377 : term,X378 : subst,X379 : subst,X380 : subst] : (((X366 @ X379 @ X377 @ (comp @ X380 @ X378)) = $true) & ($true != (X366 @ (comp @ X379 @ X380) @ (sub @ X377 @ X380) @ X378))) | ((sP83 @ X366) = $true) | ($true = (sP82 @ X366)) | ? [X370 : term] : ((X366 @ id @ X370 @ id) != (X369 @ X370)) | ($true = (X369 @ (ap @ X367 @ X368))) | ($true != (X369 @ X367)) | ((X369 @ X368) != $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f101,plain,(
% 1.70/1.50 ($true = sP85) <=> ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f102,plain,(
% 1.70/1.50 (sP86 = $true) <=> (? [X28 : term,X29 : term,X30 : term,X31 : term] : ((X30 != X31) & ((ap @ X28 @ X30) = (ap @ X29 @ X31))) | ($true = sP85))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f103,plain,(
% 1.70/1.50 ! [X236 : subst > term > subst > $o] : (($true = (sP87 @ X236)) <=> ? [X240 : subst > term > term] : (! [X242 : subst,X243 : term,X244 : subst] : ((sub @ (X240 @ X242 @ X243) @ X244) = (X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244))) & ! [X241 : term] : (((X236 @ id @ X241 @ id) != $true) | ((X236 @ id @ (X240 @ id @ X241) @ id) = $true)) & ((X236 @ id @ (lam @ (X240 @ sh @ one)) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f104,plain,(
% 1.70/1.50 ($true = sP88) <=> ! [X235 : term,X236 : subst > term > subst > $o,X237 : term > $o] : (? [X239 : term] : (($true != (X237 @ (sub @ X235 @ (push @ X239 @ id)))) & ((X237 @ X239) = $true)) | ($true = (sP87 @ X236)) | ? [X238 : term] : ((X236 @ id @ X238 @ id) != (X237 @ X238)) | ($true = (X237 @ (lam @ X235))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f105,plain,(
% 1.70/1.50 ! [X521 : subst > term > subst > $o] : (((sP89 @ X521) = $true) <=> ? [X523 : subst > term > term] : (! [X527 : term] : (((X521 @ id @ X527 @ id) != $true) | ($true = (X521 @ id @ (X523 @ id @ X527) @ id))) & ! [X524 : term,X525 : subst,X526 : subst] : ((X523 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525)) = (sub @ (X523 @ X526 @ X524) @ X525)) & ($true != (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f106,plain,(
% 1.70/1.50 ($true = sP90) <=> ! [X521 : subst > term > subst > $o,X522 : term] : (? [X528 : term] : (((X521 @ id @ (sub @ X522 @ (push @ X528 @ id)) @ id) != $true) & ((X521 @ id @ X528 @ id) = $true)) | ((X521 @ id @ (lam @ X522) @ id) = $true) | ((sP89 @ X521) = $true))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f107,plain,(
% 1.70/1.50 ! [X4 : subst > term > subst > $o] : (($true = (sP91 @ X4)) <=> ? [X10 : subst > term > term] : (! [X11 : term] : (($true = (X4 @ id @ (X10 @ id @ X11) @ id)) | ($true != (X4 @ id @ X11 @ id))) & ($true != (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) & ! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f108,plain,(
% 1.70/1.50 ! [X4 : subst > term > subst > $o] : (((sP92 @ X4) = $true) <=> ? [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (($true = (X4 @ X8 @ X6 @ (comp @ X9 @ X7))) & ((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f109,plain,(
% 1.70/1.50 ! [X4 : subst > term > subst > $o] : (((sP93 @ X4) = $true) <=> ? [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) != $true) & ((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f110,plain,(
% 1.70/1.50 ($true = sP94) <=> ! [X4 : subst > term > subst > $o,X5 : term] : (? [X19 : term] : (((X4 @ id @ X19 @ id) = $true) & ($true != (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id))) | ((sP93 @ X4) = $true) | ((sP92 @ X4) = $true) | ($true = (X4 @ id @ (lam @ X5) @ id)) | ($true = (sP91 @ X4)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f111,plain,(
% 1.70/1.50 ($true = sP95) <=> ((! [X296 : subst] : ((comp @ id @ X296) = X296) & ! [X295 : subst] : ((comp @ X295 @ id) = X295)) | ? [X293 : subst] : ((comp @ id @ X293) != X293) | ? [X294 : subst] : ((comp @ X294 @ id) != X294))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f112,plain,(
% 1.70/1.50 ! [X247 : term > $o] : (($true = (sP96 @ X247)) <=> ? [X250 : term] : (! [X251 : term] : (($true = (X247 @ (sub @ X250 @ (push @ X251 @ id)))) | ((X247 @ X251) != $true)) & ((X247 @ (lam @ X250)) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f113,plain,(
% 1.70/1.50 ! [X247 : term > $o] : (($true = (sP97 @ X247)) <=> ? [X248 : term,X249 : term] : (($true != (X247 @ (ap @ X249 @ X248))) & ($true = (X247 @ X249)) & ((X247 @ X248) = $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f114,plain,(
% 1.70/1.50 ($true = sP98) <=> ! [X245 : subst,X246 : term,X247 : term > $o] : (($true = (sP97 @ X247)) | ((X247 @ (sub @ X246 @ X245)) = $true) | ? [X252 : term] : (($true != (X247 @ (sub @ X252 @ X245))) & ($true = (var @ X252))) | ($true = (sP96 @ X247)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f115,plain,(
% 1.70/1.50 ($true = sP99) <=> ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f116,plain,(
% 1.70/1.50 (sP100 = $true) <=> (($true = sP99) | ? [X68 : term] : ((sub @ X68 @ id) != X68) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 != X70) & ((ap @ X70 @ X72) = (ap @ X69 @ X71))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f117,plain,(
% 1.70/1.50 ! [X263 : subst > term > subst > $o] : (((sP101 @ X263) = $true) <=> ? [X266 : subst > term > term] : (! [X270 : term] : (((X263 @ id @ X270 @ id) != $true) | ($true = (X263 @ id @ (X266 @ id @ X270) @ id))) & ((X263 @ id @ (lam @ (X266 @ sh @ one)) @ id) != $true) & ! [X267 : term,X268 : subst,X269 : subst] : ((X266 @ (comp @ X269 @ X268) @ (sub @ X267 @ X268)) = (sub @ (X266 @ X269 @ X267) @ X268))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f118,plain,(
% 1.70/1.50 (sP102 = $true) <=> ! [X262 : term,X263 : subst > term > subst > $o,X264 : term > $o] : (($true = (X264 @ (lam @ X262))) | ? [X271 : term] : ((X264 @ X271) != (X263 @ id @ X271 @ id)) | ((sP101 @ X263) = $true) | ? [X265 : term] : (($true = (X264 @ X265)) & ($true != (X264 @ (sub @ X262 @ (push @ X265 @ id))))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f119,plain,(
% 1.70/1.50 ! [X450 : subst > term > subst > $o] : (($true = (sP103 @ X450)) <=> ? [X451 : term,X452 : subst > term > term] : (($true != (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id)) & ! [X453 : subst,X454 : term,X455 : subst] : ((X452 @ (comp @ X453 @ X455) @ (sub @ X454 @ X455)) = (sub @ X451 @ (push @ (sub @ X454 @ X455) @ (comp @ X453 @ X455)))) & ! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ($true != (X450 @ id @ X456 @ id))) & ! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (sub @ X451 @ (push @ X458 @ X457)) @ X459) = (sub @ (X452 @ X457 @ X458) @ X459))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f120,plain,(
% 1.70/1.50 (sP104 = $true) <=> ! [X449 : term,X450 : subst > term > subst > $o] : (($true = (X450 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)) | ? [X460 : term] : (($true = (X450 @ id @ X460 @ id)) & ((X450 @ id @ (sub @ X449 @ (push @ X460 @ id)) @ id) != $true)) | ($true = (sP103 @ X450)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f121,plain,(
% 1.70/1.50 ! [X391 : subst > term > subst > $o] : (($true = (sP105 @ X391)) <=> ? [X403 : subst > term > term] : (! [X407 : term] : (((X391 @ id @ X407 @ id) != $true) | ((X391 @ id @ (X403 @ id @ X407) @ id) = $true)) & ! [X404 : term,X405 : subst,X406 : subst] : ((sub @ (X403 @ X406 @ X404) @ X405) = (X403 @ (comp @ X406 @ X405) @ (sub @ X404 @ X405))) & ((X391 @ id @ (lam @ (X403 @ sh @ one)) @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f122,plain,(
% 1.70/1.50 ! [X391 : subst > term > subst > $o] : (($true = (sP106 @ X391)) <=> ? [X392 : term,X393 : term] : (((X391 @ id @ X393 @ id) = $true) & ((X391 @ id @ (ap @ (sub @ X392 @ id) @ X393) @ id) != $true) & ($true = (X391 @ id @ X392 @ id))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f123,plain,(
% 1.70/1.50 ! [X391 : subst > term > subst > $o] : (($true = (sP107 @ X391)) <=> ? [X395 : term,X396 : subst,X397 : subst,X398 : subst] : (((X391 @ (comp @ X397 @ X398) @ (sub @ X395 @ X398) @ X396) != $true) & ($true = (X391 @ X397 @ X395 @ (comp @ X398 @ X396)))))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f124,plain,(
% 1.70/1.50 ! [X391 : subst > term > subst > $o] : (((sP108 @ X391) = $true) <=> ? [X394 : term] : (((var @ (sub @ X394 @ id)) = $true) & ((X391 @ id @ X394 @ id) != $true)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f125,plain,(
% 1.70/1.50 (sP109 = $true) <=> ! [X390 : term,X391 : subst > term > subst > $o] : (($true = (sP106 @ X391)) | ($true = (X391 @ id @ X390 @ id)) | ? [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (((X391 @ (comp @ X402 @ X401) @ (sub @ X399 @ X401) @ X400) = $true) & ($true != (X391 @ X402 @ X399 @ (comp @ X401 @ X400)))) | ((sP108 @ X391) = $true) | ($true = (sP105 @ X391)) | ($true = (sP107 @ X391)))),
% 1.70/1.50 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.70/1.50 thf(f13,plain,(
% 1.70/1.50 (hoaslamnotvar_lthm = $true) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) <=> (hoasapinj1 = $true)) & (hoasapnotvar = $true) & ((hoasinduction = $true) <=> ! [X390 : term,X391 : subst > term > subst > $o] : (? [X392 : term,X393 : term] : (((X391 @ id @ X393 @ id) = $true) & ((X391 @ id @ (ap @ (sub @ X392 @ id) @ X393) @ id) != $true) & ($true = (X391 @ id @ X392 @ id))) | ($true = (X391 @ id @ X390 @ id)) | ? [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (((X391 @ (comp @ X402 @ X401) @ (sub @ X399 @ X401) @ X400) = $true) & ($true != (X391 @ X402 @ X399 @ (comp @ X401 @ X400)))) | ? [X394 : term] : (((var @ (sub @ X394 @ id)) = $true) & ((X391 @ id @ X394 @ id) != $true)) | ? [X403 : subst > term > term] : (! [X407 : term] : (((X391 @ id @ X407 @ id) != $true) | ((X391 @ id @ (X403 @ id @ X407) @ id) = $true)) & ! [X404 : term,X405 : subst,X406 : subst] : ((sub @ (X403 @ X406 @ X404) @ X405) = (X403 @ (comp @ X406 @ X405) @ (sub @ X404 @ X405))) & ((X391 @ id @ (lam @ (X403 @ sh @ one)) @ id) != $true)) | ? [X395 : term,X396 : subst,X397 : subst,X398 : subst] : (((X391 @ (comp @ X397 @ X398) @ (sub @ X395 @ X398) @ X396) != $true) & ($true = (X391 @ X397 @ X395 @ (comp @ X398 @ X396)))))) & (substmonoid_gthm = $true) & ((apinj1 = $true) <=> ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316)))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X65 : subst > term > subst > $o] : ? [X66 : term > $o] : ! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67)) <=> (hoasinduction_lem0_lthm = $true)) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) <=> (pushprop_lem1 = $true)) & (! [X449 : term,X450 : subst > term > subst > $o] : (($true = (X450 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)) | ? [X460 : term] : (($true = (X450 @ id @ X460 @ id)) & ((X450 @ id @ (sub @ X449 @ (push @ X460 @ id)) @ id) != $true)) | ? [X451 : term,X452 : subst > term > term] : (($true != (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id)) & ! [X453 : subst,X454 : term,X455 : subst] : ((X452 @ (comp @ X453 @ X455) @ (sub @ X454 @ X455)) = (sub @ X451 @ (push @ (sub @ X454 @ X455) @ (comp @ X453 @ X455)))) & ! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ($true != (X450 @ id @ X456 @ id))) & ! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (sub @ X451 @ (push @ X458 @ X457)) @ X459) = (sub @ (X452 @ X457 @ X458) @ X459)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvarsh = $true) & (hoasinduction_gthm = $true) & (axapp = $true) & ! [X381 : d_term] : (d_one = X381) & ((? [X261 : term] : ((sub @ X261 @ id) != X261) | ! [X262 : term,X263 : subst > term > subst > $o,X264 : term > $o] : (($true = (X264 @ (lam @ X262))) | ? [X271 : term] : ((X264 @ X271) != (X263 @ id @ X271 @ id)) | ? [X266 : subst > term > term] : (! [X270 : term] : (((X263 @ id @ X270 @ id) != $true) | ($true = (X263 @ id @ (X266 @ id @ X270) @ id))) & ((X263 @ id @ (lam @ (X266 @ sh @ one)) @ id) != $true) & ! [X267 : term,X268 : subst,X269 : subst] : ((X266 @ (comp @ X269 @ X268) @ (sub @ X267 @ X268)) = (sub @ (X266 @ X269 @ X267) @ X268))) | ? [X265 : term] : (($true = (X264 @ X265)) & ($true != (X264 @ (sub @ X262 @ (push @ X265 @ id)))))) | ? [X257 : term] : ! [X258 : subst > term > term] : ? [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) != (X258 @ X259 @ X260))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_gthm = $true) & (lamnotvar = $true) & ((! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74))) | ? [X68 : term] : ((sub @ X68 @ id) != X68) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 != X70) & ((ap @ X70 @ X72) = (ap @ X69 @ X71)))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X245 : subst,X246 : term,X247 : term > $o] : (? [X248 : term,X249 : term] : (($true != (X247 @ (ap @ X249 @ X248))) & ($true = (X247 @ X249)) & ((X247 @ X248) = $true)) | ((X247 @ (sub @ X246 @ X245)) = $true) | ? [X252 : term] : (($true != (X247 @ (sub @ X252 @ X245))) & ($true = (var @ X252))) | ? [X250 : term] : (! [X251 : term] : (($true = (X247 @ (sub @ X250 @ (push @ X251 @ id)))) | ((X247 @ X251) != $true)) & ((X247 @ (lam @ X250)) != $true))) <=> (induction2lem = $true)) & ((axshiftcons = $true) <=> ! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181)) & ((shinj = $true) <=> ! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231))) & (apnotvar = $true) & ((substmonoid_lthm = $true) <=> ((! [X296 : subst] : ((comp @ id @ X296) = X296) & ! [X295 : subst] : ((comp @ X295 @ id) = X295)) | ? [X293 : subst] : ((comp @ id @ X293) != X293) | ? [X294 : subst] : ((comp @ X294 @ id) != X294))) & ((pushprop_lem0_lthm = $true) <=> ! [X272 : subst,X273 : term,X274 : term > $o] : ? [X275 : term > $o] : ! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X4 : subst > term > subst > $o,X5 : term] : (? [X19 : term] : (((X4 @ id @ X19 @ id) = $true) & ($true != (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id))) | ? [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) != $true) & ((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) = $true)) | ? [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (($true = (X4 @ X8 @ X6 @ (comp @ X9 @ X7))) & ((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) != $true)) | ($true = (X4 @ id @ (lam @ X5) @ id)) | ? [X10 : subst > term > term] : (! [X11 : term] : (($true = (X4 @ id @ (X10 @ id @ X11) @ id)) | ($true != (X4 @ id @ X11 @ id))) & ($true != (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) & ! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13)))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X521 : subst > term > subst > $o,X522 : term] : (? [X528 : term] : (((X521 @ id @ (sub @ X522 @ (push @ X528 @ id)) @ id) != $true) & ((X521 @ id @ X528 @ id) = $true)) | ((X521 @ id @ (lam @ X522) @ id) = $true) | ? [X523 : subst > term > term] : (! [X527 : term] : (((X521 @ id @ X527 @ id) != $true) | ($true = (X521 @ id @ (X523 @ id @ X527) @ id))) & ! [X524 : term,X525 : subst,X526 : subst] : ((X523 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525)) = (sub @ (X523 @ X526 @ X524) @ X525)) & ($true != (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id))))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (? [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) != (X85 @ X88)) | ((X87 @ X86) != $true) | ($true = (X85 @ one))) | ? [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) != X82)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))) | ? [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) != (sub @ (X516 @ X518 @ X519) @ X520)))) & (axvarshift = $true) & (! [X0 : term] : ? [X1 : subst > term > term] : ! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & ((substmonoid = $true) <=> (! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384))) & ! [X382 : d_term,X383 : d_term] : ((X382 = X383) | ((d2term @ X383) != (d2term @ X382))) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) <=> (hoasapinj2 = $true)) & (! [X235 : term,X236 : subst > term > subst > $o,X237 : term > $o] : (? [X239 : term] : (($true != (X237 @ (sub @ X235 @ (push @ X239 @ id)))) & ((X237 @ X239) = $true)) | ? [X240 : subst > term > term] : (! [X242 : subst,X243 : term,X244 : subst] : ((sub @ (X240 @ X242 @ X243) @ X244) = (X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244))) & ! [X241 : term] : (((X236 @ id @ X241 @ id) != $true) | ((X236 @ id @ (X240 @ id @ X241) @ id) = $true)) & ((X236 @ id @ (lam @ (X240 @ sh @ one)) @ id) != $true)) | ? [X238 : term] : ((X236 @ id @ X238 @ id) != (X237 @ X238)) | ($true = (X237 @ (lam @ X235)))) <=> (hoasinduction_lem3v2a = $true)) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & ((hoasapinj2_lthm = $true) <=> (? [X28 : term,X29 : term,X30 : term,X31 : term] : ((X30 != X31) & ((ap @ X28 @ X30) = (ap @ X29 @ X31))) | ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35)))) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X366 : subst > term > subst > $o,X367 : term,X368 : term,X369 : term > $o] : (? [X377 : term,X378 : subst,X379 : subst,X380 : subst] : (((X366 @ X379 @ X377 @ (comp @ X380 @ X378)) = $true) & ($true != (X366 @ (comp @ X379 @ X380) @ (sub @ X377 @ X380) @ X378))) | ? [X373 : subst,X374 : subst,X375 : term,X376 : subst] : (((X366 @ X376 @ X375 @ (comp @ X373 @ X374)) != $true) & ($true = (X366 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374))) | ? [X371 : term,X372 : term] : (($true = (X366 @ id @ X371 @ id)) & ($true = (X366 @ id @ X372 @ id)) & ((X366 @ id @ (ap @ (sub @ X371 @ id) @ X372) @ id) != $true)) | ? [X370 : term] : ((X366 @ id @ X370 @ id) != (X369 @ X370)) | ($true = (X369 @ (ap @ X367 @ X368))) | ($true != (X369 @ X367)) | ((X369 @ X368) != $true))) & (hoasapnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (! [X198 : term > $o,X199 : term,X200 : subst > term > subst > $o] : (? [X210 : term] : ((X200 @ id @ X210 @ id) != (X198 @ X210)) | ? [X211 : subst > term > term] : (! [X212 : term] : (($true != (X200 @ id @ X212 @ id)) | ($true = (X200 @ id @ (X211 @ id @ X212) @ id))) & ($true != (X200 @ id @ (lam @ (X211 @ sh @ one)) @ id)) & ! [X213 : term,X214 : subst,X215 : subst] : ((X211 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)) = (sub @ (X211 @ X214 @ X213) @ X215))) | ? [X201 : term,X202 : subst,X203 : subst,X204 : subst] : (($true != (X200 @ (comp @ X202 @ X204) @ (sub @ X201 @ X204) @ X203)) & ($true = (X200 @ X202 @ X201 @ (comp @ X204 @ X203)))) | ? [X205 : term] : (($true != (X198 @ (sub @ X199 @ (push @ X205 @ id)))) & ($true = (X198 @ X205))) | ? [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (((X200 @ X206 @ X209 @ (comp @ X208 @ X207)) != $true) & ((X200 @ (comp @ X206 @ X208) @ (sub @ X209 @ X208) @ X207) = $true)) | ((X198 @ (lam @ X199)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (ulamvarind = $true) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true = (X151 @ one)) | ($true != (X152 @ X150)) | ? [X154 : term] : ((X151 @ X154) != (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) <=> (pushprop_lem1v2 = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X314 : term] : ((sub @ X314 @ id) = X314) <=> (axvarid = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X322 : term,X323 : term > $o] : (($true != (X323 @ X322)) & ! [X327 : term,X328 : term] : (((X323 @ X328) != $true) | ($true = (X323 @ (ap @ X327 @ X328))) | ($true != (X323 @ X327))) & ! [X324 : term] : (((var @ X324) != $true) | ((X323 @ X324) = $true)) & ! [X325 : term] : (($true = (X323 @ (lam @ X325))) | ? [X326 : term] : (($true = (X323 @ X326)) & ((X323 @ (sub @ X325 @ (push @ X326 @ id))) != $true)))) | ? [X330 : subst > term > subst > $o,X331 : term,X332 : term > $o] : (! [X333 : subst > term > term] : (? [X334 : term] : (($true = (X330 @ id @ X334 @ id)) & ($true != (X330 @ id @ (X333 @ id @ X334) @ id))) | ? [X335 : subst,X336 : term,X337 : subst] : ((X333 @ (comp @ X337 @ X335) @ (sub @ X336 @ X335)) != (sub @ (X333 @ X337 @ X336) @ X335)) | ((X330 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)) & ! [X338 : term] : ((X330 @ id @ X338 @ id) = (X332 @ X338)) & ((X332 @ (lam @ X331)) != $true) & ! [X339 : term] : (((X332 @ X339) != $true) | ((X332 @ (sub @ X331 @ (push @ X339 @ id))) = $true))) | ! [X340 : term,X341 : subst > term > subst > $o] : (? [X344 : subst > term > term] : (! [X345 : term,X346 : subst,X347 : subst] : ((sub @ (X344 @ X346 @ X345) @ X347) = (X344 @ (comp @ X346 @ X347) @ (sub @ X345 @ X347))) & ! [X348 : term] : (($true != (X341 @ id @ X348 @ id)) | ((X341 @ id @ (X344 @ id @ X348) @ id) = $true)) & ((X341 @ id @ (lam @ (X344 @ sh @ one)) @ id) != $true)) | ((X341 @ id @ X340 @ id) = $true) | ? [X342 : term,X343 : term] : (((X341 @ id @ X342 @ id) = $true) & ((X341 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) != $true) & ((X341 @ id @ X343 @ id) = $true))) | ? [X329 : term] : ((sub @ X329 @ id) != X329) | ? [X319 : subst > term > subst > $o] : ! [X320 : term > $o] : ? [X321 : term] : ((X319 @ id @ X321 @ id) != (X320 @ X321)))) & (! [X216 : term,X217 : term > $o] : (? [X218 : term] : (((var @ X218) = $true) & ($true != (X217 @ X218))) | ? [X219 : term,X220 : term] : (((X217 @ (ap @ X219 @ X220)) != $true) & ($true = (X217 @ X219)) & ((X217 @ X220) = $true)) | ? [X221 : term] : (((X217 @ X221) = $true) & ($true != (X217 @ (lam @ X221)))) | ($true = (X217 @ X216))) <=> (induction = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X102 : term,X103 : term > $o] : (? [X106 : term] : (((var @ X106) = $true) & ($true != (X103 @ X106))) | ((X103 @ X102) = $true) | ? [X107 : term,X108 : term] : (((X103 @ X107) = $true) & ($true != (X103 @ (ap @ X108 @ X107))) & ((X103 @ X108) = $true)) | ? [X104 : term] : (! [X105 : term] : (($true != (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true)) & ($true != (X103 @ (lam @ X104))))) | ? [X93 : term] : ((sub @ X93 @ id) != X93) | ? [X94 : term,X95 : subst,X96 : term > $o] : (! [X101 : term] : (((X96 @ (sub @ X101 @ X95)) = $true) | ((var @ X101) != $true)) & ((X96 @ (sub @ X94 @ X95)) != $true) & ! [X97 : term] : (($true = (X96 @ (lam @ X97))) | ? [X98 : term] : (((X96 @ X98) = $true) & ($true != (X96 @ (sub @ X97 @ (push @ X98 @ id)))))) & ! [X99 : term,X100 : term] : (((X96 @ X100) != $true) | ($true != (X96 @ X99)) | ((X96 @ (ap @ X99 @ X100)) = $true)))) <=> (induction2_lthm = $true)) & ((! [X21 : term] : ((sub @ X21 @ id) = X21) | ? [X20 : term] : ((sub @ X20 @ id) != X20)) <=> (termmset_lthm = $true)) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X111 : subst > term > subst > $o,X112 : term] : (? [X113 : term] : (($true = (X111 @ id @ X113 @ id)) & ($true != (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id))) | ((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true) | ? [X114 : subst > term > term] : (! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) & ((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) != $true) & ! [X118 : term] : (($true = (X111 @ id @ (X114 @ id @ X118) @ id)) | ((X111 @ id @ X118 @ id) != $true))))) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X283 : term,X284 : subst > term > term,X285 : subst,X286 : subst > term > term] : (? [X287 : term,X288 : subst,X289 : subst] : ((sub @ (X284 @ X288 @ X287) @ X289) != (X284 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) | ((X286 @ X285 @ X283) = (X284 @ X285 @ X283)) | ? [X290 : subst,X291 : subst,X292 : term] : ((X286 @ (comp @ X291 @ X290) @ (sub @ X292 @ X290)) != (sub @ (X286 @ X291 @ X292) @ X290)) | ((lam @ (X284 @ sh @ one)) != (lam @ (X286 @ sh @ one)))) | ? [X277 : subst,X278 : term] : ((sub @ one @ (push @ X278 @ X277)) != X278) | ? [X281 : term,X282 : term] : ((X281 != X282) & ((lam @ X281) = (lam @ X282))) | ? [X279 : term,X280 : subst] : ((comp @ sh @ (push @ X279 @ X280)) != X280))) & (! [X408 : term] : ? [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) = (X409 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((? [X51 : term,X52 : term > $o] : (! [X55 : term,X56 : term] : (((X52 @ X56) != $true) | ($true = (X52 @ (ap @ X56 @ X55))) | ($true != (X52 @ X55))) & ! [X54 : term] : (((var @ X54) != $true) | ((X52 @ X54) = $true)) & ($true != (X52 @ X51)) & ! [X53 : term] : (($true != (X52 @ X53)) | ($true = (X52 @ (lam @ X53))))) | ! [X57 : subst,X58 : term,X59 : term > $o] : (((X59 @ (sub @ X58 @ X57)) = $true) | ? [X60 : term] : (! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ((X59 @ X61) != $true)) & ((X59 @ (lam @ X60)) != $true)) | ? [X62 : term,X63 : term] : (((X59 @ X63) = $true) & ($true = (X59 @ X62)) & ($true != (X59 @ (ap @ X62 @ X63)))) | ? [X64 : term] : (((var @ X64) = $true) & ((X59 @ (sub @ X64 @ X57)) != $true))) | ? [X50 : subst] : ((comp @ X50 @ id) != X50) | ? [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) != X47) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48)) <=> (induction2lem_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = sh) & (pushprop = $true) & ((hoasinduction_lem2 = $true) <=> ! [X301 : subst > term > subst > $o,X302 : term,X303 : term] : (? [X304 : term,X305 : term] : (($true = (X301 @ id @ X304 @ id)) & ($true != (X301 @ id @ (ap @ (sub @ X305 @ id) @ X304) @ id)) & ((X301 @ id @ X305 @ id) = $true)) | ((X301 @ id @ X302 @ id) != $true) | ($true = (X301 @ id @ (ap @ X302 @ X303) @ id)) | ? [X306 : subst,X307 : subst,X308 : term,X309 : subst] : (($true = (X301 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309) @ X306)) & ($true != (X301 @ X307 @ X308 @ (comp @ X309 @ X306)))) | ((X301 @ id @ X303 @ id) != $true) | ? [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (((X301 @ (comp @ X312 @ X313) @ (sub @ X311 @ X313) @ X310) != $true) & ($true = (X301 @ X312 @ X311 @ (comp @ X313 @ X310)))))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X156 : subst > term > subst > $o,X157 : term] : (((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id) != $true) & ! [X159 : subst > term > term] : (? [X160 : term] : (((X156 @ id @ X160 @ id) = $true) & ((X156 @ id @ (X159 @ id @ X160) @ id) != $true)) | ($true = (X156 @ id @ (lam @ (X159 @ sh @ one)) @ id)) | ? [X161 : subst,X162 : subst,X163 : term] : ((X159 @ (comp @ X161 @ X162) @ (sub @ X163 @ X162)) != (sub @ (X159 @ X161 @ X163) @ X162))) & ! [X158 : term] : (((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id) = $true) | ((X156 @ id @ X158 @ id) != $true))) | ? [X155 : term] : ((sub @ X155 @ id) != X155) | ! [X164 : subst > term > subst > $o,X165 : term] : (((X164 @ id @ (lam @ X165) @ id) = $true) | ? [X166 : term] : (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) != $true) & ($true = (X164 @ id @ X166 @ id))) | ? [X176 : subst,X177 : subst,X178 : term,X179 : subst] : (((X164 @ X177 @ X178 @ (comp @ X179 @ X176)) = $true) & ($true != (X164 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179) @ X176))) | ? [X172 : subst,X173 : subst,X174 : subst,X175 : term] : (((X164 @ X173 @ X175 @ (comp @ X174 @ X172)) != $true) & ($true = (X164 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174) @ X172))) | ? [X167 : subst > term > term] : (! [X168 : term,X169 : subst,X170 : subst] : ((sub @ (X167 @ X169 @ X168) @ X170) = (X167 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) & ! [X171 : term] : (((X164 @ id @ X171 @ id) != $true) | ($true = (X164 @ id @ (X167 @ id @ X171) @ id))) & ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) != $true))))) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (axmap = $true) & ! [X27 : d_subst] : (d_id = X27) & (pushprop_lthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((? [X420 : term] : ((sub @ X420 @ id) != X420) | ! [X431 : term,X432 : subst > term > subst > $o] : (($true = (X432 @ id @ X431 @ id)) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X432 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443) @ X440) != $true) & ($true = (X432 @ X442 @ X441 @ (comp @ X443 @ X440)))) | ? [X439 : term] : (((var @ (sub @ X439 @ id)) = $true) & ((X432 @ id @ X439 @ id) != $true)) | ? [X444 : subst > term > term] : (! [X445 : term,X446 : subst,X447 : subst] : ((X444 @ (comp @ X446 @ X447) @ (sub @ X445 @ X447)) = (sub @ (X444 @ X446 @ X445) @ X447)) & ! [X448 : term] : (($true != (X432 @ id @ X448 @ id)) | ((X432 @ id @ (X444 @ id @ X448) @ id) = $true)) & ($true != (X432 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ? [X433 : term,X434 : term] : (((X432 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) != $true) & ($true = (X432 @ id @ X433 @ id)) & ($true = (X432 @ id @ X434 @ id))) | ? [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (((X432 @ X436 @ X437 @ (comp @ X435 @ X438)) != $true) & ((X432 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435) @ X438) = $true))) | ? [X413 : term > $o,X414 : term] : (((X413 @ X414) != $true) & ! [X417 : term,X418 : term] : (($true = (X413 @ (ap @ X417 @ X418))) | ($true != (X413 @ X417)) | ($true != (X413 @ X418))) & ! [X415 : term] : (($true = (X413 @ (lam @ X415))) | ? [X416 : term] : (((X413 @ X416) = $true) & ($true != (X413 @ (sub @ X415 @ (push @ X416 @ id)))))) & ! [X419 : term] : (((var @ X419) != $true) | ((X413 @ X419) = $true))) | ? [X410 : subst > term > subst > $o] : ! [X411 : term > $o] : ? [X412 : term] : ((X410 @ id @ X412 @ id) != (X411 @ X412)) | ? [X421 : subst > term > subst > $o,X422 : term,X423 : term > $o] : (! [X424 : term] : (($true != (X423 @ X424)) | ((X423 @ (sub @ X422 @ (push @ X424 @ id))) = $true)) & ! [X426 : subst > term > term] : (? [X427 : subst,X428 : term,X429 : subst] : ((X426 @ (comp @ X427 @ X429) @ (sub @ X428 @ X429)) != (sub @ (X426 @ X427 @ X428) @ X429)) | ? [X430 : term] : (($true != (X421 @ id @ (X426 @ id @ X430) @ id)) & ((X421 @ id @ X430 @ id) = $true)) | ((X421 @ id @ (lam @ (X426 @ sh @ one)) @ id) = $true)) & ((X423 @ (lam @ X422)) != $true) & ! [X425 : term] : ((X423 @ X425) = (X421 @ id @ X425 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & (! [X297 : term] : ((sub @ X297 @ id) = X297) <=> (termmset = $true)) & (one = (d2term @ d_one)) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (? [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) != (sub @ (X37 @ X44 @ X45) @ X43)) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ? [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) != (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))))) & (hoaslamnotvar = $true) & ((pushprop_lem0 = $true) <=> ! [X186 : term,X187 : term > $o,X188 : subst] : ? [X189 : term > $o] : ! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190))) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) != (d2subst @ X253)) | (X253 = X254)) & (termmset_gthm = $true) & (! [X122 : term,X123 : subst > term > subst > $o] : (? [X129 : term,X130 : term] : (($true != (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) & ((X123 @ id @ X130 @ id) = $true) & ($true = (X123 @ id @ X129 @ id))) | ? [X124 : subst > term > term] : (($true != (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id)) & ! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) & ! [X128 : term] : (((X123 @ id @ X128 @ id) != $true) | ($true = (X123 @ id @ (X124 @ id @ X128) @ id)))) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X23 : term] : ? [X24 : subst > term > term] : ! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((induction2 = $true) <=> ! [X191 : term > $o,X192 : term] : (? [X193 : term,X194 : term] : (((X191 @ (ap @ X194 @ X193)) != $true) & ((X191 @ X193) = $true) & ($true = (X191 @ X194))) | ? [X197 : term] : (($true = (var @ X197)) & ($true != (X191 @ X197))) | ($true = (X191 @ X192)) | ? [X195 : term] : (! [X196 : term] : (((X191 @ X196) != $true) | ($true = (X191 @ (sub @ X195 @ (push @ X196 @ id))))) & ((X191 @ (lam @ X195)) != $true)))) & ((? [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) != X532) | ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)) | ? [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) != X533)) <=> (pushprop_lem1_lthm = $true)) & ((d2subst @ d_id) = id) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (lamnotap != $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (axclos = $true) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (? [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true != (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148)) & ($true = (X132 @ X147 @ X146 @ (comp @ X145 @ X148)))) | ? [X140 : term] : ((X132 @ id @ X140 @ id) != (X134 @ X140)) | ? [X149 : term] : (($true = (X134 @ X149)) & ($true != (X134 @ (sub @ X133 @ (push @ X149 @ id))))) | ? [X135 : subst > term > term] : (($true != (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) & ! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) & ! [X139 : term] : (($true = (X132 @ id @ (X135 @ id @ X139) @ id)) | ($true != (X132 @ id @ X139 @ id)))) | ($true = (X134 @ (lam @ X133))) | ? [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (($true != (X132 @ X143 @ X144 @ (comp @ X141 @ X142))) & ((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) = $true))) | ? [X131 : term] : ((sub @ X131 @ id) != X131))) & (! [X255 : term] : ? [X256 : subst > term > term] : ((X256 @ sh @ one) = (sub @ X255 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (axassoc = $true) & (pushprop_lem3v2_lthm = $true) & ((axscons = $true) <=> ! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298)) & ((hoasinduction_lthm = $true) <=> (? [X461 : term > $o,X462 : term] : (! [X465 : term,X466 : term] : (($true != (X461 @ X466)) | ((X461 @ (ap @ X466 @ X465)) = $true) | ((X461 @ X465) != $true)) & ! [X463 : term] : (? [X464 : term] : (($true != (X461 @ (sub @ X463 @ (push @ X464 @ id)))) & ($true = (X461 @ X464))) | ($true = (X461 @ (lam @ X463)))) & ! [X467 : term] : (($true != (var @ X467)) | ($true = (X461 @ X467))) & ($true != (X461 @ X462))) | ? [X468 : term,X469 : subst > term > subst > $o,X470 : term] : (! [X479 : term,X480 : term] : (($true != (X469 @ id @ X479 @ id)) | ($true = (X469 @ id @ (ap @ (sub @ X480 @ id) @ X479) @ id)) | ($true != (X469 @ id @ X480 @ id))) & ! [X475 : subst,X476 : subst,X477 : term,X478 : subst] : (((X469 @ (comp @ X476 @ X478) @ (sub @ X477 @ X478) @ X475) != $true) | ($true = (X469 @ X476 @ X477 @ (comp @ X478 @ X475)))) & ($true != (X469 @ id @ (ap @ X468 @ X470) @ id)) & ($true = (X469 @ id @ X468 @ id)) & ((X469 @ id @ X470 @ id) = $true) & ! [X471 : term,X472 : subst,X473 : subst,X474 : subst] : (((X469 @ X473 @ X471 @ (comp @ X474 @ X472)) != $true) | ((X469 @ (comp @ X473 @ X474) @ (sub @ X471 @ X474) @ X472) = $true))) | ? [X481 : subst > term > subst > $o,X482 : term] : (((X481 @ id @ (lam @ X482) @ id) != $true) & ! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (($true != (X481 @ X491 @ X490 @ (comp @ X492 @ X489))) | ($true = (X481 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492) @ X489))) & ! [X483 : subst > term > term] : (($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id)) | ? [X484 : term] : (($true = (X481 @ id @ X484 @ id)) & ($true != (X481 @ id @ (X483 @ id @ X484) @ id))) | ? [X485 : subst,X486 : term,X487 : subst] : ((sub @ (X483 @ X485 @ X486) @ X487) != (X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) & ! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (($true != (X481 @ (comp @ X493 @ X496) @ (sub @ X494 @ X496) @ X495)) | ($true = (X481 @ X493 @ X494 @ (comp @ X496 @ X495)))) & ! [X488 : term] : (((X481 @ id @ X488 @ id) != $true) | ($true = (X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id)))) | ! [X497 : subst > term > subst > $o,X498 : term] : (? [X503 : subst,X504 : subst,X505 : subst,X506 : term] : (((X497 @ X503 @ X506 @ (comp @ X505 @ X504)) = $true) & ((X497 @ (comp @ X503 @ X505) @ (sub @ X506 @ X505) @ X504) != $true)) | ($true = (X497 @ id @ X498 @ id)) | ? [X507 : term] : (($true = (var @ (sub @ X507 @ id))) & ((X497 @ id @ X507 @ id) != $true)) | ? [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (((X497 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499) = $true) & ($true != (X497 @ X501 @ X502 @ (comp @ X500 @ X499)))) | ? [X510 : subst > term > term] : (! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X510 @ X512 @ X513) @ X514) = (X510 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) & ($true != (X497 @ id @ (lam @ (X510 @ sh @ one)) @ id)) & ! [X511 : term] : (((X497 @ id @ (X510 @ id @ X511) @ id) = $true) | ($true != (X497 @ id @ X511 @ id)))) | ? [X508 : term,X509 : term] : (($true != (X497 @ id @ (ap @ (sub @ X509 @ id) @ X508) @ id)) & ((X497 @ id @ X509 @ id) = $true) & ((X497 @ id @ X508 @ id) = $true))))) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X349 : term] : ((sub @ X349 @ id) != X349) | ? [X350 : subst > term > subst > $o,X351 : term] : (($true != (X350 @ id @ (lam @ (sub @ X351 @ (push @ one @ sh))) @ id)) & ! [X352 : subst > term > term] : (? [X356 : term] : (((X350 @ id @ (X352 @ id @ X356) @ id) != $true) & ((X350 @ id @ X356 @ id) = $true)) | ? [X353 : term,X354 : subst,X355 : subst] : ((X352 @ (comp @ X355 @ X354) @ (sub @ X353 @ X354)) != (sub @ (X352 @ X355 @ X353) @ X354)) | ($true = (X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))) & ! [X357 : term] : (($true != (X350 @ id @ X357 @ id)) | ((X350 @ id @ (sub @ X351 @ (push @ X357 @ id)) @ id) = $true))) | ! [X358 : term,X359 : subst > term > subst > $o] : (? [X360 : subst > term > term] : (! [X361 : term,X362 : subst,X363 : subst] : ((sub @ (X360 @ X362 @ X361) @ X363) = (X360 @ (comp @ X362 @ X363) @ (sub @ X361 @ X363))) & ! [X364 : term] : (((X359 @ id @ (X360 @ id @ X364) @ id) = $true) | ((X359 @ id @ X364 @ id) != $true)) & ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id) != $true)) | ($true = (X359 @ id @ (lam @ X358) @ id)) | ? [X365 : term] : (($true != (X359 @ id @ (sub @ X358 @ (push @ X365 @ id)) @ id)) & ($true = (X359 @ id @ X365 @ id)))))) & ((hoasinduction_lem3aa = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (? [X225 : subst > term > term] : (! [X229 : term] : (($true = (X223 @ id @ (X225 @ id @ X229) @ id)) | ($true != (X223 @ id @ X229 @ id))) & ! [X226 : subst,X227 : term,X228 : subst] : ((X225 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226)) = (sub @ (X225 @ X228 @ X227) @ X226)) & ($true != (X223 @ id @ (lam @ (X225 @ sh @ one)) @ id))) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X232 : subst > term > subst > $o] : ? [X233 : term > $o] : ! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) <=> (hoasinduction_lem0 = $true)) & (ulamvar1 != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true))),
% 1.70/1.51 inference(flattening,[status(thm)],[f12])).
% 1.70/1.51 thf(f12,plain,(
% 1.70/1.51 (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true = (X151 @ one)) | ($true != (X152 @ X150)) | ? [X154 : term] : ((X151 @ X154) != (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (? [X225 : subst > term > term] : (! [X229 : term] : (($true = (X223 @ id @ (X225 @ id @ X229) @ id)) | ($true != (X223 @ id @ X229 @ id))) & ! [X226 : subst,X227 : term,X228 : subst] : ((X225 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226)) = (sub @ (X225 @ X228 @ X227) @ X226)) & ($true != (X223 @ id @ (lam @ (X225 @ sh @ one)) @ id))) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem3v2 = $true) & (axmap = $true) & (axabs = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X111 : subst > term > subst > $o,X112 : term] : (? [X113 : term] : (($true = (X111 @ id @ X113 @ id)) & ($true != (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id))) | ((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true) | ? [X114 : subst > term > term] : (! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) & ((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) != $true) & ! [X118 : term] : (($true = (X111 @ id @ (X114 @ id @ X118) @ id)) | ((X111 @ id @ X118 @ id) != $true))))) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & ((apinj1 = $true) <=> ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316)))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem2_gthm = $true) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & ((((! [X283 : term,X284 : subst > term > term,X285 : subst,X286 : subst > term > term] : (? [X287 : term,X288 : subst,X289 : subst] : ((sub @ (X284 @ X288 @ X287) @ X289) != (X284 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) | ((X286 @ X285 @ X283) = (X284 @ X285 @ X283)) | ? [X290 : subst,X291 : subst,X292 : term] : ((X286 @ (comp @ X291 @ X290) @ (sub @ X292 @ X290)) != (sub @ (X286 @ X291 @ X292) @ X290)) | ((lam @ (X284 @ sh @ one)) != (lam @ (X286 @ sh @ one)))) | ? [X281 : term,X282 : term] : ((X281 != X282) & ((lam @ X281) = (lam @ X282)))) | ? [X279 : term,X280 : subst] : ((comp @ sh @ (push @ X279 @ X280)) != X280)) | ? [X277 : subst,X278 : term] : ((sub @ one @ (push @ X278 @ X277)) != X278)) <=> (hoaslaminj_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (? [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) != (sub @ (X37 @ X44 @ X45) @ X43)) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ? [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) != (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))))) & ((hoasinduction_lem2 = $true) <=> ! [X301 : subst > term > subst > $o,X302 : term,X303 : term] : (? [X304 : term,X305 : term] : (($true = (X301 @ id @ X304 @ id)) & ($true != (X301 @ id @ (ap @ (sub @ X305 @ id) @ X304) @ id)) & ((X301 @ id @ X305 @ id) = $true)) | ((X301 @ id @ X302 @ id) != $true) | ($true = (X301 @ id @ (ap @ X302 @ X303) @ id)) | ? [X306 : subst,X307 : subst,X308 : term,X309 : subst] : (($true = (X301 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309) @ X306)) & ($true != (X301 @ X307 @ X308 @ (comp @ X309 @ X306)))) | ((X301 @ id @ X303 @ id) != $true) | ? [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (((X301 @ (comp @ X312 @ X313) @ (sub @ X311 @ X313) @ X310) != $true) & ($true = (X301 @ X312 @ X311 @ (comp @ X313 @ X310)))))) & (hoasapnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axassoc = $true) & ((hoasinduction_lthm = $true) <=> (((! [X497 : subst > term > subst > $o,X498 : term] : (? [X503 : subst,X504 : subst,X505 : subst,X506 : term] : (((X497 @ X503 @ X506 @ (comp @ X505 @ X504)) = $true) & ((X497 @ (comp @ X503 @ X505) @ (sub @ X506 @ X505) @ X504) != $true)) | ($true = (X497 @ id @ X498 @ id)) | ? [X507 : term] : (($true = (var @ (sub @ X507 @ id))) & ((X497 @ id @ X507 @ id) != $true)) | ? [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (((X497 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499) = $true) & ($true != (X497 @ X501 @ X502 @ (comp @ X500 @ X499)))) | ? [X510 : subst > term > term] : (! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X510 @ X512 @ X513) @ X514) = (X510 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) & ($true != (X497 @ id @ (lam @ (X510 @ sh @ one)) @ id)) & ! [X511 : term] : (((X497 @ id @ (X510 @ id @ X511) @ id) = $true) | ($true != (X497 @ id @ X511 @ id)))) | ? [X508 : term,X509 : term] : (($true != (X497 @ id @ (ap @ (sub @ X509 @ id) @ X508) @ id)) & ((X497 @ id @ X509 @ id) = $true) & ((X497 @ id @ X508 @ id) = $true))) | ? [X481 : subst > term > subst > $o,X482 : term] : (((X481 @ id @ (lam @ X482) @ id) != $true) & ! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (($true != (X481 @ X491 @ X490 @ (comp @ X492 @ X489))) | ($true = (X481 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492) @ X489))) & ! [X483 : subst > term > term] : (($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id)) | ? [X484 : term] : (($true = (X481 @ id @ X484 @ id)) & ($true != (X481 @ id @ (X483 @ id @ X484) @ id))) | ? [X485 : subst,X486 : term,X487 : subst] : ((sub @ (X483 @ X485 @ X486) @ X487) != (X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) & ! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (($true != (X481 @ (comp @ X493 @ X496) @ (sub @ X494 @ X496) @ X495)) | ($true = (X481 @ X493 @ X494 @ (comp @ X496 @ X495)))) & ! [X488 : term] : (((X481 @ id @ X488 @ id) != $true) | ($true = (X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id))))) | ? [X468 : term,X469 : subst > term > subst > $o,X470 : term] : (! [X479 : term,X480 : term] : (($true != (X469 @ id @ X479 @ id)) | ($true = (X469 @ id @ (ap @ (sub @ X480 @ id) @ X479) @ id)) | ($true != (X469 @ id @ X480 @ id))) & ! [X475 : subst,X476 : subst,X477 : term,X478 : subst] : (((X469 @ (comp @ X476 @ X478) @ (sub @ X477 @ X478) @ X475) != $true) | ($true = (X469 @ X476 @ X477 @ (comp @ X478 @ X475)))) & ($true != (X469 @ id @ (ap @ X468 @ X470) @ id)) & ($true = (X469 @ id @ X468 @ id)) & ((X469 @ id @ X470 @ id) = $true) & ! [X471 : term,X472 : subst,X473 : subst,X474 : subst] : (((X469 @ X473 @ X471 @ (comp @ X474 @ X472)) != $true) | ((X469 @ (comp @ X473 @ X474) @ (sub @ X471 @ X474) @ X472) = $true)))) | ? [X461 : term > $o,X462 : term] : (! [X465 : term,X466 : term] : (($true != (X461 @ X466)) | ((X461 @ (ap @ X466 @ X465)) = $true) | ((X461 @ X465) != $true)) & ! [X463 : term] : (? [X464 : term] : (($true != (X461 @ (sub @ X463 @ (push @ X464 @ id)))) & ($true = (X461 @ X464))) | ($true = (X461 @ (lam @ X463)))) & ! [X467 : term] : (($true != (var @ X467)) | ($true = (X461 @ X467))) & ($true != (X461 @ X462))))) & (! [X4 : subst > term > subst > $o,X5 : term] : (? [X19 : term] : (((X4 @ id @ X19 @ id) = $true) & ($true != (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id))) | ? [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) != $true) & ((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) = $true)) | ? [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (($true = (X4 @ X8 @ X6 @ (comp @ X9 @ X7))) & ((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) != $true)) | ($true = (X4 @ id @ (lam @ X5) @ id)) | ? [X10 : subst > term > term] : (! [X11 : term] : (($true = (X4 @ id @ (X10 @ id @ X11) @ id)) | ($true != (X4 @ id @ X11 @ id))) & ($true != (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) & ! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13)))) <=> (hoasinduction_lem3 = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X272 : subst,X273 : term,X274 : term > $o] : ? [X275 : term > $o] : ! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276))) & (! [X314 : term] : ((sub @ X314 @ id) = X314) <=> (axvarid = $true)) & (hoasapnotvar_lthm = $true) & (ulamvar1 != $true) & (axvarshift = $true) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((shinj = $true) <=> ! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231))) & (! [X216 : term,X217 : term > $o] : (? [X218 : term] : (((var @ X218) = $true) & ($true != (X217 @ X218))) | ? [X219 : term,X220 : term] : (((X217 @ (ap @ X219 @ X220)) != $true) & ($true = (X217 @ X219)) & ((X217 @ X220) = $true)) | ? [X221 : term] : (((X217 @ X221) = $true) & ($true != (X217 @ (lam @ X221)))) | ($true = (X217 @ X216))) <=> (induction = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)) | ? [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) != X533)) | ? [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) != X532))) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (? [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true != (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148)) & ($true = (X132 @ X147 @ X146 @ (comp @ X145 @ X148)))) | ? [X140 : term] : ((X132 @ id @ X140 @ id) != (X134 @ X140)) | ? [X149 : term] : (($true = (X134 @ X149)) & ($true != (X134 @ (sub @ X133 @ (push @ X149 @ id))))) | ? [X135 : subst > term > term] : (($true != (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) & ! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) & ! [X139 : term] : (($true = (X132 @ id @ (X135 @ id @ X139) @ id)) | ($true != (X132 @ id @ X139 @ id)))) | ($true = (X134 @ (lam @ X133))) | ? [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (($true != (X132 @ X143 @ X144 @ (comp @ X141 @ X142))) & ((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) = $true))) | ? [X131 : term] : ((sub @ X131 @ id) != X131))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (one = (d2term @ d_one)) & (induction2_gthm = $true) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) <=> (hoasapinj2 = $true)) & (pushprop_lem2v2_gthm = $true) & (! [X23 : term] : ? [X24 : subst > term > term] : ! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X186 : term,X187 : term > $o,X188 : subst] : ? [X189 : term > $o] : ! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190))) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) <=> (hoasapinj1 = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74))) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 != X70) & ((ap @ X70 @ X72) = (ap @ X69 @ X71)))) | ? [X68 : term] : ((sub @ X68 @ id) != X68))) & (pushprop_lem0_gthm = $true) & (! [X122 : term,X123 : subst > term > subst > $o] : (? [X129 : term,X130 : term] : (($true != (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) & ((X123 @ id @ X130 @ id) = $true) & ($true = (X123 @ id @ X129 @ id))) | ? [X124 : subst > term > term] : (($true != (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id)) & ! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) & ! [X128 : term] : (((X123 @ id @ X128 @ id) != $true) | ($true = (X123 @ id @ (X124 @ id @ X128) @ id)))) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X232 : subst > term > subst > $o] : ? [X233 : term > $o] : ! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem2v2_lthm = $true) & (! [X449 : term,X450 : subst > term > subst > $o] : (($true = (X450 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)) | ? [X460 : term] : (($true = (X450 @ id @ X460 @ id)) & ((X450 @ id @ (sub @ X449 @ (push @ X460 @ id)) @ id) != $true)) | ? [X451 : term,X452 : subst > term > term] : (($true != (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id)) & ! [X453 : subst,X454 : term,X455 : subst] : ((X452 @ (comp @ X453 @ X455) @ (sub @ X454 @ X455)) = (sub @ X451 @ (push @ (sub @ X454 @ X455) @ (comp @ X453 @ X455)))) & ! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ($true != (X450 @ id @ X456 @ id))) & ! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (sub @ X451 @ (push @ X458 @ X457)) @ X459) = (sub @ (X452 @ X457 @ X458) @ X459)))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (axapp = $true) & (((((! [X340 : term,X341 : subst > term > subst > $o] : (? [X344 : subst > term > term] : (! [X345 : term,X346 : subst,X347 : subst] : ((sub @ (X344 @ X346 @ X345) @ X347) = (X344 @ (comp @ X346 @ X347) @ (sub @ X345 @ X347))) & ! [X348 : term] : (($true != (X341 @ id @ X348 @ id)) | ((X341 @ id @ (X344 @ id @ X348) @ id) = $true)) & ((X341 @ id @ (lam @ (X344 @ sh @ one)) @ id) != $true)) | ((X341 @ id @ X340 @ id) = $true) | ? [X342 : term,X343 : term] : (((X341 @ id @ X342 @ id) = $true) & ((X341 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) != $true) & ((X341 @ id @ X343 @ id) = $true))) | ? [X330 : subst > term > subst > $o,X331 : term,X332 : term > $o] : (! [X333 : subst > term > term] : (? [X334 : term] : (($true = (X330 @ id @ X334 @ id)) & ($true != (X330 @ id @ (X333 @ id @ X334) @ id))) | ? [X335 : subst,X336 : term,X337 : subst] : ((X333 @ (comp @ X337 @ X335) @ (sub @ X336 @ X335)) != (sub @ (X333 @ X337 @ X336) @ X335)) | ((X330 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)) & ! [X338 : term] : ((X330 @ id @ X338 @ id) = (X332 @ X338)) & ((X332 @ (lam @ X331)) != $true) & ! [X339 : term] : (((X332 @ X339) != $true) | ((X332 @ (sub @ X331 @ (push @ X339 @ id))) = $true)))) | ? [X329 : term] : ((sub @ X329 @ id) != X329)) | ? [X322 : term,X323 : term > $o] : (($true != (X323 @ X322)) & ! [X327 : term,X328 : term] : (((X323 @ X328) != $true) | ($true = (X323 @ (ap @ X327 @ X328))) | ($true != (X323 @ X327))) & ! [X324 : term] : (((var @ X324) != $true) | ((X323 @ X324) = $true)) & ! [X325 : term] : (($true = (X323 @ (lam @ X325))) | ? [X326 : term] : (($true = (X323 @ X326)) & ((X323 @ (sub @ X325 @ (push @ X326 @ id))) != $true))))) | ? [X319 : subst > term > subst > $o] : ! [X320 : term > $o] : ? [X321 : term] : ((X319 @ id @ X321 @ id) != (X320 @ X321))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lthm = $true) & ((d2subst @ d_id) = sh) & (((! [X164 : subst > term > subst > $o,X165 : term] : (((X164 @ id @ (lam @ X165) @ id) = $true) | ? [X166 : term] : (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) != $true) & ($true = (X164 @ id @ X166 @ id))) | ? [X176 : subst,X177 : subst,X178 : term,X179 : subst] : (((X164 @ X177 @ X178 @ (comp @ X179 @ X176)) = $true) & ($true != (X164 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179) @ X176))) | ? [X172 : subst,X173 : subst,X174 : subst,X175 : term] : (((X164 @ X173 @ X175 @ (comp @ X174 @ X172)) != $true) & ($true = (X164 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174) @ X172))) | ? [X167 : subst > term > term] : (! [X168 : term,X169 : subst,X170 : subst] : ((sub @ (X167 @ X169 @ X168) @ X170) = (X167 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) & ! [X171 : term] : (((X164 @ id @ X171 @ id) != $true) | ($true = (X164 @ id @ (X167 @ id @ X171) @ id))) & ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) != $true))) | ? [X156 : subst > term > subst > $o,X157 : term] : (((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id) != $true) & ! [X159 : subst > term > term] : (? [X160 : term] : (((X156 @ id @ X160 @ id) = $true) & ((X156 @ id @ (X159 @ id @ X160) @ id) != $true)) | ($true = (X156 @ id @ (lam @ (X159 @ sh @ one)) @ id)) | ? [X161 : subst,X162 : subst,X163 : term] : ((X159 @ (comp @ X161 @ X162) @ (sub @ X163 @ X162)) != (sub @ (X159 @ X161 @ X163) @ X162))) & ! [X158 : term] : (((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id) = $true) | ((X156 @ id @ X158 @ id) != $true)))) | ? [X155 : term] : ((sub @ X155 @ id) != X155)) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop = $true) & (ulamvarsh = $true) & ((hoasinduction = $true) <=> ! [X390 : term,X391 : subst > term > subst > $o] : (? [X392 : term,X393 : term] : (((X391 @ id @ X393 @ id) = $true) & ((X391 @ id @ (ap @ (sub @ X392 @ id) @ X393) @ id) != $true) & ($true = (X391 @ id @ X392 @ id))) | ($true = (X391 @ id @ X390 @ id)) | ? [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (((X391 @ (comp @ X402 @ X401) @ (sub @ X399 @ X401) @ X400) = $true) & ($true != (X391 @ X402 @ X399 @ (comp @ X401 @ X400)))) | ? [X394 : term] : (((var @ (sub @ X394 @ id)) = $true) & ((X391 @ id @ X394 @ id) != $true)) | ? [X403 : subst > term > term] : (! [X407 : term] : (((X391 @ id @ X407 @ id) != $true) | ((X391 @ id @ (X403 @ id @ X407) @ id) = $true)) & ! [X404 : term,X405 : subst,X406 : subst] : ((sub @ (X403 @ X406 @ X404) @ X405) = (X403 @ (comp @ X406 @ X405) @ (sub @ X404 @ X405))) & ((X391 @ id @ (lam @ (X403 @ sh @ one)) @ id) != $true)) | ? [X395 : term,X396 : subst,X397 : subst,X398 : subst] : (((X391 @ (comp @ X397 @ X398) @ (sub @ X395 @ X398) @ X396) != $true) & ($true = (X391 @ X397 @ X395 @ (comp @ X398 @ X396)))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X28 : term,X29 : term,X30 : term,X31 : term] : ((X30 != X31) & ((ap @ X28 @ X30) = (ap @ X29 @ X31))) | ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35)))) & (hoasinduction_lem3b_gthm = $true) & (pushprop_gthm = $true) & (! [X408 : term] : ? [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) = (X409 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X381 : d_term] : (d_one = X381) & (hoasinduction_lem3a_gthm = $true) & ((! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (? [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) != (X85 @ X88)) | ((X87 @ X86) != $true) | ($true = (X85 @ one))) | ? [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) != X82)) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X0 : term] : ? [X1 : subst > term > term] : ! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & ((substmonoid = $true) <=> (! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384))) & (((((! [X431 : term,X432 : subst > term > subst > $o] : (($true = (X432 @ id @ X431 @ id)) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X432 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443) @ X440) != $true) & ($true = (X432 @ X442 @ X441 @ (comp @ X443 @ X440)))) | ? [X439 : term] : (((var @ (sub @ X439 @ id)) = $true) & ((X432 @ id @ X439 @ id) != $true)) | ? [X444 : subst > term > term] : (! [X445 : term,X446 : subst,X447 : subst] : ((X444 @ (comp @ X446 @ X447) @ (sub @ X445 @ X447)) = (sub @ (X444 @ X446 @ X445) @ X447)) & ! [X448 : term] : (($true != (X432 @ id @ X448 @ id)) | ((X432 @ id @ (X444 @ id @ X448) @ id) = $true)) & ($true != (X432 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ? [X433 : term,X434 : term] : (((X432 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) != $true) & ($true = (X432 @ id @ X433 @ id)) & ($true = (X432 @ id @ X434 @ id))) | ? [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (((X432 @ X436 @ X437 @ (comp @ X435 @ X438)) != $true) & ((X432 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435) @ X438) = $true))) | ? [X421 : subst > term > subst > $o,X422 : term,X423 : term > $o] : (! [X424 : term] : (($true != (X423 @ X424)) | ((X423 @ (sub @ X422 @ (push @ X424 @ id))) = $true)) & ! [X426 : subst > term > term] : (? [X427 : subst,X428 : term,X429 : subst] : ((X426 @ (comp @ X427 @ X429) @ (sub @ X428 @ X429)) != (sub @ (X426 @ X427 @ X428) @ X429)) | ? [X430 : term] : (($true != (X421 @ id @ (X426 @ id @ X430) @ id)) & ((X421 @ id @ X430 @ id) = $true)) | ((X421 @ id @ (lam @ (X426 @ sh @ one)) @ id) = $true)) & ((X423 @ (lam @ X422)) != $true) & ! [X425 : term] : ((X423 @ X425) = (X421 @ id @ X425 @ id)))) | ? [X420 : term] : ((sub @ X420 @ id) != X420)) | ? [X413 : term > $o,X414 : term] : (((X413 @ X414) != $true) & ! [X417 : term,X418 : term] : (($true = (X413 @ (ap @ X417 @ X418))) | ($true != (X413 @ X417)) | ($true != (X413 @ X418))) & ! [X415 : term] : (($true = (X413 @ (lam @ X415))) | ? [X416 : term] : (((X413 @ X416) = $true) & ($true != (X413 @ (sub @ X415 @ (push @ X416 @ id)))))) & ! [X419 : term] : (((var @ X419) != $true) | ((X413 @ X419) = $true)))) | ? [X410 : subst > term > subst > $o] : ! [X411 : term > $o] : ? [X412 : term] : ((X410 @ id @ X412 @ id) != (X411 @ X412))) <=> (hoasinduction_lthm_3 = $true)) & (! [X255 : term] : ? [X256 : subst > term > term] : ((X256 @ sh @ one) = (sub @ X255 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem_lthm = $true) <=> ((((! [X57 : subst,X58 : term,X59 : term > $o] : (((X59 @ (sub @ X58 @ X57)) = $true) | ? [X60 : term] : (! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ((X59 @ X61) != $true)) & ((X59 @ (lam @ X60)) != $true)) | ? [X62 : term,X63 : term] : (((X59 @ X63) = $true) & ($true = (X59 @ X62)) & ($true != (X59 @ (ap @ X62 @ X63)))) | ? [X64 : term] : (((var @ X64) = $true) & ((X59 @ (sub @ X64 @ X57)) != $true))) | ? [X51 : term,X52 : term > $o] : (! [X55 : term,X56 : term] : (((X52 @ X56) != $true) | ($true = (X52 @ (ap @ X56 @ X55))) | ($true != (X52 @ X55))) & ! [X54 : term] : (((var @ X54) != $true) | ((X52 @ X54) = $true)) & ($true != (X52 @ X51)) & ! [X53 : term] : (($true != (X52 @ X53)) | ($true = (X52 @ (lam @ X53)))))) | ? [X50 : subst] : ((comp @ X50 @ id) != X50)) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48)) | ? [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) != X47))) & (((! [X358 : term,X359 : subst > term > subst > $o] : (? [X360 : subst > term > term] : (! [X361 : term,X362 : subst,X363 : subst] : ((sub @ (X360 @ X362 @ X361) @ X363) = (X360 @ (comp @ X362 @ X363) @ (sub @ X361 @ X363))) & ! [X364 : term] : (((X359 @ id @ (X360 @ id @ X364) @ id) = $true) | ((X359 @ id @ X364 @ id) != $true)) & ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id) != $true)) | ($true = (X359 @ id @ (lam @ X358) @ id)) | ? [X365 : term] : (($true != (X359 @ id @ (sub @ X358 @ (push @ X365 @ id)) @ id)) & ($true = (X359 @ id @ X365 @ id)))) | ? [X350 : subst > term > subst > $o,X351 : term] : (($true != (X350 @ id @ (lam @ (sub @ X351 @ (push @ one @ sh))) @ id)) & ! [X352 : subst > term > term] : (? [X356 : term] : (((X350 @ id @ (X352 @ id @ X356) @ id) != $true) & ((X350 @ id @ X356 @ id) = $true)) | ? [X353 : term,X354 : subst,X355 : subst] : ((X352 @ (comp @ X355 @ X354) @ (sub @ X353 @ X354)) != (sub @ (X352 @ X355 @ X353) @ X354)) | ($true = (X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))) & ! [X357 : term] : (($true != (X350 @ id @ X357 @ id)) | ((X350 @ id @ (sub @ X351 @ (push @ X357 @ id)) @ id) = $true)))) | ? [X349 : term] : ((sub @ X349 @ id) != X349)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X366 : subst > term > subst > $o,X367 : term,X368 : term,X369 : term > $o] : (? [X377 : term,X378 : subst,X379 : subst,X380 : subst] : (((X366 @ X379 @ X377 @ (comp @ X380 @ X378)) = $true) & ($true != (X366 @ (comp @ X379 @ X380) @ (sub @ X377 @ X380) @ X378))) | ? [X373 : subst,X374 : subst,X375 : term,X376 : subst] : (((X366 @ X376 @ X375 @ (comp @ X373 @ X374)) != $true) & ($true = (X366 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374))) | ? [X371 : term,X372 : term] : (($true = (X366 @ id @ X371 @ id)) & ($true = (X366 @ id @ X372 @ id)) & ((X366 @ id @ (ap @ (sub @ X371 @ id) @ X372) @ id) != $true)) | ? [X370 : term] : ((X366 @ id @ X370 @ id) != (X369 @ X370)) | ($true = (X369 @ (ap @ X367 @ X368))) | ($true != (X369 @ X367)) | ((X369 @ X368) != $true))) & (hoasinduction_lem2_lthm = $true) & (((! [X262 : term,X263 : subst > term > subst > $o,X264 : term > $o] : (($true = (X264 @ (lam @ X262))) | ? [X271 : term] : ((X264 @ X271) != (X263 @ id @ X271 @ id)) | ? [X266 : subst > term > term] : (! [X270 : term] : (((X263 @ id @ X270 @ id) != $true) | ($true = (X263 @ id @ (X266 @ id @ X270) @ id))) & ((X263 @ id @ (lam @ (X266 @ sh @ one)) @ id) != $true) & ! [X267 : term,X268 : subst,X269 : subst] : ((X266 @ (comp @ X269 @ X268) @ (sub @ X267 @ X268)) = (sub @ (X266 @ X269 @ X267) @ X268))) | ? [X265 : term] : (($true = (X264 @ X265)) & ($true != (X264 @ (sub @ X262 @ (push @ X265 @ id)))))) | ? [X261 : term] : ((sub @ X261 @ id) != X261)) | ? [X257 : term] : ! [X258 : subst > term > term] : ? [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) != (X258 @ X259 @ X260))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((axscons = $true) <=> ! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (lamnotap != $true) & ((! [X21 : term] : ((sub @ X21 @ id) = X21) | ? [X20 : term] : ((sub @ X20 @ id) != X20)) <=> (termmset_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (pushprop_lthm_orig = $true) & ! [X382 : d_term,X383 : d_term] : ((X382 = X383) | ((d2term @ X383) != (d2term @ X382))) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & ((axshiftcons = $true) <=> ! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181)) & (termmset_gthm = $true) & (axclos = $true) & (! [X65 : subst > term > subst > $o] : ? [X66 : term > $o] : ! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67)) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_gthm = $true) & ((induction2_lthm = $true) <=> ((! [X102 : term,X103 : term > $o] : (? [X106 : term] : (((var @ X106) = $true) & ($true != (X103 @ X106))) | ((X103 @ X102) = $true) | ? [X107 : term,X108 : term] : (((X103 @ X107) = $true) & ($true != (X103 @ (ap @ X108 @ X107))) & ((X103 @ X108) = $true)) | ? [X104 : term] : (! [X105 : term] : (($true != (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true)) & ($true != (X103 @ (lam @ X104))))) | ? [X94 : term,X95 : subst,X96 : term > $o] : (! [X101 : term] : (((X96 @ (sub @ X101 @ X95)) = $true) | ((var @ X101) != $true)) & ((X96 @ (sub @ X94 @ X95)) != $true) & ! [X97 : term] : (($true = (X96 @ (lam @ X97))) | ? [X98 : term] : (((X96 @ X98) = $true) & ($true != (X96 @ (sub @ X97 @ (push @ X98 @ id)))))) & ! [X99 : term,X100 : term] : (((X96 @ X100) != $true) | ($true != (X96 @ X99)) | ((X96 @ (ap @ X99 @ X100)) = $true)))) | ? [X93 : term] : ((sub @ X93 @ id) != X93))) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X521 : subst > term > subst > $o,X522 : term] : (? [X528 : term] : (((X521 @ id @ (sub @ X522 @ (push @ X528 @ id)) @ id) != $true) & ((X521 @ id @ X528 @ id) = $true)) | ((X521 @ id @ (lam @ X522) @ id) = $true) | ? [X523 : subst > term > term] : (! [X527 : term] : (((X521 @ id @ X527 @ id) != $true) | ($true = (X521 @ id @ (X523 @ id @ X527) @ id))) & ! [X524 : term,X525 : subst,X526 : subst] : ((X523 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525)) = (sub @ (X523 @ X526 @ X524) @ X525)) & ($true != (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ! [X27 : d_subst] : (d_id = X27) & (hoasinduction_lem1 = $true) & ((((! [X296 : subst] : ((comp @ id @ X296) = X296) & ! [X295 : subst] : ((comp @ X295 @ id) = X295)) | ? [X294 : subst] : ((comp @ X294 @ id) != X294)) | ? [X293 : subst] : ((comp @ id @ X293) != X293)) <=> (substmonoid_lthm = $true)) & (hoasapinj2_gthm = $true) & ((d2subst @ d_id) = id) & ((var @ (d2term @ d_one)) != $true) & (! [X245 : subst,X246 : term,X247 : term > $o] : (? [X248 : term,X249 : term] : (($true != (X247 @ (ap @ X249 @ X248))) & ($true = (X247 @ X249)) & ((X247 @ X248) = $true)) | ((X247 @ (sub @ X246 @ X245)) = $true) | ? [X252 : term] : (($true != (X247 @ (sub @ X252 @ X245))) & ($true = (var @ X252))) | ? [X250 : term] : (! [X251 : term] : (($true = (X247 @ (sub @ X250 @ (push @ X251 @ id)))) | ((X247 @ X251) != $true)) & ((X247 @ (lam @ X250)) != $true))) <=> (induction2lem = $true)) & ((induction2 = $true) <=> ! [X191 : term > $o,X192 : term] : (? [X193 : term,X194 : term] : (((X191 @ (ap @ X194 @ X193)) != $true) & ((X191 @ X193) = $true) & ($true = (X191 @ X194))) | ? [X197 : term] : (($true = (var @ X197)) & ($true != (X191 @ X197))) | ($true = (X191 @ X192)) | ? [X195 : term] : (! [X196 : term] : (((X191 @ X196) != $true) | ($true = (X191 @ (sub @ X195 @ (push @ X196 @ id))))) & ((X191 @ (lam @ X195)) != $true)))) & (! [X235 : term,X236 : subst > term > subst > $o,X237 : term > $o] : (? [X239 : term] : (($true != (X237 @ (sub @ X235 @ (push @ X239 @ id)))) & ((X237 @ X239) = $true)) | ? [X240 : subst > term > term] : (! [X242 : subst,X243 : term,X244 : subst] : ((sub @ (X240 @ X242 @ X243) @ X244) = (X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244))) & ! [X241 : term] : (((X236 @ id @ X241 @ id) != $true) | ((X236 @ id @ (X240 @ id @ X241) @ id) = $true)) & ((X236 @ id @ (lam @ (X240 @ sh @ one)) @ id) != $true)) | ? [X238 : term] : ((X236 @ id @ X238 @ id) != (X237 @ X238)) | ($true = (X237 @ (lam @ X235)))) <=> (hoasinduction_lem3v2a = $true)) & (induction2lem_gthm = $true) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) != (d2subst @ X253)) | (X253 = X254)) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X515 : term,X516 : subst > term > term,X517 : term] : (((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))) | ? [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) != (sub @ (X516 @ X518 @ X519) @ X520)))) & (! [X198 : term > $o,X199 : term,X200 : subst > term > subst > $o] : (? [X210 : term] : ((X200 @ id @ X210 @ id) != (X198 @ X210)) | ? [X211 : subst > term > term] : (! [X212 : term] : (($true != (X200 @ id @ X212 @ id)) | ($true = (X200 @ id @ (X211 @ id @ X212) @ id))) & ($true != (X200 @ id @ (lam @ (X211 @ sh @ one)) @ id)) & ! [X213 : term,X214 : subst,X215 : subst] : ((X211 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)) = (sub @ (X211 @ X214 @ X213) @ X215))) | ? [X201 : term,X202 : subst,X203 : subst,X204 : subst] : (($true != (X200 @ (comp @ X202 @ X204) @ (sub @ X201 @ X204) @ X203)) & ($true = (X200 @ X202 @ X201 @ (comp @ X204 @ X203)))) | ? [X205 : term] : (($true != (X198 @ (sub @ X199 @ (push @ X205 @ id)))) & ($true = (X198 @ X205))) | ? [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (((X200 @ X206 @ X209 @ (comp @ X208 @ X207)) != $true) & ((X200 @ (comp @ X206 @ X208) @ (sub @ X209 @ X208) @ X207) = $true)) | ((X198 @ (lam @ X199)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (! [X297 : term] : ((sub @ X297 @ id) = X297) <=> (termmset = $true))),
% 1.70/1.51 inference(ennf_transformation,[status(thm)],[f11])).
% 1.70/1.51 thf(f11,plain,(
% 1.70/1.51 (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (($true != (X152 @ X150)) | ~! [X154 : term] : ((X151 @ X154) = (X152 @ (sub @ X154 @ (push @ X150 @ X153)))) | ($true = (X151 @ one))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (~! [X225 : subst > term > term] : (~! [X229 : term] : (($true = (X223 @ id @ (X225 @ id @ X229) @ id)) | ($true != (X223 @ id @ X229 @ id))) | ~! [X226 : subst,X227 : term,X228 : subst] : ((X225 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226)) = (sub @ (X225 @ X228 @ X227) @ X226)) | ($true = (X223 @ id @ (lam @ (X225 @ sh @ one)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)) | ~! [X224 : term] : (($true = (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id)) | ((X223 @ id @ X224 @ id) != $true)))) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem3v2 = $true) & (axmap = $true) & (axabs = $true) & (! [X111 : subst > term > subst > $o,X112 : term] : (((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true) | ~! [X113 : term] : (($true = (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id)) | ($true != (X111 @ id @ X113 @ id))) | ~! [X114 : subst > term > term] : (((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) = $true) | ~! [X118 : term] : (($true = (X111 @ id @ (X114 @ id @ X118) @ id)) | ((X111 @ id @ X118 @ id) != $true)) | ~! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & ((apinj1 = $true) <=> ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316)))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem2_gthm = $true) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & ((! [X277 : subst,X278 : term] : ((sub @ one @ (push @ X278 @ X277)) = X278) => (! [X279 : term,X280 : subst] : ((comp @ sh @ (push @ X279 @ X280)) = X280) => (! [X281 : term,X282 : term] : ((X281 = X282) | ((lam @ X281) != (lam @ X282))) => ! [X283 : term,X284 : subst > term > term,X285 : subst,X286 : subst > term > term] : (~! [X287 : term,X288 : subst,X289 : subst] : ((sub @ (X284 @ X288 @ X287) @ X289) = (X284 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) | ~! [X290 : subst,X291 : subst,X292 : term] : ((X286 @ (comp @ X291 @ X290) @ (sub @ X292 @ X290)) = (sub @ (X286 @ X291 @ X292) @ X290)) | ((lam @ (X284 @ sh @ one)) != (lam @ (X286 @ sh @ one))) | ((X286 @ X285 @ X283) = (X284 @ X285 @ X283)))))) <=> (hoaslaminj_lthm = $true)) & (! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (~! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))) | ~! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39))) <=> (hoaslaminj = $true)) & (! [X301 : subst > term > subst > $o,X302 : term,X303 : term] : (~! [X304 : term,X305 : term] : (($true != (X301 @ id @ X304 @ id)) | ($true = (X301 @ id @ (ap @ (sub @ X305 @ id) @ X304) @ id)) | ((X301 @ id @ X305 @ id) != $true)) | ~! [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (((X301 @ (comp @ X312 @ X313) @ (sub @ X311 @ X313) @ X310) = $true) | ($true != (X301 @ X312 @ X311 @ (comp @ X313 @ X310)))) | ~! [X306 : subst,X307 : subst,X308 : term,X309 : subst] : (($true != (X301 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309) @ X306)) | ($true = (X301 @ X307 @ X308 @ (comp @ X309 @ X306)))) | ($true = (X301 @ id @ (ap @ X302 @ X303) @ id)) | ((X301 @ id @ X302 @ id) != $true) | ((X301 @ id @ X303 @ id) != $true)) <=> (hoasinduction_lem2 = $true)) & (hoasapnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axassoc = $true) & ((hoasinduction_lthm = $true) <=> (! [X461 : term > $o,X462 : term] : (~! [X463 : term] : (~! [X464 : term] : (($true = (X461 @ (sub @ X463 @ (push @ X464 @ id)))) | ($true != (X461 @ X464))) | ($true = (X461 @ (lam @ X463)))) | ~! [X465 : term,X466 : term] : (($true != (X461 @ X466)) | ((X461 @ (ap @ X466 @ X465)) = $true) | ((X461 @ X465) != $true)) | ($true = (X461 @ X462)) | ~! [X467 : term] : (($true != (var @ X467)) | ($true = (X461 @ X467)))) => (! [X468 : term,X469 : subst > term > subst > $o,X470 : term] : (~! [X471 : term,X472 : subst,X473 : subst,X474 : subst] : (((X469 @ X473 @ X471 @ (comp @ X474 @ X472)) != $true) | ((X469 @ (comp @ X473 @ X474) @ (sub @ X471 @ X474) @ X472) = $true)) | ($true != (X469 @ id @ X468 @ id)) | ($true = (X469 @ id @ (ap @ X468 @ X470) @ id)) | ((X469 @ id @ X470 @ id) != $true) | ~! [X475 : subst,X476 : subst,X477 : term,X478 : subst] : (((X469 @ (comp @ X476 @ X478) @ (sub @ X477 @ X478) @ X475) != $true) | ($true = (X469 @ X476 @ X477 @ (comp @ X478 @ X475)))) | ~! [X479 : term,X480 : term] : (($true != (X469 @ id @ X479 @ id)) | ($true = (X469 @ id @ (ap @ (sub @ X480 @ id) @ X479) @ id)) | ($true != (X469 @ id @ X480 @ id)))) => (! [X481 : subst > term > subst > $o,X482 : term] : (~! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (($true != (X481 @ (comp @ X493 @ X496) @ (sub @ X494 @ X496) @ X495)) | ($true = (X481 @ X493 @ X494 @ (comp @ X496 @ X495)))) | ((X481 @ id @ (lam @ X482) @ id) = $true) | ~! [X488 : term] : (((X481 @ id @ X488 @ id) != $true) | ($true = (X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id))) | ~! [X483 : subst > term > term] : (($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id)) | ~! [X485 : subst,X486 : term,X487 : subst] : ((sub @ (X483 @ X485 @ X486) @ X487) = (X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487))) | ~! [X484 : term] : (($true = (X481 @ id @ (X483 @ id @ X484) @ id)) | ($true != (X481 @ id @ X484 @ id)))) | ~! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (($true != (X481 @ X491 @ X490 @ (comp @ X492 @ X489))) | ($true = (X481 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492) @ X489)))) => ! [X497 : subst > term > subst > $o,X498 : term] : (($true = (X497 @ id @ X498 @ id)) | ~! [X503 : subst,X504 : subst,X505 : subst,X506 : term] : (((X497 @ (comp @ X503 @ X505) @ (sub @ X506 @ X505) @ X504) = $true) | ((X497 @ X503 @ X506 @ (comp @ X505 @ X504)) != $true)) | ~! [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (((X497 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499) != $true) | ($true = (X497 @ X501 @ X502 @ (comp @ X500 @ X499)))) | ~! [X508 : term,X509 : term] : (($true = (X497 @ id @ (ap @ (sub @ X509 @ id) @ X508) @ id)) | ((X497 @ id @ X509 @ id) != $true) | ((X497 @ id @ X508 @ id) != $true)) | ~! [X510 : subst > term > term] : (~! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X510 @ X512 @ X513) @ X514) = (X510 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) | ($true = (X497 @ id @ (lam @ (X510 @ sh @ one)) @ id)) | ~! [X511 : term] : (((X497 @ id @ (X510 @ id @ X511) @ id) = $true) | ($true != (X497 @ id @ X511 @ id)))) | ~! [X507 : term] : (($true != (var @ (sub @ X507 @ id))) | ((X497 @ id @ X507 @ id) = $true))))))) & ((hoasinduction_lem3 = $true) <=> ! [X4 : subst > term > subst > $o,X5 : term] : (~! [X19 : term] : (((X4 @ id @ X19 @ id) != $true) | ($true = (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id))) | ~! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) = $true) | ($true != (X4 @ X8 @ X6 @ (comp @ X9 @ X7)))) | ~! [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) = $true) | ((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) != $true)) | ~! [X10 : subst > term > term] : (($true = (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) | ~! [X11 : term] : (($true = (X4 @ id @ (X10 @ id @ X11) @ id)) | ($true != (X4 @ id @ X11 @ id))) | ~! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13))) | ($true = (X4 @ id @ (lam @ X5) @ id)))) & ((pushprop_lem0_lthm = $true) <=> ! [X272 : subst,X273 : term,X274 : term > $o] : ~! [X275 : term > $o] : ~! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276))) & (! [X314 : term] : ((sub @ X314 @ id) = X314) <=> (axvarid = $true)) & (hoasapnotvar_lthm = $true) & (ulamvar1 != $true) & (axvarshift = $true) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((shinj = $true) <=> ! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231))) & (! [X216 : term,X217 : term > $o] : (($true = (X217 @ X216)) | ~! [X221 : term] : (((X217 @ X221) != $true) | ($true = (X217 @ (lam @ X221)))) | ~! [X219 : term,X220 : term] : (($true != (X217 @ X219)) | ((X217 @ X220) != $true) | ((X217 @ (ap @ X219 @ X220)) = $true)) | ~! [X218 : term] : (((var @ X218) != $true) | ($true = (X217 @ X218)))) <=> (induction = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) = X532) => (! [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) = X533) => ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (($true != (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true))))) & (hoasapinj1_gthm = $true) & ((! [X131 : term] : ((sub @ X131 @ id) = X131) => ! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (~! [X140 : term] : ((X132 @ id @ X140 @ id) = (X134 @ X140)) | ~! [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true != (X132 @ X147 @ X146 @ (comp @ X145 @ X148))) | ($true = (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148))) | ~! [X149 : term] : (($true = (X134 @ (sub @ X133 @ (push @ X149 @ id)))) | ($true != (X134 @ X149))) | ($true = (X134 @ (lam @ X133))) | ~! [X135 : subst > term > term] : (($true = (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) | ~! [X139 : term] : (($true = (X132 @ id @ (X135 @ id @ X139) @ id)) | ($true != (X132 @ id @ X139 @ id))) | ~! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137))) | ~! [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) != $true) | ($true = (X132 @ X143 @ X144 @ (comp @ X141 @ X142)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (one = (d2term @ d_one)) & (induction2_gthm = $true) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) <=> (hoasapinj2 = $true)) & (pushprop_lem2v2_gthm = $true) & (! [X23 : term] : ~! [X24 : subst > term > term] : ~! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X186 : term,X187 : term > $o,X188 : subst] : ~! [X189 : term > $o] : ~! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190))) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) <=> (hoasapinj1 = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X70 @ X72) != (ap @ X69 @ X71)) | (X69 = X70)) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74)))))) & (pushprop_lem0_gthm = $true) & (! [X122 : term,X123 : subst > term > subst > $o] : (~! [X129 : term,X130 : term] : (($true = (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) | ((X123 @ id @ X130 @ id) != $true) | ($true != (X123 @ id @ X129 @ id))) | ~! [X124 : subst > term > term] : (~! [X128 : term] : (((X123 @ id @ X128 @ id) != $true) | ($true = (X123 @ id @ (X124 @ id @ X128) @ id))) | ($true = (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id)) | ~! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126))) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X232 : subst > term > subst > $o] : ~! [X233 : term > $o] : ~! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X449 : term,X450 : subst > term > subst > $o] : (~! [X451 : term,X452 : subst > term > term] : (~! [X453 : subst,X454 : term,X455 : subst] : ((X452 @ (comp @ X453 @ X455) @ (sub @ X454 @ X455)) = (sub @ X451 @ (push @ (sub @ X454 @ X455) @ (comp @ X453 @ X455)))) | ~! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (sub @ X451 @ (push @ X458 @ X457)) @ X459) = (sub @ (X452 @ X457 @ X458) @ X459)) | ~! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ($true != (X450 @ id @ X456 @ id))) | ($true = (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id))) | ($true = (X450 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)) | ~! [X460 : term] : (((X450 @ id @ (sub @ X449 @ (push @ X460 @ id)) @ id) = $true) | ($true != (X450 @ id @ X460 @ id))))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (axapp = $true) & ((! [X319 : subst > term > subst > $o] : ~! [X320 : term > $o] : ~! [X321 : term] : ((X319 @ id @ X321 @ id) = (X320 @ X321)) => (! [X322 : term,X323 : term > $o] : (~! [X325 : term] : (($true = (X323 @ (lam @ X325))) | ~! [X326 : term] : (($true != (X323 @ X326)) | ((X323 @ (sub @ X325 @ (push @ X326 @ id))) = $true))) | ~! [X327 : term,X328 : term] : (((X323 @ X328) != $true) | ($true = (X323 @ (ap @ X327 @ X328))) | ($true != (X323 @ X327))) | ($true = (X323 @ X322)) | ~! [X324 : term] : (((var @ X324) != $true) | ((X323 @ X324) = $true))) => (! [X329 : term] : ((sub @ X329 @ id) = X329) => (! [X330 : subst > term > subst > $o,X331 : term,X332 : term > $o] : (~! [X339 : term] : (((X332 @ X339) != $true) | ((X332 @ (sub @ X331 @ (push @ X339 @ id))) = $true)) | ~! [X338 : term] : ((X330 @ id @ X338 @ id) = (X332 @ X338)) | ~! [X333 : subst > term > term] : (~! [X334 : term] : (($true = (X330 @ id @ (X333 @ id @ X334) @ id)) | ($true != (X330 @ id @ X334 @ id))) | ~! [X335 : subst,X336 : term,X337 : subst] : ((X333 @ (comp @ X337 @ X335) @ (sub @ X336 @ X335)) = (sub @ (X333 @ X337 @ X336) @ X335)) | ((X330 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)) | ((X332 @ (lam @ X331)) = $true)) => ! [X340 : term,X341 : subst > term > subst > $o] : (((X341 @ id @ X340 @ id) = $true) | ~! [X342 : term,X343 : term] : (((X341 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) = $true) | ((X341 @ id @ X343 @ id) != $true) | ((X341 @ id @ X342 @ id) != $true)) | ~! [X344 : subst > term > term] : (~! [X348 : term] : (($true != (X341 @ id @ X348 @ id)) | ((X341 @ id @ (X344 @ id @ X348) @ id) = $true)) | ((X341 @ id @ (lam @ (X344 @ sh @ one)) @ id) = $true) | ~! [X345 : term,X346 : subst,X347 : subst] : ((sub @ (X344 @ X346 @ X345) @ X347) = (X344 @ (comp @ X346 @ X347) @ (sub @ X345 @ X347))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lthm = $true) & ((d2subst @ d_id) = sh) & ((! [X155 : term] : ((sub @ X155 @ id) = X155) => (! [X156 : subst > term > subst > $o,X157 : term] : (((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id) = $true) | ~! [X158 : term] : (((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id) = $true) | ((X156 @ id @ X158 @ id) != $true)) | ~! [X159 : subst > term > term] : (~! [X161 : subst,X162 : subst,X163 : term] : ((X159 @ (comp @ X161 @ X162) @ (sub @ X163 @ X162)) = (sub @ (X159 @ X161 @ X163) @ X162)) | ~! [X160 : term] : (((X156 @ id @ X160 @ id) != $true) | ((X156 @ id @ (X159 @ id @ X160) @ id) = $true)) | ($true = (X156 @ id @ (lam @ (X159 @ sh @ one)) @ id)))) => ! [X164 : subst > term > subst > $o,X165 : term] : (~! [X176 : subst,X177 : subst,X178 : term,X179 : subst] : (($true = (X164 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179) @ X176)) | ((X164 @ X177 @ X178 @ (comp @ X179 @ X176)) != $true)) | ~! [X167 : subst > term > term] : (~! [X171 : term] : (((X164 @ id @ X171 @ id) != $true) | ($true = (X164 @ id @ (X167 @ id @ X171) @ id))) | ~! [X168 : term,X169 : subst,X170 : subst] : ((sub @ (X167 @ X169 @ X168) @ X170) = (X167 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) | ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) = $true)) | ((X164 @ id @ (lam @ X165) @ id) = $true) | ~! [X166 : term] : (($true != (X164 @ id @ X166 @ id)) | ((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) = $true)) | ~! [X172 : subst,X173 : subst,X174 : subst,X175 : term] : (($true != (X164 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174) @ X172)) | ((X164 @ X173 @ X175 @ (comp @ X174 @ X172)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop = $true) & (ulamvarsh = $true) & (! [X390 : term,X391 : subst > term > subst > $o] : (~! [X395 : term,X396 : subst,X397 : subst,X398 : subst] : (($true != (X391 @ X397 @ X395 @ (comp @ X398 @ X396))) | ((X391 @ (comp @ X397 @ X398) @ (sub @ X395 @ X398) @ X396) = $true)) | ~! [X392 : term,X393 : term] : (((X391 @ id @ (ap @ (sub @ X392 @ id) @ X393) @ id) = $true) | ((X391 @ id @ X393 @ id) != $true) | ($true != (X391 @ id @ X392 @ id))) | ~! [X394 : term] : (((X391 @ id @ X394 @ id) = $true) | ((var @ (sub @ X394 @ id)) != $true)) | ($true = (X391 @ id @ X390 @ id)) | ~! [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (($true = (X391 @ X402 @ X399 @ (comp @ X401 @ X400))) | ((X391 @ (comp @ X402 @ X401) @ (sub @ X399 @ X401) @ X400) != $true)) | ~! [X403 : subst > term > term] : (((X391 @ id @ (lam @ (X403 @ sh @ one)) @ id) = $true) | ~! [X404 : term,X405 : subst,X406 : subst] : ((sub @ (X403 @ X406 @ X404) @ X405) = (X403 @ (comp @ X406 @ X405) @ (sub @ X404 @ X405))) | ~! [X407 : term] : (((X391 @ id @ X407 @ id) != $true) | ((X391 @ id @ (X403 @ id @ X407) @ id) = $true)))) <=> (hoasinduction = $true)) & (hoasapnotvar_gthm = $true) & ((! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ X28 @ X30) != (ap @ X29 @ X31)) | (X30 = X31)) => ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (pushprop_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X408 : term] : ~! [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) != (X409 @ sh @ one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X381 : d_term] : (d_one = X381) & (hoasinduction_lem3a_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82) => ! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (($true = (X85 @ one)) | ((X87 @ X86) != $true) | ~! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88))))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X0 : term] : ~! [X1 : subst > term > term] : ~! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & ((substmonoid = $true) <=> (! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384))) & ((! [X410 : subst > term > subst > $o] : ~! [X411 : term > $o] : ~! [X412 : term] : ((X410 @ id @ X412 @ id) = (X411 @ X412)) => (! [X413 : term > $o,X414 : term] : (~! [X415 : term] : (($true = (X413 @ (lam @ X415))) | ~! [X416 : term] : (((X413 @ X416) != $true) | ($true = (X413 @ (sub @ X415 @ (push @ X416 @ id)))))) | ~! [X417 : term,X418 : term] : (($true = (X413 @ (ap @ X417 @ X418))) | ($true != (X413 @ X417)) | ($true != (X413 @ X418))) | ((X413 @ X414) = $true) | ~! [X419 : term] : (((var @ X419) != $true) | ((X413 @ X419) = $true))) => (! [X420 : term] : ((sub @ X420 @ id) = X420) => (! [X421 : subst > term > subst > $o,X422 : term,X423 : term > $o] : (~! [X425 : term] : ((X423 @ X425) = (X421 @ id @ X425 @ id)) | ~! [X426 : subst > term > term] : (((X421 @ id @ (lam @ (X426 @ sh @ one)) @ id) = $true) | ~! [X430 : term] : (((X421 @ id @ X430 @ id) != $true) | ($true = (X421 @ id @ (X426 @ id @ X430) @ id))) | ~! [X427 : subst,X428 : term,X429 : subst] : ((X426 @ (comp @ X427 @ X429) @ (sub @ X428 @ X429)) = (sub @ (X426 @ X427 @ X428) @ X429))) | ~! [X424 : term] : (($true != (X423 @ X424)) | ((X423 @ (sub @ X422 @ (push @ X424 @ id))) = $true)) | ((X423 @ (lam @ X422)) = $true)) => ! [X431 : term,X432 : subst > term > subst > $o] : (~! [X444 : subst > term > term] : (($true = (X432 @ id @ (lam @ (X444 @ sh @ one)) @ id)) | ~! [X445 : term,X446 : subst,X447 : subst] : ((X444 @ (comp @ X446 @ X447) @ (sub @ X445 @ X447)) = (sub @ (X444 @ X446 @ X445) @ X447)) | ~! [X448 : term] : (($true != (X432 @ id @ X448 @ id)) | ((X432 @ id @ (X444 @ id @ X448) @ id) = $true))) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X432 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443) @ X440) = $true) | ($true != (X432 @ X442 @ X441 @ (comp @ X443 @ X440)))) | ~! [X433 : term,X434 : term] : (($true != (X432 @ id @ X433 @ id)) | ($true != (X432 @ id @ X434 @ id)) | ((X432 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) = $true)) | ~! [X439 : term] : (((X432 @ id @ X439 @ id) = $true) | ((var @ (sub @ X439 @ id)) != $true)) | ~! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (((X432 @ X436 @ X437 @ (comp @ X435 @ X438)) = $true) | ((X432 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435) @ X438) != $true)) | ($true = (X432 @ id @ X431 @ id))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X255 : term] : ~! [X256 : subst > term > term] : ((X256 @ sh @ one) != (sub @ X255 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) => (! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48) => (! [X50 : subst] : ((comp @ X50 @ id) = X50) => (! [X51 : term,X52 : term > $o] : (~! [X55 : term,X56 : term] : (((X52 @ X56) != $true) | ($true = (X52 @ (ap @ X56 @ X55))) | ($true != (X52 @ X55))) | ~! [X53 : term] : (($true != (X52 @ X53)) | ($true = (X52 @ (lam @ X53)))) | ~! [X54 : term] : (((var @ X54) != $true) | ((X52 @ X54) = $true)) | ($true = (X52 @ X51))) => ! [X57 : subst,X58 : term,X59 : term > $o] : (~! [X60 : term] : (~! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ((X59 @ X61) != $true)) | ((X59 @ (lam @ X60)) = $true)) | ~! [X64 : term] : (((var @ X64) != $true) | ((X59 @ (sub @ X64 @ X57)) = $true)) | ~! [X62 : term,X63 : term] : (($true = (X59 @ (ap @ X62 @ X63))) | ((X59 @ X63) != $true) | ($true != (X59 @ X62))) | ((X59 @ (sub @ X58 @ X57)) = $true))))))) & ((! [X349 : term] : ((sub @ X349 @ id) = X349) => (! [X350 : subst > term > subst > $o,X351 : term] : (($true = (X350 @ id @ (lam @ (sub @ X351 @ (push @ one @ sh))) @ id)) | ~! [X357 : term] : (($true != (X350 @ id @ X357 @ id)) | ((X350 @ id @ (sub @ X351 @ (push @ X357 @ id)) @ id) = $true)) | ~! [X352 : subst > term > term] : (~! [X353 : term,X354 : subst,X355 : subst] : ((X352 @ (comp @ X355 @ X354) @ (sub @ X353 @ X354)) = (sub @ (X352 @ X355 @ X353) @ X354)) | ~! [X356 : term] : (((X350 @ id @ X356 @ id) != $true) | ((X350 @ id @ (X352 @ id @ X356) @ id) = $true)) | ($true = (X350 @ id @ (lam @ (X352 @ sh @ one)) @ id)))) => ! [X358 : term,X359 : subst > term > subst > $o] : (~! [X360 : subst > term > term] : (((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id) = $true) | ~! [X364 : term] : (((X359 @ id @ (X360 @ id @ X364) @ id) = $true) | ((X359 @ id @ X364 @ id) != $true)) | ~! [X361 : term,X362 : subst,X363 : subst] : ((sub @ (X360 @ X362 @ X361) @ X363) = (X360 @ (comp @ X362 @ X363) @ (sub @ X361 @ X363)))) | ($true = (X359 @ id @ (lam @ X358) @ id)) | ~! [X365 : term] : (($true != (X359 @ id @ X365 @ id)) | ($true = (X359 @ id @ (sub @ X358 @ (push @ X365 @ id)) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X366 : subst > term > subst > $o,X367 : term,X368 : term,X369 : term > $o] : (((X369 @ X368) != $true) | ~! [X370 : term] : ((X366 @ id @ X370 @ id) = (X369 @ X370)) | ($true != (X369 @ X367)) | ~! [X371 : term,X372 : term] : (((X366 @ id @ (ap @ (sub @ X371 @ id) @ X372) @ id) = $true) | ($true != (X366 @ id @ X372 @ id)) | ($true != (X366 @ id @ X371 @ id))) | ~! [X373 : subst,X374 : subst,X375 : term,X376 : subst] : (((X366 @ X376 @ X375 @ (comp @ X373 @ X374)) = $true) | ($true != (X366 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374))) | ($true = (X369 @ (ap @ X367 @ X368))) | ~! [X377 : term,X378 : subst,X379 : subst,X380 : subst] : (($true = (X366 @ (comp @ X379 @ X380) @ (sub @ X377 @ X380) @ X378)) | ((X366 @ X379 @ X377 @ (comp @ X380 @ X378)) != $true)))) & (hoasinduction_lem2_lthm = $true) & ((! [X257 : term] : ~! [X258 : subst > term > term] : ~! [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) = (X258 @ X259 @ X260)) => (! [X261 : term] : ((sub @ X261 @ id) = X261) => ! [X262 : term,X263 : subst > term > subst > $o,X264 : term > $o] : (~! [X265 : term] : (($true = (X264 @ (sub @ X262 @ (push @ X265 @ id)))) | ($true != (X264 @ X265))) | ~! [X266 : subst > term > term] : (((X263 @ id @ (lam @ (X266 @ sh @ one)) @ id) = $true) | ~! [X267 : term,X268 : subst,X269 : subst] : ((X266 @ (comp @ X269 @ X268) @ (sub @ X267 @ X268)) = (sub @ (X266 @ X269 @ X267) @ X268)) | ~! [X270 : term] : (((X263 @ id @ X270 @ id) != $true) | ($true = (X263 @ id @ (X266 @ id @ X270) @ id)))) | ($true = (X264 @ (lam @ X262))) | ~! [X271 : term] : ((X264 @ X271) = (X263 @ id @ X271 @ id))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((axscons = $true) <=> ! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (lamnotap != $true) & ((termmset_lthm = $true) <=> (! [X20 : term] : ((sub @ X20 @ id) = X20) => ! [X21 : term] : ((sub @ X21 @ id) = X21))) & (hoaslamnotap_lthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1v2_gthm = $true) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (pushprop_lthm_orig = $true) & ! [X382 : d_term,X383 : d_term] : (((d2term @ X383) = (d2term @ X382)) => (X382 = X383)) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & ((axshiftcons = $true) <=> ! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181)) & (termmset_gthm = $true) & (axclos = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X65 : subst > term > subst > $o] : ~! [X66 : term > $o] : ~! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67))) & (hoasinduction_gthm = $true) & ((induction2_lthm = $true) <=> (! [X93 : term] : ((sub @ X93 @ id) = X93) => (! [X94 : term,X95 : subst,X96 : term > $o] : (~! [X97 : term] : (($true = (X96 @ (lam @ X97))) | ~! [X98 : term] : (($true = (X96 @ (sub @ X97 @ (push @ X98 @ id)))) | ((X96 @ X98) != $true))) | ~! [X101 : term] : (((X96 @ (sub @ X101 @ X95)) = $true) | ((var @ X101) != $true)) | ((X96 @ (sub @ X94 @ X95)) = $true) | ~! [X99 : term,X100 : term] : (((X96 @ X100) != $true) | ($true != (X96 @ X99)) | ((X96 @ (ap @ X99 @ X100)) = $true))) => ! [X102 : term,X103 : term > $o] : (((X103 @ X102) = $true) | ~! [X107 : term,X108 : term] : (((X103 @ X107) != $true) | ((X103 @ X108) != $true) | ($true = (X103 @ (ap @ X108 @ X107)))) | ~! [X106 : term] : (((var @ X106) != $true) | ($true = (X103 @ X106))) | ~! [X104 : term] : (~! [X105 : term] : (($true != (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true)) | ($true = (X103 @ (lam @ X104)))))))) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) | ($true != (X79 @ X81))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X521 : subst > term > subst > $o,X522 : term] : (~! [X528 : term] : (((X521 @ id @ (sub @ X522 @ (push @ X528 @ id)) @ id) = $true) | ((X521 @ id @ X528 @ id) != $true)) | ~! [X523 : subst > term > term] : (($true = (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id)) | ~! [X527 : term] : (((X521 @ id @ X527 @ id) != $true) | ($true = (X521 @ id @ (X523 @ id @ X527) @ id))) | ~! [X524 : term,X525 : subst,X526 : subst] : ((X523 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525)) = (sub @ (X523 @ X526 @ X524) @ X525))) | ((X521 @ id @ (lam @ X522) @ id) = $true))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ! [X27 : d_subst] : (d_id = X27) & (hoasinduction_lem1 = $true) & ((! [X293 : subst] : ((comp @ id @ X293) = X293) => (! [X294 : subst] : ((comp @ X294 @ id) = X294) => (! [X296 : subst] : ((comp @ id @ X296) = X296) & ! [X295 : subst] : ((comp @ X295 @ id) = X295)))) <=> (substmonoid_lthm = $true)) & (hoasapinj2_gthm = $true) & ((d2subst @ d_id) = id) & ((var @ (d2term @ d_one)) != $true) & (! [X245 : subst,X246 : term,X247 : term > $o] : (~! [X250 : term] : (((X247 @ (lam @ X250)) = $true) | ~! [X251 : term] : (($true = (X247 @ (sub @ X250 @ (push @ X251 @ id)))) | ((X247 @ X251) != $true))) | ((X247 @ (sub @ X246 @ X245)) = $true) | ~! [X252 : term] : (($true = (X247 @ (sub @ X252 @ X245))) | ($true != (var @ X252))) | ~! [X248 : term,X249 : term] : (($true = (X247 @ (ap @ X249 @ X248))) | ($true != (X247 @ X249)) | ((X247 @ X248) != $true))) <=> (induction2lem = $true)) & (! [X191 : term > $o,X192 : term] : (~! [X195 : term] : (((X191 @ (lam @ X195)) = $true) | ~! [X196 : term] : (((X191 @ X196) != $true) | ($true = (X191 @ (sub @ X195 @ (push @ X196 @ id)))))) | ~! [X193 : term,X194 : term] : (((X191 @ (ap @ X194 @ X193)) = $true) | ((X191 @ X193) != $true) | ($true != (X191 @ X194))) | ($true = (X191 @ X192)) | ~! [X197 : term] : (($true != (var @ X197)) | ($true = (X191 @ X197)))) <=> (induction2 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X235 : term,X236 : subst > term > subst > $o,X237 : term > $o] : (~! [X239 : term] : (($true = (X237 @ (sub @ X235 @ (push @ X239 @ id)))) | ((X237 @ X239) != $true)) | ($true = (X237 @ (lam @ X235))) | ~! [X238 : term] : ((X236 @ id @ X238 @ id) = (X237 @ X238)) | ~! [X240 : subst > term > term] : (~! [X242 : subst,X243 : term,X244 : subst] : ((sub @ (X240 @ X242 @ X243) @ X244) = (X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244))) | ~! [X241 : term] : (((X236 @ id @ X241 @ id) != $true) | ((X236 @ id @ (X240 @ id @ X241) @ id) = $true)) | ((X236 @ id @ (lam @ (X240 @ sh @ one)) @ id) = $true)))) & (induction2lem_gthm = $true) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) = (d2subst @ X253)) => (X253 = X254)) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X515 : term,X516 : subst > term > term,X517 : term] : (~! [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) = (sub @ (X516 @ X518 @ X519) @ X520)) | ((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))))) & (! [X198 : term > $o,X199 : term,X200 : subst > term > subst > $o] : (~! [X201 : term,X202 : subst,X203 : subst,X204 : subst] : (($true != (X200 @ X202 @ X201 @ (comp @ X204 @ X203))) | ($true = (X200 @ (comp @ X202 @ X204) @ (sub @ X201 @ X204) @ X203))) | ~! [X211 : subst > term > term] : (~! [X212 : term] : (($true != (X200 @ id @ X212 @ id)) | ($true = (X200 @ id @ (X211 @ id @ X212) @ id))) | ($true = (X200 @ id @ (lam @ (X211 @ sh @ one)) @ id)) | ~! [X213 : term,X214 : subst,X215 : subst] : ((X211 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)) = (sub @ (X211 @ X214 @ X213) @ X215))) | ~! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (((X200 @ (comp @ X206 @ X208) @ (sub @ X209 @ X208) @ X207) != $true) | ((X200 @ X206 @ X209 @ (comp @ X208 @ X207)) = $true)) | ~! [X210 : term] : ((X200 @ id @ X210 @ id) = (X198 @ X210)) | ~! [X205 : term] : (($true != (X198 @ X205)) | ($true = (X198 @ (sub @ X199 @ (push @ X205 @ id))))) | ((X198 @ (lam @ X199)) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (! [X297 : term] : ((sub @ X297 @ id) = X297) <=> (termmset = $true))),
% 1.70/1.51 inference(flattening,[status(thm)],[f10])).
% 1.70/1.51 thf(f10,plain,(
% 1.70/1.51 (hoasinduction_lem2_gthm = $true) & (! [X0 : term] : ~! [X1 : subst > term > term] : ~! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & (apnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X4 : subst > term > subst > $o,X5 : term] : (~! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (~($true = (X4 @ X8 @ X6 @ (comp @ X9 @ X7))) | ((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) = $true)) | ~! [X10 : subst > term > term] : (~! [X11 : term] : (~($true = (X4 @ id @ X11 @ id)) | ($true = (X4 @ id @ (X10 @ id @ X11) @ id))) | ($true = (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) | ~! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13))) | ($true = (X4 @ id @ (lam @ X5) @ id)) | ~! [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (~((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) = $true) | ((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) = $true)) | ~! [X19 : term] : (($true = (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id)) | ~((X4 @ id @ X19 @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & ((termmset_lthm = $true) <=> (! [X20 : term] : ((sub @ X20 @ id) = X20) => ! [X21 : term] : ((sub @ X21 @ id) = X21))) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (! [X23 : term] : ~! [X24 : subst > term > term] : ~! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X27 : d_subst] : (d_id = X27) & (hoasapnotvar_lthm = $true) & ((! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ X28 @ X30) != (ap @ X29 @ X31)) | (X30 = X31)) => ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35))) <=> (hoasapinj2_lthm = $true)) & (! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (~! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))) | ~! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39))) <=> (hoaslaminj = $true)) & ~(lamnotap = $true) & ((induction2lem_lthm = $true) <=> (! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) => (! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48) => (! [X50 : subst] : ((comp @ X50 @ id) = X50) => (! [X51 : term,X52 : term > $o] : (($true = (X52 @ X51)) | ~! [X53 : term] : (~($true = (X52 @ X53)) | ($true = (X52 @ (lam @ X53)))) | ~! [X54 : term] : (~((var @ X54) = $true) | ((X52 @ X54) = $true)) | ~! [X55 : term,X56 : term] : (~($true = (X52 @ X55)) | ~((X52 @ X56) = $true) | ($true = (X52 @ (ap @ X56 @ X55))))) => ! [X57 : subst,X58 : term,X59 : term > $o] : (((X59 @ (sub @ X58 @ X57)) = $true) | ~! [X60 : term] : (((X59 @ (lam @ X60)) = $true) | ~! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ~((X59 @ X61) = $true))) | ~! [X62 : term,X63 : term] : (($true = (X59 @ (ap @ X62 @ X63))) | ~($true = (X59 @ X62)) | ~((X59 @ X63) = $true)) | ~! [X64 : term] : (~((var @ X64) = $true) | ((X59 @ (sub @ X64 @ X57)) = $true)))))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X65 : subst > term > subst > $o] : ~! [X66 : term > $o] : ~! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67))) & ((hoasapinj1_lthm = $true) <=> (! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X70 @ X72) != (ap @ X69 @ X71)) | (X69 = X70)) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74)))))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (~($true = (X79 @ X81)) | ($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & ((! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82) => ! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (~! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88)) | ($true = (X85 @ one)) | ~((X87 @ X86) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & (axabs = $true) & (one = (d2term @ d_one)) & (pushprop_lthm_orig = $true) & ((induction2_lthm = $true) <=> (! [X93 : term] : ((sub @ X93 @ id) = X93) => (! [X94 : term,X95 : subst,X96 : term > $o] : (~! [X97 : term] : (~! [X98 : term] : (($true = (X96 @ (sub @ X97 @ (push @ X98 @ id)))) | ~((X96 @ X98) = $true)) | ($true = (X96 @ (lam @ X97)))) | ((X96 @ (sub @ X94 @ X95)) = $true) | ~! [X99 : term,X100 : term] : (((X96 @ (ap @ X99 @ X100)) = $true) | ~($true = (X96 @ X99)) | ~((X96 @ X100) = $true)) | ~! [X101 : term] : (~((var @ X101) = $true) | ((X96 @ (sub @ X101 @ X95)) = $true))) => ! [X102 : term,X103 : term > $o] : (((X103 @ X102) = $true) | ~! [X104 : term] : (($true = (X103 @ (lam @ X104))) | ~! [X105 : term] : (~($true = (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true))) | ~! [X106 : term] : (($true = (X103 @ X106)) | ~((var @ X106) = $true)) | ~! [X107 : term,X108 : term] : (~((X103 @ X108) = $true) | ~((X103 @ X107) = $true) | ($true = (X103 @ (ap @ X108 @ X107)))))))) & (pushprop_gthm = $true) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & (! [X111 : subst > term > subst > $o,X112 : term] : (~! [X113 : term] : (~($true = (X111 @ id @ X113 @ id)) | ($true = (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id))) | ~! [X114 : subst > term > term] : (~! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) | ((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) = $true) | ~! [X118 : term] : (~((X111 @ id @ X118 @ id) = $true) | ($true = (X111 @ id @ (X114 @ id @ X118) @ id)))) | ((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true)) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (! [X122 : term,X123 : subst > term > subst > $o] : (~! [X124 : subst > term > term] : (~! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) | ~! [X128 : term] : (($true = (X123 @ id @ (X124 @ id @ X128) @ id)) | ~((X123 @ id @ X128 @ id) = $true)) | ($true = (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id))) | ~! [X129 : term,X130 : term] : (~((X123 @ id @ X130 @ id) = $true) | ~($true = (X123 @ id @ X129 @ id)) | ($true = (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id))) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X131 : term] : ((sub @ X131 @ id) = X131) => ! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (~! [X135 : subst > term > term] : (($true = (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) | ~! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) | ~! [X139 : term] : (~($true = (X132 @ id @ X139 @ id)) | ($true = (X132 @ id @ (X135 @ id @ X139) @ id)))) | ~! [X140 : term] : ((X132 @ id @ X140 @ id) = (X134 @ X140)) | ~! [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (($true = (X132 @ X143 @ X144 @ (comp @ X141 @ X142))) | ~((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) = $true)) | ~! [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true = (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148)) | ~($true = (X132 @ X147 @ X146 @ (comp @ X145 @ X148)))) | ($true = (X134 @ (lam @ X133))) | ~! [X149 : term] : (~($true = (X134 @ X149)) | ($true = (X134 @ (sub @ X133 @ (push @ X149 @ id))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X150 : term,X151 : term > $o,X152 : term > $o,X153 : subst] : (~($true = (X152 @ X150)) | ($true = (X151 @ one)) | ~! [X154 : term] : ((X151 @ X154) = (X152 @ (sub @ X154 @ (push @ X150 @ X153))))) <=> (pushprop_lem1v2 = $true)) & ((! [X155 : term] : ((sub @ X155 @ id) = X155) => (! [X156 : subst > term > subst > $o,X157 : term] : (~! [X158 : term] : (((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id) = $true) | ~((X156 @ id @ X158 @ id) = $true)) | ~! [X159 : subst > term > term] : (~! [X160 : term] : (((X156 @ id @ (X159 @ id @ X160) @ id) = $true) | ~((X156 @ id @ X160 @ id) = $true)) | ~! [X161 : subst,X162 : subst,X163 : term] : ((X159 @ (comp @ X161 @ X162) @ (sub @ X163 @ X162)) = (sub @ (X159 @ X161 @ X163) @ X162)) | ($true = (X156 @ id @ (lam @ (X159 @ sh @ one)) @ id))) | ((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id) = $true)) => ! [X164 : subst > term > subst > $o,X165 : term] : (~! [X166 : term] : (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) = $true) | ~($true = (X164 @ id @ X166 @ id))) | ~! [X167 : subst > term > term] : (~! [X168 : term,X169 : subst,X170 : subst] : ((sub @ (X167 @ X169 @ X168) @ X170) = (X167 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) | ~! [X171 : term] : (($true = (X164 @ id @ (X167 @ id @ X171) @ id)) | ~((X164 @ id @ X171 @ id) = $true)) | ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) = $true)) | ~! [X172 : subst,X173 : subst,X174 : subst,X175 : term] : (~($true = (X164 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174) @ X172)) | ((X164 @ X173 @ X175 @ (comp @ X174 @ X172)) = $true)) | ~! [X176 : subst,X177 : subst,X178 : term,X179 : subst] : (($true = (X164 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179) @ X176)) | ~((X164 @ X177 @ X178 @ (comp @ X179 @ X176)) = $true)) | ((X164 @ id @ (lam @ X165) @ id) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & (substmonoid_gthm = $true) & ((axshiftcons = $true) <=> ! [X180 : term,X181 : subst] : ((comp @ sh @ (push @ X180 @ X181)) = X181)) & (hoasinduction_lem1v2_gthm = $true) & (! [X182 : term,X183 : term,X184 : term,X185 : term] : (((ap @ (sub @ X184 @ id) @ X185) != (ap @ (sub @ X183 @ id) @ X182)) | (X182 = X185)) <=> (hoasapinj2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X186 : term,X187 : term > $o,X188 : subst] : ~! [X189 : term > $o] : ~! [X190 : term] : ((X187 @ (sub @ X190 @ (push @ X186 @ X188))) = (X189 @ X190))) & (hoasinduction_lem3b_gthm = $true) & (! [X191 : term > $o,X192 : term] : (~! [X193 : term,X194 : term] : (~($true = (X191 @ X194)) | ((X191 @ (ap @ X194 @ X193)) = $true) | ~((X191 @ X193) = $true)) | ~! [X195 : term] : (~! [X196 : term] : (($true = (X191 @ (sub @ X195 @ (push @ X196 @ id)))) | ~((X191 @ X196) = $true)) | ((X191 @ (lam @ X195)) = $true)) | ($true = (X191 @ X192)) | ~! [X197 : term] : (~($true = (var @ X197)) | ($true = (X191 @ X197)))) <=> (induction2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X198 : term > $o,X199 : term,X200 : subst > term > subst > $o] : (((X198 @ (lam @ X199)) = $true) | ~! [X201 : term,X202 : subst,X203 : subst,X204 : subst] : (($true = (X200 @ (comp @ X202 @ X204) @ (sub @ X201 @ X204) @ X203)) | ~($true = (X200 @ X202 @ X201 @ (comp @ X204 @ X203)))) | ~! [X205 : term] : (($true = (X198 @ (sub @ X199 @ (push @ X205 @ id)))) | ~($true = (X198 @ X205))) | ~! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : (~((X200 @ (comp @ X206 @ X208) @ (sub @ X209 @ X208) @ X207) = $true) | ((X200 @ X206 @ X209 @ (comp @ X208 @ X207)) = $true)) | ~! [X210 : term] : ((X200 @ id @ X210 @ id) = (X198 @ X210)) | ~! [X211 : subst > term > term] : (~! [X212 : term] : (~($true = (X200 @ id @ X212 @ id)) | ($true = (X200 @ id @ (X211 @ id @ X212) @ id))) | ($true = (X200 @ id @ (lam @ (X211 @ sh @ one)) @ id)) | ~! [X213 : term,X214 : subst,X215 : subst] : ((X211 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)) = (sub @ (X211 @ X214 @ X213) @ X215)))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop = $true) & ((induction = $true) <=> ! [X216 : term,X217 : term > $o] : (~! [X218 : term] : (($true = (X217 @ X218)) | ~((var @ X218) = $true)) | ~! [X219 : term,X220 : term] : (~($true = (X217 @ X219)) | ~((X217 @ X220) = $true) | ((X217 @ (ap @ X219 @ X220)) = $true)) | ~! [X221 : term] : (~((X217 @ X221) = $true) | ($true = (X217 @ (lam @ X221)))) | ($true = (X217 @ X216)))) & (! [X222 : term,X223 : subst > term > subst > $o] : (~! [X224 : term] : (~((X223 @ id @ X224 @ id) = $true) | ($true = (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ~! [X225 : subst > term > term] : (~! [X226 : subst,X227 : term,X228 : subst] : ((X225 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226)) = (sub @ (X225 @ X228 @ X227) @ X226)) | ($true = (X223 @ id @ (lam @ (X225 @ sh @ one)) @ id)) | ~! [X229 : term] : (~($true = (X223 @ id @ X229 @ id)) | ($true = (X223 @ id @ (X225 @ id @ X229) @ id)))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id))) <=> (hoasinduction_lem3aa = $true)) & ((shinj = $true) <=> ! [X230 : term,X231 : term] : (((sub @ X230 @ sh) != (sub @ X231 @ sh)) | (X230 = X231))) & (pushprop_lem2v2 = $true) & (axassoc = $true) & (termmset_gthm = $true) & (axvarshift = $true) & (! [X232 : subst > term > subst > $o] : ~! [X233 : term > $o] : ~! [X234 : term] : ((X232 @ id @ X234 @ id) = (X233 @ X234)) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem0_gthm = $true) & (! [X235 : term,X236 : subst > term > subst > $o,X237 : term > $o] : (($true = (X237 @ (lam @ X235))) | ~! [X238 : term] : ((X236 @ id @ X238 @ id) = (X237 @ X238)) | ~! [X239 : term] : (~((X237 @ X239) = $true) | ($true = (X237 @ (sub @ X235 @ (push @ X239 @ id))))) | ~! [X240 : subst > term > term] : (~! [X241 : term] : (~((X236 @ id @ X241 @ id) = $true) | ((X236 @ id @ (X240 @ id @ X241) @ id) = $true)) | ((X236 @ id @ (lam @ (X240 @ sh @ one)) @ id) = $true) | ~! [X242 : subst,X243 : term,X244 : subst] : ((sub @ (X240 @ X242 @ X243) @ X244) = (X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244))))) <=> (hoasinduction_lem3v2a = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (! [X245 : subst,X246 : term,X247 : term > $o] : (~! [X248 : term,X249 : term] : (~($true = (X247 @ X249)) | ~((X247 @ X248) = $true) | ($true = (X247 @ (ap @ X249 @ X248)))) | ~! [X250 : term] : (((X247 @ (lam @ X250)) = $true) | ~! [X251 : term] : (($true = (X247 @ (sub @ X250 @ (push @ X251 @ id)))) | ~((X247 @ X251) = $true))) | ((X247 @ (sub @ X246 @ X245)) = $true) | ~! [X252 : term] : (($true = (X247 @ (sub @ X252 @ X245))) | ~($true = (var @ X252)))) <=> (induction2lem = $true)) & (pushprop_lem3v2 = $true) & (axapp = $true) & (pushprop_lem2v2_gthm = $true) & ! [X253 : d_subst,X254 : d_subst] : (((d2subst @ X254) = (d2subst @ X253)) => (X253 = X254)) & (! [X255 : term] : ~! [X256 : subst > term > term] : ((X256 @ sh @ one) != (sub @ X255 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X257 : term] : ~! [X258 : subst > term > term] : ~! [X259 : subst,X260 : term] : ((sub @ X257 @ (push @ X260 @ X259)) = (X258 @ X259 @ X260)) => (! [X261 : term] : ((sub @ X261 @ id) = X261) => ! [X262 : term,X263 : subst > term > subst > $o,X264 : term > $o] : (~! [X265 : term] : (($true = (X264 @ (sub @ X262 @ (push @ X265 @ id)))) | ~($true = (X264 @ X265))) | ($true = (X264 @ (lam @ X262))) | ~! [X266 : subst > term > term] : (~! [X267 : term,X268 : subst,X269 : subst] : ((X266 @ (comp @ X269 @ X268) @ (sub @ X267 @ X268)) = (sub @ (X266 @ X269 @ X267) @ X268)) | ~! [X270 : term] : (~((X263 @ id @ X270 @ id) = $true) | ($true = (X263 @ id @ (X266 @ id @ X270) @ id))) | ((X263 @ id @ (lam @ (X266 @ sh @ one)) @ id) = $true)) | ~! [X271 : term] : ((X264 @ X271) = (X263 @ id @ X271 @ id)))))) & ((pushprop_lem0_lthm = $true) <=> ! [X272 : subst,X273 : term,X274 : term > $o] : ~! [X275 : term > $o] : ~! [X276 : term] : ((X274 @ (sub @ X276 @ (push @ X273 @ X272))) = (X275 @ X276))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & ((! [X277 : subst,X278 : term] : ((sub @ one @ (push @ X278 @ X277)) = X278) => (! [X279 : term,X280 : subst] : ((comp @ sh @ (push @ X279 @ X280)) = X280) => (! [X281 : term,X282 : term] : ((X281 = X282) | ((lam @ X281) != (lam @ X282))) => ! [X283 : term,X284 : subst > term > term,X285 : subst,X286 : subst > term > term] : (~! [X287 : term,X288 : subst,X289 : subst] : ((sub @ (X284 @ X288 @ X287) @ X289) = (X284 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) | ~! [X290 : subst,X291 : subst,X292 : term] : ((X286 @ (comp @ X291 @ X290) @ (sub @ X292 @ X290)) = (sub @ (X286 @ X291 @ X292) @ X290)) | ((lam @ (X284 @ sh @ one)) != (lam @ (X286 @ sh @ one))) | ((X286 @ X285 @ X283) = (X284 @ X285 @ X283)))))) <=> (hoaslaminj_lthm = $true)) & ((! [X293 : subst] : ((comp @ id @ X293) = X293) => (! [X294 : subst] : ((comp @ X294 @ id) = X294) => (! [X296 : subst] : ((comp @ id @ X296) = X296) & ! [X295 : subst] : ((comp @ X295 @ id) = X295)))) <=> (substmonoid_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoaslamnotvar_gthm = $true) & (! [X297 : term] : ((sub @ X297 @ id) = X297) <=> (termmset = $true)) & (axmap = $true) & ((axscons = $true) <=> ! [X298 : subst] : ((push @ (sub @ one @ X298) @ (comp @ sh @ X298)) = X298)) & ! [X299 : subst] : ? [X300 : d_subst] : ((d2subst @ X300) = X299) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X301 : subst > term > subst > $o,X302 : term,X303 : term] : (~! [X304 : term,X305 : term] : (~((X301 @ id @ X305 @ id) = $true) | ($true = (X301 @ id @ (ap @ (sub @ X305 @ id) @ X304) @ id)) | ~($true = (X301 @ id @ X304 @ id))) | ($true = (X301 @ id @ (ap @ X302 @ X303) @ id)) | ~! [X306 : subst,X307 : subst,X308 : term,X309 : subst] : (~($true = (X301 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309) @ X306)) | ($true = (X301 @ X307 @ X308 @ (comp @ X309 @ X306)))) | ~! [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (~($true = (X301 @ X312 @ X311 @ (comp @ X313 @ X310))) | ((X301 @ (comp @ X312 @ X313) @ (sub @ X311 @ X313) @ X310) = $true)) | ~((X301 @ id @ X302 @ id) = $true) | ~((X301 @ id @ X303 @ id) = $true))) & (hoasapnotvar = $true) & (hoasinduction_lem1_gthm = $true) & ~((var @ (d2term @ d_one)) = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (! [X314 : term] : ((sub @ X314 @ id) = X314) <=> (axvarid = $true)) & ((apinj1 = $true) <=> ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X315 = X317) | ((ap @ X317 @ X318) != (ap @ X315 @ X316)))) & ((! [X319 : subst > term > subst > $o] : ~! [X320 : term > $o] : ~! [X321 : term] : ((X319 @ id @ X321 @ id) = (X320 @ X321)) => (! [X322 : term,X323 : term > $o] : (~! [X324 : term] : (((X323 @ X324) = $true) | ~((var @ X324) = $true)) | ~! [X325 : term] : (($true = (X323 @ (lam @ X325))) | ~! [X326 : term] : (~($true = (X323 @ X326)) | ((X323 @ (sub @ X325 @ (push @ X326 @ id))) = $true))) | ~! [X327 : term,X328 : term] : (~((X323 @ X328) = $true) | ~($true = (X323 @ X327)) | ($true = (X323 @ (ap @ X327 @ X328)))) | ($true = (X323 @ X322))) => (! [X329 : term] : ((sub @ X329 @ id) = X329) => (! [X330 : subst > term > subst > $o,X331 : term,X332 : term > $o] : (~! [X333 : subst > term > term] : (~! [X334 : term] : (($true = (X330 @ id @ (X333 @ id @ X334) @ id)) | ~($true = (X330 @ id @ X334 @ id))) | ((X330 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true) | ~! [X335 : subst,X336 : term,X337 : subst] : ((X333 @ (comp @ X337 @ X335) @ (sub @ X336 @ X335)) = (sub @ (X333 @ X337 @ X336) @ X335))) | ~! [X338 : term] : ((X330 @ id @ X338 @ id) = (X332 @ X338)) | ((X332 @ (lam @ X331)) = $true) | ~! [X339 : term] : (~((X332 @ X339) = $true) | ((X332 @ (sub @ X331 @ (push @ X339 @ id))) = $true))) => ! [X340 : term,X341 : subst > term > subst > $o] : (~! [X342 : term,X343 : term] : (~((X341 @ id @ X343 @ id) = $true) | ~((X341 @ id @ X342 @ id) = $true) | ((X341 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) = $true)) | ((X341 @ id @ X340 @ id) = $true) | ~! [X344 : subst > term > term] : (~! [X345 : term,X346 : subst,X347 : subst] : ((sub @ (X344 @ X346 @ X345) @ X347) = (X344 @ (comp @ X346 @ X347) @ (sub @ X345 @ X347))) | ~! [X348 : term] : (~($true = (X341 @ id @ X348 @ id)) | ((X341 @ id @ (X344 @ id @ X348) @ id) = $true)) | ((X341 @ id @ (lam @ (X344 @ sh @ one)) @ id) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X349 : term] : ((sub @ X349 @ id) = X349) => (! [X350 : subst > term > subst > $o,X351 : term] : (($true = (X350 @ id @ (lam @ (sub @ X351 @ (push @ one @ sh))) @ id)) | ~! [X352 : subst > term > term] : (~! [X353 : term,X354 : subst,X355 : subst] : ((X352 @ (comp @ X355 @ X354) @ (sub @ X353 @ X354)) = (sub @ (X352 @ X355 @ X353) @ X354)) | ~! [X356 : term] : (~((X350 @ id @ X356 @ id) = $true) | ((X350 @ id @ (X352 @ id @ X356) @ id) = $true)) | ($true = (X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))) | ~! [X357 : term] : (((X350 @ id @ (sub @ X351 @ (push @ X357 @ id)) @ id) = $true) | ~($true = (X350 @ id @ X357 @ id)))) => ! [X358 : term,X359 : subst > term > subst > $o] : (($true = (X359 @ id @ (lam @ X358) @ id)) | ~! [X360 : subst > term > term] : (~! [X361 : term,X362 : subst,X363 : subst] : ((sub @ (X360 @ X362 @ X361) @ X363) = (X360 @ (comp @ X362 @ X363) @ (sub @ X361 @ X363))) | ~! [X364 : term] : (~((X359 @ id @ X364 @ id) = $true) | ((X359 @ id @ (X360 @ id @ X364) @ id) = $true)) | ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id) = $true)) | ~! [X365 : term] : (($true = (X359 @ id @ (sub @ X358 @ (push @ X365 @ id)) @ id)) | ~($true = (X359 @ id @ X365 @ id))))))) & (ulamvarind = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X366 : subst > term > subst > $o,X367 : term,X368 : term,X369 : term > $o] : (($true = (X369 @ (ap @ X367 @ X368))) | ~! [X370 : term] : ((X366 @ id @ X370 @ id) = (X369 @ X370)) | ~! [X371 : term,X372 : term] : (~($true = (X366 @ id @ X372 @ id)) | ~($true = (X366 @ id @ X371 @ id)) | ((X366 @ id @ (ap @ (sub @ X371 @ id) @ X372) @ id) = $true)) | ~((X369 @ X368) = $true) | ~($true = (X369 @ X367)) | ~! [X373 : subst,X374 : subst,X375 : term,X376 : subst] : (((X366 @ X376 @ X375 @ (comp @ X373 @ X374)) = $true) | ~($true = (X366 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374))) | ~! [X377 : term,X378 : subst,X379 : subst,X380 : subst] : (~((X366 @ X379 @ X377 @ (comp @ X380 @ X378)) = $true) | ($true = (X366 @ (comp @ X379 @ X380) @ (sub @ X377 @ X380) @ X378))))) & ~(ulamvar1 = $true) & (hoasinduction_lem3_gthm = $true) & ! [X381 : d_term] : (d_one = X381) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & ! [X382 : d_term,X383 : d_term] : (((d2term @ X383) = (d2term @ X382)) => (X382 = X383)) & ((d2subst @ d_id) = id) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((substmonoid = $true) <=> (! [X385 : subst] : ((comp @ X385 @ id) = X385) & ! [X384 : subst] : ((comp @ id @ X384) = X384))) & (! [X386 : term,X387 : term,X388 : term,X389 : term] : ((X386 = X388) | ((ap @ (sub @ X388 @ id) @ X389) != (ap @ (sub @ X386 @ id) @ X387))) <=> (hoasapinj1 = $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction = $true) <=> ! [X390 : term,X391 : subst > term > subst > $o] : (~! [X392 : term,X393 : term] : (~($true = (X391 @ id @ X392 @ id)) | ((X391 @ id @ (ap @ (sub @ X392 @ id) @ X393) @ id) = $true) | ~((X391 @ id @ X393 @ id) = $true)) | ~! [X394 : term] : (~((var @ (sub @ X394 @ id)) = $true) | ((X391 @ id @ X394 @ id) = $true)) | ~! [X395 : term,X396 : subst,X397 : subst,X398 : subst] : (((X391 @ (comp @ X397 @ X398) @ (sub @ X395 @ X398) @ X396) = $true) | ~($true = (X391 @ X397 @ X395 @ (comp @ X398 @ X396)))) | ~! [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (($true = (X391 @ X402 @ X399 @ (comp @ X401 @ X400))) | ~((X391 @ (comp @ X402 @ X401) @ (sub @ X399 @ X401) @ X400) = $true)) | ($true = (X391 @ id @ X390 @ id)) | ~! [X403 : subst > term > term] : (~! [X404 : term,X405 : subst,X406 : subst] : ((sub @ (X403 @ X406 @ X404) @ X405) = (X403 @ (comp @ X406 @ X405) @ (sub @ X404 @ X405))) | ~! [X407 : term] : (~((X391 @ id @ X407 @ id) = $true) | ((X391 @ id @ (X403 @ id @ X407) @ id) = $true)) | ((X391 @ id @ (lam @ (X403 @ sh @ one)) @ id) = $true)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X408 : term] : ~! [X409 : subst > term > term] : ((sub @ X408 @ (push @ one @ sh)) != (X409 @ sh @ one))) & (induction2_gthm = $true) & (pushprop_lthm = $true) & (axclos = $true) & ((! [X410 : subst > term > subst > $o] : ~! [X411 : term > $o] : ~! [X412 : term] : ((X410 @ id @ X412 @ id) = (X411 @ X412)) => (! [X413 : term > $o,X414 : term] : (~! [X415 : term] : (($true = (X413 @ (lam @ X415))) | ~! [X416 : term] : (~((X413 @ X416) = $true) | ($true = (X413 @ (sub @ X415 @ (push @ X416 @ id)))))) | ~! [X417 : term,X418 : term] : (~($true = (X413 @ X418)) | ~($true = (X413 @ X417)) | ($true = (X413 @ (ap @ X417 @ X418)))) | ((X413 @ X414) = $true) | ~! [X419 : term] : (~((var @ X419) = $true) | ((X413 @ X419) = $true))) => (! [X420 : term] : ((sub @ X420 @ id) = X420) => (! [X421 : subst > term > subst > $o,X422 : term,X423 : term > $o] : (~! [X424 : term] : (((X423 @ (sub @ X422 @ (push @ X424 @ id))) = $true) | ~($true = (X423 @ X424))) | ((X423 @ (lam @ X422)) = $true) | ~! [X425 : term] : ((X423 @ X425) = (X421 @ id @ X425 @ id)) | ~! [X426 : subst > term > term] : (((X421 @ id @ (lam @ (X426 @ sh @ one)) @ id) = $true) | ~! [X427 : subst,X428 : term,X429 : subst] : ((X426 @ (comp @ X427 @ X429) @ (sub @ X428 @ X429)) = (sub @ (X426 @ X427 @ X428) @ X429)) | ~! [X430 : term] : (($true = (X421 @ id @ (X426 @ id @ X430) @ id)) | ~((X421 @ id @ X430 @ id) = $true)))) => ! [X431 : term,X432 : subst > term > subst > $o] : (~! [X433 : term,X434 : term] : (~($true = (X432 @ id @ X433 @ id)) | ((X432 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) = $true) | ~($true = (X432 @ id @ X434 @ id))) | ($true = (X432 @ id @ X431 @ id)) | ~! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (~((X432 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435) @ X438) = $true) | ((X432 @ X436 @ X437 @ (comp @ X435 @ X438)) = $true)) | ~! [X439 : term] : (((X432 @ id @ X439 @ id) = $true) | ~((var @ (sub @ X439 @ id)) = $true)) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (~($true = (X432 @ X442 @ X441 @ (comp @ X443 @ X440))) | ((X432 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443) @ X440) = $true)) | ~! [X444 : subst > term > term] : (~! [X445 : term,X446 : subst,X447 : subst] : ((X444 @ (comp @ X446 @ X447) @ (sub @ X445 @ X447)) = (sub @ (X444 @ X446 @ X445) @ X447)) | ~! [X448 : term] : (~($true = (X432 @ id @ X448 @ id)) | ((X432 @ id @ (X444 @ id @ X448) @ id) = $true)) | ($true = (X432 @ id @ (lam @ (X444 @ sh @ one)) @ id)))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X449 : term,X450 : subst > term > subst > $o] : (~! [X451 : term,X452 : subst > term > term] : (~! [X453 : subst,X454 : term,X455 : subst] : ((X452 @ (comp @ X453 @ X455) @ (sub @ X454 @ X455)) = (sub @ X451 @ (push @ (sub @ X454 @ X455) @ (comp @ X453 @ X455)))) | ~! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ~($true = (X450 @ id @ X456 @ id))) | ~! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (sub @ X451 @ (push @ X458 @ X457)) @ X459) = (sub @ (X452 @ X457 @ X458) @ X459)) | ($true = (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id))) | ~! [X460 : term] : (~($true = (X450 @ id @ X460 @ id)) | ((X450 @ id @ (sub @ X449 @ (push @ X460 @ id)) @ id) = $true)) | ($true = (X450 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)))) & ((hoasinduction_lthm = $true) <=> (! [X461 : term > $o,X462 : term] : (($true = (X461 @ X462)) | ~! [X463 : term] : (~! [X464 : term] : (~($true = (X461 @ X464)) | ($true = (X461 @ (sub @ X463 @ (push @ X464 @ id))))) | ($true = (X461 @ (lam @ X463)))) | ~! [X465 : term,X466 : term] : (((X461 @ (ap @ X466 @ X465)) = $true) | ~($true = (X461 @ X466)) | ~((X461 @ X465) = $true)) | ~! [X467 : term] : (($true = (X461 @ X467)) | ~($true = (var @ X467)))) => (! [X468 : term,X469 : subst > term > subst > $o,X470 : term] : (($true = (X469 @ id @ (ap @ X468 @ X470) @ id)) | ~! [X471 : term,X472 : subst,X473 : subst,X474 : subst] : (((X469 @ (comp @ X473 @ X474) @ (sub @ X471 @ X474) @ X472) = $true) | ~((X469 @ X473 @ X471 @ (comp @ X474 @ X472)) = $true)) | ~($true = (X469 @ id @ X468 @ id)) | ~((X469 @ id @ X470 @ id) = $true) | ~! [X475 : subst,X476 : subst,X477 : term,X478 : subst] : (($true = (X469 @ X476 @ X477 @ (comp @ X478 @ X475))) | ~((X469 @ (comp @ X476 @ X478) @ (sub @ X477 @ X478) @ X475) = $true)) | ~! [X479 : term,X480 : term] : (($true = (X469 @ id @ (ap @ (sub @ X480 @ id) @ X479) @ id)) | ~($true = (X469 @ id @ X480 @ id)) | ~($true = (X469 @ id @ X479 @ id)))) => (! [X481 : subst > term > subst > $o,X482 : term] : (~! [X483 : subst > term > term] : (~! [X484 : term] : (($true = (X481 @ id @ (X483 @ id @ X484) @ id)) | ~($true = (X481 @ id @ X484 @ id))) | ~! [X485 : subst,X486 : term,X487 : subst] : ((sub @ (X483 @ X485 @ X486) @ X487) = (X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487))) | ($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id))) | ((X481 @ id @ (lam @ X482) @ id) = $true) | ~! [X488 : term] : (($true = (X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id)) | ~((X481 @ id @ X488 @ id) = $true)) | ~! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (~($true = (X481 @ X491 @ X490 @ (comp @ X492 @ X489))) | ($true = (X481 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492) @ X489))) | ~! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (~($true = (X481 @ (comp @ X493 @ X496) @ (sub @ X494 @ X496) @ X495)) | ($true = (X481 @ X493 @ X494 @ (comp @ X496 @ X495))))) => ! [X497 : subst > term > subst > $o,X498 : term] : (($true = (X497 @ id @ X498 @ id)) | ~! [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (($true = (X497 @ X501 @ X502 @ (comp @ X500 @ X499))) | ~((X497 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499) = $true)) | ~! [X503 : subst,X504 : subst,X505 : subst,X506 : term] : (((X497 @ (comp @ X503 @ X505) @ (sub @ X506 @ X505) @ X504) = $true) | ~((X497 @ X503 @ X506 @ (comp @ X505 @ X504)) = $true)) | ~! [X507 : term] : (~($true = (var @ (sub @ X507 @ id))) | ((X497 @ id @ X507 @ id) = $true)) | ~! [X508 : term,X509 : term] : (~((X497 @ id @ X509 @ id) = $true) | ($true = (X497 @ id @ (ap @ (sub @ X509 @ id) @ X508) @ id)) | ~((X497 @ id @ X508 @ id) = $true)) | ~! [X510 : subst > term > term] : (~! [X511 : term] : (((X497 @ id @ (X510 @ id @ X511) @ id) = $true) | ~($true = (X497 @ id @ X511 @ id))) | ~! [X512 : subst,X513 : term,X514 : subst] : ((sub @ (X510 @ X512 @ X513) @ X514) = (X510 @ (comp @ X512 @ X514) @ (sub @ X513 @ X514))) | ($true = (X497 @ id @ (lam @ (X510 @ sh @ one)) @ id)))))))) & (hoasapnotvar_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X515 : term,X516 : subst > term > term,X517 : term] : (~! [X518 : subst,X519 : term,X520 : subst] : ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)) = (sub @ (X516 @ X518 @ X519) @ X520)) | ((ap @ (sub @ X517 @ id) @ X515) != (lam @ (X516 @ sh @ one))))) & ((hoasinduction_lem3a = $true) <=> ! [X521 : subst > term > subst > $o,X522 : term] : (~! [X523 : subst > term > term] : (($true = (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id)) | ~! [X524 : term,X525 : subst,X526 : subst] : ((X523 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525)) = (sub @ (X523 @ X526 @ X524) @ X525)) | ~! [X527 : term] : (($true = (X521 @ id @ (X523 @ id @ X527) @ id)) | ~((X521 @ id @ X527 @ id) = $true))) | ((X521 @ id @ (lam @ X522) @ id) = $true) | ~! [X528 : term] : (((X521 @ id @ (sub @ X522 @ (push @ X528 @ id)) @ id) = $true) | ~((X521 @ id @ X528 @ id) = $true)))) & ((d2subst @ d_id) = sh) & ! [X529 : term] : ? [X530 : d_term] : ((d2term @ X530) = X529) & (pushprop_lem1_gthm = $true) & ((! [X531 : subst,X532 : term] : ((sub @ one @ (push @ X532 @ X531)) = X532) => (! [X533 : subst,X534 : term] : ((comp @ sh @ (push @ X534 @ X533)) = X533) => ! [X535 : term,X536 : term > $o,X537 : term > $o,X538 : subst,X539 : term] : (~($true = (X536 @ X535)) | ((X537 @ (sub @ X535 @ (push @ X539 @ X538))) = $true)))) <=> (pushprop_lem1_lthm = $true))),
% 1.70/1.51 inference(rectify,[status(thm)],[f8])).
% 1.70/1.51 thf(f8,plain,(
% 1.70/1.51 (hoasinduction_lem2_gthm = $true) & (! [X0 : term] : ~! [X1 : subst > term > term] : ~! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> (hoasinduction_lem3v2_f = $true)) & (apnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X4 : subst > term > subst > $o,X5 : term] : (~! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (~($true = (X4 @ X8 @ X6 @ (comp @ X9 @ X7))) | ((X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7) = $true)) | ~! [X10 : subst > term > term] : (~! [X11 : term] : (~($true = (X4 @ id @ X11 @ id)) | ($true = (X4 @ id @ (X10 @ id @ X11) @ id))) | ($true = (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id)) | ~! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13))) | ($true = (X4 @ id @ (lam @ X5) @ id)) | ~! [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (~((X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) = $true) | ((X4 @ X17 @ X15 @ (comp @ X16 @ X18)) = $true)) | ~! [X19 : term] : (($true = (X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id)) | ~((X4 @ id @ X19 @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & ((termmset_lthm = $true) <=> (! [X20 : term] : ((sub @ X20 @ id) = X20) => ! [X21 : term] : ((sub @ X21 @ id) = X21))) & (! [X22 : subst] : ((comp @ id @ X22) = X22) <=> (axidl = $true)) & (! [X23 : term] : ~! [X24 : subst > term > term] : ~! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X27 : d_subst] : (d_id = X27) & (hoasapnotvar_lthm = $true) & ((! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ X28 @ X30) != (ap @ X29 @ X31)) | (X30 = X31)) => ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35))) <=> (hoasapinj2_lthm = $true)) & (! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (~! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)) | ((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))) | ~! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39))) <=> (hoaslaminj = $true)) & ~(lamnotap = $true) & ((induction2lem_lthm = $true) <=> (! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) => (! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48) => (! [X50 : subst] : ((comp @ X50 @ id) = X50) => (! [X51 : term,X52 : term > $o] : (($true = (X52 @ X51)) | ~! [X53 : term] : (~($true = (X52 @ X53)) | ($true = (X52 @ (lam @ X53)))) | ~! [X54 : term] : (~((var @ X54) = $true) | ((X52 @ X54) = $true)) | ~! [X55 : term,X56 : term] : (~($true = (X52 @ X55)) | ~((X52 @ X56) = $true) | ($true = (X52 @ (ap @ X56 @ X55))))) => ! [X57 : subst,X58 : term,X59 : term > $o] : (((X59 @ (sub @ X58 @ X57)) = $true) | ~! [X60 : term] : (((X59 @ (lam @ X60)) = $true) | ~! [X61 : term] : (($true = (X59 @ (sub @ X60 @ (push @ X61 @ id)))) | ~((X59 @ X61) = $true))) | ~! [X62 : term,X63 : term] : (($true = (X59 @ (ap @ X62 @ X63))) | ~($true = (X59 @ X62)) | ~((X59 @ X63) = $true)) | ~! [X64 : term] : (~((var @ X64) = $true) | ((X59 @ (sub @ X64 @ X57)) = $true)))))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X65 : subst > term > subst > $o] : ~! [X66 : term > $o] : ~! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67))) & ((hoasapinj1_lthm = $true) <=> (! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X70 @ X72) != (ap @ X69 @ X71)) | (X69 = X70)) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74)))))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (~($true = (X79 @ X81)) | ($true = (X80 @ (sub @ X81 @ (push @ X77 @ X78))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & ((! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82) => ! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (~! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88)) | ($true = (X85 @ one)) | ~((X87 @ X86) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((apinj2 = $true) <=> ! [X89 : term,X90 : term,X91 : term,X92 : term] : ((X89 = X91) | ((ap @ X92 @ X89) != (ap @ X90 @ X91)))) & (axabs = $true) & (one = (d2term @ d_one)) & (pushprop_lthm_orig = $true) & ((induction2_lthm = $true) <=> (! [X93 : term] : ((sub @ X93 @ id) = X93) => (! [X94 : term,X95 : subst,X96 : term > $o] : (~! [X97 : term] : (~! [X98 : term] : (($true = (X96 @ (sub @ X97 @ (push @ X98 @ id)))) | ~((X96 @ X98) = $true)) | ($true = (X96 @ (lam @ X97)))) | ((X96 @ (sub @ X94 @ X95)) = $true) | ~! [X99 : term,X100 : term] : (((X96 @ (ap @ X99 @ X100)) = $true) | ~($true = (X96 @ X99)) | ~((X96 @ X100) = $true)) | ~! [X101 : term] : (~((var @ X101) = $true) | ((X96 @ (sub @ X101 @ X95)) = $true))) => ! [X102 : term,X103 : term > $o] : (((X103 @ X102) = $true) | ~! [X104 : term] : (($true = (X103 @ (lam @ X104))) | ~! [X105 : term] : (~($true = (X103 @ X105)) | ((X103 @ (sub @ X104 @ (push @ X105 @ id))) = $true))) | ~! [X106 : term] : (($true = (X103 @ X106)) | ~((var @ X106) = $true)) | ~! [X107 : term,X108 : term] : (~((X103 @ X108) = $true) | ~((X103 @ X107) = $true) | ($true = (X103 @ (ap @ X108 @ X107)))))))) & (pushprop_gthm = $true) & ((laminj = $true) <=> ! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109)))) & (! [X111 : subst > term > subst > $o,X112 : term] : (~! [X113 : term] : (~($true = (X111 @ id @ X113 @ id)) | ($true = (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id))) | ~! [X114 : subst > term > term] : (~! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) | ((X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) = $true) | ~! [X118 : term] : (~((X111 @ id @ X118 @ id) = $true) | ($true = (X111 @ id @ (X114 @ id @ X118) @ id)))) | ((X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X119 : subst] : ((comp @ X119 @ id) = X119) <=> (axidr = $true)) & ((axvarcons = $true) <=> ! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121)) & (! [X122 : term,X123 : subst > term > subst > $o] : (~! [X124 : subst > term > term] : (~! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) | ~! [X128 : term] : (($true = (X123 @ id @ (X124 @ id @ X128) @ id)) | ~((X123 @ id @ X128 @ id) = $true)) | ($true = (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id))) | ~! [X129 : term,X130 : term] : (~((X123 @ id @ X130 @ id) = $true) | ~($true = (X123 @ id @ X129 @ id)) | ($true = (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id))) | ((X123 @ id @ X122 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X131 : term] : ((sub @ X131 @ id) = X131) => ! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (~! [X135 : subst > term > term] : (($true = (X132 @ id @ (lam @ (X135 @ sh @ one)) @ id)) | ~! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) | ~! [X139 : term] : (~($true = (X132 @ id @ X139 @ id)) | ($true = (X132 @ id @ (X135 @ id @ X139) @ id)))) | ~! [X140 : term] : ((X132 @ id @ X140 @ id) = (X134 @ X140)) | ~! [X141 : subst,X142 : subst,X143 : subst,X144 : term] : (($true = (X132 @ X143 @ X144 @ (comp @ X141 @ X142))) | ~((X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142) = $true)) | ~! [X145 : subst,X146 : term,X147 : subst,X148 : subst] : (($true = (X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148)) | ~($true = (X132 @ X147 @ X146 @ (comp @ X145 @ X148)))) | ($true = (X134 @ (lam @ X133))) | ~! [X149 : term] : (~($true = (X134 @ X149)) | ($true = (X134 @ (sub @ X133 @ (push @ X149 @ id))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X153 : term,X154 : term > $o,X155 : term > $o,X156 : subst] : (~((X155 @ X153) = $true) | ($true = (X154 @ one)) | ~! [X157 : term] : ((X155 @ (sub @ X157 @ (push @ X153 @ X156))) = (X154 @ X157))) <=> (pushprop_lem1v2 = $true)) & ((! [X158 : term] : ((sub @ X158 @ id) = X158) => (! [X159 : subst > term > subst > $o,X160 : term] : (~! [X161 : term] : (($true = (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id)) | ~($true = (X159 @ id @ X161 @ id))) | ~! [X162 : subst > term > term] : (~! [X163 : term] : (($true = (X159 @ id @ (X162 @ id @ X163) @ id)) | ~((X159 @ id @ X163 @ id) = $true)) | ~! [X164 : subst,X165 : subst,X166 : term] : ((sub @ (X162 @ X164 @ X166) @ X165) = (X162 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) | ($true = (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id))) | ($true = (X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id))) => ! [X167 : subst > term > subst > $o,X168 : term] : (~! [X169 : term] : (($true = (X167 @ id @ (sub @ X168 @ (push @ X169 @ id)) @ id)) | ~($true = (X167 @ id @ X169 @ id))) | ~! [X170 : subst > term > term] : (~! [X171 : term,X172 : subst,X173 : subst] : ((sub @ (X170 @ X172 @ X171) @ X173) = (X170 @ (comp @ X172 @ X173) @ (sub @ X171 @ X173))) | ~! [X174 : term] : (($true = (X167 @ id @ (X170 @ id @ X174) @ id)) | ~($true = (X167 @ id @ X174 @ id))) | ($true = (X167 @ id @ (lam @ (X170 @ sh @ one)) @ id))) | ~! [X175 : subst,X176 : subst,X177 : subst,X178 : term] : (~($true = (X167 @ (comp @ X176 @ X177) @ (sub @ X178 @ X177) @ X175)) | ($true = (X167 @ X176 @ X178 @ (comp @ X177 @ X175)))) | ~! [X179 : subst,X180 : subst,X181 : term,X182 : subst] : (((X167 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182) @ X179) = $true) | ~((X167 @ X180 @ X181 @ (comp @ X182 @ X179)) = $true)) | ($true = (X167 @ id @ (lam @ X168) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & (substmonoid_gthm = $true) & ((axshiftcons = $true) <=> ! [X183 : term,X184 : subst] : ((comp @ sh @ (push @ X183 @ X184)) = X184)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X185 : term,X186 : term,X187 : term,X188 : term] : (((ap @ (sub @ X187 @ id) @ X188) != (ap @ (sub @ X186 @ id) @ X185)) | (X185 = X188))) & (! [X189 : term,X190 : term > $o,X191 : subst] : ~! [X192 : term > $o] : ~! [X193 : term] : ((X192 @ X193) = (X190 @ (sub @ X193 @ (push @ X189 @ X191)))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem3b_gthm = $true) & (! [X194 : term > $o,X195 : term] : (~! [X196 : term,X197 : term] : (~($true = (X194 @ X197)) | ((X194 @ (ap @ X197 @ X196)) = $true) | ~($true = (X194 @ X196))) | ~! [X198 : term] : (~! [X199 : term] : (($true = (X194 @ (sub @ X198 @ (push @ X199 @ id)))) | ~($true = (X194 @ X199))) | ($true = (X194 @ (lam @ X198)))) | ((X194 @ X195) = $true) | ~! [X200 : term] : (~($true = (var @ X200)) | ($true = (X194 @ X200)))) <=> (induction2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X206 : term > $o,X207 : term,X208 : subst > term > subst > $o] : (((X206 @ (lam @ X207)) = $true) | ~! [X209 : term,X210 : subst,X211 : subst,X212 : subst] : (($true = (X208 @ (comp @ X210 @ X212) @ (sub @ X209 @ X212) @ X211)) | ~((X208 @ X210 @ X209 @ (comp @ X212 @ X211)) = $true)) | ~! [X213 : term] : (($true = (X206 @ (sub @ X207 @ (push @ X213 @ id)))) | ~($true = (X206 @ X213))) | ~! [X214 : subst,X215 : subst,X216 : subst,X217 : term] : (~($true = (X208 @ (comp @ X214 @ X216) @ (sub @ X217 @ X216) @ X215)) | ($true = (X208 @ X214 @ X217 @ (comp @ X216 @ X215)))) | ~! [X218 : term] : ((X206 @ X218) = (X208 @ id @ X218 @ id)) | ~! [X219 : subst > term > term] : (~! [X220 : term] : (~($true = (X208 @ id @ X220 @ id)) | ($true = (X208 @ id @ (X219 @ id @ X220) @ id))) | ((X208 @ id @ (lam @ (X219 @ sh @ one)) @ id) = $true) | ~! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop = $true) & ((induction = $true) <=> ! [X224 : term,X225 : term > $o] : (~! [X226 : term] : (($true = (X225 @ X226)) | ~($true = (var @ X226))) | ~! [X227 : term,X228 : term] : (~((X225 @ X227) = $true) | ~((X225 @ X228) = $true) | ((X225 @ (ap @ X227 @ X228)) = $true)) | ~! [X229 : term] : (~((X225 @ X229) = $true) | ((X225 @ (lam @ X229)) = $true)) | ((X225 @ X224) = $true))) & (! [X230 : term,X231 : subst > term > subst > $o] : (~! [X232 : term] : (~($true = (X231 @ id @ X232 @ id)) | ($true = (X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id))) | ~! [X233 : subst > term > term] : (~! [X234 : subst,X235 : term,X236 : subst] : ((sub @ (X233 @ X236 @ X235) @ X234) = (X233 @ (comp @ X236 @ X234) @ (sub @ X235 @ X234))) | ($true = (X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) | ~! [X237 : term] : (~($true = (X231 @ id @ X237 @ id)) | ((X231 @ id @ (X233 @ id @ X237) @ id) = $true))) | ($true = (X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id))) <=> (hoasinduction_lem3aa = $true)) & (! [X238 : term,X239 : term] : (((sub @ X239 @ sh) != (sub @ X238 @ sh)) | (X238 = X239)) <=> (shinj = $true)) & (pushprop_lem2v2 = $true) & (axassoc = $true) & (termmset_gthm = $true) & (axvarshift = $true) & (! [X240 : subst > term > subst > $o] : ~! [X241 : term > $o] : ~! [X242 : term] : ((X241 @ X242) = (X240 @ id @ X242 @ id)) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem0_gthm = $true) & (! [X243 : term,X244 : subst > term > subst > $o,X245 : term > $o] : (($true = (X245 @ (lam @ X243))) | ~! [X246 : term] : ((X245 @ X246) = (X244 @ id @ X246 @ id)) | ~! [X247 : term] : (~((X245 @ X247) = $true) | ($true = (X245 @ (sub @ X243 @ (push @ X247 @ id))))) | ~! [X248 : subst > term > term] : (~! [X249 : term] : (~((X244 @ id @ X249 @ id) = $true) | ($true = (X244 @ id @ (X248 @ id @ X249) @ id))) | ($true = (X244 @ id @ (lam @ (X248 @ sh @ one)) @ id)) | ~! [X250 : subst,X251 : term,X252 : subst] : ((sub @ (X248 @ X250 @ X251) @ X252) = (X248 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252))))) <=> (hoasinduction_lem3v2a = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (! [X255 : subst,X256 : term,X257 : term > $o] : (~! [X258 : term,X259 : term] : (~($true = (X257 @ X259)) | ~($true = (X257 @ X258)) | ($true = (X257 @ (ap @ X259 @ X258)))) | ~! [X260 : term] : (((X257 @ (lam @ X260)) = $true) | ~! [X261 : term] : (((X257 @ (sub @ X260 @ (push @ X261 @ id))) = $true) | ~($true = (X257 @ X261)))) | ((X257 @ (sub @ X256 @ X255)) = $true) | ~! [X262 : term] : (($true = (X257 @ (sub @ X262 @ X255))) | ~($true = (var @ X262)))) <=> (induction2lem = $true)) & (pushprop_lem3v2 = $true) & (axapp = $true) & (pushprop_lem2v2_gthm = $true) & ! [X263 : d_subst,X264 : d_subst] : (((d2subst @ X263) = (d2subst @ X264)) => (X263 = X264)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X265 : term] : ~! [X266 : subst > term > term] : ((X266 @ sh @ one) != (sub @ X265 @ (push @ one @ sh)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X267 : term] : ~! [X268 : subst > term > term] : ~! [X269 : subst,X270 : term] : ((sub @ X267 @ (push @ X270 @ X269)) = (X268 @ X269 @ X270)) => (! [X271 : term] : ((sub @ X271 @ id) = X271) => ! [X272 : term,X273 : subst > term > subst > $o,X274 : term > $o] : (~! [X275 : term] : (((X274 @ (sub @ X272 @ (push @ X275 @ id))) = $true) | ~($true = (X274 @ X275))) | ($true = (X274 @ (lam @ X272))) | ~! [X276 : subst > term > term] : (~! [X277 : term,X278 : subst,X279 : subst] : ((X276 @ (comp @ X279 @ X278) @ (sub @ X277 @ X278)) = (sub @ (X276 @ X279 @ X277) @ X278)) | ~! [X280 : term] : (~($true = (X273 @ id @ X280 @ id)) | ($true = (X273 @ id @ (X276 @ id @ X280) @ id))) | ($true = (X273 @ id @ (lam @ (X276 @ sh @ one)) @ id))) | ~! [X281 : term] : ((X274 @ X281) = (X273 @ id @ X281 @ id)))))) & ((pushprop_lem0_lthm = $true) <=> ! [X282 : subst,X283 : term,X284 : term > $o] : ~! [X285 : term > $o] : ~! [X286 : term] : ((X285 @ X286) = (X284 @ (sub @ X286 @ (push @ X283 @ X282))))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X287 : subst,X288 : term] : ((sub @ one @ (push @ X288 @ X287)) = X288) => (! [X289 : term,X290 : subst] : ((comp @ sh @ (push @ X289 @ X290)) = X290) => (! [X291 : term,X292 : term] : ((X291 = X292) | ((lam @ X291) != (lam @ X292))) => ! [X293 : term,X294 : subst > term > term,X295 : subst,X296 : subst > term > term] : (~! [X297 : term,X298 : subst,X299 : subst] : ((X294 @ (comp @ X298 @ X299) @ (sub @ X297 @ X299)) = (sub @ (X294 @ X298 @ X297) @ X299)) | ((lam @ (X296 @ sh @ one)) != (lam @ (X294 @ sh @ one))) | ((X296 @ X295 @ X293) = (X294 @ X295 @ X293)) | ~! [X300 : subst,X301 : subst,X302 : term] : ((sub @ (X296 @ X301 @ X302) @ X300) = (X296 @ (comp @ X301 @ X300) @ (sub @ X302 @ X300)))))))) & ((! [X303 : subst] : ((comp @ id @ X303) = X303) => (! [X304 : subst] : ((comp @ X304 @ id) = X304) => (! [X305 : subst] : ((comp @ X305 @ id) = X305) & ! [X306 : subst] : ((comp @ id @ X306) = X306)))) <=> (substmonoid_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoaslamnotvar_gthm = $true) & (! [X307 : term] : ((sub @ X307 @ id) = X307) <=> (termmset = $true)) & (axmap = $true) & ((axscons = $true) <=> ! [X308 : subst] : ((push @ (sub @ one @ X308) @ (comp @ sh @ X308)) = X308)) & ! [X309 : subst] : ? [X310 : d_subst] : ((d2subst @ X310) = X309) & (induction2lem_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X311 : subst > term > subst > $o,X312 : term,X313 : term] : (~! [X314 : term,X315 : term] : (~($true = (X311 @ id @ X315 @ id)) | ((X311 @ id @ (ap @ (sub @ X315 @ id) @ X314) @ id) = $true) | ~((X311 @ id @ X314 @ id) = $true)) | ((X311 @ id @ (ap @ X312 @ X313) @ id) = $true) | ~! [X316 : subst,X317 : subst,X318 : term,X319 : subst] : (~((X311 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319) @ X316) = $true) | ((X311 @ X317 @ X318 @ (comp @ X319 @ X316)) = $true)) | ~! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (~($true = (X311 @ X322 @ X321 @ (comp @ X323 @ X320))) | ($true = (X311 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320))) | ~($true = (X311 @ id @ X312 @ id)) | ~($true = (X311 @ id @ X313 @ id)))) & (hoasapnotvar = $true) & (hoasinduction_lem1_gthm = $true) & ~((var @ (d2term @ d_one)) = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (! [X324 : term] : ((sub @ X324 @ id) = X324) <=> (axvarid = $true)) & (! [X325 : term,X326 : term,X327 : term,X328 : term] : ((X325 = X327) | ((ap @ X325 @ X326) != (ap @ X327 @ X328))) <=> (apinj1 = $true)) & ((! [X329 : subst > term > subst > $o] : ~! [X330 : term > $o] : ~! [X331 : term] : ((X329 @ id @ X331 @ id) = (X330 @ X331)) => (! [X332 : term,X333 : term > $o] : (~! [X334 : term] : (($true = (X333 @ X334)) | ~((var @ X334) = $true)) | ~! [X335 : term] : (($true = (X333 @ (lam @ X335))) | ~! [X336 : term] : (~((X333 @ X336) = $true) | ($true = (X333 @ (sub @ X335 @ (push @ X336 @ id)))))) | ~! [X337 : term,X338 : term] : (~((X333 @ X338) = $true) | ~($true = (X333 @ X337)) | ((X333 @ (ap @ X337 @ X338)) = $true)) | ((X333 @ X332) = $true)) => (! [X339 : term] : ((sub @ X339 @ id) = X339) => (! [X340 : subst > term > subst > $o,X341 : term,X342 : term > $o] : (~! [X343 : subst > term > term] : (~! [X344 : term] : (((X340 @ id @ (X343 @ id @ X344) @ id) = $true) | ~($true = (X340 @ id @ X344 @ id))) | ((X340 @ id @ (lam @ (X343 @ sh @ one)) @ id) = $true) | ~! [X345 : subst,X346 : term,X347 : subst] : ((sub @ (X343 @ X347 @ X346) @ X345) = (X343 @ (comp @ X347 @ X345) @ (sub @ X346 @ X345)))) | ~! [X348 : term] : ((X340 @ id @ X348 @ id) = (X342 @ X348)) | ($true = (X342 @ (lam @ X341))) | ~! [X349 : term] : (~((X342 @ X349) = $true) | ((X342 @ (sub @ X341 @ (push @ X349 @ id))) = $true))) => ! [X350 : term,X351 : subst > term > subst > $o] : (~! [X352 : term,X353 : term] : (~($true = (X351 @ id @ X353 @ id)) | ~($true = (X351 @ id @ X352 @ id)) | ($true = (X351 @ id @ (ap @ (sub @ X352 @ id) @ X353) @ id))) | ((X351 @ id @ X350 @ id) = $true) | ~! [X354 : subst > term > term] : (~! [X355 : term,X356 : subst,X357 : subst] : ((sub @ (X354 @ X356 @ X355) @ X357) = (X354 @ (comp @ X356 @ X357) @ (sub @ X355 @ X357))) | ~! [X358 : term] : (~($true = (X351 @ id @ X358 @ id)) | ($true = (X351 @ id @ (X354 @ id @ X358) @ id))) | ((X351 @ id @ (lam @ (X354 @ sh @ one)) @ id) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X359 : term] : ((sub @ X359 @ id) = X359) => (! [X360 : subst > term > subst > $o,X361 : term] : (($true = (X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) | ~! [X362 : subst > term > term] : (~! [X363 : term,X364 : subst,X365 : subst] : ((X362 @ (comp @ X365 @ X364) @ (sub @ X363 @ X364)) = (sub @ (X362 @ X365 @ X363) @ X364)) | ~! [X366 : term] : (~($true = (X360 @ id @ X366 @ id)) | ($true = (X360 @ id @ (X362 @ id @ X366) @ id))) | ((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id) = $true)) | ~! [X367 : term] : (($true = (X360 @ id @ (sub @ X361 @ (push @ X367 @ id)) @ id)) | ~($true = (X360 @ id @ X367 @ id)))) => ! [X368 : term,X369 : subst > term > subst > $o] : (($true = (X369 @ id @ (lam @ X368) @ id)) | ~! [X370 : subst > term > term] : (~! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X370 @ X372 @ X371) @ X373) = (X370 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373))) | ~! [X374 : term] : (~((X369 @ id @ X374 @ id) = $true) | ($true = (X369 @ id @ (X370 @ id @ X374) @ id))) | ($true = (X369 @ id @ (lam @ (X370 @ sh @ one)) @ id))) | ~! [X375 : term] : (($true = (X369 @ id @ (sub @ X368 @ (push @ X375 @ id)) @ id)) | ~($true = (X369 @ id @ X375 @ id))))))) & (ulamvarind = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X376 : subst > term > subst > $o,X377 : term,X378 : term,X379 : term > $o] : (($true = (X379 @ (ap @ X377 @ X378))) | ~! [X380 : term] : ((X376 @ id @ X380 @ id) = (X379 @ X380)) | ~! [X381 : term,X382 : term] : (~($true = (X376 @ id @ X382 @ id)) | ~($true = (X376 @ id @ X381 @ id)) | ($true = (X376 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id))) | ~($true = (X379 @ X378)) | ~($true = (X379 @ X377)) | ~! [X383 : subst,X384 : subst,X385 : term,X386 : subst] : (((X376 @ X386 @ X385 @ (comp @ X383 @ X384)) = $true) | ~($true = (X376 @ (comp @ X386 @ X383) @ (sub @ X385 @ X383) @ X384))) | ~! [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (~($true = (X376 @ X389 @ X387 @ (comp @ X390 @ X388))) | ($true = (X376 @ (comp @ X389 @ X390) @ (sub @ X387 @ X390) @ X388))))) & ~(ulamvar1 = $true) & (hoasinduction_lem3_gthm = $true) & ! [X391 : d_term] : (d_one = X391) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & ! [X392 : d_term,X393 : d_term] : (((d2term @ X392) = (d2term @ X393)) => (X392 = X393)) & ((d2subst @ d_id) = id) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((! [X394 : subst] : ((comp @ id @ X394) = X394) & ! [X395 : subst] : ((comp @ X395 @ id) = X395)) <=> (substmonoid = $true)) & ((hoasapinj1 = $true) <=> ! [X396 : term,X397 : term,X398 : term,X399 : term] : ((X396 = X398) | ((ap @ (sub @ X396 @ id) @ X397) != (ap @ (sub @ X398 @ id) @ X399)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction = $true) <=> ! [X400 : term,X401 : subst > term > subst > $o] : (~! [X402 : term,X403 : term] : (~($true = (X401 @ id @ X402 @ id)) | ($true = (X401 @ id @ (ap @ (sub @ X402 @ id) @ X403) @ id)) | ~($true = (X401 @ id @ X403 @ id))) | ~! [X404 : term] : (~($true = (var @ (sub @ X404 @ id))) | ($true = (X401 @ id @ X404 @ id))) | ~! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X401 @ (comp @ X407 @ X408) @ (sub @ X405 @ X408) @ X406)) | ~((X401 @ X407 @ X405 @ (comp @ X408 @ X406)) = $true)) | ~! [X409 : term,X410 : subst,X411 : subst,X412 : subst] : (((X401 @ X412 @ X409 @ (comp @ X411 @ X410)) = $true) | ~($true = (X401 @ (comp @ X412 @ X411) @ (sub @ X409 @ X411) @ X410))) | ($true = (X401 @ id @ X400 @ id)) | ~! [X413 : subst > term > term] : (~! [X414 : term,X415 : subst,X416 : subst] : ((X413 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415)) = (sub @ (X413 @ X416 @ X414) @ X415)) | ~! [X417 : term] : (~($true = (X401 @ id @ X417 @ id)) | ((X401 @ id @ (X413 @ id @ X417) @ id) = $true)) | ($true = (X401 @ id @ (lam @ (X413 @ sh @ one)) @ id))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotap_lthm = $true) & (! [X418 : term] : ~! [X419 : subst > term > term] : ((sub @ X418 @ (push @ one @ sh)) != (X419 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (induction2_gthm = $true) & (pushprop_lthm = $true) & (axclos = $true) & ((! [X420 : subst > term > subst > $o] : ~! [X421 : term > $o] : ~! [X422 : term] : ((X420 @ id @ X422 @ id) = (X421 @ X422)) => (! [X423 : term > $o,X424 : term] : (~! [X425 : term] : (($true = (X423 @ (lam @ X425))) | ~! [X426 : term] : (~($true = (X423 @ X426)) | ((X423 @ (sub @ X425 @ (push @ X426 @ id))) = $true))) | ~! [X427 : term,X428 : term] : (~($true = (X423 @ X428)) | ~($true = (X423 @ X427)) | ($true = (X423 @ (ap @ X427 @ X428)))) | ($true = (X423 @ X424)) | ~! [X429 : term] : (~((var @ X429) = $true) | ((X423 @ X429) = $true))) => (! [X430 : term] : ((sub @ X430 @ id) = X430) => (! [X431 : subst > term > subst > $o,X432 : term,X433 : term > $o] : (~! [X434 : term] : (($true = (X433 @ (sub @ X432 @ (push @ X434 @ id)))) | ~($true = (X433 @ X434))) | ((X433 @ (lam @ X432)) = $true) | ~! [X435 : term] : ((X431 @ id @ X435 @ id) = (X433 @ X435)) | ~! [X436 : subst > term > term] : (((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id) = $true) | ~! [X437 : subst,X438 : term,X439 : subst] : ((sub @ (X436 @ X437 @ X438) @ X439) = (X436 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439))) | ~! [X440 : term] : (($true = (X431 @ id @ (X436 @ id @ X440) @ id)) | ~($true = (X431 @ id @ X440 @ id))))) => ! [X441 : term,X442 : subst > term > subst > $o] : (~! [X443 : term,X444 : term] : (~($true = (X442 @ id @ X443 @ id)) | ((X442 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id) = $true) | ~((X442 @ id @ X444 @ id) = $true)) | ((X442 @ id @ X441 @ id) = $true) | ~! [X445 : subst,X446 : subst,X447 : term,X448 : subst] : (~($true = (X442 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445) @ X448)) | ((X442 @ X446 @ X447 @ (comp @ X445 @ X448)) = $true)) | ~! [X449 : term] : (((X442 @ id @ X449 @ id) = $true) | ~($true = (var @ (sub @ X449 @ id)))) | ~! [X450 : subst,X451 : term,X452 : subst,X453 : subst] : (~($true = (X442 @ X452 @ X451 @ (comp @ X453 @ X450))) | ((X442 @ (comp @ X452 @ X453) @ (sub @ X451 @ X453) @ X450) = $true)) | ~! [X454 : subst > term > term] : (~! [X455 : term,X456 : subst,X457 : subst] : ((X454 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457)) = (sub @ (X454 @ X456 @ X455) @ X457)) | ~! [X458 : term] : (~($true = (X442 @ id @ X458 @ id)) | ((X442 @ id @ (X454 @ id @ X458) @ id) = $true)) | ($true = (X442 @ id @ (lam @ (X454 @ sh @ one)) @ id)))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X459 : term,X460 : subst > term > subst > $o] : (~! [X461 : term,X462 : subst > term > term] : (~! [X463 : subst,X464 : term,X465 : subst] : ((sub @ X461 @ (push @ (sub @ X464 @ X465) @ (comp @ X463 @ X465))) = (X462 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465))) | ~! [X466 : term] : (((X460 @ id @ (X462 @ id @ X466) @ id) = $true) | ~($true = (X460 @ id @ X466 @ id))) | ~! [X467 : subst,X468 : term,X469 : subst] : ((sub @ (X462 @ X467 @ X468) @ X469) = (sub @ (sub @ X461 @ (push @ X468 @ X467)) @ X469)) | ($true = (X460 @ id @ (lam @ (X462 @ sh @ one)) @ id))) | ~! [X470 : term] : (~($true = (X460 @ id @ X470 @ id)) | ($true = (X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id))) | ((X460 @ id @ (lam @ (sub @ X459 @ (push @ one @ sh))) @ id) = $true))) & ((hoasinduction_lthm = $true) <=> (! [X471 : term > $o,X472 : term] : (((X471 @ X472) = $true) | ~! [X473 : term] : (~! [X474 : term] : (~((X471 @ X474) = $true) | ($true = (X471 @ (sub @ X473 @ (push @ X474 @ id))))) | ($true = (X471 @ (lam @ X473)))) | ~! [X475 : term,X476 : term] : (((X471 @ (ap @ X476 @ X475)) = $true) | ~($true = (X471 @ X476)) | ~($true = (X471 @ X475))) | ~! [X477 : term] : (((X471 @ X477) = $true) | ~($true = (var @ X477)))) => (! [X478 : term,X479 : subst > term > subst > $o,X480 : term] : (((X479 @ id @ (ap @ X478 @ X480) @ id) = $true) | ~! [X481 : term,X482 : subst,X483 : subst,X484 : subst] : (($true = (X479 @ (comp @ X483 @ X484) @ (sub @ X481 @ X484) @ X482)) | ~((X479 @ X483 @ X481 @ (comp @ X484 @ X482)) = $true)) | ~($true = (X479 @ id @ X478 @ id)) | ~($true = (X479 @ id @ X480 @ id)) | ~! [X485 : subst,X486 : subst,X487 : term,X488 : subst] : (((X479 @ X486 @ X487 @ (comp @ X488 @ X485)) = $true) | ~($true = (X479 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X485))) | ~! [X489 : term,X490 : term] : (((X479 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id) = $true) | ~($true = (X479 @ id @ X490 @ id)) | ~($true = (X479 @ id @ X489 @ id)))) => (! [X491 : subst > term > subst > $o,X492 : term] : (~! [X493 : subst > term > term] : (~! [X494 : term] : (((X491 @ id @ (X493 @ id @ X494) @ id) = $true) | ~($true = (X491 @ id @ X494 @ id))) | ~! [X495 : subst,X496 : term,X497 : subst] : ((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497)) = (sub @ (X493 @ X495 @ X496) @ X497)) | ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) = $true)) | ((X491 @ id @ (lam @ X492) @ id) = $true) | ~! [X498 : term] : (((X491 @ id @ (sub @ X492 @ (push @ X498 @ id)) @ id) = $true) | ~($true = (X491 @ id @ X498 @ id))) | ~! [X499 : subst,X500 : term,X501 : subst,X502 : subst] : (~((X491 @ X501 @ X500 @ (comp @ X502 @ X499)) = $true) | ((X491 @ (comp @ X501 @ X502) @ (sub @ X500 @ X502) @ X499) = $true)) | ~! [X503 : subst,X504 : term,X505 : subst,X506 : subst] : (~($true = (X491 @ (comp @ X503 @ X506) @ (sub @ X504 @ X506) @ X505)) | ((X491 @ X503 @ X504 @ (comp @ X506 @ X505)) = $true))) => ! [X507 : subst > term > subst > $o,X508 : term] : (($true = (X507 @ id @ X508 @ id)) | ~! [X509 : subst,X510 : subst,X511 : subst,X512 : term] : (($true = (X507 @ X511 @ X512 @ (comp @ X510 @ X509))) | ~($true = (X507 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510) @ X509))) | ~! [X513 : subst,X514 : subst,X515 : subst,X516 : term] : (($true = (X507 @ (comp @ X513 @ X515) @ (sub @ X516 @ X515) @ X514)) | ~((X507 @ X513 @ X516 @ (comp @ X515 @ X514)) = $true)) | ~! [X517 : term] : (~((var @ (sub @ X517 @ id)) = $true) | ($true = (X507 @ id @ X517 @ id))) | ~! [X518 : term,X519 : term] : (~((X507 @ id @ X519 @ id) = $true) | ((X507 @ id @ (ap @ (sub @ X519 @ id) @ X518) @ id) = $true) | ~((X507 @ id @ X518 @ id) = $true)) | ~! [X520 : subst > term > term] : (~! [X521 : term] : (((X507 @ id @ (X520 @ id @ X521) @ id) = $true) | ~($true = (X507 @ id @ X521 @ id))) | ~! [X522 : subst,X523 : term,X524 : subst] : ((X520 @ (comp @ X522 @ X524) @ (sub @ X523 @ X524)) = (sub @ (X520 @ X522 @ X523) @ X524)) | ($true = (X507 @ id @ (lam @ (X520 @ sh @ one)) @ id)))))))) & (hoasapnotvar_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X525 : term,X526 : subst > term > term,X527 : term] : (~! [X528 : subst,X529 : term,X530 : subst] : ((sub @ (X526 @ X528 @ X529) @ X530) = (X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) | ((ap @ (sub @ X527 @ id) @ X525) != (lam @ (X526 @ sh @ one))))) & ((hoasinduction_lem3a = $true) <=> ! [X531 : subst > term > subst > $o,X532 : term] : (~! [X533 : subst > term > term] : (((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id) = $true) | ~! [X534 : term,X535 : subst,X536 : subst] : ((sub @ (X533 @ X536 @ X534) @ X535) = (X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535))) | ~! [X537 : term] : (($true = (X531 @ id @ (X533 @ id @ X537) @ id)) | ~($true = (X531 @ id @ X537 @ id)))) | ((X531 @ id @ (lam @ X532) @ id) = $true) | ~! [X538 : term] : (($true = (X531 @ id @ (sub @ X532 @ (push @ X538 @ id)) @ id)) | ~((X531 @ id @ X538 @ id) = $true)))) & ((d2subst @ d_id) = sh) & ! [X539 : term] : ? [X540 : d_term] : ((d2term @ X540) = X539) & (pushprop_lem1_gthm = $true) & ((! [X541 : subst,X542 : term] : ((sub @ one @ (push @ X542 @ X541)) = X542) => (! [X543 : subst,X544 : term] : ((comp @ sh @ (push @ X544 @ X543)) = X543) => ! [X545 : term,X546 : term > $o,X547 : term > $o,X548 : subst,X549 : term] : (~((X546 @ X545) = $true) | ((X547 @ (sub @ X545 @ (push @ X549 @ X548))) = $true)))) <=> (pushprop_lem1_lthm = $true))),
% 1.70/1.51 inference(fool_elimination,[status(thm)],[f7])).
% 1.70/1.51 thf(f7,plain,(
% 1.70/1.51 hoasinduction_lem2_gthm & (! [X0 : term] : ~! [X1 : subst > term > term] : ~! [X2 : term,X3 : subst] : ((sub @ X0 @ (push @ X2 @ X3)) = (X1 @ X3 @ X2)) <=> hoasinduction_lem3v2_f) & apnotvar & hoaslamnotvar_lthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X4 : subst > term > subst > $o,X5 : term] : (~! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (~(X4 @ X8 @ X6 @ (comp @ X9 @ X7)) | (X4 @ (comp @ X8 @ X9) @ (sub @ X6 @ X9) @ X7)) | ~! [X10 : subst > term > term] : (~! [X11 : term] : (~(X4 @ id @ X11 @ id) | (X4 @ id @ (X10 @ id @ X11) @ id)) | (X4 @ id @ (lam @ (X10 @ sh @ one)) @ id) | ~! [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) = (sub @ (X10 @ X14 @ X12) @ X13))) | (X4 @ id @ (lam @ X5) @ id) | ~! [X15 : term,X16 : subst,X17 : subst,X18 : subst] : (~(X4 @ (comp @ X17 @ X16) @ (sub @ X15 @ X16) @ X18) | (X4 @ X17 @ X15 @ (comp @ X16 @ X18))) | ~! [X19 : term] : ((X4 @ id @ (sub @ X5 @ (push @ X19 @ id)) @ id) | ~(X4 @ id @ X19 @ id))) <=> hoasinduction_lem3) & (termmset_lthm <=> (! [X20 : term] : ((sub @ X20 @ id) = X20) => ! [X21 : term] : ((sub @ X21 @ id) = X21))) & (axidl <=> ! [X22 : subst] : ((comp @ id @ X22) = X22)) & (! [X23 : term] : ~! [X24 : subst > term > term] : ~! [X25 : subst,X26 : term] : ((X24 @ X25 @ X26) = (sub @ X23 @ (push @ X26 @ X25))) <=> hoasinduction_lem3v2_f_lthm) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X27 : d_subst] : (d_id = X27) & hoasapnotvar_lthm & (hoasapinj2_lthm <=> (! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ X28 @ X30) != (ap @ X29 @ X31)) | (X30 = X31)) => ! [X32 : term,X33 : term,X34 : term,X35 : term] : (((ap @ (sub @ X33 @ id) @ X34) != (ap @ (sub @ X32 @ id) @ X35)) | (X34 = X35)))) & (hoaslaminj <=> ! [X36 : subst > term > term,X37 : subst > term > term,X38 : subst,X39 : term] : (((lam @ (X36 @ sh @ one)) != (lam @ (X37 @ sh @ one))) | ~! [X40 : subst,X41 : term,X42 : subst] : ((sub @ (X36 @ X42 @ X41) @ X40) = (X36 @ (comp @ X42 @ X40) @ (sub @ X41 @ X40))) | ((X36 @ X38 @ X39) = (X37 @ X38 @ X39)) | ~! [X43 : subst,X44 : subst,X45 : term] : ((X37 @ (comp @ X44 @ X43) @ (sub @ X45 @ X43)) = (sub @ (X37 @ X44 @ X45) @ X43)))) & ~lamnotap & (induction2lem_lthm <=> (! [X46 : subst,X47 : term] : ((sub @ one @ (push @ X47 @ X46)) = X47) => (! [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) = X48) => (! [X50 : subst] : ((comp @ X50 @ id) = X50) => (! [X51 : term,X52 : term > $o] : ((X52 @ X51) | ~! [X53 : term] : (~(X52 @ X53) | (X52 @ (lam @ X53))) | ~! [X54 : term] : (~(var @ X54) | (X52 @ X54)) | ~! [X55 : term,X56 : term] : (~(X52 @ X55) | ~(X52 @ X56) | (X52 @ (ap @ X56 @ X55)))) => ! [X57 : subst,X58 : term,X59 : term > $o] : ((X59 @ (sub @ X58 @ X57)) | ~! [X60 : term] : ((X59 @ (lam @ X60)) | ~! [X61 : term] : ((X59 @ (sub @ X60 @ (push @ X61 @ id))) | ~(X59 @ X61))) | ~! [X62 : term,X63 : term] : ((X59 @ (ap @ X62 @ X63)) | ~(X59 @ X62) | ~(X59 @ X63)) | ~! [X64 : term] : (~(var @ X64) | (X59 @ (sub @ X64 @ X57))))))))) & (hoasinduction_lem0_lthm <=> ! [X65 : subst > term > subst > $o] : ~! [X66 : term > $o] : ~! [X67 : term] : ((X65 @ id @ X67 @ id) = (X66 @ X67))) & (hoasapinj1_lthm <=> (! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X70 @ X72) != (ap @ X69 @ X71)) | (X69 = X70)) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X76) != (ap @ (sub @ X75 @ id) @ X74)))))) & hoasinduction_lem3a_gthm & pushprop_lem1v2_gthm & (! [X77 : term,X78 : subst,X79 : term > $o,X80 : term > $o,X81 : term] : (~(X79 @ X81) | (X80 @ (sub @ X81 @ (push @ X77 @ X78)))) <=> pushprop_lem1) & pushprop_lem2v2_lthm & hoasinduction_lem1 & ((! [X82 : term,X83 : subst] : ((sub @ one @ (push @ X82 @ X83)) = X82) => ! [X84 : subst,X85 : term > $o,X86 : term,X87 : term > $o] : (~! [X88 : term] : ((X87 @ (sub @ X88 @ (push @ X86 @ X84))) = (X85 @ X88)) | (X85 @ one) | ~(X87 @ X86))) <=> pushprop_lem1v2_lthm) & (! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ X92 @ X89) != (ap @ X90 @ X91)) | (X89 = X91)) <=> apinj2) & axabs & (one = (d2term @ d_one)) & pushprop_lthm_orig & (induction2_lthm <=> (! [X93 : term] : ((sub @ X93 @ id) = X93) => (! [X94 : term,X95 : subst,X96 : term > $o] : (~! [X97 : term] : (~! [X98 : term] : ((X96 @ (sub @ X97 @ (push @ X98 @ id))) | ~(X96 @ X98)) | (X96 @ (lam @ X97))) | (X96 @ (sub @ X94 @ X95)) | ~! [X99 : term,X100 : term] : ((X96 @ (ap @ X99 @ X100)) | ~(X96 @ X99) | ~(X96 @ X100)) | ~! [X101 : term] : (~(var @ X101) | (X96 @ (sub @ X101 @ X95)))) => ! [X102 : term,X103 : term > $o] : ((X103 @ X102) | ~! [X104 : term] : ((X103 @ (lam @ X104)) | ~! [X105 : term] : (~(X103 @ X105) | (X103 @ (sub @ X104 @ (push @ X105 @ id))))) | ~! [X106 : term] : ((X103 @ X106) | ~(var @ X106)) | ~! [X107 : term,X108 : term] : (~(X103 @ X108) | ~(X103 @ X107) | (X103 @ (ap @ X108 @ X107))))))) & pushprop_gthm & (! [X109 : term,X110 : term] : ((X109 = X110) | ((lam @ X110) != (lam @ X109))) <=> laminj) & (! [X111 : subst > term > subst > $o,X112 : term] : (~! [X113 : term] : (~(X111 @ id @ X113 @ id) | (X111 @ id @ (sub @ X112 @ (push @ X113 @ id)) @ id)) | ~! [X114 : subst > term > term] : (~! [X115 : subst,X116 : subst,X117 : term] : ((sub @ (X114 @ X115 @ X117) @ X116) = (X114 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116))) | (X111 @ id @ (lam @ (X114 @ sh @ one)) @ id) | ~! [X118 : term] : (~(X111 @ id @ X118 @ id) | (X111 @ id @ (X114 @ id @ X118) @ id))) | (X111 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & (axidr <=> ! [X119 : subst] : ((comp @ X119 @ id) = X119)) & (! [X120 : subst,X121 : term] : ((sub @ one @ (push @ X121 @ X120)) = X121) <=> axvarcons) & (! [X122 : term,X123 : subst > term > subst > $o] : (~! [X124 : subst > term > term] : (~! [X125 : subst,X126 : subst,X127 : term] : ((X124 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X124 @ X125 @ X127) @ X126)) | ~! [X128 : term] : ((X123 @ id @ (X124 @ id @ X128) @ id) | ~(X123 @ id @ X128 @ id)) | (X123 @ id @ (lam @ (X124 @ sh @ one)) @ id)) | ~! [X129 : term,X130 : term] : (~(X123 @ id @ X130 @ id) | ~(X123 @ id @ X129 @ id) | (X123 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) | (X123 @ id @ X122 @ id)) <=> hoasinduction_no_psi_cond) & ((! [X131 : term] : ((sub @ X131 @ id) = X131) => ! [X132 : subst > term > subst > $o,X133 : term,X134 : term > $o] : (~! [X135 : subst > term > term] : ((X132 @ id @ (lam @ (X135 @ sh @ one)) @ id) | ~! [X136 : subst,X137 : subst,X138 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X138 @ X137)) = (sub @ (X135 @ X136 @ X138) @ X137)) | ~! [X139 : term] : (~(X132 @ id @ X139 @ id) | (X132 @ id @ (X135 @ id @ X139) @ id))) | ~! [X140 : term] : ((X132 @ id @ X140 @ id) = (X134 @ X140)) | ~! [X141 : subst,X142 : subst,X143 : subst,X144 : term] : ((X132 @ X143 @ X144 @ (comp @ X141 @ X142)) | ~(X132 @ (comp @ X143 @ X141) @ (sub @ X144 @ X141) @ X142)) | ~! [X145 : subst,X146 : term,X147 : subst,X148 : subst] : ((X132 @ (comp @ X147 @ X145) @ (sub @ X146 @ X145) @ X148) | ~(X132 @ X147 @ X146 @ (comp @ X145 @ X148))) | (X134 @ (lam @ X133)) | ~! [X149 : term] : (~(X134 @ X149) | (X134 @ (sub @ X133 @ (push @ X149 @ id)))))) <=> hoasinduction_lem3v2_lthm) & hoaslaminj_gthm & (hoasinduction_p_and_p_prime = (^[X150 : subst > term > subst > $o, X151 : term > $o] : (! [X152 : term] : ((X151 @ X152) = (X150 @ id @ X152 @ id))))) & (! [X153 : term,X154 : term > $o,X155 : term > $o,X156 : subst] : (~(X155 @ X153) | (X154 @ one) | ~! [X157 : term] : ((X155 @ (sub @ X157 @ (push @ X153 @ X156))) = (X154 @ X157))) <=> pushprop_lem1v2) & ((! [X158 : term] : ((sub @ X158 @ id) = X158) => (! [X159 : subst > term > subst > $o,X160 : term] : (~! [X161 : term] : ((X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id) | ~(X159 @ id @ X161 @ id)) | ~! [X162 : subst > term > term] : (~! [X163 : term] : ((X159 @ id @ (X162 @ id @ X163) @ id) | ~(X159 @ id @ X163 @ id)) | ~! [X164 : subst,X165 : subst,X166 : term] : ((sub @ (X162 @ X164 @ X166) @ X165) = (X162 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) | (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) | (X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) => ! [X167 : subst > term > subst > $o,X168 : term] : (~! [X169 : term] : ((X167 @ id @ (sub @ X168 @ (push @ X169 @ id)) @ id) | ~(X167 @ id @ X169 @ id)) | ~! [X170 : subst > term > term] : (~! [X171 : term,X172 : subst,X173 : subst] : ((sub @ (X170 @ X172 @ X171) @ X173) = (X170 @ (comp @ X172 @ X173) @ (sub @ X171 @ X173))) | ~! [X174 : term] : ((X167 @ id @ (X170 @ id @ X174) @ id) | ~(X167 @ id @ X174 @ id)) | (X167 @ id @ (lam @ (X170 @ sh @ one)) @ id)) | ~! [X175 : subst,X176 : subst,X177 : subst,X178 : term] : (~(X167 @ (comp @ X176 @ X177) @ (sub @ X178 @ X177) @ X175) | (X167 @ X176 @ X178 @ (comp @ X177 @ X175))) | ~! [X179 : subst,X180 : subst,X181 : term,X182 : subst] : ((X167 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182) @ X179) | ~(X167 @ X180 @ X181 @ (comp @ X182 @ X179))) | (X167 @ id @ (lam @ X168) @ id)))) <=> hoasinduction_lem3_lthm) & substmonoid_gthm & (axshiftcons <=> ! [X183 : term,X184 : subst] : ((comp @ sh @ (push @ X183 @ X184)) = X184)) & hoasinduction_lem1v2_gthm & (hoasapinj2 <=> ! [X185 : term,X186 : term,X187 : term,X188 : term] : (((ap @ (sub @ X187 @ id) @ X188) != (ap @ (sub @ X186 @ id) @ X185)) | (X185 = X188))) & (! [X189 : term,X190 : term > $o,X191 : subst] : ~! [X192 : term > $o] : ~! [X193 : term] : ((X192 @ X193) = (X190 @ (sub @ X193 @ (push @ X189 @ X191)))) <=> pushprop_lem0) & hoasinduction_lem3b_gthm & (! [X194 : term > $o,X195 : term] : (~! [X196 : term,X197 : term] : (~(X194 @ X197) | (X194 @ (ap @ X197 @ X196)) | ~(X194 @ X196)) | ~! [X198 : term] : (~! [X199 : term] : ((X194 @ (sub @ X198 @ (push @ X199 @ id))) | ~(X194 @ X199)) | (X194 @ (lam @ X198))) | (X194 @ X195) | ~! [X200 : term] : (~(var @ X200) | (X194 @ X200))) <=> induction2) & ((^[X201 : term, X202 : subst, X203 : term > $o, X204 : term > $o] : (! [X205 : term] : ((X203 @ (sub @ X205 @ (push @ X201 @ X202))) = (X204 @ X205)))) = pushprop_p_and_p_prime) & (! [X206 : term > $o,X207 : term,X208 : subst > term > subst > $o] : ((X206 @ (lam @ X207)) | ~! [X209 : term,X210 : subst,X211 : subst,X212 : subst] : ((X208 @ (comp @ X210 @ X212) @ (sub @ X209 @ X212) @ X211) | ~(X208 @ X210 @ X209 @ (comp @ X212 @ X211))) | ~! [X213 : term] : ((X206 @ (sub @ X207 @ (push @ X213 @ id))) | ~(X206 @ X213)) | ~! [X214 : subst,X215 : subst,X216 : subst,X217 : term] : (~(X208 @ (comp @ X214 @ X216) @ (sub @ X217 @ X216) @ X215) | (X208 @ X214 @ X217 @ (comp @ X216 @ X215))) | ~! [X218 : term] : ((X206 @ X218) = (X208 @ id @ X218 @ id)) | ~! [X219 : subst > term > term] : (~! [X220 : term] : (~(X208 @ id @ X220 @ id) | (X208 @ id @ (X219 @ id @ X220) @ id)) | (X208 @ id @ (lam @ (X219 @ sh @ one)) @ id) | ~! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))))) <=> hoasinduction_lem3v2) & pushprop & (induction <=> ! [X224 : term,X225 : term > $o] : (~! [X226 : term] : ((X225 @ X226) | ~(var @ X226)) | ~! [X227 : term,X228 : term] : (~(X225 @ X227) | ~(X225 @ X228) | (X225 @ (ap @ X227 @ X228))) | ~! [X229 : term] : (~(X225 @ X229) | (X225 @ (lam @ X229))) | (X225 @ X224))) & (! [X230 : term,X231 : subst > term > subst > $o] : (~! [X232 : term] : (~(X231 @ id @ X232 @ id) | (X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) | ~! [X233 : subst > term > term] : (~! [X234 : subst,X235 : term,X236 : subst] : ((sub @ (X233 @ X236 @ X235) @ X234) = (X233 @ (comp @ X236 @ X234) @ (sub @ X235 @ X234))) | (X231 @ id @ (lam @ (X233 @ sh @ one)) @ id) | ~! [X237 : term] : (~(X231 @ id @ X237 @ id) | (X231 @ id @ (X233 @ id @ X237) @ id))) | (X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (! [X238 : term,X239 : term] : (((sub @ X239 @ sh) != (sub @ X238 @ sh)) | (X238 = X239)) <=> shinj) & pushprop_lem2v2 & axassoc & termmset_gthm & axvarshift & (! [X240 : subst > term > subst > $o] : ~! [X241 : term > $o] : ~! [X242 : term] : ((X241 @ X242) = (X240 @ id @ X242 @ id)) <=> hoasinduction_lem0) & pushprop_lem0_gthm & (! [X243 : term,X244 : subst > term > subst > $o,X245 : term > $o] : ((X245 @ (lam @ X243)) | ~! [X246 : term] : ((X245 @ X246) = (X244 @ id @ X246 @ id)) | ~! [X247 : term] : (~(X245 @ X247) | (X245 @ (sub @ X243 @ (push @ X247 @ id)))) | ~! [X248 : subst > term > term] : (~! [X249 : term] : (~(X244 @ id @ X249 @ id) | (X244 @ id @ (X248 @ id @ X249) @ id)) | (X244 @ id @ (lam @ (X248 @ sh @ one)) @ id) | ~! [X250 : subst,X251 : term,X252 : subst] : ((sub @ (X248 @ X250 @ X251) @ X252) = (X248 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252))))) <=> hoasinduction_lem3v2a) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((^[X253 : subst, X254 : subst > term > term] : (d2term @ d_one)) = hoaslam) & pushprop_lem3v2_lthm & (! [X255 : subst,X256 : term,X257 : term > $o] : (~! [X258 : term,X259 : term] : (~(X257 @ X259) | ~(X257 @ X258) | (X257 @ (ap @ X259 @ X258))) | ~! [X260 : term] : ((X257 @ (lam @ X260)) | ~! [X261 : term] : ((X257 @ (sub @ X260 @ (push @ X261 @ id))) | ~(X257 @ X261))) | (X257 @ (sub @ X256 @ X255)) | ~! [X262 : term] : ((X257 @ (sub @ X262 @ X255)) | ~(var @ X262))) <=> induction2lem) & pushprop_lem3v2 & axapp & pushprop_lem2v2_gthm & ! [X263 : d_subst,X264 : d_subst] : (((d2subst @ X263) = (d2subst @ X264)) => (X263 = X264)) & (hoasinduction_lem3b_lthm <=> ! [X265 : term] : ~! [X266 : subst > term > term] : ((X266 @ sh @ one) != (sub @ X265 @ (push @ one @ sh)))) & hoasinduction_lem1v2 & hoasinduction_lem2v2_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X267 : term] : ~! [X268 : subst > term > term] : ~! [X269 : subst,X270 : term] : ((sub @ X267 @ (push @ X270 @ X269)) = (X268 @ X269 @ X270)) => (! [X271 : term] : ((sub @ X271 @ id) = X271) => ! [X272 : term,X273 : subst > term > subst > $o,X274 : term > $o] : (~! [X275 : term] : ((X274 @ (sub @ X272 @ (push @ X275 @ id))) | ~(X274 @ X275)) | (X274 @ (lam @ X272)) | ~! [X276 : subst > term > term] : (~! [X277 : term,X278 : subst,X279 : subst] : ((X276 @ (comp @ X279 @ X278) @ (sub @ X277 @ X278)) = (sub @ (X276 @ X279 @ X277) @ X278)) | ~! [X280 : term] : (~(X273 @ id @ X280 @ id) | (X273 @ id @ (X276 @ id @ X280) @ id)) | (X273 @ id @ (lam @ (X276 @ sh @ one)) @ id)) | ~! [X281 : term] : ((X274 @ X281) = (X273 @ id @ X281 @ id)))))) & (pushprop_lem0_lthm <=> ! [X282 : subst,X283 : term,X284 : term > $o] : ~! [X285 : term > $o] : ~! [X286 : term] : ((X285 @ X286) = (X284 @ (sub @ X286 @ (push @ X283 @ X282))))) & hoasinduction_gthm & hoaslamnotvar & (hoaslaminj_lthm <=> (! [X287 : subst,X288 : term] : ((sub @ one @ (push @ X288 @ X287)) = X288) => (! [X289 : term,X290 : subst] : ((comp @ sh @ (push @ X289 @ X290)) = X290) => (! [X291 : term,X292 : term] : ((X291 = X292) | ((lam @ X291) != (lam @ X292))) => ! [X293 : term,X294 : subst > term > term,X295 : subst,X296 : subst > term > term] : (~! [X297 : term,X298 : subst,X299 : subst] : ((X294 @ (comp @ X298 @ X299) @ (sub @ X297 @ X299)) = (sub @ (X294 @ X298 @ X297) @ X299)) | ((lam @ (X296 @ sh @ one)) != (lam @ (X294 @ sh @ one))) | ((X296 @ X295 @ X293) = (X294 @ X295 @ X293)) | ~! [X300 : subst,X301 : subst,X302 : term] : ((sub @ (X296 @ X301 @ X302) @ X300) = (X296 @ (comp @ X301 @ X300) @ (sub @ X302 @ X300)))))))) & ((! [X303 : subst] : ((comp @ id @ X303) = X303) => (! [X304 : subst] : ((comp @ X304 @ id) = X304) => (! [X305 : subst] : ((comp @ X305 @ id) = X305) & ! [X306 : subst] : ((comp @ id @ X306) = X306)))) <=> substmonoid_lthm) & hoaslamnotap_gthm & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & hoaslamnotvar_gthm & (! [X307 : term] : ((sub @ X307 @ id) = X307) <=> termmset) & axmap & (axscons <=> ! [X308 : subst] : ((push @ (sub @ one @ X308) @ (comp @ sh @ X308)) = X308)) & ! [X309 : subst] : ? [X310 : d_subst] : ((d2subst @ X310) = X309) & induction2lem_gthm & hoasapinj1_gthm & (hoasinduction_lem2 <=> ! [X311 : subst > term > subst > $o,X312 : term,X313 : term] : (~! [X314 : term,X315 : term] : (~(X311 @ id @ X315 @ id) | (X311 @ id @ (ap @ (sub @ X315 @ id) @ X314) @ id) | ~(X311 @ id @ X314 @ id)) | (X311 @ id @ (ap @ X312 @ X313) @ id) | ~! [X316 : subst,X317 : subst,X318 : term,X319 : subst] : (~(X311 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319) @ X316) | (X311 @ X317 @ X318 @ (comp @ X319 @ X316))) | ~! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (~(X311 @ X322 @ X321 @ (comp @ X323 @ X320)) | (X311 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ~(X311 @ id @ X312 @ id) | ~(X311 @ id @ X313 @ id))) & hoasapnotvar & hoasinduction_lem1_gthm & ~(var @ (d2term @ d_one)) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X324 : term] : ((sub @ X324 @ id) = X324) <=> axvarid) & (! [X325 : term,X326 : term,X327 : term,X328 : term] : ((X325 = X327) | ((ap @ X325 @ X326) != (ap @ X327 @ X328))) <=> apinj1) & ((! [X329 : subst > term > subst > $o] : ~! [X330 : term > $o] : ~! [X331 : term] : ((X329 @ id @ X331 @ id) = (X330 @ X331)) => (! [X332 : term,X333 : term > $o] : (~! [X334 : term] : ((X333 @ X334) | ~(var @ X334)) | ~! [X335 : term] : ((X333 @ (lam @ X335)) | ~! [X336 : term] : (~(X333 @ X336) | (X333 @ (sub @ X335 @ (push @ X336 @ id))))) | ~! [X337 : term,X338 : term] : (~(X333 @ X338) | ~(X333 @ X337) | (X333 @ (ap @ X337 @ X338))) | (X333 @ X332)) => (! [X339 : term] : ((sub @ X339 @ id) = X339) => (! [X340 : subst > term > subst > $o,X341 : term,X342 : term > $o] : (~! [X343 : subst > term > term] : (~! [X344 : term] : ((X340 @ id @ (X343 @ id @ X344) @ id) | ~(X340 @ id @ X344 @ id)) | (X340 @ id @ (lam @ (X343 @ sh @ one)) @ id) | ~! [X345 : subst,X346 : term,X347 : subst] : ((sub @ (X343 @ X347 @ X346) @ X345) = (X343 @ (comp @ X347 @ X345) @ (sub @ X346 @ X345)))) | ~! [X348 : term] : ((X340 @ id @ X348 @ id) = (X342 @ X348)) | (X342 @ (lam @ X341)) | ~! [X349 : term] : (~(X342 @ X349) | (X342 @ (sub @ X341 @ (push @ X349 @ id))))) => ! [X350 : term,X351 : subst > term > subst > $o] : (~! [X352 : term,X353 : term] : (~(X351 @ id @ X353 @ id) | ~(X351 @ id @ X352 @ id) | (X351 @ id @ (ap @ (sub @ X352 @ id) @ X353) @ id)) | (X351 @ id @ X350 @ id) | ~! [X354 : subst > term > term] : (~! [X355 : term,X356 : subst,X357 : subst] : ((sub @ (X354 @ X356 @ X355) @ X357) = (X354 @ (comp @ X356 @ X357) @ (sub @ X355 @ X357))) | ~! [X358 : term] : (~(X351 @ id @ X358 @ id) | (X351 @ id @ (X354 @ id @ X358) @ id)) | (X351 @ id @ (lam @ (X354 @ sh @ one)) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (hoasinduction_lem3a_lthm <=> (! [X359 : term] : ((sub @ X359 @ id) = X359) => (! [X360 : subst > term > subst > $o,X361 : term] : ((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id) | ~! [X362 : subst > term > term] : (~! [X363 : term,X364 : subst,X365 : subst] : ((X362 @ (comp @ X365 @ X364) @ (sub @ X363 @ X364)) = (sub @ (X362 @ X365 @ X363) @ X364)) | ~! [X366 : term] : (~(X360 @ id @ X366 @ id) | (X360 @ id @ (X362 @ id @ X366) @ id)) | (X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | ~! [X367 : term] : ((X360 @ id @ (sub @ X361 @ (push @ X367 @ id)) @ id) | ~(X360 @ id @ X367 @ id))) => ! [X368 : term,X369 : subst > term > subst > $o] : ((X369 @ id @ (lam @ X368) @ id) | ~! [X370 : subst > term > term] : (~! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X370 @ X372 @ X371) @ X373) = (X370 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373))) | ~! [X374 : term] : (~(X369 @ id @ X374 @ id) | (X369 @ id @ (X370 @ id @ X374) @ id)) | (X369 @ id @ (lam @ (X370 @ sh @ one)) @ id)) | ~! [X375 : term] : ((X369 @ id @ (sub @ X368 @ (push @ X375 @ id)) @ id) | ~(X369 @ id @ X375 @ id)))))) & ulamvarind & hoasinduction_lem2_lthm & (hoasinduction_lem2v2 <=> ! [X376 : subst > term > subst > $o,X377 : term,X378 : term,X379 : term > $o] : ((X379 @ (ap @ X377 @ X378)) | ~! [X380 : term] : ((X376 @ id @ X380 @ id) = (X379 @ X380)) | ~! [X381 : term,X382 : term] : (~(X376 @ id @ X382 @ id) | ~(X376 @ id @ X381 @ id) | (X376 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id)) | ~(X379 @ X378) | ~(X379 @ X377) | ~! [X383 : subst,X384 : subst,X385 : term,X386 : subst] : ((X376 @ X386 @ X385 @ (comp @ X383 @ X384)) | ~(X376 @ (comp @ X386 @ X383) @ (sub @ X385 @ X383) @ X384)) | ~! [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (~(X376 @ X389 @ X387 @ (comp @ X390 @ X388)) | (X376 @ (comp @ X389 @ X390) @ (sub @ X387 @ X390) @ X388)))) & ~ulamvar1 & hoasinduction_lem3_gthm & ! [X391 : d_term] : (d_one = X391) & ulamvarsh & hoasapinj2_gthm & ! [X392 : d_term,X393 : d_term] : (((d2term @ X392) = (d2term @ X393)) => (X392 = X393)) & ((d2subst @ d_id) = id) & lamnotvar & hoasinduction_lem3v2_gthm & hoasinduction_lem1_lthm & ((! [X394 : subst] : ((comp @ id @ X394) = X394) & ! [X395 : subst] : ((comp @ X395 @ id) = X395)) <=> substmonoid) & (hoasapinj1 <=> ! [X396 : term,X397 : term,X398 : term,X399 : term] : ((X396 = X398) | ((ap @ (sub @ X396 @ id) @ X397) != (ap @ (sub @ X398 @ id) @ X399)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction <=> ! [X400 : term,X401 : subst > term > subst > $o] : (~! [X402 : term,X403 : term] : (~(X401 @ id @ X402 @ id) | (X401 @ id @ (ap @ (sub @ X402 @ id) @ X403) @ id) | ~(X401 @ id @ X403 @ id)) | ~! [X404 : term] : (~(var @ (sub @ X404 @ id)) | (X401 @ id @ X404 @ id)) | ~! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : ((X401 @ (comp @ X407 @ X408) @ (sub @ X405 @ X408) @ X406) | ~(X401 @ X407 @ X405 @ (comp @ X408 @ X406))) | ~! [X409 : term,X410 : subst,X411 : subst,X412 : subst] : ((X401 @ X412 @ X409 @ (comp @ X411 @ X410)) | ~(X401 @ (comp @ X412 @ X411) @ (sub @ X409 @ X411) @ X410)) | (X401 @ id @ X400 @ id) | ~! [X413 : subst > term > term] : (~! [X414 : term,X415 : subst,X416 : subst] : ((X413 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415)) = (sub @ (X413 @ X416 @ X414) @ X415)) | ~! [X417 : term] : (~(X401 @ id @ X417 @ id) | (X401 @ id @ (X413 @ id @ X417) @ id)) | (X401 @ id @ (lam @ (X413 @ sh @ one)) @ id)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & hoaslamnotap_lthm & (! [X418 : term] : ~! [X419 : subst > term > term] : ((sub @ X418 @ (push @ one @ sh)) != (X419 @ sh @ one)) <=> hoasinduction_lem3b) & induction2_gthm & pushprop_lthm & axclos & ((! [X420 : subst > term > subst > $o] : ~! [X421 : term > $o] : ~! [X422 : term] : ((X420 @ id @ X422 @ id) = (X421 @ X422)) => (! [X423 : term > $o,X424 : term] : (~! [X425 : term] : ((X423 @ (lam @ X425)) | ~! [X426 : term] : (~(X423 @ X426) | (X423 @ (sub @ X425 @ (push @ X426 @ id))))) | ~! [X427 : term,X428 : term] : (~(X423 @ X428) | ~(X423 @ X427) | (X423 @ (ap @ X427 @ X428))) | (X423 @ X424) | ~! [X429 : term] : (~(var @ X429) | (X423 @ X429))) => (! [X430 : term] : ((sub @ X430 @ id) = X430) => (! [X431 : subst > term > subst > $o,X432 : term,X433 : term > $o] : (~! [X434 : term] : ((X433 @ (sub @ X432 @ (push @ X434 @ id))) | ~(X433 @ X434)) | (X433 @ (lam @ X432)) | ~! [X435 : term] : ((X431 @ id @ X435 @ id) = (X433 @ X435)) | ~! [X436 : subst > term > term] : ((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id) | ~! [X437 : subst,X438 : term,X439 : subst] : ((sub @ (X436 @ X437 @ X438) @ X439) = (X436 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439))) | ~! [X440 : term] : ((X431 @ id @ (X436 @ id @ X440) @ id) | ~(X431 @ id @ X440 @ id)))) => ! [X441 : term,X442 : subst > term > subst > $o] : (~! [X443 : term,X444 : term] : (~(X442 @ id @ X443 @ id) | (X442 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id) | ~(X442 @ id @ X444 @ id)) | (X442 @ id @ X441 @ id) | ~! [X445 : subst,X446 : subst,X447 : term,X448 : subst] : (~(X442 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445) @ X448) | (X442 @ X446 @ X447 @ (comp @ X445 @ X448))) | ~! [X449 : term] : ((X442 @ id @ X449 @ id) | ~(var @ (sub @ X449 @ id))) | ~! [X450 : subst,X451 : term,X452 : subst,X453 : subst] : (~(X442 @ X452 @ X451 @ (comp @ X453 @ X450)) | (X442 @ (comp @ X452 @ X453) @ (sub @ X451 @ X453) @ X450)) | ~! [X454 : subst > term > term] : (~! [X455 : term,X456 : subst,X457 : subst] : ((X454 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457)) = (sub @ (X454 @ X456 @ X455) @ X457)) | ~! [X458 : term] : (~(X442 @ id @ X458 @ id) | (X442 @ id @ (X454 @ id @ X458) @ id)) | (X442 @ id @ (lam @ (X454 @ sh @ one)) @ id))))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem3aaa <=> ! [X459 : term,X460 : subst > term > subst > $o] : (~! [X461 : term,X462 : subst > term > term] : (~! [X463 : subst,X464 : term,X465 : subst] : ((sub @ X461 @ (push @ (sub @ X464 @ X465) @ (comp @ X463 @ X465))) = (X462 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465))) | ~! [X466 : term] : ((X460 @ id @ (X462 @ id @ X466) @ id) | ~(X460 @ id @ X466 @ id)) | ~! [X467 : subst,X468 : term,X469 : subst] : ((sub @ (X462 @ X467 @ X468) @ X469) = (sub @ (sub @ X461 @ (push @ X468 @ X467)) @ X469)) | (X460 @ id @ (lam @ (X462 @ sh @ one)) @ id)) | ~! [X470 : term] : (~(X460 @ id @ X470 @ id) | (X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id)) | (X460 @ id @ (lam @ (sub @ X459 @ (push @ one @ sh))) @ id))) & (hoasinduction_lthm <=> (! [X471 : term > $o,X472 : term] : ((X471 @ X472) | ~! [X473 : term] : (~! [X474 : term] : (~(X471 @ X474) | (X471 @ (sub @ X473 @ (push @ X474 @ id)))) | (X471 @ (lam @ X473))) | ~! [X475 : term,X476 : term] : ((X471 @ (ap @ X476 @ X475)) | ~(X471 @ X476) | ~(X471 @ X475)) | ~! [X477 : term] : ((X471 @ X477) | ~(var @ X477))) => (! [X478 : term,X479 : subst > term > subst > $o,X480 : term] : ((X479 @ id @ (ap @ X478 @ X480) @ id) | ~! [X481 : term,X482 : subst,X483 : subst,X484 : subst] : ((X479 @ (comp @ X483 @ X484) @ (sub @ X481 @ X484) @ X482) | ~(X479 @ X483 @ X481 @ (comp @ X484 @ X482))) | ~(X479 @ id @ X478 @ id) | ~(X479 @ id @ X480 @ id) | ~! [X485 : subst,X486 : subst,X487 : term,X488 : subst] : ((X479 @ X486 @ X487 @ (comp @ X488 @ X485)) | ~(X479 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X485)) | ~! [X489 : term,X490 : term] : ((X479 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id) | ~(X479 @ id @ X490 @ id) | ~(X479 @ id @ X489 @ id))) => (! [X491 : subst > term > subst > $o,X492 : term] : (~! [X493 : subst > term > term] : (~! [X494 : term] : ((X491 @ id @ (X493 @ id @ X494) @ id) | ~(X491 @ id @ X494 @ id)) | ~! [X495 : subst,X496 : term,X497 : subst] : ((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497)) = (sub @ (X493 @ X495 @ X496) @ X497)) | (X491 @ id @ (lam @ (X493 @ sh @ one)) @ id)) | (X491 @ id @ (lam @ X492) @ id) | ~! [X498 : term] : ((X491 @ id @ (sub @ X492 @ (push @ X498 @ id)) @ id) | ~(X491 @ id @ X498 @ id)) | ~! [X499 : subst,X500 : term,X501 : subst,X502 : subst] : (~(X491 @ X501 @ X500 @ (comp @ X502 @ X499)) | (X491 @ (comp @ X501 @ X502) @ (sub @ X500 @ X502) @ X499)) | ~! [X503 : subst,X504 : term,X505 : subst,X506 : subst] : (~(X491 @ (comp @ X503 @ X506) @ (sub @ X504 @ X506) @ X505) | (X491 @ X503 @ X504 @ (comp @ X506 @ X505)))) => ! [X507 : subst > term > subst > $o,X508 : term] : ((X507 @ id @ X508 @ id) | ~! [X509 : subst,X510 : subst,X511 : subst,X512 : term] : ((X507 @ X511 @ X512 @ (comp @ X510 @ X509)) | ~(X507 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510) @ X509)) | ~! [X513 : subst,X514 : subst,X515 : subst,X516 : term] : ((X507 @ (comp @ X513 @ X515) @ (sub @ X516 @ X515) @ X514) | ~(X507 @ X513 @ X516 @ (comp @ X515 @ X514))) | ~! [X517 : term] : (~(var @ (sub @ X517 @ id)) | (X507 @ id @ X517 @ id)) | ~! [X518 : term,X519 : term] : (~(X507 @ id @ X519 @ id) | (X507 @ id @ (ap @ (sub @ X519 @ id) @ X518) @ id) | ~(X507 @ id @ X518 @ id)) | ~! [X520 : subst > term > term] : (~! [X521 : term] : ((X507 @ id @ (X520 @ id @ X521) @ id) | ~(X507 @ id @ X521 @ id)) | ~! [X522 : subst,X523 : term,X524 : subst] : ((X520 @ (comp @ X522 @ X524) @ (sub @ X523 @ X524)) = (sub @ (X520 @ X522 @ X523) @ X524)) | (X507 @ id @ (lam @ (X520 @ sh @ one)) @ id))))))) & hoasapnotvar_gthm & (hoaslamnotap <=> ! [X525 : term,X526 : subst > term > term,X527 : term] : (~! [X528 : subst,X529 : term,X530 : subst] : ((sub @ (X526 @ X528 @ X529) @ X530) = (X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) | ((ap @ (sub @ X527 @ id) @ X525) != (lam @ (X526 @ sh @ one))))) & (hoasinduction_lem3a <=> ! [X531 : subst > term > subst > $o,X532 : term] : (~! [X533 : subst > term > term] : ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id) | ~! [X534 : term,X535 : subst,X536 : subst] : ((sub @ (X533 @ X536 @ X534) @ X535) = (X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535))) | ~! [X537 : term] : ((X531 @ id @ (X533 @ id @ X537) @ id) | ~(X531 @ id @ X537 @ id))) | (X531 @ id @ (lam @ X532) @ id) | ~! [X538 : term] : ((X531 @ id @ (sub @ X532 @ (push @ X538 @ id)) @ id) | ~(X531 @ id @ X538 @ id)))) & ((d2subst @ d_id) = sh) & ! [X539 : term] : ? [X540 : d_term] : ((d2term @ X540) = X539) & pushprop_lem1_gthm & ((! [X541 : subst,X542 : term] : ((sub @ one @ (push @ X542 @ X541)) = X542) => (! [X543 : subst,X544 : term] : ((comp @ sh @ (push @ X544 @ X543)) = X543) => ! [X545 : term,X546 : term > $o,X547 : term > $o,X548 : subst,X549 : term] : (~(X546 @ X545) | (X547 @ (sub @ X545 @ (push @ X549 @ X548)))))) <=> pushprop_lem1_lthm)),
% 1.70/1.51 inference(rectify,[status(thm)],[f1])).
% 1.70/1.51 thf(f1,axiom,(
% 1.70/1.51 hoasinduction_lem2_gthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & apnotvar & hoaslamnotvar_lthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ X27) @ id) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3) & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & (axidl <=> ! [X14 : subst] : ((comp @ id @ X14) = X14)) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f_lthm) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X5 : d_subst] : (d_id = X5) & hoasapnotvar_lthm & (hoasapinj2_lthm <=> (! [X15 : term,X13 : term,X20 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) => ! [X15 : term,X13 : term,X19 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20)))) & (hoaslaminj <=> ! [X18 : subst > term > term,X31 : subst > term > term,X32 : subst,X33 : term] : (((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) & ~lamnotap & (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) => (! [X21 : term,X10 : term > $o] : ((X10 @ X21) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) => ! [X17 : subst,X16 : term,X10 : term > $o] : ((X10 @ (sub @ X16 @ X17)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))))))))) & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & (hoasapinj1_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X15 : term,X13 : term,X20 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) => ! [X15 : term,X19 : term,X13 : term,X20 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))))) & hoasinduction_lem3a_gthm & pushprop_lem1v2_gthm & (! [X15 : term,X14 : subst,X10 : term > $o,X26 : term > $o,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & pushprop_lem2v2_lthm & hoasinduction_lem1 & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X14 : subst,X11 : term > $o,X13 : term,X10 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | (X11 @ one) | ~(X10 @ X13))) <=> pushprop_lem1v2_lthm) & (! [X19 : term,X15 : term,X20 : term,X13 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) <=> apinj2) & axabs & (one = (d2term @ d_one)) & pushprop_lthm_orig & (induction2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X16 : term,X17 : subst,X10 : term > $o] : (~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))) => ! [X22 : term,X10 : term > $o] : ((X10 @ X22) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))))))) & pushprop_gthm & (! [X13 : term,X15 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15))) <=> laminj) & (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ 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))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & (axidr <=> ! [X14 : subst] : ((comp @ X14 @ id) = X14)) & (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & (! [X30 : term,X10 : subst > term > subst > $o] : (~! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X48 : term,X11 : term > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))))) <=> hoasinduction_lem3v2_lthm) & hoaslaminj_gthm & (hoasinduction_p_and_p_prime = (^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))))) & (! [X13 : term,X11 : term > $o,X10 : term > $o,X14 : subst] : (~(X10 @ X13) | (X11 @ one) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem1v2) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [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)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : subst > term > subst > $o,X27 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id)))) <=> hoasinduction_lem3_lthm) & substmonoid_gthm & (axshiftcons <=> ! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14)) & hoasinduction_lem1v2_gthm & (hoasapinj2 <=> ! [X19 : term,X13 : term,X15 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) & (! [X13 : term,X10 : term > $o,X14 : subst] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0) & hoasinduction_lem3b_gthm & (! [X10 : term > $o,X22 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))) <=> induction2) & ((^[X13 : term, X14 : subst, X10 : term > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) = pushprop_p_and_p_prime) & (! [X11 : term > $o,X48 : term,X10 : subst > term > subst > $o] : ((X11 @ (lam @ X48)) | ~! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoasinduction_lem3v2) & pushprop & (induction <=> ! [X21 : term,X10 : term > $o] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21))) & (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : (~! [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) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (! [X13 : term,X15 : term] : (((sub @ X13 @ sh) != (sub @ X15 @ sh)) | (X13 = X15)) <=> shinj) & pushprop_lem2v2 & axassoc & termmset_gthm & axvarshift & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0) & pushprop_lem0_gthm & (! [X29 : term,X10 : subst > term > subst > $o,X11 : term > $o] : ((X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoasinduction_lem3v2a) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one)) = hoaslam) & pushprop_lem3v2_lthm & (! [X17 : subst,X16 : term,X10 : term > $o] : (~! [X15 : term,X13 : 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 @ (sub @ X16 @ X17)) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))) <=> induction2lem) & pushprop_lem3v2 & axapp & pushprop_lem2v2_gthm & ! [X7 : d_subst,X6 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & hoasinduction_lem1v2 & hoasinduction_lem2v2_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X29 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~! [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)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))))) & (pushprop_lem0_lthm <=> ! [X14 : subst,X13 : term,X10 : term > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & hoasinduction_gthm & hoaslamnotvar & (hoaslaminj_lthm <=> (! [X14 : subst,X13 : term] : ((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))) => ! [X33 : term,X18 : subst > term > term,X32 : subst,X31 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) & ((! [X14 : subst] : ((comp @ id @ X14) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14)))) <=> substmonoid_lthm) & hoaslamnotap_gthm & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & hoaslamnotvar_gthm & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & axmap & (axscons <=> ! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14)) & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & induction2lem_gthm & hoasapinj1_gthm & (hoasinduction_lem2 <=> ! [X10 : subst > term > subst > $o,X23 : term,X24 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id))) & hoasapnotvar & hoasinduction_lem1_gthm & ~(var @ (d2term @ d_one)) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & (! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) <=> apinj1) & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X30 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : 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] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [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)) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X43 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))))) & ulamvarind & hoasinduction_lem2_lthm & (hoasinduction_lem2v2 <=> ! [X10 : subst > term > subst > $o,X44 : term,X45 : term,X11 : term > $o] : ((X11 @ (ap @ X44 @ X45)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X11 @ X45) | ~(X11 @ X44) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & ~ulamvar1 & hoasinduction_lem3_gthm & ! [X1 : d_term] : (d_one = X1) & ulamvarsh & hoasapinj2_gthm & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & ((d2subst @ d_id) = id) & lamnotvar & hoasinduction_lem3v2_gthm & hoasinduction_lem1_lthm & ((! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14)) <=> substmonoid) & (hoasapinj1 <=> ! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction <=> ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~! [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)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & hoaslamnotap_lthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b) & induction2_gthm & pushprop_lthm & axclos & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : (~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : subst > term > subst > $o] : (~! [X35 : term,X18 : subst > term > term] : (~! [X39 : subst,X40 : term,X41 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [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)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id))) & (hoasinduction_lthm <=> (! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X23 : term,X10 : subst > term > subst > $o,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : 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 : subst > term > subst > $o,X27 : term] : (~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : subst > term > subst > $o,X28 : term] : ((X10 @ id @ X28 @ id) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))))) & hoasapnotvar_gthm & (hoaslamnotap <=> ! [X47 : term,X18 : subst > term > term,X46 : 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)))) & (hoasinduction_lem3a <=> ! [X10 : subst > term > subst > $o,X43 : term] : (~! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ X43) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & ((d2subst @ d_id) = sh) & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & pushprop_lem1_gthm & ((! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X13 : term,X10 : term > $o,X26 : term > $o,X14 : subst,X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm)),
% 1.70/1.51 file('/export/starexec/sandbox/tmp/tmp.tVjixEyHtK/DTF2THF_10797.p',alg444_1)).
% 1.70/1.51 thf(f1310,plain,(
% 1.70/1.51 ( ! [X240 : term] : (((d2term @ (sK640 @ X240)) = X240)) )),
% 1.70/1.51 inference(cnf_transformation,[status(thm)],[f753])).
% 1.70/1.51 thf(f3842,plain,(
% 1.70/1.51 ((d2term @ d_one) != (sK610 @ sK612 @ sK613)) | spl652_309),
% 1.70/1.51 inference(forward_demodulation,[status(thm)],[f3147,f3829])).
% 1.70/1.51 thf(f3147,plain,(
% 1.70/1.51 ((sK610 @ sK612 @ sK613) != (sK611 @ sK612 @ sK613)) | spl652_309),
% 1.70/1.51 inference(avatar_component_clause,[status(thm)],[f3146])).
% 1.70/1.51 thf(f3146,definition,(
% 1.70/1.51 spl652_309 <=> ((sK610 @ sK612 @ sK613) = (sK611 @ sK612 @ sK613))),
% 1.70/1.51 introduced(definition,[new_symbols(naming,[spl652_309])],[avatar_definition])).
% 1.70/1.51 thf(f3840,plain,(
% 1.70/1.51 spl652_154),
% 1.70/1.51 inference(avatar_contradiction_clause,[status(thm)],[f3839])).
% 1.70/1.51 thf(f3839,plain,(
% 1.70/1.51 $false | spl652_154),
% 1.70/1.51 inference(subsumption_resolution,[status(thm)],[f3832,f3829])).
% 1.70/1.51 thf(f3832,plain,(
% 1.70/1.51 ((d2term @ d_one) != (sK111 @ sK112 @ sK113)) | spl652_154),
% 1.70/1.51 inference(backward_demodulation,[status(thm)],[f2494,f3829])).
% 1.70/1.51 thf(f2494,plain,(
% 1.70/1.51 ((sK111 @ sK112 @ sK113) != (sK110 @ sK112 @ sK113)) | spl652_154),
% 1.70/1.51 inference(avatar_component_clause,[status(thm)],[f2493])).
% 1.70/1.51 thf(f2493,definition,(
% 1.70/1.51 spl652_154 <=> ((sK111 @ sK112 @ sK113) = (sK110 @ sK112 @ sK113))),
% 1.70/1.51 introduced(definition,[new_symbols(naming,[spl652_154])],[avatar_definition])).
% 1.70/1.51 thf(f3148,plain,(
% 1.70/1.51 ~spl652_309 | spl652_3),
% 1.70/1.51 inference(avatar_split_clause,[status(thm)],[f1336,f1914,f3146])).
% 1.70/1.51 thf(f1914,definition,(
% 1.70/1.51 spl652_3 <=> (hoaslaminj = $true)),
% 1.70/1.51 introduced(definition,[new_symbols(naming,[spl652_3])],[avatar_definition])).
% 1.70/1.51 thf(f1336,plain,(
% 1.70/1.51 (hoaslaminj = $true) | ((sK610 @ sK612 @ sK613) != (sK611 @ sK612 @ sK613))),
% 1.70/1.51 inference(cnf_transformation,[status(thm)],[f753])).
% 1.70/1.51 thf(f2495,plain,(
% 1.70/1.51 ~spl652_3 | ~spl652_154),
% 1.70/1.51 inference(avatar_split_clause,[status(thm)],[f756,f2493,f1914])).
% 1.70/1.51 thf(f756,plain,(
% 1.70/1.51 ((sK111 @ sK112 @ sK113) != (sK110 @ sK112 @ sK113)) | (hoaslaminj != $true)),
% 1.70/1.51 inference(cnf_transformation,[status(thm)],[f134])).
% 1.70/1.51 thf(f134,plain,(
% 1.70/1.51 ((hoaslaminj != $true) | (! [X1 : subst,X2 : subst,X3 : term] : ((sK110 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (sK110 @ X2 @ X3) @ X1)) & (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK110 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK111 @ Y0 @ Y1)))))) & ((sK111 @ sK112 @ sK113) != (sK110 @ sK112 @ sK113)) & ! [X7 : subst,X8 : subst,X9 : term] : ((sub @ (sK111 @ X8 @ X9) @ X7) = (sK111 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7)))))) & ((hoaslaminj = $true) | ! [X10 : subst > term > term] : (((X10 @ (comp @ (sK115 @ X10) @ (sK114 @ X10)) @ (sub @ (sK116 @ X10) @ (sK114 @ X10))) != (sub @ (X10 @ (sK115 @ X10) @ (sK116 @ X10)) @ (sK114 @ X10))) | ! [X14 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) != (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X14 @ Y0 @ Y1)))))) | ! [X15 : subst,X16 : term] : ((X10 @ X15 @ X16) = (X14 @ X15 @ X16)) | ((sub @ (X14 @ (sK118 @ X14) @ (sK119 @ X14)) @ (sK117 @ X14)) != (X14 @ (comp @ (sK118 @ X14) @ (sK117 @ X14)) @ (sub @ (sK119 @ X14) @ (sK117 @ X14)))))))),
% 1.70/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111,sK112,sK113,sK114,sK115,sK116,sK117,sK118,sK119])],[f128,f133,f132,f131,f130,f129])).
% 1.70/1.51 thf(f129,plain,(
% 1.70/1.51 ? [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) & ? [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) & ? [X5 : subst,X6 : term] : ((X0 @ X5 @ X6) != (X4 @ X5 @ X6)) & ! [X7 : subst,X8 : subst,X9 : term] : ((sub @ (X4 @ X8 @ X9) @ X7) = (X4 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7))))) => (! [X3 : term,X2 : subst,X1 : subst] : ((sK110 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (sK110 @ X2 @ X3) @ X1)) & ? [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK110 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) & ? [X6 : term,X5 : subst] : ((sK110 @ X5 @ X6) != (X4 @ X5 @ X6)) & ! [X7 : subst,X8 : subst,X9 : term] : ((sub @ (X4 @ X8 @ X9) @ X7) = (X4 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7)))))),
% 1.70/1.51 introduced(definition,[],[choice_axiom])).
% 1.70/1.51 thf(f130,plain,(
% 1.70/1.51 ? [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK110 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) & ? [X6 : term,X5 : subst] : ((sK110 @ X5 @ X6) != (X4 @ X5 @ X6)) & ! [X7 : subst,X8 : subst,X9 : term] : ((sub @ (X4 @ X8 @ X9) @ X7) = (X4 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7)))) => (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK110 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK111 @ Y0 @ Y1)))))) & ? [X6 : term,X5 : subst] : ((sK111 @ X5 @ X6) != (sK110 @ X5 @ X6)) & ! [X9 : term,X8 : subst,X7 : subst] : ((sub @ (sK111 @ X8 @ X9) @ X7) = (sK111 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7))))),
% 1.70/1.51 introduced(definition,[],[choice_axiom])).
% 1.70/1.51 thf(f131,plain,(
% 1.70/1.51 ? [X6 : term,X5 : subst] : ((sK111 @ X5 @ X6) != (sK110 @ X5 @ X6)) => ((sK111 @ sK112 @ sK113) != (sK110 @ sK112 @ sK113))),
% 1.70/1.51 introduced(definition,[],[choice_axiom])).
% 1.70/1.51 thf(f132,plain,(
% 1.70/1.51 ! [X10 : subst > term > term] : (? [X11 : subst,X12 : subst,X13 : term] : ((X10 @ (comp @ X12 @ X11) @ (sub @ X13 @ X11)) != (sub @ (X10 @ X12 @ X13) @ X11)) => ((X10 @ (comp @ (sK115 @ X10) @ (sK114 @ X10)) @ (sub @ (sK116 @ X10) @ (sK114 @ X10))) != (sub @ (X10 @ (sK115 @ X10) @ (sK116 @ X10)) @ (sK114 @ X10))))),
% 1.70/1.51 introduced(definition,[],[choice_axiom])).
% 1.70/1.51 thf(f133,plain,(
% 1.70/1.51 ! [X14 : subst > term > term] : (? [X17 : subst,X18 : subst,X19 : term] : ((sub @ (X14 @ X18 @ X19) @ X17) != (X14 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) => ((sub @ (X14 @ (sK118 @ X14) @ (sK119 @ X14)) @ (sK117 @ X14)) != (X14 @ (comp @ (sK118 @ X14) @ (sK117 @ X14)) @ (sub @ (sK119 @ X14) @ (sK117 @ X14)))))),
% 1.70/1.51 introduced(definition,[],[choice_axiom])).
% 1.70/1.51 thf(f128,plain,(
% 1.70/1.51 ((hoaslaminj != $true) | ? [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) & ? [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) & ? [X5 : subst,X6 : term] : ((X0 @ X5 @ X6) != (X4 @ X5 @ X6)) & ! [X7 : subst,X8 : subst,X9 : term] : ((sub @ (X4 @ X8 @ X9) @ X7) = (X4 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7)))))) & ((hoaslaminj = $true) | ! [X10 : subst > term > term] : (? [X11 : subst,X12 : subst,X13 : term] : ((X10 @ (comp @ X12 @ X11) @ (sub @ X13 @ X11)) != (sub @ (X10 @ X12 @ X13) @ X11)) | ! [X14 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) != (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X14 @ Y0 @ Y1)))))) | ! [X15 : subst,X16 : term] : ((X10 @ X15 @ X16) = (X14 @ X15 @ X16)) | ? [X17 : subst,X18 : subst,X19 : term] : ((sub @ (X14 @ X18 @ X19) @ X17) != (X14 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))))))),
% 1.70/1.51 inference(rectify,[status(thm)],[f127])).
% 1.70/1.51 thf(f127,plain,(
% 1.70/1.51 ((hoaslaminj != $true) | ? [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) & ? [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) & ? [X8 : subst,X9 : term] : ((X0 @ X8 @ X9) != (X4 @ X8 @ X9)) & ! [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) = (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))))) & ((hoaslaminj = $true) | ! [X0 : subst > term > term] : (? [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) != (sub @ (X0 @ X2 @ X3) @ X1)) | ! [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) != (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) | ! [X8 : subst,X9 : term] : ((X0 @ X8 @ X9) = (X4 @ X8 @ X9)) | ? [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) != (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))))))),
% 1.70/1.51 inference(nnf_transformation,[status(thm)],[f15])).
% 1.70/1.51 thf(f15,plain,(
% 1.70/1.51 ! [X0 : subst > term > term] : (? [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) != (sub @ (X0 @ X2 @ X3) @ X1)) | ! [X4 : subst > term > term] : (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) != (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) | ! [X8 : subst,X9 : term] : ((X0 @ X8 @ X9) = (X4 @ X8 @ X9)) | ? [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) != (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))))) <~> (hoaslaminj = $true)),
% 1.70/1.51 inference(flattening,[status(thm)],[f14])).
% 1.70/1.51 thf(f14,plain,(
% 1.70/1.51 ! [X0 : subst > term > term] : (! [X4 : subst > term > term] : ((! [X8 : subst,X9 : term] : ((X0 @ X8 @ X9) = (X4 @ X8 @ X9)) | ((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) != (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1))))))) | ? [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) != (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | ? [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) != (sub @ (X0 @ X2 @ X3) @ X1))) <~> (hoaslaminj = $true)),
% 1.70/1.51 inference(ennf_transformation,[status(thm)],[f9])).
% 1.70/1.51 thf(f9,plain,(
% 1.70/1.51 ~(! [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) => ! [X4 : subst > term > term] : (! [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) = (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))) => (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) => ! [X8 : subst,X9 : term] : ((X0 @ X8 @ X9) = (X4 @ X8 @ X9))))) <=> (hoaslaminj = $true))),
% 1.70/1.51 inference(rectify,[status(thm)],[f6])).
% 1.70/1.51 thf(f6,plain,(
% 1.70/1.51 ~(! [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) => ! [X4 : subst > term > term] : (! [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) = (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))) => (((hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X0 @ Y0 @ Y1))))) = (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X4 @ Y0 @ Y1)))))) => ! [X12 : subst,X13 : term] : ((X0 @ X12 @ X13) = (X4 @ X12 @ X13))))) <=> (hoaslaminj = $true))),
% 1.70/1.51 inference(fool_elimination,[status(thm)],[f5])).
% 1.70/1.51 thf(f5,plain,(
% 1.70/1.51 ~(! [X0 : subst > term > term] : (! [X1 : subst,X2 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)) = (sub @ (X0 @ X2 @ X3) @ X1)) => ! [X4 : subst > term > term] : (! [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) = (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))) => (((hoaslam @ id @ (^[X8 : subst, X9 : term] : (X4 @ X8 @ X9))) = (hoaslam @ id @ (^[X10 : subst, X11 : term] : (X0 @ X10 @ X11)))) => ! [X12 : subst,X13 : term] : ((X0 @ X12 @ X13) = (X4 @ X12 @ X13))))) = hoaslaminj)),
% 1.70/1.51 inference(rectify,[status(thm)],[f3])).
% 1.70/1.51 thf(f3,negated_conjecture,(
% 1.70/1.51 ~(! [X18 : subst > term > term] : (! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => ! [X49 : subst > term > term] : (! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X49 @ X14 @ X13) @ X25) = (X49 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (((hoaslam @ id @ (^[X14 : subst, X13 : term] : (X49 @ X14 @ X13))) = (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13)))) => ! [X14 : subst,X13 : term] : ((X18 @ X14 @ X13) = (X49 @ X14 @ X13))))) = hoaslaminj)),
% 1.70/1.51 inference(negated_conjecture,[status(cth)],[f2])).
% 1.70/1.51 thf(f2,conjecture,(
% 1.70/1.51 (! [X18 : subst > term > term] : (! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => ! [X49 : subst > term > term] : (! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X49 @ X14 @ X13) @ X25) = (X49 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (((hoaslam @ id @ (^[X14 : subst, X13 : term] : (X49 @ X14 @ X13))) = (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13)))) => ! [X14 : subst,X13 : term] : ((X18 @ X14 @ X13) = (X49 @ X14 @ X13))))) = hoaslaminj)),
% 1.70/1.51 file('/export/starexec/sandbox/tmp/tmp.tVjixEyHtK/DTF2THF_10797.p',hoaslaminj)).
% 1.70/1.51 % SZS output end Proof for DTF2THF_10797
% 1.70/1.51 % (10943)------------------------------
% 1.70/1.51 % (10943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.51 % (10943)Termination reason: Refutation
% 1.70/1.51
% 1.70/1.51 % (10943)Memory used [KB]: 12153
% 1.70/1.51 % (10943)Time elapsed: 0.110 s
% 1.70/1.51 % (10943)Instructions burned: 263 (million)
% 1.70/1.51 % (10943)------------------------------
% 1.70/1.51 % (10943)------------------------------
% 1.70/1.51 % (10895)Success in time 0.416 s
%------------------------------------------------------------------------------