%------------------------------------------------------------------------------
% 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 : n026.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 06:58:44 PM UTC 2026
% Result : Theorem 21.29s 4.27s
% Output : Refutation 21.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 139
% Syntax : Number of formulae : 215 ( 11 unt; 0 typ; 7 def)
% Number of atoms : 11329 (5396 equ; 0 cnn)
% Maximal formula atoms : 530 ( 52 avg)
% Number of connectives : 26324 (3108 ~;2834 |;2420 &;17162 @)
% ( 515 <=>; 261 =>; 0 <=; 1 <~>)
% Maximal formula depth : 186 ( 15 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2000 (2000 >; 0 *; 0 +; 0 <<)
% Number of symbols : 734 ( 730 usr; 301 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 5767 ( 128 ^;4274 !;1365 ?;5767 :)
% 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: ( term > $o ) > $o ).
thf(func_def_145,type,
sP4: ( 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: ( term > $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_158,type,
sP17: ( subst > term > subst > $o ) > $o ).
thf(func_def_159,type,
sP18: ( subst > term > subst > $o ) > $o ).
thf(func_def_161,type,
sP20: ( subst > term > subst > $o ) > $o ).
thf(func_def_162,type,
sP21: ( subst > term > subst > $o ) > $o ).
thf(func_def_164,type,
sP23: ( term > $o ) > $o ).
thf(func_def_165,type,
sP24: ( term > $o ) > $o ).
thf(func_def_168,type,
sP27: ( term > $o ) > $o ).
thf(func_def_169,type,
sP28: ( subst > term > subst > $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_181,type,
sP40: ( subst > term > subst > $o ) > $o ).
thf(func_def_184,type,
sP43: ( term > $o ) > $o ).
thf(func_def_185,type,
sP44: ( term > $o ) > $o ).
thf(func_def_187,type,
sP46: ( subst > term > subst > $o ) > $o ).
thf(func_def_190,type,
sP49: ( subst > term > subst > $o ) > $o ).
thf(func_def_195,type,
sP54: ( term > $o ) > $o ).
thf(func_def_196,type,
sP55: ( term > $o ) > $o ).
thf(func_def_200,type,
sK59: subst > term > subst > $o ).
thf(func_def_201,type,
sK60: term ).
thf(func_def_202,type,
sK61: ( subst > term > term ) > term ).
thf(func_def_203,type,
sK62: ( subst > term > term ) > subst ).
thf(func_def_204,type,
sK63: ( subst > term > term ) > subst ).
thf(func_def_205,type,
sK64: ( subst > term > term ) > term ).
thf(func_def_206,type,
sK65: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_207,type,
sK66: term > ( subst > term > subst > $o ) > term ).
thf(func_def_208,type,
sK67: ( term > $o ) > term ).
thf(func_def_209,type,
sK68: subst > ( term > $o ) > term ).
thf(func_def_210,type,
sK69: term ).
thf(func_def_211,type,
sK70: term > $o ).
thf(func_def_212,type,
sK71: subst ).
thf(func_def_213,type,
sK72: term ).
thf(func_def_214,type,
sK73: term > term ).
thf(func_def_215,type,
sK74: term > $o ).
thf(func_def_216,type,
sK75: term ).
thf(func_def_217,type,
sK76: term > term ).
thf(func_def_218,type,
sK77: ( term > $o ) > term ).
thf(func_def_219,type,
sK78: ( term > $o ) > term ).
thf(func_def_220,type,
sK79: ( term > $o ) > term ).
thf(func_def_221,type,
sK80: ( term > $o ) > term ).
thf(func_def_222,type,
sK81: ( term > $o ) > term ).
thf(func_def_223,type,
sK82: ( term > $o ) > term ).
thf(func_def_224,type,
sK83: term > subst > term > term ).
thf(func_def_225,type,
sK84: subst > term > subst > $o ).
thf(func_def_226,type,
sK85: term > $o ).
thf(func_def_227,type,
sK86: term ).
thf(func_def_228,type,
sK87: ( subst > term > term ) > term ).
thf(func_def_229,type,
sK88: ( subst > term > term ) > subst ).
thf(func_def_230,type,
sK89: ( subst > term > term ) > subst ).
thf(func_def_231,type,
sK90: ( subst > term > term ) > term ).
thf(func_def_232,type,
sK91: term ).
thf(func_def_233,type,
sK92: term ).
thf(func_def_234,type,
sK93: ( subst > term > term ) > subst ).
thf(func_def_235,type,
sK94: ( subst > term > term ) > term ).
thf(func_def_236,type,
sK95: term > ( term > $o ) > term ).
thf(func_def_237,type,
sK96: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_238,type,
sK97: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_239,type,
sK98: term ).
thf(func_def_240,type,
sK99: subst ).
thf(func_def_241,type,
sK100: subst > term > term ).
thf(func_def_242,type,
sK101: subst > term > term ).
thf(func_def_243,type,
sK102: term ).
thf(func_def_244,type,
sK103: subst ).
thf(func_def_245,type,
sK104: term ).
thf(func_def_246,type,
sK105: subst ).
thf(func_def_247,type,
sK106: term ).
thf(func_def_248,type,
sK107: term ).
thf(func_def_249,type,
sK108: ( subst > term > term ) > subst ).
thf(func_def_250,type,
sK109: ( subst > term > term ) > term ).
thf(func_def_251,type,
sK110: ( subst > term > term ) > subst ).
thf(func_def_252,type,
sK111: ( subst > term > term ) > subst ).
thf(func_def_253,type,
sK112: ( subst > term > term ) > term ).
thf(func_def_254,type,
sK113: ( subst > term > term ) > subst ).
thf(func_def_255,type,
sK114: subst > term > subst > $o ).
thf(func_def_256,type,
sK115: term ).
thf(func_def_257,type,
sK116: ( subst > term > term ) > subst ).
thf(func_def_258,type,
sK117: ( subst > term > term ) > subst ).
thf(func_def_259,type,
sK118: ( subst > term > term ) > term ).
thf(func_def_260,type,
sK119: ( subst > term > term ) > term ).
thf(func_def_261,type,
sK120: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_262,type,
sK121: term > ( subst > term > subst > $o ) > term ).
thf(func_def_263,type,
sK122: term ).
thf(func_def_264,type,
sK123: term ).
thf(func_def_265,type,
sK124: subst > term > subst > $o ).
thf(func_def_266,type,
sK125: term > $o ).
thf(func_def_267,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_269,type,
sK128: ( subst > term > subst > $o ) > term ).
thf(func_def_270,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK130: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_272,type,
sK131: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK132: ( subst > term > subst > $o ) > subst ).
thf(func_def_274,type,
sK133: ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_276,type,
sK135: ( subst > term > subst > $o ) > term ).
thf(func_def_277,type,
sK136: ( subst > term > subst > $o ) > term ).
thf(func_def_278,type,
sK137: subst > term > subst > $o ).
thf(func_def_279,type,
sK138: term ).
thf(func_def_280,type,
sK139: ( subst > term > term ) > term ).
thf(func_def_281,type,
sK140: ( subst > term > term ) > subst ).
thf(func_def_282,type,
sK141: ( subst > term > term ) > subst ).
thf(func_def_283,type,
sK142: ( subst > term > term ) > term ).
thf(func_def_284,type,
sK143: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_285,type,
sK144: term > ( subst > term > subst > $o ) > term ).
thf(func_def_286,type,
sK145: subst > term > subst > $o ).
thf(func_def_287,type,
sK146: term ).
thf(func_def_288,type,
sK147: term > $o ).
thf(func_def_289,type,
sK148: ( term > $o ) > term > term ).
thf(func_def_290,type,
sK149: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK150: ( subst > term > subst > $o ) > term ).
thf(func_def_292,type,
sK151: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_294,type,
sK153: ( subst > term > subst > $o ) > term ).
thf(func_def_295,type,
sK154: ( subst > term > subst > $o ) > subst ).
thf(func_def_296,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_297,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK157: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_299,type,
sK158: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_300,type,
sK159: ( subst > term > term ) > subst ).
thf(func_def_301,type,
sK160: ( subst > term > term ) > term ).
thf(func_def_302,type,
sK161: ( subst > term > term ) > subst ).
thf(func_def_303,type,
sK162: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_304,type,
sK163: subst ).
thf(func_def_305,type,
sK164: term ).
thf(func_def_306,type,
sK165: term > $o ).
thf(func_def_307,type,
sK166: term > term ).
thf(func_def_308,type,
sK167: ( term > $o ) > term ).
thf(func_def_309,type,
sK168: ( term > $o ) > subst > term ).
thf(func_def_310,type,
sK169: ( term > $o ) > term ).
thf(func_def_311,type,
sK170: ( term > $o ) > term ).
thf(func_def_312,type,
sK171: ( term > $o ) > term ).
thf(func_def_313,type,
sK172: ( term > $o ) > term ).
thf(func_def_314,type,
sK173: term ).
thf(func_def_315,type,
sK174: subst > term > subst > $o ).
thf(func_def_316,type,
sK175: term ).
thf(func_def_317,type,
sK176: ( subst > term > subst > $o ) > subst ).
thf(func_def_318,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_319,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_320,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_321,type,
sK180: ( subst > term > subst > $o ) > term > term ).
thf(func_def_322,type,
sK181: ( subst > term > subst > $o ) > term ).
thf(func_def_323,type,
sK182: ( subst > term > subst > $o ) > subst ).
thf(func_def_324,type,
sK183: ( subst > term > subst > $o ) > subst ).
thf(func_def_325,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_326,type,
sK185: term > ( subst > term > subst > $o ) > term ).
thf(func_def_327,type,
sK186: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_328,type,
sK187: subst > term > subst > $o ).
thf(func_def_329,type,
sK188: term ).
thf(func_def_330,type,
sK189: ( subst > term > term ) > term ).
thf(func_def_331,type,
sK190: ( subst > term > term ) > term ).
thf(func_def_332,type,
sK191: ( subst > term > term ) > subst ).
thf(func_def_333,type,
sK192: ( subst > term > term ) > subst ).
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 > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_338,type,
sK197: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_339,type,
sK198: ( term > $o ) > term ).
thf(func_def_340,type,
sK199: ( term > $o ) > term ).
thf(func_def_341,type,
sK200: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_342,type,
sK201: term ).
thf(func_def_343,type,
sK202: term > $o ).
thf(func_def_344,type,
sK203: term > term ).
thf(func_def_345,type,
sK204: term ).
thf(func_def_346,type,
sK205: subst > term > subst > $o ).
thf(func_def_347,type,
sK206: ( term > $o ) > term ).
thf(func_def_348,type,
sK207: subst > term > subst > $o ).
thf(func_def_349,type,
sK208: term ).
thf(func_def_350,type,
sK209: ( subst > term > subst > $o ) > term ).
thf(func_def_351,type,
sK210: ( subst > term > subst > $o ) > subst ).
thf(func_def_352,type,
sK211: ( subst > term > subst > $o ) > subst ).
thf(func_def_353,type,
sK212: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_355,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_356,type,
sK215: ( subst > term > subst > $o ) > term ).
thf(func_def_357,type,
sK216: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK217: ( subst > term > subst > $o ) > term ).
thf(func_def_359,type,
sK218: term > ( term > $o ) > term ).
thf(func_def_360,type,
sK219: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_361,type,
sK220: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_362,type,
sK221: term > $o ).
thf(func_def_363,type,
sK222: term ).
thf(func_def_364,type,
sK223: subst > term > subst > $o ).
thf(func_def_365,type,
sK224: ( subst > term > term ) > term ).
thf(func_def_366,type,
sK225: ( subst > term > term ) > term ).
thf(func_def_367,type,
sK226: ( subst > term > term ) > subst ).
thf(func_def_368,type,
sK227: ( subst > term > term ) > subst ).
thf(func_def_369,type,
sK228: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_370,type,
sK229: ( subst > term > term ) > subst ).
thf(func_def_371,type,
sK230: ( subst > term > term ) > term ).
thf(func_def_372,type,
sK231: ( subst > term > term ) > subst ).
thf(func_def_373,type,
sK232: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_374,type,
sK233: ( subst > term > subst > $o ) > term ).
thf(func_def_375,type,
sK234: ( subst > term > subst > $o ) > term ).
thf(func_def_376,type,
sK235: ( term > $o ) > term ).
thf(func_def_377,type,
sK236: ( term > $o ) > term ).
thf(func_def_378,type,
sK237: term ).
thf(func_def_379,type,
sK238: term > $o ).
thf(func_def_380,type,
sK239: subst > term > subst > $o ).
thf(func_def_381,type,
sK240: ( subst > term > term ) > term ).
thf(func_def_382,type,
sK241: ( subst > term > term ) > subst ).
thf(func_def_383,type,
sK242: ( subst > term > term ) > subst ).
thf(func_def_384,type,
sK243: ( subst > term > term ) > term ).
thf(func_def_385,type,
sK244: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_386,type,
sK245: ( term > $o ) > term > term ).
thf(func_def_387,type,
sK246: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_388,type,
sK247: term ).
thf(func_def_389,type,
sK248: subst > term > subst > $o ).
thf(func_def_390,type,
sK249: term > ( subst > term > term ) > subst ).
thf(func_def_391,type,
sK250: term > ( subst > term > term ) > subst ).
thf(func_def_392,type,
sK251: term > ( subst > term > term ) > term ).
thf(func_def_393,type,
sK252: ( subst > term > term ) > term ).
thf(func_def_394,type,
sK253: term > ( subst > term > term ) > subst ).
thf(func_def_395,type,
sK254: term > ( subst > term > term ) > subst ).
thf(func_def_396,type,
sK255: term > ( subst > term > term ) > term ).
thf(func_def_397,type,
sK256: ( subst > term > subst > $o ) > term > term ).
thf(func_def_398,type,
sK257: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_399,type,
sK258: ( subst > term > subst > $o ) > term ).
thf(func_def_400,type,
sK259: subst > term > subst > $o ).
thf(func_def_401,type,
sK260: term ).
thf(func_def_402,type,
sK261: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_403,type,
sK262: ( subst > term > subst > $o ) > term ).
thf(func_def_404,type,
sK263: ( subst > term > subst > $o ) > term ).
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 > $o ) > term ).
thf(func_def_409,type,
sK268: ( term > $o ) > term ).
thf(func_def_410,type,
sK269: term > $o ).
thf(func_def_411,type,
sK270: term ).
thf(func_def_412,type,
sK271: term > term ).
thf(func_def_413,type,
sK272: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_414,type,
sK273: term > ( term > $o ) > term ).
thf(func_def_415,type,
sK274: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_416,type,
sK275: term > $o ).
thf(func_def_417,type,
sK276: term ).
thf(func_def_418,type,
sK277: subst > term > subst > $o ).
thf(func_def_419,type,
sK278: ( subst > term > term ) > term ).
thf(func_def_420,type,
sK279: ( subst > term > term ) > term ).
thf(func_def_421,type,
sK280: ( subst > term > term ) > subst ).
thf(func_def_422,type,
sK281: ( subst > term > term ) > subst ).
thf(func_def_423,type,
sK282: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_424,type,
sK283: ( subst > term > term ) > subst ).
thf(func_def_425,type,
sK284: ( subst > term > term ) > subst ).
thf(func_def_426,type,
sK285: ( subst > term > term ) > term ).
thf(func_def_427,type,
sK286: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_428,type,
sK287: ( term > $o ) > term ).
thf(func_def_429,type,
sK288: ( term > $o ) > term ).
thf(func_def_430,type,
sK289: ( term > $o ) > term ).
thf(func_def_431,type,
sK290: ( term > $o ) > term ).
thf(func_def_432,type,
sK291: term ).
thf(func_def_433,type,
sK292: subst ).
thf(func_def_434,type,
sK293: subst ).
thf(func_def_435,type,
sK294: term ).
thf(func_def_436,type,
sK295: term > $o ).
thf(func_def_437,type,
sK296: term ).
thf(func_def_438,type,
sK297: subst ).
thf(func_def_439,type,
sK298: term ).
thf(func_def_440,type,
sK299: term > $o ).
thf(func_def_441,type,
sK300: subst ).
thf(func_def_442,type,
sK301: term > term ).
thf(func_def_443,type,
sK302: subst > ( term > $o ) > term ).
thf(func_def_444,type,
sK303: ( term > $o ) > term ).
thf(func_def_445,type,
sK304: ( term > $o ) > term ).
thf(func_def_446,type,
sK305: ( term > $o ) > term ).
thf(func_def_447,type,
sK306: ( term > $o ) > term ).
thf(func_def_448,type,
sK307: ( term > $o ) > term ).
thf(func_def_449,type,
sK308: subst > term > subst > $o ).
thf(func_def_450,type,
sK309: term ).
thf(func_def_451,type,
sK310: term > $o ).
thf(func_def_452,type,
sK311: term ).
thf(func_def_453,type,
sK312: ( term > $o ) > term > term ).
thf(func_def_454,type,
sK313: ( subst > term > subst > $o ) > subst ).
thf(func_def_455,type,
sK314: ( subst > term > subst > $o ) > subst ).
thf(func_def_456,type,
sK315: ( subst > term > subst > $o ) > term ).
thf(func_def_457,type,
sK316: ( subst > term > subst > $o ) > subst ).
thf(func_def_458,type,
sK317: ( subst > term > subst > $o ) > term ).
thf(func_def_459,type,
sK318: ( subst > term > subst > $o ) > subst ).
thf(func_def_460,type,
sK319: ( subst > term > subst > $o ) > subst ).
thf(func_def_461,type,
sK320: ( subst > term > subst > $o ) > subst ).
thf(func_def_462,type,
sK321: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_463,type,
sK322: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_464,type,
sK323: ( subst > term > term ) > subst ).
thf(func_def_465,type,
sK324: ( subst > term > term ) > term ).
thf(func_def_466,type,
sK325: ( subst > term > term ) > subst ).
thf(func_def_467,type,
sK326: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_468,type,
sK327: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_469,type,
sK328: ( subst > term > term ) > subst ).
thf(func_def_470,type,
sK329: ( subst > term > term ) > subst ).
thf(func_def_471,type,
sK330: ( subst > term > term ) > term ).
thf(func_def_472,type,
sK331: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_473,type,
sK332: term ).
thf(func_def_474,type,
sK333: subst > term > subst > $o ).
thf(func_def_475,type,
sK334: ( subst > term > subst > $o ) > subst ).
thf(func_def_476,type,
sK335: ( subst > term > subst > $o ) > subst ).
thf(func_def_477,type,
sK336: ( subst > term > subst > $o ) > term ).
thf(func_def_478,type,
sK337: ( subst > term > subst > $o ) > subst ).
thf(func_def_479,type,
sK338: ( subst > term > subst > $o ) > term ).
thf(func_def_480,type,
sK339: ( subst > term > subst > $o ) > subst ).
thf(func_def_481,type,
sK340: ( subst > term > subst > $o ) > term ).
thf(func_def_482,type,
sK341: ( subst > term > subst > $o ) > subst ).
thf(func_def_483,type,
sK342: ( subst > term > subst > $o ) > subst ).
thf(func_def_484,type,
sK343: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_485,type,
sK344: ( subst > term > term ) > subst ).
thf(func_def_486,type,
sK345: ( subst > term > term ) > subst ).
thf(func_def_487,type,
sK346: ( subst > term > term ) > term ).
thf(func_def_488,type,
sK347: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_489,type,
sK348: ( subst > term > subst > $o ) > term ).
thf(func_def_490,type,
sK349: ( subst > term > subst > $o ) > term ).
thf(func_def_491,type,
sK350: term ).
thf(func_def_492,type,
sK351: subst > term > subst > $o ).
thf(func_def_493,type,
sK352: ( subst > term > term ) > subst ).
thf(func_def_494,type,
sK353: ( subst > term > term ) > subst ).
thf(func_def_495,type,
sK354: ( subst > term > term ) > term ).
thf(func_def_496,type,
sK355: ( subst > term > term ) > term ).
thf(func_def_497,type,
sK356: term ).
thf(func_def_498,type,
sK357: ( subst > term > subst > $o ) > term > term ).
thf(func_def_499,type,
sK358: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_500,type,
sK359: ( subst > term > subst > $o ) > term > term ).
thf(func_def_501,type,
sK360: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_502,type,
sK361: term ).
thf(func_def_503,type,
sK362: subst > term > subst > $o ).
thf(func_def_504,type,
sK363: ( subst > term > term ) > term ).
thf(func_def_505,type,
sK364: ( subst > term > term ) > subst ).
thf(func_def_506,type,
sK365: ( subst > term > term ) > term ).
thf(func_def_507,type,
sK366: ( subst > term > term ) > subst ).
thf(func_def_508,type,
sK367: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_512,type,
sK371: ( subst > term > subst > $o ) > subst ).
thf(func_def_513,type,
sK372: ( subst > term > subst > $o ) > subst ).
thf(func_def_514,type,
sK373: ( subst > term > subst > $o ) > subst ).
thf(func_def_515,type,
sK374: ( subst > term > subst > $o ) > term ).
thf(func_def_516,type,
sK375: term ).
thf(func_def_517,type,
sK376: term ).
thf(func_def_518,type,
sK377: subst > term > subst > $o ).
thf(func_def_519,type,
sK378: ( term > $o ) > term ).
thf(func_def_520,type,
sK379: ( term > $o ) > term ).
thf(func_def_521,type,
sK380: term ).
thf(func_def_522,type,
sK381: term > $o ).
thf(func_def_523,type,
sK382: term > term ).
thf(func_def_524,type,
sK383: term ).
thf(func_def_525,type,
sK384: subst > term > subst > $o ).
thf(func_def_526,type,
sK385: ( subst > term > subst > $o ) > subst ).
thf(func_def_527,type,
sK386: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_531,type,
sK390: ( subst > term > subst > $o ) > term ).
thf(func_def_532,type,
sK391: ( subst > term > subst > $o ) > subst ).
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 ) > subst ).
thf(func_def_536,type,
sK395: ( subst > term > subst > $o ) > term ).
thf(func_def_537,type,
sK396: ( subst > term > subst > $o ) > subst ).
thf(func_def_538,type,
sK397: ( subst > term > subst > $o ) > subst ).
thf(func_def_539,type,
sK398: term > ( subst > term > subst > $o ) > term ).
thf(func_def_540,type,
sK399: ( subst > term > subst > $o ) > subst ).
thf(func_def_541,type,
sK400: ( subst > term > subst > $o ) > subst ).
thf(func_def_542,type,
sK401: ( subst > term > subst > $o ) > subst ).
thf(func_def_543,type,
sK402: ( subst > term > subst > $o ) > term ).
thf(func_def_544,type,
sK403: subst > term > subst > $o ).
thf(func_def_545,type,
sK404: term ).
thf(func_def_546,type,
sK405: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_547,type,
sK406: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_548,type,
sK407: ( subst > term > term ) > term ).
thf(func_def_549,type,
sK408: ( subst > term > term ) > subst ).
thf(func_def_550,type,
sK409: ( subst > term > term ) > subst ).
thf(func_def_551,type,
sK410: ( subst > term > subst > $o ) > term ).
thf(func_def_552,type,
sK411: ( subst > term > subst > $o ) > term ).
thf(func_def_553,type,
sK412: ( term > $o ) > term ).
thf(func_def_554,type,
sK413: ( term > $o ) > term ).
thf(func_def_555,type,
sK414: ( subst > term > subst > $o ) > term ).
thf(func_def_556,type,
sK415: ( subst > term > subst > $o ) > term ).
thf(func_def_557,type,
sK416: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_558,type,
sK417: ( subst > term > term ) > term ).
thf(func_def_559,type,
sK418: ( subst > term > term ) > subst ).
thf(func_def_560,type,
sK419: ( subst > term > term ) > subst ).
thf(func_def_561,type,
sK420: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_562,type,
sK421: subst > term > subst > $o ).
thf(func_def_563,type,
sK422: term ).
thf(func_def_564,type,
sK423: ( subst > term > subst > $o ) > term ).
thf(func_def_565,type,
sK424: ( subst > term > subst > $o ) > subst ).
thf(func_def_566,type,
sK425: ( subst > term > subst > $o ) > subst ).
thf(func_def_567,type,
sK426: ( subst > term > subst > $o ) > subst ).
thf(func_def_568,type,
sK427: term > ( subst > term > subst > $o ) > term ).
thf(func_def_569,type,
sK428: ( subst > term > subst > $o ) > subst ).
thf(func_def_570,type,
sK429: ( subst > term > subst > $o ) > term ).
thf(func_def_571,type,
sK430: ( subst > term > subst > $o ) > subst ).
thf(func_def_572,type,
sK431: ( subst > term > subst > $o ) > subst ).
thf(func_def_573,type,
sK432: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_574,type,
sK433: ( subst > term > term ) > subst ).
thf(func_def_575,type,
sK434: ( subst > term > term ) > subst ).
thf(func_def_576,type,
sK435: ( subst > term > term ) > term ).
thf(func_def_577,type,
sK436: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_578,type,
sK437: term ).
thf(func_def_579,type,
sK438: term > $o ).
thf(func_def_580,type,
sK439: term > term ).
thf(func_def_581,type,
sK440: ( term > $o ) > term ).
thf(func_def_582,type,
sK441: ( term > $o ) > term ).
thf(func_def_583,type,
sK442: ( term > $o ) > term ).
thf(func_def_584,type,
sK443: ( term > $o ) > term ).
thf(func_def_585,type,
sK444: term ).
thf(func_def_586,type,
sK445: term ).
thf(func_def_587,type,
sK446: subst > term > subst > $o ).
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: ( subst > term > subst > $o ) > subst ).
thf(func_def_593,type,
sK452: ( subst > term > subst > $o ) > term ).
thf(func_def_594,type,
sK453: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_598,type,
sK457: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_599,type,
sK458: subst > term > subst > $o ).
thf(func_def_600,type,
sK459: ( term > $o ) > term ).
thf(func_def_601,type,
sK460: subst ).
thf(func_def_602,type,
sK461: subst > term > term ).
thf(func_def_603,type,
sK462: subst > term > term ).
thf(func_def_604,type,
sK463: term ).
thf(func_def_605,type,
sK464: ( subst > term > term ) > term ).
thf(func_def_606,type,
sK465: ( subst > term > term ) > subst ).
thf(func_def_607,type,
sK466: ( subst > term > term ) > subst ).
thf(func_def_608,type,
sK467: ( subst > term > term ) > subst ).
thf(func_def_609,type,
sK468: ( subst > term > term ) > term ).
thf(func_def_610,type,
sK469: ( subst > term > term ) > subst ).
thf(func_def_611,type,
sK470: term > subst > term > term ).
thf(func_def_612,type,
sK471: term ).
thf(func_def_613,type,
sK472: ( subst > term > term ) > subst ).
thf(func_def_614,type,
sK473: ( subst > term > term ) > term ).
thf(func_def_615,type,
sK474: subst ).
thf(func_def_616,type,
sK475: subst ).
thf(func_def_617,type,
sK476: subst ).
thf(func_def_618,type,
sK477: subst ).
thf(func_def_619,type,
sK478: term ).
thf(func_def_620,type,
sK479: subst ).
thf(func_def_621,type,
sK480: term ).
thf(func_def_622,type,
sK481: subst ).
thf(func_def_623,type,
sK482: subst ).
thf(func_def_624,type,
sK483: term ).
thf(func_def_625,type,
sK484: subst ).
thf(func_def_626,type,
sK485: term > $o ).
thf(func_def_627,type,
sK486: term ).
thf(func_def_628,type,
sK487: term ).
thf(func_def_629,type,
sK488: term > $o ).
thf(func_def_630,type,
sK489: term ).
thf(func_def_631,type,
sK490: term ).
thf(func_def_632,type,
sK491: term ).
thf(func_def_633,type,
sK492: term ).
thf(func_def_634,type,
sK493: term ).
thf(func_def_635,type,
sK494: term ).
thf(func_def_636,type,
sK495: subst ).
thf(func_def_637,type,
sK496: term > subst > term > term ).
thf(func_def_638,type,
sK497: term ).
thf(func_def_639,type,
sK498: term > subst > term > term ).
thf(func_def_640,type,
sK499: term ).
thf(func_def_641,type,
sK500: ( subst > term > term ) > subst ).
thf(func_def_642,type,
sK501: ( subst > term > term ) > term ).
thf(func_def_643,type,
sK502: ( term > $o ) > term ).
thf(func_def_644,type,
sK503: ( term > $o ) > term ).
thf(func_def_645,type,
sK504: term > $o ).
thf(func_def_646,type,
sK505: term ).
thf(func_def_647,type,
sK506: term > $o ).
thf(func_def_648,type,
sK507: subst ).
thf(func_def_649,type,
sK508: term > $o ).
thf(func_def_650,type,
sK509: term ).
thf(func_def_651,type,
sK510: term > ( term > $o ) > subst > ( term > $o ) > term ).
thf(func_def_652,type,
sK511: term ).
thf(func_def_653,type,
sK512: subst ).
thf(func_def_654,type,
sK513: subst > d_subst ).
thf(func_def_655,type,
sK514: term ).
thf(func_def_656,type,
sK515: term ).
thf(func_def_657,type,
sK516: term ).
thf(func_def_658,type,
sK517: term ).
thf(func_def_659,type,
sK518: term ).
thf(func_def_660,type,
sK519: term ).
thf(func_def_661,type,
sK520: term ).
thf(func_def_662,type,
sK521: term ).
thf(func_def_663,type,
sK522: subst ).
thf(func_def_664,type,
sK523: term ).
thf(func_def_665,type,
sK524: term > $o ).
thf(func_def_666,type,
sK525: ( term > $o ) > term ).
thf(func_def_667,type,
sK526: ( term > $o ) > term > subst > term > $o ).
thf(func_def_668,type,
sK527: subst ).
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: term > $o ).
thf(func_def_673,type,
sK532: subst ).
thf(func_def_674,type,
sK533: term ).
thf(func_def_675,type,
sK534: term > $o ).
thf(func_def_676,type,
sK535: term ).
thf(func_def_677,type,
sK536: term ).
thf(func_def_678,type,
sK537: term ).
thf(func_def_679,type,
sK538: term ).
thf(func_def_680,type,
sK539: term ).
thf(func_def_681,type,
sK540: subst > term > 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: ( subst > term > term ) > subst ).
thf(func_def_685,type,
sK544: term ).
thf(func_def_686,type,
sK545: term ).
thf(func_def_687,type,
sK546: term ).
thf(func_def_688,type,
sK547: term ).
thf(func_def_689,type,
sK548: term ).
thf(func_def_690,type,
sK549: term ).
thf(func_def_691,type,
sK550: term ).
thf(func_def_692,type,
sK551: term ).
thf(func_def_693,type,
sK552: term ).
thf(func_def_694,type,
sK553: term ).
thf(func_def_695,type,
sK554: term ).
thf(func_def_696,type,
sK555: term ).
thf(func_def_697,type,
sK556: term ).
thf(func_def_698,type,
sK557: subst > term > subst > $o ).
thf(func_def_699,type,
sK558: ( term > $o ) > term ).
thf(func_def_700,type,
sK559: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_701,type,
sK560: term > subst > term > term ).
thf(func_def_702,type,
sK561: term ).
thf(func_def_703,type,
sK562: ( subst > term > subst > $o ) > term ).
thf(func_def_704,type,
sK563: ( subst > term > subst > $o ) > term ).
thf(func_def_705,type,
sK564: subst > term > subst > $o ).
thf(func_def_706,type,
sK565: term ).
thf(func_def_707,type,
sK566: subst ).
thf(func_def_708,type,
sK567: term ).
thf(func_def_709,type,
sK568: subst ).
thf(func_def_710,type,
sK569: term ).
thf(func_def_711,type,
sK570: term ).
thf(func_def_712,type,
sK571: term ).
thf(func_def_713,type,
sK572: term ).
thf(func_def_714,type,
sK573: term ).
thf(func_def_715,type,
sK574: term ).
thf(func_def_716,type,
sK575: term > $o ).
thf(func_def_717,type,
sK576: subst ).
thf(func_def_718,type,
sK577: ( term > $o ) > term ).
thf(func_def_719,type,
sK578: subst > ( term > $o ) > term > term > $o ).
thf(func_def_720,type,
sK579: subst ).
thf(func_def_721,type,
sK580: term ).
thf(func_def_722,type,
sK581: term > $o ).
thf(func_def_723,type,
sK582: term > $o ).
thf(func_def_724,type,
sK583: ( term > $o ) > ( term > $o ) > term > subst > term ).
thf(func_def_725,type,
sK584: term > d_term ).
thf(func_def_726,type,
sK585: term ).
thf(func_def_727,type,
sK586: term ).
thf(func_def_728,type,
sK587: term ).
thf(func_def_729,type,
sK588: term ).
thf(func_def_730,type,
sK589: subst ).
thf(func_def_731,type,
sK590: subst ).
thf(func_def_732,type,
sK591: subst ).
thf(func_def_733,type,
sK592: term ).
thf(func_def_734,type,
sK593: term > $o ).
thf(func_def_735,type,
sK594: ( term > $o ) > term > subst > term > $o ).
thf(func_def_737,type,
sK596: ( term > $o ) > term ).
thf(func_def_738,type,
ph597:
!>[X0: $tType] : X0 ).
thf(f3221,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3015,f3023,f3066,f3109,f3134,f3187,f3189,f3205,f3220]) ).
thf(f3220,plain,
( ~ spl595_89
| ~ spl595_93 ),
inference(avatar_contradiction_clause,[status(thm)],[f3219]) ).
thf(f3219,plain,
( $false
| ~ spl595_89
| ~ spl595_93 ),
inference(trivial_inequality_removal,[status(thm)],[f3215]) ).
thf(f3215,plain,
( ( $true = $false )
| ~ spl595_89
| ~ spl595_93 ),
inference(superposition,[status(thm)],[f3087,f3108]) ).
thf(f3108,plain,
( ( $false
= ( sK593 @ ( d2term @ d_one ) ) )
| ~ spl595_93 ),
inference(avatar_component_clause,[status(thm)],[f3106]) ).
thf(f3106,definition,
( spl595_93
<=> ( $false
= ( sK593 @ ( d2term @ d_one ) ) ) ),
introduced(definition,[new_symbols(naming,[spl595_93])],[avatar_definition]) ).
thf(f3087,plain,
( ! [X0: term] :
( ( sK593 @ X0 )
= $true )
| ~ spl595_89 ),
inference(superposition,[status(thm)],[f3010,f2251]) ).
thf(f2251,plain,
! [X258: term] :
( ( d2term @ d_one )
= X258 ),
inference(forward_demodulation,[status(thm)],[f1060,f1117]) ).
thf(f1117,plain,
! [X203: d_term] : ( d_one = X203 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( ! [X0: subst > term > subst > $o,X2: term] :
( ( X0 @ id @ X2 @ id )
= ( sK457 @ X0 @ X2 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X4: term > $o] :
( ( sK458 @ id @ ( sK459 @ X4 ) @ id )
!= ( X4 @ ( sK459 @ X4 ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
| ( ! [X10: term,X11: subst,X12: subst] :
( ( sK462 @ ( comp @ X11 @ X12 ) @ ( sub @ X10 @ X12 ) )
= ( sub @ ( sK462 @ X11 @ X10 ) @ X12 ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( sK461 @ X15 @ X14 ) @ X13 )
= ( sK461 @ ( comp @ X15 @ X13 ) @ ( sub @ X14 @ X13 ) ) )
& ( ( lam @ ( sK461 @ sh @ one ) )
= ( lam @ ( sK462 @ sh @ one ) ) )
& ( ( sK461 @ sK460 @ sK463 )
!= ( sK462 @ sK460 @ sK463 ) ) ) )
& ( ! [X16: subst,X17: subst > term > term,X18: subst > term > term,X19: term] :
( ( ( X18 @ ( comp @ ( sK465 @ X18 ) @ ( sK466 @ X18 ) ) @ ( sub @ ( sK464 @ X18 ) @ ( sK466 @ X18 ) ) )
!= ( sub @ ( X18 @ ( sK465 @ X18 ) @ ( sK464 @ X18 ) ) @ ( sK466 @ X18 ) ) )
| ( ( sub @ ( X17 @ ( sK469 @ X17 ) @ ( sK468 @ X17 ) ) @ ( sK467 @ X17 ) )
!= ( X17 @ ( comp @ ( sK469 @ X17 ) @ ( sK467 @ X17 ) ) @ ( sub @ ( sK468 @ X17 ) @ ( sK467 @ X17 ) ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X17 @ sh @ one ) ) )
| ( ( X18 @ X16 @ X19 )
= ( X17 @ X16 @ X19 ) ) )
| ( hoaslaminj != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP58 != $true ) )
& ( ( sP58 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X26: term,X28: subst,X29: term] :
( ( sK470 @ X26 @ X28 @ X29 )
= ( sub @ X26 @ ( push @ X29 @ X28 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X31: subst > term > term] :
( ( X31 @ ( sK472 @ X31 ) @ ( sK473 @ X31 ) )
!= ( sub @ sK471 @ ( push @ ( sK473 @ X31 ) @ ( sK472 @ X31 ) ) ) ) )
& ( ( induction2_lthm = $true )
| ( sP57 != $true ) )
& ( ( sP57 = $true )
| ( induction2_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3a != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X34: subst] :
( ( comp @ X34 @ id )
= X34 )
& ( ( sK474
!= ( comp @ sK474 @ id ) )
| ( ( comp @ id @ sK475 )
!= sK475 ) )
& ! [X37: subst] :
( ( comp @ id @ X37 )
= X37 ) ) )
& ( ( sK476
!= ( comp @ sK476 @ id ) )
| ( ! [X39: subst] :
( ( comp @ X39 @ id )
= X39 )
& ! [X40: subst] :
( ( comp @ id @ X40 )
= X40 ) )
| ( sK477
!= ( comp @ id @ sK477 ) )
| ( substmonoid_lthm != $true ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X42: term,X43: subst] :
( ( sub @ one @ ( push @ X42 @ X43 ) )
= X42 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ( ( sub @ one @ ( push @ sK478 @ sK479 ) )
!= sK478 ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP50 != $true ) )
& ( ulamvarsh = $true )
& ( ( sK480
!= ( sub @ one @ ( push @ sK480 @ sK481 ) ) )
| ( ( comp @ sh @ ( push @ sK483 @ sK482 ) )
!= sK482 )
| ! [X50: subst,X51: term > $o,X52: term,X53: term,X54: term > $o] :
( ( ( X54 @ X53 )
!= $true )
| ( $true
= ( X51 @ ( sub @ X53 @ ( push @ X52 @ X50 ) ) ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X55: term,X56: subst] :
( ( sub @ one @ ( push @ X55 @ X56 ) )
= X55 )
& ! [X57: subst,X58: term] :
( ( comp @ sh @ ( push @ X58 @ X57 ) )
= X57 )
& ( ( sK488 @ sK487 )
= $true )
& ( ( sK485 @ ( sub @ sK487 @ ( push @ sK486 @ sK484 ) ) )
!= $true ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP48 != $true ) )
& ( ( sP48 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ! [X64: d_subst,X65: d_subst] :
( ( ( d2subst @ X65 )
!= ( d2subst @ X64 ) )
| ( X64 = X65 ) )
& ( ( hoasapinj2 = $true )
| ( ( sK491 != sK492 )
& ( ( ap @ ( sub @ sK489 @ id ) @ sK492 )
= ( ap @ ( sub @ sK490 @ id ) @ sK491 ) ) ) )
& ( ! [X70: term,X71: term,X72: term,X73: term] :
( ( X72 = X73 )
| ( ( ap @ ( sub @ X70 @ id ) @ X73 )
!= ( ap @ ( sub @ X71 @ id ) @ X72 ) ) )
| ( hoasapinj2 != $true ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3v2 != $true ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
| ( ( ( lam @ sK493 )
= ( lam @ sK494 ) )
& ( sK494 != sK493 ) ) )
& ( ! [X76: term,X77: term] :
( ( ( lam @ X77 )
!= ( lam @ X76 ) )
| ( X76 = X77 ) )
| ( laminj != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ( $true = sP45 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP45 ) )
& ( ( axidr = $true )
| ( sK495
!= ( comp @ sK495 @ id ) ) )
& ( ! [X79: subst] :
( ( comp @ X79 @ id )
= X79 )
| ( axidr != $true ) )
& ( ! [X80: term] :
( ( sK496 @ X80 @ sh @ one )
= ( sub @ X80 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X83: subst > term > term] :
( ( sub @ sK497 @ ( push @ one @ sh ) )
!= ( X83 @ sh @ one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X84: term,X86: subst,X87: term] :
( ( sK498 @ X84 @ X86 @ X87 )
= ( sub @ X84 @ ( push @ X87 @ X86 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X89: subst > term > term] :
( ( X89 @ ( sK500 @ X89 ) @ ( sK501 @ X89 ) )
!= ( sub @ sK499 @ ( push @ ( sK501 @ X89 ) @ ( sK500 @ X89 ) ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X92: term > $o,X93: term] :
( ( ( sP43 @ X92 )
= $true )
| ( ( ( var @ ( sK502 @ X92 ) )
= $true )
& ( $true
!= ( X92 @ ( sK502 @ X92 ) ) ) )
| ( ( ( X92 @ ( lam @ ( sK503 @ X92 ) ) )
!= $true )
& ( $true
= ( X92 @ ( sK503 @ X92 ) ) ) )
| ( ( X92 @ X93 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ( ( ( sP43 @ sK504 )
!= $true )
& ! [X98: term] :
( ( ( var @ X98 )
!= $true )
| ( ( sK504 @ X98 )
= $true ) )
& ! [X99: term] :
( ( ( sK504 @ ( lam @ X99 ) )
= $true )
| ( ( sK504 @ X99 )
!= $true ) )
& ( $true
!= ( sK504 @ sK505 ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ( ( sK506 @ one )
!= $true )
& ( ( sK508 @ sK509 )
= $true )
& ! [X104: term] :
( ( sK506 @ X104 )
= ( sK508 @ ( sub @ X104 @ ( push @ sK509 @ sK507 ) ) ) )
& ! [X105: term,X106: subst] :
( ( sub @ one @ ( push @ X105 @ X106 ) )
= X105 ) ) )
& ( ! [X107: term > $o,X108: subst,X109: term > $o,X110: term] :
( ( $true
= ( X107 @ one ) )
| ( ( X109 @ X110 )
!= $true )
| ( ( X107 @ ( sK510 @ X110 @ X109 @ X108 @ X107 ) )
!= ( X109 @ ( sub @ ( sK510 @ X110 @ X109 @ X108 @ X107 ) @ ( push @ X110 @ X108 ) ) ) ) )
| ( sK511
!= ( sub @ one @ ( push @ sK511 @ sK512 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( $true = sP42 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP42 ) )
& ! [X114: subst] :
( ( d2subst @ ( sK513 @ X114 ) )
= X114 )
& ! [X116: d_subst] : ( d_id = X116 )
& ( ! [X117: term,X118: term,X119: term,X120: term] :
( ( X117 = X119 )
| ( ( ap @ ( sub @ X118 @ id ) @ X117 )
!= ( ap @ ( sub @ X120 @ id ) @ X119 ) ) )
| ( ( sK517 != sK514 )
& ( ( ap @ sK515 @ sK517 )
= ( ap @ sK516 @ sK514 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ( sK520 != sK518 )
& ( ( ap @ ( sub @ sK519 @ id ) @ sK518 )
= ( ap @ ( sub @ sK521 @ id ) @ sK520 ) )
& ! [X129: term,X130: term,X131: term,X132: term] :
( ( X129 = X132 )
| ( ( ap @ X131 @ X129 )
!= ( ap @ X130 @ X132 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ! [X136: term > $o] :
( ( X136 @ ( sK525 @ X136 ) )
!= ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) ) ) )
& ( ! [X138: subst,X139: term,X140: term > $o,X142: term] :
( ( X140 @ ( sub @ X142 @ ( push @ X139 @ X138 ) ) )
= ( sK526 @ X140 @ X139 @ X138 @ X142 ) )
| ( pushprop_lem0 != $true ) )
& ( ! [X143: subst] :
( ( push @ ( sub @ one @ X143 ) @ ( comp @ sh @ X143 ) )
= X143 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ( sK527
!= ( push @ ( sub @ one @ sK527 ) @ ( comp @ sh @ sK527 ) ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( $true = sP39 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP39 ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
| ( ( ( sub @ sK528 @ sh )
= ( sub @ sK529 @ sh ) )
& ( sK529 != sK528 ) ) )
& ( ! [X147: term,X148: term] :
( ( ( sub @ X148 @ sh )
!= ( sub @ X147 @ sh ) )
| ( X147 = X148 ) )
| ( shinj != $true ) )
& ( induction2_gthm = $true )
& ( ! [X149: term,X150: term > $o,X151: subst,X152: term,X153: term > $o] :
( ( $true
!= ( X150 @ X149 ) )
| ( ( X153 @ ( sub @ X149 @ ( push @ X152 @ X151 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK531 @ sK530 )
= $true )
& ( ( sK534 @ ( sub @ sK530 @ ( push @ sK533 @ sK532 ) ) )
!= $true ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X159: term] :
( ( sub @ X159 @ id )
= X159 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ( sK535
!= ( sub @ sK535 @ id ) ) )
& ( ( sK536
!= ( sub @ sK536 @ id ) )
| ! [X162: term] :
( ( sub @ X162 @ id )
= X162 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X163: term] :
( ( sub @ X163 @ id )
= X163 )
& ( sK537
!= ( sub @ sK537 @ id ) ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ( ( ( lam @ ( sK540 @ sh @ one ) )
= ( ap @ ( sub @ sK538 @ id ) @ sK539 ) )
& ! [X168: subst,X169: term,X170: subst] :
( ( sK540 @ ( comp @ X170 @ X168 ) @ ( sub @ X169 @ X168 ) )
= ( sub @ ( sK540 @ X170 @ X169 ) @ X168 ) ) ) )
& ( ! [X171: term,X172: term,X173: subst > term > term] :
( ( ( lam @ ( X173 @ sh @ one ) )
!= ( ap @ ( sub @ X171 @ id ) @ X172 ) )
| ( ( sub @ ( X173 @ ( sK543 @ X173 ) @ ( sK542 @ X173 ) ) @ ( sK541 @ X173 ) )
!= ( X173 @ ( comp @ ( sK543 @ X173 ) @ ( sK541 @ X173 ) ) @ ( sub @ ( sK542 @ X173 ) @ ( sK541 @ X173 ) ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( ( ( ap @ sK545 @ sK547 )
= ( ap @ sK546 @ sK544 ) )
& ( sK545 != sK546 ) )
| ! [X181: term,X182: term,X183: term,X184: term] :
( ( X182 = X184 )
| ( ( ap @ ( sub @ X182 @ id ) @ X183 )
!= ( ap @ ( sub @ X184 @ id ) @ X181 ) ) )
| ( ( sub @ sK548 @ id )
!= sK548 )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X186: term,X187: term,X188: term,X189: term] :
( ( ( ap @ X188 @ X186 )
!= ( ap @ X187 @ X189 ) )
| ( X187 = X188 ) )
& ( sK552 != sK550 )
& ( ( ap @ ( sub @ sK552 @ id ) @ sK549 )
= ( ap @ ( sub @ sK550 @ id ) @ sK551 ) )
& ! [X194: term] :
( ( sub @ X194 @ id )
= X194 ) ) )
& ( ! [X195: term,X196: term,X197: term,X198: term] :
( ( X195 = X197 )
| ( ( ap @ ( sub @ X195 @ id ) @ X196 )
!= ( ap @ ( sub @ X197 @ id ) @ X198 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( sK555 != sK553 )
& ( ( ap @ ( sub @ sK553 @ id ) @ sK554 )
= ( ap @ ( sub @ sK555 @ id ) @ sK556 ) ) ) )
& ! [X203: d_term] : ( d_one = X203 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP31 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
| ! [X205: term > $o] :
( ( X205 @ ( sK558 @ X205 ) )
!= ( sK557 @ id @ ( sK558 @ X205 ) @ id ) ) )
& ( ! [X207: subst > term > subst > $o,X209: term] :
( ( X207 @ id @ X209 @ id )
= ( sK559 @ X207 @ X209 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( sP26 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( sP26 != $true ) )
& ( ! [X210: term] :
( ( sK560 @ X210 @ sh @ one )
= ( sub @ X210 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X213: subst > term > term] :
( ( X213 @ sh @ one )
!= ( sub @ sK561 @ ( push @ one @ sh ) ) ) )
& ( pushprop_lthm = $true )
& ( ( $true = sP22 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP22 ) )
& ( ! [X214: subst > term > subst > $o,X215: term] :
( ( ( ( X214 @ id @ ( sK562 @ X214 ) @ id )
= $true )
& ( ( X214 @ id @ ( ap @ ( sub @ ( sK562 @ X214 ) @ id ) @ ( sK563 @ X214 ) ) @ id )
!= $true )
& ( $true
= ( X214 @ id @ ( sK563 @ X214 ) @ id ) ) )
| ( ( sP20 @ X214 )
= $true )
| ( ( X214 @ id @ X215 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X220: term,X221: term] :
( ( ( sK564 @ id @ X220 @ id )
!= $true )
| ( ( sK564 @ id @ ( ap @ ( sub @ X220 @ id ) @ X221 ) @ id )
= $true )
| ( ( sK564 @ id @ X221 @ id )
!= $true ) )
& ( $true
!= ( sP20 @ sK564 ) )
& ( $true
!= ( sK564 @ id @ sK565 @ id ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X222: subst] :
( ( comp @ id @ X222 )
= X222 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ( ( comp @ id @ sK566 )
!= sK566 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK567 @ sK568 ) )
!= sK568 ) )
& ( ! [X226: term,X227: subst] :
( ( comp @ sh @ ( push @ X226 @ X227 ) )
= X227 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
| ( ( sK571 != sK572 )
& ( ( ap @ sK572 @ sK570 )
= ( ap @ sK571 @ sK569 ) ) ) )
& ( ! [X232: term,X233: term,X234: term,X235: term] :
( ( X234 = X235 )
| ( ( ap @ X234 @ X232 )
!= ( ap @ X235 @ X233 ) ) )
| ( apinj1 != $true ) )
& ( ( axvarid = $true )
| ( ( sub @ sK573 @ id )
!= sK573 ) )
& ( ! [X237: term] :
( ( sub @ X237 @ id )
= X237 )
| ( axvarid != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X241: term > $o] :
( ( sK575 @ ( sub @ ( sK577 @ X241 ) @ ( push @ sK574 @ sK576 ) ) )
!= ( X241 @ ( sK577 @ X241 ) ) ) )
& ( ! [X243: term,X244: term > $o,X245: subst,X247: term] :
( ( X244 @ ( sub @ X247 @ ( push @ X243 @ X245 ) ) )
= ( sK578 @ X245 @ X244 @ X243 @ X247 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ( ( sK582 @ sK580 )
= $true )
& ! [X252: term] :
( ( sK581 @ X252 )
= ( sK582 @ ( sub @ X252 @ ( push @ sK580 @ sK579 ) ) ) )
& ( ( sK581 @ one )
!= $true ) ) )
& ( ! [X253: subst,X254: term,X255: term > $o,X256: term > $o] :
( ( ( X256 @ X254 )
!= $true )
| ( ( X256 @ ( sub @ ( sK583 @ X256 @ X255 @ X254 @ X253 ) @ ( push @ X254 @ X253 ) ) )
!= ( X255 @ ( sK583 @ X256 @ X255 @ X254 @ X253 ) ) )
| ( ( X255 @ one )
= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP16 != $true ) )
& ( ( sP16 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( axapp = $true )
& ! [X258: term] :
( ( d2term @ ( sK584 @ X258 ) )
= X258 )
& ( ulamvarind = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP14 != $true ) )
& ( ! [X260: term,X261: term,X262: term,X263: term] :
( ( ( ap @ X261 @ X262 )
!= ( ap @ X263 @ X260 ) )
| ( X260 = X262 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( ( ap @ sK588 @ sK585 )
= ( ap @ sK586 @ sK587 ) )
& ( sK585 != sK587 ) ) )
& ( ( ! [X268: subst] :
( ( comp @ X268 @ id )
= X268 )
& ! [X269: subst] :
( ( comp @ id @ X269 )
= X269 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ( sK589
!= ( comp @ sK589 @ id ) )
| ( sK590
!= ( comp @ id @ sK590 ) ) )
& ( ( sP5 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP5 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X272: d_term,X273: d_term] :
( ( X272 = X273 )
| ( ( d2term @ X272 )
!= ( d2term @ X273 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
| ( $true != sP3 ) )
& ( ( $true = sP3 )
| ( induction2 != $true ) )
& ( ( $true = sP1 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f475,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476]) ).
thf(f476,plain,
! [X0: subst > term > subst > $o] :
( ? [X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
=> ! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( sK457 @ X0 @ X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
( ? [X3: subst > term > subst > $o] :
! [X4: term > $o] :
? [X5: term] :
( ( X4 @ X5 )
!= ( X3 @ id @ X5 @ id ) )
=> ! [X4: term > $o] :
? [X5: term] :
( ( X4 @ X5 )
!= ( sK458 @ id @ X5 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
! [X4: term > $o] :
( ? [X5: term] :
( ( X4 @ X5 )
!= ( sK458 @ id @ X5 @ id ) )
=> ( ( sK458 @ id @ ( sK459 @ X4 ) @ id )
!= ( X4 @ ( sK459 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X6: subst,X7: subst > term > term,X8: subst > term > term,X9: term] :
( ! [X10: term,X11: subst,X12: subst] :
( ( sub @ ( X8 @ X11 @ X10 ) @ X12 )
= ( X8 @ ( comp @ X11 @ X12 ) @ ( sub @ X10 @ X12 ) ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( X7 @ X15 @ X14 ) @ X13 )
= ( X7 @ ( comp @ X15 @ X13 ) @ ( sub @ X14 @ X13 ) ) )
& ( ( lam @ ( X7 @ sh @ one ) )
= ( lam @ ( X8 @ sh @ one ) ) )
& ( ( X7 @ X6 @ X9 )
!= ( X8 @ X6 @ X9 ) ) )
=> ( ! [X12: subst,X11: subst,X10: term] :
( ( sK462 @ ( comp @ X11 @ X12 ) @ ( sub @ X10 @ X12 ) )
= ( sub @ ( sK462 @ X11 @ X10 ) @ X12 ) )
& ! [X15: subst,X14: term,X13: subst] :
( ( sub @ ( sK461 @ X15 @ X14 ) @ X13 )
= ( sK461 @ ( comp @ X15 @ X13 ) @ ( sub @ X14 @ X13 ) ) )
& ( ( lam @ ( sK461 @ sh @ one ) )
= ( lam @ ( sK462 @ sh @ one ) ) )
& ( ( sK461 @ sK460 @ sK463 )
!= ( sK462 @ sK460 @ sK463 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
! [X18: subst > term > term] :
( ? [X20: term,X21: subst,X22: subst] :
( ( sub @ ( X18 @ X21 @ X20 ) @ X22 )
!= ( X18 @ ( comp @ X21 @ X22 ) @ ( sub @ X20 @ X22 ) ) )
=> ( ( X18 @ ( comp @ ( sK465 @ X18 ) @ ( sK466 @ X18 ) ) @ ( sub @ ( sK464 @ X18 ) @ ( sK466 @ X18 ) ) )
!= ( sub @ ( X18 @ ( sK465 @ X18 ) @ ( sK464 @ X18 ) ) @ ( sK466 @ X18 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
! [X17: subst > term > term] :
( ? [X23: subst,X24: term,X25: subst] :
( ( X17 @ ( comp @ X25 @ X23 ) @ ( sub @ X24 @ X23 ) )
!= ( sub @ ( X17 @ X25 @ X24 ) @ X23 ) )
=> ( ( sub @ ( X17 @ ( sK469 @ X17 ) @ ( sK468 @ X17 ) ) @ ( sK467 @ X17 ) )
!= ( X17 @ ( comp @ ( sK469 @ X17 ) @ ( sK467 @ X17 ) ) @ ( sub @ ( sK468 @ X17 ) @ ( sK467 @ X17 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
! [X26: term] :
( ? [X27: subst > term > term] :
! [X28: subst,X29: term] :
( ( X27 @ X28 @ X29 )
= ( sub @ X26 @ ( push @ X29 @ X28 ) ) )
=> ! [X29: term,X28: subst] :
( ( sK470 @ X26 @ X28 @ X29 )
= ( sub @ X26 @ ( push @ X29 @ X28 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
( ? [X30: term] :
! [X31: subst > term > term] :
? [X32: subst,X33: term] :
( ( X31 @ X32 @ X33 )
!= ( sub @ X30 @ ( push @ X33 @ X32 ) ) )
=> ! [X31: subst > term > term] :
? [X33: term,X32: subst] :
( ( X31 @ X32 @ X33 )
!= ( sub @ sK471 @ ( push @ X33 @ X32 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
! [X31: subst > term > term] :
( ? [X33: term,X32: subst] :
( ( X31 @ X32 @ X33 )
!= ( sub @ sK471 @ ( push @ X33 @ X32 ) ) )
=> ( ( X31 @ ( sK472 @ X31 ) @ ( sK473 @ X31 ) )
!= ( sub @ sK471 @ ( push @ ( sK473 @ X31 ) @ ( sK472 @ X31 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
( ? [X35: subst] :
( ( comp @ X35 @ id )
!= X35 )
=> ( sK474
!= ( comp @ sK474 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
( ? [X36: subst] :
( ( comp @ id @ X36 )
!= X36 )
=> ( ( comp @ id @ sK475 )
!= sK475 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
( ? [X38: subst] :
( ( comp @ X38 @ id )
!= X38 )
=> ( sK476
!= ( comp @ sK476 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
( ? [X41: subst] :
( ( comp @ id @ X41 )
!= X41 )
=> ( sK477
!= ( comp @ id @ sK477 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
( ? [X44: term,X45: subst] :
( ( sub @ one @ ( push @ X44 @ X45 ) )
!= X44 )
=> ( ( sub @ one @ ( push @ sK478 @ sK479 ) )
!= sK478 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
( ? [X46: term,X47: subst] :
( ( sub @ one @ ( push @ X46 @ X47 ) )
!= X46 )
=> ( sK480
!= ( sub @ one @ ( push @ sK480 @ sK481 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
( ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 )
=> ( ( comp @ sh @ ( push @ sK483 @ sK482 ) )
!= sK482 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
( ? [X59: subst,X60: term > $o,X61: term,X62: term,X63: term > $o] :
( ( ( X63 @ X62 )
= $true )
& ( ( X60 @ ( sub @ X62 @ ( push @ X61 @ X59 ) ) )
!= $true ) )
=> ( ( ( sK488 @ sK487 )
= $true )
& ( ( sK485 @ ( sub @ sK487 @ ( push @ sK486 @ sK484 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
( ? [X66: term,X67: term,X68: term,X69: term] :
( ( X68 != X69 )
& ( ( ap @ ( sub @ X67 @ id ) @ X68 )
= ( ap @ ( sub @ X66 @ id ) @ X69 ) ) )
=> ( ( sK491 != sK492 )
& ( ( ap @ ( sub @ sK489 @ id ) @ sK492 )
= ( ap @ ( sub @ sK490 @ id ) @ sK491 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
( ? [X74: term,X75: term] :
( ( ( lam @ X75 )
= ( lam @ X74 ) )
& ( X74 != X75 ) )
=> ( ( ( lam @ sK493 )
= ( lam @ sK494 ) )
& ( sK494 != sK493 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
( ? [X78: subst] :
( ( comp @ X78 @ id )
!= X78 )
=> ( sK495
!= ( comp @ sK495 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
! [X80: term] :
( ? [X81: subst > term > term] :
( ( X81 @ sh @ one )
= ( sub @ X80 @ ( push @ one @ sh ) ) )
=> ( ( sK496 @ X80 @ sh @ one )
= ( sub @ X80 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
( ? [X82: term] :
! [X83: subst > term > term] :
( ( sub @ X82 @ ( push @ one @ sh ) )
!= ( X83 @ sh @ one ) )
=> ! [X83: subst > term > term] :
( ( sub @ sK497 @ ( push @ one @ sh ) )
!= ( X83 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
! [X84: term] :
( ? [X85: subst > term > term] :
! [X86: subst,X87: term] :
( ( X85 @ X86 @ X87 )
= ( sub @ X84 @ ( push @ X87 @ X86 ) ) )
=> ! [X87: term,X86: subst] :
( ( sK498 @ X84 @ X86 @ X87 )
= ( sub @ X84 @ ( push @ X87 @ X86 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
( ? [X88: term] :
! [X89: subst > term > term] :
? [X90: subst,X91: term] :
( ( X89 @ X90 @ X91 )
!= ( sub @ X88 @ ( push @ X91 @ X90 ) ) )
=> ! [X89: subst > term > term] :
? [X91: term,X90: subst] :
( ( X89 @ X90 @ X91 )
!= ( sub @ sK499 @ ( push @ X91 @ X90 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
! [X89: subst > term > term] :
( ? [X91: term,X90: subst] :
( ( X89 @ X90 @ X91 )
!= ( sub @ sK499 @ ( push @ X91 @ X90 ) ) )
=> ( ( X89 @ ( sK500 @ X89 ) @ ( sK501 @ X89 ) )
!= ( sub @ sK499 @ ( push @ ( sK501 @ X89 ) @ ( sK500 @ X89 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
! [X92: term > $o] :
( ? [X94: term] :
( ( ( var @ X94 )
= $true )
& ( ( X92 @ X94 )
!= $true ) )
=> ( ( ( var @ ( sK502 @ X92 ) )
= $true )
& ( $true
!= ( X92 @ ( sK502 @ X92 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
! [X92: term > $o] :
( ? [X95: term] :
( ( $true
!= ( X92 @ ( lam @ X95 ) ) )
& ( $true
= ( X92 @ X95 ) ) )
=> ( ( ( X92 @ ( lam @ ( sK503 @ X92 ) ) )
!= $true )
& ( $true
= ( X92 @ ( sK503 @ X92 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
( ? [X96: term > $o,X97: term] :
( ( ( sP43 @ X96 )
!= $true )
& ! [X98: term] :
( ( ( var @ X98 )
!= $true )
| ( $true
= ( X96 @ X98 ) ) )
& ! [X99: term] :
( ( ( X96 @ ( lam @ X99 ) )
= $true )
| ( ( X96 @ X99 )
!= $true ) )
& ( $true
!= ( X96 @ X97 ) ) )
=> ( ( ( sP43 @ sK504 )
!= $true )
& ! [X98: term] :
( ( ( var @ X98 )
!= $true )
| ( ( sK504 @ X98 )
= $true ) )
& ! [X99: term] :
( ( ( sK504 @ ( lam @ X99 ) )
= $true )
| ( ( sK504 @ X99 )
!= $true ) )
& ( $true
!= ( sK504 @ sK505 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
( ? [X100: term > $o,X101: subst,X102: term > $o,X103: term] :
( ( $true
!= ( X100 @ one ) )
& ( $true
= ( X102 @ X103 ) )
& ! [X104: term] :
( ( X102 @ ( sub @ X104 @ ( push @ X103 @ X101 ) ) )
= ( X100 @ X104 ) ) )
=> ( ( ( sK506 @ one )
!= $true )
& ( ( sK508 @ sK509 )
= $true )
& ! [X104: term] :
( ( sK506 @ X104 )
= ( sK508 @ ( sub @ X104 @ ( push @ sK509 @ sK507 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
! [X107: term > $o,X108: subst,X109: term > $o,X110: term] :
( ? [X111: term] :
( ( X107 @ X111 )
!= ( X109 @ ( sub @ X111 @ ( push @ X110 @ X108 ) ) ) )
=> ( ( X107 @ ( sK510 @ X110 @ X109 @ X108 @ X107 ) )
!= ( X109 @ ( sub @ ( sK510 @ X110 @ X109 @ X108 @ X107 ) @ ( push @ X110 @ X108 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
( ? [X112: term,X113: subst] :
( ( sub @ one @ ( push @ X112 @ X113 ) )
!= X112 )
=> ( sK511
!= ( sub @ one @ ( push @ sK511 @ sK512 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
! [X114: subst] :
( ? [X115: d_subst] :
( ( d2subst @ X115 )
= X114 )
=> ( ( d2subst @ ( sK513 @ X114 ) )
= X114 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X121: term,X122: term,X123: term,X124: term] :
( ( X121 != X124 )
& ( ( ap @ X122 @ X124 )
= ( ap @ X123 @ X121 ) ) )
=> ( ( sK517 != sK514 )
& ( ( ap @ sK515 @ sK517 )
= ( ap @ sK516 @ sK514 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
( ? [X125: term,X126: term,X127: term,X128: term] :
( ( X125 != X127 )
& ( ( ap @ ( sub @ X126 @ id ) @ X125 )
= ( ap @ ( sub @ X128 @ id ) @ X127 ) ) )
=> ( ( sK520 != sK518 )
& ( ( ap @ ( sub @ sK519 @ id ) @ sK518 )
= ( ap @ ( sub @ sK521 @ id ) @ sK520 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
( ? [X133: subst,X134: term,X135: term > $o] :
! [X136: term > $o] :
? [X137: term] :
( ( X135 @ ( sub @ X137 @ ( push @ X134 @ X133 ) ) )
!= ( X136 @ X137 ) )
=> ! [X136: term > $o] :
? [X137: term] :
( ( sK524 @ ( sub @ X137 @ ( push @ sK523 @ sK522 ) ) )
!= ( X136 @ X137 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
! [X136: term > $o] :
( ? [X137: term] :
( ( sK524 @ ( sub @ X137 @ ( push @ sK523 @ sK522 ) ) )
!= ( X136 @ X137 ) )
=> ( ( X136 @ ( sK525 @ X136 ) )
!= ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
! [X138: subst,X139: term,X140: term > $o] :
( ? [X141: term > $o] :
! [X142: term] :
( ( X141 @ X142 )
= ( X140 @ ( sub @ X142 @ ( push @ X139 @ X138 ) ) ) )
=> ! [X142: term] :
( ( X140 @ ( sub @ X142 @ ( push @ X139 @ X138 ) ) )
= ( sK526 @ X140 @ X139 @ X138 @ X142 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
( ? [X144: subst] :
( ( push @ ( sub @ one @ X144 ) @ ( comp @ sh @ X144 ) )
!= X144 )
=> ( sK527
!= ( push @ ( sub @ one @ sK527 ) @ ( comp @ sh @ sK527 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ? [X145: term,X146: term] :
( ( ( sub @ X145 @ sh )
= ( sub @ X146 @ sh ) )
& ( X145 != X146 ) )
=> ( ( ( sub @ sK528 @ sh )
= ( sub @ sK529 @ sh ) )
& ( sK529 != sK528 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
( ? [X154: term,X155: term > $o,X156: subst,X157: term,X158: term > $o] :
( ( ( X155 @ X154 )
= $true )
& ( $true
!= ( X158 @ ( sub @ X154 @ ( push @ X157 @ X156 ) ) ) ) )
=> ( ( ( sK531 @ sK530 )
= $true )
& ( ( sK534 @ ( sub @ sK530 @ ( push @ sK533 @ sK532 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
( ? [X160: term] :
( ( sub @ X160 @ id )
!= X160 )
=> ( sK535
!= ( sub @ sK535 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
( ? [X161: term] :
( ( sub @ X161 @ id )
!= X161 )
=> ( sK536
!= ( sub @ sK536 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
( ? [X164: term] :
( ( sub @ X164 @ id )
!= X164 )
=> ( sK537
!= ( sub @ sK537 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
( ? [X165: term,X166: term,X167: subst > term > term] :
( ( ( ap @ ( sub @ X165 @ id ) @ X166 )
= ( lam @ ( X167 @ sh @ one ) ) )
& ! [X168: subst,X169: term,X170: subst] :
( ( X167 @ ( comp @ X170 @ X168 ) @ ( sub @ X169 @ X168 ) )
= ( sub @ ( X167 @ X170 @ X169 ) @ X168 ) ) )
=> ( ( ( lam @ ( sK540 @ sh @ one ) )
= ( ap @ ( sub @ sK538 @ id ) @ sK539 ) )
& ! [X170: subst,X169: term,X168: subst] :
( ( sK540 @ ( comp @ X170 @ X168 ) @ ( sub @ X169 @ X168 ) )
= ( sub @ ( sK540 @ X170 @ X169 ) @ X168 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
! [X173: subst > term > term] :
( ? [X174: subst,X175: term,X176: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X174 )
!= ( X173 @ ( comp @ X176 @ X174 ) @ ( sub @ X175 @ X174 ) ) )
=> ( ( sub @ ( X173 @ ( sK543 @ X173 ) @ ( sK542 @ X173 ) ) @ ( sK541 @ X173 ) )
!= ( X173 @ ( comp @ ( sK543 @ X173 ) @ ( sK541 @ X173 ) ) @ ( sub @ ( sK542 @ X173 ) @ ( sK541 @ X173 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X177: term,X178: term,X179: term,X180: term] :
( ( ( ap @ X179 @ X177 )
= ( ap @ X178 @ X180 ) )
& ( X178 != X179 ) )
=> ( ( ( ap @ sK545 @ sK547 )
= ( ap @ sK546 @ sK544 ) )
& ( sK545 != sK546 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
( ? [X185: term] :
( ( sub @ X185 @ id )
!= X185 )
=> ( ( sub @ sK548 @ id )
!= sK548 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
( ? [X190: term,X191: term,X192: term,X193: term] :
( ( X191 != X193 )
& ( ( ap @ ( sub @ X191 @ id ) @ X192 )
= ( ap @ ( sub @ X193 @ id ) @ X190 ) ) )
=> ( ( sK552 != sK550 )
& ( ( ap @ ( sub @ sK552 @ id ) @ sK549 )
= ( ap @ ( sub @ sK550 @ id ) @ sK551 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
( ? [X199: term,X200: term,X201: term,X202: term] :
( ( X199 != X201 )
& ( ( ap @ ( sub @ X199 @ id ) @ X200 )
= ( ap @ ( sub @ X201 @ id ) @ X202 ) ) )
=> ( ( sK555 != sK553 )
& ( ( ap @ ( sub @ sK553 @ id ) @ sK554 )
= ( ap @ ( sub @ sK555 @ id ) @ sK556 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
( ? [X204: subst > term > subst > $o] :
! [X205: term > $o] :
? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ id @ X206 @ id ) )
=> ! [X205: term > $o] :
? [X206: term] :
( ( X205 @ X206 )
!= ( sK557 @ id @ X206 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
! [X205: term > $o] :
( ? [X206: term] :
( ( X205 @ X206 )
!= ( sK557 @ id @ X206 @ id ) )
=> ( ( X205 @ ( sK558 @ X205 ) )
!= ( sK557 @ id @ ( sK558 @ X205 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
! [X207: subst > term > subst > $o] :
( ? [X208: term > $o] :
! [X209: term] :
( ( X208 @ X209 )
= ( X207 @ id @ X209 @ id ) )
=> ! [X209: term] :
( ( X207 @ id @ X209 @ id )
= ( sK559 @ X207 @ X209 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
! [X210: term] :
( ? [X211: subst > term > term] :
( ( X211 @ sh @ one )
= ( sub @ X210 @ ( push @ one @ sh ) ) )
=> ( ( sK560 @ X210 @ sh @ one )
= ( sub @ X210 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
( ? [X212: term] :
! [X213: subst > term > term] :
( ( X213 @ sh @ one )
!= ( sub @ X212 @ ( push @ one @ sh ) ) )
=> ! [X213: subst > term > term] :
( ( X213 @ sh @ one )
!= ( sub @ sK561 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
! [X214: subst > term > subst > $o] :
( ? [X216: term,X217: term] :
( ( ( X214 @ id @ X216 @ id )
= $true )
& ( ( X214 @ id @ ( ap @ ( sub @ X216 @ id ) @ X217 ) @ id )
!= $true )
& ( $true
= ( X214 @ id @ X217 @ id ) ) )
=> ( ( ( X214 @ id @ ( sK562 @ X214 ) @ id )
= $true )
& ( ( X214 @ id @ ( ap @ ( sub @ ( sK562 @ X214 ) @ id ) @ ( sK563 @ X214 ) ) @ id )
!= $true )
& ( $true
= ( X214 @ id @ ( sK563 @ X214 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
( ? [X218: subst > term > subst > $o,X219: term] :
( ! [X220: term,X221: term] :
( ( ( X218 @ id @ X220 @ id )
!= $true )
| ( $true
= ( X218 @ id @ ( ap @ ( sub @ X220 @ id ) @ X221 ) @ id ) )
| ( ( X218 @ id @ X221 @ id )
!= $true ) )
& ( $true
!= ( sP20 @ X218 ) )
& ( ( X218 @ id @ X219 @ id )
!= $true ) )
=> ( ! [X221: term,X220: term] :
( ( ( sK564 @ id @ X220 @ id )
!= $true )
| ( ( sK564 @ id @ ( ap @ ( sub @ X220 @ id ) @ X221 ) @ id )
= $true )
| ( ( sK564 @ id @ X221 @ id )
!= $true ) )
& ( $true
!= ( sP20 @ sK564 ) )
& ( $true
!= ( sK564 @ id @ sK565 @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X223: subst] :
( ( comp @ id @ X223 )
!= X223 )
=> ( ( comp @ id @ sK566 )
!= sK566 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
( ? [X224: term,X225: subst] :
( ( comp @ sh @ ( push @ X224 @ X225 ) )
!= X225 )
=> ( ( comp @ sh @ ( push @ sK567 @ sK568 ) )
!= sK568 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
( ? [X228: term,X229: term,X230: term,X231: term] :
( ( X230 != X231 )
& ( ( ap @ X231 @ X229 )
= ( ap @ X230 @ X228 ) ) )
=> ( ( sK571 != sK572 )
& ( ( ap @ sK572 @ sK570 )
= ( ap @ sK571 @ sK569 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
( ? [X236: term] :
( ( sub @ X236 @ id )
!= X236 )
=> ( ( sub @ sK573 @ id )
!= sK573 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
( ? [X238: term,X239: term > $o,X240: subst] :
! [X241: term > $o] :
? [X242: term] :
( ( X241 @ X242 )
!= ( X239 @ ( sub @ X242 @ ( push @ X238 @ X240 ) ) ) )
=> ! [X241: term > $o] :
? [X242: term] :
( ( X241 @ X242 )
!= ( sK575 @ ( sub @ X242 @ ( push @ sK574 @ sK576 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
! [X241: term > $o] :
( ? [X242: term] :
( ( X241 @ X242 )
!= ( sK575 @ ( sub @ X242 @ ( push @ sK574 @ sK576 ) ) ) )
=> ( ( sK575 @ ( sub @ ( sK577 @ X241 ) @ ( push @ sK574 @ sK576 ) ) )
!= ( X241 @ ( sK577 @ X241 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
! [X243: term,X244: term > $o,X245: subst] :
( ? [X246: term > $o] :
! [X247: term] :
( ( X246 @ X247 )
= ( X244 @ ( sub @ X247 @ ( push @ X243 @ X245 ) ) ) )
=> ! [X247: term] :
( ( X244 @ ( sub @ X247 @ ( push @ X243 @ X245 ) ) )
= ( sK578 @ X245 @ X244 @ X243 @ X247 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
( ? [X248: subst,X249: term,X250: term > $o,X251: term > $o] :
( ( ( X251 @ X249 )
= $true )
& ! [X252: term] :
( ( X251 @ ( sub @ X252 @ ( push @ X249 @ X248 ) ) )
= ( X250 @ X252 ) )
& ( ( X250 @ one )
!= $true ) )
=> ( ( ( sK582 @ sK580 )
= $true )
& ! [X252: term] :
( ( sK581 @ X252 )
= ( sK582 @ ( sub @ X252 @ ( push @ sK580 @ sK579 ) ) ) )
& ( ( sK581 @ one )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
! [X253: subst,X254: term,X255: term > $o,X256: term > $o] :
( ? [X257: term] :
( ( X256 @ ( sub @ X257 @ ( push @ X254 @ X253 ) ) )
!= ( X255 @ X257 ) )
=> ( ( X256 @ ( sub @ ( sK583 @ X256 @ X255 @ X254 @ X253 ) @ ( push @ X254 @ X253 ) ) )
!= ( X255 @ ( sK583 @ X256 @ X255 @ X254 @ X253 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
! [X258: term] :
( ? [X259: d_term] :
( ( d2term @ X259 )
= X258 )
=> ( ( d2term @ ( sK584 @ X258 ) )
= X258 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
( ? [X264: term,X265: term,X266: term,X267: term] :
( ( ( ap @ X265 @ X266 )
= ( ap @ X267 @ X264 ) )
& ( X264 != X266 ) )
=> ( ( ( ap @ sK588 @ sK585 )
= ( ap @ sK586 @ sK587 ) )
& ( sK585 != sK587 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
( ? [X270: subst] :
( ( comp @ X270 @ id )
!= X270 )
=> ( sK589
!= ( comp @ sK589 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
( ? [X271: subst] :
( ( comp @ id @ X271 )
!= X271 )
=> ( sK590
!= ( comp @ id @ sK590 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
( ( ! [X0: subst > term > subst > $o] :
? [X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X3: subst > term > subst > $o] :
! [X4: term > $o] :
? [X5: term] :
( ( X4 @ X5 )
!= ( X3 @ id @ X5 @ id ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X6: subst,X7: subst > term > term,X8: subst > term > term,X9: term] :
( ! [X10: term,X11: subst,X12: subst] :
( ( sub @ ( X8 @ X11 @ X10 ) @ X12 )
= ( X8 @ ( comp @ X11 @ X12 ) @ ( sub @ X10 @ X12 ) ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( X7 @ X15 @ X14 ) @ X13 )
= ( X7 @ ( comp @ X15 @ X13 ) @ ( sub @ X14 @ X13 ) ) )
& ( ( lam @ ( X7 @ sh @ one ) )
= ( lam @ ( X8 @ sh @ one ) ) )
& ( ( X7 @ X6 @ X9 )
!= ( X8 @ X6 @ X9 ) ) ) )
& ( ! [X16: subst,X17: subst > term > term,X18: subst > term > term,X19: term] :
( ? [X20: term,X21: subst,X22: subst] :
( ( sub @ ( X18 @ X21 @ X20 ) @ X22 )
!= ( X18 @ ( comp @ X21 @ X22 ) @ ( sub @ X20 @ X22 ) ) )
| ? [X23: subst,X24: term,X25: subst] :
( ( X17 @ ( comp @ X25 @ X23 ) @ ( sub @ X24 @ X23 ) )
!= ( sub @ ( X17 @ X25 @ X24 ) @ X23 ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X17 @ sh @ one ) ) )
| ( ( X18 @ X16 @ X19 )
= ( X17 @ X16 @ X19 ) ) )
| ( hoaslaminj != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP58 != $true ) )
& ( ( sP58 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X26: term] :
? [X27: subst > term > term] :
! [X28: subst,X29: term] :
( ( X27 @ X28 @ X29 )
= ( sub @ X26 @ ( push @ X29 @ X28 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X30: term] :
! [X31: subst > term > term] :
? [X32: subst,X33: term] :
( ( X31 @ X32 @ X33 )
!= ( sub @ X30 @ ( push @ X33 @ X32 ) ) ) )
& ( ( induction2_lthm = $true )
| ( sP57 != $true ) )
& ( ( sP57 = $true )
| ( induction2_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3a != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X34: subst] :
( ( comp @ X34 @ id )
= X34 )
& ( ? [X35: subst] :
( ( comp @ X35 @ id )
!= X35 )
| ? [X36: subst] :
( ( comp @ id @ X36 )
!= X36 ) )
& ! [X37: subst] :
( ( comp @ id @ X37 )
= X37 ) ) )
& ( ? [X38: subst] :
( ( comp @ X38 @ id )
!= X38 )
| ( ! [X39: subst] :
( ( comp @ X39 @ id )
= X39 )
& ! [X40: subst] :
( ( comp @ id @ X40 )
= X40 ) )
| ? [X41: subst] :
( ( comp @ id @ X41 )
!= X41 )
| ( substmonoid_lthm != $true ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X42: term,X43: subst] :
( ( sub @ one @ ( push @ X42 @ X43 ) )
= X42 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X44: term,X45: subst] :
( ( sub @ one @ ( push @ X44 @ X45 ) )
!= X44 ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP50 != $true ) )
& ( ulamvarsh = $true )
& ( ? [X46: term,X47: subst] :
( ( sub @ one @ ( push @ X46 @ X47 ) )
!= X46 )
| ? [X48: subst,X49: term] :
( ( comp @ sh @ ( push @ X49 @ X48 ) )
!= X48 )
| ! [X50: subst,X51: term > $o,X52: term,X53: term,X54: term > $o] :
( ( ( X54 @ X53 )
!= $true )
| ( $true
= ( X51 @ ( sub @ X53 @ ( push @ X52 @ X50 ) ) ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X55: term,X56: subst] :
( ( sub @ one @ ( push @ X55 @ X56 ) )
= X55 )
& ! [X57: subst,X58: term] :
( ( comp @ sh @ ( push @ X58 @ X57 ) )
= X57 )
& ? [X59: subst,X60: term > $o,X61: term,X62: term,X63: term > $o] :
( ( ( X63 @ X62 )
= $true )
& ( ( X60 @ ( sub @ X62 @ ( push @ X61 @ X59 ) ) )
!= $true ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP48 != $true ) )
& ( ( sP48 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ! [X64: d_subst,X65: d_subst] :
( ( ( d2subst @ X65 )
!= ( d2subst @ X64 ) )
| ( X64 = X65 ) )
& ( ( hoasapinj2 = $true )
| ? [X66: term,X67: term,X68: term,X69: term] :
( ( X68 != X69 )
& ( ( ap @ ( sub @ X67 @ id ) @ X68 )
= ( ap @ ( sub @ X66 @ id ) @ X69 ) ) ) )
& ( ! [X70: term,X71: term,X72: term,X73: term] :
( ( X72 = X73 )
| ( ( ap @ ( sub @ X70 @ id ) @ X73 )
!= ( ap @ ( sub @ X71 @ id ) @ X72 ) ) )
| ( hoasapinj2 != $true ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3v2 != $true ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
| ? [X74: term,X75: term] :
( ( ( lam @ X75 )
= ( lam @ X74 ) )
& ( X74 != X75 ) ) )
& ( ! [X76: term,X77: term] :
( ( ( lam @ X77 )
!= ( lam @ X76 ) )
| ( X76 = X77 ) )
| ( laminj != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ( $true = sP45 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP45 ) )
& ( ( axidr = $true )
| ? [X78: subst] :
( ( comp @ X78 @ id )
!= X78 ) )
& ( ! [X79: subst] :
( ( comp @ X79 @ id )
= X79 )
| ( axidr != $true ) )
& ( ! [X80: term] :
? [X81: subst > term > term] :
( ( X81 @ sh @ one )
= ( sub @ X80 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X82: term] :
! [X83: subst > term > term] :
( ( sub @ X82 @ ( push @ one @ sh ) )
!= ( X83 @ sh @ one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X84: term] :
? [X85: subst > term > term] :
! [X86: subst,X87: term] :
( ( X85 @ X86 @ X87 )
= ( sub @ X84 @ ( push @ X87 @ X86 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X88: term] :
! [X89: subst > term > term] :
? [X90: subst,X91: term] :
( ( X89 @ X90 @ X91 )
!= ( sub @ X88 @ ( push @ X91 @ X90 ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X92: term > $o,X93: term] :
( ( ( sP43 @ X92 )
= $true )
| ? [X94: term] :
( ( ( var @ X94 )
= $true )
& ( ( X92 @ X94 )
!= $true ) )
| ? [X95: term] :
( ( $true
!= ( X92 @ ( lam @ X95 ) ) )
& ( $true
= ( X92 @ X95 ) ) )
| ( ( X92 @ X93 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X96: term > $o,X97: term] :
( ( ( sP43 @ X96 )
!= $true )
& ! [X98: term] :
( ( ( var @ X98 )
!= $true )
| ( $true
= ( X96 @ X98 ) ) )
& ! [X99: term] :
( ( ( X96 @ ( lam @ X99 ) )
= $true )
| ( ( X96 @ X99 )
!= $true ) )
& ( $true
!= ( X96 @ X97 ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X100: term > $o,X101: subst,X102: term > $o,X103: term] :
( ( $true
!= ( X100 @ one ) )
& ( $true
= ( X102 @ X103 ) )
& ! [X104: term] :
( ( X102 @ ( sub @ X104 @ ( push @ X103 @ X101 ) ) )
= ( X100 @ X104 ) ) )
& ! [X105: term,X106: subst] :
( ( sub @ one @ ( push @ X105 @ X106 ) )
= X105 ) ) )
& ( ! [X107: term > $o,X108: subst,X109: term > $o,X110: term] :
( ( $true
= ( X107 @ one ) )
| ( ( X109 @ X110 )
!= $true )
| ? [X111: term] :
( ( X107 @ X111 )
!= ( X109 @ ( sub @ X111 @ ( push @ X110 @ X108 ) ) ) ) )
| ? [X112: term,X113: subst] :
( ( sub @ one @ ( push @ X112 @ X113 ) )
!= X112 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( $true = sP42 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP42 ) )
& ! [X114: subst] :
? [X115: d_subst] :
( ( d2subst @ X115 )
= X114 )
& ! [X116: d_subst] : ( d_id = X116 )
& ( ! [X117: term,X118: term,X119: term,X120: term] :
( ( X117 = X119 )
| ( ( ap @ ( sub @ X118 @ id ) @ X117 )
!= ( ap @ ( sub @ X120 @ id ) @ X119 ) ) )
| ? [X121: term,X122: term,X123: term,X124: term] :
( ( X121 != X124 )
& ( ( ap @ X122 @ X124 )
= ( ap @ X123 @ X121 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X125: term,X126: term,X127: term,X128: term] :
( ( X125 != X127 )
& ( ( ap @ ( sub @ X126 @ id ) @ X125 )
= ( ap @ ( sub @ X128 @ id ) @ X127 ) ) )
& ! [X129: term,X130: term,X131: term,X132: term] :
( ( X129 = X132 )
| ( ( ap @ X131 @ X129 )
!= ( ap @ X130 @ X132 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X133: subst,X134: term,X135: term > $o] :
! [X136: term > $o] :
? [X137: term] :
( ( X135 @ ( sub @ X137 @ ( push @ X134 @ X133 ) ) )
!= ( X136 @ X137 ) ) )
& ( ! [X138: subst,X139: term,X140: term > $o] :
? [X141: term > $o] :
! [X142: term] :
( ( X141 @ X142 )
= ( X140 @ ( sub @ X142 @ ( push @ X139 @ X138 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ! [X143: subst] :
( ( push @ ( sub @ one @ X143 ) @ ( comp @ sh @ X143 ) )
= X143 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X144: subst] :
( ( push @ ( sub @ one @ X144 ) @ ( comp @ sh @ X144 ) )
!= X144 ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( $true = sP39 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP39 ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
| ? [X145: term,X146: term] :
( ( ( sub @ X145 @ sh )
= ( sub @ X146 @ sh ) )
& ( X145 != X146 ) ) )
& ( ! [X147: term,X148: term] :
( ( ( sub @ X148 @ sh )
!= ( sub @ X147 @ sh ) )
| ( X147 = X148 ) )
| ( shinj != $true ) )
& ( induction2_gthm = $true )
& ( ! [X149: term,X150: term > $o,X151: subst,X152: term,X153: term > $o] :
( ( $true
!= ( X150 @ X149 ) )
| ( ( X153 @ ( sub @ X149 @ ( push @ X152 @ X151 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X154: term,X155: term > $o,X156: subst,X157: term,X158: term > $o] :
( ( ( X155 @ X154 )
= $true )
& ( $true
!= ( X158 @ ( sub @ X154 @ ( push @ X157 @ X156 ) ) ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X159: term] :
( ( sub @ X159 @ id )
= X159 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X160: term] :
( ( sub @ X160 @ id )
!= X160 ) )
& ( ? [X161: term] :
( ( sub @ X161 @ id )
!= X161 )
| ! [X162: term] :
( ( sub @ X162 @ id )
= X162 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X163: term] :
( ( sub @ X163 @ id )
= X163 )
& ? [X164: term] :
( ( sub @ X164 @ id )
!= X164 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X165: term,X166: term,X167: subst > term > term] :
( ( ( ap @ ( sub @ X165 @ id ) @ X166 )
= ( lam @ ( X167 @ sh @ one ) ) )
& ! [X168: subst,X169: term,X170: subst] :
( ( X167 @ ( comp @ X170 @ X168 ) @ ( sub @ X169 @ X168 ) )
= ( sub @ ( X167 @ X170 @ X169 ) @ X168 ) ) ) )
& ( ! [X171: term,X172: term,X173: subst > term > term] :
( ( ( lam @ ( X173 @ sh @ one ) )
!= ( ap @ ( sub @ X171 @ id ) @ X172 ) )
| ? [X174: subst,X175: term,X176: subst] :
( ( sub @ ( X173 @ X176 @ X175 ) @ X174 )
!= ( X173 @ ( comp @ X176 @ X174 ) @ ( sub @ X175 @ X174 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ? [X177: term,X178: term,X179: term,X180: term] :
( ( ( ap @ X179 @ X177 )
= ( ap @ X178 @ X180 ) )
& ( X178 != X179 ) )
| ! [X181: term,X182: term,X183: term,X184: term] :
( ( X182 = X184 )
| ( ( ap @ ( sub @ X182 @ id ) @ X183 )
!= ( ap @ ( sub @ X184 @ id ) @ X181 ) ) )
| ? [X185: term] :
( ( sub @ X185 @ id )
!= X185 )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X186: term,X187: term,X188: term,X189: term] :
( ( ( ap @ X188 @ X186 )
!= ( ap @ X187 @ X189 ) )
| ( X187 = X188 ) )
& ? [X190: term,X191: term,X192: term,X193: term] :
( ( X191 != X193 )
& ( ( ap @ ( sub @ X191 @ id ) @ X192 )
= ( ap @ ( sub @ X193 @ id ) @ X190 ) ) )
& ! [X194: term] :
( ( sub @ X194 @ id )
= X194 ) ) )
& ( ! [X195: term,X196: term,X197: term,X198: term] :
( ( X195 = X197 )
| ( ( ap @ ( sub @ X195 @ id ) @ X196 )
!= ( ap @ ( sub @ X197 @ id ) @ X198 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X199: term,X200: term,X201: term,X202: term] :
( ( X199 != X201 )
& ( ( ap @ ( sub @ X199 @ id ) @ X200 )
= ( ap @ ( sub @ X201 @ id ) @ X202 ) ) ) )
& ! [X203: d_term] : ( d_one = X203 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP31 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X204: subst > term > subst > $o] :
! [X205: term > $o] :
? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ id @ X206 @ id ) ) )
& ( ! [X207: subst > term > subst > $o] :
? [X208: term > $o] :
! [X209: term] :
( ( X208 @ X209 )
= ( X207 @ id @ X209 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( sP26 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( sP26 != $true ) )
& ( ! [X210: term] :
? [X211: subst > term > term] :
( ( X211 @ sh @ one )
= ( sub @ X210 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X212: term] :
! [X213: subst > term > term] :
( ( X213 @ sh @ one )
!= ( sub @ X212 @ ( push @ one @ sh ) ) ) )
& ( pushprop_lthm = $true )
& ( ( $true = sP22 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP22 ) )
& ( ! [X214: subst > term > subst > $o,X215: term] :
( ? [X216: term,X217: term] :
( ( ( X214 @ id @ X216 @ id )
= $true )
& ( ( X214 @ id @ ( ap @ ( sub @ X216 @ id ) @ X217 ) @ id )
!= $true )
& ( $true
= ( X214 @ id @ X217 @ id ) ) )
| ( ( sP20 @ X214 )
= $true )
| ( ( X214 @ id @ X215 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X218: subst > term > subst > $o,X219: term] :
( ! [X220: term,X221: term] :
( ( ( X218 @ id @ X220 @ id )
!= $true )
| ( $true
= ( X218 @ id @ ( ap @ ( sub @ X220 @ id ) @ X221 ) @ id ) )
| ( ( X218 @ id @ X221 @ id )
!= $true ) )
& ( $true
!= ( sP20 @ X218 ) )
& ( ( X218 @ id @ X219 @ id )
!= $true ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X222: subst] :
( ( comp @ id @ X222 )
= X222 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X223: subst] :
( ( comp @ id @ X223 )
!= X223 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X224: term,X225: subst] :
( ( comp @ sh @ ( push @ X224 @ X225 ) )
!= X225 ) )
& ( ! [X226: term,X227: subst] :
( ( comp @ sh @ ( push @ X226 @ X227 ) )
= X227 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
| ? [X228: term,X229: term,X230: term,X231: term] :
( ( X230 != X231 )
& ( ( ap @ X231 @ X229 )
= ( ap @ X230 @ X228 ) ) ) )
& ( ! [X232: term,X233: term,X234: term,X235: term] :
( ( X234 = X235 )
| ( ( ap @ X234 @ X232 )
!= ( ap @ X235 @ X233 ) ) )
| ( apinj1 != $true ) )
& ( ( axvarid = $true )
| ? [X236: term] :
( ( sub @ X236 @ id )
!= X236 ) )
& ( ! [X237: term] :
( ( sub @ X237 @ id )
= X237 )
| ( axvarid != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X238: term,X239: term > $o,X240: subst] :
! [X241: term > $o] :
? [X242: term] :
( ( X241 @ X242 )
!= ( X239 @ ( sub @ X242 @ ( push @ X238 @ X240 ) ) ) ) )
& ( ! [X243: term,X244: term > $o,X245: subst] :
? [X246: term > $o] :
! [X247: term] :
( ( X246 @ X247 )
= ( X244 @ ( sub @ X247 @ ( push @ X243 @ X245 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X248: subst,X249: term,X250: term > $o,X251: term > $o] :
( ( ( X251 @ X249 )
= $true )
& ! [X252: term] :
( ( X251 @ ( sub @ X252 @ ( push @ X249 @ X248 ) ) )
= ( X250 @ X252 ) )
& ( ( X250 @ one )
!= $true ) ) )
& ( ! [X253: subst,X254: term,X255: term > $o,X256: term > $o] :
( ( ( X256 @ X254 )
!= $true )
| ? [X257: term] :
( ( X256 @ ( sub @ X257 @ ( push @ X254 @ X253 ) ) )
!= ( X255 @ X257 ) )
| ( ( X255 @ one )
= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP16 != $true ) )
& ( ( sP16 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( axapp = $true )
& ! [X258: term] :
? [X259: d_term] :
( ( d2term @ X259 )
= X258 )
& ( ulamvarind = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP14 != $true ) )
& ( ! [X260: term,X261: term,X262: term,X263: term] :
( ( ( ap @ X261 @ X262 )
!= ( ap @ X263 @ X260 ) )
| ( X260 = X262 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X264: term,X265: term,X266: term,X267: term] :
( ( ( ap @ X265 @ X266 )
= ( ap @ X267 @ X264 ) )
& ( X264 != X266 ) ) )
& ( ( ! [X268: subst] :
( ( comp @ X268 @ id )
= X268 )
& ! [X269: subst] :
( ( comp @ id @ X269 )
= X269 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X270: subst] :
( ( comp @ X270 @ id )
!= X270 )
| ? [X271: subst] :
( ( comp @ id @ X271 )
!= X271 ) )
& ( ( sP5 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP5 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X272: d_term,X273: d_term] :
( ( X272 = X273 )
| ( ( d2term @ X272 )
!= ( d2term @ X273 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
| ( $true != sP3 ) )
& ( ( $true = sP3 )
| ( induction2 != $true ) )
& ( ( $true = sP1 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP1 ) ) ),
inference(rectify,[status(thm)],[f474]) ).
thf(f474,plain,
( ( ! [X24: subst > term > subst > $o] :
? [X25: term > $o] :
! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X24: subst > term > subst > $o] :
! [X25: term > $o] :
? [X26: term] :
( ( X24 @ id @ X26 @ id )
!= ( X25 @ X26 ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
& ! [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
& ( ( lam @ ( X219 @ sh @ one ) )
= ( lam @ ( X218 @ sh @ one ) ) )
& ( ( X219 @ X217 @ X220 )
!= ( X218 @ X217 @ X220 ) ) ) )
& ( ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ? [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
!= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ? [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
!= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) ) )
| ( hoaslaminj != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP58 != $true ) )
& ( ( sP58 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X448: term] :
? [X449: subst > term > term] :
! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X448: term] :
! [X449: subst > term > term] :
? [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
!= ( X449 @ X450 @ X451 ) ) )
& ( ( induction2_lthm = $true )
| ( sP57 != $true ) )
& ( ( sP57 = $true )
| ( induction2_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3a != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X277: subst] :
( ( comp @ X277 @ id )
= X277 )
& ( ? [X278: subst] :
( ( comp @ X278 @ id )
!= X278 )
| ? [X279: subst] :
( ( comp @ id @ X279 )
!= X279 ) )
& ! [X276: subst] :
( ( comp @ id @ X276 )
= X276 ) ) )
& ( ? [X277: subst] :
( ( comp @ X277 @ id )
!= X277 )
| ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) )
| ? [X276: subst] :
( ( comp @ id @ X276 )
!= X276 )
| ( substmonoid_lthm != $true ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
!= X114 ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP50 != $true ) )
& ( ulamvarsh = $true )
& ( ? [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
!= X499 )
| ? [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
!= X501 )
| ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
= X499 )
& ! [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
= X501 )
& ? [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
= $true )
& ( $true
!= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP48 != $true ) )
& ( ( sP48 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
!= ( d2subst @ X117 ) )
| ( X116 = X117 ) )
& ( ( hoasapinj2 = $true )
| ? [X31: term,X32: term,X33: term,X34: term] :
( ( X33 != X34 )
& ( ( ap @ ( sub @ X32 @ id ) @ X33 )
= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) )
| ( hoasapinj2 != $true ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3v2 != $true ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
| ? [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
& ( X0 != X1 ) ) )
& ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) )
| ( laminj != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ( $true = sP45 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP45 ) )
& ( ( axidr = $true )
| ? [X99: subst] :
( ( comp @ X99 @ id )
!= X99 ) )
& ( ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 )
| ( axidr != $true ) )
& ( ! [X200: term] :
? [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
= ( X201 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X200: term] :
! [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
!= ( X201 @ sh @ one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X27: term] :
? [X28: subst > term > term] :
! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X27: term] :
! [X28: subst > term > term] :
? [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
!= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X131: term > $o,X132: term] :
( ( ( sP43 @ X131 )
= $true )
| ? [X136: term] :
( ( $true
= ( var @ X136 ) )
& ( $true
!= ( X131 @ X136 ) ) )
| ? [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
!= $true )
& ( $true
= ( X131 @ X135 ) ) )
| ( ( X131 @ X132 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X131: term > $o,X132: term] :
( ( ( sP43 @ X131 )
!= $true )
& ! [X136: term] :
( ( $true
!= ( var @ X136 ) )
| ( $true
= ( X131 @ X136 ) ) )
& ! [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
= $true )
| ( $true
!= ( X131 @ X135 ) ) )
& ( ( X131 @ X132 )
!= $true ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
!= $true )
& ( $true
= ( X177 @ X178 ) )
& ! [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
= ( X175 @ X179 ) ) )
& ! [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
= X173 ) ) )
& ( ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ? [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
!= ( X175 @ X179 ) ) )
| ? [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
!= X173 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( $true = sP42 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP42 ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X535 )
& ( ( ap @ X533 @ X535 )
= ( ap @ X534 @ X532 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X536: term,X537: term,X538: term,X539: term] :
( ( X536 != X538 )
& ( ( ap @ ( sub @ X539 @ id ) @ X538 )
= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
& ! [X532: term,X533: term,X534: term,X535: term] :
( ( X532 = X535 )
| ( ( ap @ X533 @ X535 )
!= ( ap @ X534 @ X532 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X137: subst,X138: term,X139: term > $o] :
! [X140: term > $o] :
? [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
!= ( X140 @ X141 ) ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
? [X140: term > $o] :
! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
| ( pushprop_lem0 != $true ) )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
!= X102 ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( $true = sP39 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP39 ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
| ? [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
= ( sub @ X246 @ sh ) )
& ( X246 != X247 ) ) )
& ( ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) )
| ( shinj != $true ) )
& ( induction2_gthm = $true )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
= $true )
& ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
!= $true ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X216: term] :
( ( sub @ X216 @ id )
!= X216 ) )
& ( ? [X171: term] :
( ( sub @ X171 @ id )
!= X171 )
| ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
& ? [X172: term] :
( ( sub @ X172 @ id )
!= X172 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
& ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ( ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ? [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
!= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ? [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
= ( ap @ X107 @ X109 ) )
& ( X107 != X108 ) )
| ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
| ? [X105: term] :
( ( sub @ X105 @ id )
!= X105 )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) )
| ( X107 = X108 ) )
& ? [X110: term,X111: term,X112: term,X113: term] :
( ( X111 != X113 )
& ( ( ap @ ( sub @ X111 @ id ) @ X112 )
= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
& ! [X105: term] :
( ( sub @ X105 @ id )
= X105 ) ) )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X242: term,X243: term,X244: term,X245: term] :
( ( X242 != X244 )
& ( ( ap @ ( sub @ X244 @ id ) @ X245 )
= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) ) )
& ! [X170: d_term] : ( d_one = X170 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP31 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X118: subst > term > subst > $o] :
! [X119: term > $o] :
? [X120: term] :
( ( X118 @ id @ X120 @ id )
!= ( X119 @ X120 ) ) )
& ( ! [X118: subst > term > subst > $o] :
? [X119: term > $o] :
! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( sP26 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( sP26 != $true ) )
& ( ! [X129: term] :
? [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
= ( X130 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X129: term] :
! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) ) )
& ( pushprop_lthm = $true )
& ( ( $true = sP22 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP22 ) )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ? [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
= $true )
& ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
!= $true )
& ( $true
= ( X202 @ id @ X205 @ id ) ) )
| ( ( sP20 @ X202 )
= $true )
| ( ( X202 @ id @ X203 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X202: subst > term > subst > $o,X203: term] :
( ! [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
!= $true )
| ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
= $true )
| ( $true
!= ( X202 @ id @ X205 @ id ) ) )
& ( ( sP20 @ X202 )
!= $true )
& ( ( X202 @ id @ X203 @ id )
!= $true ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X299: subst] :
( ( comp @ id @ X299 )
!= X299 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
!= X104 ) )
& ( ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
| ? [X166: term,X167: term,X168: term,X169: term] :
( ( X168 != X169 )
& ( ( ap @ X169 @ X167 )
= ( ap @ X168 @ X166 ) ) ) )
& ( ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) )
| ( apinj1 != $true ) )
& ( ( axvarid = $true )
| ? [X355: term] :
( ( sub @ X355 @ id )
!= X355 ) )
& ( ! [X355: term] :
( ( sub @ X355 @ id )
= X355 )
| ( axvarid != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X211: term,X212: term > $o,X213: subst] :
! [X214: term > $o] :
? [X215: term] :
( ( X214 @ X215 )
!= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( ! [X211: term,X212: term > $o,X213: subst] :
? [X214: term > $o] :
! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
= $true )
& ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) )
& ( ( X144 @ one )
!= $true ) ) )
& ( ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
!= $true )
| ? [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
!= ( X144 @ X146 ) )
| ( ( X144 @ one )
= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP16 != $true ) )
& ( ( sP16 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( axapp = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ulamvarind = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP14 != $true ) )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
= ( ap @ X298 @ X295 ) )
& ( X295 != X297 ) ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X274: subst] :
( ( comp @ X274 @ id )
!= X274 )
| ? [X275: subst] :
( ( comp @ id @ X275 )
!= X275 ) )
& ( ( sP5 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP5 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
| ( $true != sP3 ) )
& ( ( $true = sP3 )
| ( induction2 != $true ) )
& ( ( $true = sP1 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP1 ) ) ),
inference(flattening,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ! [X24: subst > term > subst > $o] :
? [X25: term > $o] :
! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X24: subst > term > subst > $o] :
! [X25: term > $o] :
? [X26: term] :
( ( X24 @ id @ X26 @ id )
!= ( X25 @ X26 ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
| ? [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
& ! [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
& ( ( lam @ ( X219 @ sh @ one ) )
= ( lam @ ( X218 @ sh @ one ) ) )
& ( ( X219 @ X217 @ X220 )
!= ( X218 @ X217 @ X220 ) ) ) )
& ( ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ? [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
!= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ? [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
!= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) ) )
| ( hoaslaminj != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP58 != $true ) )
& ( ( sP58 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X448: term] :
? [X449: subst > term > term] :
! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X448: term] :
! [X449: subst > term > term] :
? [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
!= ( X449 @ X450 @ X451 ) ) )
& ( ( induction2_lthm = $true )
| ( sP57 != $true ) )
& ( ( sP57 = $true )
| ( induction2_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP53 != $true ) )
& ( ( sP53 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3a != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X277: subst] :
( ( comp @ X277 @ id )
= X277 )
& ( ? [X278: subst] :
( ( comp @ X278 @ id )
!= X278 )
| ? [X279: subst] :
( ( comp @ id @ X279 )
!= X279 ) )
& ! [X276: subst] :
( ( comp @ id @ X276 )
= X276 ) ) )
& ( ? [X277: subst] :
( ( comp @ X277 @ id )
!= X277 )
| ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) )
| ? [X276: subst] :
( ( comp @ id @ X276 )
!= X276 )
| ( substmonoid_lthm != $true ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
!= X114 ) )
& ( ( sP50 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP50 != $true ) )
& ( ulamvarsh = $true )
& ( ? [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
!= X499 )
| ? [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
!= X501 )
| ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
= X499 )
& ! [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
= X501 )
& ? [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
= $true )
& ( $true
!= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP48 != $true ) )
& ( ( sP48 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
!= ( d2subst @ X117 ) )
| ( X116 = X117 ) )
& ( ( hoasapinj2 = $true )
| ? [X31: term,X32: term,X33: term,X34: term] :
( ( X33 != X34 )
& ( ( ap @ ( sub @ X32 @ id ) @ X33 )
= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) )
| ( hoasapinj2 != $true ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3v2 != $true ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
| ? [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
& ( X0 != X1 ) ) )
& ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) )
| ( laminj != $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ( $true = sP45 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP45 ) )
& ( ( axidr = $true )
| ? [X99: subst] :
( ( comp @ X99 @ id )
!= X99 ) )
& ( ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 )
| ( axidr != $true ) )
& ( ! [X200: term] :
? [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
= ( X201 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X200: term] :
! [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
!= ( X201 @ sh @ one ) ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X27: term] :
? [X28: subst > term > term] :
! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X27: term] :
! [X28: subst > term > term] :
? [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
!= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X131: term > $o,X132: term] :
( ( ( sP43 @ X131 )
= $true )
| ? [X136: term] :
( ( $true
= ( var @ X136 ) )
& ( $true
!= ( X131 @ X136 ) ) )
| ? [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
!= $true )
& ( $true
= ( X131 @ X135 ) ) )
| ( ( X131 @ X132 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X131: term > $o,X132: term] :
( ( ( sP43 @ X131 )
!= $true )
& ! [X136: term] :
( ( $true
!= ( var @ X136 ) )
| ( $true
= ( X131 @ X136 ) ) )
& ! [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
= $true )
| ( $true
!= ( X131 @ X135 ) ) )
& ( ( X131 @ X132 )
!= $true ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
!= $true )
& ( $true
= ( X177 @ X178 ) )
& ! [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
= ( X175 @ X179 ) ) )
& ! [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
= X173 ) ) )
& ( ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ? [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
!= ( X175 @ X179 ) ) )
| ? [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
!= X173 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( $true = sP42 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP42 ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X535 )
& ( ( ap @ X533 @ X535 )
= ( ap @ X534 @ X532 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X536: term,X537: term,X538: term,X539: term] :
( ( X536 != X538 )
& ( ( ap @ ( sub @ X539 @ id ) @ X538 )
= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
& ! [X532: term,X533: term,X534: term,X535: term] :
( ( X532 = X535 )
| ( ( ap @ X533 @ X535 )
!= ( ap @ X534 @ X532 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
| ? [X137: subst,X138: term,X139: term > $o] :
! [X140: term > $o] :
? [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
!= ( X140 @ X141 ) ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
? [X140: term > $o] :
! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
| ( pushprop_lem0 != $true ) )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
!= X102 ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( $true = sP39 )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP39 ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
| ? [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
= ( sub @ X246 @ sh ) )
& ( X246 != X247 ) ) )
& ( ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) )
| ( shinj != $true ) )
& ( induction2_gthm = $true )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
= $true )
& ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
!= $true ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X216: term] :
( ( sub @ X216 @ id )
!= X216 ) )
& ( ? [X171: term] :
( ( sub @ X171 @ id )
!= X171 )
| ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
& ? [X172: term] :
( ( sub @ X172 @ id )
!= X172 ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
& ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ( ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ? [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
!= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP32 != $true ) )
& ( ( sP32 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ? [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
= ( ap @ X107 @ X109 ) )
& ( X107 != X108 ) )
| ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
| ? [X105: term] :
( ( sub @ X105 @ id )
!= X105 )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) )
| ( X107 = X108 ) )
& ? [X110: term,X111: term,X112: term,X113: term] :
( ( X111 != X113 )
& ( ( ap @ ( sub @ X111 @ id ) @ X112 )
= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
& ! [X105: term] :
( ( sub @ X105 @ id )
= X105 ) ) )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X242: term,X243: term,X244: term,X245: term] :
( ( X242 != X244 )
& ( ( ap @ ( sub @ X244 @ id ) @ X245 )
= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) ) )
& ! [X170: d_term] : ( d_one = X170 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP31 != $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X118: subst > term > subst > $o] :
! [X119: term > $o] :
? [X120: term] :
( ( X118 @ id @ X120 @ id )
!= ( X119 @ X120 ) ) )
& ( ! [X118: subst > term > subst > $o] :
? [X119: term > $o] :
! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( sP26 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( sP26 != $true ) )
& ( ! [X129: term] :
? [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
= ( X130 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X129: term] :
! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) ) )
& ( pushprop_lthm = $true )
& ( ( $true = sP22 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP22 ) )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ? [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
= $true )
& ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
!= $true )
& ( $true
= ( X202 @ id @ X205 @ id ) ) )
| ( ( sP20 @ X202 )
= $true )
| ( ( X202 @ id @ X203 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X202: subst > term > subst > $o,X203: term] :
( ! [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
!= $true )
| ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
= $true )
| ( $true
!= ( X202 @ id @ X205 @ id ) ) )
& ( ( sP20 @ X202 )
!= $true )
& ( ( X202 @ id @ X203 @ id )
!= $true ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X299: subst] :
( ( comp @ id @ X299 )
!= X299 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
!= X104 ) )
& ( ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
| ? [X166: term,X167: term,X168: term,X169: term] :
( ( X168 != X169 )
& ( ( ap @ X169 @ X167 )
= ( ap @ X168 @ X166 ) ) ) )
& ( ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) )
| ( apinj1 != $true ) )
& ( ( axvarid = $true )
| ? [X355: term] :
( ( sub @ X355 @ id )
!= X355 ) )
& ( ! [X355: term] :
( ( sub @ X355 @ id )
= X355 )
| ( axvarid != $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X211: term,X212: term > $o,X213: subst] :
! [X214: term > $o] :
? [X215: term] :
( ( X214 @ X215 )
!= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( ! [X211: term,X212: term > $o,X213: subst] :
? [X214: term > $o] :
! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
= $true )
& ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) )
& ( ( X144 @ one )
!= $true ) ) )
& ( ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
!= $true )
| ? [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
!= ( X144 @ X146 ) )
| ( ( X144 @ one )
= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP16 != $true ) )
& ( ( sP16 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( axapp = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ulamvarind = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP14 != $true ) )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
= ( ap @ X298 @ X295 ) )
& ( X295 != X297 ) ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X274: subst] :
( ( comp @ X274 @ id )
!= X274 )
| ? [X275: subst] :
( ( comp @ id @ X275 )
!= X275 ) )
& ( ( sP5 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP5 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
| ( $true != sP3 ) )
& ( ( $true = sP3 )
| ( induction2 != $true ) )
& ( ( $true = sP1 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP1 ) ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ! [X24: subst > term > subst > $o] :
? [X25: term > $o] :
! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ? [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
!= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ? [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
!= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ( sP58 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X448: term] :
? [X449: subst > term > term] :
! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( induction2_lthm = $true )
<=> ( sP57 = $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( sP53 = $true ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( sP52 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ( $true = sP51 ) )
& ( ( substmonoid_lthm = $true )
<=> ( ? [X277: subst] :
( ( comp @ X277 @ id )
!= X277 )
| ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) )
| ? [X276: subst] :
( ( comp @ id @ X276 )
!= X276 ) ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( ( sP50 = $true )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ulamvarsh = $true )
& ( ( ? [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
!= X499 )
| ? [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
!= X501 )
| ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ( sP48 = $true ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
!= ( d2subst @ X117 ) )
| ( X116 = X117 ) )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ( $true = sP47 ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ( $true = sP45 )
<=> ( induction2lem = $true ) )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ( ! [X200: term] :
? [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
= ( X201 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X27: term] :
? [X28: subst > term > term] :
! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X131: term > $o,X132: term] :
( ( ( sP43 @ X131 )
= $true )
| ? [X136: term] :
( ( $true
= ( var @ X136 ) )
& ( $true
!= ( X131 @ X136 ) ) )
| ? [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
!= $true )
& ( $true
= ( X131 @ X135 ) ) )
| ( ( X131 @ X132 )
= $true ) )
<=> ( induction = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ? [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
!= ( X175 @ X179 ) ) )
| ? [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
!= X173 ) ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( $true = sP42 )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ( ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X535 )
& ( ( ap @ X533 @ X535 )
= ( ap @ X534 @ X532 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X137: subst,X138: term,X139: term > $o] :
? [X140: term > $o] :
! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) ) )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( $true = sP39 )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ( $true = sP33 ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
<=> ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) ) )
& ( induction2_gthm = $true )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
<=> ( termmset = $true ) )
& ( ( ? [X171: term] :
( ( sub @ X171 @ id )
!= X171 )
| ! [X172: term] :
( ( sub @ X172 @ id )
= X172 ) )
<=> ( termmset_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ? [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
!= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ( sP32 = $true ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( ? [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
= ( ap @ X107 @ X109 ) )
& ( X107 != X108 ) )
| ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
| ? [X105: term] :
( ( sub @ X105 @ id )
!= X105 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
<=> ( hoasapinj1 = $true ) )
& ! [X170: d_term] : ( d_one = X170 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( sP31 = $true )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X118: subst > term > subst > $o] :
? [X119: term > $o] :
! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) ) )
& ( ( sP26 = $true )
<=> ( induction2lem_lthm = $true ) )
& ( ! [X129: term] :
? [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
= ( X130 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( pushprop_lthm = $true )
& ( ( $true = sP22 )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ? [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
= $true )
& ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
!= $true )
& ( $true
= ( X202 @ id @ X205 @ id ) ) )
| ( ( sP20 @ X202 )
= $true )
| ( ( X202 @ id @ X203 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
<=> ( axidl = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
<=> ( sP19 = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
<=> ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) ) )
& ( ( axvarid = $true )
<=> ! [X355: term] :
( ( sub @ X355 @ id )
= X355 ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X211: term,X212: term > $o,X213: subst] :
? [X214: term > $o] :
! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
!= $true )
| ? [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
!= ( X144 @ X146 ) )
| ( ( X144 @ one )
= $true ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( sP16 = $true ) )
& ( axapp = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ulamvarind = $true )
& ( ( sP14 = $true )
<=> ( hoasinduction_lthm = $true ) )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
<=> ( apinj2 = $true ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
<=> ( substmonoid = $true ) )
& ( ( sP5 = $true )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
<=> ( $true = sP3 ) )
& ( ( $true = sP1 )
<=> ( hoasinduction_lem2 = $true ) ) ),
inference(definition_folding,[status(thm)],[f12,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14]) ).
thf(f14,plain,
! [X182: subst > term > subst > $o] :
( ( $true
= ( sP0 @ X182 ) )
<=> ? [X191: term,X192: term] :
( ( ( X182 @ id @ X191 @ id )
= $true )
& ( $true
= ( X182 @ id @ X192 @ id ) )
& ( ( X182 @ id @ ( ap @ ( sub @ X192 @ id ) @ X191 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
( ( $true = sP1 )
<=> ! [X180: term,X181: term,X182: subst > term > subst > $o] :
( ( $true
!= ( X182 @ id @ X181 @ id ) )
| ( ( X182 @ id @ X180 @ id )
!= $true )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( ( X182 @ X184 @ X185 @ ( comp @ X183 @ X186 ) )
= $true )
& ( ( X182 @ ( comp @ X184 @ X183 ) @ ( sub @ X185 @ X183 ) @ X186 )
!= $true ) )
| ( $true
= ( sP0 @ X182 ) )
| ? [X187: subst,X188: term,X189: subst,X190: subst] :
( ( ( X182 @ ( comp @ X189 @ X187 ) @ ( sub @ X188 @ X187 ) @ X190 )
= $true )
& ( ( X182 @ X189 @ X188 @ ( comp @ X187 @ X190 ) )
!= $true ) )
| ( ( X182 @ id @ ( ap @ X180 @ X181 ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
! [X194: term > $o] :
( ( ( sP2 @ X194 )
= $true )
<=> ? [X198: term,X199: term] :
( ( $true
!= ( X194 @ ( ap @ X198 @ X199 ) ) )
& ( ( X194 @ X198 )
= $true )
& ( $true
= ( X194 @ X199 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( $true = sP3 )
<=> ! [X193: term,X194: term > $o] :
( ? [X195: term] :
( ( ( var @ X195 )
= $true )
& ( ( X194 @ X195 )
!= $true ) )
| ? [X196: term] :
( ( $true
!= ( X194 @ ( lam @ X196 ) ) )
& ! [X197: term] :
( ( ( X194 @ ( sub @ X196 @ ( push @ X197 @ id ) ) )
= $true )
| ( $true
!= ( X194 @ X197 ) ) ) )
| ( ( X194 @ X193 )
= $true )
| ( ( sP2 @ X194 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
! [X258: subst > term > subst > $o] :
( ( ( sP4 @ X258 )
= $true )
<=> ? [X269: subst > term > term] :
( ! [X273: term] :
( ( ( X258 @ id @ X273 @ id )
!= $true )
| ( ( X258 @ id @ ( X269 @ id @ X273 ) @ id )
= $true ) )
& ! [X270: subst,X271: subst,X272: term] :
( ( sub @ ( X269 @ X270 @ X272 ) @ X271 )
= ( X269 @ ( comp @ X270 @ X271 ) @ ( sub @ X272 @ X271 ) ) )
& ( ( X258 @ id @ ( lam @ ( X269 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
( ( sP5 = $true )
<=> ! [X258: subst > term > subst > $o,X259: term] :
( ( ( sP4 @ X258 )
= $true )
| ? [X264: term,X265: subst,X266: subst,X267: subst] :
( ( ( X258 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) @ X267 )
!= $true )
& ( ( X258 @ X265 @ X264 @ ( comp @ X266 @ X267 ) )
= $true ) )
| ? [X268: term] :
( ( ( X258 @ id @ ( sub @ X259 @ ( push @ X268 @ id ) ) @ id )
!= $true )
& ( $true
= ( X258 @ id @ X268 @ id ) ) )
| ( $true
= ( X258 @ id @ ( lam @ X259 ) @ id ) )
| ? [X260: subst,X261: term,X262: subst,X263: subst] :
( ( $true
= ( X258 @ ( comp @ X260 @ X263 ) @ ( sub @ X261 @ X263 ) @ X262 ) )
& ( ( X258 @ X260 @ X261 @ ( comp @ X263 @ X262 ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
! [X395: subst > term > subst > $o] :
( ( ( sP6 @ X395 )
= $true )
<=> ? [X400: subst > term > term] :
( ( ( X395 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
!= $true )
& ! [X401: term] :
( ( ( X395 @ id @ X401 @ id )
!= $true )
| ( ( X395 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
& ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X404 @ X403 ) @ ( sub @ X402 @ X403 ) )
= ( sub @ ( X400 @ X404 @ X402 ) @ X403 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
! [X395: subst > term > subst > $o] :
( ( $true
= ( sP7 @ X395 ) )
<=> ? [X405: term,X406: term] :
( ( $true
!= ( X395 @ id @ ( ap @ ( sub @ X406 @ id ) @ X405 ) @ id ) )
& ( ( X395 @ id @ X406 @ id )
= $true )
& ( ( X395 @ id @ X405 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X359: term > $o] :
( ( $true
= ( sP8 @ X359 ) )
<=> ! [X360: term,X361: term] :
( ( ( X359 @ X360 )
!= $true )
| ( ( X359 @ X361 )
!= $true )
| ( ( X359 @ ( ap @ X361 @ X360 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
! [X367: subst > term > subst > $o] :
( ( ( sP9 @ X367 )
= $true )
<=> ! [X376: term,X377: term] :
( ( ( X367 @ id @ X376 @ id )
!= $true )
| ( ( X367 @ id @ ( ap @ ( sub @ X376 @ id ) @ X377 ) @ id )
= $true )
| ( $true
!= ( X367 @ id @ X377 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
! [X378: subst > term > subst > $o] :
( ( ( sP10 @ X378 )
= $true )
<=> ! [X389: subst > term > term] :
( ? [X390: term] :
( ( ( X378 @ id @ X390 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( X389 @ id @ X390 ) @ id ) ) )
| ? [X391: term,X392: subst,X393: subst] :
( ( sub @ ( X389 @ X393 @ X391 ) @ X392 )
!= ( X389 @ ( comp @ X393 @ X392 ) @ ( sub @ X391 @ X392 ) ) )
| ( ( X378 @ id @ ( lam @ ( X389 @ sh @ one ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( $true = sP11 )
<=> ? [X378: subst > term > subst > $o,X379: term] :
( ! [X380: subst,X381: term,X382: subst,X383: subst] :
( ( ( X378 @ X383 @ X381 @ ( comp @ X382 @ X380 ) )
!= $true )
| ( ( X378 @ ( comp @ X383 @ X382 ) @ ( sub @ X381 @ X382 ) @ X380 )
= $true ) )
& ! [X388: term] :
( ( ( X378 @ id @ ( sub @ X379 @ ( push @ X388 @ id ) ) @ id )
= $true )
| ( ( X378 @ id @ X388 @ id )
!= $true ) )
& ( ( X378 @ id @ ( lam @ X379 ) @ id )
!= $true )
& ! [X384: subst,X385: subst,X386: subst,X387: term] :
( ( $true
= ( X378 @ X386 @ X387 @ ( comp @ X384 @ X385 ) ) )
| ( $true
!= ( X378 @ ( comp @ X386 @ X384 ) @ ( sub @ X387 @ X384 ) @ X385 ) ) )
& ( ( sP10 @ X378 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
( ( sP12 = $true )
<=> ! [X394: term,X395: subst > term > subst > $o] :
( ( $true
= ( sP7 @ X395 ) )
| ? [X408: subst,X409: subst,X410: subst,X411: term] :
( ( $true
= ( X395 @ ( comp @ X408 @ X409 ) @ ( sub @ X411 @ X409 ) @ X410 ) )
& ( ( X395 @ X408 @ X411 @ ( comp @ X409 @ X410 ) )
!= $true ) )
| ( ( sP6 @ X395 )
= $true )
| ? [X407: term] :
( ( ( var @ ( sub @ X407 @ id ) )
= $true )
& ( ( X395 @ id @ X407 @ id )
!= $true ) )
| ( $true
= ( X395 @ id @ X394 @ id ) )
| ? [X396: term,X397: subst,X398: subst,X399: subst] :
( ( ( X395 @ X397 @ X396 @ ( comp @ X399 @ X398 ) )
= $true )
& ( ( X395 @ ( comp @ X397 @ X399 ) @ ( sub @ X396 @ X399 ) @ X398 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( sP13 = $true )
<=> ? [X358: term,X359: term > $o] :
( ! [X362: term] :
( ? [X363: term] :
( ( $true
= ( X359 @ X363 ) )
& ( ( X359 @ ( sub @ X362 @ ( push @ X363 @ id ) ) )
!= $true ) )
| ( ( X359 @ ( lam @ X362 ) )
= $true ) )
& ( ( X359 @ X358 )
!= $true )
& ! [X364: term] :
( ( $true
= ( X359 @ X364 ) )
| ( ( var @ X364 )
!= $true ) )
& ( $true
= ( sP8 @ X359 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
( ( sP14 = $true )
<=> ( ( $true = sP11 )
| ? [X365: term,X366: term,X367: subst > term > subst > $o] :
( ! [X368: subst,X369: subst,X370: subst,X371: term] :
( ( $true
!= ( X367 @ ( comp @ X368 @ X369 ) @ ( sub @ X371 @ X369 ) @ X370 ) )
| ( $true
= ( X367 @ X368 @ X371 @ ( comp @ X369 @ X370 ) ) ) )
& ! [X372: subst,X373: subst,X374: subst,X375: term] :
( ( $true
= ( X367 @ ( comp @ X373 @ X372 ) @ ( sub @ X375 @ X372 ) @ X374 ) )
| ( $true
!= ( X367 @ X373 @ X375 @ ( comp @ X372 @ X374 ) ) ) )
& ( ( sP9 @ X367 )
= $true )
& ( $true
= ( X367 @ id @ X366 @ id ) )
& ( ( X367 @ id @ X365 @ id )
= $true )
& ( ( X367 @ id @ ( ap @ X365 @ X366 ) @ id )
!= $true ) )
| ( sP13 = $true )
| ( sP12 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
( ( $true = sP15 )
<=> ? [X8: term,X9: subst > term > subst > $o] :
( ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) )
& ( $true
!= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ? [X14: term] :
( ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
!= $true )
& ( ( X9 @ id @ X14 @ id )
= $true ) )
| ? [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
!= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
( ( sP16 = $true )
<=> ( ? [X7: term] :
( ( sub @ X7 @ id )
!= X7 )
| ! [X16: term,X17: subst > term > subst > $o] :
( ? [X18: term] :
( ( ( X17 @ id @ X18 @ id )
= $true )
& ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) )
| ? [X19: subst > term > term] :
( ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
& ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) )
& ( $true
!= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) )
| ( $true = sP15 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
! [X37: subst > term > subst > $o] :
( ( ( sP17 @ X37 )
= $true )
<=> ? [X38: term,X39: term] :
( ( ( X37 @ id @ X38 @ id )
= $true )
& ( $true
!= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
& ( ( X37 @ id @ X39 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
! [X37: subst > term > subst > $o] :
( ( $true
= ( sP18 @ X37 ) )
<=> ? [X48: subst > term > term] :
( ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) )
& ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
!= $true )
& ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
( ( sP19 = $true )
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ( $true
= ( sP18 @ X37 ) )
| ( $true
= ( X37 @ id @ X36 @ id ) )
| ? [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
= $true )
& ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
!= $true ) )
| ? [X53: term] :
( ( $true
= ( var @ ( sub @ X53 @ id ) ) )
& ( ( X37 @ id @ X53 @ id )
!= $true ) )
| ( ( sP17 @ X37 )
= $true )
| ? [X40: subst,X41: term,X42: subst,X43: subst] :
( ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
!= $true )
& ( $true
= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
! [X202: subst > term > subst > $o] :
( ( ( sP20 @ X202 )
= $true )
<=> ? [X206: subst > term > term] :
( ! [X210: term] :
( ( ( X202 @ id @ X210 @ id )
!= $true )
| ( ( X202 @ id @ ( X206 @ id @ X210 ) @ id )
= $true ) )
& ! [X207: subst,X208: subst,X209: term] :
( ( X206 @ ( comp @ X207 @ X208 ) @ ( sub @ X209 @ X208 ) )
= ( sub @ ( X206 @ X207 @ X209 ) @ X208 ) )
& ( $true
!= ( X202 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
! [X148: subst > term > subst > $o] :
( ( $true
= ( sP21 @ X148 ) )
<=> ? [X156: subst > term > term] :
( ! [X157: term] :
( ( ( X148 @ id @ X157 @ id )
!= $true )
| ( ( X148 @ id @ ( X156 @ id @ X157 ) @ id )
= $true ) )
& ! [X158: subst,X159: term,X160: subst] :
( ( sub @ ( X156 @ X158 @ X159 ) @ X160 )
= ( X156 @ ( comp @ X158 @ X160 ) @ ( sub @ X159 @ X160 ) ) )
& ( $true
!= ( X148 @ id @ ( lam @ ( X156 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( $true = sP22 )
<=> ( ? [X147: term] :
( ( sub @ X147 @ id )
!= X147 )
| ! [X148: subst > term > subst > $o,X149: term,X150: term > $o] :
( ? [X151: term] :
( ( ( X150 @ X151 )
= $true )
& ( ( X150 @ ( sub @ X149 @ ( push @ X151 @ id ) ) )
!= $true ) )
| ? [X162: subst,X163: subst,X164: term,X165: subst] :
( ( $true
= ( X148 @ ( comp @ X162 @ X163 ) @ ( sub @ X164 @ X163 ) @ X165 ) )
& ( ( X148 @ X162 @ X164 @ ( comp @ X163 @ X165 ) )
!= $true ) )
| ( ( X150 @ ( lam @ X149 ) )
= $true )
| ( $true
= ( sP21 @ X148 ) )
| ? [X152: term,X153: subst,X154: subst,X155: subst] :
( ( ( X148 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) @ X155 )
!= $true )
& ( $true
= ( X148 @ X154 @ X152 @ ( comp @ X153 @ X155 ) ) ) )
| ? [X161: term] :
( ( X150 @ X161 )
!= ( X148 @ id @ X161 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
! [X458: term > $o] :
( ( ( sP23 @ X458 )
= $true )
<=> ! [X459: term,X460: term] :
( ( ( X458 @ ( ap @ X460 @ X459 ) )
= $true )
| ( ( X458 @ X460 )
!= $true )
| ( ( X458 @ X459 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
! [X464: term > $o] :
( ( ( sP24 @ X464 )
= $true )
<=> ? [X469: term,X470: term] :
( ( ( X464 @ ( ap @ X469 @ X470 ) )
!= $true )
& ( ( X464 @ X470 )
= $true )
& ( ( X464 @ X469 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
( ( $true = sP25 )
<=> ! [X463: term,X464: term > $o,X465: subst] :
( ( ( sP24 @ X464 )
= $true )
| ? [X468: term] :
( ( ( var @ X468 )
= $true )
& ( ( X464 @ ( sub @ X468 @ X465 ) )
!= $true ) )
| ? [X466: term] :
( ( $true
!= ( X464 @ ( lam @ X466 ) ) )
& ! [X467: term] :
( ( ( X464 @ X467 )
!= $true )
| ( ( X464 @ ( sub @ X466 @ ( push @ X467 @ id ) ) )
= $true ) ) )
| ( $true
= ( X464 @ ( sub @ X463 @ X465 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
( ( sP26 = $true )
<=> ( ( $true = sP25 )
| ? [X454: term,X455: subst] :
( ( comp @ sh @ ( push @ X454 @ X455 ) )
!= X455 )
| ? [X456: subst] :
( ( comp @ X456 @ id )
!= X456 )
| ? [X457: term,X458: term > $o] :
( ! [X461: term] :
( ( ( X458 @ X461 )
= $true )
| ( ( var @ X461 )
!= $true ) )
& ! [X462: term] :
( ( ( X458 @ X462 )
!= $true )
| ( ( X458 @ ( lam @ X462 ) )
= $true ) )
& ( $true
!= ( X458 @ X457 ) )
& ( ( sP23 @ X458 )
= $true ) )
| ? [X452: term,X453: subst] :
( ( sub @ one @ ( push @ X452 @ X453 ) )
!= X452 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
! [X303: term > $o] :
( ( ( sP27 @ X303 )
= $true )
<=> ! [X305: term,X306: term] :
( ( ( X303 @ ( ap @ X305 @ X306 ) )
= $true )
| ( $true
!= ( X303 @ X305 ) )
| ( ( X303 @ X306 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
! [X321: subst > term > subst > $o] :
( ( $true
= ( sP28 @ X321 ) )
<=> ? [X323: subst > term > term] :
( ! [X324: term] :
( ( $true
= ( X321 @ id @ ( X323 @ id @ X324 ) @ id ) )
| ( ( X321 @ id @ X324 @ id )
!= $true ) )
& ! [X325: subst,X326: subst,X327: term] :
( ( sub @ ( X323 @ X326 @ X327 ) @ X325 )
= ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) ) )
& ( ( X321 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
( ( sP29 = $true )
<=> ? [X311: term > $o,X312: term,X313: subst > term > subst > $o] :
( ! [X314: term] :
( ( X311 @ X314 )
= ( X313 @ id @ X314 @ id ) )
& ( ( X311 @ ( lam @ X312 ) )
!= $true )
& ! [X315: term] :
( ( ( X311 @ ( sub @ X312 @ ( push @ X315 @ id ) ) )
= $true )
| ( ( X311 @ X315 )
!= $true ) )
& ! [X316: subst > term > term] :
( ? [X317: term] :
( ( ( X313 @ id @ X317 @ id )
= $true )
& ( ( X313 @ id @ ( X316 @ id @ X317 ) @ id )
!= $true ) )
| ? [X318: term,X319: subst,X320: subst] :
( ( sub @ ( X316 @ X320 @ X318 ) @ X319 )
!= ( X316 @ ( comp @ X320 @ X319 ) @ ( sub @ X318 @ X319 ) ) )
| ( $true
= ( X313 @ id @ ( lam @ ( X316 @ sh @ one ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( $true = sP30 )
<=> ? [X303: term > $o,X304: term] :
( ( ( X303 @ X304 )
!= $true )
& ! [X307: term] :
( ( ( X303 @ X307 )
= $true )
| ( $true
!= ( var @ X307 ) ) )
& ( ( sP27 @ X303 )
= $true )
& ! [X308: term] :
( ? [X309: term] :
( ( ( X303 @ X309 )
= $true )
& ( ( X303 @ ( sub @ X308 @ ( push @ X309 @ id ) ) )
!= $true ) )
| ( $true
= ( X303 @ ( lam @ X308 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
( ( sP31 = $true )
<=> ( ( sP29 = $true )
| ! [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ X322 @ id )
= $true )
| ? [X328: term,X329: term] :
( ( ( X321 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id )
!= $true )
& ( ( X321 @ id @ X328 @ id )
= $true )
& ( ( X321 @ id @ X329 @ id )
= $true ) )
| ( $true
= ( sP28 @ X321 ) ) )
| ? [X310: term] :
( ( sub @ X310 @ id )
!= X310 )
| ( $true = sP30 )
| ? [X300: subst > term > subst > $o] :
! [X301: term > $o] :
? [X302: term] :
( ( X301 @ X302 )
!= ( X300 @ id @ X302 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
( ( sP32 = $true )
<=> ! [X487: term,X488: subst > term > subst > $o] :
( ? [X489: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( sub @ X487 @ ( push @ X489 @ id ) ) @ id )
!= $true ) )
| ? [X490: subst > term > term,X491: term] :
( ! [X496: subst,X497: subst,X498: term] :
( ( X490 @ ( comp @ X496 @ X497 ) @ ( sub @ X498 @ X497 ) )
= ( sub @ X491 @ ( push @ ( sub @ X498 @ X497 ) @ ( comp @ X496 @ X497 ) ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X490 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ! [X492: subst,X493: subst,X494: term] :
( ( sub @ ( X490 @ X492 @ X494 ) @ X493 )
= ( sub @ ( sub @ X491 @ ( push @ X494 @ X492 ) ) @ X493 ) )
& ( $true
!= ( X488 @ id @ ( lam @ ( X490 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X488 @ id @ ( lam @ ( sub @ X487 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
( ( $true = sP33 )
<=> ! [X412: term,X413: term > $o,X414: subst > term > subst > $o] :
( ? [X421: term] :
( ( X413 @ X421 )
!= ( X414 @ id @ X421 @ id ) )
| ? [X415: term] :
( ( $true
!= ( X413 @ ( sub @ X412 @ ( push @ X415 @ id ) ) ) )
& ( $true
= ( X413 @ X415 ) ) )
| ? [X416: subst > term > term] :
( ( ( X414 @ id @ ( lam @ ( X416 @ sh @ one ) ) @ id )
!= $true )
& ! [X417: term,X418: subst,X419: subst] :
( ( sub @ ( X416 @ X419 @ X417 ) @ X418 )
= ( X416 @ ( comp @ X419 @ X418 ) @ ( sub @ X417 @ X418 ) ) )
& ! [X420: term] :
( ( ( X414 @ id @ X420 @ id )
!= $true )
| ( ( X414 @ id @ ( X416 @ id @ X420 ) @ id )
= $true ) ) )
| ( $true
= ( X413 @ ( lam @ X412 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
! [X58: term > $o] :
( ( ( sP34 @ X58 )
= $true )
<=> ! [X59: term,X60: term] :
( ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true )
| ( $true
!= ( X58 @ X59 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
! [X75: subst > term > subst > $o] :
( ( $true
= ( sP35 @ X75 ) )
<=> ? [X91: term,X92: term] :
( ( ( X75 @ id @ X91 @ id )
= $true )
& ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
!= $true )
& ( $true
= ( X75 @ id @ X92 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
! [X75: subst > term > subst > $o] :
( ( ( sP36 @ X75 )
= $true )
<=> ? [X82: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
!= $true )
& ! [X83: term] :
( ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true )
| ( ( X75 @ id @ X83 @ id )
!= $true ) )
& ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
( ( $true = sP37 )
<=> ? [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ( $true
!= ( X65 @ ( lam @ X66 ) ) )
& ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
& ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) )
& ! [X68: subst > term > term] :
( ? [X69: term] :
( ( ( X67 @ id @ X69 @ id )
= $true )
& ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
!= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true )
| ? [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
!= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
( ( sP38 = $true )
<=> ! [X75: subst > term > subst > $o,X76: term] :
( ( ( X75 @ id @ X76 @ id )
= $true )
| ( ( sP36 @ X75 )
= $true )
| ( $true
= ( sP35 @ X75 ) )
| ? [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
!= $true )
& ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
= $true ) )
| ? [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
!= $true )
& ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
= $true ) )
| ? [X77: term] :
( ( ( X75 @ id @ X77 @ id )
!= $true )
& ( ( var @ ( sub @ X77 @ id ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
( ( $true = sP39 )
<=> ( ( sP38 = $true )
| ? [X57: term,X58: term > $o] :
( ! [X61: term] :
( ( $true
= ( X58 @ ( lam @ X61 ) ) )
| ? [X62: term] :
( ( $true
= ( X58 @ X62 ) )
& ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
!= $true ) ) )
& ( ( sP34 @ X58 )
= $true )
& ! [X63: term] :
( ( ( var @ X63 )
!= $true )
| ( ( X58 @ X63 )
= $true ) )
& ( ( X58 @ X57 )
!= $true ) )
| ( $true = sP37 )
| ? [X64: term] :
( ( sub @ X64 @ id )
!= X64 )
| ? [X54: subst > term > subst > $o] :
! [X55: term > $o] :
? [X56: term] :
( ( X54 @ id @ X56 @ id )
!= ( X55 @ X56 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X340: subst > term > subst > $o] :
( ( ( sP40 @ X340 )
= $true )
<=> ? [X342: subst > term > term] :
( ( $true
!= ( X340 @ id @ ( lam @ ( X342 @ sh @ one ) ) @ id ) )
& ! [X343: term,X344: subst,X345: subst] :
( ( X342 @ ( comp @ X344 @ X345 ) @ ( sub @ X343 @ X345 ) )
= ( sub @ ( X342 @ X344 @ X343 ) @ X345 ) )
& ! [X346: term] :
( ( ( X340 @ id @ X346 @ id )
!= $true )
| ( $true
= ( X340 @ id @ ( X342 @ id @ X346 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( $true = sP41 )
<=> ? [X331: subst > term > subst > $o,X332: term] :
( ( ( X331 @ id @ ( lam @ ( sub @ X332 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X338: term] :
( ( ( X331 @ id @ X338 @ id )
!= $true )
| ( ( X331 @ id @ ( sub @ X332 @ ( push @ X338 @ id ) ) @ id )
= $true ) )
& ! [X333: subst > term > term] :
( ? [X334: term] :
( ( ( X331 @ id @ ( X333 @ id @ X334 ) @ id )
!= $true )
& ( $true
= ( X331 @ id @ X334 @ id ) ) )
| ? [X335: term,X336: subst,X337: subst] :
( ( X333 @ ( comp @ X337 @ X336 ) @ ( sub @ X335 @ X336 ) )
!= ( sub @ ( X333 @ X337 @ X335 ) @ X336 ) )
| ( ( X331 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
( ( $true = sP42 )
<=> ( ( $true = sP41 )
| ? [X330: term] :
( ( sub @ X330 @ id )
!= X330 )
| ! [X339: term,X340: subst > term > subst > $o] :
( ( ( sP40 @ X340 )
= $true )
| ? [X347: subst,X348: subst,X349: subst,X350: term] :
( ( ( X340 @ ( comp @ X349 @ X347 ) @ ( sub @ X350 @ X347 ) @ X348 )
!= $true )
& ( ( X340 @ X349 @ X350 @ ( comp @ X347 @ X348 ) )
= $true ) )
| ? [X341: term] :
( ( $true
= ( X340 @ id @ X341 @ id ) )
& ( ( X340 @ id @ ( sub @ X339 @ ( push @ X341 @ id ) ) @ id )
!= $true ) )
| ? [X351: term,X352: subst,X353: subst,X354: subst] :
( ( $true
!= ( X340 @ X353 @ X351 @ ( comp @ X354 @ X352 ) ) )
& ( ( X340 @ ( comp @ X353 @ X354 ) @ ( sub @ X351 @ X354 ) @ X352 )
= $true ) )
| ( ( X340 @ id @ ( lam @ X339 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
! [X131: term > $o] :
( ( ( sP43 @ X131 )
= $true )
<=> ? [X133: term,X134: term] :
( ( ( X131 @ X134 )
= $true )
& ( ( X131 @ X133 )
= $true )
& ( ( X131 @ ( ap @ X133 @ X134 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
! [X510: term > $o] :
( ( $true
= ( sP44 @ X510 ) )
<=> ? [X512: term,X513: term] :
( ( $true
!= ( X510 @ ( ap @ X513 @ X512 ) ) )
& ( ( X510 @ X513 )
= $true )
& ( ( X510 @ X512 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
( ( $true = sP45 )
<=> ! [X508: subst,X509: term,X510: term > $o] :
( ( ( X510 @ ( sub @ X509 @ X508 ) )
= $true )
| ( $true
= ( sP44 @ X510 ) )
| ? [X514: term] :
( ! [X515: term] :
( ( ( X510 @ X515 )
!= $true )
| ( ( X510 @ ( sub @ X514 @ ( push @ X515 @ id ) ) )
= $true ) )
& ( ( X510 @ ( lam @ X514 ) )
!= $true ) )
| ? [X511: term] :
( ( ( X510 @ ( sub @ X511 @ X508 ) )
!= $true )
& ( ( var @ X511 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
! [X422: subst > term > subst > $o] :
( ( ( sP46 @ X422 )
= $true )
<=> ? [X425: subst > term > term] :
( ( ( X422 @ id @ ( lam @ ( X425 @ sh @ one ) ) @ id )
!= $true )
& ! [X429: term] :
( ( ( X422 @ id @ X429 @ id )
!= $true )
| ( ( X422 @ id @ ( X425 @ id @ X429 ) @ id )
= $true ) )
& ! [X426: subst,X427: term,X428: subst] :
( ( X425 @ ( comp @ X428 @ X426 ) @ ( sub @ X427 @ X426 ) )
= ( sub @ ( X425 @ X428 @ X427 ) @ X426 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
( ( $true = sP47 )
<=> ! [X422: subst > term > subst > $o,X423: term,X424: term > $o] :
( ? [X439: term] :
( ( ( X424 @ X439 )
= $true )
& ( ( X424 @ ( sub @ X423 @ ( push @ X439 @ id ) ) )
!= $true ) )
| ? [X430: subst,X431: term,X432: subst,X433: subst] :
( ( ( X422 @ ( comp @ X433 @ X432 ) @ ( sub @ X431 @ X432 ) @ X430 )
!= $true )
& ( ( X422 @ X433 @ X431 @ ( comp @ X432 @ X430 ) )
= $true ) )
| ( ( X424 @ ( lam @ X423 ) )
= $true )
| ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X422 @ ( comp @ X436 @ X437 ) @ ( sub @ X434 @ X437 ) @ X435 )
= $true )
& ( $true
!= ( X422 @ X436 @ X434 @ ( comp @ X437 @ X435 ) ) ) )
| ? [X438: term] :
( ( X422 @ id @ X438 @ id )
!= ( X424 @ X438 ) )
| ( ( sP46 @ X422 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
( ( sP48 = $true )
<=> ! [X248: subst > term > subst > $o,X249: term] :
( ( $true
= ( X248 @ id @ ( lam @ ( sub @ X249 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X251: subst > term > term] :
( ( ( X248 @ id @ ( lam @ ( X251 @ sh @ one ) ) @ id )
!= $true )
& ! [X253: term,X254: subst,X255: subst] :
( ( sub @ ( X251 @ X255 @ X253 ) @ X254 )
= ( X251 @ ( comp @ X255 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X252: term] :
( ( ( X248 @ id @ ( X251 @ id @ X252 ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X252 @ id ) ) ) )
| ? [X250: term] :
( ( ( X248 @ id @ ( sub @ X249 @ ( push @ X250 @ id ) ) @ id )
!= $true )
& ( $true
= ( X248 @ id @ X250 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
! [X282: subst > term > subst > $o] :
( ( $true
= ( sP49 @ X282 ) )
<=> ? [X293: term,X294: term] :
( ( $true
!= ( X282 @ id @ ( ap @ ( sub @ X293 @ id ) @ X294 ) @ id ) )
& ( $true
= ( X282 @ id @ X293 @ id ) )
& ( ( X282 @ id @ X294 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
( ( sP50 = $true )
<=> ! [X280: term,X281: term,X282: subst > term > subst > $o,X283: term > $o] :
( ? [X289: subst,X290: subst,X291: term,X292: subst] :
( ( ( X282 @ ( comp @ X289 @ X290 ) @ ( sub @ X291 @ X290 ) @ X292 )
!= $true )
& ( ( X282 @ X289 @ X291 @ ( comp @ X290 @ X292 ) )
= $true ) )
| ? [X288: term] :
( ( X283 @ X288 )
!= ( X282 @ id @ X288 @ id ) )
| ( $true
= ( sP49 @ X282 ) )
| ( ( X283 @ X281 )
!= $true )
| ( $true
= ( X283 @ ( ap @ X280 @ X281 ) ) )
| ( ( X283 @ X280 )
!= $true )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X282 @ ( comp @ X285 @ X284 ) @ ( sub @ X286 @ X284 ) @ X287 ) )
& ( ( X282 @ X285 @ X286 @ ( comp @ X284 @ X287 ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
( ( $true = sP51 )
<=> ! [X440: subst > term > subst > $o,X441: term] :
( ? [X442: subst > term > term] :
( ! [X443: subst,X444: subst,X445: term] :
( ( X442 @ ( comp @ X443 @ X444 ) @ ( sub @ X445 @ X444 ) )
= ( sub @ ( X442 @ X443 @ X445 ) @ X444 ) )
& ( ( X440 @ id @ ( lam @ ( X442 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: term] :
( ( ( X440 @ id @ ( X442 @ id @ X446 ) @ id )
= $true )
| ( $true
!= ( X440 @ id @ X446 @ id ) ) ) )
| ( ( X440 @ id @ ( lam @ X441 ) @ id )
= $true )
| ? [X447: term] :
( ( ( X440 @ id @ X447 @ id )
= $true )
& ( ( X440 @ id @ ( sub @ X441 @ ( push @ X447 @ id ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( sP52 = $true )
<=> ( ? [X473: term,X474: subst] :
( ( comp @ sh @ ( push @ X473 @ X474 ) )
!= X474 )
| ? [X471: term,X472: subst] :
( ( sub @ one @ ( push @ X471 @ X472 ) )
!= X471 )
| ? [X475: term,X476: term] :
( ( ( lam @ X475 )
= ( lam @ X476 ) )
& ( X475 != X476 ) )
| ! [X477: term,X478: subst,X479: subst > term > term,X480: subst > term > term] :
( ? [X481: subst,X482: term,X483: subst] :
( ( sub @ ( X479 @ X483 @ X482 ) @ X481 )
!= ( X479 @ ( comp @ X483 @ X481 ) @ ( sub @ X482 @ X481 ) ) )
| ( ( lam @ ( X480 @ sh @ one ) )
!= ( lam @ ( X479 @ sh @ one ) ) )
| ( ( X479 @ X478 @ X477 )
= ( X480 @ X478 @ X477 ) )
| ? [X484: subst,X485: term,X486: subst] :
( ( X480 @ ( comp @ X484 @ X486 ) @ ( sub @ X485 @ X486 ) )
!= ( sub @ ( X480 @ X484 @ X485 ) @ X486 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
( ( sP53 = $true )
<=> ( ? [X231: term] :
( ( sub @ X231 @ id )
!= X231 )
| ? [X227: term] :
! [X228: subst > term > term] :
? [X229: subst,X230: term] :
( ( sub @ X227 @ ( push @ X230 @ X229 ) )
!= ( X228 @ X229 @ X230 ) )
| ! [X232: subst > term > subst > $o,X233: term > $o,X234: term] :
( ? [X236: term] :
( ( ( X233 @ ( sub @ X234 @ ( push @ X236 @ id ) ) )
!= $true )
& ( ( X233 @ X236 )
= $true ) )
| ( ( X233 @ ( lam @ X234 ) )
= $true )
| ? [X235: term] :
( ( X232 @ id @ X235 @ id )
!= ( X233 @ X235 ) )
| ? [X237: subst > term > term] :
( ! [X239: term,X240: subst,X241: subst] :
( ( sub @ ( X237 @ X241 @ X239 ) @ X240 )
= ( X237 @ ( comp @ X241 @ X240 ) @ ( sub @ X239 @ X240 ) ) )
& ! [X238: term] :
( ( $true
!= ( X232 @ id @ X238 @ id ) )
| ( $true
= ( X232 @ id @ ( X237 @ id @ X238 ) @ id ) ) )
& ( ( X232 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
!= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X517: term > $o] :
( ( ( sP54 @ X517 )
= $true )
<=> ! [X523: term,X524: term] :
( ( ( X517 @ ( ap @ X523 @ X524 ) )
= $true )
| ( ( X517 @ X524 )
!= $true )
| ( ( X517 @ X523 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
! [X525: term > $o] :
( ( ( sP55 @ X525 )
= $true )
<=> ? [X530: term,X531: term] :
( ( $true
= ( X525 @ X530 ) )
& ( ( X525 @ ( ap @ X530 @ X531 ) )
!= $true )
& ( $true
= ( X525 @ X531 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( sP56 = $true )
<=> ! [X525: term > $o,X526: term] :
( ? [X529: term] :
( ( ( var @ X529 )
= $true )
& ( ( X525 @ X529 )
!= $true ) )
| ? [X527: term] :
( ( ( X525 @ ( lam @ X527 ) )
!= $true )
& ! [X528: term] :
( ( ( X525 @ X528 )
!= $true )
| ( ( X525 @ ( sub @ X527 @ ( push @ X528 @ id ) ) )
= $true ) ) )
| ( $true
= ( X525 @ X526 ) )
| ( ( sP55 @ X525 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
( ( sP57 = $true )
<=> ( ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 )
| ( sP56 = $true )
| ? [X517: term > $o,X518: subst,X519: term] :
( ! [X521: term] :
( ? [X522: term] :
( ( ( X517 @ ( sub @ X521 @ ( push @ X522 @ id ) ) )
!= $true )
& ( $true
= ( X517 @ X522 ) ) )
| ( $true
= ( X517 @ ( lam @ X521 ) ) ) )
& ( $true
!= ( X517 @ ( sub @ X519 @ X518 ) ) )
& ( ( sP54 @ X517 )
= $true )
& ! [X520: term] :
( ( $true
= ( X517 @ ( sub @ X520 @ X518 ) ) )
| ( ( var @ X520 )
!= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( sP58 = $true )
<=> ! [X121: subst > term > subst > $o,X122: term] :
( ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X123: subst > term > term] :
( ! [X127: term] :
( ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) )
| ( ( X121 @ id @ X127 @ id )
!= $true ) )
& ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
!= $true )
& ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) ) )
| ? [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
!= $true )
& ( $true
= ( X121 @ id @ X128 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f12,plain,
( ( ! [X24: subst > term > subst > $o] :
? [X25: term > $o] :
! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ? [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
!= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ? [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
!= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X121: subst > term > subst > $o,X122: term] :
( ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X123: subst > term > term] :
( ! [X127: term] :
( ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) )
| ( ( X121 @ id @ X127 @ id )
!= $true ) )
& ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
!= $true )
& ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) ) )
| ? [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
!= $true )
& ( $true
= ( X121 @ id @ X128 @ id ) ) ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X448: term] :
? [X449: subst > term > term] :
! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 )
| ! [X525: term > $o,X526: term] :
( ? [X529: term] :
( ( ( var @ X529 )
= $true )
& ( ( X525 @ X529 )
!= $true ) )
| ? [X527: term] :
( ( ( X525 @ ( lam @ X527 ) )
!= $true )
& ! [X528: term] :
( ( ( X525 @ X528 )
!= $true )
| ( ( X525 @ ( sub @ X527 @ ( push @ X528 @ id ) ) )
= $true ) ) )
| ( $true
= ( X525 @ X526 ) )
| ? [X530: term,X531: term] :
( ( $true
= ( X525 @ X530 ) )
& ( ( X525 @ ( ap @ X530 @ X531 ) )
!= $true )
& ( $true
= ( X525 @ X531 ) ) ) )
| ? [X517: term > $o,X518: subst,X519: term] :
( ! [X521: term] :
( ? [X522: term] :
( ( ( X517 @ ( sub @ X521 @ ( push @ X522 @ id ) ) )
!= $true )
& ( $true
= ( X517 @ X522 ) ) )
| ( $true
= ( X517 @ ( lam @ X521 ) ) ) )
& ( $true
!= ( X517 @ ( sub @ X519 @ X518 ) ) )
& ! [X523: term,X524: term] :
( ( ( X517 @ ( ap @ X523 @ X524 ) )
= $true )
| ( ( X517 @ X524 )
!= $true )
| ( ( X517 @ X523 )
!= $true ) )
& ! [X520: term] :
( ( $true
= ( X517 @ ( sub @ X520 @ X518 ) ) )
| ( ( var @ X520 )
!= $true ) ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ? [X231: term] :
( ( sub @ X231 @ id )
!= X231 )
| ? [X227: term] :
! [X228: subst > term > term] :
? [X229: subst,X230: term] :
( ( sub @ X227 @ ( push @ X230 @ X229 ) )
!= ( X228 @ X229 @ X230 ) )
| ! [X232: subst > term > subst > $o,X233: term > $o,X234: term] :
( ? [X236: term] :
( ( ( X233 @ ( sub @ X234 @ ( push @ X236 @ id ) ) )
!= $true )
& ( ( X233 @ X236 )
= $true ) )
| ( ( X233 @ ( lam @ X234 ) )
= $true )
| ? [X235: term] :
( ( X232 @ id @ X235 @ id )
!= ( X233 @ X235 ) )
| ? [X237: subst > term > term] :
( ! [X239: term,X240: subst,X241: subst] :
( ( sub @ ( X237 @ X241 @ X239 ) @ X240 )
= ( X237 @ ( comp @ X241 @ X240 ) @ ( sub @ X239 @ X240 ) ) )
& ! [X238: term] :
( ( $true
!= ( X232 @ id @ X238 @ id ) )
| ( $true
= ( X232 @ id @ ( X237 @ id @ X238 ) @ id ) ) )
& ( ( X232 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
!= $true ) ) ) ) )
& ( pushprop_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ? [X473: term,X474: subst] :
( ( comp @ sh @ ( push @ X473 @ X474 ) )
!= X474 )
| ? [X471: term,X472: subst] :
( ( sub @ one @ ( push @ X471 @ X472 ) )
!= X471 )
| ? [X475: term,X476: term] :
( ( ( lam @ X475 )
= ( lam @ X476 ) )
& ( X475 != X476 ) )
| ! [X477: term,X478: subst,X479: subst > term > term,X480: subst > term > term] :
( ? [X481: subst,X482: term,X483: subst] :
( ( sub @ ( X479 @ X483 @ X482 ) @ X481 )
!= ( X479 @ ( comp @ X483 @ X481 ) @ ( sub @ X482 @ X481 ) ) )
| ( ( lam @ ( X480 @ sh @ one ) )
!= ( lam @ ( X479 @ sh @ one ) ) )
| ( ( X479 @ X478 @ X477 )
= ( X480 @ X478 @ X477 ) )
| ? [X484: subst,X485: term,X486: subst] :
( ( X480 @ ( comp @ X484 @ X486 ) @ ( sub @ X485 @ X486 ) )
!= ( sub @ ( X480 @ X484 @ X485 ) @ X486 ) ) ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X440: subst > term > subst > $o,X441: term] :
( ? [X442: subst > term > term] :
( ! [X443: subst,X444: subst,X445: term] :
( ( X442 @ ( comp @ X443 @ X444 ) @ ( sub @ X445 @ X444 ) )
= ( sub @ ( X442 @ X443 @ X445 ) @ X444 ) )
& ( ( X440 @ id @ ( lam @ ( X442 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: term] :
( ( ( X440 @ id @ ( X442 @ id @ X446 ) @ id )
= $true )
| ( $true
!= ( X440 @ id @ X446 @ id ) ) ) )
| ( ( X440 @ id @ ( lam @ X441 ) @ id )
= $true )
| ? [X447: term] :
( ( ( X440 @ id @ X447 @ id )
= $true )
& ( ( X440 @ id @ ( sub @ X441 @ ( push @ X447 @ id ) ) @ id )
!= $true ) ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ? [X277: subst] :
( ( comp @ X277 @ id )
!= X277 )
| ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) )
| ? [X276: subst] :
( ( comp @ id @ X276 )
!= X276 ) ) )
& ( lamnotap != $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( ! [X280: term,X281: term,X282: subst > term > subst > $o,X283: term > $o] :
( ? [X289: subst,X290: subst,X291: term,X292: subst] :
( ( ( X282 @ ( comp @ X289 @ X290 ) @ ( sub @ X291 @ X290 ) @ X292 )
!= $true )
& ( ( X282 @ X289 @ X291 @ ( comp @ X290 @ X292 ) )
= $true ) )
| ? [X288: term] :
( ( X283 @ X288 )
!= ( X282 @ id @ X288 @ id ) )
| ? [X293: term,X294: term] :
( ( $true
!= ( X282 @ id @ ( ap @ ( sub @ X293 @ id ) @ X294 ) @ id ) )
& ( $true
= ( X282 @ id @ X293 @ id ) )
& ( ( X282 @ id @ X294 @ id )
= $true ) )
| ( ( X283 @ X281 )
!= $true )
| ( $true
= ( X283 @ ( ap @ X280 @ X281 ) ) )
| ( ( X283 @ X280 )
!= $true )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X282 @ ( comp @ X285 @ X284 ) @ ( sub @ X286 @ X284 ) @ X287 ) )
& ( ( X282 @ X285 @ X286 @ ( comp @ X284 @ X287 ) )
!= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ulamvarsh = $true )
& ( ( ? [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
!= X499 )
| ? [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
!= X501 )
| ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X248: subst > term > subst > $o,X249: term] :
( ( $true
= ( X248 @ id @ ( lam @ ( sub @ X249 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X251: subst > term > term] :
( ( ( X248 @ id @ ( lam @ ( X251 @ sh @ one ) ) @ id )
!= $true )
& ! [X253: term,X254: subst,X255: subst] :
( ( sub @ ( X251 @ X255 @ X253 ) @ X254 )
= ( X251 @ ( comp @ X255 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X252: term] :
( ( ( X248 @ id @ ( X251 @ id @ X252 ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X252 @ id ) ) ) )
| ? [X250: term] :
( ( ( X248 @ id @ ( sub @ X249 @ ( push @ X250 @ id ) ) @ id )
!= $true )
& ( $true
= ( X248 @ id @ X250 @ id ) ) ) ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
!= ( d2subst @ X117 ) )
| ( X116 = X117 ) )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( axmap = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X422: subst > term > subst > $o,X423: term,X424: term > $o] :
( ? [X439: term] :
( ( ( X424 @ X439 )
= $true )
& ( ( X424 @ ( sub @ X423 @ ( push @ X439 @ id ) ) )
!= $true ) )
| ? [X430: subst,X431: term,X432: subst,X433: subst] :
( ( ( X422 @ ( comp @ X433 @ X432 ) @ ( sub @ X431 @ X432 ) @ X430 )
!= $true )
& ( ( X422 @ X433 @ X431 @ ( comp @ X432 @ X430 ) )
= $true ) )
| ( ( X424 @ ( lam @ X423 ) )
= $true )
| ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X422 @ ( comp @ X436 @ X437 ) @ ( sub @ X434 @ X437 ) @ X435 )
= $true )
& ( $true
!= ( X422 @ X436 @ X434 @ ( comp @ X437 @ X435 ) ) ) )
| ? [X438: term] :
( ( X422 @ id @ X438 @ id )
!= ( X424 @ X438 ) )
| ? [X425: subst > term > term] :
( ( ( X422 @ id @ ( lam @ ( X425 @ sh @ one ) ) @ id )
!= $true )
& ! [X429: term] :
( ( ( X422 @ id @ X429 @ id )
!= $true )
| ( ( X422 @ id @ ( X425 @ id @ X429 ) @ id )
= $true ) )
& ! [X426: subst,X427: term,X428: subst] :
( ( X425 @ ( comp @ X428 @ X426 ) @ ( sub @ X427 @ X426 ) )
= ( sub @ ( X425 @ X428 @ X427 ) @ X426 ) ) ) ) )
& ( axvarshift = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( termmset_gthm = $true )
& ( ! [X508: subst,X509: term,X510: term > $o] :
( ( ( X510 @ ( sub @ X509 @ X508 ) )
= $true )
| ? [X512: term,X513: term] :
( ( $true
!= ( X510 @ ( ap @ X513 @ X512 ) ) )
& ( ( X510 @ X513 )
= $true )
& ( ( X510 @ X512 )
= $true ) )
| ? [X514: term] :
( ! [X515: term] :
( ( ( X510 @ X515 )
!= $true )
| ( ( X510 @ ( sub @ X514 @ ( push @ X515 @ id ) ) )
= $true ) )
& ( ( X510 @ ( lam @ X514 ) )
!= $true ) )
| ? [X511: term] :
( ( ( X510 @ ( sub @ X511 @ X508 ) )
!= $true )
& ( ( var @ X511 )
= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ( ! [X200: term] :
? [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
= ( X201 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( induction2lem_gthm = $true )
& ( ! [X27: term] :
? [X28: subst > term > term] :
! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X131: term > $o,X132: term] :
( ? [X133: term,X134: term] :
( ( ( X131 @ X134 )
= $true )
& ( ( X131 @ X133 )
= $true )
& ( ( X131 @ ( ap @ X133 @ X134 ) )
!= $true ) )
| ? [X136: term] :
( ( $true
= ( var @ X136 ) )
& ( $true
!= ( X131 @ X136 ) ) )
| ? [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
!= $true )
& ( $true
= ( X131 @ X135 ) ) )
| ( ( X131 @ X132 )
= $true ) )
<=> ( induction = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ? [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
!= ( X175 @ X179 ) ) )
| ? [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
!= X173 ) ) )
& ( axabs = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( ? [X331: subst > term > subst > $o,X332: term] :
( ( ( X331 @ id @ ( lam @ ( sub @ X332 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X338: term] :
( ( ( X331 @ id @ X338 @ id )
!= $true )
| ( ( X331 @ id @ ( sub @ X332 @ ( push @ X338 @ id ) ) @ id )
= $true ) )
& ! [X333: subst > term > term] :
( ? [X334: term] :
( ( ( X331 @ id @ ( X333 @ id @ X334 ) @ id )
!= $true )
& ( $true
= ( X331 @ id @ X334 @ id ) ) )
| ? [X335: term,X336: subst,X337: subst] :
( ( X333 @ ( comp @ X337 @ X336 ) @ ( sub @ X335 @ X336 ) )
!= ( sub @ ( X333 @ X337 @ X335 ) @ X336 ) )
| ( ( X331 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X330: term] :
( ( sub @ X330 @ id )
!= X330 )
| ! [X339: term,X340: subst > term > subst > $o] :
( ? [X342: subst > term > term] :
( ( $true
!= ( X340 @ id @ ( lam @ ( X342 @ sh @ one ) ) @ id ) )
& ! [X343: term,X344: subst,X345: subst] :
( ( X342 @ ( comp @ X344 @ X345 ) @ ( sub @ X343 @ X345 ) )
= ( sub @ ( X342 @ X344 @ X343 ) @ X345 ) )
& ! [X346: term] :
( ( ( X340 @ id @ X346 @ id )
!= $true )
| ( $true
= ( X340 @ id @ ( X342 @ id @ X346 ) @ id ) ) ) )
| ? [X347: subst,X348: subst,X349: subst,X350: term] :
( ( ( X340 @ ( comp @ X349 @ X347 ) @ ( sub @ X350 @ X347 ) @ X348 )
!= $true )
& ( ( X340 @ X349 @ X350 @ ( comp @ X347 @ X348 ) )
= $true ) )
| ? [X341: term] :
( ( $true
= ( X340 @ id @ X341 @ id ) )
& ( ( X340 @ id @ ( sub @ X339 @ ( push @ X341 @ id ) ) @ id )
!= $true ) )
| ? [X351: term,X352: subst,X353: subst,X354: subst] :
( ( $true
!= ( X340 @ X353 @ X351 @ ( comp @ X354 @ X352 ) ) )
& ( ( X340 @ ( comp @ X353 @ X354 ) @ ( sub @ X351 @ X354 ) @ X352 )
= $true ) )
| ( ( X340 @ id @ ( lam @ X339 ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ( ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X535 )
& ( ( ap @ X533 @ X535 )
= ( ap @ X534 @ X532 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X137: subst,X138: term,X139: term > $o] :
? [X140: term > $o] :
! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) ) )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( ! [X75: subst > term > subst > $o,X76: term] :
( ( ( X75 @ id @ X76 @ id )
= $true )
| ? [X82: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
!= $true )
& ! [X83: term] :
( ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true )
| ( ( X75 @ id @ X83 @ id )
!= $true ) )
& ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ? [X91: term,X92: term] :
( ( ( X75 @ id @ X91 @ id )
= $true )
& ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
!= $true )
& ( $true
= ( X75 @ id @ X92 @ id ) ) )
| ? [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
!= $true )
& ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
= $true ) )
| ? [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
!= $true )
& ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
= $true ) )
| ? [X77: term] :
( ( ( X75 @ id @ X77 @ id )
!= $true )
& ( ( var @ ( sub @ X77 @ id ) )
= $true ) ) )
| ? [X57: term,X58: term > $o] :
( ! [X61: term] :
( ( $true
= ( X58 @ ( lam @ X61 ) ) )
| ? [X62: term] :
( ( $true
= ( X58 @ X62 ) )
& ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
!= $true ) ) )
& ! [X59: term,X60: term] :
( ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true )
| ( $true
!= ( X58 @ X59 ) ) )
& ! [X63: term] :
( ( ( var @ X63 )
!= $true )
| ( ( X58 @ X63 )
= $true ) )
& ( ( X58 @ X57 )
!= $true ) )
| ? [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ( $true
!= ( X65 @ ( lam @ X66 ) ) )
& ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
& ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) )
& ! [X68: subst > term > term] :
( ? [X69: term] :
( ( ( X67 @ id @ X69 @ id )
= $true )
& ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
!= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true )
| ? [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
!= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) ) )
| ? [X64: term] :
( ( sub @ X64 @ id )
!= X64 )
| ? [X54: subst > term > subst > $o] :
! [X55: term > $o] :
? [X56: term] :
( ( X54 @ id @ X56 @ id )
!= ( X55 @ X56 ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X412: term,X413: term > $o,X414: subst > term > subst > $o] :
( ? [X421: term] :
( ( X413 @ X421 )
!= ( X414 @ id @ X421 @ id ) )
| ? [X415: term] :
( ( $true
!= ( X413 @ ( sub @ X412 @ ( push @ X415 @ id ) ) ) )
& ( $true
= ( X413 @ X415 ) ) )
| ? [X416: subst > term > term] :
( ( ( X414 @ id @ ( lam @ ( X416 @ sh @ one ) ) @ id )
!= $true )
& ! [X417: term,X418: subst,X419: subst] :
( ( sub @ ( X416 @ X419 @ X417 ) @ X418 )
= ( X416 @ ( comp @ X419 @ X418 ) @ ( sub @ X417 @ X418 ) ) )
& ! [X420: term] :
( ( ( X414 @ id @ X420 @ id )
!= $true )
| ( ( X414 @ id @ ( X416 @ id @ X420 ) @ id )
= $true ) ) )
| ( $true
= ( X413 @ ( lam @ X412 ) ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( shinj = $true )
<=> ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) ) )
& ( induction2_gthm = $true )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
<=> ( termmset = $true ) )
& ( ( ? [X171: term] :
( ( sub @ X171 @ id )
!= X171 )
| ! [X172: term] :
( ( sub @ X172 @ id )
= X172 ) )
<=> ( termmset_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ? [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
!= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X487: term,X488: subst > term > subst > $o] :
( ? [X489: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( sub @ X487 @ ( push @ X489 @ id ) ) @ id )
!= $true ) )
| ? [X490: subst > term > term,X491: term] :
( ! [X496: subst,X497: subst,X498: term] :
( ( X490 @ ( comp @ X496 @ X497 ) @ ( sub @ X498 @ X497 ) )
= ( sub @ X491 @ ( push @ ( sub @ X498 @ X497 ) @ ( comp @ X496 @ X497 ) ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X490 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ! [X492: subst,X493: subst,X494: term] :
( ( sub @ ( X490 @ X492 @ X494 ) @ X493 )
= ( sub @ ( sub @ X491 @ ( push @ X494 @ X492 ) ) @ X493 ) )
& ( $true
!= ( X488 @ id @ ( lam @ ( X490 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X488 @ id @ ( lam @ ( sub @ X487 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( ? [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
= ( ap @ X107 @ X109 ) )
& ( X107 != X108 ) )
| ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
| ? [X105: term] :
( ( sub @ X105 @ id )
!= X105 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
<=> ( hoasapinj1 = $true ) )
& ! [X170: d_term] : ( d_one = X170 )
& ( hoasinduction_lem1_gthm = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ? [X311: term > $o,X312: term,X313: subst > term > subst > $o] :
( ! [X314: term] :
( ( X311 @ X314 )
= ( X313 @ id @ X314 @ id ) )
& ( ( X311 @ ( lam @ X312 ) )
!= $true )
& ! [X315: term] :
( ( ( X311 @ ( sub @ X312 @ ( push @ X315 @ id ) ) )
= $true )
| ( ( X311 @ X315 )
!= $true ) )
& ! [X316: subst > term > term] :
( ? [X317: term] :
( ( ( X313 @ id @ X317 @ id )
= $true )
& ( ( X313 @ id @ ( X316 @ id @ X317 ) @ id )
!= $true ) )
| ? [X318: term,X319: subst,X320: subst] :
( ( sub @ ( X316 @ X320 @ X318 ) @ X319 )
!= ( X316 @ ( comp @ X320 @ X319 ) @ ( sub @ X318 @ X319 ) ) )
| ( $true
= ( X313 @ id @ ( lam @ ( X316 @ sh @ one ) ) @ id ) ) ) )
| ! [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ X322 @ id )
= $true )
| ? [X328: term,X329: term] :
( ( ( X321 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id )
!= $true )
& ( ( X321 @ id @ X328 @ id )
= $true )
& ( ( X321 @ id @ X329 @ id )
= $true ) )
| ? [X323: subst > term > term] :
( ! [X324: term] :
( ( $true
= ( X321 @ id @ ( X323 @ id @ X324 ) @ id ) )
| ( ( X321 @ id @ X324 @ id )
!= $true ) )
& ! [X325: subst,X326: subst,X327: term] :
( ( sub @ ( X323 @ X326 @ X327 ) @ X325 )
= ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) ) )
& ( ( X321 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X310: term] :
( ( sub @ X310 @ id )
!= X310 )
| ? [X303: term > $o,X304: term] :
( ( ( X303 @ X304 )
!= $true )
& ! [X307: term] :
( ( ( X303 @ X307 )
= $true )
| ( $true
!= ( var @ X307 ) ) )
& ! [X305: term,X306: term] :
( ( ( X303 @ ( ap @ X305 @ X306 ) )
= $true )
| ( $true
!= ( X303 @ X305 ) )
| ( ( X303 @ X306 )
!= $true ) )
& ! [X308: term] :
( ? [X309: term] :
( ( ( X303 @ X309 )
= $true )
& ( ( X303 @ ( sub @ X308 @ ( push @ X309 @ id ) ) )
!= $true ) )
| ( $true
= ( X303 @ ( lam @ X308 ) ) ) ) )
| ? [X300: subst > term > subst > $o] :
! [X301: term > $o] :
? [X302: term] :
( ( X301 @ X302 )
!= ( X300 @ id @ X302 @ id ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( apnotvar = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X118: subst > term > subst > $o] :
? [X119: term > $o] :
! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) ) )
& ( ( ! [X463: term,X464: term > $o,X465: subst] :
( ? [X469: term,X470: term] :
( ( ( X464 @ ( ap @ X469 @ X470 ) )
!= $true )
& ( ( X464 @ X470 )
= $true )
& ( ( X464 @ X469 )
= $true ) )
| ? [X468: term] :
( ( ( var @ X468 )
= $true )
& ( ( X464 @ ( sub @ X468 @ X465 ) )
!= $true ) )
| ? [X466: term] :
( ( $true
!= ( X464 @ ( lam @ X466 ) ) )
& ! [X467: term] :
( ( ( X464 @ X467 )
!= $true )
| ( ( X464 @ ( sub @ X466 @ ( push @ X467 @ id ) ) )
= $true ) ) )
| ( $true
= ( X464 @ ( sub @ X463 @ X465 ) ) ) )
| ? [X454: term,X455: subst] :
( ( comp @ sh @ ( push @ X454 @ X455 ) )
!= X455 )
| ? [X456: subst] :
( ( comp @ X456 @ id )
!= X456 )
| ? [X457: term,X458: term > $o] :
( ! [X461: term] :
( ( ( X458 @ X461 )
= $true )
| ( ( var @ X461 )
!= $true ) )
& ! [X462: term] :
( ( ( X458 @ X462 )
!= $true )
| ( ( X458 @ ( lam @ X462 ) )
= $true ) )
& ( $true
!= ( X458 @ X457 ) )
& ! [X459: term,X460: term] :
( ( ( X458 @ ( ap @ X460 @ X459 ) )
= $true )
| ( ( X458 @ X460 )
!= $true )
| ( ( X458 @ X459 )
!= $true ) ) )
| ? [X452: term,X453: subst] :
( ( sub @ one @ ( push @ X452 @ X453 ) )
!= X452 ) )
<=> ( induction2lem_lthm = $true ) )
& ( ! [X129: term] :
? [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
= ( X130 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( pushprop_lthm = $true )
& ( ( ? [X147: term] :
( ( sub @ X147 @ id )
!= X147 )
| ! [X148: subst > term > subst > $o,X149: term,X150: term > $o] :
( ? [X151: term] :
( ( ( X150 @ X151 )
= $true )
& ( ( X150 @ ( sub @ X149 @ ( push @ X151 @ id ) ) )
!= $true ) )
| ? [X162: subst,X163: subst,X164: term,X165: subst] :
( ( $true
= ( X148 @ ( comp @ X162 @ X163 ) @ ( sub @ X164 @ X163 ) @ X165 ) )
& ( ( X148 @ X162 @ X164 @ ( comp @ X163 @ X165 ) )
!= $true ) )
| ( ( X150 @ ( lam @ X149 ) )
= $true )
| ? [X156: subst > term > term] :
( ! [X157: term] :
( ( ( X148 @ id @ X157 @ id )
!= $true )
| ( ( X148 @ id @ ( X156 @ id @ X157 ) @ id )
= $true ) )
& ! [X158: subst,X159: term,X160: subst] :
( ( sub @ ( X156 @ X158 @ X159 ) @ X160 )
= ( X156 @ ( comp @ X158 @ X160 ) @ ( sub @ X159 @ X160 ) ) )
& ( $true
!= ( X148 @ id @ ( lam @ ( X156 @ sh @ one ) ) @ id ) ) )
| ? [X152: term,X153: subst,X154: subst,X155: subst] :
( ( ( X148 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) @ X155 )
!= $true )
& ( $true
= ( X148 @ X154 @ X152 @ ( comp @ X153 @ X155 ) ) ) )
| ? [X161: term] :
( ( X150 @ X161 )
!= ( X148 @ id @ X161 @ id ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ? [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
= $true )
& ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
!= $true )
& ( $true
= ( X202 @ id @ X205 @ id ) ) )
| ? [X206: subst > term > term] :
( ! [X210: term] :
( ( ( X202 @ id @ X210 @ id )
!= $true )
| ( ( X202 @ id @ ( X206 @ id @ X210 ) @ id )
= $true ) )
& ! [X207: subst,X208: subst,X209: term] :
( ( X206 @ ( comp @ X207 @ X208 ) @ ( sub @ X209 @ X208 ) )
= ( sub @ ( X206 @ X207 @ X209 ) @ X208 ) )
& ( $true
!= ( X202 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) ) )
| ( ( X202 @ id @ X203 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
<=> ( axidl = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( hoasinduction = $true )
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ? [X48: subst > term > term] :
( ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) )
& ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
!= $true )
& ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) ) )
| ( $true
= ( X37 @ id @ X36 @ id ) )
| ? [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
= $true )
& ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
!= $true ) )
| ? [X53: term] :
( ( $true
= ( var @ ( sub @ X53 @ id ) ) )
& ( ( X37 @ id @ X53 @ id )
!= $true ) )
| ? [X38: term,X39: term] :
( ( ( X37 @ id @ X38 @ id )
= $true )
& ( $true
!= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
& ( ( X37 @ id @ X39 @ id )
= $true ) )
| ? [X40: subst,X41: term,X42: subst,X43: subst] :
( ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
!= $true )
& ( $true
= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( hoaslamnotvar = $true )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2 = $true )
& ( ( apinj1 = $true )
<=> ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) ) )
& ( ( axvarid = $true )
<=> ! [X355: term] :
( ( sub @ X355 @ id )
= X355 ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X211: term,X212: term > $o,X213: subst] :
? [X214: term > $o] :
! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
!= $true )
| ? [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
!= ( X144 @ X146 ) )
| ( ( X144 @ one )
= $true ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ? [X7: term] :
( ( sub @ X7 @ id )
!= X7 )
| ! [X16: term,X17: subst > term > subst > $o] :
( ? [X18: term] :
( ( ( X17 @ id @ X18 @ id )
= $true )
& ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) )
| ? [X19: subst > term > term] :
( ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
& ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) )
& ( $true
!= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) )
| ? [X8: term,X9: subst > term > subst > $o] :
( ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) )
& ( $true
!= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ? [X14: term] :
( ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
!= $true )
& ( ( X9 @ id @ X14 @ id )
= $true ) )
| ? [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
!= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) ) ) ) ) )
& ( axapp = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ulamvarind = $true )
& ( ( ? [X378: subst > term > subst > $o,X379: term] :
( ! [X380: subst,X381: term,X382: subst,X383: subst] :
( ( ( X378 @ X383 @ X381 @ ( comp @ X382 @ X380 ) )
!= $true )
| ( ( X378 @ ( comp @ X383 @ X382 ) @ ( sub @ X381 @ X382 ) @ X380 )
= $true ) )
& ! [X388: term] :
( ( ( X378 @ id @ ( sub @ X379 @ ( push @ X388 @ id ) ) @ id )
= $true )
| ( ( X378 @ id @ X388 @ id )
!= $true ) )
& ( ( X378 @ id @ ( lam @ X379 ) @ id )
!= $true )
& ! [X384: subst,X385: subst,X386: subst,X387: term] :
( ( $true
= ( X378 @ X386 @ X387 @ ( comp @ X384 @ X385 ) ) )
| ( $true
!= ( X378 @ ( comp @ X386 @ X384 ) @ ( sub @ X387 @ X384 ) @ X385 ) ) )
& ! [X389: subst > term > term] :
( ? [X390: term] :
( ( ( X378 @ id @ X390 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( X389 @ id @ X390 ) @ id ) ) )
| ? [X391: term,X392: subst,X393: subst] :
( ( sub @ ( X389 @ X393 @ X391 ) @ X392 )
!= ( X389 @ ( comp @ X393 @ X392 ) @ ( sub @ X391 @ X392 ) ) )
| ( ( X378 @ id @ ( lam @ ( X389 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X365: term,X366: term,X367: subst > term > subst > $o] :
( ! [X368: subst,X369: subst,X370: subst,X371: term] :
( ( $true
!= ( X367 @ ( comp @ X368 @ X369 ) @ ( sub @ X371 @ X369 ) @ X370 ) )
| ( $true
= ( X367 @ X368 @ X371 @ ( comp @ X369 @ X370 ) ) ) )
& ! [X372: subst,X373: subst,X374: subst,X375: term] :
( ( $true
= ( X367 @ ( comp @ X373 @ X372 ) @ ( sub @ X375 @ X372 ) @ X374 ) )
| ( $true
!= ( X367 @ X373 @ X375 @ ( comp @ X372 @ X374 ) ) ) )
& ! [X376: term,X377: term] :
( ( ( X367 @ id @ X376 @ id )
!= $true )
| ( ( X367 @ id @ ( ap @ ( sub @ X376 @ id ) @ X377 ) @ id )
= $true )
| ( $true
!= ( X367 @ id @ X377 @ id ) ) )
& ( $true
= ( X367 @ id @ X366 @ id ) )
& ( ( X367 @ id @ X365 @ id )
= $true )
& ( ( X367 @ id @ ( ap @ X365 @ X366 ) @ id )
!= $true ) )
| ? [X358: term,X359: term > $o] :
( ! [X362: term] :
( ? [X363: term] :
( ( $true
= ( X359 @ X363 ) )
& ( ( X359 @ ( sub @ X362 @ ( push @ X363 @ id ) ) )
!= $true ) )
| ( ( X359 @ ( lam @ X362 ) )
= $true ) )
& ( ( X359 @ X358 )
!= $true )
& ! [X364: term] :
( ( $true
= ( X359 @ X364 ) )
| ( ( var @ X364 )
!= $true ) )
& ! [X360: term,X361: term] :
( ( ( X359 @ X360 )
!= $true )
| ( ( X359 @ X361 )
!= $true )
| ( ( X359 @ ( ap @ X361 @ X360 ) )
= $true ) ) )
| ! [X394: term,X395: subst > term > subst > $o] :
( ? [X405: term,X406: term] :
( ( $true
!= ( X395 @ id @ ( ap @ ( sub @ X406 @ id ) @ X405 ) @ id ) )
& ( ( X395 @ id @ X406 @ id )
= $true )
& ( ( X395 @ id @ X405 @ id )
= $true ) )
| ? [X408: subst,X409: subst,X410: subst,X411: term] :
( ( $true
= ( X395 @ ( comp @ X408 @ X409 ) @ ( sub @ X411 @ X409 ) @ X410 ) )
& ( ( X395 @ X408 @ X411 @ ( comp @ X409 @ X410 ) )
!= $true ) )
| ? [X400: subst > term > term] :
( ( ( X395 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
!= $true )
& ! [X401: term] :
( ( ( X395 @ id @ X401 @ id )
!= $true )
| ( ( X395 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
& ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X404 @ X403 ) @ ( sub @ X402 @ X403 ) )
= ( sub @ ( X400 @ X404 @ X402 ) @ X403 ) ) )
| ? [X407: term] :
( ( ( var @ ( sub @ X407 @ id ) )
= $true )
& ( ( X395 @ id @ X407 @ id )
!= $true ) )
| ( $true
= ( X395 @ id @ X394 @ id ) )
| ? [X396: term,X397: subst,X398: subst,X399: subst] :
( ( ( X395 @ X397 @ X396 @ ( comp @ X399 @ X398 ) )
= $true )
& ( ( X395 @ ( comp @ X397 @ X399 ) @ ( sub @ X396 @ X399 ) @ X398 )
!= $true ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
<=> ( apinj2 = $true ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
<=> ( substmonoid = $true ) )
& ( ! [X258: subst > term > subst > $o,X259: term] :
( ? [X269: subst > term > term] :
( ! [X273: term] :
( ( ( X258 @ id @ X273 @ id )
!= $true )
| ( ( X258 @ id @ ( X269 @ id @ X273 ) @ id )
= $true ) )
& ! [X270: subst,X271: subst,X272: term] :
( ( sub @ ( X269 @ X270 @ X272 ) @ X271 )
= ( X269 @ ( comp @ X270 @ X271 ) @ ( sub @ X272 @ X271 ) ) )
& ( ( X258 @ id @ ( lam @ ( X269 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X264: term,X265: subst,X266: subst,X267: subst] :
( ( ( X258 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) @ X267 )
!= $true )
& ( ( X258 @ X265 @ X264 @ ( comp @ X266 @ X267 ) )
= $true ) )
| ? [X268: term] :
( ( ( X258 @ id @ ( sub @ X259 @ ( push @ X268 @ id ) ) @ id )
!= $true )
& ( $true
= ( X258 @ id @ X268 @ id ) ) )
| ( $true
= ( X258 @ id @ ( lam @ X259 ) @ id ) )
| ? [X260: subst,X261: term,X262: subst,X263: subst] :
( ( $true
= ( X258 @ ( comp @ X260 @ X263 ) @ ( sub @ X261 @ X263 ) @ X262 ) )
& ( ( X258 @ X260 @ X261 @ ( comp @ X263 @ X262 ) )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axclos = $true )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( induction2 = $true )
<=> ! [X193: term,X194: term > $o] :
( ? [X195: term] :
( ( ( var @ X195 )
= $true )
& ( ( X194 @ X195 )
!= $true ) )
| ? [X196: term] :
( ( $true
!= ( X194 @ ( lam @ X196 ) ) )
& ! [X197: term] :
( ( ( X194 @ ( sub @ X196 @ ( push @ X197 @ id ) ) )
= $true )
| ( $true
!= ( X194 @ X197 ) ) ) )
| ( ( X194 @ X193 )
= $true )
| ? [X198: term,X199: term] :
( ( $true
!= ( X194 @ ( ap @ X198 @ X199 ) ) )
& ( ( X194 @ X198 )
= $true )
& ( $true
= ( X194 @ X199 ) ) ) ) )
& ( ! [X180: term,X181: term,X182: subst > term > subst > $o] :
( ( $true
!= ( X182 @ id @ X181 @ id ) )
| ( ( X182 @ id @ X180 @ id )
!= $true )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( ( X182 @ X184 @ X185 @ ( comp @ X183 @ X186 ) )
= $true )
& ( ( X182 @ ( comp @ X184 @ X183 ) @ ( sub @ X185 @ X183 ) @ X186 )
!= $true ) )
| ? [X191: term,X192: term] :
( ( ( X182 @ id @ X191 @ id )
= $true )
& ( $true
= ( X182 @ id @ X192 @ id ) )
& ( ( X182 @ id @ ( ap @ ( sub @ X192 @ id ) @ X191 ) @ id )
!= $true ) )
| ? [X187: subst,X188: term,X189: subst,X190: subst] :
( ( ( X182 @ ( comp @ X189 @ X187 ) @ ( sub @ X188 @ X187 ) @ X190 )
= $true )
& ( ( X182 @ X189 @ X188 @ ( comp @ X187 @ X190 ) )
!= $true ) )
| ( ( X182 @ id @ ( ap @ X180 @ X181 ) @ id )
= $true ) )
<=> ( hoasinduction_lem2 = $true ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( axclos = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_gthm = $true )
& ( ( hoasinduction = $true )
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ? [X48: subst > term > term] :
( ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) )
& ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
!= $true )
& ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) ) )
| ( $true
= ( X37 @ id @ X36 @ id ) )
| ? [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
= $true )
& ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
!= $true ) )
| ? [X53: term] :
( ( $true
= ( var @ ( sub @ X53 @ id ) ) )
& ( ( X37 @ id @ X53 @ id )
!= $true ) )
| ? [X38: term,X39: term] :
( ( ( X37 @ id @ X38 @ id )
= $true )
& ( $true
!= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
& ( ( X37 @ id @ X39 @ id )
= $true ) )
| ? [X40: subst,X41: term,X42: subst,X43: subst] :
( ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
!= $true )
& ( $true
= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) ) ) ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X16: term,X17: subst > term > subst > $o] :
( ? [X18: term] :
( ( ( X17 @ id @ X18 @ id )
= $true )
& ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
!= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) )
| ? [X19: subst > term > term] :
( ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
& ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) )
& ( $true
!= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) )
| ? [X8: term,X9: subst > term > subst > $o] :
( ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) )
& ( $true
!= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ? [X14: term] :
( ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
!= $true )
& ( ( X9 @ id @ X14 @ id )
= $true ) )
| ? [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
!= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) ) ) )
| ? [X7: term] :
( ( sub @ X7 @ id )
!= X7 ) ) )
& ( lamnotvar = $true )
& ( ( induction2 = $true )
<=> ! [X193: term,X194: term > $o] :
( ? [X195: term] :
( ( ( var @ X195 )
= $true )
& ( ( X194 @ X195 )
!= $true ) )
| ? [X196: term] :
( ( $true
!= ( X194 @ ( lam @ X196 ) ) )
& ! [X197: term] :
( ( ( X194 @ ( sub @ X196 @ ( push @ X197 @ id ) ) )
= $true )
| ( $true
!= ( X194 @ X197 ) ) ) )
| ( ( X194 @ X193 )
= $true )
| ? [X198: term,X199: term] :
( ( $true
!= ( X194 @ ( ap @ X198 @ X199 ) ) )
& ( ( X194 @ X198 )
= $true )
& ( $true
= ( X194 @ X199 ) ) ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ! [X463: term,X464: term > $o,X465: subst] :
( ? [X469: term,X470: term] :
( ( ( X464 @ ( ap @ X469 @ X470 ) )
!= $true )
& ( ( X464 @ X470 )
= $true )
& ( ( X464 @ X469 )
= $true ) )
| ? [X468: term] :
( ( ( var @ X468 )
= $true )
& ( ( X464 @ ( sub @ X468 @ X465 ) )
!= $true ) )
| ? [X466: term] :
( ( $true
!= ( X464 @ ( lam @ X466 ) ) )
& ! [X467: term] :
( ( ( X464 @ X467 )
!= $true )
| ( ( X464 @ ( sub @ X466 @ ( push @ X467 @ id ) ) )
= $true ) ) )
| ( $true
= ( X464 @ ( sub @ X463 @ X465 ) ) ) )
| ? [X457: term,X458: term > $o] :
( ! [X461: term] :
( ( ( X458 @ X461 )
= $true )
| ( ( var @ X461 )
!= $true ) )
& ! [X462: term] :
( ( ( X458 @ X462 )
!= $true )
| ( ( X458 @ ( lam @ X462 ) )
= $true ) )
& ( $true
!= ( X458 @ X457 ) )
& ! [X459: term,X460: term] :
( ( ( X458 @ ( ap @ X460 @ X459 ) )
= $true )
| ( ( X458 @ X460 )
!= $true )
| ( ( X458 @ X459 )
!= $true ) ) )
| ? [X456: subst] :
( ( comp @ X456 @ id )
!= X456 )
| ? [X454: term,X455: subst] :
( ( comp @ sh @ ( push @ X454 @ X455 ) )
!= X455 )
| ? [X452: term,X453: subst] :
( ( sub @ one @ ( push @ X452 @ X453 ) )
!= X452 ) )
<=> ( induction2lem_lthm = $true ) )
& ( ! [X27: term] :
? [X28: subst > term > term] :
! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X118: subst > term > subst > $o] :
? [X119: term > $o] :
! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ! [X180: term,X181: term,X182: subst > term > subst > $o] :
( ( $true
!= ( X182 @ id @ X181 @ id ) )
| ( ( X182 @ id @ X180 @ id )
!= $true )
| ? [X183: subst,X184: subst,X185: term,X186: subst] :
( ( ( X182 @ X184 @ X185 @ ( comp @ X183 @ X186 ) )
= $true )
& ( ( X182 @ ( comp @ X184 @ X183 ) @ ( sub @ X185 @ X183 ) @ X186 )
!= $true ) )
| ? [X191: term,X192: term] :
( ( ( X182 @ id @ X191 @ id )
= $true )
& ( $true
= ( X182 @ id @ X192 @ id ) )
& ( ( X182 @ id @ ( ap @ ( sub @ X192 @ id ) @ X191 ) @ id )
!= $true ) )
| ? [X187: subst,X188: term,X189: subst,X190: subst] :
( ( ( X182 @ ( comp @ X189 @ X187 ) @ ( sub @ X188 @ X187 ) @ X190 )
= $true )
& ( ( X182 @ X189 @ X188 @ ( comp @ X187 @ X190 ) )
!= $true ) )
| ( ( X182 @ id @ ( ap @ X180 @ X181 ) @ id )
= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ! [X24: subst > term > subst > $o] :
? [X25: term > $o] :
! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( axapp = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( axvarshift = $true )
& ( ( ! [X477: term,X478: subst,X479: subst > term > term,X480: subst > term > term] :
( ? [X481: subst,X482: term,X483: subst] :
( ( sub @ ( X479 @ X483 @ X482 ) @ X481 )
!= ( X479 @ ( comp @ X483 @ X481 ) @ ( sub @ X482 @ X481 ) ) )
| ( ( lam @ ( X480 @ sh @ one ) )
!= ( lam @ ( X479 @ sh @ one ) ) )
| ( ( X479 @ X478 @ X477 )
= ( X480 @ X478 @ X477 ) )
| ? [X484: subst,X485: term,X486: subst] :
( ( X480 @ ( comp @ X484 @ X486 ) @ ( sub @ X485 @ X486 ) )
!= ( sub @ ( X480 @ X484 @ X485 ) @ X486 ) ) )
| ? [X475: term,X476: term] :
( ( ( lam @ X475 )
= ( lam @ X476 ) )
& ( X475 != X476 ) )
| ? [X473: term,X474: subst] :
( ( comp @ sh @ ( push @ X473 @ X474 ) )
!= X474 )
| ? [X471: term,X472: subst] :
( ( sub @ one @ ( push @ X471 @ X472 ) )
!= X471 ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X339: term,X340: subst > term > subst > $o] :
( ? [X342: subst > term > term] :
( ( $true
!= ( X340 @ id @ ( lam @ ( X342 @ sh @ one ) ) @ id ) )
& ! [X343: term,X344: subst,X345: subst] :
( ( X342 @ ( comp @ X344 @ X345 ) @ ( sub @ X343 @ X345 ) )
= ( sub @ ( X342 @ X344 @ X343 ) @ X345 ) )
& ! [X346: term] :
( ( ( X340 @ id @ X346 @ id )
!= $true )
| ( $true
= ( X340 @ id @ ( X342 @ id @ X346 ) @ id ) ) ) )
| ? [X347: subst,X348: subst,X349: subst,X350: term] :
( ( ( X340 @ ( comp @ X349 @ X347 ) @ ( sub @ X350 @ X347 ) @ X348 )
!= $true )
& ( ( X340 @ X349 @ X350 @ ( comp @ X347 @ X348 ) )
= $true ) )
| ? [X341: term] :
( ( $true
= ( X340 @ id @ X341 @ id ) )
& ( ( X340 @ id @ ( sub @ X339 @ ( push @ X341 @ id ) ) @ id )
!= $true ) )
| ? [X351: term,X352: subst,X353: subst,X354: subst] :
( ( $true
!= ( X340 @ X353 @ X351 @ ( comp @ X354 @ X352 ) ) )
& ( ( X340 @ ( comp @ X353 @ X354 ) @ ( sub @ X351 @ X354 ) @ X352 )
= $true ) )
| ( ( X340 @ id @ ( lam @ X339 ) @ id )
= $true ) )
| ? [X331: subst > term > subst > $o,X332: term] :
( ( ( X331 @ id @ ( lam @ ( sub @ X332 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X338: term] :
( ( ( X331 @ id @ X338 @ id )
!= $true )
| ( ( X331 @ id @ ( sub @ X332 @ ( push @ X338 @ id ) ) @ id )
= $true ) )
& ! [X333: subst > term > term] :
( ? [X334: term] :
( ( ( X331 @ id @ ( X333 @ id @ X334 ) @ id )
!= $true )
& ( $true
= ( X331 @ id @ X334 @ id ) ) )
| ? [X335: term,X336: subst,X337: subst] :
( ( X333 @ ( comp @ X337 @ X336 ) @ ( sub @ X335 @ X336 ) )
!= ( sub @ ( X333 @ X337 @ X335 ) @ X336 ) )
| ( ( X331 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X330: term] :
( ( sub @ X330 @ id )
!= X330 ) ) )
& ( induction2_gthm = $true )
& ( ( ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) )
| ? [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
!= X501 )
| ? [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
!= X499 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X440: subst > term > subst > $o,X441: term] :
( ? [X442: subst > term > term] :
( ! [X443: subst,X444: subst,X445: term] :
( ( X442 @ ( comp @ X443 @ X444 ) @ ( sub @ X445 @ X444 ) )
= ( sub @ ( X442 @ X443 @ X445 ) @ X444 ) )
& ( ( X440 @ id @ ( lam @ ( X442 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: term] :
( ( ( X440 @ id @ ( X442 @ id @ X446 ) @ id )
= $true )
| ( $true
!= ( X440 @ id @ X446 @ id ) ) ) )
| ( ( X440 @ id @ ( lam @ X441 ) @ id )
= $true )
| ? [X447: term] :
( ( ( X440 @ id @ X447 @ id )
= $true )
& ( ( X440 @ id @ ( sub @ X441 @ ( push @ X447 @ id ) ) @ id )
!= $true ) ) ) )
& ( ! [X280: term,X281: term,X282: subst > term > subst > $o,X283: term > $o] :
( ? [X289: subst,X290: subst,X291: term,X292: subst] :
( ( ( X282 @ ( comp @ X289 @ X290 ) @ ( sub @ X291 @ X290 ) @ X292 )
!= $true )
& ( ( X282 @ X289 @ X291 @ ( comp @ X290 @ X292 ) )
= $true ) )
| ? [X288: term] :
( ( X283 @ X288 )
!= ( X282 @ id @ X288 @ id ) )
| ? [X293: term,X294: term] :
( ( $true
!= ( X282 @ id @ ( ap @ ( sub @ X293 @ id ) @ X294 ) @ id ) )
& ( $true
= ( X282 @ id @ X293 @ id ) )
& ( ( X282 @ id @ X294 @ id )
= $true ) )
| ( ( X283 @ X281 )
!= $true )
| ( $true
= ( X283 @ ( ap @ X280 @ X281 ) ) )
| ( ( X283 @ X280 )
!= $true )
| ? [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
= ( X282 @ ( comp @ X285 @ X284 ) @ ( sub @ X286 @ X284 ) @ X287 ) )
& ( ( X282 @ X285 @ X286 @ ( comp @ X284 @ X287 ) )
!= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ( substmonoid_gthm = $true )
& ( ulamvarsh = $true )
& ( ( ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) )
| ? [X277: subst] :
( ( comp @ X277 @ id )
!= X277 )
| ? [X276: subst] :
( ( comp @ id @ X276 )
!= X276 ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ? [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
!= ( X175 @ X179 ) ) )
| ? [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
!= X173 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( ? [X147: term] :
( ( sub @ X147 @ id )
!= X147 )
| ! [X148: subst > term > subst > $o,X149: term,X150: term > $o] :
( ? [X151: term] :
( ( ( X150 @ X151 )
= $true )
& ( ( X150 @ ( sub @ X149 @ ( push @ X151 @ id ) ) )
!= $true ) )
| ? [X162: subst,X163: subst,X164: term,X165: subst] :
( ( $true
= ( X148 @ ( comp @ X162 @ X163 ) @ ( sub @ X164 @ X163 ) @ X165 ) )
& ( ( X148 @ X162 @ X164 @ ( comp @ X163 @ X165 ) )
!= $true ) )
| ( ( X150 @ ( lam @ X149 ) )
= $true )
| ? [X156: subst > term > term] :
( ! [X157: term] :
( ( ( X148 @ id @ X157 @ id )
!= $true )
| ( ( X148 @ id @ ( X156 @ id @ X157 ) @ id )
= $true ) )
& ! [X158: subst,X159: term,X160: subst] :
( ( sub @ ( X156 @ X158 @ X159 ) @ X160 )
= ( X156 @ ( comp @ X158 @ X160 ) @ ( sub @ X159 @ X160 ) ) )
& ( $true
!= ( X148 @ id @ ( lam @ ( X156 @ sh @ one ) ) @ id ) ) )
| ? [X152: term,X153: subst,X154: subst,X155: subst] :
( ( ( X148 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) @ X155 )
!= $true )
& ( $true
= ( X148 @ X154 @ X152 @ ( comp @ X153 @ X155 ) ) ) )
| ? [X161: term] :
( ( X150 @ X161 )
!= ( X148 @ id @ X161 @ id ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( termmset_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X248: subst > term > subst > $o,X249: term] :
( ( $true
= ( X248 @ id @ ( lam @ ( sub @ X249 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X251: subst > term > term] :
( ( ( X248 @ id @ ( lam @ ( X251 @ sh @ one ) ) @ id )
!= $true )
& ! [X253: term,X254: subst,X255: subst] :
( ( sub @ ( X251 @ X255 @ X253 ) @ X254 )
= ( X251 @ ( comp @ X255 @ X254 ) @ ( sub @ X253 @ X254 ) ) )
& ! [X252: term] :
( ( ( X248 @ id @ ( X251 @ id @ X252 ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X252 @ id ) ) ) )
| ? [X250: term] :
( ( ( X248 @ id @ ( sub @ X249 @ ( push @ X250 @ id ) ) @ id )
!= $true )
& ( $true
= ( X248 @ id @ X250 @ id ) ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X487: term,X488: subst > term > subst > $o] :
( ? [X489: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( sub @ X487 @ ( push @ X489 @ id ) ) @ id )
!= $true ) )
| ? [X490: subst > term > term,X491: term] :
( ! [X496: subst,X497: subst,X498: term] :
( ( X490 @ ( comp @ X496 @ X497 ) @ ( sub @ X498 @ X497 ) )
= ( sub @ X491 @ ( push @ ( sub @ X498 @ X497 ) @ ( comp @ X496 @ X497 ) ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X490 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ! [X492: subst,X493: subst,X494: term] :
( ( sub @ ( X490 @ X492 @ X494 ) @ X493 )
= ( sub @ ( sub @ X491 @ ( push @ X494 @ X492 ) ) @ X493 ) )
& ( $true
!= ( X488 @ id @ ( lam @ ( X490 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X488 @ id @ ( lam @ ( sub @ X487 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( ? [X171: term] :
( ( sub @ X171 @ id )
!= X171 )
| ! [X172: term] :
( ( sub @ X172 @ id )
= X172 ) )
<=> ( termmset_lthm = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( ! [X129: term] :
? [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
= ( X130 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ( ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) )
| ? [X532: term,X533: term,X534: term,X535: term] :
( ( X532 != X535 )
& ( ( ap @ X533 @ X535 )
= ( ap @ X534 @ X532 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ! [X258: subst > term > subst > $o,X259: term] :
( ? [X269: subst > term > term] :
( ! [X273: term] :
( ( ( X258 @ id @ X273 @ id )
!= $true )
| ( ( X258 @ id @ ( X269 @ id @ X273 ) @ id )
= $true ) )
& ! [X270: subst,X271: subst,X272: term] :
( ( sub @ ( X269 @ X270 @ X272 ) @ X271 )
= ( X269 @ ( comp @ X270 @ X271 ) @ ( sub @ X272 @ X271 ) ) )
& ( ( X258 @ id @ ( lam @ ( X269 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X264: term,X265: subst,X266: subst,X267: subst] :
( ( ( X258 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) @ X267 )
!= $true )
& ( ( X258 @ X265 @ X264 @ ( comp @ X266 @ X267 ) )
= $true ) )
| ? [X268: term] :
( ( ( X258 @ id @ ( sub @ X259 @ ( push @ X268 @ id ) ) @ id )
!= $true )
& ( $true
= ( X258 @ id @ X268 @ id ) ) )
| ( $true
= ( X258 @ id @ ( lam @ X259 ) @ id ) )
| ? [X260: subst,X261: term,X262: subst,X263: subst] :
( ( $true
= ( X258 @ ( comp @ X260 @ X263 ) @ ( sub @ X261 @ X263 ) @ X262 ) )
& ( ( X258 @ X260 @ X261 @ ( comp @ X263 @ X262 ) )
!= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( axmap = $true )
& ! [X256: d_term,X257: d_term] :
( ( X256 = X257 )
| ( ( d2term @ X256 )
!= ( d2term @ X257 ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X137: subst,X138: term,X139: term > $o] :
? [X140: term > $o] :
! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) ) )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ( hoaslamnotap = $true )
<=> ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ? [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
!= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X394: term,X395: subst > term > subst > $o] :
( ? [X405: term,X406: term] :
( ( $true
!= ( X395 @ id @ ( ap @ ( sub @ X406 @ id ) @ X405 ) @ id ) )
& ( ( X395 @ id @ X406 @ id )
= $true )
& ( ( X395 @ id @ X405 @ id )
= $true ) )
| ? [X408: subst,X409: subst,X410: subst,X411: term] :
( ( $true
= ( X395 @ ( comp @ X408 @ X409 ) @ ( sub @ X411 @ X409 ) @ X410 ) )
& ( ( X395 @ X408 @ X411 @ ( comp @ X409 @ X410 ) )
!= $true ) )
| ? [X400: subst > term > term] :
( ( ( X395 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
!= $true )
& ! [X401: term] :
( ( ( X395 @ id @ X401 @ id )
!= $true )
| ( ( X395 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
& ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X404 @ X403 ) @ ( sub @ X402 @ X403 ) )
= ( sub @ ( X400 @ X404 @ X402 ) @ X403 ) ) )
| ? [X407: term] :
( ( ( var @ ( sub @ X407 @ id ) )
= $true )
& ( ( X395 @ id @ X407 @ id )
!= $true ) )
| ( $true
= ( X395 @ id @ X394 @ id ) )
| ? [X396: term,X397: subst,X398: subst,X399: subst] :
( ( ( X395 @ X397 @ X396 @ ( comp @ X399 @ X398 ) )
= $true )
& ( ( X395 @ ( comp @ X397 @ X399 ) @ ( sub @ X396 @ X399 ) @ X398 )
!= $true ) ) )
| ? [X378: subst > term > subst > $o,X379: term] :
( ! [X380: subst,X381: term,X382: subst,X383: subst] :
( ( ( X378 @ X383 @ X381 @ ( comp @ X382 @ X380 ) )
!= $true )
| ( ( X378 @ ( comp @ X383 @ X382 ) @ ( sub @ X381 @ X382 ) @ X380 )
= $true ) )
& ! [X388: term] :
( ( ( X378 @ id @ ( sub @ X379 @ ( push @ X388 @ id ) ) @ id )
= $true )
| ( ( X378 @ id @ X388 @ id )
!= $true ) )
& ( ( X378 @ id @ ( lam @ X379 ) @ id )
!= $true )
& ! [X384: subst,X385: subst,X386: subst,X387: term] :
( ( $true
= ( X378 @ X386 @ X387 @ ( comp @ X384 @ X385 ) ) )
| ( $true
!= ( X378 @ ( comp @ X386 @ X384 ) @ ( sub @ X387 @ X384 ) @ X385 ) ) )
& ! [X389: subst > term > term] :
( ? [X390: term] :
( ( ( X378 @ id @ X390 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( X389 @ id @ X390 ) @ id ) ) )
| ? [X391: term,X392: subst,X393: subst] :
( ( sub @ ( X389 @ X393 @ X391 ) @ X392 )
!= ( X389 @ ( comp @ X393 @ X392 ) @ ( sub @ X391 @ X392 ) ) )
| ( ( X378 @ id @ ( lam @ ( X389 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X365: term,X366: term,X367: subst > term > subst > $o] :
( ! [X368: subst,X369: subst,X370: subst,X371: term] :
( ( $true
!= ( X367 @ ( comp @ X368 @ X369 ) @ ( sub @ X371 @ X369 ) @ X370 ) )
| ( $true
= ( X367 @ X368 @ X371 @ ( comp @ X369 @ X370 ) ) ) )
& ! [X372: subst,X373: subst,X374: subst,X375: term] :
( ( $true
= ( X367 @ ( comp @ X373 @ X372 ) @ ( sub @ X375 @ X372 ) @ X374 ) )
| ( $true
!= ( X367 @ X373 @ X375 @ ( comp @ X372 @ X374 ) ) ) )
& ! [X376: term,X377: term] :
( ( ( X367 @ id @ X376 @ id )
!= $true )
| ( ( X367 @ id @ ( ap @ ( sub @ X376 @ id ) @ X377 ) @ id )
= $true )
| ( $true
!= ( X367 @ id @ X377 @ id ) ) )
& ( $true
= ( X367 @ id @ X366 @ id ) )
& ( ( X367 @ id @ X365 @ id )
= $true )
& ( ( X367 @ id @ ( ap @ X365 @ X366 ) @ id )
!= $true ) )
| ? [X358: term,X359: term > $o] :
( ! [X362: term] :
( ? [X363: term] :
( ( $true
= ( X359 @ X363 ) )
& ( ( X359 @ ( sub @ X362 @ ( push @ X363 @ id ) ) )
!= $true ) )
| ( ( X359 @ ( lam @ X362 ) )
= $true ) )
& ( ( X359 @ X358 )
!= $true )
& ! [X364: term] :
( ( $true
= ( X359 @ X364 ) )
| ( ( var @ X364 )
!= $true ) )
& ! [X360: term,X361: term] :
( ( ( X359 @ X360 )
!= $true )
| ( ( X359 @ X361 )
!= $true )
| ( ( X359 @ ( ap @ X361 @ X360 ) )
= $true ) ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X525: term > $o,X526: term] :
( ? [X529: term] :
( ( ( var @ X529 )
= $true )
& ( ( X525 @ X529 )
!= $true ) )
| ? [X527: term] :
( ( ( X525 @ ( lam @ X527 ) )
!= $true )
& ! [X528: term] :
( ( ( X525 @ X528 )
!= $true )
| ( ( X525 @ ( sub @ X527 @ ( push @ X528 @ id ) ) )
= $true ) ) )
| ( $true
= ( X525 @ X526 ) )
| ? [X530: term,X531: term] :
( ( $true
= ( X525 @ X530 ) )
& ( ( X525 @ ( ap @ X530 @ X531 ) )
!= $true )
& ( $true
= ( X525 @ X531 ) ) ) )
| ? [X517: term > $o,X518: subst,X519: term] :
( ! [X521: term] :
( ? [X522: term] :
( ( ( X517 @ ( sub @ X521 @ ( push @ X522 @ id ) ) )
!= $true )
& ( $true
= ( X517 @ X522 ) ) )
| ( $true
= ( X517 @ ( lam @ X521 ) ) ) )
& ( $true
!= ( X517 @ ( sub @ X519 @ X518 ) ) )
& ! [X523: term,X524: term] :
( ( ( X517 @ ( ap @ X523 @ X524 ) )
= $true )
| ( ( X517 @ X524 )
!= $true )
| ( ( X517 @ X523 )
!= $true ) )
& ! [X520: term] :
( ( $true
= ( X517 @ ( sub @ X520 @ X518 ) ) )
| ( ( var @ X520 )
!= $true ) ) )
| ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 ) ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
!= ( d2subst @ X117 ) )
| ( X116 = X117 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X211: term,X212: term > $o,X213: subst] :
? [X214: term > $o] :
! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X200: term] :
? [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
= ( X201 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X131: term > $o,X132: term] :
( ? [X133: term,X134: term] :
( ( ( X131 @ X134 )
= $true )
& ( ( X131 @ X133 )
= $true )
& ( ( X131 @ ( ap @ X133 @ X134 ) )
!= $true ) )
| ? [X136: term] :
( ( $true
= ( var @ X136 ) )
& ( $true
!= ( X131 @ X136 ) ) )
| ? [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
!= $true )
& ( $true
= ( X131 @ X135 ) ) )
| ( ( X131 @ X132 )
= $true ) )
<=> ( induction = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
<=> ( substmonoid = $true ) )
& ( ( ! [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ X322 @ id )
= $true )
| ? [X328: term,X329: term] :
( ( ( X321 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id )
!= $true )
& ( ( X321 @ id @ X328 @ id )
= $true )
& ( ( X321 @ id @ X329 @ id )
= $true ) )
| ? [X323: subst > term > term] :
( ! [X324: term] :
( ( $true
= ( X321 @ id @ ( X323 @ id @ X324 ) @ id ) )
| ( ( X321 @ id @ X324 @ id )
!= $true ) )
& ! [X325: subst,X326: subst,X327: term] :
( ( sub @ ( X323 @ X326 @ X327 ) @ X325 )
= ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) ) )
& ( ( X321 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X311: term > $o,X312: term,X313: subst > term > subst > $o] :
( ! [X314: term] :
( ( X311 @ X314 )
= ( X313 @ id @ X314 @ id ) )
& ( ( X311 @ ( lam @ X312 ) )
!= $true )
& ! [X315: term] :
( ( ( X311 @ ( sub @ X312 @ ( push @ X315 @ id ) ) )
= $true )
| ( ( X311 @ X315 )
!= $true ) )
& ! [X316: subst > term > term] :
( ? [X317: term] :
( ( ( X313 @ id @ X317 @ id )
= $true )
& ( ( X313 @ id @ ( X316 @ id @ X317 ) @ id )
!= $true ) )
| ? [X318: term,X319: subst,X320: subst] :
( ( sub @ ( X316 @ X320 @ X318 ) @ X319 )
!= ( X316 @ ( comp @ X320 @ X319 ) @ ( sub @ X318 @ X319 ) ) )
| ( $true
= ( X313 @ id @ ( lam @ ( X316 @ sh @ one ) ) @ id ) ) ) )
| ? [X310: term] :
( ( sub @ X310 @ id )
!= X310 )
| ? [X303: term > $o,X304: term] :
( ( ( X303 @ X304 )
!= $true )
& ! [X307: term] :
( ( ( X303 @ X307 )
= $true )
| ( $true
!= ( var @ X307 ) ) )
& ! [X305: term,X306: term] :
( ( ( X303 @ ( ap @ X305 @ X306 ) )
= $true )
| ( $true
!= ( X303 @ X305 ) )
| ( ( X303 @ X306 )
!= $true ) )
& ! [X308: term] :
( ? [X309: term] :
( ( ( X303 @ X309 )
= $true )
& ( ( X303 @ ( sub @ X308 @ ( push @ X309 @ id ) ) )
!= $true ) )
| ( $true
= ( X303 @ ( lam @ X308 ) ) ) ) )
| ? [X300: subst > term > subst > $o] :
! [X301: term > $o] :
? [X302: term] :
( ( X301 @ X302 )
!= ( X300 @ id @ X302 @ id ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X508: subst,X509: term,X510: term > $o] :
( ( ( X510 @ ( sub @ X509 @ X508 ) )
= $true )
| ? [X512: term,X513: term] :
( ( $true
!= ( X510 @ ( ap @ X513 @ X512 ) ) )
& ( ( X510 @ X513 )
= $true )
& ( ( X510 @ X512 )
= $true ) )
| ? [X514: term] :
( ! [X515: term] :
( ( ( X510 @ X515 )
!= $true )
| ( ( X510 @ ( sub @ X514 @ ( push @ X515 @ id ) ) )
= $true ) )
& ( ( X510 @ ( lam @ X514 ) )
!= $true ) )
| ? [X511: term] :
( ( ( X510 @ ( sub @ X511 @ X508 ) )
!= $true )
& ( ( var @ X511 )
= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop = $true )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) )
| ? [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
= ( ap @ X107 @ X109 ) )
& ( X107 != X108 ) )
| ? [X105: term] :
( ( sub @ X105 @ id )
!= X105 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( lamnotap != $true )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( ( apinj1 = $true )
<=> ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X412: term,X413: term > $o,X414: subst > term > subst > $o] :
( ? [X421: term] :
( ( X413 @ X421 )
!= ( X414 @ id @ X421 @ id ) )
| ? [X415: term] :
( ( $true
!= ( X413 @ ( sub @ X412 @ ( push @ X415 @ id ) ) ) )
& ( $true
= ( X413 @ X415 ) ) )
| ? [X416: subst > term > term] :
( ( ( X414 @ id @ ( lam @ ( X416 @ sh @ one ) ) @ id )
!= $true )
& ! [X417: term,X418: subst,X419: subst] :
( ( sub @ ( X416 @ X419 @ X417 ) @ X418 )
= ( X416 @ ( comp @ X419 @ X418 ) @ ( sub @ X417 @ X418 ) ) )
& ! [X420: term] :
( ( ( X414 @ id @ X420 @ id )
!= $true )
| ( ( X414 @ id @ ( X416 @ id @ X420 ) @ id )
= $true ) ) )
| ( $true
= ( X413 @ ( lam @ X412 ) ) ) ) )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X145 @ X143 )
!= $true )
| ? [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
!= ( X144 @ X146 ) )
| ( ( X144 @ one )
= $true ) ) )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( shinj = $true )
<=> ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X422: subst > term > subst > $o,X423: term,X424: term > $o] :
( ? [X439: term] :
( ( ( X424 @ X439 )
= $true )
& ( ( X424 @ ( sub @ X423 @ ( push @ X439 @ id ) ) )
!= $true ) )
| ? [X430: subst,X431: term,X432: subst,X433: subst] :
( ( ( X422 @ ( comp @ X433 @ X432 ) @ ( sub @ X431 @ X432 ) @ X430 )
!= $true )
& ( ( X422 @ X433 @ X431 @ ( comp @ X432 @ X430 ) )
= $true ) )
| ( ( X424 @ ( lam @ X423 ) )
= $true )
| ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X422 @ ( comp @ X436 @ X437 ) @ ( sub @ X434 @ X437 ) @ X435 )
= $true )
& ( $true
!= ( X422 @ X436 @ X434 @ ( comp @ X437 @ X435 ) ) ) )
| ? [X438: term] :
( ( X422 @ id @ X438 @ id )
!= ( X424 @ X438 ) )
| ? [X425: subst > term > term] :
( ( ( X422 @ id @ ( lam @ ( X425 @ sh @ one ) ) @ id )
!= $true )
& ! [X429: term] :
( ( ( X422 @ id @ X429 @ id )
!= $true )
| ( ( X422 @ id @ ( X425 @ id @ X429 ) @ id )
= $true ) )
& ! [X426: subst,X427: term,X428: subst] :
( ( X425 @ ( comp @ X428 @ X426 ) @ ( sub @ X427 @ X426 ) )
= ( sub @ ( X425 @ X428 @ X427 ) @ X426 ) ) ) ) )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
<=> ( axidl = $true ) )
& ( hoaslamnotvar = $true )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
<=> ( apinj2 = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( pushprop_lem0_gthm = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ( hoaslaminj = $true )
<=> ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ? [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
!= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ? [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
!= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X232: subst > term > subst > $o,X233: term > $o,X234: term] :
( ? [X236: term] :
( ( ( X233 @ ( sub @ X234 @ ( push @ X236 @ id ) ) )
!= $true )
& ( ( X233 @ X236 )
= $true ) )
| ( ( X233 @ ( lam @ X234 ) )
= $true )
| ? [X235: term] :
( ( X232 @ id @ X235 @ id )
!= ( X233 @ X235 ) )
| ? [X237: subst > term > term] :
( ! [X239: term,X240: subst,X241: subst] :
( ( sub @ ( X237 @ X241 @ X239 ) @ X240 )
= ( X237 @ ( comp @ X241 @ X240 ) @ ( sub @ X239 @ X240 ) ) )
& ! [X238: term] :
( ( $true
!= ( X232 @ id @ X238 @ id ) )
| ( $true
= ( X232 @ id @ ( X237 @ id @ X238 ) @ id ) ) )
& ( ( X232 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X231: term] :
( ( sub @ X231 @ id )
!= X231 )
| ? [X227: term] :
! [X228: subst > term > term] :
? [X229: subst,X230: term] :
( ( sub @ X227 @ ( push @ X230 @ X229 ) )
!= ( X228 @ X229 @ X230 ) ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X75: subst > term > subst > $o,X76: term] :
( ( ( X75 @ id @ X76 @ id )
= $true )
| ? [X82: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
!= $true )
& ! [X83: term] :
( ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true )
| ( ( X75 @ id @ X83 @ id )
!= $true ) )
& ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ? [X91: term,X92: term] :
( ( ( X75 @ id @ X91 @ id )
= $true )
& ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
!= $true )
& ( $true
= ( X75 @ id @ X92 @ id ) ) )
| ? [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
!= $true )
& ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
= $true ) )
| ? [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
!= $true )
& ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
= $true ) )
| ? [X77: term] :
( ( ( X75 @ id @ X77 @ id )
!= $true )
& ( ( var @ ( sub @ X77 @ id ) )
= $true ) ) )
| ? [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ( $true
!= ( X65 @ ( lam @ X66 ) ) )
& ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
& ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) )
& ! [X68: subst > term > term] :
( ? [X69: term] :
( ( ( X67 @ id @ X69 @ id )
= $true )
& ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
!= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true )
| ? [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
!= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) ) )
| ? [X64: term] :
( ( sub @ X64 @ id )
!= X64 )
| ? [X57: term,X58: term > $o] :
( ! [X61: term] :
( ( $true
= ( X58 @ ( lam @ X61 ) ) )
| ? [X62: term] :
( ( $true
= ( X58 @ X62 ) )
& ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
!= $true ) ) )
& ! [X59: term,X60: term] :
( ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true )
| ( $true
!= ( X58 @ X59 ) ) )
& ! [X63: term] :
( ( ( var @ X63 )
!= $true )
| ( ( X58 @ X63 )
= $true ) )
& ( ( X58 @ X57 )
!= $true ) )
| ? [X54: subst > term > subst > $o] :
! [X55: term > $o] :
? [X56: term] :
( ( X54 @ id @ X56 @ id )
!= ( X55 @ X56 ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
<=> ( termmset = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( apnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( axvarid = $true )
<=> ! [X355: term] :
( ( sub @ X355 @ id )
= X355 ) )
& ( pushprop_lthm = $true )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ? [X204: term,X205: term] :
( ( ( X202 @ id @ X204 @ id )
= $true )
& ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
!= $true )
& ( $true
= ( X202 @ id @ X205 @ id ) ) )
| ? [X206: subst > term > term] :
( ! [X210: term] :
( ( ( X202 @ id @ X210 @ id )
!= $true )
| ( ( X202 @ id @ ( X206 @ id @ X210 ) @ id )
= $true ) )
& ! [X207: subst,X208: subst,X209: term] :
( ( X206 @ ( comp @ X207 @ X208 ) @ ( sub @ X209 @ X208 ) )
= ( sub @ ( X206 @ X207 @ X209 ) @ X208 ) )
& ( $true
!= ( X202 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) ) )
| ( ( X202 @ id @ X203 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X170: d_term] : ( d_one = X170 )
& ( ! [X448: term] :
? [X449: subst > term > term] :
! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X121: subst > term > subst > $o,X122: term] :
( ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X123: subst > term > term] :
( ! [X127: term] :
( ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) )
| ( ( X121 @ id @ X127 @ id )
!= $true ) )
& ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
!= $true )
& ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) ) )
| ? [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
!= $true )
& ( $true
= ( X121 @ id @ X128 @ id ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( axclos = $true )
& ( hoasapnotvar_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_gthm = $true )
& ( ! [X36: term,X37: subst > term > subst > $o] :
( ( $true
= ( X37 @ id @ X36 @ id ) )
| ~ ! [X38: term,X39: term] :
( ( ( X37 @ id @ X39 @ id )
!= $true )
| ( $true
= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
| ( ( X37 @ id @ X38 @ id )
!= $true ) )
| ~ ! [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
= $true )
| ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
!= $true ) )
| ~ ! [X40: subst,X41: term,X42: subst,X43: subst] :
( ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
= $true )
| ( $true
!= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) ) )
| ~ ! [X53: term] :
( ( $true
!= ( var @ ( sub @ X53 @ id ) ) )
| ( ( X37 @ id @ X53 @ id )
= $true ) )
| ~ ! [X48: subst > term > term] :
( ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) )
| ~ ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) ) ) )
<=> ( hoasinduction = $true ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X7: term] :
( ( sub @ X7 @ id )
= X7 )
=> ( ! [X8: term,X9: subst > term > subst > $o] :
( ( $true
= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) )
| ~ ! [X14: term] :
( ( ( X9 @ id @ X14 @ id )
!= $true )
| ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
= $true ) ) )
| ~ ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) ) )
=> ! [X16: term,X17: subst > term > subst > $o] :
( ~ ! [X19: subst > term > term] :
( ~ ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
| ( $true
= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) )
| ~ ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) ) )
| ~ ! [X18: term] :
( ( ( X17 @ id @ X18 @ id )
!= $true )
| ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) ) ) ) ) )
& ( lamnotvar = $true )
& ( ( induction2 = $true )
<=> ! [X193: term,X194: term > $o] :
( ~ ! [X196: term] :
( ~ ! [X197: term] :
( ( ( X194 @ ( sub @ X196 @ ( push @ X197 @ id ) ) )
= $true )
| ( $true
!= ( X194 @ X197 ) ) )
| ( $true
= ( X194 @ ( lam @ X196 ) ) ) )
| ( ( X194 @ X193 )
= $true )
| ~ ! [X198: term,X199: term] :
( ( ( X194 @ X198 )
!= $true )
| ( $true
!= ( X194 @ X199 ) )
| ( $true
= ( X194 @ ( ap @ X198 @ X199 ) ) ) )
| ~ ! [X195: term] :
( ( ( X194 @ X195 )
= $true )
| ( ( var @ X195 )
!= $true ) ) ) )
& ( ulamvar1 != $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( ! [X452: term,X453: subst] :
( ( sub @ one @ ( push @ X452 @ X453 ) )
= X452 )
=> ( ! [X454: term,X455: subst] :
( ( comp @ sh @ ( push @ X454 @ X455 ) )
= X455 )
=> ( ! [X456: subst] :
( ( comp @ X456 @ id )
= X456 )
=> ( ! [X457: term,X458: term > $o] :
( ~ ! [X459: term,X460: term] :
( ( ( X458 @ ( ap @ X460 @ X459 ) )
= $true )
| ( ( X458 @ X460 )
!= $true )
| ( ( X458 @ X459 )
!= $true ) )
| ~ ! [X462: term] :
( ( ( X458 @ X462 )
!= $true )
| ( ( X458 @ ( lam @ X462 ) )
= $true ) )
| ~ ! [X461: term] :
( ( ( X458 @ X461 )
= $true )
| ( ( var @ X461 )
!= $true ) )
| ( $true
= ( X458 @ X457 ) ) )
=> ! [X463: term,X464: term > $o,X465: subst] :
( ~ ! [X466: term] :
( ( $true
= ( X464 @ ( lam @ X466 ) ) )
| ~ ! [X467: term] :
( ( ( X464 @ X467 )
!= $true )
| ( ( X464 @ ( sub @ X466 @ ( push @ X467 @ id ) ) )
= $true ) ) )
| ( $true
= ( X464 @ ( sub @ X463 @ X465 ) ) )
| ~ ! [X469: term,X470: term] :
( ( ( X464 @ ( ap @ X469 @ X470 ) )
= $true )
| ( ( X464 @ X469 )
!= $true )
| ( ( X464 @ X470 )
!= $true ) )
| ~ ! [X468: term] :
( ( ( X464 @ ( sub @ X468 @ X465 ) )
= $true )
| ( ( var @ X468 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X27: term] :
~ ! [X28: subst > term > term] :
~ ! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( ! [X118: subst > term > subst > $o] :
~ ! [X119: term > $o] :
~ ! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ! [X180: term,X181: term,X182: subst > term > subst > $o] :
( ( ( X182 @ id @ ( ap @ X180 @ X181 ) @ id )
= $true )
| ( ( X182 @ id @ X180 @ id )
!= $true )
| ( $true
!= ( X182 @ id @ X181 @ id ) )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ( ( X182 @ X184 @ X185 @ ( comp @ X183 @ X186 ) )
!= $true )
| ( ( X182 @ ( comp @ X184 @ X183 ) @ ( sub @ X185 @ X183 ) @ X186 )
= $true ) )
| ~ ! [X191: term,X192: term] :
( ( ( X182 @ id @ ( ap @ ( sub @ X192 @ id ) @ X191 ) @ id )
= $true )
| ( ( X182 @ id @ X191 @ id )
!= $true )
| ( $true
!= ( X182 @ id @ X192 @ id ) ) )
| ~ ! [X187: subst,X188: term,X189: subst,X190: subst] :
( ( ( X182 @ X189 @ X188 @ ( comp @ X187 @ X190 ) )
= $true )
| ( ( X182 @ ( comp @ X189 @ X187 ) @ ( sub @ X188 @ X187 ) @ X190 )
!= $true ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ! [X24: subst > term > subst > $o] :
~ ! [X25: term > $o] :
~ ! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( axapp = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( axvarshift = $true )
& ( ( ! [X471: term,X472: subst] :
( ( sub @ one @ ( push @ X471 @ X472 ) )
= X471 )
=> ( ! [X473: term,X474: subst] :
( ( comp @ sh @ ( push @ X473 @ X474 ) )
= X474 )
=> ( ! [X475: term,X476: term] :
( ( ( lam @ X475 )
!= ( lam @ X476 ) )
| ( X475 = X476 ) )
=> ! [X477: term,X478: subst,X479: subst > term > term,X480: subst > term > term] :
( ~ ! [X481: subst,X482: term,X483: subst] :
( ( sub @ ( X479 @ X483 @ X482 ) @ X481 )
= ( X479 @ ( comp @ X483 @ X481 ) @ ( sub @ X482 @ X481 ) ) )
| ~ ! [X484: subst,X485: term,X486: subst] :
( ( X480 @ ( comp @ X484 @ X486 ) @ ( sub @ X485 @ X486 ) )
= ( sub @ ( X480 @ X484 @ X485 ) @ X486 ) )
| ( ( lam @ ( X480 @ sh @ one ) )
!= ( lam @ ( X479 @ sh @ one ) ) )
| ( ( X479 @ X478 @ X477 )
= ( X480 @ X478 @ X477 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X330: term] :
( ( sub @ X330 @ id )
= X330 )
=> ( ! [X331: subst > term > subst > $o,X332: term] :
( ~ ! [X333: subst > term > term] :
( ~ ! [X335: term,X336: subst,X337: subst] :
( ( X333 @ ( comp @ X337 @ X336 ) @ ( sub @ X335 @ X336 ) )
= ( sub @ ( X333 @ X337 @ X335 ) @ X336 ) )
| ( ( X331 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X334: term] :
( ( $true
!= ( X331 @ id @ X334 @ id ) )
| ( ( X331 @ id @ ( X333 @ id @ X334 ) @ id )
= $true ) ) )
| ( ( X331 @ id @ ( lam @ ( sub @ X332 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X338: term] :
( ( ( X331 @ id @ X338 @ id )
!= $true )
| ( ( X331 @ id @ ( sub @ X332 @ ( push @ X338 @ id ) ) @ id )
= $true ) ) )
=> ! [X339: term,X340: subst > term > subst > $o] :
( ~ ! [X347: subst,X348: subst,X349: subst,X350: term] :
( ( ( X340 @ X349 @ X350 @ ( comp @ X347 @ X348 ) )
!= $true )
| ( ( X340 @ ( comp @ X349 @ X347 ) @ ( sub @ X350 @ X347 ) @ X348 )
= $true ) )
| ( ( X340 @ id @ ( lam @ X339 ) @ id )
= $true )
| ~ ! [X351: term,X352: subst,X353: subst,X354: subst] :
( ( ( X340 @ ( comp @ X353 @ X354 ) @ ( sub @ X351 @ X354 ) @ X352 )
!= $true )
| ( $true
= ( X340 @ X353 @ X351 @ ( comp @ X354 @ X352 ) ) ) )
| ~ ! [X341: term] :
( ( $true
!= ( X340 @ id @ X341 @ id ) )
| ( ( X340 @ id @ ( sub @ X339 @ ( push @ X341 @ id ) ) @ id )
= $true ) )
| ~ ! [X342: subst > term > term] :
( ~ ! [X343: term,X344: subst,X345: subst] :
( ( X342 @ ( comp @ X344 @ X345 ) @ ( sub @ X343 @ X345 ) )
= ( sub @ ( X342 @ X344 @ X343 ) @ X345 ) )
| ( $true
= ( X340 @ id @ ( lam @ ( X342 @ sh @ one ) ) @ id ) )
| ~ ! [X346: term] :
( ( ( X340 @ id @ X346 @ id )
!= $true )
| ( $true
= ( X340 @ id @ ( X342 @ id @ X346 ) @ id ) ) ) ) ) ) ) )
& ( induction2_gthm = $true )
& ( ( ! [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
= X499 )
=> ( ! [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
= X501 )
=> ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( ( X507 @ X506 )
!= $true )
| ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ! [X440: subst > term > subst > $o,X441: term] :
( ( ( X440 @ id @ ( lam @ X441 ) @ id )
= $true )
| ~ ! [X442: subst > term > term] :
( ( ( X440 @ id @ ( lam @ ( X442 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X446: term] :
( ( ( X440 @ id @ ( X442 @ id @ X446 ) @ id )
= $true )
| ( $true
!= ( X440 @ id @ X446 @ id ) ) )
| ~ ! [X443: subst,X444: subst,X445: term] :
( ( X442 @ ( comp @ X443 @ X444 ) @ ( sub @ X445 @ X444 ) )
= ( sub @ ( X442 @ X443 @ X445 ) @ X444 ) ) )
| ~ ! [X447: term] :
( ( ( X440 @ id @ X447 @ id )
!= $true )
| ( ( X440 @ id @ ( sub @ X441 @ ( push @ X447 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ! [X280: term,X281: term,X282: subst > term > subst > $o,X283: term > $o] :
( ~ ! [X288: term] :
( ( X283 @ X288 )
= ( X282 @ id @ X288 @ id ) )
| ( $true
= ( X283 @ ( ap @ X280 @ X281 ) ) )
| ( ( X283 @ X281 )
!= $true )
| ( ( X283 @ X280 )
!= $true )
| ~ ! [X289: subst,X290: subst,X291: term,X292: subst] :
( ( ( X282 @ ( comp @ X289 @ X290 ) @ ( sub @ X291 @ X290 ) @ X292 )
= $true )
| ( ( X282 @ X289 @ X291 @ ( comp @ X290 @ X292 ) )
!= $true ) )
| ~ ! [X293: term,X294: term] :
( ( ( X282 @ id @ X294 @ id )
!= $true )
| ( $true
!= ( X282 @ id @ X293 @ id ) )
| ( $true
= ( X282 @ id @ ( ap @ ( sub @ X293 @ id ) @ X294 ) @ id ) ) )
| ~ ! [X284: subst,X285: subst,X286: term,X287: subst] :
( ( $true
!= ( X282 @ ( comp @ X285 @ X284 ) @ ( sub @ X286 @ X284 ) @ X287 ) )
| ( ( X282 @ X285 @ X286 @ ( comp @ X284 @ X287 ) )
= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ( substmonoid_gthm = $true )
& ( ulamvarsh = $true )
& ( ( ! [X276: subst] :
( ( comp @ id @ X276 )
= X276 )
=> ( ! [X277: subst] :
( ( comp @ X277 @ id )
= X277 )
=> ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( ! [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
= X173 )
=> ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ~ ! [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
= ( X175 @ X179 ) )
| ( $true
!= ( X177 @ X178 ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( ! [X147: term] :
( ( sub @ X147 @ id )
= X147 )
=> ! [X148: subst > term > subst > $o,X149: term,X150: term > $o] :
( ~ ! [X161: term] :
( ( X150 @ X161 )
= ( X148 @ id @ X161 @ id ) )
| ~ ! [X162: subst,X163: subst,X164: term,X165: subst] :
( ( $true
!= ( X148 @ ( comp @ X162 @ X163 ) @ ( sub @ X164 @ X163 ) @ X165 ) )
| ( ( X148 @ X162 @ X164 @ ( comp @ X163 @ X165 ) )
= $true ) )
| ~ ! [X156: subst > term > term] :
( ~ ! [X157: term] :
( ( ( X148 @ id @ X157 @ id )
!= $true )
| ( ( X148 @ id @ ( X156 @ id @ X157 ) @ id )
= $true ) )
| ( $true
= ( X148 @ id @ ( lam @ ( X156 @ sh @ one ) ) @ id ) )
| ~ ! [X158: subst,X159: term,X160: subst] :
( ( sub @ ( X156 @ X158 @ X159 ) @ X160 )
= ( X156 @ ( comp @ X158 @ X160 ) @ ( sub @ X159 @ X160 ) ) ) )
| ~ ! [X151: term] :
( ( ( X150 @ X151 )
!= $true )
| ( ( X150 @ ( sub @ X149 @ ( push @ X151 @ id ) ) )
= $true ) )
| ( ( X150 @ ( lam @ X149 ) )
= $true )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( ( X148 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) @ X155 )
= $true )
| ( $true
!= ( X148 @ X154 @ X152 @ ( comp @ X153 @ X155 ) ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( termmset_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X248: subst > term > subst > $o,X249: term] :
( ~ ! [X251: subst > term > term] :
( ( ( X248 @ id @ ( lam @ ( X251 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X252: term] :
( ( ( X248 @ id @ ( X251 @ id @ X252 ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X252 @ id ) ) )
| ~ ! [X253: term,X254: subst,X255: subst] :
( ( sub @ ( X251 @ X255 @ X253 ) @ X254 )
= ( X251 @ ( comp @ X255 @ X254 ) @ ( sub @ X253 @ X254 ) ) ) )
| ( $true
= ( X248 @ id @ ( lam @ ( sub @ X249 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X250: term] :
( ( ( X248 @ id @ ( sub @ X249 @ ( push @ X250 @ id ) ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X250 @ id ) ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ~ ! [X489: term] :
( ( $true
!= ( X488 @ id @ X489 @ id ) )
| ( ( X488 @ id @ ( sub @ X487 @ ( push @ X489 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X488 @ id @ ( lam @ ( sub @ X487 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X490: subst > term > term,X491: term] :
( ~ ! [X496: subst,X497: subst,X498: term] :
( ( X490 @ ( comp @ X496 @ X497 ) @ ( sub @ X498 @ X497 ) )
= ( sub @ X491 @ ( push @ ( sub @ X498 @ X497 ) @ ( comp @ X496 @ X497 ) ) ) )
| ~ ! [X492: subst,X493: subst,X494: term] :
( ( sub @ ( X490 @ X492 @ X494 ) @ X493 )
= ( sub @ ( sub @ X491 @ ( push @ X494 @ X492 ) ) @ X493 ) )
| ~ ! [X495: term] :
( ( ( X488 @ id @ ( X490 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
| ( $true
= ( X488 @ id @ ( lam @ ( X490 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
=> ! [X172: term] :
( ( sub @ X172 @ id )
= X172 ) )
<=> ( termmset_lthm = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X129: term] :
~ ! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X533 @ X535 )
!= ( ap @ X534 @ X532 ) )
| ( X532 = X535 ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) )
& ( ! [X258: subst > term > subst > $o,X259: term] :
( ~ ! [X268: term] :
( ( $true
!= ( X258 @ id @ X268 @ id ) )
| ( ( X258 @ id @ ( sub @ X259 @ ( push @ X268 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X258 @ id @ ( lam @ X259 ) @ id ) )
| ~ ! [X260: subst,X261: term,X262: subst,X263: subst] :
( ( ( X258 @ X260 @ X261 @ ( comp @ X263 @ X262 ) )
= $true )
| ( $true
!= ( X258 @ ( comp @ X260 @ X263 ) @ ( sub @ X261 @ X263 ) @ X262 ) ) )
| ~ ! [X264: term,X265: subst,X266: subst,X267: subst] :
( ( ( X258 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) @ X267 )
= $true )
| ( ( X258 @ X265 @ X264 @ ( comp @ X266 @ X267 ) )
!= $true ) )
| ~ ! [X269: subst > term > term] :
( ~ ! [X273: term] :
( ( ( X258 @ id @ X273 @ id )
!= $true )
| ( ( X258 @ id @ ( X269 @ id @ X273 ) @ id )
= $true ) )
| ~ ! [X270: subst,X271: subst,X272: term] :
( ( sub @ ( X269 @ X270 @ X272 ) @ X271 )
= ( X269 @ ( comp @ X270 @ X271 ) @ ( sub @ X272 @ X271 ) ) )
| ( ( X258 @ id @ ( lam @ ( X269 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( axmap = $true )
& ! [X256: d_term,X257: d_term] :
( ( ( d2term @ X256 )
= ( d2term @ X257 ) )
=> ( X256 = X257 ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
~ ! [X140: term > $o] :
~ ! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
<=> ( pushprop_lem0 = $true ) )
& ! [X35: d_subst] : ( d_id = X35 )
& ( ! [X93: term,X94: term,X95: subst > term > term] :
( ~ ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) )
| ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X358: term,X359: term > $o] :
( ~ ! [X364: term] :
( ( $true
= ( X359 @ X364 ) )
| ( ( var @ X364 )
!= $true ) )
| ~ ! [X360: term,X361: term] :
( ( ( X359 @ X360 )
!= $true )
| ( ( X359 @ X361 )
!= $true )
| ( ( X359 @ ( ap @ X361 @ X360 ) )
= $true ) )
| ( ( X359 @ X358 )
= $true )
| ~ ! [X362: term] :
( ~ ! [X363: term] :
( ( $true
!= ( X359 @ X363 ) )
| ( ( X359 @ ( sub @ X362 @ ( push @ X363 @ id ) ) )
= $true ) )
| ( ( X359 @ ( lam @ X362 ) )
= $true ) ) )
=> ( ! [X365: term,X366: term,X367: subst > term > subst > $o] :
( ~ ! [X368: subst,X369: subst,X370: subst,X371: term] :
( ( $true
!= ( X367 @ ( comp @ X368 @ X369 ) @ ( sub @ X371 @ X369 ) @ X370 ) )
| ( $true
= ( X367 @ X368 @ X371 @ ( comp @ X369 @ X370 ) ) ) )
| ( ( X367 @ id @ X365 @ id )
!= $true )
| ( ( X367 @ id @ ( ap @ X365 @ X366 ) @ id )
= $true )
| ~ ! [X372: subst,X373: subst,X374: subst,X375: term] :
( ( $true
= ( X367 @ ( comp @ X373 @ X372 ) @ ( sub @ X375 @ X372 ) @ X374 ) )
| ( $true
!= ( X367 @ X373 @ X375 @ ( comp @ X372 @ X374 ) ) ) )
| ~ ! [X376: term,X377: term] :
( ( ( X367 @ id @ X376 @ id )
!= $true )
| ( ( X367 @ id @ ( ap @ ( sub @ X376 @ id ) @ X377 ) @ id )
= $true )
| ( $true
!= ( X367 @ id @ X377 @ id ) ) )
| ( $true
!= ( X367 @ id @ X366 @ id ) ) )
=> ( ! [X378: subst > term > subst > $o,X379: term] :
( ( ( X378 @ id @ ( lam @ X379 ) @ id )
= $true )
| ~ ! [X388: term] :
( ( ( X378 @ id @ ( sub @ X379 @ ( push @ X388 @ id ) ) @ id )
= $true )
| ( ( X378 @ id @ X388 @ id )
!= $true ) )
| ~ ! [X380: subst,X381: term,X382: subst,X383: subst] :
( ( ( X378 @ X383 @ X381 @ ( comp @ X382 @ X380 ) )
!= $true )
| ( ( X378 @ ( comp @ X383 @ X382 ) @ ( sub @ X381 @ X382 ) @ X380 )
= $true ) )
| ~ ! [X389: subst > term > term] :
( ~ ! [X390: term] :
( ( ( X378 @ id @ X390 @ id )
!= $true )
| ( $true
= ( X378 @ id @ ( X389 @ id @ X390 ) @ id ) ) )
| ~ ! [X391: term,X392: subst,X393: subst] :
( ( sub @ ( X389 @ X393 @ X391 ) @ X392 )
= ( X389 @ ( comp @ X393 @ X392 ) @ ( sub @ X391 @ X392 ) ) )
| ( ( X378 @ id @ ( lam @ ( X389 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X384: subst,X385: subst,X386: subst,X387: term] :
( ( $true
= ( X378 @ X386 @ X387 @ ( comp @ X384 @ X385 ) ) )
| ( $true
!= ( X378 @ ( comp @ X386 @ X384 ) @ ( sub @ X387 @ X384 ) @ X385 ) ) ) )
=> ! [X394: term,X395: subst > term > subst > $o] :
( ~ ! [X400: subst > term > term] :
( ~ ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X404 @ X403 ) @ ( sub @ X402 @ X403 ) )
= ( sub @ ( X400 @ X404 @ X402 ) @ X403 ) )
| ~ ! [X401: term] :
( ( ( X395 @ id @ X401 @ id )
!= $true )
| ( ( X395 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
| ( ( X395 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X407: term] :
( ( ( var @ ( sub @ X407 @ id ) )
!= $true )
| ( ( X395 @ id @ X407 @ id )
= $true ) )
| ~ ! [X405: term,X406: term] :
( ( $true
= ( X395 @ id @ ( ap @ ( sub @ X406 @ id ) @ X405 ) @ id ) )
| ( ( X395 @ id @ X405 @ id )
!= $true )
| ( ( X395 @ id @ X406 @ id )
!= $true ) )
| ( $true
= ( X395 @ id @ X394 @ id ) )
| ~ ! [X396: term,X397: subst,X398: subst,X399: subst] :
( ( ( X395 @ X397 @ X396 @ ( comp @ X399 @ X398 ) )
!= $true )
| ( ( X395 @ ( comp @ X397 @ X399 ) @ ( sub @ X396 @ X399 ) @ X398 )
= $true ) )
| ~ ! [X408: subst,X409: subst,X410: subst,X411: term] :
( ( ( X395 @ X408 @ X411 @ ( comp @ X409 @ X410 ) )
= $true )
| ( $true
!= ( X395 @ ( comp @ X408 @ X409 ) @ ( sub @ X411 @ X409 ) @ X410 ) ) ) ) ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ( ! [X517: term > $o,X518: subst,X519: term] :
( ~ ! [X520: term] :
( ( $true
= ( X517 @ ( sub @ X520 @ X518 ) ) )
| ( ( var @ X520 )
!= $true ) )
| ~ ! [X521: term] :
( ~ ! [X522: term] :
( ( $true
!= ( X517 @ X522 ) )
| ( ( X517 @ ( sub @ X521 @ ( push @ X522 @ id ) ) )
= $true ) )
| ( $true
= ( X517 @ ( lam @ X521 ) ) ) )
| ~ ! [X523: term,X524: term] :
( ( ( X517 @ ( ap @ X523 @ X524 ) )
= $true )
| ( ( X517 @ X524 )
!= $true )
| ( ( X517 @ X523 )
!= $true ) )
| ( $true
= ( X517 @ ( sub @ X519 @ X518 ) ) ) )
=> ! [X525: term > $o,X526: term] :
( ~ ! [X529: term] :
( ( ( var @ X529 )
!= $true )
| ( ( X525 @ X529 )
= $true ) )
| ~ ! [X527: term] :
( ( ( X525 @ ( lam @ X527 ) )
= $true )
| ~ ! [X528: term] :
( ( ( X525 @ X528 )
!= $true )
| ( ( X525 @ ( sub @ X527 @ ( push @ X528 @ id ) ) )
= $true ) ) )
| ~ ! [X530: term,X531: term] :
( ( $true
!= ( X525 @ X531 ) )
| ( $true
!= ( X525 @ X530 ) )
| ( ( X525 @ ( ap @ X530 @ X531 ) )
= $true ) )
| ( $true
= ( X525 @ X526 ) ) ) ) ) )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
= ( d2subst @ X117 ) )
=> ( X116 = X117 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X211: term,X212: term > $o,X213: subst] :
~ ! [X214: term > $o] :
~ ! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( ! [X200: term] :
~ ! [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
!= ( X201 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
<=> ! [X131: term > $o,X132: term] :
( ( ( X131 @ X132 )
= $true )
| ~ ! [X133: term,X134: term] :
( ( ( X131 @ X134 )
!= $true )
| ( ( X131 @ X133 )
!= $true )
| ( ( X131 @ ( ap @ X133 @ X134 ) )
= $true ) )
| ~ ! [X135: term] :
( ( $true
!= ( X131 @ X135 ) )
| ( ( X131 @ ( lam @ X135 ) )
= $true ) )
| ~ ! [X136: term] :
( ( $true
!= ( var @ X136 ) )
| ( $true
= ( X131 @ X136 ) ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
<=> ( substmonoid = $true ) )
& ( ( ! [X300: subst > term > subst > $o] :
~ ! [X301: term > $o] :
~ ! [X302: term] :
( ( X301 @ X302 )
= ( X300 @ id @ X302 @ id ) )
=> ( ! [X303: term > $o,X304: term] :
( ~ ! [X305: term,X306: term] :
( ( ( X303 @ ( ap @ X305 @ X306 ) )
= $true )
| ( $true
!= ( X303 @ X305 ) )
| ( ( X303 @ X306 )
!= $true ) )
| ~ ! [X308: term] :
( ~ ! [X309: term] :
( ( ( X303 @ ( sub @ X308 @ ( push @ X309 @ id ) ) )
= $true )
| ( ( X303 @ X309 )
!= $true ) )
| ( $true
= ( X303 @ ( lam @ X308 ) ) ) )
| ~ ! [X307: term] :
( ( ( X303 @ X307 )
= $true )
| ( $true
!= ( var @ X307 ) ) )
| ( ( X303 @ X304 )
= $true ) )
=> ( ! [X310: term] :
( ( sub @ X310 @ id )
= X310 )
=> ( ! [X311: term > $o,X312: term,X313: subst > term > subst > $o] :
( ~ ! [X314: term] :
( ( X311 @ X314 )
= ( X313 @ id @ X314 @ id ) )
| ~ ! [X315: term] :
( ( ( X311 @ ( sub @ X312 @ ( push @ X315 @ id ) ) )
= $true )
| ( ( X311 @ X315 )
!= $true ) )
| ~ ! [X316: subst > term > term] :
( ( $true
= ( X313 @ id @ ( lam @ ( X316 @ sh @ one ) ) @ id ) )
| ~ ! [X317: term] :
( ( ( X313 @ id @ ( X316 @ id @ X317 ) @ id )
= $true )
| ( ( X313 @ id @ X317 @ id )
!= $true ) )
| ~ ! [X318: term,X319: subst,X320: subst] :
( ( sub @ ( X316 @ X320 @ X318 ) @ X319 )
= ( X316 @ ( comp @ X320 @ X319 ) @ ( sub @ X318 @ X319 ) ) ) )
| ( ( X311 @ ( lam @ X312 ) )
= $true ) )
=> ! [X321: subst > term > subst > $o,X322: term] :
( ~ ! [X323: subst > term > term] :
( ( ( X321 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X325: subst,X326: subst,X327: term] :
( ( sub @ ( X323 @ X326 @ X327 ) @ X325 )
= ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) ) )
| ~ ! [X324: term] :
( ( $true
= ( X321 @ id @ ( X323 @ id @ X324 ) @ id ) )
| ( ( X321 @ id @ X324 @ id )
!= $true ) ) )
| ( ( X321 @ id @ X322 @ id )
= $true )
| ~ ! [X328: term,X329: term] :
( ( ( X321 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id )
= $true )
| ( ( X321 @ id @ X328 @ id )
!= $true )
| ( ( X321 @ id @ X329 @ id )
!= $true ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( induction2lem = $true )
<=> ! [X508: subst,X509: term,X510: term > $o] :
( ~ ! [X512: term,X513: term] :
( ( $true
= ( X510 @ ( ap @ X513 @ X512 ) ) )
| ( ( X510 @ X512 )
!= $true )
| ( ( X510 @ X513 )
!= $true ) )
| ~ ! [X514: term] :
( ~ ! [X515: term] :
( ( ( X510 @ X515 )
!= $true )
| ( ( X510 @ ( sub @ X514 @ ( push @ X515 @ id ) ) )
= $true ) )
| ( ( X510 @ ( lam @ X514 ) )
= $true ) )
| ~ ! [X511: term] :
( ( ( X510 @ ( sub @ X511 @ X508 ) )
= $true )
| ( ( var @ X511 )
!= $true ) )
| ( ( X510 @ ( sub @ X509 @ X508 ) )
= $true ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop = $true )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( ! [X105: term] :
( ( sub @ X105 @ id )
= X105 )
=> ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) )
| ( X107 = X108 ) )
=> ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( lamnotap != $true )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ( ( apinj1 = $true )
<=> ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X412: term,X413: term > $o,X414: subst > term > subst > $o] :
( ~ ! [X421: term] :
( ( X413 @ X421 )
= ( X414 @ id @ X421 @ id ) )
| ( $true
= ( X413 @ ( lam @ X412 ) ) )
| ~ ! [X416: subst > term > term] :
( ~ ! [X420: term] :
( ( ( X414 @ id @ X420 @ id )
!= $true )
| ( ( X414 @ id @ ( X416 @ id @ X420 ) @ id )
= $true ) )
| ~ ! [X417: term,X418: subst,X419: subst] :
( ( sub @ ( X416 @ X419 @ X417 ) @ X418 )
= ( X416 @ ( comp @ X419 @ X418 ) @ ( sub @ X417 @ X418 ) ) )
| ( ( X414 @ id @ ( lam @ ( X416 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X415: term] :
( ( $true
= ( X413 @ ( sub @ X412 @ ( push @ X415 @ id ) ) ) )
| ( $true
!= ( X413 @ X415 ) ) ) ) )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X144 @ one )
= $true )
| ~ ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) )
| ( ( X145 @ X143 )
!= $true ) ) )
& ( axassoc = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( shinj = $true )
<=> ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X422: subst > term > subst > $o,X423: term,X424: term > $o] :
( ~ ! [X439: term] :
( ( ( X424 @ X439 )
!= $true )
| ( ( X424 @ ( sub @ X423 @ ( push @ X439 @ id ) ) )
= $true ) )
| ~ ! [X425: subst > term > term] :
( ~ ! [X426: subst,X427: term,X428: subst] :
( ( X425 @ ( comp @ X428 @ X426 ) @ ( sub @ X427 @ X426 ) )
= ( sub @ ( X425 @ X428 @ X427 ) @ X426 ) )
| ~ ! [X429: term] :
( ( ( X422 @ id @ X429 @ id )
!= $true )
| ( ( X422 @ id @ ( X425 @ id @ X429 ) @ id )
= $true ) )
| ( ( X422 @ id @ ( lam @ ( X425 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X438: term] :
( ( X422 @ id @ X438 @ id )
= ( X424 @ X438 ) )
| ( ( X424 @ ( lam @ X423 ) )
= $true )
| ~ ! [X430: subst,X431: term,X432: subst,X433: subst] :
( ( ( X422 @ X433 @ X431 @ ( comp @ X432 @ X430 ) )
!= $true )
| ( ( X422 @ ( comp @ X433 @ X432 ) @ ( sub @ X431 @ X432 ) @ X430 )
= $true ) )
| ~ ! [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X422 @ ( comp @ X436 @ X437 ) @ ( sub @ X434 @ X437 ) @ X435 )
!= $true )
| ( $true
= ( X422 @ X436 @ X434 @ ( comp @ X437 @ X435 ) ) ) ) ) )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
<=> ( axidl = $true ) )
& ( hoaslamnotvar = $true )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
<=> ( apinj2 = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( pushprop_lem0_gthm = $true )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ~ ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ~ ! [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X227: term] :
~ ! [X228: subst > term > term] :
~ ! [X229: subst,X230: term] :
( ( sub @ X227 @ ( push @ X230 @ X229 ) )
= ( X228 @ X229 @ X230 ) )
=> ( ! [X231: term] :
( ( sub @ X231 @ id )
= X231 )
=> ! [X232: subst > term > subst > $o,X233: term > $o,X234: term] :
( ~ ! [X237: subst > term > term] :
( ( ( X232 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X238: term] :
( ( $true
!= ( X232 @ id @ X238 @ id ) )
| ( $true
= ( X232 @ id @ ( X237 @ id @ X238 ) @ id ) ) )
| ~ ! [X239: term,X240: subst,X241: subst] :
( ( sub @ ( X237 @ X241 @ X239 ) @ X240 )
= ( X237 @ ( comp @ X241 @ X240 ) @ ( sub @ X239 @ X240 ) ) ) )
| ~ ! [X236: term] :
( ( ( X233 @ ( sub @ X234 @ ( push @ X236 @ id ) ) )
= $true )
| ( ( X233 @ X236 )
!= $true ) )
| ~ ! [X235: term] :
( ( X232 @ id @ X235 @ id )
= ( X233 @ X235 ) )
| ( ( X233 @ ( lam @ X234 ) )
= $true ) ) ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X54: subst > term > subst > $o] :
~ ! [X55: term > $o] :
~ ! [X56: term] :
( ( X54 @ id @ X56 @ id )
= ( X55 @ X56 ) )
=> ( ! [X57: term,X58: term > $o] :
( ~ ! [X61: term] :
( ( $true
= ( X58 @ ( lam @ X61 ) ) )
| ~ ! [X62: term] :
( ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
= $true )
| ( $true
!= ( X58 @ X62 ) ) ) )
| ~ ! [X63: term] :
( ( ( var @ X63 )
!= $true )
| ( ( X58 @ X63 )
= $true ) )
| ( ( X58 @ X57 )
= $true )
| ~ ! [X59: term,X60: term] :
( ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true )
| ( $true
!= ( X58 @ X59 ) ) ) )
=> ( ! [X64: term] :
( ( sub @ X64 @ id )
= X64 )
=> ( ! [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ~ ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
| ~ ! [X68: subst > term > term] :
( ~ ! [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) )
| ~ ! [X69: term] :
( ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
= $true )
| ( ( X67 @ id @ X69 @ id )
!= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true ) )
| ( $true
= ( X65 @ ( lam @ X66 ) ) )
| ~ ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) ) )
=> ! [X75: subst > term > subst > $o,X76: term] :
( ( ( X75 @ id @ X76 @ id )
= $true )
| ~ ! [X91: term,X92: term] :
( ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
= $true )
| ( $true
!= ( X75 @ id @ X92 @ id ) )
| ( ( X75 @ id @ X91 @ id )
!= $true ) )
| ~ ! [X82: subst > term > term] :
( ~ ! [X83: term] :
( ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true )
| ( ( X75 @ id @ X83 @ id )
!= $true ) )
| ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ~ ! [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
!= $true )
| ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
= $true ) )
| ~ ! [X77: term] :
( ( ( var @ ( sub @ X77 @ id ) )
!= $true )
| ( ( X75 @ id @ X77 @ id )
= $true ) )
| ~ ! [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
!= $true )
| ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
= $true ) ) ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
<=> ( termmset = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( apnotvar = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( axvarid = $true )
<=> ! [X355: term] :
( ( sub @ X355 @ id )
= X355 ) )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X202: subst > term > subst > $o,X203: term] :
( ~ ! [X204: term,X205: term] :
( ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
= $true )
| ( ( X202 @ id @ X204 @ id )
!= $true )
| ( $true
!= ( X202 @ id @ X205 @ id ) ) )
| ~ ! [X206: subst > term > term] :
( ~ ! [X210: term] :
( ( ( X202 @ id @ X210 @ id )
!= $true )
| ( ( X202 @ id @ ( X206 @ id @ X210 ) @ id )
= $true ) )
| ( $true
= ( X202 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) )
| ~ ! [X207: subst,X208: subst,X209: term] :
( ( X206 @ ( comp @ X207 @ X208 ) @ ( sub @ X209 @ X208 ) )
= ( sub @ ( X206 @ X207 @ X209 ) @ X208 ) ) )
| ( ( X202 @ id @ X203 @ id )
= $true ) ) )
& ( ( d2subst @ d_id )
= sh )
& ! [X170: d_term] : ( d_one = X170 )
& ( ! [X448: term] :
~ ! [X449: subst > term > term] :
~ ! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ulamvarind = $true )
& ( ! [X121: subst > term > subst > $o,X122: term] :
( ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
= $true )
| ( $true
!= ( X121 @ id @ X128 @ id ) ) )
| ~ ! [X123: subst > term > term] :
( ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X127: term] :
( ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) )
| ( ( X121 @ id @ X127 @ id )
!= $true ) )
| ~ ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( substmonoid_gthm = $true )
& ( axmap = $true )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true )
| ( ( X3 @ X2 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X7: term] :
( ( sub @ X7 @ id )
= X7 )
=> ( ! [X8: term,X9: subst > term > subst > $o] :
( ( $true
= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) )
| ~ ! [X14: term] :
( ( ( X9 @ id @ X14 @ id )
!= $true )
| ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
= $true ) ) )
| ~ ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) ) )
=> ! [X16: term,X17: subst > term > subst > $o] :
( ~ ! [X18: term] :
( ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
= $true )
| ( ( X17 @ id @ X18 @ id )
!= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) )
| ~ ! [X19: subst > term > term] :
( ~ ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
| ~ ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) )
| ( $true
= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X24: subst > term > subst > $o] :
~ ! [X25: term > $o] :
~ ! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X27: term] :
~ ! [X28: subst > term > term] :
~ ! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ! [X35: d_subst] : ( d_id = X35 )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoasinduction = $true )
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ~ ! [X38: term,X39: term] :
( ( $true
= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
| ( ( X37 @ id @ X39 @ id )
!= $true )
| ( ( X37 @ id @ X38 @ id )
!= $true ) )
| ~ ! [X40: subst,X41: term,X42: subst,X43: subst] :
( ( $true
!= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) )
| ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
= $true ) )
| ~ ! [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
!= $true )
| ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
= $true ) )
| ~ ! [X48: subst > term > term] :
( ~ ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) )
| ~ ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) )
| ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X53: term] :
( ( ( X37 @ id @ X53 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X53 @ id ) ) ) )
| ( $true
= ( X37 @ id @ X36 @ id ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X54: subst > term > subst > $o] :
~ ! [X55: term > $o] :
~ ! [X56: term] :
( ( X54 @ id @ X56 @ id )
= ( X55 @ X56 ) )
=> ( ! [X57: term,X58: term > $o] :
( ~ ! [X59: term,X60: term] :
( ( $true
!= ( X58 @ X59 ) )
| ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true ) )
| ~ ! [X61: term] :
( ~ ! [X62: term] :
( ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
= $true )
| ( $true
!= ( X58 @ X62 ) ) )
| ( $true
= ( X58 @ ( lam @ X61 ) ) ) )
| ~ ! [X63: term] :
( ( ( X58 @ X63 )
= $true )
| ( ( var @ X63 )
!= $true ) )
| ( ( X58 @ X57 )
= $true ) )
=> ( ! [X64: term] :
( ( sub @ X64 @ id )
= X64 )
=> ( ! [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ~ ! [X68: subst > term > term] :
( ~ ! [X69: term] :
( ( ( X67 @ id @ X69 @ id )
!= $true )
| ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) )
| ~ ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
| ( $true
= ( X65 @ ( lam @ X66 ) ) )
| ~ ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) ) )
=> ! [X75: subst > term > subst > $o,X76: term] :
( ~ ! [X77: term] :
( ( ( X75 @ id @ X77 @ id )
= $true )
| ( ( var @ ( sub @ X77 @ id ) )
!= $true ) )
| ~ ! [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
= $true )
| ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
!= $true ) )
| ~ ! [X82: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X83: term] :
( ( ( X75 @ id @ X83 @ id )
!= $true )
| ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true ) )
| ~ ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ~ ! [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
= $true )
| ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
!= $true ) )
| ~ ! [X91: term,X92: term] :
( ( ( X75 @ id @ X91 @ id )
!= $true )
| ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
= $true )
| ( $true
!= ( X75 @ id @ X92 @ id ) ) )
| ( ( X75 @ id @ X76 @ id )
= $true ) ) ) ) ) ) )
& ( ! [X93: term,X94: term,X95: subst > term > term] :
( ~ ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) )
| ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ulamvar1 != $true )
& ( axclos = $true )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ( hoasinduction_lem1 = $true )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( ( ! [X105: term] :
( ( sub @ X105 @ id )
= X105 )
=> ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) )
| ( X107 = X108 ) )
=> ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( lamnotap != $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
= ( d2subst @ X117 ) )
=> ( X116 = X117 ) )
& ( ! [X118: subst > term > subst > $o] :
~ ! [X119: term > $o] :
~ ! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( ! [X121: subst > term > subst > $o,X122: term] :
( ~ ! [X123: subst > term > term] :
( ~ ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) )
| ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X127: term] :
( ( ( X121 @ id @ X127 @ id )
!= $true )
| ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) ) ) )
| ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
= $true )
| ( $true
!= ( X121 @ id @ X128 @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X129: term] :
~ ! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) ) )
& ( ( induction = $true )
<=> ! [X131: term > $o,X132: term] :
( ~ ! [X133: term,X134: term] :
( ( ( X131 @ X134 )
!= $true )
| ( ( X131 @ ( ap @ X133 @ X134 ) )
= $true )
| ( ( X131 @ X133 )
!= $true ) )
| ~ ! [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
= $true )
| ( $true
!= ( X131 @ X135 ) ) )
| ~ ! [X136: term] :
( ( $true
= ( X131 @ X136 ) )
| ( $true
!= ( var @ X136 ) ) )
| ( ( X131 @ X132 )
= $true ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
~ ! [X140: term > $o] :
~ ! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
<=> ( pushprop_lem0 = $true ) )
& ( ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X144 @ one )
= $true )
| ( ( X145 @ X143 )
!= $true )
| ~ ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ( ! [X147: term] :
( ( sub @ X147 @ id )
= X147 )
=> ! [X148: subst > term > subst > $o,X149: term,X150: term > $o] :
( ~ ! [X151: term] :
( ( ( X150 @ X151 )
!= $true )
| ( ( X150 @ ( sub @ X149 @ ( push @ X151 @ id ) ) )
= $true ) )
| ~ ! [X152: term,X153: subst,X154: subst,X155: subst] :
( ( ( X148 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) @ X155 )
= $true )
| ( $true
!= ( X148 @ X154 @ X152 @ ( comp @ X153 @ X155 ) ) ) )
| ~ ! [X156: subst > term > term] :
( ~ ! [X157: term] :
( ( ( X148 @ id @ ( X156 @ id @ X157 ) @ id )
= $true )
| ( ( X148 @ id @ X157 @ id )
!= $true ) )
| ~ ! [X158: subst,X159: term,X160: subst] :
( ( sub @ ( X156 @ X158 @ X159 ) @ X160 )
= ( X156 @ ( comp @ X158 @ X160 ) @ ( sub @ X159 @ X160 ) ) )
| ( $true
= ( X148 @ id @ ( lam @ ( X156 @ sh @ one ) ) @ id ) ) )
| ( ( X150 @ ( lam @ X149 ) )
= $true )
| ~ ! [X161: term] :
( ( X150 @ X161 )
= ( X148 @ id @ X161 @ id ) )
| ~ ! [X162: subst,X163: subst,X164: term,X165: subst] :
( ( $true
!= ( X148 @ ( comp @ X162 @ X163 ) @ ( sub @ X164 @ X163 ) @ X165 ) )
| ( ( X148 @ X162 @ X164 @ ( comp @ X163 @ X165 ) )
= $true ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X166: term,X167: term,X168: term,X169: term] :
( ( X168 = X169 )
| ( ( ap @ X169 @ X167 )
!= ( ap @ X168 @ X166 ) ) ) )
& ! [X170: d_term] : ( d_one = X170 )
& ( ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
=> ! [X172: term] :
( ( sub @ X172 @ id )
= X172 ) )
<=> ( termmset_lthm = $true ) )
& ( termmset_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X173: term,X174: subst] :
( ( sub @ one @ ( push @ X173 @ X174 ) )
= X173 )
=> ! [X175: term > $o,X176: subst,X177: term > $o,X178: term] :
( ( ( X175 @ one )
= $true )
| ( $true
!= ( X177 @ X178 ) )
| ~ ! [X179: term] :
( ( X177 @ ( sub @ X179 @ ( push @ X178 @ X176 ) ) )
= ( X175 @ X179 ) ) ) ) )
& ( ! [X180: term,X181: term,X182: subst > term > subst > $o] :
( ( ( X182 @ id @ X180 @ id )
!= $true )
| ~ ! [X183: subst,X184: subst,X185: term,X186: subst] :
( ( ( X182 @ ( comp @ X184 @ X183 ) @ ( sub @ X185 @ X183 ) @ X186 )
= $true )
| ( ( X182 @ X184 @ X185 @ ( comp @ X183 @ X186 ) )
!= $true ) )
| ~ ! [X187: subst,X188: term,X189: subst,X190: subst] :
( ( ( X182 @ X189 @ X188 @ ( comp @ X187 @ X190 ) )
= $true )
| ( ( X182 @ ( comp @ X189 @ X187 ) @ ( sub @ X188 @ X187 ) @ X190 )
!= $true ) )
| ( ( X182 @ id @ ( ap @ X180 @ X181 ) @ id )
= $true )
| ~ ! [X191: term,X192: term] :
( ( $true
!= ( X182 @ id @ X192 @ id ) )
| ( ( X182 @ id @ X191 @ id )
!= $true )
| ( ( X182 @ id @ ( ap @ ( sub @ X192 @ id ) @ X191 ) @ id )
= $true ) )
| ( $true
!= ( X182 @ id @ X181 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( pushprop_lthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( axassoc = $true )
& ( ( induction2 = $true )
<=> ! [X193: term,X194: term > $o] :
( ~ ! [X195: term] :
( ( ( var @ X195 )
!= $true )
| ( ( X194 @ X195 )
= $true ) )
| ~ ! [X196: term] :
( ( $true
= ( X194 @ ( lam @ X196 ) ) )
| ~ ! [X197: term] :
( ( ( X194 @ ( sub @ X196 @ ( push @ X197 @ id ) ) )
= $true )
| ( $true
!= ( X194 @ X197 ) ) ) )
| ( ( X194 @ X193 )
= $true )
| ~ ! [X198: term,X199: term] :
( ( $true
!= ( X194 @ X199 ) )
| ( $true
= ( X194 @ ( ap @ X198 @ X199 ) ) )
| ( ( X194 @ X198 )
!= $true ) ) ) )
& ( ! [X200: term] :
~ ! [X201: subst > term > term] :
( ( sub @ X200 @ ( push @ one @ sh ) )
!= ( X201 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( induction2lem_gthm = $true )
& ( ! [X202: subst > term > subst > $o,X203: term] :
( ~ ! [X204: term,X205: term] :
( ( $true
!= ( X202 @ id @ X205 @ id ) )
| ( ( X202 @ id @ X204 @ id )
!= $true )
| ( ( X202 @ id @ ( ap @ ( sub @ X204 @ id ) @ X205 ) @ id )
= $true ) )
| ( ( X202 @ id @ X203 @ id )
= $true )
| ~ ! [X206: subst > term > term] :
( ~ ! [X207: subst,X208: subst,X209: term] :
( ( X206 @ ( comp @ X207 @ X208 ) @ ( sub @ X209 @ X208 ) )
= ( sub @ ( X206 @ X207 @ X209 ) @ X208 ) )
| ~ ! [X210: term] :
( ( ( X202 @ id @ X210 @ id )
!= $true )
| ( ( X202 @ id @ ( X206 @ id @ X210 ) @ id )
= $true ) )
| ( $true
= ( X202 @ id @ ( lam @ ( X206 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X211: term,X212: term > $o,X213: subst] :
~ ! [X214: term > $o] :
~ ! [X215: term] :
( ( X214 @ X215 )
= ( X212 @ ( sub @ X215 @ ( push @ X211 @ X213 ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X216: term] :
( ( sub @ X216 @ id )
= X216 )
<=> ( termmset = $true ) )
& ( ! [X217: subst,X218: subst > term > term,X219: subst > term > term,X220: term] :
( ~ ! [X221: term,X222: subst,X223: subst] :
( ( sub @ ( X219 @ X222 @ X221 ) @ X223 )
= ( X219 @ ( comp @ X222 @ X223 ) @ ( sub @ X221 @ X223 ) ) )
| ~ ! [X224: subst,X225: term,X226: subst] :
( ( X218 @ ( comp @ X226 @ X224 ) @ ( sub @ X225 @ X224 ) )
= ( sub @ ( X218 @ X226 @ X225 ) @ X224 ) )
| ( ( X219 @ X217 @ X220 )
= ( X218 @ X217 @ X220 ) )
| ( ( lam @ ( X219 @ sh @ one ) )
!= ( lam @ ( X218 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( ! [X227: term] :
~ ! [X228: subst > term > term] :
~ ! [X229: subst,X230: term] :
( ( sub @ X227 @ ( push @ X230 @ X229 ) )
= ( X228 @ X229 @ X230 ) )
=> ( ! [X231: term] :
( ( sub @ X231 @ id )
= X231 )
=> ! [X232: subst > term > subst > $o,X233: term > $o,X234: term] :
( ~ ! [X235: term] :
( ( X232 @ id @ X235 @ id )
= ( X233 @ X235 ) )
| ( ( X233 @ ( lam @ X234 ) )
= $true )
| ~ ! [X236: term] :
( ( ( X233 @ ( sub @ X234 @ ( push @ X236 @ id ) ) )
= $true )
| ( ( X233 @ X236 )
!= $true ) )
| ~ ! [X237: subst > term > term] :
( ~ ! [X238: term] :
( ( $true
= ( X232 @ id @ ( X237 @ id @ X238 ) @ id ) )
| ( $true
!= ( X232 @ id @ X238 @ id ) ) )
| ~ ! [X239: term,X240: subst,X241: subst] :
( ( sub @ ( X237 @ X241 @ X239 ) @ X240 )
= ( X237 @ ( comp @ X241 @ X240 ) @ ( sub @ X239 @ X240 ) ) )
| ( ( X232 @ id @ ( lam @ ( X237 @ sh @ one ) ) @ id )
= $true ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop = $true )
& ( ! [X242: term,X243: term,X244: term,X245: term] :
( ( X242 = X244 )
| ( ( ap @ ( sub @ X244 @ id ) @ X245 )
!= ( ap @ ( sub @ X242 @ id ) @ X243 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ( shinj = $true )
<=> ! [X246: term,X247: term] :
( ( ( sub @ X247 @ sh )
!= ( sub @ X246 @ sh ) )
| ( X246 = X247 ) ) )
& ( ! [X248: subst > term > subst > $o,X249: term] :
( ( $true
= ( X248 @ id @ ( lam @ ( sub @ X249 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X250: term] :
( ( $true
!= ( X248 @ id @ X250 @ id ) )
| ( ( X248 @ id @ ( sub @ X249 @ ( push @ X250 @ id ) ) @ id )
= $true ) )
| ~ ! [X251: subst > term > term] :
( ~ ! [X252: term] :
( ( ( X248 @ id @ ( X251 @ id @ X252 ) @ id )
= $true )
| ( $true
!= ( X248 @ id @ X252 @ id ) ) )
| ( ( X248 @ id @ ( lam @ ( X251 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X253: term,X254: subst,X255: subst] :
( ( sub @ ( X251 @ X255 @ X253 ) @ X254 )
= ( X251 @ ( comp @ X255 @ X254 ) @ ( sub @ X253 @ X254 ) ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ! [X256: d_term,X257: d_term] :
( ( ( d2term @ X256 )
= ( d2term @ X257 ) )
=> ( X256 = X257 ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X258: subst > term > subst > $o,X259: term] :
( ~ ! [X260: subst,X261: term,X262: subst,X263: subst] :
( ( $true
!= ( X258 @ ( comp @ X260 @ X263 ) @ ( sub @ X261 @ X263 ) @ X262 ) )
| ( ( X258 @ X260 @ X261 @ ( comp @ X263 @ X262 ) )
= $true ) )
| ~ ! [X264: term,X265: subst,X266: subst,X267: subst] :
( ( ( X258 @ ( comp @ X265 @ X266 ) @ ( sub @ X264 @ X266 ) @ X267 )
= $true )
| ( ( X258 @ X265 @ X264 @ ( comp @ X266 @ X267 ) )
!= $true ) )
| ~ ! [X268: term] :
( ( ( X258 @ id @ ( sub @ X259 @ ( push @ X268 @ id ) ) @ id )
= $true )
| ( $true
!= ( X258 @ id @ X268 @ id ) ) )
| ( $true
= ( X258 @ id @ ( lam @ X259 ) @ id ) )
| ~ ! [X269: subst > term > term] :
( ( ( X258 @ id @ ( lam @ ( X269 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X270: subst,X271: subst,X272: term] :
( ( sub @ ( X269 @ X270 @ X272 ) @ X271 )
= ( X269 @ ( comp @ X270 @ X271 ) @ ( sub @ X272 @ X271 ) ) )
| ~ ! [X273: term] :
( ( ( X258 @ id @ X273 @ id )
!= $true )
| ( ( X258 @ id @ ( X269 @ id @ X273 ) @ id )
= $true ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( ! [X274: subst] :
( ( comp @ X274 @ id )
= X274 )
& ! [X275: subst] :
( ( comp @ id @ X275 )
= X275 ) )
<=> ( substmonoid = $true ) )
& ( ( ! [X276: subst] :
( ( comp @ id @ X276 )
= X276 )
=> ( ! [X277: subst] :
( ( comp @ X277 @ id )
= X277 )
=> ( ! [X278: subst] :
( ( comp @ X278 @ id )
= X278 )
& ! [X279: subst] :
( ( comp @ id @ X279 )
= X279 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X280: term,X281: term,X282: subst > term > subst > $o,X283: term > $o] :
( ~ ! [X284: subst,X285: subst,X286: term,X287: subst] :
( ( ( X282 @ X285 @ X286 @ ( comp @ X284 @ X287 ) )
= $true )
| ( $true
!= ( X282 @ ( comp @ X285 @ X284 ) @ ( sub @ X286 @ X284 ) @ X287 ) ) )
| ~ ! [X288: term] :
( ( X283 @ X288 )
= ( X282 @ id @ X288 @ id ) )
| ~ ! [X289: subst,X290: subst,X291: term,X292: subst] :
( ( ( X282 @ X289 @ X291 @ ( comp @ X290 @ X292 ) )
!= $true )
| ( ( X282 @ ( comp @ X289 @ X290 ) @ ( sub @ X291 @ X290 ) @ X292 )
= $true ) )
| ( ( X283 @ X281 )
!= $true )
| ( ( X283 @ X280 )
!= $true )
| ( $true
= ( X283 @ ( ap @ X280 @ X281 ) ) )
| ~ ! [X293: term,X294: term] :
( ( $true
!= ( X282 @ id @ X293 @ id ) )
| ( $true
= ( X282 @ id @ ( ap @ ( sub @ X293 @ id ) @ X294 ) @ id ) )
| ( ( X282 @ id @ X294 @ id )
!= $true ) ) ) )
& ( ! [X295: term,X296: term,X297: term,X298: term] :
( ( ( ap @ X296 @ X297 )
!= ( ap @ X298 @ X295 ) )
| ( X295 = X297 ) )
<=> ( apinj2 = $true ) )
& ( lamnotvar = $true )
& ( ! [X299: subst] :
( ( comp @ id @ X299 )
= X299 )
<=> ( axidl = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasapnotvar = $true )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X300: subst > term > subst > $o] :
~ ! [X301: term > $o] :
~ ! [X302: term] :
( ( X301 @ X302 )
= ( X300 @ id @ X302 @ id ) )
=> ( ! [X303: term > $o,X304: term] :
( ~ ! [X305: term,X306: term] :
( ( ( X303 @ X306 )
!= $true )
| ( ( X303 @ ( ap @ X305 @ X306 ) )
= $true )
| ( $true
!= ( X303 @ X305 ) ) )
| ( ( X303 @ X304 )
= $true )
| ~ ! [X307: term] :
( ( ( X303 @ X307 )
= $true )
| ( $true
!= ( var @ X307 ) ) )
| ~ ! [X308: term] :
( ~ ! [X309: term] :
( ( ( X303 @ X309 )
!= $true )
| ( ( X303 @ ( sub @ X308 @ ( push @ X309 @ id ) ) )
= $true ) )
| ( $true
= ( X303 @ ( lam @ X308 ) ) ) ) )
=> ( ! [X310: term] :
( ( sub @ X310 @ id )
= X310 )
=> ( ! [X311: term > $o,X312: term,X313: subst > term > subst > $o] :
( ~ ! [X314: term] :
( ( X311 @ X314 )
= ( X313 @ id @ X314 @ id ) )
| ~ ! [X315: term] :
( ( ( X311 @ ( sub @ X312 @ ( push @ X315 @ id ) ) )
= $true )
| ( ( X311 @ X315 )
!= $true ) )
| ( ( X311 @ ( lam @ X312 ) )
= $true )
| ~ ! [X316: subst > term > term] :
( ~ ! [X317: term] :
( ( ( X313 @ id @ X317 @ id )
!= $true )
| ( ( X313 @ id @ ( X316 @ id @ X317 ) @ id )
= $true ) )
| ~ ! [X318: term,X319: subst,X320: subst] :
( ( sub @ ( X316 @ X320 @ X318 ) @ X319 )
= ( X316 @ ( comp @ X320 @ X319 ) @ ( sub @ X318 @ X319 ) ) )
| ( $true
= ( X313 @ id @ ( lam @ ( X316 @ sh @ one ) ) @ id ) ) ) )
=> ! [X321: subst > term > subst > $o,X322: term] :
( ~ ! [X323: subst > term > term] :
( ~ ! [X324: term] :
( ( ( X321 @ id @ X324 @ id )
!= $true )
| ( $true
= ( X321 @ id @ ( X323 @ id @ X324 ) @ id ) ) )
| ~ ! [X325: subst,X326: subst,X327: term] :
( ( sub @ ( X323 @ X326 @ X327 ) @ X325 )
= ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) ) )
| ( ( X321 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X328: term,X329: term] :
( ( ( X321 @ id @ X329 @ id )
!= $true )
| ( ( X321 @ id @ ( ap @ ( sub @ X329 @ id ) @ X328 ) @ id )
= $true )
| ( ( X321 @ id @ X328 @ id )
!= $true ) )
| ( ( X321 @ id @ X322 @ id )
= $true ) ) ) ) ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X330: term] :
( ( sub @ X330 @ id )
= X330 )
=> ( ! [X331: subst > term > subst > $o,X332: term] :
( ~ ! [X333: subst > term > term] :
( ( ( X331 @ id @ ( lam @ ( X333 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X334: term] :
( ( $true
!= ( X331 @ id @ X334 @ id ) )
| ( ( X331 @ id @ ( X333 @ id @ X334 ) @ id )
= $true ) )
| ~ ! [X335: term,X336: subst,X337: subst] :
( ( X333 @ ( comp @ X337 @ X336 ) @ ( sub @ X335 @ X336 ) )
= ( sub @ ( X333 @ X337 @ X335 ) @ X336 ) ) )
| ~ ! [X338: term] :
( ( ( X331 @ id @ ( sub @ X332 @ ( push @ X338 @ id ) ) @ id )
= $true )
| ( ( X331 @ id @ X338 @ id )
!= $true ) )
| ( ( X331 @ id @ ( lam @ ( sub @ X332 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X339: term,X340: subst > term > subst > $o] :
( ~ ! [X341: term] :
( ( ( X340 @ id @ ( sub @ X339 @ ( push @ X341 @ id ) ) @ id )
= $true )
| ( $true
!= ( X340 @ id @ X341 @ id ) ) )
| ~ ! [X342: subst > term > term] :
( ~ ! [X343: term,X344: subst,X345: subst] :
( ( X342 @ ( comp @ X344 @ X345 ) @ ( sub @ X343 @ X345 ) )
= ( sub @ ( X342 @ X344 @ X343 ) @ X345 ) )
| ~ ! [X346: term] :
( ( $true
= ( X340 @ id @ ( X342 @ id @ X346 ) @ id ) )
| ( ( X340 @ id @ X346 @ id )
!= $true ) )
| ( $true
= ( X340 @ id @ ( lam @ ( X342 @ sh @ one ) ) @ id ) ) )
| ( ( X340 @ id @ ( lam @ X339 ) @ id )
= $true )
| ~ ! [X347: subst,X348: subst,X349: subst,X350: term] :
( ( ( X340 @ X349 @ X350 @ ( comp @ X347 @ X348 ) )
!= $true )
| ( ( X340 @ ( comp @ X349 @ X347 ) @ ( sub @ X350 @ X347 ) @ X348 )
= $true ) )
| ~ ! [X351: term,X352: subst,X353: subst,X354: subst] :
( ( $true
= ( X340 @ X353 @ X351 @ ( comp @ X354 @ X352 ) ) )
| ( ( X340 @ ( comp @ X353 @ X354 ) @ ( sub @ X351 @ X354 ) @ X352 )
!= $true ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ( axvarid = $true )
<=> ! [X355: term] :
( ( sub @ X355 @ id )
= X355 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X356: term] :
? [X357: d_term] :
( ( d2term @ X357 )
= X356 )
& ( pushprop_lem2v2 = $true )
& ( ( ! [X358: term,X359: term > $o] :
( ~ ! [X360: term,X361: term] :
( ( ( X359 @ X360 )
!= $true )
| ( ( X359 @ X361 )
!= $true )
| ( ( X359 @ ( ap @ X361 @ X360 ) )
= $true ) )
| ( ( X359 @ X358 )
= $true )
| ~ ! [X362: term] :
( ~ ! [X363: term] :
( ( ( X359 @ ( sub @ X362 @ ( push @ X363 @ id ) ) )
= $true )
| ( $true
!= ( X359 @ X363 ) ) )
| ( ( X359 @ ( lam @ X362 ) )
= $true ) )
| ~ ! [X364: term] :
( ( $true
= ( X359 @ X364 ) )
| ( ( var @ X364 )
!= $true ) ) )
=> ( ! [X365: term,X366: term,X367: subst > term > subst > $o] :
( ( ( X367 @ id @ ( ap @ X365 @ X366 ) @ id )
= $true )
| ~ ! [X368: subst,X369: subst,X370: subst,X371: term] :
( ( $true
!= ( X367 @ ( comp @ X368 @ X369 ) @ ( sub @ X371 @ X369 ) @ X370 ) )
| ( $true
= ( X367 @ X368 @ X371 @ ( comp @ X369 @ X370 ) ) ) )
| ( ( X367 @ id @ X365 @ id )
!= $true )
| ( $true
!= ( X367 @ id @ X366 @ id ) )
| ~ ! [X372: subst,X373: subst,X374: subst,X375: term] :
( ( $true
= ( X367 @ ( comp @ X373 @ X372 ) @ ( sub @ X375 @ X372 ) @ X374 ) )
| ( $true
!= ( X367 @ X373 @ X375 @ ( comp @ X372 @ X374 ) ) ) )
| ~ ! [X376: term,X377: term] :
( ( ( X367 @ id @ X376 @ id )
!= $true )
| ( $true
!= ( X367 @ id @ X377 @ id ) )
| ( ( X367 @ id @ ( ap @ ( sub @ X376 @ id ) @ X377 ) @ id )
= $true ) ) )
=> ( ! [X378: subst > term > subst > $o,X379: term] :
( ~ ! [X380: subst,X381: term,X382: subst,X383: subst] :
( ( ( X378 @ ( comp @ X383 @ X382 ) @ ( sub @ X381 @ X382 ) @ X380 )
= $true )
| ( ( X378 @ X383 @ X381 @ ( comp @ X382 @ X380 ) )
!= $true ) )
| ( ( X378 @ id @ ( lam @ X379 ) @ id )
= $true )
| ~ ! [X384: subst,X385: subst,X386: subst,X387: term] :
( ( $true
!= ( X378 @ ( comp @ X386 @ X384 ) @ ( sub @ X387 @ X384 ) @ X385 ) )
| ( $true
= ( X378 @ X386 @ X387 @ ( comp @ X384 @ X385 ) ) ) )
| ~ ! [X388: term] :
( ( ( X378 @ id @ X388 @ id )
!= $true )
| ( ( X378 @ id @ ( sub @ X379 @ ( push @ X388 @ id ) ) @ id )
= $true ) )
| ~ ! [X389: subst > term > term] :
( ( ( X378 @ id @ ( lam @ ( X389 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X390: term] :
( ( ( X378 @ id @ X390 @ id )
!= $true )
| ( $true
= ( X378 @ id @ ( X389 @ id @ X390 ) @ id ) ) )
| ~ ! [X391: term,X392: subst,X393: subst] :
( ( sub @ ( X389 @ X393 @ X391 ) @ X392 )
= ( X389 @ ( comp @ X393 @ X392 ) @ ( sub @ X391 @ X392 ) ) ) ) )
=> ! [X394: term,X395: subst > term > subst > $o] :
( ~ ! [X396: term,X397: subst,X398: subst,X399: subst] :
( ( ( X395 @ X397 @ X396 @ ( comp @ X399 @ X398 ) )
!= $true )
| ( ( X395 @ ( comp @ X397 @ X399 ) @ ( sub @ X396 @ X399 ) @ X398 )
= $true ) )
| ~ ! [X400: subst > term > term] :
( ~ ! [X401: term] :
( ( ( X395 @ id @ X401 @ id )
!= $true )
| ( ( X395 @ id @ ( X400 @ id @ X401 ) @ id )
= $true ) )
| ~ ! [X402: term,X403: subst,X404: subst] :
( ( X400 @ ( comp @ X404 @ X403 ) @ ( sub @ X402 @ X403 ) )
= ( sub @ ( X400 @ X404 @ X402 ) @ X403 ) )
| ( ( X395 @ id @ ( lam @ ( X400 @ sh @ one ) ) @ id )
= $true ) )
| ( $true
= ( X395 @ id @ X394 @ id ) )
| ~ ! [X405: term,X406: term] :
( ( ( X395 @ id @ X405 @ id )
!= $true )
| ( ( X395 @ id @ X406 @ id )
!= $true )
| ( $true
= ( X395 @ id @ ( ap @ ( sub @ X406 @ id ) @ X405 ) @ id ) ) )
| ~ ! [X407: term] :
( ( ( X395 @ id @ X407 @ id )
= $true )
| ( ( var @ ( sub @ X407 @ id ) )
!= $true ) )
| ~ ! [X408: subst,X409: subst,X410: subst,X411: term] :
( ( ( X395 @ X408 @ X411 @ ( comp @ X409 @ X410 ) )
= $true )
| ( $true
!= ( X395 @ ( comp @ X408 @ X409 ) @ ( sub @ X411 @ X409 ) @ X410 ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X412: term,X413: term > $o,X414: subst > term > subst > $o] :
( ~ ! [X415: term] :
( ( $true
= ( X413 @ ( sub @ X412 @ ( push @ X415 @ id ) ) ) )
| ( $true
!= ( X413 @ X415 ) ) )
| ( $true
= ( X413 @ ( lam @ X412 ) ) )
| ~ ! [X416: subst > term > term] :
( ~ ! [X417: term,X418: subst,X419: subst] :
( ( sub @ ( X416 @ X419 @ X417 ) @ X418 )
= ( X416 @ ( comp @ X419 @ X418 ) @ ( sub @ X417 @ X418 ) ) )
| ( ( X414 @ id @ ( lam @ ( X416 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X420: term] :
( ( ( X414 @ id @ X420 @ id )
!= $true )
| ( ( X414 @ id @ ( X416 @ id @ X420 ) @ id )
= $true ) ) )
| ~ ! [X421: term] :
( ( X413 @ X421 )
= ( X414 @ id @ X421 @ id ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X422: subst > term > subst > $o,X423: term,X424: term > $o] :
( ( ( X424 @ ( lam @ X423 ) )
= $true )
| ~ ! [X425: subst > term > term] :
( ( ( X422 @ id @ ( lam @ ( X425 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X426: subst,X427: term,X428: subst] :
( ( X425 @ ( comp @ X428 @ X426 ) @ ( sub @ X427 @ X426 ) )
= ( sub @ ( X425 @ X428 @ X427 ) @ X426 ) )
| ~ ! [X429: term] :
( ( ( X422 @ id @ X429 @ id )
!= $true )
| ( ( X422 @ id @ ( X425 @ id @ X429 ) @ id )
= $true ) ) )
| ~ ! [X430: subst,X431: term,X432: subst,X433: subst] :
( ( ( X422 @ X433 @ X431 @ ( comp @ X432 @ X430 ) )
!= $true )
| ( ( X422 @ ( comp @ X433 @ X432 ) @ ( sub @ X431 @ X432 ) @ X430 )
= $true ) )
| ~ ! [X434: term,X435: subst,X436: subst,X437: subst] :
( ( $true
= ( X422 @ X436 @ X434 @ ( comp @ X437 @ X435 ) ) )
| ( ( X422 @ ( comp @ X436 @ X437 ) @ ( sub @ X434 @ X437 ) @ X435 )
!= $true ) )
| ~ ! [X438: term] :
( ( X422 @ id @ X438 @ id )
= ( X424 @ X438 ) )
| ~ ! [X439: term] :
( ( ( X424 @ ( sub @ X423 @ ( push @ X439 @ id ) ) )
= $true )
| ( ( X424 @ X439 )
!= $true ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X440: subst > term > subst > $o,X441: term] :
( ~ ! [X442: subst > term > term] :
( ~ ! [X443: subst,X444: subst,X445: term] :
( ( X442 @ ( comp @ X443 @ X444 ) @ ( sub @ X445 @ X444 ) )
= ( sub @ ( X442 @ X443 @ X445 ) @ X444 ) )
| ~ ! [X446: term] :
( ( ( X440 @ id @ ( X442 @ id @ X446 ) @ id )
= $true )
| ( $true
!= ( X440 @ id @ X446 @ id ) ) )
| ( ( X440 @ id @ ( lam @ ( X442 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X440 @ id @ ( lam @ X441 ) @ id )
= $true )
| ~ ! [X447: term] :
( ( ( X440 @ id @ ( sub @ X441 @ ( push @ X447 @ id ) ) @ id )
= $true )
| ( ( X440 @ id @ X447 @ id )
!= $true ) ) ) )
& ( induction2_gthm = $true )
& ( ! [X448: term] :
~ ! [X449: subst > term > term] :
~ ! [X450: subst,X451: term] :
( ( sub @ X448 @ ( push @ X451 @ X450 ) )
= ( X449 @ X450 @ X451 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( ! [X452: term,X453: subst] :
( ( sub @ one @ ( push @ X452 @ X453 ) )
= X452 )
=> ( ! [X454: term,X455: subst] :
( ( comp @ sh @ ( push @ X454 @ X455 ) )
= X455 )
=> ( ! [X456: subst] :
( ( comp @ X456 @ id )
= X456 )
=> ( ! [X457: term,X458: term > $o] :
( ~ ! [X459: term,X460: term] :
( ( ( X458 @ X459 )
!= $true )
| ( ( X458 @ ( ap @ X460 @ X459 ) )
= $true )
| ( ( X458 @ X460 )
!= $true ) )
| ( $true
= ( X458 @ X457 ) )
| ~ ! [X461: term] :
( ( ( X458 @ X461 )
= $true )
| ( ( var @ X461 )
!= $true ) )
| ~ ! [X462: term] :
( ( ( X458 @ X462 )
!= $true )
| ( ( X458 @ ( lam @ X462 ) )
= $true ) ) )
=> ! [X463: term,X464: term > $o,X465: subst] :
( ~ ! [X466: term] :
( ( $true
= ( X464 @ ( lam @ X466 ) ) )
| ~ ! [X467: term] :
( ( ( X464 @ ( sub @ X466 @ ( push @ X467 @ id ) ) )
= $true )
| ( ( X464 @ X467 )
!= $true ) ) )
| ~ ! [X468: term] :
( ( ( X464 @ ( sub @ X468 @ X465 ) )
= $true )
| ( ( var @ X468 )
!= $true ) )
| ( $true
= ( X464 @ ( sub @ X463 @ X465 ) ) )
| ~ ! [X469: term,X470: term] :
( ( ( X464 @ ( ap @ X469 @ X470 ) )
= $true )
| ( ( X464 @ X469 )
!= $true )
| ( ( X464 @ X470 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( apnotvar = $true )
& ( axabs = $true )
& ( hoaslamnotvar = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X471: term,X472: subst] :
( ( sub @ one @ ( push @ X471 @ X472 ) )
= X471 )
=> ( ! [X473: term,X474: subst] :
( ( comp @ sh @ ( push @ X473 @ X474 ) )
= X474 )
=> ( ! [X475: term,X476: term] :
( ( ( lam @ X475 )
!= ( lam @ X476 ) )
| ( X475 = X476 ) )
=> ! [X477: term,X478: subst,X479: subst > term > term,X480: subst > term > term] :
( ~ ! [X481: subst,X482: term,X483: subst] :
( ( sub @ ( X479 @ X483 @ X482 ) @ X481 )
= ( X479 @ ( comp @ X483 @ X481 ) @ ( sub @ X482 @ X481 ) ) )
| ~ ! [X484: subst,X485: term,X486: subst] :
( ( X480 @ ( comp @ X484 @ X486 ) @ ( sub @ X485 @ X486 ) )
= ( sub @ ( X480 @ X484 @ X485 ) @ X486 ) )
| ( ( lam @ ( X480 @ sh @ one ) )
!= ( lam @ ( X479 @ sh @ one ) ) )
| ( ( X479 @ X478 @ X477 )
= ( X480 @ X478 @ X477 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X487: term,X488: subst > term > subst > $o] :
( ( $true
= ( X488 @ id @ ( lam @ ( sub @ X487 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X489: term] :
( ( $true
!= ( X488 @ id @ X489 @ id ) )
| ( ( X488 @ id @ ( sub @ X487 @ ( push @ X489 @ id ) ) @ id )
= $true ) )
| ~ ! [X490: subst > term > term,X491: term] :
( ~ ! [X492: subst,X493: subst,X494: term] :
( ( sub @ ( X490 @ X492 @ X494 ) @ X493 )
= ( sub @ ( sub @ X491 @ ( push @ X494 @ X492 ) ) @ X493 ) )
| ( $true
= ( X488 @ id @ ( lam @ ( X490 @ sh @ one ) ) @ id ) )
| ~ ! [X495: term] :
( ( ( X488 @ id @ X495 @ id )
!= $true )
| ( ( X488 @ id @ ( X490 @ id @ X495 ) @ id )
= $true ) )
| ~ ! [X496: subst,X497: subst,X498: term] :
( ( X490 @ ( comp @ X496 @ X497 ) @ ( sub @ X498 @ X497 ) )
= ( sub @ X491 @ ( push @ ( sub @ X498 @ X497 ) @ ( comp @ X496 @ X497 ) ) ) ) ) ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X499: term,X500: subst] :
( ( sub @ one @ ( push @ X499 @ X500 ) )
= X499 )
=> ( ! [X501: subst,X502: term] :
( ( comp @ sh @ ( push @ X502 @ X501 ) )
= X501 )
=> ! [X503: subst,X504: term > $o,X505: term,X506: term,X507: term > $o] :
( ( $true
= ( X504 @ ( sub @ X506 @ ( push @ X505 @ X503 ) ) ) )
| ( ( X507 @ X506 )
!= $true ) ) ) ) )
& ( axvarshift = $true )
& ( ( induction2lem = $true )
<=> ! [X508: subst,X509: term,X510: term > $o] :
( ~ ! [X511: term] :
( ( ( X510 @ ( sub @ X511 @ X508 ) )
= $true )
| ( ( var @ X511 )
!= $true ) )
| ~ ! [X512: term,X513: term] :
( ( ( X510 @ X513 )
!= $true )
| ( $true
= ( X510 @ ( ap @ X513 @ X512 ) ) )
| ( ( X510 @ X512 )
!= $true ) )
| ~ ! [X514: term] :
( ( ( X510 @ ( lam @ X514 ) )
= $true )
| ~ ! [X515: term] :
( ( ( X510 @ ( sub @ X514 @ ( push @ X515 @ id ) ) )
= $true )
| ( ( X510 @ X515 )
!= $true ) ) )
| ( ( X510 @ ( sub @ X509 @ X508 ) )
= $true ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ( ! [X517: term > $o,X518: subst,X519: term] :
( ~ ! [X520: term] :
( ( ( var @ X520 )
!= $true )
| ( $true
= ( X517 @ ( sub @ X520 @ X518 ) ) ) )
| ~ ! [X521: term] :
( ~ ! [X522: term] :
( ( $true
!= ( X517 @ X522 ) )
| ( ( X517 @ ( sub @ X521 @ ( push @ X522 @ id ) ) )
= $true ) )
| ( $true
= ( X517 @ ( lam @ X521 ) ) ) )
| ~ ! [X523: term,X524: term] :
( ( ( X517 @ X524 )
!= $true )
| ( ( X517 @ X523 )
!= $true )
| ( ( X517 @ ( ap @ X523 @ X524 ) )
= $true ) )
| ( $true
= ( X517 @ ( sub @ X519 @ X518 ) ) ) )
=> ! [X525: term > $o,X526: term] :
( ( $true
= ( X525 @ X526 ) )
| ~ ! [X527: term] :
( ~ ! [X528: term] :
( ( ( X525 @ ( sub @ X527 @ ( push @ X528 @ id ) ) )
= $true )
| ( ( X525 @ X528 )
!= $true ) )
| ( ( X525 @ ( lam @ X527 ) )
= $true ) )
| ~ ! [X529: term] :
( ( ( var @ X529 )
!= $true )
| ( ( X525 @ X529 )
= $true ) )
| ~ ! [X530: term,X531: term] :
( ( $true
!= ( X525 @ X531 ) )
| ( ( X525 @ ( ap @ X530 @ X531 ) )
= $true )
| ( $true
!= ( X525 @ X530 ) ) ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X533 @ X535 )
!= ( ap @ X534 @ X532 ) )
| ( X532 = X535 ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( X536 = X538 )
| ( ( ap @ ( sub @ X539 @ id ) @ X538 )
!= ( ap @ ( sub @ X537 @ id ) @ X536 ) ) ) ) )
& ( axapp = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( substmonoid_gthm = $true )
& ( axmap = $true )
& ( ( laminj = $true )
<=> ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) ) )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
= $true )
| ( ( X3 @ X2 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X7: term] :
( ( sub @ X7 @ id )
= X7 )
=> ( ! [X8: term,X9: subst > term > subst > $o] :
( ( $true
= ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X10: subst > term > term] :
( ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) )
| ~ ! [X14: term] :
( ( ( X9 @ id @ X14 @ id )
!= $true )
| ( ( X9 @ id @ ( X10 @ id @ X14 ) @ id )
= $true ) ) )
| ~ ! [X15: term] :
( ( ( X9 @ id @ X15 @ id )
!= $true )
| ( $true
= ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) ) )
=> ! [X16: term,X17: subst > term > subst > $o] :
( ~ ! [X18: term] :
( ( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
= $true )
| ( ( X17 @ id @ X18 @ id )
!= $true ) )
| ( $true
= ( X17 @ id @ ( lam @ X16 ) @ id ) )
| ~ ! [X19: subst > term > term] :
( ~ ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
| ~ ! [X23: term] :
( ( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
= $true )
| ( $true
!= ( X17 @ id @ X23 @ id ) ) )
| ( $true
= ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X24: subst > term > subst > $o] :
~ ! [X25: term > $o] :
~ ! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X27: term] :
~ ! [X28: subst > term > term] :
~ ! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( ( hoasapinj2 = $true )
<=> ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) ) )
& ! [X35: d_subst] : ( d_id = X35 )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoasinduction = $true )
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ~ ! [X38: term,X39: term] :
( ( $true
= ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id ) )
| ( ( X37 @ id @ X39 @ id )
!= $true )
| ( ( X37 @ id @ X38 @ id )
!= $true ) )
| ~ ! [X40: subst,X41: term,X42: subst,X43: subst] :
( ( $true
!= ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 ) )
| ( ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) )
= $true ) )
| ~ ! [X44: subst,X45: subst,X46: term,X47: subst] :
( ( ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
!= $true )
| ( ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 )
= $true ) )
| ~ ! [X48: subst > term > term] :
( ~ ! [X49: term] :
( ( $true
!= ( X37 @ id @ X49 @ id ) )
| ( $true
= ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) ) )
| ~ ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) )
| ( ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X53: term] :
( ( ( X37 @ id @ X53 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X53 @ id ) ) ) )
| ( $true
= ( X37 @ id @ X36 @ id ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X54: subst > term > subst > $o] :
~ ! [X55: term > $o] :
~ ! [X56: term] :
( ( X54 @ id @ X56 @ id )
= ( X55 @ X56 ) )
=> ( ! [X57: term,X58: term > $o] :
( ~ ! [X59: term,X60: term] :
( ( $true
!= ( X58 @ X59 ) )
| ( ( X58 @ X60 )
!= $true )
| ( ( X58 @ ( ap @ X59 @ X60 ) )
= $true ) )
| ~ ! [X61: term] :
( ~ ! [X62: term] :
( ( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
= $true )
| ( $true
!= ( X58 @ X62 ) ) )
| ( $true
= ( X58 @ ( lam @ X61 ) ) ) )
| ~ ! [X63: term] :
( ( ( X58 @ X63 )
= $true )
| ( ( var @ X63 )
!= $true ) )
| ( ( X58 @ X57 )
= $true ) )
=> ( ! [X64: term] :
( ( sub @ X64 @ id )
= X64 )
=> ( ! [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ~ ! [X68: subst > term > term] :
( ~ ! [X69: term] :
( ( ( X67 @ id @ X69 @ id )
!= $true )
| ( ( X67 @ id @ ( X68 @ id @ X69 ) @ id )
= $true ) )
| ( ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) )
| ~ ! [X73: term] :
( ( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
= $true )
| ( $true
!= ( X65 @ X73 ) ) )
| ( $true
= ( X65 @ ( lam @ X66 ) ) )
| ~ ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) ) )
=> ! [X75: subst > term > subst > $o,X76: term] :
( ~ ! [X77: term] :
( ( ( X75 @ id @ X77 @ id )
= $true )
| ( ( var @ ( sub @ X77 @ id ) )
!= $true ) )
| ~ ! [X78: term,X79: subst,X80: subst,X81: subst] :
( ( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
= $true )
| ( ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 )
!= $true ) )
| ~ ! [X82: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X83: term] :
( ( ( X75 @ id @ X83 @ id )
!= $true )
| ( ( X75 @ id @ ( X82 @ id @ X83 ) @ id )
= $true ) )
| ~ ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ~ ! [X87: subst,X88: subst,X89: term,X90: subst] :
( ( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
= $true )
| ( ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) )
!= $true ) )
| ~ ! [X91: term,X92: term] :
( ( ( X75 @ id @ X91 @ id )
!= $true )
| ( ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
= $true )
| ( $true
!= ( X75 @ id @ X92 @ id ) ) )
| ( ( X75 @ id @ X76 @ id )
= $true ) ) ) ) ) ) )
& ( ! [X93: term,X94: term,X95: subst > term > term] :
( ~ ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) )
| ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ulamvar1 != $true )
& ( axclos = $true )
& ( ( axidr = $true )
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& ( hoasinduction_lem1 = $true )
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> ( axscons = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 ) )
& ( ( ! [X105: term] :
( ( sub @ X105 @ id )
= X105 )
=> ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) )
| ( X107 = X108 ) )
=> ! [X110: term,X111: term,X112: term,X113: term] :
( ( X111 = X113 )
| ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( lamnotap != $true )
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> ( axvarcons = $true ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
= ( d2subst @ X117 ) )
=> ( X116 = X117 ) )
& ( ! [X118: subst > term > subst > $o] :
~ ! [X119: term > $o] :
~ ! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( one
= ( d2term @ d_one ) )
& ( ! [X121: subst > term > subst > $o,X122: term] :
( ~ ! [X123: subst > term > term] :
( ~ ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) )
| ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X127: term] :
( ( ( X121 @ id @ X127 @ id )
!= $true )
| ( $true
= ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) ) ) )
| ( ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X128: term] :
( ( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
= $true )
| ( $true
!= ( X121 @ id @ X128 @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X129: term] :
~ ! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) ) )
& ( ( induction = $true )
<=> ! [X131: term > $o,X132: term] :
( ~ ! [X133: term,X134: term] :
( ( ( X131 @ X134 )
!= $true )
| ( ( X131 @ ( ap @ X133 @ X134 ) )
= $true )
| ( ( X131 @ X133 )
!= $true ) )
| ~ ! [X135: term] :
( ( ( X131 @ ( lam @ X135 ) )
= $true )
| ( $true
!= ( X131 @ X135 ) ) )
| ~ ! [X136: term] :
( ( $true
= ( X131 @ X136 ) )
| ( $true
!= ( var @ X136 ) ) )
| ( ( X131 @ X132 )
= $true ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
~ ! [X140: term > $o] :
~ ! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
<=> ( pushprop_lem0 = $true ) )
& ( ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( ( X144 @ one )
= $true )
| ( ( X145 @ X143 )
!= $true )
| ~ ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) )
& ( ( ! [X152: term] :
( ( sub @ X152 @ id )
= X152 )
=> ! [X153: subst > term > subst > $o,X154: term,X155: term > $o] :
( ~ ! [X156: term] :
( ( ( X155 @ X156 )
!= $true )
| ( $true
= ( X155 @ ( sub @ X154 @ ( push @ X156 @ id ) ) ) ) )
| ~ ! [X157: term,X158: subst,X159: subst,X160: subst] :
( ( ( X153 @ ( comp @ X159 @ X158 ) @ ( sub @ X157 @ X158 ) @ X160 )
= $true )
| ( ( X153 @ X159 @ X157 @ ( comp @ X158 @ X160 ) )
!= $true ) )
| ~ ! [X161: subst > term > term] :
( ~ ! [X162: term] :
( ( ( X153 @ id @ ( X161 @ id @ X162 ) @ id )
= $true )
| ( ( X153 @ id @ X162 @ id )
!= $true ) )
| ~ ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X161 @ X163 @ X164 ) @ X165 )
= ( X161 @ ( comp @ X163 @ X165 ) @ ( sub @ X164 @ X165 ) ) )
| ( ( X153 @ id @ ( lam @ ( X161 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X155 @ ( lam @ X154 ) )
= $true )
| ~ ! [X166: term] :
( ( X153 @ id @ X166 @ id )
= ( X155 @ X166 ) )
| ~ ! [X167: subst,X168: subst,X169: term,X170: subst] :
( ( ( X153 @ ( comp @ X167 @ X168 ) @ ( sub @ X169 @ X168 ) @ X170 )
!= $true )
| ( ( X153 @ X167 @ X169 @ ( comp @ X168 @ X170 ) )
= $true ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X171: term,X172: term,X173: term,X174: term] :
( ( X173 = X174 )
| ( ( ap @ X174 @ X172 )
!= ( ap @ X173 @ X171 ) ) ) )
& ! [X175: d_term] : ( d_one = X175 )
& ( ( termmset_lthm = $true )
<=> ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
=> ! [X177: term] :
( ( sub @ X177 @ id )
= X177 ) ) )
& ( termmset_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X178: term,X179: subst] :
( ( sub @ one @ ( push @ X178 @ X179 ) )
= X178 )
=> ! [X180: term > $o,X181: subst,X182: term > $o,X183: term] :
( ( ( X180 @ one )
= $true )
| ( $true
!= ( X182 @ X183 ) )
| ~ ! [X184: term] :
( ( X182 @ ( sub @ X184 @ ( push @ X183 @ X181 ) ) )
= ( X180 @ X184 ) ) ) ) )
& ( ! [X185: term,X186: term,X187: subst > term > subst > $o] :
( ( ( X187 @ id @ X185 @ id )
!= $true )
| ~ ! [X188: subst,X189: subst,X190: term,X191: subst] :
( ( ( X187 @ ( comp @ X189 @ X188 ) @ ( sub @ X190 @ X188 ) @ X191 )
= $true )
| ( ( X187 @ X189 @ X190 @ ( comp @ X188 @ X191 ) )
!= $true ) )
| ~ ! [X192: subst,X193: term,X194: subst,X195: subst] :
( ( ( X187 @ X194 @ X193 @ ( comp @ X192 @ X195 ) )
= $true )
| ( ( X187 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) @ X195 )
!= $true ) )
| ( ( X187 @ id @ ( ap @ X185 @ X186 ) @ id )
= $true )
| ~ ! [X196: term,X197: term] :
( ( ( X187 @ id @ X197 @ id )
!= $true )
| ( $true
!= ( X187 @ id @ X196 @ id ) )
| ( ( X187 @ id @ ( ap @ ( sub @ X197 @ id ) @ X196 ) @ id )
= $true ) )
| ( ( X187 @ id @ X186 @ id )
!= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( pushprop_lthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( axassoc = $true )
& ( ( induction2 = $true )
<=> ! [X198: term,X199: term > $o] :
( ~ ! [X200: term] :
( ( ( var @ X200 )
!= $true )
| ( $true
= ( X199 @ X200 ) ) )
| ~ ! [X201: term] :
( ( $true
= ( X199 @ ( lam @ X201 ) ) )
| ~ ! [X202: term] :
( ( ( X199 @ ( sub @ X201 @ ( push @ X202 @ id ) ) )
= $true )
| ( ( X199 @ X202 )
!= $true ) ) )
| ( $true
= ( X199 @ X198 ) )
| ~ ! [X203: term,X204: term] :
( ( $true
!= ( X199 @ X204 ) )
| ( ( X199 @ ( ap @ X203 @ X204 ) )
= $true )
| ( ( X199 @ X203 )
!= $true ) ) ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X205: term] :
~ ! [X206: subst > term > term] :
( ( sub @ X205 @ ( push @ one @ sh ) )
!= ( X206 @ sh @ one ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X207: subst > term > subst > $o,X208: term] :
( ~ ! [X209: term,X210: term] :
( ( ( X207 @ id @ X210 @ id )
!= $true )
| ( ( X207 @ id @ X209 @ id )
!= $true )
| ( ( X207 @ id @ ( ap @ ( sub @ X209 @ id ) @ X210 ) @ id )
= $true ) )
| ( $true
= ( X207 @ id @ X208 @ id ) )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: subst,X213: subst,X214: term] :
( ( sub @ ( X211 @ X212 @ X214 ) @ X213 )
= ( X211 @ ( comp @ X212 @ X213 ) @ ( sub @ X214 @ X213 ) ) )
| ~ ! [X215: term] :
( ( ( X207 @ id @ X215 @ id )
!= $true )
| ( ( X207 @ id @ ( X211 @ id @ X215 ) @ id )
= $true ) )
| ( ( X207 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X216: term,X217: term > $o,X218: subst] :
~ ! [X219: term > $o] :
~ ! [X220: term] :
( ( X217 @ ( sub @ X220 @ ( push @ X216 @ X218 ) ) )
= ( X219 @ X220 ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X221: term] :
( ( sub @ X221 @ id )
= X221 )
<=> ( termmset = $true ) )
& ( ( hoaslaminj = $true )
<=> ! [X222: subst,X223: subst > term > term,X224: subst > term > term,X225: term] :
( ~ ! [X226: term,X227: subst,X228: subst] :
( ( sub @ ( X224 @ X227 @ X226 ) @ X228 )
= ( X224 @ ( comp @ X227 @ X228 ) @ ( sub @ X226 @ X228 ) ) )
| ~ ! [X229: subst,X230: term,X231: subst] :
( ( sub @ ( X223 @ X231 @ X230 ) @ X229 )
= ( X223 @ ( comp @ X231 @ X229 ) @ ( sub @ X230 @ X229 ) ) )
| ( ( X224 @ X222 @ X225 )
= ( X223 @ X222 @ X225 ) )
| ( ( lam @ ( X223 @ sh @ one ) )
!= ( lam @ ( X224 @ sh @ one ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( ! [X232: term] :
~ ! [X233: subst > term > term] :
~ ! [X234: subst,X235: term] :
( ( sub @ X232 @ ( push @ X235 @ X234 ) )
= ( X233 @ X234 @ X235 ) )
=> ( ! [X236: term] :
( ( sub @ X236 @ id )
= X236 )
=> ! [X237: subst > term > subst > $o,X238: term > $o,X239: term] :
( ~ ! [X240: term] :
( ( X238 @ X240 )
= ( X237 @ id @ X240 @ id ) )
| ( ( X238 @ ( lam @ X239 ) )
= $true )
| ~ ! [X241: term] :
( ( ( X238 @ ( sub @ X239 @ ( push @ X241 @ id ) ) )
= $true )
| ( ( X238 @ X241 )
!= $true ) )
| ~ ! [X242: subst > term > term] :
( ~ ! [X243: term] :
( ( ( X237 @ id @ ( X242 @ id @ X243 ) @ id )
= $true )
| ( ( X237 @ id @ X243 @ id )
!= $true ) )
| ~ ! [X244: term,X245: subst,X246: subst] :
( ( X242 @ ( comp @ X246 @ X245 ) @ ( sub @ X244 @ X245 ) )
= ( sub @ ( X242 @ X246 @ X244 ) @ X245 ) )
| ( ( X237 @ id @ ( lam @ ( X242 @ sh @ one ) ) @ id )
= $true ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( pushprop = $true )
& ( ! [X247: term,X248: term,X249: term,X250: term] :
( ( X247 = X249 )
| ( ( ap @ ( sub @ X247 @ id ) @ X248 )
!= ( ap @ ( sub @ X249 @ id ) @ X250 ) ) )
<=> ( hoasapinj1 = $true ) )
& ( ! [X251: term,X252: term] :
( ( ( sub @ X252 @ sh )
!= ( sub @ X251 @ sh ) )
| ( X251 = X252 ) )
<=> ( shinj = $true ) )
& ( ! [X253: subst > term > subst > $o,X254: term] :
( ( ( X253 @ id @ ( lam @ ( sub @ X254 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X255: term] :
( ( ( X253 @ id @ X255 @ id )
!= $true )
| ( ( X253 @ id @ ( sub @ X254 @ ( push @ X255 @ id ) ) @ id )
= $true ) )
| ~ ! [X256: subst > term > term] :
( ~ ! [X257: term] :
( ( $true
= ( X253 @ id @ ( X256 @ id @ X257 ) @ id ) )
| ( $true
!= ( X253 @ id @ X257 @ id ) ) )
| ( ( X253 @ id @ ( lam @ ( X256 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X258: term,X259: subst,X260: subst] :
( ( X256 @ ( comp @ X260 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X256 @ X260 @ X258 ) @ X259 ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ! [X261: d_term,X262: d_term] :
( ( ( d2term @ X262 )
= ( d2term @ X261 ) )
=> ( X261 = X262 ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X263: subst > term > subst > $o,X264: term] :
( ~ ! [X265: subst,X266: term,X267: subst,X268: subst] :
( ( ( X263 @ ( comp @ X265 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 )
!= $true )
| ( $true
= ( X263 @ X265 @ X266 @ ( comp @ X268 @ X267 ) ) ) )
| ~ ! [X269: term,X270: subst,X271: subst,X272: subst] :
( ( ( X263 @ ( comp @ X270 @ X271 ) @ ( sub @ X269 @ X271 ) @ X272 )
= $true )
| ( ( X263 @ X270 @ X269 @ ( comp @ X271 @ X272 ) )
!= $true ) )
| ~ ! [X273: term] :
( ( ( X263 @ id @ ( sub @ X264 @ ( push @ X273 @ id ) ) @ id )
= $true )
| ( $true
!= ( X263 @ id @ X273 @ id ) ) )
| ( ( X263 @ id @ ( lam @ X264 ) @ id )
= $true )
| ~ ! [X274: subst > term > term] :
( ( ( X263 @ id @ ( lam @ ( X274 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X275: subst,X276: subst,X277: term] :
( ( X274 @ ( comp @ X275 @ X276 ) @ ( sub @ X277 @ X276 ) )
= ( sub @ ( X274 @ X275 @ X277 ) @ X276 ) )
| ~ ! [X278: term] :
( ( ( X263 @ id @ X278 @ id )
!= $true )
| ( $true
= ( X263 @ id @ ( X274 @ id @ X278 ) @ id ) ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( ! [X282: subst] :
( ( comp @ X282 @ id )
= X282 )
& ! [X283: subst] :
( ( comp @ id @ X283 )
= X283 ) )
<=> ( substmonoid = $true ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X284: subst] :
( ( comp @ id @ X284 )
= X284 )
=> ( ! [X285: subst] :
( ( comp @ X285 @ id )
= X285 )
=> ( ! [X286: subst] :
( ( comp @ X286 @ id )
= X286 )
& ! [X287: subst] :
( ( comp @ id @ X287 )
= X287 ) ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X288: term,X289: term,X290: subst > term > subst > $o,X291: term > $o] :
( ~ ! [X292: subst,X293: subst,X294: term,X295: subst] :
( ( ( X290 @ X293 @ X294 @ ( comp @ X292 @ X295 ) )
= $true )
| ( ( X290 @ ( comp @ X293 @ X292 ) @ ( sub @ X294 @ X292 ) @ X295 )
!= $true ) )
| ~ ! [X296: term] :
( ( X290 @ id @ X296 @ id )
= ( X291 @ X296 ) )
| ~ ! [X297: subst,X298: subst,X299: term,X300: subst] :
( ( $true
!= ( X290 @ X297 @ X299 @ ( comp @ X298 @ X300 ) ) )
| ( $true
= ( X290 @ ( comp @ X297 @ X298 ) @ ( sub @ X299 @ X298 ) @ X300 ) ) )
| ( ( X291 @ X289 )
!= $true )
| ( $true
!= ( X291 @ X288 ) )
| ( $true
= ( X291 @ ( ap @ X288 @ X289 ) ) )
| ~ ! [X301: term,X302: term] :
( ( ( X290 @ id @ X301 @ id )
!= $true )
| ( ( X290 @ id @ ( ap @ ( sub @ X301 @ id ) @ X302 ) @ id )
= $true )
| ( ( X290 @ id @ X302 @ id )
!= $true ) ) ) )
& ( ! [X303: term,X304: term,X305: term,X306: term] :
( ( X303 = X305 )
| ( ( ap @ X304 @ X305 )
!= ( ap @ X306 @ X303 ) ) )
<=> ( apinj2 = $true ) )
& ( lamnotvar = $true )
& ( ! [X307: subst] :
( ( comp @ id @ X307 )
= X307 )
<=> ( axidl = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasapnotvar = $true )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X308: subst > term > subst > $o] :
~ ! [X309: term > $o] :
~ ! [X310: term] :
( ( X309 @ X310 )
= ( X308 @ id @ X310 @ id ) )
=> ( ! [X311: term > $o,X312: term] :
( ~ ! [X313: term,X314: term] :
( ( ( X311 @ X314 )
!= $true )
| ( $true
= ( X311 @ ( ap @ X313 @ X314 ) ) )
| ( $true
!= ( X311 @ X313 ) ) )
| ( $true
= ( X311 @ X312 ) )
| ~ ! [X315: term] :
( ( ( X311 @ X315 )
= $true )
| ( $true
!= ( var @ X315 ) ) )
| ~ ! [X316: term] :
( ~ ! [X317: term] :
( ( $true
!= ( X311 @ X317 ) )
| ( ( X311 @ ( sub @ X316 @ ( push @ X317 @ id ) ) )
= $true ) )
| ( ( X311 @ ( lam @ X316 ) )
= $true ) ) )
=> ( ! [X318: term] :
( ( sub @ X318 @ id )
= X318 )
=> ( ! [X319: term > $o,X320: term,X321: subst > term > subst > $o] :
( ~ ! [X322: term] :
( ( X319 @ X322 )
= ( X321 @ id @ X322 @ id ) )
| ~ ! [X323: term] :
( ( ( X319 @ ( sub @ X320 @ ( push @ X323 @ id ) ) )
= $true )
| ( ( X319 @ X323 )
!= $true ) )
| ( ( X319 @ ( lam @ X320 ) )
= $true )
| ~ ! [X324: subst > term > term] :
( ~ ! [X325: term] :
( ( $true
!= ( X321 @ id @ X325 @ id ) )
| ( ( X321 @ id @ ( X324 @ id @ X325 ) @ id )
= $true ) )
| ~ ! [X326: term,X327: subst,X328: subst] :
( ( sub @ ( X324 @ X328 @ X326 ) @ X327 )
= ( X324 @ ( comp @ X328 @ X327 ) @ ( sub @ X326 @ X327 ) ) )
| ( $true
= ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id ) ) ) )
=> ! [X329: subst > term > subst > $o,X330: term] :
( ~ ! [X331: subst > term > term] :
( ~ ! [X332: term] :
( ( $true
!= ( X329 @ id @ X332 @ id ) )
| ( ( X329 @ id @ ( X331 @ id @ X332 ) @ id )
= $true ) )
| ~ ! [X333: subst,X334: subst,X335: term] :
( ( sub @ ( X331 @ X334 @ X335 ) @ X333 )
= ( X331 @ ( comp @ X334 @ X333 ) @ ( sub @ X335 @ X333 ) ) )
| ( $true
= ( X329 @ id @ ( lam @ ( X331 @ sh @ one ) ) @ id ) ) )
| ~ ! [X336: term,X337: term] :
( ( ( X329 @ id @ X337 @ id )
!= $true )
| ( ( X329 @ id @ ( ap @ ( sub @ X337 @ id ) @ X336 ) @ id )
= $true )
| ( ( X329 @ id @ X336 @ id )
!= $true ) )
| ( ( X329 @ id @ X330 @ id )
= $true ) ) ) ) ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X338: term] :
( ( sub @ X338 @ id )
= X338 )
=> ( ! [X339: subst > term > subst > $o,X340: term] :
( ~ ! [X341: subst > term > term] :
( ( ( X339 @ id @ ( lam @ ( X341 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X342: term] :
( ( ( X339 @ id @ X342 @ id )
!= $true )
| ( $true
= ( X339 @ id @ ( X341 @ id @ X342 ) @ id ) ) )
| ~ ! [X343: term,X344: subst,X345: subst] :
( ( sub @ ( X341 @ X345 @ X343 ) @ X344 )
= ( X341 @ ( comp @ X345 @ X344 ) @ ( sub @ X343 @ X344 ) ) ) )
| ~ ! [X346: term] :
( ( $true
= ( X339 @ id @ ( sub @ X340 @ ( push @ X346 @ id ) ) @ id ) )
| ( ( X339 @ id @ X346 @ id )
!= $true ) )
| ( ( X339 @ id @ ( lam @ ( sub @ X340 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X347: term,X348: subst > term > subst > $o] :
( ~ ! [X349: term] :
( ( ( X348 @ id @ ( sub @ X347 @ ( push @ X349 @ id ) ) @ id )
= $true )
| ( $true
!= ( X348 @ id @ X349 @ id ) ) )
| ~ ! [X350: subst > term > term] :
( ~ ! [X351: term,X352: subst,X353: subst] :
( ( X350 @ ( comp @ X352 @ X353 ) @ ( sub @ X351 @ X353 ) )
= ( sub @ ( X350 @ X352 @ X351 ) @ X353 ) )
| ~ ! [X354: term] :
( ( ( X348 @ id @ ( X350 @ id @ X354 ) @ id )
= $true )
| ( $true
!= ( X348 @ id @ X354 @ id ) ) )
| ( $true
= ( X348 @ id @ ( lam @ ( X350 @ sh @ one ) ) @ id ) ) )
| ( ( X348 @ id @ ( lam @ X347 ) @ id )
= $true )
| ~ ! [X355: subst,X356: subst,X357: subst,X358: term] :
( ( ( X348 @ X357 @ X358 @ ( comp @ X355 @ X356 ) )
!= $true )
| ( ( X348 @ ( comp @ X357 @ X355 ) @ ( sub @ X358 @ X355 ) @ X356 )
= $true ) )
| ~ ! [X359: term,X360: subst,X361: subst,X362: subst] :
( ( ( X348 @ X361 @ X359 @ ( comp @ X362 @ X360 ) )
= $true )
| ( ( X348 @ ( comp @ X361 @ X362 ) @ ( sub @ X359 @ X362 ) @ X360 )
!= $true ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
<=> ( axvarid = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X364: term] :
? [X365: d_term] :
( ( d2term @ X365 )
= X364 )
& ( pushprop_lem2v2 = $true )
& ( ( ! [X366: term,X367: term > $o] :
( ~ ! [X368: term,X369: term] :
( ( ( X367 @ X368 )
!= $true )
| ( $true
!= ( X367 @ X369 ) )
| ( ( X367 @ ( ap @ X369 @ X368 ) )
= $true ) )
| ( $true
= ( X367 @ X366 ) )
| ~ ! [X370: term] :
( ~ ! [X371: term] :
( ( ( X367 @ ( sub @ X370 @ ( push @ X371 @ id ) ) )
= $true )
| ( $true
!= ( X367 @ X371 ) ) )
| ( ( X367 @ ( lam @ X370 ) )
= $true ) )
| ~ ! [X372: term] :
( ( ( X367 @ X372 )
= $true )
| ( $true
!= ( var @ X372 ) ) ) )
=> ( ! [X373: term,X374: term,X375: subst > term > subst > $o] :
( ( ( X375 @ id @ ( ap @ X373 @ X374 ) @ id )
= $true )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X375 @ ( comp @ X376 @ X377 ) @ ( sub @ X379 @ X377 ) @ X378 )
!= $true )
| ( ( X375 @ X376 @ X379 @ ( comp @ X377 @ X378 ) )
= $true ) )
| ( ( X375 @ id @ X373 @ id )
!= $true )
| ( $true
!= ( X375 @ id @ X374 @ id ) )
| ~ ! [X380: subst,X381: subst,X382: subst,X383: term] :
( ( ( X375 @ ( comp @ X381 @ X380 ) @ ( sub @ X383 @ X380 ) @ X382 )
= $true )
| ( ( X375 @ X381 @ X383 @ ( comp @ X380 @ X382 ) )
!= $true ) )
| ~ ! [X384: term,X385: term] :
( ( $true
!= ( X375 @ id @ X384 @ id ) )
| ( ( X375 @ id @ X385 @ id )
!= $true )
| ( $true
= ( X375 @ id @ ( ap @ ( sub @ X384 @ id ) @ X385 ) @ id ) ) ) )
=> ( ! [X386: subst > term > subst > $o,X387: term] :
( ~ ! [X388: subst,X389: term,X390: subst,X391: subst] :
( ( ( X386 @ ( comp @ X391 @ X390 ) @ ( sub @ X389 @ X390 ) @ X388 )
= $true )
| ( ( X386 @ X391 @ X389 @ ( comp @ X390 @ X388 ) )
!= $true ) )
| ( ( X386 @ id @ ( lam @ X387 ) @ id )
= $true )
| ~ ! [X392: subst,X393: subst,X394: subst,X395: term] :
( ( $true
!= ( X386 @ ( comp @ X394 @ X392 ) @ ( sub @ X395 @ X392 ) @ X393 ) )
| ( ( X386 @ X394 @ X395 @ ( comp @ X392 @ X393 ) )
= $true ) )
| ~ ! [X396: term] :
( ( ( X386 @ id @ X396 @ id )
!= $true )
| ( ( X386 @ id @ ( sub @ X387 @ ( push @ X396 @ id ) ) @ id )
= $true ) )
| ~ ! [X397: subst > term > term] :
( ( ( X386 @ id @ ( lam @ ( X397 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X398: term] :
( ( $true
!= ( X386 @ id @ X398 @ id ) )
| ( ( X386 @ id @ ( X397 @ id @ X398 ) @ id )
= $true ) )
| ~ ! [X399: term,X400: subst,X401: subst] :
( ( X397 @ ( comp @ X401 @ X400 ) @ ( sub @ X399 @ X400 ) )
= ( sub @ ( X397 @ X401 @ X399 ) @ X400 ) ) ) )
=> ! [X402: term,X403: subst > term > subst > $o] :
( ~ ! [X404: term,X405: subst,X406: subst,X407: subst] :
( ( ( X403 @ X405 @ X404 @ ( comp @ X407 @ X406 ) )
!= $true )
| ( ( X403 @ ( comp @ X405 @ X407 ) @ ( sub @ X404 @ X407 ) @ X406 )
= $true ) )
| ~ ! [X408: subst > term > term] :
( ~ ! [X409: term] :
( ( ( X403 @ id @ X409 @ id )
!= $true )
| ( ( X403 @ id @ ( X408 @ id @ X409 ) @ id )
= $true ) )
| ~ ! [X410: term,X411: subst,X412: subst] :
( ( sub @ ( X408 @ X412 @ X410 ) @ X411 )
= ( X408 @ ( comp @ X412 @ X411 ) @ ( sub @ X410 @ X411 ) ) )
| ( ( X403 @ id @ ( lam @ ( X408 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X403 @ id @ X402 @ id )
= $true )
| ~ ! [X413: term,X414: term] :
( ( $true
!= ( X403 @ id @ X413 @ id ) )
| ( ( X403 @ id @ X414 @ id )
!= $true )
| ( ( X403 @ id @ ( ap @ ( sub @ X414 @ id ) @ X413 ) @ id )
= $true ) )
| ~ ! [X415: term] :
( ( $true
= ( X403 @ id @ X415 @ id ) )
| ( ( var @ ( sub @ X415 @ id ) )
!= $true ) )
| ~ ! [X416: subst,X417: subst,X418: subst,X419: term] :
( ( $true
= ( X403 @ X416 @ X419 @ ( comp @ X417 @ X418 ) ) )
| ( ( X403 @ ( comp @ X416 @ X417 ) @ ( sub @ X419 @ X417 ) @ X418 )
!= $true ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( pushprop_lthm_orig = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ! [X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ~ ! [X423: term] :
( ( $true
= ( X421 @ ( sub @ X420 @ ( push @ X423 @ id ) ) ) )
| ( ( X421 @ X423 )
!= $true ) )
| ( ( X421 @ ( lam @ X420 ) )
= $true )
| ~ ! [X424: subst > term > term] :
( ~ ! [X425: term,X426: subst,X427: subst] :
( ( X424 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) )
= ( sub @ ( X424 @ X427 @ X425 ) @ X426 ) )
| ( ( X422 @ id @ ( lam @ ( X424 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X428: term] :
( ( ( X422 @ id @ X428 @ id )
!= $true )
| ( ( X422 @ id @ ( X424 @ id @ X428 ) @ id )
= $true ) ) )
| ~ ! [X429: term] :
( ( X422 @ id @ X429 @ id )
= ( X421 @ X429 ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X432: subst > term > subst > $o,X433: term,X434: term > $o] :
( ( ( X434 @ ( lam @ X433 ) )
= $true )
| ~ ! [X435: subst > term > term] :
( ( ( X432 @ id @ ( lam @ ( X435 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X436: subst,X437: term,X438: subst] :
( ( X435 @ ( comp @ X438 @ X436 ) @ ( sub @ X437 @ X436 ) )
= ( sub @ ( X435 @ X438 @ X437 ) @ X436 ) )
| ~ ! [X439: term] :
( ( ( X432 @ id @ X439 @ id )
!= $true )
| ( ( X432 @ id @ ( X435 @ id @ X439 ) @ id )
= $true ) ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ( $true
!= ( X432 @ X443 @ X441 @ ( comp @ X442 @ X440 ) ) )
| ( ( X432 @ ( comp @ X443 @ X442 ) @ ( sub @ X441 @ X442 ) @ X440 )
= $true ) )
| ~ ! [X444: term,X445: subst,X446: subst,X447: subst] :
( ( $true
= ( X432 @ X446 @ X444 @ ( comp @ X447 @ X445 ) ) )
| ( ( X432 @ ( comp @ X446 @ X447 ) @ ( sub @ X444 @ X447 ) @ X445 )
!= $true ) )
| ~ ! [X448: term] :
( ( X434 @ X448 )
= ( X432 @ id @ X448 @ id ) )
| ~ ! [X449: term] :
( ( ( X434 @ ( sub @ X433 @ ( push @ X449 @ id ) ) )
= $true )
| ( ( X434 @ X449 )
!= $true ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X450: subst > term > subst > $o,X451: term] :
( ~ ! [X452: subst > term > term] :
( ~ ! [X453: subst,X454: subst,X455: term] :
( ( X452 @ ( comp @ X453 @ X454 ) @ ( sub @ X455 @ X454 ) )
= ( sub @ ( X452 @ X453 @ X455 ) @ X454 ) )
| ~ ! [X456: term] :
( ( $true
= ( X450 @ id @ ( X452 @ id @ X456 ) @ id ) )
| ( ( X450 @ id @ X456 @ id )
!= $true ) )
| ( $true
= ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X450 @ id @ ( lam @ X451 ) @ id ) )
| ~ ! [X457: term] :
( ( ( X450 @ id @ ( sub @ X451 @ ( push @ X457 @ id ) ) @ id )
= $true )
| ( ( X450 @ id @ X457 @ id )
!= $true ) ) ) )
& ( induction2_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X458: term] :
~ ! [X459: subst > term > term] :
~ ! [X460: subst,X461: term] :
( ( sub @ X458 @ ( push @ X461 @ X460 ) )
= ( X459 @ X460 @ X461 ) ) )
& ( ( ! [X462: term,X463: subst] :
( ( sub @ one @ ( push @ X462 @ X463 ) )
= X462 )
=> ( ! [X464: term,X465: subst] :
( ( comp @ sh @ ( push @ X464 @ X465 ) )
= X465 )
=> ( ! [X466: subst] :
( ( comp @ X466 @ id )
= X466 )
=> ( ! [X467: term,X468: term > $o] :
( ~ ! [X469: term,X470: term] :
( ( ( X468 @ X469 )
!= $true )
| ( ( X468 @ ( ap @ X470 @ X469 ) )
= $true )
| ( $true
!= ( X468 @ X470 ) ) )
| ( ( X468 @ X467 )
= $true )
| ~ ! [X471: term] :
( ( ( X468 @ X471 )
= $true )
| ( $true
!= ( var @ X471 ) ) )
| ~ ! [X472: term] :
( ( ( X468 @ X472 )
!= $true )
| ( $true
= ( X468 @ ( lam @ X472 ) ) ) ) )
=> ! [X473: term,X474: term > $o,X475: subst] :
( ~ ! [X476: term] :
( ( ( X474 @ ( lam @ X476 ) )
= $true )
| ~ ! [X477: term] :
( ( ( X474 @ ( sub @ X476 @ ( push @ X477 @ id ) ) )
= $true )
| ( $true
!= ( X474 @ X477 ) ) ) )
| ~ ! [X478: term] :
( ( $true
= ( X474 @ ( sub @ X478 @ X475 ) ) )
| ( $true
!= ( var @ X478 ) ) )
| ( ( X474 @ ( sub @ X473 @ X475 ) )
= $true )
| ~ ! [X479: term,X480: term] :
( ( ( X474 @ ( ap @ X479 @ X480 ) )
= $true )
| ( ( X474 @ X479 )
!= $true )
| ( ( X474 @ X480 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( apnotvar = $true )
& ( axabs = $true )
& ( hoaslamnotvar = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X481: term,X482: subst] :
( ( sub @ one @ ( push @ X481 @ X482 ) )
= X481 )
=> ( ! [X483: term,X484: subst] :
( ( comp @ sh @ ( push @ X483 @ X484 ) )
= X484 )
=> ( ! [X485: term,X486: term] :
( ( ( lam @ X485 )
!= ( lam @ X486 ) )
| ( X485 = X486 ) )
=> ! [X487: term,X488: subst,X489: subst > term > term,X490: subst > term > term] :
( ( ( X490 @ X488 @ X487 )
= ( X489 @ X488 @ X487 ) )
| ~ ! [X491: subst,X492: term,X493: subst] :
( ( sub @ ( X489 @ X493 @ X492 ) @ X491 )
= ( X489 @ ( comp @ X493 @ X491 ) @ ( sub @ X492 @ X491 ) ) )
| ( ( lam @ ( X490 @ sh @ one ) )
!= ( lam @ ( X489 @ sh @ one ) ) )
| ~ ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X490 @ X494 @ X495 ) @ X496 )
= ( X490 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) ) ) ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X497: term,X498: subst > term > subst > $o] :
( ( $true
= ( X498 @ id @ ( lam @ ( sub @ X497 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X499: term] :
( ( $true
!= ( X498 @ id @ X499 @ id ) )
| ( ( X498 @ id @ ( sub @ X497 @ ( push @ X499 @ id ) ) @ id )
= $true ) )
| ~ ! [X500: subst > term > term,X501: term] :
( ~ ! [X502: subst,X503: subst,X504: term] :
( ( sub @ ( X500 @ X502 @ X504 ) @ X503 )
= ( sub @ ( sub @ X501 @ ( push @ X504 @ X502 ) ) @ X503 ) )
| ( $true
= ( X498 @ id @ ( lam @ ( X500 @ sh @ one ) ) @ id ) )
| ~ ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( ( X498 @ id @ ( X500 @ id @ X505 ) @ id )
= $true ) )
| ~ ! [X506: subst,X507: subst,X508: term] :
( ( X500 @ ( comp @ X506 @ X507 ) @ ( sub @ X508 @ X507 ) )
= ( sub @ X501 @ ( push @ ( sub @ X508 @ X507 ) @ ( comp @ X506 @ X507 ) ) ) ) ) ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X509: term,X510: subst] :
( ( sub @ one @ ( push @ X509 @ X510 ) )
= X509 )
=> ( ! [X511: subst,X512: term] :
( ( comp @ sh @ ( push @ X512 @ X511 ) )
= X511 )
=> ! [X513: subst,X514: term > $o,X515: term,X516: term,X517: term > $o] :
( ( ( X514 @ ( sub @ X516 @ ( push @ X515 @ X513 ) ) )
= $true )
| ( ( X517 @ X516 )
!= $true ) ) ) ) )
& ( axvarshift = $true )
& ( ( induction2lem = $true )
<=> ! [X518: subst,X519: term,X520: term > $o] :
( ~ ! [X521: term] :
( ( ( X520 @ ( sub @ X521 @ X518 ) )
= $true )
| ( ( var @ X521 )
!= $true ) )
| ~ ! [X522: term,X523: term] :
( ( ( X520 @ X523 )
!= $true )
| ( ( X520 @ ( ap @ X523 @ X522 ) )
= $true )
| ( $true
!= ( X520 @ X522 ) ) )
| ~ ! [X524: term] :
( ( ( X520 @ ( lam @ X524 ) )
= $true )
| ~ ! [X525: term] :
( ( $true
= ( X520 @ ( sub @ X524 @ ( push @ X525 @ id ) ) ) )
| ( ( X520 @ X525 )
!= $true ) ) )
| ( $true
= ( X520 @ ( sub @ X519 @ X518 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X526: term] :
( ( sub @ X526 @ id )
= X526 )
=> ( ! [X527: term > $o,X528: subst,X529: term] :
( ~ ! [X530: term] :
( ( ( var @ X530 )
!= $true )
| ( $true
= ( X527 @ ( sub @ X530 @ X528 ) ) ) )
| ~ ! [X531: term] :
( ~ ! [X532: term] :
( ( ( X527 @ X532 )
!= $true )
| ( ( X527 @ ( sub @ X531 @ ( push @ X532 @ id ) ) )
= $true ) )
| ( ( X527 @ ( lam @ X531 ) )
= $true ) )
| ~ ! [X533: term,X534: term] :
( ( $true
!= ( X527 @ X534 ) )
| ( ( X527 @ X533 )
!= $true )
| ( ( X527 @ ( ap @ X533 @ X534 ) )
= $true ) )
| ( $true
= ( X527 @ ( sub @ X529 @ X528 ) ) ) )
=> ! [X535: term > $o,X536: term] :
( ( ( X535 @ X536 )
= $true )
| ~ ! [X537: term] :
( ~ ! [X538: term] :
( ( ( X535 @ ( sub @ X537 @ ( push @ X538 @ id ) ) )
= $true )
| ( ( X535 @ X538 )
!= $true ) )
| ( $true
= ( X535 @ ( lam @ X537 ) ) ) )
| ~ ! [X539: term] :
( ( ( var @ X539 )
!= $true )
| ( ( X535 @ X539 )
= $true ) )
| ~ ! [X540: term,X541: term] :
( ( ( X535 @ X541 )
!= $true )
| ( ( X535 @ ( ap @ X540 @ X541 ) )
= $true )
| ( ( X535 @ X540 )
!= $true ) ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasapinj1_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( ( ap @ X543 @ X545 )
!= ( ap @ X544 @ X542 ) )
| ( X542 = X545 ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( X546 = X548 )
| ( ( ap @ ( sub @ X549 @ id ) @ X548 )
!= ( ap @ ( sub @ X547 @ id ) @ X546 ) ) ) ) )
& ( axapp = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( substmonoid_gthm
& axmap
& ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( lam @ X1 ) )
| ( X0 = X1 ) )
<=> laminj )
& ( ! [X2: term,X3: term > $o,X4: subst,X5: term,X6: term > $o] :
( ( X6 @ ( sub @ X2 @ ( push @ X5 @ X4 ) ) )
| ~ ( X3 @ X2 ) )
<=> pushprop_lem1 )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X7: term] :
( ( sub @ X7 @ id )
= X7 )
=> ( ! [X8: term,X9: subst > term > subst > $o] :
( ( X9 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X10: subst > term > term] :
( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
| ~ ! [X11: subst,X12: term,X13: subst] :
( ( sub @ ( X10 @ X11 @ X12 ) @ X13 )
= ( X10 @ ( comp @ X11 @ X13 ) @ ( sub @ X12 @ X13 ) ) )
| ~ ! [X14: term] :
( ~ ( X9 @ id @ X14 @ id )
| ( X9 @ id @ ( X10 @ id @ X14 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X9 @ id @ X15 @ id )
| ( X9 @ id @ ( sub @ X8 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X16: term,X17: subst > term > subst > $o] :
( ~ ! [X18: term] :
( ( X17 @ id @ ( sub @ X16 @ ( push @ X18 @ id ) ) @ id )
| ~ ( X17 @ id @ X18 @ id ) )
| ( X17 @ id @ ( lam @ X16 ) @ id )
| ~ ! [X19: subst > term > term] :
( ~ ! [X20: subst,X21: subst,X22: term] :
( ( X19 @ ( comp @ X21 @ X20 ) @ ( sub @ X22 @ X20 ) )
= ( sub @ ( X19 @ X21 @ X22 ) @ X20 ) )
| ~ ! [X23: term] :
( ( X17 @ id @ ( X19 @ id @ X23 ) @ id )
| ~ ( X17 @ id @ X23 @ id ) )
| ( X17 @ id @ ( lam @ ( X19 @ sh @ one ) ) @ id ) ) ) ) ) )
& hoasinduction_lem3a_gthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ulamvarsh
& hoasinduction_lem3b_gthm
& ( hoasinduction_lem0_lthm
<=> ! [X24: subst > term > subst > $o] :
~ ! [X25: term > $o] :
~ ! [X26: term] :
( ( X24 @ id @ X26 @ id )
= ( X25 @ X26 ) ) )
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X27: term] :
~ ! [X28: subst > term > term] :
~ ! [X29: subst,X30: term] :
( ( X28 @ X29 @ X30 )
= ( sub @ X27 @ ( push @ X30 @ X29 ) ) ) )
& ( ! [X31: term,X32: term,X33: term,X34: term] :
( ( X33 = X34 )
| ( ( ap @ ( sub @ X32 @ id ) @ X33 )
!= ( ap @ ( sub @ X31 @ id ) @ X34 ) ) )
<=> hoasapinj2 )
& ! [X35: d_subst] : ( d_id = X35 )
& pushprop_lem1v2_gthm
& ( hoasinduction
<=> ! [X36: term,X37: subst > term > subst > $o] :
( ~ ! [X38: term,X39: term] :
( ( X37 @ id @ ( ap @ ( sub @ X39 @ id ) @ X38 ) @ id )
| ~ ( X37 @ id @ X39 @ id )
| ~ ( X37 @ id @ X38 @ id ) )
| ~ ! [X40: subst,X41: term,X42: subst,X43: subst] :
( ~ ( X37 @ ( comp @ X40 @ X43 ) @ ( sub @ X41 @ X43 ) @ X42 )
| ( X37 @ X40 @ X41 @ ( comp @ X43 @ X42 ) ) )
| ~ ! [X44: subst,X45: subst,X46: term,X47: subst] :
( ~ ( X37 @ X47 @ X46 @ ( comp @ X44 @ X45 ) )
| ( X37 @ ( comp @ X47 @ X44 ) @ ( sub @ X46 @ X44 ) @ X45 ) )
| ~ ! [X48: subst > term > term] :
( ~ ! [X49: term] :
( ~ ( X37 @ id @ X49 @ id )
| ( X37 @ id @ ( X48 @ id @ X49 ) @ id ) )
| ~ ! [X50: subst,X51: subst,X52: term] :
( ( X48 @ ( comp @ X51 @ X50 ) @ ( sub @ X52 @ X50 ) )
= ( sub @ ( X48 @ X51 @ X52 ) @ X50 ) )
| ( X37 @ id @ ( lam @ ( X48 @ sh @ one ) ) @ id ) )
| ~ ! [X53: term] :
( ( X37 @ id @ X53 @ id )
| ~ ( var @ ( sub @ X53 @ id ) ) )
| ( X37 @ id @ X36 @ id ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lthm_3
<=> ( ! [X54: subst > term > subst > $o] :
~ ! [X55: term > $o] :
~ ! [X56: term] :
( ( X54 @ id @ X56 @ id )
= ( X55 @ X56 ) )
=> ( ! [X57: term,X58: term > $o] :
( ~ ! [X59: term,X60: term] :
( ~ ( X58 @ X59 )
| ~ ( X58 @ X60 )
| ( X58 @ ( ap @ X59 @ X60 ) ) )
| ~ ! [X61: term] :
( ~ ! [X62: term] :
( ( X58 @ ( sub @ X61 @ ( push @ X62 @ id ) ) )
| ~ ( X58 @ X62 ) )
| ( X58 @ ( lam @ X61 ) ) )
| ~ ! [X63: term] :
( ( X58 @ X63 )
| ~ ( var @ X63 ) )
| ( X58 @ X57 ) )
=> ( ! [X64: term] :
( ( sub @ X64 @ id )
= X64 )
=> ( ! [X65: term > $o,X66: term,X67: subst > term > subst > $o] :
( ~ ! [X68: subst > term > term] :
( ~ ! [X69: term] :
( ~ ( X67 @ id @ X69 @ id )
| ( X67 @ id @ ( X68 @ id @ X69 ) @ id ) )
| ( X67 @ id @ ( lam @ ( X68 @ sh @ one ) ) @ id )
| ~ ! [X70: term,X71: subst,X72: subst] :
( ( X68 @ ( comp @ X72 @ X71 ) @ ( sub @ X70 @ X71 ) )
= ( sub @ ( X68 @ X72 @ X70 ) @ X71 ) ) )
| ~ ! [X73: term] :
( ( X65 @ ( sub @ X66 @ ( push @ X73 @ id ) ) )
| ~ ( X65 @ X73 ) )
| ( X65 @ ( lam @ X66 ) )
| ~ ! [X74: term] :
( ( X67 @ id @ X74 @ id )
= ( X65 @ X74 ) ) )
=> ! [X75: subst > term > subst > $o,X76: term] :
( ~ ! [X77: term] :
( ( X75 @ id @ X77 @ id )
| ~ ( var @ ( sub @ X77 @ id ) ) )
| ~ ! [X78: term,X79: subst,X80: subst,X81: subst] :
( ( X75 @ X80 @ X78 @ ( comp @ X81 @ X79 ) )
| ~ ( X75 @ ( comp @ X80 @ X81 ) @ ( sub @ X78 @ X81 ) @ X79 ) )
| ~ ! [X82: subst > term > term] :
( ( X75 @ id @ ( lam @ ( X82 @ sh @ one ) ) @ id )
| ~ ! [X83: term] :
( ~ ( X75 @ id @ X83 @ id )
| ( X75 @ id @ ( X82 @ id @ X83 ) @ id ) )
| ~ ! [X84: subst,X85: term,X86: subst] :
( ( sub @ ( X82 @ X84 @ X85 ) @ X86 )
= ( X82 @ ( comp @ X84 @ X86 ) @ ( sub @ X85 @ X86 ) ) ) )
| ~ ! [X87: subst,X88: subst,X89: term,X90: subst] :
( ( X75 @ ( comp @ X90 @ X87 ) @ ( sub @ X89 @ X87 ) @ X88 )
| ~ ( X75 @ X90 @ X89 @ ( comp @ X87 @ X88 ) ) )
| ~ ! [X91: term,X92: term] :
( ~ ( X75 @ id @ X91 @ id )
| ( X75 @ id @ ( ap @ ( sub @ X91 @ id ) @ X92 ) @ id )
| ~ ( X75 @ id @ X92 @ id ) )
| ( X75 @ id @ X76 @ id ) ) ) ) ) ) )
& ( hoaslamnotap
<=> ! [X93: term,X94: term,X95: subst > term > term] :
( ( ( lam @ ( X95 @ sh @ one ) )
!= ( ap @ ( sub @ X93 @ id ) @ X94 ) )
| ~ ! [X96: subst,X97: term,X98: subst] :
( ( X95 @ ( comp @ X98 @ X96 ) @ ( sub @ X97 @ X96 ) )
= ( sub @ ( X95 @ X98 @ X97 ) @ X96 ) ) ) )
& ~ ulamvar1
& axclos
& ( axidr
<=> ! [X99: subst] :
( ( comp @ X99 @ id )
= X99 ) )
& ! [X100: subst] :
? [X101: d_subst] :
( ( d2subst @ X101 )
= X100 )
& hoasinduction_lem1
& ( ! [X102: subst] :
( ( push @ ( sub @ one @ X102 ) @ ( comp @ sh @ X102 ) )
= X102 )
<=> axscons )
& ( ! [X103: term,X104: subst] :
( ( comp @ sh @ ( push @ X103 @ X104 ) )
= X104 )
<=> axshiftcons )
& ( ( ! [X105: term] :
( ( sub @ X105 @ id )
= X105 )
=> ( ! [X106: term,X107: term,X108: term,X109: term] :
( ( X107 = X108 )
| ( ( ap @ X108 @ X106 )
!= ( ap @ X107 @ X109 ) ) )
=> ! [X110: term,X111: term,X112: term,X113: term] :
( ( ( ap @ ( sub @ X111 @ id ) @ X112 )
!= ( ap @ ( sub @ X113 @ id ) @ X110 ) )
| ( X111 = X113 ) ) ) )
<=> hoasapinj1_lthm )
& ~ lamnotap
& ( ! [X114: term,X115: subst] :
( ( sub @ one @ ( push @ X114 @ X115 ) )
= X114 )
<=> axvarcons )
& pushprop_gthm
& pushprop_lem2v2_lthm
& ! [X116: d_subst,X117: d_subst] :
( ( ( d2subst @ X116 )
= ( d2subst @ X117 ) )
=> ( X116 = X117 ) )
& ( ! [X118: subst > term > subst > $o] :
~ ! [X119: term > $o] :
~ ! [X120: term] :
( ( X118 @ id @ X120 @ id )
= ( X119 @ X120 ) )
<=> hoasinduction_lem0 )
& ( one
= ( d2term @ d_one ) )
& ( ! [X121: subst > term > subst > $o,X122: term] :
( ~ ! [X123: subst > term > term] :
( ~ ! [X124: subst,X125: subst,X126: term] :
( ( X123 @ ( comp @ X125 @ X124 ) @ ( sub @ X126 @ X124 ) )
= ( sub @ ( X123 @ X125 @ X126 ) @ X124 ) )
| ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
| ~ ! [X127: term] :
( ~ ( X121 @ id @ X127 @ id )
| ( X121 @ id @ ( X123 @ id @ X127 ) @ id ) ) )
| ( X121 @ id @ ( lam @ ( sub @ X122 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X128: term] :
( ( X121 @ id @ ( sub @ X122 @ ( push @ X128 @ id ) ) @ id )
| ~ ( X121 @ id @ X128 @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ulamvarind
& hoasinduction_lem2v2_gthm
& hoasinduction_gthm
& hoasinduction_lem1_lthm
& pushprop_lem3v2_lthm
& ( ! [X129: term] :
~ ! [X130: subst > term > term] :
( ( sub @ X129 @ ( push @ one @ sh ) )
!= ( X130 @ sh @ one ) )
<=> hoasinduction_lem3b_lthm )
& ( induction
<=> ! [X131: term > $o,X132: term] :
( ~ ! [X133: term,X134: term] :
( ~ ( X131 @ X134 )
| ( X131 @ ( ap @ X133 @ X134 ) )
| ~ ( X131 @ X133 ) )
| ~ ! [X135: term] :
( ( X131 @ ( lam @ X135 ) )
| ~ ( X131 @ X135 ) )
| ~ ! [X136: term] :
( ( X131 @ X136 )
| ~ ( var @ X136 ) )
| ( X131 @ X132 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X137: subst,X138: term,X139: term > $o] :
~ ! [X140: term > $o] :
~ ! [X141: term] :
( ( X139 @ ( sub @ X141 @ ( push @ X138 @ X137 ) ) )
= ( X140 @ X141 ) )
<=> pushprop_lem0 )
& ( ! [X142: subst,X143: term,X144: term > $o,X145: term > $o] :
( ( X144 @ one )
| ~ ( X145 @ X143 )
| ~ ! [X146: term] :
( ( X145 @ ( sub @ X146 @ ( push @ X143 @ X142 ) ) )
= ( X144 @ X146 ) ) )
<=> pushprop_lem1v2 )
& ( pushprop_p_and_p_prime
= ( ^ [X147: term,X148: subst,X149: term > $o,X150: term > $o] :
! [X151: term] :
( ( X150 @ X151 )
= ( X149 @ ( sub @ X151 @ ( push @ X147 @ X148 ) ) ) ) ) )
& ( ( ! [X152: term] :
( ( sub @ X152 @ id )
= X152 )
=> ! [X153: subst > term > subst > $o,X154: term,X155: term > $o] :
( ~ ! [X156: term] :
( ~ ( X155 @ X156 )
| ( X155 @ ( sub @ X154 @ ( push @ X156 @ id ) ) ) )
| ~ ! [X157: term,X158: subst,X159: subst,X160: subst] :
( ( X153 @ ( comp @ X159 @ X158 ) @ ( sub @ X157 @ X158 ) @ X160 )
| ~ ( X153 @ X159 @ X157 @ ( comp @ X158 @ X160 ) ) )
| ~ ! [X161: subst > term > term] :
( ~ ! [X162: term] :
( ( X153 @ id @ ( X161 @ id @ X162 ) @ id )
| ~ ( X153 @ id @ X162 @ id ) )
| ~ ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X161 @ X163 @ X164 ) @ X165 )
= ( X161 @ ( comp @ X163 @ X165 ) @ ( sub @ X164 @ X165 ) ) )
| ( X153 @ id @ ( lam @ ( X161 @ sh @ one ) ) @ id ) )
| ( X155 @ ( lam @ X154 ) )
| ~ ! [X166: term] :
( ( X153 @ id @ X166 @ id )
= ( X155 @ X166 ) )
| ~ ! [X167: subst,X168: subst,X169: term,X170: subst] :
( ~ ( X153 @ ( comp @ X167 @ X168 ) @ ( sub @ X169 @ X168 ) @ X170 )
| ( X153 @ X167 @ X169 @ ( comp @ X168 @ X170 ) ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& hoasinduction_lem3v2_gthm
& ( apinj1
<=> ! [X171: term,X172: term,X173: term,X174: term] :
( ( X173 = X174 )
| ( ( ap @ X174 @ X172 )
!= ( ap @ X173 @ X171 ) ) ) )
& ! [X175: d_term] : ( d_one = X175 )
& ( termmset_lthm
<=> ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
=> ! [X177: term] :
( ( sub @ X177 @ id )
= X177 ) ) )
& termmset_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem1v2_lthm
<=> ( ! [X178: term,X179: subst] :
( ( sub @ one @ ( push @ X178 @ X179 ) )
= X178 )
=> ! [X180: term > $o,X181: subst,X182: term > $o,X183: term] :
( ( X180 @ one )
| ~ ( X182 @ X183 )
| ~ ! [X184: term] :
( ( X182 @ ( sub @ X184 @ ( push @ X183 @ X181 ) ) )
= ( X180 @ X184 ) ) ) ) )
& ( ! [X185: term,X186: term,X187: subst > term > subst > $o] :
( ~ ( X187 @ id @ X185 @ id )
| ~ ! [X188: subst,X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X189 @ X188 ) @ ( sub @ X190 @ X188 ) @ X191 )
| ~ ( X187 @ X189 @ X190 @ ( comp @ X188 @ X191 ) ) )
| ~ ! [X192: subst,X193: term,X194: subst,X195: subst] :
( ( X187 @ X194 @ X193 @ ( comp @ X192 @ X195 ) )
| ~ ( X187 @ ( comp @ X194 @ X192 ) @ ( sub @ X193 @ X192 ) @ X195 ) )
| ( X187 @ id @ ( ap @ X185 @ X186 ) @ id )
| ~ ! [X196: term,X197: term] :
( ~ ( X187 @ id @ X197 @ id )
| ~ ( X187 @ id @ X196 @ id )
| ( X187 @ id @ ( ap @ ( sub @ X197 @ id ) @ X196 ) @ id ) )
| ~ ( X187 @ id @ X186 @ id ) )
<=> hoasinduction_lem2 )
& pushprop_lthm
& hoasinduction_lem1_gthm
& hoaslamnotap_lthm
& hoasinduction_lem3_gthm
& axassoc
& ( induction2
<=> ! [X198: term,X199: term > $o] :
( ~ ! [X200: term] :
( ~ ( var @ X200 )
| ( X199 @ X200 ) )
| ~ ! [X201: term] :
( ( X199 @ ( lam @ X201 ) )
| ~ ! [X202: term] :
( ( X199 @ ( sub @ X201 @ ( push @ X202 @ id ) ) )
| ~ ( X199 @ X202 ) ) )
| ( X199 @ X198 )
| ~ ! [X203: term,X204: term] :
( ~ ( X199 @ X204 )
| ( X199 @ ( ap @ X203 @ X204 ) )
| ~ ( X199 @ X203 ) ) ) )
& ( hoasinduction_lem3b
<=> ! [X205: term] :
~ ! [X206: subst > term > term] :
( ( sub @ X205 @ ( push @ one @ sh ) )
!= ( X206 @ sh @ one ) ) )
& induction2lem_gthm
& ( ! [X207: subst > term > subst > $o,X208: term] :
( ~ ! [X209: term,X210: term] :
( ~ ( X207 @ id @ X210 @ id )
| ~ ( X207 @ id @ X209 @ id )
| ( X207 @ id @ ( ap @ ( sub @ X209 @ id ) @ X210 ) @ id ) )
| ( X207 @ id @ X208 @ id )
| ~ ! [X211: subst > term > term] :
( ~ ! [X212: subst,X213: subst,X214: term] :
( ( sub @ ( X211 @ X212 @ X214 ) @ X213 )
= ( X211 @ ( comp @ X212 @ X213 ) @ ( sub @ X214 @ X213 ) ) )
| ~ ! [X215: term] :
( ~ ( X207 @ id @ X215 @ id )
| ( X207 @ id @ ( X211 @ id @ X215 ) @ id ) )
| ( X207 @ id @ ( lam @ ( X211 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_no_psi_cond )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop_lem0_lthm
<=> ! [X216: term,X217: term > $o,X218: subst] :
~ ! [X219: term > $o] :
~ ! [X220: term] :
( ( X217 @ ( sub @ X220 @ ( push @ X216 @ X218 ) ) )
= ( X219 @ X220 ) ) )
& hoasapnotvar_gthm
& ( ! [X221: term] :
( ( sub @ X221 @ id )
= X221 )
<=> termmset )
& ( hoaslaminj
<=> ! [X222: subst,X223: subst > term > term,X224: subst > term > term,X225: term] :
( ~ ! [X226: term,X227: subst,X228: subst] :
( ( sub @ ( X224 @ X227 @ X226 ) @ X228 )
= ( X224 @ ( comp @ X227 @ X228 ) @ ( sub @ X226 @ X228 ) ) )
| ~ ! [X229: subst,X230: term,X231: subst] :
( ( sub @ ( X223 @ X231 @ X230 ) @ X229 )
= ( X223 @ ( comp @ X231 @ X229 ) @ ( sub @ X230 @ X229 ) ) )
| ( ( X224 @ X222 @ X225 )
= ( X223 @ X222 @ X225 ) )
| ( ( lam @ ( X223 @ sh @ one ) )
!= ( lam @ ( X224 @ sh @ one ) ) ) ) )
& hoaslamnotvar_gthm
& pushprop_lem0_gthm
& hoaslamnotap_gthm
& ( ( ! [X232: term] :
~ ! [X233: subst > term > term] :
~ ! [X234: subst,X235: term] :
( ( sub @ X232 @ ( push @ X235 @ X234 ) )
= ( X233 @ X234 @ X235 ) )
=> ( ! [X236: term] :
( ( sub @ X236 @ id )
= X236 )
=> ! [X237: subst > term > subst > $o,X238: term > $o,X239: term] :
( ~ ! [X240: term] :
( ( X238 @ X240 )
= ( X237 @ id @ X240 @ id ) )
| ( X238 @ ( lam @ X239 ) )
| ~ ! [X241: term] :
( ( X238 @ ( sub @ X239 @ ( push @ X241 @ id ) ) )
| ~ ( X238 @ X241 ) )
| ~ ! [X242: subst > term > term] :
( ~ ! [X243: term] :
( ( X237 @ id @ ( X242 @ id @ X243 ) @ id )
| ~ ( X237 @ id @ X243 @ id ) )
| ~ ! [X244: term,X245: subst,X246: subst] :
( ( X242 @ ( comp @ X246 @ X245 ) @ ( sub @ X244 @ X245 ) )
= ( sub @ ( X242 @ X246 @ X244 ) @ X245 ) )
| ( X237 @ id @ ( lam @ ( X242 @ sh @ one ) ) @ id ) ) ) ) )
<=> hoasinduction_lem3v2a_lthm )
& pushprop
& ( ! [X247: term,X248: term,X249: term,X250: term] :
( ( X247 = X249 )
| ( ( ap @ ( sub @ X247 @ id ) @ X248 )
!= ( ap @ ( sub @ X249 @ id ) @ X250 ) ) )
<=> hoasapinj1 )
& ( ! [X251: term,X252: term] :
( ( ( sub @ X252 @ sh )
!= ( sub @ X251 @ sh ) )
| ( X251 = X252 ) )
<=> shinj )
& ( ! [X253: subst > term > subst > $o,X254: term] :
( ( X253 @ id @ ( lam @ ( sub @ X254 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X255: term] :
( ~ ( X253 @ id @ X255 @ id )
| ( X253 @ id @ ( sub @ X254 @ ( push @ X255 @ id ) ) @ id ) )
| ~ ! [X256: subst > term > term] :
( ~ ! [X257: term] :
( ( X253 @ id @ ( X256 @ id @ X257 ) @ id )
| ~ ( X253 @ id @ X257 @ id ) )
| ( X253 @ id @ ( lam @ ( X256 @ sh @ one ) ) @ id )
| ~ ! [X258: term,X259: subst,X260: subst] :
( ( X256 @ ( comp @ X260 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X256 @ X260 @ X258 ) @ X259 ) ) ) )
<=> hoasinduction_lem3aa )
& ! [X261: d_term,X262: d_term] :
( ( ( d2term @ X262 )
= ( d2term @ X261 ) )
=> ( X261 = X262 ) )
& hoasapnotvar_lthm
& ( hoasinduction_lem3
<=> ! [X263: subst > term > subst > $o,X264: term] :
( ~ ! [X265: subst,X266: term,X267: subst,X268: subst] :
( ~ ( X263 @ ( comp @ X265 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 )
| ( X263 @ X265 @ X266 @ ( comp @ X268 @ X267 ) ) )
| ~ ! [X269: term,X270: subst,X271: subst,X272: subst] :
( ( X263 @ ( comp @ X270 @ X271 ) @ ( sub @ X269 @ X271 ) @ X272 )
| ~ ( X263 @ X270 @ X269 @ ( comp @ X271 @ X272 ) ) )
| ~ ! [X273: term] :
( ( X263 @ id @ ( sub @ X264 @ ( push @ X273 @ id ) ) @ id )
| ~ ( X263 @ id @ X273 @ id ) )
| ( X263 @ id @ ( lam @ X264 ) @ id )
| ~ ! [X274: subst > term > term] :
( ( X263 @ id @ ( lam @ ( X274 @ sh @ one ) ) @ id )
| ~ ! [X275: subst,X276: subst,X277: term] :
( ( X274 @ ( comp @ X275 @ X276 ) @ ( sub @ X277 @ X276 ) )
= ( sub @ ( X274 @ X275 @ X277 ) @ X276 ) )
| ~ ! [X278: term] :
( ~ ( X263 @ id @ X278 @ id )
| ( X263 @ id @ ( X274 @ id @ X278 ) @ id ) ) ) ) )
& ( ( ^ [X279: subst > term > subst > $o,X280: term > $o] :
! [X281: term] :
( ( X279 @ id @ X281 @ id )
= ( X280 @ X281 ) ) )
= hoasinduction_p_and_p_prime )
& ( ( ! [X282: subst] :
( ( comp @ X282 @ id )
= X282 )
& ! [X283: subst] :
( ( comp @ id @ X283 )
= X283 ) )
<=> substmonoid )
& ( substmonoid_lthm
<=> ( ! [X284: subst] :
( ( comp @ id @ X284 )
= X284 )
=> ( ! [X285: subst] :
( ( comp @ X285 @ id )
= X285 )
=> ( ! [X286: subst] :
( ( comp @ X286 @ id )
= X286 )
& ! [X287: subst] :
( ( comp @ id @ X287 )
= X287 ) ) ) ) )
& ( hoasinduction_lem2v2
<=> ! [X288: term,X289: term,X290: subst > term > subst > $o,X291: term > $o] :
( ~ ! [X292: subst,X293: subst,X294: term,X295: subst] :
( ( X290 @ X293 @ X294 @ ( comp @ X292 @ X295 ) )
| ~ ( X290 @ ( comp @ X293 @ X292 ) @ ( sub @ X294 @ X292 ) @ X295 ) )
| ~ ! [X296: term] :
( ( X290 @ id @ X296 @ id )
= ( X291 @ X296 ) )
| ~ ! [X297: subst,X298: subst,X299: term,X300: subst] :
( ~ ( X290 @ X297 @ X299 @ ( comp @ X298 @ X300 ) )
| ( X290 @ ( comp @ X297 @ X298 ) @ ( sub @ X299 @ X298 ) @ X300 ) )
| ~ ( X291 @ X289 )
| ~ ( X291 @ X288 )
| ( X291 @ ( ap @ X288 @ X289 ) )
| ~ ! [X301: term,X302: term] :
( ~ ( X290 @ id @ X301 @ id )
| ( X290 @ id @ ( ap @ ( sub @ X301 @ id ) @ X302 ) @ id )
| ~ ( X290 @ id @ X302 @ id ) ) ) )
& ( ! [X303: term,X304: term,X305: term,X306: term] :
( ( X303 = X305 )
| ( ( ap @ X304 @ X305 )
!= ( ap @ X306 @ X303 ) ) )
<=> apinj2 )
& lamnotvar
& ( ! [X307: subst] :
( ( comp @ id @ X307 )
= X307 )
<=> axidl )
& hoasapinj2_gthm
& ( ( d2subst @ d_id )
= id )
& hoasapnotvar
& hoaslaminj_gthm
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X308: subst > term > subst > $o] :
~ ! [X309: term > $o] :
~ ! [X310: term] :
( ( X309 @ X310 )
= ( X308 @ id @ X310 @ id ) )
=> ( ! [X311: term > $o,X312: term] :
( ~ ! [X313: term,X314: term] :
( ~ ( X311 @ X314 )
| ( X311 @ ( ap @ X313 @ X314 ) )
| ~ ( X311 @ X313 ) )
| ( X311 @ X312 )
| ~ ! [X315: term] :
( ( X311 @ X315 )
| ~ ( var @ X315 ) )
| ~ ! [X316: term] :
( ~ ! [X317: term] :
( ~ ( X311 @ X317 )
| ( X311 @ ( sub @ X316 @ ( push @ X317 @ id ) ) ) )
| ( X311 @ ( lam @ X316 ) ) ) )
=> ( ! [X318: term] :
( ( sub @ X318 @ id )
= X318 )
=> ( ! [X319: term > $o,X320: term,X321: subst > term > subst > $o] :
( ~ ! [X322: term] :
( ( X319 @ X322 )
= ( X321 @ id @ X322 @ id ) )
| ~ ! [X323: term] :
( ( X319 @ ( sub @ X320 @ ( push @ X323 @ id ) ) )
| ~ ( X319 @ X323 ) )
| ( X319 @ ( lam @ X320 ) )
| ~ ! [X324: subst > term > term] :
( ~ ! [X325: term] :
( ~ ( X321 @ id @ X325 @ id )
| ( X321 @ id @ ( X324 @ id @ X325 ) @ id ) )
| ~ ! [X326: term,X327: subst,X328: subst] :
( ( sub @ ( X324 @ X328 @ X326 ) @ X327 )
= ( X324 @ ( comp @ X328 @ X327 ) @ ( sub @ X326 @ X327 ) ) )
| ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id ) ) )
=> ! [X329: subst > term > subst > $o,X330: term] :
( ~ ! [X331: subst > term > term] :
( ~ ! [X332: term] :
( ~ ( X329 @ id @ X332 @ id )
| ( X329 @ id @ ( X331 @ id @ X332 ) @ id ) )
| ~ ! [X333: subst,X334: subst,X335: term] :
( ( sub @ ( X331 @ X334 @ X335 ) @ X333 )
= ( X331 @ ( comp @ X334 @ X333 ) @ ( sub @ X335 @ X333 ) ) )
| ( X329 @ id @ ( lam @ ( X331 @ sh @ one ) ) @ id ) )
| ~ ! [X336: term,X337: term] :
( ~ ( X329 @ id @ X337 @ id )
| ( X329 @ id @ ( ap @ ( sub @ X337 @ id ) @ X336 ) @ id )
| ~ ( X329 @ id @ X336 @ id ) )
| ( X329 @ id @ X330 @ id ) ) ) ) ) ) )
& ( hoasinduction_lem3_lthm
<=> ( ! [X338: term] :
( ( sub @ X338 @ id )
= X338 )
=> ( ! [X339: subst > term > subst > $o,X340: term] :
( ~ ! [X341: subst > term > term] :
( ( X339 @ id @ ( lam @ ( X341 @ sh @ one ) ) @ id )
| ~ ! [X342: term] :
( ~ ( X339 @ id @ X342 @ id )
| ( X339 @ id @ ( X341 @ id @ X342 ) @ id ) )
| ~ ! [X343: term,X344: subst,X345: subst] :
( ( sub @ ( X341 @ X345 @ X343 ) @ X344 )
= ( X341 @ ( comp @ X345 @ X344 ) @ ( sub @ X343 @ X344 ) ) ) )
| ~ ! [X346: term] :
( ( X339 @ id @ ( sub @ X340 @ ( push @ X346 @ id ) ) @ id )
| ~ ( X339 @ id @ X346 @ id ) )
| ( X339 @ id @ ( lam @ ( sub @ X340 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X347: term,X348: subst > term > subst > $o] :
( ~ ! [X349: term] :
( ( X348 @ id @ ( sub @ X347 @ ( push @ X349 @ id ) ) @ id )
| ~ ( X348 @ id @ X349 @ id ) )
| ~ ! [X350: subst > term > term] :
( ~ ! [X351: term,X352: subst,X353: subst] :
( ( X350 @ ( comp @ X352 @ X353 ) @ ( sub @ X351 @ X353 ) )
= ( sub @ ( X350 @ X352 @ X351 ) @ X353 ) )
| ~ ! [X354: term] :
( ( X348 @ id @ ( X350 @ id @ X354 ) @ id )
| ~ ( X348 @ id @ X354 @ id ) )
| ( X348 @ id @ ( lam @ ( X350 @ sh @ one ) ) @ id ) )
| ( X348 @ id @ ( lam @ X347 ) @ id )
| ~ ! [X355: subst,X356: subst,X357: subst,X358: term] :
( ~ ( X348 @ X357 @ X358 @ ( comp @ X355 @ X356 ) )
| ( X348 @ ( comp @ X357 @ X355 ) @ ( sub @ X358 @ X355 ) @ X356 ) )
| ~ ! [X359: term,X360: subst,X361: subst,X362: subst] :
( ( X348 @ X361 @ X359 @ ( comp @ X362 @ X360 ) )
| ~ ( X348 @ ( comp @ X361 @ X362 ) @ ( sub @ X359 @ X362 ) @ X360 ) ) ) ) ) )
& hoasinduction_lem2_lthm
& ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
<=> axvarid )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X364: term] :
? [X365: d_term] :
( ( d2term @ X365 )
= X364 )
& pushprop_lem2v2
& ( ( ! [X366: term,X367: term > $o] :
( ~ ! [X368: term,X369: term] :
( ~ ( X367 @ X368 )
| ~ ( X367 @ X369 )
| ( X367 @ ( ap @ X369 @ X368 ) ) )
| ( X367 @ X366 )
| ~ ! [X370: term] :
( ~ ! [X371: term] :
( ( X367 @ ( sub @ X370 @ ( push @ X371 @ id ) ) )
| ~ ( X367 @ X371 ) )
| ( X367 @ ( lam @ X370 ) ) )
| ~ ! [X372: term] :
( ( X367 @ X372 )
| ~ ( var @ X372 ) ) )
=> ( ! [X373: term,X374: term,X375: subst > term > subst > $o] :
( ( X375 @ id @ ( ap @ X373 @ X374 ) @ id )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ~ ( X375 @ ( comp @ X376 @ X377 ) @ ( sub @ X379 @ X377 ) @ X378 )
| ( X375 @ X376 @ X379 @ ( comp @ X377 @ X378 ) ) )
| ~ ( X375 @ id @ X373 @ id )
| ~ ( X375 @ id @ X374 @ id )
| ~ ! [X380: subst,X381: subst,X382: subst,X383: term] :
( ( X375 @ ( comp @ X381 @ X380 ) @ ( sub @ X383 @ X380 ) @ X382 )
| ~ ( X375 @ X381 @ X383 @ ( comp @ X380 @ X382 ) ) )
| ~ ! [X384: term,X385: term] :
( ~ ( X375 @ id @ X384 @ id )
| ~ ( X375 @ id @ X385 @ id )
| ( X375 @ id @ ( ap @ ( sub @ X384 @ id ) @ X385 ) @ id ) ) )
=> ( ! [X386: subst > term > subst > $o,X387: term] :
( ~ ! [X388: subst,X389: term,X390: subst,X391: subst] :
( ( X386 @ ( comp @ X391 @ X390 ) @ ( sub @ X389 @ X390 ) @ X388 )
| ~ ( X386 @ X391 @ X389 @ ( comp @ X390 @ X388 ) ) )
| ( X386 @ id @ ( lam @ X387 ) @ id )
| ~ ! [X392: subst,X393: subst,X394: subst,X395: term] :
( ~ ( X386 @ ( comp @ X394 @ X392 ) @ ( sub @ X395 @ X392 ) @ X393 )
| ( X386 @ X394 @ X395 @ ( comp @ X392 @ X393 ) ) )
| ~ ! [X396: term] :
( ~ ( X386 @ id @ X396 @ id )
| ( X386 @ id @ ( sub @ X387 @ ( push @ X396 @ id ) ) @ id ) )
| ~ ! [X397: subst > term > term] :
( ( X386 @ id @ ( lam @ ( X397 @ sh @ one ) ) @ id )
| ~ ! [X398: term] :
( ~ ( X386 @ id @ X398 @ id )
| ( X386 @ id @ ( X397 @ id @ X398 ) @ id ) )
| ~ ! [X399: term,X400: subst,X401: subst] :
( ( X397 @ ( comp @ X401 @ X400 ) @ ( sub @ X399 @ X400 ) )
= ( sub @ ( X397 @ X401 @ X399 ) @ X400 ) ) ) )
=> ! [X402: term,X403: subst > term > subst > $o] :
( ~ ! [X404: term,X405: subst,X406: subst,X407: subst] :
( ~ ( X403 @ X405 @ X404 @ ( comp @ X407 @ X406 ) )
| ( X403 @ ( comp @ X405 @ X407 ) @ ( sub @ X404 @ X407 ) @ X406 ) )
| ~ ! [X408: subst > term > term] :
( ~ ! [X409: term] :
( ~ ( X403 @ id @ X409 @ id )
| ( X403 @ id @ ( X408 @ id @ X409 ) @ id ) )
| ~ ! [X410: term,X411: subst,X412: subst] :
( ( sub @ ( X408 @ X412 @ X410 ) @ X411 )
= ( X408 @ ( comp @ X412 @ X411 ) @ ( sub @ X410 @ X411 ) ) )
| ( X403 @ id @ ( lam @ ( X408 @ sh @ one ) ) @ id ) )
| ( X403 @ id @ X402 @ id )
| ~ ! [X413: term,X414: term] :
( ~ ( X403 @ id @ X413 @ id )
| ~ ( X403 @ id @ X414 @ id )
| ( X403 @ id @ ( ap @ ( sub @ X414 @ id ) @ X413 ) @ id ) )
| ~ ! [X415: term] :
( ( X403 @ id @ X415 @ id )
| ~ ( var @ ( sub @ X415 @ id ) ) )
| ~ ! [X416: subst,X417: subst,X418: subst,X419: term] :
( ( X403 @ X416 @ X419 @ ( comp @ X417 @ X418 ) )
| ~ ( X403 @ ( comp @ X416 @ X417 ) @ ( sub @ X419 @ X417 ) @ X418 ) ) ) ) ) )
<=> hoasinduction_lthm )
& pushprop_lthm_orig
& pushprop_lem2v2_gthm
& ( ! [X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ~ ! [X423: term] :
( ( X421 @ ( sub @ X420 @ ( push @ X423 @ id ) ) )
| ~ ( X421 @ X423 ) )
| ( X421 @ ( lam @ X420 ) )
| ~ ! [X424: subst > term > term] :
( ~ ! [X425: term,X426: subst,X427: subst] :
( ( X424 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) )
= ( sub @ ( X424 @ X427 @ X425 ) @ X426 ) )
| ( X422 @ id @ ( lam @ ( X424 @ sh @ one ) ) @ id )
| ~ ! [X428: term] :
( ~ ( X422 @ id @ X428 @ id )
| ( X422 @ id @ ( X424 @ id @ X428 ) @ id ) ) )
| ~ ! [X429: term] :
( ( X422 @ id @ X429 @ id )
= ( X421 @ X429 ) ) )
<=> hoasinduction_lem3v2a )
& hoasinduction_lem1v2
& ( hoaslam
= ( ^ [X430: subst,X431: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X432: subst > term > subst > $o,X433: term,X434: term > $o] :
( ( X434 @ ( lam @ X433 ) )
| ~ ! [X435: subst > term > term] :
( ( X432 @ id @ ( lam @ ( X435 @ sh @ one ) ) @ id )
| ~ ! [X436: subst,X437: term,X438: subst] :
( ( X435 @ ( comp @ X438 @ X436 ) @ ( sub @ X437 @ X436 ) )
= ( sub @ ( X435 @ X438 @ X437 ) @ X436 ) )
| ~ ! [X439: term] :
( ~ ( X432 @ id @ X439 @ id )
| ( X432 @ id @ ( X435 @ id @ X439 ) @ id ) ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ~ ( X432 @ X443 @ X441 @ ( comp @ X442 @ X440 ) )
| ( X432 @ ( comp @ X443 @ X442 ) @ ( sub @ X441 @ X442 ) @ X440 ) )
| ~ ! [X444: term,X445: subst,X446: subst,X447: subst] :
( ( X432 @ X446 @ X444 @ ( comp @ X447 @ X445 ) )
| ~ ( X432 @ ( comp @ X446 @ X447 ) @ ( sub @ X444 @ X447 ) @ X445 ) )
| ~ ! [X448: term] :
( ( X434 @ X448 )
= ( X432 @ id @ X448 @ id ) )
| ~ ! [X449: term] :
( ( X434 @ ( sub @ X433 @ ( push @ X449 @ id ) ) )
| ~ ( X434 @ X449 ) ) )
<=> hoasinduction_lem3v2 )
& ( hoasinduction_lem3a
<=> ! [X450: subst > term > subst > $o,X451: term] :
( ~ ! [X452: subst > term > term] :
( ~ ! [X453: subst,X454: subst,X455: term] :
( ( X452 @ ( comp @ X453 @ X454 ) @ ( sub @ X455 @ X454 ) )
= ( sub @ ( X452 @ X453 @ X455 ) @ X454 ) )
| ~ ! [X456: term] :
( ( X450 @ id @ ( X452 @ id @ X456 ) @ id )
| ~ ( X450 @ id @ X456 @ id ) )
| ( X450 @ id @ ( lam @ ( X452 @ sh @ one ) ) @ id ) )
| ( X450 @ id @ ( lam @ X451 ) @ id )
| ~ ! [X457: term] :
( ( X450 @ id @ ( sub @ X451 @ ( push @ X457 @ id ) ) @ id )
| ~ ( X450 @ id @ X457 @ id ) ) ) )
& induction2_gthm
& ( hoasinduction_lem3v2_f
<=> ! [X458: term] :
~ ! [X459: subst > term > term] :
~ ! [X460: subst,X461: term] :
( ( sub @ X458 @ ( push @ X461 @ X460 ) )
= ( X459 @ X460 @ X461 ) ) )
& ( ( ! [X462: term,X463: subst] :
( ( sub @ one @ ( push @ X462 @ X463 ) )
= X462 )
=> ( ! [X464: term,X465: subst] :
( ( comp @ sh @ ( push @ X464 @ X465 ) )
= X465 )
=> ( ! [X466: subst] :
( ( comp @ X466 @ id )
= X466 )
=> ( ! [X467: term,X468: term > $o] :
( ~ ! [X469: term,X470: term] :
( ~ ( X468 @ X469 )
| ( X468 @ ( ap @ X470 @ X469 ) )
| ~ ( X468 @ X470 ) )
| ( X468 @ X467 )
| ~ ! [X471: term] :
( ( X468 @ X471 )
| ~ ( var @ X471 ) )
| ~ ! [X472: term] :
( ~ ( X468 @ X472 )
| ( X468 @ ( lam @ X472 ) ) ) )
=> ! [X473: term,X474: term > $o,X475: subst] :
( ~ ! [X476: term] :
( ( X474 @ ( lam @ X476 ) )
| ~ ! [X477: term] :
( ( X474 @ ( sub @ X476 @ ( push @ X477 @ id ) ) )
| ~ ( X474 @ X477 ) ) )
| ~ ! [X478: term] :
( ( X474 @ ( sub @ X478 @ X475 ) )
| ~ ( var @ X478 ) )
| ( X474 @ ( sub @ X473 @ X475 ) )
| ~ ! [X479: term,X480: term] :
( ( X474 @ ( ap @ X479 @ X480 ) )
| ~ ( X474 @ X479 )
| ~ ( X474 @ X480 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& apnotvar
& axabs
& hoaslamnotvar
& pushprop_lem1_gthm
& ( hoaslaminj_lthm
<=> ( ! [X481: term,X482: subst] :
( ( sub @ one @ ( push @ X481 @ X482 ) )
= X481 )
=> ( ! [X483: term,X484: subst] :
( ( comp @ sh @ ( push @ X483 @ X484 ) )
= X484 )
=> ( ! [X485: term,X486: term] :
( ( ( lam @ X485 )
!= ( lam @ X486 ) )
| ( X485 = X486 ) )
=> ! [X487: term,X488: subst,X489: subst > term > term,X490: subst > term > term] :
( ( ( X490 @ X488 @ X487 )
= ( X489 @ X488 @ X487 ) )
| ~ ! [X491: subst,X492: term,X493: subst] :
( ( sub @ ( X489 @ X493 @ X492 ) @ X491 )
= ( X489 @ ( comp @ X493 @ X491 ) @ ( sub @ X492 @ X491 ) ) )
| ( ( lam @ ( X490 @ sh @ one ) )
!= ( lam @ ( X489 @ sh @ one ) ) )
| ~ ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X490 @ X494 @ X495 ) @ X496 )
= ( X490 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) ) ) ) ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X497: term,X498: subst > term > subst > $o] :
( ( X498 @ id @ ( lam @ ( sub @ X497 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X499: term] :
( ~ ( X498 @ id @ X499 @ id )
| ( X498 @ id @ ( sub @ X497 @ ( push @ X499 @ id ) ) @ id ) )
| ~ ! [X500: subst > term > term,X501: term] :
( ~ ! [X502: subst,X503: subst,X504: term] :
( ( sub @ ( X500 @ X502 @ X504 ) @ X503 )
= ( sub @ ( sub @ X501 @ ( push @ X504 @ X502 ) ) @ X503 ) )
| ( X498 @ id @ ( lam @ ( X500 @ sh @ one ) ) @ id )
| ~ ! [X505: term] :
( ~ ( X498 @ id @ X505 @ id )
| ( X498 @ id @ ( X500 @ id @ X505 ) @ id ) )
| ~ ! [X506: subst,X507: subst,X508: term] :
( ( X500 @ ( comp @ X506 @ X507 ) @ ( sub @ X508 @ X507 ) )
= ( sub @ X501 @ ( push @ ( sub @ X508 @ X507 ) @ ( comp @ X506 @ X507 ) ) ) ) ) ) )
& ( pushprop_lem1_lthm
<=> ( ! [X509: term,X510: subst] :
( ( sub @ one @ ( push @ X509 @ X510 ) )
= X509 )
=> ( ! [X511: subst,X512: term] :
( ( comp @ sh @ ( push @ X512 @ X511 ) )
= X511 )
=> ! [X513: subst,X514: term > $o,X515: term,X516: term,X517: term > $o] :
( ( X514 @ ( sub @ X516 @ ( push @ X515 @ X513 ) ) )
| ~ ( X517 @ X516 ) ) ) ) )
& axvarshift
& ( induction2lem
<=> ! [X518: subst,X519: term,X520: term > $o] :
( ~ ! [X521: term] :
( ( X520 @ ( sub @ X521 @ X518 ) )
| ~ ( var @ X521 ) )
| ~ ! [X522: term,X523: term] :
( ~ ( X520 @ X523 )
| ( X520 @ ( ap @ X523 @ X522 ) )
| ~ ( X520 @ X522 ) )
| ~ ! [X524: term] :
( ( X520 @ ( lam @ X524 ) )
| ~ ! [X525: term] :
( ( X520 @ ( sub @ X524 @ ( push @ X525 @ id ) ) )
| ~ ( X520 @ X525 ) ) )
| ( X520 @ ( sub @ X519 @ X518 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( induction2_lthm
<=> ( ! [X526: term] :
( ( sub @ X526 @ id )
= X526 )
=> ( ! [X527: term > $o,X528: subst,X529: term] :
( ~ ! [X530: term] :
( ~ ( var @ X530 )
| ( X527 @ ( sub @ X530 @ X528 ) ) )
| ~ ! [X531: term] :
( ~ ! [X532: term] :
( ~ ( X527 @ X532 )
| ( X527 @ ( sub @ X531 @ ( push @ X532 @ id ) ) ) )
| ( X527 @ ( lam @ X531 ) ) )
| ~ ! [X533: term,X534: term] :
( ~ ( X527 @ X534 )
| ~ ( X527 @ X533 )
| ( X527 @ ( ap @ X533 @ X534 ) ) )
| ( X527 @ ( sub @ X529 @ X528 ) ) )
=> ! [X535: term > $o,X536: term] :
( ( X535 @ X536 )
| ~ ! [X537: term] :
( ~ ! [X538: term] :
( ( X535 @ ( sub @ X537 @ ( push @ X538 @ id ) ) )
| ~ ( X535 @ X538 ) )
| ( X535 @ ( lam @ X537 ) ) )
| ~ ! [X539: term] :
( ~ ( var @ X539 )
| ( X535 @ X539 ) )
| ~ ! [X540: term,X541: term] :
( ~ ( X535 @ X541 )
| ( X535 @ ( ap @ X540 @ X541 ) )
| ~ ( X535 @ X540 ) ) ) ) ) )
& hoasinduction_lem2_gthm
& hoasapinj1_gthm
& ( hoasapinj2_lthm
<=> ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( ( ap @ X543 @ X545 )
!= ( ap @ X544 @ X542 ) )
| ( X542 = X545 ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( X546 = X548 )
| ( ( ap @ ( sub @ X549 @ id ) @ X548 )
!= ( ap @ ( sub @ X547 @ id ) @ X546 ) ) ) ) )
& axapp
& pushprop_lem3v2
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_lthm
& ~ ( var @ ( d2term @ d_one ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( substmonoid_gthm
& axmap
& ( ! [X15: term,X13: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
<=> laminj )
& ( ! [X13: term,X10: term > $o,X14: subst,X15: term,X26: term > $o] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) )
<=> pushprop_lem1 )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X43: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) )
& hoasinduction_lem3a_gthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ulamvarsh
& hoasinduction_lem3b_gthm
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) ) )
& ( ! [X15: term,X13: term,X19: term,X20: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) )
<=> hoasapinj2 )
& ! [X5: d_subst] : ( d_id = X5 )
& pushprop_lem1v2_gthm
& ( hoasinduction
<=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X25: subst,X13: term,X14: 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 ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ( X10 @ id @ X28 @ id ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lthm_3
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X29: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [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] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) ) )
& ( hoaslamnotap
<=> ! [X46: term,X47: term,X18: subst > term > term] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
& ~ ulamvar1
& axclos
& ( axidr
<=> ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& hoasinduction_lem1
& ( ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 )
<=> axscons )
& ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
<=> axshiftcons )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X20: term,X13: term,X15: term,X19: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X20: term,X13: term,X19: term,X15: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) ) )
<=> hoasapinj1_lthm )
& ~ lamnotap
& ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& pushprop_gthm
& pushprop_lem2v2_lthm
& ! [X6: d_subst,X7: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0 )
& ( one
= ( d2term @ d_one ) )
& ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( 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 )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& ulamvarind
& hoasinduction_lem2v2_gthm
& hoasinduction_gthm
& hoasinduction_lem1_lthm
& pushprop_lem3v2_lthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& ( induction
<=> ! [X10: term > $o,X21: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ( X10 @ X21 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X14: subst,X13: term,X10: term > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0 )
& ( ! [X14: subst,X13: term,X11: term > $o,X10: term > $o] :
( ( X11 @ one )
| ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
<=> pushprop_lem1v2 )
& ( pushprop_p_and_p_prime
= ( ^ [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X48: term,X11: term > $o] :
( ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [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 ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X14: subst,X26: subst,X13: term,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& hoasinduction_lem3v2_gthm
& ( apinj1
<=> ! [X19: term,X20: term,X13: term,X15: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) ) )
& ! [X1: d_term] : ( d_one = X1 )
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& termmset_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem1v2_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X11: term > $o,X14: subst,X10: term > $o,X13: term] :
( ( X11 @ one )
| ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) ) )
& ( ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ~ ( X10 @ id @ X23 @ id )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ( X10 @ id @ X24 @ id ) )
<=> hoasinduction_lem2 )
& pushprop_lthm
& hoasinduction_lem1_gthm
& hoaslamnotap_lthm
& hoasinduction_lem3_gthm
& axassoc
& ( induction2
<=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) ) ) )
& ( hoasinduction_lem3b
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& induction2lem_gthm
& ( ! [X10: subst > term > subst > $o,X30: term] :
( ~ ! [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] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_no_psi_cond )
& ( ( d2subst @ d_id )
= sh )
& ( pushprop_lem0_lthm
<=> ! [X13: term,X10: term > $o,X14: subst] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& hoasapnotvar_gthm
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& ( hoaslaminj
<=> ! [X32: subst,X18: subst > term > term,X31: subst > term > term,X33: term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) ) ) )
& hoaslamnotvar_gthm
& pushprop_lem0_gthm
& hoaslamnotap_gthm
& ( ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X11: term > $o,X29: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) )
<=> hoasinduction_lem3v2a_lthm )
& pushprop
& ( ! [X13: term,X19: term,X15: term,X20: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) )
<=> hoasapinj1 )
& ( ! [X15: term,X13: term] :
( ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) )
| ( X13 = X15 ) )
<=> shinj )
& ( ! [X10: subst > term > subst > $o,X42: term] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
<=> hoasinduction_lem3aa )
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& hoasapnotvar_lthm
& ( hoasinduction_lem3
<=> ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X14: subst,X13: term,X25: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X14: subst,X26: 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 ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) ) ) )
& ( ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
= hoasinduction_p_and_p_prime )
& ( ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
<=> substmonoid )
& ( substmonoid_lthm
<=> ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) ) ) ) )
& ( hoasinduction_lem2v2
<=> ! [X44: term,X45: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X14: subst,X26: subst,X13: term,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X11 @ X45 )
| ~ ( X11 @ X44 )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ( ! [X20: term,X13: term,X19: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
<=> apinj2 )
& lamnotvar
& ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
<=> axidl )
& hoasapinj2_gthm
& ( ( d2subst @ d_id )
= id )
& hoasapnotvar
& hoaslaminj_gthm
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X29: term,X10: subst > term > subst > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
=> ! [X10: subst > term > subst > $o,X30: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ X30 @ id ) ) ) ) ) ) )
& ( hoasinduction_lem3_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [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 ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) ) ) )
& hoasinduction_lem2_lthm
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& pushprop_lem2v2
& ( ( ! [X22: term,X10: term > $o] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) ) )
=> ( ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X26: subst,X14: subst,X25: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) ) )
=> ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X14: subst,X25: 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 ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) ) ) )
<=> hoasinduction_lthm )
& pushprop_lthm_orig
& pushprop_lem2v2_gthm
& ( ! [X29: term,X11: term > $o,X10: subst > term > subst > $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 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
<=> hoasinduction_lem3v2a )
& hoasinduction_lem1v2
& ( hoaslam
= ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X10: subst > term > subst > $o,X48: term,X11: term > $o] :
( ( X11 @ ( lam @ X48 ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) )
<=> hoasinduction_lem3v2 )
& ( hoasinduction_lem3a
<=> ! [X10: subst > term > subst > $o,X43: term] :
( ~ ! [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 ) )
| ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& induction2_gthm
& ( hoasinduction_lem3v2_f
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) ) )
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X21: term,X10: term > $o] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ X21 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) ) )
=> ! [X16: term,X10: term > $o,X17: subst] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& apnotvar
& axabs
& hoaslamnotvar
& pushprop_lem1_gthm
& ( hoaslaminj_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X15: term,X13: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
=> ! [X33: term,X32: subst,X18: subst > term > term,X31: subst > term > term] :
( ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X34: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term,X35: term] :
( ~ ! [X36: subst,X38: subst,X37: term] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X39: subst,X41: subst,X40: term] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) ) ) ) )
& ( pushprop_lem1_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X14: subst,X26: term > $o,X15: term,X13: term,X10: term > $o] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) ) ) ) )
& axvarshift
& ( induction2lem
<=> ! [X17: subst,X16: term,X10: term > $o] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( induction2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: term > $o,X17: subst,X16: term] :
( ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
=> ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) ) ) ) ) )
& hoasinduction_lem2_gthm
& hoasapinj1_gthm
& ( hoasapinj2_lthm
<=> ( ! [X19: term,X15: term,X13: term,X20: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
=> ! [X19: term,X13: term,X20: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) ) )
& axapp
& pushprop_lem3v2
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_lthm
& ~ ( var @ ( d2term @ d_one ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SL7lTGeRpl/DTF2THF_17587.p',alg444_1) ).
thf(f1060,plain,
! [X258: term] :
( ( d2term @ ( sK584 @ X258 ) )
= X258 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3010,plain,
( ( $true
= ( sK593 @ ( d2term @ d_one ) ) )
| ~ spl595_89 ),
inference(avatar_component_clause,[status(thm)],[f3008]) ).
thf(f3008,definition,
( spl595_89
<=> ( $true
= ( sK593 @ ( d2term @ d_one ) ) ) ),
introduced(definition,[new_symbols(naming,[spl595_89])],[avatar_definition]) ).
thf(f3205,plain,
( ~ spl595_91
| ~ spl595_94 ),
inference(avatar_contradiction_clause,[status(thm)],[f3204]) ).
thf(f3204,plain,
( $false
| ~ spl595_91
| ~ spl595_94 ),
inference(trivial_inequality_removal,[status(thm)],[f3200]) ).
thf(f3200,plain,
( ( $true = $false )
| ~ spl595_91
| ~ spl595_94 ),
inference(superposition,[status(thm)],[f3113,f3133]) ).
thf(f3133,plain,
( ( ( sK524 @ ( d2term @ d_one ) )
= $false )
| ~ spl595_94 ),
inference(avatar_component_clause,[status(thm)],[f3131]) ).
thf(f3131,definition,
( spl595_94
<=> ( ( sK524 @ ( d2term @ d_one ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl595_94])],[avatar_definition]) ).
thf(f3113,plain,
( ! [X0: term] :
( ( sK524 @ X0 )
= $true )
| ~ spl595_91 ),
inference(superposition,[status(thm)],[f3022,f2251]) ).
thf(f3022,plain,
( ( ( sK524 @ ( d2term @ d_one ) )
= $true )
| ~ spl595_91 ),
inference(avatar_component_clause,[status(thm)],[f3020]) ).
thf(f3020,definition,
( spl595_91
<=> ( ( sK524 @ ( d2term @ d_one ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl595_91])],[avatar_definition]) ).
thf(f3189,plain,
( ~ spl595_91
| ~ spl595_92 ),
inference(avatar_contradiction_clause,[status(thm)],[f3188]) ).
thf(f3188,plain,
( $false
| ~ spl595_91
| ~ spl595_92 ),
inference(trivial_inequality_removal,[status(thm)],[f3154]) ).
thf(f3154,plain,
( ( $true = $false )
| ~ spl595_91
| ~ spl595_92 ),
inference(superposition,[status(thm)],[f3104,f3113]) ).
thf(f3104,plain,
( ! [X3: term > $o] :
( $false
= ( X3 @ ( d2term @ d_one ) ) )
| ~ spl595_92 ),
inference(avatar_component_clause,[status(thm)],[f3103]) ).
thf(f3103,definition,
( spl595_92
<=> ! [X3: term > $o] :
( $false
= ( X3 @ ( d2term @ d_one ) ) ) ),
introduced(definition,[new_symbols(naming,[spl595_92])],[avatar_definition]) ).
thf(f3187,plain,
( ~ spl595_89
| ~ spl595_92 ),
inference(avatar_contradiction_clause,[status(thm)],[f3186]) ).
thf(f3186,plain,
( $false
| ~ spl595_89
| ~ spl595_92 ),
inference(trivial_inequality_removal,[status(thm)],[f3156]) ).
thf(f3156,plain,
( ( $true = $false )
| ~ spl595_89
| ~ spl595_92 ),
inference(superposition,[status(thm)],[f3104,f3087]) ).
thf(f3134,plain,
( spl595_92
| spl595_94
| spl595_90 ),
inference(avatar_split_clause,[status(thm)],[f3129,f3012,f3131,f3103]) ).
thf(f3012,definition,
( spl595_90
<=> ( pushprop_lem0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl595_90])],[avatar_definition]) ).
thf(f3129,plain,
( ! [X136: term > $o] :
( ( ( X136 @ ( d2term @ d_one ) )
= $false )
| ( ( sK524 @ ( d2term @ d_one ) )
= $false ) )
| spl595_90 ),
inference(forward_demodulation,[status(thm)],[f3128,f2251]) ).
thf(f3128,plain,
( ! [X136: term > $o] :
( ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $false )
| ( ( X136 @ ( d2term @ d_one ) )
= $false ) )
| spl595_90 ),
inference(forward_demodulation,[status(thm)],[f3127,f2251]) ).
thf(f3127,plain,
( ! [X136: term > $o] :
( ( ( X136 @ ( sK525 @ X136 ) )
= $false )
| ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $false ) )
| spl595_90 ),
inference(subsumption_resolution,[status(thm)],[f1727,f3014]) ).
thf(f3014,plain,
( ( pushprop_lem0 != $true )
| spl595_90 ),
inference(avatar_component_clause,[status(thm)],[f3012]) ).
thf(f1727,plain,
! [X136: term > $o] :
( ( ( X136 @ ( sK525 @ X136 ) )
= $false )
| ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $false )
| ( pushprop_lem0 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1163]) ).
thf(f1163,plain,
! [X136: term > $o] :
( ( pushprop_lem0 = $true )
| ( ( X136 @ ( sK525 @ X136 ) )
!= ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3109,plain,
( spl595_92
| spl595_93
| ~ spl595_90 ),
inference(avatar_split_clause,[status(thm)],[f3101,f3012,f3106,f3103]) ).
thf(f3101,plain,
( ! [X3: term > $o] :
( ( $false
= ( sK593 @ ( d2term @ d_one ) ) )
| ( $false
= ( X3 @ ( d2term @ d_one ) ) ) )
| ~ spl595_90 ),
inference(subsumption_resolution,[status(thm)],[f3081,f3013]) ).
thf(f3013,plain,
( ( pushprop_lem0 = $true )
| ~ spl595_90 ),
inference(avatar_component_clause,[status(thm)],[f3012]) ).
thf(f3081,plain,
! [X3: term > $o] :
( ( $false
= ( sK593 @ ( d2term @ d_one ) ) )
| ( $false
= ( X3 @ ( d2term @ d_one ) ) )
| ( pushprop_lem0 != $true ) ),
inference(forward_demodulation,[status(thm)],[f3080,f2251]) ).
thf(f3080,plain,
! [X3: term > $o] :
( ( $false
= ( sK593 @ ( d2term @ d_one ) ) )
| ( $false
= ( X3 @ ( sK596 @ X3 ) ) )
| ( pushprop_lem0 != $true ) ),
inference(forward_demodulation,[status(thm)],[f1819,f2251]) ).
thf(f1819,plain,
! [X3: term > $o] :
( ( ( sK593 @ ( sub @ ( sK596 @ X3 ) @ ( push @ sK592 @ sK591 ) ) )
= $false )
| ( $false
= ( X3 @ ( sK596 @ X3 ) ) )
| ( pushprop_lem0 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1817]) ).
thf(f1817,plain,
! [X3: term > $o] :
( ( pushprop_lem0 != $true )
| ( ( sK593 @ ( sub @ ( sK596 @ X3 ) @ ( push @ sK592 @ sK591 ) ) )
!= ( X3 @ ( sK596 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1816]) ).
thf(f1816,plain,
! [X3: term > $o] :
( ( ( ( X3 @ ( sK596 @ X3 ) )
= ( sK593 @ ( sub @ ( sK596 @ X3 ) @ ( push @ sK592 @ sK591 ) ) ) )
= $false )
| ( pushprop_lem0 != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1815]) ).
thf(f1815,plain,
! [X3: term > $o] :
( ( ( ^ [Y0: term] :
( ( X3 @ Y0 )
= ( sK593 @ ( sub @ Y0 @ ( push @ sK592 @ sK591 ) ) ) )
@ ( sK596 @ X3 ) )
= $false )
| ( pushprop_lem0 != $true ) ),
inference(sigma_clausification,[status(thm)],[f1814]) ).
thf(f1814,plain,
! [X3: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( X3 @ Y0 )
= ( sK593 @ ( sub @ Y0 @ ( push @ sK592 @ sK591 ) ) ) ) )
!= $true )
| ( pushprop_lem0 != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1664]) ).
thf(f1664,plain,
! [X3: term > $o] :
( ( pushprop_lem0 != $true )
| ( ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) )
@ sK592
@ sK591
@ sK593
@ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1266,f1159]) ).
thf(f1159,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1266,plain,
! [X3: term > $o] :
( ( ( pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3 )
!= $true )
| ( pushprop_lem0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
thf(f550,plain,
( ( ! [X3: term > $o] :
( ( pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3 )
!= $true )
| ( pushprop_lem0 != $true ) )
& ( ! [X4: subst,X5: term,X6: term > $o] :
( $true
= ( pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ ( sK594 @ X6 @ X5 @ X4 ) ) )
| ( pushprop_lem0 = $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK591,sK592,sK593,sK594])],[f547,f549,f548]) ).
thf(f548,plain,
( ? [X0: subst,X1: term,X2: term > $o] :
! [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
!= $true )
=> ! [X3: term > $o] :
( ( pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f549,plain,
! [X4: subst,X5: term,X6: term > $o] :
( ? [X7: term > $o] :
( ( pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ X7 )
= $true )
=> ( $true
= ( pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ ( sK594 @ X6 @ X5 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f547,plain,
( ( ? [X0: subst,X1: term,X2: term > $o] :
! [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
!= $true )
| ( pushprop_lem0 != $true ) )
& ( ! [X4: subst,X5: term,X6: term > $o] :
? [X7: term > $o] :
( ( pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ X7 )
= $true )
| ( pushprop_lem0 = $true ) ) ),
inference(rectify,[status(thm)],[f546]) ).
thf(f546,plain,
( ( ? [X0: subst,X1: term,X2: term > $o] :
! [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
!= $true )
| ( pushprop_lem0 != $true ) )
& ( ! [X0: subst,X1: term,X2: term > $o] :
? [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
= $true )
| ( pushprop_lem0 = $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( pushprop_lem0 = $true )
<~> ! [X0: subst,X1: term,X2: term > $o] :
? [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ! [X0: subst,X1: term,X2: term > $o] :
? [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 )
= $true )
<=> ( pushprop_lem0 = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( pushprop_lem0
!= ( ! [X0: subst,X1: term,X2: term > $o] :
? [X3: term > $o] : ( pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( pushprop_lem0
!= ( ! [X14: subst,X13: term,X10: term > $o] :
? [X11: term > $o] : ( pushprop_p_and_p_prime @ X13 @ X14 @ X10 @ X11 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( pushprop_lem0
= ( ! [X14: subst,X13: term,X10: term > $o] :
? [X11: term > $o] : ( pushprop_p_and_p_prime @ X13 @ X14 @ X10 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SL7lTGeRpl/DTF2THF_17587.p',pushprop_lem0) ).
thf(f3066,plain,
~ spl595_88,
inference(avatar_contradiction_clause,[status(thm)],[f3065]) ).
thf(f3065,plain,
( $false
| ~ spl595_88 ),
inference(trivial_inequality_removal,[status(thm)],[f3038]) ).
thf(f3038,plain,
( ( $true != $true )
| ~ spl595_88 ),
inference(superposition,[status(thm)],[f2256,f2792]) ).
thf(f2792,plain,
( ! [X153: term > $o] :
( ( X153 @ ( d2term @ d_one ) )
= $true )
| ~ spl595_88 ),
inference(avatar_component_clause,[status(thm)],[f2791]) ).
thf(f2791,definition,
( spl595_88
<=> ! [X153: term > $o] :
( ( X153 @ ( d2term @ d_one ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl595_88])],[avatar_definition]) ).
thf(f2256,plain,
! [X0: term] :
( $true
!= ( var @ X0 ) ),
inference(superposition,[status(thm)],[f1048,f2251]) ).
thf(f1048,plain,
( ( var @ ( d2term @ d_one ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3023,plain,
( spl595_88
| spl595_91
| spl595_90 ),
inference(avatar_split_clause,[status(thm)],[f3018,f3012,f3020,f2791]) ).
thf(f3018,plain,
( ! [X136: term > $o] :
( ( ( sK524 @ ( d2term @ d_one ) )
= $true )
| ( ( X136 @ ( d2term @ d_one ) )
= $true ) )
| spl595_90 ),
inference(forward_demodulation,[status(thm)],[f3017,f2251]) ).
thf(f3017,plain,
( ! [X136: term > $o] :
( ( ( X136 @ ( d2term @ d_one ) )
= $true )
| ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $true ) )
| spl595_90 ),
inference(forward_demodulation,[status(thm)],[f3016,f2251]) ).
thf(f3016,plain,
( ! [X136: term > $o] :
( ( ( X136 @ ( sK525 @ X136 ) )
= $true )
| ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $true ) )
| spl595_90 ),
inference(subsumption_resolution,[status(thm)],[f1726,f3014]) ).
thf(f1726,plain,
! [X136: term > $o] :
( ( ( X136 @ ( sK525 @ X136 ) )
= $true )
| ( pushprop_lem0 = $true )
| ( ( sK524 @ ( sub @ ( sK525 @ X136 ) @ ( push @ sK523 @ sK522 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1163]) ).
thf(f3015,plain,
( spl595_89
| ~ spl595_90
| spl595_88 ),
inference(avatar_split_clause,[status(thm)],[f3006,f2791,f3012,f3008]) ).
thf(f3006,plain,
! [X3: term > $o] :
( ( $true
= ( X3 @ ( d2term @ d_one ) ) )
| ( pushprop_lem0 != $true )
| ( $true
= ( sK593 @ ( d2term @ d_one ) ) ) ),
inference(forward_demodulation,[status(thm)],[f3005,f2251]) ).
thf(f3005,plain,
! [X3: term > $o] :
( ( ( sK593 @ ( sub @ ( sK596 @ X3 ) @ ( push @ sK592 @ sK591 ) ) )
= $true )
| ( $true
= ( X3 @ ( d2term @ d_one ) ) )
| ( pushprop_lem0 != $true ) ),
inference(forward_demodulation,[status(thm)],[f1818,f2251]) ).
thf(f1818,plain,
! [X3: term > $o] :
( ( $true
= ( X3 @ ( sK596 @ X3 ) ) )
| ( pushprop_lem0 != $true )
| ( ( sK593 @ ( sub @ ( sK596 @ X3 ) @ ( push @ sK592 @ sK591 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 08:57:53 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.28/0.47 % Domain : Software Verification
% 0.28/0.47 % Problem : Benchmark: ALG444^1, Active target: pushprop_lem0
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Kon26]
% 0.28/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : ? v9.3.0
% 0.28/0.47 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.28/0.47 % Number of atoms : 255 ( 128 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 248 ( 127 avg)
% 0.28/0.47 % Number of connectives : 2573 ( 333 ~; 306 |; 129 &;1711 @)
% 0.28/0.47 % ( 56 <=>; 38 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 151 ( 76 avg)
% 0.28/0.47 % Number of types : 5 ( 4 usr)
% 0.28/0.47 % Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.28/0.47 % Number of variables : 554 ( 8 ^; 543 !; 3 ?; 554 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments :
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(term_type,type,
% 0.28/0.47 term: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(subst_type,type,
% 0.28/0.47 subst: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(one_decl,type,
% 0.28/0.47 one: term ).
% 0.28/0.47
% 0.28/0.47 thf(ap_decl,type,
% 0.28/0.47 ap: term > term > term ).
% 0.28/0.47
% 0.28/0.47 thf(lam_decl,type,
% 0.28/0.47 lam: term > term ).
% 0.28/0.47
% 0.28/0.47 thf(sub_decl,type,
% 0.28/0.47 sub: term > subst > term ).
% 0.28/0.47
% 0.28/0.47 thf(id_decl,type,
% 0.28/0.47 id: subst ).
% 0.28/0.47
% 0.28/0.47 thf(sh_decl,type,
% 0.28/0.47 sh: subst ).
% 0.28/0.47
% 0.28/0.47 thf(push_decl,type,
% 0.28/0.47 push: term > subst > subst ).
% 0.28/0.47
% 0.28/0.47 thf(comp_decl,type,
% 0.28/0.47 comp: subst > subst > subst ).
% 0.28/0.47
% 0.28/0.47 thf(var_decl,type,
% 0.28/0.47 var: term > $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1v2_decl,type,
% 0.28/0.47 pushprop_lem1v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1_gthm_decl,type,
% 0.28/0.47 pushprop_lem1_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axmap_decl,type,
% 0.28/0.47 axmap: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem0_gthm_decl,type,
% 0.28/0.47 pushprop_lem0_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(shinj_decl,type,
% 0.28/0.47 shinj: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem1v2_decl,type,
% 0.28/0.47 hoasinduction_lem1v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem1v2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasap_decl,type,
% 0.28/0.47 hoasap: subst > term > subst > term > term ).
% 0.28/0.47
% 0.28/0.47 thf(induction2lem_decl,type,
% 0.28/0.47 induction2lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2_f_decl,type,
% 0.28/0.47 hoasinduction_lem3v2_f: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axvarshift_decl,type,
% 0.28/0.47 axvarshift: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj2_decl,type,
% 0.28/0.47 hoasapinj2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapnotvar_gthm_decl,type,
% 0.28/0.47 hoasapnotvar_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj1_decl,type,
% 0.28/0.47 hoasapinj1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ulamvar1_decl,type,
% 0.28/0.47 ulamvar1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction2lem_lthm_decl,type,
% 0.28/0.47 induction2lem_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem3v2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(apnotvar_decl,type,
% 0.28/0.47 apnotvar: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lthm_orig_decl,type,
% 0.28/0.47 pushprop_lthm_orig: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3v2_f_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lthm_decl,type,
% 0.28/0.47 hoasinduction_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.28/0.47 hoasinduction_no_psi_cond_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslaminj_decl,type,
% 0.28/0.47 hoaslaminj: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3aaa_decl,type,
% 0.28/0.47 hoasinduction_lem3aaa: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction2lem_gthm_decl,type,
% 0.28/0.47 induction2lem_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3aa_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3_decl,type,
% 0.28/0.47 hoasinduction_lem3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem2_decl,type,
% 0.28/0.47 hoasinduction_lem2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(termmset_lthm_decl,type,
% 0.28/0.47 termmset_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem1_decl,type,
% 0.28/0.47 hoasinduction_lem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotap_lthm_decl,type,
% 0.28/0.47 hoaslamnotap_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1v2_lthm_decl,type,
% 0.28/0.47 pushprop_lem1v2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapnotvar_decl,type,
% 0.28/0.47 hoasapnotvar: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem0_decl,type,
% 0.28/0.47 hoasinduction_lem0: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_decl,type,
% 0.28/0.47 hoasinduction: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_gthm_decl,type,
% 0.28/0.47 hoasinduction_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axapp_decl,type,
% 0.28/0.47 axapp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotvar_lthm_decl,type,
% 0.28/0.47 hoaslamnotvar_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem3v2_lthm_decl,type,
% 0.28/0.47 pushprop_lem3v2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3b_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ulamvarind_decl,type,
% 0.28/0.47 ulamvarind: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction_decl,type,
% 0.28/0.47 induction: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3a_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(termmset_gthm_decl,type,
% 0.28/0.47 termmset_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3aa_decl,type,
% 0.28/0.47 hoasinduction_lem3aa: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1v2_gthm_decl,type,
% 0.28/0.47 pushprop_lem1v2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotap_gthm_decl,type,
% 0.28/0.47 hoaslamnotap_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotvar_gthm_decl,type,
% 0.28/0.47 hoaslamnotvar_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem3b_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem2v2_decl,type,
% 0.28/0.47 pushprop_lem2v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem3a_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axclos_decl,type,
% 0.28/0.47 axclos: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axassoc_decl,type,
% 0.28/0.47 axassoc: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem2v2_decl,type,
% 0.28/0.47 hoasinduction_lem2v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lthm_decl,type,
% 0.28/0.47 pushprop_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(apinj2_decl,type,
% 0.28/0.47 apinj2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(apinj1_decl,type,
% 0.28/0.47 apinj1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj2_lthm_decl,type,
% 0.28/0.47 hoasapinj2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2a_decl,type,
% 0.28/0.47 hoasinduction_lem3v2a: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj1_lthm_decl,type,
% 0.28/0.47 hoasapinj1_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslaminj_lthm_decl,type,
% 0.28/0.47 hoaslaminj_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axvarcons_decl,type,
% 0.28/0.47 axvarcons: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslam_decl,type,
% 0.28/0.47 hoaslam: subst > ( subst > term > term ) > term ).
% 0.28/0.47
% 0.28/0.47 thf(axscons_decl,type,
% 0.28/0.47 axscons: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem2v2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axidr_decl,type,
% 0.28/0.47 axidr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1_decl,type,
% 0.28/0.47 pushprop_lem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(laminj_decl,type,
% 0.28/0.47 laminj: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem0_decl,type,
% 0.28/0.47 pushprop_lem0: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_gthm_decl,type,
% 0.28/0.47 pushprop_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axabs_decl,type,
% 0.28/0.47 axabs: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3v2a_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem2_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj2_gthm_decl,type,
% 0.28/0.47 hoasapinj2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.28/0.47 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem1_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem1_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamnotap_decl,type,
% 0.28/0.47 lamnotap: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapinj1_gthm_decl,type,
% 0.28/0.47 hoasapinj1_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotvar_decl,type,
% 0.28/0.47 hoaslamnotvar: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axidl_decl,type,
% 0.28/0.47 axidl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslaminj_gthm_decl,type,
% 0.28/0.47 hoaslaminj_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction2_lthm_decl,type,
% 0.28/0.47 induction2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem0_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem0_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(substmonoid_lthm_decl,type,
% 0.28/0.47 substmonoid_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_decl,type,
% 0.28/0.47 pushprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem3_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem2_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3b_decl,type,
% 0.28/0.47 hoasinduction_lem3b: $o ).
% 0.28/0.47
% 0.28/0.47 thf(substmonoid_decl,type,
% 0.28/0.47 substmonoid: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamnotvar_decl,type,
% 0.28/0.47 lamnotvar: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3a_decl,type,
% 0.28/0.47 hoasinduction_lem3a: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem1_gthm_decl,type,
% 0.28/0.47 hoasinduction_lem1_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_no_psi_cond_decl,type,
% 0.28/0.47 hoasinduction_no_psi_cond: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction2_gthm_decl,type,
% 0.28/0.47 induction2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem2v2_lthm_decl,type,
% 0.28/0.47 pushprop_lem2v2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasvar_decl,type,
% 0.28/0.47 hoasvar: subst > term > subst > $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoaslamnotap_decl,type,
% 0.28/0.47 hoaslamnotap: $o ).
% 0.28/0.47
% 0.28/0.47 thf(substmonoid_gthm_decl,type,
% 0.28/0.47 substmonoid_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ulamvarsh_decl,type,
% 0.28/0.47 ulamvarsh: $o ).
% 0.28/0.47
% 0.28/0.47 thf(induction2_decl,type,
% 0.28/0.47 induction2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem3v2_decl,type,
% 0.28/0.47 pushprop_lem3v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem2v2_gthm_decl,type,
% 0.28/0.47 pushprop_lem2v2_gthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem1_lthm_decl,type,
% 0.28/0.47 pushprop_lem1_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2_decl,type,
% 0.28/0.47 hoasinduction_lem3v2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(axshiftcons_decl,type,
% 0.28/0.47 axshiftcons: $o ).
% 0.28/0.47
% 0.28/0.47 thf(termmset_decl,type,
% 0.28/0.47 termmset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem0_lthm_decl,type,
% 0.28/0.47 pushprop_lem0_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasapnotvar_lthm_decl,type,
% 0.28/0.47 hoasapnotvar_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.28/0.47 hoasinduction_lem3v2_lthm: $o ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_p_and_p_prime_decl,type,
% 0.28/0.47 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(axvarid_decl,type,
% 0.28/0.47 axvarid: $o ).
% 0.28/0.47
% 0.28/0.47 thf(hoasinduction_lthm_3_decl,type,
% 0.28/0.47 hoasinduction_lthm_3: $o ).
% 0.28/0.47
% 0.28/0.47 %----Types of the domains
% 0.28/0.47 thf(d_term_type,type,
% 0.28/0.47 d_term: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(d_subst_type,type,
% 0.28/0.47 d_subst: $tType ).
% 0.28/0.47
% 0.28/0.47 %----Types of the promotion functions
% 0.28/0.47 thf(d2term_decl,type,
% 0.28/0.47 d2term: d_term > term ).
% 0.28/0.47
% 0.28/0.47 thf(d2subst_decl,type,
% 0.28/0.47 d2subst: d_subst > subst ).
% 0.28/0.47
% 0.28/0.47 %----Types of the domain elements
% 0.28/0.47 thf(d_one_decl,type,
% 0.28/0.47 d_one: d_term ).
% 0.28/0.47
% 0.28/0.47 thf(d_id_decl,type,
% 0.28/0.47 d_id: d_subst ).
% 0.28/0.47
% 0.28/0.47 thf(alg444_1,axiom,
% 0.28/0.47 ( ! [T: term] :
% 0.28/0.47 ? [DT: d_term] :
% 0.28/0.47 ( T
% 0.28/0.47 = ( d2term @ DT ) )
% 0.28/0.47 & ! [DT: d_term] : ( DT = d_one )
% 0.28/0.47 & ! [DT1: d_term,DT2: d_term] :
% 0.28/0.47 ( ( ( d2term @ DT1 )
% 0.28/0.47 = ( d2term @ DT2 ) )
% 0.28/0.47 => ( DT1 = DT2 ) )
% 0.28/0.47 & ! [S: subst] :
% 0.28/0.47 ? [DS: d_subst] :
% 0.28/0.47 ( S
% 0.28/0.47 = ( d2subst @ DS ) )
% 0.28/0.47 & ! [DS: d_subst] : ( DS = d_id )
% 0.28/0.47 & ! [DS1: d_subst,DS2: d_subst] :
% 0.28/0.47 ( ( ( d2subst @ DS1 )
% 0.28/0.47 = ( d2subst @ DS2 ) )
% 0.28/0.47 => ( DS1 = DS2 ) )
% 0.28/0.47 & ( one
% 0.28/0.47 = ( d2term @ d_one ) )
% 0.28/0.47 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.28/0.47 = ( d2term @ d_one ) )
% 0.28/0.47 & ( ( lam @ ( d2term @ d_one ) )
% 0.28/0.47 = ( d2term @ d_one ) )
% 0.28/0.47 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.28/0.47 = ( d2term @ d_one ) )
% 0.28/0.47 & ( id
% 0.28/0.47 = ( d2subst @ d_id ) )
% 0.28/0.47 & ( sh
% 0.28/0.47 = ( d2subst @ d_id ) )
% 0.28/0.47 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.28/0.47 = ( d2subst @ d_id ) )
% 0.28/0.47 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.28/0.47 = ( d2subst @ d_id ) )
% 0.28/0.47 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.28/0.47 = ( d2term @ d_one ) )
% 0.28/0.47 & ( hoaslam
% 0.28/0.47 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.28/0.47 & ( hoasinduction_p_and_p_prime
% 0.28/0.47 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.28/0.47 ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) ) ) )
% 0.28/0.47 & ( pushprop_p_and_p_prime
% 0.28/0.47 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.28/0.47 ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.28/0.47 & ~ ( var @ ( d2term @ d_one ) )
% 0.28/0.47 & ( pushprop_lem1v2
% 0.28/0.47 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.28/0.47 | ( Q @ one ) ) )
% 0.28/0.47 & pushprop_lem1_gthm
% 0.28/0.47 & axmap
% 0.28/0.47 & pushprop_lem0_gthm
% 0.28/0.47 & ( shinj
% 0.28/0.47 <=> ! [A: term,B: term] :
% 0.28/0.47 ( ( ( sub @ A @ sh )
% 0.28/0.47 != ( sub @ B @ sh ) )
% 0.28/0.47 | ( A = B ) ) )
% 0.28/0.47 & hoasinduction_lem1v2
% 0.28/0.47 & hoasinduction_lem1v2_gthm
% 0.28/0.47 & ( induction2lem
% 0.28/0.47 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.28/0.47 ( ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( var @ B )
% 0.28/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.28/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.28/0.47 & ( hoasinduction_lem3v2_f
% 0.28/0.47 <=> ! [B: term] :
% 0.28/0.47 ~ ! [F: subst > term > term] :
% 0.28/0.47 ~ ! [A: term,M: subst] :
% 0.28/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.28/0.47 = ( F @ M @ A ) ) )
% 0.28/0.47 & axvarshift
% 0.28/0.47 & ( hoasapinj2
% 0.28/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.28/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.28/0.47 | ( C = D ) ) )
% 0.28/0.47 & hoasapnotvar_gthm
% 0.28/0.47 & ( hoasapinj1
% 0.28/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.28/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.28/0.47 | ( A = B ) ) )
% 0.28/0.47 & ~ ulamvar1
% 0.28/0.47 & ( induction2lem_lthm
% 0.28/0.47 <=> ( ! [A: term,M: subst] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.28/0.47 => ( ! [A: term,M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.28/0.47 => ( ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ M @ id ) )
% 0.28/0.47 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2140 ) )
% 0.28/0.47 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.28/0.47 ( ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( var @ B )
% 0.28/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.28/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.28/0.47 & hoasinduction_lem3v2_gthm
% 0.28/0.47 & apnotvar
% 0.28/0.47 & pushprop_lthm_orig
% 0.28/0.47 & ( hoasinduction_lem3v2_f_lthm
% 0.28/0.47 <=> ! [B: term] :
% 0.28/0.47 ~ ! [F: subst > term > term] :
% 0.28/0.47 ~ ! [A: term,M: subst] :
% 0.28/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.28/0.47 = ( F @ M @ A ) ) )
% 0.28/0.47 & ( hoasinduction_lthm
% 0.28/0.47 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2367 ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.28/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.28/0.47 | ( P @ id @ A @ id ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.28/0.47 & ( hoasinduction_no_psi_cond_lthm
% 0.28/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2367 ) )
% 0.28/0.47 => ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.28/0.47 ( ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.28/0.47 & ( hoaslaminj
% 0.28/0.47 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.28/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.28/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.28/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.28/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.28/0.47 & ( hoasinduction_lem3aaa
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.28/0.47 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.28/0.47 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.28/0.47 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.28/0.47 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.28/0.47 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.28/0.47 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.28/0.47 & induction2lem_gthm
% 0.28/0.47 & ( hoasinduction_lem3aa_lthm
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.28/0.47 & ( hoasinduction_lem3
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.28/0.47 & ( hoasinduction_lem2
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.28/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.28/0.47 & ( termmset_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) ) ) )
% 0.28/0.47 & hoasinduction_lem1
% 0.28/0.47 & hoaslamnotap_lthm
% 0.28/0.47 & ( pushprop_lem1v2_lthm
% 0.28/0.47 <=> ( ! [A: term,M: subst] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.28/0.47 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.28/0.47 | ( Q @ one ) ) ) )
% 0.28/0.47 & hoasapnotvar
% 0.28/0.47 & ( hoasinduction_lem0
% 0.28/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) ) )
% 0.28/0.47 & ( hoasinduction
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.28/0.47 | ( P @ id @ A @ id ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.28/0.47 & hoasinduction_gthm
% 0.28/0.47 & axapp
% 0.28/0.47 & hoaslamnotvar_lthm
% 0.28/0.47 & pushprop_lem3v2_lthm
% 0.28/0.47 & ( hoasinduction_lem3b_lthm
% 0.28/0.47 <=> ! [B: term] :
% 0.28/0.47 ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ( F @ sh @ one )
% 0.28/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.28/0.47 & ulamvarind
% 0.28/0.47 & ( induction
% 0.28/0.47 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2140 ) ) )
% 0.28/0.47 & ( hoasinduction_lem3a_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.28/0.47 & termmset_gthm
% 0.28/0.47 & ( hoasinduction_lem3aa
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.28/0.47 & pushprop_lem1v2_gthm
% 0.28/0.47 & hoaslamnotap_gthm
% 0.28/0.47 & hoaslamnotvar_gthm
% 0.28/0.47 & hoasinduction_lem3b_gthm
% 0.28/0.47 & pushprop_lem2v2
% 0.28/0.47 & hoasinduction_lem3a_gthm
% 0.28/0.47 & axclos
% 0.28/0.47 & axassoc
% 0.28/0.47 & ( hoasinduction_lem2v2
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ( Q @ Bound_variable_2820 )
% 0.28/0.47 | ~ ( Q @ Bound_variable_2822 )
% 0.28/0.47 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.28/0.47 & pushprop_lthm
% 0.28/0.47 & ( apinj2
% 0.28/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ A @ C )
% 0.28/0.47 != ( ap @ B @ D ) )
% 0.28/0.47 | ( C = D ) ) )
% 0.28/0.47 & ( apinj1
% 0.28/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ A @ C )
% 0.28/0.47 != ( ap @ B @ D ) )
% 0.28/0.47 | ( A = B ) ) )
% 0.28/0.47 & ( hoasapinj2_lthm
% 0.28/0.47 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ A @ C )
% 0.28/0.47 != ( ap @ B @ D ) )
% 0.28/0.47 | ( C = D ) )
% 0.28/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.28/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.28/0.47 | ( C = D ) ) ) )
% 0.28/0.47 & ( hoasinduction_lem3v2a
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.28/0.47 & ( hoasapinj1_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ A @ C )
% 0.28/0.47 != ( ap @ B @ D ) )
% 0.28/0.47 | ( A = B ) )
% 0.28/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.28/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.28/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.28/0.47 | ( A = B ) ) ) ) )
% 0.28/0.47 & ( hoaslaminj_lthm
% 0.28/0.47 <=> ( ! [A: term,M: subst] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.28/0.47 => ( ! [A: term,M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.28/0.47 => ( ! [A: term,B: term] :
% 0.28/0.47 ( ( ( lam @ A )
% 0.28/0.47 != ( lam @ B ) )
% 0.28/0.47 | ( A = B ) )
% 0.28/0.47 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.28/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.28/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.28/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.28/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.28/0.47 & ( axvarcons
% 0.28/0.47 <=> ! [A: term,M: subst] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.28/0.47 & ( axscons
% 0.28/0.47 <=> ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.28/0.47 & hoasinduction_lem2v2_gthm
% 0.28/0.47 & ( axidr
% 0.28/0.47 <=> ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ M @ id ) ) )
% 0.28/0.47 & ( pushprop_lem1
% 0.28/0.47 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.28/0.47 & ( laminj
% 0.28/0.47 <=> ! [A: term,B: term] :
% 0.28/0.47 ( ( ( lam @ A )
% 0.28/0.47 != ( lam @ B ) )
% 0.28/0.47 | ( A = B ) ) )
% 0.28/0.47 & ( hoasinduction_lem3_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.28/0.47 & ( pushprop_lem0
% 0.28/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.28/0.47 & pushprop_gthm
% 0.28/0.47 & axabs
% 0.28/0.47 & ( hoasinduction_lem3v2a_lthm
% 0.28/0.47 <=> ( ! [B: term] :
% 0.28/0.47 ~ ! [F: subst > term > term] :
% 0.28/0.47 ~ ! [A: term,M: subst] :
% 0.28/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.28/0.47 = ( F @ M @ A ) )
% 0.28/0.47 => ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.28/0.47 & hoasinduction_lem2_lthm
% 0.28/0.47 & hoasapinj2_gthm
% 0.28/0.47 & hoasinduction_lem1_lthm
% 0.28/0.47 & ~ lamnotap
% 0.28/0.47 & hoasapinj1_gthm
% 0.28/0.47 & hoaslamnotvar
% 0.28/0.47 & ( axidl
% 0.28/0.47 <=> ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ id @ M ) ) )
% 0.28/0.47 & hoaslaminj_gthm
% 0.28/0.47 & ( induction2_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.28/0.47 ( ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( var @ B )
% 0.28/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.28/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.28/0.47 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.28/0.47 & ( hoasinduction_lem0_lthm
% 0.28/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) ) )
% 0.28/0.47 & ( substmonoid_lthm
% 0.28/0.47 <=> ( ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ id @ M ) )
% 0.28/0.47 => ( ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ M @ id ) )
% 0.28/0.47 => ( ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ id @ M ) )
% 0.28/0.47 & ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ M @ id ) ) ) ) ) )
% 0.28/0.47 & pushprop
% 0.28/0.47 & hoasinduction_lem3_gthm
% 0.28/0.47 & hoasinduction_lem2_gthm
% 0.28/0.47 & ( hoasinduction_lem3b
% 0.28/0.47 <=> ! [B: term] :
% 0.28/0.47 ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ( F @ sh @ one )
% 0.28/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.28/0.47 & ( substmonoid
% 0.28/0.47 <=> ( ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ id @ M ) )
% 0.28/0.47 & ! [M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ M @ id ) ) ) )
% 0.28/0.47 & lamnotvar
% 0.28/0.47 & ( hoasinduction_lem3a
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.28/0.47 & hoasinduction_lem1_gthm
% 0.28/0.47 & ( hoasinduction_no_psi_cond
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.28/0.47 ( ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.28/0.47 & induction2_gthm
% 0.28/0.47 & pushprop_lem2v2_lthm
% 0.28/0.47 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.28/0.47 & ( hoaslamnotap
% 0.28/0.47 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.28/0.47 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.28/0.47 & substmonoid_gthm
% 0.28/0.47 & ulamvarsh
% 0.28/0.47 & ( induction2
% 0.28/0.47 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2367 ) ) )
% 0.28/0.47 & pushprop_lem3v2
% 0.28/0.47 & pushprop_lem2v2_gthm
% 0.28/0.47 & ( pushprop_lem1_lthm
% 0.28/0.47 <=> ( ! [A: term,M: subst] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.28/0.47 => ( ! [A: term,M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.28/0.47 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.28/0.47 & ( hoasinduction_lem3v2
% 0.28/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.28/0.47 & ( axshiftcons
% 0.28/0.47 <=> ! [A: term,M: subst] :
% 0.28/0.47 ( M
% 0.28/0.47 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.28/0.47 & ( termmset
% 0.28/0.47 <=> ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) ) )
% 0.28/0.47 & ( pushprop_lem0_lthm
% 0.28/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.28/0.47 & hoasapnotvar_lthm
% 0.28/0.47 & ( hoasinduction_lem3v2_lthm
% 0.28/0.47 <=> ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.28/0.47 & ( axvarid
% 0.28/0.47 <=> ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) ) )
% 0.28/0.47 & ( hoasinduction_lthm_3
% 0.28/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.28/0.47 ~ ! [Q: term > $o] :
% 0.28/0.47 ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.28/0.47 ( ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ A )
% 0.28/0.47 | ( P @ A ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ A )
% 0.28/0.47 | ~ ( P @ B )
% 0.28/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ! [B: term] :
% 0.28/0.47 ( ~ ( P @ B )
% 0.28/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( P @ ( lam @ A ) ) )
% 0.28/0.47 | ( P @ Bound_variable_2367 ) )
% 0.28/0.47 => ( ! [A: term] :
% 0.28/0.47 ( A
% 0.28/0.47 = ( sub @ A @ id ) )
% 0.28/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.28/0.47 ( ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ~ ! [X: term] :
% 0.28/0.47 ( ( Q @ X )
% 0.28/0.47 = ( P @ id @ X @ id ) )
% 0.28/0.47 | ~ ! [B: term] :
% 0.28/0.47 ( ~ ( Q @ B )
% 0.28/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.28/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.28/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.28/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.28/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.28/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.28/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.28/0.47 | ( P @ id @ A @ id ) )
% 0.28/0.47 | ~ ! [A: term,B: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ~ ( P @ id @ B @ id )
% 0.28/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.28/0.47 | ~ ! [F: subst > term > term] :
% 0.28/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.28/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.28/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.28/0.47 | ~ ! [A: term] :
% 0.28/0.47 ( ~ ( P @ id @ A @ id )
% 0.28/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.28/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.28/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(pushprop_lem0,conjecture,
% 0.28/0.47 ( pushprop_lem0
% 0.28/0.47 = ( ! [P: term > $o,A: term,M: subst] :
% 0.28/0.47 ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.41/1.43 ---- Embedded in THF ---
% 2.41/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.41/1.44 %%% Generated on Tue May 05 08:57:54 EDT 2026
% 2.41/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.41/1.44 %%% Logic specification used:
% 2.41/1.44 %%% thf(spec, logic, $$dhol).
% 2.41/1.44
% 2.41/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SL7lTGeRpl/DTF2DTF17587.p
% See solution above
% 2.41/1.44 ------------------------
% 2.41/1.46 ---- Cleaned THF ---
% 2.41/1.46 thf(term_type,type,
% 2.41/1.46 term: $tType ).
% 2.41/1.46
% 2.41/1.46 thf(subst_type,type,
% 2.41/1.46 subst: $tType ).
% 2.41/1.46
% 2.41/1.46 thf(one_decl,type,
% 2.41/1.46 one: term ).
% 2.41/1.46
% 2.41/1.46 thf(ap_decl,type,
% 2.41/1.46 ap: term > term > term ).
% 2.41/1.46
% 2.41/1.46 thf(lam_decl,type,
% 2.41/1.46 lam: term > term ).
% 2.41/1.46
% 2.41/1.46 thf(sub_decl,type,
% 2.41/1.46 sub: term > subst > term ).
% 2.41/1.46
% 2.41/1.46 thf(id_decl,type,
% 2.41/1.46 id: subst ).
% 2.41/1.46
% 2.41/1.46 thf(sh_decl,type,
% 2.41/1.46 sh: subst ).
% 2.41/1.46
% 2.41/1.46 thf(push_decl,type,
% 2.41/1.46 push: term > subst > subst ).
% 2.41/1.46
% 2.41/1.46 thf(comp_decl,type,
% 2.41/1.46 comp: subst > subst > subst ).
% 2.41/1.46
% 2.41/1.46 thf(var_decl,type,
% 2.41/1.46 var: term > $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1v2_decl,type,
% 2.41/1.46 pushprop_lem1v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1_gthm_decl,type,
% 2.41/1.46 pushprop_lem1_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axmap_decl,type,
% 2.41/1.46 axmap: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem0_gthm_decl,type,
% 2.41/1.46 pushprop_lem0_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(shinj_decl,type,
% 2.41/1.46 shinj: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem1v2_decl,type,
% 2.41/1.46 hoasinduction_lem1v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem1v2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasap_decl,type,
% 2.41/1.46 hoasap: subst > term > subst > term > term ).
% 2.41/1.46
% 2.41/1.46 thf(induction2lem_decl,type,
% 2.41/1.46 induction2lem: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2_f_decl,type,
% 2.41/1.46 hoasinduction_lem3v2_f: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axvarshift_decl,type,
% 2.41/1.46 axvarshift: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj2_decl,type,
% 2.41/1.46 hoasapinj2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapnotvar_gthm_decl,type,
% 2.41/1.46 hoasapnotvar_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj1_decl,type,
% 2.41/1.46 hoasapinj1: $o ).
% 2.41/1.46
% 2.41/1.46 thf(ulamvar1_decl,type,
% 2.41/1.46 ulamvar1: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction2lem_lthm_decl,type,
% 2.41/1.46 induction2lem_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem3v2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(apnotvar_decl,type,
% 2.41/1.46 apnotvar: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lthm_orig_decl,type,
% 2.41/1.46 pushprop_lthm_orig: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3v2_f_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lthm_decl,type,
% 2.41/1.46 hoasinduction_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.41/1.46 hoasinduction_no_psi_cond_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslaminj_decl,type,
% 2.41/1.46 hoaslaminj: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3aaa_decl,type,
% 2.41/1.46 hoasinduction_lem3aaa: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction2lem_gthm_decl,type,
% 2.41/1.46 induction2lem_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3aa_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3_decl,type,
% 2.41/1.46 hoasinduction_lem3: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem2_decl,type,
% 2.41/1.46 hoasinduction_lem2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(termmset_lthm_decl,type,
% 2.41/1.46 termmset_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem1_decl,type,
% 2.41/1.46 hoasinduction_lem1: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotap_lthm_decl,type,
% 2.41/1.46 hoaslamnotap_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1v2_lthm_decl,type,
% 2.41/1.46 pushprop_lem1v2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapnotvar_decl,type,
% 2.41/1.46 hoasapnotvar: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem0_decl,type,
% 2.41/1.46 hoasinduction_lem0: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_decl,type,
% 2.41/1.46 hoasinduction: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_gthm_decl,type,
% 2.41/1.46 hoasinduction_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axapp_decl,type,
% 2.41/1.46 axapp: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotvar_lthm_decl,type,
% 2.41/1.46 hoaslamnotvar_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem3v2_lthm_decl,type,
% 2.41/1.46 pushprop_lem3v2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3b_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(ulamvarind_decl,type,
% 2.41/1.46 ulamvarind: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction_decl,type,
% 2.41/1.46 induction: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3a_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(termmset_gthm_decl,type,
% 2.41/1.46 termmset_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3aa_decl,type,
% 2.41/1.46 hoasinduction_lem3aa: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1v2_gthm_decl,type,
% 2.41/1.46 pushprop_lem1v2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotap_gthm_decl,type,
% 2.41/1.46 hoaslamnotap_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotvar_gthm_decl,type,
% 2.41/1.46 hoaslamnotvar_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem3b_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem2v2_decl,type,
% 2.41/1.46 pushprop_lem2v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem3a_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axclos_decl,type,
% 2.41/1.46 axclos: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axassoc_decl,type,
% 2.41/1.46 axassoc: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem2v2_decl,type,
% 2.41/1.46 hoasinduction_lem2v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lthm_decl,type,
% 2.41/1.46 pushprop_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(apinj2_decl,type,
% 2.41/1.46 apinj2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(apinj1_decl,type,
% 2.41/1.46 apinj1: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj2_lthm_decl,type,
% 2.41/1.46 hoasapinj2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2a_decl,type,
% 2.41/1.46 hoasinduction_lem3v2a: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj1_lthm_decl,type,
% 2.41/1.46 hoasapinj1_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslaminj_lthm_decl,type,
% 2.41/1.46 hoaslaminj_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axvarcons_decl,type,
% 2.41/1.46 axvarcons: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslam_decl,type,
% 2.41/1.46 hoaslam: subst > ( subst > term > term ) > term ).
% 2.41/1.46
% 2.41/1.46 thf(axscons_decl,type,
% 2.41/1.46 axscons: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem2v2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axidr_decl,type,
% 2.41/1.46 axidr: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1_decl,type,
% 2.41/1.46 pushprop_lem1: $o ).
% 2.41/1.46
% 2.41/1.46 thf(laminj_decl,type,
% 2.41/1.46 laminj: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem0_decl,type,
% 2.41/1.46 pushprop_lem0: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_gthm_decl,type,
% 2.41/1.46 pushprop_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axabs_decl,type,
% 2.41/1.46 axabs: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3v2a_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem2_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj2_gthm_decl,type,
% 2.41/1.46 hoasapinj2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.41/1.46 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem1_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem1_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(lamnotap_decl,type,
% 2.41/1.46 lamnotap: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapinj1_gthm_decl,type,
% 2.41/1.46 hoasapinj1_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotvar_decl,type,
% 2.41/1.46 hoaslamnotvar: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axidl_decl,type,
% 2.41/1.46 axidl: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslaminj_gthm_decl,type,
% 2.41/1.46 hoaslaminj_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction2_lthm_decl,type,
% 2.41/1.46 induction2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem0_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem0_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(substmonoid_lthm_decl,type,
% 2.41/1.46 substmonoid_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_decl,type,
% 2.41/1.46 pushprop: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem3_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem2_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3b_decl,type,
% 2.41/1.46 hoasinduction_lem3b: $o ).
% 2.41/1.46
% 2.41/1.46 thf(substmonoid_decl,type,
% 2.41/1.46 substmonoid: $o ).
% 2.41/1.46
% 2.41/1.46 thf(lamnotvar_decl,type,
% 2.41/1.46 lamnotvar: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3a_decl,type,
% 2.41/1.46 hoasinduction_lem3a: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem1_gthm_decl,type,
% 2.41/1.46 hoasinduction_lem1_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_no_psi_cond_decl,type,
% 2.41/1.46 hoasinduction_no_psi_cond: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction2_gthm_decl,type,
% 2.41/1.46 induction2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem2v2_lthm_decl,type,
% 2.41/1.46 pushprop_lem2v2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasvar_decl,type,
% 2.41/1.46 hoasvar: subst > term > subst > $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoaslamnotap_decl,type,
% 2.41/1.46 hoaslamnotap: $o ).
% 2.41/1.46
% 2.41/1.46 thf(substmonoid_gthm_decl,type,
% 2.41/1.46 substmonoid_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(ulamvarsh_decl,type,
% 2.41/1.46 ulamvarsh: $o ).
% 2.41/1.46
% 2.41/1.46 thf(induction2_decl,type,
% 2.41/1.46 induction2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem3v2_decl,type,
% 2.41/1.46 pushprop_lem3v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem2v2_gthm_decl,type,
% 2.41/1.46 pushprop_lem2v2_gthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem1_lthm_decl,type,
% 2.41/1.46 pushprop_lem1_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2_decl,type,
% 2.41/1.46 hoasinduction_lem3v2: $o ).
% 2.41/1.46
% 2.41/1.46 thf(axshiftcons_decl,type,
% 2.41/1.46 axshiftcons: $o ).
% 2.41/1.46
% 2.41/1.46 thf(termmset_decl,type,
% 2.41/1.46 termmset: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem0_lthm_decl,type,
% 2.41/1.46 pushprop_lem0_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasapnotvar_lthm_decl,type,
% 2.41/1.46 hoasapnotvar_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.41/1.46 hoasinduction_lem3v2_lthm: $o ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_p_and_p_prime_decl,type,
% 2.41/1.46 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.41/1.46
% 2.41/1.46 thf(axvarid_decl,type,
% 2.41/1.46 axvarid: $o ).
% 2.41/1.46
% 2.41/1.46 thf(hoasinduction_lthm_3_decl,type,
% 2.41/1.46 hoasinduction_lthm_3: $o ).
% 2.41/1.46
% 2.41/1.46 thf(d_term_type,type,
% 2.41/1.46 d_term: $tType ).
% 2.41/1.46
% 2.41/1.46 thf(d_subst_type,type,
% 2.41/1.46 d_subst: $tType ).
% 2.41/1.46
% 2.41/1.46 thf(d2term_decl,type,
% 2.41/1.46 d2term: d_term > term ).
% 2.41/1.46
% 2.41/1.46 thf(d2subst_decl,type,
% 2.41/1.46 d2subst: d_subst > subst ).
% 2.41/1.46
% 2.41/1.46 thf(d_one_decl,type,
% 2.41/1.46 d_one: d_term ).
% 2.41/1.46
% 2.41/1.46 thf(d_id_decl,type,
% 2.41/1.46 d_id: d_subst ).
% 2.41/1.46
% 2.41/1.46 thf(alg444_1,axiom,
% 2.41/1.46 ( ! [T: term] :
% 2.41/1.46 ? [DT: d_term] :
% 2.41/1.46 ( T
% 2.41/1.46 = ( d2term @ DT ) )
% 2.41/1.46 & ! [DT: d_term] : ( DT = d_one )
% 2.41/1.46 & ! [DT1: d_term,DT2: d_term] :
% 2.41/1.46 ( ( ( d2term @ DT1 )
% 2.41/1.46 = ( d2term @ DT2 ) )
% 2.41/1.46 => ( DT1 = DT2 ) )
% 2.41/1.46 & ! [S: subst] :
% 2.41/1.46 ? [DS: d_subst] :
% 2.41/1.46 ( S
% 2.41/1.46 = ( d2subst @ DS ) )
% 2.41/1.46 & ! [DS: d_subst] : ( DS = d_id )
% 2.41/1.46 & ! [DS1: d_subst,DS2: d_subst] :
% 2.41/1.46 ( ( ( d2subst @ DS1 )
% 2.41/1.46 = ( d2subst @ DS2 ) )
% 2.41/1.46 => ( DS1 = DS2 ) )
% 2.41/1.46 & ( one
% 2.41/1.46 = ( d2term @ d_one ) )
% 2.41/1.46 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.41/1.46 = ( d2term @ d_one ) )
% 2.41/1.46 & ( ( lam @ ( d2term @ d_one ) )
% 2.41/1.46 = ( d2term @ d_one ) )
% 2.41/1.46 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.41/1.46 = ( d2term @ d_one ) )
% 2.41/1.46 & ( id
% 2.41/1.46 = ( d2subst @ d_id ) )
% 2.41/1.46 & ( sh
% 2.41/1.46 = ( d2subst @ d_id ) )
% 2.41/1.46 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.41/1.46 = ( d2subst @ d_id ) )
% 2.41/1.46 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.41/1.46 = ( d2subst @ d_id ) )
% 2.41/1.46 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.41/1.46 = ( d2term @ d_one ) )
% 2.41/1.46 & ( hoaslam
% 2.41/1.46 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.41/1.46 & ( hoasinduction_p_and_p_prime
% 2.41/1.46 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.41/1.46 ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) ) ) )
% 2.41/1.46 & ( pushprop_p_and_p_prime
% 2.41/1.46 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.41/1.46 ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.41/1.46 & ~ ( var @ ( d2term @ d_one ) )
% 2.41/1.46 & ( pushprop_lem1v2
% 2.41/1.46 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.41/1.46 | ( Q @ one ) ) )
% 2.41/1.46 & pushprop_lem1_gthm
% 2.41/1.46 & axmap
% 2.41/1.46 & pushprop_lem0_gthm
% 2.41/1.46 & ( shinj
% 2.41/1.46 <=> ! [A: term,B: term] :
% 2.41/1.46 ( ( ( sub @ A @ sh )
% 2.41/1.46 != ( sub @ B @ sh ) )
% 2.41/1.46 | ( A = B ) ) )
% 2.41/1.46 & hoasinduction_lem1v2
% 2.41/1.46 & hoasinduction_lem1v2_gthm
% 2.41/1.46 & ( induction2lem
% 2.41/1.46 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.41/1.46 ( ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( var @ B )
% 2.41/1.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.41/1.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.41/1.46 & ( hoasinduction_lem3v2_f
% 2.41/1.46 <=> ! [B: term] :
% 2.41/1.46 ~ ! [F: subst > term > term] :
% 2.41/1.46 ~ ! [A: term,M: subst] :
% 2.41/1.46 ( ( sub @ B @ ( push @ A @ M ) )
% 2.41/1.46 = ( F @ M @ A ) ) )
% 2.41/1.46 & axvarshift
% 2.41/1.46 & ( hoasapinj2
% 2.41/1.46 <=> ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.41/1.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.41/1.46 | ( C = D ) ) )
% 2.41/1.46 & hoasapnotvar_gthm
% 2.41/1.46 & ( hoasapinj1
% 2.41/1.46 <=> ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.41/1.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.41/1.46 | ( A = B ) ) )
% 2.41/1.46 & ~ ulamvar1
% 2.41/1.46 & ( induction2lem_lthm
% 2.41/1.46 <=> ( ! [A: term,M: subst] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.41/1.46 => ( ! [A: term,M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.41/1.46 => ( ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ M @ id ) )
% 2.41/1.46 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2140 ) )
% 2.41/1.46 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.41/1.46 ( ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( var @ B )
% 2.41/1.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.41/1.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.41/1.46 & hoasinduction_lem3v2_gthm
% 2.41/1.46 & apnotvar
% 2.41/1.46 & pushprop_lthm_orig
% 2.41/1.46 & ( hoasinduction_lem3v2_f_lthm
% 2.41/1.46 <=> ! [B: term] :
% 2.41/1.46 ~ ! [F: subst > term > term] :
% 2.41/1.46 ~ ! [A: term,M: subst] :
% 2.41/1.46 ( ( sub @ B @ ( push @ A @ M ) )
% 2.41/1.46 = ( F @ M @ A ) ) )
% 2.41/1.46 & ( hoasinduction_lthm
% 2.41/1.46 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2367 ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.41/1.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ ( sub @ A @ id ) )
% 2.41/1.46 | ( P @ id @ A @ id ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.41/1.46 & ( hoasinduction_no_psi_cond_lthm
% 2.41/1.46 <=> ( ! [P: subst > term > subst > $o] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2367 ) )
% 2.41/1.46 => ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.41/1.46 ( ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.41/1.46 & ( hoaslaminj
% 2.41/1.46 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.41/1.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ( ( lam @ ( F @ sh @ one ) )
% 2.41/1.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.41/1.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.41/1.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.41/1.46 & ( hoasinduction_lem3aaa
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.41/1.46 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.41/1.46 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.41/1.46 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.41/1.46 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.41/1.46 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.41/1.46 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.41/1.46 & induction2lem_gthm
% 2.41/1.46 & ( hoasinduction_lem3aa_lthm
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.41/1.46 & ( hoasinduction_lem3
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 2.41/1.46 & ( hoasinduction_lem2
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.41/1.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 2.41/1.46 & ( termmset_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) ) ) )
% 2.41/1.46 & hoasinduction_lem1
% 2.41/1.46 & hoaslamnotap_lthm
% 2.41/1.46 & ( pushprop_lem1v2_lthm
% 2.41/1.46 <=> ( ! [A: term,M: subst] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.41/1.46 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.41/1.46 | ( Q @ one ) ) ) )
% 2.41/1.46 & hoasapnotvar
% 2.41/1.46 & ( hoasinduction_lem0
% 2.41/1.46 <=> ! [P: subst > term > subst > $o] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) ) )
% 2.41/1.46 & ( hoasinduction
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ ( sub @ A @ id ) )
% 2.41/1.46 | ( P @ id @ A @ id ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 2.41/1.46 & hoasinduction_gthm
% 2.41/1.46 & axapp
% 2.41/1.46 & hoaslamnotvar_lthm
% 2.41/1.46 & pushprop_lem3v2_lthm
% 2.41/1.46 & ( hoasinduction_lem3b_lthm
% 2.41/1.46 <=> ! [B: term] :
% 2.41/1.46 ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ( F @ sh @ one )
% 2.41/1.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.41/1.46 & ulamvarind
% 2.41/1.46 & ( induction
% 2.41/1.46 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2140 ) ) )
% 2.41/1.46 & ( hoasinduction_lem3a_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 2.41/1.46 & termmset_gthm
% 2.41/1.46 & ( hoasinduction_lem3aa
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.41/1.46 & pushprop_lem1v2_gthm
% 2.41/1.46 & hoaslamnotap_gthm
% 2.41/1.46 & hoaslamnotvar_gthm
% 2.41/1.46 & hoasinduction_lem3b_gthm
% 2.41/1.46 & pushprop_lem2v2
% 2.41/1.46 & hoasinduction_lem3a_gthm
% 2.41/1.46 & axclos
% 2.41/1.46 & axassoc
% 2.41/1.46 & ( hoasinduction_lem2v2
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ( Q @ Bound_variable_2820 )
% 2.41/1.46 | ~ ( Q @ Bound_variable_2822 )
% 2.41/1.46 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 2.41/1.46 & pushprop_lthm
% 2.41/1.46 & ( apinj2
% 2.41/1.46 <=> ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ A @ C )
% 2.41/1.46 != ( ap @ B @ D ) )
% 2.41/1.46 | ( C = D ) ) )
% 2.41/1.46 & ( apinj1
% 2.41/1.46 <=> ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ A @ C )
% 2.41/1.46 != ( ap @ B @ D ) )
% 2.41/1.46 | ( A = B ) ) )
% 2.41/1.46 & ( hoasapinj2_lthm
% 2.41/1.46 <=> ( ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ A @ C )
% 2.41/1.46 != ( ap @ B @ D ) )
% 2.41/1.46 | ( C = D ) )
% 2.41/1.46 => ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.41/1.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.41/1.46 | ( C = D ) ) ) )
% 2.41/1.46 & ( hoasinduction_lem3v2a
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 2.41/1.46 & ( hoasapinj1_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ A @ C )
% 2.41/1.46 != ( ap @ B @ D ) )
% 2.41/1.46 | ( A = B ) )
% 2.41/1.46 => ! [A: term,B: term,C: term,D: term] :
% 2.41/1.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.41/1.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.41/1.46 | ( A = B ) ) ) ) )
% 2.41/1.46 & ( hoaslaminj_lthm
% 2.41/1.46 <=> ( ! [A: term,M: subst] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.41/1.46 => ( ! [A: term,M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.41/1.46 => ( ! [A: term,B: term] :
% 2.41/1.46 ( ( ( lam @ A )
% 2.41/1.46 != ( lam @ B ) )
% 2.41/1.46 | ( A = B ) )
% 2.41/1.46 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.41/1.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ( ( lam @ ( F @ sh @ one ) )
% 2.41/1.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.41/1.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.41/1.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 2.41/1.46 & ( axvarcons
% 2.41/1.46 <=> ! [A: term,M: subst] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 2.41/1.46 & ( axscons
% 2.41/1.46 <=> ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 2.41/1.46 & hoasinduction_lem2v2_gthm
% 2.41/1.46 & ( axidr
% 2.41/1.46 <=> ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ M @ id ) ) )
% 2.41/1.46 & ( pushprop_lem1
% 2.41/1.46 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 2.41/1.46 & ( laminj
% 2.41/1.46 <=> ! [A: term,B: term] :
% 2.41/1.46 ( ( ( lam @ A )
% 2.41/1.46 != ( lam @ B ) )
% 2.41/1.46 | ( A = B ) ) )
% 2.41/1.46 & ( hoasinduction_lem3_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 2.41/1.46 & ( pushprop_lem0
% 2.41/1.46 <=> ! [P: term > $o,A: term,M: subst] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.41/1.46 & pushprop_gthm
% 2.41/1.46 & axabs
% 2.41/1.46 & ( hoasinduction_lem3v2a_lthm
% 2.41/1.46 <=> ( ! [B: term] :
% 2.41/1.46 ~ ! [F: subst > term > term] :
% 2.41/1.46 ~ ! [A: term,M: subst] :
% 2.41/1.46 ( ( sub @ B @ ( push @ A @ M ) )
% 2.41/1.46 = ( F @ M @ A ) )
% 2.41/1.46 => ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 2.41/1.46 & hoasinduction_lem2_lthm
% 2.41/1.46 & hoasapinj2_gthm
% 2.41/1.46 & hoasinduction_lem1_lthm
% 2.41/1.46 & ~ lamnotap
% 2.41/1.46 & hoasapinj1_gthm
% 2.41/1.46 & hoaslamnotvar
% 2.41/1.46 & ( axidl
% 2.41/1.46 <=> ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ id @ M ) ) )
% 2.41/1.46 & hoaslaminj_gthm
% 2.41/1.46 & ( induction2_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.41/1.46 ( ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( var @ B )
% 2.41/1.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.41/1.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 2.41/1.46 => ! [P: term > $o,Bound_variable_2367: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2367 ) ) ) ) )
% 2.41/1.46 & ( hoasinduction_lem0_lthm
% 2.41/1.46 <=> ! [P: subst > term > subst > $o] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) ) )
% 2.41/1.46 & ( substmonoid_lthm
% 2.41/1.46 <=> ( ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ id @ M ) )
% 2.41/1.46 => ( ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ M @ id ) )
% 2.41/1.46 => ( ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ id @ M ) )
% 2.41/1.46 & ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ M @ id ) ) ) ) ) )
% 2.41/1.46 & pushprop
% 2.41/1.46 & hoasinduction_lem3_gthm
% 2.41/1.46 & hoasinduction_lem2_gthm
% 2.41/1.46 & ( hoasinduction_lem3b
% 2.41/1.46 <=> ! [B: term] :
% 2.41/1.46 ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ( F @ sh @ one )
% 2.41/1.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.41/1.46 & ( substmonoid
% 2.41/1.46 <=> ( ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ id @ M ) )
% 2.41/1.46 & ! [M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ M @ id ) ) ) )
% 2.41/1.46 & lamnotvar
% 2.41/1.46 & ( hoasinduction_lem3a
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 2.41/1.46 & hoasinduction_lem1_gthm
% 2.41/1.46 & ( hoasinduction_no_psi_cond
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.41/1.46 ( ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 2.41/1.46 & induction2_gthm
% 2.41/1.46 & pushprop_lem2v2_lthm
% 2.41/1.46 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.41/1.46 & ( hoaslamnotap
% 2.41/1.46 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ( ( lam @ ( F @ sh @ one ) )
% 2.41/1.46 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 2.41/1.46 & substmonoid_gthm
% 2.41/1.46 & ulamvarsh
% 2.41/1.46 & ( induction2
% 2.41/1.46 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2367 ) ) )
% 2.41/1.46 & pushprop_lem3v2
% 2.41/1.46 & pushprop_lem2v2_gthm
% 2.41/1.46 & ( pushprop_lem1_lthm
% 2.41/1.46 <=> ( ! [A: term,M: subst] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.41/1.46 => ( ! [A: term,M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.41/1.46 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 2.41/1.46 & ( hoasinduction_lem3v2
% 2.41/1.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 2.41/1.46 & ( axshiftcons
% 2.41/1.46 <=> ! [A: term,M: subst] :
% 2.41/1.46 ( M
% 2.41/1.46 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 2.41/1.46 & ( termmset
% 2.41/1.46 <=> ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) ) )
% 2.41/1.46 & ( pushprop_lem0_lthm
% 2.41/1.46 <=> ! [P: term > $o,A: term,M: subst] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.41/1.46 & hoasapnotvar_lthm
% 2.41/1.46 & ( hoasinduction_lem3v2_lthm
% 2.41/1.46 <=> ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 2.41/1.46 & ( axvarid
% 2.41/1.46 <=> ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) ) )
% 2.41/1.46 & ( hoasinduction_lthm_3
% 2.41/1.46 <=> ( ! [P: subst > term > subst > $o] :
% 2.41/1.46 ~ ! [Q: term > $o] :
% 2.41/1.46 ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.41/1.46 ( ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ A )
% 2.41/1.46 | ( P @ A ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ A )
% 2.41/1.46 | ~ ( P @ B )
% 2.41/1.46 | ( P @ ( ap @ A @ B ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ! [B: term] :
% 2.41/1.46 ( ~ ( P @ B )
% 2.41/1.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( P @ ( lam @ A ) ) )
% 2.41/1.46 | ( P @ Bound_variable_2367 ) )
% 2.41/1.46 => ( ! [A: term] :
% 2.41/1.46 ( A
% 2.41/1.46 = ( sub @ A @ id ) )
% 2.41/1.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.41/1.46 ( ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ~ ! [X: term] :
% 2.41/1.46 ( ( Q @ X )
% 2.41/1.46 = ( P @ id @ X @ id ) )
% 2.41/1.46 | ~ ! [B: term] :
% 2.41/1.46 ( ~ ( Q @ B )
% 2.41/1.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.41/1.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.41/1.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.41/1.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.41/1.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.41/1.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.41/1.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( var @ ( sub @ A @ id ) )
% 2.41/1.46 | ( P @ id @ A @ id ) )
% 2.41/1.46 | ~ ! [A: term,B: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ~ ( P @ id @ B @ id )
% 2.41/1.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.41/1.46 | ~ ! [F: subst > term > term] :
% 2.41/1.46 ( ~ ! [M: subst,A: term,N: subst] :
% 2.41/1.46 ( ( sub @ ( F @ M @ A ) @ N )
% 2.41/1.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.41/1.46 | ~ ! [A: term] :
% 2.41/1.46 ( ~ ( P @ id @ A @ id )
% 2.41/1.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.41/1.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.41/1.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 2.41/1.46
% 2.41/1.46 thf(pushprop_lem0,conjecture,
% 2.41/1.46 ( pushprop_lem0
% 2.41/1.46 = ( ! [P: term > $o,A: term,M: subst] :
% 2.41/1.46 ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ) ).
% 2.41/1.46 ------------------------
% 2.41/1.48 % (17871)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/183Mi)
% 2.41/1.48 % (17872)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_17587 for (2999ds/4Mi)
% 2.41/1.48 % (17877)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/18Mi)
% 2.41/1.49 % (17872)Instruction limit reached!
% 2.41/1.49 % (17872)------------------------------
% 2.41/1.49 % (17872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (17872)Termination reason: Unknown
% 2.41/1.49 % (17872)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (17872)Memory used [KB]: 1407
% 2.41/1.49 % (17872)Time elapsed: 0.003 s
% 2.41/1.49 % (17872)Instructions burned: 6 (million)
% 2.41/1.49 % (17872)------------------------------
% 2.41/1.49 % (17872)------------------------------
% 2.41/1.49 % (17877)Instruction limit reached!
% 2.41/1.49 % (17877)------------------------------
% 2.41/1.49 % (17877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (17877)Termination reason: Unknown
% 2.41/1.49 % (17877)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (17877)Memory used [KB]: 2046
% 2.41/1.49 % (17877)Time elapsed: 0.007 s
% 2.41/1.49 % (17877)Instructions burned: 18 (million)
% 2.41/1.49 % (17877)------------------------------
% 2.41/1.49 % (17877)------------------------------
% 2.41/1.49 % (17873)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_17587 for (2999ds/27Mi)
% 2.41/1.49 % (17874)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/2Mi)
% 2.41/1.49 % (17875)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_17587 for (2999ds/2Mi)
% 2.41/1.49 % (17876)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_17587 for (2999ds/275Mi)
% 2.41/1.49 % (17874)Instruction limit reached!
% 2.41/1.49 % (17874)------------------------------
% 2.41/1.49 % (17874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (17874)Termination reason: Unknown
% 2.41/1.49 % (17874)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (17874)Memory used [KB]: 1151
% 2.41/1.49 % (17874)Time elapsed: 0.003 s
% 2.41/1.49 % (17874)Instructions burned: 2 (million)
% 2.41/1.49 % (17874)------------------------------
% 2.41/1.49 % (17874)------------------------------
% 2.41/1.49 % (17875)Instruction limit reached!
% 2.41/1.49 % (17875)------------------------------
% 2.41/1.49 % (17875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (17875)Termination reason: Unknown
% 2.41/1.49 % (17875)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (17875)Memory used [KB]: 1151
% 2.41/1.49 % (17875)Time elapsed: 0.003 s
% 2.41/1.49 % (17875)Instructions burned: 2 (million)
% 2.41/1.49 % (17875)------------------------------
% 2.41/1.49 % (17875)------------------------------
% 2.51/1.50 % (17878)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/3Mi)
% 2.51/1.50 % (17878)Instruction limit reached!
% 2.51/1.50 % (17878)------------------------------
% 2.51/1.50 % (17878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.50 % (17878)Termination reason: Unknown
% 2.51/1.50 % (17878)Termination phase: shuffling
% 2.51/1.50
% 2.51/1.50 % (17878)Memory used [KB]: 1279
% 2.51/1.50 % (17878)Time elapsed: 0.003 s
% 2.51/1.50 % (17878)Instructions burned: 4 (million)
% 2.51/1.50 % (17878)------------------------------
% 2.51/1.50 % (17878)------------------------------
% 2.51/1.50 % (17879)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_17587 for (2999ds/37Mi)
% 2.51/1.51 % (17873)Instruction limit reached!
% 2.51/1.51 % (17873)------------------------------
% 2.51/1.51 % (17873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.51 % (17873)Termination reason: Unknown
% 2.51/1.51 % (17873)Termination phase: Property scanning
% 2.51/1.51
% 2.51/1.51 % (17873)Memory used [KB]: 2174
% 2.51/1.51 % (17873)Time elapsed: 0.018 s
% 2.51/1.51 % (17873)Instructions burned: 27 (million)
% 2.51/1.51 % (17873)------------------------------
% 2.51/1.51 % (17873)------------------------------
% 2.51/1.51 % (17882)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_17587 for (2999ds/1041Mi)
% 2.51/1.51 % (17880)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_17587 for (2999ds/15Mi)
% 2.51/1.51 % (17881)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_17587 for (2999ds/3Mi)
% 2.51/1.51 % (17881)Instruction limit reached!
% 2.51/1.51 % (17881)------------------------------
% 2.51/1.51 % (17881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.51 % (17881)Termination reason: Unknown
% 2.51/1.51 % (17881)Termination phase: shuffling
% 2.51/1.51
% 2.51/1.51 % (17881)Memory used [KB]: 1279
% 2.51/1.51 % (17881)Time elapsed: 0.004 s
% 2.51/1.51 % (17881)Instructions burned: 4 (million)
% 2.51/1.51 % (17881)------------------------------
% 2.51/1.51 % (17881)------------------------------
% 2.51/1.51 % (17879)Instruction limit reached!
% 2.51/1.51 % (17879)------------------------------
% 2.51/1.51 % (17879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.51 % (17879)Termination reason: Unknown
% 2.51/1.51 % (17879)Termination phase: Property scanning
% 2.51/1.51
% 2.51/1.51 % (17879)Memory used [KB]: 1918
% 2.51/1.51 % (17879)Time elapsed: 0.013 s
% 2.51/1.51 % (17879)Instructions burned: 39 (million)
% 2.51/1.51 % (17879)------------------------------
% 2.51/1.51 % (17879)------------------------------
% 2.51/1.51 % (17876)Refutation not found, incomplete strategy
% 2.51/1.51 % (17876)------------------------------
% 2.51/1.51 % (17876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.51 % (17876)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.51
% 2.51/1.51
% 2.51/1.51 % (17876)Memory used [KB]: 6652
% 2.51/1.51 % (17876)Time elapsed: 0.024 s
% 2.51/1.51 % (17876)Instructions burned: 38 (million)
% 2.51/1.51 % (17876)------------------------------
% 2.51/1.51 % (17876)------------------------------
% 2.51/1.52 % (17880)Instruction limit reached!
% 2.51/1.52 % (17880)------------------------------
% 2.51/1.52 % (17880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.52 % (17880)Termination reason: Unknown
% 2.51/1.52 % (17880)Termination phase: shuffling
% 2.51/1.52
% 2.51/1.52 % (17880)Memory used [KB]: 1918
% 2.51/1.52 % (17880)Time elapsed: 0.011 s
% 2.51/1.52 % (17880)Instructions burned: 16 (million)
% 2.51/1.52 % (17880)------------------------------
% 2.51/1.52 % (17880)------------------------------
% 2.51/1.52 % (17885)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_17587 for (2999ds/3Mi)
% 2.51/1.52 % (17885)Instruction limit reached!
% 2.51/1.52 % (17885)------------------------------
% 2.51/1.52 % (17885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.52 % (17885)Termination reason: Unknown
% 2.51/1.52 % (17885)Termination phase: shuffling
% 2.51/1.52
% 2.51/1.52 % (17885)Memory used [KB]: 1279
% 2.51/1.52 % (17885)Time elapsed: 0.002 s
% 2.51/1.52 % (17885)Instructions burned: 4 (million)
% 2.51/1.52 % (17885)------------------------------
% 2.51/1.52 % (17885)------------------------------
% 2.51/1.53 % (17883)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/7Mi)
% 2.51/1.53 % (17883)Instruction limit reached!
% 2.51/1.53 % (17883)------------------------------
% 2.51/1.53 % (17883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.53 % (17883)Termination reason: Unknown
% 2.51/1.53 % (17883)Termination phase: shuffling
% 2.51/1.53
% 2.51/1.53 % (17883)Memory used [KB]: 1407
% 2.51/1.53 % (17883)Time elapsed: 0.006 s
% 2.51/1.53 % (17883)Instructions burned: 7 (million)
% 2.51/1.53 % (17883)------------------------------
% 2.51/1.53 % (17883)------------------------------
% 2.51/1.53 % (17884)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/16Mi)
% 2.51/1.53 % (17886)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_17587 for (2999ds/3Mi)
% 2.51/1.53 % (17871)Instruction limit reached!
% 2.51/1.53 % (17871)------------------------------
% 2.51/1.53 % (17871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.53 % (17871)Termination reason: Unknown
% 2.51/1.53 % (17871)Termination phase: Property scanning
% 2.51/1.53
% 2.51/1.53 % (17871)Memory used [KB]: 4477
% 2.51/1.53 % (17871)Time elapsed: 0.051 s
% 2.51/1.53 % (17871)Instructions burned: 184 (million)
% 2.51/1.53 % (17871)------------------------------
% 2.51/1.53 % (17871)------------------------------
% 2.51/1.53 % (17888)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/3Mi)
% 2.51/1.53 % (17886)Instruction limit reached!
% 2.51/1.53 % (17886)------------------------------
% 2.51/1.53 % (17886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.53 % (17886)Termination reason: Unknown
% 2.51/1.53 % (17886)Termination phase: shuffling
% 2.51/1.53
% 2.51/1.53 % (17886)Memory used [KB]: 1279
% 2.51/1.53 % (17886)Time elapsed: 0.004 s
% 2.51/1.53 % (17886)Instructions burned: 4 (million)
% 2.51/1.53 % (17886)------------------------------
% 2.51/1.53 % (17886)------------------------------
% 2.51/1.54 % (17888)Instruction limit reached!
% 2.51/1.54 % (17888)------------------------------
% 2.51/1.54 % (17888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (17888)Termination reason: Unknown
% 2.51/1.54 % (17888)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (17888)Memory used [KB]: 1279
% 2.51/1.54 % (17888)Time elapsed: 0.003 s
% 2.51/1.54 % (17888)Instructions burned: 4 (million)
% 2.51/1.54 % (17888)------------------------------
% 2.51/1.54 % (17888)------------------------------
% 2.51/1.54 % (17887)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/7Mi)
% 2.51/1.54 % (17884)Instruction limit reached!
% 2.51/1.54 % (17884)------------------------------
% 2.51/1.54 % (17884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (17884)Termination reason: Unknown
% 2.51/1.54 % (17884)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (17884)Memory used [KB]: 1918
% 2.51/1.54 % (17884)Time elapsed: 0.011 s
% 2.51/1.54 % (17884)Instructions burned: 16 (million)
% 2.51/1.54 % (17884)------------------------------
% 2.51/1.54 % (17884)------------------------------
% 2.51/1.54 % (17887)Instruction limit reached!
% 2.51/1.54 % (17887)------------------------------
% 2.51/1.54 % (17887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.54 % (17887)Termination reason: Unknown
% 2.51/1.54 % (17887)Termination phase: shuffling
% 2.51/1.54
% 2.51/1.54 % (17887)Memory used [KB]: 1407
% 2.51/1.54 % (17887)Time elapsed: 0.006 s
% 2.51/1.54 % (17887)Instructions burned: 8 (million)
% 2.51/1.54 % (17887)------------------------------
% 2.51/1.54 % (17887)------------------------------
% 2.51/1.54 % (17890)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/18Mi)
% 2.51/1.55 % (17892)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/6Mi)
% 2.51/1.55 % (17889)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/4Mi)
% 2.51/1.55 % (17892)Instruction limit reached!
% 2.51/1.55 % (17892)------------------------------
% 2.51/1.55 % (17892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.55 % (17892)Termination reason: Unknown
% 2.51/1.55 % (17892)Termination phase: shuffling
% 2.51/1.55
% 2.51/1.55 % (17892)Memory used [KB]: 1407
% 2.51/1.55 % (17892)Time elapsed: 0.004 s
% 2.51/1.55 % (17892)Instructions burned: 7 (million)
% 2.51/1.55 % (17892)------------------------------
% 2.51/1.55 % (17892)------------------------------
% 2.51/1.55 % (17889)Instruction limit reached!
% 2.51/1.55 % (17889)------------------------------
% 2.51/1.55 % (17889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.55 % (17889)Termination reason: Unknown
% 2.51/1.55 % (17889)Termination phase: shuffling
% 2.51/1.55
% 2.51/1.55 % (17889)Memory used [KB]: 1279
% 2.51/1.55 % (17889)Time elapsed: 0.004 s
% 2.51/1.55 % (17889)Instructions burned: 4 (million)
% 2.51/1.55 % (17889)------------------------------
% 2.51/1.55 % (17889)------------------------------
% 2.51/1.55 % (17890)Instruction limit reached!
% 2.51/1.55 % (17890)------------------------------
% 2.51/1.55 % (17890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.55 % (17890)Termination reason: Unknown
% 2.51/1.55 % (17890)Termination phase: shuffling
% 2.51/1.55
% 2.51/1.55 % (17890)Memory used [KB]: 2046
% 2.51/1.55 % (17890)Time elapsed: 0.007 s
% 2.51/1.55 % (17890)Instructions burned: 19 (million)
% 2.51/1.55 % (17890)------------------------------
% 2.51/1.55 % (17890)------------------------------
% 2.51/1.55 % (17891)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/710Mi)
% 2.51/1.56 % (17893)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_17587 for (2999ds/902Mi)
% 2.51/1.56 % (17894)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_17587 for (2999ds/21Mi)
% 2.51/1.56 % (17895)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/5Mi)
% 2.51/1.56 % (17897)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/377Mi)
% 2.51/1.56 % (17895)Instruction limit reached!
% 2.51/1.56 % (17895)------------------------------
% 2.51/1.56 % (17895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.56 % (17895)Termination reason: Unknown
% 2.51/1.56 % (17895)Termination phase: shuffling
% 2.51/1.56
% 2.51/1.56 % (17895)Memory used [KB]: 1407
% 2.51/1.56 % (17895)Time elapsed: 0.003 s
% 2.51/1.56 % (17895)Instructions burned: 7 (million)
% 2.51/1.56 % (17895)------------------------------
% 2.51/1.56 % (17895)------------------------------
% 2.51/1.57 % (17894)Instruction limit reached!
% 2.51/1.57 % (17894)------------------------------
% 2.51/1.57 % (17894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.57 % (17894)Termination reason: Unknown
% 2.51/1.57 % (17894)Termination phase: shuffling
% 2.51/1.57
% 2.51/1.57 % (17894)Memory used [KB]: 2174
% 2.51/1.57 % (17894)Time elapsed: 0.010 s
% 2.51/1.57 % (17894)Instructions burned: 23 (million)
% 2.51/1.57 % (17894)------------------------------
% 2.51/1.57 % (17894)------------------------------
% 2.51/1.57 % (17896)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_17587 for (2999ds/6Mi)
% 2.51/1.57 % (17898)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_17587 for (2999ds/779Mi)
% 2.51/1.57 % (17896)Instruction limit reached!
% 2.51/1.57 % (17896)------------------------------
% 2.51/1.57 % (17896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.57 % (17896)Termination reason: Unknown
% 2.51/1.57 % (17896)Termination phase: shuffling
% 2.51/1.57
% 2.51/1.57 % (17896)Memory used [KB]: 1407
% 2.51/1.57 % (17896)Time elapsed: 0.005 s
% 2.51/1.57 % (17896)Instructions burned: 6 (million)
% 2.51/1.57 % (17896)------------------------------
% 2.51/1.57 % (17896)------------------------------
% 2.51/1.58 % (17899)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_17587 for (2999ds/19Mi)
% 2.51/1.58 % (17899)Instruction limit reached!
% 2.51/1.58 % (17899)------------------------------
% 2.51/1.58 % (17899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (17899)Termination reason: Unknown
% 2.51/1.58 % (17899)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (17899)Memory used [KB]: 1663
% 2.51/1.58 % (17899)Time elapsed: 0.007 s
% 2.51/1.58 % (17899)Instructions burned: 21 (million)
% 2.51/1.58 % (17899)------------------------------
% 2.51/1.58 % (17899)------------------------------
% 2.51/1.58 % (17900)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17587 for (2999ds/879Mi)
% 2.51/1.59 % (17901)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17587 for (2998ds/17Mi)
% 2.51/1.60 % (17901)Instruction limit reached!
% 2.51/1.60 % (17901)------------------------------
% 2.51/1.60 % (17901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (17901)Termination reason: Unknown
% 2.51/1.60 % (17901)Termination phase: shuffling
% 2.51/1.60
% 2.51/1.60 % (17901)Memory used [KB]: 2046
% 2.51/1.60 % (17901)Time elapsed: 0.007 s
% 2.51/1.60 % (17901)Instructions burned: 18 (million)
% 2.51/1.60 % (17901)------------------------------
% 2.51/1.60 % (17901)------------------------------
% 2.51/1.61 % (17902)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17587 for (2998ds/3Mi)
% 2.51/1.61 % (17902)Instruction limit reached!
% 2.51/1.61 % (17902)------------------------------
% 2.51/1.61 % (17902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.61 % (17902)Termination reason: Unknown
% 2.51/1.61 % (17902)Termination phase: shuffling
% 2.51/1.61
% 2.51/1.61 % (17902)Memory used [KB]: 1279
% 2.51/1.61 % (17902)Time elapsed: 0.003 s
% 2.51/1.61 % (17902)Instructions burned: 4 (million)
% 2.51/1.61 % (17902)------------------------------
% 2.51/1.61 % (17902)------------------------------
% 2.51/1.62 % (17903)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17587 for (2998ds/30Mi)
% 2.51/1.63 % (17893)Refutation not found, incomplete strategy
% 2.51/1.63 % (17893)------------------------------
% 2.51/1.63 % (17893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (17893)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.63
% 2.51/1.63
% 2.51/1.63 % (17893)Memory used [KB]: 9210
% 2.51/1.63 % (17893)Time elapsed: 0.074 s
% 2.51/1.63 % (17893)Instructions burned: 201 (million)
% 2.51/1.63 % (17893)------------------------------
% 2.51/1.63 % (17893)------------------------------
% 2.51/1.63 % (17903)Instruction limit reached!
% 2.51/1.63 % (17903)------------------------------
% 2.51/1.63 % (17903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (17903)Termination reason: Unknown
% 2.51/1.63 % (17903)Termination phase: Property scanning
% 2.51/1.63
% 2.51/1.63 % (17903)Memory used [KB]: 2174
% 2.51/1.63 % (17903)Time elapsed: 0.012 s
% 2.51/1.63 % (17903)Instructions burned: 31 (million)
% 2.51/1.63 % (17903)------------------------------
% 2.51/1.63 % (17903)------------------------------
% 2.51/1.64 % (17904)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17587 for (2998ds/127Mi)
% 2.51/1.64 % (17905)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17587 for (2998ds/100Mi)
% 2.51/1.67 % (17905)Instruction limit reached!
% 2.51/1.67 % (17905)------------------------------
% 2.51/1.67 % (17905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.67 % (17905)Termination reason: Unknown
% 2.51/1.67 % (17905)Termination phase: Saturation
% 2.51/1.67
% 2.51/1.67 % (17905)Memory used [KB]: 6524
% 2.51/1.67 % (17905)Time elapsed: 0.029 s
% 2.51/1.67 % (17905)Instructions burned: 100 (million)
% 2.51/1.67 % (17905)------------------------------
% 2.51/1.67 % (17905)------------------------------
% 2.51/1.67 % (17897)Instruction limit reached!
% 2.51/1.67 % (17897)------------------------------
% 2.51/1.67 % (17897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.67 % (17897)Termination reason: Unknown
% 2.51/1.67 % (17897)Termination phase: Saturation
% 2.51/1.67
% 2.51/1.67 % (17897)Memory used [KB]: 10234
% 2.51/1.67 % (17897)Time elapsed: 0.110 s
% 2.51/1.67 % (17897)Instructions burned: 380 (million)
% 2.51/1.67 % (17897)------------------------------
% 2.51/1.67 % (17897)------------------------------
% 2.51/1.68 % (17907)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_17587 for (2998ds/20Mi)
% 2.51/1.68 % (17906)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_17587 for (2998ds/3Mi)
% 2.51/1.68 % (17904)Instruction limit reached!
% 2.51/1.68 % (17904)------------------------------
% 2.51/1.68 % (17904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (17904)Termination reason: Unknown
% 2.51/1.68 % (17904)Termination phase: Property scanning
% 2.51/1.68
% 2.51/1.68 % (17904)Memory used [KB]: 4221
% 2.51/1.68 % (17904)Time elapsed: 0.039 s
% 2.51/1.68 % (17904)Instructions burned: 127 (million)
% 2.51/1.68 % (17904)------------------------------
% 2.51/1.68 % (17904)------------------------------
% 2.51/1.68 % (17906)Instruction limit reached!
% 2.51/1.68 % (17906)------------------------------
% 2.51/1.68 % (17906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (17906)Termination reason: Unknown
% 2.51/1.68 % (17906)Termination phase: shuffling
% 2.51/1.68
% 2.51/1.68 % (17906)Memory used [KB]: 1279
% 2.51/1.68 % (17906)Time elapsed: 0.002 s
% 2.51/1.68 % (17906)Instructions burned: 4 (million)
% 2.51/1.68 % (17906)------------------------------
% 2.51/1.68 % (17906)------------------------------
% 2.51/1.68 % (17907)Instruction limit reached!
% 2.51/1.68 % (17907)------------------------------
% 2.51/1.68 % (17907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (17907)Termination reason: Unknown
% 2.51/1.68 % (17907)Termination phase: shuffling
% 2.51/1.68
% 2.51/1.68 % (17907)Memory used [KB]: 2046
% 2.51/1.68 % (17907)Time elapsed: 0.008 s
% 2.51/1.68 % (17907)Instructions burned: 22 (million)
% 2.51/1.68 % (17907)------------------------------
% 2.51/1.68 % (17907)------------------------------
% 2.51/1.69 % (17908)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_17587 for (2997ds/86Mi)
% 2.51/1.69 % (17909)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_17587 for (2997ds/107Mi)
% 2.51/1.69 % (17911)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_17587 for (2997ds/39Mi)
% 2.51/1.70 % (17911)Instruction limit reached!
% 2.51/1.70 % (17911)------------------------------
% 2.51/1.70 % (17911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.70 % (17911)Termination reason: Unknown
% 2.51/1.70 % (17911)Termination phase: Property scanning
% 2.51/1.70
% 2.51/1.70 % (17911)Memory used [KB]: 1918
% 2.51/1.70 % (17911)Time elapsed: 0.011 s
% 2.51/1.70 % (17911)Instructions burned: 39 (million)
% 2.51/1.70 % (17911)------------------------------
% 2.51/1.70 % (17911)------------------------------
% 2.51/1.71 % (17912)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_17587 for (2997ds/448Mi)
% 2.51/1.72 % (17908)Instruction limit reached!
% 2.51/1.72 % (17908)------------------------------
% 2.51/1.72 % (17908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.72 % (17908)Termination reason: Unknown
% 2.51/1.72 % (17908)Termination phase: Preprocessing 3
% 2.51/1.72
% 2.51/1.72 % (17908)Memory used [KB]: 4093
% 2.51/1.72 % (17908)Time elapsed: 0.028 s
% 2.51/1.72 % (17908)Instructions burned: 87 (million)
% 2.51/1.72 % (17908)------------------------------
% 2.51/1.72 % (17908)------------------------------
% 2.51/1.72 % (17909)Instruction limit reached!
% 2.51/1.72 % (17909)------------------------------
% 2.51/1.72 % (17909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.72 % (17909)Termination reason: Unknown
% 2.51/1.72 % (17909)Termination phase: Property scanning
% 2.51/1.72
% 2.51/1.72 % (17909)Memory used [KB]: 4349
% 2.51/1.72 % (17909)Time elapsed: 0.034 s
% 2.51/1.72 % (17909)Instructions burned: 107 (million)
% 2.51/1.72 % (17909)------------------------------
% 2.51/1.72 % (17909)------------------------------
% 2.51/1.73 % (17913)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_17587 for (2997ds/46Mi)
% 2.51/1.73 % (17914)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_17587 for (2997ds/98Mi)
% 2.51/1.73 % (17912)Refutation not found, incomplete strategy
% 2.51/1.73 % (17912)------------------------------
% 2.51/1.73 % (17912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.73 % (17912)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.73
% 2.51/1.73
% 2.51/1.73 % (17912)Memory used [KB]: 6524
% 2.51/1.73 % (17912)Time elapsed: 0.021 s
% 2.51/1.73 % (17912)Instructions burned: 78 (million)
% 2.51/1.73 % (17912)------------------------------
% 2.51/1.73 % (17912)------------------------------
% 2.51/1.74 % (17913)Instruction limit reached!
% 2.51/1.74 % (17913)------------------------------
% 2.51/1.74 % (17913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.74 % (17913)Termination reason: Unknown
% 2.51/1.74 % (17913)Termination phase: shuffling
% 2.51/1.74
% 2.51/1.74 % (17913)Memory used [KB]: 2302
% 2.51/1.74 % (17913)Time elapsed: 0.016 s
% 2.51/1.74 % (17913)Instructions burned: 46 (million)
% 2.51/1.74 % (17913)------------------------------
% 2.51/1.74 % (17913)------------------------------
% 2.51/1.74 % (17915)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_17587 for (2997ds/507Mi)
% 2.51/1.75 % (17916)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_17587 for (2997ds/149Mi)
% 2.51/1.76 % (17898)Instruction limit reached!
% 2.51/1.76 % (17898)------------------------------
% 2.51/1.76 % (17898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.76 % (17898)Termination reason: Unknown
% 2.51/1.76 % (17898)Termination phase: Saturation
% 2.51/1.76
% 2.51/1.76 % (17898)Memory used [KB]: 7036
% 2.51/1.76 % (17898)Time elapsed: 0.191 s
% 2.51/1.76 % (17898)Instructions burned: 782 (million)
% 2.51/1.76 % (17898)------------------------------
% 2.51/1.76 % (17898)------------------------------
% 2.51/1.76 % (17914)Instruction limit reached!
% 2.51/1.76 % (17914)------------------------------
% 2.51/1.76 % (17914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.76 % (17914)Termination reason: Unknown
% 2.51/1.76 % (17914)Termination phase: Saturation
% 2.51/1.76
% 2.51/1.76 % (17914)Memory used [KB]: 2046
% 2.51/1.76 % (17914)Time elapsed: 0.029 s
% 2.51/1.76 % (17914)Instructions burned: 100 (million)
% 2.51/1.76 % (17914)------------------------------
% 2.51/1.76 % (17914)------------------------------
% 2.51/1.77 % (17882)Instruction limit reached!
% 2.51/1.77 % (17882)------------------------------
% 2.51/1.77 % (17882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.77 % (17882)Termination reason: Unknown
% 2.51/1.77 % (17882)Termination phase: Saturation
% 2.51/1.77
% 2.51/1.77 % (17882)Memory used [KB]: 7675
% 2.51/1.77 % (17882)Time elapsed: 0.260 s
% 2.51/1.77 % (17882)Instructions burned: 1041 (million)
% 2.51/1.77 % (17882)------------------------------
% 2.51/1.77 % (17882)------------------------------
% 2.51/1.77 % (17917)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17587 for (2997ds/39Mi)
% 2.51/1.77 % (17918)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_17587 for (2996ds/6Mi)
% 2.51/1.77 % (17918)Instruction limit reached!
% 2.51/1.77 % (17918)------------------------------
% 2.51/1.77 % (17918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.77 % (17918)Termination reason: Unknown
% 2.51/1.77 % (17918)Termination phase: shuffling
% 2.51/1.77
% 2.51/1.77 % (17918)Memory used [KB]: 1407
% 2.51/1.77 % (17918)Time elapsed: 0.003 s
% 2.51/1.77 % (17918)Instructions burned: 7 (million)
% 2.51/1.77 % (17918)------------------------------
% 2.51/1.77 % (17918)------------------------------
% 2.51/1.78 % (17919)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_17587 for (2996ds/1087Mi)
% 2.51/1.78 % (17917)Instruction limit reached!
% 2.51/1.78 % (17917)------------------------------
% 2.51/1.78 % (17917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.78 % (17917)Termination reason: Unknown
% 2.51/1.78 % (17917)Termination phase: Preprocessing 1
% 2.51/1.78
% 2.51/1.78 % (17917)Memory used [KB]: 2302
% 2.51/1.78 % (17917)Time elapsed: 0.013 s
% 2.51/1.78 % (17917)Instructions burned: 40 (million)
% 2.51/1.78 % (17917)------------------------------
% 2.51/1.78 % (17917)------------------------------
% 2.51/1.78 % (17920)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/47Mi)
% 2.51/1.79 % (17921)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_17587 for (2996ds/44Mi)
% 2.51/1.80 % (17891)Instruction limit reached!
% 2.51/1.80 % (17891)------------------------------
% 2.51/1.80 % (17891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.80 % (17891)Termination reason: Unknown
% 2.51/1.80 % (17891)Termination phase: Saturation
% 2.51/1.80
% 2.51/1.80 % (17891)Memory used [KB]: 10874
% 2.51/1.80 % (17891)Time elapsed: 0.246 s
% 2.51/1.80 % (17891)Instructions burned: 710 (million)
% 2.51/1.80 % (17891)------------------------------
% 2.51/1.80 % (17891)------------------------------
% 2.51/1.80 % (17916)Instruction limit reached!
% 2.51/1.80 % (17916)------------------------------
% 2.51/1.80 % (17916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.80 % (17916)Termination reason: Unknown
% 2.51/1.80 % (17916)Termination phase: Property scanning
% 2.51/1.80
% 2.51/1.80 % (17916)Memory used [KB]: 7803
% 2.51/1.80 % (17916)Time elapsed: 0.047 s
% 2.51/1.80 % (17916)Instructions burned: 151 (million)
% 2.51/1.80 % (17916)------------------------------
% 2.51/1.80 % (17916)------------------------------
% 2.51/1.80 % (17920)Instruction limit reached!
% 2.51/1.80 % (17920)------------------------------
% 2.51/1.80 % (17920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.80 % (17920)Termination reason: Unknown
% 2.51/1.80 % (17920)Termination phase: Naming
% 2.51/1.80
% 2.51/1.80 % (17920)Memory used [KB]: 2558
% 2.51/1.80 % (17920)Time elapsed: 0.017 s
% 2.51/1.80 % (17920)Instructions burned: 47 (million)
% 2.51/1.80 % (17920)------------------------------
% 2.51/1.80 % (17920)------------------------------
% 2.51/1.80 % (17921)Instruction limit reached!
% 2.51/1.80 % (17921)------------------------------
% 2.51/1.80 % (17921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.80 % (17921)Termination reason: Unknown
% 2.51/1.80 % (17921)Termination phase: Property scanning
% 2.51/1.80
% 2.51/1.80 % (17921)Memory used [KB]: 1918
% 2.51/1.80 % (17921)Time elapsed: 0.013 s
% 2.51/1.80 % (17921)Instructions burned: 44 (million)
% 2.51/1.80 % (17921)------------------------------
% 2.51/1.80 % (17921)------------------------------
% 2.51/1.81 % (17922)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_17587 for (2996ds/432Mi)
% 2.51/1.81 % (17923)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/62Mi)
% 2.51/1.81 % (17924)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_17587 for (2996ds/31Mi)
% 2.51/1.81 % (17925)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/96Mi)
% 2.51/1.82 % (17924)Instruction limit reached!
% 2.51/1.82 % (17924)------------------------------
% 2.51/1.82 % (17924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.82 % (17924)Termination reason: Unknown
% 2.51/1.82 % (17924)Termination phase: Property scanning
% 2.51/1.82
% 2.51/1.82 % (17924)Memory used [KB]: 2174
% 2.51/1.82 % (17924)Time elapsed: 0.012 s
% 2.51/1.82 % (17924)Instructions burned: 31 (million)
% 2.51/1.82 % (17924)------------------------------
% 2.51/1.82 % (17924)------------------------------
% 2.51/1.82 % (17915)Refutation not found, incomplete strategy
% 2.51/1.82 % (17915)------------------------------
% 2.51/1.82 % (17915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.82 % (17915)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.82
% 2.51/1.82
% 2.51/1.82 % (17915)Memory used [KB]: 9850
% 2.51/1.82 % (17915)Time elapsed: 0.079 s
% 2.51/1.82 % (17915)Instructions burned: 274 (million)
% 2.51/1.82 % (17915)------------------------------
% 2.51/1.82 % (17915)------------------------------
% 2.51/1.82 % (17923)Instruction limit reached!
% 2.51/1.82 % (17923)------------------------------
% 2.51/1.82 % (17923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.82 % (17923)Termination reason: Unknown
% 2.51/1.82 % (17923)Termination phase: Property scanning
% 2.51/1.82
% 2.51/1.82 % (17923)Memory used [KB]: 1918
% 2.51/1.82 % (17923)Time elapsed: 0.018 s
% 2.51/1.82 % (17923)Instructions burned: 62 (million)
% 2.51/1.82 % (17923)------------------------------
% 2.51/1.82 % (17923)------------------------------
% 2.51/1.83 % (17926)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_17587 for (2996ds/453Mi)
% 2.51/1.83 % (17927)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_17587 for (2996ds/71Mi)
% 2.51/1.83 % (17928)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/83Mi)
% 2.51/1.84 % (17925)Instruction limit reached!
% 2.51/1.84 % (17925)------------------------------
% 2.51/1.84 % (17925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.84 % (17925)Termination reason: Unknown
% 2.51/1.84 % (17925)Termination phase: Property scanning
% 2.51/1.84
% 2.51/1.84 % (17925)Memory used [KB]: 4349
% 2.51/1.84 % (17925)Time elapsed: 0.029 s
% 2.51/1.84 % (17925)Instructions burned: 97 (million)
% 2.51/1.84 % (17925)------------------------------
% 2.51/1.84 % (17925)------------------------------
% 2.51/1.85 % (17928)Refutation not found, incomplete strategy
% 2.51/1.85 % (17928)------------------------------
% 2.51/1.85 % (17928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.85 % (17928)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.85
% 2.51/1.85
% 2.51/1.85 % (17928)Memory used [KB]: 6652
% 2.51/1.85 % (17928)Time elapsed: 0.015 s
% 2.51/1.85 % (17928)Instructions burned: 41 (million)
% 2.51/1.85 % (17928)------------------------------
% 2.51/1.85 % (17928)------------------------------
% 2.51/1.85 % (17929)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/11Mi)
% 2.51/1.85 % (17929)Instruction limit reached!
% 2.51/1.85 % (17929)------------------------------
% 2.51/1.85 % (17929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.85 % (17929)Termination reason: Unknown
% 2.51/1.85 % (17929)Termination phase: shuffling
% 2.51/1.85
% 2.51/1.85 % (17929)Memory used [KB]: 1535
% 2.51/1.85 % (17929)Time elapsed: 0.004 s
% 2.51/1.85 % (17929)Instructions burned: 11 (million)
% 2.51/1.85 % (17929)------------------------------
% 2.51/1.85 % (17929)------------------------------
% 2.51/1.85 % (17927)Instruction limit reached!
% 2.51/1.85 % (17927)------------------------------
% 2.51/1.85 % (17927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.85 % (17927)Termination reason: Unknown
% 2.51/1.85 % (17927)Termination phase: Preprocessing 3
% 2.51/1.85
% 2.51/1.85 % (17927)Memory used [KB]: 3454
% 2.51/1.85 % (17927)Time elapsed: 0.022 s
% 2.51/1.85 % (17927)Instructions burned: 73 (million)
% 2.51/1.85 % (17927)------------------------------
% 2.51/1.85 % (17927)------------------------------
% 2.51/1.86 % (17930)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_17587 for (2996ds/41Mi)
% 2.51/1.86 % (17931)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/6Mi)
% 2.51/1.86 % (17932)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/150Mi)
% 2.51/1.86 % (17931)Instruction limit reached!
% 2.51/1.86 % (17931)------------------------------
% 2.51/1.86 % (17931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.86 % (17931)Termination reason: Unknown
% 2.51/1.86 % (17931)Termination phase: shuffling
% 2.51/1.86
% 2.51/1.86 % (17931)Memory used [KB]: 1407
% 2.51/1.86 % (17931)Time elapsed: 0.003 s
% 2.51/1.86 % (17931)Instructions burned: 7 (million)
% 2.51/1.86 % (17931)------------------------------
% 2.51/1.86 % (17931)------------------------------
% 2.51/1.87 % (17900)Instruction limit reached!
% 2.51/1.87 % (17900)------------------------------
% 2.51/1.87 % (17900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.87 % (17900)Termination reason: Unknown
% 2.51/1.87 % (17900)Termination phase: Saturation
% 2.51/1.87
% 2.51/1.87 % (17900)Memory used [KB]: 11129
% 2.51/1.87 % (17900)Time elapsed: 0.287 s
% 2.51/1.87 % (17900)Instructions burned: 879 (million)
% 2.51/1.87 % (17900)------------------------------
% 2.51/1.87 % (17900)------------------------------
% 2.51/1.87 % (17930)Instruction limit reached!
% 2.51/1.87 % (17930)------------------------------
% 2.51/1.87 % (17930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.87 % (17930)Termination reason: Unknown
% 2.51/1.87 % (17930)Termination phase: Property scanning
% 2.51/1.87
% 2.51/1.87 % (17930)Memory used [KB]: 1918
% 2.51/1.87 % (17930)Time elapsed: 0.014 s
% 2.51/1.87 % (17930)Instructions burned: 44 (million)
% 2.51/1.87 % (17930)------------------------------
% 2.51/1.87 % (17930)------------------------------
% 2.51/1.87 % (17933)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17587 for (2996ds/343Mi)
% 2.51/1.88 % (17934)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_17587 for (2995ds/109Mi)
% 2.51/1.88 % (17935)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_17587 for (2995ds/253Mi)
% 2.51/1.88 % (17933)Refutation not found, incomplete strategy
% 2.51/1.88 % (17933)------------------------------
% 2.51/1.88 % (17933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.88 % (17933)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.88
% 2.51/1.88
% 2.51/1.88 % (17933)Memory used [KB]: 6652
% 2.51/1.88 % (17933)Time elapsed: 0.013 s
% 2.51/1.88 % (17933)Instructions burned: 41 (million)
% 2.51/1.88 % (17933)------------------------------
% 2.51/1.88 % (17933)------------------------------
% 2.51/1.89 % (17935)Refutation not found, incomplete strategy
% 2.51/1.89 % (17935)------------------------------
% 2.51/1.89 % (17935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.89 % (17935)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.89
% 2.51/1.89
% 2.51/1.89 % (17935)Memory used [KB]: 6652
% 2.51/1.89 % (17935)Time elapsed: 0.014 s
% 2.51/1.89 % (17935)Instructions burned: 37 (million)
% 2.51/1.89 % (17935)------------------------------
% 2.51/1.89 % (17935)------------------------------
% 2.51/1.89 % (17936)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/140Mi)
% 2.51/1.90 % (17932)Instruction limit reached!
% 2.51/1.90 % (17932)------------------------------
% 2.51/1.90 % (17932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.90 % (17932)Termination reason: Unknown
% 2.51/1.90 % (17932)Termination phase: Property scanning
% 2.51/1.90
% 2.51/1.90 % (17932)Memory used [KB]: 4093
% 2.51/1.90 % (17932)Time elapsed: 0.042 s
% 2.51/1.90 % (17932)Instructions burned: 153 (million)
% 2.51/1.90 % (17932)------------------------------
% 2.51/1.90 % (17932)------------------------------
% 2.51/1.90 % (17937)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/614Mi)
% 2.51/1.91 % (17934)Instruction limit reached!
% 2.51/1.91 % (17934)------------------------------
% 2.51/1.91 % (17934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.91 % (17934)Termination reason: Unknown
% 2.51/1.91 % (17934)Termination phase: Property scanning
% 2.51/1.91
% 2.51/1.91 % (17934)Memory used [KB]: 4221
% 2.51/1.91 % (17934)Time elapsed: 0.035 s
% 2.51/1.91 % (17934)Instructions burned: 110 (million)
% 2.51/1.91 % (17934)------------------------------
% 2.51/1.91 % (17934)------------------------------
% 2.51/1.91 % (17938)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/202Mi)
% 2.51/1.92 % (17939)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/339Mi)
% 2.51/1.92 % (17922)Instruction limit reached!
% 2.51/1.92 % (17922)------------------------------
% 2.51/1.92 % (17922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.92 % (17922)Termination reason: Unknown
% 2.51/1.92 % (17922)Termination phase: Saturation
% 2.51/1.92
% 2.51/1.92 % (17922)Memory used [KB]: 2558
% 2.51/1.92 % (17922)Time elapsed: 0.119 s
% 2.51/1.92 % (17922)Instructions burned: 434 (million)
% 2.51/1.92 % (17922)------------------------------
% 2.51/1.92 % (17922)------------------------------
% 2.51/1.93 % (17936)Instruction limit reached!
% 2.51/1.93 % (17936)------------------------------
% 2.51/1.93 % (17936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.93 % (17936)Termination reason: Unknown
% 2.51/1.93 % (17936)Termination phase: Property scanning
% 2.51/1.93
% 2.51/1.93 % (17936)Memory used [KB]: 4221
% 2.51/1.93 % (17936)Time elapsed: 0.039 s
% 2.51/1.93 % (17936)Instructions burned: 140 (million)
% 2.51/1.93 % (17936)------------------------------
% 2.51/1.93 % (17936)------------------------------
% 2.51/1.94 % (17940)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/283Mi)
% 2.51/1.94 % (17941)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/134Mi)
% 2.51/1.95 % (17926)Instruction limit reached!
% 2.51/1.95 % (17926)------------------------------
% 2.51/1.95 % (17926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.95 % (17926)Termination reason: Unknown
% 2.51/1.95 % (17926)Termination phase: Saturation
% 2.51/1.95
% 2.51/1.95 % (17926)Memory used [KB]: 6652
% 2.51/1.95 % (17926)Time elapsed: 0.119 s
% 2.51/1.95 % (17926)Instructions burned: 454 (million)
% 2.51/1.95 % (17926)------------------------------
% 2.51/1.95 % (17926)------------------------------
% 2.51/1.96 % (17942)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/298Mi)
% 2.51/1.97 % (17938)Instruction limit reached!
% 2.51/1.97 % (17938)------------------------------
% 2.51/1.97 % (17938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.97 % (17938)Termination reason: Unknown
% 2.51/1.97 % (17938)Termination phase: Saturation
% 2.51/1.97
% 2.51/1.97 % (17938)Memory used [KB]: 4477
% 2.51/1.97 % (17938)Time elapsed: 0.057 s
% 2.51/1.97 % (17938)Instructions burned: 205 (million)
% 2.51/1.97 % (17938)------------------------------
% 2.51/1.97 % (17938)------------------------------
% 2.51/1.98 % (17943)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17587 for (2995ds/192Mi)
% 2.51/1.98 % (17941)Instruction limit reached!
% 2.51/1.98 % (17941)------------------------------
% 2.51/1.98 % (17941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.98 % (17941)Termination reason: Unknown
% 2.51/1.98 % (17941)Termination phase: Property scanning
% 2.51/1.98
% 2.51/1.98 % (17941)Memory used [KB]: 4349
% 2.51/1.98 % (17941)Time elapsed: 0.040 s
% 2.51/1.98 % (17941)Instructions burned: 138 (million)
% 2.51/1.98 % (17941)------------------------------
% 2.51/1.98 % (17941)------------------------------
% 2.51/1.99 % (17944)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/258Mi)
% 2.51/2.01 % (17940)Instruction limit reached!
% 2.51/2.01 % (17940)------------------------------
% 2.51/2.01 % (17940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.01 % (17940)Termination reason: Unknown
% 2.51/2.01 % (17940)Termination phase: Saturation
% 2.51/2.01
% 2.51/2.01 % (17940)Memory used [KB]: 7291
% 2.51/2.01 % (17940)Time elapsed: 0.073 s
% 2.51/2.01 % (17940)Instructions burned: 283 (million)
% 2.51/2.01 % (17940)------------------------------
% 2.51/2.01 % (17940)------------------------------
% 6.21/2.02 % (17945)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/90Mi)
% 6.21/2.03 % (17943)Instruction limit reached!
% 6.21/2.03 % (17943)------------------------------
% 6.21/2.03 % (17943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.03 % (17943)Termination reason: Unknown
% 6.21/2.03 % (17943)Termination phase: Property scanning
% 6.21/2.03
% 6.21/2.03 % (17943)Memory used [KB]: 4477
% 6.21/2.03 % (17943)Time elapsed: 0.053 s
% 6.21/2.03 % (17943)Instructions burned: 195 (million)
% 6.21/2.03 % (17943)------------------------------
% 6.21/2.03 % (17943)------------------------------
% 6.21/2.03 % (17942)Instruction limit reached!
% 6.21/2.03 % (17942)------------------------------
% 6.21/2.03 % (17942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.03 % (17942)Termination reason: Unknown
% 6.21/2.03 % (17942)Termination phase: Saturation
% 6.21/2.03
% 6.21/2.03 % (17942)Memory used [KB]: 6524
% 6.21/2.03 % (17942)Time elapsed: 0.077 s
% 6.21/2.03 % (17942)Instructions burned: 299 (million)
% 6.21/2.03 % (17942)------------------------------
% 6.21/2.03 % (17942)------------------------------
% 6.21/2.04 % (17939)Instruction limit reached!
% 6.21/2.04 % (17939)------------------------------
% 6.21/2.04 % (17939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.04 % (17939)Termination reason: Unknown
% 6.21/2.04 % (17939)Termination phase: Saturation
% 6.21/2.04
% 6.21/2.04 % (17939)Memory used [KB]: 11513
% 6.21/2.04 % (17939)Time elapsed: 0.118 s
% 6.21/2.04 % (17939)Instructions burned: 339 (million)
% 6.21/2.04 % (17939)------------------------------
% 6.21/2.04 % (17939)------------------------------
% 6.21/2.04 % (17946)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/231Mi)
% 6.21/2.04 % (17947)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/458Mi)
% 6.21/2.04 % (17945)Instruction limit reached!
% 6.21/2.04 % (17945)------------------------------
% 6.21/2.04 % (17945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.04 % (17945)Termination reason: Unknown
% 6.21/2.04 % (17945)Termination phase: Preprocessing 3
% 6.21/2.04
% 6.21/2.04 % (17945)Memory used [KB]: 4093
% 6.21/2.04 % (17945)Time elapsed: 0.029 s
% 6.21/2.04 % (17945)Instructions burned: 93 (million)
% 6.21/2.04 % (17945)------------------------------
% 6.21/2.04 % (17945)------------------------------
% 6.21/2.05 % (17949)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/297Mi)
% 6.21/2.06 % (17948)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_17587 for (2994ds/31Mi)
% 6.21/2.06 % (17944)Instruction limit reached!
% 6.21/2.06 % (17944)------------------------------
% 6.21/2.06 % (17944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.06 % (17944)Termination reason: Unknown
% 6.21/2.06 % (17944)Termination phase: Property scanning
% 6.21/2.06
% 6.21/2.06 % (17944)Memory used [KB]: 7803
% 6.21/2.06 % (17944)Time elapsed: 0.069 s
% 6.21/2.06 % (17944)Instructions burned: 260 (million)
% 6.21/2.06 % (17944)------------------------------
% 6.21/2.06 % (17944)------------------------------
% 6.21/2.07 % (17950)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_17587 for (2994ds/987Mi)
% 6.21/2.07 % (17949)Refutation not found, incomplete strategy
% 6.21/2.07 % (17949)------------------------------
% 6.21/2.07 % (17949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.07 % (17949)Termination reason: Refutation not found, incomplete strategy
% 6.21/2.07
% 6.21/2.07
% 6.21/2.07 % (17949)Memory used [KB]: 6524
% 6.21/2.07 % (17949)Time elapsed: 0.021 s
% 6.21/2.07 % (17949)Instructions burned: 78 (million)
% 6.21/2.07 % (17949)------------------------------
% 6.21/2.07 % (17949)------------------------------
% 6.21/2.08 % (17948)Instruction limit reached!
% 6.21/2.08 % (17948)------------------------------
% 6.21/2.08 % (17948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.08 % (17948)Termination reason: Unknown
% 6.21/2.08 % (17948)Termination phase: Property scanning
% 6.21/2.08
% 6.21/2.08 % (17948)Memory used [KB]: 2174
% 6.21/2.08 % (17948)Time elapsed: 0.020 s
% 6.21/2.08 % (17948)Instructions burned: 32 (million)
% 6.21/2.08 % (17948)------------------------------
% 6.21/2.08 % (17948)------------------------------
% 6.21/2.08 % (17951)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/182Mi)
% 6.21/2.09 % (17937)Instruction limit reached!
% 6.21/2.09 % (17937)------------------------------
% 6.21/2.09 % (17937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.09 % (17937)Termination reason: Unknown
% 6.21/2.09 % (17937)Termination phase: Saturation
% 6.21/2.09
% 6.21/2.09 % (17937)Memory used [KB]: 11769
% 6.21/2.09 % (17937)Time elapsed: 0.186 s
% 6.21/2.09 % (17937)Instructions burned: 617 (million)
% 6.21/2.09 % (17937)------------------------------
% 6.21/2.09 % (17937)------------------------------
% 6.21/2.09 % (17952)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/182Mi)
% 6.21/2.10 % (17953)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/154Mi)
% 6.21/2.10 % (17946)Instruction limit reached!
% 6.21/2.10 % (17946)------------------------------
% 6.21/2.10 % (17946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.10 % (17946)Termination reason: Unknown
% 6.21/2.10 % (17946)Termination phase: Saturation
% 6.21/2.10
% 6.21/2.10 % (17946)Memory used [KB]: 7164
% 6.21/2.10 % (17946)Time elapsed: 0.059 s
% 6.21/2.10 % (17946)Instructions burned: 234 (million)
% 6.21/2.10 % (17946)------------------------------
% 6.21/2.10 % (17946)------------------------------
% 6.21/2.11 % (17954)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/79Mi)
% 6.73/2.12 % (17919)Instruction limit reached!
% 6.73/2.12 % (17919)------------------------------
% 6.73/2.12 % (17919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.12 % (17919)Termination reason: Unknown
% 6.73/2.12 % (17919)Termination phase: Saturation
% 6.73/2.12
% 6.73/2.12 % (17919)Memory used [KB]: 11897
% 6.73/2.12 % (17919)Time elapsed: 0.345 s
% 6.73/2.12 % (17919)Instructions burned: 1089 (million)
% 6.73/2.12 % (17919)------------------------------
% 6.73/2.12 % (17919)------------------------------
% 6.73/2.13 % (17955)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/216Mi)
% 6.73/2.13 % (17954)Instruction limit reached!
% 6.73/2.13 % (17954)------------------------------
% 6.73/2.13 % (17954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.13 % (17954)Termination reason: Unknown
% 6.73/2.13 % (17954)Termination phase: Preprocessing 3
% 6.73/2.13
% 6.73/2.13 % (17954)Memory used [KB]: 3837
% 6.73/2.13 % (17954)Time elapsed: 0.025 s
% 6.73/2.13 % (17954)Instructions burned: 80 (million)
% 6.73/2.13 % (17954)------------------------------
% 6.73/2.13 % (17954)------------------------------
% 6.73/2.13 % (17951)Instruction limit reached!
% 6.73/2.13 % (17951)------------------------------
% 6.73/2.13 % (17951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.13 % (17951)Termination reason: Unknown
% 6.73/2.13 % (17951)Termination phase: Property scanning
% 6.73/2.13
% 6.73/2.13 % (17951)Memory used [KB]: 7803
% 6.73/2.13 % (17951)Time elapsed: 0.051 s
% 6.73/2.13 % (17951)Instructions burned: 182 (million)
% 6.73/2.13 % (17951)------------------------------
% 6.73/2.13 % (17951)------------------------------
% 6.73/2.14 % (17953)Instruction limit reached!
% 6.73/2.14 % (17953)------------------------------
% 6.73/2.14 % (17953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.14 % (17953)Termination reason: Unknown
% 6.73/2.14 % (17953)Termination phase: Saturation
% 6.73/2.14
% 6.73/2.14 % (17953)Memory used [KB]: 2558
% 6.73/2.14 % (17953)Time elapsed: 0.041 s
% 6.73/2.14 % (17953)Instructions burned: 157 (million)
% 6.73/2.14 % (17953)------------------------------
% 6.73/2.14 % (17953)------------------------------
% 6.73/2.14 % (17956)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/114Mi)
% 6.73/2.14 % (17957)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/922Mi)
% 6.73/2.15 % (17958)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/182Mi)
% 6.73/2.15 % (17955)Refutation not found, incomplete strategy
% 6.73/2.15 % (17955)------------------------------
% 6.73/2.15 % (17955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.15 % (17955)Termination reason: Refutation not found, incomplete strategy
% 6.73/2.15
% 6.73/2.15
% 6.73/2.15 % (17955)Memory used [KB]: 6524
% 6.73/2.15 % (17955)Time elapsed: 0.023 s
% 6.73/2.15 % (17955)Instructions burned: 81 (million)
% 6.73/2.15 % (17955)------------------------------
% 6.73/2.15 % (17955)------------------------------
% 6.73/2.16 % (17952)Instruction limit reached!
% 6.73/2.16 % (17952)------------------------------
% 6.73/2.16 % (17952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.16 % (17952)Termination reason: Unknown
% 6.73/2.16 % (17952)Termination phase: Saturation
% 6.73/2.16
% 6.73/2.16 % (17952)Memory used [KB]: 9210
% 6.73/2.16 % (17952)Time elapsed: 0.065 s
% 6.73/2.16 % (17952)Instructions burned: 184 (million)
% 6.73/2.16 % (17952)------------------------------
% 6.73/2.16 % (17952)------------------------------
% 6.73/2.16 % (17959)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/164Mi)
% 6.73/2.17 % (17960)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_17587 for (2993ds/50Mi)
% 6.73/2.18 % (17956)Instruction limit reached!
% 6.73/2.18 % (17956)------------------------------
% 6.73/2.18 % (17956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.18 % (17956)Termination reason: Unknown
% 6.73/2.18 % (17956)Termination phase: Property scanning
% 6.73/2.18
% 6.73/2.18 % (17956)Memory used [KB]: 4221
% 6.73/2.18 % (17956)Time elapsed: 0.035 s
% 6.73/2.18 % (17956)Instructions burned: 116 (million)
% 6.73/2.18 % (17956)------------------------------
% 6.73/2.18 % (17956)------------------------------
% 6.73/2.18 % (17947)Instruction limit reached!
% 6.73/2.18 % (17947)------------------------------
% 6.73/2.18 % (17947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.18 % (17947)Termination reason: Unknown
% 6.73/2.18 % (17947)Termination phase: Saturation
% 6.73/2.18
% 6.73/2.18 % (17947)Memory used [KB]: 11257
% 6.73/2.18 % (17947)Time elapsed: 0.137 s
% 6.73/2.18 % (17947)Instructions burned: 459 (million)
% 6.73/2.18 % (17947)------------------------------
% 6.73/2.18 % (17947)------------------------------
% 6.73/2.18 % (17960)Instruction limit reached!
% 6.73/2.18 % (17960)------------------------------
% 6.73/2.18 % (17960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.18 % (17960)Termination reason: Unknown
% 6.73/2.18 % (17960)Termination phase: Property scanning
% 6.73/2.18
% 6.73/2.18 % (17960)Memory used [KB]: 1918
% 6.73/2.18 % (17960)Time elapsed: 0.015 s
% 6.73/2.18 % (17960)Instructions burned: 51 (million)
% 6.73/2.18 % (17960)------------------------------
% 6.73/2.18 % (17960)------------------------------
% 6.73/2.18 % (17959)Refutation not found, incomplete strategy
% 6.73/2.18 % (17959)------------------------------
% 6.73/2.18 % (17959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.18 % (17959)Termination reason: Refutation not found, incomplete strategy
% 6.73/2.18
% 6.73/2.18
% 6.73/2.18 % (17959)Memory used [KB]: 2046
% 6.73/2.18 % (17959)Time elapsed: 0.021 s
% 6.73/2.18 % (17959)Instructions burned: 75 (million)
% 6.73/2.18 % (17959)------------------------------
% 6.73/2.18 % (17959)------------------------------
% 6.73/2.19 % (17961)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/368Mi)
% 6.73/2.19 % (17962)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/1021Mi)
% 6.73/2.19 % (17963)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/267Mi)
% 6.73/2.19 % (17964)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/204Mi)
% 6.73/2.19 % (17958)Instruction limit reached!
% 6.73/2.19 % (17958)------------------------------
% 6.73/2.19 % (17958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.19 % (17958)Termination reason: Unknown
% 6.73/2.19 % (17958)Termination phase: Saturation
% 6.73/2.19
% 6.73/2.19 % (17958)Memory used [KB]: 6524
% 6.73/2.19 % (17958)Time elapsed: 0.048 s
% 6.73/2.19 % (17958)Instructions burned: 183 (million)
% 6.73/2.19 % (17958)------------------------------
% 6.73/2.19 % (17958)------------------------------
% 7.31/2.20 % (17965)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/26Mi)
% 7.31/2.21 % (17965)Instruction limit reached!
% 7.31/2.21 % (17965)------------------------------
% 7.31/2.21 % (17965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.21 % (17965)Termination reason: Unknown
% 7.31/2.21 % (17965)Termination phase: shuffling
% 7.31/2.21
% 7.31/2.21 % (17965)Memory used [KB]: 1791
% 7.31/2.21 % (17965)Time elapsed: 0.008 s
% 7.31/2.21 % (17965)Instructions burned: 26 (million)
% 7.31/2.21 % (17965)------------------------------
% 7.31/2.21 % (17965)------------------------------
% 7.31/2.22 % (17966)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/53Mi)
% 7.31/2.24 % (17966)Instruction limit reached!
% 7.31/2.24 % (17966)------------------------------
% 7.31/2.24 % (17966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.24 % (17966)Termination reason: Unknown
% 7.31/2.24 % (17966)Termination phase: Property scanning
% 7.31/2.24
% 7.31/2.24 % (17966)Memory used [KB]: 1918
% 7.31/2.24 % (17966)Time elapsed: 0.016 s
% 7.31/2.24 % (17966)Instructions burned: 55 (million)
% 7.31/2.24 % (17966)------------------------------
% 7.31/2.24 % (17966)------------------------------
% 7.31/2.24 % (17967)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/4436Mi)
% 7.31/2.25 % (17964)Instruction limit reached!
% 7.31/2.25 % (17964)------------------------------
% 7.31/2.25 % (17964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.25 % (17964)Termination reason: Unknown
% 7.31/2.25 % (17964)Termination phase: Property scanning
% 7.31/2.25
% 7.31/2.25 % (17964)Memory used [KB]: 4605
% 7.31/2.25 % (17964)Time elapsed: 0.056 s
% 7.31/2.25 % (17964)Instructions burned: 205 (million)
% 7.31/2.25 % (17964)------------------------------
% 7.31/2.25 % (17964)------------------------------
% 7.31/2.26 % (17968)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/1539Mi)
% 7.31/2.26 % (17963)Instruction limit reached!
% 7.31/2.26 % (17963)------------------------------
% 7.31/2.26 % (17963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.26 % (17963)Termination reason: Unknown
% 7.31/2.26 % (17963)Termination phase: Saturation
% 7.31/2.26
% 7.31/2.26 % (17963)Memory used [KB]: 6652
% 7.31/2.26 % (17963)Time elapsed: 0.073 s
% 7.31/2.26 % (17963)Instructions burned: 269 (million)
% 7.31/2.26 % (17963)------------------------------
% 7.31/2.26 % (17963)------------------------------
% 7.31/2.27 % (17969)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_17587 for (2992ds/408Mi)
% 7.31/2.29 % (17961)Instruction limit reached!
% 7.31/2.29 % (17961)------------------------------
% 7.31/2.29 % (17961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.29 % (17961)Termination reason: Unknown
% 7.31/2.29 % (17961)Termination phase: Saturation
% 7.31/2.29
% 7.31/2.29 % (17961)Memory used [KB]: 11769
% 7.31/2.29 % (17961)Time elapsed: 0.108 s
% 7.31/2.29 % (17961)Instructions burned: 369 (million)
% 7.31/2.29 % (17961)------------------------------
% 7.31/2.29 % (17961)------------------------------
% 7.62/2.30 % (17970)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_17587 for (2991ds/5205Mi)
% 7.62/2.31 % (17950)Instruction limit reached!
% 7.62/2.31 % (17950)------------------------------
% 7.62/2.31 % (17950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.31 % (17950)Termination reason: Unknown
% 7.62/2.31 % (17950)Termination phase: Saturation
% 7.62/2.31
% 7.62/2.31 % (17950)Memory used [KB]: 7547
% 7.62/2.31 % (17950)Time elapsed: 0.247 s
% 7.62/2.31 % (17950)Instructions burned: 990 (million)
% 7.62/2.31 % (17950)------------------------------
% 7.62/2.31 % (17950)------------------------------
% 7.62/2.32 % (17971)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_17587 for (2991ds/1913Mi)
% 7.88/2.40 % (17969)Instruction limit reached!
% 7.88/2.40 % (17969)------------------------------
% 7.88/2.40 % (17969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.40 % (17969)Termination reason: Unknown
% 7.88/2.40 % (17969)Termination phase: Saturation
% 7.88/2.40
% 7.88/2.40 % (17969)Memory used [KB]: 10746
% 7.88/2.40 % (17969)Time elapsed: 0.126 s
% 7.88/2.40 % (17969)Instructions burned: 408 (million)
% 7.88/2.40 % (17969)------------------------------
% 7.88/2.40 % (17969)------------------------------
% 7.88/2.41 % (17972)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_17587 for (2990ds/4350Mi)
% 7.88/2.43 % (17957)Instruction limit reached!
% 7.88/2.43 % (17957)------------------------------
% 7.88/2.43 % (17957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.43 % (17957)Termination reason: Unknown
% 7.88/2.43 % (17957)Termination phase: Saturation
% 7.88/2.43
% 7.88/2.43 % (17957)Memory used [KB]: 12537
% 7.88/2.43 % (17957)Time elapsed: 0.286 s
% 7.88/2.43 % (17957)Instructions burned: 923 (million)
% 7.88/2.43 % (17957)------------------------------
% 7.88/2.43 % (17957)------------------------------
% 7.88/2.44 % (17973)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_17587 for (2990ds/68Mi)
% 7.88/2.46 % (17973)Instruction limit reached!
% 7.88/2.46 % (17973)------------------------------
% 7.88/2.46 % (17973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.46 % (17973)Termination reason: Unknown
% 7.88/2.46 % (17973)Termination phase: Preprocessing 3
% 7.88/2.46
% 7.88/2.46 % (17973)Memory used [KB]: 3198
% 7.88/2.46 % (17973)Time elapsed: 0.021 s
% 7.88/2.46 % (17973)Instructions burned: 68 (million)
% 7.88/2.46 % (17973)------------------------------
% 7.88/2.46 % (17973)------------------------------
% 7.88/2.47 % (17974)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_17587 for (2990ds/358Mi)
% 7.88/2.48 % (17962)Instruction limit reached!
% 7.88/2.48 % (17962)------------------------------
% 7.88/2.48 % (17962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.48 % (17962)Termination reason: Unknown
% 7.88/2.48 % (17962)Termination phase: Saturation
% 7.88/2.48
% 7.88/2.48 % (17962)Memory used [KB]: 11897
% 7.88/2.48 % (17962)Time elapsed: 0.295 s
% 7.88/2.48 % (17962)Instructions burned: 1024 (million)
% 7.88/2.48 % (17962)------------------------------
% 7.88/2.48 % (17962)------------------------------
% 7.88/2.49 % (17975)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_17587 for (2989ds/31Mi)
% 8.64/2.50 % (17975)Instruction limit reached!
% 8.64/2.50 % (17975)------------------------------
% 8.64/2.50 % (17975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.50 % (17975)Termination reason: Unknown
% 8.64/2.50 % (17975)Termination phase: Property scanning
% 8.64/2.50
% 8.64/2.50 % (17975)Memory used [KB]: 2174
% 8.64/2.50 % (17975)Time elapsed: 0.011 s
% 8.64/2.50 % (17975)Instructions burned: 33 (million)
% 8.64/2.50 % (17975)------------------------------
% 8.64/2.50 % (17975)------------------------------
% 8.64/2.51 % (17976)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17587 for (2989ds/279Mi)
% 8.64/2.57 % (17974)Instruction limit reached!
% 8.64/2.57 % (17974)------------------------------
% 8.64/2.57 % (17974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.57 % (17974)Termination reason: Unknown
% 8.64/2.57 % (17974)Termination phase: Saturation
% 8.64/2.57
% 8.64/2.57 % (17974)Memory used [KB]: 9722
% 8.64/2.57 % (17974)Time elapsed: 0.104 s
% 8.64/2.57 % (17974)Instructions burned: 360 (million)
% 8.64/2.57 % (17974)------------------------------
% 8.64/2.57 % (17974)------------------------------
% 8.64/2.58 % (17976)Instruction limit reached!
% 8.64/2.58 % (17976)------------------------------
% 8.64/2.58 % (17976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.58 % (17976)Termination reason: Unknown
% 8.64/2.58 % (17976)Termination phase: Saturation
% 8.64/2.58
% 8.64/2.58 % (17976)Memory used [KB]: 7675
% 8.64/2.58 % (17976)Time elapsed: 0.070 s
% 8.64/2.58 % (17976)Instructions burned: 279 (million)
% 8.64/2.58 % (17976)------------------------------
% 8.64/2.58 % (17976)------------------------------
% 8.64/2.58 % (17977)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17587 for (2988ds/258Mi)
% 8.64/2.59 % (17978)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17587 for (2988ds/26Mi)
% 8.64/2.60 % (17978)Instruction limit reached!
% 8.64/2.60 % (17978)------------------------------
% 8.64/2.60 % (17978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.60 % (17978)Termination reason: Unknown
% 8.64/2.60 % (17978)Termination phase: shuffling
% 8.64/2.60
% 8.64/2.60 % (17978)Memory used [KB]: 1791
% 8.64/2.60 % (17978)Time elapsed: 0.008 s
% 8.64/2.60 % (17978)Instructions burned: 27 (million)
% 8.64/2.60 % (17978)------------------------------
% 8.64/2.60 % (17978)------------------------------
% 8.87/2.60 % (17979)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_17587 for (2988ds/995Mi)
% 8.87/2.66 % (17977)Instruction limit reached!
% 8.87/2.66 % (17977)------------------------------
% 8.87/2.66 % (17977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.66 % (17977)Termination reason: Unknown
% 8.87/2.66 % (17977)Termination phase: Saturation
% 8.87/2.66
% 8.87/2.66 % (17977)Memory used [KB]: 9722
% 8.87/2.66 % (17977)Time elapsed: 0.076 s
% 8.87/2.66 % (17977)Instructions burned: 259 (million)
% 8.87/2.66 % (17977)------------------------------
% 8.87/2.66 % (17977)------------------------------
% 8.87/2.67 % (17980)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_17587 for (2988ds/373Mi)
% 8.96/2.70 % (17968)Instruction limit reached!
% 8.96/2.70 % (17968)------------------------------
% 8.96/2.70 % (17968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.70 % (17968)Termination reason: Unknown
% 8.96/2.70 % (17968)Termination phase: Saturation
% 8.96/2.70
% 8.96/2.70 % (17968)Memory used [KB]: 10874
% 8.96/2.70 % (17968)Time elapsed: 0.444 s
% 8.96/2.70 % (17968)Instructions burned: 1541 (million)
% 8.96/2.70 % (17968)------------------------------
% 8.96/2.70 % (17968)------------------------------
% 8.96/2.71 % (17981)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_17587 for (2987ds/253Mi)
% 8.96/2.77 % (17981)Instruction limit reached!
% 8.96/2.77 % (17981)------------------------------
% 8.96/2.77 % (17981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.77 % (17981)Termination reason: Unknown
% 8.96/2.77 % (17981)Termination phase: Saturation
% 8.96/2.77
% 8.96/2.77 % (17981)Memory used [KB]: 6780
% 8.96/2.77 % (17981)Time elapsed: 0.063 s
% 8.96/2.77 % (17981)Instructions burned: 253 (million)
% 8.96/2.77 % (17981)------------------------------
% 8.96/2.77 % (17981)------------------------------
% 8.96/2.78 % (17980)Instruction limit reached!
% 8.96/2.78 % (17980)------------------------------
% 8.96/2.78 % (17980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.78 % (17980)Termination reason: Unknown
% 8.96/2.78 % (17980)Termination phase: Saturation
% 8.96/2.78
% 8.96/2.78 % (17980)Memory used [KB]: 10106
% 8.96/2.78 % (17980)Time elapsed: 0.112 s
% 8.96/2.78 % (17980)Instructions burned: 374 (million)
% 8.96/2.78 % (17980)------------------------------
% 8.96/2.78 % (17980)------------------------------
% 8.96/2.78 % (17982)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_17587 for (2987ds/832Mi)
% 8.96/2.79 % (17983)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_17587 for (2986ds/668Mi)
% 9.60/2.85 % (17979)Instruction limit reached!
% 9.60/2.85 % (17979)------------------------------
% 9.60/2.85 % (17979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.85 % (17979)Termination reason: Unknown
% 9.60/2.85 % (17979)Termination phase: Saturation
% 9.60/2.85
% 9.60/2.85 % (17979)Memory used [KB]: 6652
% 9.60/2.85 % (17979)Time elapsed: 0.246 s
% 9.60/2.85 % (17979)Instructions burned: 996 (million)
% 9.60/2.85 % (17979)------------------------------
% 9.60/2.85 % (17979)------------------------------
% 9.60/2.86 % (17982)Refutation not found, incomplete strategy
% 9.60/2.86 % (17982)------------------------------
% 9.60/2.86 % (17982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.86 % (17982)Termination reason: Refutation not found, incomplete strategy
% 9.60/2.86
% 9.60/2.86
% 9.60/2.86 % (17982)Memory used [KB]: 9594
% 9.60/2.86 % (17982)Time elapsed: 0.074 s
% 9.60/2.86 % (17982)Instructions burned: 263 (million)
% 9.60/2.86 % (17982)------------------------------
% 9.60/2.86 % (17982)------------------------------
% 9.60/2.86 % (17984)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_17587 for (2986ds/40Mi)
% 9.60/2.87 % (17985)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_17587 for (2986ds/294Mi)
% 9.60/2.87 % (17984)Instruction limit reached!
% 9.60/2.87 % (17984)------------------------------
% 9.60/2.87 % (17984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.87 % (17984)Termination reason: Unknown
% 9.60/2.87 % (17984)Termination phase: Property scanning
% 9.60/2.87
% 9.60/2.87 % (17984)Memory used [KB]: 1918
% 9.60/2.87 % (17984)Time elapsed: 0.012 s
% 9.60/2.87 % (17984)Instructions burned: 41 (million)
% 9.60/2.87 % (17984)------------------------------
% 9.60/2.87 % (17984)------------------------------
% 9.60/2.88 % (17986)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_17587 for (2986ds/187Mi)
% 9.96/2.92 % (17971)Instruction limit reached!
% 9.96/2.92 % (17971)------------------------------
% 9.96/2.92 % (17971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.92 % (17971)Termination reason: Unknown
% 9.96/2.92 % (17971)Termination phase: Saturation
% 9.96/2.92
% 9.96/2.92 % (17971)Memory used [KB]: 6396
% 9.96/2.92 % (17971)Time elapsed: 0.593 s
% 9.96/2.92 % (17971)Instructions burned: 1914 (million)
% 9.96/2.92 % (17971)------------------------------
% 9.96/2.92 % (17971)------------------------------
% 9.96/2.93 % (17987)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17587 for (2985ds/371Mi)
% 9.96/2.93 % (17986)Instruction limit reached!
% 9.96/2.93 % (17986)------------------------------
% 9.96/2.93 % (17986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.93 % (17986)Termination reason: Unknown
% 9.96/2.93 % (17986)Termination phase: Property scanning
% 9.96/2.93
% 9.96/2.93 % (17986)Memory used [KB]: 4349
% 9.96/2.93 % (17986)Time elapsed: 0.051 s
% 9.96/2.93 % (17986)Instructions burned: 190 (million)
% 9.96/2.93 % (17986)------------------------------
% 9.96/2.93 % (17986)------------------------------
% 9.96/2.94 % (17985)Instruction limit reached!
% 9.96/2.94 % (17985)------------------------------
% 9.96/2.94 % (17985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.94 % (17985)Termination reason: Unknown
% 9.96/2.94 % (17985)Termination phase: Saturation
% 9.96/2.94
% 9.96/2.94 % (17985)Memory used [KB]: 7547
% 9.96/2.94 % (17985)Time elapsed: 0.073 s
% 9.96/2.94 % (17985)Instructions burned: 295 (million)
% 9.96/2.94 % (17985)------------------------------
% 9.96/2.94 % (17985)------------------------------
% 9.96/2.94 % (17987)Refutation not found, incomplete strategy
% 9.96/2.94 % (17987)------------------------------
% 9.96/2.94 % (17987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.94 % (17987)Termination reason: Refutation not found, incomplete strategy
% 9.96/2.94
% 9.96/2.94
% 9.96/2.94 % (17987)Memory used [KB]: 6652
% 9.96/2.94 % (17987)Time elapsed: 0.013 s
% 9.96/2.94 % (17987)Instructions burned: 39 (million)
% 9.96/2.94 % (17987)------------------------------
% 9.96/2.94 % (17987)------------------------------
% 9.96/2.94 % (17988)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17587 for (2985ds/1827Mi)
% 9.96/2.95 % (17989)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_17587 for (2985ds/70Mi)
% 9.96/2.95 % (17990)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_17587 for (2985ds/316Mi)
% 9.96/2.95 % (17983)Instruction limit reached!
% 9.96/2.95 % (17983)------------------------------
% 9.96/2.95 % (17983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.95 % (17983)Termination reason: Unknown
% 9.96/2.95 % (17983)Termination phase: Saturation
% 9.96/2.95
% 9.96/2.95 % (17983)Memory used [KB]: 11129
% 9.96/2.95 % (17983)Time elapsed: 0.166 s
% 9.96/2.95 % (17983)Instructions burned: 671 (million)
% 9.96/2.95 % (17983)------------------------------
% 9.96/2.95 % (17983)------------------------------
% 9.96/2.96 % (17991)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_17587 for (2985ds/932Mi)
% 9.96/2.97 % (17989)Instruction limit reached!
% 9.96/2.97 % (17989)------------------------------
% 9.96/2.97 % (17989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.97 % (17989)Termination reason: Unknown
% 9.96/2.97 % (17989)Termination phase: Property scanning
% 9.96/2.97
% 9.96/2.97 % (17989)Memory used [KB]: 1918
% 9.96/2.97 % (17989)Time elapsed: 0.019 s
% 9.96/2.97 % (17989)Instructions burned: 72 (million)
% 9.96/2.97 % (17989)------------------------------
% 9.96/2.97 % (17989)------------------------------
% 9.96/2.97 % (17992)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_17587 for (2984ds/4714Mi)
% 13.30/3.03 % (17990)Instruction limit reached!
% 13.30/3.03 % (17990)------------------------------
% 13.30/3.03 % (17990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.30/3.03 % (17990)Termination reason: Unknown
% 13.30/3.03 % (17990)Termination phase: Saturation
% 13.30/3.03
% 13.30/3.03 % (17990)Memory used [KB]: 7036
% 13.30/3.03 % (17990)Time elapsed: 0.080 s
% 13.30/3.03 % (17990)Instructions burned: 317 (million)
% 13.30/3.03 % (17990)------------------------------
% 13.30/3.03 % (17990)------------------------------
% 13.30/3.04 % (17993)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_17587 for (2984ds/8250Mi)
% 13.95/3.20 % (17991)Instruction limit reached!
% 13.95/3.20 % (17991)------------------------------
% 13.95/3.20 % (17991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.20 % (17991)Termination reason: Unknown
% 13.95/3.20 % (17991)Termination phase: Saturation
% 13.95/3.20
% 13.95/3.20 % (17991)Memory used [KB]: 7803
% 13.95/3.20 % (17991)Time elapsed: 0.237 s
% 13.95/3.20 % (17991)Instructions burned: 935 (million)
% 13.95/3.20 % (17991)------------------------------
% 13.95/3.20 % (17991)------------------------------
% 14.37/3.21 % (17994)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_17587 for (2982ds/770Mi)
% 14.37/3.22 % (17994)Refutation not found, incomplete strategy
% 14.37/3.22 % (17994)------------------------------
% 14.37/3.22 % (17994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.37/3.22 % (17994)Termination reason: Refutation not found, incomplete strategy
% 14.37/3.22
% 14.37/3.22
% 14.37/3.22 % (17994)Memory used [KB]: 6652
% 14.37/3.22 % (17994)Time elapsed: 0.013 s
% 14.37/3.22 % (17994)Instructions burned: 37 (million)
% 14.37/3.22 % (17994)------------------------------
% 14.37/3.22 % (17994)------------------------------
% 14.37/3.23 % (17995)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17587 for (2982ds/794Mi)
% 15.41/3.46 % (17995)Instruction limit reached!
% 15.41/3.46 % (17995)------------------------------
% 15.41/3.46 % (17995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.41/3.46 % (17995)Termination reason: Unknown
% 15.41/3.46 % (17995)Termination phase: Saturation
% 15.41/3.46
% 15.41/3.46 % (17995)Memory used [KB]: 7675
% 15.41/3.46 % (17995)Time elapsed: 0.234 s
% 15.41/3.46 % (17995)Instructions burned: 794 (million)
% 15.41/3.46 % (17995)------------------------------
% 15.41/3.46 % (17995)------------------------------
% 15.41/3.47 % (17996)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_17587 for (2980ds/464Mi)
% 16.15/3.51 % (17988)Instruction limit reached!
% 16.15/3.51 % (17988)------------------------------
% 16.15/3.51 % (17988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.51 % (17988)Termination reason: Unknown
% 16.15/3.51 % (17988)Termination phase: Saturation
% 16.15/3.51
% 16.15/3.51 % (17988)Memory used [KB]: 13048
% 16.15/3.51 % (17988)Time elapsed: 0.596 s
% 16.15/3.51 % (17988)Instructions burned: 1828 (million)
% 16.15/3.51 % (17988)------------------------------
% 16.15/3.51 % (17988)------------------------------
% 16.15/3.52 % (17997)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_17587 for (2979ds/1376Mi)
% 16.15/3.58 % (17970)Instruction limit reached!
% 16.15/3.58 % (17970)------------------------------
% 16.15/3.58 % (17970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.58 % (17970)Termination reason: Unknown
% 16.15/3.58 % (17970)Termination phase: Saturation
% 16.15/3.58
% 16.15/3.58 % (17970)Memory used [KB]: 7931
% 16.15/3.58 % (17970)Time elapsed: 1.276 s
% 16.15/3.58 % (17970)Instructions burned: 5206 (million)
% 16.15/3.58 % (17970)------------------------------
% 16.15/3.58 % (17970)------------------------------
% 16.15/3.59 % (17998)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_17587 for (2978ds/906Mi)
% 16.15/3.60 % (17972)Instruction limit reached!
% 16.15/3.60 % (17972)------------------------------
% 16.15/3.60 % (17972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.60 % (17972)Termination reason: Unknown
% 16.15/3.60 % (17972)Termination phase: Saturation
% 16.15/3.60
% 16.15/3.60 % (17972)Memory used [KB]: 15479
% 16.15/3.60 % (17972)Time elapsed: 1.187 s
% 16.15/3.60 % (17972)Instructions burned: 4352 (million)
% 16.15/3.60 % (17972)------------------------------
% 16.15/3.60 % (17972)------------------------------
% 16.58/3.61 % (17999)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_17587 for (2978ds/434Mi)
% 16.58/3.61 % (17967)Instruction limit reached!
% 16.58/3.61 % (17967)------------------------------
% 16.58/3.61 % (17967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.61 % (17967)Termination reason: Unknown
% 16.58/3.61 % (17967)Termination phase: Saturation
% 16.58/3.61
% 16.58/3.61 % (17967)Memory used [KB]: 14967
% 16.58/3.61 % (17967)Time elapsed: 1.364 s
% 16.58/3.61 % (17967)Instructions burned: 4437 (million)
% 16.58/3.61 % (17967)------------------------------
% 16.58/3.61 % (17967)------------------------------
% 16.58/3.61 % (17996)Instruction limit reached!
% 16.58/3.61 % (17996)------------------------------
% 16.58/3.61 % (17996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.61 % (17996)Termination reason: Unknown
% 16.58/3.61 % (17996)Termination phase: Saturation
% 16.58/3.61
% 16.58/3.61 % (17996)Memory used [KB]: 11385
% 16.58/3.61 % (17996)Time elapsed: 0.158 s
% 16.58/3.61 % (17996)Instructions burned: 465 (million)
% 16.58/3.61 % (17996)------------------------------
% 16.58/3.61 % (17996)------------------------------
% 16.58/3.62 % (17999)Refutation not found, incomplete strategy
% 16.58/3.62 % (17999)------------------------------
% 16.58/3.62 % (17999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.62 % (17999)Termination reason: Refutation not found, incomplete strategy
% 16.58/3.62
% 16.58/3.62
% 16.58/3.62 % (17999)Memory used [KB]: 6652
% 16.58/3.62 % (17999)Time elapsed: 0.012 s
% 16.58/3.62 % (17999)Instructions burned: 37 (million)
% 16.58/3.62 % (17999)------------------------------
% 16.58/3.62 % (17999)------------------------------
% 16.58/3.62 % (18000)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_17587 for (2978ds/865Mi)
% 16.58/3.62 % (18001)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_17587 for (2978ds/593Mi)
% 16.58/3.63 % (18002)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_17587 for (2978ds/443Mi)
% 16.88/3.75 % (18002)Instruction limit reached!
% 16.88/3.75 % (18002)------------------------------
% 16.88/3.75 % (18002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.88/3.75 % (18002)Termination reason: Unknown
% 16.88/3.75 % (18002)Termination phase: Saturation
% 16.88/3.75
% 16.88/3.75 % (18002)Memory used [KB]: 11641
% 16.88/3.75 % (18002)Time elapsed: 0.129 s
% 16.88/3.75 % (18002)Instructions burned: 443 (million)
% 16.88/3.75 % (18002)------------------------------
% 16.88/3.75 % (18002)------------------------------
% 16.88/3.76 % (18001)Instruction limit reached!
% 16.88/3.76 % (18001)------------------------------
% 16.88/3.76 % (18001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.88/3.76 % (18001)Termination reason: Unknown
% 16.88/3.76 % (18001)Termination phase: Saturation
% 16.88/3.76
% 16.88/3.76 % (18001)Memory used [KB]: 6780
% 16.88/3.76 % (18001)Time elapsed: 0.146 s
% 16.88/3.76 % (18001)Instructions burned: 596 (million)
% 16.88/3.76 % (18001)------------------------------
% 16.88/3.76 % (18001)------------------------------
% 16.88/3.77 % (18003)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_17587 for (2977ds/594Mi)
% 16.88/3.77 % (18004)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_17587 for (2976ds/327Mi)
% 17.27/3.83 % (18000)Instruction limit reached!
% 17.27/3.83 % (18000)------------------------------
% 17.27/3.83 % (18000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.83 % (18000)Termination reason: Unknown
% 17.27/3.83 % (18000)Termination phase: Saturation
% 17.27/3.83
% 17.27/3.83 % (18000)Memory used [KB]: 6908
% 17.27/3.83 % (18000)Time elapsed: 0.213 s
% 17.27/3.83 % (18000)Instructions burned: 865 (million)
% 17.27/3.83 % (18000)------------------------------
% 17.27/3.83 % (18000)------------------------------
% 17.27/3.84 % (18005)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_17587 for (2976ds/5411Mi)
% 17.27/3.85 % (18005)Refutation not found, incomplete strategy
% 17.27/3.85 % (18005)------------------------------
% 17.27/3.85 % (18005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.85 % (18005)Termination reason: Refutation not found, incomplete strategy
% 17.27/3.85
% 17.27/3.85
% 17.27/3.85 % (18005)Memory used [KB]: 6652
% 17.27/3.85 % (18005)Time elapsed: 0.012 s
% 17.27/3.85 % (18005)Instructions burned: 36 (million)
% 17.27/3.85 % (18005)------------------------------
% 17.27/3.85 % (18005)------------------------------
% 17.27/3.86 % (18006)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_17587 for (2976ds/1762Mi)
% 17.27/3.87 % (17997)Instruction limit reached!
% 17.27/3.87 % (17997)------------------------------
% 17.27/3.87 % (17997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.87 % (17997)Termination reason: Unknown
% 17.27/3.87 % (17997)Termination phase: Saturation
% 17.27/3.87
% 17.27/3.87 % (17997)Memory used [KB]: 8315
% 17.27/3.87 % (17997)Time elapsed: 0.369 s
% 17.27/3.87 % (17997)Instructions burned: 1376 (million)
% 17.27/3.87 % (17997)------------------------------
% 17.27/3.87 % (17997)------------------------------
% 17.27/3.87 % (18004)Instruction limit reached!
% 17.27/3.87 % (18004)------------------------------
% 17.27/3.87 % (18004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.87 % (18004)Termination reason: Unknown
% 17.27/3.87 % (18004)Termination phase: Saturation
% 17.27/3.87
% 17.27/3.87 % (18004)Memory used [KB]: 10618
% 17.27/3.87 % (18004)Time elapsed: 0.101 s
% 17.27/3.87 % (18004)Instructions burned: 327 (million)
% 17.27/3.87 % (18004)------------------------------
% 17.27/3.87 % (18004)------------------------------
% 17.27/3.88 % (18007)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/96Mi)
% 17.27/3.88 % (17998)Instruction limit reached!
% 17.27/3.88 % (17998)------------------------------
% 17.27/3.88 % (17998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.88 % (17998)Termination reason: Unknown
% 17.27/3.88 % (17998)Termination phase: Saturation
% 17.27/3.88
% 17.27/3.88 % (17998)Memory used [KB]: 16119
% 17.27/3.88 % (17998)Time elapsed: 0.316 s
% 17.27/3.88 % (17998)Instructions burned: 907 (million)
% 17.27/3.88 % (17998)------------------------------
% 17.27/3.88 % (17998)------------------------------
% 17.27/3.88 % (18008)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/503Mi)
% 17.27/3.89 % (18009)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/90Mi)
% 17.27/3.89 % (18008)Refutation not found, incomplete strategy
% 17.27/3.89 % (18008)------------------------------
% 17.27/3.89 % (18008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.27/3.89 % (18008)Termination reason: Refutation not found, incomplete strategy
% 17.27/3.89
% 17.27/3.89
% 17.27/3.89 % (18008)Memory used [KB]: 6652
% 17.27/3.89 % (18008)Time elapsed: 0.013 s
% 17.27/3.89 % (18008)Instructions burned: 37 (million)
% 17.27/3.89 % (18008)------------------------------
% 17.27/3.89 % (18008)------------------------------
% 18.39/3.90 % (18007)Instruction limit reached!
% 18.39/3.90 % (18007)------------------------------
% 18.39/3.90 % (18007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.39/3.90 % (18007)Termination reason: Unknown
% 18.39/3.90 % (18007)Termination phase: Saturation
% 18.39/3.90
% 18.39/3.90 % (18007)Memory used [KB]: 6524
% 18.39/3.90 % (18007)Time elapsed: 0.026 s
% 18.39/3.90 % (18007)Instructions burned: 98 (million)
% 18.39/3.90 % (18007)------------------------------
% 18.39/3.90 % (18007)------------------------------
% 18.39/3.90 % (18010)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/593Mi)
% 18.39/3.91 % (18011)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/1512Mi)
% 18.39/3.92 % (18009)Instruction limit reached!
% 18.39/3.92 % (18009)------------------------------
% 18.39/3.92 % (18009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.39/3.92 % (18009)Termination reason: Unknown
% 18.39/3.92 % (18009)Termination phase: Preprocessing 3
% 18.39/3.92
% 18.39/3.92 % (18009)Memory used [KB]: 4093
% 18.39/3.92 % (18009)Time elapsed: 0.028 s
% 18.39/3.92 % (18009)Instructions burned: 93 (million)
% 18.39/3.92 % (18009)------------------------------
% 18.39/3.92 % (18009)------------------------------
% 18.39/3.93 % (18012)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/569Mi)
% 18.39/3.94 % (18003)Instruction limit reached!
% 18.39/3.94 % (18003)------------------------------
% 18.39/3.94 % (18003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.39/3.94 % (18003)Termination reason: Unknown
% 18.39/3.94 % (18003)Termination phase: Saturation
% 18.39/3.94
% 18.39/3.94 % (18003)Memory used [KB]: 9978
% 18.39/3.94 % (18003)Time elapsed: 0.174 s
% 18.39/3.94 % (18003)Instructions burned: 595 (million)
% 18.39/3.94 % (18003)------------------------------
% 18.39/3.94 % (18003)------------------------------
% 18.39/3.95 % (18013)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_17587 for (2975ds/501Mi)
% 18.39/3.98 % (18011)Refutation not found, incomplete strategy
% 18.39/3.98 % (18011)------------------------------
% 18.39/3.98 % (18011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.39/3.98 % (18011)Termination reason: Refutation not found, incomplete strategy
% 18.39/3.98
% 18.39/3.98
% 18.39/3.98 % (18011)Memory used [KB]: 9722
% 18.39/3.98 % (18011)Time elapsed: 0.074 s
% 18.39/3.98 % (18011)Instructions burned: 261 (million)
% 18.39/3.98 % (18011)------------------------------
% 18.39/3.98 % (18011)------------------------------
% 18.39/3.99 % (18014)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_17587 for (2974ds/562Mi)
% 20.34/4.06 % (18012)Instruction limit reached!
% 20.34/4.06 % (18012)------------------------------
% 20.34/4.06 % (18012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.06 % (18012)Termination reason: Unknown
% 20.34/4.06 % (18012)Termination phase: Saturation
% 20.34/4.06
% 20.34/4.06 % (18012)Memory used [KB]: 6652
% 20.34/4.06 % (18012)Time elapsed: 0.140 s
% 20.34/4.06 % (18012)Instructions burned: 570 (million)
% 20.34/4.06 % (18012)------------------------------
% 20.34/4.06 % (18012)------------------------------
% 20.34/4.08 % (18015)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17587 for (2973ds/406Mi)
% 20.34/4.08 % (18010)Instruction limit reached!
% 20.34/4.08 % (18010)------------------------------
% 20.34/4.08 % (18010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.08 % (18010)Termination reason: Unknown
% 20.34/4.08 % (18010)Termination phase: Saturation
% 20.34/4.08
% 20.34/4.08 % (18010)Memory used [KB]: 11257
% 20.34/4.08 % (18010)Time elapsed: 0.175 s
% 20.34/4.08 % (18010)Instructions burned: 594 (million)
% 20.34/4.08 % (18010)------------------------------
% 20.34/4.08 % (18010)------------------------------
% 20.34/4.09 % (18013)Instruction limit reached!
% 20.34/4.09 % (18013)------------------------------
% 20.34/4.09 % (18013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.09 % (18013)Termination reason: Unknown
% 20.34/4.09 % (18013)Termination phase: Saturation
% 20.34/4.09
% 20.34/4.09 % (18013)Memory used [KB]: 10874
% 20.34/4.09 % (18013)Time elapsed: 0.140 s
% 20.34/4.09 % (18013)Instructions burned: 503 (million)
% 20.34/4.09 % (18013)------------------------------
% 20.34/4.09 % (18013)------------------------------
% 20.34/4.09 % (18016)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_17587 for (2973ds/582Mi)
% 20.34/4.10 % (18017)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_17587 for (2973ds/456Mi)
% 20.94/4.14 % (18014)Instruction limit reached!
% 20.94/4.14 % (18014)------------------------------
% 20.94/4.14 % (18014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.14 % (18014)Termination reason: Unknown
% 20.94/4.14 % (18014)Termination phase: Saturation
% 20.94/4.14
% 20.94/4.14 % (18014)Memory used [KB]: 7164
% 20.94/4.14 % (18014)Time elapsed: 0.144 s
% 20.94/4.14 % (18014)Instructions burned: 562 (million)
% 20.94/4.14 % (18014)------------------------------
% 20.94/4.14 % (18014)------------------------------
% 20.94/4.14 % (17992)Instruction limit reached!
% 20.94/4.14 % (17992)------------------------------
% 20.94/4.14 % (17992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.14 % (17992)Termination reason: Unknown
% 20.94/4.14 % (17992)Termination phase: Saturation
% 20.94/4.14
% 20.94/4.14 % (17992)Memory used [KB]: 11129
% 20.94/4.14 % (17992)Time elapsed: 1.166 s
% 20.94/4.14 % (17992)Instructions burned: 4717 (million)
% 20.94/4.14 % (17992)------------------------------
% 20.94/4.14 % (17992)------------------------------
% 20.94/4.15 % (18018)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_17587 for (2973ds/393Mi)
% 20.94/4.15 % (18019)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_17587 for (2973ds/1335Mi)
% 20.94/4.17 % (18019)Refutation not found, incomplete strategy
% 20.94/4.17 % (18019)------------------------------
% 20.94/4.17 % (18019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.17 % (18019)Termination reason: Refutation not found, incomplete strategy
% 20.94/4.17
% 20.94/4.17
% 20.94/4.17 % (18019)Memory used [KB]: 6524
% 20.94/4.17 % (18019)Time elapsed: 0.021 s
% 20.94/4.17 % (18019)Instructions burned: 79 (million)
% 20.94/4.17 % (18019)------------------------------
% 20.94/4.17 % (18019)------------------------------
% 20.94/4.18 % (18020)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_17587 for (2972ds/3373Mi)
% 20.94/4.19 % (18015)Instruction limit reached!
% 20.94/4.19 % (18015)------------------------------
% 20.94/4.19 % (18015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.19 % (18015)Termination reason: Unknown
% 20.94/4.19 % (18015)Termination phase: Saturation
% 20.94/4.19
% 20.94/4.19 % (18015)Memory used [KB]: 9978
% 20.94/4.19 % (18015)Time elapsed: 0.119 s
% 20.94/4.19 % (18015)Instructions burned: 409 (million)
% 20.94/4.19 % (18015)------------------------------
% 20.94/4.19 % (18015)------------------------------
% 21.29/4.20 % (18021)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17587 for (2972ds/474Mi)
% 21.29/4.22 % (18017)Instruction limit reached!
% 21.29/4.22 % (18017)------------------------------
% 21.29/4.22 % (18017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.29/4.22 % (18017)Termination reason: Unknown
% 21.29/4.22 % (18017)Termination phase: Saturation
% 21.29/4.22
% 21.29/4.22 % (18017)Memory used [KB]: 11641
% 21.29/4.22 % (18017)Time elapsed: 0.129 s
% 21.29/4.22 % (18017)Instructions burned: 457 (million)
% 21.29/4.22 % (18017)------------------------------
% 21.29/4.22 % (18017)------------------------------
% 21.29/4.23 % (18022)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17587 for (2972ds/157Mi)
% 21.29/4.24 % (18016)First to succeed.
% 21.29/4.24 % (18018)Instruction limit reached!
% 21.29/4.24 % (18018)------------------------------
% 21.29/4.24 % (18018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.29/4.24 % (18018)Termination reason: Unknown
% 21.29/4.24 % (18018)Termination phase: Saturation
% 21.29/4.24
% 21.29/4.24 % (18018)Memory used [KB]: 6652
% 21.29/4.24 % (18018)Time elapsed: 0.097 s
% 21.29/4.24 % (18018)Instructions burned: 396 (million)
% 21.29/4.24 % (18018)------------------------------
% 21.29/4.24 % (18018)------------------------------
% 21.29/4.25 % (18023)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_17587 for (2972ds/590Mi)
% 21.29/4.27 % (18016)Refutation found. Thanks to Tanya!
% 21.29/4.27 % SZS status Theorem for DTF2THF_17587
% 21.29/4.27 % SZS output start Proof for DTF2THF_17587
% 21.29/4.27 thf(type_def_5, type, term: $tType).
% 21.29/4.27 thf(type_def_7, type, subst: $tType).
% 21.29/4.27 thf(type_def_8, type, d_term: $tType).
% 21.29/4.27 thf(type_def_9, type, d_subst: $tType).
% 21.29/4.27 thf(func_def_0, type, term: $tType).
% 21.29/4.27 thf(func_def_1, type, subst: $tType).
% 21.29/4.27 thf(func_def_2, type, one: term).
% 21.29/4.27 thf(func_def_3, type, ap: term > term > term).
% 21.29/4.27 thf(func_def_4, type, lam: term > term).
% 21.29/4.27 thf(func_def_5, type, sub: term > subst > term).
% 21.29/4.27 thf(func_def_6, type, id: subst).
% 21.29/4.27 thf(func_def_7, type, sh: subst).
% 21.29/4.27 thf(func_def_8, type, push: term > subst > subst).
% 21.29/4.27 thf(func_def_9, type, comp: subst > subst > subst).
% 21.29/4.27 thf(func_def_10, type, var: term > $o).
% 21.29/4.27 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 21.29/4.27 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 21.29/4.27 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 21.29/4.27 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 21.29/4.27 thf(func_def_124, type, d_term: $tType).
% 21.29/4.27 thf(func_def_125, type, d_subst: $tType).
% 21.29/4.27 thf(func_def_126, type, d2term: d_term > term).
% 21.29/4.27 thf(func_def_127, type, d2subst: d_subst > subst).
% 21.29/4.27 thf(func_def_128, type, d_one: d_term).
% 21.29/4.27 thf(func_def_129, type, d_id: d_subst).
% 21.29/4.27 thf(func_def_141, type, sP0: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_143, type, sP2: (term > $o) > $o).
% 21.29/4.27 thf(func_def_145, type, sP4: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_147, type, sP6: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_148, type, sP7: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_149, type, sP8: (term > $o) > $o).
% 21.29/4.27 thf(func_def_150, type, sP9: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_151, type, sP10: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_158, type, sP17: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_159, type, sP18: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_161, type, sP20: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_162, type, sP21: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_164, type, sP23: (term > $o) > $o).
% 21.29/4.27 thf(func_def_165, type, sP24: (term > $o) > $o).
% 21.29/4.27 thf(func_def_168, type, sP27: (term > $o) > $o).
% 21.29/4.27 thf(func_def_169, type, sP28: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_175, type, sP34: (term > $o) > $o).
% 21.29/4.27 thf(func_def_176, type, sP35: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_177, type, sP36: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_181, type, sP40: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_184, type, sP43: (term > $o) > $o).
% 21.29/4.27 thf(func_def_185, type, sP44: (term > $o) > $o).
% 21.29/4.27 thf(func_def_187, type, sP46: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_190, type, sP49: (subst > term > subst > $o) > $o).
% 21.29/4.27 thf(func_def_195, type, sP54: (term > $o) > $o).
% 21.29/4.27 thf(func_def_196, type, sP55: (term > $o) > $o).
% 21.29/4.27 thf(func_def_200, type, sK59: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_201, type, sK60: term).
% 21.29/4.27 thf(func_def_202, type, sK61: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_203, type, sK62: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_204, type, sK63: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_205, type, sK64: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_206, type, sK65: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_207, type, sK66: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_208, type, sK67: (term > $o) > term).
% 21.29/4.27 thf(func_def_209, type, sK68: subst > (term > $o) > term).
% 21.29/4.27 thf(func_def_210, type, sK69: term).
% 21.29/4.27 thf(func_def_211, type, sK70: term > $o).
% 21.29/4.27 thf(func_def_212, type, sK71: subst).
% 21.29/4.27 thf(func_def_213, type, sK72: term).
% 21.29/4.27 thf(func_def_214, type, sK73: term > term).
% 21.29/4.27 thf(func_def_215, type, sK74: term > $o).
% 21.29/4.27 thf(func_def_216, type, sK75: term).
% 21.29/4.27 thf(func_def_217, type, sK76: term > term).
% 21.29/4.27 thf(func_def_218, type, sK77: (term > $o) > term).
% 21.29/4.27 thf(func_def_219, type, sK78: (term > $o) > term).
% 21.29/4.27 thf(func_def_220, type, sK79: (term > $o) > term).
% 21.29/4.27 thf(func_def_221, type, sK80: (term > $o) > term).
% 21.29/4.27 thf(func_def_222, type, sK81: (term > $o) > term).
% 21.29/4.27 thf(func_def_223, type, sK82: (term > $o) > term).
% 21.29/4.27 thf(func_def_224, type, sK83: term > subst > term > term).
% 21.29/4.27 thf(func_def_225, type, sK84: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_226, type, sK85: term > $o).
% 21.29/4.27 thf(func_def_227, type, sK86: term).
% 21.29/4.27 thf(func_def_228, type, sK87: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_229, type, sK88: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_230, type, sK89: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_231, type, sK90: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_232, type, sK91: term).
% 21.29/4.27 thf(func_def_233, type, sK92: term).
% 21.29/4.27 thf(func_def_234, type, sK93: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_235, type, sK94: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_236, type, sK95: term > (term > $o) > term).
% 21.29/4.27 thf(func_def_237, type, sK96: (term > $o) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_238, type, sK97: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_239, type, sK98: term).
% 21.29/4.27 thf(func_def_240, type, sK99: subst).
% 21.29/4.27 thf(func_def_241, type, sK100: subst > term > term).
% 21.29/4.27 thf(func_def_242, type, sK101: subst > term > term).
% 21.29/4.27 thf(func_def_243, type, sK102: term).
% 21.29/4.27 thf(func_def_244, type, sK103: subst).
% 21.29/4.27 thf(func_def_245, type, sK104: term).
% 21.29/4.27 thf(func_def_246, type, sK105: subst).
% 21.29/4.27 thf(func_def_247, type, sK106: term).
% 21.29/4.27 thf(func_def_248, type, sK107: term).
% 21.29/4.27 thf(func_def_249, type, sK108: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_250, type, sK109: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_251, type, sK110: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_252, type, sK111: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_253, type, sK112: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_254, type, sK113: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_255, type, sK114: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_256, type, sK115: term).
% 21.29/4.27 thf(func_def_257, type, sK116: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_258, type, sK117: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_259, type, sK118: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_260, type, sK119: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_261, type, sK120: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_262, type, sK121: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_263, type, sK122: term).
% 21.29/4.27 thf(func_def_264, type, sK123: term).
% 21.29/4.27 thf(func_def_265, type, sK124: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_266, type, sK125: term > $o).
% 21.29/4.27 thf(func_def_267, type, sK126: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_268, type, sK127: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_269, type, sK128: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_270, type, sK129: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_271, type, sK130: (term > $o) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_272, type, sK131: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_273, type, sK132: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_274, type, sK133: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_275, type, sK134: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_276, type, sK135: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_277, type, sK136: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_278, type, sK137: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_279, type, sK138: term).
% 21.29/4.27 thf(func_def_280, type, sK139: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_281, type, sK140: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_282, type, sK141: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_283, type, sK142: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_284, type, sK143: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_285, type, sK144: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_286, type, sK145: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_287, type, sK146: term).
% 21.29/4.27 thf(func_def_288, type, sK147: term > $o).
% 21.29/4.27 thf(func_def_289, type, sK148: (term > $o) > term > term).
% 21.29/4.27 thf(func_def_290, type, sK149: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_291, type, sK150: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_292, type, sK151: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_293, type, sK152: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_294, type, sK153: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_295, type, sK154: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_296, type, sK155: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_297, type, sK156: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_298, type, sK157: (term > $o) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_299, type, sK158: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_300, type, sK159: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_301, type, sK160: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_302, type, sK161: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_303, type, sK162: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_304, type, sK163: subst).
% 21.29/4.27 thf(func_def_305, type, sK164: term).
% 21.29/4.27 thf(func_def_306, type, sK165: term > $o).
% 21.29/4.27 thf(func_def_307, type, sK166: term > term).
% 21.29/4.27 thf(func_def_308, type, sK167: (term > $o) > term).
% 21.29/4.27 thf(func_def_309, type, sK168: (term > $o) > subst > term).
% 21.29/4.27 thf(func_def_310, type, sK169: (term > $o) > term).
% 21.29/4.27 thf(func_def_311, type, sK170: (term > $o) > term).
% 21.29/4.27 thf(func_def_312, type, sK171: (term > $o) > term).
% 21.29/4.27 thf(func_def_313, type, sK172: (term > $o) > term).
% 21.29/4.27 thf(func_def_314, type, sK173: term).
% 21.29/4.27 thf(func_def_315, type, sK174: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_316, type, sK175: term).
% 21.29/4.27 thf(func_def_317, type, sK176: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_318, type, sK177: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_319, type, sK178: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_320, type, sK179: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_321, type, sK180: (subst > term > subst > $o) > term > term).
% 21.29/4.27 thf(func_def_322, type, sK181: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_323, type, sK182: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_324, type, sK183: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_325, type, sK184: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_326, type, sK185: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_327, type, sK186: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_328, type, sK187: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_329, type, sK188: term).
% 21.29/4.27 thf(func_def_330, type, sK189: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_331, type, sK190: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_332, type, sK191: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_333, type, sK192: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_334, type, sK193: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_335, type, sK194: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_336, type, sK195: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_337, type, sK196: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_338, type, sK197: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_339, type, sK198: (term > $o) > term).
% 21.29/4.27 thf(func_def_340, type, sK199: (term > $o) > term).
% 21.29/4.27 thf(func_def_341, type, sK200: (subst > term > subst > $o) > term > $o).
% 21.29/4.27 thf(func_def_342, type, sK201: term).
% 21.29/4.27 thf(func_def_343, type, sK202: term > $o).
% 21.29/4.27 thf(func_def_344, type, sK203: term > term).
% 21.29/4.27 thf(func_def_345, type, sK204: term).
% 21.29/4.27 thf(func_def_346, type, sK205: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_347, type, sK206: (term > $o) > term).
% 21.29/4.27 thf(func_def_348, type, sK207: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_349, type, sK208: term).
% 21.29/4.27 thf(func_def_350, type, sK209: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_351, type, sK210: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_352, type, sK211: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_353, type, sK212: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_354, type, sK213: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_355, type, sK214: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_356, type, sK215: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_357, type, sK216: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_358, type, sK217: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_359, type, sK218: term > (term > $o) > term).
% 21.29/4.27 thf(func_def_360, type, sK219: (subst > term > subst > $o) > (term > $o) > term).
% 21.29/4.27 thf(func_def_361, type, sK220: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_362, type, sK221: term > $o).
% 21.29/4.27 thf(func_def_363, type, sK222: term).
% 21.29/4.27 thf(func_def_364, type, sK223: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_365, type, sK224: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_366, type, sK225: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_367, type, sK226: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_368, type, sK227: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_369, type, sK228: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_370, type, sK229: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_371, type, sK230: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_372, type, sK231: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_373, type, sK232: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_374, type, sK233: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_375, type, sK234: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_376, type, sK235: (term > $o) > term).
% 21.29/4.27 thf(func_def_377, type, sK236: (term > $o) > term).
% 21.29/4.27 thf(func_def_378, type, sK237: term).
% 21.29/4.27 thf(func_def_379, type, sK238: term > $o).
% 21.29/4.27 thf(func_def_380, type, sK239: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_381, type, sK240: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_382, type, sK241: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_383, type, sK242: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_384, type, sK243: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_385, type, sK244: (subst > term > subst > $o) > (term > $o) > term).
% 21.29/4.27 thf(func_def_386, type, sK245: (term > $o) > term > term).
% 21.29/4.27 thf(func_def_387, type, sK246: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_388, type, sK247: term).
% 21.29/4.27 thf(func_def_389, type, sK248: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_390, type, sK249: term > (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_391, type, sK250: term > (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_392, type, sK251: term > (subst > term > term) > term).
% 21.29/4.27 thf(func_def_393, type, sK252: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_394, type, sK253: term > (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_395, type, sK254: term > (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_396, type, sK255: term > (subst > term > term) > term).
% 21.29/4.27 thf(func_def_397, type, sK256: (subst > term > subst > $o) > term > term).
% 21.29/4.27 thf(func_def_398, type, sK257: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_399, type, sK258: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_400, type, sK259: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_401, type, sK260: term).
% 21.29/4.27 thf(func_def_402, type, sK261: (subst > term > subst > $o) > term > $o).
% 21.29/4.27 thf(func_def_403, type, sK262: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_404, type, sK263: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_405, type, sK264: term).
% 21.29/4.27 thf(func_def_406, type, sK265: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_407, type, sK266: (term > $o) > term).
% 21.29/4.27 thf(func_def_408, type, sK267: (term > $o) > term).
% 21.29/4.27 thf(func_def_409, type, sK268: (term > $o) > term).
% 21.29/4.27 thf(func_def_410, type, sK269: term > $o).
% 21.29/4.27 thf(func_def_411, type, sK270: term).
% 21.29/4.27 thf(func_def_412, type, sK271: term > term).
% 21.29/4.27 thf(func_def_413, type, sK272: (subst > term > subst > $o) > (term > $o) > term).
% 21.29/4.27 thf(func_def_414, type, sK273: term > (term > $o) > term).
% 21.29/4.27 thf(func_def_415, type, sK274: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_416, type, sK275: term > $o).
% 21.29/4.27 thf(func_def_417, type, sK276: term).
% 21.29/4.27 thf(func_def_418, type, sK277: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_419, type, sK278: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_420, type, sK279: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_421, type, sK280: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_422, type, sK281: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_423, type, sK282: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_424, type, sK283: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_425, type, sK284: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_426, type, sK285: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_427, type, sK286: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_428, type, sK287: (term > $o) > term).
% 21.29/4.27 thf(func_def_429, type, sK288: (term > $o) > term).
% 21.29/4.27 thf(func_def_430, type, sK289: (term > $o) > term).
% 21.29/4.27 thf(func_def_431, type, sK290: (term > $o) > term).
% 21.29/4.27 thf(func_def_432, type, sK291: term).
% 21.29/4.27 thf(func_def_433, type, sK292: subst).
% 21.29/4.27 thf(func_def_434, type, sK293: subst).
% 21.29/4.27 thf(func_def_435, type, sK294: term).
% 21.29/4.27 thf(func_def_436, type, sK295: term > $o).
% 21.29/4.27 thf(func_def_437, type, sK296: term).
% 21.29/4.27 thf(func_def_438, type, sK297: subst).
% 21.29/4.27 thf(func_def_439, type, sK298: term).
% 21.29/4.27 thf(func_def_440, type, sK299: term > $o).
% 21.29/4.27 thf(func_def_441, type, sK300: subst).
% 21.29/4.27 thf(func_def_442, type, sK301: term > term).
% 21.29/4.27 thf(func_def_443, type, sK302: subst > (term > $o) > term).
% 21.29/4.27 thf(func_def_444, type, sK303: (term > $o) > term).
% 21.29/4.27 thf(func_def_445, type, sK304: (term > $o) > term).
% 21.29/4.27 thf(func_def_446, type, sK305: (term > $o) > term).
% 21.29/4.27 thf(func_def_447, type, sK306: (term > $o) > term).
% 21.29/4.27 thf(func_def_448, type, sK307: (term > $o) > term).
% 21.29/4.27 thf(func_def_449, type, sK308: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_450, type, sK309: term).
% 21.29/4.27 thf(func_def_451, type, sK310: term > $o).
% 21.29/4.27 thf(func_def_452, type, sK311: term).
% 21.29/4.27 thf(func_def_453, type, sK312: (term > $o) > term > term).
% 21.29/4.27 thf(func_def_454, type, sK313: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_455, type, sK314: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_456, type, sK315: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_457, type, sK316: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_458, type, sK317: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_459, type, sK318: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_460, type, sK319: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_461, type, sK320: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_462, type, sK321: (term > $o) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_463, type, sK322: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_464, type, sK323: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_465, type, sK324: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_466, type, sK325: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_467, type, sK326: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_468, type, sK327: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_469, type, sK328: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_470, type, sK329: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_471, type, sK330: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_472, type, sK331: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_473, type, sK332: term).
% 21.29/4.27 thf(func_def_474, type, sK333: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_475, type, sK334: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_476, type, sK335: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_477, type, sK336: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_478, type, sK337: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_479, type, sK338: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_480, type, sK339: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_481, type, sK340: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_482, type, sK341: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_483, type, sK342: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_484, type, sK343: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_485, type, sK344: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_486, type, sK345: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_487, type, sK346: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_488, type, sK347: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_489, type, sK348: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_490, type, sK349: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_491, type, sK350: term).
% 21.29/4.27 thf(func_def_492, type, sK351: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_493, type, sK352: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_494, type, sK353: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_495, type, sK354: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_496, type, sK355: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_497, type, sK356: term).
% 21.29/4.27 thf(func_def_498, type, sK357: (subst > term > subst > $o) > term > term).
% 21.29/4.27 thf(func_def_499, type, sK358: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_500, type, sK359: (subst > term > subst > $o) > term > term).
% 21.29/4.27 thf(func_def_501, type, sK360: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_502, type, sK361: term).
% 21.29/4.27 thf(func_def_503, type, sK362: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_504, type, sK363: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_505, type, sK364: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_506, type, sK365: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_507, type, sK366: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_508, type, sK367: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_509, type, sK368: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_510, type, sK369: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_511, type, sK370: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_512, type, sK371: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_513, type, sK372: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_514, type, sK373: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_515, type, sK374: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_516, type, sK375: term).
% 21.29/4.27 thf(func_def_517, type, sK376: term).
% 21.29/4.27 thf(func_def_518, type, sK377: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_519, type, sK378: (term > $o) > term).
% 21.29/4.27 thf(func_def_520, type, sK379: (term > $o) > term).
% 21.29/4.27 thf(func_def_521, type, sK380: term).
% 21.29/4.27 thf(func_def_522, type, sK381: term > $o).
% 21.29/4.27 thf(func_def_523, type, sK382: term > term).
% 21.29/4.27 thf(func_def_524, type, sK383: term).
% 21.29/4.27 thf(func_def_525, type, sK384: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_526, type, sK385: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_527, type, sK386: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_528, type, sK387: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_529, type, sK388: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_530, type, sK389: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_531, type, sK390: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_532, type, sK391: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_533, type, sK392: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_534, type, sK393: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_535, type, sK394: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_536, type, sK395: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_537, type, sK396: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_538, type, sK397: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_539, type, sK398: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_540, type, sK399: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_541, type, sK400: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_542, type, sK401: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_543, type, sK402: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_544, type, sK403: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_545, type, sK404: term).
% 21.29/4.27 thf(func_def_546, type, sK405: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_547, type, sK406: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_548, type, sK407: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_549, type, sK408: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_550, type, sK409: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_551, type, sK410: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_552, type, sK411: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_553, type, sK412: (term > $o) > term).
% 21.29/4.27 thf(func_def_554, type, sK413: (term > $o) > term).
% 21.29/4.27 thf(func_def_555, type, sK414: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_556, type, sK415: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_557, type, sK416: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_558, type, sK417: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_559, type, sK418: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_560, type, sK419: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_561, type, sK420: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_562, type, sK421: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_563, type, sK422: term).
% 21.29/4.27 thf(func_def_564, type, sK423: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_565, type, sK424: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_566, type, sK425: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_567, type, sK426: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_568, type, sK427: term > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_569, type, sK428: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_570, type, sK429: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_571, type, sK430: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_572, type, sK431: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_573, type, sK432: (subst > term > term) > (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_574, type, sK433: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_575, type, sK434: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_576, type, sK435: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_577, type, sK436: (subst > term > subst > $o) > subst > term > term).
% 21.29/4.27 thf(func_def_578, type, sK437: term).
% 21.29/4.27 thf(func_def_579, type, sK438: term > $o).
% 21.29/4.27 thf(func_def_580, type, sK439: term > term).
% 21.29/4.27 thf(func_def_581, type, sK440: (term > $o) > term).
% 21.29/4.27 thf(func_def_582, type, sK441: (term > $o) > term).
% 21.29/4.27 thf(func_def_583, type, sK442: (term > $o) > term).
% 21.29/4.27 thf(func_def_584, type, sK443: (term > $o) > term).
% 21.29/4.27 thf(func_def_585, type, sK444: term).
% 21.29/4.27 thf(func_def_586, type, sK445: term).
% 21.29/4.27 thf(func_def_587, type, sK446: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_588, type, sK447: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_589, type, sK448: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_590, type, sK449: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_591, type, sK450: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_592, type, sK451: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_593, type, sK452: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_594, type, sK453: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_595, type, sK454: (subst > term > subst > $o) > subst).
% 21.29/4.27 thf(func_def_596, type, sK455: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_597, type, sK456: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_598, type, sK457: (subst > term > subst > $o) > term > $o).
% 21.29/4.27 thf(func_def_599, type, sK458: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_600, type, sK459: (term > $o) > term).
% 21.29/4.27 thf(func_def_601, type, sK460: subst).
% 21.29/4.27 thf(func_def_602, type, sK461: subst > term > term).
% 21.29/4.27 thf(func_def_603, type, sK462: subst > term > term).
% 21.29/4.27 thf(func_def_604, type, sK463: term).
% 21.29/4.27 thf(func_def_605, type, sK464: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_606, type, sK465: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_607, type, sK466: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_608, type, sK467: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_609, type, sK468: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_610, type, sK469: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_611, type, sK470: term > subst > term > term).
% 21.29/4.27 thf(func_def_612, type, sK471: term).
% 21.29/4.27 thf(func_def_613, type, sK472: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_614, type, sK473: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_615, type, sK474: subst).
% 21.29/4.27 thf(func_def_616, type, sK475: subst).
% 21.29/4.27 thf(func_def_617, type, sK476: subst).
% 21.29/4.27 thf(func_def_618, type, sK477: subst).
% 21.29/4.27 thf(func_def_619, type, sK478: term).
% 21.29/4.27 thf(func_def_620, type, sK479: subst).
% 21.29/4.27 thf(func_def_621, type, sK480: term).
% 21.29/4.27 thf(func_def_622, type, sK481: subst).
% 21.29/4.27 thf(func_def_623, type, sK482: subst).
% 21.29/4.27 thf(func_def_624, type, sK483: term).
% 21.29/4.27 thf(func_def_625, type, sK484: subst).
% 21.29/4.27 thf(func_def_626, type, sK485: term > $o).
% 21.29/4.27 thf(func_def_627, type, sK486: term).
% 21.29/4.27 thf(func_def_628, type, sK487: term).
% 21.29/4.27 thf(func_def_629, type, sK488: term > $o).
% 21.29/4.27 thf(func_def_630, type, sK489: term).
% 21.29/4.27 thf(func_def_631, type, sK490: term).
% 21.29/4.27 thf(func_def_632, type, sK491: term).
% 21.29/4.27 thf(func_def_633, type, sK492: term).
% 21.29/4.27 thf(func_def_634, type, sK493: term).
% 21.29/4.27 thf(func_def_635, type, sK494: term).
% 21.29/4.27 thf(func_def_636, type, sK495: subst).
% 21.29/4.27 thf(func_def_637, type, sK496: term > subst > term > term).
% 21.29/4.27 thf(func_def_638, type, sK497: term).
% 21.29/4.27 thf(func_def_639, type, sK498: term > subst > term > term).
% 21.29/4.27 thf(func_def_640, type, sK499: term).
% 21.29/4.27 thf(func_def_641, type, sK500: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_642, type, sK501: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_643, type, sK502: (term > $o) > term).
% 21.29/4.27 thf(func_def_644, type, sK503: (term > $o) > term).
% 21.29/4.27 thf(func_def_645, type, sK504: term > $o).
% 21.29/4.27 thf(func_def_646, type, sK505: term).
% 21.29/4.27 thf(func_def_647, type, sK506: term > $o).
% 21.29/4.27 thf(func_def_648, type, sK507: subst).
% 21.29/4.27 thf(func_def_649, type, sK508: term > $o).
% 21.29/4.27 thf(func_def_650, type, sK509: term).
% 21.29/4.27 thf(func_def_651, type, sK510: term > (term > $o) > subst > (term > $o) > term).
% 21.29/4.27 thf(func_def_652, type, sK511: term).
% 21.29/4.27 thf(func_def_653, type, sK512: subst).
% 21.29/4.27 thf(func_def_654, type, sK513: subst > d_subst).
% 21.29/4.27 thf(func_def_655, type, sK514: term).
% 21.29/4.27 thf(func_def_656, type, sK515: term).
% 21.29/4.27 thf(func_def_657, type, sK516: term).
% 21.29/4.27 thf(func_def_658, type, sK517: term).
% 21.29/4.27 thf(func_def_659, type, sK518: term).
% 21.29/4.27 thf(func_def_660, type, sK519: term).
% 21.29/4.27 thf(func_def_661, type, sK520: term).
% 21.29/4.27 thf(func_def_662, type, sK521: term).
% 21.29/4.27 thf(func_def_663, type, sK522: subst).
% 21.29/4.27 thf(func_def_664, type, sK523: term).
% 21.29/4.27 thf(func_def_665, type, sK524: term > $o).
% 21.29/4.27 thf(func_def_666, type, sK525: (term > $o) > term).
% 21.29/4.27 thf(func_def_667, type, sK526: (term > $o) > term > subst > term > $o).
% 21.29/4.27 thf(func_def_668, type, sK527: subst).
% 21.29/4.27 thf(func_def_669, type, sK528: term).
% 21.29/4.27 thf(func_def_670, type, sK529: term).
% 21.29/4.27 thf(func_def_671, type, sK530: term).
% 21.29/4.27 thf(func_def_672, type, sK531: term > $o).
% 21.29/4.27 thf(func_def_673, type, sK532: subst).
% 21.29/4.27 thf(func_def_674, type, sK533: term).
% 21.29/4.27 thf(func_def_675, type, sK534: term > $o).
% 21.29/4.27 thf(func_def_676, type, sK535: term).
% 21.29/4.27 thf(func_def_677, type, sK536: term).
% 21.29/4.27 thf(func_def_678, type, sK537: term).
% 21.29/4.27 thf(func_def_679, type, sK538: term).
% 21.29/4.27 thf(func_def_680, type, sK539: term).
% 21.29/4.27 thf(func_def_681, type, sK540: subst > term > term).
% 21.29/4.27 thf(func_def_682, type, sK541: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_683, type, sK542: (subst > term > term) > term).
% 21.29/4.27 thf(func_def_684, type, sK543: (subst > term > term) > subst).
% 21.29/4.27 thf(func_def_685, type, sK544: term).
% 21.29/4.27 thf(func_def_686, type, sK545: term).
% 21.29/4.27 thf(func_def_687, type, sK546: term).
% 21.29/4.27 thf(func_def_688, type, sK547: term).
% 21.29/4.27 thf(func_def_689, type, sK548: term).
% 21.29/4.27 thf(func_def_690, type, sK549: term).
% 21.29/4.27 thf(func_def_691, type, sK550: term).
% 21.29/4.27 thf(func_def_692, type, sK551: term).
% 21.29/4.27 thf(func_def_693, type, sK552: term).
% 21.29/4.27 thf(func_def_694, type, sK553: term).
% 21.29/4.27 thf(func_def_695, type, sK554: term).
% 21.29/4.27 thf(func_def_696, type, sK555: term).
% 21.29/4.27 thf(func_def_697, type, sK556: term).
% 21.29/4.27 thf(func_def_698, type, sK557: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_699, type, sK558: (term > $o) > term).
% 21.29/4.27 thf(func_def_700, type, sK559: (subst > term > subst > $o) > term > $o).
% 21.29/4.27 thf(func_def_701, type, sK560: term > subst > term > term).
% 21.29/4.27 thf(func_def_702, type, sK561: term).
% 21.29/4.27 thf(func_def_703, type, sK562: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_704, type, sK563: (subst > term > subst > $o) > term).
% 21.29/4.27 thf(func_def_705, type, sK564: subst > term > subst > $o).
% 21.29/4.27 thf(func_def_706, type, sK565: term).
% 21.29/4.27 thf(func_def_707, type, sK566: subst).
% 21.29/4.27 thf(func_def_708, type, sK567: term).
% 21.29/4.27 thf(func_def_709, type, sK568: subst).
% 21.29/4.27 thf(func_def_710, type, sK569: term).
% 21.29/4.27 thf(func_def_711, type, sK570: term).
% 21.29/4.27 thf(func_def_712, type, sK571: term).
% 21.29/4.27 thf(func_def_713, type, sK572: term).
% 21.29/4.27 thf(func_def_714, type, sK573: term).
% 21.29/4.27 thf(func_def_715, type, sK574: term).
% 21.29/4.27 thf(func_def_716, type, sK575: term > $o).
% 21.29/4.27 thf(func_def_717, type, sK576: subst).
% 21.29/4.27 thf(func_def_718, type, sK577: (term > $o) > term).
% 21.29/4.27 thf(func_def_719, type, sK578: subst > (term > $o) > term > term > $o).
% 21.29/4.27 thf(func_def_720, type, sK579: subst).
% 21.29/4.27 thf(func_def_721, type, sK580: term).
% 21.29/4.27 thf(func_def_722, type, sK581: term > $o).
% 21.29/4.27 thf(func_def_723, type, sK582: term > $o).
% 21.29/4.27 thf(func_def_724, type, sK583: (term > $o) > (term > $o) > term > subst > term).
% 21.29/4.27 thf(func_def_725, type, sK584: term > d_term).
% 21.29/4.27 thf(func_def_726, type, sK585: term).
% 21.29/4.27 thf(func_def_727, type, sK586: term).
% 21.29/4.27 thf(func_def_728, type, sK587: term).
% 21.29/4.27 thf(func_def_729, type, sK588: term).
% 21.29/4.27 thf(func_def_730, type, sK589: subst).
% 21.29/4.27 thf(func_def_731, type, sK590: subst).
% 21.29/4.27 thf(func_def_732, type, sK591: subst).
% 21.29/4.27 thf(func_def_733, type, sK592: term).
% 21.29/4.27 thf(func_def_734, type, sK593: term > $o).
% 21.29/4.27 thf(func_def_735, type, sK594: (term > $o) > term > subst > term > $o).
% 21.29/4.27 thf(func_def_737, type, sK596: (term > $o) > term).
% 21.29/4.27 thf(func_def_738, type, ph597: !>[X0: $tType]:(X0)).
% 21.29/4.27 thf(f3221,plain,(
% 21.29/4.27 $false),
% 21.29/4.27 inference(avatar_sat_refutation,[status(thm)],[f3015,f3023,f3066,f3109,f3134,f3187,f3189,f3205,f3220])).
% 21.29/4.27 thf(f3220,plain,(
% 21.29/4.27 ~spl595_89 | ~spl595_93),
% 21.29/4.27 inference(avatar_contradiction_clause,[status(thm)],[f3219])).
% 21.29/4.27 thf(f3219,plain,(
% 21.29/4.27 $false | (~spl595_89 | ~spl595_93)),
% 21.29/4.27 inference(trivial_inequality_removal,[status(thm)],[f3215])).
% 21.29/4.27 thf(f3215,plain,(
% 21.29/4.27 ($true = $false) | (~spl595_89 | ~spl595_93)),
% 21.29/4.27 inference(superposition,[status(thm)],[f3087,f3108])).
% 21.29/4.27 thf(f3108,plain,(
% 21.29/4.27 ($false = (sK593 @ (d2term @ d_one))) | ~spl595_93),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3106])).
% 21.29/4.27 thf(f3106,definition,(
% 21.29/4.27 spl595_93 <=> ($false = (sK593 @ (d2term @ d_one)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_93])],[avatar_definition])).
% 21.29/4.27 thf(f3087,plain,(
% 21.29/4.27 ( ! [X0 : term] : (((sK593 @ X0) = $true)) ) | ~spl595_89),
% 21.29/4.27 inference(superposition,[status(thm)],[f3010,f2251])).
% 21.29/4.27 thf(f2251,plain,(
% 21.29/4.27 ( ! [X258 : term] : (((d2term @ d_one) = X258)) )),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f1060,f1117])).
% 21.29/4.27 thf(f1117,plain,(
% 21.29/4.27 ( ! [X203 : d_term] : ((d_one = X203)) )),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f545])).
% 21.29/4.27 thf(f545,plain,(
% 21.29/4.27 (! [X0 : subst > term > subst > $o] : ! [X2 : term] : ((X0 @ id @ X2 @ id) = (sK457 @ X0 @ X2)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X4 : term > $o] : ((sK458 @ id @ (sK459 @ X4) @ id) != (X4 @ (sK459 @ X4)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj = $true) | (! [X10 : term,X11 : subst,X12 : subst] : ((sK462 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12)) = (sub @ (sK462 @ X11 @ X10) @ X12)) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (sK461 @ X15 @ X14) @ X13) = (sK461 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) & ((lam @ (sK461 @ sh @ one)) = (lam @ (sK462 @ sh @ one))) & ((sK461 @ sK460 @ sK463) != (sK462 @ sK460 @ sK463)))) & (! [X16 : subst,X17 : subst > term > term,X18 : subst > term > term,X19 : term] : (((X18 @ (comp @ (sK465 @ X18) @ (sK466 @ X18)) @ (sub @ (sK464 @ X18) @ (sK466 @ X18))) != (sub @ (X18 @ (sK465 @ X18) @ (sK464 @ X18)) @ (sK466 @ X18))) | ((sub @ (X17 @ (sK469 @ X17) @ (sK468 @ X17)) @ (sK467 @ X17)) != (X17 @ (comp @ (sK469 @ X17) @ (sK467 @ X17)) @ (sub @ (sK468 @ X17) @ (sK467 @ X17)))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X17 @ sh @ one))) | ((X18 @ X16 @ X19) = (X17 @ X16 @ X19))) | (hoaslaminj != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((d2subst @ d_id) = id) & (! [X26 : term] : ! [X28 : subst,X29 : term] : ((sK470 @ X26 @ X28 @ X29) = (sub @ X26 @ (push @ X29 @ X28))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X31 : subst > term > term] : ((X31 @ (sK472 @ X31) @ (sK473 @ X31)) != (sub @ sK471 @ (push @ (sK473 @ X31) @ (sK472 @ X31))))) & ((induction2_lthm = $true) | (sP57 != $true)) & ((sP57 = $true) | (induction2_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (! [X34 : subst] : ((comp @ X34 @ id) = X34) & ((sK474 != (comp @ sK474 @ id)) | ((comp @ id @ sK475) != sK475)) & ! [X37 : subst] : ((comp @ id @ X37) = X37))) & ((sK476 != (comp @ sK476 @ id)) | (! [X39 : subst] : ((comp @ X39 @ id) = X39) & ! [X40 : subst] : ((comp @ id @ X40) = X40)) | (sK477 != (comp @ id @ sK477)) | (substmonoid_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (! [X42 : term,X43 : subst] : ((sub @ one @ (push @ X42 @ X43)) = X42) | (axvarcons != $true)) & ((axvarcons = $true) | ((sub @ one @ (push @ sK478 @ sK479)) != sK478)) & ((sP50 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP50 != $true)) & (ulamvarsh = $true) & ((sK480 != (sub @ one @ (push @ sK480 @ sK481))) | ((comp @ sh @ (push @ sK483 @ sK482)) != sK482) | ! [X50 : subst,X51 : term > $o,X52 : term,X53 : term,X54 : term > $o] : (((X54 @ X53) != $true) | ($true = (X51 @ (sub @ X53 @ (push @ X52 @ X50))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X55 : term,X56 : subst] : ((sub @ one @ (push @ X55 @ X56)) = X55) & ! [X57 : subst,X58 : term] : ((comp @ sh @ (push @ X58 @ X57)) = X57) & (((sK488 @ sK487) = $true) & ((sK485 @ (sub @ sK487 @ (push @ sK486 @ sK484))) != $true)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lem3aa = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lem3aa != $true)) & ! [X64 : d_subst,X65 : d_subst] : (((d2subst @ X65) != (d2subst @ X64)) | (X64 = X65)) & ((hoasapinj2 = $true) | ((sK491 != sK492) & ((ap @ (sub @ sK489 @ id) @ sK492) = (ap @ (sub @ sK490 @ id) @ sK491)))) & (! [X70 : term,X71 : term,X72 : term,X73 : term] : ((X72 = X73) | ((ap @ (sub @ X70 @ id) @ X73) != (ap @ (sub @ X71 @ id) @ X72))) | (hoasapinj2 != $true)) & (axmap = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((laminj = $true) | (((lam @ sK493) = (lam @ sK494)) & (sK494 != sK493))) & (! [X76 : term,X77 : term] : (((lam @ X77) != (lam @ X76)) | (X76 = X77)) | (laminj != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & (($true = sP45) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP45)) & ((axidr = $true) | (sK495 != (comp @ sK495 @ id))) & (! [X79 : subst] : ((comp @ X79 @ id) = X79) | (axidr != $true)) & (! [X80 : term] : ((sK496 @ X80 @ sh @ one) = (sub @ X80 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X83 : subst > term > term] : ((sub @ sK497 @ (push @ one @ sh)) != (X83 @ sh @ one))) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & (! [X84 : term] : ! [X86 : subst,X87 : term] : ((sK498 @ X84 @ X86 @ X87) = (sub @ X84 @ (push @ X87 @ X86))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X89 : subst > term > term] : ((X89 @ (sK500 @ X89) @ (sK501 @ X89)) != (sub @ sK499 @ (push @ (sK501 @ X89) @ (sK500 @ X89))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X92 : term > $o,X93 : term] : (((sP43 @ X92) = $true) | (((var @ (sK502 @ X92)) = $true) & ($true != (X92 @ (sK502 @ X92)))) | (((X92 @ (lam @ (sK503 @ X92))) != $true) & ($true = (X92 @ (sK503 @ X92)))) | ((X92 @ X93) = $true)) | (induction != $true)) & ((induction = $true) | (((sP43 @ sK504) != $true) & ! [X98 : term] : (((var @ X98) != $true) | ((sK504 @ X98) = $true)) & ! [X99 : term] : (((sK504 @ (lam @ X99)) = $true) | ((sK504 @ X99) != $true)) & ($true != (sK504 @ sK505)))) & ((pushprop_lem1v2_lthm = $true) | ((((sK506 @ one) != $true) & ((sK508 @ sK509) = $true) & ! [X104 : term] : ((sK506 @ X104) = (sK508 @ (sub @ X104 @ (push @ sK509 @ sK507))))) & ! [X105 : term,X106 : subst] : ((sub @ one @ (push @ X105 @ X106)) = X105))) & (! [X107 : term > $o,X108 : subst,X109 : term > $o,X110 : term] : (($true = (X107 @ one)) | ((X109 @ X110) != $true) | ((X107 @ (sK510 @ X110 @ X109 @ X108 @ X107)) != (X109 @ (sub @ (sK510 @ X110 @ X109 @ X108 @ X107) @ (push @ X110 @ X108))))) | (sK511 != (sub @ one @ (push @ sK511 @ sK512))) | (pushprop_lem1v2_lthm != $true)) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP42) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP42)) & ! [X114 : subst] : ((d2subst @ (sK513 @ X114)) = X114) & ! [X116 : d_subst] : (d_id = X116) & (! [X117 : term,X118 : term,X119 : term,X120 : term] : ((X117 = X119) | ((ap @ (sub @ X118 @ id) @ X117) != (ap @ (sub @ X120 @ id) @ X119))) | ((sK517 != sK514) & ((ap @ sK515 @ sK517) = (ap @ sK516 @ sK514))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((sK520 != sK518) & ((ap @ (sub @ sK519 @ id) @ sK518) = (ap @ (sub @ sK521 @ id) @ sK520))) & ! [X129 : term,X130 : term,X131 : term,X132 : term] : ((X129 = X132) | ((ap @ X131 @ X129) != (ap @ X130 @ X132))))) & (lamnotvar = $true) & ((pushprop_lem0 = $true) | ! [X136 : term > $o] : ((X136 @ (sK525 @ X136)) != (sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))))) & (! [X138 : subst,X139 : term,X140 : term > $o] : ! [X142 : term] : ((X140 @ (sub @ X142 @ (push @ X139 @ X138))) = (sK526 @ X140 @ X139 @ X138 @ X142)) | (pushprop_lem0 != $true)) & (! [X143 : subst] : ((push @ (sub @ one @ X143) @ (comp @ sh @ X143)) = X143) | (axscons != $true)) & ((axscons = $true) | (sK527 != (push @ (sub @ one @ sK527) @ (comp @ sh @ sK527)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & (($true = sP39) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP39)) & ((hoasinduction_lem3v2a = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2a != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((shinj = $true) | (((sub @ sK528 @ sh) = (sub @ sK529 @ sh)) & (sK529 != sK528))) & (! [X147 : term,X148 : term] : (((sub @ X148 @ sh) != (sub @ X147 @ sh)) | (X147 = X148)) | (shinj != $true)) & (induction2_gthm = $true) & (! [X149 : term,X150 : term > $o,X151 : subst,X152 : term,X153 : term > $o] : (($true != (X150 @ X149)) | ((X153 @ (sub @ X149 @ (push @ X152 @ X151))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (((sK531 @ sK530) = $true) & ((sK534 @ (sub @ sK530 @ (push @ sK533 @ sK532))) != $true))) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & (! [X159 : term] : ((sub @ X159 @ id) = X159) | (termmset != $true)) & ((termmset = $true) | (sK535 != (sub @ sK535 @ id))) & ((sK536 != (sub @ sK536 @ id)) | ! [X162 : term] : ((sub @ X162 @ id) = X162) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X163 : term] : ((sub @ X163 @ id) = X163) & (sK537 != (sub @ sK537 @ id)))) & (pushprop_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | (((lam @ (sK540 @ sh @ one)) = (ap @ (sub @ sK538 @ id) @ sK539)) & ! [X168 : subst,X169 : term,X170 : subst] : ((sK540 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)) = (sub @ (sK540 @ X170 @ X169) @ X168)))) & (! [X171 : term,X172 : term,X173 : subst > term > term] : (((lam @ (X173 @ sh @ one)) != (ap @ (sub @ X171 @ id) @ X172)) | ((sub @ (X173 @ (sK543 @ X173) @ (sK542 @ X173)) @ (sK541 @ X173)) != (X173 @ (comp @ (sK543 @ X173) @ (sK541 @ X173)) @ (sub @ (sK542 @ X173) @ (sK541 @ X173))))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) | (sP32 != $true)) & ((sP32 = $true) | (hoasinduction_lem3aaa != $true)) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & ((((ap @ sK545 @ sK547) = (ap @ sK546 @ sK544)) & (sK545 != sK546)) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X182 = X184) | ((ap @ (sub @ X182 @ id) @ X183) != (ap @ (sub @ X184 @ id) @ X181))) | ((sub @ sK548 @ id) != sK548) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X186 : term,X187 : term,X188 : term,X189 : term] : (((ap @ X188 @ X186) != (ap @ X187 @ X189)) | (X187 = X188)) & ((sK552 != sK550) & ((ap @ (sub @ sK552 @ id) @ sK549) = (ap @ (sub @ sK550 @ id) @ sK551))) & ! [X194 : term] : ((sub @ X194 @ id) = X194))) & (! [X195 : term,X196 : term,X197 : term,X198 : term] : ((X195 = X197) | ((ap @ (sub @ X195 @ id) @ X196) != (ap @ (sub @ X197 @ id) @ X198))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((sK555 != sK553) & ((ap @ (sub @ sK553 @ id) @ sK554) = (ap @ (sub @ sK555 @ id) @ sK556)))) & ! [X203 : d_term] : (d_one = X203) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP31 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP31 != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & ((hoasinduction_lem0 = $true) | ! [X205 : term > $o] : ((X205 @ (sK558 @ X205)) != (sK557 @ id @ (sK558 @ X205) @ id))) & (! [X207 : subst > term > subst > $o] : ! [X209 : term] : ((X207 @ id @ X209 @ id) = (sK559 @ X207 @ X209)) | (hoasinduction_lem0 != $true)) & ((sP26 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP26 != $true)) & (! [X210 : term] : ((sK560 @ X210 @ sh @ one) = (sub @ X210 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X213 : subst > term > term] : ((X213 @ sh @ one) != (sub @ sK561 @ (push @ one @ sh)))) & (pushprop_lthm = $true) & (($true = sP22) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP22)) & (! [X214 : subst > term > subst > $o,X215 : term] : ((((X214 @ id @ (sK562 @ X214) @ id) = $true) & ((X214 @ id @ (ap @ (sub @ (sK562 @ X214) @ id) @ (sK563 @ X214)) @ id) != $true) & ($true = (X214 @ id @ (sK563 @ X214) @ id))) | ((sP20 @ X214) = $true) | ((X214 @ id @ X215 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X220 : term,X221 : term] : (((sK564 @ id @ X220 @ id) != $true) | ((sK564 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id) = $true) | ((sK564 @ id @ X221 @ id) != $true)) & ($true != (sP20 @ sK564)) & ($true != (sK564 @ id @ sK565 @ id)))) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (! [X222 : subst] : ((comp @ id @ X222) = X222) | (axidl != $true)) & ((axidl = $true) | ((comp @ id @ sK566) != sK566)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK567 @ sK568)) != sK568)) & (! [X226 : term,X227 : subst] : ((comp @ sh @ (push @ X226 @ X227)) = X227) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((apinj1 = $true) | ((sK571 != sK572) & ((ap @ sK572 @ sK570) = (ap @ sK571 @ sK569)))) & (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X234 = X235) | ((ap @ X234 @ X232) != (ap @ X235 @ X233))) | (apinj1 != $true)) & ((axvarid = $true) | ((sub @ sK573 @ id) != sK573)) & (! [X237 : term] : ((sub @ X237 @ id) = X237) | (axvarid != $true)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) | ! [X241 : term > $o] : ((sK575 @ (sub @ (sK577 @ X241) @ (push @ sK574 @ sK576))) != (X241 @ (sK577 @ X241)))) & (! [X243 : term,X244 : term > $o,X245 : subst] : ! [X247 : term] : ((X244 @ (sub @ X247 @ (push @ X243 @ X245))) = (sK578 @ X245 @ X244 @ X243 @ X247)) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem1v2 = $true) | (((sK582 @ sK580) = $true) & ! [X252 : term] : ((sK581 @ X252) = (sK582 @ (sub @ X252 @ (push @ sK580 @ sK579)))) & ((sK581 @ one) != $true))) & (! [X253 : subst,X254 : term,X255 : term > $o,X256 : term > $o] : (((X256 @ X254) != $true) | ((X256 @ (sub @ (sK583 @ X256 @ X255 @ X254 @ X253) @ (push @ X254 @ X253))) != (X255 @ (sK583 @ X256 @ X255 @ X254 @ X253))) | ((X255 @ one) = $true)) | (pushprop_lem1v2 != $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP16 != $true)) & ((sP16 = $true) | (hoasinduction_lem3a_lthm != $true)) & (axapp = $true) & ! [X258 : term] : ((d2term @ (sK584 @ X258)) = X258) & (ulamvarind = $true) & ((sP14 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP14 != $true)) & (! [X260 : term,X261 : term,X262 : term,X263 : term] : (((ap @ X261 @ X262) != (ap @ X263 @ X260)) | (X260 = X262)) | (apinj2 != $true)) & ((apinj2 = $true) | (((ap @ sK588 @ sK585) = (ap @ sK586 @ sK587)) & (sK585 != sK587))) & ((! [X268 : subst] : ((comp @ X268 @ id) = X268) & ! [X269 : subst] : ((comp @ id @ X269) = X269)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK589 != (comp @ sK589 @ id)) | (sK590 != (comp @ id @ sK590))) & ((sP5 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP5 != $true)) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X272 : d_term,X273 : d_term] : ((X272 = X273) | ((d2term @ X272) != (d2term @ X273))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((induction2 = $true) | ($true != sP3)) & (($true = sP3) | (induction2 != $true)) & (($true = sP1) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP1))),
% 21.29/4.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f475,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476])).
% 21.29/4.27 thf(f476,plain,(
% 21.29/4.27 ! [X0 : subst > term > subst > $o] : (? [X1 : term > $o] : ! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) => ! [X2 : term] : ((X0 @ id @ X2 @ id) = (sK457 @ X0 @ X2)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f477,plain,(
% 21.29/4.27 ? [X3 : subst > term > subst > $o] : ! [X4 : term > $o] : ? [X5 : term] : ((X4 @ X5) != (X3 @ id @ X5 @ id)) => ! [X4 : term > $o] : ? [X5 : term] : ((X4 @ X5) != (sK458 @ id @ X5 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f478,plain,(
% 21.29/4.27 ! [X4 : term > $o] : (? [X5 : term] : ((X4 @ X5) != (sK458 @ id @ X5 @ id)) => ((sK458 @ id @ (sK459 @ X4) @ id) != (X4 @ (sK459 @ X4))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f479,plain,(
% 21.29/4.27 ? [X6 : subst,X7 : subst > term > term,X8 : subst > term > term,X9 : term] : (! [X10 : term,X11 : subst,X12 : subst] : ((sub @ (X8 @ X11 @ X10) @ X12) = (X8 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12))) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (X7 @ X15 @ X14) @ X13) = (X7 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) & ((lam @ (X7 @ sh @ one)) = (lam @ (X8 @ sh @ one))) & ((X7 @ X6 @ X9) != (X8 @ X6 @ X9))) => (! [X12 : subst,X11 : subst,X10 : term] : ((sK462 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12)) = (sub @ (sK462 @ X11 @ X10) @ X12)) & ! [X15 : subst,X14 : term,X13 : subst] : ((sub @ (sK461 @ X15 @ X14) @ X13) = (sK461 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) & ((lam @ (sK461 @ sh @ one)) = (lam @ (sK462 @ sh @ one))) & ((sK461 @ sK460 @ sK463) != (sK462 @ sK460 @ sK463)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f480,plain,(
% 21.29/4.27 ! [X18 : subst > term > term] : (? [X20 : term,X21 : subst,X22 : subst] : ((sub @ (X18 @ X21 @ X20) @ X22) != (X18 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22))) => ((X18 @ (comp @ (sK465 @ X18) @ (sK466 @ X18)) @ (sub @ (sK464 @ X18) @ (sK466 @ X18))) != (sub @ (X18 @ (sK465 @ X18) @ (sK464 @ X18)) @ (sK466 @ X18))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f481,plain,(
% 21.29/4.27 ! [X17 : subst > term > term] : (? [X23 : subst,X24 : term,X25 : subst] : ((X17 @ (comp @ X25 @ X23) @ (sub @ X24 @ X23)) != (sub @ (X17 @ X25 @ X24) @ X23)) => ((sub @ (X17 @ (sK469 @ X17) @ (sK468 @ X17)) @ (sK467 @ X17)) != (X17 @ (comp @ (sK469 @ X17) @ (sK467 @ X17)) @ (sub @ (sK468 @ X17) @ (sK467 @ X17)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f482,plain,(
% 21.29/4.27 ! [X26 : term] : (? [X27 : subst > term > term] : ! [X28 : subst,X29 : term] : ((X27 @ X28 @ X29) = (sub @ X26 @ (push @ X29 @ X28))) => ! [X29 : term,X28 : subst] : ((sK470 @ X26 @ X28 @ X29) = (sub @ X26 @ (push @ X29 @ X28))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f483,plain,(
% 21.29/4.27 ? [X30 : term] : ! [X31 : subst > term > term] : ? [X32 : subst,X33 : term] : ((X31 @ X32 @ X33) != (sub @ X30 @ (push @ X33 @ X32))) => ! [X31 : subst > term > term] : ? [X33 : term,X32 : subst] : ((X31 @ X32 @ X33) != (sub @ sK471 @ (push @ X33 @ X32)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f484,plain,(
% 21.29/4.27 ! [X31 : subst > term > term] : (? [X33 : term,X32 : subst] : ((X31 @ X32 @ X33) != (sub @ sK471 @ (push @ X33 @ X32))) => ((X31 @ (sK472 @ X31) @ (sK473 @ X31)) != (sub @ sK471 @ (push @ (sK473 @ X31) @ (sK472 @ X31)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f485,plain,(
% 21.29/4.27 ? [X35 : subst] : ((comp @ X35 @ id) != X35) => (sK474 != (comp @ sK474 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f486,plain,(
% 21.29/4.27 ? [X36 : subst] : ((comp @ id @ X36) != X36) => ((comp @ id @ sK475) != sK475)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f487,plain,(
% 21.29/4.27 ? [X38 : subst] : ((comp @ X38 @ id) != X38) => (sK476 != (comp @ sK476 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f488,plain,(
% 21.29/4.27 ? [X41 : subst] : ((comp @ id @ X41) != X41) => (sK477 != (comp @ id @ sK477))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f489,plain,(
% 21.29/4.27 ? [X44 : term,X45 : subst] : ((sub @ one @ (push @ X44 @ X45)) != X44) => ((sub @ one @ (push @ sK478 @ sK479)) != sK478)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f490,plain,(
% 21.29/4.27 ? [X46 : term,X47 : subst] : ((sub @ one @ (push @ X46 @ X47)) != X46) => (sK480 != (sub @ one @ (push @ sK480 @ sK481)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f491,plain,(
% 21.29/4.27 ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48) => ((comp @ sh @ (push @ sK483 @ sK482)) != sK482)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f492,plain,(
% 21.29/4.27 ? [X59 : subst,X60 : term > $o,X61 : term,X62 : term,X63 : term > $o] : (((X63 @ X62) = $true) & ((X60 @ (sub @ X62 @ (push @ X61 @ X59))) != $true)) => (((sK488 @ sK487) = $true) & ((sK485 @ (sub @ sK487 @ (push @ sK486 @ sK484))) != $true))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f493,plain,(
% 21.29/4.27 ? [X66 : term,X67 : term,X68 : term,X69 : term] : ((X68 != X69) & ((ap @ (sub @ X67 @ id) @ X68) = (ap @ (sub @ X66 @ id) @ X69))) => ((sK491 != sK492) & ((ap @ (sub @ sK489 @ id) @ sK492) = (ap @ (sub @ sK490 @ id) @ sK491)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f494,plain,(
% 21.29/4.27 ? [X74 : term,X75 : term] : (((lam @ X75) = (lam @ X74)) & (X74 != X75)) => (((lam @ sK493) = (lam @ sK494)) & (sK494 != sK493))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f495,plain,(
% 21.29/4.27 ? [X78 : subst] : ((comp @ X78 @ id) != X78) => (sK495 != (comp @ sK495 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f496,plain,(
% 21.29/4.27 ! [X80 : term] : (? [X81 : subst > term > term] : ((X81 @ sh @ one) = (sub @ X80 @ (push @ one @ sh))) => ((sK496 @ X80 @ sh @ one) = (sub @ X80 @ (push @ one @ sh))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f497,plain,(
% 21.29/4.27 ? [X82 : term] : ! [X83 : subst > term > term] : ((sub @ X82 @ (push @ one @ sh)) != (X83 @ sh @ one)) => ! [X83 : subst > term > term] : ((sub @ sK497 @ (push @ one @ sh)) != (X83 @ sh @ one))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f498,plain,(
% 21.29/4.27 ! [X84 : term] : (? [X85 : subst > term > term] : ! [X86 : subst,X87 : term] : ((X85 @ X86 @ X87) = (sub @ X84 @ (push @ X87 @ X86))) => ! [X87 : term,X86 : subst] : ((sK498 @ X84 @ X86 @ X87) = (sub @ X84 @ (push @ X87 @ X86))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f499,plain,(
% 21.29/4.27 ? [X88 : term] : ! [X89 : subst > term > term] : ? [X90 : subst,X91 : term] : ((X89 @ X90 @ X91) != (sub @ X88 @ (push @ X91 @ X90))) => ! [X89 : subst > term > term] : ? [X91 : term,X90 : subst] : ((X89 @ X90 @ X91) != (sub @ sK499 @ (push @ X91 @ X90)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f500,plain,(
% 21.29/4.27 ! [X89 : subst > term > term] : (? [X91 : term,X90 : subst] : ((X89 @ X90 @ X91) != (sub @ sK499 @ (push @ X91 @ X90))) => ((X89 @ (sK500 @ X89) @ (sK501 @ X89)) != (sub @ sK499 @ (push @ (sK501 @ X89) @ (sK500 @ X89)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f501,plain,(
% 21.29/4.27 ! [X92 : term > $o] : (? [X94 : term] : (((var @ X94) = $true) & ((X92 @ X94) != $true)) => (((var @ (sK502 @ X92)) = $true) & ($true != (X92 @ (sK502 @ X92)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f502,plain,(
% 21.29/4.27 ! [X92 : term > $o] : (? [X95 : term] : (($true != (X92 @ (lam @ X95))) & ($true = (X92 @ X95))) => (((X92 @ (lam @ (sK503 @ X92))) != $true) & ($true = (X92 @ (sK503 @ X92)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f503,plain,(
% 21.29/4.27 ? [X96 : term > $o,X97 : term] : (((sP43 @ X96) != $true) & ! [X98 : term] : (((var @ X98) != $true) | ($true = (X96 @ X98))) & ! [X99 : term] : (((X96 @ (lam @ X99)) = $true) | ((X96 @ X99) != $true)) & ($true != (X96 @ X97))) => (((sP43 @ sK504) != $true) & ! [X98 : term] : (((var @ X98) != $true) | ((sK504 @ X98) = $true)) & ! [X99 : term] : (((sK504 @ (lam @ X99)) = $true) | ((sK504 @ X99) != $true)) & ($true != (sK504 @ sK505)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f504,plain,(
% 21.29/4.27 ? [X100 : term > $o,X101 : subst,X102 : term > $o,X103 : term] : (($true != (X100 @ one)) & ($true = (X102 @ X103)) & ! [X104 : term] : ((X102 @ (sub @ X104 @ (push @ X103 @ X101))) = (X100 @ X104))) => (((sK506 @ one) != $true) & ((sK508 @ sK509) = $true) & ! [X104 : term] : ((sK506 @ X104) = (sK508 @ (sub @ X104 @ (push @ sK509 @ sK507)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f505,plain,(
% 21.29/4.27 ! [X107 : term > $o,X108 : subst,X109 : term > $o,X110 : term] : (? [X111 : term] : ((X107 @ X111) != (X109 @ (sub @ X111 @ (push @ X110 @ X108)))) => ((X107 @ (sK510 @ X110 @ X109 @ X108 @ X107)) != (X109 @ (sub @ (sK510 @ X110 @ X109 @ X108 @ X107) @ (push @ X110 @ X108)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f506,plain,(
% 21.29/4.27 ? [X112 : term,X113 : subst] : ((sub @ one @ (push @ X112 @ X113)) != X112) => (sK511 != (sub @ one @ (push @ sK511 @ sK512)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f507,plain,(
% 21.29/4.27 ! [X114 : subst] : (? [X115 : d_subst] : ((d2subst @ X115) = X114) => ((d2subst @ (sK513 @ X114)) = X114))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f508,plain,(
% 21.29/4.27 ? [X121 : term,X122 : term,X123 : term,X124 : term] : ((X121 != X124) & ((ap @ X122 @ X124) = (ap @ X123 @ X121))) => ((sK517 != sK514) & ((ap @ sK515 @ sK517) = (ap @ sK516 @ sK514)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f509,plain,(
% 21.29/4.27 ? [X125 : term,X126 : term,X127 : term,X128 : term] : ((X125 != X127) & ((ap @ (sub @ X126 @ id) @ X125) = (ap @ (sub @ X128 @ id) @ X127))) => ((sK520 != sK518) & ((ap @ (sub @ sK519 @ id) @ sK518) = (ap @ (sub @ sK521 @ id) @ sK520)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f510,plain,(
% 21.29/4.27 ? [X133 : subst,X134 : term,X135 : term > $o] : ! [X136 : term > $o] : ? [X137 : term] : ((X135 @ (sub @ X137 @ (push @ X134 @ X133))) != (X136 @ X137)) => ! [X136 : term > $o] : ? [X137 : term] : ((sK524 @ (sub @ X137 @ (push @ sK523 @ sK522))) != (X136 @ X137))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f511,plain,(
% 21.29/4.27 ! [X136 : term > $o] : (? [X137 : term] : ((sK524 @ (sub @ X137 @ (push @ sK523 @ sK522))) != (X136 @ X137)) => ((X136 @ (sK525 @ X136)) != (sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f512,plain,(
% 21.29/4.27 ! [X138 : subst,X139 : term,X140 : term > $o] : (? [X141 : term > $o] : ! [X142 : term] : ((X141 @ X142) = (X140 @ (sub @ X142 @ (push @ X139 @ X138)))) => ! [X142 : term] : ((X140 @ (sub @ X142 @ (push @ X139 @ X138))) = (sK526 @ X140 @ X139 @ X138 @ X142)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f513,plain,(
% 21.29/4.27 ? [X144 : subst] : ((push @ (sub @ one @ X144) @ (comp @ sh @ X144)) != X144) => (sK527 != (push @ (sub @ one @ sK527) @ (comp @ sh @ sK527)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f514,plain,(
% 21.29/4.27 ? [X145 : term,X146 : term] : (((sub @ X145 @ sh) = (sub @ X146 @ sh)) & (X145 != X146)) => (((sub @ sK528 @ sh) = (sub @ sK529 @ sh)) & (sK529 != sK528))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f515,plain,(
% 21.29/4.27 ? [X154 : term,X155 : term > $o,X156 : subst,X157 : term,X158 : term > $o] : (((X155 @ X154) = $true) & ($true != (X158 @ (sub @ X154 @ (push @ X157 @ X156))))) => (((sK531 @ sK530) = $true) & ((sK534 @ (sub @ sK530 @ (push @ sK533 @ sK532))) != $true))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f516,plain,(
% 21.29/4.27 ? [X160 : term] : ((sub @ X160 @ id) != X160) => (sK535 != (sub @ sK535 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f517,plain,(
% 21.29/4.27 ? [X161 : term] : ((sub @ X161 @ id) != X161) => (sK536 != (sub @ sK536 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f518,plain,(
% 21.29/4.27 ? [X164 : term] : ((sub @ X164 @ id) != X164) => (sK537 != (sub @ sK537 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f519,plain,(
% 21.29/4.27 ? [X165 : term,X166 : term,X167 : subst > term > term] : (((ap @ (sub @ X165 @ id) @ X166) = (lam @ (X167 @ sh @ one))) & ! [X168 : subst,X169 : term,X170 : subst] : ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)) = (sub @ (X167 @ X170 @ X169) @ X168))) => (((lam @ (sK540 @ sh @ one)) = (ap @ (sub @ sK538 @ id) @ sK539)) & ! [X170 : subst,X169 : term,X168 : subst] : ((sK540 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)) = (sub @ (sK540 @ X170 @ X169) @ X168)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f520,plain,(
% 21.29/4.27 ! [X173 : subst > term > term] : (? [X174 : subst,X175 : term,X176 : subst] : ((sub @ (X173 @ X176 @ X175) @ X174) != (X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) => ((sub @ (X173 @ (sK543 @ X173) @ (sK542 @ X173)) @ (sK541 @ X173)) != (X173 @ (comp @ (sK543 @ X173) @ (sK541 @ X173)) @ (sub @ (sK542 @ X173) @ (sK541 @ X173)))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f521,plain,(
% 21.29/4.27 ? [X177 : term,X178 : term,X179 : term,X180 : term] : (((ap @ X179 @ X177) = (ap @ X178 @ X180)) & (X178 != X179)) => (((ap @ sK545 @ sK547) = (ap @ sK546 @ sK544)) & (sK545 != sK546))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f522,plain,(
% 21.29/4.27 ? [X185 : term] : ((sub @ X185 @ id) != X185) => ((sub @ sK548 @ id) != sK548)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f523,plain,(
% 21.29/4.27 ? [X190 : term,X191 : term,X192 : term,X193 : term] : ((X191 != X193) & ((ap @ (sub @ X191 @ id) @ X192) = (ap @ (sub @ X193 @ id) @ X190))) => ((sK552 != sK550) & ((ap @ (sub @ sK552 @ id) @ sK549) = (ap @ (sub @ sK550 @ id) @ sK551)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f524,plain,(
% 21.29/4.27 ? [X199 : term,X200 : term,X201 : term,X202 : term] : ((X199 != X201) & ((ap @ (sub @ X199 @ id) @ X200) = (ap @ (sub @ X201 @ id) @ X202))) => ((sK555 != sK553) & ((ap @ (sub @ sK553 @ id) @ sK554) = (ap @ (sub @ sK555 @ id) @ sK556)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f525,plain,(
% 21.29/4.27 ? [X204 : subst > term > subst > $o] : ! [X205 : term > $o] : ? [X206 : term] : ((X205 @ X206) != (X204 @ id @ X206 @ id)) => ! [X205 : term > $o] : ? [X206 : term] : ((X205 @ X206) != (sK557 @ id @ X206 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f526,plain,(
% 21.29/4.27 ! [X205 : term > $o] : (? [X206 : term] : ((X205 @ X206) != (sK557 @ id @ X206 @ id)) => ((X205 @ (sK558 @ X205)) != (sK557 @ id @ (sK558 @ X205) @ id)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f527,plain,(
% 21.29/4.27 ! [X207 : subst > term > subst > $o] : (? [X208 : term > $o] : ! [X209 : term] : ((X208 @ X209) = (X207 @ id @ X209 @ id)) => ! [X209 : term] : ((X207 @ id @ X209 @ id) = (sK559 @ X207 @ X209)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f528,plain,(
% 21.29/4.27 ! [X210 : term] : (? [X211 : subst > term > term] : ((X211 @ sh @ one) = (sub @ X210 @ (push @ one @ sh))) => ((sK560 @ X210 @ sh @ one) = (sub @ X210 @ (push @ one @ sh))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f529,plain,(
% 21.29/4.27 ? [X212 : term] : ! [X213 : subst > term > term] : ((X213 @ sh @ one) != (sub @ X212 @ (push @ one @ sh))) => ! [X213 : subst > term > term] : ((X213 @ sh @ one) != (sub @ sK561 @ (push @ one @ sh)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f530,plain,(
% 21.29/4.27 ! [X214 : subst > term > subst > $o] : (? [X216 : term,X217 : term] : (((X214 @ id @ X216 @ id) = $true) & ((X214 @ id @ (ap @ (sub @ X216 @ id) @ X217) @ id) != $true) & ($true = (X214 @ id @ X217 @ id))) => (((X214 @ id @ (sK562 @ X214) @ id) = $true) & ((X214 @ id @ (ap @ (sub @ (sK562 @ X214) @ id) @ (sK563 @ X214)) @ id) != $true) & ($true = (X214 @ id @ (sK563 @ X214) @ id))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f531,plain,(
% 21.29/4.27 ? [X218 : subst > term > subst > $o,X219 : term] : (! [X220 : term,X221 : term] : (((X218 @ id @ X220 @ id) != $true) | ($true = (X218 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) | ((X218 @ id @ X221 @ id) != $true)) & ($true != (sP20 @ X218)) & ((X218 @ id @ X219 @ id) != $true)) => (! [X221 : term,X220 : term] : (((sK564 @ id @ X220 @ id) != $true) | ((sK564 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id) = $true) | ((sK564 @ id @ X221 @ id) != $true)) & ($true != (sP20 @ sK564)) & ($true != (sK564 @ id @ sK565 @ id)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f532,plain,(
% 21.29/4.27 ? [X223 : subst] : ((comp @ id @ X223) != X223) => ((comp @ id @ sK566) != sK566)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f533,plain,(
% 21.29/4.27 ? [X224 : term,X225 : subst] : ((comp @ sh @ (push @ X224 @ X225)) != X225) => ((comp @ sh @ (push @ sK567 @ sK568)) != sK568)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f534,plain,(
% 21.29/4.27 ? [X228 : term,X229 : term,X230 : term,X231 : term] : ((X230 != X231) & ((ap @ X231 @ X229) = (ap @ X230 @ X228))) => ((sK571 != sK572) & ((ap @ sK572 @ sK570) = (ap @ sK571 @ sK569)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f535,plain,(
% 21.29/4.27 ? [X236 : term] : ((sub @ X236 @ id) != X236) => ((sub @ sK573 @ id) != sK573)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f536,plain,(
% 21.29/4.27 ? [X238 : term,X239 : term > $o,X240 : subst] : ! [X241 : term > $o] : ? [X242 : term] : ((X241 @ X242) != (X239 @ (sub @ X242 @ (push @ X238 @ X240)))) => ! [X241 : term > $o] : ? [X242 : term] : ((X241 @ X242) != (sK575 @ (sub @ X242 @ (push @ sK574 @ sK576))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f537,plain,(
% 21.29/4.27 ! [X241 : term > $o] : (? [X242 : term] : ((X241 @ X242) != (sK575 @ (sub @ X242 @ (push @ sK574 @ sK576)))) => ((sK575 @ (sub @ (sK577 @ X241) @ (push @ sK574 @ sK576))) != (X241 @ (sK577 @ X241))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f538,plain,(
% 21.29/4.27 ! [X243 : term,X244 : term > $o,X245 : subst] : (? [X246 : term > $o] : ! [X247 : term] : ((X246 @ X247) = (X244 @ (sub @ X247 @ (push @ X243 @ X245)))) => ! [X247 : term] : ((X244 @ (sub @ X247 @ (push @ X243 @ X245))) = (sK578 @ X245 @ X244 @ X243 @ X247)))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f539,plain,(
% 21.29/4.27 ? [X248 : subst,X249 : term,X250 : term > $o,X251 : term > $o] : (((X251 @ X249) = $true) & ! [X252 : term] : ((X251 @ (sub @ X252 @ (push @ X249 @ X248))) = (X250 @ X252)) & ((X250 @ one) != $true)) => (((sK582 @ sK580) = $true) & ! [X252 : term] : ((sK581 @ X252) = (sK582 @ (sub @ X252 @ (push @ sK580 @ sK579)))) & ((sK581 @ one) != $true))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f540,plain,(
% 21.29/4.27 ! [X253 : subst,X254 : term,X255 : term > $o,X256 : term > $o] : (? [X257 : term] : ((X256 @ (sub @ X257 @ (push @ X254 @ X253))) != (X255 @ X257)) => ((X256 @ (sub @ (sK583 @ X256 @ X255 @ X254 @ X253) @ (push @ X254 @ X253))) != (X255 @ (sK583 @ X256 @ X255 @ X254 @ X253))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f541,plain,(
% 21.29/4.27 ! [X258 : term] : (? [X259 : d_term] : ((d2term @ X259) = X258) => ((d2term @ (sK584 @ X258)) = X258))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f542,plain,(
% 21.29/4.27 ? [X264 : term,X265 : term,X266 : term,X267 : term] : (((ap @ X265 @ X266) = (ap @ X267 @ X264)) & (X264 != X266)) => (((ap @ sK588 @ sK585) = (ap @ sK586 @ sK587)) & (sK585 != sK587))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f543,plain,(
% 21.29/4.27 ? [X270 : subst] : ((comp @ X270 @ id) != X270) => (sK589 != (comp @ sK589 @ id))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f544,plain,(
% 21.29/4.27 ? [X271 : subst] : ((comp @ id @ X271) != X271) => (sK590 != (comp @ id @ sK590))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f475,plain,(
% 21.29/4.27 (! [X0 : subst > term > subst > $o] : ? [X1 : term > $o] : ! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X3 : subst > term > subst > $o] : ! [X4 : term > $o] : ? [X5 : term] : ((X4 @ X5) != (X3 @ id @ X5 @ id))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj = $true) | ? [X6 : subst,X7 : subst > term > term,X8 : subst > term > term,X9 : term] : (! [X10 : term,X11 : subst,X12 : subst] : ((sub @ (X8 @ X11 @ X10) @ X12) = (X8 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12))) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (X7 @ X15 @ X14) @ X13) = (X7 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) & ((lam @ (X7 @ sh @ one)) = (lam @ (X8 @ sh @ one))) & ((X7 @ X6 @ X9) != (X8 @ X6 @ X9)))) & (! [X16 : subst,X17 : subst > term > term,X18 : subst > term > term,X19 : term] : (? [X20 : term,X21 : subst,X22 : subst] : ((sub @ (X18 @ X21 @ X20) @ X22) != (X18 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22))) | ? [X23 : subst,X24 : term,X25 : subst] : ((X17 @ (comp @ X25 @ X23) @ (sub @ X24 @ X23)) != (sub @ (X17 @ X25 @ X24) @ X23)) | ((lam @ (X18 @ sh @ one)) != (lam @ (X17 @ sh @ one))) | ((X18 @ X16 @ X19) = (X17 @ X16 @ X19))) | (hoaslaminj != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((d2subst @ d_id) = id) & (! [X26 : term] : ? [X27 : subst > term > term] : ! [X28 : subst,X29 : term] : ((X27 @ X28 @ X29) = (sub @ X26 @ (push @ X29 @ X28))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X30 : term] : ! [X31 : subst > term > term] : ? [X32 : subst,X33 : term] : ((X31 @ X32 @ X33) != (sub @ X30 @ (push @ X33 @ X32)))) & ((induction2_lthm = $true) | (sP57 != $true)) & ((sP57 = $true) | (induction2_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (! [X34 : subst] : ((comp @ X34 @ id) = X34) & (? [X35 : subst] : ((comp @ X35 @ id) != X35) | ? [X36 : subst] : ((comp @ id @ X36) != X36)) & ! [X37 : subst] : ((comp @ id @ X37) = X37))) & (? [X38 : subst] : ((comp @ X38 @ id) != X38) | (! [X39 : subst] : ((comp @ X39 @ id) = X39) & ! [X40 : subst] : ((comp @ id @ X40) = X40)) | ? [X41 : subst] : ((comp @ id @ X41) != X41) | (substmonoid_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (! [X42 : term,X43 : subst] : ((sub @ one @ (push @ X42 @ X43)) = X42) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X44 : term,X45 : subst] : ((sub @ one @ (push @ X44 @ X45)) != X44)) & ((sP50 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP50 != $true)) & (ulamvarsh = $true) & (? [X46 : term,X47 : subst] : ((sub @ one @ (push @ X46 @ X47)) != X46) | ? [X48 : subst,X49 : term] : ((comp @ sh @ (push @ X49 @ X48)) != X48) | ! [X50 : subst,X51 : term > $o,X52 : term,X53 : term,X54 : term > $o] : (((X54 @ X53) != $true) | ($true = (X51 @ (sub @ X53 @ (push @ X52 @ X50))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X55 : term,X56 : subst] : ((sub @ one @ (push @ X55 @ X56)) = X55) & ! [X57 : subst,X58 : term] : ((comp @ sh @ (push @ X58 @ X57)) = X57) & ? [X59 : subst,X60 : term > $o,X61 : term,X62 : term,X63 : term > $o] : (((X63 @ X62) = $true) & ((X60 @ (sub @ X62 @ (push @ X61 @ X59))) != $true)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lem3aa = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lem3aa != $true)) & ! [X64 : d_subst,X65 : d_subst] : (((d2subst @ X65) != (d2subst @ X64)) | (X64 = X65)) & ((hoasapinj2 = $true) | ? [X66 : term,X67 : term,X68 : term,X69 : term] : ((X68 != X69) & ((ap @ (sub @ X67 @ id) @ X68) = (ap @ (sub @ X66 @ id) @ X69)))) & (! [X70 : term,X71 : term,X72 : term,X73 : term] : ((X72 = X73) | ((ap @ (sub @ X70 @ id) @ X73) != (ap @ (sub @ X71 @ id) @ X72))) | (hoasapinj2 != $true)) & (axmap = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((laminj = $true) | ? [X74 : term,X75 : term] : (((lam @ X75) = (lam @ X74)) & (X74 != X75))) & (! [X76 : term,X77 : term] : (((lam @ X77) != (lam @ X76)) | (X76 = X77)) | (laminj != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & (($true = sP45) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP45)) & ((axidr = $true) | ? [X78 : subst] : ((comp @ X78 @ id) != X78)) & (! [X79 : subst] : ((comp @ X79 @ id) = X79) | (axidr != $true)) & (! [X80 : term] : ? [X81 : subst > term > term] : ((X81 @ sh @ one) = (sub @ X80 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X82 : term] : ! [X83 : subst > term > term] : ((sub @ X82 @ (push @ one @ sh)) != (X83 @ sh @ one))) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & (! [X84 : term] : ? [X85 : subst > term > term] : ! [X86 : subst,X87 : term] : ((X85 @ X86 @ X87) = (sub @ X84 @ (push @ X87 @ X86))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X88 : term] : ! [X89 : subst > term > term] : ? [X90 : subst,X91 : term] : ((X89 @ X90 @ X91) != (sub @ X88 @ (push @ X91 @ X90)))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X92 : term > $o,X93 : term] : (((sP43 @ X92) = $true) | ? [X94 : term] : (((var @ X94) = $true) & ((X92 @ X94) != $true)) | ? [X95 : term] : (($true != (X92 @ (lam @ X95))) & ($true = (X92 @ X95))) | ((X92 @ X93) = $true)) | (induction != $true)) & ((induction = $true) | ? [X96 : term > $o,X97 : term] : (((sP43 @ X96) != $true) & ! [X98 : term] : (((var @ X98) != $true) | ($true = (X96 @ X98))) & ! [X99 : term] : (((X96 @ (lam @ X99)) = $true) | ((X96 @ X99) != $true)) & ($true != (X96 @ X97)))) & ((pushprop_lem1v2_lthm = $true) | (? [X100 : term > $o,X101 : subst,X102 : term > $o,X103 : term] : (($true != (X100 @ one)) & ($true = (X102 @ X103)) & ! [X104 : term] : ((X102 @ (sub @ X104 @ (push @ X103 @ X101))) = (X100 @ X104))) & ! [X105 : term,X106 : subst] : ((sub @ one @ (push @ X105 @ X106)) = X105))) & (! [X107 : term > $o,X108 : subst,X109 : term > $o,X110 : term] : (($true = (X107 @ one)) | ((X109 @ X110) != $true) | ? [X111 : term] : ((X107 @ X111) != (X109 @ (sub @ X111 @ (push @ X110 @ X108))))) | ? [X112 : term,X113 : subst] : ((sub @ one @ (push @ X112 @ X113)) != X112) | (pushprop_lem1v2_lthm != $true)) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP42) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP42)) & ! [X114 : subst] : ? [X115 : d_subst] : ((d2subst @ X115) = X114) & ! [X116 : d_subst] : (d_id = X116) & (! [X117 : term,X118 : term,X119 : term,X120 : term] : ((X117 = X119) | ((ap @ (sub @ X118 @ id) @ X117) != (ap @ (sub @ X120 @ id) @ X119))) | ? [X121 : term,X122 : term,X123 : term,X124 : term] : ((X121 != X124) & ((ap @ X122 @ X124) = (ap @ X123 @ X121))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X125 : term,X126 : term,X127 : term,X128 : term] : ((X125 != X127) & ((ap @ (sub @ X126 @ id) @ X125) = (ap @ (sub @ X128 @ id) @ X127))) & ! [X129 : term,X130 : term,X131 : term,X132 : term] : ((X129 = X132) | ((ap @ X131 @ X129) != (ap @ X130 @ X132))))) & (lamnotvar = $true) & ((pushprop_lem0 = $true) | ? [X133 : subst,X134 : term,X135 : term > $o] : ! [X136 : term > $o] : ? [X137 : term] : ((X135 @ (sub @ X137 @ (push @ X134 @ X133))) != (X136 @ X137))) & (! [X138 : subst,X139 : term,X140 : term > $o] : ? [X141 : term > $o] : ! [X142 : term] : ((X141 @ X142) = (X140 @ (sub @ X142 @ (push @ X139 @ X138)))) | (pushprop_lem0 != $true)) & (! [X143 : subst] : ((push @ (sub @ one @ X143) @ (comp @ sh @ X143)) = X143) | (axscons != $true)) & ((axscons = $true) | ? [X144 : subst] : ((push @ (sub @ one @ X144) @ (comp @ sh @ X144)) != X144)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & (($true = sP39) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP39)) & ((hoasinduction_lem3v2a = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2a != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((shinj = $true) | ? [X145 : term,X146 : term] : (((sub @ X145 @ sh) = (sub @ X146 @ sh)) & (X145 != X146))) & (! [X147 : term,X148 : term] : (((sub @ X148 @ sh) != (sub @ X147 @ sh)) | (X147 = X148)) | (shinj != $true)) & (induction2_gthm = $true) & (! [X149 : term,X150 : term > $o,X151 : subst,X152 : term,X153 : term > $o] : (($true != (X150 @ X149)) | ((X153 @ (sub @ X149 @ (push @ X152 @ X151))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X154 : term,X155 : term > $o,X156 : subst,X157 : term,X158 : term > $o] : (((X155 @ X154) = $true) & ($true != (X158 @ (sub @ X154 @ (push @ X157 @ X156)))))) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & (! [X159 : term] : ((sub @ X159 @ id) = X159) | (termmset != $true)) & ((termmset = $true) | ? [X160 : term] : ((sub @ X160 @ id) != X160)) & (? [X161 : term] : ((sub @ X161 @ id) != X161) | ! [X162 : term] : ((sub @ X162 @ id) = X162) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X163 : term] : ((sub @ X163 @ id) = X163) & ? [X164 : term] : ((sub @ X164 @ id) != X164))) & (pushprop_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X165 : term,X166 : term,X167 : subst > term > term] : (((ap @ (sub @ X165 @ id) @ X166) = (lam @ (X167 @ sh @ one))) & ! [X168 : subst,X169 : term,X170 : subst] : ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)) = (sub @ (X167 @ X170 @ X169) @ X168)))) & (! [X171 : term,X172 : term,X173 : subst > term > term] : (((lam @ (X173 @ sh @ one)) != (ap @ (sub @ X171 @ id) @ X172)) | ? [X174 : subst,X175 : term,X176 : subst] : ((sub @ (X173 @ X176 @ X175) @ X174) != (X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174)))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) | (sP32 != $true)) & ((sP32 = $true) | (hoasinduction_lem3aaa != $true)) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & (? [X177 : term,X178 : term,X179 : term,X180 : term] : (((ap @ X179 @ X177) = (ap @ X178 @ X180)) & (X178 != X179)) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X182 = X184) | ((ap @ (sub @ X182 @ id) @ X183) != (ap @ (sub @ X184 @ id) @ X181))) | ? [X185 : term] : ((sub @ X185 @ id) != X185) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X186 : term,X187 : term,X188 : term,X189 : term] : (((ap @ X188 @ X186) != (ap @ X187 @ X189)) | (X187 = X188)) & ? [X190 : term,X191 : term,X192 : term,X193 : term] : ((X191 != X193) & ((ap @ (sub @ X191 @ id) @ X192) = (ap @ (sub @ X193 @ id) @ X190))) & ! [X194 : term] : ((sub @ X194 @ id) = X194))) & (! [X195 : term,X196 : term,X197 : term,X198 : term] : ((X195 = X197) | ((ap @ (sub @ X195 @ id) @ X196) != (ap @ (sub @ X197 @ id) @ X198))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X199 : term,X200 : term,X201 : term,X202 : term] : ((X199 != X201) & ((ap @ (sub @ X199 @ id) @ X200) = (ap @ (sub @ X201 @ id) @ X202)))) & ! [X203 : d_term] : (d_one = X203) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP31 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP31 != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & ((hoasinduction_lem0 = $true) | ? [X204 : subst > term > subst > $o] : ! [X205 : term > $o] : ? [X206 : term] : ((X205 @ X206) != (X204 @ id @ X206 @ id))) & (! [X207 : subst > term > subst > $o] : ? [X208 : term > $o] : ! [X209 : term] : ((X208 @ X209) = (X207 @ id @ X209 @ id)) | (hoasinduction_lem0 != $true)) & ((sP26 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP26 != $true)) & (! [X210 : term] : ? [X211 : subst > term > term] : ((X211 @ sh @ one) = (sub @ X210 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X212 : term] : ! [X213 : subst > term > term] : ((X213 @ sh @ one) != (sub @ X212 @ (push @ one @ sh)))) & (pushprop_lthm = $true) & (($true = sP22) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP22)) & (! [X214 : subst > term > subst > $o,X215 : term] : (? [X216 : term,X217 : term] : (((X214 @ id @ X216 @ id) = $true) & ((X214 @ id @ (ap @ (sub @ X216 @ id) @ X217) @ id) != $true) & ($true = (X214 @ id @ X217 @ id))) | ((sP20 @ X214) = $true) | ((X214 @ id @ X215 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X218 : subst > term > subst > $o,X219 : term] : (! [X220 : term,X221 : term] : (((X218 @ id @ X220 @ id) != $true) | ($true = (X218 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) | ((X218 @ id @ X221 @ id) != $true)) & ($true != (sP20 @ X218)) & ((X218 @ id @ X219 @ id) != $true))) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (! [X222 : subst] : ((comp @ id @ X222) = X222) | (axidl != $true)) & ((axidl = $true) | ? [X223 : subst] : ((comp @ id @ X223) != X223)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X224 : term,X225 : subst] : ((comp @ sh @ (push @ X224 @ X225)) != X225)) & (! [X226 : term,X227 : subst] : ((comp @ sh @ (push @ X226 @ X227)) = X227) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((apinj1 = $true) | ? [X228 : term,X229 : term,X230 : term,X231 : term] : ((X230 != X231) & ((ap @ X231 @ X229) = (ap @ X230 @ X228)))) & (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X234 = X235) | ((ap @ X234 @ X232) != (ap @ X235 @ X233))) | (apinj1 != $true)) & ((axvarid = $true) | ? [X236 : term] : ((sub @ X236 @ id) != X236)) & (! [X237 : term] : ((sub @ X237 @ id) = X237) | (axvarid != $true)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) | ? [X238 : term,X239 : term > $o,X240 : subst] : ! [X241 : term > $o] : ? [X242 : term] : ((X241 @ X242) != (X239 @ (sub @ X242 @ (push @ X238 @ X240))))) & (! [X243 : term,X244 : term > $o,X245 : subst] : ? [X246 : term > $o] : ! [X247 : term] : ((X246 @ X247) = (X244 @ (sub @ X247 @ (push @ X243 @ X245)))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem1v2 = $true) | ? [X248 : subst,X249 : term,X250 : term > $o,X251 : term > $o] : (((X251 @ X249) = $true) & ! [X252 : term] : ((X251 @ (sub @ X252 @ (push @ X249 @ X248))) = (X250 @ X252)) & ((X250 @ one) != $true))) & (! [X253 : subst,X254 : term,X255 : term > $o,X256 : term > $o] : (((X256 @ X254) != $true) | ? [X257 : term] : ((X256 @ (sub @ X257 @ (push @ X254 @ X253))) != (X255 @ X257)) | ((X255 @ one) = $true)) | (pushprop_lem1v2 != $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP16 != $true)) & ((sP16 = $true) | (hoasinduction_lem3a_lthm != $true)) & (axapp = $true) & ! [X258 : term] : ? [X259 : d_term] : ((d2term @ X259) = X258) & (ulamvarind = $true) & ((sP14 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP14 != $true)) & (! [X260 : term,X261 : term,X262 : term,X263 : term] : (((ap @ X261 @ X262) != (ap @ X263 @ X260)) | (X260 = X262)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X264 : term,X265 : term,X266 : term,X267 : term] : (((ap @ X265 @ X266) = (ap @ X267 @ X264)) & (X264 != X266))) & ((! [X268 : subst] : ((comp @ X268 @ id) = X268) & ! [X269 : subst] : ((comp @ id @ X269) = X269)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X270 : subst] : ((comp @ X270 @ id) != X270) | ? [X271 : subst] : ((comp @ id @ X271) != X271)) & ((sP5 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP5 != $true)) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X272 : d_term,X273 : d_term] : ((X272 = X273) | ((d2term @ X272) != (d2term @ X273))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((induction2 = $true) | ($true != sP3)) & (($true = sP3) | (induction2 != $true)) & (($true = sP1) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP1))),
% 21.29/4.27 inference(rectify,[status(thm)],[f474])).
% 21.29/4.27 thf(f474,plain,(
% 21.29/4.27 (! [X24 : subst > term > subst > $o] : ? [X25 : term > $o] : ! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X24 : subst > term > subst > $o] : ! [X25 : term > $o] : ? [X26 : term] : ((X24 @ id @ X26 @ id) != (X25 @ X26))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj = $true) | ? [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) & ! [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) = (sub @ (X218 @ X226 @ X225) @ X224)) & ((lam @ (X219 @ sh @ one)) = (lam @ (X218 @ sh @ one))) & ((X219 @ X217 @ X220) != (X218 @ X217 @ X220)))) & (! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (? [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) != (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ? [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) != (sub @ (X218 @ X226 @ X225) @ X224)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one))) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220))) | (hoaslaminj != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((d2subst @ d_id) = id) & (! [X448 : term] : ? [X449 : subst > term > term] : ! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X448 : term] : ! [X449 : subst > term > term] : ? [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) != (X449 @ X450 @ X451))) & ((induction2_lthm = $true) | (sP57 != $true)) & ((sP57 = $true) | (induction2_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (! [X277 : subst] : ((comp @ X277 @ id) = X277) & (? [X278 : subst] : ((comp @ X278 @ id) != X278) | ? [X279 : subst] : ((comp @ id @ X279) != X279)) & ! [X276 : subst] : ((comp @ id @ X276) = X276))) & (? [X277 : subst] : ((comp @ X277 @ id) != X277) | (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)) | ? [X276 : subst] : ((comp @ id @ X276) != X276) | (substmonoid_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) != X114)) & ((sP50 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP50 != $true)) & (ulamvarsh = $true) & (? [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) != X499) | ? [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) != X501) | ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) = X499) & ! [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) = X501) & ? [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) = $true) & ($true != (X504 @ (sub @ X506 @ (push @ X505 @ X503))))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lem3aa = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lem3aa != $true)) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) != (d2subst @ X117)) | (X116 = X117)) & ((hoasapinj2 = $true) | ? [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 != X34) & ((ap @ (sub @ X32 @ id) @ X33) = (ap @ (sub @ X31 @ id) @ X34)))) & (! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34))) | (hoasapinj2 != $true)) & (axmap = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((laminj = $true) | ? [X0 : term,X1 : term] : (((lam @ X0) = (lam @ X1)) & (X0 != X1))) & (! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1)) | (laminj != $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & (($true = sP45) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP45)) & ((axidr = $true) | ? [X99 : subst] : ((comp @ X99 @ id) != X99)) & (! [X99 : subst] : ((comp @ X99 @ id) = X99) | (axidr != $true)) & (! [X200 : term] : ? [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) = (X201 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X200 : term] : ! [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) != (X201 @ sh @ one))) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & (! [X27 : term] : ? [X28 : subst > term > term] : ! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X27 : term] : ! [X28 : subst > term > term] : ? [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) != (sub @ X27 @ (push @ X30 @ X29)))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X131 : term > $o,X132 : term] : (((sP43 @ X131) = $true) | ? [X136 : term] : (($true = (var @ X136)) & ($true != (X131 @ X136))) | ? [X135 : term] : (((X131 @ (lam @ X135)) != $true) & ($true = (X131 @ X135))) | ((X131 @ X132) = $true)) | (induction != $true)) & ((induction = $true) | ? [X131 : term > $o,X132 : term] : (((sP43 @ X131) != $true) & ! [X136 : term] : (($true != (var @ X136)) | ($true = (X131 @ X136))) & ! [X135 : term] : (((X131 @ (lam @ X135)) = $true) | ($true != (X131 @ X135))) & ((X131 @ X132) != $true))) & ((pushprop_lem1v2_lthm = $true) | (? [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) != $true) & ($true = (X177 @ X178)) & ! [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) = (X175 @ X179))) & ! [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) = X173))) & (! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ($true != (X177 @ X178)) | ? [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) != (X175 @ X179))) | ? [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) != X173) | (pushprop_lem1v2_lthm != $true)) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP42) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP42)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ! [X35 : d_subst] : (d_id = X35) & (! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | ? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X535) & ((ap @ X533 @ X535) = (ap @ X534 @ X532))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 != X538) & ((ap @ (sub @ X539 @ id) @ X538) = (ap @ (sub @ X537 @ id) @ X536))) & ! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 = X535) | ((ap @ X533 @ X535) != (ap @ X534 @ X532))))) & (lamnotvar = $true) & ((pushprop_lem0 = $true) | ? [X137 : subst,X138 : term,X139 : term > $o] : ! [X140 : term > $o] : ? [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) != (X140 @ X141))) & (! [X137 : subst,X138 : term,X139 : term > $o] : ? [X140 : term > $o] : ! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) | (pushprop_lem0 != $true)) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) | (axscons != $true)) & ((axscons = $true) | ? [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) != X102)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & (($true = sP39) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP39)) & ((hoasinduction_lem3v2a = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2a != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((shinj = $true) | ? [X246 : term,X247 : term] : (((sub @ X247 @ sh) = (sub @ X246 @ sh)) & (X246 != X247))) & (! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247)) | (shinj != $true)) & (induction2_gthm = $true) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) = $true) & ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) != $true))) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & (! [X216 : term] : ((sub @ X216 @ id) = X216) | (termmset != $true)) & ((termmset = $true) | ? [X216 : term] : ((sub @ X216 @ id) != X216)) & (? [X171 : term] : ((sub @ X171 @ id) != X171) | ! [X172 : term] : ((sub @ X172 @ id) = X172) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X171 : term] : ((sub @ X171 @ id) = X171) & ? [X172 : term] : ((sub @ X172 @ id) != X172))) & (pushprop_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) = (ap @ (sub @ X93 @ id) @ X94)) & ! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)))) & (! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ? [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) != (sub @ (X95 @ X98 @ X97) @ X96))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) | (sP32 != $true)) & ((sP32 = $true) | (hoasinduction_lem3aaa != $true)) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & (? [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) = (ap @ X107 @ X109)) & (X107 != X108)) | ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))) | ? [X105 : term] : ((sub @ X105 @ id) != X105) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) != (ap @ X107 @ X109)) | (X107 = X108)) & ? [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 != X113) & ((ap @ (sub @ X111 @ id) @ X112) = (ap @ (sub @ X113 @ id) @ X110))) & ! [X105 : term] : ((sub @ X105 @ id) = X105))) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 != X244) & ((ap @ (sub @ X244 @ id) @ X245) = (ap @ (sub @ X242 @ id) @ X243)))) & ! [X170 : d_term] : (d_one = X170) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP31 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP31 != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & ((hoasinduction_lem0 = $true) | ? [X118 : subst > term > subst > $o] : ! [X119 : term > $o] : ? [X120 : term] : ((X118 @ id @ X120 @ id) != (X119 @ X120))) & (! [X118 : subst > term > subst > $o] : ? [X119 : term > $o] : ! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) | (hoasinduction_lem0 != $true)) & ((sP26 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP26 != $true)) & (! [X129 : term] : ? [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) = (X130 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X129 : term] : ! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one))) & (pushprop_lthm = $true) & (($true = sP22) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP22)) & (! [X202 : subst > term > subst > $o,X203 : term] : (? [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) = $true) & ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) != $true) & ($true = (X202 @ id @ X205 @ id))) | ((sP20 @ X202) = $true) | ((X202 @ id @ X203 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X202 : subst > term > subst > $o,X203 : term] : (! [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) != $true) | ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) = $true) | ($true != (X202 @ id @ X205 @ id))) & ((sP20 @ X202) != $true) & ((X202 @ id @ X203 @ id) != $true))) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (! [X299 : subst] : ((comp @ id @ X299) = X299) | (axidl != $true)) & ((axidl = $true) | ? [X299 : subst] : ((comp @ id @ X299) != X299)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) != X104)) & (! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((apinj1 = $true) | ? [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 != X169) & ((ap @ X169 @ X167) = (ap @ X168 @ X166)))) & (! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166))) | (apinj1 != $true)) & ((axvarid = $true) | ? [X355 : term] : ((sub @ X355 @ id) != X355)) & (! [X355 : term] : ((sub @ X355 @ id) = X355) | (axvarid != $true)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) | ? [X211 : term,X212 : term > $o,X213 : subst] : ! [X214 : term > $o] : ? [X215 : term] : ((X214 @ X215) != (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & (! [X211 : term,X212 : term > $o,X213 : subst] : ? [X214 : term > $o] : ! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213)))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem1v2 = $true) | ? [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) = $true) & ! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146)) & ((X144 @ one) != $true))) & (! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) != $true) | ? [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) != (X144 @ X146)) | ((X144 @ one) = $true)) | (pushprop_lem1v2 != $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP16 != $true)) & ((sP16 = $true) | (hoasinduction_lem3a_lthm != $true)) & (axapp = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (ulamvarind = $true) & ((sP14 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP14 != $true)) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) = (ap @ X298 @ X295)) & (X295 != X297))) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X274 : subst] : ((comp @ X274 @ id) != X274) | ? [X275 : subst] : ((comp @ id @ X275) != X275)) & ((sP5 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP5 != $true)) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((induction2 = $true) | ($true != sP3)) & (($true = sP3) | (induction2 != $true)) & (($true = sP1) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP1))),
% 21.29/4.27 inference(flattening,[status(thm)],[f473])).
% 21.29/4.27 thf(f473,plain,(
% 21.29/4.27 ((! [X24 : subst > term > subst > $o] : ? [X25 : term > $o] : ! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X24 : subst > term > subst > $o] : ! [X25 : term > $o] : ? [X26 : term] : ((X24 @ id @ X26 @ id) != (X25 @ X26)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (((hoaslaminj = $true) | ? [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) & ! [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) = (sub @ (X218 @ X226 @ X225) @ X224)) & ((lam @ (X219 @ sh @ one)) = (lam @ (X218 @ sh @ one))) & ((X219 @ X217 @ X220) != (X218 @ X217 @ X220)))) & (! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (? [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) != (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ? [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) != (sub @ (X218 @ X226 @ X225) @ X224)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one))) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220))) | (hoaslaminj != $true))) & (hoasapnotvar_gthm = $true) & (((hoasinduction_lem3aa_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa_lthm != $true))) & ((d2subst @ d_id) = id) & ((! [X448 : term] : ? [X449 : subst > term > term] : ! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X448 : term] : ! [X449 : subst > term > term] : ? [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) != (X449 @ X450 @ X451)))) & (((induction2_lthm = $true) | (sP57 != $true)) & ((sP57 = $true) | (induction2_lthm != $true))) & (((hoasinduction_lem3v2a_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a_lthm != $true))) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (((hoaslaminj_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoaslaminj_lthm != $true))) & (pushprop_lem2v2_lthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3a != $true))) & (((substmonoid_lthm = $true) | (! [X277 : subst] : ((comp @ X277 @ id) = X277) & (? [X278 : subst] : ((comp @ X278 @ id) != X278) | ? [X279 : subst] : ((comp @ id @ X279) != X279)) & ! [X276 : subst] : ((comp @ id @ X276) = X276))) & ((? [X277 : subst] : ((comp @ X277 @ id) != X277) | (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)) | ? [X276 : subst] : ((comp @ id @ X276) != X276)) | (substmonoid_lthm != $true))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & ((! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) != X114))) & (((sP50 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP50 != $true))) & (ulamvarsh = $true) & (((? [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) != X499) | ? [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) != X501) | ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503)))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) = X499) & ! [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) = X501) & ? [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) = $true) & ($true != (X504 @ (sub @ X506 @ (push @ X505 @ X503)))))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (((hoasinduction_lem3aa = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lem3aa != $true))) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) != (d2subst @ X117)) | (X116 = X117)) & (((hoasapinj2 = $true) | ? [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 != X34) & ((ap @ (sub @ X32 @ id) @ X33) = (ap @ (sub @ X31 @ id) @ X34)))) & (! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34))) | (hoasapinj2 != $true))) & (axmap = $true) & (((hoasinduction_lem3v2 = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2 != $true))) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (((laminj = $true) | ? [X0 : term,X1 : term] : (((lam @ X0) = (lam @ X1)) & (X0 != X1))) & (! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1)) | (laminj != $true))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & ((($true = sP45) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP45))) & (((axidr = $true) | ? [X99 : subst] : ((comp @ X99 @ id) != X99)) & (! [X99 : subst] : ((comp @ X99 @ id) = X99) | (axidr != $true))) & ((! [X200 : term] : ? [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) = (X201 @ sh @ one)) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X200 : term] : ! [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) != (X201 @ sh @ one)))) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ((! [X27 : term] : ? [X28 : subst > term > term] : ! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X27 : term] : ! [X28 : subst > term > term] : ? [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) != (sub @ X27 @ (push @ X30 @ X29))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & ((! [X131 : term > $o,X132 : term] : (((sP43 @ X131) = $true) | ? [X136 : term] : (($true = (var @ X136)) & ($true != (X131 @ X136))) | ? [X135 : term] : (((X131 @ (lam @ X135)) != $true) & ($true = (X131 @ X135))) | ((X131 @ X132) = $true)) | (induction != $true)) & ((induction = $true) | ? [X131 : term > $o,X132 : term] : (((sP43 @ X131) != $true) & ! [X136 : term] : (($true != (var @ X136)) | ($true = (X131 @ X136))) & ! [X135 : term] : (((X131 @ (lam @ X135)) = $true) | ($true != (X131 @ X135))) & ((X131 @ X132) != $true)))) & (((pushprop_lem1v2_lthm = $true) | (? [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) != $true) & ($true = (X177 @ X178)) & ! [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) = (X175 @ X179))) & ! [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) = X173))) & ((! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ($true != (X177 @ X178)) | ? [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) != (X175 @ X179))) | ? [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) != X173)) | (pushprop_lem1v2_lthm != $true))) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & ((($true = sP42) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP42))) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ! [X35 : d_subst] : (d_id = X35) & (((! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | ? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X535) & ((ap @ X533 @ X535) = (ap @ X534 @ X532)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 != X538) & ((ap @ (sub @ X539 @ id) @ X538) = (ap @ (sub @ X537 @ id) @ X536))) & ! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 = X535) | ((ap @ X533 @ X535) != (ap @ X534 @ X532)))))) & (lamnotvar = $true) & (((pushprop_lem0 = $true) | ? [X137 : subst,X138 : term,X139 : term > $o] : ! [X140 : term > $o] : ? [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) != (X140 @ X141))) & (! [X137 : subst,X138 : term,X139 : term > $o] : ? [X140 : term > $o] : ! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) | (pushprop_lem0 != $true))) & ((! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) | (axscons != $true)) & ((axscons = $true) | ? [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) != X102))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & ((($true = sP39) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP39))) & (((hoasinduction_lem3v2a = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2a != $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (((shinj = $true) | ? [X246 : term,X247 : term] : (((sub @ X247 @ sh) = (sub @ X246 @ sh)) & (X246 != X247))) & (! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247)) | (shinj != $true))) & (induction2_gthm = $true) & ((! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) = $true) & ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) != $true)))) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & ((! [X216 : term] : ((sub @ X216 @ id) = X216) | (termmset != $true)) & ((termmset = $true) | ? [X216 : term] : ((sub @ X216 @ id) != X216))) & (((? [X171 : term] : ((sub @ X171 @ id) != X171) | ! [X172 : term] : ((sub @ X172 @ id) = X172)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X171 : term] : ((sub @ X171 @ id) = X171) & ? [X172 : term] : ((sub @ X172 @ id) != X172)))) & (pushprop_lem2v2_gthm = $true) & (((hoaslamnotap = $true) | ? [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) = (ap @ (sub @ X93 @ id) @ X94)) & ! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)))) & (! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ? [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) != (sub @ (X95 @ X98 @ X97) @ X96))) | (hoaslamnotap != $true))) & (hoasinduction_lem1v2_gthm = $true) & (((hoasinduction_lem3aaa = $true) | (sP32 != $true)) & ((sP32 = $true) | (hoasinduction_lem3aaa != $true))) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & (((? [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) = (ap @ X107 @ X109)) & (X107 != X108)) | ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))) | ? [X105 : term] : ((sub @ X105 @ id) != X105)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) != (ap @ X107 @ X109)) | (X107 = X108)) & ? [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 != X113) & ((ap @ (sub @ X111 @ id) @ X112) = (ap @ (sub @ X113 @ id) @ X110))) & ! [X105 : term] : ((sub @ X105 @ id) = X105)))) & ((! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 != X244) & ((ap @ (sub @ X244 @ id) @ X245) = (ap @ (sub @ X242 @ id) @ X243))))) & ! [X170 : d_term] : (d_one = X170) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((sP31 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP31 != $true))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (((hoasinduction_lem0 = $true) | ? [X118 : subst > term > subst > $o] : ! [X119 : term > $o] : ? [X120 : term] : ((X118 @ id @ X120 @ id) != (X119 @ X120))) & (! [X118 : subst > term > subst > $o] : ? [X119 : term > $o] : ! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) | (hoasinduction_lem0 != $true))) & (((sP26 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP26 != $true))) & ((! [X129 : term] : ? [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) = (X130 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X129 : term] : ! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one)))) & (pushprop_lthm = $true) & ((($true = sP22) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP22))) & ((! [X202 : subst > term > subst > $o,X203 : term] : (? [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) = $true) & ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) != $true) & ($true = (X202 @ id @ X205 @ id))) | ((sP20 @ X202) = $true) | ((X202 @ id @ X203 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X202 : subst > term > subst > $o,X203 : term] : (! [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) != $true) | ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) = $true) | ($true != (X202 @ id @ X205 @ id))) & ((sP20 @ X202) != $true) & ((X202 @ id @ X203 @ id) != $true)))) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & ((! [X299 : subst] : ((comp @ id @ X299) = X299) | (axidl != $true)) & ((axidl = $true) | ? [X299 : subst] : ((comp @ id @ X299) != X299))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((hoasinduction = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction != $true))) & (((axshiftcons = $true) | ? [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) != X104)) & (! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104) | (axshiftcons != $true))) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & (((apinj1 = $true) | ? [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 != X169) & ((ap @ X169 @ X167) = (ap @ X168 @ X166)))) & (! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166))) | (apinj1 != $true))) & (((axvarid = $true) | ? [X355 : term] : ((sub @ X355 @ id) != X355)) & (! [X355 : term] : ((sub @ X355 @ id) = X355) | (axvarid != $true))) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (((pushprop_lem0_lthm = $true) | ? [X211 : term,X212 : term > $o,X213 : subst] : ! [X214 : term > $o] : ? [X215 : term] : ((X214 @ X215) != (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & (! [X211 : term,X212 : term > $o,X213 : subst] : ? [X214 : term > $o] : ! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213)))) | (pushprop_lem0_lthm != $true))) & (((pushprop_lem1v2 = $true) | ? [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) = $true) & ! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146)) & ((X144 @ one) != $true))) & (! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) != $true) | ? [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) != (X144 @ X146)) | ((X144 @ one) = $true)) | (pushprop_lem1v2 != $true))) & (pushprop_lem0_gthm = $true) & (((hoasinduction_lem3a_lthm = $true) | (sP16 != $true)) & ((sP16 = $true) | (hoasinduction_lem3a_lthm != $true))) & (axapp = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (ulamvarind = $true) & (((sP14 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP14 != $true))) & ((! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) = (ap @ X298 @ X295)) & (X295 != X297)))) & (((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X274 : subst] : ((comp @ X274 @ id) != X274) | ? [X275 : subst] : ((comp @ id @ X275) != X275)))) & (((sP5 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP5 != $true))) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & (((induction2 = $true) | ($true != sP3)) & (($true = sP3) | (induction2 != $true))) & ((($true = sP1) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP1)))),
% 21.29/4.27 inference(nnf_transformation,[status(thm)],[f73])).
% 21.29/4.27 thf(f73,plain,(
% 21.29/4.27 (! [X24 : subst > term > subst > $o] : ? [X25 : term > $o] : ! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj = $true) <=> ! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (? [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) != (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ? [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) != (sub @ (X218 @ X226 @ X225) @ X224)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one))) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220)))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP58 = $true)) & ((d2subst @ d_id) = id) & (! [X448 : term] : ? [X449 : subst > term > term] : ! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) <=> (hoasinduction_lem3v2_f = $true)) & ((induction2_lthm = $true) <=> (sP57 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (sP53 = $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (sP52 = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP51)) & ((substmonoid_lthm = $true) <=> (? [X277 : subst] : ((comp @ X277 @ id) != X277) | (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)) | ? [X276 : subst] : ((comp @ id @ X276) != X276))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & ((sP50 = $true) <=> (hoasinduction_lem2v2 = $true)) & (ulamvarsh = $true) & ((? [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) != X499) | ? [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) != X501) | ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503)))))) <=> (pushprop_lem1_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lem3aa = $true) <=> (sP48 = $true)) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) != (d2subst @ X117)) | (X116 = X117)) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & (axmap = $true) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP47)) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & (($true = sP45) <=> (induction2lem = $true)) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & (! [X200 : term] : ? [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) = (X201 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & (! [X27 : term] : ? [X28 : subst > term > term] : ! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X131 : term > $o,X132 : term] : (((sP43 @ X131) = $true) | ? [X136 : term] : (($true = (var @ X136)) & ($true != (X131 @ X136))) | ? [X135 : term] : (((X131 @ (lam @ X135)) != $true) & ($true = (X131 @ X135))) | ((X131 @ X132) = $true)) <=> (induction = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ($true != (X177 @ X178)) | ? [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) != (X175 @ X179))) | ? [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) != X173))) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP42) <=> (hoasinduction_lem3_lthm = $true)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ! [X35 : d_subst] : (d_id = X35) & ((! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | ? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X535) & ((ap @ X533 @ X535) = (ap @ X534 @ X532)))) <=> (hoasapinj2_lthm = $true)) & (lamnotvar = $true) & ((pushprop_lem0 = $true) <=> ! [X137 : subst,X138 : term,X139 : term > $o] : ? [X140 : term > $o] : ! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141))) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & (($true = sP39) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP33)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((shinj = $true) <=> ! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247))) & (induction2_gthm = $true) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & (! [X216 : term] : ((sub @ X216 @ id) = X216) <=> (termmset = $true)) & ((? [X171 : term] : ((sub @ X171 @ id) != X171) | ! [X172 : term] : ((sub @ X172 @ id) = X172)) <=> (termmset_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ? [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) != (sub @ (X95 @ X98 @ X97) @ X96)))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> (sP32 = $true)) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & ((? [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) = (ap @ X107 @ X109)) & (X107 != X108)) | ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))) | ? [X105 : term] : ((sub @ X105 @ id) != X105)) <=> (hoasapinj1_lthm = $true)) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) <=> (hoasapinj1 = $true)) & ! [X170 : d_term] : (d_one = X170) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((sP31 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & ((hoasinduction_lem0 = $true) <=> ! [X118 : subst > term > subst > $o] : ? [X119 : term > $o] : ! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120))) & ((sP26 = $true) <=> (induction2lem_lthm = $true)) & (! [X129 : term] : ? [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) = (X130 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lthm = $true) & (($true = sP22) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X202 : subst > term > subst > $o,X203 : term] : (? [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) = $true) & ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) != $true) & ($true = (X202 @ id @ X205 @ id))) | ((sP20 @ X202) = $true) | ((X202 @ id @ X203 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (! [X299 : subst] : ((comp @ id @ X299) = X299) <=> (axidl = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction = $true) <=> (sP19 = $true)) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((apinj1 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166)))) & ((axvarid = $true) <=> ! [X355 : term] : ((sub @ X355 @ id) = X355)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) <=> ! [X211 : term,X212 : term > $o,X213 : subst] : ? [X214 : term > $o] : ! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & ((pushprop_lem1v2 = $true) <=> ! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) != $true) | ? [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) != (X144 @ X146)) | ((X144 @ one) = $true))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (sP16 = $true)) & (axapp = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (ulamvarind = $true) & ((sP14 = $true) <=> (hoasinduction_lthm = $true)) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) <=> (apinj2 = $true)) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) <=> (substmonoid = $true)) & ((sP5 = $true) <=> (hoasinduction_lem3 = $true)) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((induction2 = $true) <=> ($true = sP3)) & (($true = sP1) <=> (hoasinduction_lem2 = $true))),
% 21.29/4.27 inference(definition_folding,[status(thm)],[f12,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 21.29/4.27 thf(f14,plain,(
% 21.29/4.27 ! [X182 : subst > term > subst > $o] : (($true = (sP0 @ X182)) <=> ? [X191 : term,X192 : term] : (((X182 @ id @ X191 @ id) = $true) & ($true = (X182 @ id @ X192 @ id)) & ((X182 @ id @ (ap @ (sub @ X192 @ id) @ X191) @ id) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f15,plain,(
% 21.29/4.27 ($true = sP1) <=> ! [X180 : term,X181 : term,X182 : subst > term > subst > $o] : (($true != (X182 @ id @ X181 @ id)) | ((X182 @ id @ X180 @ id) != $true) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (((X182 @ X184 @ X185 @ (comp @ X183 @ X186)) = $true) & ((X182 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183) @ X186) != $true)) | ($true = (sP0 @ X182)) | ? [X187 : subst,X188 : term,X189 : subst,X190 : subst] : (((X182 @ (comp @ X189 @ X187) @ (sub @ X188 @ X187) @ X190) = $true) & ((X182 @ X189 @ X188 @ (comp @ X187 @ X190)) != $true)) | ((X182 @ id @ (ap @ X180 @ X181) @ id) = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f16,plain,(
% 21.29/4.27 ! [X194 : term > $o] : (((sP2 @ X194) = $true) <=> ? [X198 : term,X199 : term] : (($true != (X194 @ (ap @ X198 @ X199))) & ((X194 @ X198) = $true) & ($true = (X194 @ X199))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f17,plain,(
% 21.29/4.27 ($true = sP3) <=> ! [X193 : term,X194 : term > $o] : (? [X195 : term] : (((var @ X195) = $true) & ((X194 @ X195) != $true)) | ? [X196 : term] : (($true != (X194 @ (lam @ X196))) & ! [X197 : term] : (((X194 @ (sub @ X196 @ (push @ X197 @ id))) = $true) | ($true != (X194 @ X197)))) | ((X194 @ X193) = $true) | ((sP2 @ X194) = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f18,plain,(
% 21.29/4.27 ! [X258 : subst > term > subst > $o] : (((sP4 @ X258) = $true) <=> ? [X269 : subst > term > term] : (! [X273 : term] : (((X258 @ id @ X273 @ id) != $true) | ((X258 @ id @ (X269 @ id @ X273) @ id) = $true)) & ! [X270 : subst,X271 : subst,X272 : term] : ((sub @ (X269 @ X270 @ X272) @ X271) = (X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271))) & ((X258 @ id @ (lam @ (X269 @ sh @ one)) @ id) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f19,plain,(
% 21.29/4.27 (sP5 = $true) <=> ! [X258 : subst > term > subst > $o,X259 : term] : (((sP4 @ X258) = $true) | ? [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (((X258 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X267) != $true) & ((X258 @ X265 @ X264 @ (comp @ X266 @ X267)) = $true)) | ? [X268 : term] : (((X258 @ id @ (sub @ X259 @ (push @ X268 @ id)) @ id) != $true) & ($true = (X258 @ id @ X268 @ id))) | ($true = (X258 @ id @ (lam @ X259) @ id)) | ? [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (($true = (X258 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) & ((X258 @ X260 @ X261 @ (comp @ X263 @ X262)) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f20,plain,(
% 21.29/4.27 ! [X395 : subst > term > subst > $o] : (((sP6 @ X395) = $true) <=> ? [X400 : subst > term > term] : (((X395 @ id @ (lam @ (X400 @ sh @ one)) @ id) != $true) & ! [X401 : term] : (((X395 @ id @ X401 @ id) != $true) | ((X395 @ id @ (X400 @ id @ X401) @ id) = $true)) & ! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X404 @ X403) @ (sub @ X402 @ X403)) = (sub @ (X400 @ X404 @ X402) @ X403))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f21,plain,(
% 21.29/4.27 ! [X395 : subst > term > subst > $o] : (($true = (sP7 @ X395)) <=> ? [X405 : term,X406 : term] : (($true != (X395 @ id @ (ap @ (sub @ X406 @ id) @ X405) @ id)) & ((X395 @ id @ X406 @ id) = $true) & ((X395 @ id @ X405 @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f22,plain,(
% 21.29/4.27 ! [X359 : term > $o] : (($true = (sP8 @ X359)) <=> ! [X360 : term,X361 : term] : (((X359 @ X360) != $true) | ((X359 @ X361) != $true) | ((X359 @ (ap @ X361 @ X360)) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f23,plain,(
% 21.29/4.27 ! [X367 : subst > term > subst > $o] : (((sP9 @ X367) = $true) <=> ! [X376 : term,X377 : term] : (((X367 @ id @ X376 @ id) != $true) | ((X367 @ id @ (ap @ (sub @ X376 @ id) @ X377) @ id) = $true) | ($true != (X367 @ id @ X377 @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f24,plain,(
% 21.29/4.27 ! [X378 : subst > term > subst > $o] : (((sP10 @ X378) = $true) <=> ! [X389 : subst > term > term] : (? [X390 : term] : (((X378 @ id @ X390 @ id) = $true) & ($true != (X378 @ id @ (X389 @ id @ X390) @ id))) | ? [X391 : term,X392 : subst,X393 : subst] : ((sub @ (X389 @ X393 @ X391) @ X392) != (X389 @ (comp @ X393 @ X392) @ (sub @ X391 @ X392))) | ((X378 @ id @ (lam @ (X389 @ sh @ one)) @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f25,plain,(
% 21.29/4.27 ($true = sP11) <=> ? [X378 : subst > term > subst > $o,X379 : term] : (! [X380 : subst,X381 : term,X382 : subst,X383 : subst] : (((X378 @ X383 @ X381 @ (comp @ X382 @ X380)) != $true) | ((X378 @ (comp @ X383 @ X382) @ (sub @ X381 @ X382) @ X380) = $true)) & ! [X388 : term] : (((X378 @ id @ (sub @ X379 @ (push @ X388 @ id)) @ id) = $true) | ((X378 @ id @ X388 @ id) != $true)) & ((X378 @ id @ (lam @ X379) @ id) != $true) & ! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (($true = (X378 @ X386 @ X387 @ (comp @ X384 @ X385))) | ($true != (X378 @ (comp @ X386 @ X384) @ (sub @ X387 @ X384) @ X385))) & ((sP10 @ X378) = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f26,plain,(
% 21.29/4.27 (sP12 = $true) <=> ! [X394 : term,X395 : subst > term > subst > $o] : (($true = (sP7 @ X395)) | ? [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (($true = (X395 @ (comp @ X408 @ X409) @ (sub @ X411 @ X409) @ X410)) & ((X395 @ X408 @ X411 @ (comp @ X409 @ X410)) != $true)) | ((sP6 @ X395) = $true) | ? [X407 : term] : (((var @ (sub @ X407 @ id)) = $true) & ((X395 @ id @ X407 @ id) != $true)) | ($true = (X395 @ id @ X394 @ id)) | ? [X396 : term,X397 : subst,X398 : subst,X399 : subst] : (((X395 @ X397 @ X396 @ (comp @ X399 @ X398)) = $true) & ((X395 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f27,plain,(
% 21.29/4.27 (sP13 = $true) <=> ? [X358 : term,X359 : term > $o] : (! [X362 : term] : (? [X363 : term] : (($true = (X359 @ X363)) & ((X359 @ (sub @ X362 @ (push @ X363 @ id))) != $true)) | ((X359 @ (lam @ X362)) = $true)) & ((X359 @ X358) != $true) & ! [X364 : term] : (($true = (X359 @ X364)) | ((var @ X364) != $true)) & ($true = (sP8 @ X359)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f28,plain,(
% 21.29/4.27 (sP14 = $true) <=> (($true = sP11) | ? [X365 : term,X366 : term,X367 : subst > term > subst > $o] : (! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (($true != (X367 @ (comp @ X368 @ X369) @ (sub @ X371 @ X369) @ X370)) | ($true = (X367 @ X368 @ X371 @ (comp @ X369 @ X370)))) & ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (($true = (X367 @ (comp @ X373 @ X372) @ (sub @ X375 @ X372) @ X374)) | ($true != (X367 @ X373 @ X375 @ (comp @ X372 @ X374)))) & ((sP9 @ X367) = $true) & ($true = (X367 @ id @ X366 @ id)) & ((X367 @ id @ X365 @ id) = $true) & ((X367 @ id @ (ap @ X365 @ X366) @ id) != $true)) | (sP13 = $true) | (sP12 = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f29,plain,(
% 21.29/4.27 ($true = sP15) <=> ? [X8 : term,X9 : subst > term > subst > $o] : (! [X15 : term] : (((X9 @ id @ X15 @ id) != $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id))) & ($true != (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) & ! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ? [X14 : term] : (((X9 @ id @ (X10 @ id @ X14) @ id) != $true) & ((X9 @ id @ X14 @ id) = $true)) | ? [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) != (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13)))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f30,plain,(
% 21.29/4.27 (sP16 = $true) <=> (? [X7 : term] : ((sub @ X7 @ id) != X7) | ! [X16 : term,X17 : subst > term > subst > $o] : (? [X18 : term] : (((X17 @ id @ X18 @ id) = $true) & ((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) != $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)) | ? [X19 : subst > term > term] : (! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) & ! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ($true != (X17 @ id @ X23 @ id))) & ($true != (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id)))) | ($true = sP15))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f31,plain,(
% 21.29/4.27 ! [X37 : subst > term > subst > $o] : (((sP17 @ X37) = $true) <=> ? [X38 : term,X39 : term] : (((X37 @ id @ X38 @ id) = $true) & ($true != (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) & ((X37 @ id @ X39 @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f32,plain,(
% 21.29/4.27 ! [X37 : subst > term > subst > $o] : (($true = (sP18 @ X37)) <=> ? [X48 : subst > term > term] : (! [X49 : term] : (($true != (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))) & ((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) != $true) & ! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f33,plain,(
% 21.29/4.27 (sP19 = $true) <=> ! [X36 : term,X37 : subst > term > subst > $o] : (($true = (sP18 @ X37)) | ($true = (X37 @ id @ X36 @ id)) | ? [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) = $true) & ((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) != $true)) | ? [X53 : term] : (($true = (var @ (sub @ X53 @ id))) & ((X37 @ id @ X53 @ id) != $true)) | ((sP17 @ X37) = $true) | ? [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) != $true) & ($true = (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f34,plain,(
% 21.29/4.27 ! [X202 : subst > term > subst > $o] : (((sP20 @ X202) = $true) <=> ? [X206 : subst > term > term] : (! [X210 : term] : (((X202 @ id @ X210 @ id) != $true) | ((X202 @ id @ (X206 @ id @ X210) @ id) = $true)) & ! [X207 : subst,X208 : subst,X209 : term] : ((X206 @ (comp @ X207 @ X208) @ (sub @ X209 @ X208)) = (sub @ (X206 @ X207 @ X209) @ X208)) & ($true != (X202 @ id @ (lam @ (X206 @ sh @ one)) @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f35,plain,(
% 21.29/4.27 ! [X148 : subst > term > subst > $o] : (($true = (sP21 @ X148)) <=> ? [X156 : subst > term > term] : (! [X157 : term] : (((X148 @ id @ X157 @ id) != $true) | ((X148 @ id @ (X156 @ id @ X157) @ id) = $true)) & ! [X158 : subst,X159 : term,X160 : subst] : ((sub @ (X156 @ X158 @ X159) @ X160) = (X156 @ (comp @ X158 @ X160) @ (sub @ X159 @ X160))) & ($true != (X148 @ id @ (lam @ (X156 @ sh @ one)) @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f36,plain,(
% 21.29/4.27 ($true = sP22) <=> (? [X147 : term] : ((sub @ X147 @ id) != X147) | ! [X148 : subst > term > subst > $o,X149 : term,X150 : term > $o] : (? [X151 : term] : (((X150 @ X151) = $true) & ((X150 @ (sub @ X149 @ (push @ X151 @ id))) != $true)) | ? [X162 : subst,X163 : subst,X164 : term,X165 : subst] : (($true = (X148 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163) @ X165)) & ((X148 @ X162 @ X164 @ (comp @ X163 @ X165)) != $true)) | ((X150 @ (lam @ X149)) = $true) | ($true = (sP21 @ X148)) | ? [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (((X148 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153) @ X155) != $true) & ($true = (X148 @ X154 @ X152 @ (comp @ X153 @ X155)))) | ? [X161 : term] : ((X150 @ X161) != (X148 @ id @ X161 @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f37,plain,(
% 21.29/4.27 ! [X458 : term > $o] : (((sP23 @ X458) = $true) <=> ! [X459 : term,X460 : term] : (((X458 @ (ap @ X460 @ X459)) = $true) | ((X458 @ X460) != $true) | ((X458 @ X459) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f38,plain,(
% 21.29/4.27 ! [X464 : term > $o] : (((sP24 @ X464) = $true) <=> ? [X469 : term,X470 : term] : (((X464 @ (ap @ X469 @ X470)) != $true) & ((X464 @ X470) = $true) & ((X464 @ X469) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f39,plain,(
% 21.29/4.27 ($true = sP25) <=> ! [X463 : term,X464 : term > $o,X465 : subst] : (((sP24 @ X464) = $true) | ? [X468 : term] : (((var @ X468) = $true) & ((X464 @ (sub @ X468 @ X465)) != $true)) | ? [X466 : term] : (($true != (X464 @ (lam @ X466))) & ! [X467 : term] : (((X464 @ X467) != $true) | ((X464 @ (sub @ X466 @ (push @ X467 @ id))) = $true))) | ($true = (X464 @ (sub @ X463 @ X465))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f40,plain,(
% 21.29/4.27 (sP26 = $true) <=> (($true = sP25) | ? [X454 : term,X455 : subst] : ((comp @ sh @ (push @ X454 @ X455)) != X455) | ? [X456 : subst] : ((comp @ X456 @ id) != X456) | ? [X457 : term,X458 : term > $o] : (! [X461 : term] : (((X458 @ X461) = $true) | ((var @ X461) != $true)) & ! [X462 : term] : (((X458 @ X462) != $true) | ((X458 @ (lam @ X462)) = $true)) & ($true != (X458 @ X457)) & ((sP23 @ X458) = $true)) | ? [X452 : term,X453 : subst] : ((sub @ one @ (push @ X452 @ X453)) != X452))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f41,plain,(
% 21.29/4.27 ! [X303 : term > $o] : (((sP27 @ X303) = $true) <=> ! [X305 : term,X306 : term] : (((X303 @ (ap @ X305 @ X306)) = $true) | ($true != (X303 @ X305)) | ((X303 @ X306) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f42,plain,(
% 21.29/4.27 ! [X321 : subst > term > subst > $o] : (($true = (sP28 @ X321)) <=> ? [X323 : subst > term > term] : (! [X324 : term] : (($true = (X321 @ id @ (X323 @ id @ X324) @ id)) | ((X321 @ id @ X324 @ id) != $true)) & ! [X325 : subst,X326 : subst,X327 : term] : ((sub @ (X323 @ X326 @ X327) @ X325) = (X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325))) & ((X321 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f43,plain,(
% 21.29/4.27 (sP29 = $true) <=> ? [X311 : term > $o,X312 : term,X313 : subst > term > subst > $o] : (! [X314 : term] : ((X311 @ X314) = (X313 @ id @ X314 @ id)) & ((X311 @ (lam @ X312)) != $true) & ! [X315 : term] : (((X311 @ (sub @ X312 @ (push @ X315 @ id))) = $true) | ((X311 @ X315) != $true)) & ! [X316 : subst > term > term] : (? [X317 : term] : (((X313 @ id @ X317 @ id) = $true) & ((X313 @ id @ (X316 @ id @ X317) @ id) != $true)) | ? [X318 : term,X319 : subst,X320 : subst] : ((sub @ (X316 @ X320 @ X318) @ X319) != (X316 @ (comp @ X320 @ X319) @ (sub @ X318 @ X319))) | ($true = (X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f44,plain,(
% 21.29/4.27 ($true = sP30) <=> ? [X303 : term > $o,X304 : term] : (((X303 @ X304) != $true) & ! [X307 : term] : (((X303 @ X307) = $true) | ($true != (var @ X307))) & ((sP27 @ X303) = $true) & ! [X308 : term] : (? [X309 : term] : (((X303 @ X309) = $true) & ((X303 @ (sub @ X308 @ (push @ X309 @ id))) != $true)) | ($true = (X303 @ (lam @ X308)))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f45,plain,(
% 21.29/4.27 (sP31 = $true) <=> ((sP29 = $true) | ! [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ X322 @ id) = $true) | ? [X328 : term,X329 : term] : (((X321 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id) != $true) & ((X321 @ id @ X328 @ id) = $true) & ((X321 @ id @ X329 @ id) = $true)) | ($true = (sP28 @ X321))) | ? [X310 : term] : ((sub @ X310 @ id) != X310) | ($true = sP30) | ? [X300 : subst > term > subst > $o] : ! [X301 : term > $o] : ? [X302 : term] : ((X301 @ X302) != (X300 @ id @ X302 @ id)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f46,plain,(
% 21.29/4.27 (sP32 = $true) <=> ! [X487 : term,X488 : subst > term > subst > $o] : (? [X489 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (sub @ X487 @ (push @ X489 @ id)) @ id) != $true)) | ? [X490 : subst > term > term,X491 : term] : (! [X496 : subst,X497 : subst,X498 : term] : ((X490 @ (comp @ X496 @ X497) @ (sub @ X498 @ X497)) = (sub @ X491 @ (push @ (sub @ X498 @ X497) @ (comp @ X496 @ X497)))) & ! [X495 : term] : (((X488 @ id @ (X490 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ! [X492 : subst,X493 : subst,X494 : term] : ((sub @ (X490 @ X492 @ X494) @ X493) = (sub @ (sub @ X491 @ (push @ X494 @ X492)) @ X493)) & ($true != (X488 @ id @ (lam @ (X490 @ sh @ one)) @ id))) | ($true = (X488 @ id @ (lam @ (sub @ X487 @ (push @ one @ sh))) @ id)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f47,plain,(
% 21.29/4.27 ($true = sP33) <=> ! [X412 : term,X413 : term > $o,X414 : subst > term > subst > $o] : (? [X421 : term] : ((X413 @ X421) != (X414 @ id @ X421 @ id)) | ? [X415 : term] : (($true != (X413 @ (sub @ X412 @ (push @ X415 @ id)))) & ($true = (X413 @ X415))) | ? [X416 : subst > term > term] : (((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) != $true) & ! [X417 : term,X418 : subst,X419 : subst] : ((sub @ (X416 @ X419 @ X417) @ X418) = (X416 @ (comp @ X419 @ X418) @ (sub @ X417 @ X418))) & ! [X420 : term] : (((X414 @ id @ X420 @ id) != $true) | ((X414 @ id @ (X416 @ id @ X420) @ id) = $true))) | ($true = (X413 @ (lam @ X412))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f48,plain,(
% 21.29/4.27 ! [X58 : term > $o] : (((sP34 @ X58) = $true) <=> ! [X59 : term,X60 : term] : (((X58 @ X60) != $true) | ((X58 @ (ap @ X59 @ X60)) = $true) | ($true != (X58 @ X59))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f49,plain,(
% 21.29/4.27 ! [X75 : subst > term > subst > $o] : (($true = (sP35 @ X75)) <=> ? [X91 : term,X92 : term] : (((X75 @ id @ X91 @ id) = $true) & ((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) != $true) & ($true = (X75 @ id @ X92 @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f50,plain,(
% 21.29/4.27 ! [X75 : subst > term > subst > $o] : (((sP36 @ X75) = $true) <=> ? [X82 : subst > term > term] : (((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) != $true) & ! [X83 : term] : (((X75 @ id @ (X82 @ id @ X83) @ id) = $true) | ((X75 @ id @ X83 @ id) != $true)) & ! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f51,plain,(
% 21.29/4.27 ($true = sP37) <=> ? [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (($true != (X65 @ (lam @ X66))) & ! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ($true != (X65 @ X73))) & ! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74)) & ! [X68 : subst > term > term] : (? [X69 : term] : (((X67 @ id @ X69 @ id) = $true) & ((X67 @ id @ (X68 @ id @ X69) @ id) != $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true) | ? [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) != (sub @ (X68 @ X72 @ X70) @ X71))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f52,plain,(
% 21.29/4.27 (sP38 = $true) <=> ! [X75 : subst > term > subst > $o,X76 : term] : (((X75 @ id @ X76 @ id) = $true) | ((sP36 @ X75) = $true) | ($true = (sP35 @ X75)) | ? [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) != $true) & ((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) = $true)) | ? [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) != $true) & ((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) = $true)) | ? [X77 : term] : (((X75 @ id @ X77 @ id) != $true) & ((var @ (sub @ X77 @ id)) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f53,plain,(
% 21.29/4.27 ($true = sP39) <=> ((sP38 = $true) | ? [X57 : term,X58 : term > $o] : (! [X61 : term] : (($true = (X58 @ (lam @ X61))) | ? [X62 : term] : (($true = (X58 @ X62)) & ((X58 @ (sub @ X61 @ (push @ X62 @ id))) != $true))) & ((sP34 @ X58) = $true) & ! [X63 : term] : (((var @ X63) != $true) | ((X58 @ X63) = $true)) & ((X58 @ X57) != $true)) | ($true = sP37) | ? [X64 : term] : ((sub @ X64 @ id) != X64) | ? [X54 : subst > term > subst > $o] : ! [X55 : term > $o] : ? [X56 : term] : ((X54 @ id @ X56 @ id) != (X55 @ X56)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f54,plain,(
% 21.29/4.27 ! [X340 : subst > term > subst > $o] : (((sP40 @ X340) = $true) <=> ? [X342 : subst > term > term] : (($true != (X340 @ id @ (lam @ (X342 @ sh @ one)) @ id)) & ! [X343 : term,X344 : subst,X345 : subst] : ((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345)) = (sub @ (X342 @ X344 @ X343) @ X345)) & ! [X346 : term] : (((X340 @ id @ X346 @ id) != $true) | ($true = (X340 @ id @ (X342 @ id @ X346) @ id)))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f55,plain,(
% 21.29/4.27 ($true = sP41) <=> ? [X331 : subst > term > subst > $o,X332 : term] : (((X331 @ id @ (lam @ (sub @ X332 @ (push @ one @ sh))) @ id) != $true) & ! [X338 : term] : (((X331 @ id @ X338 @ id) != $true) | ((X331 @ id @ (sub @ X332 @ (push @ X338 @ id)) @ id) = $true)) & ! [X333 : subst > term > term] : (? [X334 : term] : (((X331 @ id @ (X333 @ id @ X334) @ id) != $true) & ($true = (X331 @ id @ X334 @ id))) | ? [X335 : term,X336 : subst,X337 : subst] : ((X333 @ (comp @ X337 @ X336) @ (sub @ X335 @ X336)) != (sub @ (X333 @ X337 @ X335) @ X336)) | ((X331 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f56,plain,(
% 21.29/4.27 ($true = sP42) <=> (($true = sP41) | ? [X330 : term] : ((sub @ X330 @ id) != X330) | ! [X339 : term,X340 : subst > term > subst > $o] : (((sP40 @ X340) = $true) | ? [X347 : subst,X348 : subst,X349 : subst,X350 : term] : (((X340 @ (comp @ X349 @ X347) @ (sub @ X350 @ X347) @ X348) != $true) & ((X340 @ X349 @ X350 @ (comp @ X347 @ X348)) = $true)) | ? [X341 : term] : (($true = (X340 @ id @ X341 @ id)) & ((X340 @ id @ (sub @ X339 @ (push @ X341 @ id)) @ id) != $true)) | ? [X351 : term,X352 : subst,X353 : subst,X354 : subst] : (($true != (X340 @ X353 @ X351 @ (comp @ X354 @ X352))) & ((X340 @ (comp @ X353 @ X354) @ (sub @ X351 @ X354) @ X352) = $true)) | ((X340 @ id @ (lam @ X339) @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f57,plain,(
% 21.29/4.27 ! [X131 : term > $o] : (((sP43 @ X131) = $true) <=> ? [X133 : term,X134 : term] : (((X131 @ X134) = $true) & ((X131 @ X133) = $true) & ((X131 @ (ap @ X133 @ X134)) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f58,plain,(
% 21.29/4.27 ! [X510 : term > $o] : (($true = (sP44 @ X510)) <=> ? [X512 : term,X513 : term] : (($true != (X510 @ (ap @ X513 @ X512))) & ((X510 @ X513) = $true) & ((X510 @ X512) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f59,plain,(
% 21.29/4.27 ($true = sP45) <=> ! [X508 : subst,X509 : term,X510 : term > $o] : (((X510 @ (sub @ X509 @ X508)) = $true) | ($true = (sP44 @ X510)) | ? [X514 : term] : (! [X515 : term] : (((X510 @ X515) != $true) | ((X510 @ (sub @ X514 @ (push @ X515 @ id))) = $true)) & ((X510 @ (lam @ X514)) != $true)) | ? [X511 : term] : (((X510 @ (sub @ X511 @ X508)) != $true) & ((var @ X511) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f60,plain,(
% 21.29/4.27 ! [X422 : subst > term > subst > $o] : (((sP46 @ X422) = $true) <=> ? [X425 : subst > term > term] : (((X422 @ id @ (lam @ (X425 @ sh @ one)) @ id) != $true) & ! [X429 : term] : (((X422 @ id @ X429 @ id) != $true) | ((X422 @ id @ (X425 @ id @ X429) @ id) = $true)) & ! [X426 : subst,X427 : term,X428 : subst] : ((X425 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426)) = (sub @ (X425 @ X428 @ X427) @ X426))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f61,plain,(
% 21.29/4.27 ($true = sP47) <=> ! [X422 : subst > term > subst > $o,X423 : term,X424 : term > $o] : (? [X439 : term] : (((X424 @ X439) = $true) & ((X424 @ (sub @ X423 @ (push @ X439 @ id))) != $true)) | ? [X430 : subst,X431 : term,X432 : subst,X433 : subst] : (((X422 @ (comp @ X433 @ X432) @ (sub @ X431 @ X432) @ X430) != $true) & ((X422 @ X433 @ X431 @ (comp @ X432 @ X430)) = $true)) | ((X424 @ (lam @ X423)) = $true) | ? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X422 @ (comp @ X436 @ X437) @ (sub @ X434 @ X437) @ X435) = $true) & ($true != (X422 @ X436 @ X434 @ (comp @ X437 @ X435)))) | ? [X438 : term] : ((X422 @ id @ X438 @ id) != (X424 @ X438)) | ((sP46 @ X422) = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f62,plain,(
% 21.29/4.27 (sP48 = $true) <=> ! [X248 : subst > term > subst > $o,X249 : term] : (($true = (X248 @ id @ (lam @ (sub @ X249 @ (push @ one @ sh))) @ id)) | ? [X251 : subst > term > term] : (((X248 @ id @ (lam @ (X251 @ sh @ one)) @ id) != $true) & ! [X253 : term,X254 : subst,X255 : subst] : ((sub @ (X251 @ X255 @ X253) @ X254) = (X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254))) & ! [X252 : term] : (((X248 @ id @ (X251 @ id @ X252) @ id) = $true) | ($true != (X248 @ id @ X252 @ id)))) | ? [X250 : term] : (((X248 @ id @ (sub @ X249 @ (push @ X250 @ id)) @ id) != $true) & ($true = (X248 @ id @ X250 @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f63,plain,(
% 21.29/4.27 ! [X282 : subst > term > subst > $o] : (($true = (sP49 @ X282)) <=> ? [X293 : term,X294 : term] : (($true != (X282 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)) & ($true = (X282 @ id @ X293 @ id)) & ((X282 @ id @ X294 @ id) = $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f64,plain,(
% 21.29/4.27 (sP50 = $true) <=> ! [X280 : term,X281 : term,X282 : subst > term > subst > $o,X283 : term > $o] : (? [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (((X282 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290) @ X292) != $true) & ((X282 @ X289 @ X291 @ (comp @ X290 @ X292)) = $true)) | ? [X288 : term] : ((X283 @ X288) != (X282 @ id @ X288 @ id)) | ($true = (sP49 @ X282)) | ((X283 @ X281) != $true) | ($true = (X283 @ (ap @ X280 @ X281))) | ((X283 @ X280) != $true) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X282 @ (comp @ X285 @ X284) @ (sub @ X286 @ X284) @ X287)) & ((X282 @ X285 @ X286 @ (comp @ X284 @ X287)) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f65,plain,(
% 21.29/4.27 ($true = sP51) <=> ! [X440 : subst > term > subst > $o,X441 : term] : (? [X442 : subst > term > term] : (! [X443 : subst,X444 : subst,X445 : term] : ((X442 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444)) = (sub @ (X442 @ X443 @ X445) @ X444)) & ((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id) != $true) & ! [X446 : term] : (((X440 @ id @ (X442 @ id @ X446) @ id) = $true) | ($true != (X440 @ id @ X446 @ id)))) | ((X440 @ id @ (lam @ X441) @ id) = $true) | ? [X447 : term] : (((X440 @ id @ X447 @ id) = $true) & ((X440 @ id @ (sub @ X441 @ (push @ X447 @ id)) @ id) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f66,plain,(
% 21.29/4.27 (sP52 = $true) <=> (? [X473 : term,X474 : subst] : ((comp @ sh @ (push @ X473 @ X474)) != X474) | ? [X471 : term,X472 : subst] : ((sub @ one @ (push @ X471 @ X472)) != X471) | ? [X475 : term,X476 : term] : (((lam @ X475) = (lam @ X476)) & (X475 != X476)) | ! [X477 : term,X478 : subst,X479 : subst > term > term,X480 : subst > term > term] : (? [X481 : subst,X482 : term,X483 : subst] : ((sub @ (X479 @ X483 @ X482) @ X481) != (X479 @ (comp @ X483 @ X481) @ (sub @ X482 @ X481))) | ((lam @ (X480 @ sh @ one)) != (lam @ (X479 @ sh @ one))) | ((X479 @ X478 @ X477) = (X480 @ X478 @ X477)) | ? [X484 : subst,X485 : term,X486 : subst] : ((X480 @ (comp @ X484 @ X486) @ (sub @ X485 @ X486)) != (sub @ (X480 @ X484 @ X485) @ X486))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f67,plain,(
% 21.29/4.27 (sP53 = $true) <=> (? [X231 : term] : ((sub @ X231 @ id) != X231) | ? [X227 : term] : ! [X228 : subst > term > term] : ? [X229 : subst,X230 : term] : ((sub @ X227 @ (push @ X230 @ X229)) != (X228 @ X229 @ X230)) | ! [X232 : subst > term > subst > $o,X233 : term > $o,X234 : term] : (? [X236 : term] : (((X233 @ (sub @ X234 @ (push @ X236 @ id))) != $true) & ((X233 @ X236) = $true)) | ((X233 @ (lam @ X234)) = $true) | ? [X235 : term] : ((X232 @ id @ X235 @ id) != (X233 @ X235)) | ? [X237 : subst > term > term] : (! [X239 : term,X240 : subst,X241 : subst] : ((sub @ (X237 @ X241 @ X239) @ X240) = (X237 @ (comp @ X241 @ X240) @ (sub @ X239 @ X240))) & ! [X238 : term] : (($true != (X232 @ id @ X238 @ id)) | ($true = (X232 @ id @ (X237 @ id @ X238) @ id))) & ((X232 @ id @ (lam @ (X237 @ sh @ one)) @ id) != $true))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f68,plain,(
% 21.29/4.27 ! [X517 : term > $o] : (((sP54 @ X517) = $true) <=> ! [X523 : term,X524 : term] : (((X517 @ (ap @ X523 @ X524)) = $true) | ((X517 @ X524) != $true) | ((X517 @ X523) != $true)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f69,plain,(
% 21.29/4.27 ! [X525 : term > $o] : (((sP55 @ X525) = $true) <=> ? [X530 : term,X531 : term] : (($true = (X525 @ X530)) & ((X525 @ (ap @ X530 @ X531)) != $true) & ($true = (X525 @ X531))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f70,plain,(
% 21.29/4.27 (sP56 = $true) <=> ! [X525 : term > $o,X526 : term] : (? [X529 : term] : (((var @ X529) = $true) & ((X525 @ X529) != $true)) | ? [X527 : term] : (((X525 @ (lam @ X527)) != $true) & ! [X528 : term] : (((X525 @ X528) != $true) | ((X525 @ (sub @ X527 @ (push @ X528 @ id))) = $true))) | ($true = (X525 @ X526)) | ((sP55 @ X525) = $true))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f71,plain,(
% 21.29/4.27 (sP57 = $true) <=> (? [X516 : term] : ((sub @ X516 @ id) != X516) | (sP56 = $true) | ? [X517 : term > $o,X518 : subst,X519 : term] : (! [X521 : term] : (? [X522 : term] : (((X517 @ (sub @ X521 @ (push @ X522 @ id))) != $true) & ($true = (X517 @ X522))) | ($true = (X517 @ (lam @ X521)))) & ($true != (X517 @ (sub @ X519 @ X518))) & ((sP54 @ X517) = $true) & ! [X520 : term] : (($true = (X517 @ (sub @ X520 @ X518))) | ((var @ X520) != $true))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f72,plain,(
% 21.29/4.27 (sP58 = $true) <=> ! [X121 : subst > term > subst > $o,X122 : term] : (((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ? [X123 : subst > term > term] : (! [X127 : term] : (($true = (X121 @ id @ (X123 @ id @ X127) @ id)) | ((X121 @ id @ X127 @ id) != $true)) & ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) != $true) & ! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124))) | ? [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) != $true) & ($true = (X121 @ id @ X128 @ id))))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 21.29/4.27 thf(f12,plain,(
% 21.29/4.27 (! [X24 : subst > term > subst > $o] : ? [X25 : term > $o] : ! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj = $true) <=> ! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (? [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) != (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ? [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) != (sub @ (X218 @ X226 @ X225) @ X224)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one))) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220)))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X121 : subst > term > subst > $o,X122 : term] : (((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ? [X123 : subst > term > term] : (! [X127 : term] : (($true = (X121 @ id @ (X123 @ id @ X127) @ id)) | ((X121 @ id @ X127 @ id) != $true)) & ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) != $true) & ! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124))) | ? [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) != $true) & ($true = (X121 @ id @ X128 @ id))))) & ((d2subst @ d_id) = id) & (! [X448 : term] : ? [X449 : subst > term > term] : ! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) <=> (hoasinduction_lem3v2_f = $true)) & ((induction2_lthm = $true) <=> (? [X516 : term] : ((sub @ X516 @ id) != X516) | ! [X525 : term > $o,X526 : term] : (? [X529 : term] : (((var @ X529) = $true) & ((X525 @ X529) != $true)) | ? [X527 : term] : (((X525 @ (lam @ X527)) != $true) & ! [X528 : term] : (((X525 @ X528) != $true) | ((X525 @ (sub @ X527 @ (push @ X528 @ id))) = $true))) | ($true = (X525 @ X526)) | ? [X530 : term,X531 : term] : (($true = (X525 @ X530)) & ((X525 @ (ap @ X530 @ X531)) != $true) & ($true = (X525 @ X531)))) | ? [X517 : term > $o,X518 : subst,X519 : term] : (! [X521 : term] : (? [X522 : term] : (((X517 @ (sub @ X521 @ (push @ X522 @ id))) != $true) & ($true = (X517 @ X522))) | ($true = (X517 @ (lam @ X521)))) & ($true != (X517 @ (sub @ X519 @ X518))) & ! [X523 : term,X524 : term] : (((X517 @ (ap @ X523 @ X524)) = $true) | ((X517 @ X524) != $true) | ((X517 @ X523) != $true)) & ! [X520 : term] : (($true = (X517 @ (sub @ X520 @ X518))) | ((var @ X520) != $true))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X231 : term] : ((sub @ X231 @ id) != X231) | ? [X227 : term] : ! [X228 : subst > term > term] : ? [X229 : subst,X230 : term] : ((sub @ X227 @ (push @ X230 @ X229)) != (X228 @ X229 @ X230)) | ! [X232 : subst > term > subst > $o,X233 : term > $o,X234 : term] : (? [X236 : term] : (((X233 @ (sub @ X234 @ (push @ X236 @ id))) != $true) & ((X233 @ X236) = $true)) | ((X233 @ (lam @ X234)) = $true) | ? [X235 : term] : ((X232 @ id @ X235 @ id) != (X233 @ X235)) | ? [X237 : subst > term > term] : (! [X239 : term,X240 : subst,X241 : subst] : ((sub @ (X237 @ X241 @ X239) @ X240) = (X237 @ (comp @ X241 @ X240) @ (sub @ X239 @ X240))) & ! [X238 : term] : (($true != (X232 @ id @ X238 @ id)) | ($true = (X232 @ id @ (X237 @ id @ X238) @ id))) & ((X232 @ id @ (lam @ (X237 @ sh @ one)) @ id) != $true))))) & (pushprop_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (? [X473 : term,X474 : subst] : ((comp @ sh @ (push @ X473 @ X474)) != X474) | ? [X471 : term,X472 : subst] : ((sub @ one @ (push @ X471 @ X472)) != X471) | ? [X475 : term,X476 : term] : (((lam @ X475) = (lam @ X476)) & (X475 != X476)) | ! [X477 : term,X478 : subst,X479 : subst > term > term,X480 : subst > term > term] : (? [X481 : subst,X482 : term,X483 : subst] : ((sub @ (X479 @ X483 @ X482) @ X481) != (X479 @ (comp @ X483 @ X481) @ (sub @ X482 @ X481))) | ((lam @ (X480 @ sh @ one)) != (lam @ (X479 @ sh @ one))) | ((X479 @ X478 @ X477) = (X480 @ X478 @ X477)) | ? [X484 : subst,X485 : term,X486 : subst] : ((X480 @ (comp @ X484 @ X486) @ (sub @ X485 @ X486)) != (sub @ (X480 @ X484 @ X485) @ X486))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X440 : subst > term > subst > $o,X441 : term] : (? [X442 : subst > term > term] : (! [X443 : subst,X444 : subst,X445 : term] : ((X442 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444)) = (sub @ (X442 @ X443 @ X445) @ X444)) & ((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id) != $true) & ! [X446 : term] : (((X440 @ id @ (X442 @ id @ X446) @ id) = $true) | ($true != (X440 @ id @ X446 @ id)))) | ((X440 @ id @ (lam @ X441) @ id) = $true) | ? [X447 : term] : (((X440 @ id @ X447 @ id) = $true) & ((X440 @ id @ (sub @ X441 @ (push @ X447 @ id)) @ id) != $true)))) & ((substmonoid_lthm = $true) <=> (? [X277 : subst] : ((comp @ X277 @ id) != X277) | (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)) | ? [X276 : subst] : ((comp @ id @ X276) != X276))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & (! [X280 : term,X281 : term,X282 : subst > term > subst > $o,X283 : term > $o] : (? [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (((X282 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290) @ X292) != $true) & ((X282 @ X289 @ X291 @ (comp @ X290 @ X292)) = $true)) | ? [X288 : term] : ((X283 @ X288) != (X282 @ id @ X288 @ id)) | ? [X293 : term,X294 : term] : (($true != (X282 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)) & ($true = (X282 @ id @ X293 @ id)) & ((X282 @ id @ X294 @ id) = $true)) | ((X283 @ X281) != $true) | ($true = (X283 @ (ap @ X280 @ X281))) | ((X283 @ X280) != $true) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X282 @ (comp @ X285 @ X284) @ (sub @ X286 @ X284) @ X287)) & ((X282 @ X285 @ X286 @ (comp @ X284 @ X287)) != $true))) <=> (hoasinduction_lem2v2 = $true)) & (ulamvarsh = $true) & ((? [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) != X499) | ? [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) != X501) | ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503)))))) <=> (pushprop_lem1_lthm = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lem3aa = $true) <=> ! [X248 : subst > term > subst > $o,X249 : term] : (($true = (X248 @ id @ (lam @ (sub @ X249 @ (push @ one @ sh))) @ id)) | ? [X251 : subst > term > term] : (((X248 @ id @ (lam @ (X251 @ sh @ one)) @ id) != $true) & ! [X253 : term,X254 : subst,X255 : subst] : ((sub @ (X251 @ X255 @ X253) @ X254) = (X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254))) & ! [X252 : term] : (((X248 @ id @ (X251 @ id @ X252) @ id) = $true) | ($true != (X248 @ id @ X252 @ id)))) | ? [X250 : term] : (((X248 @ id @ (sub @ X249 @ (push @ X250 @ id)) @ id) != $true) & ($true = (X248 @ id @ X250 @ id))))) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) != (d2subst @ X117)) | (X116 = X117)) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & (axmap = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X422 : subst > term > subst > $o,X423 : term,X424 : term > $o] : (? [X439 : term] : (((X424 @ X439) = $true) & ((X424 @ (sub @ X423 @ (push @ X439 @ id))) != $true)) | ? [X430 : subst,X431 : term,X432 : subst,X433 : subst] : (((X422 @ (comp @ X433 @ X432) @ (sub @ X431 @ X432) @ X430) != $true) & ((X422 @ X433 @ X431 @ (comp @ X432 @ X430)) = $true)) | ((X424 @ (lam @ X423)) = $true) | ? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X422 @ (comp @ X436 @ X437) @ (sub @ X434 @ X437) @ X435) = $true) & ($true != (X422 @ X436 @ X434 @ (comp @ X437 @ X435)))) | ? [X438 : term] : ((X422 @ id @ X438 @ id) != (X424 @ X438)) | ? [X425 : subst > term > term] : (((X422 @ id @ (lam @ (X425 @ sh @ one)) @ id) != $true) & ! [X429 : term] : (((X422 @ id @ X429 @ id) != $true) | ((X422 @ id @ (X425 @ id @ X429) @ id) = $true)) & ! [X426 : subst,X427 : term,X428 : subst] : ((X425 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426)) = (sub @ (X425 @ X428 @ X427) @ X426))))) & (axvarshift = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (termmset_gthm = $true) & (! [X508 : subst,X509 : term,X510 : term > $o] : (((X510 @ (sub @ X509 @ X508)) = $true) | ? [X512 : term,X513 : term] : (($true != (X510 @ (ap @ X513 @ X512))) & ((X510 @ X513) = $true) & ((X510 @ X512) = $true)) | ? [X514 : term] : (! [X515 : term] : (((X510 @ X515) != $true) | ((X510 @ (sub @ X514 @ (push @ X515 @ id))) = $true)) & ((X510 @ (lam @ X514)) != $true)) | ? [X511 : term] : (((X510 @ (sub @ X511 @ X508)) != $true) & ((var @ X511) = $true))) <=> (induction2lem = $true)) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & (! [X200 : term] : ? [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) = (X201 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & (! [X27 : term] : ? [X28 : subst > term > term] : ! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X131 : term > $o,X132 : term] : (? [X133 : term,X134 : term] : (((X131 @ X134) = $true) & ((X131 @ X133) = $true) & ((X131 @ (ap @ X133 @ X134)) != $true)) | ? [X136 : term] : (($true = (var @ X136)) & ($true != (X131 @ X136))) | ? [X135 : term] : (((X131 @ (lam @ X135)) != $true) & ($true = (X131 @ X135))) | ((X131 @ X132) = $true)) <=> (induction = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ($true != (X177 @ X178)) | ? [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) != (X175 @ X179))) | ? [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) != X173))) & (axabs = $true) & (pushprop_lem1v2_gthm = $true) & ((? [X331 : subst > term > subst > $o,X332 : term] : (((X331 @ id @ (lam @ (sub @ X332 @ (push @ one @ sh))) @ id) != $true) & ! [X338 : term] : (((X331 @ id @ X338 @ id) != $true) | ((X331 @ id @ (sub @ X332 @ (push @ X338 @ id)) @ id) = $true)) & ! [X333 : subst > term > term] : (? [X334 : term] : (((X331 @ id @ (X333 @ id @ X334) @ id) != $true) & ($true = (X331 @ id @ X334 @ id))) | ? [X335 : term,X336 : subst,X337 : subst] : ((X333 @ (comp @ X337 @ X336) @ (sub @ X335 @ X336)) != (sub @ (X333 @ X337 @ X335) @ X336)) | ((X331 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true))) | ? [X330 : term] : ((sub @ X330 @ id) != X330) | ! [X339 : term,X340 : subst > term > subst > $o] : (? [X342 : subst > term > term] : (($true != (X340 @ id @ (lam @ (X342 @ sh @ one)) @ id)) & ! [X343 : term,X344 : subst,X345 : subst] : ((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345)) = (sub @ (X342 @ X344 @ X343) @ X345)) & ! [X346 : term] : (((X340 @ id @ X346 @ id) != $true) | ($true = (X340 @ id @ (X342 @ id @ X346) @ id)))) | ? [X347 : subst,X348 : subst,X349 : subst,X350 : term] : (((X340 @ (comp @ X349 @ X347) @ (sub @ X350 @ X347) @ X348) != $true) & ((X340 @ X349 @ X350 @ (comp @ X347 @ X348)) = $true)) | ? [X341 : term] : (($true = (X340 @ id @ X341 @ id)) & ((X340 @ id @ (sub @ X339 @ (push @ X341 @ id)) @ id) != $true)) | ? [X351 : term,X352 : subst,X353 : subst,X354 : subst] : (($true != (X340 @ X353 @ X351 @ (comp @ X354 @ X352))) & ((X340 @ (comp @ X353 @ X354) @ (sub @ X351 @ X354) @ X352) = $true)) | ((X340 @ id @ (lam @ X339) @ id) = $true))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ! [X35 : d_subst] : (d_id = X35) & ((! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | ? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X535) & ((ap @ X533 @ X535) = (ap @ X534 @ X532)))) <=> (hoasapinj2_lthm = $true)) & (lamnotvar = $true) & ((pushprop_lem0 = $true) <=> ! [X137 : subst,X138 : term,X139 : term > $o] : ? [X140 : term > $o] : ! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141))) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapinj2_gthm = $true) & ((! [X75 : subst > term > subst > $o,X76 : term] : (((X75 @ id @ X76 @ id) = $true) | ? [X82 : subst > term > term] : (((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) != $true) & ! [X83 : term] : (((X75 @ id @ (X82 @ id @ X83) @ id) = $true) | ((X75 @ id @ X83 @ id) != $true)) & ! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ? [X91 : term,X92 : term] : (((X75 @ id @ X91 @ id) = $true) & ((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) != $true) & ($true = (X75 @ id @ X92 @ id))) | ? [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) != $true) & ((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) = $true)) | ? [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) != $true) & ((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) = $true)) | ? [X77 : term] : (((X75 @ id @ X77 @ id) != $true) & ((var @ (sub @ X77 @ id)) = $true))) | ? [X57 : term,X58 : term > $o] : (! [X61 : term] : (($true = (X58 @ (lam @ X61))) | ? [X62 : term] : (($true = (X58 @ X62)) & ((X58 @ (sub @ X61 @ (push @ X62 @ id))) != $true))) & ! [X59 : term,X60 : term] : (((X58 @ X60) != $true) | ((X58 @ (ap @ X59 @ X60)) = $true) | ($true != (X58 @ X59))) & ! [X63 : term] : (((var @ X63) != $true) | ((X58 @ X63) = $true)) & ((X58 @ X57) != $true)) | ? [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (($true != (X65 @ (lam @ X66))) & ! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ($true != (X65 @ X73))) & ! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74)) & ! [X68 : subst > term > term] : (? [X69 : term] : (((X67 @ id @ X69 @ id) = $true) & ((X67 @ id @ (X68 @ id @ X69) @ id) != $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true) | ? [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) != (sub @ (X68 @ X72 @ X70) @ X71)))) | ? [X64 : term] : ((sub @ X64 @ id) != X64) | ? [X54 : subst > term > subst > $o] : ! [X55 : term > $o] : ? [X56 : term] : ((X54 @ id @ X56 @ id) != (X55 @ X56))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X412 : term,X413 : term > $o,X414 : subst > term > subst > $o] : (? [X421 : term] : ((X413 @ X421) != (X414 @ id @ X421 @ id)) | ? [X415 : term] : (($true != (X413 @ (sub @ X412 @ (push @ X415 @ id)))) & ($true = (X413 @ X415))) | ? [X416 : subst > term > term] : (((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) != $true) & ! [X417 : term,X418 : subst,X419 : subst] : ((sub @ (X416 @ X419 @ X417) @ X418) = (X416 @ (comp @ X419 @ X418) @ (sub @ X417 @ X418))) & ! [X420 : term] : (((X414 @ id @ X420 @ id) != $true) | ((X414 @ id @ (X416 @ id @ X420) @ id) = $true))) | ($true = (X413 @ (lam @ X412))))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((shinj = $true) <=> ! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247))) & (induction2_gthm = $true) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_lthm = $true) & (! [X216 : term] : ((sub @ X216 @ id) = X216) <=> (termmset = $true)) & ((? [X171 : term] : ((sub @ X171 @ id) != X171) | ! [X172 : term] : ((sub @ X172 @ id) = X172)) <=> (termmset_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ? [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) != (sub @ (X95 @ X98 @ X97) @ X96)))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X487 : term,X488 : subst > term > subst > $o] : (? [X489 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (sub @ X487 @ (push @ X489 @ id)) @ id) != $true)) | ? [X490 : subst > term > term,X491 : term] : (! [X496 : subst,X497 : subst,X498 : term] : ((X490 @ (comp @ X496 @ X497) @ (sub @ X498 @ X497)) = (sub @ X491 @ (push @ (sub @ X498 @ X497) @ (comp @ X496 @ X497)))) & ! [X495 : term] : (((X488 @ id @ (X490 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ! [X492 : subst,X493 : subst,X494 : term] : ((sub @ (X490 @ X492 @ X494) @ X493) = (sub @ (sub @ X491 @ (push @ X494 @ X492)) @ X493)) & ($true != (X488 @ id @ (lam @ (X490 @ sh @ one)) @ id))) | ($true = (X488 @ id @ (lam @ (sub @ X487 @ (push @ one @ sh))) @ id)))) & (hoasapinj1_gthm = $true) & (substmonoid_gthm = $true) & ((? [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) = (ap @ X107 @ X109)) & (X107 != X108)) | ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))) | ? [X105 : term] : ((sub @ X105 @ id) != X105)) <=> (hoasapinj1_lthm = $true)) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) <=> (hoasapinj1 = $true)) & ! [X170 : d_term] : (d_one = X170) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((? [X311 : term > $o,X312 : term,X313 : subst > term > subst > $o] : (! [X314 : term] : ((X311 @ X314) = (X313 @ id @ X314 @ id)) & ((X311 @ (lam @ X312)) != $true) & ! [X315 : term] : (((X311 @ (sub @ X312 @ (push @ X315 @ id))) = $true) | ((X311 @ X315) != $true)) & ! [X316 : subst > term > term] : (? [X317 : term] : (((X313 @ id @ X317 @ id) = $true) & ((X313 @ id @ (X316 @ id @ X317) @ id) != $true)) | ? [X318 : term,X319 : subst,X320 : subst] : ((sub @ (X316 @ X320 @ X318) @ X319) != (X316 @ (comp @ X320 @ X319) @ (sub @ X318 @ X319))) | ($true = (X313 @ id @ (lam @ (X316 @ sh @ one)) @ id)))) | ! [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ X322 @ id) = $true) | ? [X328 : term,X329 : term] : (((X321 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id) != $true) & ((X321 @ id @ X328 @ id) = $true) & ((X321 @ id @ X329 @ id) = $true)) | ? [X323 : subst > term > term] : (! [X324 : term] : (($true = (X321 @ id @ (X323 @ id @ X324) @ id)) | ((X321 @ id @ X324 @ id) != $true)) & ! [X325 : subst,X326 : subst,X327 : term] : ((sub @ (X323 @ X326 @ X327) @ X325) = (X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325))) & ((X321 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true))) | ? [X310 : term] : ((sub @ X310 @ id) != X310) | ? [X303 : term > $o,X304 : term] : (((X303 @ X304) != $true) & ! [X307 : term] : (((X303 @ X307) = $true) | ($true != (var @ X307))) & ! [X305 : term,X306 : term] : (((X303 @ (ap @ X305 @ X306)) = $true) | ($true != (X303 @ X305)) | ((X303 @ X306) != $true)) & ! [X308 : term] : (? [X309 : term] : (((X303 @ X309) = $true) & ((X303 @ (sub @ X308 @ (push @ X309 @ id))) != $true)) | ($true = (X303 @ (lam @ X308))))) | ? [X300 : subst > term > subst > $o] : ! [X301 : term > $o] : ? [X302 : term] : ((X301 @ X302) != (X300 @ id @ X302 @ id))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & ((hoasinduction_lem0 = $true) <=> ! [X118 : subst > term > subst > $o] : ? [X119 : term > $o] : ! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120))) & ((! [X463 : term,X464 : term > $o,X465 : subst] : (? [X469 : term,X470 : term] : (((X464 @ (ap @ X469 @ X470)) != $true) & ((X464 @ X470) = $true) & ((X464 @ X469) = $true)) | ? [X468 : term] : (((var @ X468) = $true) & ((X464 @ (sub @ X468 @ X465)) != $true)) | ? [X466 : term] : (($true != (X464 @ (lam @ X466))) & ! [X467 : term] : (((X464 @ X467) != $true) | ((X464 @ (sub @ X466 @ (push @ X467 @ id))) = $true))) | ($true = (X464 @ (sub @ X463 @ X465)))) | ? [X454 : term,X455 : subst] : ((comp @ sh @ (push @ X454 @ X455)) != X455) | ? [X456 : subst] : ((comp @ X456 @ id) != X456) | ? [X457 : term,X458 : term > $o] : (! [X461 : term] : (((X458 @ X461) = $true) | ((var @ X461) != $true)) & ! [X462 : term] : (((X458 @ X462) != $true) | ((X458 @ (lam @ X462)) = $true)) & ($true != (X458 @ X457)) & ! [X459 : term,X460 : term] : (((X458 @ (ap @ X460 @ X459)) = $true) | ((X458 @ X460) != $true) | ((X458 @ X459) != $true))) | ? [X452 : term,X453 : subst] : ((sub @ one @ (push @ X452 @ X453)) != X452)) <=> (induction2lem_lthm = $true)) & (! [X129 : term] : ? [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) = (X130 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lthm = $true) & ((? [X147 : term] : ((sub @ X147 @ id) != X147) | ! [X148 : subst > term > subst > $o,X149 : term,X150 : term > $o] : (? [X151 : term] : (((X150 @ X151) = $true) & ((X150 @ (sub @ X149 @ (push @ X151 @ id))) != $true)) | ? [X162 : subst,X163 : subst,X164 : term,X165 : subst] : (($true = (X148 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163) @ X165)) & ((X148 @ X162 @ X164 @ (comp @ X163 @ X165)) != $true)) | ((X150 @ (lam @ X149)) = $true) | ? [X156 : subst > term > term] : (! [X157 : term] : (((X148 @ id @ X157 @ id) != $true) | ((X148 @ id @ (X156 @ id @ X157) @ id) = $true)) & ! [X158 : subst,X159 : term,X160 : subst] : ((sub @ (X156 @ X158 @ X159) @ X160) = (X156 @ (comp @ X158 @ X160) @ (sub @ X159 @ X160))) & ($true != (X148 @ id @ (lam @ (X156 @ sh @ one)) @ id))) | ? [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (((X148 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153) @ X155) != $true) & ($true = (X148 @ X154 @ X152 @ (comp @ X153 @ X155)))) | ? [X161 : term] : ((X150 @ X161) != (X148 @ id @ X161 @ id)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X202 : subst > term > subst > $o,X203 : term] : (? [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) = $true) & ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) != $true) & ($true = (X202 @ id @ X205 @ id))) | ? [X206 : subst > term > term] : (! [X210 : term] : (((X202 @ id @ X210 @ id) != $true) | ((X202 @ id @ (X206 @ id @ X210) @ id) = $true)) & ! [X207 : subst,X208 : subst,X209 : term] : ((X206 @ (comp @ X207 @ X208) @ (sub @ X209 @ X208)) = (sub @ (X206 @ X207 @ X209) @ X208)) & ($true != (X202 @ id @ (lam @ (X206 @ sh @ one)) @ id))) | ((X202 @ id @ X203 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (one = (d2term @ d_one)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (! [X299 : subst] : ((comp @ id @ X299) = X299) <=> (axidl = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction = $true) <=> ! [X36 : term,X37 : subst > term > subst > $o] : (? [X48 : subst > term > term] : (! [X49 : term] : (($true != (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))) & ((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) != $true) & ! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50))) | ($true = (X37 @ id @ X36 @ id)) | ? [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) = $true) & ((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) != $true)) | ? [X53 : term] : (($true = (var @ (sub @ X53 @ id))) & ((X37 @ id @ X53 @ id) != $true)) | ? [X38 : term,X39 : term] : (((X37 @ id @ X38 @ id) = $true) & ($true != (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) & ((X37 @ id @ X39 @ id) = $true)) | ? [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) != $true) & ($true = (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42))))) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((apinj1 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166)))) & ((axvarid = $true) <=> ! [X355 : term] : ((sub @ X355 @ id) = X355)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) <=> ! [X211 : term,X212 : term > $o,X213 : subst] : ? [X214 : term > $o] : ! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & ((pushprop_lem1v2 = $true) <=> ! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) != $true) | ? [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) != (X144 @ X146)) | ((X144 @ one) = $true))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X7 : term] : ((sub @ X7 @ id) != X7) | ! [X16 : term,X17 : subst > term > subst > $o] : (? [X18 : term] : (((X17 @ id @ X18 @ id) = $true) & ((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) != $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)) | ? [X19 : subst > term > term] : (! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) & ! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ($true != (X17 @ id @ X23 @ id))) & ($true != (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id)))) | ? [X8 : term,X9 : subst > term > subst > $o] : (! [X15 : term] : (((X9 @ id @ X15 @ id) != $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id))) & ($true != (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) & ! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ? [X14 : term] : (((X9 @ id @ (X10 @ id @ X14) @ id) != $true) & ((X9 @ id @ X14 @ id) = $true)) | ? [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) != (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13))))))) & (axapp = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (ulamvarind = $true) & ((? [X378 : subst > term > subst > $o,X379 : term] : (! [X380 : subst,X381 : term,X382 : subst,X383 : subst] : (((X378 @ X383 @ X381 @ (comp @ X382 @ X380)) != $true) | ((X378 @ (comp @ X383 @ X382) @ (sub @ X381 @ X382) @ X380) = $true)) & ! [X388 : term] : (((X378 @ id @ (sub @ X379 @ (push @ X388 @ id)) @ id) = $true) | ((X378 @ id @ X388 @ id) != $true)) & ((X378 @ id @ (lam @ X379) @ id) != $true) & ! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (($true = (X378 @ X386 @ X387 @ (comp @ X384 @ X385))) | ($true != (X378 @ (comp @ X386 @ X384) @ (sub @ X387 @ X384) @ X385))) & ! [X389 : subst > term > term] : (? [X390 : term] : (((X378 @ id @ X390 @ id) = $true) & ($true != (X378 @ id @ (X389 @ id @ X390) @ id))) | ? [X391 : term,X392 : subst,X393 : subst] : ((sub @ (X389 @ X393 @ X391) @ X392) != (X389 @ (comp @ X393 @ X392) @ (sub @ X391 @ X392))) | ((X378 @ id @ (lam @ (X389 @ sh @ one)) @ id) = $true))) | ? [X365 : term,X366 : term,X367 : subst > term > subst > $o] : (! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (($true != (X367 @ (comp @ X368 @ X369) @ (sub @ X371 @ X369) @ X370)) | ($true = (X367 @ X368 @ X371 @ (comp @ X369 @ X370)))) & ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (($true = (X367 @ (comp @ X373 @ X372) @ (sub @ X375 @ X372) @ X374)) | ($true != (X367 @ X373 @ X375 @ (comp @ X372 @ X374)))) & ! [X376 : term,X377 : term] : (((X367 @ id @ X376 @ id) != $true) | ((X367 @ id @ (ap @ (sub @ X376 @ id) @ X377) @ id) = $true) | ($true != (X367 @ id @ X377 @ id))) & ($true = (X367 @ id @ X366 @ id)) & ((X367 @ id @ X365 @ id) = $true) & ((X367 @ id @ (ap @ X365 @ X366) @ id) != $true)) | ? [X358 : term,X359 : term > $o] : (! [X362 : term] : (? [X363 : term] : (($true = (X359 @ X363)) & ((X359 @ (sub @ X362 @ (push @ X363 @ id))) != $true)) | ((X359 @ (lam @ X362)) = $true)) & ((X359 @ X358) != $true) & ! [X364 : term] : (($true = (X359 @ X364)) | ((var @ X364) != $true)) & ! [X360 : term,X361 : term] : (((X359 @ X360) != $true) | ((X359 @ X361) != $true) | ((X359 @ (ap @ X361 @ X360)) = $true))) | ! [X394 : term,X395 : subst > term > subst > $o] : (? [X405 : term,X406 : term] : (($true != (X395 @ id @ (ap @ (sub @ X406 @ id) @ X405) @ id)) & ((X395 @ id @ X406 @ id) = $true) & ((X395 @ id @ X405 @ id) = $true)) | ? [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (($true = (X395 @ (comp @ X408 @ X409) @ (sub @ X411 @ X409) @ X410)) & ((X395 @ X408 @ X411 @ (comp @ X409 @ X410)) != $true)) | ? [X400 : subst > term > term] : (((X395 @ id @ (lam @ (X400 @ sh @ one)) @ id) != $true) & ! [X401 : term] : (((X395 @ id @ X401 @ id) != $true) | ((X395 @ id @ (X400 @ id @ X401) @ id) = $true)) & ! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X404 @ X403) @ (sub @ X402 @ X403)) = (sub @ (X400 @ X404 @ X402) @ X403))) | ? [X407 : term] : (((var @ (sub @ X407 @ id)) = $true) & ((X395 @ id @ X407 @ id) != $true)) | ($true = (X395 @ id @ X394 @ id)) | ? [X396 : term,X397 : subst,X398 : subst,X399 : subst] : (((X395 @ X397 @ X396 @ (comp @ X399 @ X398)) = $true) & ((X395 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398) != $true)))) <=> (hoasinduction_lthm = $true)) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) <=> (apinj2 = $true)) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) <=> (substmonoid = $true)) & (! [X258 : subst > term > subst > $o,X259 : term] : (? [X269 : subst > term > term] : (! [X273 : term] : (((X258 @ id @ X273 @ id) != $true) | ((X258 @ id @ (X269 @ id @ X273) @ id) = $true)) & ! [X270 : subst,X271 : subst,X272 : term] : ((sub @ (X269 @ X270 @ X272) @ X271) = (X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271))) & ((X258 @ id @ (lam @ (X269 @ sh @ one)) @ id) != $true)) | ? [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (((X258 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X267) != $true) & ((X258 @ X265 @ X264 @ (comp @ X266 @ X267)) = $true)) | ? [X268 : term] : (((X258 @ id @ (sub @ X259 @ (push @ X268 @ id)) @ id) != $true) & ($true = (X258 @ id @ X268 @ id))) | ($true = (X258 @ id @ (lam @ X259) @ id)) | ? [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (($true = (X258 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) & ((X258 @ X260 @ X261 @ (comp @ X263 @ X262)) != $true))) <=> (hoasinduction_lem3 = $true)) & ((var @ (d2term @ d_one)) != $true) & (axclos = $true) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((induction2 = $true) <=> ! [X193 : term,X194 : term > $o] : (? [X195 : term] : (((var @ X195) = $true) & ((X194 @ X195) != $true)) | ? [X196 : term] : (($true != (X194 @ (lam @ X196))) & ! [X197 : term] : (((X194 @ (sub @ X196 @ (push @ X197 @ id))) = $true) | ($true != (X194 @ X197)))) | ((X194 @ X193) = $true) | ? [X198 : term,X199 : term] : (($true != (X194 @ (ap @ X198 @ X199))) & ((X194 @ X198) = $true) & ($true = (X194 @ X199))))) & (! [X180 : term,X181 : term,X182 : subst > term > subst > $o] : (($true != (X182 @ id @ X181 @ id)) | ((X182 @ id @ X180 @ id) != $true) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (((X182 @ X184 @ X185 @ (comp @ X183 @ X186)) = $true) & ((X182 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183) @ X186) != $true)) | ? [X191 : term,X192 : term] : (((X182 @ id @ X191 @ id) = $true) & ($true = (X182 @ id @ X192 @ id)) & ((X182 @ id @ (ap @ (sub @ X192 @ id) @ X191) @ id) != $true)) | ? [X187 : subst,X188 : term,X189 : subst,X190 : subst] : (((X182 @ (comp @ X189 @ X187) @ (sub @ X188 @ X187) @ X190) = $true) & ((X182 @ X189 @ X188 @ (comp @ X187 @ X190)) != $true)) | ((X182 @ id @ (ap @ X180 @ X181) @ id) = $true)) <=> (hoasinduction_lem2 = $true))),
% 21.29/4.27 inference(flattening,[status(thm)],[f11])).
% 21.29/4.27 thf(f11,plain,(
% 21.29/4.27 (axclos = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X36 : term,X37 : subst > term > subst > $o] : (? [X48 : subst > term > term] : (! [X49 : term] : (($true != (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))) & ((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) != $true) & ! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50))) | ($true = (X37 @ id @ X36 @ id)) | ? [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) = $true) & ((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) != $true)) | ? [X53 : term] : (($true = (var @ (sub @ X53 @ id))) & ((X37 @ id @ X53 @ id) != $true)) | ? [X38 : term,X39 : term] : (((X37 @ id @ X38 @ id) = $true) & ($true != (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) & ((X37 @ id @ X39 @ id) = $true)) | ? [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) != $true) & ($true = (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42))))) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X16 : term,X17 : subst > term > subst > $o] : (? [X18 : term] : (((X17 @ id @ X18 @ id) = $true) & ((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) != $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)) | ? [X19 : subst > term > term] : (! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) & ! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ($true != (X17 @ id @ X23 @ id))) & ($true != (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id)))) | ? [X8 : term,X9 : subst > term > subst > $o] : (! [X15 : term] : (((X9 @ id @ X15 @ id) != $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id))) & ($true != (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) & ! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ? [X14 : term] : (((X9 @ id @ (X10 @ id @ X14) @ id) != $true) & ((X9 @ id @ X14 @ id) = $true)) | ? [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) != (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13)))))) | ? [X7 : term] : ((sub @ X7 @ id) != X7))) & (lamnotvar = $true) & ((induction2 = $true) <=> ! [X193 : term,X194 : term > $o] : (? [X195 : term] : (((var @ X195) = $true) & ((X194 @ X195) != $true)) | ? [X196 : term] : (($true != (X194 @ (lam @ X196))) & ! [X197 : term] : (((X194 @ (sub @ X196 @ (push @ X197 @ id))) = $true) | ($true != (X194 @ X197)))) | ((X194 @ X193) = $true) | ? [X198 : term,X199 : term] : (($true != (X194 @ (ap @ X198 @ X199))) & ((X194 @ X198) = $true) & ($true = (X194 @ X199))))) & (ulamvar1 != $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (((((! [X463 : term,X464 : term > $o,X465 : subst] : (? [X469 : term,X470 : term] : (((X464 @ (ap @ X469 @ X470)) != $true) & ((X464 @ X470) = $true) & ((X464 @ X469) = $true)) | ? [X468 : term] : (((var @ X468) = $true) & ((X464 @ (sub @ X468 @ X465)) != $true)) | ? [X466 : term] : (($true != (X464 @ (lam @ X466))) & ! [X467 : term] : (((X464 @ X467) != $true) | ((X464 @ (sub @ X466 @ (push @ X467 @ id))) = $true))) | ($true = (X464 @ (sub @ X463 @ X465)))) | ? [X457 : term,X458 : term > $o] : (! [X461 : term] : (((X458 @ X461) = $true) | ((var @ X461) != $true)) & ! [X462 : term] : (((X458 @ X462) != $true) | ((X458 @ (lam @ X462)) = $true)) & ($true != (X458 @ X457)) & ! [X459 : term,X460 : term] : (((X458 @ (ap @ X460 @ X459)) = $true) | ((X458 @ X460) != $true) | ((X458 @ X459) != $true)))) | ? [X456 : subst] : ((comp @ X456 @ id) != X456)) | ? [X454 : term,X455 : subst] : ((comp @ sh @ (push @ X454 @ X455)) != X455)) | ? [X452 : term,X453 : subst] : ((sub @ one @ (push @ X452 @ X453)) != X452)) <=> (induction2lem_lthm = $true)) & (! [X27 : term] : ? [X28 : subst > term > term] : ! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X118 : subst > term > subst > $o] : ? [X119 : term > $o] : ! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120))) & (one = (d2term @ d_one)) & (hoasinduction_lem3a_gthm = $true) & (! [X180 : term,X181 : term,X182 : subst > term > subst > $o] : (($true != (X182 @ id @ X181 @ id)) | ((X182 @ id @ X180 @ id) != $true) | ? [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (((X182 @ X184 @ X185 @ (comp @ X183 @ X186)) = $true) & ((X182 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183) @ X186) != $true)) | ? [X191 : term,X192 : term] : (((X182 @ id @ X191 @ id) = $true) & ($true = (X182 @ id @ X192 @ id)) & ((X182 @ id @ (ap @ (sub @ X192 @ id) @ X191) @ id) != $true)) | ? [X187 : subst,X188 : term,X189 : subst,X190 : subst] : (((X182 @ (comp @ X189 @ X187) @ (sub @ X188 @ X187) @ X190) = $true) & ((X182 @ X189 @ X188 @ (comp @ X187 @ X190)) != $true)) | ((X182 @ id @ (ap @ X180 @ X181) @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & (! [X24 : subst > term > subst > $o] : ? [X25 : term > $o] : ! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & (axapp = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem1 = $true) & (axvarshift = $true) & ((((! [X477 : term,X478 : subst,X479 : subst > term > term,X480 : subst > term > term] : (? [X481 : subst,X482 : term,X483 : subst] : ((sub @ (X479 @ X483 @ X482) @ X481) != (X479 @ (comp @ X483 @ X481) @ (sub @ X482 @ X481))) | ((lam @ (X480 @ sh @ one)) != (lam @ (X479 @ sh @ one))) | ((X479 @ X478 @ X477) = (X480 @ X478 @ X477)) | ? [X484 : subst,X485 : term,X486 : subst] : ((X480 @ (comp @ X484 @ X486) @ (sub @ X485 @ X486)) != (sub @ (X480 @ X484 @ X485) @ X486))) | ? [X475 : term,X476 : term] : (((lam @ X475) = (lam @ X476)) & (X475 != X476))) | ? [X473 : term,X474 : subst] : ((comp @ sh @ (push @ X473 @ X474)) != X474)) | ? [X471 : term,X472 : subst] : ((sub @ one @ (push @ X471 @ X472)) != X471)) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X339 : term,X340 : subst > term > subst > $o] : (? [X342 : subst > term > term] : (($true != (X340 @ id @ (lam @ (X342 @ sh @ one)) @ id)) & ! [X343 : term,X344 : subst,X345 : subst] : ((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345)) = (sub @ (X342 @ X344 @ X343) @ X345)) & ! [X346 : term] : (((X340 @ id @ X346 @ id) != $true) | ($true = (X340 @ id @ (X342 @ id @ X346) @ id)))) | ? [X347 : subst,X348 : subst,X349 : subst,X350 : term] : (((X340 @ (comp @ X349 @ X347) @ (sub @ X350 @ X347) @ X348) != $true) & ((X340 @ X349 @ X350 @ (comp @ X347 @ X348)) = $true)) | ? [X341 : term] : (($true = (X340 @ id @ X341 @ id)) & ((X340 @ id @ (sub @ X339 @ (push @ X341 @ id)) @ id) != $true)) | ? [X351 : term,X352 : subst,X353 : subst,X354 : subst] : (($true != (X340 @ X353 @ X351 @ (comp @ X354 @ X352))) & ((X340 @ (comp @ X353 @ X354) @ (sub @ X351 @ X354) @ X352) = $true)) | ((X340 @ id @ (lam @ X339) @ id) = $true)) | ? [X331 : subst > term > subst > $o,X332 : term] : (((X331 @ id @ (lam @ (sub @ X332 @ (push @ one @ sh))) @ id) != $true) & ! [X338 : term] : (((X331 @ id @ X338 @ id) != $true) | ((X331 @ id @ (sub @ X332 @ (push @ X338 @ id)) @ id) = $true)) & ! [X333 : subst > term > term] : (? [X334 : term] : (((X331 @ id @ (X333 @ id @ X334) @ id) != $true) & ($true = (X331 @ id @ X334 @ id))) | ? [X335 : term,X336 : subst,X337 : subst] : ((X333 @ (comp @ X337 @ X336) @ (sub @ X335 @ X336)) != (sub @ (X333 @ X337 @ X335) @ X336)) | ((X331 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true)))) | ? [X330 : term] : ((sub @ X330 @ id) != X330))) & (induction2_gthm = $true) & (((! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503))))) | ? [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) != X501)) | ? [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) != X499)) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X440 : subst > term > subst > $o,X441 : term] : (? [X442 : subst > term > term] : (! [X443 : subst,X444 : subst,X445 : term] : ((X442 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444)) = (sub @ (X442 @ X443 @ X445) @ X444)) & ((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id) != $true) & ! [X446 : term] : (((X440 @ id @ (X442 @ id @ X446) @ id) = $true) | ($true != (X440 @ id @ X446 @ id)))) | ((X440 @ id @ (lam @ X441) @ id) = $true) | ? [X447 : term] : (((X440 @ id @ X447 @ id) = $true) & ((X440 @ id @ (sub @ X441 @ (push @ X447 @ id)) @ id) != $true)))) & (! [X280 : term,X281 : term,X282 : subst > term > subst > $o,X283 : term > $o] : (? [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (((X282 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290) @ X292) != $true) & ((X282 @ X289 @ X291 @ (comp @ X290 @ X292)) = $true)) | ? [X288 : term] : ((X283 @ X288) != (X282 @ id @ X288 @ id)) | ? [X293 : term,X294 : term] : (($true != (X282 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)) & ($true = (X282 @ id @ X293 @ id)) & ((X282 @ id @ X294 @ id) = $true)) | ((X283 @ X281) != $true) | ($true = (X283 @ (ap @ X280 @ X281))) | ((X283 @ X280) != $true) | ? [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true = (X282 @ (comp @ X285 @ X284) @ (sub @ X286 @ X284) @ X287)) & ((X282 @ X285 @ X286 @ (comp @ X284 @ X287)) != $true))) <=> (hoasinduction_lem2v2 = $true)) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & (substmonoid_gthm = $true) & (ulamvarsh = $true) & ((((! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)) | ? [X277 : subst] : ((comp @ X277 @ id) != X277)) | ? [X276 : subst] : ((comp @ id @ X276) != X276)) <=> (substmonoid_lthm = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ($true != (X177 @ X178)) | ? [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) != (X175 @ X179))) | ? [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) != X173))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((? [X147 : term] : ((sub @ X147 @ id) != X147) | ! [X148 : subst > term > subst > $o,X149 : term,X150 : term > $o] : (? [X151 : term] : (((X150 @ X151) = $true) & ((X150 @ (sub @ X149 @ (push @ X151 @ id))) != $true)) | ? [X162 : subst,X163 : subst,X164 : term,X165 : subst] : (($true = (X148 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163) @ X165)) & ((X148 @ X162 @ X164 @ (comp @ X163 @ X165)) != $true)) | ((X150 @ (lam @ X149)) = $true) | ? [X156 : subst > term > term] : (! [X157 : term] : (((X148 @ id @ X157 @ id) != $true) | ((X148 @ id @ (X156 @ id @ X157) @ id) = $true)) & ! [X158 : subst,X159 : term,X160 : subst] : ((sub @ (X156 @ X158 @ X159) @ X160) = (X156 @ (comp @ X158 @ X160) @ (sub @ X159 @ X160))) & ($true != (X148 @ id @ (lam @ (X156 @ sh @ one)) @ id))) | ? [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (((X148 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153) @ X155) != $true) & ($true = (X148 @ X154 @ X152 @ (comp @ X153 @ X155)))) | ? [X161 : term] : ((X150 @ X161) != (X148 @ id @ X161 @ id)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapnotvar_gthm = $true) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3aa = $true) <=> ! [X248 : subst > term > subst > $o,X249 : term] : (($true = (X248 @ id @ (lam @ (sub @ X249 @ (push @ one @ sh))) @ id)) | ? [X251 : subst > term > term] : (((X248 @ id @ (lam @ (X251 @ sh @ one)) @ id) != $true) & ! [X253 : term,X254 : subst,X255 : subst] : ((sub @ (X251 @ X255 @ X253) @ X254) = (X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254))) & ! [X252 : term] : (((X248 @ id @ (X251 @ id @ X252) @ id) = $true) | ($true != (X248 @ id @ X252 @ id)))) | ? [X250 : term] : (((X248 @ id @ (sub @ X249 @ (push @ X250 @ id)) @ id) != $true) & ($true = (X248 @ id @ X250 @ id))))) & (pushprop_lthm_orig = $true) & ((var @ (d2term @ d_one)) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X487 : term,X488 : subst > term > subst > $o] : (? [X489 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (sub @ X487 @ (push @ X489 @ id)) @ id) != $true)) | ? [X490 : subst > term > term,X491 : term] : (! [X496 : subst,X497 : subst,X498 : term] : ((X490 @ (comp @ X496 @ X497) @ (sub @ X498 @ X497)) = (sub @ X491 @ (push @ (sub @ X498 @ X497) @ (comp @ X496 @ X497)))) & ! [X495 : term] : (((X488 @ id @ (X490 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ! [X492 : subst,X493 : subst,X494 : term] : ((sub @ (X490 @ X492 @ X494) @ X493) = (sub @ (sub @ X491 @ (push @ X494 @ X492)) @ X493)) & ($true != (X488 @ id @ (lam @ (X490 @ sh @ one)) @ id))) | ($true = (X488 @ id @ (lam @ (sub @ X487 @ (push @ one @ sh))) @ id)))) & (induction2lem_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((? [X171 : term] : ((sub @ X171 @ id) != X171) | ! [X172 : term] : ((sub @ X172 @ id) = X172)) <=> (termmset_lthm = $true)) & (pushprop_lem1_gthm = $true) & (! [X129 : term] : ? [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) = (X130 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & ((! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))) | ? [X532 : term,X533 : term,X534 : term,X535 : term] : ((X532 != X535) & ((ap @ X533 @ X535) = (ap @ X534 @ X532)))) <=> (hoasapinj2_lthm = $true)) & (! [X258 : subst > term > subst > $o,X259 : term] : (? [X269 : subst > term > term] : (! [X273 : term] : (((X258 @ id @ X273 @ id) != $true) | ((X258 @ id @ (X269 @ id @ X273) @ id) = $true)) & ! [X270 : subst,X271 : subst,X272 : term] : ((sub @ (X269 @ X270 @ X272) @ X271) = (X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271))) & ((X258 @ id @ (lam @ (X269 @ sh @ one)) @ id) != $true)) | ? [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (((X258 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X267) != $true) & ((X258 @ X265 @ X264 @ (comp @ X266 @ X267)) = $true)) | ? [X268 : term] : (((X258 @ id @ (sub @ X259 @ (push @ X268 @ id)) @ id) != $true) & ($true = (X258 @ id @ X268 @ id))) | ($true = (X258 @ id @ (lam @ X259) @ id)) | ? [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (($true = (X258 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) & ((X258 @ X260 @ X261 @ (comp @ X263 @ X262)) != $true))) <=> (hoasinduction_lem3 = $true)) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslaminj_gthm = $true) & (axmap = $true) & ! [X256 : d_term,X257 : d_term] : ((X256 = X257) | ((d2term @ X256) != (d2term @ X257))) & ((pushprop_lem0 = $true) <=> ! [X137 : subst,X138 : term,X139 : term > $o] : ? [X140 : term > $o] : ! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141))) & ! [X35 : d_subst] : (d_id = X35) & ((hoaslamnotap = $true) <=> ! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ? [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) != (sub @ (X95 @ X98 @ X97) @ X96)))) & ((hoasinduction_lthm = $true) <=> (((! [X394 : term,X395 : subst > term > subst > $o] : (? [X405 : term,X406 : term] : (($true != (X395 @ id @ (ap @ (sub @ X406 @ id) @ X405) @ id)) & ((X395 @ id @ X406 @ id) = $true) & ((X395 @ id @ X405 @ id) = $true)) | ? [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (($true = (X395 @ (comp @ X408 @ X409) @ (sub @ X411 @ X409) @ X410)) & ((X395 @ X408 @ X411 @ (comp @ X409 @ X410)) != $true)) | ? [X400 : subst > term > term] : (((X395 @ id @ (lam @ (X400 @ sh @ one)) @ id) != $true) & ! [X401 : term] : (((X395 @ id @ X401 @ id) != $true) | ((X395 @ id @ (X400 @ id @ X401) @ id) = $true)) & ! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X404 @ X403) @ (sub @ X402 @ X403)) = (sub @ (X400 @ X404 @ X402) @ X403))) | ? [X407 : term] : (((var @ (sub @ X407 @ id)) = $true) & ((X395 @ id @ X407 @ id) != $true)) | ($true = (X395 @ id @ X394 @ id)) | ? [X396 : term,X397 : subst,X398 : subst,X399 : subst] : (((X395 @ X397 @ X396 @ (comp @ X399 @ X398)) = $true) & ((X395 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398) != $true))) | ? [X378 : subst > term > subst > $o,X379 : term] : (! [X380 : subst,X381 : term,X382 : subst,X383 : subst] : (((X378 @ X383 @ X381 @ (comp @ X382 @ X380)) != $true) | ((X378 @ (comp @ X383 @ X382) @ (sub @ X381 @ X382) @ X380) = $true)) & ! [X388 : term] : (((X378 @ id @ (sub @ X379 @ (push @ X388 @ id)) @ id) = $true) | ((X378 @ id @ X388 @ id) != $true)) & ((X378 @ id @ (lam @ X379) @ id) != $true) & ! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (($true = (X378 @ X386 @ X387 @ (comp @ X384 @ X385))) | ($true != (X378 @ (comp @ X386 @ X384) @ (sub @ X387 @ X384) @ X385))) & ! [X389 : subst > term > term] : (? [X390 : term] : (((X378 @ id @ X390 @ id) = $true) & ($true != (X378 @ id @ (X389 @ id @ X390) @ id))) | ? [X391 : term,X392 : subst,X393 : subst] : ((sub @ (X389 @ X393 @ X391) @ X392) != (X389 @ (comp @ X393 @ X392) @ (sub @ X391 @ X392))) | ((X378 @ id @ (lam @ (X389 @ sh @ one)) @ id) = $true)))) | ? [X365 : term,X366 : term,X367 : subst > term > subst > $o] : (! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (($true != (X367 @ (comp @ X368 @ X369) @ (sub @ X371 @ X369) @ X370)) | ($true = (X367 @ X368 @ X371 @ (comp @ X369 @ X370)))) & ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (($true = (X367 @ (comp @ X373 @ X372) @ (sub @ X375 @ X372) @ X374)) | ($true != (X367 @ X373 @ X375 @ (comp @ X372 @ X374)))) & ! [X376 : term,X377 : term] : (((X367 @ id @ X376 @ id) != $true) | ((X367 @ id @ (ap @ (sub @ X376 @ id) @ X377) @ id) = $true) | ($true != (X367 @ id @ X377 @ id))) & ($true = (X367 @ id @ X366 @ id)) & ((X367 @ id @ X365 @ id) = $true) & ((X367 @ id @ (ap @ X365 @ X366) @ id) != $true))) | ? [X358 : term,X359 : term > $o] : (! [X362 : term] : (? [X363 : term] : (($true = (X359 @ X363)) & ((X359 @ (sub @ X362 @ (push @ X363 @ id))) != $true)) | ((X359 @ (lam @ X362)) = $true)) & ((X359 @ X358) != $true) & ! [X364 : term] : (($true = (X359 @ X364)) | ((var @ X364) != $true)) & ! [X360 : term,X361 : term] : (((X359 @ X360) != $true) | ((X359 @ X361) != $true) | ((X359 @ (ap @ X361 @ X360)) = $true))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & ((induction2_lthm = $true) <=> ((! [X525 : term > $o,X526 : term] : (? [X529 : term] : (((var @ X529) = $true) & ((X525 @ X529) != $true)) | ? [X527 : term] : (((X525 @ (lam @ X527)) != $true) & ! [X528 : term] : (((X525 @ X528) != $true) | ((X525 @ (sub @ X527 @ (push @ X528 @ id))) = $true))) | ($true = (X525 @ X526)) | ? [X530 : term,X531 : term] : (($true = (X525 @ X530)) & ((X525 @ (ap @ X530 @ X531)) != $true) & ($true = (X525 @ X531)))) | ? [X517 : term > $o,X518 : subst,X519 : term] : (! [X521 : term] : (? [X522 : term] : (((X517 @ (sub @ X521 @ (push @ X522 @ id))) != $true) & ($true = (X517 @ X522))) | ($true = (X517 @ (lam @ X521)))) & ($true != (X517 @ (sub @ X519 @ X518))) & ! [X523 : term,X524 : term] : (((X517 @ (ap @ X523 @ X524)) = $true) | ((X517 @ X524) != $true) | ((X517 @ X523) != $true)) & ! [X520 : term] : (($true = (X517 @ (sub @ X520 @ X518))) | ((var @ X520) != $true)))) | ? [X516 : term] : ((sub @ X516 @ id) != X516))) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) != (d2subst @ X117)) | (X116 = X117)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X211 : term,X212 : term > $o,X213 : subst] : ? [X214 : term > $o] : ! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X200 : term] : ? [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) = (X201 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X131 : term > $o,X132 : term] : (? [X133 : term,X134 : term] : (((X131 @ X134) = $true) & ((X131 @ X133) = $true) & ((X131 @ (ap @ X133 @ X134)) != $true)) | ? [X136 : term] : (($true = (var @ X136)) & ($true != (X131 @ X136))) | ? [X135 : term] : (((X131 @ (lam @ X135)) != $true) & ($true = (X131 @ X135))) | ((X131 @ X132) = $true)) <=> (induction = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) <=> (hoasapinj1 = $true)) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) <=> (substmonoid = $true)) & (((((! [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ X322 @ id) = $true) | ? [X328 : term,X329 : term] : (((X321 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id) != $true) & ((X321 @ id @ X328 @ id) = $true) & ((X321 @ id @ X329 @ id) = $true)) | ? [X323 : subst > term > term] : (! [X324 : term] : (($true = (X321 @ id @ (X323 @ id @ X324) @ id)) | ((X321 @ id @ X324 @ id) != $true)) & ! [X325 : subst,X326 : subst,X327 : term] : ((sub @ (X323 @ X326 @ X327) @ X325) = (X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325))) & ((X321 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true))) | ? [X311 : term > $o,X312 : term,X313 : subst > term > subst > $o] : (! [X314 : term] : ((X311 @ X314) = (X313 @ id @ X314 @ id)) & ((X311 @ (lam @ X312)) != $true) & ! [X315 : term] : (((X311 @ (sub @ X312 @ (push @ X315 @ id))) = $true) | ((X311 @ X315) != $true)) & ! [X316 : subst > term > term] : (? [X317 : term] : (((X313 @ id @ X317 @ id) = $true) & ((X313 @ id @ (X316 @ id @ X317) @ id) != $true)) | ? [X318 : term,X319 : subst,X320 : subst] : ((sub @ (X316 @ X320 @ X318) @ X319) != (X316 @ (comp @ X320 @ X319) @ (sub @ X318 @ X319))) | ($true = (X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))))) | ? [X310 : term] : ((sub @ X310 @ id) != X310)) | ? [X303 : term > $o,X304 : term] : (((X303 @ X304) != $true) & ! [X307 : term] : (((X303 @ X307) = $true) | ($true != (var @ X307))) & ! [X305 : term,X306 : term] : (((X303 @ (ap @ X305 @ X306)) = $true) | ($true != (X303 @ X305)) | ((X303 @ X306) != $true)) & ! [X308 : term] : (? [X309 : term] : (((X303 @ X309) = $true) & ((X303 @ (sub @ X308 @ (push @ X309 @ id))) != $true)) | ($true = (X303 @ (lam @ X308)))))) | ? [X300 : subst > term > subst > $o] : ! [X301 : term > $o] : ? [X302 : term] : ((X301 @ X302) != (X300 @ id @ X302 @ id))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X508 : subst,X509 : term,X510 : term > $o] : (((X510 @ (sub @ X509 @ X508)) = $true) | ? [X512 : term,X513 : term] : (($true != (X510 @ (ap @ X513 @ X512))) & ((X510 @ X513) = $true) & ((X510 @ X512) = $true)) | ? [X514 : term] : (! [X515 : term] : (((X510 @ X515) != $true) | ((X510 @ (sub @ X514 @ (push @ X515 @ id))) = $true)) & ((X510 @ (lam @ X514)) != $true)) | ? [X511 : term] : (((X510 @ (sub @ X511 @ X508)) != $true) & ((var @ X511) = $true))) <=> (induction2lem = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))) | ? [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) = (ap @ X107 @ X109)) & (X107 != X108))) | ? [X105 : term] : ((sub @ X105 @ id) != X105)) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (lamnotap != $true) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & ((apinj1 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X412 : term,X413 : term > $o,X414 : subst > term > subst > $o] : (? [X421 : term] : ((X413 @ X421) != (X414 @ id @ X421 @ id)) | ? [X415 : term] : (($true != (X413 @ (sub @ X412 @ (push @ X415 @ id)))) & ($true = (X413 @ X415))) | ? [X416 : subst > term > term] : (((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) != $true) & ! [X417 : term,X418 : subst,X419 : subst] : ((sub @ (X416 @ X419 @ X417) @ X418) = (X416 @ (comp @ X419 @ X418) @ (sub @ X417 @ X418))) & ! [X420 : term] : (((X414 @ id @ X420 @ id) != $true) | ((X414 @ id @ (X416 @ id @ X420) @ id) = $true))) | ($true = (X413 @ (lam @ X412))))) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & ((pushprop_lem1v2 = $true) <=> ! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X145 @ X143) != $true) | ? [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) != (X144 @ X146)) | ((X144 @ one) = $true))) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & (hoasinduction_lem1_lthm = $true) & ((shinj = $true) <=> ! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247))) & ((hoasinduction_lem3v2 = $true) <=> ! [X422 : subst > term > subst > $o,X423 : term,X424 : term > $o] : (? [X439 : term] : (((X424 @ X439) = $true) & ((X424 @ (sub @ X423 @ (push @ X439 @ id))) != $true)) | ? [X430 : subst,X431 : term,X432 : subst,X433 : subst] : (((X422 @ (comp @ X433 @ X432) @ (sub @ X431 @ X432) @ X430) != $true) & ((X422 @ X433 @ X431 @ (comp @ X432 @ X430)) = $true)) | ((X424 @ (lam @ X423)) = $true) | ? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X422 @ (comp @ X436 @ X437) @ (sub @ X434 @ X437) @ X435) = $true) & ($true != (X422 @ X436 @ X434 @ (comp @ X437 @ X435)))) | ? [X438 : term] : ((X422 @ id @ X438 @ id) != (X424 @ X438)) | ? [X425 : subst > term > term] : (((X422 @ id @ (lam @ (X425 @ sh @ one)) @ id) != $true) & ! [X429 : term] : (((X422 @ id @ X429 @ id) != $true) | ((X422 @ id @ (X425 @ id @ X429) @ id) = $true)) & ! [X426 : subst,X427 : term,X428 : subst] : ((X425 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426)) = (sub @ (X425 @ X428 @ X427) @ X426))))) & (! [X299 : subst] : ((comp @ id @ X299) = X299) <=> (axidl = $true)) & (hoaslamnotvar = $true) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) <=> (apinj2 = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & (pushprop_lem0_gthm = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & ((hoaslaminj = $true) <=> ! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (? [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) != (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ? [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) != (sub @ (X218 @ X226 @ X225) @ X224)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one))) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220)))) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X232 : subst > term > subst > $o,X233 : term > $o,X234 : term] : (? [X236 : term] : (((X233 @ (sub @ X234 @ (push @ X236 @ id))) != $true) & ((X233 @ X236) = $true)) | ((X233 @ (lam @ X234)) = $true) | ? [X235 : term] : ((X232 @ id @ X235 @ id) != (X233 @ X235)) | ? [X237 : subst > term > term] : (! [X239 : term,X240 : subst,X241 : subst] : ((sub @ (X237 @ X241 @ X239) @ X240) = (X237 @ (comp @ X241 @ X240) @ (sub @ X239 @ X240))) & ! [X238 : term] : (($true != (X232 @ id @ X238 @ id)) | ($true = (X232 @ id @ (X237 @ id @ X238) @ id))) & ((X232 @ id @ (lam @ (X237 @ sh @ one)) @ id) != $true))) | ? [X231 : term] : ((sub @ X231 @ id) != X231)) | ? [X227 : term] : ! [X228 : subst > term > term] : ? [X229 : subst,X230 : term] : ((sub @ X227 @ (push @ X230 @ X229)) != (X228 @ X229 @ X230)))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X75 : subst > term > subst > $o,X76 : term] : (((X75 @ id @ X76 @ id) = $true) | ? [X82 : subst > term > term] : (((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) != $true) & ! [X83 : term] : (((X75 @ id @ (X82 @ id @ X83) @ id) = $true) | ((X75 @ id @ X83 @ id) != $true)) & ! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ? [X91 : term,X92 : term] : (((X75 @ id @ X91 @ id) = $true) & ((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) != $true) & ($true = (X75 @ id @ X92 @ id))) | ? [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) != $true) & ((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) = $true)) | ? [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) != $true) & ((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) = $true)) | ? [X77 : term] : (((X75 @ id @ X77 @ id) != $true) & ((var @ (sub @ X77 @ id)) = $true))) | ? [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (($true != (X65 @ (lam @ X66))) & ! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ($true != (X65 @ X73))) & ! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74)) & ! [X68 : subst > term > term] : (? [X69 : term] : (((X67 @ id @ X69 @ id) = $true) & ((X67 @ id @ (X68 @ id @ X69) @ id) != $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true) | ? [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) != (sub @ (X68 @ X72 @ X70) @ X71))))) | ? [X64 : term] : ((sub @ X64 @ id) != X64)) | ? [X57 : term,X58 : term > $o] : (! [X61 : term] : (($true = (X58 @ (lam @ X61))) | ? [X62 : term] : (($true = (X58 @ X62)) & ((X58 @ (sub @ X61 @ (push @ X62 @ id))) != $true))) & ! [X59 : term,X60 : term] : (((X58 @ X60) != $true) | ((X58 @ (ap @ X59 @ X60)) = $true) | ($true != (X58 @ X59))) & ! [X63 : term] : (((var @ X63) != $true) | ((X58 @ X63) = $true)) & ((X58 @ X57) != $true))) | ? [X54 : subst > term > subst > $o] : ! [X55 : term > $o] : ? [X56 : term] : ((X54 @ id @ X56 @ id) != (X55 @ X56)))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X216 : term] : ((sub @ X216 @ id) = X216) <=> (termmset = $true)) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & (apnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((axvarid = $true) <=> ! [X355 : term] : ((sub @ X355 @ id) = X355)) & (pushprop_lthm = $true) & (! [X202 : subst > term > subst > $o,X203 : term] : (? [X204 : term,X205 : term] : (((X202 @ id @ X204 @ id) = $true) & ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) != $true) & ($true = (X202 @ id @ X205 @ id))) | ? [X206 : subst > term > term] : (! [X210 : term] : (((X202 @ id @ X210 @ id) != $true) | ((X202 @ id @ (X206 @ id @ X210) @ id) = $true)) & ! [X207 : subst,X208 : subst,X209 : term] : ((X206 @ (comp @ X207 @ X208) @ (sub @ X209 @ X208)) = (sub @ (X206 @ X207 @ X209) @ X208)) & ($true != (X202 @ id @ (lam @ (X206 @ sh @ one)) @ id))) | ((X202 @ id @ X203 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((d2subst @ d_id) = sh) & ! [X170 : d_term] : (d_one = X170) & (! [X448 : term] : ? [X449 : subst > term > term] : ! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) <=> (hoasinduction_lem3v2_f = $true)) & (ulamvarind = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X121 : subst > term > subst > $o,X122 : term] : (((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ? [X123 : subst > term > term] : (! [X127 : term] : (($true = (X121 @ id @ (X123 @ id @ X127) @ id)) | ((X121 @ id @ X127 @ id) != $true)) & ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) != $true) & ! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124))) | ? [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) != $true) & ($true = (X121 @ id @ X128 @ id)))))),
% 21.29/4.27 inference(ennf_transformation,[status(thm)],[f10])).
% 21.29/4.27 thf(f10,plain,(
% 21.29/4.27 (axclos = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_gthm = $true) & (! [X36 : term,X37 : subst > term > subst > $o] : (($true = (X37 @ id @ X36 @ id)) | ~! [X38 : term,X39 : term] : (((X37 @ id @ X39 @ id) != $true) | ($true = (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) | ((X37 @ id @ X38 @ id) != $true)) | ~! [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) = $true) | ((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) != $true)) | ~! [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) = $true) | ($true != (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42))) | ~! [X53 : term] : (($true != (var @ (sub @ X53 @ id))) | ((X37 @ id @ X53 @ id) = $true)) | ~! [X48 : subst > term > term] : (((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) = $true) | ~! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50)) | ~! [X49 : term] : (($true != (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))))) <=> (hoasinduction = $true)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X7 : term] : ((sub @ X7 @ id) = X7) => (! [X8 : term,X9 : subst > term > subst > $o] : (($true = (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) | ~! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ~! [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) = (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13))) | ~! [X14 : term] : (((X9 @ id @ X14 @ id) != $true) | ((X9 @ id @ (X10 @ id @ X14) @ id) = $true))) | ~! [X15 : term] : (((X9 @ id @ X15 @ id) != $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id)))) => ! [X16 : term,X17 : subst > term > subst > $o] : (~! [X19 : subst > term > term] : (~! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) | ($true = (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id)) | ~! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ($true != (X17 @ id @ X23 @ id)))) | ~! [X18 : term] : (((X17 @ id @ X18 @ id) != $true) | ((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) = $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)))))) & (lamnotvar = $true) & ((induction2 = $true) <=> ! [X193 : term,X194 : term > $o] : (~! [X196 : term] : (~! [X197 : term] : (((X194 @ (sub @ X196 @ (push @ X197 @ id))) = $true) | ($true != (X194 @ X197))) | ($true = (X194 @ (lam @ X196)))) | ((X194 @ X193) = $true) | ~! [X198 : term,X199 : term] : (((X194 @ X198) != $true) | ($true != (X194 @ X199)) | ($true = (X194 @ (ap @ X198 @ X199)))) | ~! [X195 : term] : (((X194 @ X195) = $true) | ((var @ X195) != $true)))) & (ulamvar1 != $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((! [X452 : term,X453 : subst] : ((sub @ one @ (push @ X452 @ X453)) = X452) => (! [X454 : term,X455 : subst] : ((comp @ sh @ (push @ X454 @ X455)) = X455) => (! [X456 : subst] : ((comp @ X456 @ id) = X456) => (! [X457 : term,X458 : term > $o] : (~! [X459 : term,X460 : term] : (((X458 @ (ap @ X460 @ X459)) = $true) | ((X458 @ X460) != $true) | ((X458 @ X459) != $true)) | ~! [X462 : term] : (((X458 @ X462) != $true) | ((X458 @ (lam @ X462)) = $true)) | ~! [X461 : term] : (((X458 @ X461) = $true) | ((var @ X461) != $true)) | ($true = (X458 @ X457))) => ! [X463 : term,X464 : term > $o,X465 : subst] : (~! [X466 : term] : (($true = (X464 @ (lam @ X466))) | ~! [X467 : term] : (((X464 @ X467) != $true) | ((X464 @ (sub @ X466 @ (push @ X467 @ id))) = $true))) | ($true = (X464 @ (sub @ X463 @ X465))) | ~! [X469 : term,X470 : term] : (((X464 @ (ap @ X469 @ X470)) = $true) | ((X464 @ X469) != $true) | ((X464 @ X470) != $true)) | ~! [X468 : term] : (((X464 @ (sub @ X468 @ X465)) = $true) | ((var @ X468) != $true))))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X27 : term] : ~! [X28 : subst > term > term] : ~! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29)))) & (pushprop_lem2v2 = $true) & (! [X118 : subst > term > subst > $o] : ~! [X119 : term > $o] : ~! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) <=> (hoasinduction_lem0 = $true)) & (one = (d2term @ d_one)) & (hoasinduction_lem3a_gthm = $true) & (! [X180 : term,X181 : term,X182 : subst > term > subst > $o] : (((X182 @ id @ (ap @ X180 @ X181) @ id) = $true) | ((X182 @ id @ X180 @ id) != $true) | ($true != (X182 @ id @ X181 @ id)) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (((X182 @ X184 @ X185 @ (comp @ X183 @ X186)) != $true) | ((X182 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183) @ X186) = $true)) | ~! [X191 : term,X192 : term] : (((X182 @ id @ (ap @ (sub @ X192 @ id) @ X191) @ id) = $true) | ((X182 @ id @ X191 @ id) != $true) | ($true != (X182 @ id @ X192 @ id))) | ~! [X187 : subst,X188 : term,X189 : subst,X190 : subst] : (((X182 @ X189 @ X188 @ (comp @ X187 @ X190)) = $true) | ((X182 @ (comp @ X189 @ X187) @ (sub @ X188 @ X187) @ X190) != $true))) <=> (hoasinduction_lem2 = $true)) & (! [X24 : subst > term > subst > $o] : ~! [X25 : term > $o] : ~! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & (axapp = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem1 = $true) & (axvarshift = $true) & ((! [X471 : term,X472 : subst] : ((sub @ one @ (push @ X471 @ X472)) = X471) => (! [X473 : term,X474 : subst] : ((comp @ sh @ (push @ X473 @ X474)) = X474) => (! [X475 : term,X476 : term] : (((lam @ X475) != (lam @ X476)) | (X475 = X476)) => ! [X477 : term,X478 : subst,X479 : subst > term > term,X480 : subst > term > term] : (~! [X481 : subst,X482 : term,X483 : subst] : ((sub @ (X479 @ X483 @ X482) @ X481) = (X479 @ (comp @ X483 @ X481) @ (sub @ X482 @ X481))) | ~! [X484 : subst,X485 : term,X486 : subst] : ((X480 @ (comp @ X484 @ X486) @ (sub @ X485 @ X486)) = (sub @ (X480 @ X484 @ X485) @ X486)) | ((lam @ (X480 @ sh @ one)) != (lam @ (X479 @ sh @ one))) | ((X479 @ X478 @ X477) = (X480 @ X478 @ X477)))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X330 : term] : ((sub @ X330 @ id) = X330) => (! [X331 : subst > term > subst > $o,X332 : term] : (~! [X333 : subst > term > term] : (~! [X335 : term,X336 : subst,X337 : subst] : ((X333 @ (comp @ X337 @ X336) @ (sub @ X335 @ X336)) = (sub @ (X333 @ X337 @ X335) @ X336)) | ((X331 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true) | ~! [X334 : term] : (($true != (X331 @ id @ X334 @ id)) | ((X331 @ id @ (X333 @ id @ X334) @ id) = $true))) | ((X331 @ id @ (lam @ (sub @ X332 @ (push @ one @ sh))) @ id) = $true) | ~! [X338 : term] : (((X331 @ id @ X338 @ id) != $true) | ((X331 @ id @ (sub @ X332 @ (push @ X338 @ id)) @ id) = $true))) => ! [X339 : term,X340 : subst > term > subst > $o] : (~! [X347 : subst,X348 : subst,X349 : subst,X350 : term] : (((X340 @ X349 @ X350 @ (comp @ X347 @ X348)) != $true) | ((X340 @ (comp @ X349 @ X347) @ (sub @ X350 @ X347) @ X348) = $true)) | ((X340 @ id @ (lam @ X339) @ id) = $true) | ~! [X351 : term,X352 : subst,X353 : subst,X354 : subst] : (((X340 @ (comp @ X353 @ X354) @ (sub @ X351 @ X354) @ X352) != $true) | ($true = (X340 @ X353 @ X351 @ (comp @ X354 @ X352)))) | ~! [X341 : term] : (($true != (X340 @ id @ X341 @ id)) | ((X340 @ id @ (sub @ X339 @ (push @ X341 @ id)) @ id) = $true)) | ~! [X342 : subst > term > term] : (~! [X343 : term,X344 : subst,X345 : subst] : ((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345)) = (sub @ (X342 @ X344 @ X343) @ X345)) | ($true = (X340 @ id @ (lam @ (X342 @ sh @ one)) @ id)) | ~! [X346 : term] : (((X340 @ id @ X346 @ id) != $true) | ($true = (X340 @ id @ (X342 @ id @ X346) @ id)))))))) & (induction2_gthm = $true) & ((! [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) = X499) => (! [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) = X501) => ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (((X507 @ X506) != $true) | ($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503))))))) <=> (pushprop_lem1_lthm = $true)) & (! [X440 : subst > term > subst > $o,X441 : term] : (((X440 @ id @ (lam @ X441) @ id) = $true) | ~! [X442 : subst > term > term] : (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id) = $true) | ~! [X446 : term] : (((X440 @ id @ (X442 @ id @ X446) @ id) = $true) | ($true != (X440 @ id @ X446 @ id))) | ~! [X443 : subst,X444 : subst,X445 : term] : ((X442 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444)) = (sub @ (X442 @ X443 @ X445) @ X444))) | ~! [X447 : term] : (((X440 @ id @ X447 @ id) != $true) | ((X440 @ id @ (sub @ X441 @ (push @ X447 @ id)) @ id) = $true))) <=> (hoasinduction_lem3a = $true)) & (! [X280 : term,X281 : term,X282 : subst > term > subst > $o,X283 : term > $o] : (~! [X288 : term] : ((X283 @ X288) = (X282 @ id @ X288 @ id)) | ($true = (X283 @ (ap @ X280 @ X281))) | ((X283 @ X281) != $true) | ((X283 @ X280) != $true) | ~! [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (((X282 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290) @ X292) = $true) | ((X282 @ X289 @ X291 @ (comp @ X290 @ X292)) != $true)) | ~! [X293 : term,X294 : term] : (((X282 @ id @ X294 @ id) != $true) | ($true != (X282 @ id @ X293 @ id)) | ($true = (X282 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))) | ~! [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (($true != (X282 @ (comp @ X285 @ X284) @ (sub @ X286 @ X284) @ X287)) | ((X282 @ X285 @ X286 @ (comp @ X284 @ X287)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & (substmonoid_gthm = $true) & (ulamvarsh = $true) & ((! [X276 : subst] : ((comp @ id @ X276) = X276) => (! [X277 : subst] : ((comp @ X277 @ id) = X277) => (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)))) <=> (substmonoid_lthm = $true)) & ((! [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) = X173) => ! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ~! [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) = (X175 @ X179)) | ($true != (X177 @ X178)))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((! [X147 : term] : ((sub @ X147 @ id) = X147) => ! [X148 : subst > term > subst > $o,X149 : term,X150 : term > $o] : (~! [X161 : term] : ((X150 @ X161) = (X148 @ id @ X161 @ id)) | ~! [X162 : subst,X163 : subst,X164 : term,X165 : subst] : (($true != (X148 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163) @ X165)) | ((X148 @ X162 @ X164 @ (comp @ X163 @ X165)) = $true)) | ~! [X156 : subst > term > term] : (~! [X157 : term] : (((X148 @ id @ X157 @ id) != $true) | ((X148 @ id @ (X156 @ id @ X157) @ id) = $true)) | ($true = (X148 @ id @ (lam @ (X156 @ sh @ one)) @ id)) | ~! [X158 : subst,X159 : term,X160 : subst] : ((sub @ (X156 @ X158 @ X159) @ X160) = (X156 @ (comp @ X158 @ X160) @ (sub @ X159 @ X160)))) | ~! [X151 : term] : (((X150 @ X151) != $true) | ((X150 @ (sub @ X149 @ (push @ X151 @ id))) = $true)) | ((X150 @ (lam @ X149)) = $true) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (((X148 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153) @ X155) = $true) | ($true != (X148 @ X154 @ X152 @ (comp @ X153 @ X155)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapnotvar_gthm = $true) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3aa = $true) <=> ! [X248 : subst > term > subst > $o,X249 : term] : (~! [X251 : subst > term > term] : (((X248 @ id @ (lam @ (X251 @ sh @ one)) @ id) = $true) | ~! [X252 : term] : (((X248 @ id @ (X251 @ id @ X252) @ id) = $true) | ($true != (X248 @ id @ X252 @ id))) | ~! [X253 : term,X254 : subst,X255 : subst] : ((sub @ (X251 @ X255 @ X253) @ X254) = (X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254)))) | ($true = (X248 @ id @ (lam @ (sub @ X249 @ (push @ one @ sh))) @ id)) | ~! [X250 : term] : (((X248 @ id @ (sub @ X249 @ (push @ X250 @ id)) @ id) = $true) | ($true != (X248 @ id @ X250 @ id))))) & (pushprop_lthm_orig = $true) & ((var @ (d2term @ d_one)) != $true) & (! [X487 : term,X488 : subst > term > subst > $o] : (~! [X489 : term] : (($true != (X488 @ id @ X489 @ id)) | ((X488 @ id @ (sub @ X487 @ (push @ X489 @ id)) @ id) = $true)) | ($true = (X488 @ id @ (lam @ (sub @ X487 @ (push @ one @ sh))) @ id)) | ~! [X490 : subst > term > term,X491 : term] : (~! [X496 : subst,X497 : subst,X498 : term] : ((X490 @ (comp @ X496 @ X497) @ (sub @ X498 @ X497)) = (sub @ X491 @ (push @ (sub @ X498 @ X497) @ (comp @ X496 @ X497)))) | ~! [X492 : subst,X493 : subst,X494 : term] : ((sub @ (X490 @ X492 @ X494) @ X493) = (sub @ (sub @ X491 @ (push @ X494 @ X492)) @ X493)) | ~! [X495 : term] : (((X488 @ id @ (X490 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) | ($true = (X488 @ id @ (lam @ (X490 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (induction2lem_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((! [X171 : term] : ((sub @ X171 @ id) = X171) => ! [X172 : term] : ((sub @ X172 @ id) = X172)) <=> (termmset_lthm = $true)) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X129 : term] : ~! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one))) & (pushprop_lem1v2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X533 @ X535) != (ap @ X534 @ X532)) | (X532 = X535)) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))))) & (! [X258 : subst > term > subst > $o,X259 : term] : (~! [X268 : term] : (($true != (X258 @ id @ X268 @ id)) | ((X258 @ id @ (sub @ X259 @ (push @ X268 @ id)) @ id) = $true)) | ($true = (X258 @ id @ (lam @ X259) @ id)) | ~! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (((X258 @ X260 @ X261 @ (comp @ X263 @ X262)) = $true) | ($true != (X258 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262))) | ~! [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (((X258 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X267) = $true) | ((X258 @ X265 @ X264 @ (comp @ X266 @ X267)) != $true)) | ~! [X269 : subst > term > term] : (~! [X273 : term] : (((X258 @ id @ X273 @ id) != $true) | ((X258 @ id @ (X269 @ id @ X273) @ id) = $true)) | ~! [X270 : subst,X271 : subst,X272 : term] : ((sub @ (X269 @ X270 @ X272) @ X271) = (X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271))) | ((X258 @ id @ (lam @ (X269 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X3 @ X2) != $true) | ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslaminj_gthm = $true) & (axmap = $true) & ! [X256 : d_term,X257 : d_term] : (((d2term @ X256) = (d2term @ X257)) => (X256 = X257)) & (! [X137 : subst,X138 : term,X139 : term > $o] : ~! [X140 : term > $o] : ~! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) <=> (pushprop_lem0 = $true)) & ! [X35 : d_subst] : (d_id = X35) & (! [X93 : term,X94 : term,X95 : subst > term > term] : (~! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)) | ((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lthm = $true) <=> (! [X358 : term,X359 : term > $o] : (~! [X364 : term] : (($true = (X359 @ X364)) | ((var @ X364) != $true)) | ~! [X360 : term,X361 : term] : (((X359 @ X360) != $true) | ((X359 @ X361) != $true) | ((X359 @ (ap @ X361 @ X360)) = $true)) | ((X359 @ X358) = $true) | ~! [X362 : term] : (~! [X363 : term] : (($true != (X359 @ X363)) | ((X359 @ (sub @ X362 @ (push @ X363 @ id))) = $true)) | ((X359 @ (lam @ X362)) = $true))) => (! [X365 : term,X366 : term,X367 : subst > term > subst > $o] : (~! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (($true != (X367 @ (comp @ X368 @ X369) @ (sub @ X371 @ X369) @ X370)) | ($true = (X367 @ X368 @ X371 @ (comp @ X369 @ X370)))) | ((X367 @ id @ X365 @ id) != $true) | ((X367 @ id @ (ap @ X365 @ X366) @ id) = $true) | ~! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (($true = (X367 @ (comp @ X373 @ X372) @ (sub @ X375 @ X372) @ X374)) | ($true != (X367 @ X373 @ X375 @ (comp @ X372 @ X374)))) | ~! [X376 : term,X377 : term] : (((X367 @ id @ X376 @ id) != $true) | ((X367 @ id @ (ap @ (sub @ X376 @ id) @ X377) @ id) = $true) | ($true != (X367 @ id @ X377 @ id))) | ($true != (X367 @ id @ X366 @ id))) => (! [X378 : subst > term > subst > $o,X379 : term] : (((X378 @ id @ (lam @ X379) @ id) = $true) | ~! [X388 : term] : (((X378 @ id @ (sub @ X379 @ (push @ X388 @ id)) @ id) = $true) | ((X378 @ id @ X388 @ id) != $true)) | ~! [X380 : subst,X381 : term,X382 : subst,X383 : subst] : (((X378 @ X383 @ X381 @ (comp @ X382 @ X380)) != $true) | ((X378 @ (comp @ X383 @ X382) @ (sub @ X381 @ X382) @ X380) = $true)) | ~! [X389 : subst > term > term] : (~! [X390 : term] : (((X378 @ id @ X390 @ id) != $true) | ($true = (X378 @ id @ (X389 @ id @ X390) @ id))) | ~! [X391 : term,X392 : subst,X393 : subst] : ((sub @ (X389 @ X393 @ X391) @ X392) = (X389 @ (comp @ X393 @ X392) @ (sub @ X391 @ X392))) | ((X378 @ id @ (lam @ (X389 @ sh @ one)) @ id) = $true)) | ~! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (($true = (X378 @ X386 @ X387 @ (comp @ X384 @ X385))) | ($true != (X378 @ (comp @ X386 @ X384) @ (sub @ X387 @ X384) @ X385)))) => ! [X394 : term,X395 : subst > term > subst > $o] : (~! [X400 : subst > term > term] : (~! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X404 @ X403) @ (sub @ X402 @ X403)) = (sub @ (X400 @ X404 @ X402) @ X403)) | ~! [X401 : term] : (((X395 @ id @ X401 @ id) != $true) | ((X395 @ id @ (X400 @ id @ X401) @ id) = $true)) | ((X395 @ id @ (lam @ (X400 @ sh @ one)) @ id) = $true)) | ~! [X407 : term] : (((var @ (sub @ X407 @ id)) != $true) | ((X395 @ id @ X407 @ id) = $true)) | ~! [X405 : term,X406 : term] : (($true = (X395 @ id @ (ap @ (sub @ X406 @ id) @ X405) @ id)) | ((X395 @ id @ X405 @ id) != $true) | ((X395 @ id @ X406 @ id) != $true)) | ($true = (X395 @ id @ X394 @ id)) | ~! [X396 : term,X397 : subst,X398 : subst,X399 : subst] : (((X395 @ X397 @ X396 @ (comp @ X399 @ X398)) != $true) | ((X395 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398) = $true)) | ~! [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (((X395 @ X408 @ X411 @ (comp @ X409 @ X410)) = $true) | ($true != (X395 @ (comp @ X408 @ X409) @ (sub @ X411 @ X409) @ X410)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & ((induction2_lthm = $true) <=> (! [X516 : term] : ((sub @ X516 @ id) = X516) => (! [X517 : term > $o,X518 : subst,X519 : term] : (~! [X520 : term] : (($true = (X517 @ (sub @ X520 @ X518))) | ((var @ X520) != $true)) | ~! [X521 : term] : (~! [X522 : term] : (($true != (X517 @ X522)) | ((X517 @ (sub @ X521 @ (push @ X522 @ id))) = $true)) | ($true = (X517 @ (lam @ X521)))) | ~! [X523 : term,X524 : term] : (((X517 @ (ap @ X523 @ X524)) = $true) | ((X517 @ X524) != $true) | ((X517 @ X523) != $true)) | ($true = (X517 @ (sub @ X519 @ X518)))) => ! [X525 : term > $o,X526 : term] : (~! [X529 : term] : (((var @ X529) != $true) | ((X525 @ X529) = $true)) | ~! [X527 : term] : (((X525 @ (lam @ X527)) = $true) | ~! [X528 : term] : (((X525 @ X528) != $true) | ((X525 @ (sub @ X527 @ (push @ X528 @ id))) = $true))) | ~! [X530 : term,X531 : term] : (($true != (X525 @ X531)) | ($true != (X525 @ X530)) | ((X525 @ (ap @ X530 @ X531)) = $true)) | ($true = (X525 @ X526)))))) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) = (d2subst @ X117)) => (X116 = X117)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X211 : term,X212 : term > $o,X213 : subst] : ~! [X214 : term > $o] : ~! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X200 : term] : ~! [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) != (X201 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) <=> ! [X131 : term > $o,X132 : term] : (((X131 @ X132) = $true) | ~! [X133 : term,X134 : term] : (((X131 @ X134) != $true) | ((X131 @ X133) != $true) | ((X131 @ (ap @ X133 @ X134)) = $true)) | ~! [X135 : term] : (($true != (X131 @ X135)) | ((X131 @ (lam @ X135)) = $true)) | ~! [X136 : term] : (($true != (var @ X136)) | ($true = (X131 @ X136))))) & (hoasinduction_lem3_gthm = $true) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) <=> (hoasapinj1 = $true)) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) <=> (substmonoid = $true)) & ((! [X300 : subst > term > subst > $o] : ~! [X301 : term > $o] : ~! [X302 : term] : ((X301 @ X302) = (X300 @ id @ X302 @ id)) => (! [X303 : term > $o,X304 : term] : (~! [X305 : term,X306 : term] : (((X303 @ (ap @ X305 @ X306)) = $true) | ($true != (X303 @ X305)) | ((X303 @ X306) != $true)) | ~! [X308 : term] : (~! [X309 : term] : (((X303 @ (sub @ X308 @ (push @ X309 @ id))) = $true) | ((X303 @ X309) != $true)) | ($true = (X303 @ (lam @ X308)))) | ~! [X307 : term] : (((X303 @ X307) = $true) | ($true != (var @ X307))) | ((X303 @ X304) = $true)) => (! [X310 : term] : ((sub @ X310 @ id) = X310) => (! [X311 : term > $o,X312 : term,X313 : subst > term > subst > $o] : (~! [X314 : term] : ((X311 @ X314) = (X313 @ id @ X314 @ id)) | ~! [X315 : term] : (((X311 @ (sub @ X312 @ (push @ X315 @ id))) = $true) | ((X311 @ X315) != $true)) | ~! [X316 : subst > term > term] : (($true = (X313 @ id @ (lam @ (X316 @ sh @ one)) @ id)) | ~! [X317 : term] : (((X313 @ id @ (X316 @ id @ X317) @ id) = $true) | ((X313 @ id @ X317 @ id) != $true)) | ~! [X318 : term,X319 : subst,X320 : subst] : ((sub @ (X316 @ X320 @ X318) @ X319) = (X316 @ (comp @ X320 @ X319) @ (sub @ X318 @ X319)))) | ((X311 @ (lam @ X312)) = $true)) => ! [X321 : subst > term > subst > $o,X322 : term] : (~! [X323 : subst > term > term] : (((X321 @ id @ (lam @ (X323 @ sh @ one)) @ id) = $true) | ~! [X325 : subst,X326 : subst,X327 : term] : ((sub @ (X323 @ X326 @ X327) @ X325) = (X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325))) | ~! [X324 : term] : (($true = (X321 @ id @ (X323 @ id @ X324) @ id)) | ((X321 @ id @ X324 @ id) != $true))) | ((X321 @ id @ X322 @ id) = $true) | ~! [X328 : term,X329 : term] : (((X321 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id) = $true) | ((X321 @ id @ X328 @ id) != $true) | ((X321 @ id @ X329 @ id) != $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((induction2lem = $true) <=> ! [X508 : subst,X509 : term,X510 : term > $o] : (~! [X512 : term,X513 : term] : (($true = (X510 @ (ap @ X513 @ X512))) | ((X510 @ X512) != $true) | ((X510 @ X513) != $true)) | ~! [X514 : term] : (~! [X515 : term] : (((X510 @ X515) != $true) | ((X510 @ (sub @ X514 @ (push @ X515 @ id))) = $true)) | ((X510 @ (lam @ X514)) = $true)) | ~! [X511 : term] : (((X510 @ (sub @ X511 @ X508)) = $true) | ((var @ X511) != $true)) | ((X510 @ (sub @ X509 @ X508)) = $true))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X105 : term] : ((sub @ X105 @ id) = X105) => (! [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) != (ap @ X107 @ X109)) | (X107 = X108)) => ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (lamnotap != $true) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & ((apinj1 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X412 : term,X413 : term > $o,X414 : subst > term > subst > $o] : (~! [X421 : term] : ((X413 @ X421) = (X414 @ id @ X421 @ id)) | ($true = (X413 @ (lam @ X412))) | ~! [X416 : subst > term > term] : (~! [X420 : term] : (((X414 @ id @ X420 @ id) != $true) | ((X414 @ id @ (X416 @ id @ X420) @ id) = $true)) | ~! [X417 : term,X418 : subst,X419 : subst] : ((sub @ (X416 @ X419 @ X417) @ X418) = (X416 @ (comp @ X419 @ X418) @ (sub @ X417 @ X418))) | ((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) = $true)) | ~! [X415 : term] : (($true = (X413 @ (sub @ X412 @ (push @ X415 @ id)))) | ($true != (X413 @ X415))))) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & ((pushprop_lem1v2 = $true) <=> ! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X144 @ one) = $true) | ~! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146)) | ((X145 @ X143) != $true))) & (axassoc = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & (hoasinduction_lem1_lthm = $true) & ((shinj = $true) <=> ! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247))) & ((hoasinduction_lem3v2 = $true) <=> ! [X422 : subst > term > subst > $o,X423 : term,X424 : term > $o] : (~! [X439 : term] : (((X424 @ X439) != $true) | ((X424 @ (sub @ X423 @ (push @ X439 @ id))) = $true)) | ~! [X425 : subst > term > term] : (~! [X426 : subst,X427 : term,X428 : subst] : ((X425 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426)) = (sub @ (X425 @ X428 @ X427) @ X426)) | ~! [X429 : term] : (((X422 @ id @ X429 @ id) != $true) | ((X422 @ id @ (X425 @ id @ X429) @ id) = $true)) | ((X422 @ id @ (lam @ (X425 @ sh @ one)) @ id) = $true)) | ~! [X438 : term] : ((X422 @ id @ X438 @ id) = (X424 @ X438)) | ((X424 @ (lam @ X423)) = $true) | ~! [X430 : subst,X431 : term,X432 : subst,X433 : subst] : (((X422 @ X433 @ X431 @ (comp @ X432 @ X430)) != $true) | ((X422 @ (comp @ X433 @ X432) @ (sub @ X431 @ X432) @ X430) = $true)) | ~! [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X422 @ (comp @ X436 @ X437) @ (sub @ X434 @ X437) @ X435) != $true) | ($true = (X422 @ X436 @ X434 @ (comp @ X437 @ X435)))))) & (! [X299 : subst] : ((comp @ id @ X299) = X299) <=> (axidl = $true)) & (hoaslamnotvar = $true) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) <=> (apinj2 = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & (pushprop_lem0_gthm = $true) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (~! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ~! [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) = (sub @ (X218 @ X226 @ X225) @ X224)) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one)))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X227 : term] : ~! [X228 : subst > term > term] : ~! [X229 : subst,X230 : term] : ((sub @ X227 @ (push @ X230 @ X229)) = (X228 @ X229 @ X230)) => (! [X231 : term] : ((sub @ X231 @ id) = X231) => ! [X232 : subst > term > subst > $o,X233 : term > $o,X234 : term] : (~! [X237 : subst > term > term] : (((X232 @ id @ (lam @ (X237 @ sh @ one)) @ id) = $true) | ~! [X238 : term] : (($true != (X232 @ id @ X238 @ id)) | ($true = (X232 @ id @ (X237 @ id @ X238) @ id))) | ~! [X239 : term,X240 : subst,X241 : subst] : ((sub @ (X237 @ X241 @ X239) @ X240) = (X237 @ (comp @ X241 @ X240) @ (sub @ X239 @ X240)))) | ~! [X236 : term] : (((X233 @ (sub @ X234 @ (push @ X236 @ id))) = $true) | ((X233 @ X236) != $true)) | ~! [X235 : term] : ((X232 @ id @ X235 @ id) = (X233 @ X235)) | ((X233 @ (lam @ X234)) = $true))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X54 : subst > term > subst > $o] : ~! [X55 : term > $o] : ~! [X56 : term] : ((X54 @ id @ X56 @ id) = (X55 @ X56)) => (! [X57 : term,X58 : term > $o] : (~! [X61 : term] : (($true = (X58 @ (lam @ X61))) | ~! [X62 : term] : (((X58 @ (sub @ X61 @ (push @ X62 @ id))) = $true) | ($true != (X58 @ X62)))) | ~! [X63 : term] : (((var @ X63) != $true) | ((X58 @ X63) = $true)) | ((X58 @ X57) = $true) | ~! [X59 : term,X60 : term] : (((X58 @ X60) != $true) | ((X58 @ (ap @ X59 @ X60)) = $true) | ($true != (X58 @ X59)))) => (! [X64 : term] : ((sub @ X64 @ id) = X64) => (! [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (~! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ($true != (X65 @ X73))) | ~! [X68 : subst > term > term] : (~! [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) = (sub @ (X68 @ X72 @ X70) @ X71)) | ~! [X69 : term] : (((X67 @ id @ (X68 @ id @ X69) @ id) = $true) | ((X67 @ id @ X69 @ id) != $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true)) | ($true = (X65 @ (lam @ X66))) | ~! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74))) => ! [X75 : subst > term > subst > $o,X76 : term] : (((X75 @ id @ X76 @ id) = $true) | ~! [X91 : term,X92 : term] : (((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) = $true) | ($true != (X75 @ id @ X92 @ id)) | ((X75 @ id @ X91 @ id) != $true)) | ~! [X82 : subst > term > term] : (~! [X83 : term] : (((X75 @ id @ (X82 @ id @ X83) @ id) = $true) | ((X75 @ id @ X83 @ id) != $true)) | ((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) = $true) | ~! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ~! [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) != $true) | ((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) = $true)) | ~! [X77 : term] : (((var @ (sub @ X77 @ id)) != $true) | ((X75 @ id @ X77 @ id) = $true)) | ~! [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) != $true) | ((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) = $true)))))))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X216 : term] : ((sub @ X216 @ id) = X216) <=> (termmset = $true)) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & (apnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((axvarid = $true) <=> ! [X355 : term] : ((sub @ X355 @ id) = X355)) & (pushprop_lthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X202 : subst > term > subst > $o,X203 : term] : (~! [X204 : term,X205 : term] : (((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) = $true) | ((X202 @ id @ X204 @ id) != $true) | ($true != (X202 @ id @ X205 @ id))) | ~! [X206 : subst > term > term] : (~! [X210 : term] : (((X202 @ id @ X210 @ id) != $true) | ((X202 @ id @ (X206 @ id @ X210) @ id) = $true)) | ($true = (X202 @ id @ (lam @ (X206 @ sh @ one)) @ id)) | ~! [X207 : subst,X208 : subst,X209 : term] : ((X206 @ (comp @ X207 @ X208) @ (sub @ X209 @ X208)) = (sub @ (X206 @ X207 @ X209) @ X208))) | ((X202 @ id @ X203 @ id) = $true))) & ((d2subst @ d_id) = sh) & ! [X170 : d_term] : (d_one = X170) & (! [X448 : term] : ~! [X449 : subst > term > term] : ~! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) <=> (hoasinduction_lem3v2_f = $true)) & (ulamvarind = $true) & (! [X121 : subst > term > subst > $o,X122 : term] : (((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ~! [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) = $true) | ($true != (X121 @ id @ X128 @ id))) | ~! [X123 : subst > term > term] : (((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) = $true) | ~! [X127 : term] : (($true = (X121 @ id @ (X123 @ id @ X127) @ id)) | ((X121 @ id @ X127 @ id) != $true)) | ~! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124)))) <=> (hoasinduction_lem3aa_lthm = $true))),
% 21.29/4.27 inference(flattening,[status(thm)],[f9])).
% 21.29/4.27 thf(f9,plain,(
% 21.29/4.27 (substmonoid_gthm = $true) & (axmap = $true) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true) | ~((X3 @ X2) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X7 : term] : ((sub @ X7 @ id) = X7) => (! [X8 : term,X9 : subst > term > subst > $o] : (($true = (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) | ~! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ~! [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) = (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13))) | ~! [X14 : term] : (~((X9 @ id @ X14 @ id) = $true) | ((X9 @ id @ (X10 @ id @ X14) @ id) = $true))) | ~! [X15 : term] : (~((X9 @ id @ X15 @ id) = $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id)))) => ! [X16 : term,X17 : subst > term > subst > $o] : (~! [X18 : term] : (((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) = $true) | ~((X17 @ id @ X18 @ id) = $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)) | ~! [X19 : subst > term > term] : (~! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) | ~! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ~($true = (X17 @ id @ X23 @ id))) | ($true = (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id))))))) & (hoasinduction_lem3a_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X24 : subst > term > subst > $o] : ~! [X25 : term > $o] : ~! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X27 : term] : ~! [X28 : subst > term > term] : ~! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29)))) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & ! [X35 : d_subst] : (d_id = X35) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X36 : term,X37 : subst > term > subst > $o] : (~! [X38 : term,X39 : term] : (($true = (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) | ~((X37 @ id @ X39 @ id) = $true) | ~((X37 @ id @ X38 @ id) = $true)) | ~! [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (~($true = (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42)) | ((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) = $true)) | ~! [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (~((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) = $true) | ((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) = $true)) | ~! [X48 : subst > term > term] : (~! [X49 : term] : (~($true = (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))) | ~! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50)) | ((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) = $true)) | ~! [X53 : term] : (((X37 @ id @ X53 @ id) = $true) | ~($true = (var @ (sub @ X53 @ id)))) | ($true = (X37 @ id @ X36 @ id)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) <=> (! [X54 : subst > term > subst > $o] : ~! [X55 : term > $o] : ~! [X56 : term] : ((X54 @ id @ X56 @ id) = (X55 @ X56)) => (! [X57 : term,X58 : term > $o] : (~! [X59 : term,X60 : term] : (~($true = (X58 @ X59)) | ~((X58 @ X60) = $true) | ((X58 @ (ap @ X59 @ X60)) = $true)) | ~! [X61 : term] : (~! [X62 : term] : (((X58 @ (sub @ X61 @ (push @ X62 @ id))) = $true) | ~($true = (X58 @ X62))) | ($true = (X58 @ (lam @ X61)))) | ~! [X63 : term] : (((X58 @ X63) = $true) | ~((var @ X63) = $true)) | ((X58 @ X57) = $true)) => (! [X64 : term] : ((sub @ X64 @ id) = X64) => (! [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (~! [X68 : subst > term > term] : (~! [X69 : term] : (~((X67 @ id @ X69 @ id) = $true) | ((X67 @ id @ (X68 @ id @ X69) @ id) = $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true) | ~! [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) = (sub @ (X68 @ X72 @ X70) @ X71))) | ~! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ~($true = (X65 @ X73))) | ($true = (X65 @ (lam @ X66))) | ~! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74))) => ! [X75 : subst > term > subst > $o,X76 : term] : (~! [X77 : term] : (((X75 @ id @ X77 @ id) = $true) | ~((var @ (sub @ X77 @ id)) = $true)) | ~! [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) = $true) | ~((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) = $true)) | ~! [X82 : subst > term > term] : (((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) = $true) | ~! [X83 : term] : (~((X75 @ id @ X83 @ id) = $true) | ((X75 @ id @ (X82 @ id @ X83) @ id) = $true)) | ~! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ~! [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) = $true) | ~((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) = $true)) | ~! [X91 : term,X92 : term] : (~((X75 @ id @ X91 @ id) = $true) | ((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) = $true) | ~($true = (X75 @ id @ X92 @ id))) | ((X75 @ id @ X76 @ id) = $true))))))) & (! [X93 : term,X94 : term,X95 : subst > term > term] : (~! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)) | ((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94))) <=> (hoaslamnotap = $true)) & ~(ulamvar1 = $true) & (axclos = $true) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & (hoasinduction_lem1 = $true) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & ((! [X105 : term] : ((sub @ X105 @ id) = X105) => (! [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) != (ap @ X107 @ X109)) | (X107 = X108)) => ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))))) <=> (hoasapinj1_lthm = $true)) & ~(lamnotap = $true) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) = (d2subst @ X117)) => (X116 = X117)) & (! [X118 : subst > term > subst > $o] : ~! [X119 : term > $o] : ~! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) <=> (hoasinduction_lem0 = $true)) & (one = (d2term @ d_one)) & (! [X121 : subst > term > subst > $o,X122 : term] : (~! [X123 : subst > term > term] : (~! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124)) | ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) = $true) | ~! [X127 : term] : (~((X121 @ id @ X127 @ id) = $true) | ($true = (X121 @ id @ (X123 @ id @ X127) @ id)))) | ((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ~! [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) = $true) | ~($true = (X121 @ id @ X128 @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X129 : term] : ~! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one))) & ((induction = $true) <=> ! [X131 : term > $o,X132 : term] : (~! [X133 : term,X134 : term] : (~((X131 @ X134) = $true) | ((X131 @ (ap @ X133 @ X134)) = $true) | ~((X131 @ X133) = $true)) | ~! [X135 : term] : (((X131 @ (lam @ X135)) = $true) | ~($true = (X131 @ X135))) | ~! [X136 : term] : (($true = (X131 @ X136)) | ~($true = (var @ X136))) | ((X131 @ X132) = $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X137 : subst,X138 : term,X139 : term > $o] : ~! [X140 : term > $o] : ~! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) <=> (pushprop_lem0 = $true)) & (! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X144 @ one) = $true) | ~((X145 @ X143) = $true) | ~! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146))) <=> (pushprop_lem1v2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((! [X147 : term] : ((sub @ X147 @ id) = X147) => ! [X148 : subst > term > subst > $o,X149 : term,X150 : term > $o] : (~! [X151 : term] : (~((X150 @ X151) = $true) | ((X150 @ (sub @ X149 @ (push @ X151 @ id))) = $true)) | ~! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (((X148 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153) @ X155) = $true) | ~($true = (X148 @ X154 @ X152 @ (comp @ X153 @ X155)))) | ~! [X156 : subst > term > term] : (~! [X157 : term] : (((X148 @ id @ (X156 @ id @ X157) @ id) = $true) | ~((X148 @ id @ X157 @ id) = $true)) | ~! [X158 : subst,X159 : term,X160 : subst] : ((sub @ (X156 @ X158 @ X159) @ X160) = (X156 @ (comp @ X158 @ X160) @ (sub @ X159 @ X160))) | ($true = (X148 @ id @ (lam @ (X156 @ sh @ one)) @ id))) | ((X150 @ (lam @ X149)) = $true) | ~! [X161 : term] : ((X150 @ X161) = (X148 @ id @ X161 @ id)) | ~! [X162 : subst,X163 : subst,X164 : term,X165 : subst] : (~($true = (X148 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163) @ X165)) | ((X148 @ X162 @ X164 @ (comp @ X163 @ X165)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((apinj1 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X168 = X169) | ((ap @ X169 @ X167) != (ap @ X168 @ X166)))) & ! [X170 : d_term] : (d_one = X170) & ((! [X171 : term] : ((sub @ X171 @ id) = X171) => ! [X172 : term] : ((sub @ X172 @ id) = X172)) <=> (termmset_lthm = $true)) & (termmset_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X173 : term,X174 : subst] : ((sub @ one @ (push @ X173 @ X174)) = X173) => ! [X175 : term > $o,X176 : subst,X177 : term > $o,X178 : term] : (((X175 @ one) = $true) | ~($true = (X177 @ X178)) | ~! [X179 : term] : ((X177 @ (sub @ X179 @ (push @ X178 @ X176))) = (X175 @ X179))))) & (! [X180 : term,X181 : term,X182 : subst > term > subst > $o] : (~((X182 @ id @ X180 @ id) = $true) | ~! [X183 : subst,X184 : subst,X185 : term,X186 : subst] : (((X182 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183) @ X186) = $true) | ~((X182 @ X184 @ X185 @ (comp @ X183 @ X186)) = $true)) | ~! [X187 : subst,X188 : term,X189 : subst,X190 : subst] : (((X182 @ X189 @ X188 @ (comp @ X187 @ X190)) = $true) | ~((X182 @ (comp @ X189 @ X187) @ (sub @ X188 @ X187) @ X190) = $true)) | ((X182 @ id @ (ap @ X180 @ X181) @ id) = $true) | ~! [X191 : term,X192 : term] : (~($true = (X182 @ id @ X192 @ id)) | ~((X182 @ id @ X191 @ id) = $true) | ((X182 @ id @ (ap @ (sub @ X192 @ id) @ X191) @ id) = $true)) | ~($true = (X182 @ id @ X181 @ id))) <=> (hoasinduction_lem2 = $true)) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (axassoc = $true) & ((induction2 = $true) <=> ! [X193 : term,X194 : term > $o] : (~! [X195 : term] : (~((var @ X195) = $true) | ((X194 @ X195) = $true)) | ~! [X196 : term] : (($true = (X194 @ (lam @ X196))) | ~! [X197 : term] : (((X194 @ (sub @ X196 @ (push @ X197 @ id))) = $true) | ~($true = (X194 @ X197)))) | ((X194 @ X193) = $true) | ~! [X198 : term,X199 : term] : (~($true = (X194 @ X199)) | ($true = (X194 @ (ap @ X198 @ X199))) | ~((X194 @ X198) = $true)))) & (! [X200 : term] : ~! [X201 : subst > term > term] : ((sub @ X200 @ (push @ one @ sh)) != (X201 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (induction2lem_gthm = $true) & (! [X202 : subst > term > subst > $o,X203 : term] : (~! [X204 : term,X205 : term] : (~($true = (X202 @ id @ X205 @ id)) | ~((X202 @ id @ X204 @ id) = $true) | ((X202 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id) = $true)) | ((X202 @ id @ X203 @ id) = $true) | ~! [X206 : subst > term > term] : (~! [X207 : subst,X208 : subst,X209 : term] : ((X206 @ (comp @ X207 @ X208) @ (sub @ X209 @ X208)) = (sub @ (X206 @ X207 @ X209) @ X208)) | ~! [X210 : term] : (~((X202 @ id @ X210 @ id) = $true) | ((X202 @ id @ (X206 @ id @ X210) @ id) = $true)) | ($true = (X202 @ id @ (lam @ (X206 @ sh @ one)) @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((d2subst @ d_id) = sh) & ((pushprop_lem0_lthm = $true) <=> ! [X211 : term,X212 : term > $o,X213 : subst] : ~! [X214 : term > $o] : ~! [X215 : term] : ((X214 @ X215) = (X212 @ (sub @ X215 @ (push @ X211 @ X213))))) & (hoasapnotvar_gthm = $true) & (! [X216 : term] : ((sub @ X216 @ id) = X216) <=> (termmset = $true)) & (! [X217 : subst,X218 : subst > term > term,X219 : subst > term > term,X220 : term] : (~! [X221 : term,X222 : subst,X223 : subst] : ((sub @ (X219 @ X222 @ X221) @ X223) = (X219 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) | ~! [X224 : subst,X225 : term,X226 : subst] : ((X218 @ (comp @ X226 @ X224) @ (sub @ X225 @ X224)) = (sub @ (X218 @ X226 @ X225) @ X224)) | ((X219 @ X217 @ X220) = (X218 @ X217 @ X220)) | ((lam @ (X219 @ sh @ one)) != (lam @ (X218 @ sh @ one)))) <=> (hoaslaminj = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_gthm = $true) & ((! [X227 : term] : ~! [X228 : subst > term > term] : ~! [X229 : subst,X230 : term] : ((sub @ X227 @ (push @ X230 @ X229)) = (X228 @ X229 @ X230)) => (! [X231 : term] : ((sub @ X231 @ id) = X231) => ! [X232 : subst > term > subst > $o,X233 : term > $o,X234 : term] : (~! [X235 : term] : ((X232 @ id @ X235 @ id) = (X233 @ X235)) | ((X233 @ (lam @ X234)) = $true) | ~! [X236 : term] : (((X233 @ (sub @ X234 @ (push @ X236 @ id))) = $true) | ~((X233 @ X236) = $true)) | ~! [X237 : subst > term > term] : (~! [X238 : term] : (($true = (X232 @ id @ (X237 @ id @ X238) @ id)) | ~($true = (X232 @ id @ X238 @ id))) | ~! [X239 : term,X240 : subst,X241 : subst] : ((sub @ (X237 @ X241 @ X239) @ X240) = (X237 @ (comp @ X241 @ X240) @ (sub @ X239 @ X240))) | ((X232 @ id @ (lam @ (X237 @ sh @ one)) @ id) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop = $true) & (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 = X244) | ((ap @ (sub @ X244 @ id) @ X245) != (ap @ (sub @ X242 @ id) @ X243))) <=> (hoasapinj1 = $true)) & ((shinj = $true) <=> ! [X246 : term,X247 : term] : (((sub @ X247 @ sh) != (sub @ X246 @ sh)) | (X246 = X247))) & (! [X248 : subst > term > subst > $o,X249 : term] : (($true = (X248 @ id @ (lam @ (sub @ X249 @ (push @ one @ sh))) @ id)) | ~! [X250 : term] : (~($true = (X248 @ id @ X250 @ id)) | ((X248 @ id @ (sub @ X249 @ (push @ X250 @ id)) @ id) = $true)) | ~! [X251 : subst > term > term] : (~! [X252 : term] : (((X248 @ id @ (X251 @ id @ X252) @ id) = $true) | ~($true = (X248 @ id @ X252 @ id))) | ((X248 @ id @ (lam @ (X251 @ sh @ one)) @ id) = $true) | ~! [X253 : term,X254 : subst,X255 : subst] : ((sub @ (X251 @ X255 @ X253) @ X254) = (X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254))))) <=> (hoasinduction_lem3aa = $true)) & ! [X256 : d_term,X257 : d_term] : (((d2term @ X256) = (d2term @ X257)) => (X256 = X257)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X258 : subst > term > subst > $o,X259 : term] : (~! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (~($true = (X258 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) | ((X258 @ X260 @ X261 @ (comp @ X263 @ X262)) = $true)) | ~! [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (((X258 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X267) = $true) | ~((X258 @ X265 @ X264 @ (comp @ X266 @ X267)) = $true)) | ~! [X268 : term] : (((X258 @ id @ (sub @ X259 @ (push @ X268 @ id)) @ id) = $true) | ~($true = (X258 @ id @ X268 @ id))) | ($true = (X258 @ id @ (lam @ X259) @ id)) | ~! [X269 : subst > term > term] : (((X258 @ id @ (lam @ (X269 @ sh @ one)) @ id) = $true) | ~! [X270 : subst,X271 : subst,X272 : term] : ((sub @ (X269 @ X270 @ X272) @ X271) = (X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271))) | ~! [X273 : term] : (~((X258 @ id @ X273 @ id) = $true) | ((X258 @ id @ (X269 @ id @ X273) @ id) = $true))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X274 : subst] : ((comp @ X274 @ id) = X274) & ! [X275 : subst] : ((comp @ id @ X275) = X275)) <=> (substmonoid = $true)) & ((! [X276 : subst] : ((comp @ id @ X276) = X276) => (! [X277 : subst] : ((comp @ X277 @ id) = X277) => (! [X278 : subst] : ((comp @ X278 @ id) = X278) & ! [X279 : subst] : ((comp @ id @ X279) = X279)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X280 : term,X281 : term,X282 : subst > term > subst > $o,X283 : term > $o] : (~! [X284 : subst,X285 : subst,X286 : term,X287 : subst] : (((X282 @ X285 @ X286 @ (comp @ X284 @ X287)) = $true) | ~($true = (X282 @ (comp @ X285 @ X284) @ (sub @ X286 @ X284) @ X287))) | ~! [X288 : term] : ((X283 @ X288) = (X282 @ id @ X288 @ id)) | ~! [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (~((X282 @ X289 @ X291 @ (comp @ X290 @ X292)) = $true) | ((X282 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290) @ X292) = $true)) | ~((X283 @ X281) = $true) | ~((X283 @ X280) = $true) | ($true = (X283 @ (ap @ X280 @ X281))) | ~! [X293 : term,X294 : term] : (~($true = (X282 @ id @ X293 @ id)) | ($true = (X282 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)) | ~((X282 @ id @ X294 @ id) = $true)))) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : (((ap @ X296 @ X297) != (ap @ X298 @ X295)) | (X295 = X297)) <=> (apinj2 = $true)) & (lamnotvar = $true) & (! [X299 : subst] : ((comp @ id @ X299) = X299) <=> (axidl = $true)) & (hoasapinj2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasapnotvar = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X300 : subst > term > subst > $o] : ~! [X301 : term > $o] : ~! [X302 : term] : ((X301 @ X302) = (X300 @ id @ X302 @ id)) => (! [X303 : term > $o,X304 : term] : (~! [X305 : term,X306 : term] : (~((X303 @ X306) = $true) | ((X303 @ (ap @ X305 @ X306)) = $true) | ~($true = (X303 @ X305))) | ((X303 @ X304) = $true) | ~! [X307 : term] : (((X303 @ X307) = $true) | ~($true = (var @ X307))) | ~! [X308 : term] : (~! [X309 : term] : (~((X303 @ X309) = $true) | ((X303 @ (sub @ X308 @ (push @ X309 @ id))) = $true)) | ($true = (X303 @ (lam @ X308))))) => (! [X310 : term] : ((sub @ X310 @ id) = X310) => (! [X311 : term > $o,X312 : term,X313 : subst > term > subst > $o] : (~! [X314 : term] : ((X311 @ X314) = (X313 @ id @ X314 @ id)) | ~! [X315 : term] : (((X311 @ (sub @ X312 @ (push @ X315 @ id))) = $true) | ~((X311 @ X315) = $true)) | ((X311 @ (lam @ X312)) = $true) | ~! [X316 : subst > term > term] : (~! [X317 : term] : (~((X313 @ id @ X317 @ id) = $true) | ((X313 @ id @ (X316 @ id @ X317) @ id) = $true)) | ~! [X318 : term,X319 : subst,X320 : subst] : ((sub @ (X316 @ X320 @ X318) @ X319) = (X316 @ (comp @ X320 @ X319) @ (sub @ X318 @ X319))) | ($true = (X313 @ id @ (lam @ (X316 @ sh @ one)) @ id)))) => ! [X321 : subst > term > subst > $o,X322 : term] : (~! [X323 : subst > term > term] : (~! [X324 : term] : (~((X321 @ id @ X324 @ id) = $true) | ($true = (X321 @ id @ (X323 @ id @ X324) @ id))) | ~! [X325 : subst,X326 : subst,X327 : term] : ((sub @ (X323 @ X326 @ X327) @ X325) = (X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325))) | ((X321 @ id @ (lam @ (X323 @ sh @ one)) @ id) = $true)) | ~! [X328 : term,X329 : term] : (~((X321 @ id @ X329 @ id) = $true) | ((X321 @ id @ (ap @ (sub @ X329 @ id) @ X328) @ id) = $true) | ~((X321 @ id @ X328 @ id) = $true)) | ((X321 @ id @ X322 @ id) = $true))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X330 : term] : ((sub @ X330 @ id) = X330) => (! [X331 : subst > term > subst > $o,X332 : term] : (~! [X333 : subst > term > term] : (((X331 @ id @ (lam @ (X333 @ sh @ one)) @ id) = $true) | ~! [X334 : term] : (~($true = (X331 @ id @ X334 @ id)) | ((X331 @ id @ (X333 @ id @ X334) @ id) = $true)) | ~! [X335 : term,X336 : subst,X337 : subst] : ((X333 @ (comp @ X337 @ X336) @ (sub @ X335 @ X336)) = (sub @ (X333 @ X337 @ X335) @ X336))) | ~! [X338 : term] : (((X331 @ id @ (sub @ X332 @ (push @ X338 @ id)) @ id) = $true) | ~((X331 @ id @ X338 @ id) = $true)) | ((X331 @ id @ (lam @ (sub @ X332 @ (push @ one @ sh))) @ id) = $true)) => ! [X339 : term,X340 : subst > term > subst > $o] : (~! [X341 : term] : (((X340 @ id @ (sub @ X339 @ (push @ X341 @ id)) @ id) = $true) | ~($true = (X340 @ id @ X341 @ id))) | ~! [X342 : subst > term > term] : (~! [X343 : term,X344 : subst,X345 : subst] : ((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345)) = (sub @ (X342 @ X344 @ X343) @ X345)) | ~! [X346 : term] : (($true = (X340 @ id @ (X342 @ id @ X346) @ id)) | ~((X340 @ id @ X346 @ id) = $true)) | ($true = (X340 @ id @ (lam @ (X342 @ sh @ one)) @ id))) | ((X340 @ id @ (lam @ X339) @ id) = $true) | ~! [X347 : subst,X348 : subst,X349 : subst,X350 : term] : (~((X340 @ X349 @ X350 @ (comp @ X347 @ X348)) = $true) | ((X340 @ (comp @ X349 @ X347) @ (sub @ X350 @ X347) @ X348) = $true)) | ~! [X351 : term,X352 : subst,X353 : subst,X354 : subst] : (($true = (X340 @ X353 @ X351 @ (comp @ X354 @ X352))) | ~((X340 @ (comp @ X353 @ X354) @ (sub @ X351 @ X354) @ X352) = $true)))))) & (hoasinduction_lem2_lthm = $true) & ((axvarid = $true) <=> ! [X355 : term] : ((sub @ X355 @ id) = X355)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X356 : term] : ? [X357 : d_term] : ((d2term @ X357) = X356) & (pushprop_lem2v2 = $true) & ((! [X358 : term,X359 : term > $o] : (~! [X360 : term,X361 : term] : (~((X359 @ X360) = $true) | ~((X359 @ X361) = $true) | ((X359 @ (ap @ X361 @ X360)) = $true)) | ((X359 @ X358) = $true) | ~! [X362 : term] : (~! [X363 : term] : (((X359 @ (sub @ X362 @ (push @ X363 @ id))) = $true) | ~($true = (X359 @ X363))) | ((X359 @ (lam @ X362)) = $true)) | ~! [X364 : term] : (($true = (X359 @ X364)) | ~((var @ X364) = $true))) => (! [X365 : term,X366 : term,X367 : subst > term > subst > $o] : (((X367 @ id @ (ap @ X365 @ X366) @ id) = $true) | ~! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (~($true = (X367 @ (comp @ X368 @ X369) @ (sub @ X371 @ X369) @ X370)) | ($true = (X367 @ X368 @ X371 @ (comp @ X369 @ X370)))) | ~((X367 @ id @ X365 @ id) = $true) | ~($true = (X367 @ id @ X366 @ id)) | ~! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (($true = (X367 @ (comp @ X373 @ X372) @ (sub @ X375 @ X372) @ X374)) | ~($true = (X367 @ X373 @ X375 @ (comp @ X372 @ X374)))) | ~! [X376 : term,X377 : term] : (~((X367 @ id @ X376 @ id) = $true) | ~($true = (X367 @ id @ X377 @ id)) | ((X367 @ id @ (ap @ (sub @ X376 @ id) @ X377) @ id) = $true))) => (! [X378 : subst > term > subst > $o,X379 : term] : (~! [X380 : subst,X381 : term,X382 : subst,X383 : subst] : (((X378 @ (comp @ X383 @ X382) @ (sub @ X381 @ X382) @ X380) = $true) | ~((X378 @ X383 @ X381 @ (comp @ X382 @ X380)) = $true)) | ((X378 @ id @ (lam @ X379) @ id) = $true) | ~! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (~($true = (X378 @ (comp @ X386 @ X384) @ (sub @ X387 @ X384) @ X385)) | ($true = (X378 @ X386 @ X387 @ (comp @ X384 @ X385)))) | ~! [X388 : term] : (~((X378 @ id @ X388 @ id) = $true) | ((X378 @ id @ (sub @ X379 @ (push @ X388 @ id)) @ id) = $true)) | ~! [X389 : subst > term > term] : (((X378 @ id @ (lam @ (X389 @ sh @ one)) @ id) = $true) | ~! [X390 : term] : (~((X378 @ id @ X390 @ id) = $true) | ($true = (X378 @ id @ (X389 @ id @ X390) @ id))) | ~! [X391 : term,X392 : subst,X393 : subst] : ((sub @ (X389 @ X393 @ X391) @ X392) = (X389 @ (comp @ X393 @ X392) @ (sub @ X391 @ X392))))) => ! [X394 : term,X395 : subst > term > subst > $o] : (~! [X396 : term,X397 : subst,X398 : subst,X399 : subst] : (~((X395 @ X397 @ X396 @ (comp @ X399 @ X398)) = $true) | ((X395 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398) = $true)) | ~! [X400 : subst > term > term] : (~! [X401 : term] : (~((X395 @ id @ X401 @ id) = $true) | ((X395 @ id @ (X400 @ id @ X401) @ id) = $true)) | ~! [X402 : term,X403 : subst,X404 : subst] : ((X400 @ (comp @ X404 @ X403) @ (sub @ X402 @ X403)) = (sub @ (X400 @ X404 @ X402) @ X403)) | ((X395 @ id @ (lam @ (X400 @ sh @ one)) @ id) = $true)) | ($true = (X395 @ id @ X394 @ id)) | ~! [X405 : term,X406 : term] : (~((X395 @ id @ X405 @ id) = $true) | ~((X395 @ id @ X406 @ id) = $true) | ($true = (X395 @ id @ (ap @ (sub @ X406 @ id) @ X405) @ id))) | ~! [X407 : term] : (((X395 @ id @ X407 @ id) = $true) | ~((var @ (sub @ X407 @ id)) = $true)) | ~! [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (((X395 @ X408 @ X411 @ (comp @ X409 @ X410)) = $true) | ~($true = (X395 @ (comp @ X408 @ X409) @ (sub @ X411 @ X409) @ X410))))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2_gthm = $true) & (! [X412 : term,X413 : term > $o,X414 : subst > term > subst > $o] : (~! [X415 : term] : (($true = (X413 @ (sub @ X412 @ (push @ X415 @ id)))) | ~($true = (X413 @ X415))) | ($true = (X413 @ (lam @ X412))) | ~! [X416 : subst > term > term] : (~! [X417 : term,X418 : subst,X419 : subst] : ((sub @ (X416 @ X419 @ X417) @ X418) = (X416 @ (comp @ X419 @ X418) @ (sub @ X417 @ X418))) | ((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) = $true) | ~! [X420 : term] : (~((X414 @ id @ X420 @ id) = $true) | ((X414 @ id @ (X416 @ id @ X420) @ id) = $true))) | ~! [X421 : term] : ((X413 @ X421) = (X414 @ id @ X421 @ id))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X422 : subst > term > subst > $o,X423 : term,X424 : term > $o] : (((X424 @ (lam @ X423)) = $true) | ~! [X425 : subst > term > term] : (((X422 @ id @ (lam @ (X425 @ sh @ one)) @ id) = $true) | ~! [X426 : subst,X427 : term,X428 : subst] : ((X425 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426)) = (sub @ (X425 @ X428 @ X427) @ X426)) | ~! [X429 : term] : (~((X422 @ id @ X429 @ id) = $true) | ((X422 @ id @ (X425 @ id @ X429) @ id) = $true))) | ~! [X430 : subst,X431 : term,X432 : subst,X433 : subst] : (~((X422 @ X433 @ X431 @ (comp @ X432 @ X430)) = $true) | ((X422 @ (comp @ X433 @ X432) @ (sub @ X431 @ X432) @ X430) = $true)) | ~! [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (($true = (X422 @ X436 @ X434 @ (comp @ X437 @ X435))) | ~((X422 @ (comp @ X436 @ X437) @ (sub @ X434 @ X437) @ X435) = $true)) | ~! [X438 : term] : ((X422 @ id @ X438 @ id) = (X424 @ X438)) | ~! [X439 : term] : (((X424 @ (sub @ X423 @ (push @ X439 @ id))) = $true) | ~((X424 @ X439) = $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X440 : subst > term > subst > $o,X441 : term] : (~! [X442 : subst > term > term] : (~! [X443 : subst,X444 : subst,X445 : term] : ((X442 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444)) = (sub @ (X442 @ X443 @ X445) @ X444)) | ~! [X446 : term] : (((X440 @ id @ (X442 @ id @ X446) @ id) = $true) | ~($true = (X440 @ id @ X446 @ id))) | ((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id) = $true)) | ((X440 @ id @ (lam @ X441) @ id) = $true) | ~! [X447 : term] : (((X440 @ id @ (sub @ X441 @ (push @ X447 @ id)) @ id) = $true) | ~((X440 @ id @ X447 @ id) = $true)))) & (induction2_gthm = $true) & (! [X448 : term] : ~! [X449 : subst > term > term] : ~! [X450 : subst,X451 : term] : ((sub @ X448 @ (push @ X451 @ X450)) = (X449 @ X450 @ X451)) <=> (hoasinduction_lem3v2_f = $true)) & ((! [X452 : term,X453 : subst] : ((sub @ one @ (push @ X452 @ X453)) = X452) => (! [X454 : term,X455 : subst] : ((comp @ sh @ (push @ X454 @ X455)) = X455) => (! [X456 : subst] : ((comp @ X456 @ id) = X456) => (! [X457 : term,X458 : term > $o] : (~! [X459 : term,X460 : term] : (~((X458 @ X459) = $true) | ((X458 @ (ap @ X460 @ X459)) = $true) | ~((X458 @ X460) = $true)) | ($true = (X458 @ X457)) | ~! [X461 : term] : (((X458 @ X461) = $true) | ~((var @ X461) = $true)) | ~! [X462 : term] : (~((X458 @ X462) = $true) | ((X458 @ (lam @ X462)) = $true))) => ! [X463 : term,X464 : term > $o,X465 : subst] : (~! [X466 : term] : (($true = (X464 @ (lam @ X466))) | ~! [X467 : term] : (((X464 @ (sub @ X466 @ (push @ X467 @ id))) = $true) | ~((X464 @ X467) = $true))) | ~! [X468 : term] : (((X464 @ (sub @ X468 @ X465)) = $true) | ~((var @ X468) = $true)) | ($true = (X464 @ (sub @ X463 @ X465))) | ~! [X469 : term,X470 : term] : (((X464 @ (ap @ X469 @ X470)) = $true) | ~((X464 @ X469) = $true) | ~((X464 @ X470) = $true))))))) <=> (induction2lem_lthm = $true)) & (apnotvar = $true) & (axabs = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X471 : term,X472 : subst] : ((sub @ one @ (push @ X471 @ X472)) = X471) => (! [X473 : term,X474 : subst] : ((comp @ sh @ (push @ X473 @ X474)) = X474) => (! [X475 : term,X476 : term] : (((lam @ X475) != (lam @ X476)) | (X475 = X476)) => ! [X477 : term,X478 : subst,X479 : subst > term > term,X480 : subst > term > term] : (~! [X481 : subst,X482 : term,X483 : subst] : ((sub @ (X479 @ X483 @ X482) @ X481) = (X479 @ (comp @ X483 @ X481) @ (sub @ X482 @ X481))) | ~! [X484 : subst,X485 : term,X486 : subst] : ((X480 @ (comp @ X484 @ X486) @ (sub @ X485 @ X486)) = (sub @ (X480 @ X484 @ X485) @ X486)) | ((lam @ (X480 @ sh @ one)) != (lam @ (X479 @ sh @ one))) | ((X479 @ X478 @ X477) = (X480 @ X478 @ X477)))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X487 : term,X488 : subst > term > subst > $o] : (($true = (X488 @ id @ (lam @ (sub @ X487 @ (push @ one @ sh))) @ id)) | ~! [X489 : term] : (~($true = (X488 @ id @ X489 @ id)) | ((X488 @ id @ (sub @ X487 @ (push @ X489 @ id)) @ id) = $true)) | ~! [X490 : subst > term > term,X491 : term] : (~! [X492 : subst,X493 : subst,X494 : term] : ((sub @ (X490 @ X492 @ X494) @ X493) = (sub @ (sub @ X491 @ (push @ X494 @ X492)) @ X493)) | ($true = (X488 @ id @ (lam @ (X490 @ sh @ one)) @ id)) | ~! [X495 : term] : (~((X488 @ id @ X495 @ id) = $true) | ((X488 @ id @ (X490 @ id @ X495) @ id) = $true)) | ~! [X496 : subst,X497 : subst,X498 : term] : ((X490 @ (comp @ X496 @ X497) @ (sub @ X498 @ X497)) = (sub @ X491 @ (push @ (sub @ X498 @ X497) @ (comp @ X496 @ X497))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X499 : term,X500 : subst] : ((sub @ one @ (push @ X499 @ X500)) = X499) => (! [X501 : subst,X502 : term] : ((comp @ sh @ (push @ X502 @ X501)) = X501) => ! [X503 : subst,X504 : term > $o,X505 : term,X506 : term,X507 : term > $o] : (($true = (X504 @ (sub @ X506 @ (push @ X505 @ X503)))) | ~((X507 @ X506) = $true))))) & (axvarshift = $true) & ((induction2lem = $true) <=> ! [X508 : subst,X509 : term,X510 : term > $o] : (~! [X511 : term] : (((X510 @ (sub @ X511 @ X508)) = $true) | ~((var @ X511) = $true)) | ~! [X512 : term,X513 : term] : (~((X510 @ X513) = $true) | ($true = (X510 @ (ap @ X513 @ X512))) | ~((X510 @ X512) = $true)) | ~! [X514 : term] : (((X510 @ (lam @ X514)) = $true) | ~! [X515 : term] : (((X510 @ (sub @ X514 @ (push @ X515 @ id))) = $true) | ~((X510 @ X515) = $true))) | ((X510 @ (sub @ X509 @ X508)) = $true))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((induction2_lthm = $true) <=> (! [X516 : term] : ((sub @ X516 @ id) = X516) => (! [X517 : term > $o,X518 : subst,X519 : term] : (~! [X520 : term] : (~((var @ X520) = $true) | ($true = (X517 @ (sub @ X520 @ X518)))) | ~! [X521 : term] : (~! [X522 : term] : (~($true = (X517 @ X522)) | ((X517 @ (sub @ X521 @ (push @ X522 @ id))) = $true)) | ($true = (X517 @ (lam @ X521)))) | ~! [X523 : term,X524 : term] : (~((X517 @ X524) = $true) | ~((X517 @ X523) = $true) | ((X517 @ (ap @ X523 @ X524)) = $true)) | ($true = (X517 @ (sub @ X519 @ X518)))) => ! [X525 : term > $o,X526 : term] : (($true = (X525 @ X526)) | ~! [X527 : term] : (~! [X528 : term] : (((X525 @ (sub @ X527 @ (push @ X528 @ id))) = $true) | ~((X525 @ X528) = $true)) | ((X525 @ (lam @ X527)) = $true)) | ~! [X529 : term] : (~((var @ X529) = $true) | ((X525 @ X529) = $true)) | ~! [X530 : term,X531 : term] : (~($true = (X525 @ X531)) | ((X525 @ (ap @ X530 @ X531)) = $true) | ~($true = (X525 @ X530))))))) & (hoasinduction_lem2_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X533 @ X535) != (ap @ X534 @ X532)) | (X532 = X535)) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : ((X536 = X538) | ((ap @ (sub @ X539 @ id) @ X538) != (ap @ (sub @ X537 @ id) @ X536))))) & (axapp = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ~((var @ (d2term @ d_one)) = $true)),
% 21.29/4.27 inference(rectify,[status(thm)],[f6])).
% 21.29/4.27 thf(f6,plain,(
% 21.29/4.27 (substmonoid_gthm = $true) & (axmap = $true) & ((laminj = $true) <=> ! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1))) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : (((X6 @ (sub @ X2 @ (push @ X5 @ X4))) = $true) | ~((X3 @ X2) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X7 : term] : ((sub @ X7 @ id) = X7) => (! [X8 : term,X9 : subst > term > subst > $o] : (($true = (X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) | ~! [X10 : subst > term > term] : (((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true) | ~! [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) = (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13))) | ~! [X14 : term] : (~((X9 @ id @ X14 @ id) = $true) | ((X9 @ id @ (X10 @ id @ X14) @ id) = $true))) | ~! [X15 : term] : (~((X9 @ id @ X15 @ id) = $true) | ($true = (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id)))) => ! [X16 : term,X17 : subst > term > subst > $o] : (~! [X18 : term] : (((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) = $true) | ~((X17 @ id @ X18 @ id) = $true)) | ($true = (X17 @ id @ (lam @ X16) @ id)) | ~! [X19 : subst > term > term] : (~! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) | ~! [X23 : term] : (((X17 @ id @ (X19 @ id @ X23) @ id) = $true) | ~($true = (X17 @ id @ X23 @ id))) | ($true = (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id))))))) & (hoasinduction_lem3a_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X24 : subst > term > subst > $o] : ~! [X25 : term > $o] : ~! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26)) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X27 : term] : ~! [X28 : subst > term > term] : ~! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29)))) & ((hoasapinj2 = $true) <=> ! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34)))) & ! [X35 : d_subst] : (d_id = X35) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X36 : term,X37 : subst > term > subst > $o] : (~! [X38 : term,X39 : term] : (($true = (X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id)) | ~((X37 @ id @ X39 @ id) = $true) | ~((X37 @ id @ X38 @ id) = $true)) | ~! [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (~($true = (X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42)) | ((X37 @ X40 @ X41 @ (comp @ X43 @ X42)) = $true)) | ~! [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (~((X37 @ X47 @ X46 @ (comp @ X44 @ X45)) = $true) | ((X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45) = $true)) | ~! [X48 : subst > term > term] : (~! [X49 : term] : (~($true = (X37 @ id @ X49 @ id)) | ($true = (X37 @ id @ (X48 @ id @ X49) @ id))) | ~! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50)) | ((X37 @ id @ (lam @ (X48 @ sh @ one)) @ id) = $true)) | ~! [X53 : term] : (((X37 @ id @ X53 @ id) = $true) | ~($true = (var @ (sub @ X53 @ id)))) | ($true = (X37 @ id @ X36 @ id)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) <=> (! [X54 : subst > term > subst > $o] : ~! [X55 : term > $o] : ~! [X56 : term] : ((X54 @ id @ X56 @ id) = (X55 @ X56)) => (! [X57 : term,X58 : term > $o] : (~! [X59 : term,X60 : term] : (~($true = (X58 @ X59)) | ~((X58 @ X60) = $true) | ((X58 @ (ap @ X59 @ X60)) = $true)) | ~! [X61 : term] : (~! [X62 : term] : (((X58 @ (sub @ X61 @ (push @ X62 @ id))) = $true) | ~($true = (X58 @ X62))) | ($true = (X58 @ (lam @ X61)))) | ~! [X63 : term] : (((X58 @ X63) = $true) | ~((var @ X63) = $true)) | ((X58 @ X57) = $true)) => (! [X64 : term] : ((sub @ X64 @ id) = X64) => (! [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (~! [X68 : subst > term > term] : (~! [X69 : term] : (~((X67 @ id @ X69 @ id) = $true) | ((X67 @ id @ (X68 @ id @ X69) @ id) = $true)) | ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) = $true) | ~! [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) = (sub @ (X68 @ X72 @ X70) @ X71))) | ~! [X73 : term] : (((X65 @ (sub @ X66 @ (push @ X73 @ id))) = $true) | ~($true = (X65 @ X73))) | ($true = (X65 @ (lam @ X66))) | ~! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74))) => ! [X75 : subst > term > subst > $o,X76 : term] : (~! [X77 : term] : (((X75 @ id @ X77 @ id) = $true) | ~((var @ (sub @ X77 @ id)) = $true)) | ~! [X78 : term,X79 : subst,X80 : subst,X81 : subst] : (((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) = $true) | ~((X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79) = $true)) | ~! [X82 : subst > term > term] : (((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) = $true) | ~! [X83 : term] : (~((X75 @ id @ X83 @ id) = $true) | ((X75 @ id @ (X82 @ id @ X83) @ id) = $true)) | ~! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ~! [X87 : subst,X88 : subst,X89 : term,X90 : subst] : (((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) = $true) | ~((X75 @ X90 @ X89 @ (comp @ X87 @ X88)) = $true)) | ~! [X91 : term,X92 : term] : (~((X75 @ id @ X91 @ id) = $true) | ((X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) = $true) | ~($true = (X75 @ id @ X92 @ id))) | ((X75 @ id @ X76 @ id) = $true))))))) & (! [X93 : term,X94 : term,X95 : subst > term > term] : (~! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)) | ((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94))) <=> (hoaslamnotap = $true)) & ~(ulamvar1 = $true) & (axclos = $true) & ((axidr = $true) <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & (hoasinduction_lem1 = $true) & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> (axscons = $true)) & ((axshiftcons = $true) <=> ! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104)) & ((! [X105 : term] : ((sub @ X105 @ id) = X105) => (! [X106 : term,X107 : term,X108 : term,X109 : term] : (((ap @ X108 @ X106) != (ap @ X107 @ X109)) | (X107 = X108)) => ! [X110 : term,X111 : term,X112 : term,X113 : term] : ((X111 = X113) | ((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110))))) <=> (hoasapinj1_lthm = $true)) & ~(lamnotap = $true) & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> (axvarcons = $true)) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) = (d2subst @ X117)) => (X116 = X117)) & (! [X118 : subst > term > subst > $o] : ~! [X119 : term > $o] : ~! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) <=> (hoasinduction_lem0 = $true)) & (one = (d2term @ d_one)) & (! [X121 : subst > term > subst > $o,X122 : term] : (~! [X123 : subst > term > term] : (~! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124)) | ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) = $true) | ~! [X127 : term] : (~((X121 @ id @ X127 @ id) = $true) | ($true = (X121 @ id @ (X123 @ id @ X127) @ id)))) | ((X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) = $true) | ~! [X128 : term] : (((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) = $true) | ~($true = (X121 @ id @ X128 @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X129 : term] : ~! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one))) & ((induction = $true) <=> ! [X131 : term > $o,X132 : term] : (~! [X133 : term,X134 : term] : (~((X131 @ X134) = $true) | ((X131 @ (ap @ X133 @ X134)) = $true) | ~((X131 @ X133) = $true)) | ~! [X135 : term] : (((X131 @ (lam @ X135)) = $true) | ~($true = (X131 @ X135))) | ~! [X136 : term] : (($true = (X131 @ X136)) | ~($true = (var @ X136))) | ((X131 @ X132) = $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X137 : subst,X138 : term,X139 : term > $o] : ~! [X140 : term > $o] : ~! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) <=> (pushprop_lem0 = $true)) & (! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : (((X144 @ one) = $true) | ~((X145 @ X143) = $true) | ~! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146))) <=> (pushprop_lem1v2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((! [X152 : term] : ((sub @ X152 @ id) = X152) => ! [X153 : subst > term > subst > $o,X154 : term,X155 : term > $o] : (~! [X156 : term] : (~((X155 @ X156) = $true) | ($true = (X155 @ (sub @ X154 @ (push @ X156 @ id))))) | ~! [X157 : term,X158 : subst,X159 : subst,X160 : subst] : (((X153 @ (comp @ X159 @ X158) @ (sub @ X157 @ X158) @ X160) = $true) | ~((X153 @ X159 @ X157 @ (comp @ X158 @ X160)) = $true)) | ~! [X161 : subst > term > term] : (~! [X162 : term] : (((X153 @ id @ (X161 @ id @ X162) @ id) = $true) | ~((X153 @ id @ X162 @ id) = $true)) | ~! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X161 @ X163 @ X164) @ X165) = (X161 @ (comp @ X163 @ X165) @ (sub @ X164 @ X165))) | ((X153 @ id @ (lam @ (X161 @ sh @ one)) @ id) = $true)) | ((X155 @ (lam @ X154)) = $true) | ~! [X166 : term] : ((X153 @ id @ X166 @ id) = (X155 @ X166)) | ~! [X167 : subst,X168 : subst,X169 : term,X170 : subst] : (~((X153 @ (comp @ X167 @ X168) @ (sub @ X169 @ X168) @ X170) = $true) | ((X153 @ X167 @ X169 @ (comp @ X168 @ X170)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((apinj1 = $true) <=> ! [X171 : term,X172 : term,X173 : term,X174 : term] : ((X173 = X174) | ((ap @ X174 @ X172) != (ap @ X173 @ X171)))) & ! [X175 : d_term] : (d_one = X175) & ((termmset_lthm = $true) <=> (! [X176 : term] : ((sub @ X176 @ id) = X176) => ! [X177 : term] : ((sub @ X177 @ id) = X177))) & (termmset_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X178 : term,X179 : subst] : ((sub @ one @ (push @ X178 @ X179)) = X178) => ! [X180 : term > $o,X181 : subst,X182 : term > $o,X183 : term] : (((X180 @ one) = $true) | ~($true = (X182 @ X183)) | ~! [X184 : term] : ((X182 @ (sub @ X184 @ (push @ X183 @ X181))) = (X180 @ X184))))) & (! [X185 : term,X186 : term,X187 : subst > term > subst > $o] : (~((X187 @ id @ X185 @ id) = $true) | ~! [X188 : subst,X189 : subst,X190 : term,X191 : subst] : (((X187 @ (comp @ X189 @ X188) @ (sub @ X190 @ X188) @ X191) = $true) | ~((X187 @ X189 @ X190 @ (comp @ X188 @ X191)) = $true)) | ~! [X192 : subst,X193 : term,X194 : subst,X195 : subst] : (((X187 @ X194 @ X193 @ (comp @ X192 @ X195)) = $true) | ~((X187 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192) @ X195) = $true)) | ((X187 @ id @ (ap @ X185 @ X186) @ id) = $true) | ~! [X196 : term,X197 : term] : (~((X187 @ id @ X197 @ id) = $true) | ~($true = (X187 @ id @ X196 @ id)) | ((X187 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id) = $true)) | ~((X187 @ id @ X186 @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (axassoc = $true) & ((induction2 = $true) <=> ! [X198 : term,X199 : term > $o] : (~! [X200 : term] : (~((var @ X200) = $true) | ($true = (X199 @ X200))) | ~! [X201 : term] : (($true = (X199 @ (lam @ X201))) | ~! [X202 : term] : (((X199 @ (sub @ X201 @ (push @ X202 @ id))) = $true) | ~((X199 @ X202) = $true))) | ($true = (X199 @ X198)) | ~! [X203 : term,X204 : term] : (~($true = (X199 @ X204)) | ((X199 @ (ap @ X203 @ X204)) = $true) | ~((X199 @ X203) = $true)))) & ((hoasinduction_lem3b = $true) <=> ! [X205 : term] : ~! [X206 : subst > term > term] : ((sub @ X205 @ (push @ one @ sh)) != (X206 @ sh @ one))) & (induction2lem_gthm = $true) & (! [X207 : subst > term > subst > $o,X208 : term] : (~! [X209 : term,X210 : term] : (~((X207 @ id @ X210 @ id) = $true) | ~((X207 @ id @ X209 @ id) = $true) | ((X207 @ id @ (ap @ (sub @ X209 @ id) @ X210) @ id) = $true)) | ($true = (X207 @ id @ X208 @ id)) | ~! [X211 : subst > term > term] : (~! [X212 : subst,X213 : subst,X214 : term] : ((sub @ (X211 @ X212 @ X214) @ X213) = (X211 @ (comp @ X212 @ X213) @ (sub @ X214 @ X213))) | ~! [X215 : term] : (~((X207 @ id @ X215 @ id) = $true) | ((X207 @ id @ (X211 @ id @ X215) @ id) = $true)) | ((X207 @ id @ (lam @ (X211 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & ((d2subst @ d_id) = sh) & ((pushprop_lem0_lthm = $true) <=> ! [X216 : term,X217 : term > $o,X218 : subst] : ~! [X219 : term > $o] : ~! [X220 : term] : ((X217 @ (sub @ X220 @ (push @ X216 @ X218))) = (X219 @ X220))) & (hoasapnotvar_gthm = $true) & (! [X221 : term] : ((sub @ X221 @ id) = X221) <=> (termmset = $true)) & ((hoaslaminj = $true) <=> ! [X222 : subst,X223 : subst > term > term,X224 : subst > term > term,X225 : term] : (~! [X226 : term,X227 : subst,X228 : subst] : ((sub @ (X224 @ X227 @ X226) @ X228) = (X224 @ (comp @ X227 @ X228) @ (sub @ X226 @ X228))) | ~! [X229 : subst,X230 : term,X231 : subst] : ((sub @ (X223 @ X231 @ X230) @ X229) = (X223 @ (comp @ X231 @ X229) @ (sub @ X230 @ X229))) | ((X224 @ X222 @ X225) = (X223 @ X222 @ X225)) | ((lam @ (X223 @ sh @ one)) != (lam @ (X224 @ sh @ one))))) & (hoaslamnotvar_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_gthm = $true) & ((! [X232 : term] : ~! [X233 : subst > term > term] : ~! [X234 : subst,X235 : term] : ((sub @ X232 @ (push @ X235 @ X234)) = (X233 @ X234 @ X235)) => (! [X236 : term] : ((sub @ X236 @ id) = X236) => ! [X237 : subst > term > subst > $o,X238 : term > $o,X239 : term] : (~! [X240 : term] : ((X238 @ X240) = (X237 @ id @ X240 @ id)) | ((X238 @ (lam @ X239)) = $true) | ~! [X241 : term] : (((X238 @ (sub @ X239 @ (push @ X241 @ id))) = $true) | ~((X238 @ X241) = $true)) | ~! [X242 : subst > term > term] : (~! [X243 : term] : (((X237 @ id @ (X242 @ id @ X243) @ id) = $true) | ~((X237 @ id @ X243 @ id) = $true)) | ~! [X244 : term,X245 : subst,X246 : subst] : ((X242 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245)) = (sub @ (X242 @ X246 @ X244) @ X245)) | ((X237 @ id @ (lam @ (X242 @ sh @ one)) @ id) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop = $true) & (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X247 = X249) | ((ap @ (sub @ X247 @ id) @ X248) != (ap @ (sub @ X249 @ id) @ X250))) <=> (hoasapinj1 = $true)) & (! [X251 : term,X252 : term] : (((sub @ X252 @ sh) != (sub @ X251 @ sh)) | (X251 = X252)) <=> (shinj = $true)) & (! [X253 : subst > term > subst > $o,X254 : term] : (((X253 @ id @ (lam @ (sub @ X254 @ (push @ one @ sh))) @ id) = $true) | ~! [X255 : term] : (~((X253 @ id @ X255 @ id) = $true) | ((X253 @ id @ (sub @ X254 @ (push @ X255 @ id)) @ id) = $true)) | ~! [X256 : subst > term > term] : (~! [X257 : term] : (($true = (X253 @ id @ (X256 @ id @ X257) @ id)) | ~($true = (X253 @ id @ X257 @ id))) | ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id) = $true) | ~! [X258 : term,X259 : subst,X260 : subst] : ((X256 @ (comp @ X260 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X256 @ X260 @ X258) @ X259)))) <=> (hoasinduction_lem3aa = $true)) & ! [X261 : d_term,X262 : d_term] : (((d2term @ X262) = (d2term @ X261)) => (X261 = X262)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X263 : subst > term > subst > $o,X264 : term] : (~! [X265 : subst,X266 : term,X267 : subst,X268 : subst] : (~((X263 @ (comp @ X265 @ X268) @ (sub @ X266 @ X268) @ X267) = $true) | ($true = (X263 @ X265 @ X266 @ (comp @ X268 @ X267)))) | ~! [X269 : term,X270 : subst,X271 : subst,X272 : subst] : (((X263 @ (comp @ X270 @ X271) @ (sub @ X269 @ X271) @ X272) = $true) | ~((X263 @ X270 @ X269 @ (comp @ X271 @ X272)) = $true)) | ~! [X273 : term] : (((X263 @ id @ (sub @ X264 @ (push @ X273 @ id)) @ id) = $true) | ~($true = (X263 @ id @ X273 @ id))) | ((X263 @ id @ (lam @ X264) @ id) = $true) | ~! [X274 : subst > term > term] : (((X263 @ id @ (lam @ (X274 @ sh @ one)) @ id) = $true) | ~! [X275 : subst,X276 : subst,X277 : term] : ((X274 @ (comp @ X275 @ X276) @ (sub @ X277 @ X276)) = (sub @ (X274 @ X275 @ X277) @ X276)) | ~! [X278 : term] : (~((X263 @ id @ X278 @ id) = $true) | ($true = (X263 @ id @ (X274 @ id @ X278) @ id)))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X282 : subst] : ((comp @ X282 @ id) = X282) & ! [X283 : subst] : ((comp @ id @ X283) = X283)) <=> (substmonoid = $true)) & ((substmonoid_lthm = $true) <=> (! [X284 : subst] : ((comp @ id @ X284) = X284) => (! [X285 : subst] : ((comp @ X285 @ id) = X285) => (! [X286 : subst] : ((comp @ X286 @ id) = X286) & ! [X287 : subst] : ((comp @ id @ X287) = X287))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X288 : term,X289 : term,X290 : subst > term > subst > $o,X291 : term > $o] : (~! [X292 : subst,X293 : subst,X294 : term,X295 : subst] : (((X290 @ X293 @ X294 @ (comp @ X292 @ X295)) = $true) | ~((X290 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295) = $true)) | ~! [X296 : term] : ((X290 @ id @ X296 @ id) = (X291 @ X296)) | ~! [X297 : subst,X298 : subst,X299 : term,X300 : subst] : (~($true = (X290 @ X297 @ X299 @ (comp @ X298 @ X300))) | ($true = (X290 @ (comp @ X297 @ X298) @ (sub @ X299 @ X298) @ X300))) | ~((X291 @ X289) = $true) | ~($true = (X291 @ X288)) | ($true = (X291 @ (ap @ X288 @ X289))) | ~! [X301 : term,X302 : term] : (~((X290 @ id @ X301 @ id) = $true) | ((X290 @ id @ (ap @ (sub @ X301 @ id) @ X302) @ id) = $true) | ~((X290 @ id @ X302 @ id) = $true)))) & (! [X303 : term,X304 : term,X305 : term,X306 : term] : ((X303 = X305) | ((ap @ X304 @ X305) != (ap @ X306 @ X303))) <=> (apinj2 = $true)) & (lamnotvar = $true) & (! [X307 : subst] : ((comp @ id @ X307) = X307) <=> (axidl = $true)) & (hoasapinj2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasapnotvar = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X308 : subst > term > subst > $o] : ~! [X309 : term > $o] : ~! [X310 : term] : ((X309 @ X310) = (X308 @ id @ X310 @ id)) => (! [X311 : term > $o,X312 : term] : (~! [X313 : term,X314 : term] : (~((X311 @ X314) = $true) | ($true = (X311 @ (ap @ X313 @ X314))) | ~($true = (X311 @ X313))) | ($true = (X311 @ X312)) | ~! [X315 : term] : (((X311 @ X315) = $true) | ~($true = (var @ X315))) | ~! [X316 : term] : (~! [X317 : term] : (~($true = (X311 @ X317)) | ((X311 @ (sub @ X316 @ (push @ X317 @ id))) = $true)) | ((X311 @ (lam @ X316)) = $true))) => (! [X318 : term] : ((sub @ X318 @ id) = X318) => (! [X319 : term > $o,X320 : term,X321 : subst > term > subst > $o] : (~! [X322 : term] : ((X319 @ X322) = (X321 @ id @ X322 @ id)) | ~! [X323 : term] : (((X319 @ (sub @ X320 @ (push @ X323 @ id))) = $true) | ~((X319 @ X323) = $true)) | ((X319 @ (lam @ X320)) = $true) | ~! [X324 : subst > term > term] : (~! [X325 : term] : (~($true = (X321 @ id @ X325 @ id)) | ((X321 @ id @ (X324 @ id @ X325) @ id) = $true)) | ~! [X326 : term,X327 : subst,X328 : subst] : ((sub @ (X324 @ X328 @ X326) @ X327) = (X324 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))) | ($true = (X321 @ id @ (lam @ (X324 @ sh @ one)) @ id)))) => ! [X329 : subst > term > subst > $o,X330 : term] : (~! [X331 : subst > term > term] : (~! [X332 : term] : (~($true = (X329 @ id @ X332 @ id)) | ((X329 @ id @ (X331 @ id @ X332) @ id) = $true)) | ~! [X333 : subst,X334 : subst,X335 : term] : ((sub @ (X331 @ X334 @ X335) @ X333) = (X331 @ (comp @ X334 @ X333) @ (sub @ X335 @ X333))) | ($true = (X329 @ id @ (lam @ (X331 @ sh @ one)) @ id))) | ~! [X336 : term,X337 : term] : (~((X329 @ id @ X337 @ id) = $true) | ((X329 @ id @ (ap @ (sub @ X337 @ id) @ X336) @ id) = $true) | ~((X329 @ id @ X336 @ id) = $true)) | ((X329 @ id @ X330 @ id) = $true))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X338 : term] : ((sub @ X338 @ id) = X338) => (! [X339 : subst > term > subst > $o,X340 : term] : (~! [X341 : subst > term > term] : (((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id) = $true) | ~! [X342 : term] : (~((X339 @ id @ X342 @ id) = $true) | ($true = (X339 @ id @ (X341 @ id @ X342) @ id))) | ~! [X343 : term,X344 : subst,X345 : subst] : ((sub @ (X341 @ X345 @ X343) @ X344) = (X341 @ (comp @ X345 @ X344) @ (sub @ X343 @ X344)))) | ~! [X346 : term] : (($true = (X339 @ id @ (sub @ X340 @ (push @ X346 @ id)) @ id)) | ~((X339 @ id @ X346 @ id) = $true)) | ((X339 @ id @ (lam @ (sub @ X340 @ (push @ one @ sh))) @ id) = $true)) => ! [X347 : term,X348 : subst > term > subst > $o] : (~! [X349 : term] : (((X348 @ id @ (sub @ X347 @ (push @ X349 @ id)) @ id) = $true) | ~($true = (X348 @ id @ X349 @ id))) | ~! [X350 : subst > term > term] : (~! [X351 : term,X352 : subst,X353 : subst] : ((X350 @ (comp @ X352 @ X353) @ (sub @ X351 @ X353)) = (sub @ (X350 @ X352 @ X351) @ X353)) | ~! [X354 : term] : (((X348 @ id @ (X350 @ id @ X354) @ id) = $true) | ~($true = (X348 @ id @ X354 @ id))) | ($true = (X348 @ id @ (lam @ (X350 @ sh @ one)) @ id))) | ((X348 @ id @ (lam @ X347) @ id) = $true) | ~! [X355 : subst,X356 : subst,X357 : subst,X358 : term] : (~((X348 @ X357 @ X358 @ (comp @ X355 @ X356)) = $true) | ((X348 @ (comp @ X357 @ X355) @ (sub @ X358 @ X355) @ X356) = $true)) | ~! [X359 : term,X360 : subst,X361 : subst,X362 : subst] : (((X348 @ X361 @ X359 @ (comp @ X362 @ X360)) = $true) | ~((X348 @ (comp @ X361 @ X362) @ (sub @ X359 @ X362) @ X360) = $true)))))) & (hoasinduction_lem2_lthm = $true) & (! [X363 : term] : ((sub @ X363 @ id) = X363) <=> (axvarid = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X364 : term] : ? [X365 : d_term] : ((d2term @ X365) = X364) & (pushprop_lem2v2 = $true) & ((! [X366 : term,X367 : term > $o] : (~! [X368 : term,X369 : term] : (~((X367 @ X368) = $true) | ~($true = (X367 @ X369)) | ((X367 @ (ap @ X369 @ X368)) = $true)) | ($true = (X367 @ X366)) | ~! [X370 : term] : (~! [X371 : term] : (((X367 @ (sub @ X370 @ (push @ X371 @ id))) = $true) | ~($true = (X367 @ X371))) | ((X367 @ (lam @ X370)) = $true)) | ~! [X372 : term] : (((X367 @ X372) = $true) | ~($true = (var @ X372)))) => (! [X373 : term,X374 : term,X375 : subst > term > subst > $o] : (((X375 @ id @ (ap @ X373 @ X374) @ id) = $true) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (~((X375 @ (comp @ X376 @ X377) @ (sub @ X379 @ X377) @ X378) = $true) | ((X375 @ X376 @ X379 @ (comp @ X377 @ X378)) = $true)) | ~((X375 @ id @ X373 @ id) = $true) | ~($true = (X375 @ id @ X374 @ id)) | ~! [X380 : subst,X381 : subst,X382 : subst,X383 : term] : (((X375 @ (comp @ X381 @ X380) @ (sub @ X383 @ X380) @ X382) = $true) | ~((X375 @ X381 @ X383 @ (comp @ X380 @ X382)) = $true)) | ~! [X384 : term,X385 : term] : (~($true = (X375 @ id @ X384 @ id)) | ~((X375 @ id @ X385 @ id) = $true) | ($true = (X375 @ id @ (ap @ (sub @ X384 @ id) @ X385) @ id)))) => (! [X386 : subst > term > subst > $o,X387 : term] : (~! [X388 : subst,X389 : term,X390 : subst,X391 : subst] : (((X386 @ (comp @ X391 @ X390) @ (sub @ X389 @ X390) @ X388) = $true) | ~((X386 @ X391 @ X389 @ (comp @ X390 @ X388)) = $true)) | ((X386 @ id @ (lam @ X387) @ id) = $true) | ~! [X392 : subst,X393 : subst,X394 : subst,X395 : term] : (~($true = (X386 @ (comp @ X394 @ X392) @ (sub @ X395 @ X392) @ X393)) | ((X386 @ X394 @ X395 @ (comp @ X392 @ X393)) = $true)) | ~! [X396 : term] : (~((X386 @ id @ X396 @ id) = $true) | ((X386 @ id @ (sub @ X387 @ (push @ X396 @ id)) @ id) = $true)) | ~! [X397 : subst > term > term] : (((X386 @ id @ (lam @ (X397 @ sh @ one)) @ id) = $true) | ~! [X398 : term] : (~($true = (X386 @ id @ X398 @ id)) | ((X386 @ id @ (X397 @ id @ X398) @ id) = $true)) | ~! [X399 : term,X400 : subst,X401 : subst] : ((X397 @ (comp @ X401 @ X400) @ (sub @ X399 @ X400)) = (sub @ (X397 @ X401 @ X399) @ X400)))) => ! [X402 : term,X403 : subst > term > subst > $o] : (~! [X404 : term,X405 : subst,X406 : subst,X407 : subst] : (~((X403 @ X405 @ X404 @ (comp @ X407 @ X406)) = $true) | ((X403 @ (comp @ X405 @ X407) @ (sub @ X404 @ X407) @ X406) = $true)) | ~! [X408 : subst > term > term] : (~! [X409 : term] : (~((X403 @ id @ X409 @ id) = $true) | ((X403 @ id @ (X408 @ id @ X409) @ id) = $true)) | ~! [X410 : term,X411 : subst,X412 : subst] : ((sub @ (X408 @ X412 @ X410) @ X411) = (X408 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411))) | ((X403 @ id @ (lam @ (X408 @ sh @ one)) @ id) = $true)) | ((X403 @ id @ X402 @ id) = $true) | ~! [X413 : term,X414 : term] : (~($true = (X403 @ id @ X413 @ id)) | ~((X403 @ id @ X414 @ id) = $true) | ((X403 @ id @ (ap @ (sub @ X414 @ id) @ X413) @ id) = $true)) | ~! [X415 : term] : (($true = (X403 @ id @ X415 @ id)) | ~((var @ (sub @ X415 @ id)) = $true)) | ~! [X416 : subst,X417 : subst,X418 : subst,X419 : term] : (($true = (X403 @ X416 @ X419 @ (comp @ X417 @ X418))) | ~((X403 @ (comp @ X416 @ X417) @ (sub @ X419 @ X417) @ X418) = $true)))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2_gthm = $true) & (! [X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (~! [X423 : term] : (($true = (X421 @ (sub @ X420 @ (push @ X423 @ id)))) | ~((X421 @ X423) = $true)) | ((X421 @ (lam @ X420)) = $true) | ~! [X424 : subst > term > term] : (~! [X425 : term,X426 : subst,X427 : subst] : ((X424 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426)) = (sub @ (X424 @ X427 @ X425) @ X426)) | ((X422 @ id @ (lam @ (X424 @ sh @ one)) @ id) = $true) | ~! [X428 : term] : (~((X422 @ id @ X428 @ id) = $true) | ((X422 @ id @ (X424 @ id @ X428) @ id) = $true))) | ~! [X429 : term] : ((X422 @ id @ X429 @ id) = (X421 @ X429))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X432 : subst > term > subst > $o,X433 : term,X434 : term > $o] : (((X434 @ (lam @ X433)) = $true) | ~! [X435 : subst > term > term] : (((X432 @ id @ (lam @ (X435 @ sh @ one)) @ id) = $true) | ~! [X436 : subst,X437 : term,X438 : subst] : ((X435 @ (comp @ X438 @ X436) @ (sub @ X437 @ X436)) = (sub @ (X435 @ X438 @ X437) @ X436)) | ~! [X439 : term] : (~((X432 @ id @ X439 @ id) = $true) | ((X432 @ id @ (X435 @ id @ X439) @ id) = $true))) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (~($true = (X432 @ X443 @ X441 @ (comp @ X442 @ X440))) | ((X432 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442) @ X440) = $true)) | ~! [X444 : term,X445 : subst,X446 : subst,X447 : subst] : (($true = (X432 @ X446 @ X444 @ (comp @ X447 @ X445))) | ~((X432 @ (comp @ X446 @ X447) @ (sub @ X444 @ X447) @ X445) = $true)) | ~! [X448 : term] : ((X434 @ X448) = (X432 @ id @ X448 @ id)) | ~! [X449 : term] : (((X434 @ (sub @ X433 @ (push @ X449 @ id))) = $true) | ~((X434 @ X449) = $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X450 : subst > term > subst > $o,X451 : term] : (~! [X452 : subst > term > term] : (~! [X453 : subst,X454 : subst,X455 : term] : ((X452 @ (comp @ X453 @ X454) @ (sub @ X455 @ X454)) = (sub @ (X452 @ X453 @ X455) @ X454)) | ~! [X456 : term] : (($true = (X450 @ id @ (X452 @ id @ X456) @ id)) | ~((X450 @ id @ X456 @ id) = $true)) | ($true = (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id))) | ($true = (X450 @ id @ (lam @ X451) @ id)) | ~! [X457 : term] : (((X450 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id) = $true) | ~((X450 @ id @ X457 @ id) = $true)))) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X458 : term] : ~! [X459 : subst > term > term] : ~! [X460 : subst,X461 : term] : ((sub @ X458 @ (push @ X461 @ X460)) = (X459 @ X460 @ X461))) & ((! [X462 : term,X463 : subst] : ((sub @ one @ (push @ X462 @ X463)) = X462) => (! [X464 : term,X465 : subst] : ((comp @ sh @ (push @ X464 @ X465)) = X465) => (! [X466 : subst] : ((comp @ X466 @ id) = X466) => (! [X467 : term,X468 : term > $o] : (~! [X469 : term,X470 : term] : (~((X468 @ X469) = $true) | ((X468 @ (ap @ X470 @ X469)) = $true) | ~($true = (X468 @ X470))) | ((X468 @ X467) = $true) | ~! [X471 : term] : (((X468 @ X471) = $true) | ~($true = (var @ X471))) | ~! [X472 : term] : (~((X468 @ X472) = $true) | ($true = (X468 @ (lam @ X472))))) => ! [X473 : term,X474 : term > $o,X475 : subst] : (~! [X476 : term] : (((X474 @ (lam @ X476)) = $true) | ~! [X477 : term] : (((X474 @ (sub @ X476 @ (push @ X477 @ id))) = $true) | ~($true = (X474 @ X477)))) | ~! [X478 : term] : (($true = (X474 @ (sub @ X478 @ X475))) | ~($true = (var @ X478))) | ((X474 @ (sub @ X473 @ X475)) = $true) | ~! [X479 : term,X480 : term] : (((X474 @ (ap @ X479 @ X480)) = $true) | ~((X474 @ X479) = $true) | ~((X474 @ X480) = $true))))))) <=> (induction2lem_lthm = $true)) & (apnotvar = $true) & (axabs = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X481 : term,X482 : subst] : ((sub @ one @ (push @ X481 @ X482)) = X481) => (! [X483 : term,X484 : subst] : ((comp @ sh @ (push @ X483 @ X484)) = X484) => (! [X485 : term,X486 : term] : (((lam @ X485) != (lam @ X486)) | (X485 = X486)) => ! [X487 : term,X488 : subst,X489 : subst > term > term,X490 : subst > term > term] : (((X490 @ X488 @ X487) = (X489 @ X488 @ X487)) | ~! [X491 : subst,X492 : term,X493 : subst] : ((sub @ (X489 @ X493 @ X492) @ X491) = (X489 @ (comp @ X493 @ X491) @ (sub @ X492 @ X491))) | ((lam @ (X490 @ sh @ one)) != (lam @ (X489 @ sh @ one))) | ~! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X490 @ X494 @ X495) @ X496) = (X490 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496)))))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X497 : term,X498 : subst > term > subst > $o] : (($true = (X498 @ id @ (lam @ (sub @ X497 @ (push @ one @ sh))) @ id)) | ~! [X499 : term] : (~($true = (X498 @ id @ X499 @ id)) | ((X498 @ id @ (sub @ X497 @ (push @ X499 @ id)) @ id) = $true)) | ~! [X500 : subst > term > term,X501 : term] : (~! [X502 : subst,X503 : subst,X504 : term] : ((sub @ (X500 @ X502 @ X504) @ X503) = (sub @ (sub @ X501 @ (push @ X504 @ X502)) @ X503)) | ($true = (X498 @ id @ (lam @ (X500 @ sh @ one)) @ id)) | ~! [X505 : term] : (~($true = (X498 @ id @ X505 @ id)) | ((X498 @ id @ (X500 @ id @ X505) @ id) = $true)) | ~! [X506 : subst,X507 : subst,X508 : term] : ((X500 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507)) = (sub @ X501 @ (push @ (sub @ X508 @ X507) @ (comp @ X506 @ X507))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X509 : term,X510 : subst] : ((sub @ one @ (push @ X509 @ X510)) = X509) => (! [X511 : subst,X512 : term] : ((comp @ sh @ (push @ X512 @ X511)) = X511) => ! [X513 : subst,X514 : term > $o,X515 : term,X516 : term,X517 : term > $o] : (((X514 @ (sub @ X516 @ (push @ X515 @ X513))) = $true) | ~((X517 @ X516) = $true))))) & (axvarshift = $true) & ((induction2lem = $true) <=> ! [X518 : subst,X519 : term,X520 : term > $o] : (~! [X521 : term] : (((X520 @ (sub @ X521 @ X518)) = $true) | ~((var @ X521) = $true)) | ~! [X522 : term,X523 : term] : (~((X520 @ X523) = $true) | ((X520 @ (ap @ X523 @ X522)) = $true) | ~($true = (X520 @ X522))) | ~! [X524 : term] : (((X520 @ (lam @ X524)) = $true) | ~! [X525 : term] : (($true = (X520 @ (sub @ X524 @ (push @ X525 @ id)))) | ~((X520 @ X525) = $true))) | ($true = (X520 @ (sub @ X519 @ X518))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((induction2_lthm = $true) <=> (! [X526 : term] : ((sub @ X526 @ id) = X526) => (! [X527 : term > $o,X528 : subst,X529 : term] : (~! [X530 : term] : (~((var @ X530) = $true) | ($true = (X527 @ (sub @ X530 @ X528)))) | ~! [X531 : term] : (~! [X532 : term] : (~((X527 @ X532) = $true) | ((X527 @ (sub @ X531 @ (push @ X532 @ id))) = $true)) | ((X527 @ (lam @ X531)) = $true)) | ~! [X533 : term,X534 : term] : (~($true = (X527 @ X534)) | ~((X527 @ X533) = $true) | ((X527 @ (ap @ X533 @ X534)) = $true)) | ($true = (X527 @ (sub @ X529 @ X528)))) => ! [X535 : term > $o,X536 : term] : (((X535 @ X536) = $true) | ~! [X537 : term] : (~! [X538 : term] : (((X535 @ (sub @ X537 @ (push @ X538 @ id))) = $true) | ~((X535 @ X538) = $true)) | ($true = (X535 @ (lam @ X537)))) | ~! [X539 : term] : (~((var @ X539) = $true) | ((X535 @ X539) = $true)) | ~! [X540 : term,X541 : term] : (~((X535 @ X541) = $true) | ((X535 @ (ap @ X540 @ X541)) = $true) | ~((X535 @ X540) = $true)))))) & (hoasinduction_lem2_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X542 : term,X543 : term,X544 : term,X545 : term] : (((ap @ X543 @ X545) != (ap @ X544 @ X542)) | (X542 = X545)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X546 = X548) | ((ap @ (sub @ X549 @ id) @ X548) != (ap @ (sub @ X547 @ id) @ X546))))) & (axapp = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ~((var @ (d2term @ d_one)) = $true)),
% 21.29/4.27 inference(fool_elimination,[status(thm)],[f5])).
% 21.29/4.27 thf(f5,plain,(
% 21.29/4.27 substmonoid_gthm & axmap & (! [X0 : term,X1 : term] : (((lam @ X0) != (lam @ X1)) | (X0 = X1)) <=> laminj) & (! [X2 : term,X3 : term > $o,X4 : subst,X5 : term,X6 : term > $o] : ((X6 @ (sub @ X2 @ (push @ X5 @ X4))) | ~(X3 @ X2)) <=> pushprop_lem1) & (hoasinduction_lem3a_lthm <=> (! [X7 : term] : ((sub @ X7 @ id) = X7) => (! [X8 : term,X9 : subst > term > subst > $o] : ((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id) | ~! [X10 : subst > term > term] : ((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) | ~! [X11 : subst,X12 : term,X13 : subst] : ((sub @ (X10 @ X11 @ X12) @ X13) = (X10 @ (comp @ X11 @ X13) @ (sub @ X12 @ X13))) | ~! [X14 : term] : (~(X9 @ id @ X14 @ id) | (X9 @ id @ (X10 @ id @ X14) @ id))) | ~! [X15 : term] : (~(X9 @ id @ X15 @ id) | (X9 @ id @ (sub @ X8 @ (push @ X15 @ id)) @ id))) => ! [X16 : term,X17 : subst > term > subst > $o] : (~! [X18 : term] : ((X17 @ id @ (sub @ X16 @ (push @ X18 @ id)) @ id) | ~(X17 @ id @ X18 @ id)) | (X17 @ id @ (lam @ X16) @ id) | ~! [X19 : subst > term > term] : (~! [X20 : subst,X21 : subst,X22 : term] : ((X19 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)) = (sub @ (X19 @ X21 @ X22) @ X20)) | ~! [X23 : term] : ((X17 @ id @ (X19 @ id @ X23) @ id) | ~(X17 @ id @ X23 @ id)) | (X17 @ id @ (lam @ (X19 @ sh @ one)) @ id)))))) & hoasinduction_lem3a_gthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ulamvarsh & hoasinduction_lem3b_gthm & (hoasinduction_lem0_lthm <=> ! [X24 : subst > term > subst > $o] : ~! [X25 : term > $o] : ~! [X26 : term] : ((X24 @ id @ X26 @ id) = (X25 @ X26))) & (hoasinduction_lem3v2_f_lthm <=> ! [X27 : term] : ~! [X28 : subst > term > term] : ~! [X29 : subst,X30 : term] : ((X28 @ X29 @ X30) = (sub @ X27 @ (push @ X30 @ X29)))) & (! [X31 : term,X32 : term,X33 : term,X34 : term] : ((X33 = X34) | ((ap @ (sub @ X32 @ id) @ X33) != (ap @ (sub @ X31 @ id) @ X34))) <=> hoasapinj2) & ! [X35 : d_subst] : (d_id = X35) & pushprop_lem1v2_gthm & (hoasinduction <=> ! [X36 : term,X37 : subst > term > subst > $o] : (~! [X38 : term,X39 : term] : ((X37 @ id @ (ap @ (sub @ X39 @ id) @ X38) @ id) | ~(X37 @ id @ X39 @ id) | ~(X37 @ id @ X38 @ id)) | ~! [X40 : subst,X41 : term,X42 : subst,X43 : subst] : (~(X37 @ (comp @ X40 @ X43) @ (sub @ X41 @ X43) @ X42) | (X37 @ X40 @ X41 @ (comp @ X43 @ X42))) | ~! [X44 : subst,X45 : subst,X46 : term,X47 : subst] : (~(X37 @ X47 @ X46 @ (comp @ X44 @ X45)) | (X37 @ (comp @ X47 @ X44) @ (sub @ X46 @ X44) @ X45)) | ~! [X48 : subst > term > term] : (~! [X49 : term] : (~(X37 @ id @ X49 @ id) | (X37 @ id @ (X48 @ id @ X49) @ id)) | ~! [X50 : subst,X51 : subst,X52 : term] : ((X48 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50)) = (sub @ (X48 @ X51 @ X52) @ X50)) | (X37 @ id @ (lam @ (X48 @ sh @ one)) @ id)) | ~! [X53 : term] : ((X37 @ id @ X53 @ id) | ~(var @ (sub @ X53 @ id))) | (X37 @ id @ X36 @ id))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lthm_3 <=> (! [X54 : subst > term > subst > $o] : ~! [X55 : term > $o] : ~! [X56 : term] : ((X54 @ id @ X56 @ id) = (X55 @ X56)) => (! [X57 : term,X58 : term > $o] : (~! [X59 : term,X60 : term] : (~(X58 @ X59) | ~(X58 @ X60) | (X58 @ (ap @ X59 @ X60))) | ~! [X61 : term] : (~! [X62 : term] : ((X58 @ (sub @ X61 @ (push @ X62 @ id))) | ~(X58 @ X62)) | (X58 @ (lam @ X61))) | ~! [X63 : term] : ((X58 @ X63) | ~(var @ X63)) | (X58 @ X57)) => (! [X64 : term] : ((sub @ X64 @ id) = X64) => (! [X65 : term > $o,X66 : term,X67 : subst > term > subst > $o] : (~! [X68 : subst > term > term] : (~! [X69 : term] : (~(X67 @ id @ X69 @ id) | (X67 @ id @ (X68 @ id @ X69) @ id)) | (X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) | ~! [X70 : term,X71 : subst,X72 : subst] : ((X68 @ (comp @ X72 @ X71) @ (sub @ X70 @ X71)) = (sub @ (X68 @ X72 @ X70) @ X71))) | ~! [X73 : term] : ((X65 @ (sub @ X66 @ (push @ X73 @ id))) | ~(X65 @ X73)) | (X65 @ (lam @ X66)) | ~! [X74 : term] : ((X67 @ id @ X74 @ id) = (X65 @ X74))) => ! [X75 : subst > term > subst > $o,X76 : term] : (~! [X77 : term] : ((X75 @ id @ X77 @ id) | ~(var @ (sub @ X77 @ id))) | ~! [X78 : term,X79 : subst,X80 : subst,X81 : subst] : ((X75 @ X80 @ X78 @ (comp @ X81 @ X79)) | ~(X75 @ (comp @ X80 @ X81) @ (sub @ X78 @ X81) @ X79)) | ~! [X82 : subst > term > term] : ((X75 @ id @ (lam @ (X82 @ sh @ one)) @ id) | ~! [X83 : term] : (~(X75 @ id @ X83 @ id) | (X75 @ id @ (X82 @ id @ X83) @ id)) | ~! [X84 : subst,X85 : term,X86 : subst] : ((sub @ (X82 @ X84 @ X85) @ X86) = (X82 @ (comp @ X84 @ X86) @ (sub @ X85 @ X86)))) | ~! [X87 : subst,X88 : subst,X89 : term,X90 : subst] : ((X75 @ (comp @ X90 @ X87) @ (sub @ X89 @ X87) @ X88) | ~(X75 @ X90 @ X89 @ (comp @ X87 @ X88))) | ~! [X91 : term,X92 : term] : (~(X75 @ id @ X91 @ id) | (X75 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) | ~(X75 @ id @ X92 @ id)) | (X75 @ id @ X76 @ id))))))) & (hoaslamnotap <=> ! [X93 : term,X94 : term,X95 : subst > term > term] : (((lam @ (X95 @ sh @ one)) != (ap @ (sub @ X93 @ id) @ X94)) | ~! [X96 : subst,X97 : term,X98 : subst] : ((X95 @ (comp @ X98 @ X96) @ (sub @ X97 @ X96)) = (sub @ (X95 @ X98 @ X97) @ X96)))) & ~ulamvar1 & axclos & (axidr <=> ! [X99 : subst] : ((comp @ X99 @ id) = X99)) & ! [X100 : subst] : ? [X101 : d_subst] : ((d2subst @ X101) = X100) & hoasinduction_lem1 & (! [X102 : subst] : ((push @ (sub @ one @ X102) @ (comp @ sh @ X102)) = X102) <=> axscons) & (! [X103 : term,X104 : subst] : ((comp @ sh @ (push @ X103 @ X104)) = X104) <=> axshiftcons) & ((! [X105 : term] : ((sub @ X105 @ id) = X105) => (! [X106 : term,X107 : term,X108 : term,X109 : term] : ((X107 = X108) | ((ap @ X108 @ X106) != (ap @ X107 @ X109))) => ! [X110 : term,X111 : term,X112 : term,X113 : term] : (((ap @ (sub @ X111 @ id) @ X112) != (ap @ (sub @ X113 @ id) @ X110)) | (X111 = X113)))) <=> hoasapinj1_lthm) & ~lamnotap & (! [X114 : term,X115 : subst] : ((sub @ one @ (push @ X114 @ X115)) = X114) <=> axvarcons) & pushprop_gthm & pushprop_lem2v2_lthm & ! [X116 : d_subst,X117 : d_subst] : (((d2subst @ X116) = (d2subst @ X117)) => (X116 = X117)) & (! [X118 : subst > term > subst > $o] : ~! [X119 : term > $o] : ~! [X120 : term] : ((X118 @ id @ X120 @ id) = (X119 @ X120)) <=> hoasinduction_lem0) & (one = (d2term @ d_one)) & (! [X121 : subst > term > subst > $o,X122 : term] : (~! [X123 : subst > term > term] : (~! [X124 : subst,X125 : subst,X126 : term] : ((X123 @ (comp @ X125 @ X124) @ (sub @ X126 @ X124)) = (sub @ (X123 @ X125 @ X126) @ X124)) | (X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) | ~! [X127 : term] : (~(X121 @ id @ X127 @ id) | (X121 @ id @ (X123 @ id @ X127) @ id))) | (X121 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id) | ~! [X128 : term] : ((X121 @ id @ (sub @ X122 @ (push @ X128 @ id)) @ id) | ~(X121 @ id @ X128 @ id))) <=> hoasinduction_lem3aa_lthm) & ulamvarind & hoasinduction_lem2v2_gthm & hoasinduction_gthm & hoasinduction_lem1_lthm & pushprop_lem3v2_lthm & (! [X129 : term] : ~! [X130 : subst > term > term] : ((sub @ X129 @ (push @ one @ sh)) != (X130 @ sh @ one)) <=> hoasinduction_lem3b_lthm) & (induction <=> ! [X131 : term > $o,X132 : term] : (~! [X133 : term,X134 : term] : (~(X131 @ X134) | (X131 @ (ap @ X133 @ X134)) | ~(X131 @ X133)) | ~! [X135 : term] : ((X131 @ (lam @ X135)) | ~(X131 @ X135)) | ~! [X136 : term] : ((X131 @ X136) | ~(var @ X136)) | (X131 @ X132))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X137 : subst,X138 : term,X139 : term > $o] : ~! [X140 : term > $o] : ~! [X141 : term] : ((X139 @ (sub @ X141 @ (push @ X138 @ X137))) = (X140 @ X141)) <=> pushprop_lem0) & (! [X142 : subst,X143 : term,X144 : term > $o,X145 : term > $o] : ((X144 @ one) | ~(X145 @ X143) | ~! [X146 : term] : ((X145 @ (sub @ X146 @ (push @ X143 @ X142))) = (X144 @ X146))) <=> pushprop_lem1v2) & (pushprop_p_and_p_prime = (^[X147 : term, X148 : subst, X149 : term > $o, X150 : term > $o] : (! [X151 : term] : ((X150 @ X151) = (X149 @ (sub @ X151 @ (push @ X147 @ X148))))))) & ((! [X152 : term] : ((sub @ X152 @ id) = X152) => ! [X153 : subst > term > subst > $o,X154 : term,X155 : term > $o] : (~! [X156 : term] : (~(X155 @ X156) | (X155 @ (sub @ X154 @ (push @ X156 @ id)))) | ~! [X157 : term,X158 : subst,X159 : subst,X160 : subst] : ((X153 @ (comp @ X159 @ X158) @ (sub @ X157 @ X158) @ X160) | ~(X153 @ X159 @ X157 @ (comp @ X158 @ X160))) | ~! [X161 : subst > term > term] : (~! [X162 : term] : ((X153 @ id @ (X161 @ id @ X162) @ id) | ~(X153 @ id @ X162 @ id)) | ~! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X161 @ X163 @ X164) @ X165) = (X161 @ (comp @ X163 @ X165) @ (sub @ X164 @ X165))) | (X153 @ id @ (lam @ (X161 @ sh @ one)) @ id)) | (X155 @ (lam @ X154)) | ~! [X166 : term] : ((X153 @ id @ X166 @ id) = (X155 @ X166)) | ~! [X167 : subst,X168 : subst,X169 : term,X170 : subst] : (~(X153 @ (comp @ X167 @ X168) @ (sub @ X169 @ X168) @ X170) | (X153 @ X167 @ X169 @ (comp @ X168 @ X170))))) <=> hoasinduction_lem3v2_lthm) & hoasinduction_lem3v2_gthm & (apinj1 <=> ! [X171 : term,X172 : term,X173 : term,X174 : term] : ((X173 = X174) | ((ap @ X174 @ X172) != (ap @ X173 @ X171)))) & ! [X175 : d_term] : (d_one = X175) & (termmset_lthm <=> (! [X176 : term] : ((sub @ X176 @ id) = X176) => ! [X177 : term] : ((sub @ X177 @ id) = X177))) & termmset_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem1v2_lthm <=> (! [X178 : term,X179 : subst] : ((sub @ one @ (push @ X178 @ X179)) = X178) => ! [X180 : term > $o,X181 : subst,X182 : term > $o,X183 : term] : ((X180 @ one) | ~(X182 @ X183) | ~! [X184 : term] : ((X182 @ (sub @ X184 @ (push @ X183 @ X181))) = (X180 @ X184))))) & (! [X185 : term,X186 : term,X187 : subst > term > subst > $o] : (~(X187 @ id @ X185 @ id) | ~! [X188 : subst,X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X189 @ X188) @ (sub @ X190 @ X188) @ X191) | ~(X187 @ X189 @ X190 @ (comp @ X188 @ X191))) | ~! [X192 : subst,X193 : term,X194 : subst,X195 : subst] : ((X187 @ X194 @ X193 @ (comp @ X192 @ X195)) | ~(X187 @ (comp @ X194 @ X192) @ (sub @ X193 @ X192) @ X195)) | (X187 @ id @ (ap @ X185 @ X186) @ id) | ~! [X196 : term,X197 : term] : (~(X187 @ id @ X197 @ id) | ~(X187 @ id @ X196 @ id) | (X187 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) | ~(X187 @ id @ X186 @ id)) <=> hoasinduction_lem2) & pushprop_lthm & hoasinduction_lem1_gthm & hoaslamnotap_lthm & hoasinduction_lem3_gthm & axassoc & (induction2 <=> ! [X198 : term,X199 : term > $o] : (~! [X200 : term] : (~(var @ X200) | (X199 @ X200)) | ~! [X201 : term] : ((X199 @ (lam @ X201)) | ~! [X202 : term] : ((X199 @ (sub @ X201 @ (push @ X202 @ id))) | ~(X199 @ X202))) | (X199 @ X198) | ~! [X203 : term,X204 : term] : (~(X199 @ X204) | (X199 @ (ap @ X203 @ X204)) | ~(X199 @ X203)))) & (hoasinduction_lem3b <=> ! [X205 : term] : ~! [X206 : subst > term > term] : ((sub @ X205 @ (push @ one @ sh)) != (X206 @ sh @ one))) & induction2lem_gthm & (! [X207 : subst > term > subst > $o,X208 : term] : (~! [X209 : term,X210 : term] : (~(X207 @ id @ X210 @ id) | ~(X207 @ id @ X209 @ id) | (X207 @ id @ (ap @ (sub @ X209 @ id) @ X210) @ id)) | (X207 @ id @ X208 @ id) | ~! [X211 : subst > term > term] : (~! [X212 : subst,X213 : subst,X214 : term] : ((sub @ (X211 @ X212 @ X214) @ X213) = (X211 @ (comp @ X212 @ X213) @ (sub @ X214 @ X213))) | ~! [X215 : term] : (~(X207 @ id @ X215 @ id) | (X207 @ id @ (X211 @ id @ X215) @ id)) | (X207 @ id @ (lam @ (X211 @ sh @ one)) @ id))) <=> hoasinduction_no_psi_cond) & ((d2subst @ d_id) = sh) & (pushprop_lem0_lthm <=> ! [X216 : term,X217 : term > $o,X218 : subst] : ~! [X219 : term > $o] : ~! [X220 : term] : ((X217 @ (sub @ X220 @ (push @ X216 @ X218))) = (X219 @ X220))) & hoasapnotvar_gthm & (! [X221 : term] : ((sub @ X221 @ id) = X221) <=> termmset) & (hoaslaminj <=> ! [X222 : subst,X223 : subst > term > term,X224 : subst > term > term,X225 : term] : (~! [X226 : term,X227 : subst,X228 : subst] : ((sub @ (X224 @ X227 @ X226) @ X228) = (X224 @ (comp @ X227 @ X228) @ (sub @ X226 @ X228))) | ~! [X229 : subst,X230 : term,X231 : subst] : ((sub @ (X223 @ X231 @ X230) @ X229) = (X223 @ (comp @ X231 @ X229) @ (sub @ X230 @ X229))) | ((X224 @ X222 @ X225) = (X223 @ X222 @ X225)) | ((lam @ (X223 @ sh @ one)) != (lam @ (X224 @ sh @ one))))) & hoaslamnotvar_gthm & pushprop_lem0_gthm & hoaslamnotap_gthm & ((! [X232 : term] : ~! [X233 : subst > term > term] : ~! [X234 : subst,X235 : term] : ((sub @ X232 @ (push @ X235 @ X234)) = (X233 @ X234 @ X235)) => (! [X236 : term] : ((sub @ X236 @ id) = X236) => ! [X237 : subst > term > subst > $o,X238 : term > $o,X239 : term] : (~! [X240 : term] : ((X238 @ X240) = (X237 @ id @ X240 @ id)) | (X238 @ (lam @ X239)) | ~! [X241 : term] : ((X238 @ (sub @ X239 @ (push @ X241 @ id))) | ~(X238 @ X241)) | ~! [X242 : subst > term > term] : (~! [X243 : term] : ((X237 @ id @ (X242 @ id @ X243) @ id) | ~(X237 @ id @ X243 @ id)) | ~! [X244 : term,X245 : subst,X246 : subst] : ((X242 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245)) = (sub @ (X242 @ X246 @ X244) @ X245)) | (X237 @ id @ (lam @ (X242 @ sh @ one)) @ id))))) <=> hoasinduction_lem3v2a_lthm) & pushprop & (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X247 = X249) | ((ap @ (sub @ X247 @ id) @ X248) != (ap @ (sub @ X249 @ id) @ X250))) <=> hoasapinj1) & (! [X251 : term,X252 : term] : (((sub @ X252 @ sh) != (sub @ X251 @ sh)) | (X251 = X252)) <=> shinj) & (! [X253 : subst > term > subst > $o,X254 : term] : ((X253 @ id @ (lam @ (sub @ X254 @ (push @ one @ sh))) @ id) | ~! [X255 : term] : (~(X253 @ id @ X255 @ id) | (X253 @ id @ (sub @ X254 @ (push @ X255 @ id)) @ id)) | ~! [X256 : subst > term > term] : (~! [X257 : term] : ((X253 @ id @ (X256 @ id @ X257) @ id) | ~(X253 @ id @ X257 @ id)) | (X253 @ id @ (lam @ (X256 @ sh @ one)) @ id) | ~! [X258 : term,X259 : subst,X260 : subst] : ((X256 @ (comp @ X260 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X256 @ X260 @ X258) @ X259)))) <=> hoasinduction_lem3aa) & ! [X261 : d_term,X262 : d_term] : (((d2term @ X262) = (d2term @ X261)) => (X261 = X262)) & hoasapnotvar_lthm & (hoasinduction_lem3 <=> ! [X263 : subst > term > subst > $o,X264 : term] : (~! [X265 : subst,X266 : term,X267 : subst,X268 : subst] : (~(X263 @ (comp @ X265 @ X268) @ (sub @ X266 @ X268) @ X267) | (X263 @ X265 @ X266 @ (comp @ X268 @ X267))) | ~! [X269 : term,X270 : subst,X271 : subst,X272 : subst] : ((X263 @ (comp @ X270 @ X271) @ (sub @ X269 @ X271) @ X272) | ~(X263 @ X270 @ X269 @ (comp @ X271 @ X272))) | ~! [X273 : term] : ((X263 @ id @ (sub @ X264 @ (push @ X273 @ id)) @ id) | ~(X263 @ id @ X273 @ id)) | (X263 @ id @ (lam @ X264) @ id) | ~! [X274 : subst > term > term] : ((X263 @ id @ (lam @ (X274 @ sh @ one)) @ id) | ~! [X275 : subst,X276 : subst,X277 : term] : ((X274 @ (comp @ X275 @ X276) @ (sub @ X277 @ X276)) = (sub @ (X274 @ X275 @ X277) @ X276)) | ~! [X278 : term] : (~(X263 @ id @ X278 @ id) | (X263 @ id @ (X274 @ id @ X278) @ id))))) & ((^[X279 : subst > term > subst > $o, X280 : term > $o] : (! [X281 : term] : ((X279 @ id @ X281 @ id) = (X280 @ X281)))) = hoasinduction_p_and_p_prime) & ((! [X282 : subst] : ((comp @ X282 @ id) = X282) & ! [X283 : subst] : ((comp @ id @ X283) = X283)) <=> substmonoid) & (substmonoid_lthm <=> (! [X284 : subst] : ((comp @ id @ X284) = X284) => (! [X285 : subst] : ((comp @ X285 @ id) = X285) => (! [X286 : subst] : ((comp @ X286 @ id) = X286) & ! [X287 : subst] : ((comp @ id @ X287) = X287))))) & (hoasinduction_lem2v2 <=> ! [X288 : term,X289 : term,X290 : subst > term > subst > $o,X291 : term > $o] : (~! [X292 : subst,X293 : subst,X294 : term,X295 : subst] : ((X290 @ X293 @ X294 @ (comp @ X292 @ X295)) | ~(X290 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) | ~! [X296 : term] : ((X290 @ id @ X296 @ id) = (X291 @ X296)) | ~! [X297 : subst,X298 : subst,X299 : term,X300 : subst] : (~(X290 @ X297 @ X299 @ (comp @ X298 @ X300)) | (X290 @ (comp @ X297 @ X298) @ (sub @ X299 @ X298) @ X300)) | ~(X291 @ X289) | ~(X291 @ X288) | (X291 @ (ap @ X288 @ X289)) | ~! [X301 : term,X302 : term] : (~(X290 @ id @ X301 @ id) | (X290 @ id @ (ap @ (sub @ X301 @ id) @ X302) @ id) | ~(X290 @ id @ X302 @ id)))) & (! [X303 : term,X304 : term,X305 : term,X306 : term] : ((X303 = X305) | ((ap @ X304 @ X305) != (ap @ X306 @ X303))) <=> apinj2) & lamnotvar & (! [X307 : subst] : ((comp @ id @ X307) = X307) <=> axidl) & hoasapinj2_gthm & ((d2subst @ d_id) = id) & hoasapnotvar & hoaslaminj_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X308 : subst > term > subst > $o] : ~! [X309 : term > $o] : ~! [X310 : term] : ((X309 @ X310) = (X308 @ id @ X310 @ id)) => (! [X311 : term > $o,X312 : term] : (~! [X313 : term,X314 : term] : (~(X311 @ X314) | (X311 @ (ap @ X313 @ X314)) | ~(X311 @ X313)) | (X311 @ X312) | ~! [X315 : term] : ((X311 @ X315) | ~(var @ X315)) | ~! [X316 : term] : (~! [X317 : term] : (~(X311 @ X317) | (X311 @ (sub @ X316 @ (push @ X317 @ id)))) | (X311 @ (lam @ X316)))) => (! [X318 : term] : ((sub @ X318 @ id) = X318) => (! [X319 : term > $o,X320 : term,X321 : subst > term > subst > $o] : (~! [X322 : term] : ((X319 @ X322) = (X321 @ id @ X322 @ id)) | ~! [X323 : term] : ((X319 @ (sub @ X320 @ (push @ X323 @ id))) | ~(X319 @ X323)) | (X319 @ (lam @ X320)) | ~! [X324 : subst > term > term] : (~! [X325 : term] : (~(X321 @ id @ X325 @ id) | (X321 @ id @ (X324 @ id @ X325) @ id)) | ~! [X326 : term,X327 : subst,X328 : subst] : ((sub @ (X324 @ X328 @ X326) @ X327) = (X324 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))) | (X321 @ id @ (lam @ (X324 @ sh @ one)) @ id))) => ! [X329 : subst > term > subst > $o,X330 : term] : (~! [X331 : subst > term > term] : (~! [X332 : term] : (~(X329 @ id @ X332 @ id) | (X329 @ id @ (X331 @ id @ X332) @ id)) | ~! [X333 : subst,X334 : subst,X335 : term] : ((sub @ (X331 @ X334 @ X335) @ X333) = (X331 @ (comp @ X334 @ X333) @ (sub @ X335 @ X333))) | (X329 @ id @ (lam @ (X331 @ sh @ one)) @ id)) | ~! [X336 : term,X337 : term] : (~(X329 @ id @ X337 @ id) | (X329 @ id @ (ap @ (sub @ X337 @ id) @ X336) @ id) | ~(X329 @ id @ X336 @ id)) | (X329 @ id @ X330 @ id))))))) & (hoasinduction_lem3_lthm <=> (! [X338 : term] : ((sub @ X338 @ id) = X338) => (! [X339 : subst > term > subst > $o,X340 : term] : (~! [X341 : subst > term > term] : ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id) | ~! [X342 : term] : (~(X339 @ id @ X342 @ id) | (X339 @ id @ (X341 @ id @ X342) @ id)) | ~! [X343 : term,X344 : subst,X345 : subst] : ((sub @ (X341 @ X345 @ X343) @ X344) = (X341 @ (comp @ X345 @ X344) @ (sub @ X343 @ X344)))) | ~! [X346 : term] : ((X339 @ id @ (sub @ X340 @ (push @ X346 @ id)) @ id) | ~(X339 @ id @ X346 @ id)) | (X339 @ id @ (lam @ (sub @ X340 @ (push @ one @ sh))) @ id)) => ! [X347 : term,X348 : subst > term > subst > $o] : (~! [X349 : term] : ((X348 @ id @ (sub @ X347 @ (push @ X349 @ id)) @ id) | ~(X348 @ id @ X349 @ id)) | ~! [X350 : subst > term > term] : (~! [X351 : term,X352 : subst,X353 : subst] : ((X350 @ (comp @ X352 @ X353) @ (sub @ X351 @ X353)) = (sub @ (X350 @ X352 @ X351) @ X353)) | ~! [X354 : term] : ((X348 @ id @ (X350 @ id @ X354) @ id) | ~(X348 @ id @ X354 @ id)) | (X348 @ id @ (lam @ (X350 @ sh @ one)) @ id)) | (X348 @ id @ (lam @ X347) @ id) | ~! [X355 : subst,X356 : subst,X357 : subst,X358 : term] : (~(X348 @ X357 @ X358 @ (comp @ X355 @ X356)) | (X348 @ (comp @ X357 @ X355) @ (sub @ X358 @ X355) @ X356)) | ~! [X359 : term,X360 : subst,X361 : subst,X362 : subst] : ((X348 @ X361 @ X359 @ (comp @ X362 @ X360)) | ~(X348 @ (comp @ X361 @ X362) @ (sub @ X359 @ X362) @ X360)))))) & hoasinduction_lem2_lthm & (! [X363 : term] : ((sub @ X363 @ id) = X363) <=> axvarid) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X364 : term] : ? [X365 : d_term] : ((d2term @ X365) = X364) & pushprop_lem2v2 & ((! [X366 : term,X367 : term > $o] : (~! [X368 : term,X369 : term] : (~(X367 @ X368) | ~(X367 @ X369) | (X367 @ (ap @ X369 @ X368))) | (X367 @ X366) | ~! [X370 : term] : (~! [X371 : term] : ((X367 @ (sub @ X370 @ (push @ X371 @ id))) | ~(X367 @ X371)) | (X367 @ (lam @ X370))) | ~! [X372 : term] : ((X367 @ X372) | ~(var @ X372))) => (! [X373 : term,X374 : term,X375 : subst > term > subst > $o] : ((X375 @ id @ (ap @ X373 @ X374) @ id) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (~(X375 @ (comp @ X376 @ X377) @ (sub @ X379 @ X377) @ X378) | (X375 @ X376 @ X379 @ (comp @ X377 @ X378))) | ~(X375 @ id @ X373 @ id) | ~(X375 @ id @ X374 @ id) | ~! [X380 : subst,X381 : subst,X382 : subst,X383 : term] : ((X375 @ (comp @ X381 @ X380) @ (sub @ X383 @ X380) @ X382) | ~(X375 @ X381 @ X383 @ (comp @ X380 @ X382))) | ~! [X384 : term,X385 : term] : (~(X375 @ id @ X384 @ id) | ~(X375 @ id @ X385 @ id) | (X375 @ id @ (ap @ (sub @ X384 @ id) @ X385) @ id))) => (! [X386 : subst > term > subst > $o,X387 : term] : (~! [X388 : subst,X389 : term,X390 : subst,X391 : subst] : ((X386 @ (comp @ X391 @ X390) @ (sub @ X389 @ X390) @ X388) | ~(X386 @ X391 @ X389 @ (comp @ X390 @ X388))) | (X386 @ id @ (lam @ X387) @ id) | ~! [X392 : subst,X393 : subst,X394 : subst,X395 : term] : (~(X386 @ (comp @ X394 @ X392) @ (sub @ X395 @ X392) @ X393) | (X386 @ X394 @ X395 @ (comp @ X392 @ X393))) | ~! [X396 : term] : (~(X386 @ id @ X396 @ id) | (X386 @ id @ (sub @ X387 @ (push @ X396 @ id)) @ id)) | ~! [X397 : subst > term > term] : ((X386 @ id @ (lam @ (X397 @ sh @ one)) @ id) | ~! [X398 : term] : (~(X386 @ id @ X398 @ id) | (X386 @ id @ (X397 @ id @ X398) @ id)) | ~! [X399 : term,X400 : subst,X401 : subst] : ((X397 @ (comp @ X401 @ X400) @ (sub @ X399 @ X400)) = (sub @ (X397 @ X401 @ X399) @ X400)))) => ! [X402 : term,X403 : subst > term > subst > $o] : (~! [X404 : term,X405 : subst,X406 : subst,X407 : subst] : (~(X403 @ X405 @ X404 @ (comp @ X407 @ X406)) | (X403 @ (comp @ X405 @ X407) @ (sub @ X404 @ X407) @ X406)) | ~! [X408 : subst > term > term] : (~! [X409 : term] : (~(X403 @ id @ X409 @ id) | (X403 @ id @ (X408 @ id @ X409) @ id)) | ~! [X410 : term,X411 : subst,X412 : subst] : ((sub @ (X408 @ X412 @ X410) @ X411) = (X408 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411))) | (X403 @ id @ (lam @ (X408 @ sh @ one)) @ id)) | (X403 @ id @ X402 @ id) | ~! [X413 : term,X414 : term] : (~(X403 @ id @ X413 @ id) | ~(X403 @ id @ X414 @ id) | (X403 @ id @ (ap @ (sub @ X414 @ id) @ X413) @ id)) | ~! [X415 : term] : ((X403 @ id @ X415 @ id) | ~(var @ (sub @ X415 @ id))) | ~! [X416 : subst,X417 : subst,X418 : subst,X419 : term] : ((X403 @ X416 @ X419 @ (comp @ X417 @ X418)) | ~(X403 @ (comp @ X416 @ X417) @ (sub @ X419 @ X417) @ X418)))))) <=> hoasinduction_lthm) & pushprop_lthm_orig & pushprop_lem2v2_gthm & (! [X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (~! [X423 : term] : ((X421 @ (sub @ X420 @ (push @ X423 @ id))) | ~(X421 @ X423)) | (X421 @ (lam @ X420)) | ~! [X424 : subst > term > term] : (~! [X425 : term,X426 : subst,X427 : subst] : ((X424 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426)) = (sub @ (X424 @ X427 @ X425) @ X426)) | (X422 @ id @ (lam @ (X424 @ sh @ one)) @ id) | ~! [X428 : term] : (~(X422 @ id @ X428 @ id) | (X422 @ id @ (X424 @ id @ X428) @ id))) | ~! [X429 : term] : ((X422 @ id @ X429 @ id) = (X421 @ X429))) <=> hoasinduction_lem3v2a) & hoasinduction_lem1v2 & (hoaslam = (^[X430 : subst, X431 : subst > term > term] : (d2term @ d_one))) & (! [X432 : subst > term > subst > $o,X433 : term,X434 : term > $o] : ((X434 @ (lam @ X433)) | ~! [X435 : subst > term > term] : ((X432 @ id @ (lam @ (X435 @ sh @ one)) @ id) | ~! [X436 : subst,X437 : term,X438 : subst] : ((X435 @ (comp @ X438 @ X436) @ (sub @ X437 @ X436)) = (sub @ (X435 @ X438 @ X437) @ X436)) | ~! [X439 : term] : (~(X432 @ id @ X439 @ id) | (X432 @ id @ (X435 @ id @ X439) @ id))) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (~(X432 @ X443 @ X441 @ (comp @ X442 @ X440)) | (X432 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442) @ X440)) | ~! [X444 : term,X445 : subst,X446 : subst,X447 : subst] : ((X432 @ X446 @ X444 @ (comp @ X447 @ X445)) | ~(X432 @ (comp @ X446 @ X447) @ (sub @ X444 @ X447) @ X445)) | ~! [X448 : term] : ((X434 @ X448) = (X432 @ id @ X448 @ id)) | ~! [X449 : term] : ((X434 @ (sub @ X433 @ (push @ X449 @ id))) | ~(X434 @ X449))) <=> hoasinduction_lem3v2) & (hoasinduction_lem3a <=> ! [X450 : subst > term > subst > $o,X451 : term] : (~! [X452 : subst > term > term] : (~! [X453 : subst,X454 : subst,X455 : term] : ((X452 @ (comp @ X453 @ X454) @ (sub @ X455 @ X454)) = (sub @ (X452 @ X453 @ X455) @ X454)) | ~! [X456 : term] : ((X450 @ id @ (X452 @ id @ X456) @ id) | ~(X450 @ id @ X456 @ id)) | (X450 @ id @ (lam @ (X452 @ sh @ one)) @ id)) | (X450 @ id @ (lam @ X451) @ id) | ~! [X457 : term] : ((X450 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id) | ~(X450 @ id @ X457 @ id)))) & induction2_gthm & (hoasinduction_lem3v2_f <=> ! [X458 : term] : ~! [X459 : subst > term > term] : ~! [X460 : subst,X461 : term] : ((sub @ X458 @ (push @ X461 @ X460)) = (X459 @ X460 @ X461))) & ((! [X462 : term,X463 : subst] : ((sub @ one @ (push @ X462 @ X463)) = X462) => (! [X464 : term,X465 : subst] : ((comp @ sh @ (push @ X464 @ X465)) = X465) => (! [X466 : subst] : ((comp @ X466 @ id) = X466) => (! [X467 : term,X468 : term > $o] : (~! [X469 : term,X470 : term] : (~(X468 @ X469) | (X468 @ (ap @ X470 @ X469)) | ~(X468 @ X470)) | (X468 @ X467) | ~! [X471 : term] : ((X468 @ X471) | ~(var @ X471)) | ~! [X472 : term] : (~(X468 @ X472) | (X468 @ (lam @ X472)))) => ! [X473 : term,X474 : term > $o,X475 : subst] : (~! [X476 : term] : ((X474 @ (lam @ X476)) | ~! [X477 : term] : ((X474 @ (sub @ X476 @ (push @ X477 @ id))) | ~(X474 @ X477))) | ~! [X478 : term] : ((X474 @ (sub @ X478 @ X475)) | ~(var @ X478)) | (X474 @ (sub @ X473 @ X475)) | ~! [X479 : term,X480 : term] : ((X474 @ (ap @ X479 @ X480)) | ~(X474 @ X479) | ~(X474 @ X480))))))) <=> induction2lem_lthm) & apnotvar & axabs & hoaslamnotvar & pushprop_lem1_gthm & (hoaslaminj_lthm <=> (! [X481 : term,X482 : subst] : ((sub @ one @ (push @ X481 @ X482)) = X481) => (! [X483 : term,X484 : subst] : ((comp @ sh @ (push @ X483 @ X484)) = X484) => (! [X485 : term,X486 : term] : (((lam @ X485) != (lam @ X486)) | (X485 = X486)) => ! [X487 : term,X488 : subst,X489 : subst > term > term,X490 : subst > term > term] : (((X490 @ X488 @ X487) = (X489 @ X488 @ X487)) | ~! [X491 : subst,X492 : term,X493 : subst] : ((sub @ (X489 @ X493 @ X492) @ X491) = (X489 @ (comp @ X493 @ X491) @ (sub @ X492 @ X491))) | ((lam @ (X490 @ sh @ one)) != (lam @ (X489 @ sh @ one))) | ~! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X490 @ X494 @ X495) @ X496) = (X490 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496)))))))) & (hoasinduction_lem3aaa <=> ! [X497 : term,X498 : subst > term > subst > $o] : ((X498 @ id @ (lam @ (sub @ X497 @ (push @ one @ sh))) @ id) | ~! [X499 : term] : (~(X498 @ id @ X499 @ id) | (X498 @ id @ (sub @ X497 @ (push @ X499 @ id)) @ id)) | ~! [X500 : subst > term > term,X501 : term] : (~! [X502 : subst,X503 : subst,X504 : term] : ((sub @ (X500 @ X502 @ X504) @ X503) = (sub @ (sub @ X501 @ (push @ X504 @ X502)) @ X503)) | (X498 @ id @ (lam @ (X500 @ sh @ one)) @ id) | ~! [X505 : term] : (~(X498 @ id @ X505 @ id) | (X498 @ id @ (X500 @ id @ X505) @ id)) | ~! [X506 : subst,X507 : subst,X508 : term] : ((X500 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507)) = (sub @ X501 @ (push @ (sub @ X508 @ X507) @ (comp @ X506 @ X507))))))) & (pushprop_lem1_lthm <=> (! [X509 : term,X510 : subst] : ((sub @ one @ (push @ X509 @ X510)) = X509) => (! [X511 : subst,X512 : term] : ((comp @ sh @ (push @ X512 @ X511)) = X511) => ! [X513 : subst,X514 : term > $o,X515 : term,X516 : term,X517 : term > $o] : ((X514 @ (sub @ X516 @ (push @ X515 @ X513))) | ~(X517 @ X516))))) & axvarshift & (induction2lem <=> ! [X518 : subst,X519 : term,X520 : term > $o] : (~! [X521 : term] : ((X520 @ (sub @ X521 @ X518)) | ~(var @ X521)) | ~! [X522 : term,X523 : term] : (~(X520 @ X523) | (X520 @ (ap @ X523 @ X522)) | ~(X520 @ X522)) | ~! [X524 : term] : ((X520 @ (lam @ X524)) | ~! [X525 : term] : ((X520 @ (sub @ X524 @ (push @ X525 @ id))) | ~(X520 @ X525))) | (X520 @ (sub @ X519 @ X518)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (induction2_lthm <=> (! [X526 : term] : ((sub @ X526 @ id) = X526) => (! [X527 : term > $o,X528 : subst,X529 : term] : (~! [X530 : term] : (~(var @ X530) | (X527 @ (sub @ X530 @ X528))) | ~! [X531 : term] : (~! [X532 : term] : (~(X527 @ X532) | (X527 @ (sub @ X531 @ (push @ X532 @ id)))) | (X527 @ (lam @ X531))) | ~! [X533 : term,X534 : term] : (~(X527 @ X534) | ~(X527 @ X533) | (X527 @ (ap @ X533 @ X534))) | (X527 @ (sub @ X529 @ X528))) => ! [X535 : term > $o,X536 : term] : ((X535 @ X536) | ~! [X537 : term] : (~! [X538 : term] : ((X535 @ (sub @ X537 @ (push @ X538 @ id))) | ~(X535 @ X538)) | (X535 @ (lam @ X537))) | ~! [X539 : term] : (~(var @ X539) | (X535 @ X539)) | ~! [X540 : term,X541 : term] : (~(X535 @ X541) | (X535 @ (ap @ X540 @ X541)) | ~(X535 @ X540)))))) & hoasinduction_lem2_gthm & hoasapinj1_gthm & (hoasapinj2_lthm <=> (! [X542 : term,X543 : term,X544 : term,X545 : term] : (((ap @ X543 @ X545) != (ap @ X544 @ X542)) | (X542 = X545)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X546 = X548) | ((ap @ (sub @ X549 @ id) @ X548) != (ap @ (sub @ X547 @ id) @ X546))))) & axapp & pushprop_lem3v2 & hoasinduction_lem1v2_gthm & hoaslamnotvar_lthm & ~(var @ (d2term @ d_one))),
% 21.29/4.27 inference(rectify,[status(thm)],[f1])).
% 21.29/4.27 thf(f1,axiom,(
% 21.29/4.27 substmonoid_gthm & axmap & (! [X15 : term,X13 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) <=> laminj) & (! [X13 : term,X10 : term > $o,X14 : subst,X15 : term,X26 : term > $o] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X43 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))) & hoasinduction_lem3a_gthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ulamvarsh & hoasinduction_lem3b_gthm & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13))) & (! [X15 : term,X13 : term,X19 : term,X20 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))) <=> hoasapinj2) & ! [X5 : d_subst] : (d_id = X5) & pushprop_lem1v2_gthm & (hoasinduction <=> ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : 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)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lthm_3 <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X29 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) => ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [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] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id))))))) & (hoaslamnotap <=> ! [X46 : term,X47 : term,X18 : subst > term > term] : (((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) & ~ulamvar1 & axclos & (axidr <=> ! [X14 : subst] : ((comp @ X14 @ id) = X14)) & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & hoasinduction_lem1 & (! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14) <=> axscons) & (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) <=> axshiftcons) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X20 : term,X13 : term,X15 : term,X19 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X20 : term,X13 : term,X19 : term,X15 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)))) <=> hoasapinj1_lthm) & ~lamnotap & (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & pushprop_gthm & pushprop_lem2v2_lthm & ! [X6 : d_subst,X7 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0) & (one = (d2term @ d_one)) & (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (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) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aa_lthm) & ulamvarind & hoasinduction_lem2v2_gthm & hoasinduction_gthm & hoasinduction_lem1_lthm & pushprop_lem3v2_lthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & (induction <=> ! [X10 : term > $o,X21 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X21))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X14 : subst,X13 : term,X10 : term > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0) & (! [X14 : subst,X13 : term,X11 : term > $o,X10 : term > $o] : ((X11 @ one) | ~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem1v2) & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : term > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X48 : term,X11 : term > $o] : (~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [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)) | (X11 @ (lam @ X48)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) <=> hoasinduction_lem3v2_lthm) & hoasinduction_lem3v2_gthm & (apinj1 <=> ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20)))) & ! [X1 : d_term] : (d_one = X1) & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & termmset_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X11 : term > $o,X14 : subst,X10 : term > $o,X13 : term] : ((X11 @ one) | ~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & (! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : (~(X10 @ id @ X23 @ id) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X10 @ id @ X24 @ id)) <=> hoasinduction_lem2) & pushprop_lthm & hoasinduction_lem1_gthm & hoaslamnotap_lthm & hoasinduction_lem3_gthm & axassoc & (induction2 <=> ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & induction2lem_gthm & (! [X10 : subst > term > subst > $o,X30 : term] : (~! [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] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_no_psi_cond) & ((d2subst @ d_id) = sh) & (pushprop_lem0_lthm <=> ! [X13 : term,X10 : term > $o,X14 : subst] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & hoasapnotvar_gthm & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & (hoaslaminj <=> ! [X32 : subst,X18 : subst > term > term,X31 : subst > term > term,X33 : term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))))) & hoaslamnotvar_gthm & pushprop_lem0_gthm & hoaslamnotap_gthm & ((! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X11 : term > $o,X29 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))) <=> hoasinduction_lem3v2a_lthm) & pushprop & (! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))) <=> hoasapinj1) & (! [X15 : term,X13 : term] : (((sub @ X13 @ sh) != (sub @ X15 @ sh)) | (X13 = X15)) <=> shinj) & (! [X10 : subst > term > subst > $o,X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoasinduction_lem3aa) & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & hoasapnotvar_lthm & (hoasinduction_lem3 <=> ! [X10 : subst > term > subst > $o,X27 : term] : (~! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X14 : subst,X26 : 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)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & ((^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) = hoasinduction_p_and_p_prime) & ((! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14)) <=> substmonoid) & (substmonoid_lthm <=> (! [X14 : subst] : ((comp @ id @ X14) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14))))) & (hoasinduction_lem2v2 <=> ! [X44 : term,X45 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X45) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & (! [X20 : term,X13 : term,X19 : term,X15 : term] : ((X19 = X20) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) <=> apinj2) & lamnotvar & (! [X14 : subst] : ((comp @ id @ X14) = X14) <=> axidl) & hoasapinj2_gthm & ((d2subst @ d_id) = id) & hoasapnotvar & hoaslaminj_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X29 : term,X10 : subst > term > subst > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X10 : subst > term > subst > $o,X30 : term] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X30 @ id))))))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X27 : term,X10 : subst > term > subst > $o] : (~! [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)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) & hoasinduction_lem2_lthm & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & pushprop_lem2v2 & ((! [X22 : term,X10 : term > $o] : (~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id) | ~! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) => (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X14 : subst,X25 : 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)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) <=> hoasinduction_lthm) & pushprop_lthm_orig & pushprop_lem2v2_gthm & (! [X29 : term,X11 : term > $o,X10 : subst > term > subst > $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))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) <=> hoasinduction_lem3v2a) & hoasinduction_lem1v2 & (hoaslam = (^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one))) & (! [X10 : subst > term > subst > $o,X48 : term,X11 : term > $o] : ((X11 @ (lam @ X48)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15))) <=> hoasinduction_lem3v2) & (hoasinduction_lem3a <=> ! [X10 : subst > term > subst > $o,X43 : term] : (~! [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)) | (X10 @ id @ (lam @ X43) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & induction2_gthm & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13))) & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X21 : term,X10 : term > $o] : (~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X21) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13)))) => ! [X16 : term,X10 : term > $o,X17 : subst] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))))))) <=> induction2lem_lthm) & apnotvar & axabs & hoaslamnotvar & pushprop_lem1_gthm & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X15 : term,X13 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) => ! [X33 : term,X32 : subst,X18 : subst > term > term,X31 : subst > term > term] : (((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term,X35 : term] : (~! [X36 : subst,X38 : subst,X37 : term] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X39 : subst,X41 : subst,X40 : term] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X14 : subst,X26 : term > $o,X15 : term,X13 : term,X10 : term > $o] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & axvarshift & (induction2lem <=> ! [X17 : subst,X16 : term,X10 : term > $o] : (~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (induction2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : term > $o,X17 : subst,X16 : term] : (~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17))) => ! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)))))) & hoasinduction_lem2_gthm & hoasapinj1_gthm & (hoasapinj2_lthm <=> (! [X19 : term,X15 : term,X13 : term,X20 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) => ! [X19 : term,X13 : term,X20 : term,X15 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))))) & axapp & pushprop_lem3v2 & hoasinduction_lem1v2_gthm & hoaslamnotvar_lthm & ~(var @ (d2term @ d_one))),
% 21.29/4.27 file('/export/starexec/sandbox/tmp/tmp.SL7lTGeRpl/DTF2THF_17587.p',alg444_1)).
% 21.29/4.27 thf(f1060,plain,(
% 21.29/4.27 ( ! [X258 : term] : (((d2term @ (sK584 @ X258)) = X258)) )),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f545])).
% 21.29/4.27 thf(f3010,plain,(
% 21.29/4.27 ($true = (sK593 @ (d2term @ d_one))) | ~spl595_89),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3008])).
% 21.29/4.27 thf(f3008,definition,(
% 21.29/4.27 spl595_89 <=> ($true = (sK593 @ (d2term @ d_one)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_89])],[avatar_definition])).
% 21.29/4.27 thf(f3205,plain,(
% 21.29/4.27 ~spl595_91 | ~spl595_94),
% 21.29/4.27 inference(avatar_contradiction_clause,[status(thm)],[f3204])).
% 21.29/4.27 thf(f3204,plain,(
% 21.29/4.27 $false | (~spl595_91 | ~spl595_94)),
% 21.29/4.27 inference(trivial_inequality_removal,[status(thm)],[f3200])).
% 21.29/4.27 thf(f3200,plain,(
% 21.29/4.27 ($true = $false) | (~spl595_91 | ~spl595_94)),
% 21.29/4.27 inference(superposition,[status(thm)],[f3113,f3133])).
% 21.29/4.27 thf(f3133,plain,(
% 21.29/4.27 ((sK524 @ (d2term @ d_one)) = $false) | ~spl595_94),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3131])).
% 21.29/4.27 thf(f3131,definition,(
% 21.29/4.27 spl595_94 <=> ((sK524 @ (d2term @ d_one)) = $false)),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_94])],[avatar_definition])).
% 21.29/4.27 thf(f3113,plain,(
% 21.29/4.27 ( ! [X0 : term] : (((sK524 @ X0) = $true)) ) | ~spl595_91),
% 21.29/4.27 inference(superposition,[status(thm)],[f3022,f2251])).
% 21.29/4.27 thf(f3022,plain,(
% 21.29/4.27 ((sK524 @ (d2term @ d_one)) = $true) | ~spl595_91),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3020])).
% 21.29/4.27 thf(f3020,definition,(
% 21.29/4.27 spl595_91 <=> ((sK524 @ (d2term @ d_one)) = $true)),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_91])],[avatar_definition])).
% 21.29/4.27 thf(f3189,plain,(
% 21.29/4.27 ~spl595_91 | ~spl595_92),
% 21.29/4.27 inference(avatar_contradiction_clause,[status(thm)],[f3188])).
% 21.29/4.27 thf(f3188,plain,(
% 21.29/4.27 $false | (~spl595_91 | ~spl595_92)),
% 21.29/4.27 inference(trivial_inequality_removal,[status(thm)],[f3154])).
% 21.29/4.27 thf(f3154,plain,(
% 21.29/4.27 ($true = $false) | (~spl595_91 | ~spl595_92)),
% 21.29/4.27 inference(superposition,[status(thm)],[f3104,f3113])).
% 21.29/4.27 thf(f3104,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($false = (X3 @ (d2term @ d_one)))) ) | ~spl595_92),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3103])).
% 21.29/4.27 thf(f3103,definition,(
% 21.29/4.27 spl595_92 <=> ! [X3 : term > $o] : ($false = (X3 @ (d2term @ d_one)))),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_92])],[avatar_definition])).
% 21.29/4.27 thf(f3187,plain,(
% 21.29/4.27 ~spl595_89 | ~spl595_92),
% 21.29/4.27 inference(avatar_contradiction_clause,[status(thm)],[f3186])).
% 21.29/4.27 thf(f3186,plain,(
% 21.29/4.27 $false | (~spl595_89 | ~spl595_92)),
% 21.29/4.27 inference(trivial_inequality_removal,[status(thm)],[f3156])).
% 21.29/4.27 thf(f3156,plain,(
% 21.29/4.27 ($true = $false) | (~spl595_89 | ~spl595_92)),
% 21.29/4.27 inference(superposition,[status(thm)],[f3104,f3087])).
% 21.29/4.27 thf(f3134,plain,(
% 21.29/4.27 spl595_92 | spl595_94 | spl595_90),
% 21.29/4.27 inference(avatar_split_clause,[status(thm)],[f3129,f3012,f3131,f3103])).
% 21.29/4.27 thf(f3012,definition,(
% 21.29/4.27 spl595_90 <=> (pushprop_lem0 = $true)),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_90])],[avatar_definition])).
% 21.29/4.27 thf(f3129,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (d2term @ d_one)) = $false) | ((sK524 @ (d2term @ d_one)) = $false)) ) | spl595_90),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3128,f2251])).
% 21.29/4.27 thf(f3128,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $false) | ((X136 @ (d2term @ d_one)) = $false)) ) | spl595_90),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3127,f2251])).
% 21.29/4.27 thf(f3127,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (sK525 @ X136)) = $false) | ((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $false)) ) | spl595_90),
% 21.29/4.27 inference(subsumption_resolution,[status(thm)],[f1727,f3014])).
% 21.29/4.27 thf(f3014,plain,(
% 21.29/4.27 (pushprop_lem0 != $true) | spl595_90),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3012])).
% 21.29/4.27 thf(f1727,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (sK525 @ X136)) = $false) | ((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $false) | (pushprop_lem0 = $true)) )),
% 21.29/4.27 inference(binary_proxy_clausification,[status(thm)],[f1163])).
% 21.29/4.27 thf(f1163,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : ((pushprop_lem0 = $true) | ((X136 @ (sK525 @ X136)) != (sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))))) )),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f545])).
% 21.29/4.27 thf(f3109,plain,(
% 21.29/4.27 spl595_92 | spl595_93 | ~spl595_90),
% 21.29/4.27 inference(avatar_split_clause,[status(thm)],[f3101,f3012,f3106,f3103])).
% 21.29/4.27 thf(f3101,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($false = (sK593 @ (d2term @ d_one))) | ($false = (X3 @ (d2term @ d_one)))) ) | ~spl595_90),
% 21.29/4.27 inference(subsumption_resolution,[status(thm)],[f3081,f3013])).
% 21.29/4.27 thf(f3013,plain,(
% 21.29/4.27 (pushprop_lem0 = $true) | ~spl595_90),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f3012])).
% 21.29/4.27 thf(f3081,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($false = (sK593 @ (d2term @ d_one))) | ($false = (X3 @ (d2term @ d_one))) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3080,f2251])).
% 21.29/4.27 thf(f3080,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($false = (sK593 @ (d2term @ d_one))) | ($false = (X3 @ (sK596 @ X3))) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f1819,f2251])).
% 21.29/4.27 thf(f1819,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (((sK593 @ (sub @ (sK596 @ X3) @ (push @ sK592 @ sK591))) = $false) | ($false = (X3 @ (sK596 @ X3))) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(binary_proxy_clausification,[status(thm)],[f1817])).
% 21.29/4.27 thf(f1817,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : ((pushprop_lem0 != $true) | ((sK593 @ (sub @ (sK596 @ X3) @ (push @ sK592 @ sK591))) != (X3 @ (sK596 @ X3)))) )),
% 21.29/4.27 inference(equality_proxy_clausification,[status(thm)],[f1816])).
% 21.29/4.27 thf(f1816,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : ((((X3 @ (sK596 @ X3)) = (sK593 @ (sub @ (sK596 @ X3) @ (push @ sK592 @ sK591)))) = $false) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(beta_eta_normalization,[status(thm)],[f1815])).
% 21.29/4.27 thf(f1815,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : ((((^[Y0 : term]: ((X3 @ Y0) = (sK593 @ (sub @ Y0 @ (push @ sK592 @ sK591))))) @ (sK596 @ X3)) = $false) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(sigma_clausification,[status(thm)],[f1814])).
% 21.29/4.27 thf(f1814,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (((!! @ term @ (^[Y0 : term]: ((X3 @ Y0) = (sK593 @ (sub @ Y0 @ (push @ sK592 @ sK591)))))) != $true) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(beta_eta_normalization,[status(thm)],[f1664])).
% 21.29/4.27 thf(f1664,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : ((pushprop_lem0 != $true) | (((^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))))))))))))) @ sK592 @ sK591 @ sK593 @ X3) != $true)) )),
% 21.29/4.27 inference(definition_unfolding,[status(thm)],[f1266,f1159])).
% 21.29/4.27 thf(f1159,plain,(
% 21.29/4.27 (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))))))))))))))),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f545])).
% 21.29/4.27 thf(f1266,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (((pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3) != $true) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f550])).
% 21.29/4.27 thf(f550,plain,(
% 21.29/4.27 (! [X3 : term > $o] : ((pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3) != $true) | (pushprop_lem0 != $true)) & (! [X4 : subst,X5 : term,X6 : term > $o] : ($true = (pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ (sK594 @ X6 @ X5 @ X4))) | (pushprop_lem0 = $true))),
% 21.29/4.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK591,sK592,sK593,sK594])],[f547,f549,f548])).
% 21.29/4.27 thf(f548,plain,(
% 21.29/4.27 ? [X0 : subst,X1 : term,X2 : term > $o] : ! [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) != $true) => ! [X3 : term > $o] : ((pushprop_p_and_p_prime @ sK592 @ sK591 @ sK593 @ X3) != $true)),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f549,plain,(
% 21.29/4.27 ! [X4 : subst,X5 : term,X6 : term > $o] : (? [X7 : term > $o] : ((pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ X7) = $true) => ($true = (pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ (sK594 @ X6 @ X5 @ X4))))),
% 21.29/4.27 introduced(definition,[],[choice_axiom])).
% 21.29/4.27 thf(f547,plain,(
% 21.29/4.27 (? [X0 : subst,X1 : term,X2 : term > $o] : ! [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) != $true) | (pushprop_lem0 != $true)) & (! [X4 : subst,X5 : term,X6 : term > $o] : ? [X7 : term > $o] : ((pushprop_p_and_p_prime @ X5 @ X4 @ X6 @ X7) = $true) | (pushprop_lem0 = $true))),
% 21.29/4.27 inference(rectify,[status(thm)],[f546])).
% 21.29/4.27 thf(f546,plain,(
% 21.29/4.27 (? [X0 : subst,X1 : term,X2 : term > $o] : ! [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) != $true) | (pushprop_lem0 != $true)) & (! [X0 : subst,X1 : term,X2 : term > $o] : ? [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) = $true) | (pushprop_lem0 = $true))),
% 21.29/4.27 inference(nnf_transformation,[status(thm)],[f13])).
% 21.29/4.27 thf(f13,plain,(
% 21.29/4.27 (pushprop_lem0 = $true) <~> ! [X0 : subst,X1 : term,X2 : term > $o] : ? [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) = $true)),
% 21.29/4.27 inference(ennf_transformation,[status(thm)],[f8])).
% 21.29/4.27 thf(f8,plain,(
% 21.29/4.27 ~(! [X0 : subst,X1 : term,X2 : term > $o] : ? [X3 : term > $o] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3) = $true) <=> (pushprop_lem0 = $true))),
% 21.29/4.27 inference(fool_elimination,[status(thm)],[f7])).
% 21.29/4.27 thf(f7,plain,(
% 21.29/4.27 ~(pushprop_lem0 = ! [X0 : subst,X1 : term,X2 : term > $o] : ? [X3 : term > $o] : (pushprop_p_and_p_prime @ X1 @ X0 @ X2 @ X3))),
% 21.29/4.27 inference(rectify,[status(thm)],[f3])).
% 21.29/4.27 thf(f3,negated_conjecture,(
% 21.29/4.27 ~(pushprop_lem0 = ! [X14 : subst,X13 : term,X10 : term > $o] : ? [X11 : term > $o] : (pushprop_p_and_p_prime @ X13 @ X14 @ X10 @ X11))),
% 21.29/4.27 inference(negated_conjecture,[status(cth)],[f2])).
% 21.29/4.27 thf(f2,conjecture,(
% 21.29/4.27 (pushprop_lem0 = ! [X14 : subst,X13 : term,X10 : term > $o] : ? [X11 : term > $o] : (pushprop_p_and_p_prime @ X13 @ X14 @ X10 @ X11))),
% 21.29/4.27 file('/export/starexec/sandbox/tmp/tmp.SL7lTGeRpl/DTF2THF_17587.p',pushprop_lem0)).
% 21.29/4.27 thf(f3066,plain,(
% 21.29/4.27 ~spl595_88),
% 21.29/4.27 inference(avatar_contradiction_clause,[status(thm)],[f3065])).
% 21.29/4.27 thf(f3065,plain,(
% 21.29/4.27 $false | ~spl595_88),
% 21.29/4.27 inference(trivial_inequality_removal,[status(thm)],[f3038])).
% 21.29/4.27 thf(f3038,plain,(
% 21.29/4.27 ($true != $true) | ~spl595_88),
% 21.29/4.27 inference(superposition,[status(thm)],[f2256,f2792])).
% 21.29/4.27 thf(f2792,plain,(
% 21.29/4.27 ( ! [X153 : term > $o] : (((X153 @ (d2term @ d_one)) = $true)) ) | ~spl595_88),
% 21.29/4.27 inference(avatar_component_clause,[status(thm)],[f2791])).
% 21.29/4.27 thf(f2791,definition,(
% 21.29/4.27 spl595_88 <=> ! [X153 : term > $o] : ((X153 @ (d2term @ d_one)) = $true)),
% 21.29/4.27 introduced(definition,[new_symbols(naming,[spl595_88])],[avatar_definition])).
% 21.29/4.27 thf(f2256,plain,(
% 21.29/4.27 ( ! [X0 : term] : (($true != (var @ X0))) )),
% 21.29/4.27 inference(superposition,[status(thm)],[f1048,f2251])).
% 21.29/4.27 thf(f1048,plain,(
% 21.29/4.27 ((var @ (d2term @ d_one)) != $true)),
% 21.29/4.27 inference(cnf_transformation,[status(thm)],[f545])).
% 21.29/4.27 thf(f3023,plain,(
% 21.29/4.27 spl595_88 | spl595_91 | spl595_90),
% 21.29/4.27 inference(avatar_split_clause,[status(thm)],[f3018,f3012,f3020,f2791])).
% 21.29/4.27 thf(f3018,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((sK524 @ (d2term @ d_one)) = $true) | ((X136 @ (d2term @ d_one)) = $true)) ) | spl595_90),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3017,f2251])).
% 21.29/4.27 thf(f3017,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (d2term @ d_one)) = $true) | ((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $true)) ) | spl595_90),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3016,f2251])).
% 21.29/4.27 thf(f3016,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (sK525 @ X136)) = $true) | ((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $true)) ) | spl595_90),
% 21.29/4.27 inference(subsumption_resolution,[status(thm)],[f1726,f3014])).
% 21.29/4.27 thf(f1726,plain,(
% 21.29/4.27 ( ! [X136 : term > $o] : (((X136 @ (sK525 @ X136)) = $true) | (pushprop_lem0 = $true) | ((sK524 @ (sub @ (sK525 @ X136) @ (push @ sK523 @ sK522))) = $true)) )),
% 21.29/4.27 inference(binary_proxy_clausification,[status(thm)],[f1163])).
% 21.29/4.27 thf(f3015,plain,(
% 21.29/4.27 spl595_89 | ~spl595_90 | spl595_88),
% 21.29/4.27 inference(avatar_split_clause,[status(thm)],[f3006,f2791,f3012,f3008])).
% 21.29/4.27 thf(f3006,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($true = (X3 @ (d2term @ d_one))) | (pushprop_lem0 != $true) | ($true = (sK593 @ (d2term @ d_one)))) )),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f3005,f2251])).
% 21.29/4.27 thf(f3005,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (((sK593 @ (sub @ (sK596 @ X3) @ (push @ sK592 @ sK591))) = $true) | ($true = (X3 @ (d2term @ d_one))) | (pushprop_lem0 != $true)) )),
% 21.29/4.27 inference(forward_demodulation,[status(thm)],[f1818,f2251])).
% 21.29/4.27 thf(f1818,plain,(
% 21.29/4.27 ( ! [X3 : term > $o] : (($true = (X3 @ (sK596 @ X3))) | (pushprop_lem0 != $true) | ((sK593 @ (sub @ (sK596 @ X3) @ (push @ sK592 @ sK591))) = $true)) )),
% 21.29/4.27 inference(binary_proxy_clausification,[status(thm)],[f1817])).
% 21.29/4.27 % SZS output end Proof for DTF2THF_17587
% 21.29/4.27 % (18016)------------------------------
% 21.29/4.27 % (18016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.29/4.27 % (18016)Termination reason: Refutation
% 21.29/4.27
% 21.29/4.27 % (18016)Memory used [KB]: 11385
% 21.29/4.27 % (18016)Time elapsed: 0.182 s
% 21.29/4.27 % (18016)Instructions burned: 496 (million)
% 21.29/4.27 % (18016)------------------------------
% 21.29/4.27 % (18016)------------------------------
% 21.29/4.27 % (17870)Success in time 2.813 s
%------------------------------------------------------------------------------