%------------------------------------------------------------------------------
% 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 : n018.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 06:58:48 PM UTC 2026
% Result : Theorem 32.60s 5.94s
% Output : Refutation 32.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 155
% Syntax : Number of formulae : 286 ( 20 unt; 0 typ; 12 def)
% Number of atoms : 12362 (5746 equ; 0 cnn)
% Maximal formula atoms : 530 ( 43 avg)
% Number of connectives : 30535 (3237 ~;3004 |;2504 &;20556 @)
% ( 519 <=>; 461 =>; 0 <=; 0 <~>)
% Maximal formula depth : 187 ( 13 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2329 (2329 >; 0 *; 0 +; 0 <<)
% Number of symbols : 769 ( 765 usr; 305 con; 0-4 aty)
% ( 254 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 6304 ( 383 ^;4484 !;1437 ?;6304 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(type_def_8,type,
d_term: $tType ).
thf(type_def_9,type,
d_subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_124,type,
d_term: $tType ).
thf(func_def_125,type,
d_subst: $tType ).
thf(func_def_126,type,
d2term: d_term > term ).
thf(func_def_127,type,
d2subst: d_subst > subst ).
thf(func_def_128,type,
d_one: d_term ).
thf(func_def_129,type,
d_id: d_subst ).
thf(func_def_142,type,
sP0: ( term > $o ) > $o ).
thf(func_def_143,type,
sP1: ( term > $o ) > $o ).
thf(func_def_147,type,
sP5: ( subst > term > subst > $o ) > $o ).
thf(func_def_149,type,
sP7: ( term > $o ) > $o ).
thf(func_def_150,type,
sP8: ( subst > term > subst > $o ) > $o ).
thf(func_def_156,type,
sP14: ( term > $o ) > $o ).
thf(func_def_159,type,
sP17: ( subst > term > subst > $o ) > $o ).
thf(func_def_162,type,
sP20: ( term > $o ) > $o ).
thf(func_def_165,type,
sP23: ( term > $o ) > $o ).
thf(func_def_166,type,
sP24: ( subst > term > subst > $o ) > $o ).
thf(func_def_167,type,
sP25: ( subst > term > subst > $o ) > $o ).
thf(func_def_168,type,
sP26: ( subst > term > subst > $o ) > $o ).
thf(func_def_169,type,
sP27: ( subst > term > subst > $o ) > $o ).
thf(func_def_176,type,
sP34: ( subst > term > subst > $o ) > $o ).
thf(func_def_178,type,
sP36: ( subst > term > subst > $o ) > $o ).
thf(func_def_179,type,
sP37: ( subst > term > subst > $o ) > $o ).
thf(func_def_181,type,
sP39: ( term > $o ) > $o ).
thf(func_def_182,type,
sP40: ( subst > term > subst > $o ) > $o ).
thf(func_def_184,type,
sP42: ( subst > term > subst > $o ) > $o ).
thf(func_def_185,type,
sP43: ( term > $o ) > $o ).
thf(func_def_186,type,
sP44: ( term > $o ) > $o ).
thf(func_def_189,type,
sP47: ( term > $o ) > $o ).
thf(func_def_190,type,
sP48: ( subst > term > subst > $o ) > $o ).
thf(func_def_191,type,
sP49: ( subst > term > subst > $o ) > $o ).
thf(func_def_197,type,
sP55: ( subst > term > subst > $o ) > $o ).
thf(func_def_199,type,
sP57: ( subst > term > subst > $o ) > $o ).
thf(func_def_201,type,
sK59: subst > term > subst > $o ).
thf(func_def_202,type,
sK60: term > $o ).
thf(func_def_203,type,
sK61: term ).
thf(func_def_204,type,
sK62: ( subst > term > subst > $o ) > term ).
thf(func_def_205,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_207,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_208,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_210,type,
sK68: ( subst > term > subst > $o ) > subst ).
thf(func_def_211,type,
sK69: ( subst > term > subst > $o ) > term ).
thf(func_def_212,type,
sK70: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK71: term > ( term > $o ) > term ).
thf(func_def_214,type,
sK72: ( subst > term > term ) > term ).
thf(func_def_215,type,
sK73: ( subst > term > term ) > subst ).
thf(func_def_216,type,
sK74: ( subst > term > term ) > subst ).
thf(func_def_217,type,
sK75: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_218,type,
sK76: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_219,type,
sK77: subst > term > subst > $o ).
thf(func_def_220,type,
sK78: term ).
thf(func_def_221,type,
sK79: term > $o ).
thf(func_def_222,type,
sK80: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_223,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_224,type,
sK82: ( subst > term > subst > $o ) > term ).
thf(func_def_225,type,
sK83: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK84: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK85: ( subst > term > subst > $o ) > subst ).
thf(func_def_228,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK88: ( subst > term > subst > $o ) > term ).
thf(func_def_231,type,
sK89: ( term > $o ) > term > term ).
thf(func_def_232,type,
sK90: term ).
thf(func_def_233,type,
sK91: ( subst > term > term ) > term ).
thf(func_def_234,type,
sK92: ( subst > term > term ) > subst ).
thf(func_def_235,type,
sK93: ( subst > term > term ) > subst ).
thf(func_def_236,type,
sK94: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_237,type,
sK95: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_238,type,
sK96: subst > term > subst > $o ).
thf(func_def_239,type,
sK97: term ).
thf(func_def_240,type,
sK98: ( subst > term > term ) > term ).
thf(func_def_241,type,
sK99: ( subst > term > term ) > term ).
thf(func_def_242,type,
sK100: ( subst > term > term ) > subst ).
thf(func_def_243,type,
sK101: ( subst > term > term ) > subst ).
thf(func_def_244,type,
sK102: term > ( subst > term > subst > $o ) > term ).
thf(func_def_245,type,
sK103: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_246,type,
sK104: subst > term > subst > $o ).
thf(func_def_247,type,
sK105: term ).
thf(func_def_248,type,
sK106: ( subst > term > term ) > subst ).
thf(func_def_249,type,
sK107: ( subst > term > term ) > subst ).
thf(func_def_250,type,
sK108: ( subst > term > term ) > term ).
thf(func_def_251,type,
sK109: ( subst > term > term ) > term ).
thf(func_def_252,type,
sK110: term > ( subst > term > subst > $o ) > term ).
thf(func_def_253,type,
sK111: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_254,type,
sK112: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_255,type,
sK113: ( term > $o ) > term ).
thf(func_def_256,type,
sK114: ( term > $o ) > term ).
thf(func_def_257,type,
sK115: subst > term > subst > $o ).
thf(func_def_258,type,
sK116: ( term > $o ) > term ).
thf(func_def_259,type,
sK117: term ).
thf(func_def_260,type,
sK118: term > $o ).
thf(func_def_261,type,
sK119: term ).
thf(func_def_262,type,
sK120: term > term ).
thf(func_def_263,type,
sK121: subst > term > subst > $o ).
thf(func_def_264,type,
sK122: term ).
thf(func_def_265,type,
sK123: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK124: ( subst > term > subst > $o ) > subst ).
thf(func_def_267,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK126: ( subst > term > subst > $o ) > term ).
thf(func_def_269,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK128: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK129: ( subst > term > subst > $o ) > term ).
thf(func_def_272,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK131: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK132: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK133: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_276,type,
sK134: term > ( term > $o ) > term ).
thf(func_def_277,type,
sK135: subst > term > subst > $o ).
thf(func_def_278,type,
sK136: term > $o ).
thf(func_def_279,type,
sK137: term ).
thf(func_def_280,type,
sK138: ( subst > term > term ) > term ).
thf(func_def_281,type,
sK139: ( subst > term > term ) > subst ).
thf(func_def_282,type,
sK140: ( subst > term > term ) > term ).
thf(func_def_283,type,
sK141: ( subst > term > term ) > subst ).
thf(func_def_284,type,
sK142: ( subst > term > subst > $o ) > term ).
thf(func_def_285,type,
sK143: ( subst > term > subst > $o ) > term ).
thf(func_def_286,type,
sK144: ( subst > term > term ) > subst ).
thf(func_def_287,type,
sK145: ( subst > term > term ) > term ).
thf(func_def_288,type,
sK146: ( subst > term > term ) > subst ).
thf(func_def_289,type,
sK147: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK148: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_291,type,
sK149: ( term > $o ) > term ).
thf(func_def_292,type,
sK150: ( term > $o ) > term ).
thf(func_def_293,type,
sK151: ( term > $o ) > term ).
thf(func_def_294,type,
sK152: subst > ( term > $o ) > term ).
thf(func_def_295,type,
sK153: term ).
thf(func_def_296,type,
sK154: term > $o ).
thf(func_def_297,type,
sK155: subst ).
thf(func_def_298,type,
sK156: term ).
thf(func_def_299,type,
sK157: term > term ).
thf(func_def_300,type,
sK158: term > $o ).
thf(func_def_301,type,
sK159: term ).
thf(func_def_302,type,
sK160: term > term ).
thf(func_def_303,type,
sK161: ( term > $o ) > term ).
thf(func_def_304,type,
sK162: ( term > $o ) > term ).
thf(func_def_305,type,
sK163: ( term > $o ) > term ).
thf(func_def_306,type,
sK164: ( term > $o ) > term ).
thf(func_def_307,type,
sK165: ( term > $o ) > term ).
thf(func_def_308,type,
sK166: ( term > $o ) > term ).
thf(func_def_309,type,
sK167: ( subst > term > subst > $o ) > term ).
thf(func_def_310,type,
sK168: ( subst > term > subst > $o ) > term ).
thf(func_def_311,type,
sK169: subst > term > subst > $o ).
thf(func_def_312,type,
sK170: term ).
thf(func_def_313,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_314,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_315,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_316,type,
sK174: ( subst > term > subst > $o ) > term ).
thf(func_def_317,type,
sK175: ( subst > term > subst > $o ) > term ).
thf(func_def_318,type,
sK176: ( subst > term > subst > $o ) > subst ).
thf(func_def_319,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_320,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_321,type,
sK179: term > ( subst > term > subst > $o ) > term ).
thf(func_def_322,type,
sK180: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_323,type,
sK181: ( subst > term > term ) > subst ).
thf(func_def_324,type,
sK182: ( subst > term > term ) > subst ).
thf(func_def_325,type,
sK183: ( subst > term > term ) > term ).
thf(func_def_326,type,
sK184: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_327,type,
sK185: ( term > $o ) > term ).
thf(func_def_328,type,
sK186: ( term > $o ) > term ).
thf(func_def_329,type,
sK187: term ).
thf(func_def_330,type,
sK188: subst > term > subst > $o ).
thf(func_def_331,type,
sK189: ( subst > term > subst > $o ) > term ).
thf(func_def_332,type,
sK190: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK191: ( subst > term > subst > $o ) > subst ).
thf(func_def_334,type,
sK192: ( subst > term > subst > $o ) > subst ).
thf(func_def_335,type,
sK193: ( subst > term > subst > $o ) > term ).
thf(func_def_336,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK195: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK196: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK197: ( subst > term > subst > $o ) > term ).
thf(func_def_340,type,
sK198: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_341,type,
sK199: ( subst > term > term ) > subst ).
thf(func_def_342,type,
sK200: ( subst > term > term ) > term ).
thf(func_def_343,type,
sK201: ( subst > term > term ) > subst ).
thf(func_def_344,type,
sK202: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_345,type,
sK203: ( subst > term > subst > $o ) > term ).
thf(func_def_346,type,
sK204: ( subst > term > subst > $o ) > term ).
thf(func_def_347,type,
sK205: term ).
thf(func_def_348,type,
sK206: term > $o ).
thf(func_def_349,type,
sK207: subst > term > subst > $o ).
thf(func_def_350,type,
sK208: term ).
thf(func_def_351,type,
sK209: ( subst > term > subst > $o ) > subst ).
thf(func_def_352,type,
sK210: ( subst > term > subst > $o ) > term ).
thf(func_def_353,type,
sK211: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK212: ( subst > term > subst > $o ) > subst ).
thf(func_def_355,type,
sK213: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_356,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_357,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK216: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK217: ( subst > term > subst > $o ) > term ).
thf(func_def_360,type,
sK218: ( subst > term > subst > $o ) > term ).
thf(func_def_361,type,
sK219: ( subst > term > subst > $o ) > term ).
thf(func_def_362,type,
sK220: subst > term > subst > $o ).
thf(func_def_363,type,
sK221: term > $o ).
thf(func_def_364,type,
sK222: term ).
thf(func_def_365,type,
sK223: ( subst > term > term ) > subst ).
thf(func_def_366,type,
sK224: ( subst > term > term ) > subst ).
thf(func_def_367,type,
sK225: ( subst > term > term ) > term ).
thf(func_def_368,type,
sK226: ( subst > term > term ) > term ).
thf(func_def_369,type,
sK227: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_370,type,
sK228: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_371,type,
sK229: term > ( term > $o ) > term ).
thf(func_def_372,type,
sK230: term ).
thf(func_def_373,type,
sK231: subst > term > subst > $o ).
thf(func_def_374,type,
sK232: ( subst > term > term ) > subst ).
thf(func_def_375,type,
sK233: ( subst > term > term ) > term ).
thf(func_def_376,type,
sK234: ( subst > term > term ) > subst ).
thf(func_def_377,type,
sK235: ( subst > term > term ) > term ).
thf(func_def_378,type,
sK236: ( subst > term > subst > $o ) > term > term ).
thf(func_def_379,type,
sK237: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_380,type,
sK238: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK239: ( subst > term > subst > $o ) > term ).
thf(func_def_382,type,
sK240: ( subst > term > subst > $o ) > subst ).
thf(func_def_383,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_384,type,
sK242: ( subst > term > subst > $o ) > term ).
thf(func_def_385,type,
sK243: ( subst > term > subst > $o ) > subst ).
thf(func_def_386,type,
sK244: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_388,type,
sK246: subst > term > subst > $o ).
thf(func_def_389,type,
sK247: term ).
thf(func_def_390,type,
sK248: term ).
thf(func_def_391,type,
sK249: ( term > $o ) > term ).
thf(func_def_392,type,
sK250: ( term > $o ) > term ).
thf(func_def_393,type,
sK251: term > $o ).
thf(func_def_394,type,
sK252: term ).
thf(func_def_395,type,
sK253: term > term ).
thf(func_def_396,type,
sK254: subst > term > subst > $o ).
thf(func_def_397,type,
sK255: term ).
thf(func_def_398,type,
sK256: ( subst > term > subst > $o ) > subst ).
thf(func_def_399,type,
sK257: ( subst > term > subst > $o ) > subst ).
thf(func_def_400,type,
sK258: ( subst > term > subst > $o ) > term ).
thf(func_def_401,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_402,type,
sK260: ( subst > term > subst > $o ) > subst ).
thf(func_def_403,type,
sK261: ( subst > term > subst > $o ) > term ).
thf(func_def_404,type,
sK262: ( subst > term > subst > $o ) > subst ).
thf(func_def_405,type,
sK263: ( subst > term > subst > $o ) > subst ).
thf(func_def_406,type,
sK264: ( subst > term > subst > $o ) > term ).
thf(func_def_407,type,
sK265: ( subst > term > subst > $o ) > subst ).
thf(func_def_408,type,
sK266: ( subst > term > subst > $o ) > subst ).
thf(func_def_409,type,
sK267: ( subst > term > subst > $o ) > term ).
thf(func_def_410,type,
sK268: ( subst > term > subst > $o ) > subst ).
thf(func_def_411,type,
sK269: ( subst > term > subst > $o ) > term > term ).
thf(func_def_412,type,
sK270: ( subst > term > subst > $o ) > subst ).
thf(func_def_413,type,
sK271: ( subst > term > subst > $o ) > term ).
thf(func_def_414,type,
sK272: ( subst > term > subst > $o ) > subst ).
thf(func_def_415,type,
sK273: ( subst > term > subst > $o ) > subst ).
thf(func_def_416,type,
sK274: term ).
thf(func_def_417,type,
sK275: subst > term > subst > $o ).
thf(func_def_418,type,
sK276: ( subst > term > subst > $o ) > term ).
thf(func_def_419,type,
sK277: ( subst > term > subst > $o ) > term ).
thf(func_def_420,type,
sK278: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_421,type,
sK279: ( subst > term > term ) > term ).
thf(func_def_422,type,
sK280: ( subst > term > term ) > subst ).
thf(func_def_423,type,
sK281: ( subst > term > term ) > subst ).
thf(func_def_424,type,
sK282: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_425,type,
sK283: ( subst > term > subst > $o ) > term ).
thf(func_def_426,type,
sK284: ( subst > term > subst > $o ) > term ).
thf(func_def_427,type,
sK285: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_428,type,
sK286: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_429,type,
sK287: ( subst > term > term ) > subst ).
thf(func_def_430,type,
sK288: ( subst > term > term ) > subst ).
thf(func_def_431,type,
sK289: ( subst > term > term ) > term ).
thf(func_def_432,type,
sK290: ( term > $o ) > term ).
thf(func_def_433,type,
sK291: ( term > $o ) > term ).
thf(func_def_434,type,
sK292: subst ).
thf(func_def_435,type,
sK293: subst > term > term ).
thf(func_def_436,type,
sK294: term ).
thf(func_def_437,type,
sK295: subst > term > term ).
thf(func_def_438,type,
sK296: ( subst > term > term ) > subst ).
thf(func_def_439,type,
sK297: ( subst > term > term ) > term ).
thf(func_def_440,type,
sK298: ( subst > term > term ) > subst ).
thf(func_def_441,type,
sK299: ( subst > term > term ) > subst ).
thf(func_def_442,type,
sK300: ( subst > term > term ) > term ).
thf(func_def_443,type,
sK301: ( subst > term > term ) > subst ).
thf(func_def_444,type,
sK302: subst ).
thf(func_def_445,type,
sK303: term ).
thf(func_def_446,type,
sK304: term ).
thf(func_def_447,type,
sK305: subst ).
thf(func_def_448,type,
sK306: term ).
thf(func_def_449,type,
sK307: term ).
thf(func_def_450,type,
sK308: term > $o ).
thf(func_def_451,type,
sK309: term ).
thf(func_def_452,type,
sK310: term > term ).
thf(func_def_453,type,
sK311: ( term > $o ) > term ).
thf(func_def_454,type,
sK312: ( term > $o ) > term ).
thf(func_def_455,type,
sK313: ( term > $o ) > term ).
thf(func_def_456,type,
sK314: ( term > $o ) > term ).
thf(func_def_457,type,
sK315: subst > term > subst > $o ).
thf(func_def_458,type,
sK316: term ).
thf(func_def_459,type,
sK317: term ).
thf(func_def_460,type,
sK318: ( subst > term > subst > $o ) > subst ).
thf(func_def_461,type,
sK319: ( subst > term > subst > $o ) > subst ).
thf(func_def_462,type,
sK320: ( subst > term > subst > $o ) > subst ).
thf(func_def_463,type,
sK321: ( subst > term > subst > $o ) > term ).
thf(func_def_464,type,
sK322: ( subst > term > subst > $o ) > subst ).
thf(func_def_465,type,
sK323: ( subst > term > subst > $o ) > subst ).
thf(func_def_466,type,
sK324: ( subst > term > subst > $o ) > subst ).
thf(func_def_467,type,
sK325: ( subst > term > subst > $o ) > term ).
thf(func_def_468,type,
sK326: term > ( subst > term > subst > $o ) > term ).
thf(func_def_469,type,
sK327: ( subst > term > subst > $o ) > term > term ).
thf(func_def_470,type,
sK328: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_471,type,
sK329: term ).
thf(func_def_472,type,
sK330: subst > term > subst > $o ).
thf(func_def_473,type,
sK331: ( subst > term > term ) > term ).
thf(func_def_474,type,
sK332: ( subst > term > term ) > term ).
thf(func_def_475,type,
sK333: ( subst > term > term ) > subst ).
thf(func_def_476,type,
sK334: ( subst > term > term ) > subst ).
thf(func_def_477,type,
sK335: ( subst > term > term ) > subst ).
thf(func_def_478,type,
sK336: ( subst > term > term ) > subst ).
thf(func_def_479,type,
sK337: ( subst > term > term ) > term ).
thf(func_def_480,type,
sK338: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_481,type,
sK339: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_482,type,
sK340: term ).
thf(func_def_483,type,
sK341: subst > term > subst > $o ).
thf(func_def_484,type,
sK342: term > ( subst > term > term ) > subst ).
thf(func_def_485,type,
sK343: term > ( subst > term > term ) > term ).
thf(func_def_486,type,
sK344: term > ( subst > term > term ) > subst ).
thf(func_def_487,type,
sK345: term > ( subst > term > term ) > subst ).
thf(func_def_488,type,
sK346: term > ( subst > term > term ) > subst ).
thf(func_def_489,type,
sK347: term > ( subst > term > term ) > term ).
thf(func_def_490,type,
sK348: ( subst > term > term ) > term ).
thf(func_def_491,type,
sK349: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_492,type,
sK350: ( subst > term > subst > $o ) > term ).
thf(func_def_493,type,
sK351: ( subst > term > subst > $o ) > term > term ).
thf(func_def_494,type,
sK352: term ).
thf(func_def_495,type,
sK353: subst ).
thf(func_def_496,type,
sK354: term > $o ).
thf(func_def_497,type,
sK355: term > term ).
thf(func_def_498,type,
sK356: ( term > $o ) > subst > term ).
thf(func_def_499,type,
sK357: ( term > $o ) > term ).
thf(func_def_500,type,
sK358: ( term > $o ) > term ).
thf(func_def_501,type,
sK359: ( term > $o ) > term ).
thf(func_def_502,type,
sK360: subst > term > subst > $o ).
thf(func_def_503,type,
sK361: term ).
thf(func_def_504,type,
sK362: ( subst > term > term ) > term ).
thf(func_def_505,type,
sK363: ( subst > term > term ) > subst ).
thf(func_def_506,type,
sK364: ( subst > term > term ) > term ).
thf(func_def_507,type,
sK365: ( subst > term > term ) > subst ).
thf(func_def_508,type,
sK366: term > ( subst > term > subst > $o ) > term ).
thf(func_def_509,type,
sK367: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_510,type,
sK368: term ).
thf(func_def_511,type,
sK369: term > ( subst > term > subst > $o ) > term ).
thf(func_def_512,type,
sK370: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_513,type,
sK371: subst > term > subst > $o ).
thf(func_def_514,type,
sK372: term ).
thf(func_def_515,type,
sK373: ( subst > term > term ) > term ).
thf(func_def_516,type,
sK374: ( subst > term > term ) > subst ).
thf(func_def_517,type,
sK375: ( subst > term > term ) > subst ).
thf(func_def_518,type,
sK376: ( subst > term > term ) > term ).
thf(func_def_519,type,
sK377: subst > term > subst > $o ).
thf(func_def_520,type,
sK378: term ).
thf(func_def_521,type,
sK379: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_522,type,
sK380: ( subst > term > subst > $o ) > term ).
thf(func_def_523,type,
sK381: ( subst > term > subst > $o ) > term ).
thf(func_def_524,type,
sK382: subst > term > subst > $o ).
thf(func_def_525,type,
sK383: ( term > $o ) > term ).
thf(func_def_526,type,
sK384: term ).
thf(func_def_527,type,
sK385: ( term > $o ) > term ).
thf(func_def_528,type,
sK386: ( term > $o ) > term ).
thf(func_def_529,type,
sK387: term ).
thf(func_def_530,type,
sK388: term > $o ).
thf(func_def_531,type,
sK389: term > term ).
thf(func_def_532,type,
sK390: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_533,type,
sK391: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_534,type,
sK392: ( term > $o ) > term > term ).
thf(func_def_535,type,
sK393: subst > term > subst > $o ).
thf(func_def_536,type,
sK394: term ).
thf(func_def_537,type,
sK395: term > $o ).
thf(func_def_538,type,
sK396: ( subst > term > term ) > term ).
thf(func_def_539,type,
sK397: ( subst > term > term ) > subst ).
thf(func_def_540,type,
sK398: ( subst > term > term ) > term ).
thf(func_def_541,type,
sK399: ( subst > term > term ) > subst ).
thf(func_def_542,type,
sK400: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_543,type,
sK401: ( subst > term > term ) > term ).
thf(func_def_544,type,
sK402: ( subst > term > term ) > subst ).
thf(func_def_545,type,
sK403: ( subst > term > term ) > subst ).
thf(func_def_546,type,
sK404: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_547,type,
sK405: ( term > $o ) > term ).
thf(func_def_548,type,
sK406: ( term > $o ) > term ).
thf(func_def_549,type,
sK407: term ).
thf(func_def_550,type,
sK408: term ).
thf(func_def_551,type,
sK409: subst > term > subst > $o ).
thf(func_def_552,type,
sK410: ( subst > term > subst > $o ) > term ).
thf(func_def_553,type,
sK411: ( subst > term > subst > $o ) > subst ).
thf(func_def_554,type,
sK412: ( subst > term > subst > $o ) > subst ).
thf(func_def_555,type,
sK413: ( subst > term > subst > $o ) > subst ).
thf(func_def_556,type,
sK414: ( subst > term > subst > $o ) > subst ).
thf(func_def_557,type,
sK415: ( subst > term > subst > $o ) > term ).
thf(func_def_558,type,
sK416: ( subst > term > subst > $o ) > subst ).
thf(func_def_559,type,
sK417: ( subst > term > subst > $o ) > subst ).
thf(func_def_560,type,
sK418: ( subst > term > subst > $o ) > term ).
thf(func_def_561,type,
sK419: ( subst > term > subst > $o ) > term ).
thf(func_def_562,type,
sK420: term > subst > term > term ).
thf(func_def_563,type,
sK421: subst > term > subst > $o ).
thf(func_def_564,type,
sK422: term > $o ).
thf(func_def_565,type,
sK423: term ).
thf(func_def_566,type,
sK424: ( subst > term > term ) > term ).
thf(func_def_567,type,
sK425: ( subst > term > term ) > subst ).
thf(func_def_568,type,
sK426: ( subst > term > term ) > subst ).
thf(func_def_569,type,
sK427: ( subst > term > term ) > term ).
thf(func_def_570,type,
sK428: term ).
thf(func_def_571,type,
sK429: term ).
thf(func_def_572,type,
sK430: ( subst > term > term ) > term ).
thf(func_def_573,type,
sK431: ( subst > term > term ) > subst ).
thf(func_def_574,type,
sK432: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_575,type,
sK433: term > ( term > $o ) > term ).
thf(func_def_576,type,
sK434: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_577,type,
sK435: ( term > $o ) > term ).
thf(func_def_578,type,
sK436: ( term > $o ) > term ).
thf(func_def_579,type,
sK437: subst ).
thf(func_def_580,type,
sK438: term > $o ).
thf(func_def_581,type,
sK439: term ).
thf(func_def_582,type,
sK440: term ).
thf(func_def_583,type,
sK441: subst ).
thf(func_def_584,type,
sK442: subst ).
thf(func_def_585,type,
sK443: term ).
thf(func_def_586,type,
sK444: term > $o ).
thf(func_def_587,type,
sK445: term ).
thf(func_def_588,type,
sK446: subst ).
thf(func_def_589,type,
sK447: term > term ).
thf(func_def_590,type,
sK448: ( term > $o ) > term ).
thf(func_def_591,type,
sK449: subst > ( term > $o ) > term ).
thf(func_def_592,type,
sK450: ( term > $o ) > term ).
thf(func_def_593,type,
sK451: ( term > $o ) > term ).
thf(func_def_594,type,
sK452: ( term > $o ) > term ).
thf(func_def_595,type,
sK453: ( term > $o ) > term ).
thf(func_def_596,type,
sK454: term ).
thf(func_def_597,type,
sK455: ( subst > term > term ) > subst ).
thf(func_def_598,type,
sK456: ( subst > term > term ) > term ).
thf(func_def_599,type,
sK457: term > subst > term > term ).
thf(func_def_600,type,
sK458: term ).
thf(func_def_601,type,
sK459: term ).
thf(func_def_602,type,
sK460: term ).
thf(func_def_603,type,
sK461: term ).
thf(func_def_604,type,
sK462: term ).
thf(func_def_605,type,
sK463: term ).
thf(func_def_606,type,
sK464: term ).
thf(func_def_607,type,
sK465: term ).
thf(func_def_608,type,
sK466: term ).
thf(func_def_609,type,
sK467: term ).
thf(func_def_610,type,
sK468: term ).
thf(func_def_611,type,
sK469: term ).
thf(func_def_612,type,
sK470: term ).
thf(func_def_613,type,
sK471: term ).
thf(func_def_614,type,
sK472: term ).
thf(func_def_615,type,
sK473: ( subst > term > term ) > subst ).
thf(func_def_616,type,
sK474: ( subst > term > term ) > term ).
thf(func_def_617,type,
sK475: term > subst > term > term ).
thf(func_def_618,type,
sK476: subst > term > subst > $o ).
thf(func_def_619,type,
sK477: ( term > $o ) > term ).
thf(func_def_620,type,
sK478: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_621,type,
sK479: term ).
thf(func_def_622,type,
sK480: term > subst > term > term ).
thf(func_def_623,type,
sK481: term > d_term ).
thf(func_def_624,type,
sK482: subst ).
thf(func_def_625,type,
sK483: term ).
thf(func_def_626,type,
sK484: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_627,type,
sK485: term ).
thf(func_def_628,type,
sK486: subst > term > subst > $o ).
thf(func_def_629,type,
sK487: ( subst > term > term ) > subst ).
thf(func_def_630,type,
sK488: ( subst > term > term ) > term ).
thf(func_def_631,type,
sK489: ( subst > term > term ) > subst ).
thf(func_def_632,type,
sK490: ( subst > term > term ) > term ).
thf(func_def_633,type,
sK491: subst > d_subst ).
thf(func_def_634,type,
sK492: subst ).
thf(func_def_635,type,
sK493: term > $o ).
thf(func_def_636,type,
sK494: term ).
thf(func_def_637,type,
sK495: ( term > $o ) > term ).
thf(func_def_638,type,
sK496: term > ( term > $o ) > subst > term > $o ).
thf(func_def_639,type,
sK497: term ).
thf(func_def_640,type,
sK498: term ).
thf(func_def_641,type,
sK499: term ).
thf(func_def_642,type,
sK500: term ).
thf(func_def_643,type,
sK501: term ).
thf(func_def_644,type,
sK502: term ).
thf(func_def_645,type,
sK503: term ).
thf(func_def_646,type,
sK504: term ).
thf(func_def_647,type,
sK505: term ).
thf(func_def_648,type,
sK506: ( term > $o ) > term ).
thf(func_def_649,type,
sK507: ( term > $o ) > term ).
thf(func_def_650,type,
sK508: term > $o ).
thf(func_def_651,type,
sK509: term ).
thf(func_def_652,type,
sK510: subst ).
thf(func_def_653,type,
sK511: subst ).
thf(func_def_654,type,
sK512: term ).
thf(func_def_655,type,
sK513: term > subst > term > term ).
thf(func_def_656,type,
sK514: term ).
thf(func_def_657,type,
sK515: term ).
thf(func_def_658,type,
sK516: term ).
thf(func_def_659,type,
sK517: term ).
thf(func_def_660,type,
sK518: term > $o ).
thf(func_def_661,type,
sK519: term ).
thf(func_def_662,type,
sK520: subst ).
thf(func_def_663,type,
sK521: ( term > $o ) > term ).
thf(func_def_664,type,
sK522: subst > term > ( term > $o ) > term > $o ).
thf(func_def_665,type,
sK523: term ).
thf(func_def_666,type,
sK524: term ).
thf(func_def_667,type,
sK525: subst ).
thf(func_def_668,type,
sK526: subst ).
thf(func_def_669,type,
sK527: subst ).
thf(func_def_670,type,
sK528: subst ).
thf(func_def_671,type,
sK529: term > $o ).
thf(func_def_672,type,
sK530: subst ).
thf(func_def_673,type,
sK531: term > $o ).
thf(func_def_674,type,
sK532: term ).
thf(func_def_675,type,
sK533: term ).
thf(func_def_676,type,
sK534: term ).
thf(func_def_677,type,
sK535: term ).
thf(func_def_678,type,
sK536: term ).
thf(func_def_679,type,
sK537: ( subst > term > term ) > term ).
thf(func_def_680,type,
sK538: ( subst > term > term ) > subst ).
thf(func_def_681,type,
sK539: ( subst > term > term ) > subst ).
thf(func_def_682,type,
sK540: ( subst > term > term ) > subst ).
thf(func_def_683,type,
sK541: ( subst > term > term ) > term ).
thf(func_def_684,type,
sK542: ( subst > term > term ) > subst ).
thf(func_def_685,type,
sK543: subst > term > term ).
thf(func_def_686,type,
sK544: subst ).
thf(func_def_687,type,
sK545: subst > term > term ).
thf(func_def_688,type,
sK546: term ).
thf(func_def_689,type,
sK547: subst ).
thf(func_def_690,type,
sK548: subst > term > term ).
thf(func_def_691,type,
sK549: term ).
thf(func_def_692,type,
sK550: term ).
thf(func_def_693,type,
sK551: ( subst > term > term ) > subst ).
thf(func_def_694,type,
sK552: ( subst > term > term ) > term ).
thf(func_def_695,type,
sK553: ( subst > term > term ) > subst ).
thf(func_def_696,type,
sK554: term ).
thf(func_def_697,type,
sK555: term ).
thf(func_def_698,type,
sK556: term ).
thf(func_def_699,type,
sK557: term ).
thf(func_def_700,type,
sK558: term > subst > ( term > $o ) > ( term > $o ) > term ).
thf(func_def_701,type,
sK559: term > $o ).
thf(func_def_702,type,
sK560: term > $o ).
thf(func_def_703,type,
sK561: subst ).
thf(func_def_704,type,
sK562: term ).
thf(func_def_705,type,
sK563: subst ).
thf(func_def_706,type,
sK564: term ).
thf(func_def_707,type,
sK565: term > $o ).
thf(func_def_708,type,
sK566: term > $o ).
thf(func_def_709,type,
sK567: subst ).
thf(func_def_710,type,
sK568: term ).
thf(func_def_711,type,
sK569: term ).
thf(func_def_712,type,
sK570: subst ).
thf(func_def_713,type,
sK571: subst ).
thf(func_def_714,type,
sK572: term ).
thf(func_def_715,type,
sK573: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_716,type,
sK574: subst > term > subst > $o ).
thf(func_def_717,type,
sK575: ( term > $o ) > term ).
thf(func_def_718,type,
sK576: subst ).
thf(func_def_719,type,
sK577: term ).
thf(func_def_720,type,
sK578: subst ).
thf(func_def_721,type,
sK579: term ).
thf(func_def_722,type,
sK580: subst ).
thf(func_def_723,type,
sK581: term ).
thf(func_def_724,type,
sK582: ( term > $o ) > ( term > $o ) > subst > term > term ).
thf(func_def_725,type,
sK583: term ).
thf(func_def_726,type,
sK584: subst ).
thf(func_def_727,type,
sK585: term > $o ).
thf(func_def_728,type,
sK586: term > $o ).
thf(func_def_729,type,
sK587: term ).
thf(func_def_730,type,
sK588: term ).
thf(func_def_731,type,
sK589: term ).
thf(func_def_732,type,
sK590: term ).
thf(func_def_734,type,
sK592: term > $o ).
thf(func_def_735,type,
sK593: subst > term > subst > $o ).
thf(func_def_736,type,
sK594: ( subst > term > term ) > term ).
thf(func_def_737,type,
sK595: ( subst > term > term ) > term ).
thf(func_def_738,type,
sK596: ( subst > term > term ) > subst ).
thf(func_def_739,type,
sK597: ( subst > term > term ) > subst ).
thf(func_def_740,type,
sK598: term ).
thf(func_def_741,type,
sK599: ( subst > term > subst > $o ) > subst ).
thf(func_def_742,type,
sK600: ( subst > term > subst > $o ) > term ).
thf(func_def_743,type,
sK601: ( subst > term > subst > $o ) > subst ).
thf(func_def_744,type,
sK602: ( subst > term > subst > $o ) > subst ).
thf(func_def_745,type,
sK603: ( subst > term > subst > $o ) > subst ).
thf(func_def_746,type,
sK604: ( subst > term > subst > $o ) > term ).
thf(func_def_747,type,
sK605: ( subst > term > subst > $o ) > subst ).
thf(func_def_748,type,
sK606: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_749,type,
sK607: ( subst > term > subst > $o ) > subst ).
thf(func_def_750,type,
sK608: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_751,type,
sK609: ( term > $o ) > term > term ).
thf(func_def_752,type,
sK610: ( subst > term > subst > $o ) > subst ).
thf(func_def_753,type,
sK611: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_754,type,
sK612: term > ( term > $o ) > term ).
thf(func_def_755,type,
sK613: term > ( term > $o ) > term ).
thf(func_def_756,type,
sK614: term > ( term > $o ) > term ).
thf(func_def_757,type,
sK615: term > ( term > $o ) > term ).
thf(func_def_758,type,
sK616: ( subst > term > subst > $o ) > subst ).
thf(func_def_759,type,
sK617: term > ( term > $o ) > term ).
thf(func_def_760,type,
sK618: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_761,type,
sK619: term > ( term > $o ) > term ).
thf(func_def_762,type,
sK620: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_763,type,
sK621: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_764,type,
sK622: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_765,type,
sK623: ( subst > term > subst > $o ) > subst ).
thf(func_def_766,type,
sK624: ( subst > term > subst > $o ) > subst ).
thf(func_def_767,type,
sK625: term > ( term > $o ) > term ).
thf(func_def_768,type,
sK626: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_770,type,
ph627:
!>[X0: $tType] : X0 ).
thf(f12740,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3220,f3834,f3842,f3858,f4559,f4613,f4848,f5545,f7223,f7333,f7414,f12736,f12738]) ).
thf(f12738,plain,
( spl591_545
| spl591_255
| ~ spl591_515
| ~ spl591_517 ),
inference(avatar_split_clause,[status(thm)],[f12672,f4611,f4597,f3217,f4845]) ).
thf(f4845,definition,
( spl591_545
<=> ( ( sP57 @ sK59 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_545])],[avatar_definition]) ).
thf(f3217,definition,
( spl591_255
<=> ( $true
= ( sK60 @ ( lam @ sK61 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_255])],[avatar_definition]) ).
thf(f4597,definition,
( spl591_515
<=> ! [X9: term,X10: term] : ( X9 = X10 ) ),
introduced(definition,[new_symbols(naming,[spl591_515])],[avatar_definition]) ).
thf(f4611,definition,
( spl591_517
<=> ! [X11: term] :
( ( ( sK60 @ X11 )
= $true )
| ( $false
= ( sK59 @ ( d2subst @ d_id ) @ X11 @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_517])],[avatar_definition]) ).
thf(f12672,plain,
( ( ( sP57 @ sK59 )
= $true )
| spl591_255
| ~ spl591_515
| ~ spl591_517 ),
inference(trivial_inequality_removal,[status(thm)],[f12636]) ).
thf(f12636,plain,
( ( ( sP57 @ sK59 )
= $true )
| ( $false = $true )
| spl591_255
| ~ spl591_515
| ~ spl591_517 ),
inference(superposition,[status(thm)],[f7678,f4237]) ).
thf(f4237,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP57 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4236,f4138]) ).
thf(f4138,plain,
! [X55: term] :
( ( d2term @ d_one )
= X55 ),
inference(forward_demodulation,[status(thm)],[f1217,f1180]) ).
thf(f1180,plain,
! [X113: d_term] : ( d_one = X113 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X1: subst > term > term] :
( ( X1 @ ( sK455 @ X1 ) @ ( sK456 @ X1 ) )
!= ( sub @ sK454 @ ( push @ ( sK456 @ X1 ) @ ( sK455 @ X1 ) ) ) ) )
& ( ! [X4: term,X6: subst,X7: term] :
( ( sK457 @ X4 @ X6 @ X7 )
= ( sub @ X4 @ ( push @ X7 @ X6 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X8: term,X9: term,X10: term,X11: term] :
( ( ( ap @ X9 @ X8 )
!= ( ap @ X10 @ X11 ) )
| ( X9 = X10 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ( ( ( ap @ sK459 @ sK458 )
= ( ap @ sK460 @ sK461 ) )
& ( sK460 != sK459 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP58 != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X16: term,X17: term,X18: term,X19: term] :
( ( ( ap @ X19 @ X17 )
!= ( ap @ X16 @ X18 ) )
| ( X17 = X18 ) )
& ( ( ap @ ( sub @ sK465 @ id ) @ sK462 )
= ( ap @ ( sub @ sK464 @ id ) @ sK463 ) )
& ( sK462 != sK463 ) ) )
& ( ( ( ( ap @ sK469 @ sK467 )
= ( ap @ sK466 @ sK468 ) )
& ( sK468 != sK467 ) )
| ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ ( sub @ X30 @ id ) @ X29 )
!= ( ap @ ( sub @ X31 @ id ) @ X28 ) )
| ( X28 = X29 ) )
| ( hoasapinj2_lthm != $true ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X32: d_subst] : ( d_id = X32 )
& ( ( termmset_lthm = $true )
| ( ( ( sub @ sK470 @ id )
!= sK470 )
& ! [X34: term] :
( ( sub @ X34 @ id )
= X34 ) ) )
& ( ! [X35: term] :
( ( sub @ X35 @ id )
= X35 )
| ( ( sub @ sK471 @ id )
!= sK471 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X38: subst > term > term] :
( ( sub @ sK472 @ ( push @ ( sK474 @ X38 ) @ ( sK473 @ X38 ) ) )
!= ( X38 @ ( sK473 @ X38 ) @ ( sK474 @ X38 ) ) ) )
& ( ! [X41: term,X43: subst,X44: term] :
( ( sub @ X41 @ ( push @ X44 @ X43 ) )
= ( sK475 @ X41 @ X43 @ X44 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP56 != $true ) )
& ( ( sP56 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ulamvarind = $true )
& ( ( sP54 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP54 != $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X46: term > $o] :
( ( sK476 @ id @ ( sK477 @ X46 ) @ id )
!= ( X46 @ ( sK477 @ X46 ) ) ) )
& ( ! [X48: subst > term > subst > $o,X50: term] :
( ( sK478 @ X48 @ X50 )
= ( X48 @ id @ X50 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X52: subst > term > term] :
( ( sub @ sK479 @ ( push @ one @ sh ) )
!= ( X52 @ sh @ one ) ) )
& ( ! [X53: term] :
( ( sK480 @ X53 @ sh @ one )
= ( sub @ X53 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP53 ) )
& ( ( $true = sP53 )
| ( hoasinduction_lem3a != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X55: term] :
( ( d2term @ ( sK481 @ X55 ) )
= X55 )
& ( hoasapinj2_gthm = $true )
& ( ! [X57: subst,X58: term] :
( ( sub @ one @ ( push @ X58 @ X57 ) )
= X58 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ( sK483
!= ( sub @ one @ ( push @ sK483 @ sK482 ) ) ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP46 ) )
& ( ( $true = sP46 )
| ( induction2_lthm != $true ) )
& ( ! [X61: term,X62: subst > term > subst > $o] :
( ( ! [X64: subst,X65: term,X66: subst] :
( ( sK484 @ X62 @ ( comp @ X64 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( sK484 @ X62 @ X64 @ X65 ) @ X66 ) )
& ! [X67: term] :
( ( $true
= ( X62 @ id @ ( sK484 @ X62 @ id @ X67 ) @ id ) )
| ( ( X62 @ id @ X67 @ id )
!= $true ) )
& ( ( X62 @ id @ ( lam @ ( sK484 @ X62 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X62 @ id @ X61 @ id )
= $true )
| ( ( sP42 @ X62 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X70: subst > term > term] :
( ( ( X70 @ ( comp @ ( sK487 @ X70 ) @ ( sK489 @ X70 ) ) @ ( sub @ ( sK488 @ X70 ) @ ( sK489 @ X70 ) ) )
!= ( sub @ ( X70 @ ( sK487 @ X70 ) @ ( sK488 @ X70 ) ) @ ( sK489 @ X70 ) ) )
| ( ( $true
!= ( sK486 @ id @ ( X70 @ id @ ( sK490 @ X70 ) ) @ id ) )
& ( ( sK486 @ id @ ( sK490 @ X70 ) @ id )
= $true ) )
| ( $true
= ( sK486 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) )
& ( ( sK486 @ id @ sK485 @ id )
!= $true )
& ( ( sP42 @ sK486 )
!= $true ) ) )
& ! [X75: subst] :
( ( d2subst @ ( sK491 @ X75 ) )
= X75 )
& ( ( pushprop_lem0 = $true )
| ! [X80: term > $o] :
( ( sK493 @ ( sub @ ( sK495 @ X80 ) @ ( push @ sK494 @ sK492 ) ) )
!= ( X80 @ ( sK495 @ X80 ) ) ) )
& ( ! [X82: subst,X83: term > $o,X84: term,X86: term] :
( ( X83 @ ( sub @ X86 @ ( push @ X84 @ X82 ) ) )
= ( sK496 @ X84 @ X83 @ X82 @ X86 ) )
| ( pushprop_lem0 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ! [X87: term,X88: term,X89: term,X90: term] :
( ( ( ap @ ( sub @ X90 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) )
| ( X87 = X90 ) )
| ( sK497
!= ( sub @ sK497 @ id ) )
| ( ( sK500 != sK501 )
& ( ( ap @ sK501 @ sK499 )
= ( ap @ sK500 @ sK498 ) ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ( ( ap @ ( sub @ sK502 @ id ) @ sK503 )
= ( ap @ ( sub @ sK505 @ id ) @ sK504 ) )
& ( sK505 != sK502 )
& ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
& ! [X101: term,X102: term,X103: term,X104: term] :
( ( X103 = X104 )
| ( ( ap @ X104 @ X102 )
!= ( ap @ X103 @ X101 ) ) ) ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ! [X105: term > $o,X106: term] :
( ( ( $true
!= ( X105 @ ( sK506 @ X105 ) ) )
& ( ( var @ ( sK506 @ X105 ) )
= $true ) )
| ( ( sP39 @ X105 )
= $true )
| ( ( X105 @ X106 )
= $true )
| ( ( ( X105 @ ( sK507 @ X105 ) )
= $true )
& ( ( X105 @ ( lam @ ( sK507 @ X105 ) ) )
!= $true ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ( ! [X111: term] :
( ( ( sK508 @ X111 )
= $true )
| ( ( var @ X111 )
!= $true ) )
& ( ( sP39 @ sK508 )
!= $true )
& ( ( sK508 @ sK509 )
!= $true )
& ! [X112: term] :
( ( ( sK508 @ X112 )
!= $true )
| ( ( sK508 @ ( lam @ X112 ) )
= $true ) ) ) )
& ( hoasinduction_gthm = $true )
& ! [X113: d_term] : ( d_one = X113 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
| ( sP38 != $true ) )
& ( ( sP38 = $true )
| ( hoasinduction != $true ) )
& ( ( ! [X114: subst] :
( ( comp @ id @ X114 )
= X114 )
& ! [X115: subst] :
( ( comp @ X115 @ id )
= X115 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ( sK510
!= ( comp @ id @ sK510 ) )
| ( sK511
!= ( comp @ sK511 @ id ) ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
| ! [X119: subst > term > term] :
( ( X119 @ sh @ one )
!= ( sub @ sK512 @ ( push @ one @ sh ) ) ) )
& ( ! [X120: term] :
( ( sub @ X120 @ ( push @ one @ sh ) )
= ( sK513 @ X120 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
| ( ( sK514 != sK517 )
& ( ( ap @ ( sub @ sK514 @ id ) @ sK515 )
= ( ap @ ( sub @ sK517 @ id ) @ sK516 ) ) ) )
& ( ! [X126: term,X127: term,X128: term,X129: term] :
( ( X126 = X129 )
| ( ( ap @ ( sub @ X126 @ id ) @ X127 )
!= ( ap @ ( sub @ X129 @ id ) @ X128 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X133: term > $o] :
( ( sK518 @ ( sub @ ( sK521 @ X133 ) @ ( push @ sK519 @ sK520 ) ) )
!= ( X133 @ ( sK521 @ X133 ) ) ) )
& ( ! [X135: term > $o,X136: term,X137: subst,X139: term] :
( ( sK522 @ X137 @ X136 @ X135 @ X139 )
= ( X135 @ ( sub @ X139 @ ( push @ X136 @ X137 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
| ( ( ( lam @ sK523 )
= ( lam @ sK524 ) )
& ( sK523 != sK524 ) ) )
& ( ! [X142: term,X143: term] :
( ( ( lam @ X142 )
!= ( lam @ X143 ) )
| ( X142 = X143 ) )
| ( laminj != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X144: d_term,X145: d_term] :
( ( X144 = X145 )
| ( ( d2term @ X144 )
!= ( d2term @ X145 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP35 != $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP33 != $true ) )
& ( ( sP33 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( ( comp @ id @ sK525 )
!= sK525 )
| ( sK526
!= ( comp @ sK526 @ id ) )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X149: subst] :
( ( comp @ X149 @ id )
= X149 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X150: subst] :
( ( comp @ id @ X150 )
= X150 )
& ! [X151: subst] :
( ( comp @ X151 @ id )
= X151 )
& ( ( sK527
!= ( comp @ id @ sK527 ) )
| ( sK528
!= ( comp @ sK528 @ id ) ) ) ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP32 ) )
& ( ! [X154: term > $o,X155: subst,X156: term > $o,X157: term,X158: term] :
( ( ( X156 @ ( sub @ X158 @ ( push @ X157 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X158 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK531 @ ( sub @ sK533 @ ( push @ sK532 @ sK530 ) ) )
!= $true )
& ( ( sK529 @ sK533 )
= $true ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP31 != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
| ( ( ( sub @ sK535 @ sh )
= ( sub @ sK534 @ sh ) )
& ( sK534 != sK535 ) ) )
& ( ! [X166: term,X167: term] :
( ( ( sub @ X167 @ sh )
!= ( sub @ X166 @ sh ) )
| ( X166 = X167 ) )
| ( shinj != $true ) )
& ( ! [X168: term] :
( ( sub @ X168 @ id )
= X168 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ( ( sub @ sK536 @ id )
!= sK536 ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X170: subst > term > term,X171: subst,X172: subst > term > term,X173: term] :
( ( ( lam @ ( X172 @ sh @ one ) )
!= ( lam @ ( X170 @ sh @ one ) ) )
| ( ( X172 @ X171 @ X173 )
= ( X170 @ X171 @ X173 ) )
| ( ( X170 @ ( comp @ ( sK538 @ X170 ) @ ( sK539 @ X170 ) ) @ ( sub @ ( sK537 @ X170 ) @ ( sK539 @ X170 ) ) )
!= ( sub @ ( X170 @ ( sK538 @ X170 ) @ ( sK537 @ X170 ) ) @ ( sK539 @ X170 ) ) )
| ( ( X172 @ ( comp @ ( sK540 @ X172 ) @ ( sK542 @ X172 ) ) @ ( sub @ ( sK541 @ X172 ) @ ( sK542 @ X172 ) ) )
!= ( sub @ ( X172 @ ( sK540 @ X172 ) @ ( sK541 @ X172 ) ) @ ( sK542 @ X172 ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ( ( ( lam @ ( sK543 @ sh @ one ) )
= ( lam @ ( sK545 @ sh @ one ) ) )
& ( ( sK543 @ sK544 @ sK546 )
!= ( sK545 @ sK544 @ sK546 ) )
& ! [X184: term,X185: subst,X186: subst] :
( ( sK543 @ ( comp @ X185 @ X186 ) @ ( sub @ X184 @ X186 ) )
= ( sub @ ( sK543 @ X185 @ X184 ) @ X186 ) )
& ! [X187: subst,X188: term,X189: subst] :
( ( sub @ ( sK545 @ X187 @ X188 ) @ X189 )
= ( sK545 @ ( comp @ X187 @ X189 ) @ ( sub @ X188 @ X189 ) ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
| ( sP21 != $true ) )
& ( ( sP21 = $true )
| ( induction2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X190: subst] :
( ( push @ ( sub @ one @ X190 ) @ ( comp @ sh @ X190 ) )
= X190 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ( ( push @ ( sub @ one @ sK547 ) @ ( comp @ sh @ sK547 ) )
!= sK547 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ( ! [X195: subst,X196: term,X197: subst] :
( ( sK548 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) )
= ( sub @ ( sK548 @ X197 @ X196 ) @ X195 ) )
& ( ( ap @ ( sub @ sK549 @ id ) @ sK550 )
= ( lam @ ( sK548 @ sh @ one ) ) ) ) )
& ( ! [X198: subst > term > term,X199: term,X200: term] :
( ( ( X198 @ ( comp @ ( sK553 @ X198 ) @ ( sK551 @ X198 ) ) @ ( sub @ ( sK552 @ X198 ) @ ( sK551 @ X198 ) ) )
!= ( sub @ ( X198 @ ( sK553 @ X198 ) @ ( sK552 @ X198 ) ) @ ( sK551 @ X198 ) ) )
| ( ( ap @ ( sub @ X199 @ id ) @ X200 )
!= ( lam @ ( X198 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ( $true = sP16 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP16 ) )
& ( ( sP15 = $true )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( sP15 != $true ) )
& ( ! [X204: term,X205: term,X206: term,X207: term] :
( ( ( ap @ ( sub @ X204 @ id ) @ X205 )
!= ( ap @ ( sub @ X207 @ id ) @ X206 ) )
| ( X205 = X206 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( ( ap @ ( sub @ sK554 @ id ) @ sK555 )
= ( ap @ ( sub @ sK557 @ id ) @ sK556 ) )
& ( sK555 != sK556 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP13 != $true ) )
& ( ( sP13 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ! [X212: term > $o,X213: term > $o,X214: subst,X215: term] :
( ( ( X213 @ ( sub @ ( sK558 @ X215 @ X214 @ X213 @ X212 ) @ ( push @ X215 @ X214 ) ) )
!= ( X212 @ ( sK558 @ X215 @ X214 @ X213 @ X212 ) ) )
| ( ( X212 @ one )
= $true )
| ( ( X213 @ X215 )
!= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ! [X221: term] :
( ( sK560 @ ( sub @ X221 @ ( push @ sK562 @ sK561 ) ) )
= ( sK559 @ X221 ) )
& ( ( sK559 @ one )
!= $true )
& ( $true
= ( sK560 @ sK562 ) ) ) )
& ( ( axidr = $true )
| ( sK563
!= ( comp @ sK563 @ id ) ) )
& ( ! [X223: subst] :
( ( comp @ X223 @ id )
= X223 )
| ( axidr != $true ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X224: term,X225: subst] :
( ( sub @ one @ ( push @ X224 @ X225 ) )
= X224 )
& ! [X226: subst,X227: term] :
( ( comp @ sh @ ( push @ X227 @ X226 ) )
= X226 )
& ( ( sK565 @ sK568 )
= $true )
& ( ( sK566 @ ( sub @ sK568 @ ( push @ sK564 @ sK567 ) ) )
!= $true ) ) )
& ( ( sK569
!= ( sub @ one @ ( push @ sK569 @ sK570 ) ) )
| ( sK571
!= ( comp @ sh @ ( push @ sK572 @ sK571 ) ) )
| ! [X237: term,X238: term > $o,X239: term > $o,X240: subst,X241: term] :
( ( ( X238 @ X241 )
!= $true )
| ( ( X239 @ ( sub @ X241 @ ( push @ X237 @ X240 ) ) )
= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ! [X242: subst > term > subst > $o,X244: term] :
( ( sK573 @ X242 @ X244 )
= ( X242 @ id @ X244 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ! [X246: term > $o] :
( ( X246 @ ( sK575 @ X246 ) )
!= ( sK574 @ id @ ( sK575 @ X246 ) @ id ) ) )
& ( ( sP11 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP11 != $true ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK577 @ sK576 ) )
!= sK576 ) )
& ( ! [X250: subst,X251: term] :
( ( comp @ sh @ ( push @ X251 @ X250 ) )
= X250 )
| ( axshiftcons != $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X252: d_subst,X253: d_subst] :
( ( X252 = X253 )
| ( ( d2subst @ X253 )
!= ( d2subst @ X252 ) ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP6 != $true ) )
& ( ( axidl = $true )
| ( ( comp @ id @ sK578 )
!= sK578 ) )
& ( ! [X255: subst] :
( ( comp @ id @ X255 )
= X255 )
| ( axidl != $true ) )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ( ( sub @ sK579 @ id )
!= sK579 ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP4 != $true ) )
& ( ( sP4 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ( sK581
!= ( sub @ one @ ( push @ sK581 @ sK580 ) ) )
| ! [X260: term,X261: subst,X262: term > $o,X263: term > $o] :
( ( ( X263 @ ( sub @ ( sK582 @ X263 @ X262 @ X261 @ X260 ) @ ( push @ X260 @ X261 ) ) )
!= ( X262 @ ( sK582 @ X263 @ X262 @ X261 @ X260 ) ) )
| ( ( X262 @ one )
= $true )
| ( ( X263 @ X260 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X265: subst,X266: term] :
( ( sub @ one @ ( push @ X266 @ X265 ) )
= X266 )
& ! [X271: term] :
( ( sK585 @ X271 )
= ( sK586 @ ( sub @ X271 @ ( push @ sK583 @ sK584 ) ) ) )
& ( $true
!= ( sK585 @ one ) )
& ( ( sK586 @ sK583 )
= $true ) ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X272: term,X273: term,X274: term,X275: term] :
( ( ( ap @ X273 @ X275 )
!= ( ap @ X272 @ X274 ) )
| ( X274 = X275 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( ( ap @ sK587 @ sK589 )
= ( ap @ sK588 @ sK590 ) )
& ( sK590 != sK589 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
| ( sP3 != $true ) )
& ( ( sP3 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474]) ).
thf(f474,plain,
( ? [X0: term] :
! [X1: subst > term > term] :
? [X2: subst,X3: term] :
( ( sub @ X0 @ ( push @ X3 @ X2 ) )
!= ( X1 @ X2 @ X3 ) )
=> ! [X1: subst > term > term] :
? [X3: term,X2: subst] :
( ( X1 @ X2 @ X3 )
!= ( sub @ sK454 @ ( push @ X3 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
! [X1: subst > term > term] :
( ? [X3: term,X2: subst] :
( ( X1 @ X2 @ X3 )
!= ( sub @ sK454 @ ( push @ X3 @ X2 ) ) )
=> ( ( X1 @ ( sK455 @ X1 ) @ ( sK456 @ X1 ) )
!= ( sub @ sK454 @ ( push @ ( sK456 @ X1 ) @ ( sK455 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f476,plain,
! [X4: term] :
( ? [X5: subst > term > term] :
! [X6: subst,X7: term] :
( ( X5 @ X6 @ X7 )
= ( sub @ X4 @ ( push @ X7 @ X6 ) ) )
=> ! [X7: term,X6: subst] :
( ( sK457 @ X4 @ X6 @ X7 )
= ( sub @ X4 @ ( push @ X7 @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
( ? [X12: term,X13: term,X14: term,X15: term] :
( ( ( ap @ X14 @ X15 )
= ( ap @ X13 @ X12 ) )
& ( X13 != X14 ) )
=> ( ( ( ap @ sK459 @ sK458 )
= ( ap @ sK460 @ sK461 ) )
& ( sK460 != sK459 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
( ? [X20: term,X21: term,X22: term,X23: term] :
( ( ( ap @ ( sub @ X23 @ id ) @ X20 )
= ( ap @ ( sub @ X22 @ id ) @ X21 ) )
& ( X20 != X21 ) )
=> ( ( ( ap @ ( sub @ sK465 @ id ) @ sK462 )
= ( ap @ ( sub @ sK464 @ id ) @ sK463 ) )
& ( sK462 != sK463 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X24: term,X25: term,X26: term,X27: term] :
( ( ( ap @ X27 @ X25 )
= ( ap @ X24 @ X26 ) )
& ( X25 != X26 ) )
=> ( ( ( ap @ sK469 @ sK467 )
= ( ap @ sK466 @ sK468 ) )
& ( sK468 != sK467 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
( ? [X33: term] :
( ( sub @ X33 @ id )
!= X33 )
=> ( ( sub @ sK470 @ id )
!= sK470 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
( ? [X36: term] :
( ( sub @ X36 @ id )
!= X36 )
=> ( ( sub @ sK471 @ id )
!= sK471 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ? [X37: term] :
! [X38: subst > term > term] :
? [X39: subst,X40: term] :
( ( X38 @ X39 @ X40 )
!= ( sub @ X37 @ ( push @ X40 @ X39 ) ) )
=> ! [X38: subst > term > term] :
? [X40: term,X39: subst] :
( ( X38 @ X39 @ X40 )
!= ( sub @ sK472 @ ( push @ X40 @ X39 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
! [X38: subst > term > term] :
( ? [X40: term,X39: subst] :
( ( X38 @ X39 @ X40 )
!= ( sub @ sK472 @ ( push @ X40 @ X39 ) ) )
=> ( ( sub @ sK472 @ ( push @ ( sK474 @ X38 ) @ ( sK473 @ X38 ) ) )
!= ( X38 @ ( sK473 @ X38 ) @ ( sK474 @ X38 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
! [X41: term] :
( ? [X42: subst > term > term] :
! [X43: subst,X44: term] :
( ( X42 @ X43 @ X44 )
= ( sub @ X41 @ ( push @ X44 @ X43 ) ) )
=> ! [X44: term,X43: subst] :
( ( sub @ X41 @ ( push @ X44 @ X43 ) )
= ( sK475 @ X41 @ X43 @ X44 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
( ? [X45: subst > term > subst > $o] :
! [X46: term > $o] :
? [X47: term] :
( ( X45 @ id @ X47 @ id )
!= ( X46 @ X47 ) )
=> ! [X46: term > $o] :
? [X47: term] :
( ( sK476 @ id @ X47 @ id )
!= ( X46 @ X47 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
! [X46: term > $o] :
( ? [X47: term] :
( ( sK476 @ id @ X47 @ id )
!= ( X46 @ X47 ) )
=> ( ( sK476 @ id @ ( sK477 @ X46 ) @ id )
!= ( X46 @ ( sK477 @ X46 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
! [X48: subst > term > subst > $o] :
( ? [X49: term > $o] :
! [X50: term] :
( ( X48 @ id @ X50 @ id )
= ( X49 @ X50 ) )
=> ! [X50: term] :
( ( sK478 @ X48 @ X50 )
= ( X48 @ id @ X50 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
( ? [X51: term] :
! [X52: subst > term > term] :
( ( X52 @ sh @ one )
!= ( sub @ X51 @ ( push @ one @ sh ) ) )
=> ! [X52: subst > term > term] :
( ( sub @ sK479 @ ( push @ one @ sh ) )
!= ( X52 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
! [X53: term] :
( ? [X54: subst > term > term] :
( ( sub @ X53 @ ( push @ one @ sh ) )
= ( X54 @ sh @ one ) )
=> ( ( sK480 @ X53 @ sh @ one )
= ( sub @ X53 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
! [X55: term] :
( ? [X56: d_term] :
( ( d2term @ X56 )
= X55 )
=> ( ( d2term @ ( sK481 @ X55 ) )
= X55 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
( ? [X59: subst,X60: term] :
( ( sub @ one @ ( push @ X60 @ X59 ) )
!= X60 )
=> ( sK483
!= ( sub @ one @ ( push @ sK483 @ sK482 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
! [X62: subst > term > subst > $o] :
( ? [X63: subst > term > term] :
( ! [X64: subst,X65: term,X66: subst] :
( ( sub @ ( X63 @ X64 @ X65 ) @ X66 )
= ( X63 @ ( comp @ X64 @ X66 ) @ ( sub @ X65 @ X66 ) ) )
& ! [X67: term] :
( ( ( X62 @ id @ ( X63 @ id @ X67 ) @ id )
= $true )
| ( ( X62 @ id @ X67 @ id )
!= $true ) )
& ( ( X62 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id )
!= $true ) )
=> ( ! [X66: subst,X65: term,X64: subst] :
( ( sK484 @ X62 @ ( comp @ X64 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( sK484 @ X62 @ X64 @ X65 ) @ X66 ) )
& ! [X67: term] :
( ( $true
= ( X62 @ id @ ( sK484 @ X62 @ id @ X67 ) @ id ) )
| ( ( X62 @ id @ X67 @ id )
!= $true ) )
& ( ( X62 @ id @ ( lam @ ( sK484 @ X62 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
( ? [X68: term,X69: subst > term > subst > $o] :
( ! [X70: subst > term > term] :
( ? [X71: subst,X72: term,X73: subst] :
( ( sub @ ( X70 @ X71 @ X72 ) @ X73 )
!= ( X70 @ ( comp @ X71 @ X73 ) @ ( sub @ X72 @ X73 ) ) )
| ? [X74: term] :
( ( ( X69 @ id @ ( X70 @ id @ X74 ) @ id )
!= $true )
& ( ( X69 @ id @ X74 @ id )
= $true ) )
| ( ( X69 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X69 @ id @ X68 @ id )
!= $true )
& ( ( sP42 @ X69 )
!= $true ) )
=> ( ! [X70: subst > term > term] :
( ? [X71: subst,X72: term,X73: subst] :
( ( sub @ ( X70 @ X71 @ X72 ) @ X73 )
!= ( X70 @ ( comp @ X71 @ X73 ) @ ( sub @ X72 @ X73 ) ) )
| ? [X74: term] :
( ( ( sK486 @ id @ ( X70 @ id @ X74 ) @ id )
!= $true )
& ( ( sK486 @ id @ X74 @ id )
= $true ) )
| ( $true
= ( sK486 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) )
& ( ( sK486 @ id @ sK485 @ id )
!= $true )
& ( ( sP42 @ sK486 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
! [X70: subst > term > term] :
( ? [X71: subst,X72: term,X73: subst] :
( ( sub @ ( X70 @ X71 @ X72 ) @ X73 )
!= ( X70 @ ( comp @ X71 @ X73 ) @ ( sub @ X72 @ X73 ) ) )
=> ( ( X70 @ ( comp @ ( sK487 @ X70 ) @ ( sK489 @ X70 ) ) @ ( sub @ ( sK488 @ X70 ) @ ( sK489 @ X70 ) ) )
!= ( sub @ ( X70 @ ( sK487 @ X70 ) @ ( sK488 @ X70 ) ) @ ( sK489 @ X70 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
! [X70: subst > term > term] :
( ? [X74: term] :
( ( ( sK486 @ id @ ( X70 @ id @ X74 ) @ id )
!= $true )
& ( ( sK486 @ id @ X74 @ id )
= $true ) )
=> ( ( $true
!= ( sK486 @ id @ ( X70 @ id @ ( sK490 @ X70 ) ) @ id ) )
& ( ( sK486 @ id @ ( sK490 @ X70 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
! [X75: subst] :
( ? [X76: d_subst] :
( ( d2subst @ X76 )
= X75 )
=> ( ( d2subst @ ( sK491 @ X75 ) )
= X75 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
( ? [X77: subst,X78: term > $o,X79: term] :
! [X80: term > $o] :
? [X81: term] :
( ( X80 @ X81 )
!= ( X78 @ ( sub @ X81 @ ( push @ X79 @ X77 ) ) ) )
=> ! [X80: term > $o] :
? [X81: term] :
( ( sK493 @ ( sub @ X81 @ ( push @ sK494 @ sK492 ) ) )
!= ( X80 @ X81 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
! [X80: term > $o] :
( ? [X81: term] :
( ( sK493 @ ( sub @ X81 @ ( push @ sK494 @ sK492 ) ) )
!= ( X80 @ X81 ) )
=> ( ( sK493 @ ( sub @ ( sK495 @ X80 ) @ ( push @ sK494 @ sK492 ) ) )
!= ( X80 @ ( sK495 @ X80 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
! [X82: subst,X83: term > $o,X84: term] :
( ? [X85: term > $o] :
! [X86: term] :
( ( X83 @ ( sub @ X86 @ ( push @ X84 @ X82 ) ) )
= ( X85 @ X86 ) )
=> ! [X86: term] :
( ( X83 @ ( sub @ X86 @ ( push @ X84 @ X82 ) ) )
= ( sK496 @ X84 @ X83 @ X82 @ X86 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
( ? [X91: term] :
( ( sub @ X91 @ id )
!= X91 )
=> ( sK497
!= ( sub @ sK497 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
( ? [X92: term,X93: term,X94: term,X95: term] :
( ( X94 != X95 )
& ( ( ap @ X94 @ X92 )
= ( ap @ X95 @ X93 ) ) )
=> ( ( sK500 != sK501 )
& ( ( ap @ sK501 @ sK499 )
= ( ap @ sK500 @ sK498 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
( ? [X96: term,X97: term,X98: term,X99: term] :
( ( ( ap @ ( sub @ X96 @ id ) @ X97 )
= ( ap @ ( sub @ X99 @ id ) @ X98 ) )
& ( X96 != X99 ) )
=> ( ( ( ap @ ( sub @ sK502 @ id ) @ sK503 )
= ( ap @ ( sub @ sK505 @ id ) @ sK504 ) )
& ( sK505 != sK502 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
! [X105: term > $o] :
( ? [X107: term] :
( ( ( X105 @ X107 )
!= $true )
& ( ( var @ X107 )
= $true ) )
=> ( ( $true
!= ( X105 @ ( sK506 @ X105 ) ) )
& ( ( var @ ( sK506 @ X105 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
! [X105: term > $o] :
( ? [X108: term] :
( ( ( X105 @ X108 )
= $true )
& ( ( X105 @ ( lam @ X108 ) )
!= $true ) )
=> ( ( ( X105 @ ( sK507 @ X105 ) )
= $true )
& ( ( X105 @ ( lam @ ( sK507 @ X105 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
( ? [X109: term > $o,X110: term] :
( ! [X111: term] :
( ( ( X109 @ X111 )
= $true )
| ( ( var @ X111 )
!= $true ) )
& ( ( sP39 @ X109 )
!= $true )
& ( ( X109 @ X110 )
!= $true )
& ! [X112: term] :
( ( ( X109 @ X112 )
!= $true )
| ( ( X109 @ ( lam @ X112 ) )
= $true ) ) )
=> ( ! [X111: term] :
( ( ( sK508 @ X111 )
= $true )
| ( ( var @ X111 )
!= $true ) )
& ( ( sP39 @ sK508 )
!= $true )
& ( ( sK508 @ sK509 )
!= $true )
& ! [X112: term] :
( ( ( sK508 @ X112 )
!= $true )
| ( ( sK508 @ ( lam @ X112 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
( ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 )
=> ( sK510
!= ( comp @ id @ sK510 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
( ? [X117: subst] :
( ( comp @ X117 @ id )
!= X117 )
=> ( sK511
!= ( comp @ sK511 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X118: term] :
! [X119: subst > term > term] :
( ( X119 @ sh @ one )
!= ( sub @ X118 @ ( push @ one @ sh ) ) )
=> ! [X119: subst > term > term] :
( ( X119 @ sh @ one )
!= ( sub @ sK512 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
! [X120: term] :
( ? [X121: subst > term > term] :
( ( sub @ X120 @ ( push @ one @ sh ) )
= ( X121 @ sh @ one ) )
=> ( ( sub @ X120 @ ( push @ one @ sh ) )
= ( sK513 @ X120 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
( ? [X122: term,X123: term,X124: term,X125: term] :
( ( X122 != X125 )
& ( ( ap @ ( sub @ X125 @ id ) @ X124 )
= ( ap @ ( sub @ X122 @ id ) @ X123 ) ) )
=> ( ( sK514 != sK517 )
& ( ( ap @ ( sub @ sK514 @ id ) @ sK515 )
= ( ap @ ( sub @ sK517 @ id ) @ sK516 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
( ? [X130: term > $o,X131: term,X132: subst] :
! [X133: term > $o] :
? [X134: term] :
( ( X133 @ X134 )
!= ( X130 @ ( sub @ X134 @ ( push @ X131 @ X132 ) ) ) )
=> ! [X133: term > $o] :
? [X134: term] :
( ( X133 @ X134 )
!= ( sK518 @ ( sub @ X134 @ ( push @ sK519 @ sK520 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
! [X133: term > $o] :
( ? [X134: term] :
( ( X133 @ X134 )
!= ( sK518 @ ( sub @ X134 @ ( push @ sK519 @ sK520 ) ) ) )
=> ( ( sK518 @ ( sub @ ( sK521 @ X133 ) @ ( push @ sK519 @ sK520 ) ) )
!= ( X133 @ ( sK521 @ X133 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
! [X135: term > $o,X136: term,X137: subst] :
( ? [X138: term > $o] :
! [X139: term] :
( ( X138 @ X139 )
= ( X135 @ ( sub @ X139 @ ( push @ X136 @ X137 ) ) ) )
=> ! [X139: term] :
( ( sK522 @ X137 @ X136 @ X135 @ X139 )
= ( X135 @ ( sub @ X139 @ ( push @ X136 @ X137 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ? [X140: term,X141: term] :
( ( ( lam @ X141 )
= ( lam @ X140 ) )
& ( X140 != X141 ) )
=> ( ( ( lam @ sK523 )
= ( lam @ sK524 ) )
& ( sK523 != sK524 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
( ? [X146: subst] :
( ( comp @ id @ X146 )
!= X146 )
=> ( ( comp @ id @ sK525 )
!= sK525 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
( ? [X147: subst] :
( ( comp @ X147 @ id )
!= X147 )
=> ( sK526
!= ( comp @ sK526 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
( ? [X152: subst] :
( ( comp @ id @ X152 )
!= X152 )
=> ( sK527
!= ( comp @ id @ sK527 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
( ? [X153: subst] :
( ( comp @ X153 @ id )
!= X153 )
=> ( sK528
!= ( comp @ sK528 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
( ? [X159: term > $o,X160: subst,X161: term > $o,X162: term,X163: term] :
( ( ( X161 @ ( sub @ X163 @ ( push @ X162 @ X160 ) ) )
!= $true )
& ( $true
= ( X159 @ X163 ) ) )
=> ( ( ( sK531 @ ( sub @ sK533 @ ( push @ sK532 @ sK530 ) ) )
!= $true )
& ( ( sK529 @ sK533 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
( ? [X164: term,X165: term] :
( ( ( sub @ X164 @ sh )
= ( sub @ X165 @ sh ) )
& ( X164 != X165 ) )
=> ( ( ( sub @ sK535 @ sh )
= ( sub @ sK534 @ sh ) )
& ( sK534 != sK535 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X169: term] :
( ( sub @ X169 @ id )
!= X169 )
=> ( ( sub @ sK536 @ id )
!= sK536 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
! [X170: subst > term > term] :
( ? [X174: term,X175: subst,X176: subst] :
( ( sub @ ( X170 @ X175 @ X174 ) @ X176 )
!= ( X170 @ ( comp @ X175 @ X176 ) @ ( sub @ X174 @ X176 ) ) )
=> ( ( X170 @ ( comp @ ( sK538 @ X170 ) @ ( sK539 @ X170 ) ) @ ( sub @ ( sK537 @ X170 ) @ ( sK539 @ X170 ) ) )
!= ( sub @ ( X170 @ ( sK538 @ X170 ) @ ( sK537 @ X170 ) ) @ ( sK539 @ X170 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
! [X172: subst > term > term] :
( ? [X177: subst,X178: term,X179: subst] :
( ( X172 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) )
!= ( sub @ ( X172 @ X177 @ X178 ) @ X179 ) )
=> ( ( X172 @ ( comp @ ( sK540 @ X172 ) @ ( sK542 @ X172 ) ) @ ( sub @ ( sK541 @ X172 ) @ ( sK542 @ X172 ) ) )
!= ( sub @ ( X172 @ ( sK540 @ X172 ) @ ( sK541 @ X172 ) ) @ ( sK542 @ X172 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
( ? [X180: subst > term > term,X181: subst,X182: subst > term > term,X183: term] :
( ( ( lam @ ( X182 @ sh @ one ) )
= ( lam @ ( X180 @ sh @ one ) ) )
& ( ( X182 @ X181 @ X183 )
!= ( X180 @ X181 @ X183 ) )
& ! [X184: term,X185: subst,X186: subst] :
( ( sub @ ( X180 @ X185 @ X184 ) @ X186 )
= ( X180 @ ( comp @ X185 @ X186 ) @ ( sub @ X184 @ X186 ) ) )
& ! [X187: subst,X188: term,X189: subst] :
( ( X182 @ ( comp @ X187 @ X189 ) @ ( sub @ X188 @ X189 ) )
= ( sub @ ( X182 @ X187 @ X188 ) @ X189 ) ) )
=> ( ( ( lam @ ( sK543 @ sh @ one ) )
= ( lam @ ( sK545 @ sh @ one ) ) )
& ( ( sK543 @ sK544 @ sK546 )
!= ( sK545 @ sK544 @ sK546 ) )
& ! [X186: subst,X185: subst,X184: term] :
( ( sK543 @ ( comp @ X185 @ X186 ) @ ( sub @ X184 @ X186 ) )
= ( sub @ ( sK543 @ X185 @ X184 ) @ X186 ) )
& ! [X189: subst,X188: term,X187: subst] :
( ( sub @ ( sK545 @ X187 @ X188 ) @ X189 )
= ( sK545 @ ( comp @ X187 @ X189 ) @ ( sub @ X188 @ X189 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
( ? [X191: subst] :
( ( push @ ( sub @ one @ X191 ) @ ( comp @ sh @ X191 ) )
!= X191 )
=> ( ( push @ ( sub @ one @ sK547 ) @ ( comp @ sh @ sK547 ) )
!= sK547 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
( ? [X192: subst > term > term,X193: term,X194: term] :
( ! [X195: subst,X196: term,X197: subst] :
( ( sub @ ( X192 @ X197 @ X196 ) @ X195 )
= ( X192 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) ) )
& ( ( ap @ ( sub @ X193 @ id ) @ X194 )
= ( lam @ ( X192 @ sh @ one ) ) ) )
=> ( ! [X197: subst,X196: term,X195: subst] :
( ( sK548 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) )
= ( sub @ ( sK548 @ X197 @ X196 ) @ X195 ) )
& ( ( ap @ ( sub @ sK549 @ id ) @ sK550 )
= ( lam @ ( sK548 @ sh @ one ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
! [X198: subst > term > term] :
( ? [X201: subst,X202: term,X203: subst] :
( ( sub @ ( X198 @ X203 @ X202 ) @ X201 )
!= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
=> ( ( X198 @ ( comp @ ( sK553 @ X198 ) @ ( sK551 @ X198 ) ) @ ( sub @ ( sK552 @ X198 ) @ ( sK551 @ X198 ) ) )
!= ( sub @ ( X198 @ ( sK553 @ X198 ) @ ( sK552 @ X198 ) ) @ ( sK551 @ X198 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
( ? [X208: term,X209: term,X210: term,X211: term] :
( ( ( ap @ ( sub @ X208 @ id ) @ X209 )
= ( ap @ ( sub @ X211 @ id ) @ X210 ) )
& ( X209 != X210 ) )
=> ( ( ( ap @ ( sub @ sK554 @ id ) @ sK555 )
= ( ap @ ( sub @ sK557 @ id ) @ sK556 ) )
& ( sK555 != sK556 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
! [X212: term > $o,X213: term > $o,X214: subst,X215: term] :
( ? [X216: term] :
( ( X213 @ ( sub @ X216 @ ( push @ X215 @ X214 ) ) )
!= ( X212 @ X216 ) )
=> ( ( X213 @ ( sub @ ( sK558 @ X215 @ X214 @ X213 @ X212 ) @ ( push @ X215 @ X214 ) ) )
!= ( X212 @ ( sK558 @ X215 @ X214 @ X213 @ X212 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
( ? [X217: term > $o,X218: term > $o,X219: subst,X220: term] :
( ! [X221: term] :
( ( X217 @ X221 )
= ( X218 @ ( sub @ X221 @ ( push @ X220 @ X219 ) ) ) )
& ( ( X217 @ one )
!= $true )
& ( ( X218 @ X220 )
= $true ) )
=> ( ! [X221: term] :
( ( sK560 @ ( sub @ X221 @ ( push @ sK562 @ sK561 ) ) )
= ( sK559 @ X221 ) )
& ( ( sK559 @ one )
!= $true )
& ( $true
= ( sK560 @ sK562 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
( ? [X222: subst] :
( ( comp @ X222 @ id )
!= X222 )
=> ( sK563
!= ( comp @ sK563 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X228: term,X229: term > $o,X230: term > $o,X231: subst,X232: term] :
( ( ( X229 @ X232 )
= $true )
& ( $true
!= ( X230 @ ( sub @ X232 @ ( push @ X228 @ X231 ) ) ) ) )
=> ( ( ( sK565 @ sK568 )
= $true )
& ( ( sK566 @ ( sub @ sK568 @ ( push @ sK564 @ sK567 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
( ? [X233: term,X234: subst] :
( ( sub @ one @ ( push @ X233 @ X234 ) )
!= X233 )
=> ( sK569
!= ( sub @ one @ ( push @ sK569 @ sK570 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
( ? [X235: subst,X236: term] :
( ( comp @ sh @ ( push @ X236 @ X235 ) )
!= X235 )
=> ( sK571
!= ( comp @ sh @ ( push @ sK572 @ sK571 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
! [X242: subst > term > subst > $o] :
( ? [X243: term > $o] :
! [X244: term] :
( ( X243 @ X244 )
= ( X242 @ id @ X244 @ id ) )
=> ! [X244: term] :
( ( sK573 @ X242 @ X244 )
= ( X242 @ id @ X244 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
( ? [X245: subst > term > subst > $o] :
! [X246: term > $o] :
? [X247: term] :
( ( X246 @ X247 )
!= ( X245 @ id @ X247 @ id ) )
=> ! [X246: term > $o] :
? [X247: term] :
( ( X246 @ X247 )
!= ( sK574 @ id @ X247 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
! [X246: term > $o] :
( ? [X247: term] :
( ( X246 @ X247 )
!= ( sK574 @ id @ X247 @ id ) )
=> ( ( X246 @ ( sK575 @ X246 ) )
!= ( sK574 @ id @ ( sK575 @ X246 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
( ? [X248: subst,X249: term] :
( ( comp @ sh @ ( push @ X249 @ X248 ) )
!= X248 )
=> ( ( comp @ sh @ ( push @ sK577 @ sK576 ) )
!= sK576 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
( ? [X254: subst] :
( ( comp @ id @ X254 )
!= X254 )
=> ( ( comp @ id @ sK578 )
!= sK578 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
( ? [X257: term] :
( ( sub @ X257 @ id )
!= X257 )
=> ( ( sub @ sK579 @ id )
!= sK579 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
( ? [X258: subst,X259: term] :
( ( sub @ one @ ( push @ X259 @ X258 ) )
!= X259 )
=> ( sK581
!= ( sub @ one @ ( push @ sK581 @ sK580 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
! [X260: term,X261: subst,X262: term > $o,X263: term > $o] :
( ? [X264: term] :
( ( X262 @ X264 )
!= ( X263 @ ( sub @ X264 @ ( push @ X260 @ X261 ) ) ) )
=> ( ( X263 @ ( sub @ ( sK582 @ X263 @ X262 @ X261 @ X260 ) @ ( push @ X260 @ X261 ) ) )
!= ( X262 @ ( sK582 @ X263 @ X262 @ X261 @ X260 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
( ? [X267: term,X268: subst,X269: term > $o,X270: term > $o] :
( ! [X271: term] :
( ( X269 @ X271 )
= ( X270 @ ( sub @ X271 @ ( push @ X267 @ X268 ) ) ) )
& ( ( X269 @ one )
!= $true )
& ( ( X270 @ X267 )
= $true ) )
=> ( ! [X271: term] :
( ( sK585 @ X271 )
= ( sK586 @ ( sub @ X271 @ ( push @ sK583 @ sK584 ) ) ) )
& ( $true
!= ( sK585 @ one ) )
& ( ( sK586 @ sK583 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
( ? [X276: term,X277: term,X278: term,X279: term] :
( ( ( ap @ X277 @ X279 )
= ( ap @ X276 @ X278 ) )
& ( X278 != X279 ) )
=> ( ( ( ap @ sK587 @ sK589 )
= ( ap @ sK588 @ sK590 ) )
& ( sK590 != sK589 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f473,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X0: term] :
! [X1: subst > term > term] :
? [X2: subst,X3: term] :
( ( sub @ X0 @ ( push @ X3 @ X2 ) )
!= ( X1 @ X2 @ X3 ) ) )
& ( ! [X4: term] :
? [X5: subst > term > term] :
! [X6: subst,X7: term] :
( ( X5 @ X6 @ X7 )
= ( sub @ X4 @ ( push @ X7 @ X6 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X8: term,X9: term,X10: term,X11: term] :
( ( ( ap @ X9 @ X8 )
!= ( ap @ X10 @ X11 ) )
| ( X9 = X10 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X12: term,X13: term,X14: term,X15: term] :
( ( ( ap @ X14 @ X15 )
= ( ap @ X13 @ X12 ) )
& ( X13 != X14 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP58 != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X16: term,X17: term,X18: term,X19: term] :
( ( ( ap @ X19 @ X17 )
!= ( ap @ X16 @ X18 ) )
| ( X17 = X18 ) )
& ? [X20: term,X21: term,X22: term,X23: term] :
( ( ( ap @ ( sub @ X23 @ id ) @ X20 )
= ( ap @ ( sub @ X22 @ id ) @ X21 ) )
& ( X20 != X21 ) ) ) )
& ( ? [X24: term,X25: term,X26: term,X27: term] :
( ( ( ap @ X27 @ X25 )
= ( ap @ X24 @ X26 ) )
& ( X25 != X26 ) )
| ! [X28: term,X29: term,X30: term,X31: term] :
( ( ( ap @ ( sub @ X30 @ id ) @ X29 )
!= ( ap @ ( sub @ X31 @ id ) @ X28 ) )
| ( X28 = X29 ) )
| ( hoasapinj2_lthm != $true ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X32: d_subst] : ( d_id = X32 )
& ( ( termmset_lthm = $true )
| ( ? [X33: term] :
( ( sub @ X33 @ id )
!= X33 )
& ! [X34: term] :
( ( sub @ X34 @ id )
= X34 ) ) )
& ( ! [X35: term] :
( ( sub @ X35 @ id )
= X35 )
| ? [X36: term] :
( ( sub @ X36 @ id )
!= X36 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X37: term] :
! [X38: subst > term > term] :
? [X39: subst,X40: term] :
( ( X38 @ X39 @ X40 )
!= ( sub @ X37 @ ( push @ X40 @ X39 ) ) ) )
& ( ! [X41: term] :
? [X42: subst > term > term] :
! [X43: subst,X44: term] :
( ( X42 @ X43 @ X44 )
= ( sub @ X41 @ ( push @ X44 @ X43 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP56 != $true ) )
& ( ( sP56 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ulamvarind = $true )
& ( ( sP54 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP54 != $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X45: subst > term > subst > $o] :
! [X46: term > $o] :
? [X47: term] :
( ( X45 @ id @ X47 @ id )
!= ( X46 @ X47 ) ) )
& ( ! [X48: subst > term > subst > $o] :
? [X49: term > $o] :
! [X50: term] :
( ( X48 @ id @ X50 @ id )
= ( X49 @ X50 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X51: term] :
! [X52: subst > term > term] :
( ( X52 @ sh @ one )
!= ( sub @ X51 @ ( push @ one @ sh ) ) ) )
& ( ! [X53: term] :
? [X54: subst > term > term] :
( ( sub @ X53 @ ( push @ one @ sh ) )
= ( X54 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP53 ) )
& ( ( $true = sP53 )
| ( hoasinduction_lem3a != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X55: term] :
? [X56: d_term] :
( ( d2term @ X56 )
= X55 )
& ( hoasapinj2_gthm = $true )
& ( ! [X57: subst,X58: term] :
( ( sub @ one @ ( push @ X58 @ X57 ) )
= X58 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X59: subst,X60: term] :
( ( sub @ one @ ( push @ X60 @ X59 ) )
!= X60 ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP46 ) )
& ( ( $true = sP46 )
| ( induction2_lthm != $true ) )
& ( ! [X61: term,X62: subst > term > subst > $o] :
( ? [X63: subst > term > term] :
( ! [X64: subst,X65: term,X66: subst] :
( ( sub @ ( X63 @ X64 @ X65 ) @ X66 )
= ( X63 @ ( comp @ X64 @ X66 ) @ ( sub @ X65 @ X66 ) ) )
& ! [X67: term] :
( ( ( X62 @ id @ ( X63 @ id @ X67 ) @ id )
= $true )
| ( ( X62 @ id @ X67 @ id )
!= $true ) )
& ( ( X62 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X62 @ id @ X61 @ id )
= $true )
| ( ( sP42 @ X62 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X68: term,X69: subst > term > subst > $o] :
( ! [X70: subst > term > term] :
( ? [X71: subst,X72: term,X73: subst] :
( ( sub @ ( X70 @ X71 @ X72 ) @ X73 )
!= ( X70 @ ( comp @ X71 @ X73 ) @ ( sub @ X72 @ X73 ) ) )
| ? [X74: term] :
( ( ( X69 @ id @ ( X70 @ id @ X74 ) @ id )
!= $true )
& ( ( X69 @ id @ X74 @ id )
= $true ) )
| ( ( X69 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X69 @ id @ X68 @ id )
!= $true )
& ( ( sP42 @ X69 )
!= $true ) ) )
& ! [X75: subst] :
? [X76: d_subst] :
( ( d2subst @ X76 )
= X75 )
& ( ( pushprop_lem0 = $true )
| ? [X77: subst,X78: term > $o,X79: term] :
! [X80: term > $o] :
? [X81: term] :
( ( X80 @ X81 )
!= ( X78 @ ( sub @ X81 @ ( push @ X79 @ X77 ) ) ) ) )
& ( ! [X82: subst,X83: term > $o,X84: term] :
? [X85: term > $o] :
! [X86: term] :
( ( X83 @ ( sub @ X86 @ ( push @ X84 @ X82 ) ) )
= ( X85 @ X86 ) )
| ( pushprop_lem0 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ! [X87: term,X88: term,X89: term,X90: term] :
( ( ( ap @ ( sub @ X90 @ id ) @ X89 )
!= ( ap @ ( sub @ X87 @ id ) @ X88 ) )
| ( X87 = X90 ) )
| ? [X91: term] :
( ( sub @ X91 @ id )
!= X91 )
| ? [X92: term,X93: term,X94: term,X95: term] :
( ( X94 != X95 )
& ( ( ap @ X94 @ X92 )
= ( ap @ X95 @ X93 ) ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X96: term,X97: term,X98: term,X99: term] :
( ( ( ap @ ( sub @ X96 @ id ) @ X97 )
= ( ap @ ( sub @ X99 @ id ) @ X98 ) )
& ( X96 != X99 ) )
& ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
& ! [X101: term,X102: term,X103: term,X104: term] :
( ( X103 = X104 )
| ( ( ap @ X104 @ X102 )
!= ( ap @ X103 @ X101 ) ) ) ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ! [X105: term > $o,X106: term] :
( ? [X107: term] :
( ( ( X105 @ X107 )
!= $true )
& ( ( var @ X107 )
= $true ) )
| ( ( sP39 @ X105 )
= $true )
| ( ( X105 @ X106 )
= $true )
| ? [X108: term] :
( ( ( X105 @ X108 )
= $true )
& ( ( X105 @ ( lam @ X108 ) )
!= $true ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X109: term > $o,X110: term] :
( ! [X111: term] :
( ( ( X109 @ X111 )
= $true )
| ( ( var @ X111 )
!= $true ) )
& ( ( sP39 @ X109 )
!= $true )
& ( ( X109 @ X110 )
!= $true )
& ! [X112: term] :
( ( ( X109 @ X112 )
!= $true )
| ( ( X109 @ ( lam @ X112 ) )
= $true ) ) ) )
& ( hoasinduction_gthm = $true )
& ! [X113: d_term] : ( d_one = X113 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
| ( sP38 != $true ) )
& ( ( sP38 = $true )
| ( hoasinduction != $true ) )
& ( ( ! [X114: subst] :
( ( comp @ id @ X114 )
= X114 )
& ! [X115: subst] :
( ( comp @ X115 @ id )
= X115 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 )
| ? [X117: subst] :
( ( comp @ X117 @ id )
!= X117 ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
| ? [X118: term] :
! [X119: subst > term > term] :
( ( X119 @ sh @ one )
!= ( sub @ X118 @ ( push @ one @ sh ) ) ) )
& ( ! [X120: term] :
? [X121: subst > term > term] :
( ( sub @ X120 @ ( push @ one @ sh ) )
= ( X121 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
| ? [X122: term,X123: term,X124: term,X125: term] :
( ( X122 != X125 )
& ( ( ap @ ( sub @ X125 @ id ) @ X124 )
= ( ap @ ( sub @ X122 @ id ) @ X123 ) ) ) )
& ( ! [X126: term,X127: term,X128: term,X129: term] :
( ( X126 = X129 )
| ( ( ap @ ( sub @ X126 @ id ) @ X127 )
!= ( ap @ ( sub @ X129 @ id ) @ X128 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X130: term > $o,X131: term,X132: subst] :
! [X133: term > $o] :
? [X134: term] :
( ( X133 @ X134 )
!= ( X130 @ ( sub @ X134 @ ( push @ X131 @ X132 ) ) ) ) )
& ( ! [X135: term > $o,X136: term,X137: subst] :
? [X138: term > $o] :
! [X139: term] :
( ( X138 @ X139 )
= ( X135 @ ( sub @ X139 @ ( push @ X136 @ X137 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
| ? [X140: term,X141: term] :
( ( ( lam @ X141 )
= ( lam @ X140 ) )
& ( X140 != X141 ) ) )
& ( ! [X142: term,X143: term] :
( ( ( lam @ X142 )
!= ( lam @ X143 ) )
| ( X142 = X143 ) )
| ( laminj != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X144: d_term,X145: d_term] :
( ( X144 = X145 )
| ( ( d2term @ X144 )
!= ( d2term @ X145 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP35 != $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP33 != $true ) )
& ( ( sP33 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ? [X146: subst] :
( ( comp @ id @ X146 )
!= X146 )
| ? [X147: subst] :
( ( comp @ X147 @ id )
!= X147 )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X149: subst] :
( ( comp @ X149 @ id )
= X149 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X150: subst] :
( ( comp @ id @ X150 )
= X150 )
& ! [X151: subst] :
( ( comp @ X151 @ id )
= X151 )
& ( ? [X152: subst] :
( ( comp @ id @ X152 )
!= X152 )
| ? [X153: subst] :
( ( comp @ X153 @ id )
!= X153 ) ) ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP32 ) )
& ( ! [X154: term > $o,X155: subst,X156: term > $o,X157: term,X158: term] :
( ( ( X156 @ ( sub @ X158 @ ( push @ X157 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X158 ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X159: term > $o,X160: subst,X161: term > $o,X162: term,X163: term] :
( ( ( X161 @ ( sub @ X163 @ ( push @ X162 @ X160 ) ) )
!= $true )
& ( $true
= ( X159 @ X163 ) ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP31 != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
| ? [X164: term,X165: term] :
( ( ( sub @ X164 @ sh )
= ( sub @ X165 @ sh ) )
& ( X164 != X165 ) ) )
& ( ! [X166: term,X167: term] :
( ( ( sub @ X167 @ sh )
!= ( sub @ X166 @ sh ) )
| ( X166 = X167 ) )
| ( shinj != $true ) )
& ( ! [X168: term] :
( ( sub @ X168 @ id )
= X168 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X169: term] :
( ( sub @ X169 @ id )
!= X169 ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X170: subst > term > term,X171: subst,X172: subst > term > term,X173: term] :
( ( ( lam @ ( X172 @ sh @ one ) )
!= ( lam @ ( X170 @ sh @ one ) ) )
| ( ( X172 @ X171 @ X173 )
= ( X170 @ X171 @ X173 ) )
| ? [X174: term,X175: subst,X176: subst] :
( ( sub @ ( X170 @ X175 @ X174 ) @ X176 )
!= ( X170 @ ( comp @ X175 @ X176 ) @ ( sub @ X174 @ X176 ) ) )
| ? [X177: subst,X178: term,X179: subst] :
( ( X172 @ ( comp @ X177 @ X179 ) @ ( sub @ X178 @ X179 ) )
!= ( sub @ ( X172 @ X177 @ X178 ) @ X179 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X180: subst > term > term,X181: subst,X182: subst > term > term,X183: term] :
( ( ( lam @ ( X182 @ sh @ one ) )
= ( lam @ ( X180 @ sh @ one ) ) )
& ( ( X182 @ X181 @ X183 )
!= ( X180 @ X181 @ X183 ) )
& ! [X184: term,X185: subst,X186: subst] :
( ( sub @ ( X180 @ X185 @ X184 ) @ X186 )
= ( X180 @ ( comp @ X185 @ X186 ) @ ( sub @ X184 @ X186 ) ) )
& ! [X187: subst,X188: term,X189: subst] :
( ( X182 @ ( comp @ X187 @ X189 ) @ ( sub @ X188 @ X189 ) )
= ( sub @ ( X182 @ X187 @ X188 ) @ X189 ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
| ( sP21 != $true ) )
& ( ( sP21 = $true )
| ( induction2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X190: subst] :
( ( push @ ( sub @ one @ X190 ) @ ( comp @ sh @ X190 ) )
= X190 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X191: subst] :
( ( push @ ( sub @ one @ X191 ) @ ( comp @ sh @ X191 ) )
!= X191 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X192: subst > term > term,X193: term,X194: term] :
( ! [X195: subst,X196: term,X197: subst] :
( ( sub @ ( X192 @ X197 @ X196 ) @ X195 )
= ( X192 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) ) )
& ( ( ap @ ( sub @ X193 @ id ) @ X194 )
= ( lam @ ( X192 @ sh @ one ) ) ) ) )
& ( ! [X198: subst > term > term,X199: term,X200: term] :
( ? [X201: subst,X202: term,X203: subst] :
( ( sub @ ( X198 @ X203 @ X202 ) @ X201 )
!= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
| ( ( ap @ ( sub @ X199 @ id ) @ X200 )
!= ( lam @ ( X198 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ( $true = sP16 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP16 ) )
& ( ( sP15 = $true )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( sP15 != $true ) )
& ( ! [X204: term,X205: term,X206: term,X207: term] :
( ( ( ap @ ( sub @ X204 @ id ) @ X205 )
!= ( ap @ ( sub @ X207 @ id ) @ X206 ) )
| ( X205 = X206 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X208: term,X209: term,X210: term,X211: term] :
( ( ( ap @ ( sub @ X208 @ id ) @ X209 )
= ( ap @ ( sub @ X211 @ id ) @ X210 ) )
& ( X209 != X210 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP13 != $true ) )
& ( ( sP13 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ! [X212: term > $o,X213: term > $o,X214: subst,X215: term] :
( ? [X216: term] :
( ( X213 @ ( sub @ X216 @ ( push @ X215 @ X214 ) ) )
!= ( X212 @ X216 ) )
| ( ( X212 @ one )
= $true )
| ( ( X213 @ X215 )
!= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X217: term > $o,X218: term > $o,X219: subst,X220: term] :
( ! [X221: term] :
( ( X217 @ X221 )
= ( X218 @ ( sub @ X221 @ ( push @ X220 @ X219 ) ) ) )
& ( ( X217 @ one )
!= $true )
& ( ( X218 @ X220 )
= $true ) ) )
& ( ( axidr = $true )
| ? [X222: subst] :
( ( comp @ X222 @ id )
!= X222 ) )
& ( ! [X223: subst] :
( ( comp @ X223 @ id )
= X223 )
| ( axidr != $true ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X224: term,X225: subst] :
( ( sub @ one @ ( push @ X224 @ X225 ) )
= X224 )
& ! [X226: subst,X227: term] :
( ( comp @ sh @ ( push @ X227 @ X226 ) )
= X226 )
& ? [X228: term,X229: term > $o,X230: term > $o,X231: subst,X232: term] :
( ( ( X229 @ X232 )
= $true )
& ( $true
!= ( X230 @ ( sub @ X232 @ ( push @ X228 @ X231 ) ) ) ) ) ) )
& ( ? [X233: term,X234: subst] :
( ( sub @ one @ ( push @ X233 @ X234 ) )
!= X233 )
| ? [X235: subst,X236: term] :
( ( comp @ sh @ ( push @ X236 @ X235 ) )
!= X235 )
| ! [X237: term,X238: term > $o,X239: term > $o,X240: subst,X241: term] :
( ( ( X238 @ X241 )
!= $true )
| ( ( X239 @ ( sub @ X241 @ ( push @ X237 @ X240 ) ) )
= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ! [X242: subst > term > subst > $o] :
? [X243: term > $o] :
! [X244: term] :
( ( X243 @ X244 )
= ( X242 @ id @ X244 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X245: subst > term > subst > $o] :
! [X246: term > $o] :
? [X247: term] :
( ( X246 @ X247 )
!= ( X245 @ id @ X247 @ id ) ) )
& ( ( sP11 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP11 != $true ) )
& ( ( axshiftcons = $true )
| ? [X248: subst,X249: term] :
( ( comp @ sh @ ( push @ X249 @ X248 ) )
!= X248 ) )
& ( ! [X250: subst,X251: term] :
( ( comp @ sh @ ( push @ X251 @ X250 ) )
= X250 )
| ( axshiftcons != $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X252: d_subst,X253: d_subst] :
( ( X252 = X253 )
| ( ( d2subst @ X253 )
!= ( d2subst @ X252 ) ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP6 != $true ) )
& ( ( axidl = $true )
| ? [X254: subst] :
( ( comp @ id @ X254 )
!= X254 ) )
& ( ! [X255: subst] :
( ( comp @ id @ X255 )
= X255 )
| ( axidl != $true ) )
& ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X257: term] :
( ( sub @ X257 @ id )
!= X257 ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP4 != $true ) )
& ( ( sP4 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ? [X258: subst,X259: term] :
( ( sub @ one @ ( push @ X259 @ X258 ) )
!= X259 )
| ! [X260: term,X261: subst,X262: term > $o,X263: term > $o] :
( ? [X264: term] :
( ( X262 @ X264 )
!= ( X263 @ ( sub @ X264 @ ( push @ X260 @ X261 ) ) ) )
| ( ( X262 @ one )
= $true )
| ( ( X263 @ X260 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X265: subst,X266: term] :
( ( sub @ one @ ( push @ X266 @ X265 ) )
= X266 )
& ? [X267: term,X268: subst,X269: term > $o,X270: term > $o] :
( ! [X271: term] :
( ( X269 @ X271 )
= ( X270 @ ( sub @ X271 @ ( push @ X267 @ X268 ) ) ) )
& ( ( X269 @ one )
!= $true )
& ( ( X270 @ X267 )
= $true ) ) ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X272: term,X273: term,X274: term,X275: term] :
( ( ( ap @ X273 @ X275 )
!= ( ap @ X272 @ X274 ) )
| ( X274 = X275 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X276: term,X277: term,X278: term,X279: term] :
( ( ( ap @ X277 @ X279 )
= ( ap @ X276 @ X278 ) )
& ( X278 != X279 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
| ( sP3 != $true ) )
& ( ( sP3 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(rectify,[status(thm)],[f472]) ).
thf(f472,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X34: term] :
! [X35: subst > term > term] :
? [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
!= ( sub @ X34 @ ( push @ X37 @ X36 ) ) ) )
& ( ! [X34: term] :
? [X35: subst > term > term] :
! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
= ( ap @ X413 @ X414 ) )
& ( X412 != X413 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP58 != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
!= ( ap @ X59 @ X57 ) )
| ( X57 = X58 ) )
& ? [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
& ( X60 != X61 ) ) ) )
& ( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
= ( ap @ X59 @ X57 ) )
& ( X57 != X58 ) )
| ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) )
| ( hoasapinj2_lthm != $true ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( termmset_lthm = $true )
| ( ? [X418: term] :
( ( sub @ X418 @ id )
!= X418 )
& ! [X417: term] :
( ( sub @ X417 @ id )
= X417 ) ) )
& ( ! [X418: term] :
( ( sub @ X418 @ id )
= X418 )
| ? [X417: term] :
( ( sub @ X417 @ id )
!= X417 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X483: term] :
! [X484: subst > term > term] :
? [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
!= ( X484 @ X485 @ X486 ) ) )
& ( ! [X483: term] :
? [X484: subst > term > term] :
! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP56 != $true ) )
& ( ( sP56 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ulamvarind = $true )
& ( ( sP54 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP54 != $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X311: subst > term > subst > $o] :
! [X312: term > $o] :
? [X313: term] :
( ( X311 @ id @ X313 @ id )
!= ( X312 @ X313 ) ) )
& ( ! [X311: subst > term > subst > $o] :
? [X312: term > $o] :
! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X28: term] :
! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) ) )
& ( ! [X28: term] :
? [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
= ( X29 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP53 ) )
& ( ( $true = sP53 )
| ( hoasinduction_lem3a != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasapinj2_gthm = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
!= X156 ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP46 ) )
& ( ( $true = sP46 )
| ( induction2_lthm != $true ) )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ? [X491: subst > term > term] :
( ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X488 @ id @ X487 @ id )
= $true )
| ( ( sP42 @ X488 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X487: term,X488: subst > term > subst > $o] :
( ! [X491: subst > term > term] :
( ? [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
!= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
| ? [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
!= $true )
& ( ( X488 @ id @ X495 @ id )
= $true ) )
| ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X488 @ id @ X487 @ id )
!= $true )
& ( ( sP42 @ X488 )
!= $true ) ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( ( pushprop_lem0 = $true )
| ? [X456: subst,X457: term > $o,X458: term] :
! [X459: term > $o] :
? [X460: term] :
( ( X459 @ X460 )
!= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ! [X456: subst,X457: term > $o,X458: term] :
? [X459: term > $o] :
! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) )
| ? [X5: term] :
( ( sub @ X5 @ id )
!= X5 )
| ? [X6: term,X7: term,X8: term,X9: term] :
( ( X8 != X9 )
& ( ( ap @ X8 @ X6 )
= ( ap @ X9 @ X7 ) ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
& ( X10 != X13 ) )
& ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
& ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) ) ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ! [X149: term > $o,X150: term] :
( ? [X154: term] :
( ( ( X149 @ X154 )
!= $true )
& ( ( var @ X154 )
= $true ) )
| ( ( sP39 @ X149 )
= $true )
| ( ( X149 @ X150 )
= $true )
| ? [X153: term] :
( ( ( X149 @ X153 )
= $true )
& ( ( X149 @ ( lam @ X153 ) )
!= $true ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X149: term > $o,X150: term] :
( ! [X154: term] :
( ( ( X149 @ X154 )
= $true )
| ( ( var @ X154 )
!= $true ) )
& ( ( sP39 @ X149 )
!= $true )
& ( ( X149 @ X150 )
!= $true )
& ! [X153: term] :
( ( ( X149 @ X153 )
!= $true )
| ( ( X149 @ ( lam @ X153 ) )
= $true ) ) ) )
& ( hoasinduction_gthm = $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
| ( sP38 != $true ) )
& ( ( sP38 = $true )
| ( hoasinduction != $true ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X408: subst] :
( ( comp @ id @ X408 )
!= X408 )
| ? [X407: subst] :
( ( comp @ X407 @ id )
!= X407 ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
| ? [X415: term] :
! [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
!= ( X416 @ sh @ one ) ) )
& ( ! [X415: term] :
? [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
= ( X416 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
| ? [X30: term,X31: term,X32: term,X33: term] :
( ( X30 != X33 )
& ( ( ap @ ( sub @ X30 @ id ) @ X31 )
= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X14: term > $o,X15: term,X16: subst] :
! [X17: term > $o] :
? [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
!= ( X17 @ X18 ) ) )
& ( ! [X14: term > $o,X15: term,X16: subst] :
? [X17: term > $o] :
! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
| ? [X461: term,X462: term] :
( ( ( lam @ X461 )
= ( lam @ X462 ) )
& ( X461 != X462 ) ) )
& ( ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) )
| ( laminj != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X199: d_term,X200: d_term] :
( ( X199 = X200 )
| ( ( d2term @ X200 )
!= ( d2term @ X199 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP35 != $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP33 != $true ) )
& ( ( sP33 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ? [X145: subst] :
( ( comp @ id @ X145 )
!= X145 )
| ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X145: subst] :
( ( comp @ id @ X145 )
= X145 )
& ! [X146: subst] :
( ( comp @ X146 @ id )
= X146 )
& ( ? [X148: subst] :
( ( comp @ id @ X148 )
!= X148 )
| ? [X147: subst] :
( ( comp @ X147 @ id )
!= X147 ) ) ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP32 ) )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
!= $true )
& ( ( X204 @ X208 )
= $true ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP31 != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
| ? [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
= ( sub @ X198 @ sh ) )
& ( X197 != X198 ) ) )
& ( ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) )
| ( shinj != $true ) )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X383: term] :
( ( sub @ X383 @ id )
!= X383 ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ? [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
!= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
| ? [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
!= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
= ( lam @ ( X524 @ sh @ one ) ) )
& ( ( X524 @ X523 @ X525 )
!= ( X522 @ X523 @ X525 ) )
& ! [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
& ! [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
| ( sP21 != $true ) )
& ( ( sP21 = $true )
| ( induction2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
!= X196 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X314: subst > term > term,X315: term,X316: term] :
( ! [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
& ( ( ap @ ( sub @ X315 @ id ) @ X316 )
= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( ! [X314: subst > term > term,X315: term,X316: term] :
( ? [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
!= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ( $true = sP16 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP16 ) )
& ( ( sP15 = $true )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( sP15 != $true ) )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
& ( X453 != X454 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP13 != $true ) )
& ( ( sP13 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ? [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
!= ( X0 @ X4 ) )
| ( ( X0 @ one )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) )
& ( ( X0 @ one )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) )
& ( ( axidr = $true )
| ? [X172: subst] :
( ( comp @ X172 @ id )
!= X172 ) )
& ( ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 )
| ( axidr != $true ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
& ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
& ? [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
= $true )
& ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
!= $true ) ) ) )
& ( ? [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
!= X19 )
| ? [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
!= X21 )
| ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ! [X201: subst > term > subst > $o] :
? [X202: term > $o] :
! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X201: subst > term > subst > $o] :
! [X202: term > $o] :
? [X203: term] :
( ( X202 @ X203 )
!= ( X201 @ id @ X203 @ id ) ) )
& ( ( sP11 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP11 != $true ) )
& ( ( axshiftcons = $true )
| ? [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
!= X463 ) )
& ( ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 )
| ( axshiftcons != $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( X54 = X55 )
| ( ( d2subst @ X55 )
!= ( d2subst @ X54 ) ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP6 != $true ) )
& ( ( axidl = $true )
| ? [X409: subst] :
( ( comp @ id @ X409 )
!= X409 ) )
& ( ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 )
| ( axidl != $true ) )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X374: term] :
( ( sub @ X374 @ id )
!= X374 ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP4 != $true ) )
& ( ( sP4 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ? [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
!= X211 )
| ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ? [X216: term] :
( ( X214 @ X216 )
!= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
| ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
= X211 )
& ? [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ! [X216: term] :
( ( X214 @ X216 )
= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
& ( $true
!= ( X214 @ one ) )
& ( ( X215 @ X212 )
= $true ) ) ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
= ( ap @ X174 @ X176 ) )
& ( X175 != X176 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
| ( sP3 != $true ) )
& ( ( sP3 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(flattening,[status(thm)],[f471]) ).
thf(f471,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X34: term] :
! [X35: subst > term > term] :
? [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
!= ( sub @ X34 @ ( push @ X37 @ X36 ) ) ) )
& ( ! [X34: term] :
? [X35: subst > term > term] :
! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
= ( ap @ X413 @ X414 ) )
& ( X412 != X413 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP58 != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
!= ( ap @ X59 @ X57 ) )
| ( X57 = X58 ) )
& ? [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
& ( X60 != X61 ) ) ) )
& ( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
= ( ap @ X59 @ X57 ) )
& ( X57 != X58 ) )
| ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) )
| ( hoasapinj2_lthm != $true ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( termmset_lthm = $true )
| ( ? [X418: term] :
( ( sub @ X418 @ id )
!= X418 )
& ! [X417: term] :
( ( sub @ X417 @ id )
= X417 ) ) )
& ( ! [X418: term] :
( ( sub @ X418 @ id )
= X418 )
| ? [X417: term] :
( ( sub @ X417 @ id )
!= X417 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X483: term] :
! [X484: subst > term > term] :
? [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
!= ( X484 @ X485 @ X486 ) ) )
& ( ! [X483: term] :
? [X484: subst > term > term] :
! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( sP56 != $true ) )
& ( ( sP56 = $true )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ulamvarind = $true )
& ( ( sP54 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP54 != $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X311: subst > term > subst > $o] :
! [X312: term > $o] :
? [X313: term] :
( ( X311 @ id @ X313 @ id )
!= ( X312 @ X313 ) ) )
& ( ! [X311: subst > term > subst > $o] :
? [X312: term > $o] :
! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X28: term] :
! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) ) )
& ( ! [X28: term] :
? [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
= ( X29 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP53 ) )
& ( ( $true = sP53 )
| ( hoasinduction_lem3a != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasapinj2_gthm = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
| ( axvarcons != $true ) )
& ( ( axvarcons = $true )
| ? [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
!= X156 ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP46 ) )
& ( ( $true = sP46 )
| ( induction2_lthm != $true ) )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ? [X491: subst > term > term] :
( ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X488 @ id @ X487 @ id )
= $true )
| ( ( sP42 @ X488 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X487: term,X488: subst > term > subst > $o] :
( ! [X491: subst > term > term] :
( ? [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
!= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
| ? [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
!= $true )
& ( ( X488 @ id @ X495 @ id )
= $true ) )
| ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
= $true ) )
& ( ( X488 @ id @ X487 @ id )
!= $true )
& ( ( sP42 @ X488 )
!= $true ) ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( ( pushprop_lem0 = $true )
| ? [X456: subst,X457: term > $o,X458: term] :
! [X459: term > $o] :
? [X460: term] :
( ( X459 @ X460 )
!= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ! [X456: subst,X457: term > $o,X458: term] :
? [X459: term > $o] :
! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) )
| ? [X5: term] :
( ( sub @ X5 @ id )
!= X5 )
| ? [X6: term,X7: term,X8: term,X9: term] :
( ( X8 != X9 )
& ( ( ap @ X8 @ X6 )
= ( ap @ X9 @ X7 ) ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ? [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
& ( X10 != X13 ) )
& ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
& ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) ) ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP41 != $true ) )
& ( ( sP41 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ! [X149: term > $o,X150: term] :
( ? [X154: term] :
( ( ( X149 @ X154 )
!= $true )
& ( ( var @ X154 )
= $true ) )
| ( ( sP39 @ X149 )
= $true )
| ( ( X149 @ X150 )
= $true )
| ? [X153: term] :
( ( ( X149 @ X153 )
= $true )
& ( ( X149 @ ( lam @ X153 ) )
!= $true ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X149: term > $o,X150: term] :
( ! [X154: term] :
( ( ( X149 @ X154 )
= $true )
| ( ( var @ X154 )
!= $true ) )
& ( ( sP39 @ X149 )
!= $true )
& ( ( X149 @ X150 )
!= $true )
& ! [X153: term] :
( ( ( X149 @ X153 )
!= $true )
| ( ( X149 @ ( lam @ X153 ) )
= $true ) ) ) )
& ( hoasinduction_gthm = $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
| ( sP38 != $true ) )
& ( ( sP38 = $true )
| ( hoasinduction != $true ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X408: subst] :
( ( comp @ id @ X408 )
!= X408 )
| ? [X407: subst] :
( ( comp @ X407 @ id )
!= X407 ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
| ? [X415: term] :
! [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
!= ( X416 @ sh @ one ) ) )
& ( ! [X415: term] :
? [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
= ( X416 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
| ? [X30: term,X31: term,X32: term,X33: term] :
( ( X30 != X33 )
& ( ( ap @ ( sub @ X30 @ id ) @ X31 )
= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) )
| ( hoasapinj1 != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X14: term > $o,X15: term,X16: subst] :
! [X17: term > $o] :
? [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
!= ( X17 @ X18 ) ) )
& ( ! [X14: term > $o,X15: term,X16: subst] :
? [X17: term > $o] :
! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
| ? [X461: term,X462: term] :
( ( ( lam @ X461 )
= ( lam @ X462 ) )
& ( X461 != X462 ) ) )
& ( ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) )
| ( laminj != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X199: d_term,X200: d_term] :
( ( X199 = X200 )
| ( ( d2term @ X200 )
!= ( d2term @ X199 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ( sP35 = $true )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( sP35 != $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP33 != $true ) )
& ( ( sP33 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ? [X145: subst] :
( ( comp @ id @ X145 )
!= X145 )
| ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X145: subst] :
( ( comp @ id @ X145 )
= X145 )
& ! [X146: subst] :
( ( comp @ X146 @ id )
= X146 )
& ( ? [X148: subst] :
( ( comp @ id @ X148 )
!= X148 )
| ? [X147: subst] :
( ( comp @ X147 @ id )
!= X147 ) ) ) )
& ( ( $true = sP32 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP32 ) )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
!= $true )
& ( ( X204 @ X208 )
= $true ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( sP31 = $true )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( sP31 != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP22 != $true ) )
& ( ( sP22 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
| ? [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
= ( sub @ X198 @ sh ) )
& ( X197 != X198 ) ) )
& ( ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) )
| ( shinj != $true ) )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X383: term] :
( ( sub @ X383 @ id )
!= X383 ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ? [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
!= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
| ? [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
!= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
= ( lam @ ( X524 @ sh @ one ) ) )
& ( ( X524 @ X523 @ X525 )
!= ( X522 @ X523 @ X525 ) )
& ! [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
& ! [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
| ( sP21 != $true ) )
& ( ( sP21 = $true )
| ( induction2 != $true ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
!= X196 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( sP19 != $true ) )
& ( ( sP19 = $true )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
| ? [X314: subst > term > term,X315: term,X316: term] :
( ! [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
& ( ( ap @ ( sub @ X315 @ id ) @ X316 )
= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( ! [X314: subst > term > term,X315: term,X316: term] :
( ? [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
!= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ( $true = sP16 )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP16 ) )
& ( ( sP15 = $true )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( sP15 != $true ) )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
& ( X453 != X454 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( sP13 != $true ) )
& ( ( sP13 = $true )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ? [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
!= ( X0 @ X4 ) )
| ( ( X0 @ one )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) )
& ( ( X0 @ one )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) )
& ( ( axidr = $true )
| ? [X172: subst] :
( ( comp @ X172 @ id )
!= X172 ) )
& ( ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 )
| ( axidr != $true ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
& ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
& ? [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
= $true )
& ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
!= $true ) ) ) )
& ( ? [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
!= X19 )
| ? [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
!= X21 )
| ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ! [X201: subst > term > subst > $o] :
? [X202: term > $o] :
! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X201: subst > term > subst > $o] :
! [X202: term > $o] :
? [X203: term] :
( ( X202 @ X203 )
!= ( X201 @ id @ X203 @ id ) ) )
& ( ( sP11 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( sP11 != $true ) )
& ( ( axshiftcons = $true )
| ? [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
!= X463 ) )
& ( ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 )
| ( axshiftcons != $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( X54 = X55 )
| ( ( d2subst @ X55 )
!= ( d2subst @ X54 ) ) )
& ( ( sP6 = $true )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( sP6 != $true ) )
& ( ( axidl = $true )
| ? [X409: subst] :
( ( comp @ id @ X409 )
!= X409 ) )
& ( ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 )
| ( axidl != $true ) )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X374: term] :
( ( sub @ X374 @ id )
!= X374 ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( sP4 != $true ) )
& ( ( sP4 = $true )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ? [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
!= X211 )
| ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ? [X216: term] :
( ( X214 @ X216 )
!= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
| ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
= X211 )
& ? [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ! [X216: term] :
( ( X214 @ X216 )
= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
& ( $true
!= ( X214 @ one ) )
& ( ( X215 @ X212 )
= $true ) ) ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
= ( ap @ X174 @ X176 ) )
& ( X175 != X176 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
| ( sP3 != $true ) )
& ( ( sP3 = $true )
| ( induction2lem_lthm != $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X34: term] :
? [X35: subst > term > term] :
! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
<=> ( apinj1 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ( sP58 = $true )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
= ( ap @ X59 @ X57 ) )
& ( X57 != X58 ) )
| ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) ) ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( termmset_lthm = $true )
<=> ( ! [X418: term] :
( ( sub @ X418 @ id )
= X418 )
| ? [X417: term] :
( ( sub @ X417 @ id )
!= X417 ) ) )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X483: term] :
? [X484: subst > term > term] :
! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( sP56 = $true ) )
& ( ulamvarind = $true )
& ( ( sP54 = $true )
<=> ( hoasinduction_lem3aa = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X311: subst > term > subst > $o] :
? [X312: term > $o] :
! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
? [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
= ( X29 @ sh @ one ) ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ( $true = sP53 ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasapinj2_gthm = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( sP52 = $true ) )
& ( ( induction2_lthm = $true )
<=> ( $true = sP46 ) )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ? [X491: subst > term > term] :
( ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X488 @ id @ X487 @ id )
= $true )
| ( ( sP42 @ X488 )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( ( pushprop_lem0 = $true )
<=> ! [X456: subst,X457: term > $o,X458: term] :
? [X459: term > $o] :
! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ( ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) )
| ? [X5: term] :
( ( sub @ X5 @ id )
!= X5 )
| ? [X6: term,X7: term,X8: term,X9: term] :
( ( X8 != X9 )
& ( ( ap @ X8 @ X6 )
= ( ap @ X9 @ X7 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ( sP41 = $true ) )
& ( ! [X149: term > $o,X150: term] :
( ? [X154: term] :
( ( ( X149 @ X154 )
!= $true )
& ( ( var @ X154 )
= $true ) )
| ( ( sP39 @ X149 )
= $true )
| ( ( X149 @ X150 )
= $true )
| ? [X153: term] :
( ( ( X149 @ X153 )
= $true )
& ( ( X149 @ ( lam @ X153 ) )
!= $true ) ) )
<=> ( induction = $true ) )
& ( hoasinduction_gthm = $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
<=> ( sP38 = $true ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
<=> ( substmonoid = $true ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X415: term] :
? [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
= ( X416 @ sh @ one ) ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X14: term > $o,X15: term,X16: subst] :
? [X17: term > $o] :
! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
<=> ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X199: d_term,X200: d_term] :
( ( X199 = X200 )
| ( ( d2term @ X200 )
!= ( d2term @ X199 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ( sP35 = $true )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ( sP33 = $true ) )
& ( ( ? [X145: subst] :
( ( comp @ id @ X145 )
!= X145 )
| ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( $true = sP32 )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( sP31 = $true )
<=> ( hoasinduction_lthm = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( sP22 = $true ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
<=> ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) ) )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
<=> ( termmset = $true ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ? [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
!= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
| ? [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
!= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) )
<=> ( hoaslaminj = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
<=> ( sP21 = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
<=> ( axscons = $true ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( sP19 = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X314: subst > term > term,X315: term,X316: term] :
( ? [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
!= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ( $true = sP16 )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( sP15 = $true )
<=> ( induction2lem = $true ) )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( sP13 = $true ) )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ? [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
!= ( X0 @ X4 ) )
| ( ( X0 @ one )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( axidr = $true )
<=> ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ? [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
!= X19 )
| ? [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
!= X21 )
| ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) ) ) )
& ( ! [X201: subst > term > subst > $o] :
? [X202: term > $o] :
! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( sP11 = $true )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( X54 = X55 )
| ( ( d2subst @ X55 )
!= ( d2subst @ X54 ) ) )
& ( ( sP6 = $true )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( axidl = $true )
<=> ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 ) )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
<=> ( axvarid = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( sP4 = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ( ? [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
!= X211 )
| ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ? [X216: term] :
( ( X214 @ X216 )
!= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
| ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
<=> ( apinj2 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( sP3 = $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14]) ).
thf(f14,plain,
! [X342: term > $o] :
( ( ( sP0 @ X342 )
= $true )
<=> ! [X344: term,X345: term] :
( ( ( X342 @ ( ap @ X345 @ X344 ) )
= $true )
| ( ( X342 @ X344 )
!= $true )
| ( ( X342 @ X345 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
! [X348: term > $o] :
( ( ( sP1 @ X348 )
= $true )
<=> ? [X351: term,X352: term] :
( ( ( X348 @ X351 )
= $true )
& ( ( X348 @ ( ap @ X352 @ X351 ) )
!= $true )
& ( ( X348 @ X352 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( $true = sP2 )
<=> ! [X348: term > $o,X349: term,X350: subst] :
( ( ( X348 @ ( sub @ X349 @ X350 ) )
= $true )
| ( ( sP1 @ X348 )
= $true )
| ? [X353: term] :
( ! [X354: term] :
( ( $true
= ( X348 @ ( sub @ X353 @ ( push @ X354 @ id ) ) ) )
| ( ( X348 @ X354 )
!= $true ) )
& ( ( X348 @ ( lam @ X353 ) )
!= $true ) )
| ? [X355: term] :
( ( $true
!= ( X348 @ ( sub @ X355 @ X350 ) ) )
& ( ( var @ X355 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( sP3 = $true )
<=> ( ( $true = sP2 )
| ? [X341: subst] :
( ( comp @ X341 @ id )
!= X341 )
| ? [X342: term > $o,X343: term] :
( ( ( X342 @ X343 )
!= $true )
& ! [X346: term] :
( ( ( X342 @ X346 )
!= $true )
| ( ( X342 @ ( lam @ X346 ) )
= $true ) )
& ( ( sP0 @ X342 )
= $true )
& ! [X347: term] :
( ( $true
!= ( var @ X347 ) )
| ( ( X342 @ X347 )
= $true ) ) )
| ? [X339: term,X340: subst] :
( ( comp @ sh @ ( push @ X339 @ X340 ) )
!= X340 )
| ? [X337: subst,X338: term] :
( ( sub @ one @ ( push @ X338 @ X337 ) )
!= X338 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
( ( sP4 = $true )
<=> ( ? [X161: term] :
( ( sub @ X161 @ id )
!= X161 )
| ? [X157: term] :
! [X158: subst > term > term] :
? [X159: term,X160: subst] :
( ( X158 @ X160 @ X159 )
!= ( sub @ X157 @ ( push @ X159 @ X160 ) ) )
| ! [X162: subst > term > subst > $o,X163: term > $o,X164: term] :
( ( ( X163 @ ( lam @ X164 ) )
= $true )
| ? [X171: term] :
( ( X163 @ X171 )
!= ( X162 @ id @ X171 @ id ) )
| ? [X165: term] :
( ( ( X163 @ ( sub @ X164 @ ( push @ X165 @ id ) ) )
!= $true )
& ( ( X163 @ X165 )
= $true ) )
| ? [X166: subst > term > term] :
( ( ( X162 @ id @ ( lam @ ( X166 @ sh @ one ) ) @ id )
!= $true )
& ! [X167: term] :
( ( ( X162 @ id @ X167 @ id )
!= $true )
| ( ( X162 @ id @ ( X166 @ id @ X167 ) @ id )
= $true ) )
& ! [X168: subst,X169: subst,X170: term] :
( ( sub @ ( X166 @ X168 @ X170 ) @ X169 )
= ( X166 @ ( comp @ X168 @ X169 ) @ ( sub @ X170 @ X169 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X431: subst > term > subst > $o] :
( ( $true
= ( sP5 @ X431 ) )
<=> ? [X432: term,X433: term] :
( ( ( X431 @ id @ X433 @ id )
= $true )
& ( ( X431 @ id @ X432 @ id )
= $true )
& ( ( X431 @ id @ ( ap @ ( sub @ X432 @ id ) @ X433 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
( ( sP6 = $true )
<=> ! [X429: term,X430: term,X431: subst > term > subst > $o] :
( ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X431 @ X436 @ X434 @ ( comp @ X435 @ X437 ) )
= $true )
& ( ( X431 @ ( comp @ X436 @ X435 ) @ ( sub @ X434 @ X435 ) @ X437 )
!= $true ) )
| ? [X438: subst,X439: term,X440: subst,X441: subst] :
( ( ( X431 @ X438 @ X439 @ ( comp @ X441 @ X440 ) )
!= $true )
& ( ( X431 @ ( comp @ X438 @ X441 ) @ ( sub @ X439 @ X441 ) @ X440 )
= $true ) )
| ( ( X431 @ id @ X429 @ id )
!= $true )
| ( $true
= ( sP5 @ X431 ) )
| ( ( X431 @ id @ ( ap @ X430 @ X429 ) @ id )
= $true )
| ( $true
!= ( X431 @ id @ X430 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
! [X119: term > $o] :
( ( $true
= ( sP7 @ X119 ) )
<=> ! [X120: term,X121: term] :
( ( ( X119 @ ( ap @ X120 @ X121 ) )
= $true )
| ( ( X119 @ X121 )
!= $true )
| ( ( X119 @ X120 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X136: subst > term > subst > $o] :
( ( ( sP8 @ X136 )
= $true )
<=> ? [X138: subst > term > term] :
( ! [X139: term] :
( ( ( X136 @ id @ ( X138 @ id @ X139 ) @ id )
= $true )
| ( ( X136 @ id @ X139 @ id )
!= $true ) )
& ( ( X136 @ id @ ( lam @ ( X138 @ sh @ one ) ) @ id )
!= $true )
& ! [X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X142 @ X141 ) @ ( sub @ X140 @ X141 ) )
= ( sub @ ( X138 @ X142 @ X140 ) @ X141 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
( ( $true = sP9 )
<=> ? [X126: subst > term > subst > $o,X127: term,X128: term > $o] :
( ! [X130: term] :
( ( X126 @ id @ X130 @ id )
= ( X128 @ X130 ) )
& ! [X131: subst > term > term] :
( ( ( X126 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id )
= $true )
| ? [X132: term] :
( ( $true
= ( X126 @ id @ X132 @ id ) )
& ( ( X126 @ id @ ( X131 @ id @ X132 ) @ id )
!= $true ) )
| ? [X133: subst,X134: term,X135: subst] :
( ( X131 @ ( comp @ X133 @ X135 ) @ ( sub @ X134 @ X135 ) )
!= ( sub @ ( X131 @ X133 @ X134 ) @ X135 ) ) )
& ( ( X128 @ ( lam @ X127 ) )
!= $true )
& ! [X129: term] :
( ( ( X128 @ ( sub @ X127 @ ( push @ X129 @ id ) ) )
= $true )
| ( ( X128 @ X129 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
( ( sP10 = $true )
<=> ? [X118: term,X119: term > $o] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X119 @ X122 )
= $true ) )
& ! [X123: term] :
( ? [X124: term] :
( ( ( X119 @ X124 )
= $true )
& ( ( X119 @ ( sub @ X123 @ ( push @ X124 @ id ) ) )
!= $true ) )
| ( ( X119 @ ( lam @ X123 ) )
= $true ) )
& ( $true
!= ( X119 @ X118 ) )
& ( $true
= ( sP7 @ X119 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( sP11 = $true )
<=> ( ! [X136: subst > term > subst > $o,X137: term] :
( ? [X143: term,X144: term] :
( ( ( X136 @ id @ ( ap @ ( sub @ X144 @ id ) @ X143 ) @ id )
!= $true )
& ( ( X136 @ id @ X143 @ id )
= $true )
& ( ( X136 @ id @ X144 @ id )
= $true ) )
| ( ( sP8 @ X136 )
= $true )
| ( ( X136 @ id @ X137 @ id )
= $true ) )
| ? [X115: subst > term > subst > $o] :
! [X116: term > $o] :
? [X117: term] :
( ( X116 @ X117 )
!= ( X115 @ id @ X117 @ id ) )
| ( $true = sP9 )
| ? [X125: term] :
( ( sub @ X125 @ id )
!= X125 )
| ( sP10 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
( ( sP12 = $true )
<=> ? [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ ( lam @ ( sub @ X322 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X323: term] :
( ( ( X321 @ id @ ( sub @ X322 @ ( push @ X323 @ id ) ) @ id )
= $true )
| ( $true
!= ( X321 @ id @ X323 @ id ) ) )
& ! [X324: subst > term > term] :
( ? [X328: term] :
( ( $true
!= ( X321 @ id @ ( X324 @ id @ X328 ) @ id ) )
& ( ( X321 @ id @ X328 @ id )
= $true ) )
| ( ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id )
= $true )
| ? [X325: subst,X326: subst,X327: term] :
( ( X324 @ ( comp @ X325 @ X326 ) @ ( sub @ X327 @ X326 ) )
!= ( sub @ ( X324 @ X325 @ X327 ) @ X326 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( sP13 = $true )
<=> ( ( sP12 = $true )
| ! [X329: subst > term > subst > $o,X330: term] :
( ? [X331: term] :
( ( $true
!= ( X329 @ id @ ( sub @ X330 @ ( push @ X331 @ id ) ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( ( X329 @ id @ ( lam @ X330 ) @ id )
= $true )
| ? [X332: subst > term > term] :
( ! [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
| ( ( X329 @ id @ ( X332 @ id @ X336 ) @ id )
= $true ) )
& ( ( X329 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id )
!= $true )
& ! [X333: subst,X334: term,X335: subst] :
( ( X332 @ ( comp @ X333 @ X335 ) @ ( sub @ X334 @ X335 ) )
= ( sub @ ( X332 @ X333 @ X334 ) @ X335 ) ) ) )
| ? [X320: term] :
( ( sub @ X320 @ id )
!= X320 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X534: term > $o] :
( ( ( sP14 @ X534 )
= $true )
<=> ? [X538: term,X539: term] :
( ( ( X534 @ X538 )
= $true )
& ( ( X534 @ X539 )
= $true )
& ( ( X534 @ ( ap @ X538 @ X539 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
( ( sP15 = $true )
<=> ! [X532: term,X533: subst,X534: term > $o] :
( ( ( X534 @ ( sub @ X532 @ X533 ) )
= $true )
| ? [X537: term] :
( ( ( X534 @ ( sub @ X537 @ X533 ) )
!= $true )
& ( ( var @ X537 )
= $true ) )
| ? [X535: term] :
( ! [X536: term] :
( ( ( X534 @ X536 )
!= $true )
| ( ( X534 @ ( sub @ X535 @ ( push @ X536 @ id ) ) )
= $true ) )
& ( ( X534 @ ( lam @ X535 ) )
!= $true ) )
| ( ( sP14 @ X534 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
( ( $true = sP16 )
<=> ! [X64: term,X65: subst > term > subst > $o] :
( ? [X67: subst > term > term,X68: term] :
( ! [X72: subst,X73: term,X74: subst] :
( ( X67 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) )
= ( sub @ X68 @ ( push @ ( sub @ X73 @ X74 ) @ ( comp @ X72 @ X74 ) ) ) )
& ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
!= $true )
& ! [X69: subst,X70: subst,X71: term] :
( ( sub @ ( sub @ X68 @ ( push @ X71 @ X69 ) ) @ X70 )
= ( sub @ ( X67 @ X69 @ X71 ) @ X70 ) )
& ! [X75: term] :
( ( ( X65 @ id @ X75 @ id )
!= $true )
| ( ( X65 @ id @ ( X67 @ id @ X75 ) @ id )
= $true ) ) )
| ( ( X65 @ id @ ( lam @ ( sub @ X64 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X66: term] :
( ( ( X65 @ id @ ( sub @ X64 @ ( push @ X66 @ id ) ) @ id )
!= $true )
& ( ( X65 @ id @ X66 @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
! [X295: subst > term > subst > $o] :
( ( ( sP17 @ X295 )
= $true )
<=> ? [X301: subst > term > term] :
( ! [X302: subst,X303: subst,X304: term] :
( ( X301 @ ( comp @ X303 @ X302 ) @ ( sub @ X304 @ X302 ) )
= ( sub @ ( X301 @ X303 @ X304 ) @ X302 ) )
& ( $true
!= ( X295 @ id @ ( lam @ ( X301 @ sh @ one ) ) @ id ) )
& ! [X305: term] :
( ( ( X295 @ id @ ( X301 @ id @ X305 ) @ id )
= $true )
| ( ( X295 @ id @ X305 @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
( ( sP18 = $true )
<=> ? [X287: term,X288: subst > term > subst > $o] :
( ! [X294: term] :
( ( ( X288 @ id @ X294 @ id )
!= $true )
| ( $true
= ( X288 @ id @ ( sub @ X287 @ ( push @ X294 @ id ) ) @ id ) ) )
& ! [X289: subst > term > term] :
( ? [X290: term] :
( ( $true
= ( X288 @ id @ X290 @ id ) )
& ( ( X288 @ id @ ( X289 @ id @ X290 ) @ id )
!= $true ) )
| ( $true
= ( X288 @ id @ ( lam @ ( X289 @ sh @ one ) ) @ id ) )
| ? [X291: term,X292: subst,X293: subst] :
( ( sub @ ( X289 @ X292 @ X291 ) @ X293 )
!= ( X289 @ ( comp @ X292 @ X293 ) @ ( sub @ X291 @ X293 ) ) ) )
& ( ( X288 @ id @ ( lam @ ( sub @ X287 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
( ( sP19 = $true )
<=> ( ( sP18 = $true )
| ? [X286: term] :
( ( sub @ X286 @ id )
!= X286 )
| ! [X295: subst > term > subst > $o,X296: term] :
( ? [X307: subst,X308: subst,X309: subst,X310: term] :
( ( ( X295 @ X307 @ X310 @ ( comp @ X308 @ X309 ) )
= $true )
& ( ( X295 @ ( comp @ X307 @ X308 ) @ ( sub @ X310 @ X308 ) @ X309 )
!= $true ) )
| ( ( sP17 @ X295 )
= $true )
| ? [X297: subst,X298: subst,X299: subst,X300: term] :
( ( $true
= ( X295 @ ( comp @ X297 @ X298 ) @ ( sub @ X300 @ X298 ) @ X299 ) )
& ( ( X295 @ X297 @ X300 @ ( comp @ X298 @ X299 ) )
!= $true ) )
| ? [X306: term] :
( ( ( X295 @ id @ X306 @ id )
= $true )
& ( ( X295 @ id @ ( sub @ X296 @ ( push @ X306 @ id ) ) @ id )
!= $true ) )
| ( ( X295 @ id @ ( lam @ X296 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
! [X400: term > $o] :
( ( ( sP20 @ X400 )
= $true )
<=> ? [X402: term,X403: term] :
( ( ( X400 @ X403 )
= $true )
& ( $true
!= ( X400 @ ( ap @ X403 @ X402 ) ) )
& ( ( X400 @ X402 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
( ( sP21 = $true )
<=> ! [X400: term > $o,X401: term] :
( ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( ( X400 @ X404 )
!= $true ) )
| ? [X405: term] :
( ( ( X400 @ ( lam @ X405 ) )
!= $true )
& ! [X406: term] :
( ( ( X400 @ ( sub @ X405 @ ( push @ X406 @ id ) ) )
= $true )
| ( ( X400 @ X406 )
!= $true ) ) )
| ( ( sP20 @ X400 )
= $true )
| ( ( X400 @ X401 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( sP22 = $true )
<=> ( ! [X390: subst,X391: subst > term > term,X392: term,X393: subst > term > term] :
( ? [X394: subst,X395: term,X396: subst] :
( ( X393 @ ( comp @ X396 @ X394 ) @ ( sub @ X395 @ X394 ) )
!= ( sub @ ( X393 @ X396 @ X395 ) @ X394 ) )
| ( ( lam @ ( X391 @ sh @ one ) )
!= ( lam @ ( X393 @ sh @ one ) ) )
| ( ( X391 @ X390 @ X392 )
= ( X393 @ X390 @ X392 ) )
| ? [X397: subst,X398: term,X399: subst] :
( ( X391 @ ( comp @ X397 @ X399 ) @ ( sub @ X398 @ X399 ) )
!= ( sub @ ( X391 @ X397 @ X398 ) @ X399 ) ) )
| ? [X386: subst,X387: term] :
( ( comp @ sh @ ( push @ X387 @ X386 ) )
!= X386 )
| ? [X384: term,X385: subst] :
( ( sub @ one @ ( push @ X384 @ X385 ) )
!= X384 )
| ? [X388: term,X389: term] :
( ( ( lam @ X389 )
= ( lam @ X388 ) )
& ( X388 != X389 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
! [X217: term > $o] :
( ( ( sP23 @ X217 )
= $true )
<=> ! [X222: term,X223: term] :
( ( ( X217 @ ( ap @ X222 @ X223 ) )
= $true )
| ( ( X217 @ X222 )
!= $true )
| ( ( X217 @ X223 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
! [X238: subst > term > subst > $o] :
( ( $true
= ( sP24 @ X238 ) )
<=> ! [X247: subst > term > term] :
( ( ( X238 @ id @ ( lam @ ( X247 @ sh @ one ) ) @ id )
= $true )
| ? [X248: term] :
( ( ( X238 @ id @ ( X247 @ id @ X248 ) @ id )
!= $true )
& ( $true
= ( X238 @ id @ X248 @ id ) ) )
| ? [X249: subst,X250: subst,X251: term] :
( ( X247 @ ( comp @ X249 @ X250 ) @ ( sub @ X251 @ X250 ) )
!= ( sub @ ( X247 @ X249 @ X251 ) @ X250 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
! [X224: subst > term > subst > $o] :
( ( ( sP25 @ X224 )
= $true )
<=> ! [X227: term,X228: term] :
( ( ( X224 @ id @ X228 @ id )
!= $true )
| ( ( X224 @ id @ ( ap @ ( sub @ X227 @ id ) @ X228 ) @ id )
= $true )
| ( ( X224 @ id @ X227 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
! [X253: subst > term > subst > $o] :
( ( ( sP26 @ X253 )
= $true )
<=> ? [X261: subst > term > term] :
( ( ( X253 @ id @ ( lam @ ( X261 @ sh @ one ) ) @ id )
!= $true )
& ! [X262: term] :
( ( $true
!= ( X253 @ id @ X262 @ id ) )
| ( $true
= ( X253 @ id @ ( X261 @ id @ X262 ) @ id ) ) )
& ! [X263: term,X264: subst,X265: subst] :
( ( X261 @ ( comp @ X265 @ X264 ) @ ( sub @ X263 @ X264 ) )
= ( sub @ ( X261 @ X265 @ X263 ) @ X264 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
! [X253: subst > term > subst > $o] :
( ( ( sP27 @ X253 )
= $true )
<=> ? [X259: term,X260: term] :
( ( $true
!= ( X253 @ id @ ( ap @ ( sub @ X259 @ id ) @ X260 ) @ id ) )
& ( ( X253 @ id @ X260 @ id )
= $true )
& ( ( X253 @ id @ X259 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
( ( sP28 = $true )
<=> ? [X237: term,X238: subst > term > subst > $o] :
( ( ( X238 @ id @ ( lam @ X237 ) @ id )
!= $true )
& ( $true
= ( sP24 @ X238 ) )
& ! [X243: subst,X244: subst,X245: term,X246: subst] :
( ( ( X238 @ ( comp @ X244 @ X243 ) @ ( sub @ X245 @ X243 ) @ X246 )
= $true )
| ( ( X238 @ X244 @ X245 @ ( comp @ X243 @ X246 ) )
!= $true ) )
& ! [X252: term] :
( ( ( X238 @ id @ ( sub @ X237 @ ( push @ X252 @ id ) ) @ id )
= $true )
| ( ( X238 @ id @ X252 @ id )
!= $true ) )
& ! [X239: subst,X240: term,X241: subst,X242: subst] :
( ( ( X238 @ ( comp @ X241 @ X242 ) @ ( sub @ X240 @ X242 ) @ X239 )
!= $true )
| ( ( X238 @ X241 @ X240 @ ( comp @ X242 @ X239 ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
( ( sP29 = $true )
<=> ! [X253: subst > term > subst > $o,X254: term] :
( ( ( sP27 @ X253 )
= $true )
| ? [X266: subst,X267: subst,X268: term,X269: subst] :
( ( ( X253 @ X267 @ X268 @ ( comp @ X269 @ X266 ) )
!= $true )
& ( ( X253 @ ( comp @ X267 @ X269 ) @ ( sub @ X268 @ X269 ) @ X266 )
= $true ) )
| ( ( X253 @ id @ X254 @ id )
= $true )
| ? [X255: subst,X256: term,X257: subst,X258: subst] :
( ( ( X253 @ ( comp @ X258 @ X257 ) @ ( sub @ X256 @ X257 ) @ X255 )
!= $true )
& ( $true
= ( X253 @ X258 @ X256 @ ( comp @ X257 @ X255 ) ) ) )
| ? [X270: term] :
( ( $true
= ( var @ ( sub @ X270 @ id ) ) )
& ( ( X253 @ id @ X270 @ id )
!= $true ) )
| ( ( sP26 @ X253 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( sP30 = $true )
<=> ? [X217: term > $o,X218: term] :
( ( ( sP23 @ X217 )
= $true )
& ! [X219: term] :
( ( ( X217 @ X219 )
= $true )
| ( ( var @ X219 )
!= $true ) )
& ! [X220: term] :
( ( ( X217 @ ( lam @ X220 ) )
= $true )
| ? [X221: term] :
( ( ( X217 @ ( sub @ X220 @ ( push @ X221 @ id ) ) )
!= $true )
& ( ( X217 @ X221 )
= $true ) ) )
& ( ( X217 @ X218 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
( ( sP31 = $true )
<=> ( ( sP29 = $true )
| ? [X224: subst > term > subst > $o,X225: term,X226: term] :
( ! [X233: subst,X234: term,X235: subst,X236: subst] :
( ( ( X224 @ X235 @ X234 @ ( comp @ X233 @ X236 ) )
!= $true )
| ( ( X224 @ ( comp @ X235 @ X233 ) @ ( sub @ X234 @ X233 ) @ X236 )
= $true ) )
& ! [X229: term,X230: subst,X231: subst,X232: subst] :
( ( ( X224 @ X230 @ X229 @ ( comp @ X231 @ X232 ) )
= $true )
| ( ( X224 @ ( comp @ X230 @ X231 ) @ ( sub @ X229 @ X231 ) @ X232 )
!= $true ) )
& ( ( X224 @ id @ X226 @ id )
= $true )
& ( ( X224 @ id @ X225 @ id )
= $true )
& ( ( sP25 @ X224 )
= $true )
& ( $true
!= ( X224 @ id @ ( ap @ X225 @ X226 ) @ id ) ) )
| ( sP28 = $true )
| ( sP30 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
( ( $true = sP32 )
<=> ! [X442: term,X443: subst > term > subst > $o] :
( ( ( X443 @ id @ ( lam @ ( sub @ X442 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X444: term] :
( ( ( X443 @ id @ ( sub @ X442 @ ( push @ X444 @ id ) ) @ id )
!= $true )
& ( ( X443 @ id @ X444 @ id )
= $true ) )
| ? [X445: subst > term > term] :
( ! [X446: subst,X447: term,X448: subst] :
( ( sub @ ( X445 @ X446 @ X447 ) @ X448 )
= ( X445 @ ( comp @ X446 @ X448 ) @ ( sub @ X447 @ X448 ) ) )
& ! [X449: term] :
( ( ( X443 @ id @ X449 @ id )
!= $true )
| ( ( X443 @ id @ ( X445 @ id @ X449 ) @ id )
= $true ) )
& ( ( X443 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
( ( sP33 = $true )
<=> ! [X512: subst > term > subst > $o,X513: term > $o,X514: term] :
( ? [X515: term] :
( ( X513 @ X515 )
!= ( X512 @ id @ X515 @ id ) )
| ? [X516: subst > term > term] :
( ( ( X512 @ id @ ( lam @ ( X516 @ sh @ one ) ) @ id )
!= $true )
& ! [X517: subst,X518: subst,X519: term] :
( ( sub @ ( X516 @ X518 @ X519 ) @ X517 )
= ( X516 @ ( comp @ X518 @ X517 ) @ ( sub @ X519 @ X517 ) ) )
& ! [X520: term] :
( ( ( X512 @ id @ X520 @ id )
!= $true )
| ( ( X512 @ id @ ( X516 @ id @ X520 ) @ id )
= $true ) ) )
| ( $true
= ( X513 @ ( lam @ X514 ) ) )
| ? [X521: term] :
( ( ( X513 @ ( sub @ X514 @ ( push @ X521 @ id ) ) )
!= $true )
& ( ( X513 @ X521 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
! [X273: subst > term > subst > $o] :
( ( $true
= ( sP34 @ X273 ) )
<=> ? [X280: term,X281: term] :
( ( ( X273 @ id @ ( ap @ ( sub @ X281 @ id ) @ X280 ) @ id )
!= $true )
& ( ( X273 @ id @ X281 @ id )
= $true )
& ( ( X273 @ id @ X280 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
( ( sP35 = $true )
<=> ! [X271: term,X272: term > $o,X273: subst > term > subst > $o,X274: term] :
( ? [X282: subst,X283: term,X284: subst,X285: subst] :
( ( ( X273 @ ( comp @ X285 @ X282 ) @ ( sub @ X283 @ X282 ) @ X284 )
= $true )
& ( ( X273 @ X285 @ X283 @ ( comp @ X282 @ X284 ) )
!= $true ) )
| ( $true
= ( sP34 @ X273 ) )
| ( $true
!= ( X272 @ X274 ) )
| ( ( X272 @ X271 )
!= $true )
| ( ( X272 @ ( ap @ X274 @ X271 ) )
= $true )
| ? [X275: term] :
( ( X272 @ X275 )
!= ( X273 @ id @ X275 @ id ) )
| ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( ( X273 @ ( comp @ X276 @ X278 ) @ ( sub @ X279 @ X278 ) @ X277 )
!= $true )
& ( ( X273 @ X276 @ X279 @ ( comp @ X278 @ X277 ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
! [X466: subst > term > subst > $o] :
( ( ( sP36 @ X466 )
= $true )
<=> ? [X481: term,X482: term] :
( ( ( X466 @ id @ X481 @ id )
= $true )
& ( $true
= ( X466 @ id @ X482 @ id ) )
& ( ( X466 @ id @ ( ap @ ( sub @ X482 @ id ) @ X481 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
! [X466: subst > term > subst > $o] :
( ( ( sP37 @ X466 )
= $true )
<=> ? [X472: subst > term > term] :
( ! [X476: term] :
( ( ( X466 @ id @ X476 @ id )
!= $true )
| ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true ) )
& ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
!= $true )
& ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
( ( sP38 = $true )
<=> ! [X465: term,X466: subst > term > subst > $o] :
( ( ( X466 @ id @ X465 @ id )
= $true )
| ( ( sP37 @ X466 )
= $true )
| ? [X468: term,X469: subst,X470: subst,X471: subst] :
( ( ( X466 @ X470 @ X468 @ ( comp @ X471 @ X469 ) )
= $true )
& ( ( X466 @ ( comp @ X470 @ X471 ) @ ( sub @ X468 @ X471 ) @ X469 )
!= $true ) )
| ( ( sP36 @ X466 )
= $true )
| ? [X467: term] :
( ( $true
!= ( X466 @ id @ X467 @ id ) )
& ( ( var @ ( sub @ X467 @ id ) )
= $true ) )
| ? [X477: subst,X478: subst,X479: subst,X480: term] :
( ( $true
= ( X466 @ ( comp @ X479 @ X478 ) @ ( sub @ X480 @ X478 ) @ X477 ) )
& ( $true
!= ( X466 @ X479 @ X480 @ ( comp @ X478 @ X477 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
! [X149: term > $o] :
( ( ( sP39 @ X149 )
= $true )
<=> ? [X151: term,X152: term] :
( ( ( X149 @ ( ap @ X152 @ X151 ) )
!= $true )
& ( $true
= ( X149 @ X151 ) )
& ( ( X149 @ X152 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X38: subst > term > subst > $o] :
( ( ( sP40 @ X38 )
= $true )
<=> ? [X49: subst > term > term] :
( ! [X53: term] :
( ( ( X38 @ id @ X53 @ id )
!= $true )
| ( ( X38 @ id @ ( X49 @ id @ X53 ) @ id )
= $true ) )
& ! [X50: subst,X51: subst,X52: term] :
( ( X49 @ ( comp @ X50 @ X51 ) @ ( sub @ X52 @ X51 ) )
= ( sub @ ( X49 @ X50 @ X52 ) @ X51 ) )
& ( ( X38 @ id @ ( lam @ ( X49 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( sP41 = $true )
<=> ! [X38: subst > term > subst > $o,X39: term] :
( ( ( X38 @ id @ ( lam @ X39 ) @ id )
= $true )
| ? [X44: subst,X45: subst,X46: subst,X47: term] :
( ( ( X38 @ ( comp @ X44 @ X46 ) @ ( sub @ X47 @ X46 ) @ X45 )
= $true )
& ( ( X38 @ X44 @ X47 @ ( comp @ X46 @ X45 ) )
!= $true ) )
| ( ( sP40 @ X38 )
= $true )
| ? [X40: term,X41: subst,X42: subst,X43: subst] :
( ( $true
!= ( X38 @ ( comp @ X42 @ X43 ) @ ( sub @ X40 @ X43 ) @ X41 ) )
& ( ( X38 @ X42 @ X40 @ ( comp @ X43 @ X41 ) )
= $true ) )
| ? [X48: term] :
( ( ( X38 @ id @ ( sub @ X39 @ ( push @ X48 @ id ) ) @ id )
!= $true )
& ( $true
= ( X38 @ id @ X48 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
! [X488: subst > term > subst > $o] :
( ( ( sP42 @ X488 )
= $true )
<=> ? [X489: term,X490: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( ap @ ( sub @ X489 @ id ) @ X490 ) @ id )
!= $true )
& ( ( X488 @ id @ X490 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
! [X497: term > $o] :
( ( ( sP43 @ X497 )
= $true )
<=> ! [X500: term,X501: term] :
( ( ( X497 @ X501 )
!= $true )
| ( ( X497 @ X500 )
!= $true )
| ( ( X497 @ ( ap @ X500 @ X501 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
! [X505: term > $o] :
( ( $true
= ( sP44 @ X505 ) )
<=> ? [X509: term,X510: term] :
( ( ( X505 @ X510 )
= $true )
& ( ( X505 @ X509 )
= $true )
& ( ( X505 @ ( ap @ X509 @ X510 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
( ( sP45 = $true )
<=> ! [X505: term > $o,X506: term] :
( ? [X507: term] :
( ! [X508: term] :
( ( ( X505 @ X508 )
!= $true )
| ( ( X505 @ ( sub @ X507 @ ( push @ X508 @ id ) ) )
= $true ) )
& ( $true
!= ( X505 @ ( lam @ X507 ) ) ) )
| ? [X511: term] :
( ( ( var @ X511 )
= $true )
& ( ( X505 @ X511 )
!= $true ) )
| ( $true
= ( sP44 @ X505 ) )
| ( $true
= ( X505 @ X506 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
( ( $true = sP46 )
<=> ( ? [X496: term] :
( ( sub @ X496 @ id )
!= X496 )
| ( sP45 = $true )
| ? [X497: term > $o,X498: subst,X499: term] :
( ! [X502: term] :
( ( ( X497 @ ( lam @ X502 ) )
= $true )
| ? [X503: term] :
( ( ( X497 @ X503 )
= $true )
& ( ( X497 @ ( sub @ X502 @ ( push @ X503 @ id ) ) )
!= $true ) ) )
& ( ( sP43 @ X497 )
= $true )
& ( ( X497 @ ( sub @ X499 @ X498 ) )
!= $true )
& ! [X504: term] :
( ( $true
= ( X497 @ ( sub @ X504 @ X498 ) ) )
| ( ( var @ X504 )
!= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
! [X79: term > $o] :
( ( ( sP47 @ X79 )
= $true )
<=> ! [X81: term,X82: term] :
( ( $true
!= ( X79 @ X82 ) )
| ( ( X79 @ ( ap @ X82 @ X81 ) )
= $true )
| ( ( X79 @ X81 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
! [X97: subst > term > subst > $o] :
( ( ( sP48 @ X97 )
= $true )
<=> ? [X110: subst > term > term] :
( ! [X111: subst,X112: term,X113: subst] :
( ( X110 @ ( comp @ X113 @ X111 ) @ ( sub @ X112 @ X111 ) )
= ( sub @ ( X110 @ X113 @ X112 ) @ X111 ) )
& ! [X114: term] :
( ( ( X97 @ id @ ( X110 @ id @ X114 ) @ id )
= $true )
| ( ( X97 @ id @ X114 @ id )
!= $true ) )
& ( ( X97 @ id @ ( lam @ ( X110 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
! [X97: subst > term > subst > $o] :
( ( ( sP49 @ X97 )
= $true )
<=> ? [X107: term,X108: term] :
( ( ( X97 @ id @ X107 @ id )
= $true )
& ( ( X97 @ id @ X108 @ id )
= $true )
& ( ( X97 @ id @ ( ap @ ( sub @ X108 @ id ) @ X107 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
( ( sP50 = $true )
<=> ? [X87: subst > term > subst > $o,X88: term > $o,X89: term] :
( ! [X90: term] :
( ( X87 @ id @ X90 @ id )
= ( X88 @ X90 ) )
& ! [X91: subst > term > term] :
( ( ( X87 @ id @ ( lam @ ( X91 @ sh @ one ) ) @ id )
= $true )
| ? [X92: term] :
( ( $true
!= ( X87 @ id @ ( X91 @ id @ X92 ) @ id ) )
& ( ( X87 @ id @ X92 @ id )
= $true ) )
| ? [X93: subst,X94: term,X95: subst] :
( ( X91 @ ( comp @ X95 @ X93 ) @ ( sub @ X94 @ X93 ) )
!= ( sub @ ( X91 @ X95 @ X94 ) @ X93 ) ) )
& ! [X96: term] :
( ( ( X88 @ ( sub @ X89 @ ( push @ X96 @ id ) ) )
= $true )
| ( ( X88 @ X96 )
!= $true ) )
& ( ( X88 @ ( lam @ X89 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
( ( sP51 = $true )
<=> ! [X97: subst > term > subst > $o,X98: term] :
( ? [X103: subst,X104: subst,X105: subst,X106: term] :
( ( ( X97 @ ( comp @ X103 @ X104 ) @ ( sub @ X106 @ X104 ) @ X105 )
= $true )
& ( ( X97 @ X103 @ X106 @ ( comp @ X104 @ X105 ) )
!= $true ) )
| ( ( sP49 @ X97 )
= $true )
| ? [X99: subst,X100: subst,X101: term,X102: subst] :
( ( ( X97 @ X99 @ X101 @ ( comp @ X102 @ X100 ) )
= $true )
& ( ( X97 @ ( comp @ X99 @ X102 ) @ ( sub @ X101 @ X102 ) @ X100 )
!= $true ) )
| ( ( sP48 @ X97 )
= $true )
| ? [X109: term] :
( ( ( var @ ( sub @ X109 @ id ) )
= $true )
& ( $true
!= ( X97 @ id @ X109 @ id ) ) )
| ( ( X97 @ id @ X98 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( sP52 = $true )
<=> ( ? [X76: subst > term > subst > $o] :
! [X77: term > $o] :
? [X78: term] :
( ( X76 @ id @ X78 @ id )
!= ( X77 @ X78 ) )
| ( sP51 = $true )
| ? [X86: term] :
( ( sub @ X86 @ id )
!= X86 )
| ( sP50 = $true )
| ? [X79: term > $o,X80: term] :
( ! [X84: term] :
( ( ( X79 @ ( lam @ X84 ) )
= $true )
| ? [X85: term] :
( ( ( X79 @ ( sub @ X84 @ ( push @ X85 @ id ) ) )
!= $true )
& ( ( X79 @ X85 )
= $true ) ) )
& ( ( sP47 @ X79 )
= $true )
& ! [X83: term] :
( ( ( var @ X83 )
!= $true )
| ( ( X79 @ X83 )
= $true ) )
& ( ( X79 @ X80 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
( ( $true = sP53 )
<=> ! [X375: subst > term > subst > $o,X376: term] :
( ( ( X375 @ id @ ( lam @ X376 ) @ id )
= $true )
| ? [X377: term] :
( ( $true
= ( X375 @ id @ X377 @ id ) )
& ( ( X375 @ id @ ( sub @ X376 @ ( push @ X377 @ id ) ) @ id )
!= $true ) )
| ? [X378: subst > term > term] :
( ! [X380: subst,X381: subst,X382: term] :
( ( sub @ ( X378 @ X380 @ X382 ) @ X381 )
= ( X378 @ ( comp @ X380 @ X381 ) @ ( sub @ X382 @ X381 ) ) )
& ( ( X375 @ id @ ( lam @ ( X378 @ sh @ one ) ) @ id )
!= $true )
& ! [X379: term] :
( ( ( X375 @ id @ X379 @ id )
!= $true )
| ( ( X375 @ id @ ( X378 @ id @ X379 ) @ id )
= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
( ( sP54 = $true )
<=> ! [X421: subst > term > subst > $o,X422: term] :
( ? [X428: term] :
( ( ( X421 @ id @ ( sub @ X422 @ ( push @ X428 @ id ) ) @ id )
!= $true )
& ( ( X421 @ id @ X428 @ id )
= $true ) )
| ? [X423: subst > term > term] :
( ! [X424: term] :
( ( ( X421 @ id @ X424 @ id )
!= $true )
| ( ( X421 @ id @ ( X423 @ id @ X424 ) @ id )
= $true ) )
& ! [X425: term,X426: subst,X427: subst] :
( ( sub @ ( X423 @ X427 @ X425 ) @ X426 )
= ( X423 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) ) )
& ( ( X421 @ id @ ( lam @ ( X423 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X421 @ id @ ( lam @ ( sub @ X422 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
! [X178: subst > term > subst > $o] :
( ( ( sP55 @ X178 )
= $true )
<=> ? [X186: subst > term > term] :
( ( ( X178 @ id @ ( lam @ ( X186 @ sh @ one ) ) @ id )
!= $true )
& ! [X188: term,X189: subst,X190: subst] :
( ( X186 @ ( comp @ X189 @ X190 ) @ ( sub @ X188 @ X190 ) )
= ( sub @ ( X186 @ X189 @ X188 ) @ X190 ) )
& ! [X187: term] :
( ( ( X178 @ id @ ( X186 @ id @ X187 ) @ id )
= $true )
| ( ( X178 @ id @ X187 @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( sP56 = $true )
<=> ( ! [X178: subst > term > subst > $o,X179: term,X180: term > $o] :
( ( ( sP55 @ X178 )
= $true )
| ( ( X180 @ ( lam @ X179 ) )
= $true )
| ? [X195: term] :
( ( X180 @ X195 )
!= ( X178 @ id @ X195 @ id ) )
| ? [X191: subst,X192: term,X193: subst,X194: subst] :
( ( $true
!= ( X178 @ X191 @ X192 @ ( comp @ X193 @ X194 ) ) )
& ( ( X178 @ ( comp @ X191 @ X193 ) @ ( sub @ X192 @ X193 ) @ X194 )
= $true ) )
| ? [X181: subst,X182: subst,X183: subst,X184: term] :
( ( ( X178 @ X183 @ X184 @ ( comp @ X182 @ X181 ) )
= $true )
& ( ( X178 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) @ X181 )
!= $true ) )
| ? [X185: term] :
( ( ( X180 @ X185 )
= $true )
& ( ( X180 @ ( sub @ X179 @ ( push @ X185 @ id ) ) )
!= $true ) ) )
| ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
! [X356: subst > term > subst > $o] :
( ( ( sP57 @ X356 )
= $true )
<=> ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
& ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) )
& ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( sP58 = $true )
<=> ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ? [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
!= $true )
& ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
= $true ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ( ( sP57 @ X356 )
= $true )
| ? [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
= $true )
& ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
!= $true ) )
| ? [X359: term] :
( ( X357 @ X359 )
!= ( X356 @ id @ X359 @ id ) )
| ? [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
!= $true )
& ( $true
= ( X357 @ X364 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X34: term] :
? [X35: subst > term > term] :
! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
<=> ( apinj1 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ? [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
!= $true )
& ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
= $true ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
& ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) )
& ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
= $true )
& ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
!= $true ) )
| ? [X359: term] :
( ( X357 @ X359 )
!= ( X356 @ id @ X359 @ id ) )
| ? [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
!= $true )
& ( $true
= ( X357 @ X364 ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
= ( ap @ X59 @ X57 ) )
& ( X57 != X58 ) )
| ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) ) ) )
& ( axapp = $true )
& ( induction2_gthm = $true )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( termmset_lthm = $true )
<=> ( ! [X418: term] :
( ( sub @ X418 @ id )
= X418 )
| ? [X417: term] :
( ( sub @ X417 @ id )
!= X417 ) ) )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X483: term] :
? [X484: subst > term > term] :
! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X178: subst > term > subst > $o,X179: term,X180: term > $o] :
( ? [X186: subst > term > term] :
( ( ( X178 @ id @ ( lam @ ( X186 @ sh @ one ) ) @ id )
!= $true )
& ! [X188: term,X189: subst,X190: subst] :
( ( X186 @ ( comp @ X189 @ X190 ) @ ( sub @ X188 @ X190 ) )
= ( sub @ ( X186 @ X189 @ X188 ) @ X190 ) )
& ! [X187: term] :
( ( ( X178 @ id @ ( X186 @ id @ X187 ) @ id )
= $true )
| ( ( X178 @ id @ X187 @ id )
!= $true ) ) )
| ( ( X180 @ ( lam @ X179 ) )
= $true )
| ? [X195: term] :
( ( X180 @ X195 )
!= ( X178 @ id @ X195 @ id ) )
| ? [X191: subst,X192: term,X193: subst,X194: subst] :
( ( $true
!= ( X178 @ X191 @ X192 @ ( comp @ X193 @ X194 ) ) )
& ( ( X178 @ ( comp @ X191 @ X193 ) @ ( sub @ X192 @ X193 ) @ X194 )
= $true ) )
| ? [X181: subst,X182: subst,X183: subst,X184: term] :
( ( ( X178 @ X183 @ X184 @ ( comp @ X182 @ X181 ) )
= $true )
& ( ( X178 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) @ X181 )
!= $true ) )
| ? [X185: term] :
( ( ( X180 @ X185 )
= $true )
& ( ( X180 @ ( sub @ X179 @ ( push @ X185 @ id ) ) )
!= $true ) ) )
| ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 ) ) )
& ( ulamvarind = $true )
& ( ! [X421: subst > term > subst > $o,X422: term] :
( ? [X428: term] :
( ( ( X421 @ id @ ( sub @ X422 @ ( push @ X428 @ id ) ) @ id )
!= $true )
& ( ( X421 @ id @ X428 @ id )
= $true ) )
| ? [X423: subst > term > term] :
( ! [X424: term] :
( ( ( X421 @ id @ X424 @ id )
!= $true )
| ( ( X421 @ id @ ( X423 @ id @ X424 ) @ id )
= $true ) )
& ! [X425: term,X426: subst,X427: subst] :
( ( sub @ ( X423 @ X427 @ X425 ) @ X426 )
= ( X423 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) ) )
& ( ( X421 @ id @ ( lam @ ( X423 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X421 @ id @ ( lam @ ( sub @ X422 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X311: subst > term > subst > $o] :
? [X312: term > $o] :
! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
? [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
= ( X29 @ sh @ one ) ) )
& ( pushprop_lem3v2 = $true )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X375: subst > term > subst > $o,X376: term] :
( ( ( X375 @ id @ ( lam @ X376 ) @ id )
= $true )
| ? [X377: term] :
( ( $true
= ( X375 @ id @ X377 @ id ) )
& ( ( X375 @ id @ ( sub @ X376 @ ( push @ X377 @ id ) ) @ id )
!= $true ) )
| ? [X378: subst > term > term] :
( ! [X380: subst,X381: subst,X382: term] :
( ( sub @ ( X378 @ X380 @ X382 ) @ X381 )
= ( X378 @ ( comp @ X380 @ X381 ) @ ( sub @ X382 @ X381 ) ) )
& ( ( X375 @ id @ ( lam @ ( X378 @ sh @ one ) ) @ id )
!= $true )
& ! [X379: term] :
( ( ( X375 @ id @ X379 @ id )
!= $true )
| ( ( X375 @ id @ ( X378 @ id @ X379 ) @ id )
= $true ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasapinj2_gthm = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ? [X76: subst > term > subst > $o] :
! [X77: term > $o] :
? [X78: term] :
( ( X76 @ id @ X78 @ id )
!= ( X77 @ X78 ) )
| ! [X97: subst > term > subst > $o,X98: term] :
( ? [X103: subst,X104: subst,X105: subst,X106: term] :
( ( ( X97 @ ( comp @ X103 @ X104 ) @ ( sub @ X106 @ X104 ) @ X105 )
= $true )
& ( ( X97 @ X103 @ X106 @ ( comp @ X104 @ X105 ) )
!= $true ) )
| ? [X107: term,X108: term] :
( ( ( X97 @ id @ X107 @ id )
= $true )
& ( ( X97 @ id @ X108 @ id )
= $true )
& ( ( X97 @ id @ ( ap @ ( sub @ X108 @ id ) @ X107 ) @ id )
!= $true ) )
| ? [X99: subst,X100: subst,X101: term,X102: subst] :
( ( ( X97 @ X99 @ X101 @ ( comp @ X102 @ X100 ) )
= $true )
& ( ( X97 @ ( comp @ X99 @ X102 ) @ ( sub @ X101 @ X102 ) @ X100 )
!= $true ) )
| ? [X110: subst > term > term] :
( ! [X111: subst,X112: term,X113: subst] :
( ( X110 @ ( comp @ X113 @ X111 ) @ ( sub @ X112 @ X111 ) )
= ( sub @ ( X110 @ X113 @ X112 ) @ X111 ) )
& ! [X114: term] :
( ( ( X97 @ id @ ( X110 @ id @ X114 ) @ id )
= $true )
| ( ( X97 @ id @ X114 @ id )
!= $true ) )
& ( ( X97 @ id @ ( lam @ ( X110 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X109: term] :
( ( ( var @ ( sub @ X109 @ id ) )
= $true )
& ( $true
!= ( X97 @ id @ X109 @ id ) ) )
| ( ( X97 @ id @ X98 @ id )
= $true ) )
| ? [X86: term] :
( ( sub @ X86 @ id )
!= X86 )
| ? [X87: subst > term > subst > $o,X88: term > $o,X89: term] :
( ! [X90: term] :
( ( X87 @ id @ X90 @ id )
= ( X88 @ X90 ) )
& ! [X91: subst > term > term] :
( ( ( X87 @ id @ ( lam @ ( X91 @ sh @ one ) ) @ id )
= $true )
| ? [X92: term] :
( ( $true
!= ( X87 @ id @ ( X91 @ id @ X92 ) @ id ) )
& ( ( X87 @ id @ X92 @ id )
= $true ) )
| ? [X93: subst,X94: term,X95: subst] :
( ( X91 @ ( comp @ X95 @ X93 ) @ ( sub @ X94 @ X93 ) )
!= ( sub @ ( X91 @ X95 @ X94 ) @ X93 ) ) )
& ! [X96: term] :
( ( ( X88 @ ( sub @ X89 @ ( push @ X96 @ id ) ) )
= $true )
| ( ( X88 @ X96 )
!= $true ) )
& ( ( X88 @ ( lam @ X89 ) )
!= $true ) )
| ? [X79: term > $o,X80: term] :
( ! [X84: term] :
( ( ( X79 @ ( lam @ X84 ) )
= $true )
| ? [X85: term] :
( ( ( X79 @ ( sub @ X84 @ ( push @ X85 @ id ) ) )
!= $true )
& ( ( X79 @ X85 )
= $true ) ) )
& ! [X81: term,X82: term] :
( ( $true
!= ( X79 @ X82 ) )
| ( ( X79 @ ( ap @ X82 @ X81 ) )
= $true )
| ( ( X79 @ X81 )
!= $true ) )
& ! [X83: term] :
( ( ( var @ X83 )
!= $true )
| ( ( X79 @ X83 )
= $true ) )
& ( ( X79 @ X80 )
!= $true ) ) ) )
& ( ( induction2_lthm = $true )
<=> ( ? [X496: term] :
( ( sub @ X496 @ id )
!= X496 )
| ! [X505: term > $o,X506: term] :
( ? [X507: term] :
( ! [X508: term] :
( ( ( X505 @ X508 )
!= $true )
| ( ( X505 @ ( sub @ X507 @ ( push @ X508 @ id ) ) )
= $true ) )
& ( $true
!= ( X505 @ ( lam @ X507 ) ) ) )
| ? [X511: term] :
( ( ( var @ X511 )
= $true )
& ( ( X505 @ X511 )
!= $true ) )
| ? [X509: term,X510: term] :
( ( ( X505 @ X510 )
= $true )
& ( ( X505 @ X509 )
= $true )
& ( ( X505 @ ( ap @ X509 @ X510 ) )
!= $true ) )
| ( $true
= ( X505 @ X506 ) ) )
| ? [X497: term > $o,X498: subst,X499: term] :
( ! [X502: term] :
( ( ( X497 @ ( lam @ X502 ) )
= $true )
| ? [X503: term] :
( ( ( X497 @ X503 )
= $true )
& ( ( X497 @ ( sub @ X502 @ ( push @ X503 @ id ) ) )
!= $true ) ) )
& ! [X500: term,X501: term] :
( ( ( X497 @ X501 )
!= $true )
| ( ( X497 @ X500 )
!= $true )
| ( ( X497 @ ( ap @ X500 @ X501 ) )
= $true ) )
& ( ( X497 @ ( sub @ X499 @ X498 ) )
!= $true )
& ! [X504: term] :
( ( $true
= ( X497 @ ( sub @ X504 @ X498 ) ) )
| ( ( var @ X504 )
!= $true ) ) ) ) )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ? [X491: subst > term > term] :
( ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X488 @ id @ X487 @ id )
= $true )
| ? [X489: term,X490: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( ap @ ( sub @ X489 @ id ) @ X490 ) @ id )
!= $true )
& ( ( X488 @ id @ X490 @ id )
= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( ( pushprop_lem0 = $true )
<=> ! [X456: subst,X457: term > $o,X458: term] :
? [X459: term > $o] :
! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( pushprop = $true )
& ( ( ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) )
| ? [X5: term] :
( ( sub @ X5 @ id )
!= X5 )
| ? [X6: term,X7: term,X8: term,X9: term] :
( ( X8 != X9 )
& ( ( ap @ X8 @ X6 )
= ( ap @ X9 @ X7 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X38: subst > term > subst > $o,X39: term] :
( ( ( X38 @ id @ ( lam @ X39 ) @ id )
= $true )
| ? [X44: subst,X45: subst,X46: subst,X47: term] :
( ( ( X38 @ ( comp @ X44 @ X46 ) @ ( sub @ X47 @ X46 ) @ X45 )
= $true )
& ( ( X38 @ X44 @ X47 @ ( comp @ X46 @ X45 ) )
!= $true ) )
| ? [X49: subst > term > term] :
( ! [X53: term] :
( ( ( X38 @ id @ X53 @ id )
!= $true )
| ( ( X38 @ id @ ( X49 @ id @ X53 ) @ id )
= $true ) )
& ! [X50: subst,X51: subst,X52: term] :
( ( X49 @ ( comp @ X50 @ X51 ) @ ( sub @ X52 @ X51 ) )
= ( sub @ ( X49 @ X50 @ X52 ) @ X51 ) )
& ( ( X38 @ id @ ( lam @ ( X49 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X40: term,X41: subst,X42: subst,X43: subst] :
( ( $true
!= ( X38 @ ( comp @ X42 @ X43 ) @ ( sub @ X40 @ X43 ) @ X41 ) )
& ( ( X38 @ X42 @ X40 @ ( comp @ X43 @ X41 ) )
= $true ) )
| ? [X48: term] :
( ( ( X38 @ id @ ( sub @ X39 @ ( push @ X48 @ id ) ) @ id )
!= $true )
& ( $true
= ( X38 @ id @ X48 @ id ) ) ) ) )
& ( ! [X149: term > $o,X150: term] :
( ? [X154: term] :
( ( ( X149 @ X154 )
!= $true )
& ( ( var @ X154 )
= $true ) )
| ? [X151: term,X152: term] :
( ( ( X149 @ ( ap @ X152 @ X151 ) )
!= $true )
& ( $true
= ( X149 @ X151 ) )
& ( ( X149 @ X152 )
= $true ) )
| ( ( X149 @ X150 )
= $true )
| ? [X153: term] :
( ( ( X149 @ X153 )
= $true )
& ( ( X149 @ ( lam @ X153 ) )
!= $true ) ) )
<=> ( induction = $true ) )
& ( hoasinduction_gthm = $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction = $true )
<=> ! [X465: term,X466: subst > term > subst > $o] :
( ( ( X466 @ id @ X465 @ id )
= $true )
| ? [X472: subst > term > term] :
( ! [X476: term] :
( ( ( X466 @ id @ X476 @ id )
!= $true )
| ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true ) )
& ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
!= $true )
& ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) ) )
| ? [X468: term,X469: subst,X470: subst,X471: subst] :
( ( ( X466 @ X470 @ X468 @ ( comp @ X471 @ X469 ) )
= $true )
& ( ( X466 @ ( comp @ X470 @ X471 ) @ ( sub @ X468 @ X471 ) @ X469 )
!= $true ) )
| ? [X481: term,X482: term] :
( ( ( X466 @ id @ X481 @ id )
= $true )
& ( $true
= ( X466 @ id @ X482 @ id ) )
& ( ( X466 @ id @ ( ap @ ( sub @ X482 @ id ) @ X481 ) @ id )
!= $true ) )
| ? [X467: term] :
( ( $true
!= ( X466 @ id @ X467 @ id ) )
& ( ( var @ ( sub @ X467 @ id ) )
= $true ) )
| ? [X477: subst,X478: subst,X479: subst,X480: term] :
( ( $true
= ( X466 @ ( comp @ X479 @ X478 ) @ ( sub @ X480 @ X478 ) @ X477 ) )
& ( $true
!= ( X466 @ X479 @ X480 @ ( comp @ X478 @ X477 ) ) ) ) ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
<=> ( substmonoid = $true ) )
& ( axclos = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X415: term] :
? [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
= ( X416 @ sh @ one ) ) )
& ( ulamvar1 != $true )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X14: term > $o,X15: term,X16: subst] :
? [X17: term > $o] :
! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) ) )
& ( ulamvarsh = $true )
& ( ( laminj = $true )
<=> ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ! [X199: d_term,X200: d_term] :
( ( X199 = X200 )
| ( ( d2term @ X200 )
!= ( d2term @ X199 ) ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ! [X271: term,X272: term > $o,X273: subst > term > subst > $o,X274: term] :
( ? [X282: subst,X283: term,X284: subst,X285: subst] :
( ( ( X273 @ ( comp @ X285 @ X282 ) @ ( sub @ X283 @ X282 ) @ X284 )
= $true )
& ( ( X273 @ X285 @ X283 @ ( comp @ X282 @ X284 ) )
!= $true ) )
| ? [X280: term,X281: term] :
( ( ( X273 @ id @ ( ap @ ( sub @ X281 @ id ) @ X280 ) @ id )
!= $true )
& ( ( X273 @ id @ X281 @ id )
= $true )
& ( ( X273 @ id @ X280 @ id )
= $true ) )
| ( $true
!= ( X272 @ X274 ) )
| ( ( X272 @ X271 )
!= $true )
| ( ( X272 @ ( ap @ X274 @ X271 ) )
= $true )
| ? [X275: term] :
( ( X272 @ X275 )
!= ( X273 @ id @ X275 @ id ) )
| ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( ( X273 @ ( comp @ X276 @ X278 ) @ ( sub @ X279 @ X278 ) @ X277 )
!= $true )
& ( ( X273 @ X276 @ X279 @ ( comp @ X278 @ X277 ) )
= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X512: subst > term > subst > $o,X513: term > $o,X514: term] :
( ? [X515: term] :
( ( X513 @ X515 )
!= ( X512 @ id @ X515 @ id ) )
| ? [X516: subst > term > term] :
( ( ( X512 @ id @ ( lam @ ( X516 @ sh @ one ) ) @ id )
!= $true )
& ! [X517: subst,X518: subst,X519: term] :
( ( sub @ ( X516 @ X518 @ X519 ) @ X517 )
= ( X516 @ ( comp @ X518 @ X517 ) @ ( sub @ X519 @ X517 ) ) )
& ! [X520: term] :
( ( ( X512 @ id @ X520 @ id )
!= $true )
| ( ( X512 @ id @ ( X516 @ id @ X520 ) @ id )
= $true ) ) )
| ( $true
= ( X513 @ ( lam @ X514 ) ) )
| ? [X521: term] :
( ( ( X513 @ ( sub @ X514 @ ( push @ X521 @ id ) ) )
!= $true )
& ( ( X513 @ X521 )
= $true ) ) ) )
& ( ( ? [X145: subst] :
( ( comp @ id @ X145 )
!= X145 )
| ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ! [X442: term,X443: subst > term > subst > $o] :
( ( ( X443 @ id @ ( lam @ ( sub @ X442 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X444: term] :
( ( ( X443 @ id @ ( sub @ X442 @ ( push @ X444 @ id ) ) @ id )
!= $true )
& ( ( X443 @ id @ X444 @ id )
= $true ) )
| ? [X445: subst > term > term] :
( ! [X446: subst,X447: term,X448: subst] :
( ( sub @ ( X445 @ X446 @ X447 ) @ X448 )
= ( X445 @ ( comp @ X446 @ X448 ) @ ( sub @ X447 @ X448 ) ) )
& ! [X449: term] :
( ( ( X443 @ id @ X449 @ id )
!= $true )
| ( ( X443 @ id @ ( X445 @ id @ X449 ) @ id )
= $true ) )
& ( ( X443 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( ! [X253: subst > term > subst > $o,X254: term] :
( ? [X259: term,X260: term] :
( ( $true
!= ( X253 @ id @ ( ap @ ( sub @ X259 @ id ) @ X260 ) @ id ) )
& ( ( X253 @ id @ X260 @ id )
= $true )
& ( ( X253 @ id @ X259 @ id )
= $true ) )
| ? [X266: subst,X267: subst,X268: term,X269: subst] :
( ( ( X253 @ X267 @ X268 @ ( comp @ X269 @ X266 ) )
!= $true )
& ( ( X253 @ ( comp @ X267 @ X269 ) @ ( sub @ X268 @ X269 ) @ X266 )
= $true ) )
| ( ( X253 @ id @ X254 @ id )
= $true )
| ? [X255: subst,X256: term,X257: subst,X258: subst] :
( ( ( X253 @ ( comp @ X258 @ X257 ) @ ( sub @ X256 @ X257 ) @ X255 )
!= $true )
& ( $true
= ( X253 @ X258 @ X256 @ ( comp @ X257 @ X255 ) ) ) )
| ? [X270: term] :
( ( $true
= ( var @ ( sub @ X270 @ id ) ) )
& ( ( X253 @ id @ X270 @ id )
!= $true ) )
| ? [X261: subst > term > term] :
( ( ( X253 @ id @ ( lam @ ( X261 @ sh @ one ) ) @ id )
!= $true )
& ! [X262: term] :
( ( $true
!= ( X253 @ id @ X262 @ id ) )
| ( $true
= ( X253 @ id @ ( X261 @ id @ X262 ) @ id ) ) )
& ! [X263: term,X264: subst,X265: subst] :
( ( X261 @ ( comp @ X265 @ X264 ) @ ( sub @ X263 @ X264 ) )
= ( sub @ ( X261 @ X265 @ X263 ) @ X264 ) ) ) )
| ? [X224: subst > term > subst > $o,X225: term,X226: term] :
( ! [X233: subst,X234: term,X235: subst,X236: subst] :
( ( ( X224 @ X235 @ X234 @ ( comp @ X233 @ X236 ) )
!= $true )
| ( ( X224 @ ( comp @ X235 @ X233 ) @ ( sub @ X234 @ X233 ) @ X236 )
= $true ) )
& ! [X229: term,X230: subst,X231: subst,X232: subst] :
( ( ( X224 @ X230 @ X229 @ ( comp @ X231 @ X232 ) )
= $true )
| ( ( X224 @ ( comp @ X230 @ X231 ) @ ( sub @ X229 @ X231 ) @ X232 )
!= $true ) )
& ( ( X224 @ id @ X226 @ id )
= $true )
& ( ( X224 @ id @ X225 @ id )
= $true )
& ! [X227: term,X228: term] :
( ( ( X224 @ id @ X228 @ id )
!= $true )
| ( ( X224 @ id @ ( ap @ ( sub @ X227 @ id ) @ X228 ) @ id )
= $true )
| ( ( X224 @ id @ X227 @ id )
!= $true ) )
& ( $true
!= ( X224 @ id @ ( ap @ X225 @ X226 ) @ id ) ) )
| ? [X237: term,X238: subst > term > subst > $o] :
( ( ( X238 @ id @ ( lam @ X237 ) @ id )
!= $true )
& ! [X247: subst > term > term] :
( ( ( X238 @ id @ ( lam @ ( X247 @ sh @ one ) ) @ id )
= $true )
| ? [X248: term] :
( ( ( X238 @ id @ ( X247 @ id @ X248 ) @ id )
!= $true )
& ( $true
= ( X238 @ id @ X248 @ id ) ) )
| ? [X249: subst,X250: subst,X251: term] :
( ( X247 @ ( comp @ X249 @ X250 ) @ ( sub @ X251 @ X250 ) )
!= ( sub @ ( X247 @ X249 @ X251 ) @ X250 ) ) )
& ! [X243: subst,X244: subst,X245: term,X246: subst] :
( ( ( X238 @ ( comp @ X244 @ X243 ) @ ( sub @ X245 @ X243 ) @ X246 )
= $true )
| ( ( X238 @ X244 @ X245 @ ( comp @ X243 @ X246 ) )
!= $true ) )
& ! [X252: term] :
( ( ( X238 @ id @ ( sub @ X237 @ ( push @ X252 @ id ) ) @ id )
= $true )
| ( ( X238 @ id @ X252 @ id )
!= $true ) )
& ! [X239: subst,X240: term,X241: subst,X242: subst] :
( ( ( X238 @ ( comp @ X241 @ X242 ) @ ( sub @ X240 @ X242 ) @ X239 )
!= $true )
| ( ( X238 @ X241 @ X240 @ ( comp @ X242 @ X239 ) )
= $true ) ) )
| ? [X217: term > $o,X218: term] :
( ! [X222: term,X223: term] :
( ( ( X217 @ ( ap @ X222 @ X223 ) )
= $true )
| ( ( X217 @ X222 )
!= $true )
| ( ( X217 @ X223 )
!= $true ) )
& ! [X219: term] :
( ( ( X217 @ X219 )
= $true )
| ( ( var @ X219 )
!= $true ) )
& ! [X220: term] :
( ( ( X217 @ ( lam @ X220 ) )
= $true )
| ? [X221: term] :
( ( ( X217 @ ( sub @ X220 @ ( push @ X221 @ id ) ) )
!= $true )
& ( ( X217 @ X221 )
= $true ) ) )
& ( ( X217 @ X218 )
!= $true ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X390: subst,X391: subst > term > term,X392: term,X393: subst > term > term] :
( ? [X394: subst,X395: term,X396: subst] :
( ( X393 @ ( comp @ X396 @ X394 ) @ ( sub @ X395 @ X394 ) )
!= ( sub @ ( X393 @ X396 @ X395 ) @ X394 ) )
| ( ( lam @ ( X391 @ sh @ one ) )
!= ( lam @ ( X393 @ sh @ one ) ) )
| ( ( X391 @ X390 @ X392 )
= ( X393 @ X390 @ X392 ) )
| ? [X397: subst,X398: term,X399: subst] :
( ( X391 @ ( comp @ X397 @ X399 ) @ ( sub @ X398 @ X399 ) )
!= ( sub @ ( X391 @ X397 @ X398 ) @ X399 ) ) )
| ? [X386: subst,X387: term] :
( ( comp @ sh @ ( push @ X387 @ X386 ) )
!= X386 )
| ? [X384: term,X385: subst] :
( ( sub @ one @ ( push @ X384 @ X385 ) )
!= X384 )
| ? [X388: term,X389: term] :
( ( ( lam @ X389 )
= ( lam @ X388 ) )
& ( X388 != X389 ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( shinj = $true )
<=> ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) ) )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
<=> ( termmset = $true ) )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ? [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
!= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
| ? [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
!= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) )
<=> ( hoaslaminj = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( ( induction2 = $true )
<=> ! [X400: term > $o,X401: term] :
( ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( ( X400 @ X404 )
!= $true ) )
| ? [X405: term] :
( ( ( X400 @ ( lam @ X405 ) )
!= $true )
& ! [X406: term] :
( ( ( X400 @ ( sub @ X405 @ ( push @ X406 @ id ) ) )
= $true )
| ( ( X400 @ X406 )
!= $true ) ) )
| ? [X402: term,X403: term] :
( ( ( X400 @ X403 )
= $true )
& ( $true
!= ( X400 @ ( ap @ X403 @ X402 ) ) )
& ( ( X400 @ X402 )
= $true ) )
| ( ( X400 @ X401 )
= $true ) ) )
& ( pushprop_lem0_gthm = $true )
& ( lamnotap != $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
<=> ( axscons = $true ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ? [X287: term,X288: subst > term > subst > $o] :
( ! [X294: term] :
( ( ( X288 @ id @ X294 @ id )
!= $true )
| ( $true
= ( X288 @ id @ ( sub @ X287 @ ( push @ X294 @ id ) ) @ id ) ) )
& ! [X289: subst > term > term] :
( ? [X290: term] :
( ( $true
= ( X288 @ id @ X290 @ id ) )
& ( ( X288 @ id @ ( X289 @ id @ X290 ) @ id )
!= $true ) )
| ( $true
= ( X288 @ id @ ( lam @ ( X289 @ sh @ one ) ) @ id ) )
| ? [X291: term,X292: subst,X293: subst] :
( ( sub @ ( X289 @ X292 @ X291 ) @ X293 )
!= ( X289 @ ( comp @ X292 @ X293 ) @ ( sub @ X291 @ X293 ) ) ) )
& ( ( X288 @ id @ ( lam @ ( sub @ X287 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) )
| ? [X286: term] :
( ( sub @ X286 @ id )
!= X286 )
| ! [X295: subst > term > subst > $o,X296: term] :
( ? [X307: subst,X308: subst,X309: subst,X310: term] :
( ( ( X295 @ X307 @ X310 @ ( comp @ X308 @ X309 ) )
= $true )
& ( ( X295 @ ( comp @ X307 @ X308 ) @ ( sub @ X310 @ X308 ) @ X309 )
!= $true ) )
| ? [X301: subst > term > term] :
( ! [X302: subst,X303: subst,X304: term] :
( ( X301 @ ( comp @ X303 @ X302 ) @ ( sub @ X304 @ X302 ) )
= ( sub @ ( X301 @ X303 @ X304 ) @ X302 ) )
& ( $true
!= ( X295 @ id @ ( lam @ ( X301 @ sh @ one ) ) @ id ) )
& ! [X305: term] :
( ( ( X295 @ id @ ( X301 @ id @ X305 ) @ id )
= $true )
| ( ( X295 @ id @ X305 @ id )
!= $true ) ) )
| ? [X297: subst,X298: subst,X299: subst,X300: term] :
( ( $true
= ( X295 @ ( comp @ X297 @ X298 ) @ ( sub @ X300 @ X298 ) @ X299 ) )
& ( ( X295 @ X297 @ X300 @ ( comp @ X298 @ X299 ) )
!= $true ) )
| ? [X306: term] :
( ( ( X295 @ id @ X306 @ id )
= $true )
& ( ( X295 @ id @ ( sub @ X296 @ ( push @ X306 @ id ) ) @ id )
!= $true ) )
| ( ( X295 @ id @ ( lam @ X296 ) @ id )
= $true ) ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( axmap = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X314: subst > term > term,X315: term,X316: term] :
( ? [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
!= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop_gthm = $true )
& ( ! [X64: term,X65: subst > term > subst > $o] :
( ? [X67: subst > term > term,X68: term] :
( ! [X72: subst,X73: term,X74: subst] :
( ( X67 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) )
= ( sub @ X68 @ ( push @ ( sub @ X73 @ X74 ) @ ( comp @ X72 @ X74 ) ) ) )
& ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
!= $true )
& ! [X69: subst,X70: subst,X71: term] :
( ( sub @ ( sub @ X68 @ ( push @ X71 @ X69 ) ) @ X70 )
= ( sub @ ( X67 @ X69 @ X71 ) @ X70 ) )
& ! [X75: term] :
( ( ( X65 @ id @ X75 @ id )
!= $true )
| ( ( X65 @ id @ ( X67 @ id @ X75 ) @ id )
= $true ) ) )
| ( ( X65 @ id @ ( lam @ ( sub @ X64 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X66: term] :
( ( ( X65 @ id @ ( sub @ X64 @ ( push @ X66 @ id ) ) @ id )
!= $true )
& ( ( X65 @ id @ X66 @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ! [X532: term,X533: subst,X534: term > $o] :
( ( ( X534 @ ( sub @ X532 @ X533 ) )
= $true )
| ? [X537: term] :
( ( ( X534 @ ( sub @ X537 @ X533 ) )
!= $true )
& ( ( var @ X537 )
= $true ) )
| ? [X535: term] :
( ! [X536: term] :
( ( ( X534 @ X536 )
!= $true )
| ( ( X534 @ ( sub @ X535 @ ( push @ X536 @ id ) ) )
= $true ) )
& ( ( X534 @ ( lam @ X535 ) )
!= $true ) )
| ? [X538: term,X539: term] :
( ( ( X534 @ X538 )
= $true )
& ( ( X534 @ X539 )
= $true )
& ( ( X534 @ ( ap @ X538 @ X539 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ? [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ ( lam @ ( sub @ X322 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X323: term] :
( ( ( X321 @ id @ ( sub @ X322 @ ( push @ X323 @ id ) ) @ id )
= $true )
| ( $true
!= ( X321 @ id @ X323 @ id ) ) )
& ! [X324: subst > term > term] :
( ? [X328: term] :
( ( $true
!= ( X321 @ id @ ( X324 @ id @ X328 ) @ id ) )
& ( ( X321 @ id @ X328 @ id )
= $true ) )
| ( ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id )
= $true )
| ? [X325: subst,X326: subst,X327: term] :
( ( X324 @ ( comp @ X325 @ X326 ) @ ( sub @ X327 @ X326 ) )
!= ( sub @ ( X324 @ X325 @ X327 ) @ X326 ) ) ) )
| ! [X329: subst > term > subst > $o,X330: term] :
( ? [X331: term] :
( ( $true
!= ( X329 @ id @ ( sub @ X330 @ ( push @ X331 @ id ) ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( ( X329 @ id @ ( lam @ X330 ) @ id )
= $true )
| ? [X332: subst > term > term] :
( ! [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
| ( ( X329 @ id @ ( X332 @ id @ X336 ) @ id )
= $true ) )
& ( ( X329 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id )
!= $true )
& ! [X333: subst,X334: term,X335: subst] :
( ( X332 @ ( comp @ X333 @ X335 ) @ ( sub @ X334 @ X335 ) )
= ( sub @ ( X332 @ X333 @ X334 ) @ X335 ) ) ) )
| ? [X320: term] :
( ( sub @ X320 @ id )
!= X320 ) ) )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ? [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
!= ( X0 @ X4 ) )
| ( ( X0 @ one )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( axidr = $true )
<=> ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 ) )
& ( pushprop_lthm_orig = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ? [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
!= X19 )
| ? [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
!= X21 )
| ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) ) ) )
& ( ! [X201: subst > term > subst > $o] :
? [X202: term > $o] :
! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( ! [X136: subst > term > subst > $o,X137: term] :
( ? [X143: term,X144: term] :
( ( ( X136 @ id @ ( ap @ ( sub @ X144 @ id ) @ X143 ) @ id )
!= $true )
& ( ( X136 @ id @ X143 @ id )
= $true )
& ( ( X136 @ id @ X144 @ id )
= $true ) )
| ? [X138: subst > term > term] :
( ! [X139: term] :
( ( ( X136 @ id @ ( X138 @ id @ X139 ) @ id )
= $true )
| ( ( X136 @ id @ X139 @ id )
!= $true ) )
& ( ( X136 @ id @ ( lam @ ( X138 @ sh @ one ) ) @ id )
!= $true )
& ! [X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X142 @ X141 ) @ ( sub @ X140 @ X141 ) )
= ( sub @ ( X138 @ X142 @ X140 ) @ X141 ) ) )
| ( ( X136 @ id @ X137 @ id )
= $true ) )
| ? [X115: subst > term > subst > $o] :
! [X116: term > $o] :
? [X117: term] :
( ( X116 @ X117 )
!= ( X115 @ id @ X117 @ id ) )
| ? [X126: subst > term > subst > $o,X127: term,X128: term > $o] :
( ! [X130: term] :
( ( X126 @ id @ X130 @ id )
= ( X128 @ X130 ) )
& ! [X131: subst > term > term] :
( ( ( X126 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id )
= $true )
| ? [X132: term] :
( ( $true
= ( X126 @ id @ X132 @ id ) )
& ( ( X126 @ id @ ( X131 @ id @ X132 ) @ id )
!= $true ) )
| ? [X133: subst,X134: term,X135: subst] :
( ( X131 @ ( comp @ X133 @ X135 ) @ ( sub @ X134 @ X135 ) )
!= ( sub @ ( X131 @ X133 @ X134 ) @ X135 ) ) )
& ( ( X128 @ ( lam @ X127 ) )
!= $true )
& ! [X129: term] :
( ( ( X128 @ ( sub @ X127 @ ( push @ X129 @ id ) ) )
= $true )
| ( ( X128 @ X129 )
!= $true ) ) )
| ? [X125: term] :
( ( sub @ X125 @ id )
!= X125 )
| ? [X118: term,X119: term > $o] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X119 @ X122 )
= $true ) )
& ! [X123: term] :
( ? [X124: term] :
( ( ( X119 @ X124 )
= $true )
& ( ( X119 @ ( sub @ X123 @ ( push @ X124 @ id ) ) )
!= $true ) )
| ( ( X119 @ ( lam @ X123 ) )
= $true ) )
& ( $true
!= ( X119 @ X118 ) )
& ! [X120: term,X121: term] :
( ( ( X119 @ ( ap @ X120 @ X121 ) )
= $true )
| ( ( X119 @ X121 )
!= $true )
| ( ( X119 @ X120 )
!= $true ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 ) )
& ( axassoc = $true )
& ( hoasinduction_lem2_lthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( X54 = X55 )
| ( ( d2subst @ X55 )
!= ( d2subst @ X54 ) ) )
& ( ! [X429: term,X430: term,X431: subst > term > subst > $o] :
( ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X431 @ X436 @ X434 @ ( comp @ X435 @ X437 ) )
= $true )
& ( ( X431 @ ( comp @ X436 @ X435 ) @ ( sub @ X434 @ X435 ) @ X437 )
!= $true ) )
| ? [X438: subst,X439: term,X440: subst,X441: subst] :
( ( ( X431 @ X438 @ X439 @ ( comp @ X441 @ X440 ) )
!= $true )
& ( ( X431 @ ( comp @ X438 @ X441 ) @ ( sub @ X439 @ X441 ) @ X440 )
= $true ) )
| ( ( X431 @ id @ X429 @ id )
!= $true )
| ? [X432: term,X433: term] :
( ( ( X431 @ id @ X433 @ id )
= $true )
& ( ( X431 @ id @ X432 @ id )
= $true )
& ( ( X431 @ id @ ( ap @ ( sub @ X432 @ id ) @ X433 ) @ id )
!= $true ) )
| ( ( X431 @ id @ ( ap @ X430 @ X429 ) @ id )
= $true )
| ( $true
!= ( X431 @ id @ X430 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( axidl = $true )
<=> ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 ) )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
<=> ( axvarid = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ? [X161: term] :
( ( sub @ X161 @ id )
!= X161 )
| ? [X157: term] :
! [X158: subst > term > term] :
? [X159: term,X160: subst] :
( ( X158 @ X160 @ X159 )
!= ( sub @ X157 @ ( push @ X159 @ X160 ) ) )
| ! [X162: subst > term > subst > $o,X163: term > $o,X164: term] :
( ( ( X163 @ ( lam @ X164 ) )
= $true )
| ? [X171: term] :
( ( X163 @ X171 )
!= ( X162 @ id @ X171 @ id ) )
| ? [X165: term] :
( ( ( X163 @ ( sub @ X164 @ ( push @ X165 @ id ) ) )
!= $true )
& ( ( X163 @ X165 )
= $true ) )
| ? [X166: subst > term > term] :
( ( ( X162 @ id @ ( lam @ ( X166 @ sh @ one ) ) @ id )
!= $true )
& ! [X167: term] :
( ( ( X162 @ id @ X167 @ id )
!= $true )
| ( ( X162 @ id @ ( X166 @ id @ X167 ) @ id )
= $true ) )
& ! [X168: subst,X169: subst,X170: term] :
( ( sub @ ( X166 @ X168 @ X170 ) @ X169 )
= ( X166 @ ( comp @ X168 @ X169 ) @ ( sub @ X170 @ X169 ) ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( ( ? [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
!= X211 )
| ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ? [X216: term] :
( ( X214 @ X216 )
!= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
| ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( d2subst @ d_id )
= id )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( axabs = $true )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
<=> ( apinj2 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X348: term > $o,X349: term,X350: subst] :
( ( ( X348 @ ( sub @ X349 @ X350 ) )
= $true )
| ? [X351: term,X352: term] :
( ( ( X348 @ X351 )
= $true )
& ( ( X348 @ ( ap @ X352 @ X351 ) )
!= $true )
& ( ( X348 @ X352 )
= $true ) )
| ? [X353: term] :
( ! [X354: term] :
( ( $true
= ( X348 @ ( sub @ X353 @ ( push @ X354 @ id ) ) ) )
| ( ( X348 @ X354 )
!= $true ) )
& ( ( X348 @ ( lam @ X353 ) )
!= $true ) )
| ? [X355: term] :
( ( $true
!= ( X348 @ ( sub @ X355 @ X350 ) ) )
& ( ( var @ X355 )
= $true ) ) )
| ? [X341: subst] :
( ( comp @ X341 @ id )
!= X341 )
| ? [X342: term > $o,X343: term] :
( ( ( X342 @ X343 )
!= $true )
& ! [X346: term] :
( ( ( X342 @ X346 )
!= $true )
| ( ( X342 @ ( lam @ X346 ) )
= $true ) )
& ! [X344: term,X345: term] :
( ( ( X342 @ ( ap @ X345 @ X344 ) )
= $true )
| ( ( X342 @ X344 )
!= $true )
| ( ( X342 @ X345 )
!= $true ) )
& ! [X347: term] :
( ( $true
!= ( var @ X347 ) )
| ( ( X342 @ X347 )
= $true ) ) )
| ? [X339: term,X340: subst] :
( ( comp @ sh @ ( push @ X339 @ X340 ) )
!= X340 )
| ? [X337: subst,X338: term] :
( ( sub @ one @ ( push @ X338 @ X337 ) )
!= X338 ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lthm = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) )
| ? [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
!= X21 )
| ? [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
!= X19 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X314: subst > term > term,X315: term,X316: term] :
( ? [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
!= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ X56 @ X58 )
= ( ap @ X59 @ X57 ) )
& ( X57 != X58 ) )
| ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X162: subst > term > subst > $o,X163: term > $o,X164: term] :
( ( ( X163 @ ( lam @ X164 ) )
= $true )
| ? [X171: term] :
( ( X163 @ X171 )
!= ( X162 @ id @ X171 @ id ) )
| ? [X165: term] :
( ( ( X163 @ ( sub @ X164 @ ( push @ X165 @ id ) ) )
!= $true )
& ( ( X163 @ X165 )
= $true ) )
| ? [X166: subst > term > term] :
( ( ( X162 @ id @ ( lam @ ( X166 @ sh @ one ) ) @ id )
!= $true )
& ! [X167: term] :
( ( ( X162 @ id @ X167 @ id )
!= $true )
| ( ( X162 @ id @ ( X166 @ id @ X167 ) @ id )
= $true ) )
& ! [X168: subst,X169: subst,X170: term] :
( ( sub @ ( X166 @ X168 @ X170 ) @ X169 )
= ( X166 @ ( comp @ X168 @ X169 ) @ ( sub @ X170 @ X169 ) ) ) ) )
| ? [X161: term] :
( ( sub @ X161 @ id )
!= X161 )
| ? [X157: term] :
! [X158: subst > term > term] :
? [X159: term,X160: subst] :
( ( X158 @ X160 @ X159 )
!= ( sub @ X157 @ ( push @ X159 @ X160 ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( ? [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
!= X211 )
| ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ? [X216: term] :
( ( X214 @ X216 )
!= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) )
| ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X253: subst > term > subst > $o,X254: term] :
( ? [X259: term,X260: term] :
( ( $true
!= ( X253 @ id @ ( ap @ ( sub @ X259 @ id ) @ X260 ) @ id ) )
& ( ( X253 @ id @ X260 @ id )
= $true )
& ( ( X253 @ id @ X259 @ id )
= $true ) )
| ? [X266: subst,X267: subst,X268: term,X269: subst] :
( ( ( X253 @ X267 @ X268 @ ( comp @ X269 @ X266 ) )
!= $true )
& ( ( X253 @ ( comp @ X267 @ X269 ) @ ( sub @ X268 @ X269 ) @ X266 )
= $true ) )
| ( ( X253 @ id @ X254 @ id )
= $true )
| ? [X255: subst,X256: term,X257: subst,X258: subst] :
( ( ( X253 @ ( comp @ X258 @ X257 ) @ ( sub @ X256 @ X257 ) @ X255 )
!= $true )
& ( $true
= ( X253 @ X258 @ X256 @ ( comp @ X257 @ X255 ) ) ) )
| ? [X270: term] :
( ( $true
= ( var @ ( sub @ X270 @ id ) ) )
& ( ( X253 @ id @ X270 @ id )
!= $true ) )
| ? [X261: subst > term > term] :
( ( ( X253 @ id @ ( lam @ ( X261 @ sh @ one ) ) @ id )
!= $true )
& ! [X262: term] :
( ( $true
!= ( X253 @ id @ X262 @ id ) )
| ( $true
= ( X253 @ id @ ( X261 @ id @ X262 ) @ id ) ) )
& ! [X263: term,X264: subst,X265: subst] :
( ( X261 @ ( comp @ X265 @ X264 ) @ ( sub @ X263 @ X264 ) )
= ( sub @ ( X261 @ X265 @ X263 ) @ X264 ) ) ) )
| ? [X237: term,X238: subst > term > subst > $o] :
( ( ( X238 @ id @ ( lam @ X237 ) @ id )
!= $true )
& ! [X247: subst > term > term] :
( ( ( X238 @ id @ ( lam @ ( X247 @ sh @ one ) ) @ id )
= $true )
| ? [X248: term] :
( ( ( X238 @ id @ ( X247 @ id @ X248 ) @ id )
!= $true )
& ( $true
= ( X238 @ id @ X248 @ id ) ) )
| ? [X249: subst,X250: subst,X251: term] :
( ( X247 @ ( comp @ X249 @ X250 ) @ ( sub @ X251 @ X250 ) )
!= ( sub @ ( X247 @ X249 @ X251 ) @ X250 ) ) )
& ! [X243: subst,X244: subst,X245: term,X246: subst] :
( ( ( X238 @ ( comp @ X244 @ X243 ) @ ( sub @ X245 @ X243 ) @ X246 )
= $true )
| ( ( X238 @ X244 @ X245 @ ( comp @ X243 @ X246 ) )
!= $true ) )
& ! [X252: term] :
( ( ( X238 @ id @ ( sub @ X237 @ ( push @ X252 @ id ) ) @ id )
= $true )
| ( ( X238 @ id @ X252 @ id )
!= $true ) )
& ! [X239: subst,X240: term,X241: subst,X242: subst] :
( ( ( X238 @ ( comp @ X241 @ X242 ) @ ( sub @ X240 @ X242 ) @ X239 )
!= $true )
| ( ( X238 @ X241 @ X240 @ ( comp @ X242 @ X239 ) )
= $true ) ) )
| ? [X224: subst > term > subst > $o,X225: term,X226: term] :
( ! [X233: subst,X234: term,X235: subst,X236: subst] :
( ( ( X224 @ X235 @ X234 @ ( comp @ X233 @ X236 ) )
!= $true )
| ( ( X224 @ ( comp @ X235 @ X233 ) @ ( sub @ X234 @ X233 ) @ X236 )
= $true ) )
& ! [X229: term,X230: subst,X231: subst,X232: subst] :
( ( ( X224 @ X230 @ X229 @ ( comp @ X231 @ X232 ) )
= $true )
| ( ( X224 @ ( comp @ X230 @ X231 ) @ ( sub @ X229 @ X231 ) @ X232 )
!= $true ) )
& ( ( X224 @ id @ X226 @ id )
= $true )
& ( ( X224 @ id @ X225 @ id )
= $true )
& ! [X227: term,X228: term] :
( ( ( X224 @ id @ X228 @ id )
!= $true )
| ( ( X224 @ id @ ( ap @ ( sub @ X227 @ id ) @ X228 ) @ id )
= $true )
| ( ( X224 @ id @ X227 @ id )
!= $true ) )
& ( $true
!= ( X224 @ id @ ( ap @ X225 @ X226 ) @ id ) ) )
| ? [X217: term > $o,X218: term] :
( ! [X222: term,X223: term] :
( ( ( X217 @ ( ap @ X222 @ X223 ) )
= $true )
| ( ( X217 @ X222 )
!= $true )
| ( ( X217 @ X223 )
!= $true ) )
& ! [X219: term] :
( ( ( X217 @ X219 )
= $true )
| ( ( var @ X219 )
!= $true ) )
& ! [X220: term] :
( ( ( X217 @ ( lam @ X220 ) )
= $true )
| ? [X221: term] :
( ( ( X217 @ ( sub @ X220 @ ( push @ X221 @ id ) ) )
!= $true )
& ( ( X217 @ X221 )
= $true ) ) )
& ( ( X217 @ X218 )
!= $true ) ) ) )
& ( pushprop_gthm = $true )
& ( ( ! [X97: subst > term > subst > $o,X98: term] :
( ? [X103: subst,X104: subst,X105: subst,X106: term] :
( ( ( X97 @ ( comp @ X103 @ X104 ) @ ( sub @ X106 @ X104 ) @ X105 )
= $true )
& ( ( X97 @ X103 @ X106 @ ( comp @ X104 @ X105 ) )
!= $true ) )
| ? [X107: term,X108: term] :
( ( ( X97 @ id @ X107 @ id )
= $true )
& ( ( X97 @ id @ X108 @ id )
= $true )
& ( ( X97 @ id @ ( ap @ ( sub @ X108 @ id ) @ X107 ) @ id )
!= $true ) )
| ? [X99: subst,X100: subst,X101: term,X102: subst] :
( ( ( X97 @ X99 @ X101 @ ( comp @ X102 @ X100 ) )
= $true )
& ( ( X97 @ ( comp @ X99 @ X102 ) @ ( sub @ X101 @ X102 ) @ X100 )
!= $true ) )
| ? [X110: subst > term > term] :
( ! [X111: subst,X112: term,X113: subst] :
( ( X110 @ ( comp @ X113 @ X111 ) @ ( sub @ X112 @ X111 ) )
= ( sub @ ( X110 @ X113 @ X112 ) @ X111 ) )
& ! [X114: term] :
( ( ( X97 @ id @ ( X110 @ id @ X114 ) @ id )
= $true )
| ( ( X97 @ id @ X114 @ id )
!= $true ) )
& ( ( X97 @ id @ ( lam @ ( X110 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X109: term] :
( ( ( var @ ( sub @ X109 @ id ) )
= $true )
& ( $true
!= ( X97 @ id @ X109 @ id ) ) )
| ( ( X97 @ id @ X98 @ id )
= $true ) )
| ? [X87: subst > term > subst > $o,X88: term > $o,X89: term] :
( ! [X90: term] :
( ( X87 @ id @ X90 @ id )
= ( X88 @ X90 ) )
& ! [X91: subst > term > term] :
( ( ( X87 @ id @ ( lam @ ( X91 @ sh @ one ) ) @ id )
= $true )
| ? [X92: term] :
( ( $true
!= ( X87 @ id @ ( X91 @ id @ X92 ) @ id ) )
& ( ( X87 @ id @ X92 @ id )
= $true ) )
| ? [X93: subst,X94: term,X95: subst] :
( ( X91 @ ( comp @ X95 @ X93 ) @ ( sub @ X94 @ X93 ) )
!= ( sub @ ( X91 @ X95 @ X94 ) @ X93 ) ) )
& ! [X96: term] :
( ( ( X88 @ ( sub @ X89 @ ( push @ X96 @ id ) ) )
= $true )
| ( ( X88 @ X96 )
!= $true ) )
& ( ( X88 @ ( lam @ X89 ) )
!= $true ) )
| ? [X86: term] :
( ( sub @ X86 @ id )
!= X86 )
| ? [X79: term > $o,X80: term] :
( ! [X84: term] :
( ( ( X79 @ ( lam @ X84 ) )
= $true )
| ? [X85: term] :
( ( ( X79 @ ( sub @ X84 @ ( push @ X85 @ id ) ) )
!= $true )
& ( ( X79 @ X85 )
= $true ) ) )
& ! [X81: term,X82: term] :
( ( $true
!= ( X79 @ X82 ) )
| ( ( X79 @ ( ap @ X82 @ X81 ) )
= $true )
| ( ( X79 @ X81 )
!= $true ) )
& ! [X83: term] :
( ( ( var @ X83 )
!= $true )
| ( ( X79 @ X83 )
= $true ) )
& ( ( X79 @ X80 )
!= $true ) )
| ? [X76: subst > term > subst > $o] :
! [X77: term > $o] :
? [X78: term] :
( ( X76 @ id @ X78 @ id )
!= ( X77 @ X78 ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ! [X201: subst > term > subst > $o] :
? [X202: term > $o] :
! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X38: subst > term > subst > $o,X39: term] :
( ( ( X38 @ id @ ( lam @ X39 ) @ id )
= $true )
| ? [X44: subst,X45: subst,X46: subst,X47: term] :
( ( ( X38 @ ( comp @ X44 @ X46 ) @ ( sub @ X47 @ X46 ) @ X45 )
= $true )
& ( ( X38 @ X44 @ X47 @ ( comp @ X46 @ X45 ) )
!= $true ) )
| ? [X49: subst > term > term] :
( ! [X53: term] :
( ( ( X38 @ id @ X53 @ id )
!= $true )
| ( ( X38 @ id @ ( X49 @ id @ X53 ) @ id )
= $true ) )
& ! [X50: subst,X51: subst,X52: term] :
( ( X49 @ ( comp @ X50 @ X51 ) @ ( sub @ X52 @ X51 ) )
= ( sub @ ( X49 @ X50 @ X52 ) @ X51 ) )
& ( ( X38 @ id @ ( lam @ ( X49 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X40: term,X41: subst,X42: subst,X43: subst] :
( ( $true
!= ( X38 @ ( comp @ X42 @ X43 ) @ ( sub @ X40 @ X43 ) @ X41 ) )
& ( ( X38 @ X42 @ X40 @ ( comp @ X43 @ X41 ) )
= $true ) )
| ? [X48: term] :
( ( ( X38 @ id @ ( sub @ X39 @ ( push @ X48 @ id ) ) @ id )
!= $true )
& ( $true
= ( X38 @ id @ X48 @ id ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X512: subst > term > subst > $o,X513: term > $o,X514: term] :
( ? [X515: term] :
( ( X513 @ X515 )
!= ( X512 @ id @ X515 @ id ) )
| ? [X516: subst > term > term] :
( ( ( X512 @ id @ ( lam @ ( X516 @ sh @ one ) ) @ id )
!= $true )
& ! [X517: subst,X518: subst,X519: term] :
( ( sub @ ( X516 @ X518 @ X519 ) @ X517 )
= ( X516 @ ( comp @ X518 @ X517 ) @ ( sub @ X519 @ X517 ) ) )
& ! [X520: term] :
( ( ( X512 @ id @ X520 @ id )
!= $true )
| ( ( X512 @ id @ ( X516 @ id @ X520 ) @ id )
= $true ) ) )
| ( $true
= ( X513 @ ( lam @ X514 ) ) )
| ? [X521: term] :
( ( ( X513 @ ( sub @ X514 @ ( push @ X521 @ id ) ) )
!= $true )
& ( ( X513 @ X521 )
= $true ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( X54 = X55 )
| ( ( d2subst @ X55 )
!= ( d2subst @ X54 ) ) )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( ! [X136: subst > term > subst > $o,X137: term] :
( ? [X143: term,X144: term] :
( ( ( X136 @ id @ ( ap @ ( sub @ X144 @ id ) @ X143 ) @ id )
!= $true )
& ( ( X136 @ id @ X143 @ id )
= $true )
& ( ( X136 @ id @ X144 @ id )
= $true ) )
| ? [X138: subst > term > term] :
( ! [X139: term] :
( ( ( X136 @ id @ ( X138 @ id @ X139 ) @ id )
= $true )
| ( ( X136 @ id @ X139 @ id )
!= $true ) )
& ( ( X136 @ id @ ( lam @ ( X138 @ sh @ one ) ) @ id )
!= $true )
& ! [X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X142 @ X141 ) @ ( sub @ X140 @ X141 ) )
= ( sub @ ( X138 @ X142 @ X140 ) @ X141 ) ) )
| ( ( X136 @ id @ X137 @ id )
= $true ) )
| ? [X126: subst > term > subst > $o,X127: term,X128: term > $o] :
( ! [X130: term] :
( ( X126 @ id @ X130 @ id )
= ( X128 @ X130 ) )
& ! [X131: subst > term > term] :
( ( ( X126 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id )
= $true )
| ? [X132: term] :
( ( $true
= ( X126 @ id @ X132 @ id ) )
& ( ( X126 @ id @ ( X131 @ id @ X132 ) @ id )
!= $true ) )
| ? [X133: subst,X134: term,X135: subst] :
( ( X131 @ ( comp @ X133 @ X135 ) @ ( sub @ X134 @ X135 ) )
!= ( sub @ ( X131 @ X133 @ X134 ) @ X135 ) ) )
& ( ( X128 @ ( lam @ X127 ) )
!= $true )
& ! [X129: term] :
( ( ( X128 @ ( sub @ X127 @ ( push @ X129 @ id ) ) )
= $true )
| ( ( X128 @ X129 )
!= $true ) ) )
| ? [X125: term] :
( ( sub @ X125 @ id )
!= X125 )
| ? [X118: term,X119: term > $o] :
( ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X119 @ X122 )
= $true ) )
& ! [X123: term] :
( ? [X124: term] :
( ( ( X119 @ X124 )
= $true )
& ( ( X119 @ ( sub @ X123 @ ( push @ X124 @ id ) ) )
!= $true ) )
| ( ( X119 @ ( lam @ X123 ) )
= $true ) )
& ( $true
!= ( X119 @ X118 ) )
& ! [X120: term,X121: term] :
( ( ( X119 @ ( ap @ X120 @ X121 ) )
= $true )
| ( ( X119 @ X121 )
!= $true )
| ( ( X119 @ X120 )
!= $true ) ) )
| ? [X115: subst > term > subst > $o] :
! [X116: term > $o] :
? [X117: term] :
( ( X116 @ X117 )
!= ( X115 @ id @ X117 @ id ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axidr = $true )
<=> ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 ) )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
<=> ( apinj2 = $true ) )
& ( ! [X532: term,X533: subst,X534: term > $o] :
( ( ( X534 @ ( sub @ X532 @ X533 ) )
= $true )
| ? [X537: term] :
( ( ( X534 @ ( sub @ X537 @ X533 ) )
!= $true )
& ( ( var @ X537 )
= $true ) )
| ? [X535: term] :
( ! [X536: term] :
( ( ( X534 @ X536 )
!= $true )
| ( ( X534 @ ( sub @ X535 @ ( push @ X536 @ id ) ) )
= $true ) )
& ( ( X534 @ ( lam @ X535 ) )
!= $true ) )
| ? [X538: term,X539: term] :
( ( ( X534 @ X538 )
= $true )
& ( ( X534 @ X539 )
= $true )
& ( ( X534 @ ( ap @ X538 @ X539 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X311: subst > term > subst > $o] :
? [X312: term > $o] :
! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) ) )
& ( ( induction2 = $true )
<=> ! [X400: term > $o,X401: term] :
( ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( ( X400 @ X404 )
!= $true ) )
| ? [X405: term] :
( ( ( X400 @ ( lam @ X405 ) )
!= $true )
& ! [X406: term] :
( ( ( X400 @ ( sub @ X405 @ ( push @ X406 @ id ) ) )
= $true )
| ( ( X400 @ X406 )
!= $true ) ) )
| ? [X402: term,X403: term] :
( ( ( X400 @ X403 )
= $true )
& ( $true
!= ( X400 @ ( ap @ X403 @ X402 ) ) )
& ( ( X400 @ X402 )
= $true ) )
| ( ( X400 @ X401 )
= $true ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapinj2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ? [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
!= $true )
& ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
= $true ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
& ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) )
& ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
= $true )
& ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
!= $true ) )
| ? [X359: term] :
( ( X357 @ X359 )
!= ( X356 @ id @ X359 @ id ) )
| ? [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
!= $true )
& ( $true
= ( X357 @ X364 ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ! [X442: term,X443: subst > term > subst > $o] :
( ( ( X443 @ id @ ( lam @ ( sub @ X442 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X444: term] :
( ( ( X443 @ id @ ( sub @ X442 @ ( push @ X444 @ id ) ) @ id )
!= $true )
& ( ( X443 @ id @ X444 @ id )
= $true ) )
| ? [X445: subst > term > term] :
( ! [X446: subst,X447: term,X448: subst] :
( ( sub @ ( X445 @ X446 @ X447 ) @ X448 )
= ( X445 @ ( comp @ X446 @ X448 ) @ ( sub @ X447 @ X448 ) ) )
& ! [X449: term] :
( ( ( X443 @ id @ X449 @ id )
!= $true )
| ( ( X443 @ id @ ( X445 @ id @ X449 ) @ id )
= $true ) )
& ( ( X443 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X295: subst > term > subst > $o,X296: term] :
( ? [X307: subst,X308: subst,X309: subst,X310: term] :
( ( ( X295 @ X307 @ X310 @ ( comp @ X308 @ X309 ) )
= $true )
& ( ( X295 @ ( comp @ X307 @ X308 ) @ ( sub @ X310 @ X308 ) @ X309 )
!= $true ) )
| ? [X301: subst > term > term] :
( ! [X302: subst,X303: subst,X304: term] :
( ( X301 @ ( comp @ X303 @ X302 ) @ ( sub @ X304 @ X302 ) )
= ( sub @ ( X301 @ X303 @ X304 ) @ X302 ) )
& ( $true
!= ( X295 @ id @ ( lam @ ( X301 @ sh @ one ) ) @ id ) )
& ! [X305: term] :
( ( ( X295 @ id @ ( X301 @ id @ X305 ) @ id )
= $true )
| ( ( X295 @ id @ X305 @ id )
!= $true ) ) )
| ? [X297: subst,X298: subst,X299: subst,X300: term] :
( ( $true
= ( X295 @ ( comp @ X297 @ X298 ) @ ( sub @ X300 @ X298 ) @ X299 ) )
& ( ( X295 @ X297 @ X300 @ ( comp @ X298 @ X299 ) )
!= $true ) )
| ? [X306: term] :
( ( ( X295 @ id @ X306 @ id )
= $true )
& ( ( X295 @ id @ ( sub @ X296 @ ( push @ X306 @ id ) ) @ id )
!= $true ) )
| ( ( X295 @ id @ ( lam @ X296 ) @ id )
= $true ) )
| ? [X287: term,X288: subst > term > subst > $o] :
( ! [X294: term] :
( ( ( X288 @ id @ X294 @ id )
!= $true )
| ( $true
= ( X288 @ id @ ( sub @ X287 @ ( push @ X294 @ id ) ) @ id ) ) )
& ! [X289: subst > term > term] :
( ? [X290: term] :
( ( $true
= ( X288 @ id @ X290 @ id ) )
& ( ( X288 @ id @ ( X289 @ id @ X290 ) @ id )
!= $true ) )
| ( $true
= ( X288 @ id @ ( lam @ ( X289 @ sh @ one ) ) @ id ) )
| ? [X291: term,X292: subst,X293: subst] :
( ( sub @ ( X289 @ X292 @ X291 ) @ X293 )
!= ( X289 @ ( comp @ X292 @ X293 ) @ ( sub @ X291 @ X293 ) ) ) )
& ( ( X288 @ id @ ( lam @ ( sub @ X287 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) )
| ? [X286: term] :
( ( sub @ X286 @ id )
!= X286 ) ) )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
<=> ( apinj1 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvar1 != $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ulamvarsh = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X329: subst > term > subst > $o,X330: term] :
( ? [X331: term] :
( ( $true
!= ( X329 @ id @ ( sub @ X330 @ ( push @ X331 @ id ) ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( ( X329 @ id @ ( lam @ X330 ) @ id )
= $true )
| ? [X332: subst > term > term] :
( ! [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
| ( ( X329 @ id @ ( X332 @ id @ X336 ) @ id )
= $true ) )
& ( ( X329 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id )
!= $true )
& ! [X333: subst,X334: term,X335: subst] :
( ( X332 @ ( comp @ X333 @ X335 ) @ ( sub @ X334 @ X335 ) )
= ( sub @ ( X332 @ X333 @ X334 ) @ X335 ) ) ) )
| ? [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ ( lam @ ( sub @ X322 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X323: term] :
( ( ( X321 @ id @ ( sub @ X322 @ ( push @ X323 @ id ) ) @ id )
= $true )
| ( $true
!= ( X321 @ id @ X323 @ id ) ) )
& ! [X324: subst > term > term] :
( ? [X328: term] :
( ( $true
!= ( X321 @ id @ ( X324 @ id @ X328 ) @ id ) )
& ( ( X321 @ id @ X328 @ id )
= $true ) )
| ( ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id )
= $true )
| ? [X325: subst,X326: subst,X327: term] :
( ( X324 @ ( comp @ X325 @ X326 ) @ ( sub @ X327 @ X326 ) )
!= ( sub @ ( X324 @ X325 @ X327 ) @ X326 ) ) ) )
| ? [X320: term] :
( ( sub @ X320 @ id )
!= X320 ) ) )
& ( hoasapinj1_gthm = $true )
& ( ( ! [X348: term > $o,X349: term,X350: subst] :
( ( ( X348 @ ( sub @ X349 @ X350 ) )
= $true )
| ? [X351: term,X352: term] :
( ( ( X348 @ X351 )
= $true )
& ( ( X348 @ ( ap @ X352 @ X351 ) )
!= $true )
& ( ( X348 @ X352 )
= $true ) )
| ? [X353: term] :
( ! [X354: term] :
( ( $true
= ( X348 @ ( sub @ X353 @ ( push @ X354 @ id ) ) ) )
| ( ( X348 @ X354 )
!= $true ) )
& ( ( X348 @ ( lam @ X353 ) )
!= $true ) )
| ? [X355: term] :
( ( $true
!= ( X348 @ ( sub @ X355 @ X350 ) ) )
& ( ( var @ X355 )
= $true ) ) )
| ? [X342: term > $o,X343: term] :
( ( ( X342 @ X343 )
!= $true )
& ! [X346: term] :
( ( ( X342 @ X346 )
!= $true )
| ( ( X342 @ ( lam @ X346 ) )
= $true ) )
& ! [X344: term,X345: term] :
( ( ( X342 @ ( ap @ X345 @ X344 ) )
= $true )
| ( ( X342 @ X344 )
!= $true )
| ( ( X342 @ X345 )
!= $true ) )
& ! [X347: term] :
( ( $true
!= ( var @ X347 ) )
| ( ( X342 @ X347 )
= $true ) ) )
| ? [X341: subst] :
( ( comp @ X341 @ id )
!= X341 )
| ? [X339: term,X340: subst] :
( ( comp @ sh @ ( push @ X339 @ X340 ) )
!= X340 )
| ? [X337: subst,X338: term] :
( ( sub @ one @ ( push @ X338 @ X337 ) )
!= X338 ) )
<=> ( induction2lem_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( ! [X390: subst,X391: subst > term > term,X392: term,X393: subst > term > term] :
( ? [X394: subst,X395: term,X396: subst] :
( ( X393 @ ( comp @ X396 @ X394 ) @ ( sub @ X395 @ X394 ) )
!= ( sub @ ( X393 @ X396 @ X395 ) @ X394 ) )
| ( ( lam @ ( X391 @ sh @ one ) )
!= ( lam @ ( X393 @ sh @ one ) ) )
| ( ( X391 @ X390 @ X392 )
= ( X393 @ X390 @ X392 ) )
| ? [X397: subst,X398: term,X399: subst] :
( ( X391 @ ( comp @ X397 @ X399 ) @ ( sub @ X398 @ X399 ) )
!= ( sub @ ( X391 @ X397 @ X398 ) @ X399 ) ) )
| ? [X388: term,X389: term] :
( ( ( lam @ X389 )
= ( lam @ X388 ) )
& ( X388 != X389 ) )
| ? [X386: subst,X387: term] :
( ( comp @ sh @ ( push @ X387 @ X386 ) )
!= X386 )
| ? [X384: term,X385: subst] :
( ( sub @ one @ ( push @ X384 @ X385 ) )
!= X384 ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
? [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
= ( X29 @ sh @ one ) ) )
& ( ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ? [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
!= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) )
| ? [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
!= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) ) )
<=> ( hoaslaminj = $true ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X415: term] :
? [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
= ( X416 @ sh @ one ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop = $true )
& ( axvarshift = $true )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X483: term] :
? [X484: subst > term > term] :
! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X34: term] :
? [X35: subst > term > term] :
! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) ) )
& ! [X199: d_term,X200: d_term] :
( ( X199 = X200 )
| ( ( d2term @ X200 )
!= ( d2term @ X199 ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X418: term] :
( ( sub @ X418 @ id )
= X418 )
| ? [X417: term] :
( ( sub @ X417 @ id )
!= X417 ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X14: term > $o,X15: term,X16: subst] :
? [X17: term > $o] :
! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X456: subst,X457: term > $o,X458: term] :
? [X459: term > $o] :
! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ! [X421: subst > term > subst > $o,X422: term] :
( ? [X428: term] :
( ( ( X421 @ id @ ( sub @ X422 @ ( push @ X428 @ id ) ) @ id )
!= $true )
& ( ( X421 @ id @ X428 @ id )
= $true ) )
| ? [X423: subst > term > term] :
( ! [X424: term] :
( ( ( X421 @ id @ X424 @ id )
!= $true )
| ( ( X421 @ id @ ( X423 @ id @ X424 ) @ id )
= $true ) )
& ! [X425: term,X426: subst,X427: subst] :
( ( sub @ ( X423 @ X427 @ X425 ) @ X426 )
= ( X423 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) ) )
& ( ( X421 @ id @ ( lam @ ( X423 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X421 @ id @ ( lam @ ( sub @ X422 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) )
| ? [X6: term,X7: term,X8: term,X9: term] :
( ( X8 != X9 )
& ( ( ap @ X8 @ X6 )
= ( ap @ X9 @ X7 ) ) )
| ? [X5: term] :
( ( sub @ X5 @ id )
!= X5 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
<=> ( axscons = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X178: subst > term > subst > $o,X179: term,X180: term > $o] :
( ? [X186: subst > term > term] :
( ( ( X178 @ id @ ( lam @ ( X186 @ sh @ one ) ) @ id )
!= $true )
& ! [X188: term,X189: subst,X190: subst] :
( ( X186 @ ( comp @ X189 @ X190 ) @ ( sub @ X188 @ X190 ) )
= ( sub @ ( X186 @ X189 @ X188 ) @ X190 ) )
& ! [X187: term] :
( ( ( X178 @ id @ ( X186 @ id @ X187 ) @ id )
= $true )
| ( ( X178 @ id @ X187 @ id )
!= $true ) ) )
| ( ( X180 @ ( lam @ X179 ) )
= $true )
| ? [X195: term] :
( ( X180 @ X195 )
!= ( X178 @ id @ X195 @ id ) )
| ? [X191: subst,X192: term,X193: subst,X194: subst] :
( ( $true
!= ( X178 @ X191 @ X192 @ ( comp @ X193 @ X194 ) ) )
& ( ( X178 @ ( comp @ X191 @ X193 ) @ ( sub @ X192 @ X193 ) @ X194 )
= $true ) )
| ? [X181: subst,X182: subst,X183: subst,X184: term] :
( ( ( X178 @ X183 @ X184 @ ( comp @ X182 @ X181 ) )
= $true )
& ( ( X178 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) @ X181 )
!= $true ) )
| ? [X185: term] :
( ( ( X180 @ X185 )
= $true )
& ( ( X180 @ ( sub @ X179 @ ( push @ X185 @ id ) ) )
!= $true ) ) )
| ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 ) ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( substmonoid_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( ( shinj = $true )
<=> ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ( ! [X505: term > $o,X506: term] :
( ? [X507: term] :
( ! [X508: term] :
( ( ( X505 @ X508 )
!= $true )
| ( ( X505 @ ( sub @ X507 @ ( push @ X508 @ id ) ) )
= $true ) )
& ( $true
!= ( X505 @ ( lam @ X507 ) ) ) )
| ? [X511: term] :
( ( ( var @ X511 )
= $true )
& ( ( X505 @ X511 )
!= $true ) )
| ? [X509: term,X510: term] :
( ( ( X505 @ X510 )
= $true )
& ( ( X505 @ X509 )
= $true )
& ( ( X505 @ ( ap @ X509 @ X510 ) )
!= $true ) )
| ( $true
= ( X505 @ X506 ) ) )
| ? [X497: term > $o,X498: subst,X499: term] :
( ! [X502: term] :
( ( ( X497 @ ( lam @ X502 ) )
= $true )
| ? [X503: term] :
( ( ( X497 @ X503 )
= $true )
& ( ( X497 @ ( sub @ X502 @ ( push @ X503 @ id ) ) )
!= $true ) ) )
& ! [X500: term,X501: term] :
( ( ( X497 @ X501 )
!= $true )
| ( ( X497 @ X500 )
!= $true )
| ( ( X497 @ ( ap @ X500 @ X501 ) )
= $true ) )
& ( ( X497 @ ( sub @ X499 @ X498 ) )
!= $true )
& ! [X504: term] :
( ( $true
= ( X497 @ ( sub @ X504 @ X498 ) ) )
| ( ( var @ X504 )
!= $true ) ) )
| ? [X496: term] :
( ( sub @ X496 @ id )
!= X496 ) )
<=> ( induction2_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ? [X491: subst > term > term] :
( ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
& ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
& ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( X488 @ id @ X487 @ id )
= $true )
| ? [X489: term,X490: term] :
( ( $true
= ( X488 @ id @ X489 @ id ) )
& ( ( X488 @ id @ ( ap @ ( sub @ X489 @ id ) @ X490 ) @ id )
!= $true )
& ( ( X488 @ id @ X490 @ id )
= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X375: subst > term > subst > $o,X376: term] :
( ( ( X375 @ id @ ( lam @ X376 ) @ id )
= $true )
| ? [X377: term] :
( ( $true
= ( X375 @ id @ X377 @ id ) )
& ( ( X375 @ id @ ( sub @ X376 @ ( push @ X377 @ id ) ) @ id )
!= $true ) )
| ? [X378: subst > term > term] :
( ! [X380: subst,X381: subst,X382: term] :
( ( sub @ ( X378 @ X380 @ X382 ) @ X381 )
= ( X378 @ ( comp @ X380 @ X381 ) @ ( sub @ X382 @ X381 ) ) )
& ( ( X375 @ id @ ( lam @ ( X378 @ sh @ one ) ) @ id )
!= $true )
& ! [X379: term] :
( ( ( X375 @ id @ X379 @ id )
!= $true )
| ( ( X375 @ id @ ( X378 @ id @ X379 ) @ id )
= $true ) ) ) ) )
& ( axapp = $true )
& ( ! [X429: term,X430: term,X431: subst > term > subst > $o] :
( ? [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X431 @ X436 @ X434 @ ( comp @ X435 @ X437 ) )
= $true )
& ( ( X431 @ ( comp @ X436 @ X435 ) @ ( sub @ X434 @ X435 ) @ X437 )
!= $true ) )
| ? [X438: subst,X439: term,X440: subst,X441: subst] :
( ( ( X431 @ X438 @ X439 @ ( comp @ X441 @ X440 ) )
!= $true )
& ( ( X431 @ ( comp @ X438 @ X441 ) @ ( sub @ X439 @ X441 ) @ X440 )
= $true ) )
| ( ( X431 @ id @ X429 @ id )
!= $true )
| ? [X432: term,X433: term] :
( ( ( X431 @ id @ X433 @ id )
= $true )
& ( ( X431 @ id @ X432 @ id )
= $true )
& ( ( X431 @ id @ ( ap @ ( sub @ X432 @ id ) @ X433 ) @ id )
!= $true ) )
| ( ( X431 @ id @ ( ap @ X430 @ X429 ) @ id )
= $true )
| ( $true
!= ( X431 @ id @ X430 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( laminj = $true )
<=> ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) ) )
& ( apnotvar = $true )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
<=> ( termmset = $true ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
<=> ( substmonoid = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
<=> ( hoasapinj2 = $true ) )
& ( axabs = $true )
& ( pushprop_lthm = $true )
& ( ! [X64: term,X65: subst > term > subst > $o] :
( ? [X67: subst > term > term,X68: term] :
( ! [X72: subst,X73: term,X74: subst] :
( ( X67 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) )
= ( sub @ X68 @ ( push @ ( sub @ X73 @ X74 ) @ ( comp @ X72 @ X74 ) ) ) )
& ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
!= $true )
& ! [X69: subst,X70: subst,X71: term] :
( ( sub @ ( sub @ X68 @ ( push @ X71 @ X69 ) ) @ X70 )
= ( sub @ ( X67 @ X69 @ X71 ) @ X70 ) )
& ! [X75: term] :
( ( ( X65 @ id @ X75 @ id )
!= $true )
| ( ( X65 @ id @ ( X67 @ id @ X75 ) @ id )
= $true ) ) )
| ( ( X65 @ id @ ( lam @ ( sub @ X64 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X66: term] :
( ( ( X65 @ id @ ( sub @ X64 @ ( push @ X66 @ id ) ) @ id )
!= $true )
& ( ( X65 @ id @ X66 @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X149: term > $o,X150: term] :
( ? [X154: term] :
( ( ( X149 @ X154 )
!= $true )
& ( ( var @ X154 )
= $true ) )
| ? [X151: term,X152: term] :
( ( ( X149 @ ( ap @ X152 @ X151 ) )
!= $true )
& ( $true
= ( X149 @ X151 ) )
& ( ( X149 @ X152 )
= $true ) )
| ( ( X149 @ X150 )
= $true )
| ? [X153: term] :
( ( ( X149 @ X153 )
= $true )
& ( ( X149 @ ( lam @ X153 ) )
!= $true ) ) )
<=> ( induction = $true ) )
& ( ! [X271: term,X272: term > $o,X273: subst > term > subst > $o,X274: term] :
( ? [X282: subst,X283: term,X284: subst,X285: subst] :
( ( ( X273 @ ( comp @ X285 @ X282 ) @ ( sub @ X283 @ X282 ) @ X284 )
= $true )
& ( ( X273 @ X285 @ X283 @ ( comp @ X282 @ X284 ) )
!= $true ) )
| ? [X280: term,X281: term] :
( ( ( X273 @ id @ ( ap @ ( sub @ X281 @ id ) @ X280 ) @ id )
!= $true )
& ( ( X273 @ id @ X281 @ id )
= $true )
& ( ( X273 @ id @ X280 @ id )
= $true ) )
| ( $true
!= ( X272 @ X274 ) )
| ( ( X272 @ X271 )
!= $true )
| ( ( X272 @ ( ap @ X274 @ X271 ) )
= $true )
| ? [X275: term] :
( ( X272 @ X275 )
!= ( X273 @ id @ X275 @ id ) )
| ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( ( X273 @ ( comp @ X276 @ X278 ) @ ( sub @ X279 @ X278 ) @ X277 )
!= $true )
& ( ( X273 @ X276 @ X279 @ ( comp @ X278 @ X277 ) )
= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( pushprop_lthm_orig = $true )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ? [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
!= ( X0 @ X4 ) )
| ( ( X0 @ one )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( induction2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
<=> ( axvarid = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= id )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axassoc = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) )
| ? [X146: subst] :
( ( comp @ X146 @ id )
!= X146 )
| ? [X145: subst] :
( ( comp @ id @ X145 )
!= X145 ) ) )
& ( ( axidl = $true )
<=> ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 ) )
& ( pushprop_lem3v2 = $true )
& ( ( hoasinduction = $true )
<=> ! [X465: term,X466: subst > term > subst > $o] :
( ( ( X466 @ id @ X465 @ id )
= $true )
| ? [X472: subst > term > term] :
( ! [X476: term] :
( ( ( X466 @ id @ X476 @ id )
!= $true )
| ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true ) )
& ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
!= $true )
& ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) ) )
| ? [X468: term,X469: subst,X470: subst,X471: subst] :
( ( ( X466 @ X470 @ X468 @ ( comp @ X471 @ X469 ) )
= $true )
& ( ( X466 @ ( comp @ X470 @ X471 ) @ ( sub @ X468 @ X471 ) @ X469 )
!= $true ) )
| ? [X481: term,X482: term] :
( ( ( X466 @ id @ X481 @ id )
= $true )
& ( $true
= ( X466 @ id @ X482 @ id ) )
& ( ( X466 @ id @ ( ap @ ( sub @ X482 @ id ) @ X481 ) @ id )
!= $true ) )
| ? [X467: term] :
( ( $true
!= ( X466 @ id @ X467 @ id ) )
& ( ( var @ ( sub @ X467 @ id ) )
= $true ) )
| ? [X477: subst,X478: subst,X479: subst,X480: term] :
( ( $true
= ( X466 @ ( comp @ X479 @ X478 ) @ ( sub @ X480 @ X478 ) @ X477 ) )
& ( $true
!= ( X466 @ X479 @ X480 @ ( comp @ X478 @ X477 ) ) ) ) ) )
& ( hoasinduction_lem2_lthm = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
=> ( ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
=> ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X24 @ X27 )
!= $true )
| ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X314: subst > term > term,X315: term,X316: term] :
( ~ ! [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( ( ! [X56: term,X57: term,X58: term,X59: term] :
( ( X57 = X58 )
| ( ( ap @ X56 @ X58 )
!= ( ap @ X59 @ X57 ) ) )
=> ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X157: term] :
~ ! [X158: subst > term > term] :
~ ! [X159: term,X160: subst] :
( ( X158 @ X160 @ X159 )
= ( sub @ X157 @ ( push @ X159 @ X160 ) ) )
=> ( ! [X161: term] :
( ( sub @ X161 @ id )
= X161 )
=> ! [X162: subst > term > subst > $o,X163: term > $o,X164: term] :
( ~ ! [X166: subst > term > term] :
( ( ( X162 @ id @ ( lam @ ( X166 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X167: term] :
( ( ( X162 @ id @ X167 @ id )
!= $true )
| ( ( X162 @ id @ ( X166 @ id @ X167 ) @ id )
= $true ) )
| ~ ! [X168: subst,X169: subst,X170: term] :
( ( sub @ ( X166 @ X168 @ X170 ) @ X169 )
= ( X166 @ ( comp @ X168 @ X169 ) @ ( sub @ X170 @ X169 ) ) ) )
| ~ ! [X171: term] :
( ( X163 @ X171 )
= ( X162 @ id @ X171 @ id ) )
| ~ ! [X165: term] :
( ( ( X163 @ X165 )
!= $true )
| ( ( X163 @ ( sub @ X164 @ ( push @ X165 @ id ) ) )
= $true ) )
| ( ( X163 @ ( lam @ X164 ) )
= $true ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
= X211 )
=> ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ( $true
= ( X214 @ one ) )
| ( ( X215 @ X212 )
!= $true )
| ~ ! [X216: term] :
( ( X214 @ X216 )
= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X217: term > $o,X218: term] :
( ~ ! [X220: term] :
( ~ ! [X221: term] :
( ( ( X217 @ ( sub @ X220 @ ( push @ X221 @ id ) ) )
= $true )
| ( ( X217 @ X221 )
!= $true ) )
| ( ( X217 @ ( lam @ X220 ) )
= $true ) )
| ~ ! [X222: term,X223: term] :
( ( ( X217 @ ( ap @ X222 @ X223 ) )
= $true )
| ( ( X217 @ X222 )
!= $true )
| ( ( X217 @ X223 )
!= $true ) )
| ( ( X217 @ X218 )
= $true )
| ~ ! [X219: term] :
( ( ( X217 @ X219 )
= $true )
| ( ( var @ X219 )
!= $true ) ) )
=> ( ! [X224: subst > term > subst > $o,X225: term,X226: term] :
( ( ( X224 @ id @ X226 @ id )
!= $true )
| ~ ! [X229: term,X230: subst,X231: subst,X232: subst] :
( ( ( X224 @ X230 @ X229 @ ( comp @ X231 @ X232 ) )
= $true )
| ( ( X224 @ ( comp @ X230 @ X231 ) @ ( sub @ X229 @ X231 ) @ X232 )
!= $true ) )
| ~ ! [X227: term,X228: term] :
( ( ( X224 @ id @ X228 @ id )
!= $true )
| ( ( X224 @ id @ ( ap @ ( sub @ X227 @ id ) @ X228 ) @ id )
= $true )
| ( ( X224 @ id @ X227 @ id )
!= $true ) )
| ( $true
= ( X224 @ id @ ( ap @ X225 @ X226 ) @ id ) )
| ( ( X224 @ id @ X225 @ id )
!= $true )
| ~ ! [X233: subst,X234: term,X235: subst,X236: subst] :
( ( ( X224 @ X235 @ X234 @ ( comp @ X233 @ X236 ) )
!= $true )
| ( ( X224 @ ( comp @ X235 @ X233 ) @ ( sub @ X234 @ X233 ) @ X236 )
= $true ) ) )
=> ( ! [X237: term,X238: subst > term > subst > $o] :
( ~ ! [X247: subst > term > term] :
( ~ ! [X249: subst,X250: subst,X251: term] :
( ( X247 @ ( comp @ X249 @ X250 ) @ ( sub @ X251 @ X250 ) )
= ( sub @ ( X247 @ X249 @ X251 ) @ X250 ) )
| ~ ! [X248: term] :
( ( ( X238 @ id @ ( X247 @ id @ X248 ) @ id )
= $true )
| ( $true
!= ( X238 @ id @ X248 @ id ) ) )
| ( ( X238 @ id @ ( lam @ ( X247 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X243: subst,X244: subst,X245: term,X246: subst] :
( ( ( X238 @ ( comp @ X244 @ X243 ) @ ( sub @ X245 @ X243 ) @ X246 )
= $true )
| ( ( X238 @ X244 @ X245 @ ( comp @ X243 @ X246 ) )
!= $true ) )
| ~ ! [X252: term] :
( ( ( X238 @ id @ ( sub @ X237 @ ( push @ X252 @ id ) ) @ id )
= $true )
| ( ( X238 @ id @ X252 @ id )
!= $true ) )
| ( ( X238 @ id @ ( lam @ X237 ) @ id )
= $true )
| ~ ! [X239: subst,X240: term,X241: subst,X242: subst] :
( ( ( X238 @ ( comp @ X241 @ X242 ) @ ( sub @ X240 @ X242 ) @ X239 )
!= $true )
| ( ( X238 @ X241 @ X240 @ ( comp @ X242 @ X239 ) )
= $true ) ) )
=> ! [X253: subst > term > subst > $o,X254: term] :
( ~ ! [X270: term] :
( ( $true
!= ( var @ ( sub @ X270 @ id ) ) )
| ( ( X253 @ id @ X270 @ id )
= $true ) )
| ~ ! [X255: subst,X256: term,X257: subst,X258: subst] :
( ( $true
!= ( X253 @ X258 @ X256 @ ( comp @ X257 @ X255 ) ) )
| ( ( X253 @ ( comp @ X258 @ X257 ) @ ( sub @ X256 @ X257 ) @ X255 )
= $true ) )
| ~ ! [X266: subst,X267: subst,X268: term,X269: subst] :
( ( ( X253 @ X267 @ X268 @ ( comp @ X269 @ X266 ) )
= $true )
| ( ( X253 @ ( comp @ X267 @ X269 ) @ ( sub @ X268 @ X269 ) @ X266 )
!= $true ) )
| ~ ! [X261: subst > term > term] :
( ( ( X253 @ id @ ( lam @ ( X261 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X262: term] :
( ( $true
!= ( X253 @ id @ X262 @ id ) )
| ( $true
= ( X253 @ id @ ( X261 @ id @ X262 ) @ id ) ) )
| ~ ! [X263: term,X264: subst,X265: subst] :
( ( X261 @ ( comp @ X265 @ X264 ) @ ( sub @ X263 @ X264 ) )
= ( sub @ ( X261 @ X265 @ X263 ) @ X264 ) ) )
| ( ( X253 @ id @ X254 @ id )
= $true )
| ~ ! [X259: term,X260: term] :
( ( ( X253 @ id @ X260 @ id )
!= $true )
| ( ( X253 @ id @ X259 @ id )
!= $true )
| ( $true
= ( X253 @ id @ ( ap @ ( sub @ X259 @ id ) @ X260 ) @ id ) ) ) ) ) ) ) )
& ( pushprop_gthm = $true )
& ( ( ! [X76: subst > term > subst > $o] :
~ ! [X77: term > $o] :
~ ! [X78: term] :
( ( X76 @ id @ X78 @ id )
= ( X77 @ X78 ) )
=> ( ! [X79: term > $o,X80: term] :
( ( ( X79 @ X80 )
= $true )
| ~ ! [X81: term,X82: term] :
( ( $true
!= ( X79 @ X82 ) )
| ( ( X79 @ ( ap @ X82 @ X81 ) )
= $true )
| ( ( X79 @ X81 )
!= $true ) )
| ~ ! [X84: term] :
( ( ( X79 @ ( lam @ X84 ) )
= $true )
| ~ ! [X85: term] :
( ( ( X79 @ ( sub @ X84 @ ( push @ X85 @ id ) ) )
= $true )
| ( ( X79 @ X85 )
!= $true ) ) )
| ~ ! [X83: term] :
( ( ( var @ X83 )
!= $true )
| ( ( X79 @ X83 )
= $true ) ) )
=> ( ! [X86: term] :
( ( sub @ X86 @ id )
= X86 )
=> ( ! [X87: subst > term > subst > $o,X88: term > $o,X89: term] :
( ~ ! [X96: term] :
( ( ( X88 @ ( sub @ X89 @ ( push @ X96 @ id ) ) )
= $true )
| ( ( X88 @ X96 )
!= $true ) )
| ( ( X88 @ ( lam @ X89 ) )
= $true )
| ~ ! [X90: term] :
( ( X87 @ id @ X90 @ id )
= ( X88 @ X90 ) )
| ~ ! [X91: subst > term > term] :
( ~ ! [X93: subst,X94: term,X95: subst] :
( ( X91 @ ( comp @ X95 @ X93 ) @ ( sub @ X94 @ X93 ) )
= ( sub @ ( X91 @ X95 @ X94 ) @ X93 ) )
| ~ ! [X92: term] :
( ( $true
= ( X87 @ id @ ( X91 @ id @ X92 ) @ id ) )
| ( ( X87 @ id @ X92 @ id )
!= $true ) )
| ( ( X87 @ id @ ( lam @ ( X91 @ sh @ one ) ) @ id )
= $true ) ) )
=> ! [X97: subst > term > subst > $o,X98: term] :
( ~ ! [X109: term] :
( ( ( var @ ( sub @ X109 @ id ) )
!= $true )
| ( $true
= ( X97 @ id @ X109 @ id ) ) )
| ~ ! [X107: term,X108: term] :
( ( ( X97 @ id @ X108 @ id )
!= $true )
| ( ( X97 @ id @ ( ap @ ( sub @ X108 @ id ) @ X107 ) @ id )
= $true )
| ( ( X97 @ id @ X107 @ id )
!= $true ) )
| ~ ! [X110: subst > term > term] :
( ~ ! [X114: term] :
( ( ( X97 @ id @ ( X110 @ id @ X114 ) @ id )
= $true )
| ( ( X97 @ id @ X114 @ id )
!= $true ) )
| ( ( X97 @ id @ ( lam @ ( X110 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X111: subst,X112: term,X113: subst] :
( ( X110 @ ( comp @ X113 @ X111 ) @ ( sub @ X112 @ X111 ) )
= ( sub @ ( X110 @ X113 @ X112 ) @ X111 ) ) )
| ~ ! [X99: subst,X100: subst,X101: term,X102: subst] :
( ( ( X97 @ ( comp @ X99 @ X102 ) @ ( sub @ X101 @ X102 ) @ X100 )
= $true )
| ( ( X97 @ X99 @ X101 @ ( comp @ X102 @ X100 ) )
!= $true ) )
| ~ ! [X103: subst,X104: subst,X105: subst,X106: term] :
( ( ( X97 @ X103 @ X106 @ ( comp @ X104 @ X105 ) )
= $true )
| ( ( X97 @ ( comp @ X103 @ X104 ) @ ( sub @ X106 @ X104 ) @ X105 )
!= $true ) )
| ( ( X97 @ id @ X98 @ id )
= $true ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X201: subst > term > subst > $o] :
~ ! [X202: term > $o] :
~ ! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X38: subst > term > subst > $o,X39: term] :
( ~ ! [X49: subst > term > term] :
( ( ( X38 @ id @ ( lam @ ( X49 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X53: term] :
( ( ( X38 @ id @ X53 @ id )
!= $true )
| ( ( X38 @ id @ ( X49 @ id @ X53 ) @ id )
= $true ) )
| ~ ! [X50: subst,X51: subst,X52: term] :
( ( X49 @ ( comp @ X50 @ X51 ) @ ( sub @ X52 @ X51 ) )
= ( sub @ ( X49 @ X50 @ X52 ) @ X51 ) ) )
| ~ ! [X48: term] :
( ( ( X38 @ id @ ( sub @ X39 @ ( push @ X48 @ id ) ) @ id )
= $true )
| ( $true
!= ( X38 @ id @ X48 @ id ) ) )
| ~ ! [X40: term,X41: subst,X42: subst,X43: subst] :
( ( $true
= ( X38 @ ( comp @ X42 @ X43 ) @ ( sub @ X40 @ X43 ) @ X41 ) )
| ( ( X38 @ X42 @ X40 @ ( comp @ X43 @ X41 ) )
!= $true ) )
| ( ( X38 @ id @ ( lam @ X39 ) @ id )
= $true )
| ~ ! [X44: subst,X45: subst,X46: subst,X47: term] :
( ( ( X38 @ ( comp @ X44 @ X46 ) @ ( sub @ X47 @ X46 ) @ X45 )
!= $true )
| ( ( X38 @ X44 @ X47 @ ( comp @ X46 @ X45 ) )
= $true ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ! [X512: subst > term > subst > $o,X513: term > $o,X514: term] :
( ~ ! [X515: term] :
( ( X513 @ X515 )
= ( X512 @ id @ X515 @ id ) )
| ( $true
= ( X513 @ ( lam @ X514 ) ) )
| ~ ! [X516: subst > term > term] :
( ~ ! [X520: term] :
( ( ( X512 @ id @ X520 @ id )
!= $true )
| ( ( X512 @ id @ ( X516 @ id @ X520 ) @ id )
= $true ) )
| ( ( X512 @ id @ ( lam @ ( X516 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X517: subst,X518: subst,X519: term] :
( ( sub @ ( X516 @ X518 @ X519 ) @ X517 )
= ( X516 @ ( comp @ X518 @ X517 ) @ ( sub @ X519 @ X517 ) ) ) )
| ~ ! [X521: term] :
( ( ( X513 @ X521 )
!= $true )
| ( ( X513 @ ( sub @ X514 @ ( push @ X521 @ id ) ) )
= $true ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ! [X54: d_subst,X55: d_subst] :
( ( ( d2subst @ X55 )
= ( d2subst @ X54 ) )
=> ( X54 = X55 ) )
& ! [X209: d_subst] : ( d_id = X209 )
& ( ( ! [X115: subst > term > subst > $o] :
~ ! [X116: term > $o] :
~ ! [X117: term] :
( ( X116 @ X117 )
= ( X115 @ id @ X117 @ id ) )
=> ( ! [X118: term,X119: term > $o] :
( ( $true
= ( X119 @ X118 ) )
| ~ ! [X123: term] :
( ~ ! [X124: term] :
( ( ( X119 @ ( sub @ X123 @ ( push @ X124 @ id ) ) )
= $true )
| ( ( X119 @ X124 )
!= $true ) )
| ( ( X119 @ ( lam @ X123 ) )
= $true ) )
| ~ ! [X122: term] :
( ( ( var @ X122 )
!= $true )
| ( ( X119 @ X122 )
= $true ) )
| ~ ! [X120: term,X121: term] :
( ( ( X119 @ ( ap @ X120 @ X121 ) )
= $true )
| ( ( X119 @ X121 )
!= $true )
| ( ( X119 @ X120 )
!= $true ) ) )
=> ( ! [X125: term] :
( ( sub @ X125 @ id )
= X125 )
=> ( ! [X126: subst > term > subst > $o,X127: term,X128: term > $o] :
( ( ( X128 @ ( lam @ X127 ) )
= $true )
| ~ ! [X131: subst > term > term] :
( ~ ! [X133: subst,X134: term,X135: subst] :
( ( X131 @ ( comp @ X133 @ X135 ) @ ( sub @ X134 @ X135 ) )
= ( sub @ ( X131 @ X133 @ X134 ) @ X135 ) )
| ( ( X126 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X132: term] :
( ( ( X126 @ id @ ( X131 @ id @ X132 ) @ id )
= $true )
| ( $true
!= ( X126 @ id @ X132 @ id ) ) ) )
| ~ ! [X130: term] :
( ( X126 @ id @ X130 @ id )
= ( X128 @ X130 ) )
| ~ ! [X129: term] :
( ( ( X128 @ ( sub @ X127 @ ( push @ X129 @ id ) ) )
= $true )
| ( ( X128 @ X129 )
!= $true ) ) )
=> ! [X136: subst > term > subst > $o,X137: term] :
( ~ ! [X138: subst > term > term] :
( ~ ! [X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X142 @ X141 ) @ ( sub @ X140 @ X141 ) )
= ( sub @ ( X138 @ X142 @ X140 ) @ X141 ) )
| ( ( X136 @ id @ ( lam @ ( X138 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X139: term] :
( ( ( X136 @ id @ ( X138 @ id @ X139 ) @ id )
= $true )
| ( ( X136 @ id @ X139 @ id )
!= $true ) ) )
| ~ ! [X143: term,X144: term] :
( ( ( X136 @ id @ ( ap @ ( sub @ X144 @ id ) @ X143 ) @ id )
= $true )
| ( ( X136 @ id @ X143 @ id )
!= $true )
| ( ( X136 @ id @ X144 @ id )
!= $true ) )
| ( ( X136 @ id @ X137 @ id )
= $true ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axidr = $true )
<=> ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 ) )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
<=> ( apinj2 = $true ) )
& ( ( induction2lem = $true )
<=> ! [X532: term,X533: subst,X534: term > $o] :
( ~ ! [X537: term] :
( ( ( X534 @ ( sub @ X537 @ X533 ) )
= $true )
| ( ( var @ X537 )
!= $true ) )
| ~ ! [X538: term,X539: term] :
( ( ( X534 @ X538 )
!= $true )
| ( ( X534 @ ( ap @ X538 @ X539 ) )
= $true )
| ( ( X534 @ X539 )
!= $true ) )
| ( ( X534 @ ( sub @ X532 @ X533 ) )
= $true )
| ~ ! [X535: term] :
( ~ ! [X536: term] :
( ( ( X534 @ X536 )
!= $true )
| ( ( X534 @ ( sub @ X535 @ ( push @ X536 @ id ) ) )
= $true ) )
| ( ( X534 @ ( lam @ X535 ) )
= $true ) ) ) )
& ( ! [X311: subst > term > subst > $o] :
~ ! [X312: term > $o] :
~ ! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( induction2 = $true )
<=> ! [X400: term > $o,X401: term] :
( ~ ! [X404: term] :
( ( ( var @ X404 )
!= $true )
| ( ( X400 @ X404 )
= $true ) )
| ( ( X400 @ X401 )
= $true )
| ~ ! [X402: term,X403: term] :
( ( ( X400 @ X403 )
!= $true )
| ( $true
= ( X400 @ ( ap @ X403 @ X402 ) ) )
| ( ( X400 @ X402 )
!= $true ) )
| ~ ! [X405: term] :
( ( ( X400 @ ( lam @ X405 ) )
= $true )
| ~ ! [X406: term] :
( ( ( X400 @ ( sub @ X405 @ ( push @ X406 @ id ) ) )
= $true )
| ( ( X400 @ X406 )
!= $true ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapinj2_gthm = $true )
& ( axclos = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ~ ! [X359: term] :
( ( X357 @ X359 )
= ( X356 @ id @ X359 @ id ) )
| ~ ! [X369: subst > term > term] :
( ~ ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
| ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ~ ! [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
!= $true )
| ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
= $true ) )
| ~ ! [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
= $true )
| ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
!= $true ) )
| ~ ! [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
= $true )
| ( $true
!= ( X357 @ X364 ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ! [X442: term,X443: subst > term > subst > $o] :
( ( ( X443 @ id @ ( lam @ ( sub @ X442 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X444: term] :
( ( ( X443 @ id @ X444 @ id )
!= $true )
| ( ( X443 @ id @ ( sub @ X442 @ ( push @ X444 @ id ) ) @ id )
= $true ) )
| ~ ! [X445: subst > term > term] :
( ( ( X443 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X446: subst,X447: term,X448: subst] :
( ( sub @ ( X445 @ X446 @ X447 ) @ X448 )
= ( X445 @ ( comp @ X446 @ X448 ) @ ( sub @ X447 @ X448 ) ) )
| ~ ! [X449: term] :
( ( ( X443 @ id @ X449 @ id )
!= $true )
| ( ( X443 @ id @ ( X445 @ id @ X449 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X286: term] :
( ( sub @ X286 @ id )
= X286 )
=> ( ! [X287: term,X288: subst > term > subst > $o] :
( ~ ! [X289: subst > term > term] :
( ~ ! [X290: term] :
( ( $true
!= ( X288 @ id @ X290 @ id ) )
| ( ( X288 @ id @ ( X289 @ id @ X290 ) @ id )
= $true ) )
| ( $true
= ( X288 @ id @ ( lam @ ( X289 @ sh @ one ) ) @ id ) )
| ~ ! [X291: term,X292: subst,X293: subst] :
( ( sub @ ( X289 @ X292 @ X291 ) @ X293 )
= ( X289 @ ( comp @ X292 @ X293 ) @ ( sub @ X291 @ X293 ) ) ) )
| ( ( X288 @ id @ ( lam @ ( sub @ X287 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X294: term] :
( ( ( X288 @ id @ X294 @ id )
!= $true )
| ( $true
= ( X288 @ id @ ( sub @ X287 @ ( push @ X294 @ id ) ) @ id ) ) ) )
=> ! [X295: subst > term > subst > $o,X296: term] :
( ~ ! [X307: subst,X308: subst,X309: subst,X310: term] :
( ( ( X295 @ ( comp @ X307 @ X308 ) @ ( sub @ X310 @ X308 ) @ X309 )
= $true )
| ( ( X295 @ X307 @ X310 @ ( comp @ X308 @ X309 ) )
!= $true ) )
| ~ ! [X301: subst > term > term] :
( ( $true
= ( X295 @ id @ ( lam @ ( X301 @ sh @ one ) ) @ id ) )
| ~ ! [X305: term] :
( ( ( X295 @ id @ ( X301 @ id @ X305 ) @ id )
= $true )
| ( ( X295 @ id @ X305 @ id )
!= $true ) )
| ~ ! [X302: subst,X303: subst,X304: term] :
( ( X301 @ ( comp @ X303 @ X302 ) @ ( sub @ X304 @ X302 ) )
= ( sub @ ( X301 @ X303 @ X304 ) @ X302 ) ) )
| ~ ! [X306: term] :
( ( ( X295 @ id @ X306 @ id )
!= $true )
| ( ( X295 @ id @ ( sub @ X296 @ ( push @ X306 @ id ) ) @ id )
= $true ) )
| ( ( X295 @ id @ ( lam @ X296 ) @ id )
= $true )
| ~ ! [X297: subst,X298: subst,X299: subst,X300: term] :
( ( $true
!= ( X295 @ ( comp @ X297 @ X298 ) @ ( sub @ X300 @ X298 ) @ X299 ) )
| ( ( X295 @ X297 @ X300 @ ( comp @ X298 @ X299 ) )
= $true ) ) ) ) ) )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
<=> ( apinj1 = $true ) )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ulamvar1 != $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ulamvarsh = $true )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X320: term] :
( ( sub @ X320 @ id )
= X320 )
=> ( ! [X321: subst > term > subst > $o,X322: term] :
( ( ( X321 @ id @ ( lam @ ( sub @ X322 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X324: subst > term > term] :
( ( ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X325: subst,X326: subst,X327: term] :
( ( X324 @ ( comp @ X325 @ X326 ) @ ( sub @ X327 @ X326 ) )
= ( sub @ ( X324 @ X325 @ X327 ) @ X326 ) )
| ~ ! [X328: term] :
( ( ( X321 @ id @ X328 @ id )
!= $true )
| ( $true
= ( X321 @ id @ ( X324 @ id @ X328 ) @ id ) ) ) )
| ~ ! [X323: term] :
( ( ( X321 @ id @ ( sub @ X322 @ ( push @ X323 @ id ) ) @ id )
= $true )
| ( $true
!= ( X321 @ id @ X323 @ id ) ) ) )
=> ! [X329: subst > term > subst > $o,X330: term] :
( ~ ! [X332: subst > term > term] :
( ( ( X329 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
| ( ( X329 @ id @ ( X332 @ id @ X336 ) @ id )
= $true ) )
| ~ ! [X333: subst,X334: term,X335: subst] :
( ( X332 @ ( comp @ X333 @ X335 ) @ ( sub @ X334 @ X335 ) )
= ( sub @ ( X332 @ X333 @ X334 ) @ X335 ) ) )
| ~ ! [X331: term] :
( ( ( X329 @ id @ X331 @ id )
!= $true )
| ( $true
= ( X329 @ id @ ( sub @ X330 @ ( push @ X331 @ id ) ) @ id ) ) )
| ( ( X329 @ id @ ( lam @ X330 ) @ id )
= $true ) ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( ( ! [X337: subst,X338: term] :
( ( sub @ one @ ( push @ X338 @ X337 ) )
= X338 )
=> ( ! [X339: term,X340: subst] :
( ( comp @ sh @ ( push @ X339 @ X340 ) )
= X340 )
=> ( ! [X341: subst] :
( ( comp @ X341 @ id )
= X341 )
=> ( ! [X342: term > $o,X343: term] :
( ( ( X342 @ X343 )
= $true )
| ~ ! [X344: term,X345: term] :
( ( ( X342 @ ( ap @ X345 @ X344 ) )
= $true )
| ( ( X342 @ X344 )
!= $true )
| ( ( X342 @ X345 )
!= $true ) )
| ~ ! [X347: term] :
( ( $true
!= ( var @ X347 ) )
| ( ( X342 @ X347 )
= $true ) )
| ~ ! [X346: term] :
( ( ( X342 @ X346 )
!= $true )
| ( ( X342 @ ( lam @ X346 ) )
= $true ) ) )
=> ! [X348: term > $o,X349: term,X350: subst] :
( ~ ! [X355: term] :
( ( ( var @ X355 )
!= $true )
| ( $true
= ( X348 @ ( sub @ X355 @ X350 ) ) ) )
| ~ ! [X353: term] :
( ( ( X348 @ ( lam @ X353 ) )
= $true )
| ~ ! [X354: term] :
( ( $true
= ( X348 @ ( sub @ X353 @ ( push @ X354 @ id ) ) ) )
| ( ( X348 @ X354 )
!= $true ) ) )
| ( ( X348 @ ( sub @ X349 @ X350 ) )
= $true )
| ~ ! [X351: term,X352: term] :
( ( ( X348 @ X352 )
!= $true )
| ( ( X348 @ ( ap @ X352 @ X351 ) )
= $true )
| ( ( X348 @ X351 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( ! [X384: term,X385: subst] :
( ( sub @ one @ ( push @ X384 @ X385 ) )
= X384 )
=> ( ! [X386: subst,X387: term] :
( ( comp @ sh @ ( push @ X387 @ X386 ) )
= X386 )
=> ( ! [X388: term,X389: term] :
( ( ( lam @ X389 )
!= ( lam @ X388 ) )
| ( X388 = X389 ) )
=> ! [X390: subst,X391: subst > term > term,X392: term,X393: subst > term > term] :
( ( ( X391 @ X390 @ X392 )
= ( X393 @ X390 @ X392 ) )
| ~ ! [X394: subst,X395: term,X396: subst] :
( ( X393 @ ( comp @ X396 @ X394 ) @ ( sub @ X395 @ X394 ) )
= ( sub @ ( X393 @ X396 @ X395 ) @ X394 ) )
| ( ( lam @ ( X391 @ sh @ one ) )
!= ( lam @ ( X393 @ sh @ one ) ) )
| ~ ! [X397: subst,X398: term,X399: subst] :
( ( X391 @ ( comp @ X397 @ X399 ) @ ( sub @ X398 @ X399 ) )
= ( sub @ ( X391 @ X397 @ X398 ) @ X399 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
~ ! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ~ ! [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) )
| ~ ! [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) ) ) )
& ( ! [X415: term] :
~ ! [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
!= ( X416 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( pushprop = $true )
& ( axvarshift = $true )
& ( ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axmap = $true )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
<=> ( axvarcons = $true ) )
& ( ! [X483: term] :
~ ! [X484: subst > term > term] :
~ ! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( lamnotap != $true )
& ( ! [X34: term] :
~ ! [X35: subst > term > term] :
~ ! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ! [X199: d_term,X200: d_term] :
( ( ( d2term @ X200 )
= ( d2term @ X199 ) )
=> ( X199 = X200 ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( ! [X417: term] :
( ( sub @ X417 @ id )
= X417 )
=> ! [X418: term] :
( ( sub @ X418 @ id )
= X418 ) )
<=> ( termmset_lthm = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X14: term > $o,X15: term,X16: subst] :
~ ! [X17: term > $o] :
~ ! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X456: subst,X457: term > $o,X458: term] :
~ ! [X459: term > $o] :
~ ! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X421: subst > term > subst > $o,X422: term] :
( ~ ! [X423: subst > term > term] :
( ~ ! [X424: term] :
( ( ( X421 @ id @ X424 @ id )
!= $true )
| ( ( X421 @ id @ ( X423 @ id @ X424 ) @ id )
= $true ) )
| ~ ! [X425: term,X426: subst,X427: subst] :
( ( sub @ ( X423 @ X427 @ X425 ) @ X426 )
= ( X423 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) ) )
| ( ( X421 @ id @ ( lam @ ( X423 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X421 @ id @ ( lam @ ( sub @ X422 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X428: term] :
( ( ( X421 @ id @ X428 @ id )
!= $true )
| ( ( X421 @ id @ ( sub @ X422 @ ( push @ X428 @ id ) ) @ id )
= $true ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
=> ( ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) )
=> ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
<=> ( axscons = $true ) )
& ( ( ! [X177: term] :
( ( sub @ X177 @ id )
= X177 )
=> ! [X178: subst > term > subst > $o,X179: term,X180: term > $o] :
( ~ ! [X191: subst,X192: term,X193: subst,X194: subst] :
( ( ( X178 @ ( comp @ X191 @ X193 ) @ ( sub @ X192 @ X193 ) @ X194 )
!= $true )
| ( $true
= ( X178 @ X191 @ X192 @ ( comp @ X193 @ X194 ) ) ) )
| ~ ! [X185: term] :
( ( ( X180 @ X185 )
!= $true )
| ( ( X180 @ ( sub @ X179 @ ( push @ X185 @ id ) ) )
= $true ) )
| ~ ! [X195: term] :
( ( X180 @ X195 )
= ( X178 @ id @ X195 @ id ) )
| ( ( X180 @ ( lam @ X179 ) )
= $true )
| ~ ! [X186: subst > term > term] :
( ~ ! [X188: term,X189: subst,X190: subst] :
( ( X186 @ ( comp @ X189 @ X190 ) @ ( sub @ X188 @ X190 ) )
= ( sub @ ( X186 @ X189 @ X188 ) @ X190 ) )
| ( ( X178 @ id @ ( lam @ ( X186 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X187: term] :
( ( ( X178 @ id @ ( X186 @ id @ X187 ) @ id )
= $true )
| ( ( X178 @ id @ X187 @ id )
!= $true ) ) )
| ~ ! [X181: subst,X182: subst,X183: subst,X184: term] :
( ( ( X178 @ X183 @ X184 @ ( comp @ X182 @ X181 ) )
!= $true )
| ( ( X178 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) @ X181 )
= $true ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( substmonoid_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ! [X410: d_term] : ( d_one = X410 )
& ( ( shinj = $true )
<=> ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) ) )
& ( induction2lem_gthm = $true )
& ( hoasapnotvar = $true )
& ( ulamvarind = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( ( ! [X496: term] :
( ( sub @ X496 @ id )
= X496 )
=> ( ! [X497: term > $o,X498: subst,X499: term] :
( ~ ! [X504: term] :
( ( $true
= ( X497 @ ( sub @ X504 @ X498 ) ) )
| ( ( var @ X504 )
!= $true ) )
| ~ ! [X502: term] :
( ( ( X497 @ ( lam @ X502 ) )
= $true )
| ~ ! [X503: term] :
( ( ( X497 @ X503 )
!= $true )
| ( ( X497 @ ( sub @ X502 @ ( push @ X503 @ id ) ) )
= $true ) ) )
| ( ( X497 @ ( sub @ X499 @ X498 ) )
= $true )
| ~ ! [X500: term,X501: term] :
( ( ( X497 @ X501 )
!= $true )
| ( ( X497 @ X500 )
!= $true )
| ( ( X497 @ ( ap @ X500 @ X501 ) )
= $true ) ) )
=> ! [X505: term > $o,X506: term] :
( ~ ! [X507: term] :
( ( $true
= ( X505 @ ( lam @ X507 ) ) )
| ~ ! [X508: term] :
( ( ( X505 @ X508 )
!= $true )
| ( ( X505 @ ( sub @ X507 @ ( push @ X508 @ id ) ) )
= $true ) ) )
| ~ ! [X509: term,X510: term] :
( ( ( X505 @ X510 )
!= $true )
| ( ( X505 @ ( ap @ X509 @ X510 ) )
= $true )
| ( ( X505 @ X509 )
!= $true ) )
| ~ ! [X511: term] :
( ( ( var @ X511 )
!= $true )
| ( ( X505 @ X511 )
= $true ) )
| ( $true
= ( X505 @ X506 ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X487: term,X488: subst > term > subst > $o] :
( ~ ! [X491: subst > term > term] :
( ~ ! [X495: term] :
( ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true )
| ( ( X488 @ id @ X495 @ id )
!= $true ) )
| ~ ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
| ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X489: term,X490: term] :
( ( ( X488 @ id @ X490 @ id )
!= $true )
| ( ( X488 @ id @ ( ap @ ( sub @ X489 @ id ) @ X490 ) @ id )
= $true )
| ( $true
!= ( X488 @ id @ X489 @ id ) ) )
| ( ( X488 @ id @ X487 @ id )
= $true ) ) )
& ( ! [X375: subst > term > subst > $o,X376: term] :
( ~ ! [X377: term] :
( ( $true
!= ( X375 @ id @ X377 @ id ) )
| ( ( X375 @ id @ ( sub @ X376 @ ( push @ X377 @ id ) ) @ id )
= $true ) )
| ( ( X375 @ id @ ( lam @ X376 ) @ id )
= $true )
| ~ ! [X378: subst > term > term] :
( ( ( X375 @ id @ ( lam @ ( X378 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X380: subst,X381: subst,X382: term] :
( ( sub @ ( X378 @ X380 @ X382 ) @ X381 )
= ( X378 @ ( comp @ X380 @ X381 ) @ ( sub @ X382 @ X381 ) ) )
| ~ ! [X379: term] :
( ( ( X375 @ id @ X379 @ id )
!= $true )
| ( ( X375 @ id @ ( X378 @ id @ X379 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( axapp = $true )
& ( ! [X429: term,X430: term,X431: subst > term > subst > $o] :
( ( ( X431 @ id @ ( ap @ X430 @ X429 ) @ id )
= $true )
| ( $true
!= ( X431 @ id @ X430 @ id ) )
| ( ( X431 @ id @ X429 @ id )
!= $true )
| ~ ! [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X431 @ ( comp @ X436 @ X435 ) @ ( sub @ X434 @ X435 ) @ X437 )
= $true )
| ( ( X431 @ X436 @ X434 @ ( comp @ X435 @ X437 ) )
!= $true ) )
| ~ ! [X432: term,X433: term] :
( ( ( X431 @ id @ ( ap @ ( sub @ X432 @ id ) @ X433 ) @ id )
= $true )
| ( ( X431 @ id @ X433 @ id )
!= $true )
| ( ( X431 @ id @ X432 @ id )
!= $true ) )
| ~ ! [X438: subst,X439: term,X440: subst,X441: subst] :
( ( ( X431 @ ( comp @ X438 @ X441 ) @ ( sub @ X439 @ X441 ) @ X440 )
!= $true )
| ( ( X431 @ X438 @ X439 @ ( comp @ X441 @ X440 ) )
= $true ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( laminj = $true )
<=> ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) ) )
& ( apnotvar = $true )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
<=> ( termmset = $true ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
<=> ( substmonoid = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
<=> ( hoasapinj2 = $true ) )
& ( axabs = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X64: term,X65: subst > term > subst > $o] :
( ~ ! [X67: subst > term > term,X68: term] :
( ~ ! [X75: term] :
( ( ( X65 @ id @ X75 @ id )
!= $true )
| ( ( X65 @ id @ ( X67 @ id @ X75 ) @ id )
= $true ) )
| ~ ! [X69: subst,X70: subst,X71: term] :
( ( sub @ ( sub @ X68 @ ( push @ X71 @ X69 ) ) @ X70 )
= ( sub @ ( X67 @ X69 @ X71 ) @ X70 ) )
| ~ ! [X72: subst,X73: term,X74: subst] :
( ( X67 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) )
= ( sub @ X68 @ ( push @ ( sub @ X73 @ X74 ) @ ( comp @ X72 @ X74 ) ) ) )
| ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X66: term] :
( ( ( X65 @ id @ X66 @ id )
!= $true )
| ( ( X65 @ id @ ( sub @ X64 @ ( push @ X66 @ id ) ) @ id )
= $true ) )
| ( ( X65 @ id @ ( lam @ ( sub @ X64 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( induction = $true )
<=> ! [X149: term > $o,X150: term] :
( ~ ! [X154: term] :
( ( ( X149 @ X154 )
= $true )
| ( ( var @ X154 )
!= $true ) )
| ( ( X149 @ X150 )
= $true )
| ~ ! [X153: term] :
( ( ( X149 @ X153 )
!= $true )
| ( ( X149 @ ( lam @ X153 ) )
= $true ) )
| ~ ! [X151: term,X152: term] :
( ( ( X149 @ ( ap @ X152 @ X151 ) )
= $true )
| ( $true
!= ( X149 @ X151 ) )
| ( ( X149 @ X152 )
!= $true ) ) ) )
& ( ! [X271: term,X272: term > $o,X273: subst > term > subst > $o,X274: term] :
( ( ( X272 @ X271 )
!= $true )
| ( $true
!= ( X272 @ X274 ) )
| ~ ! [X280: term,X281: term] :
( ( ( X273 @ id @ X280 @ id )
!= $true )
| ( ( X273 @ id @ ( ap @ ( sub @ X281 @ id ) @ X280 ) @ id )
= $true )
| ( ( X273 @ id @ X281 @ id )
!= $true ) )
| ~ ! [X275: term] :
( ( X272 @ X275 )
= ( X273 @ id @ X275 @ id ) )
| ~ ! [X276: subst,X277: subst,X278: subst,X279: term] :
( ( ( X273 @ ( comp @ X276 @ X278 ) @ ( sub @ X279 @ X278 ) @ X277 )
= $true )
| ( ( X273 @ X276 @ X279 @ ( comp @ X278 @ X277 ) )
!= $true ) )
| ~ ! [X282: subst,X283: term,X284: subst,X285: subst] :
( ( ( X273 @ ( comp @ X285 @ X282 ) @ ( sub @ X283 @ X282 ) @ X284 )
!= $true )
| ( ( X273 @ X285 @ X283 @ ( comp @ X282 @ X284 ) )
= $true ) )
| ( ( X272 @ ( ap @ X274 @ X271 ) )
= $true ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( pushprop_lthm_orig = $true )
& ( ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ one )
= $true )
| ~ ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( induction2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
<=> ( axvarid = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( d2subst @ d_id )
= id )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axassoc = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X145: subst] :
( ( comp @ id @ X145 )
= X145 )
=> ( ! [X146: subst] :
( ( comp @ X146 @ id )
= X146 )
=> ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) ) ) ) )
& ( ( axidl = $true )
<=> ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 ) )
& ( pushprop_lem3v2 = $true )
& ( ! [X465: term,X466: subst > term > subst > $o] :
( ( ( X466 @ id @ X465 @ id )
= $true )
| ~ ! [X468: term,X469: subst,X470: subst,X471: subst] :
( ( ( X466 @ X470 @ X468 @ ( comp @ X471 @ X469 ) )
!= $true )
| ( ( X466 @ ( comp @ X470 @ X471 ) @ ( sub @ X468 @ X471 ) @ X469 )
= $true ) )
| ~ ! [X477: subst,X478: subst,X479: subst,X480: term] :
( ( $true
= ( X466 @ X479 @ X480 @ ( comp @ X478 @ X477 ) ) )
| ( $true
!= ( X466 @ ( comp @ X479 @ X478 ) @ ( sub @ X480 @ X478 ) @ X477 ) ) )
| ~ ! [X467: term] :
( ( ( var @ ( sub @ X467 @ id ) )
!= $true )
| ( $true
= ( X466 @ id @ X467 @ id ) ) )
| ~ ! [X472: subst > term > term] :
( ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) )
| ~ ! [X476: term] :
( ( ( X466 @ id @ X476 @ id )
!= $true )
| ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true ) ) )
| ~ ! [X481: term,X482: term] :
( ( ( X466 @ id @ X481 @ id )
!= $true )
| ( ( X466 @ id @ ( ap @ ( sub @ X482 @ id ) @ X481 ) @ id )
= $true )
| ( $true
!= ( X466 @ id @ X482 @ id ) ) ) )
<=> ( hoasinduction = $true ) )
& ( hoasinduction_lem2_lthm = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( hoasinduction_lem1v2 = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ~ ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) )
| ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ one )
= $true ) ) )
& ( ( ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
=> ( ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) )
=> ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( pushprop_lthm = $true )
& ( ! [X14: term > $o,X15: term,X16: subst] :
~ ! [X17: term > $o] :
~ ! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
=> ( ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
=> ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true )
| ( ( X24 @ X27 )
!= $true ) ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
~ ! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( axabs = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ! [X34: term] :
~ ! [X35: subst > term > term] :
~ ! [X36: subst,X37: term] :
( ( X35 @ X36 @ X37 )
= ( sub @ X34 @ ( push @ X37 @ X36 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X38: subst > term > subst > $o,X39: term] :
( ~ ! [X40: term,X41: subst,X42: subst,X43: subst] :
( ( $true
= ( X38 @ ( comp @ X42 @ X43 ) @ ( sub @ X40 @ X43 ) @ X41 ) )
| ( ( X38 @ X42 @ X40 @ ( comp @ X43 @ X41 ) )
!= $true ) )
| ~ ! [X44: subst,X45: subst,X46: subst,X47: term] :
( ( ( X38 @ ( comp @ X44 @ X46 ) @ ( sub @ X47 @ X46 ) @ X45 )
!= $true )
| ( ( X38 @ X44 @ X47 @ ( comp @ X46 @ X45 ) )
= $true ) )
| ~ ! [X48: term] :
( ( $true
!= ( X38 @ id @ X48 @ id ) )
| ( ( X38 @ id @ ( sub @ X39 @ ( push @ X48 @ id ) ) @ id )
= $true ) )
| ( ( X38 @ id @ ( lam @ X39 ) @ id )
= $true )
| ~ ! [X49: subst > term > term] :
( ~ ! [X50: subst,X51: subst,X52: term] :
( ( X49 @ ( comp @ X50 @ X51 ) @ ( sub @ X52 @ X51 ) )
= ( sub @ ( X49 @ X50 @ X52 ) @ X51 ) )
| ~ ! [X53: term] :
( ( ( X38 @ id @ ( X49 @ id @ X53 ) @ id )
= $true )
| ( ( X38 @ id @ X53 @ id )
!= $true ) )
| ( ( X38 @ id @ ( lam @ ( X49 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ! [X54: d_subst,X55: d_subst] :
( ( ( d2subst @ X55 )
= ( d2subst @ X54 ) )
=> ( X54 = X55 ) )
& ( ( ! [X56: term,X57: term,X58: term,X59: term] :
( ( X57 = X58 )
| ( ( ap @ X56 @ X58 )
!= ( ap @ X59 @ X57 ) ) )
=> ! [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ ( sub @ X63 @ id ) @ X60 )
!= ( ap @ ( sub @ X62 @ id ) @ X61 ) )
| ( X60 = X61 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X64: term,X65: subst > term > subst > $o] :
( ( ( X65 @ id @ ( lam @ ( sub @ X64 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X66: term] :
( ( ( X65 @ id @ ( sub @ X64 @ ( push @ X66 @ id ) ) @ id )
= $true )
| ( ( X65 @ id @ X66 @ id )
!= $true ) )
| ~ ! [X67: subst > term > term,X68: term] :
( ~ ! [X69: subst,X70: subst,X71: term] :
( ( sub @ ( sub @ X68 @ ( push @ X71 @ X69 ) ) @ X70 )
= ( sub @ ( X67 @ X69 @ X71 ) @ X70 ) )
| ~ ! [X72: subst,X73: term,X74: subst] :
( ( X67 @ ( comp @ X72 @ X74 ) @ ( sub @ X73 @ X74 ) )
= ( sub @ X68 @ ( push @ ( sub @ X73 @ X74 ) @ ( comp @ X72 @ X74 ) ) ) )
| ~ ! [X75: term] :
( ( ( X65 @ id @ X75 @ id )
!= $true )
| ( ( X65 @ id @ ( X67 @ id @ X75 ) @ id )
= $true ) )
| ( ( X65 @ id @ ( lam @ ( X67 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( apnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X76: subst > term > subst > $o] :
~ ! [X77: term > $o] :
~ ! [X78: term] :
( ( X76 @ id @ X78 @ id )
= ( X77 @ X78 ) )
=> ( ! [X79: term > $o,X80: term] :
( ( ( X79 @ X80 )
= $true )
| ~ ! [X81: term,X82: term] :
( ( $true
!= ( X79 @ X82 ) )
| ( ( X79 @ ( ap @ X82 @ X81 ) )
= $true )
| ( ( X79 @ X81 )
!= $true ) )
| ~ ! [X83: term] :
( ( ( var @ X83 )
!= $true )
| ( ( X79 @ X83 )
= $true ) )
| ~ ! [X84: term] :
( ( ( X79 @ ( lam @ X84 ) )
= $true )
| ~ ! [X85: term] :
( ( ( X79 @ ( sub @ X84 @ ( push @ X85 @ id ) ) )
= $true )
| ( ( X79 @ X85 )
!= $true ) ) ) )
=> ( ! [X86: term] :
( ( sub @ X86 @ id )
= X86 )
=> ( ! [X87: subst > term > subst > $o,X88: term > $o,X89: term] :
( ( ( X88 @ ( lam @ X89 ) )
= $true )
| ~ ! [X90: term] :
( ( X87 @ id @ X90 @ id )
= ( X88 @ X90 ) )
| ~ ! [X91: subst > term > term] :
( ( ( X87 @ id @ ( lam @ ( X91 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X92: term] :
( ( ( X87 @ id @ X92 @ id )
!= $true )
| ( $true
= ( X87 @ id @ ( X91 @ id @ X92 ) @ id ) ) )
| ~ ! [X93: subst,X94: term,X95: subst] :
( ( X91 @ ( comp @ X95 @ X93 ) @ ( sub @ X94 @ X93 ) )
= ( sub @ ( X91 @ X95 @ X94 ) @ X93 ) ) )
| ~ ! [X96: term] :
( ( ( X88 @ ( sub @ X89 @ ( push @ X96 @ id ) ) )
= $true )
| ( ( X88 @ X96 )
!= $true ) ) )
=> ! [X97: subst > term > subst > $o,X98: term] :
( ~ ! [X99: subst,X100: subst,X101: term,X102: subst] :
( ( ( X97 @ ( comp @ X99 @ X102 ) @ ( sub @ X101 @ X102 ) @ X100 )
= $true )
| ( ( X97 @ X99 @ X101 @ ( comp @ X102 @ X100 ) )
!= $true ) )
| ~ ! [X103: subst,X104: subst,X105: subst,X106: term] :
( ( ( X97 @ X103 @ X106 @ ( comp @ X104 @ X105 ) )
= $true )
| ( ( X97 @ ( comp @ X103 @ X104 ) @ ( sub @ X106 @ X104 ) @ X105 )
!= $true ) )
| ~ ! [X107: term,X108: term] :
( ( ( X97 @ id @ X107 @ id )
!= $true )
| ( ( X97 @ id @ X108 @ id )
!= $true )
| ( ( X97 @ id @ ( ap @ ( sub @ X108 @ id ) @ X107 ) @ id )
= $true ) )
| ~ ! [X109: term] :
( ( $true
= ( X97 @ id @ X109 @ id ) )
| ( ( var @ ( sub @ X109 @ id ) )
!= $true ) )
| ( ( X97 @ id @ X98 @ id )
= $true )
| ~ ! [X110: subst > term > term] :
( ~ ! [X111: subst,X112: term,X113: subst] :
( ( X110 @ ( comp @ X113 @ X111 ) @ ( sub @ X112 @ X111 ) )
= ( sub @ ( X110 @ X113 @ X112 ) @ X111 ) )
| ~ ! [X114: term] :
( ( ( X97 @ id @ X114 @ id )
!= $true )
| ( ( X97 @ id @ ( X110 @ id @ X114 ) @ id )
= $true ) )
| ( ( X97 @ id @ ( lam @ ( X110 @ sh @ one ) ) @ id )
= $true ) ) ) ) ) ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X115: subst > term > subst > $o] :
~ ! [X116: term > $o] :
~ ! [X117: term] :
( ( X116 @ X117 )
= ( X115 @ id @ X117 @ id ) )
=> ( ! [X118: term,X119: term > $o] :
( ~ ! [X120: term,X121: term] :
( ( ( X119 @ X121 )
!= $true )
| ( ( X119 @ ( ap @ X120 @ X121 ) )
= $true )
| ( ( X119 @ X120 )
!= $true ) )
| ~ ! [X122: term] :
( ( ( X119 @ X122 )
= $true )
| ( ( var @ X122 )
!= $true ) )
| ~ ! [X123: term] :
( ( ( X119 @ ( lam @ X123 ) )
= $true )
| ~ ! [X124: term] :
( ( ( X119 @ X124 )
!= $true )
| ( ( X119 @ ( sub @ X123 @ ( push @ X124 @ id ) ) )
= $true ) ) )
| ( $true
= ( X119 @ X118 ) ) )
=> ( ! [X125: term] :
( ( sub @ X125 @ id )
= X125 )
=> ( ! [X126: subst > term > subst > $o,X127: term,X128: term > $o] :
( ( ( X128 @ ( lam @ X127 ) )
= $true )
| ~ ! [X129: term] :
( ( ( X128 @ X129 )
!= $true )
| ( ( X128 @ ( sub @ X127 @ ( push @ X129 @ id ) ) )
= $true ) )
| ~ ! [X130: term] :
( ( X126 @ id @ X130 @ id )
= ( X128 @ X130 ) )
| ~ ! [X131: subst > term > term] :
( ( ( X126 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X132: term] :
( ( $true
!= ( X126 @ id @ X132 @ id ) )
| ( ( X126 @ id @ ( X131 @ id @ X132 ) @ id )
= $true ) )
| ~ ! [X133: subst,X134: term,X135: subst] :
( ( X131 @ ( comp @ X133 @ X135 ) @ ( sub @ X134 @ X135 ) )
= ( sub @ ( X131 @ X133 @ X134 ) @ X135 ) ) ) )
=> ! [X136: subst > term > subst > $o,X137: term] :
( ( ( X136 @ id @ X137 @ id )
= $true )
| ~ ! [X138: subst > term > term] :
( ~ ! [X139: term] :
( ( ( X136 @ id @ X139 @ id )
!= $true )
| ( ( X136 @ id @ ( X138 @ id @ X139 ) @ id )
= $true ) )
| ( ( X136 @ id @ ( lam @ ( X138 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X142 @ X141 ) @ ( sub @ X140 @ X141 ) )
= ( sub @ ( X138 @ X142 @ X140 ) @ X141 ) ) )
| ~ ! [X143: term,X144: term] :
( ( ( X136 @ id @ X144 @ id )
!= $true )
| ( ( X136 @ id @ X143 @ id )
!= $true )
| ( ( X136 @ id @ ( ap @ ( sub @ X144 @ id ) @ X143 ) @ id )
= $true ) ) ) ) ) ) ) )
& ( axapp = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ulamvar1 != $true )
& ( hoasinduction_lem1 = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X145: subst] :
( ( comp @ id @ X145 )
= X145 )
=> ( ! [X146: subst] :
( ( comp @ X146 @ id )
= X146 )
=> ( ! [X148: subst] :
( ( comp @ id @ X148 )
= X148 )
& ! [X147: subst] :
( ( comp @ X147 @ id )
= X147 ) ) ) ) )
& ( ! [X149: term > $o,X150: term] :
( ~ ! [X151: term,X152: term] :
( ( ( X149 @ ( ap @ X152 @ X151 ) )
= $true )
| ( ( X149 @ X152 )
!= $true )
| ( $true
!= ( X149 @ X151 ) ) )
| ~ ! [X153: term] :
( ( ( X149 @ X153 )
!= $true )
| ( ( X149 @ ( lam @ X153 ) )
= $true ) )
| ( ( X149 @ X150 )
= $true )
| ~ ! [X154: term] :
( ( ( X149 @ X154 )
= $true )
| ( ( var @ X154 )
!= $true ) ) )
<=> ( induction = $true ) )
& ( ! [X155: subst,X156: term] :
( ( sub @ one @ ( push @ X156 @ X155 ) )
= X156 )
<=> ( axvarcons = $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X157: term] :
~ ! [X158: subst > term > term] :
~ ! [X159: term,X160: subst] :
( ( X158 @ X160 @ X159 )
= ( sub @ X157 @ ( push @ X159 @ X160 ) ) )
=> ( ! [X161: term] :
( ( sub @ X161 @ id )
= X161 )
=> ! [X162: subst > term > subst > $o,X163: term > $o,X164: term] :
( ~ ! [X165: term] :
( ( ( X163 @ ( sub @ X164 @ ( push @ X165 @ id ) ) )
= $true )
| ( ( X163 @ X165 )
!= $true ) )
| ~ ! [X166: subst > term > term] :
( ~ ! [X167: term] :
( ( ( X162 @ id @ X167 @ id )
!= $true )
| ( ( X162 @ id @ ( X166 @ id @ X167 ) @ id )
= $true ) )
| ~ ! [X168: subst,X169: subst,X170: term] :
( ( sub @ ( X166 @ X168 @ X170 ) @ X169 )
= ( X166 @ ( comp @ X168 @ X169 ) @ ( sub @ X170 @ X169 ) ) )
| ( ( X162 @ id @ ( lam @ ( X166 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X163 @ ( lam @ X164 ) )
= $true )
| ~ ! [X171: term] :
( ( X163 @ X171 )
= ( X162 @ id @ X171 @ id ) ) ) ) ) )
& ( ( axidr = $true )
<=> ! [X172: subst] :
( ( comp @ X172 @ id )
= X172 ) )
& ( ! [X173: term,X174: term,X175: term,X176: term] :
( ( ( ap @ X173 @ X175 )
!= ( ap @ X174 @ X176 ) )
| ( X175 = X176 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoasinduction_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X177: term] :
( ( sub @ X177 @ id )
= X177 )
=> ! [X178: subst > term > subst > $o,X179: term,X180: term > $o] :
( ( ( X180 @ ( lam @ X179 ) )
= $true )
| ~ ! [X181: subst,X182: subst,X183: subst,X184: term] :
( ( ( X178 @ ( comp @ X183 @ X182 ) @ ( sub @ X184 @ X182 ) @ X181 )
= $true )
| ( ( X178 @ X183 @ X184 @ ( comp @ X182 @ X181 ) )
!= $true ) )
| ~ ! [X185: term] :
( ( ( X180 @ ( sub @ X179 @ ( push @ X185 @ id ) ) )
= $true )
| ( ( X180 @ X185 )
!= $true ) )
| ~ ! [X186: subst > term > term] :
( ( ( X178 @ id @ ( lam @ ( X186 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X187: term] :
( ( ( X178 @ id @ ( X186 @ id @ X187 ) @ id )
= $true )
| ( ( X178 @ id @ X187 @ id )
!= $true ) )
| ~ ! [X188: term,X189: subst,X190: subst] :
( ( X186 @ ( comp @ X189 @ X190 ) @ ( sub @ X188 @ X190 ) )
= ( sub @ ( X186 @ X189 @ X188 ) @ X190 ) ) )
| ~ ! [X191: subst,X192: term,X193: subst,X194: subst] :
( ( ( X178 @ ( comp @ X191 @ X193 ) @ ( sub @ X192 @ X193 ) @ X194 )
!= $true )
| ( $true
= ( X178 @ X191 @ X192 @ ( comp @ X193 @ X194 ) ) ) )
| ~ ! [X195: term] :
( ( X180 @ X195 )
= ( X178 @ id @ X195 @ id ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true )
& ( termmset_gthm = $true )
& ( ! [X196: subst] :
( ( push @ ( sub @ one @ X196 ) @ ( comp @ sh @ X196 ) )
= X196 )
<=> ( axscons = $true ) )
& ( ( shinj = $true )
<=> ! [X197: term,X198: term] :
( ( ( sub @ X197 @ sh )
!= ( sub @ X198 @ sh ) )
| ( X197 = X198 ) ) )
& ! [X199: d_term,X200: d_term] :
( ( ( d2term @ X200 )
= ( d2term @ X199 ) )
=> ( X199 = X200 ) )
& ( pushprop_lem0_gthm = $true )
& ( axclos = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X201: subst > term > subst > $o] :
~ ! [X202: term > $o] :
~ ! [X203: term] :
( ( X202 @ X203 )
= ( X201 @ id @ X203 @ id ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X204: term > $o,X205: subst,X206: term > $o,X207: term,X208: term] :
( ( ( X206 @ ( sub @ X208 @ ( push @ X207 @ X205 ) ) )
= $true )
| ( ( X204 @ X208 )
!= $true ) ) )
& ! [X209: d_subst] : ( d_id = X209 )
& ( hoaslamnotap_lthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X210: subst,X211: term] :
( ( sub @ one @ ( push @ X211 @ X210 ) )
= X211 )
=> ! [X212: term,X213: subst,X214: term > $o,X215: term > $o] :
( ( ( X215 @ X212 )
!= $true )
| ( $true
= ( X214 @ one ) )
| ~ ! [X216: term] :
( ( X214 @ X216 )
= ( X215 @ ( sub @ X216 @ ( push @ X212 @ X213 ) ) ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X217: term > $o,X218: term] :
( ( ( X217 @ X218 )
= $true )
| ~ ! [X219: term] :
( ( ( var @ X219 )
!= $true )
| ( ( X217 @ X219 )
= $true ) )
| ~ ! [X220: term] :
( ( ( X217 @ ( lam @ X220 ) )
= $true )
| ~ ! [X221: term] :
( ( ( X217 @ X221 )
!= $true )
| ( ( X217 @ ( sub @ X220 @ ( push @ X221 @ id ) ) )
= $true ) ) )
| ~ ! [X222: term,X223: term] :
( ( ( X217 @ X222 )
!= $true )
| ( ( X217 @ ( ap @ X222 @ X223 ) )
= $true )
| ( ( X217 @ X223 )
!= $true ) ) )
=> ( ! [X224: subst > term > subst > $o,X225: term,X226: term] :
( ~ ! [X227: term,X228: term] :
( ( ( X224 @ id @ X228 @ id )
!= $true )
| ( ( X224 @ id @ ( ap @ ( sub @ X227 @ id ) @ X228 ) @ id )
= $true )
| ( ( X224 @ id @ X227 @ id )
!= $true ) )
| ( ( X224 @ id @ X226 @ id )
!= $true )
| ( $true
= ( X224 @ id @ ( ap @ X225 @ X226 ) @ id ) )
| ( ( X224 @ id @ X225 @ id )
!= $true )
| ~ ! [X229: term,X230: subst,X231: subst,X232: subst] :
( ( ( X224 @ X230 @ X229 @ ( comp @ X231 @ X232 ) )
= $true )
| ( ( X224 @ ( comp @ X230 @ X231 ) @ ( sub @ X229 @ X231 ) @ X232 )
!= $true ) )
| ~ ! [X233: subst,X234: term,X235: subst,X236: subst] :
( ( ( X224 @ X235 @ X234 @ ( comp @ X233 @ X236 ) )
!= $true )
| ( ( X224 @ ( comp @ X235 @ X233 ) @ ( sub @ X234 @ X233 ) @ X236 )
= $true ) ) )
=> ( ! [X237: term,X238: subst > term > subst > $o] :
( ~ ! [X239: subst,X240: term,X241: subst,X242: subst] :
( ( ( X238 @ X241 @ X240 @ ( comp @ X242 @ X239 ) )
= $true )
| ( ( X238 @ ( comp @ X241 @ X242 ) @ ( sub @ X240 @ X242 ) @ X239 )
!= $true ) )
| ~ ! [X243: subst,X244: subst,X245: term,X246: subst] :
( ( ( X238 @ X244 @ X245 @ ( comp @ X243 @ X246 ) )
!= $true )
| ( ( X238 @ ( comp @ X244 @ X243 ) @ ( sub @ X245 @ X243 ) @ X246 )
= $true ) )
| ~ ! [X247: subst > term > term] :
( ~ ! [X248: term] :
( ( $true
!= ( X238 @ id @ X248 @ id ) )
| ( ( X238 @ id @ ( X247 @ id @ X248 ) @ id )
= $true ) )
| ~ ! [X249: subst,X250: subst,X251: term] :
( ( X247 @ ( comp @ X249 @ X250 ) @ ( sub @ X251 @ X250 ) )
= ( sub @ ( X247 @ X249 @ X251 ) @ X250 ) )
| ( ( X238 @ id @ ( lam @ ( X247 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X238 @ id @ ( lam @ X237 ) @ id )
= $true )
| ~ ! [X252: term] :
( ( ( X238 @ id @ X252 @ id )
!= $true )
| ( ( X238 @ id @ ( sub @ X237 @ ( push @ X252 @ id ) ) @ id )
= $true ) ) )
=> ! [X253: subst > term > subst > $o,X254: term] :
( ~ ! [X255: subst,X256: term,X257: subst,X258: subst] :
( ( ( X253 @ ( comp @ X258 @ X257 ) @ ( sub @ X256 @ X257 ) @ X255 )
= $true )
| ( $true
!= ( X253 @ X258 @ X256 @ ( comp @ X257 @ X255 ) ) ) )
| ~ ! [X259: term,X260: term] :
( ( ( X253 @ id @ X259 @ id )
!= $true )
| ( $true
= ( X253 @ id @ ( ap @ ( sub @ X259 @ id ) @ X260 ) @ id ) )
| ( ( X253 @ id @ X260 @ id )
!= $true ) )
| ~ ! [X261: subst > term > term] :
( ~ ! [X262: term] :
( ( $true
!= ( X253 @ id @ X262 @ id ) )
| ( $true
= ( X253 @ id @ ( X261 @ id @ X262 ) @ id ) ) )
| ( ( X253 @ id @ ( lam @ ( X261 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X263: term,X264: subst,X265: subst] :
( ( X261 @ ( comp @ X265 @ X264 ) @ ( sub @ X263 @ X264 ) )
= ( sub @ ( X261 @ X265 @ X263 ) @ X264 ) ) )
| ~ ! [X266: subst,X267: subst,X268: term,X269: subst] :
( ( ( X253 @ X267 @ X268 @ ( comp @ X269 @ X266 ) )
= $true )
| ( ( X253 @ ( comp @ X267 @ X269 ) @ ( sub @ X268 @ X269 ) @ X266 )
!= $true ) )
| ~ ! [X270: term] :
( ( ( X253 @ id @ X270 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X270 @ id ) ) ) )
| ( ( X253 @ id @ X254 @ id )
= $true ) ) ) ) ) )
& ( ! [X271: term,X272: term > $o,X273: subst > term > subst > $o,X274: term] :
( ( $true
!= ( X272 @ X274 ) )
| ~ ! [X275: term] :
( ( X272 @ X275 )
= ( X273 @ id @ X275 @ id ) )
| ~ ! [X276: subst,X277: subst,X278: subst,X279: term] :
( ( ( X273 @ X276 @ X279 @ ( comp @ X278 @ X277 ) )
!= $true )
| ( ( X273 @ ( comp @ X276 @ X278 ) @ ( sub @ X279 @ X278 ) @ X277 )
= $true ) )
| ~ ! [X280: term,X281: term] :
( ( ( X273 @ id @ ( ap @ ( sub @ X281 @ id ) @ X280 ) @ id )
= $true )
| ( ( X273 @ id @ X280 @ id )
!= $true )
| ( ( X273 @ id @ X281 @ id )
!= $true ) )
| ~ ! [X282: subst,X283: term,X284: subst,X285: subst] :
( ( ( X273 @ ( comp @ X285 @ X282 ) @ ( sub @ X283 @ X282 ) @ X284 )
!= $true )
| ( ( X273 @ X285 @ X283 @ ( comp @ X282 @ X284 ) )
= $true ) )
| ( ( X272 @ X271 )
!= $true )
| ( ( X272 @ ( ap @ X274 @ X271 ) )
= $true ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X286: term] :
( ( sub @ X286 @ id )
= X286 )
=> ( ! [X287: term,X288: subst > term > subst > $o] :
( ~ ! [X289: subst > term > term] :
( ~ ! [X290: term] :
( ( ( X288 @ id @ ( X289 @ id @ X290 ) @ id )
= $true )
| ( $true
!= ( X288 @ id @ X290 @ id ) ) )
| ~ ! [X291: term,X292: subst,X293: subst] :
( ( sub @ ( X289 @ X292 @ X291 ) @ X293 )
= ( X289 @ ( comp @ X292 @ X293 ) @ ( sub @ X291 @ X293 ) ) )
| ( $true
= ( X288 @ id @ ( lam @ ( X289 @ sh @ one ) ) @ id ) ) )
| ~ ! [X294: term] :
( ( $true
= ( X288 @ id @ ( sub @ X287 @ ( push @ X294 @ id ) ) @ id ) )
| ( ( X288 @ id @ X294 @ id )
!= $true ) )
| ( ( X288 @ id @ ( lam @ ( sub @ X287 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X295: subst > term > subst > $o,X296: term] :
( ( ( X295 @ id @ ( lam @ X296 ) @ id )
= $true )
| ~ ! [X297: subst,X298: subst,X299: subst,X300: term] :
( ( $true
!= ( X295 @ ( comp @ X297 @ X298 ) @ ( sub @ X300 @ X298 ) @ X299 ) )
| ( ( X295 @ X297 @ X300 @ ( comp @ X298 @ X299 ) )
= $true ) )
| ~ ! [X301: subst > term > term] :
( ~ ! [X302: subst,X303: subst,X304: term] :
( ( X301 @ ( comp @ X303 @ X302 ) @ ( sub @ X304 @ X302 ) )
= ( sub @ ( X301 @ X303 @ X304 ) @ X302 ) )
| ~ ! [X305: term] :
( ( ( X295 @ id @ X305 @ id )
!= $true )
| ( ( X295 @ id @ ( X301 @ id @ X305 ) @ id )
= $true ) )
| ( $true
= ( X295 @ id @ ( lam @ ( X301 @ sh @ one ) ) @ id ) ) )
| ~ ! [X306: term] :
( ( ( X295 @ id @ X306 @ id )
!= $true )
| ( ( X295 @ id @ ( sub @ X296 @ ( push @ X306 @ id ) ) @ id )
= $true ) )
| ~ ! [X307: subst,X308: subst,X309: subst,X310: term] :
( ( ( X295 @ ( comp @ X307 @ X308 ) @ ( sub @ X310 @ X308 ) @ X309 )
= $true )
| ( ( X295 @ X307 @ X310 @ ( comp @ X308 @ X309 ) )
!= $true ) ) ) ) ) )
& ( ! [X311: subst > term > subst > $o] :
~ ! [X312: term > $o] :
~ ! [X313: term] :
( ( X311 @ id @ X313 @ id )
= ( X312 @ X313 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X314: subst > term > term,X315: term,X316: term] :
( ~ ! [X317: subst,X318: term,X319: subst] :
( ( X314 @ ( comp @ X319 @ X317 ) @ ( sub @ X318 @ X317 ) )
= ( sub @ ( X314 @ X319 @ X318 ) @ X317 ) )
| ( ( ap @ ( sub @ X315 @ id ) @ X316 )
!= ( lam @ ( X314 @ sh @ one ) ) ) ) )
& ( lamnotvar = $true )
& ( ( ! [X320: term] :
( ( sub @ X320 @ id )
= X320 )
=> ( ! [X321: subst > term > subst > $o,X322: term] :
( ~ ! [X323: term] :
( ( ( X321 @ id @ ( sub @ X322 @ ( push @ X323 @ id ) ) @ id )
= $true )
| ( $true
!= ( X321 @ id @ X323 @ id ) ) )
| ( ( X321 @ id @ ( lam @ ( sub @ X322 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X324: subst > term > term] :
( ~ ! [X325: subst,X326: subst,X327: term] :
( ( X324 @ ( comp @ X325 @ X326 ) @ ( sub @ X327 @ X326 ) )
= ( sub @ ( X324 @ X325 @ X327 ) @ X326 ) )
| ( ( X321 @ id @ ( lam @ ( X324 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X328: term] :
( ( $true
= ( X321 @ id @ ( X324 @ id @ X328 ) @ id ) )
| ( ( X321 @ id @ X328 @ id )
!= $true ) ) ) )
=> ! [X329: subst > term > subst > $o,X330: term] :
( ~ ! [X331: term] :
( ( $true
= ( X329 @ id @ ( sub @ X330 @ ( push @ X331 @ id ) ) @ id ) )
| ( ( X329 @ id @ X331 @ id )
!= $true ) )
| ~ ! [X332: subst > term > term] :
( ~ ! [X333: subst,X334: term,X335: subst] :
( ( X332 @ ( comp @ X333 @ X335 ) @ ( sub @ X334 @ X335 ) )
= ( sub @ ( X332 @ X333 @ X334 ) @ X335 ) )
| ( ( X329 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X336: term] :
( ( ( X329 @ id @ ( X332 @ id @ X336 ) @ id )
= $true )
| ( $true
!= ( X329 @ id @ X336 @ id ) ) ) )
| ( ( X329 @ id @ ( lam @ X330 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X337: subst,X338: term] :
( ( sub @ one @ ( push @ X338 @ X337 ) )
= X338 )
=> ( ! [X339: term,X340: subst] :
( ( comp @ sh @ ( push @ X339 @ X340 ) )
= X340 )
=> ( ! [X341: subst] :
( ( comp @ X341 @ id )
= X341 )
=> ( ! [X342: term > $o,X343: term] :
( ~ ! [X344: term,X345: term] :
( ( ( X342 @ ( ap @ X345 @ X344 ) )
= $true )
| ( ( X342 @ X345 )
!= $true )
| ( ( X342 @ X344 )
!= $true ) )
| ~ ! [X346: term] :
( ( ( X342 @ ( lam @ X346 ) )
= $true )
| ( ( X342 @ X346 )
!= $true ) )
| ~ ! [X347: term] :
( ( $true
!= ( var @ X347 ) )
| ( ( X342 @ X347 )
= $true ) )
| ( ( X342 @ X343 )
= $true ) )
=> ! [X348: term > $o,X349: term,X350: subst] :
( ~ ! [X351: term,X352: term] :
( ( ( X348 @ ( ap @ X352 @ X351 ) )
= $true )
| ( ( X348 @ X351 )
!= $true )
| ( ( X348 @ X352 )
!= $true ) )
| ~ ! [X353: term] :
( ~ ! [X354: term] :
( ( $true
= ( X348 @ ( sub @ X353 @ ( push @ X354 @ id ) ) ) )
| ( ( X348 @ X354 )
!= $true ) )
| ( ( X348 @ ( lam @ X353 ) )
= $true ) )
| ~ ! [X355: term] :
( ( ( var @ X355 )
!= $true )
| ( $true
= ( X348 @ ( sub @ X355 @ X350 ) ) ) )
| ( ( X348 @ ( sub @ X349 @ X350 ) )
= $true ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ~ ! [X359: term] :
( ( X357 @ X359 )
= ( X356 @ id @ X359 @ id ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ~ ! [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
!= $true )
| ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
= $true ) )
| ~ ! [X364: term] :
( ( $true
!= ( X357 @ X364 ) )
| ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
= $true ) )
| ~ ! [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
!= $true )
| ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
= $true ) )
| ~ ! [X369: subst > term > term] :
( ~ ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) )
| ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X374: term] :
( ( sub @ X374 @ id )
= X374 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X375: subst > term > subst > $o,X376: term] :
( ( ( X375 @ id @ ( lam @ X376 ) @ id )
= $true )
| ~ ! [X377: term] :
( ( ( X375 @ id @ ( sub @ X376 @ ( push @ X377 @ id ) ) @ id )
= $true )
| ( $true
!= ( X375 @ id @ X377 @ id ) ) )
| ~ ! [X378: subst > term > term] :
( ~ ! [X379: term] :
( ( ( X375 @ id @ ( X378 @ id @ X379 ) @ id )
= $true )
| ( ( X375 @ id @ X379 @ id )
!= $true ) )
| ( ( X375 @ id @ ( lam @ ( X378 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X380: subst,X381: subst,X382: term] :
( ( sub @ ( X378 @ X380 @ X382 ) @ X381 )
= ( X378 @ ( comp @ X380 @ X381 ) @ ( sub @ X382 @ X381 ) ) ) ) ) )
& ( ! [X383: term] :
( ( sub @ X383 @ id )
= X383 )
<=> ( termmset = $true ) )
& ( ( ! [X384: term,X385: subst] :
( ( sub @ one @ ( push @ X384 @ X385 ) )
= X384 )
=> ( ! [X386: subst,X387: term] :
( ( comp @ sh @ ( push @ X387 @ X386 ) )
= X386 )
=> ( ! [X388: term,X389: term] :
( ( ( lam @ X389 )
!= ( lam @ X388 ) )
| ( X388 = X389 ) )
=> ! [X390: subst,X391: subst > term > term,X392: term,X393: subst > term > term] :
( ( ( X391 @ X390 @ X392 )
= ( X393 @ X390 @ X392 ) )
| ~ ! [X394: subst,X395: term,X396: subst] :
( ( X393 @ ( comp @ X396 @ X394 ) @ ( sub @ X395 @ X394 ) )
= ( sub @ ( X393 @ X396 @ X395 ) @ X394 ) )
| ( ( lam @ ( X391 @ sh @ one ) )
!= ( lam @ ( X393 @ sh @ one ) ) )
| ~ ! [X397: subst,X398: term,X399: subst] :
( ( X391 @ ( comp @ X397 @ X399 ) @ ( sub @ X398 @ X399 ) )
= ( sub @ ( X391 @ X397 @ X398 ) @ X399 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( induction2 = $true )
<=> ! [X400: term > $o,X401: term] :
( ~ ! [X402: term,X403: term] :
( ( $true
= ( X400 @ ( ap @ X403 @ X402 ) ) )
| ( ( X400 @ X402 )
!= $true )
| ( ( X400 @ X403 )
!= $true ) )
| ( ( X400 @ X401 )
= $true )
| ~ ! [X404: term] :
( ( ( var @ X404 )
!= $true )
| ( ( X400 @ X404 )
= $true ) )
| ~ ! [X405: term] :
( ~ ! [X406: term] :
( ( ( X400 @ X406 )
!= $true )
| ( ( X400 @ ( sub @ X405 @ ( push @ X406 @ id ) ) )
= $true ) )
| ( ( X400 @ ( lam @ X405 ) )
= $true ) ) ) )
& ( ( ! [X408: subst] :
( ( comp @ id @ X408 )
= X408 )
& ! [X407: subst] :
( ( comp @ X407 @ id )
= X407 ) )
<=> ( substmonoid = $true ) )
& ( ( axidl = $true )
<=> ! [X409: subst] :
( ( comp @ id @ X409 )
= X409 ) )
& ! [X410: d_term] : ( d_one = X410 )
& ( pushprop_lthm_orig = $true )
& ( ! [X411: term,X412: term,X413: term,X414: term] :
( ( ( ap @ X412 @ X411 )
!= ( ap @ X413 @ X414 ) )
| ( X412 = X413 ) )
<=> ( apinj1 = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop = $true )
& ( axvarshift = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X415: term] :
~ ! [X416: subst > term > term] :
( ( sub @ X415 @ ( push @ one @ sh ) )
!= ( X416 @ sh @ one ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( ! [X417: term] :
( ( sub @ X417 @ id )
= X417 )
=> ! [X418: term] :
( ( sub @ X418 @ id )
= X418 ) )
<=> ( termmset_lthm = $true ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axmap = $true )
& ! [X419: subst] :
? [X420: d_subst] :
( ( d2subst @ X420 )
= X419 )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X421: subst > term > subst > $o,X422: term] :
( ~ ! [X423: subst > term > term] :
( ~ ! [X424: term] :
( ( ( X421 @ id @ ( X423 @ id @ X424 ) @ id )
= $true )
| ( ( X421 @ id @ X424 @ id )
!= $true ) )
| ~ ! [X425: term,X426: subst,X427: subst] :
( ( sub @ ( X423 @ X427 @ X425 ) @ X426 )
= ( X423 @ ( comp @ X427 @ X426 ) @ ( sub @ X425 @ X426 ) ) )
| ( ( X421 @ id @ ( lam @ ( X423 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X421 @ id @ ( lam @ ( sub @ X422 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X428: term] :
( ( ( X421 @ id @ ( sub @ X422 @ ( push @ X428 @ id ) ) @ id )
= $true )
| ( ( X421 @ id @ X428 @ id )
!= $true ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X429: term,X430: term,X431: subst > term > subst > $o] :
( ( ( X431 @ id @ X429 @ id )
!= $true )
| ~ ! [X432: term,X433: term] :
( ( ( X431 @ id @ X432 @ id )
!= $true )
| ( ( X431 @ id @ ( ap @ ( sub @ X432 @ id ) @ X433 ) @ id )
= $true )
| ( ( X431 @ id @ X433 @ id )
!= $true ) )
| ( ( X431 @ id @ ( ap @ X430 @ X429 ) @ id )
= $true )
| ~ ! [X434: term,X435: subst,X436: subst,X437: subst] :
( ( ( X431 @ ( comp @ X436 @ X435 ) @ ( sub @ X434 @ X435 ) @ X437 )
= $true )
| ( ( X431 @ X436 @ X434 @ ( comp @ X435 @ X437 ) )
!= $true ) )
| ~ ! [X438: subst,X439: term,X440: subst,X441: subst] :
( ( ( X431 @ X438 @ X439 @ ( comp @ X441 @ X440 ) )
= $true )
| ( ( X431 @ ( comp @ X438 @ X441 ) @ ( sub @ X439 @ X441 ) @ X440 )
!= $true ) )
| ( $true
!= ( X431 @ id @ X430 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X442: term,X443: subst > term > subst > $o] :
( ~ ! [X444: term] :
( ( ( X443 @ id @ ( sub @ X442 @ ( push @ X444 @ id ) ) @ id )
= $true )
| ( ( X443 @ id @ X444 @ id )
!= $true ) )
| ~ ! [X445: subst > term > term] :
( ~ ! [X446: subst,X447: term,X448: subst] :
( ( sub @ ( X445 @ X446 @ X447 ) @ X448 )
= ( X445 @ ( comp @ X446 @ X448 ) @ ( sub @ X447 @ X448 ) ) )
| ~ ! [X449: term] :
( ( ( X443 @ id @ X449 @ id )
!= $true )
| ( ( X443 @ id @ ( X445 @ id @ X449 ) @ id )
= $true ) )
| ( ( X443 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X443 @ id @ ( lam @ ( sub @ X442 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) )
& ( hoaslamnotap_gthm = $true )
& ! [X450: term] :
? [X451: d_term] :
( ( d2term @ X451 )
= X450 )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ ( sub @ X455 @ id ) @ X454 )
!= ( ap @ ( sub @ X452 @ id ) @ X453 ) )
| ( X453 = X454 ) )
<=> ( hoasapinj2 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X456: subst,X457: term > $o,X458: term] :
~ ! [X459: term > $o] :
~ ! [X460: term] :
( ( X459 @ X460 )
= ( X457 @ ( sub @ X460 @ ( push @ X458 @ X456 ) ) ) ) )
& ( ( laminj = $true )
<=> ! [X461: term,X462: term] :
( ( ( lam @ X461 )
!= ( lam @ X462 ) )
| ( X461 = X462 ) ) )
& ( induction2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ( axshiftcons = $true )
<=> ! [X463: subst,X464: term] :
( ( comp @ sh @ ( push @ X464 @ X463 ) )
= X463 ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( hoasinduction = $true )
<=> ! [X465: term,X466: subst > term > subst > $o] :
( ~ ! [X467: term] :
( ( $true
= ( X466 @ id @ X467 @ id ) )
| ( ( var @ ( sub @ X467 @ id ) )
!= $true ) )
| ~ ! [X468: term,X469: subst,X470: subst,X471: subst] :
( ( ( X466 @ X470 @ X468 @ ( comp @ X471 @ X469 ) )
!= $true )
| ( ( X466 @ ( comp @ X470 @ X471 ) @ ( sub @ X468 @ X471 ) @ X469 )
= $true ) )
| ~ ! [X472: subst > term > term] :
( ~ ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) )
| ~ ! [X476: term] :
( ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true )
| ( ( X466 @ id @ X476 @ id )
!= $true ) )
| ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X466 @ id @ X465 @ id )
= $true )
| ~ ! [X477: subst,X478: subst,X479: subst,X480: term] :
( ( $true
= ( X466 @ X479 @ X480 @ ( comp @ X478 @ X477 ) ) )
| ( $true
!= ( X466 @ ( comp @ X479 @ X478 ) @ ( sub @ X480 @ X478 ) @ X477 ) ) )
| ~ ! [X481: term,X482: term] :
( ( ( X466 @ id @ ( ap @ ( sub @ X482 @ id ) @ X481 ) @ id )
= $true )
| ( ( X466 @ id @ X481 @ id )
!= $true )
| ( $true
!= ( X466 @ id @ X482 @ id ) ) ) ) )
& ( ! [X483: term] :
~ ! [X484: subst > term > term] :
~ ! [X485: subst,X486: term] :
( ( sub @ X483 @ ( push @ X486 @ X485 ) )
= ( X484 @ X485 @ X486 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ! [X487: term,X488: subst > term > subst > $o] :
( ~ ! [X489: term,X490: term] :
( ( ( X488 @ id @ X490 @ id )
!= $true )
| ( ( X488 @ id @ ( ap @ ( sub @ X489 @ id ) @ X490 ) @ id )
= $true )
| ( $true
!= ( X488 @ id @ X489 @ id ) ) )
| ~ ! [X491: subst > term > term] :
( ~ ! [X492: subst,X493: term,X494: subst] :
( ( sub @ ( X491 @ X492 @ X493 ) @ X494 )
= ( X491 @ ( comp @ X492 @ X494 ) @ ( sub @ X493 @ X494 ) ) )
| ( ( X488 @ id @ ( lam @ ( X491 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X495: term] :
( ( ( X488 @ id @ X495 @ id )
!= $true )
| ( ( X488 @ id @ ( X491 @ id @ X495 ) @ id )
= $true ) ) )
| ( ( X488 @ id @ X487 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( ! [X496: term] :
( ( sub @ X496 @ id )
= X496 )
=> ( ! [X497: term > $o,X498: subst,X499: term] :
( ( ( X497 @ ( sub @ X499 @ X498 ) )
= $true )
| ~ ! [X500: term,X501: term] :
( ( ( X497 @ X500 )
!= $true )
| ( ( X497 @ ( ap @ X500 @ X501 ) )
= $true )
| ( ( X497 @ X501 )
!= $true ) )
| ~ ! [X502: term] :
( ( ( X497 @ ( lam @ X502 ) )
= $true )
| ~ ! [X503: term] :
( ( ( X497 @ X503 )
!= $true )
| ( ( X497 @ ( sub @ X502 @ ( push @ X503 @ id ) ) )
= $true ) ) )
| ~ ! [X504: term] :
( ( ( var @ X504 )
!= $true )
| ( $true
= ( X497 @ ( sub @ X504 @ X498 ) ) ) ) )
=> ! [X505: term > $o,X506: term] :
( ( $true
= ( X505 @ X506 ) )
| ~ ! [X507: term] :
( ~ ! [X508: term] :
( ( ( X505 @ X508 )
!= $true )
| ( ( X505 @ ( sub @ X507 @ ( push @ X508 @ id ) ) )
= $true ) )
| ( $true
= ( X505 @ ( lam @ X507 ) ) ) )
| ~ ! [X509: term,X510: term] :
( ( ( X505 @ ( ap @ X509 @ X510 ) )
= $true )
| ( ( X505 @ X509 )
!= $true )
| ( ( X505 @ X510 )
!= $true ) )
| ~ ! [X511: term] :
( ( ( var @ X511 )
!= $true )
| ( ( X505 @ X511 )
= $true ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X512: subst > term > subst > $o,X513: term > $o,X514: term] :
( ~ ! [X515: term] :
( ( X513 @ X515 )
= ( X512 @ id @ X515 @ id ) )
| ( $true
= ( X513 @ ( lam @ X514 ) ) )
| ~ ! [X516: subst > term > term] :
( ~ ! [X517: subst,X518: subst,X519: term] :
( ( sub @ ( X516 @ X518 @ X519 ) @ X517 )
= ( X516 @ ( comp @ X518 @ X517 ) @ ( sub @ X519 @ X517 ) ) )
| ( ( X512 @ id @ ( lam @ ( X516 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X520: term] :
( ( ( X512 @ id @ ( X516 @ id @ X520 ) @ id )
= $true )
| ( ( X512 @ id @ X520 @ id )
!= $true ) ) )
| ~ ! [X521: term] :
( ( ( X513 @ ( sub @ X514 @ ( push @ X521 @ id ) ) )
= $true )
| ( ( X513 @ X521 )
!= $true ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X522: subst > term > term,X523: subst,X524: subst > term > term,X525: term] :
( ( ( lam @ ( X522 @ sh @ one ) )
!= ( lam @ ( X524 @ sh @ one ) ) )
| ( ( X524 @ X523 @ X525 )
= ( X522 @ X523 @ X525 ) )
| ~ ! [X526: subst,X527: term,X528: subst] :
( ( X524 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) )
= ( sub @ ( X524 @ X526 @ X527 ) @ X528 ) )
| ~ ! [X529: term,X530: subst,X531: subst] :
( ( X522 @ ( comp @ X530 @ X531 ) @ ( sub @ X529 @ X531 ) )
= ( sub @ ( X522 @ X530 @ X529 ) @ X531 ) ) ) )
& ( pushprop_gthm = $true )
& ( ( induction2lem = $true )
<=> ! [X532: term,X533: subst,X534: term > $o] :
( ~ ! [X535: term] :
( ( ( X534 @ ( lam @ X535 ) )
= $true )
| ~ ! [X536: term] :
( ( ( X534 @ ( sub @ X535 @ ( push @ X536 @ id ) ) )
= $true )
| ( ( X534 @ X536 )
!= $true ) ) )
| ( ( X534 @ ( sub @ X532 @ X533 ) )
= $true )
| ~ ! [X537: term] :
( ( ( var @ X537 )
!= $true )
| ( ( X534 @ ( sub @ X537 @ X533 ) )
= $true ) )
| ~ ! [X538: term,X539: term] :
( ( ( X534 @ X539 )
!= $true )
| ( ( X534 @ X538 )
!= $true )
| ( ( X534 @ ( ap @ X538 @ X539 ) )
= $true ) ) ) )
& ( hoasapnotvar_gthm = $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( hoasinduction_lem1v2 = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ~ ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) )
| ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ one )
= $true ) ) )
& ( ( ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
=> ( ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) )
=> ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( pushprop_lthm = $true )
& ( ! [X14: term > $o,X15: term,X16: subst] :
~ ! [X17: term > $o] :
~ ! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
=> ( ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
=> ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
= $true )
| ( ( X24 @ X27 )
!= $true ) ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X28: term] :
~ ! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X30: term,X31: term,X32: term,X33: term] :
( ( X30 = X33 )
| ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( axabs = $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( ! [X39: term] :
~ ! [X40: subst > term > term] :
~ ! [X41: subst,X42: term] :
( ( sub @ X39 @ ( push @ X42 @ X41 ) )
= ( X40 @ X41 @ X42 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_lem3v2 = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X43: subst > term > subst > $o,X44: term] :
( ~ ! [X45: term,X46: subst,X47: subst,X48: subst] :
( ( ( X43 @ ( comp @ X47 @ X48 ) @ ( sub @ X45 @ X48 ) @ X46 )
= $true )
| ( ( X43 @ X47 @ X45 @ ( comp @ X48 @ X46 ) )
!= $true ) )
| ~ ! [X49: subst,X50: subst,X51: subst,X52: term] :
( ( ( X43 @ ( comp @ X49 @ X51 ) @ ( sub @ X52 @ X51 ) @ X50 )
!= $true )
| ( $true
= ( X43 @ X49 @ X52 @ ( comp @ X51 @ X50 ) ) ) )
| ~ ! [X53: term] :
( ( $true
!= ( X43 @ id @ X53 @ id ) )
| ( ( X43 @ id @ ( sub @ X44 @ ( push @ X53 @ id ) ) @ id )
= $true ) )
| ( ( X43 @ id @ ( lam @ X44 ) @ id )
= $true )
| ~ ! [X54: subst > term > term] :
( ~ ! [X55: subst,X56: subst,X57: term] :
( ( sub @ ( X54 @ X55 @ X57 ) @ X56 )
= ( X54 @ ( comp @ X55 @ X56 ) @ ( sub @ X57 @ X56 ) ) )
| ~ ! [X58: term] :
( ( ( X43 @ id @ ( X54 @ id @ X58 ) @ id )
= $true )
| ( ( X43 @ id @ X58 @ id )
!= $true ) )
| ( ( X43 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ! [X59: d_subst,X60: d_subst] :
( ( ( d2subst @ X59 )
= ( d2subst @ X60 ) )
=> ( X59 = X60 ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X61: term,X62: term,X63: term,X64: term] :
( ( X62 = X63 )
| ( ( ap @ X61 @ X63 )
!= ( ap @ X64 @ X62 ) ) )
=> ! [X65: term,X66: term,X67: term,X68: term] :
( ( ( ap @ ( sub @ X68 @ id ) @ X65 )
!= ( ap @ ( sub @ X67 @ id ) @ X66 ) )
| ( X65 = X66 ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X69: term,X70: subst > term > subst > $o] :
( ( ( X70 @ id @ ( lam @ ( sub @ X69 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X71: term] :
( ( $true
= ( X70 @ id @ ( sub @ X69 @ ( push @ X71 @ id ) ) @ id ) )
| ( ( X70 @ id @ X71 @ id )
!= $true ) )
| ~ ! [X72: subst > term > term,X73: term] :
( ~ ! [X74: subst,X75: subst,X76: term] :
( ( sub @ ( X72 @ X74 @ X76 ) @ X75 )
= ( sub @ ( sub @ X73 @ ( push @ X76 @ X74 ) ) @ X75 ) )
| ~ ! [X77: subst,X78: term,X79: subst] :
( ( sub @ X73 @ ( push @ ( sub @ X78 @ X79 ) @ ( comp @ X77 @ X79 ) ) )
= ( X72 @ ( comp @ X77 @ X79 ) @ ( sub @ X78 @ X79 ) ) )
| ~ ! [X80: term] :
( ( ( X70 @ id @ X80 @ id )
!= $true )
| ( $true
= ( X70 @ id @ ( X72 @ id @ X80 ) @ id ) ) )
| ( ( X70 @ id @ ( lam @ ( X72 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( apnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X81: subst > term > subst > $o] :
~ ! [X82: term > $o] :
~ ! [X83: term] :
( ( X81 @ id @ X83 @ id )
= ( X82 @ X83 ) )
=> ( ! [X84: term > $o,X85: term] :
( ( $true
= ( X84 @ X85 ) )
| ~ ! [X86: term,X87: term] :
( ( ( X84 @ X87 )
!= $true )
| ( ( X84 @ ( ap @ X87 @ X86 ) )
= $true )
| ( ( X84 @ X86 )
!= $true ) )
| ~ ! [X88: term] :
( ( ( var @ X88 )
!= $true )
| ( ( X84 @ X88 )
= $true ) )
| ~ ! [X89: term] :
( ( ( X84 @ ( lam @ X89 ) )
= $true )
| ~ ! [X90: term] :
( ( ( X84 @ ( sub @ X89 @ ( push @ X90 @ id ) ) )
= $true )
| ( ( X84 @ X90 )
!= $true ) ) ) )
=> ( ! [X91: term] :
( ( sub @ X91 @ id )
= X91 )
=> ( ! [X92: subst > term > subst > $o,X93: term > $o,X94: term] :
( ( $true
= ( X93 @ ( lam @ X94 ) ) )
| ~ ! [X95: term] :
( ( X93 @ X95 )
= ( X92 @ id @ X95 @ id ) )
| ~ ! [X96: subst > term > term] :
( ( $true
= ( X92 @ id @ ( lam @ ( X96 @ sh @ one ) ) @ id ) )
| ~ ! [X97: term] :
( ( ( X92 @ id @ X97 @ id )
!= $true )
| ( ( X92 @ id @ ( X96 @ id @ X97 ) @ id )
= $true ) )
| ~ ! [X98: subst,X99: term,X100: subst] :
( ( X96 @ ( comp @ X100 @ X98 ) @ ( sub @ X99 @ X98 ) )
= ( sub @ ( X96 @ X100 @ X99 ) @ X98 ) ) )
| ~ ! [X101: term] :
( ( ( X93 @ ( sub @ X94 @ ( push @ X101 @ id ) ) )
= $true )
| ( ( X93 @ X101 )
!= $true ) ) )
=> ! [X102: subst > term > subst > $o,X103: term] :
( ~ ! [X104: subst,X105: subst,X106: term,X107: subst] :
( ( $true
= ( X102 @ ( comp @ X104 @ X107 ) @ ( sub @ X106 @ X107 ) @ X105 ) )
| ( ( X102 @ X104 @ X106 @ ( comp @ X107 @ X105 ) )
!= $true ) )
| ~ ! [X108: subst,X109: subst,X110: subst,X111: term] :
( ( ( X102 @ X108 @ X111 @ ( comp @ X109 @ X110 ) )
= $true )
| ( ( X102 @ ( comp @ X108 @ X109 ) @ ( sub @ X111 @ X109 ) @ X110 )
!= $true ) )
| ~ ! [X112: term,X113: term] :
( ( ( X102 @ id @ X112 @ id )
!= $true )
| ( ( X102 @ id @ X113 @ id )
!= $true )
| ( ( X102 @ id @ ( ap @ ( sub @ X113 @ id ) @ X112 ) @ id )
= $true ) )
| ~ ! [X114: term] :
( ( ( X102 @ id @ X114 @ id )
= $true )
| ( ( var @ ( sub @ X114 @ id ) )
!= $true ) )
| ( ( X102 @ id @ X103 @ id )
= $true )
| ~ ! [X115: subst > term > term] :
( ~ ! [X116: subst,X117: term,X118: subst] :
( ( sub @ ( X115 @ X118 @ X117 ) @ X116 )
= ( X115 @ ( comp @ X118 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
| ~ ! [X119: term] :
( ( ( X102 @ id @ X119 @ id )
!= $true )
| ( ( X102 @ id @ ( X115 @ id @ X119 ) @ id )
= $true ) )
| ( $true
= ( X102 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X120: subst > term > subst > $o] :
~ ! [X121: term > $o] :
~ ! [X122: term] :
( ( X121 @ X122 )
= ( X120 @ id @ X122 @ id ) )
=> ( ! [X123: term,X124: term > $o] :
( ~ ! [X125: term,X126: term] :
( ( $true
!= ( X124 @ X126 ) )
| ( ( X124 @ ( ap @ X125 @ X126 ) )
= $true )
| ( ( X124 @ X125 )
!= $true ) )
| ~ ! [X127: term] :
( ( $true
= ( X124 @ X127 ) )
| ( ( var @ X127 )
!= $true ) )
| ~ ! [X128: term] :
( ( ( X124 @ ( lam @ X128 ) )
= $true )
| ~ ! [X129: term] :
( ( ( X124 @ X129 )
!= $true )
| ( ( X124 @ ( sub @ X128 @ ( push @ X129 @ id ) ) )
= $true ) ) )
| ( ( X124 @ X123 )
= $true ) )
=> ( ! [X130: term] :
( ( sub @ X130 @ id )
= X130 )
=> ( ! [X131: subst > term > subst > $o,X132: term,X133: term > $o] :
( ( $true
= ( X133 @ ( lam @ X132 ) ) )
| ~ ! [X134: term] :
( ( ( X133 @ X134 )
!= $true )
| ( ( X133 @ ( sub @ X132 @ ( push @ X134 @ id ) ) )
= $true ) )
| ~ ! [X135: term] :
( ( X131 @ id @ X135 @ id )
= ( X133 @ X135 ) )
| ~ ! [X136: subst > term > term] :
( ( ( X131 @ id @ ( lam @ ( X136 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X137: term] :
( ( ( X131 @ id @ X137 @ id )
!= $true )
| ( ( X131 @ id @ ( X136 @ id @ X137 ) @ id )
= $true ) )
| ~ ! [X138: subst,X139: term,X140: subst] :
( ( sub @ ( X136 @ X138 @ X139 ) @ X140 )
= ( X136 @ ( comp @ X138 @ X140 ) @ ( sub @ X139 @ X140 ) ) ) ) )
=> ! [X141: subst > term > subst > $o,X142: term] :
( ( ( X141 @ id @ X142 @ id )
= $true )
| ~ ! [X143: subst > term > term] :
( ~ ! [X144: term] :
( ( $true
!= ( X141 @ id @ X144 @ id ) )
| ( ( X141 @ id @ ( X143 @ id @ X144 ) @ id )
= $true ) )
| ( ( X141 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X145: term,X146: subst,X147: subst] :
( ( X143 @ ( comp @ X147 @ X146 ) @ ( sub @ X145 @ X146 ) )
= ( sub @ ( X143 @ X147 @ X145 ) @ X146 ) ) )
| ~ ! [X148: term,X149: term] :
( ( ( X141 @ id @ X149 @ id )
!= $true )
| ( ( X141 @ id @ X148 @ id )
!= $true )
| ( ( X141 @ id @ ( ap @ ( sub @ X149 @ id ) @ X148 ) @ id )
= $true ) ) ) ) ) ) ) )
& ( axapp = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ulamvar1 != $true )
& ( hoasinduction_lem1 = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X150: subst] :
( ( comp @ id @ X150 )
= X150 )
=> ( ! [X151: subst] :
( ( comp @ X151 @ id )
= X151 )
=> ( ! [X152: subst] :
( ( comp @ X152 @ id )
= X152 )
& ! [X153: subst] :
( ( comp @ id @ X153 )
= X153 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ! [X154: term > $o,X155: term] :
( ~ ! [X156: term,X157: term] :
( ( ( X154 @ ( ap @ X157 @ X156 ) )
= $true )
| ( ( X154 @ X157 )
!= $true )
| ( ( X154 @ X156 )
!= $true ) )
| ~ ! [X158: term] :
( ( $true
!= ( X154 @ X158 ) )
| ( ( X154 @ ( lam @ X158 ) )
= $true ) )
| ( ( X154 @ X155 )
= $true )
| ~ ! [X159: term] :
( ( $true
= ( X154 @ X159 ) )
| ( $true
!= ( var @ X159 ) ) ) )
<=> ( induction = $true ) )
& ( ( axvarcons = $true )
<=> ! [X160: subst,X161: term] :
( ( sub @ one @ ( push @ X161 @ X160 ) )
= X161 ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X162: term] :
~ ! [X163: subst > term > term] :
~ ! [X164: term,X165: subst] :
( ( X163 @ X165 @ X164 )
= ( sub @ X162 @ ( push @ X164 @ X165 ) ) )
=> ( ! [X166: term] :
( ( sub @ X166 @ id )
= X166 )
=> ! [X167: subst > term > subst > $o,X168: term > $o,X169: term] :
( ~ ! [X170: term] :
( ( $true
= ( X168 @ ( sub @ X169 @ ( push @ X170 @ id ) ) ) )
| ( $true
!= ( X168 @ X170 ) ) )
| ~ ! [X171: subst > term > term] :
( ~ ! [X172: term] :
( ( ( X167 @ id @ X172 @ id )
!= $true )
| ( ( X167 @ id @ ( X171 @ id @ X172 ) @ id )
= $true ) )
| ~ ! [X173: subst,X174: subst,X175: term] :
( ( sub @ ( X171 @ X173 @ X175 ) @ X174 )
= ( X171 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) ) )
| ( $true
= ( X167 @ id @ ( lam @ ( X171 @ sh @ one ) ) @ id ) ) )
| ( ( X168 @ ( lam @ X169 ) )
= $true )
| ~ ! [X176: term] :
( ( X168 @ X176 )
= ( X167 @ id @ X176 @ id ) ) ) ) ) )
& ( ! [X177: subst] :
( ( comp @ X177 @ id )
= X177 )
<=> ( axidr = $true ) )
& ( ! [X178: term,X179: term,X180: term,X181: term] :
( ( ( ap @ X178 @ X180 )
!= ( ap @ X179 @ X181 ) )
| ( X180 = X181 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( hoasinduction_gthm = $true )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X182: term] :
( ( sub @ X182 @ id )
= X182 )
=> ! [X183: subst > term > subst > $o,X184: term,X185: term > $o] :
( ( $true
= ( X185 @ ( lam @ X184 ) ) )
| ~ ! [X186: subst,X187: subst,X188: subst,X189: term] :
( ( ( X183 @ ( comp @ X188 @ X187 ) @ ( sub @ X189 @ X187 ) @ X186 )
= $true )
| ( ( X183 @ X188 @ X189 @ ( comp @ X187 @ X186 ) )
!= $true ) )
| ~ ! [X190: term] :
( ( ( X185 @ ( sub @ X184 @ ( push @ X190 @ id ) ) )
= $true )
| ( ( X185 @ X190 )
!= $true ) )
| ~ ! [X191: subst > term > term] :
( ( $true
= ( X183 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id ) )
| ~ ! [X192: term] :
( ( ( X183 @ id @ ( X191 @ id @ X192 ) @ id )
= $true )
| ( $true
!= ( X183 @ id @ X192 @ id ) ) )
| ~ ! [X193: term,X194: subst,X195: subst] :
( ( X191 @ ( comp @ X194 @ X195 ) @ ( sub @ X193 @ X195 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X195 ) ) )
| ~ ! [X196: subst,X197: term,X198: subst,X199: subst] :
( ( $true
!= ( X183 @ ( comp @ X196 @ X198 ) @ ( sub @ X197 @ X198 ) @ X199 ) )
| ( ( X183 @ X196 @ X197 @ ( comp @ X198 @ X199 ) )
= $true ) )
| ~ ! [X200: term] :
( ( X183 @ id @ X200 @ id )
= ( X185 @ X200 ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true )
& ( termmset_gthm = $true )
& ( ! [X201: subst] :
( ( push @ ( sub @ one @ X201 ) @ ( comp @ sh @ X201 ) )
= X201 )
<=> ( axscons = $true ) )
& ( ! [X202: term,X203: term] :
( ( X202 = X203 )
| ( ( sub @ X202 @ sh )
!= ( sub @ X203 @ sh ) ) )
<=> ( shinj = $true ) )
& ! [X204: d_term,X205: d_term] :
( ( ( d2term @ X205 )
= ( d2term @ X204 ) )
=> ( X204 = X205 ) )
& ( pushprop_lem0_gthm = $true )
& ( axclos = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ulamvarind = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X206: subst > term > subst > $o] :
~ ! [X207: term > $o] :
~ ! [X208: term] :
( ( X206 @ id @ X208 @ id )
= ( X207 @ X208 ) ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X209: term > $o,X210: subst,X211: term > $o,X212: term,X213: term] :
( ( ( X211 @ ( sub @ X213 @ ( push @ X212 @ X210 ) ) )
= $true )
| ( ( X209 @ X213 )
!= $true ) ) )
& ! [X214: d_subst] : ( d_id = X214 )
& ( hoaslamnotap_lthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X215: subst,X216: term] :
( ( sub @ one @ ( push @ X216 @ X215 ) )
= X216 )
=> ! [X217: term,X218: subst,X219: term > $o,X220: term > $o] :
( ( ( X220 @ X217 )
!= $true )
| ( ( X219 @ one )
= $true )
| ~ ! [X221: term] :
( ( X219 @ X221 )
= ( X220 @ ( sub @ X221 @ ( push @ X217 @ X218 ) ) ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X222: term > $o,X223: term] :
( ( ( X222 @ X223 )
= $true )
| ~ ! [X224: term] :
( ( ( var @ X224 )
!= $true )
| ( ( X222 @ X224 )
= $true ) )
| ~ ! [X225: term] :
( ( ( X222 @ ( lam @ X225 ) )
= $true )
| ~ ! [X226: term] :
( ( ( X222 @ X226 )
!= $true )
| ( ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) )
= $true ) ) )
| ~ ! [X227: term,X228: term] :
( ( $true
!= ( X222 @ X227 ) )
| ( ( X222 @ ( ap @ X227 @ X228 ) )
= $true )
| ( ( X222 @ X228 )
!= $true ) ) )
=> ( ! [X229: subst > term > subst > $o,X230: term,X231: term] :
( ~ ! [X232: term,X233: term] :
( ( ( X229 @ id @ X233 @ id )
!= $true )
| ( ( X229 @ id @ ( ap @ ( sub @ X232 @ id ) @ X233 ) @ id )
= $true )
| ( ( X229 @ id @ X232 @ id )
!= $true ) )
| ( ( X229 @ id @ X231 @ id )
!= $true )
| ( ( X229 @ id @ ( ap @ X230 @ X231 ) @ id )
= $true )
| ( ( X229 @ id @ X230 @ id )
!= $true )
| ~ ! [X234: term,X235: subst,X236: subst,X237: subst] :
( ( ( X229 @ X235 @ X234 @ ( comp @ X236 @ X237 ) )
= $true )
| ( ( X229 @ ( comp @ X235 @ X236 ) @ ( sub @ X234 @ X236 ) @ X237 )
!= $true ) )
| ~ ! [X238: subst,X239: term,X240: subst,X241: subst] :
( ( ( X229 @ X240 @ X239 @ ( comp @ X238 @ X241 ) )
!= $true )
| ( ( X229 @ ( comp @ X240 @ X238 ) @ ( sub @ X239 @ X238 ) @ X241 )
= $true ) ) )
=> ( ! [X242: term,X243: subst > term > subst > $o] :
( ~ ! [X244: subst,X245: term,X246: subst,X247: subst] :
( ( ( X243 @ X246 @ X245 @ ( comp @ X247 @ X244 ) )
= $true )
| ( ( X243 @ ( comp @ X246 @ X247 ) @ ( sub @ X245 @ X247 ) @ X244 )
!= $true ) )
| ~ ! [X248: subst,X249: subst,X250: term,X251: subst] :
( ( ( X243 @ X249 @ X250 @ ( comp @ X248 @ X251 ) )
!= $true )
| ( ( X243 @ ( comp @ X249 @ X248 ) @ ( sub @ X250 @ X248 ) @ X251 )
= $true ) )
| ~ ! [X252: subst > term > term] :
( ~ ! [X253: term] :
( ( ( X243 @ id @ X253 @ id )
!= $true )
| ( ( X243 @ id @ ( X252 @ id @ X253 ) @ id )
= $true ) )
| ~ ! [X254: subst,X255: subst,X256: term] :
( ( X252 @ ( comp @ X254 @ X255 ) @ ( sub @ X256 @ X255 ) )
= ( sub @ ( X252 @ X254 @ X256 ) @ X255 ) )
| ( ( X243 @ id @ ( lam @ ( X252 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X243 @ id @ ( lam @ X242 ) @ id )
= $true )
| ~ ! [X257: term] :
( ( ( X243 @ id @ X257 @ id )
!= $true )
| ( ( X243 @ id @ ( sub @ X242 @ ( push @ X257 @ id ) ) @ id )
= $true ) ) )
=> ! [X258: subst > term > subst > $o,X259: term] :
( ~ ! [X260: subst,X261: term,X262: subst,X263: subst] :
( ( ( X258 @ ( comp @ X263 @ X262 ) @ ( sub @ X261 @ X262 ) @ X260 )
= $true )
| ( $true
!= ( X258 @ X263 @ X261 @ ( comp @ X262 @ X260 ) ) ) )
| ~ ! [X264: term,X265: term] :
( ( ( X258 @ id @ X264 @ id )
!= $true )
| ( $true
= ( X258 @ id @ ( ap @ ( sub @ X264 @ id ) @ X265 ) @ id ) )
| ( ( X258 @ id @ X265 @ id )
!= $true ) )
| ~ ! [X266: subst > term > term] :
( ~ ! [X267: term] :
( ( ( X258 @ id @ X267 @ id )
!= $true )
| ( ( X258 @ id @ ( X266 @ id @ X267 ) @ id )
= $true ) )
| ( ( X258 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X268: term,X269: subst,X270: subst] :
( ( X266 @ ( comp @ X270 @ X269 ) @ ( sub @ X268 @ X269 ) )
= ( sub @ ( X266 @ X270 @ X268 ) @ X269 ) ) )
| ~ ! [X271: subst,X272: subst,X273: term,X274: subst] :
( ( ( X258 @ X272 @ X273 @ ( comp @ X274 @ X271 ) )
= $true )
| ( ( X258 @ ( comp @ X272 @ X274 ) @ ( sub @ X273 @ X274 ) @ X271 )
!= $true ) )
| ~ ! [X275: term] :
( ( ( X258 @ id @ X275 @ id )
= $true )
| ( ( var @ ( sub @ X275 @ id ) )
!= $true ) )
| ( ( X258 @ id @ X259 @ id )
= $true ) ) ) ) ) )
& ( ! [X276: term,X277: term > $o,X278: subst > term > subst > $o,X279: term] :
( ( $true
!= ( X277 @ X279 ) )
| ~ ! [X280: term] :
( ( X278 @ id @ X280 @ id )
= ( X277 @ X280 ) )
| ~ ! [X281: subst,X282: subst,X283: subst,X284: term] :
( ( ( X278 @ X281 @ X284 @ ( comp @ X283 @ X282 ) )
!= $true )
| ( ( X278 @ ( comp @ X281 @ X283 ) @ ( sub @ X284 @ X283 ) @ X282 )
= $true ) )
| ~ ! [X285: term,X286: term] :
( ( ( X278 @ id @ ( ap @ ( sub @ X286 @ id ) @ X285 ) @ id )
= $true )
| ( ( X278 @ id @ X285 @ id )
!= $true )
| ( ( X278 @ id @ X286 @ id )
!= $true ) )
| ~ ! [X287: subst,X288: term,X289: subst,X290: subst] :
( ( ( X278 @ ( comp @ X290 @ X287 ) @ ( sub @ X288 @ X287 ) @ X289 )
!= $true )
| ( ( X278 @ X290 @ X288 @ ( comp @ X287 @ X289 ) )
= $true ) )
| ( $true
!= ( X277 @ X276 ) )
| ( ( X277 @ ( ap @ X279 @ X276 ) )
= $true ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X291: term] :
( ( sub @ X291 @ id )
= X291 )
=> ( ! [X292: term,X293: subst > term > subst > $o] :
( ~ ! [X294: subst > term > term] :
( ~ ! [X295: term] :
( ( $true
= ( X293 @ id @ ( X294 @ id @ X295 ) @ id ) )
| ( $true
!= ( X293 @ id @ X295 @ id ) ) )
| ~ ! [X296: term,X297: subst,X298: subst] :
( ( sub @ ( X294 @ X297 @ X296 ) @ X298 )
= ( X294 @ ( comp @ X297 @ X298 ) @ ( sub @ X296 @ X298 ) ) )
| ( ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X299: term] :
( ( ( X293 @ id @ ( sub @ X292 @ ( push @ X299 @ id ) ) @ id )
= $true )
| ( ( X293 @ id @ X299 @ id )
!= $true ) )
| ( ( X293 @ id @ ( lam @ ( sub @ X292 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X300: subst > term > subst > $o,X301: term] :
( ( ( X300 @ id @ ( lam @ X301 ) @ id )
= $true )
| ~ ! [X302: subst,X303: subst,X304: subst,X305: term] :
( ( ( X300 @ ( comp @ X302 @ X303 ) @ ( sub @ X305 @ X303 ) @ X304 )
!= $true )
| ( ( X300 @ X302 @ X305 @ ( comp @ X303 @ X304 ) )
= $true ) )
| ~ ! [X306: subst > term > term] :
( ~ ! [X307: subst,X308: subst,X309: term] :
( ( X306 @ ( comp @ X308 @ X307 ) @ ( sub @ X309 @ X307 ) )
= ( sub @ ( X306 @ X308 @ X309 ) @ X307 ) )
| ~ ! [X310: term] :
( ( $true
!= ( X300 @ id @ X310 @ id ) )
| ( $true
= ( X300 @ id @ ( X306 @ id @ X310 ) @ id ) ) )
| ( ( X300 @ id @ ( lam @ ( X306 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X311: term] :
( ( ( X300 @ id @ X311 @ id )
!= $true )
| ( ( X300 @ id @ ( sub @ X301 @ ( push @ X311 @ id ) ) @ id )
= $true ) )
| ~ ! [X312: subst,X313: subst,X314: subst,X315: term] :
( ( ( X300 @ ( comp @ X312 @ X313 ) @ ( sub @ X315 @ X313 ) @ X314 )
= $true )
| ( ( X300 @ X312 @ X315 @ ( comp @ X313 @ X314 ) )
!= $true ) ) ) ) ) )
& ( ! [X316: subst > term > subst > $o] :
~ ! [X317: term > $o] :
~ ! [X318: term] :
( ( X316 @ id @ X318 @ id )
= ( X317 @ X318 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X319: subst > term > term,X320: term,X321: term] :
( ( ( ap @ ( sub @ X320 @ id ) @ X321 )
!= ( lam @ ( X319 @ sh @ one ) ) )
| ~ ! [X322: subst,X323: term,X324: subst] :
( ( sub @ ( X319 @ X324 @ X323 ) @ X322 )
= ( X319 @ ( comp @ X324 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( ! [X325: term] :
( ( sub @ X325 @ id )
= X325 )
=> ( ! [X326: subst > term > subst > $o,X327: term] :
( ~ ! [X328: term] :
( ( $true
= ( X326 @ id @ ( sub @ X327 @ ( push @ X328 @ id ) ) @ id ) )
| ( ( X326 @ id @ X328 @ id )
!= $true ) )
| ( ( X326 @ id @ ( lam @ ( sub @ X327 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X329: subst > term > term] :
( ~ ! [X330: subst,X331: subst,X332: term] :
( ( sub @ ( X329 @ X330 @ X332 ) @ X331 )
= ( X329 @ ( comp @ X330 @ X331 ) @ ( sub @ X332 @ X331 ) ) )
| ( ( X326 @ id @ ( lam @ ( X329 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X333: term] :
( ( ( X326 @ id @ ( X329 @ id @ X333 ) @ id )
= $true )
| ( ( X326 @ id @ X333 @ id )
!= $true ) ) ) )
=> ! [X334: subst > term > subst > $o,X335: term] :
( ~ ! [X336: term] :
( ( ( X334 @ id @ ( sub @ X335 @ ( push @ X336 @ id ) ) @ id )
= $true )
| ( ( X334 @ id @ X336 @ id )
!= $true ) )
| ~ ! [X337: subst > term > term] :
( ~ ! [X338: subst,X339: term,X340: subst] :
( ( X337 @ ( comp @ X338 @ X340 ) @ ( sub @ X339 @ X340 ) )
= ( sub @ ( X337 @ X338 @ X339 ) @ X340 ) )
| ( $true
= ( X334 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
| ~ ! [X341: term] :
( ( ( X334 @ id @ ( X337 @ id @ X341 ) @ id )
= $true )
| ( ( X334 @ id @ X341 @ id )
!= $true ) ) )
| ( ( X334 @ id @ ( lam @ X335 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X342: subst,X343: term] :
( ( sub @ one @ ( push @ X343 @ X342 ) )
= X343 )
=> ( ! [X344: term,X345: subst] :
( ( comp @ sh @ ( push @ X344 @ X345 ) )
= X345 )
=> ( ! [X346: subst] :
( ( comp @ X346 @ id )
= X346 )
=> ( ! [X347: term > $o,X348: term] :
( ~ ! [X349: term,X350: term] :
( ( ( X347 @ ( ap @ X350 @ X349 ) )
= $true )
| ( ( X347 @ X350 )
!= $true )
| ( ( X347 @ X349 )
!= $true ) )
| ~ ! [X351: term] :
( ( ( X347 @ ( lam @ X351 ) )
= $true )
| ( ( X347 @ X351 )
!= $true ) )
| ~ ! [X352: term] :
( ( ( var @ X352 )
!= $true )
| ( ( X347 @ X352 )
= $true ) )
| ( ( X347 @ X348 )
= $true ) )
=> ! [X353: term > $o,X354: term,X355: subst] :
( ~ ! [X356: term,X357: term] :
( ( ( X353 @ ( ap @ X357 @ X356 ) )
= $true )
| ( ( X353 @ X356 )
!= $true )
| ( ( X353 @ X357 )
!= $true ) )
| ~ ! [X358: term] :
( ~ ! [X359: term] :
( ( ( X353 @ ( sub @ X358 @ ( push @ X359 @ id ) ) )
= $true )
| ( ( X353 @ X359 )
!= $true ) )
| ( ( X353 @ ( lam @ X358 ) )
= $true ) )
| ~ ! [X360: term] :
( ( ( var @ X360 )
!= $true )
| ( $true
= ( X353 @ ( sub @ X360 @ X355 ) ) ) )
| ( ( X353 @ ( sub @ X354 @ X355 ) )
= $true ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X361: subst > term > subst > $o,X362: term > $o,X363: term] :
( ~ ! [X364: term] :
( ( X361 @ id @ X364 @ id )
= ( X362 @ X364 ) )
| ( ( X362 @ ( lam @ X363 ) )
= $true )
| ~ ! [X365: term,X366: subst,X367: subst,X368: subst] :
( ( ( X361 @ X366 @ X365 @ ( comp @ X367 @ X368 ) )
!= $true )
| ( ( X361 @ ( comp @ X366 @ X367 ) @ ( sub @ X365 @ X367 ) @ X368 )
= $true ) )
| ~ ! [X369: term] :
( ( ( X362 @ X369 )
!= $true )
| ( ( X362 @ ( sub @ X363 @ ( push @ X369 @ id ) ) )
= $true ) )
| ~ ! [X370: subst,X371: subst,X372: subst,X373: term] :
( ( ( X361 @ ( comp @ X372 @ X370 ) @ ( sub @ X373 @ X370 ) @ X371 )
!= $true )
| ( ( X361 @ X372 @ X373 @ ( comp @ X370 @ X371 ) )
= $true ) )
| ~ ! [X374: subst > term > term] :
( ~ ! [X375: term] :
( ( ( X361 @ id @ ( X374 @ id @ X375 ) @ id )
= $true )
| ( ( X361 @ id @ X375 @ id )
!= $true ) )
| ( $true
= ( X361 @ id @ ( lam @ ( X374 @ sh @ one ) ) @ id ) )
| ~ ! [X376: term,X377: subst,X378: subst] :
( ( X374 @ ( comp @ X377 @ X378 ) @ ( sub @ X376 @ X378 ) )
= ( sub @ ( X374 @ X377 @ X376 ) @ X378 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X382: term] :
( ( sub @ X382 @ id )
= X382 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X383: subst > term > subst > $o,X384: term] :
( ( ( X383 @ id @ ( lam @ X384 ) @ id )
= $true )
| ~ ! [X385: term] :
( ( ( X383 @ id @ ( sub @ X384 @ ( push @ X385 @ id ) ) @ id )
= $true )
| ( ( X383 @ id @ X385 @ id )
!= $true ) )
| ~ ! [X386: subst > term > term] :
( ~ ! [X387: term] :
( ( ( X383 @ id @ ( X386 @ id @ X387 ) @ id )
= $true )
| ( ( X383 @ id @ X387 @ id )
!= $true ) )
| ( $true
= ( X383 @ id @ ( lam @ ( X386 @ sh @ one ) ) @ id ) )
| ~ ! [X388: subst,X389: subst,X390: term] :
( ( sub @ ( X386 @ X388 @ X390 ) @ X389 )
= ( X386 @ ( comp @ X388 @ X389 ) @ ( sub @ X390 @ X389 ) ) ) ) ) )
& ( ! [X391: term] :
( ( sub @ X391 @ id )
= X391 )
<=> ( termmset = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X392: term,X393: subst] :
( ( sub @ one @ ( push @ X392 @ X393 ) )
= X392 )
=> ( ! [X394: subst,X395: term] :
( ( comp @ sh @ ( push @ X395 @ X394 ) )
= X394 )
=> ( ! [X396: term,X397: term] :
( ( X396 = X397 )
| ( ( lam @ X396 )
!= ( lam @ X397 ) ) )
=> ! [X398: subst,X399: subst > term > term,X400: term,X401: subst > term > term] :
( ~ ! [X402: subst,X403: term,X404: subst] :
( ( sub @ ( X401 @ X404 @ X403 ) @ X402 )
= ( X401 @ ( comp @ X404 @ X402 ) @ ( sub @ X403 @ X402 ) ) )
| ~ ! [X405: subst,X406: term,X407: subst] :
( ( X399 @ ( comp @ X405 @ X407 ) @ ( sub @ X406 @ X407 ) )
= ( sub @ ( X399 @ X405 @ X406 ) @ X407 ) )
| ( ( X399 @ X398 @ X400 )
= ( X401 @ X398 @ X400 ) )
| ( ( lam @ ( X399 @ sh @ one ) )
!= ( lam @ ( X401 @ sh @ one ) ) ) ) ) ) ) )
& ( ( induction2 = $true )
<=> ! [X408: term > $o,X409: term] :
( ~ ! [X410: term,X411: term] :
( ( ( X408 @ ( ap @ X411 @ X410 ) )
= $true )
| ( ( X408 @ X410 )
!= $true )
| ( ( X408 @ X411 )
!= $true ) )
| ( $true
= ( X408 @ X409 ) )
| ~ ! [X412: term] :
( ( ( var @ X412 )
!= $true )
| ( $true
= ( X408 @ X412 ) ) )
| ~ ! [X413: term] :
( ~ ! [X414: term] :
( ( ( X408 @ X414 )
!= $true )
| ( ( X408 @ ( sub @ X413 @ ( push @ X414 @ id ) ) )
= $true ) )
| ( ( X408 @ ( lam @ X413 ) )
= $true ) ) ) )
& ( ( ! [X415: subst] :
( ( comp @ X415 @ id )
= X415 )
& ! [X416: subst] :
( ( comp @ id @ X416 )
= X416 ) )
<=> ( substmonoid = $true ) )
& ( ( axidl = $true )
<=> ! [X417: subst] :
( ( comp @ id @ X417 )
= X417 ) )
& ! [X418: d_term] : ( d_one = X418 )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
<=> ! [X419: term,X420: term,X421: term,X422: term] :
( ( X420 = X421 )
| ( ( ap @ X421 @ X422 )
!= ( ap @ X420 @ X419 ) ) ) )
& ( pushprop_lem2v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop = $true )
& ( axvarshift = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ! [X423: term] :
~ ! [X424: subst > term > term] :
( ( X424 @ sh @ one )
!= ( sub @ X423 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X425: term] :
( ( sub @ X425 @ id )
= X425 )
=> ! [X426: term] :
( ( sub @ X426 @ id )
= X426 ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axmap = $true )
& ! [X427: subst] :
? [X428: d_subst] :
( ( d2subst @ X428 )
= X427 )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X429: subst > term > subst > $o,X430: term] :
( ~ ! [X431: subst > term > term] :
( ~ ! [X432: term] :
( ( ( X429 @ id @ ( X431 @ id @ X432 ) @ id )
= $true )
| ( ( X429 @ id @ X432 @ id )
!= $true ) )
| ~ ! [X433: term,X434: subst,X435: subst] :
( ( X431 @ ( comp @ X435 @ X434 ) @ ( sub @ X433 @ X434 ) )
= ( sub @ ( X431 @ X435 @ X433 ) @ X434 ) )
| ( ( X429 @ id @ ( lam @ ( X431 @ sh @ one ) ) @ id )
= $true ) )
| ( $true
= ( X429 @ id @ ( lam @ ( sub @ X430 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X436: term] :
( ( ( X429 @ id @ ( sub @ X430 @ ( push @ X436 @ id ) ) @ id )
= $true )
| ( ( X429 @ id @ X436 @ id )
!= $true ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X437: term,X438: term,X439: subst > term > subst > $o] :
( ( ( X439 @ id @ X437 @ id )
!= $true )
| ~ ! [X440: term,X441: term] :
( ( ( X439 @ id @ X440 @ id )
!= $true )
| ( ( X439 @ id @ ( ap @ ( sub @ X440 @ id ) @ X441 ) @ id )
= $true )
| ( ( X439 @ id @ X441 @ id )
!= $true ) )
| ( ( X439 @ id @ ( ap @ X438 @ X437 ) @ id )
= $true )
| ~ ! [X442: term,X443: subst,X444: subst,X445: subst] :
( ( ( X439 @ ( comp @ X444 @ X443 ) @ ( sub @ X442 @ X443 ) @ X445 )
= $true )
| ( ( X439 @ X444 @ X442 @ ( comp @ X443 @ X445 ) )
!= $true ) )
| ~ ! [X446: subst,X447: term,X448: subst,X449: subst] :
( ( $true
= ( X439 @ X446 @ X447 @ ( comp @ X449 @ X448 ) ) )
| ( ( X439 @ ( comp @ X446 @ X449 ) @ ( sub @ X447 @ X449 ) @ X448 )
!= $true ) )
| ( ( X439 @ id @ X438 @ id )
!= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X450: term,X451: subst > term > subst > $o] :
( ~ ! [X452: term] :
( ( ( X451 @ id @ ( sub @ X450 @ ( push @ X452 @ id ) ) @ id )
= $true )
| ( ( X451 @ id @ X452 @ id )
!= $true ) )
| ~ ! [X453: subst > term > term] :
( ~ ! [X454: subst,X455: term,X456: subst] :
( ( sub @ ( X453 @ X454 @ X455 ) @ X456 )
= ( X453 @ ( comp @ X454 @ X456 ) @ ( sub @ X455 @ X456 ) ) )
| ~ ! [X457: term] :
( ( $true
!= ( X451 @ id @ X457 @ id ) )
| ( ( X451 @ id @ ( X453 @ id @ X457 ) @ id )
= $true ) )
| ( $true
= ( X451 @ id @ ( lam @ ( X453 @ sh @ one ) ) @ id ) ) )
| ( ( X451 @ id @ ( lam @ ( sub @ X450 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) )
& ( hoaslamnotap_gthm = $true )
& ! [X458: term] :
? [X459: d_term] :
( ( d2term @ X459 )
= X458 )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X462: term,X463: term,X464: term,X465: term] :
( ( ( ap @ ( sub @ X465 @ id ) @ X464 )
!= ( ap @ ( sub @ X462 @ id ) @ X463 ) )
| ( X463 = X464 ) )
<=> ( hoasapinj2 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X466: subst,X467: term > $o,X468: term] :
~ ! [X469: term > $o] :
~ ! [X470: term] :
( ( X467 @ ( sub @ X470 @ ( push @ X468 @ X466 ) ) )
= ( X469 @ X470 ) )
<=> ( pushprop_lem0 = $true ) )
& ( ( laminj = $true )
<=> ! [X471: term,X472: term] :
( ( ( lam @ X472 )
!= ( lam @ X471 ) )
| ( X471 = X472 ) ) )
& ( induction2_gthm = $true )
& ( substmonoid_gthm = $true )
& ( ! [X473: subst,X474: term] :
( ( comp @ sh @ ( push @ X474 @ X473 ) )
= X473 )
<=> ( axshiftcons = $true ) )
& ( induction2lem_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( hoasinduction = $true )
<=> ! [X475: term,X476: subst > term > subst > $o] :
( ~ ! [X477: term] :
( ( ( X476 @ id @ X477 @ id )
= $true )
| ( ( var @ ( sub @ X477 @ id ) )
!= $true ) )
| ~ ! [X478: term,X479: subst,X480: subst,X481: subst] :
( ( ( X476 @ X480 @ X478 @ ( comp @ X481 @ X479 ) )
!= $true )
| ( $true
= ( X476 @ ( comp @ X480 @ X481 ) @ ( sub @ X478 @ X481 ) @ X479 ) ) )
| ~ ! [X482: subst > term > term] :
( ~ ! [X483: subst,X484: term,X485: subst] :
( ( sub @ ( X482 @ X485 @ X484 ) @ X483 )
= ( X482 @ ( comp @ X485 @ X483 ) @ ( sub @ X484 @ X483 ) ) )
| ~ ! [X486: term] :
( ( ( X476 @ id @ ( X482 @ id @ X486 ) @ id )
= $true )
| ( $true
!= ( X476 @ id @ X486 @ id ) ) )
| ( ( X476 @ id @ ( lam @ ( X482 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X476 @ id @ X475 @ id )
= $true )
| ~ ! [X487: subst,X488: subst,X489: subst,X490: term] :
( ( ( X476 @ X489 @ X490 @ ( comp @ X488 @ X487 ) )
= $true )
| ( $true
!= ( X476 @ ( comp @ X489 @ X488 ) @ ( sub @ X490 @ X488 ) @ X487 ) ) )
| ~ ! [X491: term,X492: term] :
( ( ( X476 @ id @ ( ap @ ( sub @ X492 @ id ) @ X491 ) @ id )
= $true )
| ( ( X476 @ id @ X491 @ id )
!= $true )
| ( ( X476 @ id @ X492 @ id )
!= $true ) ) ) )
& ( ! [X493: term] :
~ ! [X494: subst > term > term] :
~ ! [X495: subst,X496: term] :
( ( sub @ X493 @ ( push @ X496 @ X495 ) )
= ( X494 @ X495 @ X496 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ! [X497: term,X498: subst > term > subst > $o] :
( ~ ! [X499: term,X500: term] :
( ( ( X498 @ id @ X500 @ id )
!= $true )
| ( ( X498 @ id @ ( ap @ ( sub @ X499 @ id ) @ X500 ) @ id )
= $true )
| ( ( X498 @ id @ X499 @ id )
!= $true ) )
| ~ ! [X501: subst > term > term] :
( ~ ! [X502: subst,X503: term,X504: subst] :
( ( sub @ ( X501 @ X502 @ X503 ) @ X504 )
= ( X501 @ ( comp @ X502 @ X504 ) @ ( sub @ X503 @ X504 ) ) )
| ( ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X505: term] :
( ( ( X498 @ id @ X505 @ id )
!= $true )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) ) )
| ( ( X498 @ id @ X497 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( ! [X506: term] :
( ( sub @ X506 @ id )
= X506 )
=> ( ! [X507: term > $o,X508: subst,X509: term] :
( ( ( X507 @ ( sub @ X509 @ X508 ) )
= $true )
| ~ ! [X510: term,X511: term] :
( ( ( X507 @ X510 )
!= $true )
| ( ( X507 @ ( ap @ X510 @ X511 ) )
= $true )
| ( ( X507 @ X511 )
!= $true ) )
| ~ ! [X512: term] :
( ( ( X507 @ ( lam @ X512 ) )
= $true )
| ~ ! [X513: term] :
( ( ( X507 @ X513 )
!= $true )
| ( ( X507 @ ( sub @ X512 @ ( push @ X513 @ id ) ) )
= $true ) ) )
| ~ ! [X514: term] :
( ( $true
!= ( var @ X514 ) )
| ( $true
= ( X507 @ ( sub @ X514 @ X508 ) ) ) ) )
=> ! [X515: term > $o,X516: term] :
( ( ( X515 @ X516 )
= $true )
| ~ ! [X517: term] :
( ~ ! [X518: term] :
( ( ( X515 @ X518 )
!= $true )
| ( ( X515 @ ( sub @ X517 @ ( push @ X518 @ id ) ) )
= $true ) )
| ( ( X515 @ ( lam @ X517 ) )
= $true ) )
| ~ ! [X519: term,X520: term] :
( ( $true
= ( X515 @ ( ap @ X519 @ X520 ) ) )
| ( ( X515 @ X519 )
!= $true )
| ( $true
!= ( X515 @ X520 ) ) )
| ~ ! [X521: term] :
( ( $true
!= ( var @ X521 ) )
| ( ( X515 @ X521 )
= $true ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X522: subst > term > subst > $o,X523: term > $o,X524: term] :
( ~ ! [X525: term] :
( ( X523 @ X525 )
= ( X522 @ id @ X525 @ id ) )
| ( ( X523 @ ( lam @ X524 ) )
= $true )
| ~ ! [X526: subst > term > term] :
( ~ ! [X527: subst,X528: subst,X529: term] :
( ( sub @ ( X526 @ X528 @ X529 ) @ X527 )
= ( X526 @ ( comp @ X528 @ X527 ) @ ( sub @ X529 @ X527 ) ) )
| ( ( X522 @ id @ ( lam @ ( X526 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X530: term] :
( ( $true
= ( X522 @ id @ ( X526 @ id @ X530 ) @ id ) )
| ( ( X522 @ id @ X530 @ id )
!= $true ) ) )
| ~ ! [X531: term] :
( ( ( X523 @ ( sub @ X524 @ ( push @ X531 @ id ) ) )
= $true )
| ( ( X523 @ X531 )
!= $true ) ) ) )
& ( ( hoaslaminj = $true )
<=> ! [X532: subst > term > term,X533: subst,X534: subst > term > term,X535: term] :
( ( ( X532 @ X533 @ X535 )
= ( X534 @ X533 @ X535 ) )
| ~ ! [X536: subst,X537: term,X538: subst] :
( ( X534 @ ( comp @ X536 @ X538 ) @ ( sub @ X537 @ X538 ) )
= ( sub @ ( X534 @ X536 @ X537 ) @ X538 ) )
| ~ ! [X539: term,X540: subst,X541: subst] :
( ( sub @ ( X532 @ X540 @ X539 ) @ X541 )
= ( X532 @ ( comp @ X540 @ X541 ) @ ( sub @ X539 @ X541 ) ) )
| ( ( lam @ ( X534 @ sh @ one ) )
!= ( lam @ ( X532 @ sh @ one ) ) ) ) )
& ( pushprop_gthm = $true )
& ( ( induction2lem = $true )
<=> ! [X542: term,X543: subst,X544: term > $o] :
( ~ ! [X545: term] :
( ( ( X544 @ ( lam @ X545 ) )
= $true )
| ~ ! [X546: term] :
( ( ( X544 @ ( sub @ X545 @ ( push @ X546 @ id ) ) )
= $true )
| ( ( X544 @ X546 )
!= $true ) ) )
| ( $true
= ( X544 @ ( sub @ X542 @ X543 ) ) )
| ~ ! [X547: term] :
( ( $true
!= ( var @ X547 ) )
| ( $true
= ( X544 @ ( sub @ X547 @ X543 ) ) ) )
| ~ ! [X548: term,X549: term] :
( ( ( X544 @ X549 )
!= $true )
| ( ( X544 @ X548 )
!= $true )
| ( ( X544 @ ( ap @ X548 @ X549 ) )
= $true ) ) ) )
& ( hoasapnotvar_gthm = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( hoasinduction_lem1v2
& ( pushprop_lem1v2
<=> ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
( ~ ! [X4: term] :
( ( X1 @ ( sub @ X4 @ ( push @ X3 @ X2 ) ) )
= ( X0 @ X4 ) )
| ~ ( X1 @ X3 )
| ( X0 @ one ) ) )
& ( ( ! [X5: term] :
( ( sub @ X5 @ id )
= X5 )
=> ( ! [X6: term,X7: term,X8: term,X9: term] :
( ( X8 = X9 )
| ( ( ap @ X8 @ X6 )
!= ( ap @ X9 @ X7 ) ) )
=> ! [X10: term,X11: term,X12: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X12 )
!= ( ap @ ( sub @ X10 @ id ) @ X11 ) )
| ( X10 = X13 ) ) ) )
<=> hoasapinj1_lthm )
& pushprop_lthm
& ( pushprop_lem0_lthm
<=> ! [X14: term > $o,X15: term,X16: subst] :
~ ! [X17: term > $o] :
~ ! [X18: term] :
( ( X14 @ ( sub @ X18 @ ( push @ X15 @ X16 ) ) )
= ( X17 @ X18 ) ) )
& hoaslamnotvar
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem1_lthm
<=> ( ! [X19: term,X20: subst] :
( ( sub @ one @ ( push @ X19 @ X20 ) )
= X19 )
=> ( ! [X21: subst,X22: term] :
( ( comp @ sh @ ( push @ X22 @ X21 ) )
= X21 )
=> ! [X23: term,X24: term > $o,X25: term > $o,X26: subst,X27: term] :
( ( X25 @ ( sub @ X27 @ ( push @ X23 @ X26 ) ) )
| ~ ( X24 @ X27 ) ) ) ) )
& hoasapnotvar
& hoasinduction_lem1_lthm
& ( ! [X28: term] :
~ ! [X29: subst > term > term] :
( ( sub @ X28 @ ( push @ one @ sh ) )
!= ( X29 @ sh @ one ) )
<=> hoasinduction_lem3b_lthm )
& ( ! [X30: term,X31: term,X32: term,X33: term] :
( ( ( ap @ ( sub @ X30 @ id ) @ X31 )
!= ( ap @ ( sub @ X33 @ id ) @ X32 ) )
| ( X30 = X33 ) )
<=> hoasapinj1 )
& hoasapinj1_gthm
& axabs
& ( pushprop_p_and_p_prime
= ( ^ [X34: term,X35: subst,X36: term > $o,X37: term > $o] :
! [X38: term] :
( ( X36 @ ( sub @ X38 @ ( push @ X34 @ X35 ) ) )
= ( X37 @ X38 ) ) ) )
& ( ! [X39: term] :
~ ! [X40: subst > term > term] :
~ ! [X41: subst,X42: term] :
( ( sub @ X39 @ ( push @ X42 @ X41 ) )
= ( X40 @ X41 @ X42 ) )
<=> hoasinduction_lem3v2_f_lthm )
& pushprop_lem3v2
& hoasinduction_lem3a_gthm
& hoaslamnotvar_gthm
& ( ( d2subst @ d_id )
= sh )
& hoasinduction_lem3v2_gthm
& pushprop_lem2v2
& ( ! [X43: subst > term > subst > $o,X44: term] :
( ~ ! [X45: term,X46: subst,X47: subst,X48: subst] :
( ( X43 @ ( comp @ X47 @ X48 ) @ ( sub @ X45 @ X48 ) @ X46 )
| ~ ( X43 @ X47 @ X45 @ ( comp @ X48 @ X46 ) ) )
| ~ ! [X49: subst,X50: subst,X51: subst,X52: term] :
( ~ ( X43 @ ( comp @ X49 @ X51 ) @ ( sub @ X52 @ X51 ) @ X50 )
| ( X43 @ X49 @ X52 @ ( comp @ X51 @ X50 ) ) )
| ~ ! [X53: term] :
( ~ ( X43 @ id @ X53 @ id )
| ( X43 @ id @ ( sub @ X44 @ ( push @ X53 @ id ) ) @ id ) )
| ( X43 @ id @ ( lam @ X44 ) @ id )
| ~ ! [X54: subst > term > term] :
( ~ ! [X55: subst,X56: subst,X57: term] :
( ( sub @ ( X54 @ X55 @ X57 ) @ X56 )
= ( X54 @ ( comp @ X55 @ X56 ) @ ( sub @ X57 @ X56 ) ) )
| ~ ! [X58: term] :
( ( X43 @ id @ ( X54 @ id @ X58 ) @ id )
| ~ ( X43 @ id @ X58 @ id ) )
| ( X43 @ id @ ( lam @ ( X54 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3 )
& ! [X59: d_subst,X60: d_subst] :
( ( ( d2subst @ X59 )
= ( d2subst @ X60 ) )
=> ( X59 = X60 ) )
& ( hoasapinj2_lthm
<=> ( ! [X61: term,X62: term,X63: term,X64: term] :
( ( X62 = X63 )
| ( ( ap @ X61 @ X63 )
!= ( ap @ X64 @ X62 ) ) )
=> ! [X65: term,X66: term,X67: term,X68: term] :
( ( ( ap @ ( sub @ X68 @ id ) @ X65 )
!= ( ap @ ( sub @ X67 @ id ) @ X66 ) )
| ( X65 = X66 ) ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X69: term,X70: subst > term > subst > $o] :
( ( X70 @ id @ ( lam @ ( sub @ X69 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X71: term] :
( ( X70 @ id @ ( sub @ X69 @ ( push @ X71 @ id ) ) @ id )
| ~ ( X70 @ id @ X71 @ id ) )
| ~ ! [X72: subst > term > term,X73: term] :
( ~ ! [X74: subst,X75: subst,X76: term] :
( ( sub @ ( X72 @ X74 @ X76 ) @ X75 )
= ( sub @ ( sub @ X73 @ ( push @ X76 @ X74 ) ) @ X75 ) )
| ~ ! [X77: subst,X78: term,X79: subst] :
( ( sub @ X73 @ ( push @ ( sub @ X78 @ X79 ) @ ( comp @ X77 @ X79 ) ) )
= ( X72 @ ( comp @ X77 @ X79 ) @ ( sub @ X78 @ X79 ) ) )
| ~ ! [X80: term] :
( ~ ( X70 @ id @ X80 @ id )
| ( X70 @ id @ ( X72 @ id @ X80 ) @ id ) )
| ( X70 @ id @ ( lam @ ( X72 @ sh @ one ) ) @ id ) ) ) )
& apnotvar
& hoasinduction_lem2v2_gthm
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lthm_3
<=> ( ! [X81: subst > term > subst > $o] :
~ ! [X82: term > $o] :
~ ! [X83: term] :
( ( X81 @ id @ X83 @ id )
= ( X82 @ X83 ) )
=> ( ! [X84: term > $o,X85: term] :
( ( X84 @ X85 )
| ~ ! [X86: term,X87: term] :
( ~ ( X84 @ X87 )
| ( X84 @ ( ap @ X87 @ X86 ) )
| ~ ( X84 @ X86 ) )
| ~ ! [X88: term] :
( ~ ( var @ X88 )
| ( X84 @ X88 ) )
| ~ ! [X89: term] :
( ( X84 @ ( lam @ X89 ) )
| ~ ! [X90: term] :
( ( X84 @ ( sub @ X89 @ ( push @ X90 @ id ) ) )
| ~ ( X84 @ X90 ) ) ) )
=> ( ! [X91: term] :
( ( sub @ X91 @ id )
= X91 )
=> ( ! [X92: subst > term > subst > $o,X93: term > $o,X94: term] :
( ( X93 @ ( lam @ X94 ) )
| ~ ! [X95: term] :
( ( X93 @ X95 )
= ( X92 @ id @ X95 @ id ) )
| ~ ! [X96: subst > term > term] :
( ( X92 @ id @ ( lam @ ( X96 @ sh @ one ) ) @ id )
| ~ ! [X97: term] :
( ~ ( X92 @ id @ X97 @ id )
| ( X92 @ id @ ( X96 @ id @ X97 ) @ id ) )
| ~ ! [X98: subst,X99: term,X100: subst] :
( ( X96 @ ( comp @ X100 @ X98 ) @ ( sub @ X99 @ X98 ) )
= ( sub @ ( X96 @ X100 @ X99 ) @ X98 ) ) )
| ~ ! [X101: term] :
( ( X93 @ ( sub @ X94 @ ( push @ X101 @ id ) ) )
| ~ ( X93 @ X101 ) ) )
=> ! [X102: subst > term > subst > $o,X103: term] :
( ~ ! [X104: subst,X105: subst,X106: term,X107: subst] :
( ( X102 @ ( comp @ X104 @ X107 ) @ ( sub @ X106 @ X107 ) @ X105 )
| ~ ( X102 @ X104 @ X106 @ ( comp @ X107 @ X105 ) ) )
| ~ ! [X108: subst,X109: subst,X110: subst,X111: term] :
( ( X102 @ X108 @ X111 @ ( comp @ X109 @ X110 ) )
| ~ ( X102 @ ( comp @ X108 @ X109 ) @ ( sub @ X111 @ X109 ) @ X110 ) )
| ~ ! [X112: term,X113: term] :
( ~ ( X102 @ id @ X112 @ id )
| ~ ( X102 @ id @ X113 @ id )
| ( X102 @ id @ ( ap @ ( sub @ X113 @ id ) @ X112 ) @ id ) )
| ~ ! [X114: term] :
( ( X102 @ id @ X114 @ id )
| ~ ( var @ ( sub @ X114 @ id ) ) )
| ( X102 @ id @ X103 @ id )
| ~ ! [X115: subst > term > term] :
( ~ ! [X116: subst,X117: term,X118: subst] :
( ( sub @ ( X115 @ X118 @ X117 ) @ X116 )
= ( X115 @ ( comp @ X118 @ X116 ) @ ( sub @ X117 @ X116 ) ) )
| ~ ! [X119: term] :
( ~ ( X102 @ id @ X119 @ id )
| ( X102 @ id @ ( X115 @ id @ X119 ) @ id ) )
| ( X102 @ id @ ( lam @ ( X115 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X120: subst > term > subst > $o] :
~ ! [X121: term > $o] :
~ ! [X122: term] :
( ( X121 @ X122 )
= ( X120 @ id @ X122 @ id ) )
=> ( ! [X123: term,X124: term > $o] :
( ~ ! [X125: term,X126: term] :
( ~ ( X124 @ X126 )
| ( X124 @ ( ap @ X125 @ X126 ) )
| ~ ( X124 @ X125 ) )
| ~ ! [X127: term] :
( ( X124 @ X127 )
| ~ ( var @ X127 ) )
| ~ ! [X128: term] :
( ( X124 @ ( lam @ X128 ) )
| ~ ! [X129: term] :
( ~ ( X124 @ X129 )
| ( X124 @ ( sub @ X128 @ ( push @ X129 @ id ) ) ) ) )
| ( X124 @ X123 ) )
=> ( ! [X130: term] :
( ( sub @ X130 @ id )
= X130 )
=> ( ! [X131: subst > term > subst > $o,X132: term,X133: term > $o] :
( ( X133 @ ( lam @ X132 ) )
| ~ ! [X134: term] :
( ~ ( X133 @ X134 )
| ( X133 @ ( sub @ X132 @ ( push @ X134 @ id ) ) ) )
| ~ ! [X135: term] :
( ( X131 @ id @ X135 @ id )
= ( X133 @ X135 ) )
| ~ ! [X136: subst > term > term] :
( ( X131 @ id @ ( lam @ ( X136 @ sh @ one ) ) @ id )
| ~ ! [X137: term] :
( ~ ( X131 @ id @ X137 @ id )
| ( X131 @ id @ ( X136 @ id @ X137 ) @ id ) )
| ~ ! [X138: subst,X139: term,X140: subst] :
( ( sub @ ( X136 @ X138 @ X139 ) @ X140 )
= ( X136 @ ( comp @ X138 @ X140 ) @ ( sub @ X139 @ X140 ) ) ) ) )
=> ! [X141: subst > term > subst > $o,X142: term] :
( ( X141 @ id @ X142 @ id )
| ~ ! [X143: subst > term > term] :
( ~ ! [X144: term] :
( ~ ( X141 @ id @ X144 @ id )
| ( X141 @ id @ ( X143 @ id @ X144 ) @ id ) )
| ( X141 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id )
| ~ ! [X145: term,X146: subst,X147: subst] :
( ( X143 @ ( comp @ X147 @ X146 ) @ ( sub @ X145 @ X146 ) )
= ( sub @ ( X143 @ X147 @ X145 ) @ X146 ) ) )
| ~ ! [X148: term,X149: term] :
( ~ ( X141 @ id @ X149 @ id )
| ~ ( X141 @ id @ X148 @ id )
| ( X141 @ id @ ( ap @ ( sub @ X149 @ id ) @ X148 ) @ id ) ) ) ) ) ) ) )
& axapp
& hoasinduction_lem2_gthm
& ~ ulamvar1
& hoasinduction_lem1
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X150: subst] :
( ( comp @ id @ X150 )
= X150 )
=> ( ! [X151: subst] :
( ( comp @ X151 @ id )
= X151 )
=> ( ! [X152: subst] :
( ( comp @ X152 @ id )
= X152 )
& ! [X153: subst] :
( ( comp @ id @ X153 )
= X153 ) ) ) )
<=> substmonoid_lthm )
& ( ! [X154: term > $o,X155: term] :
( ~ ! [X156: term,X157: term] :
( ( X154 @ ( ap @ X157 @ X156 ) )
| ~ ( X154 @ X157 )
| ~ ( X154 @ X156 ) )
| ~ ! [X158: term] :
( ~ ( X154 @ X158 )
| ( X154 @ ( lam @ X158 ) ) )
| ( X154 @ X155 )
| ~ ! [X159: term] :
( ( X154 @ X159 )
| ~ ( var @ X159 ) ) )
<=> induction )
& ( axvarcons
<=> ! [X160: subst,X161: term] :
( ( sub @ one @ ( push @ X161 @ X160 ) )
= X161 ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X162: term] :
~ ! [X163: subst > term > term] :
~ ! [X164: term,X165: subst] :
( ( X163 @ X165 @ X164 )
= ( sub @ X162 @ ( push @ X164 @ X165 ) ) )
=> ( ! [X166: term] :
( ( sub @ X166 @ id )
= X166 )
=> ! [X167: subst > term > subst > $o,X168: term > $o,X169: term] :
( ~ ! [X170: term] :
( ( X168 @ ( sub @ X169 @ ( push @ X170 @ id ) ) )
| ~ ( X168 @ X170 ) )
| ~ ! [X171: subst > term > term] :
( ~ ! [X172: term] :
( ~ ( X167 @ id @ X172 @ id )
| ( X167 @ id @ ( X171 @ id @ X172 ) @ id ) )
| ~ ! [X173: subst,X174: subst,X175: term] :
( ( sub @ ( X171 @ X173 @ X175 ) @ X174 )
= ( X171 @ ( comp @ X173 @ X174 ) @ ( sub @ X175 @ X174 ) ) )
| ( X167 @ id @ ( lam @ ( X171 @ sh @ one ) ) @ id ) )
| ( X168 @ ( lam @ X169 ) )
| ~ ! [X176: term] :
( ( X168 @ X176 )
= ( X167 @ id @ X176 @ id ) ) ) ) ) )
& ( ! [X177: subst] :
( ( comp @ X177 @ id )
= X177 )
<=> axidr )
& ( ! [X178: term,X179: term,X180: term,X181: term] :
( ( ( ap @ X178 @ X180 )
!= ( ap @ X179 @ X181 ) )
| ( X180 = X181 ) )
<=> apinj2 )
& hoasinduction_lem3_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& hoasinduction_gthm
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X182: term] :
( ( sub @ X182 @ id )
= X182 )
=> ! [X183: subst > term > subst > $o,X184: term,X185: term > $o] :
( ( X185 @ ( lam @ X184 ) )
| ~ ! [X186: subst,X187: subst,X188: subst,X189: term] :
( ( X183 @ ( comp @ X188 @ X187 ) @ ( sub @ X189 @ X187 ) @ X186 )
| ~ ( X183 @ X188 @ X189 @ ( comp @ X187 @ X186 ) ) )
| ~ ! [X190: term] :
( ( X185 @ ( sub @ X184 @ ( push @ X190 @ id ) ) )
| ~ ( X185 @ X190 ) )
| ~ ! [X191: subst > term > term] :
( ( X183 @ id @ ( lam @ ( X191 @ sh @ one ) ) @ id )
| ~ ! [X192: term] :
( ( X183 @ id @ ( X191 @ id @ X192 ) @ id )
| ~ ( X183 @ id @ X192 @ id ) )
| ~ ! [X193: term,X194: subst,X195: subst] :
( ( X191 @ ( comp @ X194 @ X195 ) @ ( sub @ X193 @ X195 ) )
= ( sub @ ( X191 @ X194 @ X193 ) @ X195 ) ) )
| ~ ! [X196: subst,X197: term,X198: subst,X199: subst] :
( ~ ( X183 @ ( comp @ X196 @ X198 ) @ ( sub @ X197 @ X198 ) @ X199 )
| ( X183 @ X196 @ X197 @ ( comp @ X198 @ X199 ) ) )
| ~ ! [X200: term] :
( ( X183 @ id @ X200 @ id )
= ( X185 @ X200 ) ) ) ) )
& axassoc
& hoasapinj2_gthm
& termmset_gthm
& ( ! [X201: subst] :
( ( push @ ( sub @ one @ X201 ) @ ( comp @ sh @ X201 ) )
= X201 )
<=> axscons )
& ( ! [X202: term,X203: term] :
( ( X202 = X203 )
| ( ( sub @ X202 @ sh )
!= ( sub @ X203 @ sh ) ) )
<=> shinj )
& ! [X204: d_term,X205: d_term] :
( ( ( d2term @ X205 )
= ( d2term @ X204 ) )
=> ( X204 = X205 ) )
& pushprop_lem0_gthm
& axclos
& hoasinduction_lem3b_gthm
& ulamvarind
& ( hoasinduction_lem0
<=> ! [X206: subst > term > subst > $o] :
~ ! [X207: term > $o] :
~ ! [X208: term] :
( ( X206 @ id @ X208 @ id )
= ( X207 @ X208 ) ) )
& hoasinduction_lem1v2_gthm
& ( pushprop_lem1
<=> ! [X209: term > $o,X210: subst,X211: term > $o,X212: term,X213: term] :
( ( X211 @ ( sub @ X213 @ ( push @ X212 @ X210 ) ) )
| ~ ( X209 @ X213 ) ) )
& ! [X214: d_subst] : ( d_id = X214 )
& hoaslamnotap_lthm
& ( pushprop_lem1v2_lthm
<=> ( ! [X215: subst,X216: term] :
( ( sub @ one @ ( push @ X216 @ X215 ) )
= X216 )
=> ! [X217: term,X218: subst,X219: term > $o,X220: term > $o] :
( ~ ( X220 @ X217 )
| ( X219 @ one )
| ~ ! [X221: term] :
( ( X219 @ X221 )
= ( X220 @ ( sub @ X221 @ ( push @ X217 @ X218 ) ) ) ) ) ) )
& hoaslaminj_gthm
& ( hoasinduction_lthm
<=> ( ! [X222: term > $o,X223: term] :
( ( X222 @ X223 )
| ~ ! [X224: term] :
( ~ ( var @ X224 )
| ( X222 @ X224 ) )
| ~ ! [X225: term] :
( ( X222 @ ( lam @ X225 ) )
| ~ ! [X226: term] :
( ~ ( X222 @ X226 )
| ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) ) )
| ~ ! [X227: term,X228: term] :
( ~ ( X222 @ X227 )
| ( X222 @ ( ap @ X227 @ X228 ) )
| ~ ( X222 @ X228 ) ) )
=> ( ! [X229: subst > term > subst > $o,X230: term,X231: term] :
( ~ ! [X232: term,X233: term] :
( ~ ( X229 @ id @ X233 @ id )
| ( X229 @ id @ ( ap @ ( sub @ X232 @ id ) @ X233 ) @ id )
| ~ ( X229 @ id @ X232 @ id ) )
| ~ ( X229 @ id @ X231 @ id )
| ( X229 @ id @ ( ap @ X230 @ X231 ) @ id )
| ~ ( X229 @ id @ X230 @ id )
| ~ ! [X234: term,X235: subst,X236: subst,X237: subst] :
( ( X229 @ X235 @ X234 @ ( comp @ X236 @ X237 ) )
| ~ ( X229 @ ( comp @ X235 @ X236 ) @ ( sub @ X234 @ X236 ) @ X237 ) )
| ~ ! [X238: subst,X239: term,X240: subst,X241: subst] :
( ~ ( X229 @ X240 @ X239 @ ( comp @ X238 @ X241 ) )
| ( X229 @ ( comp @ X240 @ X238 ) @ ( sub @ X239 @ X238 ) @ X241 ) ) )
=> ( ! [X242: term,X243: subst > term > subst > $o] :
( ~ ! [X244: subst,X245: term,X246: subst,X247: subst] :
( ( X243 @ X246 @ X245 @ ( comp @ X247 @ X244 ) )
| ~ ( X243 @ ( comp @ X246 @ X247 ) @ ( sub @ X245 @ X247 ) @ X244 ) )
| ~ ! [X248: subst,X249: subst,X250: term,X251: subst] :
( ~ ( X243 @ X249 @ X250 @ ( comp @ X248 @ X251 ) )
| ( X243 @ ( comp @ X249 @ X248 ) @ ( sub @ X250 @ X248 ) @ X251 ) )
| ~ ! [X252: subst > term > term] :
( ~ ! [X253: term] :
( ~ ( X243 @ id @ X253 @ id )
| ( X243 @ id @ ( X252 @ id @ X253 ) @ id ) )
| ~ ! [X254: subst,X255: subst,X256: term] :
( ( X252 @ ( comp @ X254 @ X255 ) @ ( sub @ X256 @ X255 ) )
= ( sub @ ( X252 @ X254 @ X256 ) @ X255 ) )
| ( X243 @ id @ ( lam @ ( X252 @ sh @ one ) ) @ id ) )
| ( X243 @ id @ ( lam @ X242 ) @ id )
| ~ ! [X257: term] :
( ~ ( X243 @ id @ X257 @ id )
| ( X243 @ id @ ( sub @ X242 @ ( push @ X257 @ id ) ) @ id ) ) )
=> ! [X258: subst > term > subst > $o,X259: term] :
( ~ ! [X260: subst,X261: term,X262: subst,X263: subst] :
( ( X258 @ ( comp @ X263 @ X262 ) @ ( sub @ X261 @ X262 ) @ X260 )
| ~ ( X258 @ X263 @ X261 @ ( comp @ X262 @ X260 ) ) )
| ~ ! [X264: term,X265: term] :
( ~ ( X258 @ id @ X264 @ id )
| ( X258 @ id @ ( ap @ ( sub @ X264 @ id ) @ X265 ) @ id )
| ~ ( X258 @ id @ X265 @ id ) )
| ~ ! [X266: subst > term > term] :
( ~ ! [X267: term] :
( ~ ( X258 @ id @ X267 @ id )
| ( X258 @ id @ ( X266 @ id @ X267 ) @ id ) )
| ( X258 @ id @ ( lam @ ( X266 @ sh @ one ) ) @ id )
| ~ ! [X268: term,X269: subst,X270: subst] :
( ( X266 @ ( comp @ X270 @ X269 ) @ ( sub @ X268 @ X269 ) )
= ( sub @ ( X266 @ X270 @ X268 ) @ X269 ) ) )
| ~ ! [X271: subst,X272: subst,X273: term,X274: subst] :
( ( X258 @ X272 @ X273 @ ( comp @ X274 @ X271 ) )
| ~ ( X258 @ ( comp @ X272 @ X274 ) @ ( sub @ X273 @ X274 ) @ X271 ) )
| ~ ! [X275: term] :
( ( X258 @ id @ X275 @ id )
| ~ ( var @ ( sub @ X275 @ id ) ) )
| ( X258 @ id @ X259 @ id ) ) ) ) ) )
& ( ! [X276: term,X277: term > $o,X278: subst > term > subst > $o,X279: term] :
( ~ ( X277 @ X279 )
| ~ ! [X280: term] :
( ( X278 @ id @ X280 @ id )
= ( X277 @ X280 ) )
| ~ ! [X281: subst,X282: subst,X283: subst,X284: term] :
( ~ ( X278 @ X281 @ X284 @ ( comp @ X283 @ X282 ) )
| ( X278 @ ( comp @ X281 @ X283 ) @ ( sub @ X284 @ X283 ) @ X282 ) )
| ~ ! [X285: term,X286: term] :
( ( X278 @ id @ ( ap @ ( sub @ X286 @ id ) @ X285 ) @ id )
| ~ ( X278 @ id @ X285 @ id )
| ~ ( X278 @ id @ X286 @ id ) )
| ~ ! [X287: subst,X288: term,X289: subst,X290: subst] :
( ~ ( X278 @ ( comp @ X290 @ X287 ) @ ( sub @ X288 @ X287 ) @ X289 )
| ( X278 @ X290 @ X288 @ ( comp @ X287 @ X289 ) ) )
| ~ ( X277 @ X276 )
| ( X277 @ ( ap @ X279 @ X276 ) ) )
<=> hoasinduction_lem2v2 )
& hoasapnotvar_lthm
& ( hoasinduction_lem3_lthm
<=> ( ! [X291: term] :
( ( sub @ X291 @ id )
= X291 )
=> ( ! [X292: term,X293: subst > term > subst > $o] :
( ~ ! [X294: subst > term > term] :
( ~ ! [X295: term] :
( ( X293 @ id @ ( X294 @ id @ X295 ) @ id )
| ~ ( X293 @ id @ X295 @ id ) )
| ~ ! [X296: term,X297: subst,X298: subst] :
( ( sub @ ( X294 @ X297 @ X296 ) @ X298 )
= ( X294 @ ( comp @ X297 @ X298 ) @ ( sub @ X296 @ X298 ) ) )
| ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) )
| ~ ! [X299: term] :
( ( X293 @ id @ ( sub @ X292 @ ( push @ X299 @ id ) ) @ id )
| ~ ( X293 @ id @ X299 @ id ) )
| ( X293 @ id @ ( lam @ ( sub @ X292 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X300: subst > term > subst > $o,X301: term] :
( ( X300 @ id @ ( lam @ X301 ) @ id )
| ~ ! [X302: subst,X303: subst,X304: subst,X305: term] :
( ~ ( X300 @ ( comp @ X302 @ X303 ) @ ( sub @ X305 @ X303 ) @ X304 )
| ( X300 @ X302 @ X305 @ ( comp @ X303 @ X304 ) ) )
| ~ ! [X306: subst > term > term] :
( ~ ! [X307: subst,X308: subst,X309: term] :
( ( X306 @ ( comp @ X308 @ X307 ) @ ( sub @ X309 @ X307 ) )
= ( sub @ ( X306 @ X308 @ X309 ) @ X307 ) )
| ~ ! [X310: term] :
( ~ ( X300 @ id @ X310 @ id )
| ( X300 @ id @ ( X306 @ id @ X310 ) @ id ) )
| ( X300 @ id @ ( lam @ ( X306 @ sh @ one ) ) @ id ) )
| ~ ! [X311: term] :
( ~ ( X300 @ id @ X311 @ id )
| ( X300 @ id @ ( sub @ X301 @ ( push @ X311 @ id ) ) @ id ) )
| ~ ! [X312: subst,X313: subst,X314: subst,X315: term] :
( ( X300 @ ( comp @ X312 @ X313 ) @ ( sub @ X315 @ X313 ) @ X314 )
| ~ ( X300 @ X312 @ X315 @ ( comp @ X313 @ X314 ) ) ) ) ) ) )
& ( ! [X316: subst > term > subst > $o] :
~ ! [X317: term > $o] :
~ ! [X318: term] :
( ( X316 @ id @ X318 @ id )
= ( X317 @ X318 ) )
<=> hoasinduction_lem0_lthm )
& hoaslamnotvar_lthm
& pushprop_lem1_gthm
& ( hoaslamnotap
<=> ! [X319: subst > term > term,X320: term,X321: term] :
( ( ( ap @ ( sub @ X320 @ id ) @ X321 )
!= ( lam @ ( X319 @ sh @ one ) ) )
| ~ ! [X322: subst,X323: term,X324: subst] :
( ( sub @ ( X319 @ X324 @ X323 ) @ X322 )
= ( X319 @ ( comp @ X324 @ X322 ) @ ( sub @ X323 @ X322 ) ) ) ) )
& lamnotvar
& ( ( ! [X325: term] :
( ( sub @ X325 @ id )
= X325 )
=> ( ! [X326: subst > term > subst > $o,X327: term] :
( ~ ! [X328: term] :
( ( X326 @ id @ ( sub @ X327 @ ( push @ X328 @ id ) ) @ id )
| ~ ( X326 @ id @ X328 @ id ) )
| ( X326 @ id @ ( lam @ ( sub @ X327 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X329: subst > term > term] :
( ~ ! [X330: subst,X331: subst,X332: term] :
( ( sub @ ( X329 @ X330 @ X332 ) @ X331 )
= ( X329 @ ( comp @ X330 @ X331 ) @ ( sub @ X332 @ X331 ) ) )
| ( X326 @ id @ ( lam @ ( X329 @ sh @ one ) ) @ id )
| ~ ! [X333: term] :
( ( X326 @ id @ ( X329 @ id @ X333 ) @ id )
| ~ ( X326 @ id @ X333 @ id ) ) ) )
=> ! [X334: subst > term > subst > $o,X335: term] :
( ~ ! [X336: term] :
( ( X334 @ id @ ( sub @ X335 @ ( push @ X336 @ id ) ) @ id )
| ~ ( X334 @ id @ X336 @ id ) )
| ~ ! [X337: subst > term > term] :
( ~ ! [X338: subst,X339: term,X340: subst] :
( ( X337 @ ( comp @ X338 @ X340 ) @ ( sub @ X339 @ X340 ) )
= ( sub @ ( X337 @ X338 @ X339 ) @ X340 ) )
| ( X334 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id )
| ~ ! [X341: term] :
( ( X334 @ id @ ( X337 @ id @ X341 ) @ id )
| ~ ( X334 @ id @ X341 @ id ) ) )
| ( X334 @ id @ ( lam @ X335 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( induction2lem_lthm
<=> ( ! [X342: subst,X343: term] :
( ( sub @ one @ ( push @ X343 @ X342 ) )
= X343 )
=> ( ! [X344: term,X345: subst] :
( ( comp @ sh @ ( push @ X344 @ X345 ) )
= X345 )
=> ( ! [X346: subst] :
( ( comp @ X346 @ id )
= X346 )
=> ( ! [X347: term > $o,X348: term] :
( ~ ! [X349: term,X350: term] :
( ( X347 @ ( ap @ X350 @ X349 ) )
| ~ ( X347 @ X350 )
| ~ ( X347 @ X349 ) )
| ~ ! [X351: term] :
( ( X347 @ ( lam @ X351 ) )
| ~ ( X347 @ X351 ) )
| ~ ! [X352: term] :
( ~ ( var @ X352 )
| ( X347 @ X352 ) )
| ( X347 @ X348 ) )
=> ! [X353: term > $o,X354: term,X355: subst] :
( ~ ! [X356: term,X357: term] :
( ( X353 @ ( ap @ X357 @ X356 ) )
| ~ ( X353 @ X356 )
| ~ ( X353 @ X357 ) )
| ~ ! [X358: term] :
( ~ ! [X359: term] :
( ( X353 @ ( sub @ X358 @ ( push @ X359 @ id ) ) )
| ~ ( X353 @ X359 ) )
| ( X353 @ ( lam @ X358 ) ) )
| ~ ! [X360: term] :
( ~ ( var @ X360 )
| ( X353 @ ( sub @ X360 @ X355 ) ) )
| ( X353 @ ( sub @ X354 @ X355 ) ) ) ) ) ) ) )
& ( hoasinduction_lem3v2
<=> ! [X361: subst > term > subst > $o,X362: term > $o,X363: term] :
( ~ ! [X364: term] :
( ( X361 @ id @ X364 @ id )
= ( X362 @ X364 ) )
| ( X362 @ ( lam @ X363 ) )
| ~ ! [X365: term,X366: subst,X367: subst,X368: subst] :
( ~ ( X361 @ X366 @ X365 @ ( comp @ X367 @ X368 ) )
| ( X361 @ ( comp @ X366 @ X367 ) @ ( sub @ X365 @ X367 ) @ X368 ) )
| ~ ! [X369: term] :
( ~ ( X362 @ X369 )
| ( X362 @ ( sub @ X363 @ ( push @ X369 @ id ) ) ) )
| ~ ! [X370: subst,X371: subst,X372: subst,X373: term] :
( ~ ( X361 @ ( comp @ X372 @ X370 ) @ ( sub @ X373 @ X370 ) @ X371 )
| ( X361 @ X372 @ X373 @ ( comp @ X370 @ X371 ) ) )
| ~ ! [X374: subst > term > term] :
( ~ ! [X375: term] :
( ( X361 @ id @ ( X374 @ id @ X375 ) @ id )
| ~ ( X361 @ id @ X375 @ id ) )
| ( X361 @ id @ ( lam @ ( X374 @ sh @ one ) ) @ id )
| ~ ! [X376: term,X377: subst,X378: subst] :
( ( X374 @ ( comp @ X377 @ X378 ) @ ( sub @ X376 @ X378 ) )
= ( sub @ ( X374 @ X377 @ X376 ) @ X378 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [X379: subst > term > subst > $o,X380: term > $o] :
! [X381: term] :
( ( X380 @ X381 )
= ( X379 @ id @ X381 @ id ) ) ) )
& ( ! [X382: term] :
( ( sub @ X382 @ id )
= X382 )
<=> axvarid )
& ( hoasinduction_lem3a
<=> ! [X383: subst > term > subst > $o,X384: term] :
( ( X383 @ id @ ( lam @ X384 ) @ id )
| ~ ! [X385: term] :
( ( X383 @ id @ ( sub @ X384 @ ( push @ X385 @ id ) ) @ id )
| ~ ( X383 @ id @ X385 @ id ) )
| ~ ! [X386: subst > term > term] :
( ~ ! [X387: term] :
( ( X383 @ id @ ( X386 @ id @ X387 ) @ id )
| ~ ( X383 @ id @ X387 @ id ) )
| ( X383 @ id @ ( lam @ ( X386 @ sh @ one ) ) @ id )
| ~ ! [X388: subst,X389: subst,X390: term] :
( ( sub @ ( X386 @ X388 @ X390 ) @ X389 )
= ( X386 @ ( comp @ X388 @ X389 ) @ ( sub @ X390 @ X389 ) ) ) ) ) )
& ( ! [X391: term] :
( ( sub @ X391 @ id )
= X391 )
<=> termmset )
& ( hoaslaminj_lthm
<=> ( ! [X392: term,X393: subst] :
( ( sub @ one @ ( push @ X392 @ X393 ) )
= X392 )
=> ( ! [X394: subst,X395: term] :
( ( comp @ sh @ ( push @ X395 @ X394 ) )
= X394 )
=> ( ! [X396: term,X397: term] :
( ( X396 = X397 )
| ( ( lam @ X396 )
!= ( lam @ X397 ) ) )
=> ! [X398: subst,X399: subst > term > term,X400: term,X401: subst > term > term] :
( ~ ! [X402: subst,X403: term,X404: subst] :
( ( sub @ ( X401 @ X404 @ X403 ) @ X402 )
= ( X401 @ ( comp @ X404 @ X402 ) @ ( sub @ X403 @ X402 ) ) )
| ~ ! [X405: subst,X406: term,X407: subst] :
( ( X399 @ ( comp @ X405 @ X407 ) @ ( sub @ X406 @ X407 ) )
= ( sub @ ( X399 @ X405 @ X406 ) @ X407 ) )
| ( ( X399 @ X398 @ X400 )
= ( X401 @ X398 @ X400 ) )
| ( ( lam @ ( X399 @ sh @ one ) )
!= ( lam @ ( X401 @ sh @ one ) ) ) ) ) ) ) )
& ( induction2
<=> ! [X408: term > $o,X409: term] :
( ~ ! [X410: term,X411: term] :
( ( X408 @ ( ap @ X411 @ X410 ) )
| ~ ( X408 @ X410 )
| ~ ( X408 @ X411 ) )
| ( X408 @ X409 )
| ~ ! [X412: term] :
( ~ ( var @ X412 )
| ( X408 @ X412 ) )
| ~ ! [X413: term] :
( ~ ! [X414: term] :
( ~ ( X408 @ X414 )
| ( X408 @ ( sub @ X413 @ ( push @ X414 @ id ) ) ) )
| ( X408 @ ( lam @ X413 ) ) ) ) )
& ( ( ! [X415: subst] :
( ( comp @ X415 @ id )
= X415 )
& ! [X416: subst] :
( ( comp @ id @ X416 )
= X416 ) )
<=> substmonoid )
& ( axidl
<=> ! [X417: subst] :
( ( comp @ id @ X417 )
= X417 ) )
& ! [X418: d_term] : ( d_one = X418 )
& pushprop_lthm_orig
& ( apinj1
<=> ! [X419: term,X420: term,X421: term,X422: term] :
( ( X420 = X421 )
| ( ( ap @ X421 @ X422 )
!= ( ap @ X420 @ X419 ) ) ) )
& pushprop_lem2v2_gthm
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop
& axvarshift
& pushprop_lem1v2_gthm
& ~ ( var @ ( d2term @ d_one ) )
& ( ! [X423: term] :
~ ! [X424: subst > term > term] :
( ( X424 @ sh @ one )
!= ( sub @ X423 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b )
& hoasinduction_lem1_gthm
& ( termmset_lthm
<=> ( ! [X425: term] :
( ( sub @ X425 @ id )
= X425 )
=> ! [X426: term] :
( ( sub @ X426 @ id )
= X426 ) ) )
& pushprop_lem2v2_lthm
& axmap
& ! [X427: subst] :
? [X428: d_subst] :
( ( d2subst @ X428 )
= X427 )
& ~ lamnotap
& ( hoasinduction_lem3aa
<=> ! [X429: subst > term > subst > $o,X430: term] :
( ~ ! [X431: subst > term > term] :
( ~ ! [X432: term] :
( ( X429 @ id @ ( X431 @ id @ X432 ) @ id )
| ~ ( X429 @ id @ X432 @ id ) )
| ~ ! [X433: term,X434: subst,X435: subst] :
( ( X431 @ ( comp @ X435 @ X434 ) @ ( sub @ X433 @ X434 ) )
= ( sub @ ( X431 @ X435 @ X433 ) @ X434 ) )
| ( X429 @ id @ ( lam @ ( X431 @ sh @ one ) ) @ id ) )
| ( X429 @ id @ ( lam @ ( sub @ X430 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X436: term] :
( ( X429 @ id @ ( sub @ X430 @ ( push @ X436 @ id ) ) @ id )
| ~ ( X429 @ id @ X436 @ id ) ) ) )
& ulamvarsh
& ( ! [X437: term,X438: term,X439: subst > term > subst > $o] :
( ~ ( X439 @ id @ X437 @ id )
| ~ ! [X440: term,X441: term] :
( ~ ( X439 @ id @ X440 @ id )
| ( X439 @ id @ ( ap @ ( sub @ X440 @ id ) @ X441 ) @ id )
| ~ ( X439 @ id @ X441 @ id ) )
| ( X439 @ id @ ( ap @ X438 @ X437 ) @ id )
| ~ ! [X442: term,X443: subst,X444: subst,X445: subst] :
( ( X439 @ ( comp @ X444 @ X443 ) @ ( sub @ X442 @ X443 ) @ X445 )
| ~ ( X439 @ X444 @ X442 @ ( comp @ X443 @ X445 ) ) )
| ~ ! [X446: subst,X447: term,X448: subst,X449: subst] :
( ( X439 @ X446 @ X447 @ ( comp @ X449 @ X448 ) )
| ~ ( X439 @ ( comp @ X446 @ X449 ) @ ( sub @ X447 @ X449 ) @ X448 ) )
| ~ ( X439 @ id @ X438 @ id ) )
<=> hoasinduction_lem2 )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3aa_lthm
<=> ! [X450: term,X451: subst > term > subst > $o] :
( ~ ! [X452: term] :
( ( X451 @ id @ ( sub @ X450 @ ( push @ X452 @ id ) ) @ id )
| ~ ( X451 @ id @ X452 @ id ) )
| ~ ! [X453: subst > term > term] :
( ~ ! [X454: subst,X455: term,X456: subst] :
( ( sub @ ( X453 @ X454 @ X455 ) @ X456 )
= ( X453 @ ( comp @ X454 @ X456 ) @ ( sub @ X455 @ X456 ) ) )
| ~ ! [X457: term] :
( ~ ( X451 @ id @ X457 @ id )
| ( X451 @ id @ ( X453 @ id @ X457 ) @ id ) )
| ( X451 @ id @ ( lam @ ( X453 @ sh @ one ) ) @ id ) )
| ( X451 @ id @ ( lam @ ( sub @ X450 @ ( push @ one @ sh ) ) ) @ id ) ) )
& hoaslamnotap_gthm
& ! [X458: term] :
? [X459: d_term] :
( ( d2term @ X459 )
= X458 )
& ( hoaslam
= ( ^ [X460: subst,X461: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X462: term,X463: term,X464: term,X465: term] :
( ( ( ap @ ( sub @ X465 @ id ) @ X464 )
!= ( ap @ ( sub @ X462 @ id ) @ X463 ) )
| ( X463 = X464 ) )
<=> hoasapinj2 )
& pushprop_lem3v2_lthm
& ( ! [X466: subst,X467: term > $o,X468: term] :
~ ! [X469: term > $o] :
~ ! [X470: term] :
( ( X467 @ ( sub @ X470 @ ( push @ X468 @ X466 ) ) )
= ( X469 @ X470 ) )
<=> pushprop_lem0 )
& ( laminj
<=> ! [X471: term,X472: term] :
( ( ( lam @ X472 )
!= ( lam @ X471 ) )
| ( X471 = X472 ) ) )
& induction2_gthm
& substmonoid_gthm
& ( ! [X473: subst,X474: term] :
( ( comp @ sh @ ( push @ X474 @ X473 ) )
= X473 )
<=> axshiftcons )
& induction2lem_gthm
& hoasinduction_lem2_lthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction
<=> ! [X475: term,X476: subst > term > subst > $o] :
( ~ ! [X477: term] :
( ( X476 @ id @ X477 @ id )
| ~ ( var @ ( sub @ X477 @ id ) ) )
| ~ ! [X478: term,X479: subst,X480: subst,X481: subst] :
( ~ ( X476 @ X480 @ X478 @ ( comp @ X481 @ X479 ) )
| ( X476 @ ( comp @ X480 @ X481 ) @ ( sub @ X478 @ X481 ) @ X479 ) )
| ~ ! [X482: subst > term > term] :
( ~ ! [X483: subst,X484: term,X485: subst] :
( ( sub @ ( X482 @ X485 @ X484 ) @ X483 )
= ( X482 @ ( comp @ X485 @ X483 ) @ ( sub @ X484 @ X483 ) ) )
| ~ ! [X486: term] :
( ( X476 @ id @ ( X482 @ id @ X486 ) @ id )
| ~ ( X476 @ id @ X486 @ id ) )
| ( X476 @ id @ ( lam @ ( X482 @ sh @ one ) ) @ id ) )
| ( X476 @ id @ X475 @ id )
| ~ ! [X487: subst,X488: subst,X489: subst,X490: term] :
( ( X476 @ X489 @ X490 @ ( comp @ X488 @ X487 ) )
| ~ ( X476 @ ( comp @ X489 @ X488 ) @ ( sub @ X490 @ X488 ) @ X487 ) )
| ~ ! [X491: term,X492: term] :
( ( X476 @ id @ ( ap @ ( sub @ X492 @ id ) @ X491 ) @ id )
| ~ ( X476 @ id @ X491 @ id )
| ~ ( X476 @ id @ X492 @ id ) ) ) )
& ( ! [X493: term] :
~ ! [X494: subst > term > term] :
~ ! [X495: subst,X496: term] :
( ( sub @ X493 @ ( push @ X496 @ X495 ) )
= ( X494 @ X495 @ X496 ) )
<=> hoasinduction_lem3v2_f )
& ( ! [X497: term,X498: subst > term > subst > $o] :
( ~ ! [X499: term,X500: term] :
( ~ ( X498 @ id @ X500 @ id )
| ( X498 @ id @ ( ap @ ( sub @ X499 @ id ) @ X500 ) @ id )
| ~ ( X498 @ id @ X499 @ id ) )
| ~ ! [X501: subst > term > term] :
( ~ ! [X502: subst,X503: term,X504: subst] :
( ( sub @ ( X501 @ X502 @ X503 ) @ X504 )
= ( X501 @ ( comp @ X502 @ X504 ) @ ( sub @ X503 @ X504 ) ) )
| ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id )
| ~ ! [X505: term] :
( ~ ( X498 @ id @ X505 @ id )
| ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) )
| ( X498 @ id @ X497 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ( ! [X506: term] :
( ( sub @ X506 @ id )
= X506 )
=> ( ! [X507: term > $o,X508: subst,X509: term] :
( ( X507 @ ( sub @ X509 @ X508 ) )
| ~ ! [X510: term,X511: term] :
( ~ ( X507 @ X510 )
| ( X507 @ ( ap @ X510 @ X511 ) )
| ~ ( X507 @ X511 ) )
| ~ ! [X512: term] :
( ( X507 @ ( lam @ X512 ) )
| ~ ! [X513: term] :
( ~ ( X507 @ X513 )
| ( X507 @ ( sub @ X512 @ ( push @ X513 @ id ) ) ) ) )
| ~ ! [X514: term] :
( ~ ( var @ X514 )
| ( X507 @ ( sub @ X514 @ X508 ) ) ) )
=> ! [X515: term > $o,X516: term] :
( ( X515 @ X516 )
| ~ ! [X517: term] :
( ~ ! [X518: term] :
( ~ ( X515 @ X518 )
| ( X515 @ ( sub @ X517 @ ( push @ X518 @ id ) ) ) )
| ( X515 @ ( lam @ X517 ) ) )
| ~ ! [X519: term,X520: term] :
( ( X515 @ ( ap @ X519 @ X520 ) )
| ~ ( X515 @ X519 )
| ~ ( X515 @ X520 ) )
| ~ ! [X521: term] :
( ~ ( var @ X521 )
| ( X515 @ X521 ) ) ) ) )
<=> induction2_lthm )
& ( hoasinduction_lem3v2a
<=> ! [X522: subst > term > subst > $o,X523: term > $o,X524: term] :
( ~ ! [X525: term] :
( ( X523 @ X525 )
= ( X522 @ id @ X525 @ id ) )
| ( X523 @ ( lam @ X524 ) )
| ~ ! [X526: subst > term > term] :
( ~ ! [X527: subst,X528: subst,X529: term] :
( ( sub @ ( X526 @ X528 @ X529 ) @ X527 )
= ( X526 @ ( comp @ X528 @ X527 ) @ ( sub @ X529 @ X527 ) ) )
| ( X522 @ id @ ( lam @ ( X526 @ sh @ one ) ) @ id )
| ~ ! [X530: term] :
( ( X522 @ id @ ( X526 @ id @ X530 ) @ id )
| ~ ( X522 @ id @ X530 @ id ) ) )
| ~ ! [X531: term] :
( ( X523 @ ( sub @ X524 @ ( push @ X531 @ id ) ) )
| ~ ( X523 @ X531 ) ) ) )
& ( hoaslaminj
<=> ! [X532: subst > term > term,X533: subst,X534: subst > term > term,X535: term] :
( ( ( X532 @ X533 @ X535 )
= ( X534 @ X533 @ X535 ) )
| ~ ! [X536: subst,X537: term,X538: subst] :
( ( X534 @ ( comp @ X536 @ X538 ) @ ( sub @ X537 @ X538 ) )
= ( sub @ ( X534 @ X536 @ X537 ) @ X538 ) )
| ~ ! [X539: term,X540: subst,X541: subst] :
( ( sub @ ( X532 @ X540 @ X539 ) @ X541 )
= ( X532 @ ( comp @ X540 @ X541 ) @ ( sub @ X539 @ X541 ) ) )
| ( ( lam @ ( X534 @ sh @ one ) )
!= ( lam @ ( X532 @ sh @ one ) ) ) ) )
& pushprop_gthm
& ( induction2lem
<=> ! [X542: term,X543: subst,X544: term > $o] :
( ~ ! [X545: term] :
( ( X544 @ ( lam @ X545 ) )
| ~ ! [X546: term] :
( ( X544 @ ( sub @ X545 @ ( push @ X546 @ id ) ) )
| ~ ( X544 @ X546 ) ) )
| ( X544 @ ( sub @ X542 @ X543 ) )
| ~ ! [X547: term] :
( ~ ( var @ X547 )
| ( X544 @ ( sub @ X547 @ X543 ) ) )
| ~ ! [X548: term,X549: term] :
( ~ ( X544 @ X549 )
| ~ ( X544 @ X548 )
| ( X544 @ ( ap @ X548 @ X549 ) ) ) ) )
& hoasapnotvar_gthm ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( hoasinduction_lem1v2
& ( pushprop_lem1v2
<=> ! [X11: term > $o,X10: term > $o,X14: subst,X13: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ~ ( X10 @ X13 )
| ( X11 @ one ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X19: term,X20: term,X13: term,X15: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X15: term,X20: term,X19: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) ) )
<=> hoasapinj1_lthm )
& pushprop_lthm
& ( pushprop_lem0_lthm
<=> ! [X10: term > $o,X13: term,X14: subst] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& hoaslamnotvar
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem1_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X15: term,X10: term > $o,X26: term > $o,X14: subst,X13: term] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) ) ) ) )
& hoasapnotvar
& hoasinduction_lem1_lthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& ( ! [X15: term,X20: term,X19: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) )
<=> hoasapinj1 )
& hoasapinj1_gthm
& axabs
& ( 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 ) ) ) ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f_lthm )
& pushprop_lem3v2
& hoasinduction_lem3a_gthm
& hoaslamnotvar_gthm
& ( ( d2subst @ d_id )
= sh )
& hoasinduction_lem3v2_gthm
& pushprop_lem2v2
& ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X14: subst,X25: subst,X26: 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 ) )
| ( X10 @ id @ ( lam @ X27 ) @ 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 @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3 )
& ! [X6: d_subst,X7: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( hoasapinj2_lthm
<=> ( ! [X13: term,X20: term,X19: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X19: term,X20: term,X15: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X34: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term,X35: term] :
( ~ ! [X36: subst,X38: subst,X37: term] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ~ ! [X39: subst,X40: term,X41: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) )
& apnotvar
& hoasinduction_lem2v2_gthm
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lthm_3
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X11: term > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X14: subst,X25: subst,X13: term,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) ) ) ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [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 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ( X10 @ X22 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
=> ! [X10: subst > term > subst > $o,X30: term] :
( ( X10 @ id @ X30 @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) ) ) ) ) ) ) )
& axapp
& hoasinduction_lem2_gthm
& ~ ulamvar1
& hoasinduction_lem1
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) ) ) )
<=> substmonoid_lthm )
& ( ! [X10: term > $o,X21: term] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X21 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) ) )
<=> induction )
& ( axvarcons
<=> ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X11: term > $o,X29: term] :
( ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) ) ) )
& ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
<=> axidr )
& ( ! [X13: term,X15: term,X19: term,X20: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
<=> apinj2 )
& hoasinduction_lem3_gthm
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& hoasinduction_gthm
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X48: term,X11: term > $o] :
( ( X11 @ ( lam @ X48 ) )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X14: subst,X13: term,X26: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) ) )
& axassoc
& hoasapinj2_gthm
& termmset_gthm
& ( ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 )
<=> axscons )
& ( ! [X15: term,X13: term] :
( ( X13 = X15 )
| ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) ) )
<=> shinj )
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& pushprop_lem0_gthm
& axclos
& hoasinduction_lem3b_gthm
& ulamvarind
& ( hoasinduction_lem0
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& hoasinduction_lem1v2_gthm
& ( pushprop_lem1
<=> ! [X10: term > $o,X14: subst,X26: term > $o,X15: term,X13: term] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) ) )
& ! [X5: d_subst] : ( d_id = X5 )
& hoaslamnotap_lthm
& ( pushprop_lem1v2_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X13: term,X14: subst,X11: term > $o,X10: term > $o] :
( ~ ( X10 @ X13 )
| ( X11 @ one )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) ) )
& hoaslaminj_gthm
& ( hoasinduction_lthm
<=> ( ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) ) )
=> ( ! [X10: subst > term > subst > $o,X23: term,X24: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ( X10 @ id @ X24 @ id )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) )
=> ( ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: 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 ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X25: subst,X13: term,X26: subst,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 ) )
| ~ ! [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 ) ) ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) )
& ( ! [X45: term,X11: term > $o,X10: subst > term > subst > $o,X44: term] :
( ~ ( X11 @ X44 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X11 @ X45 )
| ( X11 @ ( ap @ X44 @ X45 ) ) )
<=> hoasinduction_lem2v2 )
& hoasapnotvar_lthm
& ( hoasinduction_lem3_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
=> ! [X10: subst > term > subst > $o,X27: term] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [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 @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) ) ) )
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0_lthm )
& hoaslamnotvar_lthm
& pushprop_lem1_gthm
& ( hoaslamnotap
<=> ! [X18: subst > term > term,X46: term,X47: 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 ) ) ) ) )
& lamnotvar
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
=> ! [X10: subst > term > subst > $o,X43: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ( X10 @ id @ ( lam @ X43 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( induction2lem_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X10: term > $o,X21: term] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( X10 @ X21 ) )
=> ! [X10: term > $o,X16: term,X17: subst] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) ) ) ) ) ) )
& ( hoasinduction_lem3v2
<=> ! [X10: subst > term > subst > $o,X11: term > $o,X48: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ~ ( 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 ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& ( hoasinduction_lem3a
<=> ! [X10: subst > term > subst > $o,X43: term] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& ( hoaslaminj_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X13: term,X15: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) )
=> ! [X32: subst,X18: subst > term > term,X33: term,X31: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X14: subst,X13: term,X25: 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 ) ) ) ) ) ) ) )
& ( induction2
<=> ! [X10: term > $o,X22: term] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) ) ) )
& ( ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
& ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
<=> substmonoid )
& ( axidl
<=> ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
& ! [X1: d_term] : ( d_one = X1 )
& pushprop_lthm_orig
& ( apinj1
<=> ! [X20: term,X15: term,X13: term,X19: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) ) )
& pushprop_lem2v2_gthm
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop
& axvarshift
& pushprop_lem1v2_gthm
& ~ ( var @ ( d2term @ d_one ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b )
& hoasinduction_lem1_gthm
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& pushprop_lem2v2_lthm
& axmap
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ~ lamnotap
& ( hoasinduction_lem3aa
<=> ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [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 ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ulamvarsh
& ( ! [X24: term,X23: term,X10: subst > term > subst > $o] :
( ~ ( X10 @ id @ X24 @ id )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X14: subst,X13: term,X25: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X10 @ id @ X23 @ id ) )
<=> hoasinduction_lem2 )
& ( ( d2subst @ d_id )
= id )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3aa_lthm
<=> ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) ) )
& hoaslamnotap_gthm
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( hoaslam
= ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X15: term,X20: term,X19: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) )
<=> hoasapinj2 )
& pushprop_lem3v2_lthm
& ( ! [X14: subst,X10: term > $o,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0 )
& ( laminj
<=> ! [X13: term,X15: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) ) )
& induction2_gthm
& substmonoid_gthm
& ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
<=> axshiftcons )
& induction2lem_gthm
& hoasinduction_lem2_lthm
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( hoasinduction
<=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [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] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& ( ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ X30 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: term > $o,X17: subst,X16: term] :
( ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) ) )
=> ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) ) ) )
<=> induction2_lthm )
& ( hoasinduction_lem3v2a
<=> ! [X10: subst > term > subst > $o,X11: term > $o,X29: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) ) )
& ( hoaslaminj
<=> ! [X18: subst > term > term,X32: subst,X31: subst > term > term,X33: term] :
( ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) ) ) )
& pushprop_gthm
& ( induction2lem
<=> ! [X16: term,X17: subst,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) ) ) )
& hoasapnotvar_gthm ),
file('/export/starexec/sandbox/tmp/tmp.SwuThMpGUN/DTF2THF_19838.p',alg444_1) ).
thf(f1217,plain,
! [X55: term] :
( ( d2term @ ( sK481 @ X55 ) )
= X55 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f4236,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( d2term @ d_one )
!= ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP57 @ X0 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4235,f4138]) ).
thf(f4235,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) )
| ( ( sP57 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4140,f4232]) ).
thf(f4232,plain,
! [X0: subst > term > subst > $o,X7: term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ X7 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4181,f4213]) ).
thf(f4213,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP37 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4212,f4138]) ).
thf(f4212,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( d2term @ d_one )
!= ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP37 @ X0 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4211,f4138]) ).
thf(f4211,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) )
| ( ( sP37 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f4210]) ).
thf(f4210,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP37 @ X0 )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4145,f4138]) ).
thf(f4145,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK198 @ X1 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( sP37 @ X0 )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1388,f4138]) ).
thf(f1388,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK198 @ X1 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP37 @ X0 )
= $true )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f729,f1046,f1046,f1046,f1116,f1078,f1046]) ).
thf(f1078,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1116,plain,
( ( d2subst @ d_id )
= sh ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1046,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f729,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP37 @ X0 )
= $true )
| ( ( X0 @ id @ ( sK198 @ X1 @ X0 ) @ id )
= $true )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
thf(f219,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP37 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ( ( ( X0 @ id @ ( sK198 @ X1 @ X0 ) @ id )
= $true )
& ( ( X0 @ id @ ( X1 @ id @ ( sK198 @ X1 @ X0 ) ) @ id )
!= $true ) )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ) )
& ( ( ! [X7: term] :
( ( ( X0 @ id @ X7 @ id )
!= $true )
| ( $true
= ( X0 @ id @ ( sK202 @ X0 @ id @ X7 ) @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( sK202 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X8: subst,X9: term,X10: subst] :
( ( sK202 @ X0 @ ( comp @ X10 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( sK202 @ X0 @ X10 @ X9 ) @ X8 ) ) )
| ( ( sP37 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199,sK200,sK201,sK202])],[f215,f218,f217,f216]) ).
thf(f216,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X2: term] :
( ( ( X0 @ id @ X2 @ id )
= $true )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
=> ( ( ( X0 @ id @ ( sK198 @ X1 @ X0 ) @ id )
= $true )
& ( ( X0 @ id @ ( X1 @ id @ ( sK198 @ X1 @ X0 ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f217,plain,
! [X1: subst > term > term] :
( ? [X3: subst,X4: term,X5: subst] :
( ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) )
!= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) )
=> ( ( sub @ ( X1 @ ( sK201 @ X1 ) @ ( sK200 @ X1 ) ) @ ( sK199 @ X1 ) )
!= ( X1 @ ( comp @ ( sK201 @ X1 ) @ ( sK199 @ X1 ) ) @ ( sub @ ( sK200 @ X1 ) @ ( sK199 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f218,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ! [X7: term] :
( ( ( X0 @ id @ X7 @ id )
!= $true )
| ( ( X0 @ id @ ( X6 @ id @ X7 ) @ id )
= $true ) )
& ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X8: subst,X9: term,X10: subst] :
( ( sub @ ( X6 @ X10 @ X9 ) @ X8 )
= ( X6 @ ( comp @ X10 @ X8 ) @ ( sub @ X9 @ X8 ) ) ) )
=> ( ! [X7: term] :
( ( ( X0 @ id @ X7 @ id )
!= $true )
| ( $true
= ( X0 @ id @ ( sK202 @ X0 @ id @ X7 ) @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( sK202 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X10: subst,X9: term,X8: subst] :
( ( sK202 @ X0 @ ( comp @ X10 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( sK202 @ X0 @ X10 @ X9 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f215,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP37 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ? [X2: term] :
( ( ( X0 @ id @ X2 @ id )
= $true )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ X2 ) @ id ) ) )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ? [X3: subst,X4: term,X5: subst] :
( ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) )
!= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) ) )
& ( ? [X6: subst > term > term] :
( ! [X7: term] :
( ( ( X0 @ id @ X7 @ id )
!= $true )
| ( ( X0 @ id @ ( X6 @ id @ X7 ) @ id )
= $true ) )
& ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X8: subst,X9: term,X10: subst] :
( ( sub @ ( X6 @ X10 @ X9 ) @ X8 )
= ( X6 @ ( comp @ X10 @ X8 ) @ ( sub @ X9 @ X8 ) ) ) )
| ( ( sP37 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f214]) ).
thf(f214,plain,
! [X466: subst > term > subst > $o] :
( ( ( ( sP37 @ X466 )
= $true )
| ! [X472: subst > term > term] :
( ? [X476: term] :
( ( ( X466 @ id @ X476 @ id )
= $true )
& ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
!= $true ) )
| ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
= $true )
| ? [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
!= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) ) ) )
& ( ? [X472: subst > term > term] :
( ! [X476: term] :
( ( ( X466 @ id @ X476 @ id )
!= $true )
| ( ( X466 @ id @ ( X472 @ id @ X476 ) @ id )
= $true ) )
& ( ( X466 @ id @ ( lam @ ( X472 @ sh @ one ) ) @ id )
!= $true )
& ! [X473: subst,X474: term,X475: subst] :
( ( X472 @ ( comp @ X475 @ X473 ) @ ( sub @ X474 @ X473 ) )
= ( sub @ ( X472 @ X475 @ X474 ) @ X473 ) ) )
| ( ( sP37 @ X466 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
thf(f4181,plain,
! [X0: subst > term > subst > $o,X7: term] :
( ( ( X0 @ ( d2subst @ d_id ) @ X7 @ ( d2subst @ d_id ) )
!= $true )
| ( ( sP37 @ X0 )
!= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1390,f4138]) ).
thf(f1390,plain,
! [X0: subst > term > subst > $o,X7: term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( sK202 @ X0 @ ( d2subst @ d_id ) @ X7 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP37 @ X0 )
!= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ X7 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f727,f1046,f1046,f1046,f1046,f1046]) ).
thf(f727,plain,
! [X0: subst > term > subst > $o,X7: term] :
( ( ( X0 @ id @ X7 @ id )
!= $true )
| ( $true
= ( X0 @ id @ ( sK202 @ X0 @ id @ X7 ) @ id ) )
| ( ( sP37 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
thf(f4140,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP57 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK75 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1274,f4138]) ).
thf(f1274,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK75 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) )
| ( ( sP57 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f564,f1046,f1046,f1046,f1116,f1078,f1046]) ).
thf(f564,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP57 @ X0 )
= $true )
| ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) )
| ( ( X0 @ id @ ( sK75 @ X1 @ X0 ) @ id )
= $true )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP57 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) )
| ( ( ( X0 @ id @ ( X1 @ id @ ( sK75 @ X1 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK75 @ X1 @ X0 ) @ id )
= $true ) )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ) )
& ( ( ! [X7: term,X8: subst,X9: subst] :
( ( sub @ ( sK76 @ X0 @ X8 @ X7 ) @ X9 )
= ( sK76 @ X0 @ ( comp @ X8 @ X9 ) @ ( sub @ X7 @ X9 ) ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( sK76 @ X0 @ id @ X10 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( sK76 @ X0 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( sP57 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74,sK75,sK76])],[f83,f86,f85,f84]) ).
thf(f84,plain,
! [X1: subst > term > term] :
( ? [X2: term,X3: subst,X4: subst] :
( ( X1 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) )
!= ( sub @ ( X1 @ X3 @ X2 ) @ X4 ) )
=> ( ( X1 @ ( comp @ ( sK73 @ X1 ) @ ( sK74 @ X1 ) ) @ ( sub @ ( sK72 @ X1 ) @ ( sK74 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK73 @ X1 ) @ ( sK72 @ X1 ) ) @ ( sK74 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f85,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X5: term] :
( ( ( X0 @ id @ ( X1 @ id @ X5 ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ X5 @ id ) ) )
=> ( ( ( X0 @ id @ ( X1 @ id @ ( sK75 @ X1 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK75 @ X1 @ X0 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f86,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ! [X7: term,X8: subst,X9: subst] :
( ( X6 @ ( comp @ X8 @ X9 ) @ ( sub @ X7 @ X9 ) )
= ( sub @ ( X6 @ X8 @ X7 ) @ X9 ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( X6 @ id @ X10 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true ) )
=> ( ! [X9: subst,X8: subst,X7: term] :
( ( sub @ ( sK76 @ X0 @ X8 @ X7 ) @ X9 )
= ( sK76 @ X0 @ ( comp @ X8 @ X9 ) @ ( sub @ X7 @ X9 ) ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( sK76 @ X0 @ id @ X10 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( sK76 @ X0 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f83,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP57 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ? [X2: term,X3: subst,X4: subst] :
( ( X1 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) )
!= ( sub @ ( X1 @ X3 @ X2 ) @ X4 ) )
| ? [X5: term] :
( ( ( X0 @ id @ ( X1 @ id @ X5 ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ X5 @ id ) ) )
| ( ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ) )
& ( ? [X6: subst > term > term] :
( ! [X7: term,X8: subst,X9: subst] :
( ( X6 @ ( comp @ X8 @ X9 ) @ ( sub @ X7 @ X9 ) )
= ( sub @ ( X6 @ X8 @ X7 ) @ X9 ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( X6 @ id @ X10 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( sP57 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f82]) ).
thf(f82,plain,
! [X356: subst > term > subst > $o] :
( ( ( ( sP57 @ X356 )
= $true )
| ! [X369: subst > term > term] :
( ? [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
!= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
| ? [X370: term] :
( ( $true
!= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
& ( ( X356 @ id @ X370 @ id )
= $true ) )
| ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
= $true ) ) )
& ( ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( X369 @ ( comp @ X372 @ X373 ) @ ( sub @ X371 @ X373 ) )
= ( sub @ ( X369 @ X372 @ X371 ) @ X373 ) )
& ! [X370: term] :
( ( $true
= ( X356 @ id @ ( X369 @ id @ X370 ) @ id ) )
| ( ( X356 @ id @ X370 @ id )
!= $true ) )
& ( ( X356 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id )
!= $true ) )
| ( ( sP57 @ X356 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f71]) ).
thf(f7678,plain,
( ! [X11: term] :
( $false
= ( sK59 @ ( d2subst @ d_id ) @ X11 @ ( d2subst @ d_id ) ) )
| spl591_255
| ~ spl591_515
| ~ spl591_517 ),
inference(subsumption_resolution,[status(thm)],[f4612,f7546]) ).
thf(f7546,plain,
( ! [X0: term] :
( $true
!= ( sK60 @ X0 ) )
| spl591_255
| ~ spl591_515 ),
inference(superposition,[status(thm)],[f3219,f4598]) ).
thf(f4598,plain,
( ! [X10: term,X9: term] : ( X9 = X10 )
| ~ spl591_515 ),
inference(avatar_component_clause,[status(thm)],[f4597]) ).
thf(f3219,plain,
( ( $true
!= ( sK60 @ ( lam @ sK61 ) ) )
| spl591_255 ),
inference(avatar_component_clause,[status(thm)],[f3217]) ).
thf(f4612,plain,
( ! [X11: term] :
( ( ( sK60 @ X11 )
= $true )
| ( $false
= ( sK59 @ ( d2subst @ d_id ) @ X11 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_517 ),
inference(avatar_component_clause,[status(thm)],[f4611]) ).
thf(f12736,plain,
( spl591_633
| ~ spl591_401
| ~ spl591_515 ),
inference(avatar_split_clause,[status(thm)],[f7436,f4597,f3827,f6777]) ).
thf(f6777,definition,
( spl591_633
<=> ! [X1: term] :
( $false
= ( sK592 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_633])],[avatar_definition]) ).
thf(f3827,definition,
( spl591_401
<=> ( $false
= ( sK592 @ ( lam @ sK598 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_401])],[avatar_definition]) ).
thf(f7436,plain,
( ! [X0: term] :
( $false
= ( sK592 @ X0 ) )
| ~ spl591_401
| ~ spl591_515 ),
inference(superposition,[status(thm)],[f3829,f4598]) ).
thf(f3829,plain,
( ( $false
= ( sK592 @ ( lam @ sK598 ) ) )
| ~ spl591_401 ),
inference(avatar_component_clause,[status(thm)],[f3827]) ).
thf(f7414,plain,
spl591_515,
inference(avatar_split_clause,[status(thm)],[f7410,f4597]) ).
thf(f7410,plain,
! [X0: term,X1: term] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f4138,f4138]) ).
thf(f7333,plain,
( ~ spl591_404
| ~ spl591_406
| ~ spl591_633 ),
inference(avatar_contradiction_clause,[status(thm)],[f7332]) ).
thf(f7332,plain,
( $false
| ~ spl591_404
| ~ spl591_406
| ~ spl591_633 ),
inference(trivial_inequality_removal,[status(thm)],[f7331]) ).
thf(f7331,plain,
( ( $false = $true )
| ~ spl591_404
| ~ spl591_406
| ~ spl591_633 ),
inference(forward_demodulation,[status(thm)],[f3850,f7217]) ).
thf(f7217,plain,
( ! [X1: term] :
( $false
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ~ spl591_404
| ~ spl591_633 ),
inference(trivial_inequality_removal,[status(thm)],[f7216]) ).
thf(f7216,plain,
( ! [X1: term] :
( ( $false
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( $false = $true ) )
| ~ spl591_404
| ~ spl591_633 ),
inference(backward_demodulation,[status(thm)],[f3841,f6778]) ).
thf(f6778,plain,
( ! [X1: term] :
( $false
= ( sK592 @ X1 ) )
| ~ spl591_633 ),
inference(avatar_component_clause,[status(thm)],[f6777]) ).
thf(f3841,plain,
( ! [X1: term] :
( ( $false
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( ( sK592 @ X1 )
= $true ) )
| ~ spl591_404 ),
inference(avatar_component_clause,[status(thm)],[f3840]) ).
thf(f3840,definition,
( spl591_404
<=> ! [X1: term] :
( ( $false
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( ( sK592 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl591_404])],[avatar_definition]) ).
thf(f3850,plain,
( ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ~ spl591_406 ),
inference(avatar_component_clause,[status(thm)],[f3848]) ).
thf(f3848,definition,
( spl591_406
<=> ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_406])],[avatar_definition]) ).
thf(f7223,plain,
( ~ spl591_404
| ~ spl591_408
| ~ spl591_633 ),
inference(avatar_contradiction_clause,[status(thm)],[f7222]) ).
thf(f7222,plain,
( $false
| ~ spl591_404
| ~ spl591_408
| ~ spl591_633 ),
inference(subsumption_resolution,[status(thm)],[f7221,f4138]) ).
thf(f7221,plain,
( ! [X1: subst > term > term] :
( ( d2term @ d_one )
!= ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) ) )
| ~ spl591_404
| ~ spl591_408
| ~ spl591_633 ),
inference(forward_demodulation,[status(thm)],[f7220,f4138]) ).
thf(f7220,plain,
( ! [X1: subst > term > term] :
( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) )
| ~ spl591_404
| ~ spl591_408
| ~ spl591_633 ),
inference(trivial_inequality_removal,[status(thm)],[f7219]) ).
thf(f7219,plain,
( ! [X1: subst > term > term] :
( ( $false = $true )
| ( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) ) )
| ~ spl591_404
| ~ spl591_408
| ~ spl591_633 ),
inference(forward_demodulation,[status(thm)],[f3857,f7217]) ).
thf(f3857,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) ) )
| ~ spl591_408 ),
inference(avatar_component_clause,[status(thm)],[f3856]) ).
thf(f3856,definition,
( spl591_408
<=> ! [X1: subst > term > term] :
( ( $true
= ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_408])],[avatar_definition]) ).
thf(f5545,plain,
( ~ spl591_197
| ~ spl591_402 ),
inference(avatar_contradiction_clause,[status(thm)],[f5544]) ).
thf(f5544,plain,
( $false
| ~ spl591_197
| ~ spl591_402 ),
inference(trivial_inequality_removal,[status(thm)],[f5543]) ).
thf(f5543,plain,
( ( $false = $true )
| ~ spl591_197
| ~ spl591_402 ),
inference(forward_demodulation,[status(thm)],[f2966,f3833]) ).
thf(f3833,plain,
( ( hoasinduction_lem3v2 = $false )
| ~ spl591_402 ),
inference(avatar_component_clause,[status(thm)],[f3831]) ).
thf(f3831,definition,
( spl591_402
<=> ( hoasinduction_lem3v2 = $false ) ),
introduced(definition,[new_symbols(naming,[spl591_402])],[avatar_definition]) ).
thf(f2966,plain,
( ( hoasinduction_lem3v2 = $true )
| ~ spl591_197 ),
inference(avatar_component_clause,[status(thm)],[f2965]) ).
thf(f2965,definition,
( spl591_197
<=> ( hoasinduction_lem3v2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_197])],[avatar_definition]) ).
thf(f4848,plain,
( spl591_191
| ~ spl591_545 ),
inference(avatar_split_clause,[status(thm)],[f558,f4845,f2940]) ).
thf(f2940,definition,
( spl591_191
<=> ( sP58 = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_191])],[avatar_definition]) ).
thf(f558,plain,
( ( ( sP57 @ sK59 )
!= $true )
| ( sP58 = $true ) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( sP58 = $true )
| ( ! [X3: term,X4: subst,X5: subst,X6: subst] :
( ( ( sK59 @ ( comp @ X4 @ X5 ) @ ( sub @ X3 @ X5 ) @ X6 )
= $true )
| ( ( sK59 @ X4 @ X3 @ ( comp @ X5 @ X6 ) )
!= $true ) )
& ( $true
!= ( sK60 @ ( lam @ sK61 ) ) )
& ( ( sP57 @ sK59 )
!= $true )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( ( sK59 @ ( comp @ X9 @ X7 ) @ ( sub @ X10 @ X7 ) @ X8 )
!= $true )
| ( ( sK59 @ X9 @ X10 @ ( comp @ X7 @ X8 ) )
= $true ) )
& ! [X11: term] :
( ( sK59 @ id @ X11 @ id )
= ( sK60 @ X11 ) )
& ! [X12: term] :
( ( $true
= ( sK60 @ ( sub @ sK61 @ ( push @ X12 @ id ) ) ) )
| ( ( sK60 @ X12 )
!= $true ) ) ) )
& ( ! [X13: subst > term > subst > $o,X14: term > $o,X15: term] :
( ( ( ( X13 @ ( comp @ ( sK63 @ X13 ) @ ( sK64 @ X13 ) ) @ ( sub @ ( sK62 @ X13 ) @ ( sK64 @ X13 ) ) @ ( sK65 @ X13 ) )
!= $true )
& ( ( X13 @ ( sK63 @ X13 ) @ ( sK62 @ X13 ) @ ( comp @ ( sK64 @ X13 ) @ ( sK65 @ X13 ) ) )
= $true ) )
| ( ( X14 @ ( lam @ X15 ) )
= $true )
| ( ( sP57 @ X13 )
= $true )
| ( ( ( X13 @ ( comp @ ( sK68 @ X13 ) @ ( sK66 @ X13 ) ) @ ( sub @ ( sK69 @ X13 ) @ ( sK66 @ X13 ) ) @ ( sK67 @ X13 ) )
= $true )
& ( $true
!= ( X13 @ ( sK68 @ X13 ) @ ( sK69 @ X13 ) @ ( comp @ ( sK66 @ X13 ) @ ( sK67 @ X13 ) ) ) ) )
| ( ( X13 @ id @ ( sK70 @ X14 @ X13 ) @ id )
!= ( X14 @ ( sK70 @ X14 @ X13 ) ) )
| ( ( ( X14 @ ( sub @ X15 @ ( push @ ( sK71 @ X15 @ X14 ) @ id ) ) )
!= $true )
& ( $true
= ( X14 @ ( sK71 @ X15 @ X14 ) ) ) ) )
| ( sP58 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63,sK64,sK65,sK66,sK67,sK68,sK69,sK70,sK71])],[f75,f80,f79,f78,f77,f76]) ).
thf(f76,plain,
( ? [X0: subst > term > subst > $o,X1: term > $o,X2: term] :
( ! [X3: term,X4: subst,X5: subst,X6: subst] :
( ( ( X0 @ ( comp @ X4 @ X5 ) @ ( sub @ X3 @ X5 ) @ X6 )
= $true )
| ( ( X0 @ X4 @ X3 @ ( comp @ X5 @ X6 ) )
!= $true ) )
& ( ( X1 @ ( lam @ X2 ) )
!= $true )
& ( ( sP57 @ X0 )
!= $true )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X0 @ ( comp @ X9 @ X7 ) @ ( sub @ X10 @ X7 ) @ X8 ) )
| ( ( X0 @ X9 @ X10 @ ( comp @ X7 @ X8 ) )
= $true ) )
& ! [X11: term] :
( ( X0 @ id @ X11 @ id )
= ( X1 @ X11 ) )
& ! [X12: term] :
( ( ( X1 @ ( sub @ X2 @ ( push @ X12 @ id ) ) )
= $true )
| ( ( X1 @ X12 )
!= $true ) ) )
=> ( ! [X6: subst,X5: subst,X4: subst,X3: term] :
( ( ( sK59 @ ( comp @ X4 @ X5 ) @ ( sub @ X3 @ X5 ) @ X6 )
= $true )
| ( ( sK59 @ X4 @ X3 @ ( comp @ X5 @ X6 ) )
!= $true ) )
& ( $true
!= ( sK60 @ ( lam @ sK61 ) ) )
& ( ( sP57 @ sK59 )
!= $true )
& ! [X10: term,X9: subst,X8: subst,X7: subst] :
( ( ( sK59 @ ( comp @ X9 @ X7 ) @ ( sub @ X10 @ X7 ) @ X8 )
!= $true )
| ( ( sK59 @ X9 @ X10 @ ( comp @ X7 @ X8 ) )
= $true ) )
& ! [X11: term] :
( ( sK59 @ id @ X11 @ id )
= ( sK60 @ X11 ) )
& ! [X12: term] :
( ( $true
= ( sK60 @ ( sub @ sK61 @ ( push @ X12 @ id ) ) ) )
| ( ( sK60 @ X12 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f77,plain,
! [X13: subst > term > subst > $o] :
( ? [X16: term,X17: subst,X18: subst,X19: subst] :
( ( ( X13 @ ( comp @ X17 @ X18 ) @ ( sub @ X16 @ X18 ) @ X19 )
!= $true )
& ( $true
= ( X13 @ X17 @ X16 @ ( comp @ X18 @ X19 ) ) ) )
=> ( ( ( X13 @ ( comp @ ( sK63 @ X13 ) @ ( sK64 @ X13 ) ) @ ( sub @ ( sK62 @ X13 ) @ ( sK64 @ X13 ) ) @ ( sK65 @ X13 ) )
!= $true )
& ( ( X13 @ ( sK63 @ X13 ) @ ( sK62 @ X13 ) @ ( comp @ ( sK64 @ X13 ) @ ( sK65 @ X13 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f78,plain,
! [X13: subst > term > subst > $o] :
( ? [X20: subst,X21: subst,X22: subst,X23: term] :
( ( ( X13 @ ( comp @ X22 @ X20 ) @ ( sub @ X23 @ X20 ) @ X21 )
= $true )
& ( $true
!= ( X13 @ X22 @ X23 @ ( comp @ X20 @ X21 ) ) ) )
=> ( ( ( X13 @ ( comp @ ( sK68 @ X13 ) @ ( sK66 @ X13 ) ) @ ( sub @ ( sK69 @ X13 ) @ ( sK66 @ X13 ) ) @ ( sK67 @ X13 ) )
= $true )
& ( $true
!= ( X13 @ ( sK68 @ X13 ) @ ( sK69 @ X13 ) @ ( comp @ ( sK66 @ X13 ) @ ( sK67 @ X13 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f79,plain,
! [X13: subst > term > subst > $o,X14: term > $o] :
( ? [X24: term] :
( ( X14 @ X24 )
!= ( X13 @ id @ X24 @ id ) )
=> ( ( X13 @ id @ ( sK70 @ X14 @ X13 ) @ id )
!= ( X14 @ ( sK70 @ X14 @ X13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f80,plain,
! [X14: term > $o,X15: term] :
( ? [X25: term] :
( ( ( X14 @ ( sub @ X15 @ ( push @ X25 @ id ) ) )
!= $true )
& ( ( X14 @ X25 )
= $true ) )
=> ( ( ( X14 @ ( sub @ X15 @ ( push @ ( sK71 @ X15 @ X14 ) @ id ) ) )
!= $true )
& ( $true
= ( X14 @ ( sK71 @ X15 @ X14 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f75,plain,
( ( ( sP58 = $true )
| ? [X0: subst > term > subst > $o,X1: term > $o,X2: term] :
( ! [X3: term,X4: subst,X5: subst,X6: subst] :
( ( ( X0 @ ( comp @ X4 @ X5 ) @ ( sub @ X3 @ X5 ) @ X6 )
= $true )
| ( ( X0 @ X4 @ X3 @ ( comp @ X5 @ X6 ) )
!= $true ) )
& ( ( X1 @ ( lam @ X2 ) )
!= $true )
& ( ( sP57 @ X0 )
!= $true )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X0 @ ( comp @ X9 @ X7 ) @ ( sub @ X10 @ X7 ) @ X8 ) )
| ( ( X0 @ X9 @ X10 @ ( comp @ X7 @ X8 ) )
= $true ) )
& ! [X11: term] :
( ( X0 @ id @ X11 @ id )
= ( X1 @ X11 ) )
& ! [X12: term] :
( ( ( X1 @ ( sub @ X2 @ ( push @ X12 @ id ) ) )
= $true )
| ( ( X1 @ X12 )
!= $true ) ) ) )
& ( ! [X13: subst > term > subst > $o,X14: term > $o,X15: term] :
( ? [X16: term,X17: subst,X18: subst,X19: subst] :
( ( ( X13 @ ( comp @ X17 @ X18 ) @ ( sub @ X16 @ X18 ) @ X19 )
!= $true )
& ( $true
= ( X13 @ X17 @ X16 @ ( comp @ X18 @ X19 ) ) ) )
| ( ( X14 @ ( lam @ X15 ) )
= $true )
| ( ( sP57 @ X13 )
= $true )
| ? [X20: subst,X21: subst,X22: subst,X23: term] :
( ( ( X13 @ ( comp @ X22 @ X20 ) @ ( sub @ X23 @ X20 ) @ X21 )
= $true )
& ( $true
!= ( X13 @ X22 @ X23 @ ( comp @ X20 @ X21 ) ) ) )
| ? [X24: term] :
( ( X14 @ X24 )
!= ( X13 @ id @ X24 @ id ) )
| ? [X25: term] :
( ( ( X14 @ ( sub @ X15 @ ( push @ X25 @ id ) ) )
!= $true )
& ( ( X14 @ X25 )
= $true ) ) )
| ( sP58 != $true ) ) ),
inference(rectify,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( sP58 = $true )
| ? [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ! [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
= $true )
| ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
!= $true ) )
& ( ( X357 @ ( lam @ X358 ) )
!= $true )
& ( ( sP57 @ X356 )
!= $true )
& ! [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
!= $true )
| ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
= $true ) )
& ! [X359: term] :
( ( X357 @ X359 )
= ( X356 @ id @ X359 @ id ) )
& ! [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
= $true )
| ( $true
!= ( X357 @ X364 ) ) ) ) )
& ( ! [X356: subst > term > subst > $o,X357: term > $o,X358: term] :
( ? [X360: term,X361: subst,X362: subst,X363: subst] :
( ( ( X356 @ ( comp @ X361 @ X362 ) @ ( sub @ X360 @ X362 ) @ X363 )
!= $true )
& ( ( X356 @ X361 @ X360 @ ( comp @ X362 @ X363 ) )
= $true ) )
| ( ( X357 @ ( lam @ X358 ) )
= $true )
| ( ( sP57 @ X356 )
= $true )
| ? [X365: subst,X366: subst,X367: subst,X368: term] :
( ( ( X356 @ ( comp @ X367 @ X365 ) @ ( sub @ X368 @ X365 ) @ X366 )
= $true )
& ( ( X356 @ X367 @ X368 @ ( comp @ X365 @ X366 ) )
!= $true ) )
| ? [X359: term] :
( ( X357 @ X359 )
!= ( X356 @ id @ X359 @ id ) )
| ? [X364: term] :
( ( ( X357 @ ( sub @ X358 @ ( push @ X364 @ id ) ) )
!= $true )
& ( $true
= ( X357 @ X364 ) ) ) )
| ( sP58 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f72]) ).
thf(f4613,plain,
( spl591_517
| spl591_191 ),
inference(avatar_split_clause,[status(thm)],[f1702,f2940,f4611]) ).
thf(f1702,plain,
! [X11: term] :
( ( sP58 = $true )
| ( ( sK60 @ X11 )
= $true )
| ( $false
= ( sK59 @ ( d2subst @ d_id ) @ X11 @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1263]) ).
thf(f1263,plain,
! [X11: term] :
( ( ( sK60 @ X11 )
= ( sK59 @ ( d2subst @ d_id ) @ X11 @ ( d2subst @ d_id ) ) )
| ( sP58 = $true ) ),
inference(definition_unfolding,[status(thm)],[f556,f1046,f1046]) ).
thf(f556,plain,
! [X11: term] :
( ( sP58 = $true )
| ( ( sK59 @ id @ X11 @ id )
= ( sK60 @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
thf(f4559,plain,
( ~ spl591_191
| spl591_197 ),
inference(avatar_split_clause,[status(thm)],[f1251,f2965,f2940]) ).
thf(f1251,plain,
( ( sP58 != $true )
| ( hoasinduction_lem3v2 = $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3858,plain,
( spl591_406
| spl591_408
| spl591_402 ),
inference(avatar_split_clause,[status(thm)],[f1785,f3831,f3856,f3848]) ).
thf(f1785,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2 = $false )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1783]) ).
thf(f1783,plain,
! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) )
!= ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) ) )
| ( hoasinduction_lem3v2 = $false )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1782]) ).
thf(f1782,plain,
! [X1: subst > term > term] :
( ( $false
= ( ( X1 @ ( comp @ ( sK596 @ X1 ) @ ( sK597 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK597 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK597 @ X1 ) ) ) )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1781]) ).
thf(f1781,plain,
! [X1: subst > term > term] :
( ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( $false
= ( ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK596 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) )
@ ( sK597 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1780]) ).
thf(f1780,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK596 @ X1 ) @ Y0 ) @ ( sub @ ( sK595 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK596 @ X1 ) @ ( sK595 @ X1 ) ) @ Y0 ) ) ) )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1779]) ).
thf(f1779,plain,
! [X1: subst > term > term] :
( ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ ( sK595 @ X1 ) @ Y1 ) )
= ( sub @ ( X1 @ Y0 @ ( sK595 @ X1 ) ) @ Y1 ) ) )
@ ( sK596 @ X1 ) ) )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1778]) ).
thf(f1778,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ ( sK595 @ X1 ) @ Y1 ) )
= ( sub @ ( X1 @ Y0 @ ( sK595 @ X1 ) ) @ Y1 ) ) ) ) )
| ( hoasinduction_lem3v2 = $false )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1777]) ).
thf(f1777,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ ( sK595 @ X1 ) ) )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1776]) ).
thf(f1776,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
| ( $false
= ( ( sK593 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction_lem3v2 = $false )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1775]) ).
thf(f1775,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
| ( ( ^ [Y0: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) )
@ ( sK594 @ X1 ) )
= $false )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1774]) ).
thf(f1774,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2 = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
| ( ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1773]) ).
thf(f1773,plain,
! [X1: subst > term > term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
= $true )
| ( hoasinduction_lem3v2 = $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1772]) ).
thf(f1772,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2 = $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1771]) ).
thf(f1771,plain,
! [X1: subst > term > term] :
( ( ( ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
@ X1 )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(pi_clausification,[status(thm)],[f1770]) ).
thf(f1770,plain,
( ( hoasinduction_lem3v2 = $false )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1758]) ).
thf(f1758,plain,
( ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1747]) ).
thf(f1747,plain,
( ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK593 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y3 )
=> ( sK593 @ Y2 @ Y1 @ ( comp @ Y0 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1746]) ).
thf(f1746,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK593 @ Y0 @ Y1 @ ( comp @ Y3 @ Y2 ) )
=> ( sK593 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK593 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y3 )
=> ( sK593 @ Y2 @ Y1 @ ( comp @ Y0 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK593 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK593 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3v2 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1745]) ).
thf(f1745,plain,
( ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
= ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK592 @ Y2 )
=> ( sK592 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y1 ) ) ) ) ) ) ) )
@ sK593 ) ) ),
inference(sigma_clausification,[status(thm)],[f1744]) ).
thf(f1744,plain,
( ( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
= ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK592 @ Y2 )
=> ( sK592 @ ( sub @ Y1 @ ( push @ Y2 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y1 ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1743]) ).
thf(f1743,plain,
( ( ( ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
= ( Y1 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) )
@ sK592 )
= $false )
| ( hoasinduction_lem3v2 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1742]) ).
thf(f1742,plain,
( ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
= ( Y1 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1740]) ).
thf(f1740,plain,
( hoasinduction_lem3v2
!= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
= ( Y1 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1262]) ).
thf(f1262,plain,
( hoasinduction_lem3v2
!= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( d2subst @ d_id ) @ Y3 @ ( d2subst @ d_id ) )
=> ( Y1 @ ( d2subst @ d_id ) @ ( Y2 @ ( d2subst @ d_id ) @ Y3 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y1 @ ( d2subst @ d_id )
@ ( ^ [Y3: subst,Y4: subst > term > term] : ( d2term @ d_one )
@ ( d2subst @ d_id )
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ ( d2subst @ d_id ) ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( d2subst @ d_id ) @ Y4 @ ( d2subst @ d_id ) ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f546,f1046,f1046,f1046,f1046,f1046,f1046,f1115,f1046,f1046,f1261,f1046]) ).
thf(f1261,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1108,f1046,f1046]) ).
thf(f1108,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1115,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f546,plain,
( hoasinduction_lem3v2
!= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( hoasinduction_lem3v2
!= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( hoasinduction_lem3v2
!= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y3 @ ( comp @ Y5 @ Y4 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y5 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y2 @ Y5 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y2 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) )
= ( sub @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: subst > term > subst > $o,X1: term > $o] :
( ( ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( X0 @ X5 @ X4 @ ( comp @ X2 @ X3 ) )
=> ( X0 @ ( comp @ X5 @ X2 ) @ ( sub @ X4 @ X2 ) @ X3 ) )
=> ( ! [X6: subst,X7: subst,X8: term,X9: subst] :
( ( X0 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) @ X6 )
=> ( X0 @ X7 @ X8 @ ( comp @ X9 @ X6 ) ) )
=> ( ! [X10: subst > term > term] :
( ! [X11: subst,X12: subst,X13: term] :
( ( X10 @ ( comp @ X12 @ X11 ) @ ( sub @ X13 @ X11 ) )
= ( sub @ ( X10 @ X12 @ X13 ) @ X11 ) )
=> ( ! [X14: term] :
( ( X0 @ id @ X14 @ id )
=> ( X0 @ id @ ( X10 @ id @ X14 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X15: subst,X16: term] : ( X10 @ X15 @ X16 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
=> ! [X17: term] :
( ! [X18: term] :
( ( X1 @ X18 )
=> ( X1 @ ( sub @ X17 @ ( push @ X18 @ id ) ) ) )
=> ( X1 @ ( lam @ X17 ) ) ) ) ) ) )
= hoasinduction_lem3v2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X10: subst > term > subst > $o,X11: term > $o] :
( ( ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
=> ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
=> ( ! [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 @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
=> ! [X13: term] :
( ! [X15: term] :
( ( X11 @ X15 )
=> ( X11 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
=> ( X11 @ ( lam @ X13 ) ) ) ) ) ) )
= hoasinduction_lem3v2 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X10: subst > term > subst > $o,X11: term > $o] :
( ( ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
=> ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
=> ( ! [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 @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X10 @ X11 )
=> ! [X13: term] :
( ! [X15: term] :
( ( X11 @ X15 )
=> ( X11 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
=> ( X11 @ ( lam @ X13 ) ) ) ) ) ) )
= hoasinduction_lem3v2 ),
file('/export/starexec/sandbox/tmp/tmp.SwuThMpGUN/DTF2THF_19838.p',hoasinduction_lem3v2) ).
thf(f3842,plain,
( spl591_404
| spl591_402 ),
inference(avatar_split_clause,[status(thm)],[f1791,f3831,f3840]) ).
thf(f1791,plain,
! [X1: term] :
( ( $false
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( ( sK592 @ X1 )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1790]) ).
thf(f1790,plain,
! [X1: term] :
( ( ( sK592 @ X1 )
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f1789]) ).
thf(f1789,plain,
! [X1: term] :
( ( hoasinduction_lem3v2 = $false )
| ( ( ( sK592 @ X1 )
= ( sK593 @ ( d2subst @ d_id ) @ X1 @ ( d2subst @ d_id ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1788]) ).
thf(f1788,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) )
@ X1 )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(pi_clausification,[status(thm)],[f1787]) ).
thf(f1787,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
= $true )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1769]) ).
thf(f1769,plain,
( ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
= ( sK593 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) ) ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1758]) ).
thf(f3834,plain,
( spl591_401
| spl591_402 ),
inference(avatar_split_clause,[status(thm)],[f1795,f3831,f3827]) ).
thf(f1795,plain,
( ( $false
= ( sK592 @ ( lam @ sK598 ) ) )
| ( hoasinduction_lem3v2 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1794]) ).
thf(f1794,plain,
( ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ Y0 )
=> ( sK592 @ ( sub @ sK598 @ ( push @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ sK598 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1793]) ).
thf(f1793,plain,
( ( hoasinduction_lem3v2 = $false )
| ( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) )
@ sK598 ) ) ),
inference(sigma_clausification,[status(thm)],[f1786]) ).
thf(f1786,plain,
( ( hoasinduction_lem3v2 = $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ Y1 )
=> ( sK592 @ ( sub @ Y0 @ ( push @ Y1 @ ( d2subst @ d_id ) ) ) ) ) )
=> ( sK592 @ ( lam @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1769]) ).
thf(f3220,plain,
( ~ spl591_255
| spl591_191 ),
inference(avatar_split_clause,[status(thm)],[f559,f2940,f3217]) ).
thf(f559,plain,
( ( $true
!= ( sK60 @ ( lam @ sK61 ) ) )
| ( sP58 = $true ) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:04:31 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.19/0.46 % Domain : Software Verification
% 0.19/0.46 % Problem : Benchmark: ALG444^1, Active target: hoasinduction_lem3v2
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Kon26]
% 0.19/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : ? v9.3.0
% 0.19/0.46 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.19/0.46 % Number of atoms : 256 ( 129 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 248 ( 128 avg)
% 0.19/0.46 % Number of connectives : 2639 ( 333 ~; 306 |; 129 &;1766 @)
% 0.19/0.46 % ( 56 <=>; 49 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 151 ( 76 avg)
% 0.19/0.46 % Number of types : 5 ( 4 usr)
% 0.19/0.46 % Number of type conns : 228 ( 228 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.19/0.46 % Number of variables : 569 ( 10 ^; 557 !; 2 ?; 569 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(term_type,type,
% 0.19/0.46 term: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(subst_type,type,
% 0.19/0.46 subst: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(one_decl,type,
% 0.19/0.46 one: term ).
% 0.19/0.46
% 0.19/0.46 thf(ap_decl,type,
% 0.19/0.46 ap: term > term > term ).
% 0.19/0.46
% 0.19/0.46 thf(lam_decl,type,
% 0.19/0.46 lam: term > term ).
% 0.19/0.46
% 0.19/0.46 thf(sub_decl,type,
% 0.19/0.46 sub: term > subst > term ).
% 0.19/0.46
% 0.19/0.46 thf(id_decl,type,
% 0.19/0.46 id: subst ).
% 0.19/0.46
% 0.19/0.46 thf(sh_decl,type,
% 0.19/0.46 sh: subst ).
% 0.19/0.46
% 0.19/0.46 thf(push_decl,type,
% 0.19/0.46 push: term > subst > subst ).
% 0.19/0.46
% 0.19/0.46 thf(comp_decl,type,
% 0.19/0.46 comp: subst > subst > subst ).
% 0.19/0.46
% 0.19/0.46 thf(var_decl,type,
% 0.19/0.46 var: term > $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1v2_decl,type,
% 0.19/0.46 pushprop_lem1v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1_gthm_decl,type,
% 0.19/0.46 pushprop_lem1_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axmap_decl,type,
% 0.19/0.46 axmap: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem0_gthm_decl,type,
% 0.19/0.46 pushprop_lem0_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(shinj_decl,type,
% 0.19/0.46 shinj: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem1v2_decl,type,
% 0.19/0.46 hoasinduction_lem1v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem1v2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasap_decl,type,
% 0.19/0.46 hoasap: subst > term > subst > term > term ).
% 0.19/0.46
% 0.19/0.46 thf(induction2lem_decl,type,
% 0.19/0.46 induction2lem: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2_f_decl,type,
% 0.19/0.46 hoasinduction_lem3v2_f: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axvarshift_decl,type,
% 0.19/0.46 axvarshift: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj2_decl,type,
% 0.19/0.46 hoasapinj2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapnotvar_gthm_decl,type,
% 0.19/0.46 hoasapnotvar_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj1_decl,type,
% 0.19/0.46 hoasapinj1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(ulamvar1_decl,type,
% 0.19/0.46 ulamvar1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction2lem_lthm_decl,type,
% 0.19/0.46 induction2lem_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem3v2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(apnotvar_decl,type,
% 0.19/0.46 apnotvar: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lthm_orig_decl,type,
% 0.19/0.46 pushprop_lthm_orig: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3v2_f_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lthm_decl,type,
% 0.19/0.46 hoasinduction_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.19/0.46 hoasinduction_no_psi_cond_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslaminj_decl,type,
% 0.19/0.46 hoaslaminj: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3aaa_decl,type,
% 0.19/0.46 hoasinduction_lem3aaa: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction2lem_gthm_decl,type,
% 0.19/0.46 induction2lem_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3aa_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3_decl,type,
% 0.19/0.46 hoasinduction_lem3: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem2_decl,type,
% 0.19/0.46 hoasinduction_lem2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(termmset_lthm_decl,type,
% 0.19/0.46 termmset_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem1_decl,type,
% 0.19/0.46 hoasinduction_lem1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotap_lthm_decl,type,
% 0.19/0.46 hoaslamnotap_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1v2_lthm_decl,type,
% 0.19/0.46 pushprop_lem1v2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapnotvar_decl,type,
% 0.19/0.46 hoasapnotvar: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem0_decl,type,
% 0.19/0.46 hoasinduction_lem0: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_decl,type,
% 0.19/0.46 hoasinduction: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_gthm_decl,type,
% 0.19/0.46 hoasinduction_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axapp_decl,type,
% 0.19/0.46 axapp: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotvar_lthm_decl,type,
% 0.19/0.46 hoaslamnotvar_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem3v2_lthm_decl,type,
% 0.19/0.46 pushprop_lem3v2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3b_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(ulamvarind_decl,type,
% 0.19/0.46 ulamvarind: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction_decl,type,
% 0.19/0.46 induction: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3a_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(termmset_gthm_decl,type,
% 0.19/0.46 termmset_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3aa_decl,type,
% 0.19/0.46 hoasinduction_lem3aa: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1v2_gthm_decl,type,
% 0.19/0.46 pushprop_lem1v2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotap_gthm_decl,type,
% 0.19/0.46 hoaslamnotap_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotvar_gthm_decl,type,
% 0.19/0.46 hoaslamnotvar_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem3b_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem2v2_decl,type,
% 0.19/0.46 pushprop_lem2v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem3a_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axclos_decl,type,
% 0.19/0.46 axclos: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axassoc_decl,type,
% 0.19/0.46 axassoc: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem2v2_decl,type,
% 0.19/0.46 hoasinduction_lem2v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lthm_decl,type,
% 0.19/0.46 pushprop_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(apinj2_decl,type,
% 0.19/0.46 apinj2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(apinj1_decl,type,
% 0.19/0.46 apinj1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj2_lthm_decl,type,
% 0.19/0.46 hoasapinj2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2a_decl,type,
% 0.19/0.46 hoasinduction_lem3v2a: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj1_lthm_decl,type,
% 0.19/0.46 hoasapinj1_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslaminj_lthm_decl,type,
% 0.19/0.46 hoaslaminj_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axvarcons_decl,type,
% 0.19/0.46 axvarcons: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslam_decl,type,
% 0.19/0.46 hoaslam: subst > ( subst > term > term ) > term ).
% 0.19/0.46
% 0.19/0.46 thf(axscons_decl,type,
% 0.19/0.46 axscons: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem2v2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axidr_decl,type,
% 0.19/0.46 axidr: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1_decl,type,
% 0.19/0.46 pushprop_lem1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(laminj_decl,type,
% 0.19/0.46 laminj: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem0_decl,type,
% 0.19/0.46 pushprop_lem0: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_gthm_decl,type,
% 0.19/0.46 pushprop_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axabs_decl,type,
% 0.19/0.46 axabs: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3v2a_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem2_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj2_gthm_decl,type,
% 0.19/0.46 hoasapinj2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.19/0.46 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem1_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem1_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(lamnotap_decl,type,
% 0.19/0.46 lamnotap: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapinj1_gthm_decl,type,
% 0.19/0.46 hoasapinj1_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotvar_decl,type,
% 0.19/0.46 hoaslamnotvar: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axidl_decl,type,
% 0.19/0.46 axidl: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslaminj_gthm_decl,type,
% 0.19/0.46 hoaslaminj_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction2_lthm_decl,type,
% 0.19/0.46 induction2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem0_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem0_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(substmonoid_lthm_decl,type,
% 0.19/0.46 substmonoid_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_decl,type,
% 0.19/0.46 pushprop: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem3_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem2_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3b_decl,type,
% 0.19/0.46 hoasinduction_lem3b: $o ).
% 0.19/0.46
% 0.19/0.46 thf(substmonoid_decl,type,
% 0.19/0.46 substmonoid: $o ).
% 0.19/0.46
% 0.19/0.46 thf(lamnotvar_decl,type,
% 0.19/0.46 lamnotvar: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3a_decl,type,
% 0.19/0.46 hoasinduction_lem3a: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem1_gthm_decl,type,
% 0.19/0.46 hoasinduction_lem1_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_no_psi_cond_decl,type,
% 0.19/0.46 hoasinduction_no_psi_cond: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction2_gthm_decl,type,
% 0.19/0.46 induction2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem2v2_lthm_decl,type,
% 0.19/0.46 pushprop_lem2v2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasvar_decl,type,
% 0.19/0.46 hoasvar: subst > term > subst > $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoaslamnotap_decl,type,
% 0.19/0.46 hoaslamnotap: $o ).
% 0.19/0.46
% 0.19/0.46 thf(substmonoid_gthm_decl,type,
% 0.19/0.46 substmonoid_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(ulamvarsh_decl,type,
% 0.19/0.46 ulamvarsh: $o ).
% 0.19/0.46
% 0.19/0.46 thf(induction2_decl,type,
% 0.19/0.46 induction2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem3v2_decl,type,
% 0.19/0.46 pushprop_lem3v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem2v2_gthm_decl,type,
% 0.19/0.46 pushprop_lem2v2_gthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem1_lthm_decl,type,
% 0.19/0.46 pushprop_lem1_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2_decl,type,
% 0.19/0.46 hoasinduction_lem3v2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(axshiftcons_decl,type,
% 0.19/0.46 axshiftcons: $o ).
% 0.19/0.46
% 0.19/0.46 thf(termmset_decl,type,
% 0.19/0.46 termmset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_lem0_lthm_decl,type,
% 0.19/0.46 pushprop_lem0_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasapnotvar_lthm_decl,type,
% 0.19/0.46 hoasapnotvar_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.19/0.46 hoasinduction_lem3v2_lthm: $o ).
% 0.19/0.46
% 0.19/0.46 thf(pushprop_p_and_p_prime_decl,type,
% 0.19/0.46 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(axvarid_decl,type,
% 0.19/0.46 axvarid: $o ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lthm_3_decl,type,
% 0.19/0.46 hoasinduction_lthm_3: $o ).
% 0.19/0.46
% 0.19/0.46 %----Types of the domains
% 0.19/0.46 thf(d_term_type,type,
% 0.19/0.46 d_term: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(d_subst_type,type,
% 0.19/0.46 d_subst: $tType ).
% 0.19/0.46
% 0.19/0.46 %----Types of the promotion functions
% 0.19/0.46 thf(d2term_decl,type,
% 0.19/0.46 d2term: d_term > term ).
% 0.19/0.46
% 0.19/0.46 thf(d2subst_decl,type,
% 0.19/0.46 d2subst: d_subst > subst ).
% 0.19/0.46
% 0.19/0.46 %----Types of the domain elements
% 0.19/0.46 thf(d_one_decl,type,
% 0.19/0.46 d_one: d_term ).
% 0.19/0.46
% 0.19/0.46 thf(d_id_decl,type,
% 0.19/0.46 d_id: d_subst ).
% 0.19/0.46
% 0.19/0.46 thf(alg444_1,axiom,
% 0.19/0.46 ( ! [T: term] :
% 0.19/0.46 ? [DT: d_term] :
% 0.19/0.46 ( T
% 0.19/0.46 = ( d2term @ DT ) )
% 0.19/0.46 & ! [DT: d_term] : ( DT = d_one )
% 0.19/0.46 & ! [DT1: d_term,DT2: d_term] :
% 0.19/0.46 ( ( ( d2term @ DT1 )
% 0.19/0.46 = ( d2term @ DT2 ) )
% 0.19/0.46 => ( DT1 = DT2 ) )
% 0.19/0.46 & ! [S: subst] :
% 0.19/0.46 ? [DS: d_subst] :
% 0.19/0.46 ( S
% 0.19/0.46 = ( d2subst @ DS ) )
% 0.19/0.46 & ! [DS: d_subst] : ( DS = d_id )
% 0.19/0.46 & ! [DS1: d_subst,DS2: d_subst] :
% 0.19/0.46 ( ( ( d2subst @ DS1 )
% 0.19/0.46 = ( d2subst @ DS2 ) )
% 0.19/0.46 => ( DS1 = DS2 ) )
% 0.19/0.46 & ( one
% 0.19/0.46 = ( d2term @ d_one ) )
% 0.19/0.46 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.19/0.46 = ( d2term @ d_one ) )
% 0.19/0.46 & ( ( lam @ ( d2term @ d_one ) )
% 0.19/0.46 = ( d2term @ d_one ) )
% 0.19/0.46 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.46 = ( d2term @ d_one ) )
% 0.19/0.46 & ( id
% 0.19/0.46 = ( d2subst @ d_id ) )
% 0.19/0.46 & ( sh
% 0.19/0.46 = ( d2subst @ d_id ) )
% 0.19/0.46 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.46 = ( d2subst @ d_id ) )
% 0.19/0.46 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.19/0.46 = ( d2subst @ d_id ) )
% 0.19/0.46 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.19/0.46 = ( d2term @ d_one ) )
% 0.19/0.46 & ( hoaslam
% 0.19/0.46 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.19/0.46 & ( hoasinduction_p_and_p_prime
% 0.19/0.46 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.19/0.46 ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) ) ) )
% 0.19/0.46 & ( pushprop_p_and_p_prime
% 0.19/0.46 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.19/0.46 ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.19/0.46 & ~ ( var @ ( d2term @ d_one ) )
% 0.19/0.46 & ( pushprop_lem1v2
% 0.19/0.46 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.19/0.46 | ( Q @ one ) ) )
% 0.19/0.46 & pushprop_lem1_gthm
% 0.19/0.46 & axmap
% 0.19/0.46 & pushprop_lem0_gthm
% 0.19/0.46 & ( shinj
% 0.19/0.46 <=> ! [A: term,B: term] :
% 0.19/0.46 ( ( ( sub @ A @ sh )
% 0.19/0.46 != ( sub @ B @ sh ) )
% 0.19/0.46 | ( A = B ) ) )
% 0.19/0.46 & hoasinduction_lem1v2
% 0.19/0.46 & hoasinduction_lem1v2_gthm
% 0.19/0.46 & ( induction2lem
% 0.19/0.46 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.46 ( ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( var @ B )
% 0.19/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.19/0.46 & ( hoasinduction_lem3v2_f
% 0.19/0.46 <=> ! [B: term] :
% 0.19/0.46 ~ ! [F: subst > term > term] :
% 0.19/0.46 ~ ! [A: term,M: subst] :
% 0.19/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.46 = ( F @ M @ A ) ) )
% 0.19/0.46 & axvarshift
% 0.19/0.46 & ( hoasapinj2
% 0.19/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.46 | ( C = D ) ) )
% 0.19/0.46 & hoasapnotvar_gthm
% 0.19/0.46 & ( hoasapinj1
% 0.19/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.46 | ( A = B ) ) )
% 0.19/0.46 & ~ ulamvar1
% 0.19/0.46 & ( induction2lem_lthm
% 0.19/0.46 <=> ( ! [A: term,M: subst] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.46 => ( ! [A: term,M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.46 => ( ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ M @ id ) )
% 0.19/0.46 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2140 ) )
% 0.19/0.46 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.46 ( ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( var @ B )
% 0.19/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.19/0.46 & hoasinduction_lem3v2_gthm
% 0.19/0.46 & apnotvar
% 0.19/0.46 & pushprop_lthm_orig
% 0.19/0.46 & ( hoasinduction_lem3v2_f_lthm
% 0.19/0.46 <=> ! [B: term] :
% 0.19/0.46 ~ ! [F: subst > term > term] :
% 0.19/0.46 ~ ! [A: term,M: subst] :
% 0.19/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.46 = ( F @ M @ A ) ) )
% 0.19/0.46 & ( hoasinduction_lthm
% 0.19/0.46 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2367 ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.19/0.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.46 | ( P @ id @ A @ id ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.19/0.46 & ( hoasinduction_no_psi_cond_lthm
% 0.19/0.46 <=> ( ! [P: subst > term > subst > $o] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2367 ) )
% 0.19/0.46 => ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.19/0.46 ( ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.19/0.46 & ( hoaslaminj
% 0.19/0.46 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.19/0.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.19/0.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.19/0.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.19/0.46 & ( hoasinduction_lem3aaa
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.19/0.46 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.19/0.46 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.19/0.46 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.19/0.46 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.19/0.46 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.19/0.46 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.46 & induction2lem_gthm
% 0.19/0.46 & ( hoasinduction_lem3aa_lthm
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.46 & ( hoasinduction_lem3
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.19/0.46 & ( hoasinduction_lem2
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.19/0.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.19/0.46 & ( termmset_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) ) ) )
% 0.19/0.46 & hoasinduction_lem1
% 0.19/0.46 & hoaslamnotap_lthm
% 0.19/0.46 & ( pushprop_lem1v2_lthm
% 0.19/0.46 <=> ( ! [A: term,M: subst] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.46 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.19/0.46 | ( Q @ one ) ) ) )
% 0.19/0.46 & hoasapnotvar
% 0.19/0.46 & ( hoasinduction_lem0
% 0.19/0.46 <=> ! [P: subst > term > subst > $o] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) ) )
% 0.19/0.46 & ( hoasinduction
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.46 | ( P @ id @ A @ id ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.19/0.46 & hoasinduction_gthm
% 0.19/0.46 & axapp
% 0.19/0.46 & hoaslamnotvar_lthm
% 0.19/0.46 & pushprop_lem3v2_lthm
% 0.19/0.46 & ( hoasinduction_lem3b_lthm
% 0.19/0.46 <=> ! [B: term] :
% 0.19/0.46 ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ( F @ sh @ one )
% 0.19/0.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.19/0.46 & ulamvarind
% 0.19/0.46 & ( induction
% 0.19/0.46 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2140 ) ) )
% 0.19/0.46 & ( hoasinduction_lem3a_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.19/0.46 & termmset_gthm
% 0.19/0.46 & ( hoasinduction_lem3aa
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.46 & pushprop_lem1v2_gthm
% 0.19/0.46 & hoaslamnotap_gthm
% 0.19/0.46 & hoaslamnotvar_gthm
% 0.19/0.46 & hoasinduction_lem3b_gthm
% 0.19/0.46 & pushprop_lem2v2
% 0.19/0.46 & hoasinduction_lem3a_gthm
% 0.19/0.46 & axclos
% 0.19/0.46 & axassoc
% 0.19/0.46 & ( hoasinduction_lem2v2
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ( Q @ Bound_variable_2820 )
% 0.19/0.46 | ~ ( Q @ Bound_variable_2822 )
% 0.19/0.46 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.19/0.46 & pushprop_lthm
% 0.19/0.46 & ( apinj2
% 0.19/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ A @ C )
% 0.19/0.46 != ( ap @ B @ D ) )
% 0.19/0.46 | ( C = D ) ) )
% 0.19/0.46 & ( apinj1
% 0.19/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ A @ C )
% 0.19/0.46 != ( ap @ B @ D ) )
% 0.19/0.46 | ( A = B ) ) )
% 0.19/0.46 & ( hoasapinj2_lthm
% 0.19/0.46 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ A @ C )
% 0.19/0.46 != ( ap @ B @ D ) )
% 0.19/0.46 | ( C = D ) )
% 0.19/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.46 | ( C = D ) ) ) )
% 0.19/0.46 & ( hoasinduction_lem3v2a
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.19/0.46 & ( hoasapinj1_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ A @ C )
% 0.19/0.46 != ( ap @ B @ D ) )
% 0.19/0.46 | ( A = B ) )
% 0.19/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.19/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.46 | ( A = B ) ) ) ) )
% 0.19/0.46 & ( hoaslaminj_lthm
% 0.19/0.46 <=> ( ! [A: term,M: subst] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.46 => ( ! [A: term,M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.46 => ( ! [A: term,B: term] :
% 0.19/0.46 ( ( ( lam @ A )
% 0.19/0.46 != ( lam @ B ) )
% 0.19/0.46 | ( A = B ) )
% 0.19/0.46 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.19/0.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.19/0.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.19/0.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.19/0.46 & ( axvarcons
% 0.19/0.46 <=> ! [A: term,M: subst] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.19/0.46 & ( axscons
% 0.19/0.46 <=> ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.19/0.46 & hoasinduction_lem2v2_gthm
% 0.19/0.46 & ( axidr
% 0.19/0.46 <=> ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ M @ id ) ) )
% 0.19/0.46 & ( pushprop_lem1
% 0.19/0.46 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.19/0.46 & ( laminj
% 0.19/0.46 <=> ! [A: term,B: term] :
% 0.19/0.46 ( ( ( lam @ A )
% 0.19/0.46 != ( lam @ B ) )
% 0.19/0.46 | ( A = B ) ) )
% 0.19/0.46 & ( hoasinduction_lem3_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.19/0.46 & ( pushprop_lem0
% 0.19/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.19/0.46 & pushprop_gthm
% 0.19/0.46 & axabs
% 0.19/0.46 & ( hoasinduction_lem3v2a_lthm
% 0.19/0.46 <=> ( ! [B: term] :
% 0.19/0.46 ~ ! [F: subst > term > term] :
% 0.19/0.46 ~ ! [A: term,M: subst] :
% 0.19/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.46 = ( F @ M @ A ) )
% 0.19/0.46 => ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.19/0.46 & hoasinduction_lem2_lthm
% 0.19/0.46 & hoasapinj2_gthm
% 0.19/0.46 & hoasinduction_lem1_lthm
% 0.19/0.46 & ~ lamnotap
% 0.19/0.46 & hoasapinj1_gthm
% 0.19/0.46 & hoaslamnotvar
% 0.19/0.46 & ( axidl
% 0.19/0.46 <=> ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ id @ M ) ) )
% 0.19/0.46 & hoaslaminj_gthm
% 0.19/0.46 & ( induction2_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.46 ( ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( var @ B )
% 0.19/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.19/0.46 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.19/0.46 & ( hoasinduction_lem0_lthm
% 0.19/0.46 <=> ! [P: subst > term > subst > $o] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) ) )
% 0.19/0.46 & ( substmonoid_lthm
% 0.19/0.46 <=> ( ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ id @ M ) )
% 0.19/0.46 => ( ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ M @ id ) )
% 0.19/0.46 => ( ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ id @ M ) )
% 0.19/0.46 & ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ M @ id ) ) ) ) ) )
% 0.19/0.46 & pushprop
% 0.19/0.46 & hoasinduction_lem3_gthm
% 0.19/0.46 & hoasinduction_lem2_gthm
% 0.19/0.46 & ( hoasinduction_lem3b
% 0.19/0.46 <=> ! [B: term] :
% 0.19/0.46 ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ( F @ sh @ one )
% 0.19/0.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.19/0.46 & ( substmonoid
% 0.19/0.46 <=> ( ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ id @ M ) )
% 0.19/0.46 & ! [M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ M @ id ) ) ) )
% 0.19/0.46 & lamnotvar
% 0.19/0.46 & ( hoasinduction_lem3a
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.19/0.46 & hoasinduction_lem1_gthm
% 0.19/0.46 & ( hoasinduction_no_psi_cond
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.19/0.46 ( ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.19/0.46 & induction2_gthm
% 0.19/0.46 & pushprop_lem2v2_lthm
% 0.19/0.46 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.46 & ( hoaslamnotap
% 0.19/0.46 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.46 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.19/0.46 & substmonoid_gthm
% 0.19/0.46 & ulamvarsh
% 0.19/0.46 & ( induction2
% 0.19/0.46 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2367 ) ) )
% 0.19/0.46 & pushprop_lem3v2
% 0.19/0.46 & pushprop_lem2v2_gthm
% 0.19/0.46 & ( pushprop_lem1_lthm
% 0.19/0.46 <=> ( ! [A: term,M: subst] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.46 => ( ! [A: term,M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.46 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.19/0.46 & ( hoasinduction_lem3v2
% 0.19/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.19/0.46 & ( axshiftcons
% 0.19/0.46 <=> ! [A: term,M: subst] :
% 0.19/0.46 ( M
% 0.19/0.46 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.19/0.46 & ( termmset
% 0.19/0.46 <=> ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) ) )
% 0.19/0.46 & ( pushprop_lem0_lthm
% 0.19/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.19/0.46 & hoasapnotvar_lthm
% 0.19/0.46 & ( hoasinduction_lem3v2_lthm
% 0.19/0.46 <=> ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.19/0.46 & ( axvarid
% 0.19/0.46 <=> ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) ) )
% 0.19/0.46 & ( hoasinduction_lthm_3
% 0.19/0.46 <=> ( ! [P: subst > term > subst > $o] :
% 0.19/0.46 ~ ! [Q: term > $o] :
% 0.19/0.46 ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.46 ( ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ A )
% 0.19/0.46 | ( P @ A ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ A )
% 0.19/0.46 | ~ ( P @ B )
% 0.19/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ! [B: term] :
% 0.19/0.46 ( ~ ( P @ B )
% 0.19/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( P @ ( lam @ A ) ) )
% 0.19/0.46 | ( P @ Bound_variable_2367 ) )
% 0.19/0.46 => ( ! [A: term] :
% 0.19/0.46 ( A
% 0.19/0.46 = ( sub @ A @ id ) )
% 0.19/0.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.46 ( ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ~ ! [X: term] :
% 0.19/0.46 ( ( Q @ X )
% 0.19/0.46 = ( P @ id @ X @ id ) )
% 0.19/0.46 | ~ ! [B: term] :
% 0.19/0.46 ( ~ ( Q @ B )
% 0.19/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.19/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.46 | ( P @ id @ A @ id ) )
% 0.19/0.46 | ~ ! [A: term,B: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ~ ( P @ id @ B @ id )
% 0.19/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.46 | ~ ! [F: subst > term > term] :
% 0.19/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 | ~ ! [A: term] :
% 0.19/0.46 ( ~ ( P @ id @ A @ id )
% 0.19/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(hoasinduction_lem3v2,conjecture,
% 0.19/0.46 ( hoasinduction_lem3v2
% 0.19/0.46 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.19/0.46 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.46 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.46 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.46 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.46 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.46 => ( ! [F: subst > term > term] :
% 0.19/0.46 ( ! [M: subst,A: term,N: subst] :
% 0.19/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.46 => ( ! [A: term] :
% 0.19/0.46 ( ( P @ id @ A @ id )
% 0.19/0.46 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.46 => ( P @ id
% 0.19/0.46 @ ( hoaslam @ id
% 0.19/0.46 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.19/0.46 @ id ) ) )
% 0.19/0.46 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.19/0.46 => ! [A: term] :
% 0.19/0.46 ( ! [B: term] :
% 0.19/0.46 ( ( Q @ B )
% 0.19/0.46 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.46 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 2.27/1.49 ---- Embedded in THF ---
% 2.27/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.27/1.49 %%% Generated on Tue May 05 09:04:32 EDT 2026
% 2.27/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.27/1.49 %%% Logic specification used:
% 2.27/1.49 %%% thf(spec, logic, $$dhol).
% 2.27/1.49
% 2.27/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SwuThMpGUN/DTF2DTF19838.p
% See solution above
% 2.27/1.49 ------------------------
% 2.54/1.51 ---- Cleaned THF ---
% 2.54/1.51 thf(term_type,type,
% 2.54/1.51 term: $tType ).
% 2.54/1.51
% 2.54/1.51 thf(subst_type,type,
% 2.54/1.51 subst: $tType ).
% 2.54/1.51
% 2.54/1.51 thf(one_decl,type,
% 2.54/1.51 one: term ).
% 2.54/1.51
% 2.54/1.51 thf(ap_decl,type,
% 2.54/1.51 ap: term > term > term ).
% 2.54/1.51
% 2.54/1.51 thf(lam_decl,type,
% 2.54/1.51 lam: term > term ).
% 2.54/1.51
% 2.54/1.51 thf(sub_decl,type,
% 2.54/1.51 sub: term > subst > term ).
% 2.54/1.51
% 2.54/1.51 thf(id_decl,type,
% 2.54/1.51 id: subst ).
% 2.54/1.51
% 2.54/1.51 thf(sh_decl,type,
% 2.54/1.51 sh: subst ).
% 2.54/1.51
% 2.54/1.51 thf(push_decl,type,
% 2.54/1.51 push: term > subst > subst ).
% 2.54/1.51
% 2.54/1.51 thf(comp_decl,type,
% 2.54/1.51 comp: subst > subst > subst ).
% 2.54/1.51
% 2.54/1.51 thf(var_decl,type,
% 2.54/1.51 var: term > $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1v2_decl,type,
% 2.54/1.51 pushprop_lem1v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1_gthm_decl,type,
% 2.54/1.51 pushprop_lem1_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axmap_decl,type,
% 2.54/1.51 axmap: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem0_gthm_decl,type,
% 2.54/1.51 pushprop_lem0_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(shinj_decl,type,
% 2.54/1.51 shinj: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem1v2_decl,type,
% 2.54/1.51 hoasinduction_lem1v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem1v2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasap_decl,type,
% 2.54/1.51 hoasap: subst > term > subst > term > term ).
% 2.54/1.51
% 2.54/1.51 thf(induction2lem_decl,type,
% 2.54/1.51 induction2lem: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2_f_decl,type,
% 2.54/1.51 hoasinduction_lem3v2_f: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axvarshift_decl,type,
% 2.54/1.51 axvarshift: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj2_decl,type,
% 2.54/1.51 hoasapinj2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapnotvar_gthm_decl,type,
% 2.54/1.51 hoasapnotvar_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj1_decl,type,
% 2.54/1.51 hoasapinj1: $o ).
% 2.54/1.51
% 2.54/1.51 thf(ulamvar1_decl,type,
% 2.54/1.51 ulamvar1: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction2lem_lthm_decl,type,
% 2.54/1.51 induction2lem_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem3v2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(apnotvar_decl,type,
% 2.54/1.51 apnotvar: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lthm_orig_decl,type,
% 2.54/1.51 pushprop_lthm_orig: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3v2_f_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lthm_decl,type,
% 2.54/1.51 hoasinduction_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.54/1.51 hoasinduction_no_psi_cond_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslaminj_decl,type,
% 2.54/1.51 hoaslaminj: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3aaa_decl,type,
% 2.54/1.51 hoasinduction_lem3aaa: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction2lem_gthm_decl,type,
% 2.54/1.51 induction2lem_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3aa_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3_decl,type,
% 2.54/1.51 hoasinduction_lem3: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem2_decl,type,
% 2.54/1.51 hoasinduction_lem2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(termmset_lthm_decl,type,
% 2.54/1.51 termmset_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem1_decl,type,
% 2.54/1.51 hoasinduction_lem1: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotap_lthm_decl,type,
% 2.54/1.51 hoaslamnotap_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1v2_lthm_decl,type,
% 2.54/1.51 pushprop_lem1v2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapnotvar_decl,type,
% 2.54/1.51 hoasapnotvar: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem0_decl,type,
% 2.54/1.51 hoasinduction_lem0: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_decl,type,
% 2.54/1.51 hoasinduction: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_gthm_decl,type,
% 2.54/1.51 hoasinduction_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axapp_decl,type,
% 2.54/1.51 axapp: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotvar_lthm_decl,type,
% 2.54/1.51 hoaslamnotvar_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem3v2_lthm_decl,type,
% 2.54/1.51 pushprop_lem3v2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3b_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(ulamvarind_decl,type,
% 2.54/1.51 ulamvarind: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction_decl,type,
% 2.54/1.51 induction: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3a_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(termmset_gthm_decl,type,
% 2.54/1.51 termmset_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3aa_decl,type,
% 2.54/1.51 hoasinduction_lem3aa: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1v2_gthm_decl,type,
% 2.54/1.51 pushprop_lem1v2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotap_gthm_decl,type,
% 2.54/1.51 hoaslamnotap_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotvar_gthm_decl,type,
% 2.54/1.51 hoaslamnotvar_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem3b_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem2v2_decl,type,
% 2.54/1.51 pushprop_lem2v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem3a_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axclos_decl,type,
% 2.54/1.51 axclos: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axassoc_decl,type,
% 2.54/1.51 axassoc: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem2v2_decl,type,
% 2.54/1.51 hoasinduction_lem2v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lthm_decl,type,
% 2.54/1.51 pushprop_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(apinj2_decl,type,
% 2.54/1.51 apinj2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(apinj1_decl,type,
% 2.54/1.51 apinj1: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj2_lthm_decl,type,
% 2.54/1.51 hoasapinj2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2a_decl,type,
% 2.54/1.51 hoasinduction_lem3v2a: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj1_lthm_decl,type,
% 2.54/1.51 hoasapinj1_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslaminj_lthm_decl,type,
% 2.54/1.51 hoaslaminj_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axvarcons_decl,type,
% 2.54/1.51 axvarcons: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslam_decl,type,
% 2.54/1.51 hoaslam: subst > ( subst > term > term ) > term ).
% 2.54/1.51
% 2.54/1.51 thf(axscons_decl,type,
% 2.54/1.51 axscons: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem2v2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axidr_decl,type,
% 2.54/1.51 axidr: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1_decl,type,
% 2.54/1.51 pushprop_lem1: $o ).
% 2.54/1.51
% 2.54/1.51 thf(laminj_decl,type,
% 2.54/1.51 laminj: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem0_decl,type,
% 2.54/1.51 pushprop_lem0: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_gthm_decl,type,
% 2.54/1.51 pushprop_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axabs_decl,type,
% 2.54/1.51 axabs: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3v2a_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem2_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj2_gthm_decl,type,
% 2.54/1.51 hoasapinj2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.54/1.51 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem1_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem1_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(lamnotap_decl,type,
% 2.54/1.51 lamnotap: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapinj1_gthm_decl,type,
% 2.54/1.51 hoasapinj1_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotvar_decl,type,
% 2.54/1.51 hoaslamnotvar: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axidl_decl,type,
% 2.54/1.51 axidl: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslaminj_gthm_decl,type,
% 2.54/1.51 hoaslaminj_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction2_lthm_decl,type,
% 2.54/1.51 induction2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem0_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem0_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(substmonoid_lthm_decl,type,
% 2.54/1.51 substmonoid_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_decl,type,
% 2.54/1.51 pushprop: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem3_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem2_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3b_decl,type,
% 2.54/1.51 hoasinduction_lem3b: $o ).
% 2.54/1.51
% 2.54/1.51 thf(substmonoid_decl,type,
% 2.54/1.51 substmonoid: $o ).
% 2.54/1.51
% 2.54/1.51 thf(lamnotvar_decl,type,
% 2.54/1.51 lamnotvar: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3a_decl,type,
% 2.54/1.51 hoasinduction_lem3a: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem1_gthm_decl,type,
% 2.54/1.51 hoasinduction_lem1_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_no_psi_cond_decl,type,
% 2.54/1.51 hoasinduction_no_psi_cond: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction2_gthm_decl,type,
% 2.54/1.51 induction2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem2v2_lthm_decl,type,
% 2.54/1.51 pushprop_lem2v2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasvar_decl,type,
% 2.54/1.51 hoasvar: subst > term > subst > $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoaslamnotap_decl,type,
% 2.54/1.51 hoaslamnotap: $o ).
% 2.54/1.51
% 2.54/1.51 thf(substmonoid_gthm_decl,type,
% 2.54/1.51 substmonoid_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(ulamvarsh_decl,type,
% 2.54/1.51 ulamvarsh: $o ).
% 2.54/1.51
% 2.54/1.51 thf(induction2_decl,type,
% 2.54/1.51 induction2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem3v2_decl,type,
% 2.54/1.51 pushprop_lem3v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem2v2_gthm_decl,type,
% 2.54/1.51 pushprop_lem2v2_gthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem1_lthm_decl,type,
% 2.54/1.51 pushprop_lem1_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2_decl,type,
% 2.54/1.51 hoasinduction_lem3v2: $o ).
% 2.54/1.51
% 2.54/1.51 thf(axshiftcons_decl,type,
% 2.54/1.51 axshiftcons: $o ).
% 2.54/1.51
% 2.54/1.51 thf(termmset_decl,type,
% 2.54/1.51 termmset: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_lem0_lthm_decl,type,
% 2.54/1.51 pushprop_lem0_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasapnotvar_lthm_decl,type,
% 2.54/1.51 hoasapnotvar_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.54/1.51 hoasinduction_lem3v2_lthm: $o ).
% 2.54/1.51
% 2.54/1.51 thf(pushprop_p_and_p_prime_decl,type,
% 2.54/1.51 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.54/1.51
% 2.54/1.51 thf(axvarid_decl,type,
% 2.54/1.51 axvarid: $o ).
% 2.54/1.51
% 2.54/1.51 thf(hoasinduction_lthm_3_decl,type,
% 2.54/1.51 hoasinduction_lthm_3: $o ).
% 2.54/1.51
% 2.54/1.51 thf(d_term_type,type,
% 2.54/1.51 d_term: $tType ).
% 2.54/1.51
% 2.54/1.51 thf(d_subst_type,type,
% 2.54/1.51 d_subst: $tType ).
% 2.54/1.51
% 2.54/1.51 thf(d2term_decl,type,
% 2.54/1.51 d2term: d_term > term ).
% 2.54/1.51
% 2.54/1.51 thf(d2subst_decl,type,
% 2.54/1.51 d2subst: d_subst > subst ).
% 2.54/1.51
% 2.54/1.51 thf(d_one_decl,type,
% 2.54/1.51 d_one: d_term ).
% 2.54/1.51
% 2.54/1.51 thf(d_id_decl,type,
% 2.54/1.51 d_id: d_subst ).
% 2.54/1.51
% 2.54/1.51 thf(alg444_1,axiom,
% 2.54/1.51 ( ! [T: term] :
% 2.54/1.51 ? [DT: d_term] :
% 2.54/1.51 ( T
% 2.54/1.51 = ( d2term @ DT ) )
% 2.54/1.51 & ! [DT: d_term] : ( DT = d_one )
% 2.54/1.51 & ! [DT1: d_term,DT2: d_term] :
% 2.54/1.51 ( ( ( d2term @ DT1 )
% 2.54/1.51 = ( d2term @ DT2 ) )
% 2.54/1.51 => ( DT1 = DT2 ) )
% 2.54/1.51 & ! [S: subst] :
% 2.54/1.51 ? [DS: d_subst] :
% 2.54/1.51 ( S
% 2.54/1.51 = ( d2subst @ DS ) )
% 2.54/1.51 & ! [DS: d_subst] : ( DS = d_id )
% 2.54/1.51 & ! [DS1: d_subst,DS2: d_subst] :
% 2.54/1.51 ( ( ( d2subst @ DS1 )
% 2.54/1.51 = ( d2subst @ DS2 ) )
% 2.54/1.51 => ( DS1 = DS2 ) )
% 2.54/1.51 & ( one
% 2.54/1.51 = ( d2term @ d_one ) )
% 2.54/1.51 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.54/1.51 = ( d2term @ d_one ) )
% 2.54/1.51 & ( ( lam @ ( d2term @ d_one ) )
% 2.54/1.51 = ( d2term @ d_one ) )
% 2.54/1.51 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.54/1.51 = ( d2term @ d_one ) )
% 2.54/1.51 & ( id
% 2.54/1.51 = ( d2subst @ d_id ) )
% 2.54/1.51 & ( sh
% 2.54/1.51 = ( d2subst @ d_id ) )
% 2.54/1.51 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.54/1.51 = ( d2subst @ d_id ) )
% 2.54/1.51 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.54/1.51 = ( d2subst @ d_id ) )
% 2.54/1.51 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.54/1.51 = ( d2term @ d_one ) )
% 2.54/1.51 & ( hoaslam
% 2.54/1.51 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.54/1.51 & ( hoasinduction_p_and_p_prime
% 2.54/1.51 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.54/1.51 ! [X: term] :
% 2.54/1.51 ( ( Q @ X )
% 2.54/1.51 = ( P @ id @ X @ id ) ) ) )
% 2.54/1.51 & ( pushprop_p_and_p_prime
% 2.54/1.51 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.54/1.51 ! [X: term] :
% 2.54/1.51 ( ( Q @ X )
% 2.54/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.54/1.51 & ~ ( var @ ( d2term @ d_one ) )
% 2.54/1.51 & ( pushprop_lem1v2
% 2.54/1.51 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ~ ! [X: term] :
% 2.54/1.51 ( ( Q @ X )
% 2.54/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.54/1.51 | ( Q @ one ) ) )
% 2.54/1.51 & pushprop_lem1_gthm
% 2.54/1.51 & axmap
% 2.54/1.51 & pushprop_lem0_gthm
% 2.54/1.51 & ( shinj
% 2.54/1.51 <=> ! [A: term,B: term] :
% 2.54/1.51 ( ( ( sub @ A @ sh )
% 2.54/1.51 != ( sub @ B @ sh ) )
% 2.54/1.51 | ( A = B ) ) )
% 2.54/1.51 & hoasinduction_lem1v2
% 2.54/1.51 & hoasinduction_lem1v2_gthm
% 2.54/1.51 & ( induction2lem
% 2.54/1.51 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.54/1.51 ( ~ ! [A: term,B: term] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ~ ( P @ B )
% 2.54/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ! [B: term] :
% 2.54/1.51 ( ~ ( P @ B )
% 2.54/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.51 | ( P @ ( lam @ A ) ) )
% 2.54/1.51 | ~ ! [B: term] :
% 2.54/1.51 ( ~ ( var @ B )
% 2.54/1.51 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.54/1.51 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.54/1.51 & ( hoasinduction_lem3v2_f
% 2.54/1.51 <=> ! [B: term] :
% 2.54/1.51 ~ ! [F: subst > term > term] :
% 2.54/1.51 ~ ! [A: term,M: subst] :
% 2.54/1.51 ( ( sub @ B @ ( push @ A @ M ) )
% 2.54/1.51 = ( F @ M @ A ) ) )
% 2.54/1.51 & axvarshift
% 2.54/1.51 & ( hoasapinj2
% 2.54/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.54/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.54/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.54/1.51 | ( C = D ) ) )
% 2.54/1.51 & hoasapnotvar_gthm
% 2.54/1.51 & ( hoasapinj1
% 2.54/1.51 <=> ! [A: term,B: term,C: term,D: term] :
% 2.54/1.51 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.54/1.51 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.54/1.51 | ( A = B ) ) )
% 2.54/1.51 & ~ ulamvar1
% 2.54/1.51 & ( induction2lem_lthm
% 2.54/1.51 <=> ( ! [A: term,M: subst] :
% 2.54/1.51 ( A
% 2.54/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.54/1.51 => ( ! [A: term,M: subst] :
% 2.54/1.51 ( M
% 2.54/1.51 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.54/1.51 => ( ! [M: subst] :
% 2.54/1.51 ( M
% 2.54/1.51 = ( comp @ M @ id ) )
% 2.54/1.51 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.54/1.51 ( ~ ! [A: term] :
% 2.54/1.51 ( ~ ( var @ A )
% 2.54/1.51 | ( P @ A ) )
% 2.54/1.51 | ~ ! [A: term,B: term] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ~ ( P @ B )
% 2.54/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ( P @ ( lam @ A ) ) )
% 2.54/1.51 | ( P @ Bound_variable_2140 ) )
% 2.54/1.51 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.54/1.51 ( ~ ! [A: term,B: term] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ~ ( P @ B )
% 2.54/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ! [B: term] :
% 2.54/1.51 ( ~ ( P @ B )
% 2.54/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.51 | ( P @ ( lam @ A ) ) )
% 2.54/1.51 | ~ ! [B: term] :
% 2.54/1.51 ( ~ ( var @ B )
% 2.54/1.51 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.54/1.51 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.54/1.51 & hoasinduction_lem3v2_gthm
% 2.54/1.51 & apnotvar
% 2.54/1.51 & pushprop_lthm_orig
% 2.54/1.51 & ( hoasinduction_lem3v2_f_lthm
% 2.54/1.51 <=> ! [B: term] :
% 2.54/1.51 ~ ! [F: subst > term > term] :
% 2.54/1.51 ~ ! [A: term,M: subst] :
% 2.54/1.51 ( ( sub @ B @ ( push @ A @ M ) )
% 2.54/1.51 = ( F @ M @ A ) ) )
% 2.54/1.51 & ( hoasinduction_lthm
% 2.54/1.51 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.54/1.51 ( ~ ! [A: term] :
% 2.54/1.51 ( ~ ( var @ A )
% 2.54/1.51 | ( P @ A ) )
% 2.54/1.51 | ~ ! [A: term,B: term] :
% 2.54/1.51 ( ~ ( P @ A )
% 2.54/1.51 | ~ ( P @ B )
% 2.54/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ! [B: term] :
% 2.54/1.51 ( ~ ( P @ B )
% 2.54/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.51 | ( P @ ( lam @ A ) ) )
% 2.54/1.51 | ( P @ Bound_variable_2367 ) )
% 2.54/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.54/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.51 | ~ ! [A: term,B: term] :
% 2.54/1.51 ( ~ ( P @ id @ A @ id )
% 2.54/1.51 | ~ ( P @ id @ B @ id )
% 2.54/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.51 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.54/1.51 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.54/1.51 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.54/1.51 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.54/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.51 | ~ ! [F: subst > term > term] :
% 2.54/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ( P @ id @ A @ id )
% 2.54/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.51 | ~ ! [B: term] :
% 2.54/1.51 ( ~ ( P @ id @ B @ id )
% 2.54/1.51 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.51 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.54/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.54/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.51 | ~ ! [A: term] :
% 2.54/1.51 ( ~ ( var @ ( sub @ A @ id ) )
% 2.54/1.51 | ( P @ id @ A @ id ) )
% 2.54/1.51 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.54/1.52 & ( hoasinduction_no_psi_cond_lthm
% 2.54/1.52 <=> ( ! [P: subst > term > subst > $o] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ A )
% 2.54/1.52 | ( P @ A ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ B )
% 2.54/1.52 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ( P @ Bound_variable_2367 ) )
% 2.54/1.52 => ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.54/1.52 ( ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.54/1.52 & ( hoaslaminj
% 2.54/1.52 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.54/1.52 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ( ( lam @ ( F @ sh @ one ) )
% 2.54/1.52 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.54/1.52 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.54/1.52 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.54/1.52 & ( hoasinduction_lem3aaa
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.54/1.52 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.54/1.52 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.54/1.52 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.54/1.52 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.54/1.52 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.54/1.52 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.54/1.52 & induction2lem_gthm
% 2.54/1.52 & ( hoasinduction_lem3aa_lthm
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.54/1.52 & ( hoasinduction_lem3
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 2.54/1.52 & ( hoasinduction_lem2
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.54/1.52 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 2.54/1.52 & ( termmset_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) ) ) )
% 2.54/1.52 & hoasinduction_lem1
% 2.54/1.52 & hoaslamnotap_lthm
% 2.54/1.52 & ( pushprop_lem1v2_lthm
% 2.54/1.52 <=> ( ! [A: term,M: subst] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.54/1.52 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.54/1.52 | ( Q @ one ) ) ) )
% 2.54/1.52 & hoasapnotvar
% 2.54/1.52 & ( hoasinduction_lem0
% 2.54/1.52 <=> ! [P: subst > term > subst > $o] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) ) )
% 2.54/1.52 & ( hoasinduction
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ ( sub @ A @ id ) )
% 2.54/1.52 | ( P @ id @ A @ id ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 2.54/1.52 & hoasinduction_gthm
% 2.54/1.52 & axapp
% 2.54/1.52 & hoaslamnotvar_lthm
% 2.54/1.52 & pushprop_lem3v2_lthm
% 2.54/1.52 & ( hoasinduction_lem3b_lthm
% 2.54/1.52 <=> ! [B: term] :
% 2.54/1.52 ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ( F @ sh @ one )
% 2.54/1.52 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.54/1.52 & ulamvarind
% 2.54/1.52 & ( induction
% 2.54/1.52 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ A )
% 2.54/1.52 | ( P @ A ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ( P @ Bound_variable_2140 ) ) )
% 2.54/1.52 & ( hoasinduction_lem3a_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 2.54/1.52 & termmset_gthm
% 2.54/1.52 & ( hoasinduction_lem3aa
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.54/1.52 & pushprop_lem1v2_gthm
% 2.54/1.52 & hoaslamnotap_gthm
% 2.54/1.52 & hoaslamnotvar_gthm
% 2.54/1.52 & hoasinduction_lem3b_gthm
% 2.54/1.52 & pushprop_lem2v2
% 2.54/1.52 & hoasinduction_lem3a_gthm
% 2.54/1.52 & axclos
% 2.54/1.52 & axassoc
% 2.54/1.52 & ( hoasinduction_lem2v2
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ( Q @ Bound_variable_2820 )
% 2.54/1.52 | ~ ( Q @ Bound_variable_2822 )
% 2.54/1.52 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 2.54/1.52 & pushprop_lthm
% 2.54/1.52 & ( apinj2
% 2.54/1.52 <=> ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ A @ C )
% 2.54/1.52 != ( ap @ B @ D ) )
% 2.54/1.52 | ( C = D ) ) )
% 2.54/1.52 & ( apinj1
% 2.54/1.52 <=> ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ A @ C )
% 2.54/1.52 != ( ap @ B @ D ) )
% 2.54/1.52 | ( A = B ) ) )
% 2.54/1.52 & ( hoasapinj2_lthm
% 2.54/1.52 <=> ( ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ A @ C )
% 2.54/1.52 != ( ap @ B @ D ) )
% 2.54/1.52 | ( C = D ) )
% 2.54/1.52 => ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.54/1.52 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.54/1.52 | ( C = D ) ) ) )
% 2.54/1.52 & ( hoasinduction_lem3v2a
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 2.54/1.52 & ( hoasapinj1_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ A @ C )
% 2.54/1.52 != ( ap @ B @ D ) )
% 2.54/1.52 | ( A = B ) )
% 2.54/1.52 => ! [A: term,B: term,C: term,D: term] :
% 2.54/1.52 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.54/1.52 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.54/1.52 | ( A = B ) ) ) ) )
% 2.54/1.52 & ( hoaslaminj_lthm
% 2.54/1.52 <=> ( ! [A: term,M: subst] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.54/1.52 => ( ! [A: term,M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.54/1.52 => ( ! [A: term,B: term] :
% 2.54/1.52 ( ( ( lam @ A )
% 2.54/1.52 != ( lam @ B ) )
% 2.54/1.52 | ( A = B ) )
% 2.54/1.52 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.54/1.52 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ( ( lam @ ( F @ sh @ one ) )
% 2.54/1.52 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.54/1.52 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.54/1.52 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 2.54/1.52 & ( axvarcons
% 2.54/1.52 <=> ! [A: term,M: subst] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 2.54/1.52 & ( axscons
% 2.54/1.52 <=> ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 2.54/1.52 & hoasinduction_lem2v2_gthm
% 2.54/1.52 & ( axidr
% 2.54/1.52 <=> ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ M @ id ) ) )
% 2.54/1.52 & ( pushprop_lem1
% 2.54/1.52 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 2.54/1.52 & ( laminj
% 2.54/1.52 <=> ! [A: term,B: term] :
% 2.54/1.52 ( ( ( lam @ A )
% 2.54/1.52 != ( lam @ B ) )
% 2.54/1.52 | ( A = B ) ) )
% 2.54/1.52 & ( hoasinduction_lem3_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 2.54/1.52 & ( pushprop_lem0
% 2.54/1.52 <=> ! [P: term > $o,A: term,M: subst] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.54/1.52 & pushprop_gthm
% 2.54/1.52 & axabs
% 2.54/1.52 & ( hoasinduction_lem3v2a_lthm
% 2.54/1.52 <=> ( ! [B: term] :
% 2.54/1.52 ~ ! [F: subst > term > term] :
% 2.54/1.52 ~ ! [A: term,M: subst] :
% 2.54/1.52 ( ( sub @ B @ ( push @ A @ M ) )
% 2.54/1.52 = ( F @ M @ A ) )
% 2.54/1.52 => ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 2.54/1.52 & hoasinduction_lem2_lthm
% 2.54/1.52 & hoasapinj2_gthm
% 2.54/1.52 & hoasinduction_lem1_lthm
% 2.54/1.52 & ~ lamnotap
% 2.54/1.52 & hoasapinj1_gthm
% 2.54/1.52 & hoaslamnotvar
% 2.54/1.52 & ( axidl
% 2.54/1.52 <=> ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ id @ M ) ) )
% 2.54/1.52 & hoaslaminj_gthm
% 2.54/1.52 & ( induction2_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.54/1.52 ( ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ B )
% 2.54/1.52 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( var @ B )
% 2.54/1.52 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.54/1.52 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 2.54/1.52 => ! [P: term > $o,Bound_variable_2367: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ A )
% 2.54/1.52 | ( P @ A ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ B )
% 2.54/1.52 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ( P @ Bound_variable_2367 ) ) ) ) )
% 2.54/1.52 & ( hoasinduction_lem0_lthm
% 2.54/1.52 <=> ! [P: subst > term > subst > $o] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) ) )
% 2.54/1.52 & ( substmonoid_lthm
% 2.54/1.52 <=> ( ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ id @ M ) )
% 2.54/1.52 => ( ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ M @ id ) )
% 2.54/1.52 => ( ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ id @ M ) )
% 2.54/1.52 & ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ M @ id ) ) ) ) ) )
% 2.54/1.52 & pushprop
% 2.54/1.52 & hoasinduction_lem3_gthm
% 2.54/1.52 & hoasinduction_lem2_gthm
% 2.54/1.52 & ( hoasinduction_lem3b
% 2.54/1.52 <=> ! [B: term] :
% 2.54/1.52 ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ( F @ sh @ one )
% 2.54/1.52 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.54/1.52 & ( substmonoid
% 2.54/1.52 <=> ( ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ id @ M ) )
% 2.54/1.52 & ! [M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ M @ id ) ) ) )
% 2.54/1.52 & lamnotvar
% 2.54/1.52 & ( hoasinduction_lem3a
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 2.54/1.52 & hoasinduction_lem1_gthm
% 2.54/1.52 & ( hoasinduction_no_psi_cond
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.54/1.52 ( ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 2.54/1.52 & induction2_gthm
% 2.54/1.52 & pushprop_lem2v2_lthm
% 2.54/1.52 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.54/1.52 & ( hoaslamnotap
% 2.54/1.52 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ( ( lam @ ( F @ sh @ one ) )
% 2.54/1.52 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 2.54/1.52 & substmonoid_gthm
% 2.54/1.52 & ulamvarsh
% 2.54/1.52 & ( induction2
% 2.54/1.52 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ A )
% 2.54/1.52 | ( P @ A ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ B )
% 2.54/1.52 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ( P @ Bound_variable_2367 ) ) )
% 2.54/1.52 & pushprop_lem3v2
% 2.54/1.52 & pushprop_lem2v2_gthm
% 2.54/1.52 & ( pushprop_lem1_lthm
% 2.54/1.52 <=> ( ! [A: term,M: subst] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.54/1.52 => ( ! [A: term,M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.54/1.52 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 2.54/1.52 & ( hoasinduction_lem3v2
% 2.54/1.52 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 2.54/1.52 & ( axshiftcons
% 2.54/1.52 <=> ! [A: term,M: subst] :
% 2.54/1.52 ( M
% 2.54/1.52 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 2.54/1.52 & ( termmset
% 2.54/1.52 <=> ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) ) )
% 2.54/1.52 & ( pushprop_lem0_lthm
% 2.54/1.52 <=> ! [P: term > $o,A: term,M: subst] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.54/1.52 & hoasapnotvar_lthm
% 2.54/1.52 & ( hoasinduction_lem3v2_lthm
% 2.54/1.52 <=> ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 2.54/1.52 & ( axvarid
% 2.54/1.52 <=> ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) ) )
% 2.54/1.52 & ( hoasinduction_lthm_3
% 2.54/1.52 <=> ( ! [P: subst > term > subst > $o] :
% 2.54/1.52 ~ ! [Q: term > $o] :
% 2.54/1.52 ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.54/1.52 ( ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ A )
% 2.54/1.52 | ( P @ A ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ A )
% 2.54/1.52 | ~ ( P @ B )
% 2.54/1.52 | ( P @ ( ap @ A @ B ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ! [B: term] :
% 2.54/1.52 ( ~ ( P @ B )
% 2.54/1.52 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( P @ ( lam @ A ) ) )
% 2.54/1.52 | ( P @ Bound_variable_2367 ) )
% 2.54/1.52 => ( ! [A: term] :
% 2.54/1.52 ( A
% 2.54/1.52 = ( sub @ A @ id ) )
% 2.54/1.52 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.54/1.52 ( ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ~ ! [X: term] :
% 2.54/1.52 ( ( Q @ X )
% 2.54/1.52 = ( P @ id @ X @ id ) )
% 2.54/1.52 | ~ ! [B: term] :
% 2.54/1.52 ( ~ ( Q @ B )
% 2.54/1.52 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.54/1.52 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.54/1.52 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( var @ ( sub @ A @ id ) )
% 2.54/1.52 | ( P @ id @ A @ id ) )
% 2.54/1.52 | ~ ! [A: term,B: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ~ ( P @ id @ B @ id )
% 2.54/1.52 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.54/1.52 | ~ ! [F: subst > term > term] :
% 2.54/1.52 ( ~ ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 | ~ ! [A: term] :
% 2.54/1.52 ( ~ ( P @ id @ A @ id )
% 2.54/1.52 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.54/1.52 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(hoasinduction_lem3v2,conjecture,
% 2.54/1.52 ( hoasinduction_lem3v2
% 2.54/1.52 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 2.54/1.52 ( ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 2.54/1.52 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.54/1.52 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 2.54/1.52 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.54/1.52 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.54/1.52 => ( ! [F: subst > term > term] :
% 2.54/1.52 ( ! [M: subst,A: term,N: subst] :
% 2.54/1.52 ( ( sub @ ( F @ M @ A ) @ N )
% 2.54/1.52 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.54/1.52 => ( ! [A: term] :
% 2.54/1.52 ( ( P @ id @ A @ id )
% 2.54/1.52 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.54/1.52 => ( P @ id
% 2.54/1.52 @ ( hoaslam @ id
% 2.54/1.52 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 2.54/1.52 @ id ) ) )
% 2.54/1.52 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 2.54/1.52 => ! [A: term] :
% 2.54/1.52 ( ! [B: term] :
% 2.54/1.52 ( ( Q @ B )
% 2.54/1.52 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.54/1.52 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ) ).
% 2.54/1.52 ------------------------
% 2.54/1.53 % (20172)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/183Mi)
% 2.54/1.53 % (20173)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_19838 for (2999ds/4Mi)
% 2.54/1.53 % (20174)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_19838 for (2999ds/27Mi)
% 2.54/1.54 % (20173)Instruction limit reached!
% 2.54/1.54 % (20173)------------------------------
% 2.54/1.54 % (20173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (20173)Termination reason: Unknown
% 2.54/1.54 % (20173)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (20173)Memory used [KB]: 1407
% 2.54/1.54 % (20173)Time elapsed: 0.003 s
% 2.54/1.54 % (20173)Instructions burned: 6 (million)
% 2.54/1.54 % (20173)------------------------------
% 2.54/1.54 % (20173)------------------------------
% 2.54/1.54 % (20175)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/2Mi)
% 2.54/1.54 % (20176)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_19838 for (2999ds/2Mi)
% 2.54/1.54 % (20177)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_19838 for (2999ds/275Mi)
% 2.54/1.54 % (20178)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/18Mi)
% 2.54/1.54 % (20175)Instruction limit reached!
% 2.54/1.54 % (20175)------------------------------
% 2.54/1.54 % (20175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (20175)Termination reason: Unknown
% 2.54/1.54 % (20175)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (20175)Memory used [KB]: 1279
% 2.54/1.54 % (20175)Time elapsed: 0.004 s
% 2.54/1.54 % (20175)Instructions burned: 3 (million)
% 2.54/1.54 % (20175)------------------------------
% 2.54/1.54 % (20175)------------------------------
% 2.54/1.54 % (20176)Instruction limit reached!
% 2.54/1.54 % (20176)------------------------------
% 2.54/1.54 % (20176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (20176)Termination reason: Unknown
% 2.54/1.54 % (20176)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (20176)Memory used [KB]: 1279
% 2.54/1.54 % (20176)Time elapsed: 0.004 s
% 2.54/1.54 % (20176)Instructions burned: 3 (million)
% 2.54/1.54 % (20176)------------------------------
% 2.54/1.54 % (20176)------------------------------
% 2.54/1.54 % (20174)Instruction limit reached!
% 2.54/1.54 % (20174)------------------------------
% 2.54/1.54 % (20174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (20174)Termination reason: Unknown
% 2.54/1.54 % (20174)Termination phase: Property scanning
% 2.54/1.54
% 2.54/1.54 % (20174)Memory used [KB]: 2174
% 2.54/1.54 % (20174)Time elapsed: 0.011 s
% 2.54/1.54 % (20174)Instructions burned: 30 (million)
% 2.54/1.54 % (20174)------------------------------
% 2.54/1.54 % (20174)------------------------------
% 2.54/1.55 % (20179)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/3Mi)
% 2.54/1.55 % (20179)Instruction limit reached!
% 2.54/1.55 % (20179)------------------------------
% 2.54/1.55 % (20179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (20179)Termination reason: Unknown
% 2.54/1.55 % (20179)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (20179)Memory used [KB]: 1279
% 2.54/1.55 % (20179)Time elapsed: 0.003 s
% 2.54/1.55 % (20179)Instructions burned: 4 (million)
% 2.54/1.55 % (20179)------------------------------
% 2.54/1.55 % (20179)------------------------------
% 2.54/1.55 % (20178)Instruction limit reached!
% 2.54/1.55 % (20178)------------------------------
% 2.54/1.55 % (20178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (20178)Termination reason: Unknown
% 2.54/1.55 % (20178)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (20178)Memory used [KB]: 2046
% 2.54/1.55 % (20178)Time elapsed: 0.013 s
% 2.54/1.55 % (20178)Instructions burned: 18 (million)
% 2.54/1.55 % (20178)------------------------------
% 2.54/1.55 % (20178)------------------------------
% 2.54/1.55 % (20182)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_19838 for (2999ds/3Mi)
% 2.54/1.56 % (20182)Instruction limit reached!
% 2.54/1.56 % (20182)------------------------------
% 2.54/1.56 % (20182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (20182)Termination reason: Unknown
% 2.54/1.56 % (20182)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (20182)Memory used [KB]: 1279
% 2.54/1.56 % (20182)Time elapsed: 0.003 s
% 2.54/1.56 % (20182)Instructions burned: 4 (million)
% 2.54/1.56 % (20182)------------------------------
% 2.54/1.56 % (20182)------------------------------
% 2.54/1.56 % (20183)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_19838 for (2999ds/1041Mi)
% 2.54/1.56 % (20180)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_19838 for (2999ds/37Mi)
% 2.54/1.56 % (20181)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_19838 for (2999ds/15Mi)
% 2.54/1.57 % (20185)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/16Mi)
% 2.54/1.57 % (20177)Refutation not found, incomplete strategy
% 2.54/1.57 % (20177)------------------------------
% 2.54/1.57 % (20177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (20177)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.57
% 2.54/1.57
% 2.54/1.57 % (20177)Memory used [KB]: 6780
% 2.54/1.57 % (20177)Time elapsed: 0.028 s
% 2.54/1.57 % (20177)Instructions burned: 45 (million)
% 2.54/1.57 % (20177)------------------------------
% 2.54/1.57 % (20177)------------------------------
% 2.54/1.57 % (20181)Instruction limit reached!
% 2.54/1.57 % (20181)------------------------------
% 2.54/1.57 % (20181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (20181)Termination reason: Unknown
% 2.54/1.57 % (20181)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (20181)Memory used [KB]: 1791
% 2.54/1.57 % (20181)Time elapsed: 0.011 s
% 2.54/1.57 % (20181)Instructions burned: 16 (million)
% 2.54/1.57 % (20181)------------------------------
% 2.54/1.57 % (20181)------------------------------
% 2.54/1.57 % (20184)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/7Mi)
% 2.54/1.57 % (20185)Instruction limit reached!
% 2.54/1.57 % (20185)------------------------------
% 2.54/1.57 % (20185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (20185)Termination reason: Unknown
% 2.54/1.57 % (20185)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (20185)Memory used [KB]: 1791
% 2.54/1.57 % (20185)Time elapsed: 0.007 s
% 2.54/1.57 % (20185)Instructions burned: 16 (million)
% 2.54/1.57 % (20185)------------------------------
% 2.54/1.57 % (20185)------------------------------
% 2.54/1.57 % (20184)Instruction limit reached!
% 2.54/1.57 % (20184)------------------------------
% 2.54/1.57 % (20184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (20184)Termination reason: Unknown
% 2.54/1.57 % (20184)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (20184)Memory used [KB]: 1407
% 2.54/1.57 % (20184)Time elapsed: 0.006 s
% 2.54/1.57 % (20184)Instructions burned: 7 (million)
% 2.54/1.57 % (20184)------------------------------
% 2.54/1.57 % (20184)------------------------------
% 2.54/1.58 % (20180)Instruction limit reached!
% 2.54/1.58 % (20180)------------------------------
% 2.54/1.58 % (20180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (20180)Termination reason: Unknown
% 2.54/1.58 % (20180)Termination phase: Property scanning
% 2.54/1.58
% 2.54/1.58 % (20180)Memory used [KB]: 1918
% 2.54/1.58 % (20180)Time elapsed: 0.019 s
% 2.54/1.58 % (20180)Instructions burned: 39 (million)
% 2.54/1.58 % (20180)------------------------------
% 2.54/1.58 % (20180)------------------------------
% 2.54/1.58 % (20187)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_19838 for (2999ds/3Mi)
% 2.54/1.58 % (20188)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/7Mi)
% 2.54/1.58 % (20187)Instruction limit reached!
% 2.54/1.58 % (20187)------------------------------
% 2.54/1.58 % (20187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (20187)Termination reason: Unknown
% 2.54/1.58 % (20187)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (20187)Memory used [KB]: 1279
% 2.54/1.58 % (20187)Time elapsed: 0.002 s
% 2.54/1.58 % (20187)Instructions burned: 4 (million)
% 2.54/1.58 % (20187)------------------------------
% 2.54/1.58 % (20187)------------------------------
% 2.54/1.58 % (20188)Instruction limit reached!
% 2.54/1.58 % (20188)------------------------------
% 2.54/1.58 % (20188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (20188)Termination reason: Unknown
% 2.54/1.58 % (20188)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (20188)Memory used [KB]: 1407
% 2.54/1.58 % (20188)Time elapsed: 0.004 s
% 2.54/1.58 % (20188)Instructions burned: 8 (million)
% 2.54/1.58 % (20188)------------------------------
% 2.54/1.58 % (20188)------------------------------
% 2.54/1.58 % (20172)Instruction limit reached!
% 2.54/1.58 % (20172)------------------------------
% 2.54/1.58 % (20172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (20172)Termination reason: Unknown
% 2.54/1.58 % (20172)Termination phase: Property scanning
% 2.54/1.58
% 2.54/1.58 % (20172)Memory used [KB]: 4605
% 2.54/1.58 % (20172)Time elapsed: 0.052 s
% 2.54/1.58 % (20172)Instructions burned: 186 (million)
% 2.54/1.58 % (20172)------------------------------
% 2.54/1.58 % (20172)------------------------------
% 2.54/1.59 % (20186)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_19838 for (2999ds/3Mi)
% 2.54/1.59 % (20186)Instruction limit reached!
% 2.54/1.59 % (20186)------------------------------
% 2.54/1.59 % (20186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (20186)Termination reason: Unknown
% 2.54/1.59 % (20186)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (20186)Memory used [KB]: 1279
% 2.54/1.59 % (20186)Time elapsed: 0.004 s
% 2.54/1.59 % (20186)Instructions burned: 4 (million)
% 2.54/1.59 % (20186)------------------------------
% 2.54/1.59 % (20186)------------------------------
% 2.54/1.59 % (20190)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/4Mi)
% 2.54/1.59 % (20190)Instruction limit reached!
% 2.54/1.59 % (20190)------------------------------
% 2.54/1.59 % (20190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (20190)Termination reason: Unknown
% 2.54/1.59 % (20190)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (20190)Memory used [KB]: 1407
% 2.54/1.59 % (20190)Time elapsed: 0.003 s
% 2.54/1.59 % (20190)Instructions burned: 6 (million)
% 2.54/1.59 % (20190)------------------------------
% 2.54/1.59 % (20190)------------------------------
% 2.54/1.59 % (20191)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/18Mi)
% 2.54/1.59 % (20189)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/3Mi)
% 2.54/1.59 % (20192)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/710Mi)
% 2.54/1.59 % (20189)Instruction limit reached!
% 2.54/1.59 % (20189)------------------------------
% 2.54/1.59 % (20189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (20189)Termination reason: Unknown
% 2.54/1.59 % (20189)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (20189)Memory used [KB]: 1279
% 2.54/1.59 % (20189)Time elapsed: 0.004 s
% 2.54/1.59 % (20189)Instructions burned: 4 (million)
% 2.54/1.59 % (20189)------------------------------
% 2.54/1.59 % (20189)------------------------------
% 2.54/1.59 % (20193)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/6Mi)
% 2.54/1.60 % (20193)Instruction limit reached!
% 2.54/1.60 % (20193)------------------------------
% 2.54/1.60 % (20193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.60 % (20193)Termination reason: Unknown
% 2.54/1.60 % (20193)Termination phase: shuffling
% 2.54/1.60
% 2.54/1.60 % (20193)Memory used [KB]: 1407
% 2.54/1.60 % (20193)Time elapsed: 0.003 s
% 2.54/1.60 % (20193)Instructions burned: 7 (million)
% 2.54/1.60 % (20193)------------------------------
% 2.54/1.60 % (20193)------------------------------
% 2.57/1.60 % (20191)Instruction limit reached!
% 2.57/1.60 % (20191)------------------------------
% 2.57/1.60 % (20191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.60 % (20191)Termination reason: Unknown
% 2.57/1.60 % (20191)Termination phase: shuffling
% 2.57/1.60
% 2.57/1.60 % (20191)Memory used [KB]: 2046
% 2.57/1.60 % (20191)Time elapsed: 0.008 s
% 2.57/1.60 % (20191)Instructions burned: 19 (million)
% 2.57/1.60 % (20191)------------------------------
% 2.57/1.60 % (20191)------------------------------
% 2.57/1.60 % (20195)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_19838 for (2999ds/21Mi)
% 2.57/1.61 % (20197)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_19838 for (2999ds/6Mi)
% 2.57/1.61 % (20194)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_19838 for (2999ds/902Mi)
% 2.57/1.61 % (20197)Instruction limit reached!
% 2.57/1.61 % (20197)------------------------------
% 2.57/1.61 % (20197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.61 % (20197)Termination reason: Unknown
% 2.57/1.61 % (20197)Termination phase: shuffling
% 2.57/1.61
% 2.57/1.61 % (20197)Memory used [KB]: 1407
% 2.57/1.61 % (20197)Time elapsed: 0.003 s
% 2.57/1.61 % (20197)Instructions burned: 7 (million)
% 2.57/1.61 % (20197)------------------------------
% 2.57/1.61 % (20197)------------------------------
% 2.57/1.61 % (20195)Instruction limit reached!
% 2.57/1.61 % (20195)------------------------------
% 2.57/1.61 % (20195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.61 % (20195)Termination reason: Unknown
% 2.57/1.61 % (20195)Termination phase: shuffling
% 2.57/1.61
% 2.57/1.61 % (20195)Memory used [KB]: 2174
% 2.57/1.61 % (20195)Time elapsed: 0.009 s
% 2.57/1.61 % (20195)Instructions burned: 21 (million)
% 2.57/1.61 % (20195)------------------------------
% 2.57/1.61 % (20195)------------------------------
% 2.57/1.61 % (20198)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/377Mi)
% 2.57/1.61 % (20196)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/5Mi)
% 2.57/1.61 % (20196)Instruction limit reached!
% 2.57/1.61 % (20196)------------------------------
% 2.57/1.61 % (20196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.61 % (20196)Termination reason: Unknown
% 2.57/1.61 % (20196)Termination phase: shuffling
% 2.57/1.61
% 2.57/1.61 % (20196)Memory used [KB]: 1407
% 2.57/1.61 % (20196)Time elapsed: 0.005 s
% 2.57/1.61 % (20196)Instructions burned: 6 (million)
% 2.57/1.61 % (20196)------------------------------
% 2.57/1.61 % (20196)------------------------------
% 2.57/1.62 % (20200)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_19838 for (2999ds/19Mi)
% 2.57/1.62 % (20200)Instruction limit reached!
% 2.57/1.62 % (20200)------------------------------
% 2.57/1.62 % (20200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.62 % (20200)Termination reason: Unknown
% 2.57/1.62 % (20200)Termination phase: shuffling
% 2.57/1.62
% 2.57/1.62 % (20200)Memory used [KB]: 1663
% 2.57/1.62 % (20200)Time elapsed: 0.008 s
% 2.57/1.62 % (20200)Instructions burned: 22 (million)
% 2.57/1.62 % (20200)------------------------------
% 2.57/1.62 % (20200)------------------------------
% 2.57/1.62 % (20199)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_19838 for (2999ds/779Mi)
% 2.57/1.63 % (20201)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/879Mi)
% 2.57/1.63 % (20202)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19838 for (2999ds/17Mi)
% 2.57/1.64 % (20202)Instruction limit reached!
% 2.57/1.64 % (20202)------------------------------
% 2.57/1.64 % (20202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.64 % (20202)Termination reason: Unknown
% 2.57/1.64 % (20202)Termination phase: shuffling
% 2.57/1.64
% 2.57/1.64 % (20202)Memory used [KB]: 2046
% 2.57/1.64 % (20202)Time elapsed: 0.008 s
% 2.57/1.64 % (20202)Instructions burned: 18 (million)
% 2.57/1.64 % (20202)------------------------------
% 2.57/1.64 % (20202)------------------------------
% 2.57/1.65 % (20203)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19838 for (2998ds/3Mi)
% 2.57/1.65 % (20203)Instruction limit reached!
% 2.57/1.65 % (20203)------------------------------
% 2.57/1.65 % (20203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.65 % (20203)Termination reason: Unknown
% 2.57/1.65 % (20203)Termination phase: shuffling
% 2.57/1.65
% 2.57/1.65 % (20203)Memory used [KB]: 1279
% 2.57/1.65 % (20203)Time elapsed: 0.003 s
% 2.57/1.65 % (20203)Instructions burned: 4 (million)
% 2.57/1.65 % (20203)------------------------------
% 2.57/1.65 % (20203)------------------------------
% 2.57/1.66 % (20204)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19838 for (2998ds/30Mi)
% 2.57/1.67 % (20204)Instruction limit reached!
% 2.57/1.67 % (20204)------------------------------
% 2.57/1.67 % (20204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.67 % (20204)Termination reason: Unknown
% 2.57/1.67 % (20204)Termination phase: Property scanning
% 2.57/1.67
% 2.57/1.67 % (20204)Memory used [KB]: 2174
% 2.57/1.67 % (20204)Time elapsed: 0.012 s
% 2.57/1.67 % (20204)Instructions burned: 31 (million)
% 2.57/1.67 % (20204)------------------------------
% 2.57/1.67 % (20204)------------------------------
% 2.57/1.68 % (20205)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19838 for (2998ds/127Mi)
% 2.57/1.68 % (20194)Refutation not found, incomplete strategy
% 2.57/1.68 % (20194)------------------------------
% 2.57/1.68 % (20194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.68 % (20194)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.68
% 2.57/1.68
% 2.57/1.68 % (20194)Memory used [KB]: 9338
% 2.57/1.68 % (20194)Time elapsed: 0.080 s
% 2.57/1.68 % (20194)Instructions burned: 206 (million)
% 2.57/1.68 % (20194)------------------------------
% 2.57/1.68 % (20194)------------------------------
% 2.57/1.70 % (20206)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19838 for (2998ds/100Mi)
% 2.57/1.72 % (20205)Instruction limit reached!
% 2.57/1.72 % (20205)------------------------------
% 2.57/1.72 % (20205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.72 % (20205)Termination reason: Unknown
% 2.57/1.72 % (20205)Termination phase: Property scanning
% 2.57/1.72
% 2.57/1.72 % (20205)Memory used [KB]: 4221
% 2.57/1.72 % (20205)Time elapsed: 0.040 s
% 2.57/1.72 % (20205)Instructions burned: 127 (million)
% 2.57/1.72 % (20205)------------------------------
% 2.57/1.72 % (20205)------------------------------
% 2.57/1.72 % (20198)Instruction limit reached!
% 2.57/1.72 % (20198)------------------------------
% 2.57/1.72 % (20198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.72 % (20198)Termination reason: Unknown
% 2.57/1.72 % (20198)Termination phase: Saturation
% 2.57/1.72
% 2.57/1.72 % (20198)Memory used [KB]: 10106
% 2.57/1.72 % (20198)Time elapsed: 0.116 s
% 2.57/1.72 % (20198)Instructions burned: 377 (million)
% 2.57/1.72 % (20198)------------------------------
% 2.57/1.72 % (20198)------------------------------
% 2.57/1.72 % (20206)Instruction limit reached!
% 2.57/1.72 % (20206)------------------------------
% 2.57/1.72 % (20206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.72 % (20206)Termination reason: Unknown
% 2.57/1.72 % (20206)Termination phase: Saturation
% 2.57/1.72
% 2.57/1.72 % (20206)Memory used [KB]: 6524
% 2.57/1.72 % (20206)Time elapsed: 0.028 s
% 2.57/1.72 % (20206)Instructions burned: 100 (million)
% 2.57/1.72 % (20206)------------------------------
% 2.57/1.72 % (20206)------------------------------
% 2.57/1.73 % (20207)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_19838 for (2998ds/3Mi)
% 2.57/1.73 % (20207)Instruction limit reached!
% 2.57/1.73 % (20207)------------------------------
% 2.57/1.73 % (20207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.73 % (20207)Termination reason: Unknown
% 2.57/1.73 % (20207)Termination phase: shuffling
% 2.57/1.73
% 2.57/1.73 % (20207)Memory used [KB]: 1279
% 2.57/1.73 % (20207)Time elapsed: 0.002 s
% 2.57/1.73 % (20207)Instructions burned: 4 (million)
% 2.57/1.73 % (20207)------------------------------
% 2.57/1.73 % (20207)------------------------------
% 2.57/1.73 % (20208)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_19838 for (2998ds/20Mi)
% 2.57/1.73 % (20209)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_19838 for (2998ds/86Mi)
% 2.57/1.74 % (20208)Instruction limit reached!
% 2.57/1.74 % (20208)------------------------------
% 2.57/1.74 % (20208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.74 % (20208)Termination reason: Unknown
% 2.57/1.74 % (20208)Termination phase: shuffling
% 2.57/1.74
% 2.57/1.74 % (20208)Memory used [KB]: 2046
% 2.57/1.74 % (20208)Time elapsed: 0.009 s
% 2.57/1.74 % (20208)Instructions burned: 21 (million)
% 2.57/1.74 % (20208)------------------------------
% 2.57/1.74 % (20208)------------------------------
% 2.57/1.74 % (20210)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_19838 for (2997ds/107Mi)
% 2.57/1.75 % (20211)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_19838 for (2997ds/39Mi)
% 2.57/1.76 % (20209)Instruction limit reached!
% 2.57/1.76 % (20209)------------------------------
% 2.57/1.76 % (20209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.76 % (20209)Termination reason: Unknown
% 2.57/1.76 % (20209)Termination phase: Preprocessing 3
% 2.57/1.76
% 2.57/1.76 % (20209)Memory used [KB]: 3965
% 2.57/1.76 % (20209)Time elapsed: 0.029 s
% 2.57/1.76 % (20209)Instructions burned: 87 (million)
% 2.57/1.76 % (20209)------------------------------
% 2.57/1.76 % (20209)------------------------------
% 2.57/1.76 % (20211)Instruction limit reached!
% 2.57/1.76 % (20211)------------------------------
% 2.57/1.76 % (20211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.76 % (20211)Termination reason: Unknown
% 2.57/1.76 % (20211)Termination phase: Property scanning
% 2.57/1.76
% 2.57/1.76 % (20211)Memory used [KB]: 1918
% 2.57/1.76 % (20211)Time elapsed: 0.013 s
% 2.57/1.76 % (20211)Instructions burned: 40 (million)
% 2.57/1.76 % (20211)------------------------------
% 2.57/1.76 % (20211)------------------------------
% 2.57/1.77 % (20212)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_19838 for (2997ds/448Mi)
% 2.57/1.77 % (20213)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_19838 for (2997ds/46Mi)
% 2.57/1.78 % (20210)Instruction limit reached!
% 2.57/1.78 % (20210)------------------------------
% 2.57/1.78 % (20210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.78 % (20210)Termination reason: Unknown
% 2.57/1.78 % (20210)Termination phase: Property scanning
% 2.57/1.78
% 2.57/1.78 % (20210)Memory used [KB]: 4221
% 2.57/1.78 % (20210)Time elapsed: 0.035 s
% 2.57/1.78 % (20210)Instructions burned: 108 (million)
% 2.57/1.78 % (20210)------------------------------
% 2.57/1.78 % (20210)------------------------------
% 2.57/1.79 % (20214)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_19838 for (2997ds/98Mi)
% 2.57/1.79 % (20213)Instruction limit reached!
% 2.57/1.79 % (20213)------------------------------
% 2.57/1.79 % (20213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.79 % (20213)Termination reason: Unknown
% 2.57/1.79 % (20213)Termination phase: Preprocessing 1
% 2.57/1.79
% 2.57/1.79 % (20213)Memory used [KB]: 2302
% 2.57/1.79 % (20213)Time elapsed: 0.016 s
% 2.57/1.79 % (20213)Instructions burned: 46 (million)
% 2.57/1.79 % (20213)------------------------------
% 2.57/1.79 % (20213)------------------------------
% 2.57/1.80 % (20215)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_19838 for (2997ds/507Mi)
% 2.57/1.81 % (20192)Instruction limit reached!
% 2.57/1.81 % (20192)------------------------------
% 2.57/1.81 % (20192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.81 % (20192)Termination reason: Unknown
% 2.57/1.81 % (20192)Termination phase: Saturation
% 2.57/1.81
% 2.57/1.81 % (20192)Memory used [KB]: 10362
% 2.57/1.81 % (20192)Time elapsed: 0.216 s
% 2.57/1.81 % (20192)Instructions burned: 710 (million)
% 2.57/1.81 % (20192)------------------------------
% 2.57/1.81 % (20192)------------------------------
% 2.57/1.81 % (20214)Instruction limit reached!
% 2.57/1.81 % (20214)------------------------------
% 2.57/1.81 % (20214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.81 % (20214)Termination reason: Unknown
% 2.57/1.81 % (20214)Termination phase: Saturation
% 2.57/1.81
% 2.57/1.81 % (20214)Memory used [KB]: 2046
% 2.57/1.81 % (20214)Time elapsed: 0.029 s
% 2.57/1.81 % (20214)Instructions burned: 101 (million)
% 2.57/1.81 % (20214)------------------------------
% 2.57/1.81 % (20214)------------------------------
% 2.57/1.82 % (20216)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_19838 for (2997ds/149Mi)
% 2.57/1.82 % (20183)Instruction limit reached!
% 2.57/1.82 % (20183)------------------------------
% 2.57/1.82 % (20183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.82 % (20183)Termination reason: Unknown
% 2.57/1.82 % (20183)Termination phase: Saturation
% 2.57/1.82
% 2.57/1.82 % (20183)Memory used [KB]: 8059
% 2.57/1.82 % (20183)Time elapsed: 0.263 s
% 2.57/1.82 % (20183)Instructions burned: 1042 (million)
% 2.57/1.82 % (20183)------------------------------
% 2.57/1.82 % (20183)------------------------------
% 2.57/1.82 % (20217)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/39Mi)
% 2.57/1.83 % (20218)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_19838 for (2996ds/6Mi)
% 2.57/1.83 % (20199)Instruction limit reached!
% 2.57/1.83 % (20199)------------------------------
% 2.57/1.83 % (20199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.83 % (20199)Termination reason: Unknown
% 2.57/1.83 % (20199)Termination phase: Saturation
% 2.57/1.83
% 2.57/1.83 % (20199)Memory used [KB]: 6780
% 2.57/1.83 % (20199)Time elapsed: 0.206 s
% 2.57/1.83 % (20199)Instructions burned: 779 (million)
% 2.57/1.83 % (20199)------------------------------
% 2.57/1.83 % (20199)------------------------------
% 2.57/1.83 % (20218)Instruction limit reached!
% 2.57/1.83 % (20218)------------------------------
% 2.57/1.83 % (20218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.83 % (20218)Termination reason: Unknown
% 2.57/1.83 % (20218)Termination phase: shuffling
% 2.57/1.83
% 2.57/1.83 % (20218)Memory used [KB]: 1407
% 2.57/1.83 % (20218)Time elapsed: 0.003 s
% 2.57/1.83 % (20218)Instructions burned: 7 (million)
% 2.57/1.83 % (20218)------------------------------
% 2.57/1.83 % (20218)------------------------------
% 2.57/1.84 % (20217)Instruction limit reached!
% 2.57/1.84 % (20217)------------------------------
% 2.57/1.84 % (20217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.84 % (20217)Termination reason: Unknown
% 2.57/1.84 % (20217)Termination phase: Naming
% 2.57/1.84
% 2.57/1.84 % (20217)Memory used [KB]: 2302
% 2.57/1.84 % (20217)Time elapsed: 0.015 s
% 2.57/1.84 % (20217)Instructions burned: 41 (million)
% 2.57/1.84 % (20217)------------------------------
% 2.57/1.84 % (20217)------------------------------
% 2.57/1.84 % (20219)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_19838 for (2996ds/1087Mi)
% 2.57/1.84 % (20220)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/47Mi)
% 2.57/1.85 % (20221)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_19838 for (2996ds/44Mi)
% 2.57/1.85 % (20220)Instruction limit reached!
% 2.57/1.85 % (20220)------------------------------
% 2.57/1.85 % (20220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.85 % (20220)Termination reason: Unknown
% 2.57/1.85 % (20220)Termination phase: Naming
% 2.57/1.85
% 2.57/1.85 % (20220)Memory used [KB]: 2686
% 2.57/1.85 % (20220)Time elapsed: 0.016 s
% 2.57/1.85 % (20220)Instructions burned: 48 (million)
% 2.57/1.85 % (20220)------------------------------
% 2.57/1.85 % (20220)------------------------------
% 2.57/1.86 % (20221)Instruction limit reached!
% 2.57/1.86 % (20221)------------------------------
% 2.57/1.86 % (20221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.86 % (20221)Termination reason: Unknown
% 2.57/1.86 % (20221)Termination phase: Property scanning
% 2.57/1.86
% 2.57/1.86 % (20221)Memory used [KB]: 1918
% 2.57/1.86 % (20221)Time elapsed: 0.014 s
% 2.57/1.86 % (20221)Instructions burned: 46 (million)
% 2.57/1.86 % (20221)------------------------------
% 2.57/1.86 % (20221)------------------------------
% 2.57/1.86 % (20216)Instruction limit reached!
% 2.57/1.86 % (20216)------------------------------
% 2.57/1.86 % (20216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.86 % (20216)Termination reason: Unknown
% 2.57/1.86 % (20216)Termination phase: Property scanning
% 2.57/1.86
% 2.57/1.86 % (20216)Memory used [KB]: 7931
% 2.57/1.86 % (20216)Time elapsed: 0.044 s
% 2.57/1.86 % (20216)Instructions burned: 151 (million)
% 2.57/1.86 % (20216)------------------------------
% 2.57/1.86 % (20216)------------------------------
% 2.57/1.86 % (20222)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_19838 for (2996ds/432Mi)
% 2.57/1.87 % (20223)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/62Mi)
% 2.57/1.87 % (20224)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_19838 for (2996ds/31Mi)
% 2.57/1.88 % (20224)Instruction limit reached!
% 2.57/1.88 % (20224)------------------------------
% 2.57/1.88 % (20224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.88 % (20224)Termination reason: Unknown
% 2.57/1.88 % (20224)Termination phase: Property scanning
% 2.57/1.88
% 2.57/1.88 % (20224)Memory used [KB]: 2174
% 2.57/1.88 % (20224)Time elapsed: 0.011 s
% 2.57/1.88 % (20224)Instructions burned: 34 (million)
% 2.57/1.88 % (20224)------------------------------
% 2.57/1.88 % (20224)------------------------------
% 2.57/1.88 % (20215)Refutation not found, incomplete strategy
% 2.57/1.88 % (20215)------------------------------
% 2.57/1.88 % (20215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.88 % (20215)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.88
% 2.57/1.88
% 2.57/1.88 % (20215)Memory used [KB]: 9978
% 2.57/1.88 % (20215)Time elapsed: 0.087 s
% 2.57/1.88 % (20215)Instructions burned: 283 (million)
% 2.57/1.88 % (20215)------------------------------
% 2.57/1.88 % (20215)------------------------------
% 2.57/1.89 % (20223)Instruction limit reached!
% 2.57/1.89 % (20223)------------------------------
% 2.57/1.89 % (20223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.89 % (20223)Termination reason: Unknown
% 2.57/1.89 % (20223)Termination phase: Property scanning
% 2.57/1.89
% 2.57/1.89 % (20223)Memory used [KB]: 2046
% 2.57/1.89 % (20223)Time elapsed: 0.018 s
% 2.57/1.89 % (20223)Instructions burned: 62 (million)
% 2.57/1.89 % (20223)------------------------------
% 2.57/1.89 % (20223)------------------------------
% 2.57/1.89 % (20225)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/96Mi)
% 2.57/1.89 % (20226)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_19838 for (2996ds/453Mi)
% 2.57/1.90 % (20227)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_19838 for (2996ds/71Mi)
% 2.57/1.90 % (20212)Instruction limit reached!
% 2.57/1.90 % (20212)------------------------------
% 2.57/1.90 % (20212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.90 % (20212)Termination reason: Unknown
% 2.57/1.90 % (20212)Termination phase: Saturation
% 2.57/1.90
% 2.57/1.90 % (20212)Memory used [KB]: 7419
% 2.57/1.90 % (20212)Time elapsed: 0.131 s
% 2.57/1.90 % (20212)Instructions burned: 449 (million)
% 2.57/1.90 % (20212)------------------------------
% 2.57/1.90 % (20212)------------------------------
% 2.57/1.91 % (20228)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/83Mi)
% 2.57/1.92 % (20225)Instruction limit reached!
% 2.57/1.92 % (20225)------------------------------
% 2.57/1.92 % (20225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.92 % (20225)Termination reason: Unknown
% 2.57/1.92 % (20225)Termination phase: Preprocessing 3
% 2.57/1.92
% 2.57/1.92 % (20225)Memory used [KB]: 4093
% 2.57/1.92 % (20225)Time elapsed: 0.029 s
% 2.57/1.92 % (20225)Instructions burned: 96 (million)
% 2.57/1.92 % (20225)------------------------------
% 2.57/1.92 % (20225)------------------------------
% 2.57/1.92 % (20227)Instruction limit reached!
% 2.57/1.92 % (20227)------------------------------
% 2.57/1.92 % (20227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.92 % (20227)Termination reason: Unknown
% 2.57/1.92 % (20227)Termination phase: Preprocessing 3
% 2.57/1.92
% 2.57/1.92 % (20227)Memory used [KB]: 3454
% 2.57/1.92 % (20227)Time elapsed: 0.025 s
% 2.57/1.92 % (20227)Instructions burned: 74 (million)
% 2.57/1.92 % (20227)------------------------------
% 2.57/1.92 % (20227)------------------------------
% 2.57/1.93 % (20201)Instruction limit reached!
% 2.57/1.93 % (20201)------------------------------
% 2.57/1.93 % (20201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.93 % (20201)Termination reason: Unknown
% 2.57/1.93 % (20201)Termination phase: Saturation
% 2.57/1.93
% 2.57/1.93 % (20201)Memory used [KB]: 11129
% 2.57/1.93 % (20201)Time elapsed: 0.297 s
% 2.57/1.93 % (20201)Instructions burned: 880 (million)
% 2.57/1.93 % (20201)------------------------------
% 2.57/1.93 % (20201)------------------------------
% 2.57/1.93 % (20229)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19838 for (2996ds/11Mi)
% 2.57/1.93 % (20229)Instruction limit reached!
% 2.57/1.93 % (20229)------------------------------
% 2.57/1.93 % (20229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.93 % (20229)Termination reason: Unknown
% 2.57/1.93 % (20229)Termination phase: shuffling
% 2.57/1.93
% 2.57/1.93 % (20229)Memory used [KB]: 1535
% 2.57/1.93 % (20229)Time elapsed: 0.004 s
% 2.57/1.93 % (20229)Instructions burned: 11 (million)
% 2.57/1.93 % (20229)------------------------------
% 2.57/1.93 % (20229)------------------------------
% 2.57/1.93 % (20230)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_19838 for (2996ds/41Mi)
% 2.57/1.93 % (20228)Instruction limit reached!
% 2.57/1.93 % (20228)------------------------------
% 2.57/1.93 % (20228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.93 % (20228)Termination reason: Unknown
% 2.57/1.93 % (20228)Termination phase: Saturation
% 2.57/1.93
% 2.57/1.93 % (20228)Memory used [KB]: 7164
% 2.57/1.93 % (20228)Time elapsed: 0.025 s
% 2.57/1.93 % (20228)Instructions burned: 83 (million)
% 2.57/1.93 % (20228)------------------------------
% 2.57/1.93 % (20228)------------------------------
% 2.57/1.94 % (20231)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19838 for (2995ds/6Mi)
% 2.57/1.94 % (20231)Instruction limit reached!
% 2.57/1.94 % (20231)------------------------------
% 2.57/1.94 % (20231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.94 % (20231)Termination reason: Unknown
% 2.57/1.94 % (20231)Termination phase: shuffling
% 2.57/1.94
% 2.57/1.94 % (20231)Memory used [KB]: 1407
% 2.57/1.94 % (20231)Time elapsed: 0.003 s
% 2.57/1.94 % (20231)Instructions burned: 7 (million)
% 2.57/1.94 % (20231)------------------------------
% 2.57/1.94 % (20231)------------------------------
% 2.57/1.94 % (20232)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19838 for (2995ds/150Mi)
% 2.57/1.94 % (20230)Instruction limit reached!
% 2.57/1.94 % (20230)------------------------------
% 2.57/1.94 % (20230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.94 % (20230)Termination reason: Unknown
% 2.57/1.94 % (20230)Termination phase: Property scanning
% 2.57/1.94
% 2.57/1.94 % (20230)Memory used [KB]: 1918
% 2.57/1.94 % (20230)Time elapsed: 0.013 s
% 2.57/1.94 % (20230)Instructions burned: 41 (million)
% 2.57/1.94 % (20230)------------------------------
% 2.57/1.94 % (20230)------------------------------
% 2.57/1.94 % (20233)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19838 for (2995ds/343Mi)
% 2.57/1.95 % (20234)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_19838 for (2995ds/109Mi)
% 2.57/1.95 % (20235)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_19838 for (2995ds/253Mi)
% 2.57/1.97 % (20222)Instruction limit reached!
% 2.57/1.97 % (20222)------------------------------
% 2.57/1.97 % (20222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.97 % (20222)Termination reason: Unknown
% 2.57/1.97 % (20222)Termination phase: Saturation
% 2.57/1.97
% 2.57/1.97 % (20222)Memory used [KB]: 2430
% 2.57/1.97 % (20222)Time elapsed: 0.111 s
% 2.57/1.97 % (20222)Instructions burned: 435 (million)
% 2.57/1.97 % (20222)------------------------------
% 2.57/1.97 % (20222)------------------------------
% 2.57/1.98 % (20232)Instruction limit reached!
% 2.57/1.98 % (20232)------------------------------
% 2.57/1.98 % (20232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.98 % (20232)Termination reason: Unknown
% 2.57/1.98 % (20232)Termination phase: Property scanning
% 2.57/1.98
% 2.57/1.98 % (20232)Memory used [KB]: 4221
% 2.57/1.98 % (20232)Time elapsed: 0.044 s
% 2.57/1.98 % (20232)Instructions burned: 153 (million)
% 2.57/1.98 % (20232)------------------------------
% 2.57/1.98 % (20232)------------------------------
% 2.57/1.98 % (20234)Instruction limit reached!
% 2.57/1.98 % (20234)------------------------------
% 2.57/1.98 % (20234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.98 % (20234)Termination reason: Unknown
% 2.57/1.98 % (20234)Termination phase: Property scanning
% 2.57/1.98
% 2.57/1.98 % (20234)Memory used [KB]: 4349
% 2.57/1.98 % (20234)Time elapsed: 0.036 s
% 2.57/1.98 % (20234)Instructions burned: 110 (million)
% 2.57/1.98 % (20234)------------------------------
% 2.57/1.98 % (20234)------------------------------
% 2.57/1.98 % (20236)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19838 for (2995ds/140Mi)
% 2.57/1.99 % (20237)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_19838 for (2995ds/614Mi)
% 2.57/2.00 % (20238)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_19838 for (2995ds/202Mi)
% 5.92/2.01 % (20226)Instruction limit reached!
% 5.92/2.01 % (20226)------------------------------
% 5.92/2.01 % (20226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.01 % (20226)Termination reason: Unknown
% 5.92/2.01 % (20226)Termination phase: Saturation
% 5.92/2.01
% 5.92/2.01 % (20226)Memory used [KB]: 6652
% 5.92/2.01 % (20226)Time elapsed: 0.122 s
% 5.92/2.01 % (20226)Instructions burned: 456 (million)
% 5.92/2.01 % (20226)------------------------------
% 5.92/2.01 % (20226)------------------------------
% 5.92/2.02 % (20236)Instruction limit reached!
% 5.92/2.02 % (20236)------------------------------
% 5.92/2.02 % (20236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.02 % (20236)Termination reason: Unknown
% 5.92/2.02 % (20236)Termination phase: Property scanning
% 5.92/2.02
% 5.92/2.02 % (20236)Memory used [KB]: 4221
% 5.92/2.02 % (20236)Time elapsed: 0.040 s
% 5.92/2.02 % (20236)Instructions burned: 142 (million)
% 5.92/2.02 % (20236)------------------------------
% 5.92/2.02 % (20236)------------------------------
% 5.92/2.02 % (20239)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_19838 for (2995ds/339Mi)
% 5.92/2.03 % (20235)Instruction limit reached!
% 5.92/2.03 % (20235)------------------------------
% 5.92/2.03 % (20235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.03 % (20235)Termination reason: Unknown
% 5.92/2.03 % (20235)Termination phase: Saturation
% 5.92/2.03
% 5.92/2.03 % (20235)Memory used [KB]: 7291
% 5.92/2.03 % (20235)Time elapsed: 0.079 s
% 5.92/2.03 % (20235)Instructions burned: 255 (million)
% 5.92/2.03 % (20235)------------------------------
% 5.92/2.03 % (20235)------------------------------
% 5.92/2.03 % (20240)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_19838 for (2995ds/283Mi)
% 5.92/2.04 % (20241)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19838 for (2994ds/134Mi)
% 5.92/2.05 % (20233)Instruction limit reached!
% 5.92/2.05 % (20233)------------------------------
% 5.92/2.05 % (20233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.05 % (20233)Termination reason: Unknown
% 5.92/2.05 % (20233)Termination phase: Saturation
% 5.92/2.05
% 5.92/2.05 % (20233)Memory used [KB]: 7803
% 5.92/2.05 % (20233)Time elapsed: 0.105 s
% 5.92/2.05 % (20233)Instructions burned: 346 (million)
% 5.92/2.05 % (20233)------------------------------
% 5.92/2.05 % (20233)------------------------------
% 5.92/2.06 % (20242)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19838 for (2994ds/298Mi)
% 5.92/2.08 % (20241)Instruction limit reached!
% 5.92/2.08 % (20241)------------------------------
% 5.92/2.08 % (20241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.08 % (20241)Termination reason: Unknown
% 5.92/2.08 % (20241)Termination phase: Property scanning
% 5.92/2.08
% 5.92/2.08 % (20241)Memory used [KB]: 4093
% 5.92/2.08 % (20241)Time elapsed: 0.038 s
% 5.92/2.08 % (20241)Instructions burned: 136 (million)
% 5.92/2.08 % (20241)------------------------------
% 5.92/2.08 % (20241)------------------------------
% 5.92/2.09 % (20243)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19838 for (2994ds/192Mi)
% 5.92/2.10 % (20238)Instruction limit reached!
% 5.92/2.10 % (20238)------------------------------
% 5.92/2.10 % (20238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.10 % (20238)Termination reason: Unknown
% 5.92/2.10 % (20238)Termination phase: Saturation
% 5.92/2.10
% 5.92/2.10 % (20238)Memory used [KB]: 4477
% 5.92/2.10 % (20238)Time elapsed: 0.100 s
% 5.92/2.10 % (20238)Instructions burned: 202 (million)
% 5.92/2.10 % (20238)------------------------------
% 5.92/2.10 % (20238)------------------------------
% 5.92/2.10 % (20240)Instruction limit reached!
% 5.92/2.10 % (20240)------------------------------
% 5.92/2.10 % (20240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.10 % (20240)Termination reason: Unknown
% 5.92/2.10 % (20240)Termination phase: Saturation
% 5.92/2.10
% 5.92/2.10 % (20240)Memory used [KB]: 6780
% 5.92/2.10 % (20240)Time elapsed: 0.094 s
% 5.92/2.10 % (20240)Instructions burned: 286 (million)
% 5.92/2.10 % (20240)------------------------------
% 5.92/2.10 % (20240)------------------------------
% 5.92/2.11 % (20244)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_19838 for (2994ds/258Mi)
% 6.44/2.11 % (20245)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_19838 for (2994ds/90Mi)
% 6.44/2.12 % (20239)Instruction limit reached!
% 6.44/2.12 % (20239)------------------------------
% 6.44/2.12 % (20239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.12 % (20239)Termination reason: Unknown
% 6.44/2.12 % (20239)Termination phase: Saturation
% 6.44/2.12
% 6.44/2.12 % (20239)Memory used [KB]: 9594
% 6.44/2.12 % (20239)Time elapsed: 0.094 s
% 6.44/2.12 % (20239)Instructions burned: 341 (million)
% 6.44/2.12 % (20239)------------------------------
% 6.44/2.12 % (20239)------------------------------
% 6.44/2.13 % (20246)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_19838 for (2993ds/231Mi)
% 6.44/2.14 % (20242)Instruction limit reached!
% 6.44/2.14 % (20242)------------------------------
% 6.44/2.14 % (20242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (20242)Termination reason: Unknown
% 6.44/2.14 % (20242)Termination phase: Saturation
% 6.44/2.14
% 6.44/2.14 % (20242)Memory used [KB]: 7164
% 6.44/2.14 % (20242)Time elapsed: 0.082 s
% 6.44/2.14 % (20242)Instructions burned: 299 (million)
% 6.44/2.14 % (20242)------------------------------
% 6.44/2.14 % (20242)------------------------------
% 6.44/2.14 % (20243)Instruction limit reached!
% 6.44/2.14 % (20243)------------------------------
% 6.44/2.14 % (20243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (20243)Termination reason: Unknown
% 6.44/2.14 % (20243)Termination phase: Property scanning
% 6.44/2.14
% 6.44/2.14 % (20243)Memory used [KB]: 4605
% 6.44/2.14 % (20243)Time elapsed: 0.054 s
% 6.44/2.14 % (20243)Instructions burned: 193 (million)
% 6.44/2.14 % (20243)------------------------------
% 6.44/2.14 % (20243)------------------------------
% 6.44/2.14 % (20245)Instruction limit reached!
% 6.44/2.14 % (20245)------------------------------
% 6.44/2.14 % (20245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (20245)Termination reason: Unknown
% 6.44/2.14 % (20245)Termination phase: Preprocessing 3
% 6.44/2.14
% 6.44/2.14 % (20245)Memory used [KB]: 4093
% 6.44/2.14 % (20245)Time elapsed: 0.028 s
% 6.44/2.14 % (20245)Instructions burned: 91 (million)
% 6.44/2.14 % (20245)------------------------------
% 6.44/2.14 % (20245)------------------------------
% 6.44/2.15 % (20247)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_19838 for (2993ds/458Mi)
% 6.44/2.15 % (20248)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_19838 for (2993ds/31Mi)
% 6.44/2.15 % (20249)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_19838 for (2993ds/297Mi)
% 6.44/2.16 % (20248)Instruction limit reached!
% 6.44/2.16 % (20248)------------------------------
% 6.44/2.16 % (20248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.16 % (20248)Termination reason: Unknown
% 6.44/2.16 % (20248)Termination phase: Property scanning
% 6.44/2.16
% 6.44/2.16 % (20248)Memory used [KB]: 2174
% 6.44/2.16 % (20248)Time elapsed: 0.011 s
% 6.44/2.16 % (20248)Instructions burned: 33 (million)
% 6.44/2.16 % (20248)------------------------------
% 6.44/2.16 % (20248)------------------------------
% 6.44/2.17 % (20250)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_19838 for (2993ds/987Mi)
% 6.44/2.17 % (20237)Instruction limit reached!
% 6.44/2.17 % (20237)------------------------------
% 6.44/2.17 % (20237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.17 % (20237)Termination reason: Unknown
% 6.44/2.17 % (20237)Termination phase: Saturation
% 6.44/2.17
% 6.44/2.17 % (20237)Memory used [KB]: 12537
% 6.44/2.17 % (20237)Time elapsed: 0.202 s
% 6.44/2.17 % (20237)Instructions burned: 615 (million)
% 6.44/2.17 % (20237)------------------------------
% 6.44/2.17 % (20237)------------------------------
% 6.44/2.18 % (20244)Instruction limit reached!
% 6.44/2.18 % (20244)------------------------------
% 6.44/2.18 % (20244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (20244)Termination reason: Unknown
% 6.44/2.18 % (20244)Termination phase: Property scanning
% 6.44/2.18
% 6.44/2.18 % (20244)Memory used [KB]: 7931
% 6.44/2.18 % (20244)Time elapsed: 0.068 s
% 6.44/2.18 % (20244)Instructions burned: 258 (million)
% 6.44/2.18 % (20244)------------------------------
% 6.44/2.18 % (20244)------------------------------
% 6.44/2.18 % (20251)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_19838 for (2993ds/182Mi)
% 6.44/2.18 % (20246)Instruction limit reached!
% 6.44/2.18 % (20246)------------------------------
% 6.44/2.18 % (20246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (20246)Termination reason: Unknown
% 6.44/2.18 % (20246)Termination phase: Saturation
% 6.44/2.18
% 6.44/2.18 % (20246)Memory used [KB]: 7036
% 6.44/2.18 % (20246)Time elapsed: 0.059 s
% 6.44/2.18 % (20246)Instructions burned: 232 (million)
% 6.44/2.18 % (20246)------------------------------
% 6.44/2.18 % (20246)------------------------------
% 6.44/2.19 % (20252)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_19838 for (2993ds/182Mi)
% 6.44/2.19 % (20253)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_19838 for (2993ds/154Mi)
% 6.44/2.20 % (20219)Instruction limit reached!
% 6.44/2.20 % (20219)------------------------------
% 6.44/2.20 % (20219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.20 % (20219)Termination reason: Unknown
% 6.44/2.20 % (20219)Termination phase: Saturation
% 6.44/2.20
% 6.44/2.20 % (20219)Memory used [KB]: 12281
% 6.44/2.20 % (20219)Time elapsed: 0.357 s
% 6.44/2.20 % (20219)Instructions burned: 1087 (million)
% 6.44/2.20 % (20219)------------------------------
% 6.44/2.20 % (20219)------------------------------
% 7.08/2.21 % (20254)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_19838 for (2993ds/79Mi)
% 7.08/2.23 % (20254)Instruction limit reached!
% 7.08/2.23 % (20254)------------------------------
% 7.08/2.23 % (20254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (20254)Termination reason: Unknown
% 7.08/2.23 % (20254)Termination phase: Preprocessing 3
% 7.08/2.23
% 7.08/2.23 % (20254)Memory used [KB]: 3582
% 7.08/2.23 % (20254)Time elapsed: 0.024 s
% 7.08/2.23 % (20254)Instructions burned: 79 (million)
% 7.08/2.23 % (20254)------------------------------
% 7.08/2.23 % (20254)------------------------------
% 7.08/2.23 % (20249)Instruction limit reached!
% 7.08/2.23 % (20249)------------------------------
% 7.08/2.23 % (20249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (20249)Termination reason: Unknown
% 7.08/2.23 % (20249)Termination phase: Saturation
% 7.08/2.23
% 7.08/2.23 % (20249)Memory used [KB]: 7036
% 7.08/2.23 % (20249)Time elapsed: 0.081 s
% 7.08/2.23 % (20249)Instructions burned: 297 (million)
% 7.08/2.23 % (20249)------------------------------
% 7.08/2.23 % (20249)------------------------------
% 7.08/2.23 % (20253)Instruction limit reached!
% 7.08/2.23 % (20253)------------------------------
% 7.08/2.23 % (20253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (20253)Termination reason: Unknown
% 7.08/2.23 % (20253)Termination phase: Saturation
% 7.08/2.23
% 7.08/2.23 % (20253)Memory used [KB]: 2430
% 7.08/2.23 % (20253)Time elapsed: 0.040 s
% 7.08/2.23 % (20253)Instructions burned: 155 (million)
% 7.08/2.23 % (20253)------------------------------
% 7.08/2.23 % (20253)------------------------------
% 7.08/2.23 % (20251)Instruction limit reached!
% 7.08/2.23 % (20251)------------------------------
% 7.08/2.23 % (20251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.23 % (20251)Termination reason: Unknown
% 7.08/2.23 % (20251)Termination phase: Property scanning
% 7.08/2.23
% 7.08/2.23 % (20251)Memory used [KB]: 7803
% 7.08/2.23 % (20251)Time elapsed: 0.051 s
% 7.08/2.23 % (20251)Instructions burned: 184 (million)
% 7.08/2.23 % (20251)------------------------------
% 7.08/2.23 % (20251)------------------------------
% 7.08/2.24 % (20255)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_19838 for (2992ds/216Mi)
% 7.08/2.24 % (20252)Instruction limit reached!
% 7.08/2.24 % (20252)------------------------------
% 7.08/2.24 % (20252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.24 % (20252)Termination reason: Unknown
% 7.08/2.24 % (20252)Termination phase: Saturation
% 7.08/2.24
% 7.08/2.24 % (20252)Memory used [KB]: 8955
% 7.08/2.24 % (20252)Time elapsed: 0.052 s
% 7.08/2.24 % (20252)Instructions burned: 182 (million)
% 7.08/2.24 % (20252)------------------------------
% 7.08/2.24 % (20252)------------------------------
% 7.08/2.24 % (20256)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19838 for (2992ds/114Mi)
% 7.08/2.24 % (20257)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_19838 for (2992ds/922Mi)
% 7.08/2.25 % (20259)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_19838 for (2992ds/164Mi)
% 7.08/2.25 % (20258)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_19838 for (2992ds/182Mi)
% 7.08/2.27 % (20256)Instruction limit reached!
% 7.08/2.27 % (20256)------------------------------
% 7.08/2.27 % (20256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.27 % (20256)Termination reason: Unknown
% 7.08/2.27 % (20256)Termination phase: Property scanning
% 7.08/2.27
% 7.08/2.27 % (20256)Memory used [KB]: 4221
% 7.08/2.27 % (20256)Time elapsed: 0.035 s
% 7.08/2.27 % (20256)Instructions burned: 115 (million)
% 7.08/2.27 % (20256)------------------------------
% 7.08/2.27 % (20256)------------------------------
% 7.08/2.28 % (20247)Instruction limit reached!
% 7.08/2.28 % (20247)------------------------------
% 7.08/2.28 % (20247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.28 % (20247)Termination reason: Unknown
% 7.08/2.28 % (20247)Termination phase: Saturation
% 7.08/2.28
% 7.08/2.28 % (20247)Memory used [KB]: 10874
% 7.08/2.28 % (20247)Time elapsed: 0.135 s
% 7.08/2.28 % (20247)Instructions burned: 459 (million)
% 7.08/2.28 % (20247)------------------------------
% 7.08/2.28 % (20247)------------------------------
% 7.08/2.28 % (20260)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_19838 for (2992ds/50Mi)
% 7.08/2.29 % (20261)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19838 for (2992ds/368Mi)
% 7.08/2.29 % (20259)Instruction limit reached!
% 7.08/2.29 % (20259)------------------------------
% 7.08/2.29 % (20259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.29 % (20259)Termination reason: Unknown
% 7.08/2.29 % (20259)Termination phase: Saturation
% 7.08/2.29
% 7.08/2.29 % (20259)Memory used [KB]: 2302
% 7.08/2.29 % (20259)Time elapsed: 0.048 s
% 7.08/2.29 % (20259)Instructions burned: 165 (million)
% 7.08/2.29 % (20259)------------------------------
% 7.08/2.29 % (20259)------------------------------
% 7.60/2.30 % (20260)Instruction limit reached!
% 7.60/2.30 % (20260)------------------------------
% 7.60/2.30 % (20260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.30 % (20260)Termination reason: Unknown
% 7.60/2.30 % (20260)Termination phase: Property scanning
% 7.60/2.30
% 7.60/2.30 % (20260)Memory used [KB]: 1918
% 7.60/2.30 % (20260)Time elapsed: 0.015 s
% 7.60/2.30 % (20260)Instructions burned: 51 (million)
% 7.60/2.30 % (20260)------------------------------
% 7.60/2.30 % (20260)------------------------------
% 7.60/2.30 % (20255)Instruction limit reached!
% 7.60/2.30 % (20255)------------------------------
% 7.60/2.30 % (20255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.30 % (20255)Termination reason: Unknown
% 7.60/2.30 % (20255)Termination phase: Saturation
% 7.60/2.30
% 7.60/2.30 % (20255)Memory used [KB]: 6780
% 7.60/2.30 % (20255)Time elapsed: 0.064 s
% 7.60/2.30 % (20255)Instructions burned: 216 (million)
% 7.60/2.30 % (20255)------------------------------
% 7.60/2.30 % (20255)------------------------------
% 7.60/2.30 % (20262)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_19838 for (2992ds/1021Mi)
% 7.60/2.31 % (20263)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_19838 for (2992ds/267Mi)
% 7.60/2.31 % (20264)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_19838 for (2992ds/204Mi)
% 7.60/2.31 % (20258)Instruction limit reached!
% 7.60/2.31 % (20258)------------------------------
% 7.60/2.31 % (20258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (20258)Termination reason: Unknown
% 7.60/2.31 % (20258)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (20258)Memory used [KB]: 6652
% 7.60/2.31 % (20258)Time elapsed: 0.063 s
% 7.60/2.31 % (20258)Instructions burned: 185 (million)
% 7.60/2.31 % (20258)------------------------------
% 7.60/2.31 % (20258)------------------------------
% 7.60/2.32 % (20265)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_19838 for (2992ds/26Mi)
% 7.60/2.33 % (20265)Instruction limit reached!
% 7.60/2.33 % (20265)------------------------------
% 7.60/2.33 % (20265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.33 % (20265)Termination reason: Unknown
% 7.60/2.33 % (20265)Termination phase: shuffling
% 7.60/2.33
% 7.60/2.33 % (20265)Memory used [KB]: 1791
% 7.60/2.33 % (20265)Time elapsed: 0.009 s
% 7.60/2.33 % (20265)Instructions burned: 27 (million)
% 7.60/2.33 % (20265)------------------------------
% 7.60/2.33 % (20265)------------------------------
% 7.60/2.34 % (20266)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_19838 for (2991ds/53Mi)
% 7.60/2.35 % (20266)Instruction limit reached!
% 7.60/2.35 % (20266)------------------------------
% 7.60/2.35 % (20266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.35 % (20266)Termination reason: Unknown
% 7.60/2.35 % (20266)Termination phase: Property scanning
% 7.60/2.35
% 7.60/2.35 % (20266)Memory used [KB]: 1918
% 7.60/2.35 % (20266)Time elapsed: 0.015 s
% 7.60/2.35 % (20266)Instructions burned: 55 (million)
% 7.60/2.35 % (20266)------------------------------
% 7.60/2.35 % (20266)------------------------------
% 7.60/2.36 % (20267)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_19838 for (2991ds/4436Mi)
% 7.60/2.37 % (20264)Instruction limit reached!
% 7.60/2.37 % (20264)------------------------------
% 7.60/2.37 % (20264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (20264)Termination reason: Unknown
% 7.60/2.37 % (20264)Termination phase: Property scanning
% 7.60/2.37
% 7.60/2.37 % (20264)Memory used [KB]: 4605
% 7.60/2.37 % (20264)Time elapsed: 0.057 s
% 7.60/2.37 % (20264)Instructions burned: 207 (million)
% 7.60/2.37 % (20264)------------------------------
% 7.60/2.37 % (20264)------------------------------
% 7.60/2.37 % (20263)Instruction limit reached!
% 7.60/2.37 % (20263)------------------------------
% 7.60/2.37 % (20263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (20263)Termination reason: Unknown
% 7.60/2.37 % (20263)Termination phase: Saturation
% 7.60/2.37
% 7.60/2.37 % (20263)Memory used [KB]: 7419
% 7.60/2.37 % (20263)Time elapsed: 0.068 s
% 7.60/2.37 % (20263)Instructions burned: 267 (million)
% 7.60/2.37 % (20263)------------------------------
% 7.60/2.37 % (20263)------------------------------
% 7.60/2.38 % (20268)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_19838 for (2991ds/1539Mi)
% 7.60/2.38 % (20269)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_19838 for (2991ds/408Mi)
% 7.60/2.40 % (20261)Instruction limit reached!
% 7.60/2.40 % (20261)------------------------------
% 7.60/2.40 % (20261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.40 % (20261)Termination reason: Unknown
% 7.60/2.40 % (20261)Termination phase: Saturation
% 7.60/2.40
% 7.60/2.40 % (20261)Memory used [KB]: 11641
% 7.60/2.40 % (20261)Time elapsed: 0.106 s
% 7.60/2.40 % (20261)Instructions burned: 371 (million)
% 7.60/2.40 % (20261)------------------------------
% 7.60/2.40 % (20261)------------------------------
% 7.96/2.41 % (20270)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_19838 for (2991ds/5205Mi)
% 7.96/2.41 % (20250)Instruction limit reached!
% 7.96/2.41 % (20250)------------------------------
% 7.96/2.41 % (20250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.41 % (20250)Termination reason: Unknown
% 7.96/2.41 % (20250)Termination phase: Saturation
% 7.96/2.41
% 7.96/2.41 % (20250)Memory used [KB]: 7931
% 7.96/2.41 % (20250)Time elapsed: 0.247 s
% 7.96/2.41 % (20250)Instructions burned: 989 (million)
% 7.96/2.41 % (20250)------------------------------
% 7.96/2.41 % (20250)------------------------------
% 7.96/2.42 % (20271)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_19838 for (2991ds/1913Mi)
% 8.35/2.50 % (20269)Instruction limit reached!
% 8.35/2.50 % (20269)------------------------------
% 8.35/2.50 % (20269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.50 % (20269)Termination reason: Unknown
% 8.35/2.50 % (20269)Termination phase: Saturation
% 8.35/2.50
% 8.35/2.50 % (20269)Memory used [KB]: 11001
% 8.35/2.50 % (20269)Time elapsed: 0.121 s
% 8.35/2.50 % (20269)Instructions burned: 410 (million)
% 8.35/2.50 % (20269)------------------------------
% 8.35/2.50 % (20269)------------------------------
% 8.35/2.51 % (20272)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_19838 for (2990ds/4350Mi)
% 8.35/2.52 % (20257)Instruction limit reached!
% 8.35/2.52 % (20257)------------------------------
% 8.35/2.52 % (20257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.52 % (20257)Termination reason: Unknown
% 8.35/2.52 % (20257)Termination phase: Saturation
% 8.35/2.52
% 8.35/2.52 % (20257)Memory used [KB]: 13048
% 8.35/2.52 % (20257)Time elapsed: 0.284 s
% 8.35/2.52 % (20257)Instructions burned: 922 (million)
% 8.35/2.52 % (20257)------------------------------
% 8.35/2.52 % (20257)------------------------------
% 8.35/2.53 % (20273)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_19838 for (2989ds/68Mi)
% 8.35/2.55 % (20273)Instruction limit reached!
% 8.35/2.55 % (20273)------------------------------
% 8.35/2.55 % (20273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.55 % (20273)Termination reason: Unknown
% 8.35/2.55 % (20273)Termination phase: Preprocessing 3
% 8.35/2.55
% 8.35/2.55 % (20273)Memory used [KB]: 3070
% 8.35/2.55 % (20273)Time elapsed: 0.021 s
% 8.35/2.55 % (20273)Instructions burned: 69 (million)
% 8.35/2.55 % (20273)------------------------------
% 8.35/2.55 % (20273)------------------------------
% 8.35/2.56 % (20274)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_19838 for (2989ds/358Mi)
% 8.79/2.61 % (20262)Instruction limit reached!
% 8.79/2.61 % (20262)------------------------------
% 8.79/2.61 % (20262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.61 % (20262)Termination reason: Unknown
% 8.79/2.61 % (20262)Termination phase: Saturation
% 8.79/2.61
% 8.79/2.61 % (20262)Memory used [KB]: 12537
% 8.79/2.61 % (20262)Time elapsed: 0.310 s
% 8.79/2.61 % (20262)Instructions burned: 1023 (million)
% 8.79/2.61 % (20262)------------------------------
% 8.79/2.61 % (20262)------------------------------
% 8.79/2.62 % (20275)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_19838 for (2989ds/31Mi)
% 8.79/2.63 % (20275)Instruction limit reached!
% 8.79/2.63 % (20275)------------------------------
% 8.79/2.63 % (20275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.63 % (20275)Termination reason: Unknown
% 8.79/2.63 % (20275)Termination phase: Property scanning
% 8.79/2.63
% 8.79/2.63 % (20275)Memory used [KB]: 2174
% 8.79/2.63 % (20275)Time elapsed: 0.011 s
% 8.79/2.63 % (20275)Instructions burned: 33 (million)
% 8.79/2.63 % (20275)------------------------------
% 8.79/2.63 % (20275)------------------------------
% 8.79/2.64 % (20276)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19838 for (2988ds/279Mi)
% 8.79/2.67 % (20274)Instruction limit reached!
% 8.79/2.67 % (20274)------------------------------
% 8.79/2.67 % (20274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.67 % (20274)Termination reason: Unknown
% 8.79/2.67 % (20274)Termination phase: Saturation
% 8.79/2.67
% 8.79/2.67 % (20274)Memory used [KB]: 9594
% 8.79/2.67 % (20274)Time elapsed: 0.103 s
% 8.79/2.67 % (20274)Instructions burned: 358 (million)
% 8.79/2.67 % (20274)------------------------------
% 8.79/2.67 % (20274)------------------------------
% 8.79/2.68 % (20277)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19838 for (2988ds/258Mi)
% 9.24/2.72 % (20276)Instruction limit reached!
% 9.24/2.72 % (20276)------------------------------
% 9.24/2.72 % (20276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.72 % (20276)Termination reason: Unknown
% 9.24/2.72 % (20276)Termination phase: Saturation
% 9.24/2.72
% 9.24/2.72 % (20276)Memory used [KB]: 8059
% 9.24/2.72 % (20276)Time elapsed: 0.076 s
% 9.24/2.72 % (20276)Instructions burned: 279 (million)
% 9.24/2.72 % (20276)------------------------------
% 9.24/2.72 % (20276)------------------------------
% 9.24/2.73 % (20278)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_19838 for (2988ds/26Mi)
% 9.24/2.73 % (20278)Instruction limit reached!
% 9.24/2.73 % (20278)------------------------------
% 9.24/2.73 % (20278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.73 % (20278)Termination reason: Unknown
% 9.24/2.73 % (20278)Termination phase: shuffling
% 9.24/2.73
% 9.24/2.73 % (20278)Memory used [KB]: 1791
% 9.24/2.73 % (20278)Time elapsed: 0.008 s
% 9.24/2.73 % (20278)Instructions burned: 26 (million)
% 9.24/2.73 % (20278)------------------------------
% 9.24/2.73 % (20278)------------------------------
% 9.24/2.74 % (20279)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_19838 for (2987ds/995Mi)
% 9.24/2.75 % (20277)Instruction limit reached!
% 9.24/2.75 % (20277)------------------------------
% 9.24/2.75 % (20277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.75 % (20277)Termination reason: Unknown
% 9.24/2.75 % (20277)Termination phase: Saturation
% 9.24/2.75
% 9.24/2.75 % (20277)Memory used [KB]: 9594
% 9.24/2.75 % (20277)Time elapsed: 0.077 s
% 9.24/2.75 % (20277)Instructions burned: 259 (million)
% 9.24/2.75 % (20277)------------------------------
% 9.24/2.75 % (20277)------------------------------
% 9.24/2.76 % (20280)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_19838 for (2987ds/373Mi)
% 9.44/2.82 % (20268)Instruction limit reached!
% 9.44/2.82 % (20268)------------------------------
% 9.44/2.82 % (20268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.82 % (20268)Termination reason: Unknown
% 9.44/2.82 % (20268)Termination phase: Saturation
% 9.44/2.82
% 9.44/2.82 % (20268)Memory used [KB]: 11513
% 9.44/2.82 % (20268)Time elapsed: 0.447 s
% 9.44/2.82 % (20268)Instructions burned: 1541 (million)
% 9.44/2.82 % (20268)------------------------------
% 9.44/2.82 % (20268)------------------------------
% 9.44/2.83 % (20281)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_19838 for (2987ds/253Mi)
% 9.44/2.87 % (20280)Instruction limit reached!
% 9.44/2.87 % (20280)------------------------------
% 9.44/2.87 % (20280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.87 % (20280)Termination reason: Unknown
% 9.44/2.87 % (20280)Termination phase: Saturation
% 9.44/2.87
% 9.44/2.87 % (20280)Memory used [KB]: 10490
% 9.44/2.87 % (20280)Time elapsed: 0.131 s
% 9.44/2.87 % (20280)Instructions burned: 376 (million)
% 9.44/2.87 % (20280)------------------------------
% 9.44/2.87 % (20280)------------------------------
% 9.44/2.88 % (20282)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_19838 for (2986ds/832Mi)
% 10.02/2.90 % (20281)Instruction limit reached!
% 10.02/2.90 % (20281)------------------------------
% 10.02/2.90 % (20281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.90 % (20281)Termination reason: Unknown
% 10.02/2.90 % (20281)Termination phase: Saturation
% 10.02/2.90
% 10.02/2.90 % (20281)Memory used [KB]: 6780
% 10.02/2.90 % (20281)Time elapsed: 0.065 s
% 10.02/2.90 % (20281)Instructions burned: 256 (million)
% 10.02/2.90 % (20281)------------------------------
% 10.02/2.90 % (20281)------------------------------
% 10.02/2.91 % (20283)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_19838 for (2986ds/668Mi)
% 10.02/2.96 % (20282)Refutation not found, incomplete strategy
% 10.02/2.96 % (20282)------------------------------
% 10.02/2.96 % (20282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.96 % (20282)Termination reason: Refutation not found, incomplete strategy
% 10.02/2.96
% 10.02/2.96
% 10.02/2.96 % (20282)Memory used [KB]: 9850
% 10.02/2.96 % (20282)Time elapsed: 0.076 s
% 10.02/2.96 % (20282)Instructions burned: 272 (million)
% 10.02/2.96 % (20282)------------------------------
% 10.02/2.96 % (20282)------------------------------
% 10.02/2.97 % (20284)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_19838 for (2985ds/40Mi)
% 10.02/2.98 % (20284)Instruction limit reached!
% 10.02/2.98 % (20284)------------------------------
% 10.02/2.98 % (20284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.98 % (20284)Termination reason: Unknown
% 10.02/2.98 % (20284)Termination phase: Property scanning
% 10.02/2.98
% 10.02/2.98 % (20284)Memory used [KB]: 1918
% 10.02/2.98 % (20284)Time elapsed: 0.012 s
% 10.02/2.98 % (20284)Instructions burned: 41 (million)
% 10.02/2.98 % (20284)------------------------------
% 10.02/2.98 % (20284)------------------------------
% 10.02/2.99 % (20285)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_19838 for (2985ds/294Mi)
% 10.02/2.99 % (20279)Instruction limit reached!
% 10.02/2.99 % (20279)------------------------------
% 10.02/2.99 % (20279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.99 % (20279)Termination reason: Unknown
% 10.02/2.99 % (20279)Termination phase: Saturation
% 10.02/2.99
% 10.02/2.99 % (20279)Memory used [KB]: 6652
% 10.02/2.99 % (20279)Time elapsed: 0.244 s
% 10.02/2.99 % (20279)Instructions burned: 995 (million)
% 10.02/2.99 % (20279)------------------------------
% 10.02/2.99 % (20279)------------------------------
% 10.02/3.00 % (20286)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_19838 for (2985ds/187Mi)
% 10.02/3.01 % (20271)Instruction limit reached!
% 10.02/3.01 % (20271)------------------------------
% 10.02/3.01 % (20271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/3.01 % (20271)Termination reason: Unknown
% 10.02/3.01 % (20271)Termination phase: Saturation
% 10.02/3.01
% 10.02/3.01 % (20271)Memory used [KB]: 6524
% 10.02/3.01 % (20271)Time elapsed: 0.583 s
% 10.02/3.01 % (20271)Instructions burned: 1914 (million)
% 10.02/3.01 % (20271)------------------------------
% 10.02/3.01 % (20271)------------------------------
% 12.95/3.02 % (20287)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_19838 for (2985ds/371Mi)
% 12.95/3.05 % (20286)Instruction limit reached!
% 12.95/3.05 % (20286)------------------------------
% 12.95/3.05 % (20286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.05 % (20286)Termination reason: Unknown
% 12.95/3.05 % (20286)Termination phase: Property scanning
% 12.95/3.05
% 12.95/3.05 % (20286)Memory used [KB]: 4477
% 12.95/3.05 % (20286)Time elapsed: 0.051 s
% 12.95/3.05 % (20286)Instructions burned: 190 (million)
% 12.95/3.05 % (20286)------------------------------
% 12.95/3.05 % (20286)------------------------------
% 12.95/3.06 % (20288)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_19838 for (2984ds/1827Mi)
% 12.95/3.06 % (20285)Instruction limit reached!
% 12.95/3.06 % (20285)------------------------------
% 12.95/3.06 % (20285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.06 % (20285)Termination reason: Unknown
% 12.95/3.06 % (20285)Termination phase: Saturation
% 12.95/3.06
% 12.95/3.06 % (20285)Memory used [KB]: 7675
% 12.95/3.06 % (20285)Time elapsed: 0.073 s
% 12.95/3.06 % (20285)Instructions burned: 294 (million)
% 12.95/3.06 % (20285)------------------------------
% 12.95/3.06 % (20285)------------------------------
% 12.95/3.07 % (20283)Instruction limit reached!
% 12.95/3.07 % (20283)------------------------------
% 12.95/3.07 % (20283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.07 % (20283)Termination reason: Unknown
% 12.95/3.07 % (20283)Termination phase: Saturation
% 12.95/3.07
% 12.95/3.07 % (20283)Memory used [KB]: 11129
% 12.95/3.07 % (20283)Time elapsed: 0.163 s
% 12.95/3.07 % (20283)Instructions burned: 669 (million)
% 12.95/3.07 % (20283)------------------------------
% 12.95/3.07 % (20283)------------------------------
% 12.95/3.07 % (20289)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_19838 for (2984ds/70Mi)
% 12.95/3.08 % (20290)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_19838 for (2984ds/316Mi)
% 12.95/3.09 % (20289)Instruction limit reached!
% 12.95/3.09 % (20289)------------------------------
% 12.95/3.09 % (20289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.09 % (20289)Termination reason: Unknown
% 12.95/3.09 % (20289)Termination phase: Property scanning
% 12.95/3.09
% 12.95/3.09 % (20289)Memory used [KB]: 1918
% 12.95/3.09 % (20289)Time elapsed: 0.020 s
% 12.95/3.09 % (20289)Instructions burned: 73 (million)
% 12.95/3.09 % (20289)------------------------------
% 12.95/3.09 % (20289)------------------------------
% 12.95/3.10 % (20291)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_19838 for (2984ds/932Mi)
% 13.44/3.13 % (20287)Instruction limit reached!
% 13.44/3.13 % (20287)------------------------------
% 13.44/3.13 % (20287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.13 % (20287)Termination reason: Unknown
% 13.44/3.13 % (20287)Termination phase: Saturation
% 13.44/3.13
% 13.44/3.13 % (20287)Memory used [KB]: 8187
% 13.44/3.13 % (20287)Time elapsed: 0.114 s
% 13.44/3.13 % (20287)Instructions burned: 372 (million)
% 13.44/3.13 % (20287)------------------------------
% 13.44/3.13 % (20287)------------------------------
% 13.44/3.14 % (20292)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_19838 for (2983ds/4714Mi)
% 13.44/3.16 % (20290)Instruction limit reached!
% 13.44/3.16 % (20290)------------------------------
% 13.44/3.16 % (20290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.16 % (20290)Termination reason: Unknown
% 13.44/3.16 % (20290)Termination phase: Saturation
% 13.44/3.16
% 13.44/3.16 % (20290)Memory used [KB]: 7036
% 13.44/3.16 % (20290)Time elapsed: 0.088 s
% 13.44/3.16 % (20290)Instructions burned: 317 (million)
% 13.44/3.16 % (20290)------------------------------
% 13.44/3.16 % (20290)------------------------------
% 13.44/3.17 % (20293)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_19838 for (2983ds/8250Mi)
% 14.21/3.33 % (20291)Instruction limit reached!
% 14.21/3.33 % (20291)------------------------------
% 14.21/3.33 % (20291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.33 % (20291)Termination reason: Unknown
% 14.21/3.33 % (20291)Termination phase: Saturation
% 14.21/3.33
% 14.21/3.33 % (20291)Memory used [KB]: 8059
% 14.21/3.33 % (20291)Time elapsed: 0.235 s
% 14.21/3.33 % (20291)Instructions burned: 934 (million)
% 14.21/3.33 % (20291)------------------------------
% 14.21/3.33 % (20291)------------------------------
% 14.21/3.34 % (20294)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_19838 for (2981ds/770Mi)
% 14.21/3.35 % (20294)Refutation not found, incomplete strategy
% 14.21/3.35 % (20294)------------------------------
% 14.21/3.35 % (20294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.35 % (20294)Termination reason: Refutation not found, incomplete strategy
% 14.21/3.35
% 14.21/3.35
% 14.21/3.35 % (20294)Memory used [KB]: 6780
% 14.21/3.35 % (20294)Time elapsed: 0.014 s
% 14.21/3.35 % (20294)Instructions burned: 43 (million)
% 14.21/3.35 % (20294)------------------------------
% 14.21/3.35 % (20294)------------------------------
% 14.21/3.36 % (20295)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_19838 for (2981ds/794Mi)
% 15.38/3.61 % (20295)Instruction limit reached!
% 15.38/3.61 % (20295)------------------------------
% 15.38/3.61 % (20295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.38/3.61 % (20295)Termination reason: Unknown
% 15.38/3.61 % (20295)Termination phase: Saturation
% 15.38/3.61
% 15.38/3.61 % (20295)Memory used [KB]: 7547
% 15.38/3.61 % (20295)Time elapsed: 0.247 s
% 15.38/3.61 % (20295)Instructions burned: 796 (million)
% 15.38/3.61 % (20295)------------------------------
% 15.38/3.61 % (20295)------------------------------
% 15.38/3.62 % (20296)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_19838 for (2979ds/464Mi)
% 15.38/3.64 % (20288)Instruction limit reached!
% 15.38/3.64 % (20288)------------------------------
% 15.38/3.64 % (20288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.38/3.64 % (20288)Termination reason: Unknown
% 15.38/3.64 % (20288)Termination phase: Saturation
% 15.38/3.64
% 15.38/3.64 % (20288)Memory used [KB]: 13176
% 15.38/3.64 % (20288)Time elapsed: 0.582 s
% 15.38/3.64 % (20288)Instructions burned: 1828 (million)
% 15.38/3.64 % (20288)------------------------------
% 15.38/3.64 % (20288)------------------------------
% 15.38/3.65 % (20297)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_19838 for (2978ds/1376Mi)
% 16.53/3.70 % (20270)Instruction limit reached!
% 16.53/3.70 % (20270)------------------------------
% 16.53/3.70 % (20270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.70 % (20270)Termination reason: Unknown
% 16.53/3.70 % (20270)Termination phase: Saturation
% 16.53/3.70
% 16.53/3.70 % (20270)Memory used [KB]: 8187
% 16.53/3.70 % (20270)Time elapsed: 1.293 s
% 16.53/3.70 % (20270)Instructions burned: 5209 (million)
% 16.53/3.70 % (20270)------------------------------
% 16.53/3.70 % (20270)------------------------------
% 16.53/3.71 % (20298)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_19838 for (2978ds/906Mi)
% 16.53/3.72 % (20272)Instruction limit reached!
% 16.53/3.72 % (20272)------------------------------
% 16.53/3.72 % (20272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.72 % (20272)Termination reason: Unknown
% 16.53/3.72 % (20272)Termination phase: Saturation
% 16.53/3.72
% 16.53/3.72 % (20272)Memory used [KB]: 18293
% 16.53/3.72 % (20272)Time elapsed: 1.203 s
% 16.53/3.72 % (20272)Instructions burned: 4351 (million)
% 16.53/3.72 % (20272)------------------------------
% 16.53/3.72 % (20272)------------------------------
% 16.53/3.73 % (20299)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_19838 for (2978ds/434Mi)
% 16.53/3.75 % (20296)Instruction limit reached!
% 16.53/3.75 % (20296)------------------------------
% 16.53/3.75 % (20296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.75 % (20296)Termination reason: Unknown
% 16.53/3.75 % (20296)Termination phase: Saturation
% 16.53/3.75
% 16.53/3.75 % (20296)Memory used [KB]: 11897
% 16.53/3.75 % (20296)Time elapsed: 0.134 s
% 16.53/3.75 % (20296)Instructions burned: 466 (million)
% 16.53/3.75 % (20296)------------------------------
% 16.53/3.75 % (20296)------------------------------
% 16.53/3.76 % (20300)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_19838 for (2977ds/865Mi)
% 16.82/3.81 % (20267)Instruction limit reached!
% 16.82/3.81 % (20267)------------------------------
% 16.82/3.81 % (20267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.81 % (20267)Termination reason: Unknown
% 16.82/3.81 % (20267)Termination phase: Saturation
% 16.82/3.81
% 16.82/3.81 % (20267)Memory used [KB]: 15095
% 16.82/3.81 % (20267)Time elapsed: 1.446 s
% 16.82/3.81 % (20267)Instructions burned: 4438 (million)
% 16.82/3.81 % (20267)------------------------------
% 16.82/3.81 % (20267)------------------------------
% 16.82/3.82 % (20301)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_19838 for (2977ds/593Mi)
% 16.82/3.85 % (20299)Instruction limit reached!
% 16.82/3.85 % (20299)------------------------------
% 16.82/3.85 % (20299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.85 % (20299)Termination reason: Unknown
% 16.82/3.85 % (20299)Termination phase: Saturation
% 16.82/3.85
% 16.82/3.85 % (20299)Memory used [KB]: 7675
% 16.82/3.85 % (20299)Time elapsed: 0.122 s
% 16.82/3.85 % (20299)Instructions burned: 434 (million)
% 16.82/3.85 % (20299)------------------------------
% 16.82/3.85 % (20299)------------------------------
% 16.82/3.86 % (20302)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_19838 for (2976ds/443Mi)
% 16.98/3.96 % (20301)Instruction limit reached!
% 16.98/3.96 % (20301)------------------------------
% 16.98/3.96 % (20301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/3.96 % (20301)Termination reason: Unknown
% 16.98/3.96 % (20301)Termination phase: Saturation
% 16.98/3.96
% 16.98/3.96 % (20301)Memory used [KB]: 7164
% 16.98/3.96 % (20301)Time elapsed: 0.148 s
% 16.98/3.96 % (20301)Instructions burned: 595 (million)
% 16.98/3.96 % (20301)------------------------------
% 16.98/3.96 % (20301)------------------------------
% 16.98/3.97 % (20303)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_19838 for (2975ds/594Mi)
% 16.98/3.98 % (20302)Instruction limit reached!
% 16.98/3.98 % (20302)------------------------------
% 16.98/3.98 % (20302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/3.98 % (20302)Termination reason: Unknown
% 16.98/3.98 % (20302)Termination phase: Saturation
% 16.98/3.98
% 16.98/3.98 % (20302)Memory used [KB]: 12025
% 16.98/3.98 % (20302)Time elapsed: 0.129 s
% 16.98/3.98 % (20302)Instructions burned: 444 (million)
% 16.98/3.98 % (20302)------------------------------
% 16.98/3.98 % (20302)------------------------------
% 16.98/3.99 % (20304)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_19838 for (2975ds/327Mi)
% 16.98/4.00 % (20297)Instruction limit reached!
% 16.98/4.00 % (20297)------------------------------
% 16.98/4.00 % (20297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/4.00 % (20297)Termination reason: Unknown
% 16.98/4.00 % (20297)Termination phase: Saturation
% 16.98/4.00
% 16.98/4.00 % (20297)Memory used [KB]: 7803
% 16.98/4.00 % (20297)Time elapsed: 0.351 s
% 16.98/4.00 % (20297)Instructions burned: 1377 (million)
% 16.98/4.00 % (20297)------------------------------
% 16.98/4.00 % (20297)------------------------------
% 16.98/4.00 % (20298)Instruction limit reached!
% 16.98/4.00 % (20298)------------------------------
% 16.98/4.00 % (20298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/4.00 % (20298)Termination reason: Unknown
% 16.98/4.00 % (20298)Termination phase: Saturation
% 16.98/4.00
% 16.98/4.00 % (20298)Memory used [KB]: 16119
% 16.98/4.00 % (20298)Time elapsed: 0.291 s
% 16.98/4.00 % (20298)Instructions burned: 908 (million)
% 16.98/4.00 % (20298)------------------------------
% 16.98/4.00 % (20298)------------------------------
% 16.98/4.01 % (20300)Instruction limit reached!
% 16.98/4.01 % (20300)------------------------------
% 16.98/4.01 % (20300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/4.01 % (20300)Termination reason: Unknown
% 16.98/4.01 % (20300)Termination phase: Saturation
% 16.98/4.01
% 16.98/4.01 % (20300)Memory used [KB]: 7931
% 16.98/4.01 % (20300)Time elapsed: 0.245 s
% 16.98/4.01 % (20300)Instructions burned: 866 (million)
% 16.98/4.01 % (20300)------------------------------
% 16.98/4.01 % (20300)------------------------------
% 16.98/4.01 % (20305)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_19838 for (2975ds/5411Mi)
% 16.98/4.01 % (20306)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_19838 for (2975ds/1762Mi)
% 16.98/4.02 % (20307)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_19838 for (2975ds/96Mi)
% 16.98/4.02 % (20305)Refutation not found, incomplete strategy
% 16.98/4.02 % (20305)------------------------------
% 16.98/4.02 % (20305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.98/4.02 % (20305)Termination reason: Refutation not found, incomplete strategy
% 16.98/4.02
% 16.98/4.02
% 16.98/4.02 % (20305)Memory used [KB]: 6780
% 16.98/4.02 % (20305)Time elapsed: 0.014 s
% 16.98/4.02 % (20305)Instructions burned: 44 (million)
% 16.98/4.02 % (20305)------------------------------
% 16.98/4.02 % (20305)------------------------------
% 20.02/4.03 % (20308)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_19838 for (2975ds/503Mi)
% 20.02/4.04 % (20307)Instruction limit reached!
% 20.02/4.04 % (20307)------------------------------
% 20.02/4.04 % (20307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.04 % (20307)Termination reason: Unknown
% 20.02/4.04 % (20307)Termination phase: Saturation
% 20.02/4.04
% 20.02/4.04 % (20307)Memory used [KB]: 6524
% 20.02/4.04 % (20307)Time elapsed: 0.026 s
% 20.02/4.04 % (20307)Instructions burned: 99 (million)
% 20.02/4.04 % (20307)------------------------------
% 20.02/4.04 % (20307)------------------------------
% 20.02/4.05 % (20309)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_19838 for (2974ds/90Mi)
% 20.02/4.08 % (20309)Instruction limit reached!
% 20.02/4.08 % (20309)------------------------------
% 20.02/4.08 % (20309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.08 % (20309)Termination reason: Unknown
% 20.02/4.08 % (20309)Termination phase: Preprocessing 3
% 20.02/4.08
% 20.02/4.08 % (20309)Memory used [KB]: 4093
% 20.02/4.08 % (20309)Time elapsed: 0.028 s
% 20.02/4.08 % (20309)Instructions burned: 93 (million)
% 20.02/4.08 % (20309)------------------------------
% 20.02/4.08 % (20309)------------------------------
% 20.02/4.09 % (20310)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_19838 for (2974ds/593Mi)
% 20.02/4.09 % (20304)Instruction limit reached!
% 20.02/4.09 % (20304)------------------------------
% 20.02/4.09 % (20304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.09 % (20304)Termination reason: Unknown
% 20.02/4.09 % (20304)Termination phase: Saturation
% 20.02/4.09
% 20.02/4.09 % (20304)Memory used [KB]: 10618
% 20.02/4.09 % (20304)Time elapsed: 0.101 s
% 20.02/4.09 % (20304)Instructions burned: 329 (million)
% 20.02/4.09 % (20304)------------------------------
% 20.02/4.09 % (20304)------------------------------
% 20.02/4.10 % (20311)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_19838 for (2974ds/1512Mi)
% 20.49/4.15 % (20303)Instruction limit reached!
% 20.49/4.15 % (20303)------------------------------
% 20.49/4.15 % (20303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.49/4.15 % (20303)Termination reason: Unknown
% 20.49/4.15 % (20303)Termination phase: Saturation
% 20.49/4.15
% 20.49/4.15 % (20303)Memory used [KB]: 9978
% 20.49/4.15 % (20303)Time elapsed: 0.174 s
% 20.49/4.15 % (20303)Instructions burned: 596 (million)
% 20.49/4.15 % (20303)------------------------------
% 20.49/4.15 % (20303)------------------------------
% 20.49/4.16 % (20312)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_19838 for (2973ds/569Mi)
% 20.49/4.17 % (20308)Instruction limit reached!
% 20.49/4.17 % (20308)------------------------------
% 20.49/4.17 % (20308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.49/4.17 % (20308)Termination reason: Unknown
% 20.49/4.17 % (20308)Termination phase: Saturation
% 20.49/4.17
% 20.49/4.17 % (20308)Memory used [KB]: 8315
% 20.49/4.17 % (20308)Time elapsed: 0.144 s
% 20.49/4.17 % (20308)Instructions burned: 504 (million)
% 20.49/4.17 % (20308)------------------------------
% 20.49/4.17 % (20308)------------------------------
% 20.49/4.18 % (20311)Refutation not found, incomplete strategy
% 20.49/4.18 % (20311)------------------------------
% 20.49/4.18 % (20311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.49/4.18 % (20311)Termination reason: Refutation not found, incomplete strategy
% 20.49/4.18
% 20.49/4.18
% 20.49/4.18 % (20311)Memory used [KB]: 9722
% 20.49/4.18 % (20311)Time elapsed: 0.077 s
% 20.49/4.18 % (20311)Instructions burned: 267 (million)
% 20.49/4.18 % (20311)------------------------------
% 20.49/4.18 % (20311)------------------------------
% 20.49/4.18 % (20313)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_19838 for (2973ds/501Mi)
% 20.49/4.19 % (20314)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_19838 for (2973ds/562Mi)
% 20.89/4.26 % (20310)Instruction limit reached!
% 20.89/4.26 % (20310)------------------------------
% 20.89/4.26 % (20310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.26 % (20310)Termination reason: Unknown
% 20.89/4.26 % (20310)Termination phase: Saturation
% 20.89/4.26
% 20.89/4.26 % (20310)Memory used [KB]: 11001
% 20.89/4.26 % (20310)Time elapsed: 0.174 s
% 20.89/4.26 % (20310)Instructions burned: 594 (million)
% 20.89/4.26 % (20310)------------------------------
% 20.89/4.26 % (20310)------------------------------
% 20.89/4.27 % (20315)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_19838 for (2972ds/406Mi)
% 20.89/4.30 % (20312)Instruction limit reached!
% 20.89/4.30 % (20312)------------------------------
% 20.89/4.30 % (20312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.30 % (20312)Termination reason: Unknown
% 20.89/4.30 % (20312)Termination phase: Saturation
% 20.89/4.30
% 20.89/4.30 % (20312)Memory used [KB]: 6652
% 20.89/4.30 % (20312)Time elapsed: 0.141 s
% 20.89/4.30 % (20312)Instructions burned: 569 (million)
% 20.89/4.30 % (20312)------------------------------
% 20.89/4.30 % (20312)------------------------------
% 21.28/4.30 % (20292)Instruction limit reached!
% 21.28/4.30 % (20292)------------------------------
% 21.28/4.30 % (20292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.28/4.30 % (20292)Termination reason: Unknown
% 21.28/4.30 % (20292)Termination phase: Saturation
% 21.28/4.30
% 21.28/4.30 % (20292)Memory used [KB]: 9850
% 21.28/4.30 % (20292)Time elapsed: 1.161 s
% 21.28/4.30 % (20292)Instructions burned: 4716 (million)
% 21.28/4.30 % (20292)------------------------------
% 21.28/4.30 % (20292)------------------------------
% 21.28/4.31 % (20316)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_19838 for (2972ds/582Mi)
% 21.28/4.31 % (20317)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_19838 for (2972ds/456Mi)
% 21.28/4.32 % (20313)Instruction limit reached!
% 21.28/4.32 % (20313)------------------------------
% 21.28/4.32 % (20313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.28/4.32 % (20313)Termination reason: Unknown
% 21.28/4.32 % (20313)Termination phase: Saturation
% 21.28/4.32
% 21.28/4.32 % (20313)Memory used [KB]: 11001
% 21.28/4.32 % (20313)Time elapsed: 0.143 s
% 21.28/4.32 % (20313)Instructions burned: 503 (million)
% 21.28/4.32 % (20313)------------------------------
% 21.28/4.32 % (20313)------------------------------
% 21.28/4.34 % (20318)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_19838 for (2971ds/393Mi)
% 21.28/4.35 % (20314)Instruction limit reached!
% 21.28/4.35 % (20314)------------------------------
% 21.28/4.35 % (20314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.28/4.35 % (20314)Termination reason: Unknown
% 21.28/4.35 % (20314)Termination phase: Saturation
% 21.28/4.35
% 21.28/4.35 % (20314)Memory used [KB]: 7547
% 21.28/4.35 % (20314)Time elapsed: 0.159 s
% 21.28/4.35 % (20314)Instructions burned: 563 (million)
% 21.28/4.35 % (20314)------------------------------
% 21.28/4.35 % (20314)------------------------------
% 21.28/4.36 % (20319)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_19838 for (2971ds/1335Mi)
% 21.28/4.39 % (20315)Instruction limit reached!
% 21.28/4.39 % (20315)------------------------------
% 21.28/4.39 % (20315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.28/4.39 % (20315)Termination reason: Unknown
% 21.28/4.39 % (20315)Termination phase: Saturation
% 21.28/4.39
% 21.28/4.39 % (20315)Memory used [KB]: 10106
% 21.28/4.39 % (20315)Time elapsed: 0.122 s
% 21.28/4.39 % (20315)Instructions burned: 407 (million)
% 21.28/4.39 % (20315)------------------------------
% 21.28/4.39 % (20315)------------------------------
% 21.28/4.39 % (20319)Refutation not found, incomplete strategy
% 21.28/4.39 % (20319)------------------------------
% 21.28/4.39 % (20319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.28/4.39 % (20319)Termination reason: Refutation not found, incomplete strategy
% 21.28/4.39
% 21.28/4.39
% 21.28/4.39 % (20319)Memory used [KB]: 6780
% 21.28/4.39 % (20319)Time elapsed: 0.034 s
% 21.28/4.39 % (20319)Instructions burned: 124 (million)
% 21.28/4.39 % (20319)------------------------------
% 21.28/4.39 % (20319)------------------------------
% 22.04/4.40 % (20320)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_19838 for (2971ds/3373Mi)
% 22.04/4.40 % (20321)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_19838 for (2971ds/474Mi)
% 22.04/4.43 % (20318)Instruction limit reached!
% 22.04/4.43 % (20318)------------------------------
% 22.04/4.43 % (20318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.43 % (20318)Termination reason: Unknown
% 22.04/4.43 % (20318)Termination phase: Saturation
% 22.04/4.43
% 22.04/4.43 % (20318)Memory used [KB]: 6780
% 22.04/4.43 % (20318)Time elapsed: 0.101 s
% 22.04/4.43 % (20318)Instructions burned: 394 (million)
% 22.04/4.43 % (20318)------------------------------
% 22.04/4.43 % (20318)------------------------------
% 22.04/4.44 % (20317)Instruction limit reached!
% 22.04/4.44 % (20317)------------------------------
% 22.04/4.44 % (20317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.44 % (20317)Termination reason: Unknown
% 22.04/4.44 % (20317)Termination phase: Saturation
% 22.04/4.44
% 22.04/4.44 % (20317)Memory used [KB]: 11385
% 22.04/4.44 % (20317)Time elapsed: 0.133 s
% 22.04/4.44 % (20317)Instructions burned: 457 (million)
% 22.04/4.44 % (20317)------------------------------
% 22.04/4.44 % (20317)------------------------------
% 22.04/4.44 % (20322)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_19838 for (2970ds/157Mi)
% 22.04/4.45 % (20306)Instruction limit reached!
% 22.04/4.45 % (20306)------------------------------
% 22.04/4.45 % (20306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.45 % (20306)Termination reason: Unknown
% 22.04/4.45 % (20306)Termination phase: Saturation
% 22.04/4.45
% 22.04/4.45 % (20306)Memory used [KB]: 15607
% 22.04/4.45 % (20306)Time elapsed: 0.441 s
% 22.04/4.45 % (20306)Instructions burned: 1764 (million)
% 22.04/4.45 % (20306)------------------------------
% 22.04/4.45 % (20306)------------------------------
% 22.04/4.45 % (20323)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_19838 for (2970ds/590Mi)
% 22.04/4.46 % (20324)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_19838 for (2970ds/104Mi)
% 22.04/4.48 % (20316)Instruction limit reached!
% 22.04/4.48 % (20316)------------------------------
% 22.04/4.48 % (20316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.48 % (20316)Termination reason: Unknown
% 22.04/4.48 % (20316)Termination phase: Saturation
% 22.04/4.48
% 22.04/4.48 % (20316)Memory used [KB]: 10106
% 22.04/4.48 % (20316)Time elapsed: 0.178 s
% 22.04/4.48 % (20316)Instructions burned: 582 (million)
% 22.04/4.48 % (20316)------------------------------
% 22.04/4.48 % (20316)------------------------------
% 22.04/4.48 % (20322)Instruction limit reached!
% 22.04/4.48 % (20322)------------------------------
% 22.04/4.48 % (20322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.48 % (20322)Termination reason: Unknown
% 22.04/4.48 % (20322)Termination phase: Saturation
% 22.04/4.48
% 22.04/4.48 % (20322)Memory used [KB]: 6524
% 22.04/4.48 % (20322)Time elapsed: 0.041 s
% 22.04/4.48 % (20322)Instructions burned: 161 (million)
% 22.04/4.48 % (20322)------------------------------
% 22.04/4.48 % (20322)------------------------------
% 22.04/4.49 % (20324)Instruction limit reached!
% 22.04/4.49 % (20324)------------------------------
% 22.04/4.49 % (20324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.04/4.49 % (20324)Termination reason: Unknown
% 22.04/4.49 % (20324)Termination phase: Property scanning
% 22.04/4.49
% 22.04/4.49 % (20324)Memory used [KB]: 4093
% 22.04/4.49 % (20324)Time elapsed: 0.031 s
% 22.04/4.49 % (20324)Instructions burned: 105 (million)
% 22.04/4.49 % (20324)------------------------------
% 22.04/4.49 % (20324)------------------------------
% 22.04/4.49 % (20325)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_19838 for (2970ds/414Mi)
% 22.04/4.49 % (20326)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_19838 for (2970ds/715Mi)
% 23.13/4.50 % (20327)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_19838 for (2970ds/961Mi)
% 23.13/4.53 % (20321)Instruction limit reached!
% 23.13/4.53 % (20321)------------------------------
% 23.13/4.53 % (20321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.13/4.53 % (20321)Termination reason: Unknown
% 23.13/4.53 % (20321)Termination phase: Saturation
% 23.13/4.53
% 23.13/4.53 % (20321)Memory used [KB]: 7675
% 23.13/4.53 % (20321)Time elapsed: 0.125 s
% 23.13/4.53 % (20321)Instructions burned: 476 (million)
% 23.13/4.53 % (20321)------------------------------
% 23.13/4.53 % (20321)------------------------------
% 23.13/4.54 % (20328)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_19838 for (2969ds/1213Mi)
% 23.13/4.60 % (20325)Instruction limit reached!
% 23.13/4.60 % (20325)------------------------------
% 23.13/4.60 % (20325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.13/4.60 % (20325)Termination reason: Unknown
% 23.13/4.60 % (20325)Termination phase: Saturation
% 23.13/4.60
% 23.13/4.60 % (20325)Memory used [KB]: 6652
% 23.13/4.60 % (20325)Time elapsed: 0.104 s
% 23.13/4.60 % (20325)Instructions burned: 414 (million)
% 23.13/4.60 % (20325)------------------------------
% 23.13/4.60 % (20325)------------------------------
% 23.36/4.61 % (20323)Instruction limit reached!
% 23.36/4.61 % (20323)------------------------------
% 23.36/4.61 % (20323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.61 % (20323)Termination reason: Unknown
% 23.36/4.61 % (20323)Termination phase: Saturation
% 23.36/4.61
% 23.36/4.61 % (20323)Memory used [KB]: 9978
% 23.36/4.61 % (20323)Time elapsed: 0.165 s
% 23.36/4.61 % (20323)Instructions burned: 590 (million)
% 23.36/4.61 % (20323)------------------------------
% 23.36/4.61 % (20323)------------------------------
% 23.36/4.61 % (20329)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_19838 for (2969ds/1979Mi)
% 23.36/4.62 % (20330)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_19838 for (2969ds/481Mi)
% 23.75/4.70 % (20326)Instruction limit reached!
% 23.75/4.70 % (20326)------------------------------
% 23.75/4.70 % (20326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.70 % (20326)Termination reason: Unknown
% 23.75/4.70 % (20326)Termination phase: Saturation
% 23.75/4.70
% 23.75/4.70 % (20326)Memory used [KB]: 6268
% 23.75/4.70 % (20326)Time elapsed: 0.212 s
% 23.75/4.70 % (20326)Instructions burned: 718 (million)
% 23.75/4.70 % (20326)------------------------------
% 23.75/4.70 % (20326)------------------------------
% 23.75/4.72 % (20331)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_19838 for (2968ds/783Mi)
% 23.75/4.74 % (20330)Instruction limit reached!
% 23.75/4.74 % (20330)------------------------------
% 23.75/4.74 % (20330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.74 % (20330)Termination reason: Unknown
% 23.75/4.74 % (20330)Termination phase: Saturation
% 23.75/4.74
% 23.75/4.74 % (20330)Memory used [KB]: 7419
% 23.75/4.74 % (20330)Time elapsed: 0.122 s
% 23.75/4.74 % (20330)Instructions burned: 482 (million)
% 23.75/4.74 % (20330)------------------------------
% 23.75/4.74 % (20330)------------------------------
% 23.75/4.75 % (20332)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_19838 for (2967ds/432Mi)
% 23.75/4.78 % (20327)Instruction limit reached!
% 23.75/4.78 % (20327)------------------------------
% 23.75/4.78 % (20327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.78 % (20327)Termination reason: Unknown
% 23.75/4.78 % (20327)Termination phase: Saturation
% 23.75/4.78
% 23.75/4.78 % (20327)Memory used [KB]: 12281
% 23.75/4.78 % (20327)Time elapsed: 0.286 s
% 23.75/4.78 % (20327)Instructions burned: 962 (million)
% 23.75/4.78 % (20327)------------------------------
% 23.75/4.78 % (20327)------------------------------
% 23.75/4.79 % (20333)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_19838 for (2967ds/1670Mi)
% 24.49/4.88 % (20332)Instruction limit reached!
% 24.49/4.88 % (20332)------------------------------
% 24.49/4.88 % (20332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.88 % (20332)Termination reason: Unknown
% 24.49/4.88 % (20332)Termination phase: Saturation
% 24.49/4.88
% 24.49/4.88 % (20332)Memory used [KB]: 8059
% 24.49/4.88 % (20332)Time elapsed: 0.126 s
% 24.49/4.88 % (20332)Instructions burned: 434 (million)
% 24.49/4.88 % (20332)------------------------------
% 24.49/4.88 % (20332)------------------------------
% 24.49/4.89 % (20334)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_19838 for (2966ds/90Mi)
% 24.72/4.91 % (20328)Instruction limit reached!
% 24.72/4.91 % (20328)------------------------------
% 24.72/4.91 % (20328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/4.91 % (20328)Termination reason: Unknown
% 24.72/4.91 % (20328)Termination phase: Saturation
% 24.72/4.91
% 24.72/4.91 % (20328)Memory used [KB]: 11257
% 24.72/4.91 % (20328)Time elapsed: 0.377 s
% 24.72/4.91 % (20328)Instructions burned: 1213 (million)
% 24.72/4.91 % (20328)------------------------------
% 24.72/4.91 % (20328)------------------------------
% 24.72/4.92 % (20334)Instruction limit reached!
% 24.72/4.92 % (20334)------------------------------
% 24.72/4.92 % (20334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/4.92 % (20334)Termination reason: Unknown
% 24.72/4.92 % (20334)Termination phase: Preprocessing 3
% 24.72/4.92
% 24.72/4.92 % (20334)Memory used [KB]: 4093
% 24.72/4.92 % (20334)Time elapsed: 0.028 s
% 24.72/4.92 % (20334)Instructions burned: 92 (million)
% 24.72/4.92 % (20334)------------------------------
% 24.72/4.92 % (20334)------------------------------
% 24.72/4.92 % (20335)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_19838 for (2966ds/346Mi)
% 24.72/4.93 % (20336)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_19838 for (2966ds/401Mi)
% 24.72/4.95 % (20331)Instruction limit reached!
% 24.72/4.95 % (20331)------------------------------
% 24.72/4.95 % (20331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/4.95 % (20331)Termination reason: Unknown
% 24.72/4.95 % (20331)Termination phase: Saturation
% 24.72/4.95
% 24.72/4.95 % (20331)Memory used [KB]: 9083
% 24.72/4.95 % (20331)Time elapsed: 0.233 s
% 24.72/4.95 % (20331)Instructions burned: 783 (million)
% 24.72/4.95 % (20331)------------------------------
% 24.72/4.95 % (20331)------------------------------
% 24.72/4.96 % (20337)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_19838 for (2965ds/6454Mi)
% 24.72/5.01 % (20335)Instruction limit reached!
% 24.72/5.01 % (20335)------------------------------
% 24.72/5.01 % (20335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.72/5.01 % (20335)Termination reason: Unknown
% 24.72/5.01 % (20335)Termination phase: Saturation
% 24.72/5.01
% 24.72/5.01 % (20335)Memory used [KB]: 7164
% 24.72/5.01 % (20335)Time elapsed: 0.086 s
% 24.72/5.01 % (20335)Instructions burned: 349 (million)
% 24.72/5.01 % (20335)------------------------------
% 24.72/5.01 % (20335)------------------------------
% 26.97/5.02 % (20338)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_19838 for (2965ds/283Mi)
% 26.97/5.02 % (20336)Instruction limit reached!
% 26.97/5.02 % (20336)------------------------------
% 26.97/5.02 % (20336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.97/5.02 % (20336)Termination reason: Unknown
% 26.97/5.02 % (20336)Termination phase: Saturation
% 26.97/5.02
% 26.97/5.02 % (20336)Memory used [KB]: 6780
% 26.97/5.02 % (20336)Time elapsed: 0.099 s
% 26.97/5.02 % (20336)Instructions burned: 402 (million)
% 26.97/5.02 % (20336)------------------------------
% 26.97/5.02 % (20336)------------------------------
% 26.97/5.03 % (20339)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_19838 for (2964ds/865Mi)
% 26.97/5.09 % (20338)Instruction limit reached!
% 26.97/5.09 % (20338)------------------------------
% 26.97/5.09 % (20338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.97/5.09 % (20338)Termination reason: Unknown
% 26.97/5.09 % (20338)Termination phase: Saturation
% 26.97/5.09
% 26.97/5.09 % (20338)Memory used [KB]: 9594
% 26.97/5.09 % (20338)Time elapsed: 0.078 s
% 26.97/5.09 % (20338)Instructions burned: 284 (million)
% 26.97/5.09 % (20338)------------------------------
% 26.97/5.09 % (20338)------------------------------
% 26.97/5.10 % (20340)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_19838 for (2964ds/4528Mi)
% 27.59/5.12 % (20340)Refutation not found, incomplete strategy
% 27.59/5.12 % (20340)------------------------------
% 27.59/5.12 % (20340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.59/5.12 % (20340)Termination reason: Refutation not found, incomplete strategy
% 27.59/5.12
% 27.59/5.12
% 27.59/5.12 % (20340)Memory used [KB]: 2174
% 27.59/5.12 % (20340)Time elapsed: 0.014 s
% 27.59/5.12 % (20340)Instructions burned: 41 (million)
% 27.59/5.12 % (20340)------------------------------
% 27.59/5.12 % (20340)------------------------------
% 27.59/5.13 % (20341)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_19838 for (2963ds/1001Mi)
% 27.59/5.14 % (20339)Refutation not found, incomplete strategy
% 27.59/5.14 % (20339)------------------------------
% 27.59/5.14 % (20339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.59/5.14 % (20339)Termination reason: Refutation not found, incomplete strategy
% 27.59/5.14
% 27.59/5.14
% 27.59/5.14 % (20339)Memory used [KB]: 10874
% 27.59/5.14 % (20339)Time elapsed: 0.105 s
% 27.59/5.14 % (20339)Instructions burned: 358 (million)
% 27.59/5.14 % (20339)------------------------------
% 27.59/5.14 % (20339)------------------------------
% 27.59/5.15 % (20342)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_19838 for (2963ds/102Mi)
% 27.59/5.17 % (20342)Instruction limit reached!
% 27.59/5.17 % (20342)------------------------------
% 27.59/5.17 % (20342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.59/5.17 % (20342)Termination reason: Unknown
% 27.59/5.17 % (20342)Termination phase: Saturation
% 27.59/5.17
% 27.59/5.17 % (20342)Memory used [KB]: 6524
% 27.59/5.17 % (20342)Time elapsed: 0.027 s
% 27.59/5.17 % (20342)Instructions burned: 104 (million)
% 27.59/5.17 % (20342)------------------------------
% 27.59/5.17 % (20342)------------------------------
% 27.59/5.18 % (20343)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_19838 for (2963ds/952Mi)
% 28.19/5.20 % (20333)Instruction limit reached!
% 28.19/5.20 % (20333)------------------------------
% 28.19/5.20 % (20333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.19/5.20 % (20333)Termination reason: Unknown
% 28.19/5.20 % (20333)Termination phase: Saturation
% 28.19/5.20
% 28.19/5.20 % (20333)Memory used [KB]: 6780
% 28.19/5.20 % (20333)Time elapsed: 0.413 s
% 28.19/5.20 % (20333)Instructions burned: 1670 (million)
% 28.19/5.20 % (20333)------------------------------
% 28.19/5.20 % (20333)------------------------------
% 28.19/5.21 % (20344)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_19838 for (2963ds/578Mi)
% 28.60/5.33 % (20329)Instruction limit reached!
% 28.60/5.33 % (20329)------------------------------
% 28.60/5.33 % (20329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.60/5.33 % (20329)Termination reason: Unknown
% 28.60/5.33 % (20329)Termination phase: Saturation
% 28.60/5.33
% 28.60/5.33 % (20329)Memory used [KB]: 12792
% 28.60/5.33 % (20329)Time elapsed: 0.723 s
% 28.60/5.33 % (20329)Instructions burned: 1979 (million)
% 28.60/5.33 % (20329)------------------------------
% 28.60/5.33 % (20329)------------------------------
% 28.60/5.35 % (20345)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_19838 for (2961ds/643Mi)
% 28.60/5.37 % (20344)Instruction limit reached!
% 28.60/5.37 % (20344)------------------------------
% 28.60/5.37 % (20344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.60/5.37 % (20344)Termination reason: Unknown
% 28.60/5.37 % (20344)Termination phase: Saturation
% 28.60/5.37
% 28.60/5.37 % (20344)Memory used [KB]: 7931
% 28.60/5.37 % (20344)Time elapsed: 0.153 s
% 28.60/5.37 % (20344)Instructions burned: 578 (million)
% 28.60/5.37 % (20344)------------------------------
% 28.60/5.37 % (20344)------------------------------
% 28.60/5.38 % (20346)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_19838 for (2961ds/865Mi)
% 29.11/5.41 % (20320)Instruction limit reached!
% 29.11/5.41 % (20320)------------------------------
% 29.11/5.41 % (20320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.41 % (20320)Termination reason: Unknown
% 29.11/5.41 % (20320)Termination phase: Saturation
% 29.11/5.41
% 29.11/5.41 % (20320)Memory used [KB]: 15351
% 29.11/5.41 % (20320)Time elapsed: 1.013 s
% 29.11/5.41 % (20320)Instructions burned: 3373 (million)
% 29.11/5.41 % (20320)------------------------------
% 29.11/5.41 % (20320)------------------------------
% 29.11/5.42 % (20341)Instruction limit reached!
% 29.11/5.42 % (20341)------------------------------
% 29.11/5.42 % (20341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.42 % (20341)Termination reason: Unknown
% 29.11/5.42 % (20341)Termination phase: Saturation
% 29.11/5.42
% 29.11/5.42 % (20341)Memory used [KB]: 15991
% 29.11/5.42 % (20341)Time elapsed: 0.291 s
% 29.11/5.42 % (20341)Instructions burned: 1002 (million)
% 29.11/5.42 % (20341)------------------------------
% 29.11/5.42 % (20341)------------------------------
% 29.11/5.42 % (20347)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_19838 for (2960ds/1174Mi)
% 29.11/5.43 % (20348)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_19838 for (2960ds/644Mi)
% 29.11/5.46 % (20343)Instruction limit reached!
% 29.11/5.46 % (20343)------------------------------
% 29.11/5.46 % (20343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.46 % (20343)Termination reason: Unknown
% 29.11/5.46 % (20343)Termination phase: Saturation
% 29.11/5.46
% 29.11/5.46 % (20343)Memory used [KB]: 11129
% 29.11/5.46 % (20343)Time elapsed: 0.283 s
% 29.11/5.46 % (20343)Instructions burned: 953 (million)
% 29.11/5.46 % (20343)------------------------------
% 29.11/5.46 % (20343)------------------------------
% 29.11/5.48 % (20349)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_19838 for (2960ds/1201Mi)
% 29.93/5.50 % (20345)Instruction limit reached!
% 29.93/5.50 % (20345)------------------------------
% 29.93/5.50 % (20345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.93/5.50 % (20345)Termination reason: Unknown
% 29.93/5.50 % (20345)Termination phase: Saturation
% 29.93/5.50
% 29.93/5.50 % (20345)Memory used [KB]: 6652
% 29.93/5.50 % (20345)Time elapsed: 0.160 s
% 29.93/5.50 % (20345)Instructions burned: 644 (million)
% 29.93/5.50 % (20345)------------------------------
% 29.93/5.50 % (20345)------------------------------
% 29.93/5.51 % (20350)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_19838 for (2960ds/1046Mi)
% 29.93/5.53 % (20348)Refutation not found, incomplete strategy
% 29.93/5.53 % (20348)------------------------------
% 29.93/5.53 % (20348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.93/5.53 % (20348)Termination reason: Refutation not found, incomplete strategy
% 29.93/5.53
% 29.93/5.53
% 29.93/5.53 % (20348)Memory used [KB]: 10874
% 29.93/5.53 % (20348)Time elapsed: 0.099 s
% 29.93/5.53 % (20348)Instructions burned: 339 (million)
% 29.93/5.53 % (20348)------------------------------
% 29.93/5.53 % (20348)------------------------------
% 29.93/5.54 % (20351)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_19838 for (2959ds/222Mi)
% 29.93/5.60 % (20351)Instruction limit reached!
% 29.93/5.60 % (20351)------------------------------
% 29.93/5.60 % (20351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.93/5.60 % (20351)Termination reason: Unknown
% 29.93/5.60 % (20351)Termination phase: Saturation
% 29.93/5.60
% 29.93/5.60 % (20351)Memory used [KB]: 6780
% 29.93/5.60 % (20351)Time elapsed: 0.061 s
% 29.93/5.60 % (20351)Instructions burned: 224 (million)
% 29.93/5.60 % (20351)------------------------------
% 29.93/5.60 % (20351)------------------------------
% 30.49/5.61 % (20352)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_19838 for (2959ds/68Mi)
% 30.49/5.63 % (20352)Instruction limit reached!
% 30.49/5.63 % (20352)------------------------------
% 30.49/5.63 % (20352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.49/5.63 % (20352)Termination reason: Unknown
% 30.49/5.63 % (20352)Termination phase: Preprocessing 3
% 30.49/5.63
% 30.49/5.63 % (20352)Memory used [KB]: 3070
% 30.49/5.63 % (20352)Time elapsed: 0.021 s
% 30.49/5.63 % (20352)Instructions burned: 70 (million)
% 30.49/5.63 % (20352)------------------------------
% 30.49/5.63 % (20352)------------------------------
% 30.49/5.64 % (20353)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=454:si=on:rtra=on_0 on DTF2THF_19838 for (2958ds/454Mi)
% 30.49/5.64 % (20346)Instruction limit reached!
% 30.49/5.64 % (20346)------------------------------
% 30.49/5.64 % (20346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.49/5.64 % (20346)Termination reason: Unknown
% 30.49/5.64 % (20346)Termination phase: Saturation
% 30.49/5.64
% 30.49/5.64 % (20346)Memory used [KB]: 11257
% 30.49/5.64 % (20346)Time elapsed: 0.267 s
% 30.49/5.64 % (20346)Instructions burned: 867 (million)
% 30.49/5.64 % (20346)------------------------------
% 30.49/5.64 % (20346)------------------------------
% 30.49/5.65 % (20354)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_19838 for (2958ds/360Mi)
% 30.99/5.70 % (20293)Instruction limit reached!
% 30.99/5.70 % (20293)------------------------------
% 30.99/5.70 % (20293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.70 % (20293)Termination reason: Unknown
% 30.99/5.70 % (20293)Termination phase: Saturation
% 30.99/5.70
% 30.99/5.70 % (20293)Memory used [KB]: 20980
% 30.99/5.70 % (20293)Time elapsed: 2.527 s
% 30.99/5.70 % (20293)Instructions burned: 8252 (million)
% 30.99/5.70 % (20293)------------------------------
% 30.99/5.70 % (20293)------------------------------
% 30.99/5.71 % (20355)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_19838 for (2958ds/157Mi)
% 30.99/5.74 % (20354)Instruction limit reached!
% 30.99/5.74 % (20354)------------------------------
% 30.99/5.74 % (20354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.74 % (20354)Termination reason: Unknown
% 30.99/5.74 % (20354)Termination phase: Saturation
% 30.99/5.74
% 30.99/5.74 % (20354)Memory used [KB]: 6524
% 30.99/5.74 % (20354)Time elapsed: 0.091 s
% 30.99/5.74 % (20354)Instructions burned: 362 (million)
% 30.99/5.74 % (20354)------------------------------
% 30.99/5.74 % (20354)------------------------------
% 30.99/5.75 % (20353)Instruction limit reached!
% 30.99/5.75 % (20353)------------------------------
% 30.99/5.75 % (20353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.75 % (20353)Termination reason: Unknown
% 30.99/5.75 % (20353)Termination phase: Saturation
% 30.99/5.75
% 30.99/5.75 % (20353)Memory used [KB]: 11129
% 30.99/5.75 % (20353)Time elapsed: 0.115 s
% 30.99/5.75 % (20353)Instructions burned: 456 (million)
% 30.99/5.75 % (20353)------------------------------
% 30.99/5.75 % (20353)------------------------------
% 30.99/5.75 % (20355)Instruction limit reached!
% 30.99/5.75 % (20355)------------------------------
% 30.99/5.75 % (20355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.75 % (20355)Termination reason: Unknown
% 30.99/5.75 % (20355)Termination phase: Saturation
% 30.99/5.75
% 30.99/5.75 % (20355)Memory used [KB]: 6524
% 30.99/5.75 % (20355)Time elapsed: 0.041 s
% 30.99/5.75 % (20355)Instructions burned: 161 (million)
% 30.99/5.75 % (20355)------------------------------
% 30.99/5.75 % (20355)------------------------------
% 30.99/5.75 % (20356)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_19838 for (2957ds/5061Mi)
% 30.99/5.76 % (20357)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_19838 for (2957ds/2401Mi)
% 30.99/5.76 % (20358)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_19838 for (2957ds/5798Mi)
% 30.99/5.77 % (20350)Instruction limit reached!
% 30.99/5.77 % (20350)------------------------------
% 30.99/5.77 % (20350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.77 % (20350)Termination reason: Unknown
% 30.99/5.77 % (20350)Termination phase: Saturation
% 30.99/5.77
% 30.99/5.77 % (20350)Memory used [KB]: 6652
% 30.99/5.77 % (20350)Time elapsed: 0.258 s
% 30.99/5.77 % (20350)Instructions burned: 1046 (million)
% 30.99/5.77 % (20350)------------------------------
% 30.99/5.77 % (20350)------------------------------
% 30.99/5.78 % (20359)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_19838 for (2957ds/346Mi)
% 30.99/5.79 % (20347)Instruction limit reached!
% 30.99/5.79 % (20347)------------------------------
% 30.99/5.79 % (20347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.79 % (20347)Termination reason: Unknown
% 30.99/5.79 % (20347)Termination phase: Saturation
% 30.99/5.79
% 30.99/5.79 % (20347)Memory used [KB]: 13176
% 30.99/5.79 % (20347)Time elapsed: 0.366 s
% 30.99/5.79 % (20347)Instructions burned: 1176 (million)
% 30.99/5.79 % (20347)------------------------------
% 30.99/5.79 % (20347)------------------------------
% 32.02/5.80 % (20360)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_19838 for (2957ds/1321Mi)
% 32.02/5.85 % (20349)Instruction limit reached!
% 32.02/5.85 % (20349)------------------------------
% 32.02/5.85 % (20349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.85 % (20349)Termination reason: Unknown
% 32.02/5.85 % (20349)Termination phase: Saturation
% 32.02/5.85
% 32.02/5.85 % (20349)Memory used [KB]: 12025
% 32.02/5.85 % (20349)Time elapsed: 0.372 s
% 32.02/5.85 % (20349)Instructions burned: 1204 (million)
% 32.02/5.85 % (20349)------------------------------
% 32.02/5.85 % (20349)------------------------------
% 32.02/5.86 % (20361)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_19838 for (2956ds/1312Mi)
% 32.02/5.87 % (20359)Instruction limit reached!
% 32.02/5.87 % (20359)------------------------------
% 32.02/5.87 % (20359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.87 % (20359)Termination reason: Unknown
% 32.02/5.87 % (20359)Termination phase: Saturation
% 32.02/5.87
% 32.02/5.87 % (20359)Memory used [KB]: 7291
% 32.02/5.87 % (20359)Time elapsed: 0.088 s
% 32.02/5.87 % (20359)Instructions burned: 346 (million)
% 32.02/5.87 % (20359)------------------------------
% 32.02/5.87 % (20359)------------------------------
% 32.02/5.88 % (20362)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_19838 for (2956ds/672Mi)
% 32.60/5.90 % (20337)First to succeed.
% 32.60/5.94 % (20337)Refutation found. Thanks to Tanya!
% 32.60/5.94 % SZS status Theorem for DTF2THF_19838
% 32.60/5.94 % SZS output start Proof for DTF2THF_19838
% 32.60/5.94 thf(type_def_5, type, term: $tType).
% 32.60/5.94 thf(type_def_7, type, subst: $tType).
% 32.60/5.94 thf(type_def_8, type, d_term: $tType).
% 32.60/5.94 thf(type_def_9, type, d_subst: $tType).
% 32.60/5.94 thf(func_def_0, type, term: $tType).
% 32.60/5.94 thf(func_def_1, type, subst: $tType).
% 32.60/5.94 thf(func_def_2, type, one: term).
% 32.60/5.94 thf(func_def_3, type, ap: term > term > term).
% 32.60/5.94 thf(func_def_4, type, lam: term > term).
% 32.60/5.94 thf(func_def_5, type, sub: term > subst > term).
% 32.60/5.94 thf(func_def_6, type, id: subst).
% 32.60/5.94 thf(func_def_7, type, sh: subst).
% 32.60/5.94 thf(func_def_8, type, push: term > subst > subst).
% 32.60/5.94 thf(func_def_9, type, comp: subst > subst > subst).
% 32.60/5.94 thf(func_def_10, type, var: term > $o).
% 32.60/5.94 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 32.60/5.94 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 32.60/5.94 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 32.60/5.94 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 32.60/5.94 thf(func_def_124, type, d_term: $tType).
% 32.60/5.94 thf(func_def_125, type, d_subst: $tType).
% 32.60/5.94 thf(func_def_126, type, d2term: d_term > term).
% 32.60/5.94 thf(func_def_127, type, d2subst: d_subst > subst).
% 32.60/5.94 thf(func_def_128, type, d_one: d_term).
% 32.60/5.94 thf(func_def_129, type, d_id: d_subst).
% 32.60/5.94 thf(func_def_142, type, sP0: (term > $o) > $o).
% 32.60/5.94 thf(func_def_143, type, sP1: (term > $o) > $o).
% 32.60/5.94 thf(func_def_147, type, sP5: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_149, type, sP7: (term > $o) > $o).
% 32.60/5.94 thf(func_def_150, type, sP8: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_156, type, sP14: (term > $o) > $o).
% 32.60/5.94 thf(func_def_159, type, sP17: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_162, type, sP20: (term > $o) > $o).
% 32.60/5.94 thf(func_def_165, type, sP23: (term > $o) > $o).
% 32.60/5.94 thf(func_def_166, type, sP24: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_167, type, sP25: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_168, type, sP26: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_169, type, sP27: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_176, type, sP34: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_178, type, sP36: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_179, type, sP37: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_181, type, sP39: (term > $o) > $o).
% 32.60/5.94 thf(func_def_182, type, sP40: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_184, type, sP42: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_185, type, sP43: (term > $o) > $o).
% 32.60/5.94 thf(func_def_186, type, sP44: (term > $o) > $o).
% 32.60/5.94 thf(func_def_189, type, sP47: (term > $o) > $o).
% 32.60/5.94 thf(func_def_190, type, sP48: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_191, type, sP49: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_197, type, sP55: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_199, type, sP57: (subst > term > subst > $o) > $o).
% 32.60/5.94 thf(func_def_201, type, sK59: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_202, type, sK60: term > $o).
% 32.60/5.94 thf(func_def_203, type, sK61: term).
% 32.60/5.94 thf(func_def_204, type, sK62: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_205, type, sK63: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_206, type, sK64: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_207, type, sK65: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_208, type, sK66: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_209, type, sK67: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_210, type, sK68: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_211, type, sK69: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_212, type, sK70: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_213, type, sK71: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_214, type, sK72: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_215, type, sK73: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_216, type, sK74: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_217, type, sK75: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_218, type, sK76: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_219, type, sK77: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_220, type, sK78: term).
% 32.60/5.94 thf(func_def_221, type, sK79: term > $o).
% 32.60/5.94 thf(func_def_222, type, sK80: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_223, type, sK81: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_224, type, sK82: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_225, type, sK83: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_226, type, sK84: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_227, type, sK85: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_228, type, sK86: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_229, type, sK87: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_230, type, sK88: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_231, type, sK89: (term > $o) > term > term).
% 32.60/5.94 thf(func_def_232, type, sK90: term).
% 32.60/5.94 thf(func_def_233, type, sK91: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_234, type, sK92: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_235, type, sK93: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_236, type, sK94: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_237, type, sK95: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_238, type, sK96: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_239, type, sK97: term).
% 32.60/5.94 thf(func_def_240, type, sK98: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_241, type, sK99: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_242, type, sK100: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_243, type, sK101: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_244, type, sK102: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_245, type, sK103: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_246, type, sK104: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_247, type, sK105: term).
% 32.60/5.94 thf(func_def_248, type, sK106: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_249, type, sK107: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_250, type, sK108: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_251, type, sK109: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_252, type, sK110: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_253, type, sK111: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_254, type, sK112: (subst > term > subst > $o) > term > $o).
% 32.60/5.94 thf(func_def_255, type, sK113: (term > $o) > term).
% 32.60/5.94 thf(func_def_256, type, sK114: (term > $o) > term).
% 32.60/5.94 thf(func_def_257, type, sK115: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_258, type, sK116: (term > $o) > term).
% 32.60/5.94 thf(func_def_259, type, sK117: term).
% 32.60/5.94 thf(func_def_260, type, sK118: term > $o).
% 32.60/5.94 thf(func_def_261, type, sK119: term).
% 32.60/5.94 thf(func_def_262, type, sK120: term > term).
% 32.60/5.94 thf(func_def_263, type, sK121: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_264, type, sK122: term).
% 32.60/5.94 thf(func_def_265, type, sK123: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_266, type, sK124: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_267, type, sK125: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_268, type, sK126: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_269, type, sK127: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_270, type, sK128: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_271, type, sK129: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_272, type, sK130: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_273, type, sK131: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_274, type, sK132: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_275, type, sK133: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_276, type, sK134: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_277, type, sK135: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_278, type, sK136: term > $o).
% 32.60/5.94 thf(func_def_279, type, sK137: term).
% 32.60/5.94 thf(func_def_280, type, sK138: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_281, type, sK139: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_282, type, sK140: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_283, type, sK141: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_284, type, sK142: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_285, type, sK143: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_286, type, sK144: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_287, type, sK145: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_288, type, sK146: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_289, type, sK147: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_290, type, sK148: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_291, type, sK149: (term > $o) > term).
% 32.60/5.94 thf(func_def_292, type, sK150: (term > $o) > term).
% 32.60/5.94 thf(func_def_293, type, sK151: (term > $o) > term).
% 32.60/5.94 thf(func_def_294, type, sK152: subst > (term > $o) > term).
% 32.60/5.94 thf(func_def_295, type, sK153: term).
% 32.60/5.94 thf(func_def_296, type, sK154: term > $o).
% 32.60/5.94 thf(func_def_297, type, sK155: subst).
% 32.60/5.94 thf(func_def_298, type, sK156: term).
% 32.60/5.94 thf(func_def_299, type, sK157: term > term).
% 32.60/5.94 thf(func_def_300, type, sK158: term > $o).
% 32.60/5.94 thf(func_def_301, type, sK159: term).
% 32.60/5.94 thf(func_def_302, type, sK160: term > term).
% 32.60/5.94 thf(func_def_303, type, sK161: (term > $o) > term).
% 32.60/5.94 thf(func_def_304, type, sK162: (term > $o) > term).
% 32.60/5.94 thf(func_def_305, type, sK163: (term > $o) > term).
% 32.60/5.94 thf(func_def_306, type, sK164: (term > $o) > term).
% 32.60/5.94 thf(func_def_307, type, sK165: (term > $o) > term).
% 32.60/5.94 thf(func_def_308, type, sK166: (term > $o) > term).
% 32.60/5.94 thf(func_def_309, type, sK167: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_310, type, sK168: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_311, type, sK169: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_312, type, sK170: term).
% 32.60/5.94 thf(func_def_313, type, sK171: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_314, type, sK172: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_315, type, sK173: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_316, type, sK174: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_317, type, sK175: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_318, type, sK176: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_319, type, sK177: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_320, type, sK178: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_321, type, sK179: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_322, type, sK180: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_323, type, sK181: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_324, type, sK182: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_325, type, sK183: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_326, type, sK184: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_327, type, sK185: (term > $o) > term).
% 32.60/5.94 thf(func_def_328, type, sK186: (term > $o) > term).
% 32.60/5.94 thf(func_def_329, type, sK187: term).
% 32.60/5.94 thf(func_def_330, type, sK188: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_331, type, sK189: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_332, type, sK190: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_333, type, sK191: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_334, type, sK192: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_335, type, sK193: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_336, type, sK194: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_337, type, sK195: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_338, type, sK196: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_339, type, sK197: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_340, type, sK198: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_341, type, sK199: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_342, type, sK200: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_343, type, sK201: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_344, type, sK202: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_345, type, sK203: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_346, type, sK204: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_347, type, sK205: term).
% 32.60/5.94 thf(func_def_348, type, sK206: term > $o).
% 32.60/5.94 thf(func_def_349, type, sK207: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_350, type, sK208: term).
% 32.60/5.94 thf(func_def_351, type, sK209: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_352, type, sK210: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_353, type, sK211: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_354, type, sK212: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_355, type, sK213: (subst > term > subst > $o) > (term > $o) > term).
% 32.60/5.94 thf(func_def_356, type, sK214: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_357, type, sK215: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_358, type, sK216: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_359, type, sK217: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_360, type, sK218: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_361, type, sK219: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_362, type, sK220: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_363, type, sK221: term > $o).
% 32.60/5.94 thf(func_def_364, type, sK222: term).
% 32.60/5.94 thf(func_def_365, type, sK223: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_366, type, sK224: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_367, type, sK225: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_368, type, sK226: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_369, type, sK227: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_370, type, sK228: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_371, type, sK229: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_372, type, sK230: term).
% 32.60/5.94 thf(func_def_373, type, sK231: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_374, type, sK232: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_375, type, sK233: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_376, type, sK234: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_377, type, sK235: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_378, type, sK236: (subst > term > subst > $o) > term > term).
% 32.60/5.94 thf(func_def_379, type, sK237: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_380, type, sK238: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_381, type, sK239: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_382, type, sK240: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_383, type, sK241: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_384, type, sK242: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_385, type, sK243: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_386, type, sK244: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_387, type, sK245: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_388, type, sK246: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_389, type, sK247: term).
% 32.60/5.94 thf(func_def_390, type, sK248: term).
% 32.60/5.94 thf(func_def_391, type, sK249: (term > $o) > term).
% 32.60/5.94 thf(func_def_392, type, sK250: (term > $o) > term).
% 32.60/5.94 thf(func_def_393, type, sK251: term > $o).
% 32.60/5.94 thf(func_def_394, type, sK252: term).
% 32.60/5.94 thf(func_def_395, type, sK253: term > term).
% 32.60/5.94 thf(func_def_396, type, sK254: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_397, type, sK255: term).
% 32.60/5.94 thf(func_def_398, type, sK256: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_399, type, sK257: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_400, type, sK258: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_401, type, sK259: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_402, type, sK260: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_403, type, sK261: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_404, type, sK262: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_405, type, sK263: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_406, type, sK264: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_407, type, sK265: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_408, type, sK266: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_409, type, sK267: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_410, type, sK268: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_411, type, sK269: (subst > term > subst > $o) > term > term).
% 32.60/5.94 thf(func_def_412, type, sK270: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_413, type, sK271: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_414, type, sK272: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_415, type, sK273: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_416, type, sK274: term).
% 32.60/5.94 thf(func_def_417, type, sK275: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_418, type, sK276: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_419, type, sK277: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_420, type, sK278: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_421, type, sK279: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_422, type, sK280: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_423, type, sK281: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_424, type, sK282: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_425, type, sK283: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_426, type, sK284: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_427, type, sK285: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_428, type, sK286: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_429, type, sK287: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_430, type, sK288: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_431, type, sK289: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_432, type, sK290: (term > $o) > term).
% 32.60/5.94 thf(func_def_433, type, sK291: (term > $o) > term).
% 32.60/5.94 thf(func_def_434, type, sK292: subst).
% 32.60/5.94 thf(func_def_435, type, sK293: subst > term > term).
% 32.60/5.94 thf(func_def_436, type, sK294: term).
% 32.60/5.94 thf(func_def_437, type, sK295: subst > term > term).
% 32.60/5.94 thf(func_def_438, type, sK296: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_439, type, sK297: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_440, type, sK298: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_441, type, sK299: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_442, type, sK300: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_443, type, sK301: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_444, type, sK302: subst).
% 32.60/5.94 thf(func_def_445, type, sK303: term).
% 32.60/5.94 thf(func_def_446, type, sK304: term).
% 32.60/5.94 thf(func_def_447, type, sK305: subst).
% 32.60/5.94 thf(func_def_448, type, sK306: term).
% 32.60/5.94 thf(func_def_449, type, sK307: term).
% 32.60/5.94 thf(func_def_450, type, sK308: term > $o).
% 32.60/5.94 thf(func_def_451, type, sK309: term).
% 32.60/5.94 thf(func_def_452, type, sK310: term > term).
% 32.60/5.94 thf(func_def_453, type, sK311: (term > $o) > term).
% 32.60/5.94 thf(func_def_454, type, sK312: (term > $o) > term).
% 32.60/5.94 thf(func_def_455, type, sK313: (term > $o) > term).
% 32.60/5.94 thf(func_def_456, type, sK314: (term > $o) > term).
% 32.60/5.94 thf(func_def_457, type, sK315: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_458, type, sK316: term).
% 32.60/5.94 thf(func_def_459, type, sK317: term).
% 32.60/5.94 thf(func_def_460, type, sK318: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_461, type, sK319: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_462, type, sK320: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_463, type, sK321: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_464, type, sK322: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_465, type, sK323: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_466, type, sK324: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_467, type, sK325: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_468, type, sK326: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_469, type, sK327: (subst > term > subst > $o) > term > term).
% 32.60/5.94 thf(func_def_470, type, sK328: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_471, type, sK329: term).
% 32.60/5.94 thf(func_def_472, type, sK330: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_473, type, sK331: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_474, type, sK332: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_475, type, sK333: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_476, type, sK334: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_477, type, sK335: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_478, type, sK336: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_479, type, sK337: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_480, type, sK338: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_481, type, sK339: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_482, type, sK340: term).
% 32.60/5.94 thf(func_def_483, type, sK341: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_484, type, sK342: term > (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_485, type, sK343: term > (subst > term > term) > term).
% 32.60/5.94 thf(func_def_486, type, sK344: term > (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_487, type, sK345: term > (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_488, type, sK346: term > (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_489, type, sK347: term > (subst > term > term) > term).
% 32.60/5.94 thf(func_def_490, type, sK348: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_491, type, sK349: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_492, type, sK350: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_493, type, sK351: (subst > term > subst > $o) > term > term).
% 32.60/5.94 thf(func_def_494, type, sK352: term).
% 32.60/5.94 thf(func_def_495, type, sK353: subst).
% 32.60/5.94 thf(func_def_496, type, sK354: term > $o).
% 32.60/5.94 thf(func_def_497, type, sK355: term > term).
% 32.60/5.94 thf(func_def_498, type, sK356: (term > $o) > subst > term).
% 32.60/5.94 thf(func_def_499, type, sK357: (term > $o) > term).
% 32.60/5.94 thf(func_def_500, type, sK358: (term > $o) > term).
% 32.60/5.94 thf(func_def_501, type, sK359: (term > $o) > term).
% 32.60/5.94 thf(func_def_502, type, sK360: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_503, type, sK361: term).
% 32.60/5.94 thf(func_def_504, type, sK362: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_505, type, sK363: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_506, type, sK364: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_507, type, sK365: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_508, type, sK366: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_509, type, sK367: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_510, type, sK368: term).
% 32.60/5.94 thf(func_def_511, type, sK369: term > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_512, type, sK370: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_513, type, sK371: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_514, type, sK372: term).
% 32.60/5.94 thf(func_def_515, type, sK373: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_516, type, sK374: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_517, type, sK375: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_518, type, sK376: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_519, type, sK377: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_520, type, sK378: term).
% 32.60/5.94 thf(func_def_521, type, sK379: (subst > term > subst > $o) > term > $o).
% 32.60/5.94 thf(func_def_522, type, sK380: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_523, type, sK381: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_524, type, sK382: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_525, type, sK383: (term > $o) > term).
% 32.60/5.94 thf(func_def_526, type, sK384: term).
% 32.60/5.94 thf(func_def_527, type, sK385: (term > $o) > term).
% 32.60/5.94 thf(func_def_528, type, sK386: (term > $o) > term).
% 32.60/5.94 thf(func_def_529, type, sK387: term).
% 32.60/5.94 thf(func_def_530, type, sK388: term > $o).
% 32.60/5.94 thf(func_def_531, type, sK389: term > term).
% 32.60/5.94 thf(func_def_532, type, sK390: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_533, type, sK391: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_534, type, sK392: (term > $o) > term > term).
% 32.60/5.94 thf(func_def_535, type, sK393: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_536, type, sK394: term).
% 32.60/5.94 thf(func_def_537, type, sK395: term > $o).
% 32.60/5.94 thf(func_def_538, type, sK396: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_539, type, sK397: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_540, type, sK398: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_541, type, sK399: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_542, type, sK400: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_543, type, sK401: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_544, type, sK402: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_545, type, sK403: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_546, type, sK404: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_547, type, sK405: (term > $o) > term).
% 32.60/5.94 thf(func_def_548, type, sK406: (term > $o) > term).
% 32.60/5.94 thf(func_def_549, type, sK407: term).
% 32.60/5.94 thf(func_def_550, type, sK408: term).
% 32.60/5.94 thf(func_def_551, type, sK409: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_552, type, sK410: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_553, type, sK411: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_554, type, sK412: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_555, type, sK413: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_556, type, sK414: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_557, type, sK415: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_558, type, sK416: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_559, type, sK417: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_560, type, sK418: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_561, type, sK419: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_562, type, sK420: term > subst > term > term).
% 32.60/5.94 thf(func_def_563, type, sK421: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_564, type, sK422: term > $o).
% 32.60/5.94 thf(func_def_565, type, sK423: term).
% 32.60/5.94 thf(func_def_566, type, sK424: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_567, type, sK425: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_568, type, sK426: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_569, type, sK427: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_570, type, sK428: term).
% 32.60/5.94 thf(func_def_571, type, sK429: term).
% 32.60/5.94 thf(func_def_572, type, sK430: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_573, type, sK431: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_574, type, sK432: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_575, type, sK433: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_576, type, sK434: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_577, type, sK435: (term > $o) > term).
% 32.60/5.94 thf(func_def_578, type, sK436: (term > $o) > term).
% 32.60/5.94 thf(func_def_579, type, sK437: subst).
% 32.60/5.94 thf(func_def_580, type, sK438: term > $o).
% 32.60/5.94 thf(func_def_581, type, sK439: term).
% 32.60/5.94 thf(func_def_582, type, sK440: term).
% 32.60/5.94 thf(func_def_583, type, sK441: subst).
% 32.60/5.94 thf(func_def_584, type, sK442: subst).
% 32.60/5.94 thf(func_def_585, type, sK443: term).
% 32.60/5.94 thf(func_def_586, type, sK444: term > $o).
% 32.60/5.94 thf(func_def_587, type, sK445: term).
% 32.60/5.94 thf(func_def_588, type, sK446: subst).
% 32.60/5.94 thf(func_def_589, type, sK447: term > term).
% 32.60/5.94 thf(func_def_590, type, sK448: (term > $o) > term).
% 32.60/5.94 thf(func_def_591, type, sK449: subst > (term > $o) > term).
% 32.60/5.94 thf(func_def_592, type, sK450: (term > $o) > term).
% 32.60/5.94 thf(func_def_593, type, sK451: (term > $o) > term).
% 32.60/5.94 thf(func_def_594, type, sK452: (term > $o) > term).
% 32.60/5.94 thf(func_def_595, type, sK453: (term > $o) > term).
% 32.60/5.94 thf(func_def_596, type, sK454: term).
% 32.60/5.94 thf(func_def_597, type, sK455: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_598, type, sK456: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_599, type, sK457: term > subst > term > term).
% 32.60/5.94 thf(func_def_600, type, sK458: term).
% 32.60/5.94 thf(func_def_601, type, sK459: term).
% 32.60/5.94 thf(func_def_602, type, sK460: term).
% 32.60/5.94 thf(func_def_603, type, sK461: term).
% 32.60/5.94 thf(func_def_604, type, sK462: term).
% 32.60/5.94 thf(func_def_605, type, sK463: term).
% 32.60/5.94 thf(func_def_606, type, sK464: term).
% 32.60/5.94 thf(func_def_607, type, sK465: term).
% 32.60/5.94 thf(func_def_608, type, sK466: term).
% 32.60/5.94 thf(func_def_609, type, sK467: term).
% 32.60/5.94 thf(func_def_610, type, sK468: term).
% 32.60/5.94 thf(func_def_611, type, sK469: term).
% 32.60/5.94 thf(func_def_612, type, sK470: term).
% 32.60/5.94 thf(func_def_613, type, sK471: term).
% 32.60/5.94 thf(func_def_614, type, sK472: term).
% 32.60/5.94 thf(func_def_615, type, sK473: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_616, type, sK474: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_617, type, sK475: term > subst > term > term).
% 32.60/5.94 thf(func_def_618, type, sK476: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_619, type, sK477: (term > $o) > term).
% 32.60/5.94 thf(func_def_620, type, sK478: (subst > term > subst > $o) > term > $o).
% 32.60/5.94 thf(func_def_621, type, sK479: term).
% 32.60/5.94 thf(func_def_622, type, sK480: term > subst > term > term).
% 32.60/5.94 thf(func_def_623, type, sK481: term > d_term).
% 32.60/5.94 thf(func_def_624, type, sK482: subst).
% 32.60/5.94 thf(func_def_625, type, sK483: term).
% 32.60/5.94 thf(func_def_626, type, sK484: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_627, type, sK485: term).
% 32.60/5.94 thf(func_def_628, type, sK486: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_629, type, sK487: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_630, type, sK488: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_631, type, sK489: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_632, type, sK490: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_633, type, sK491: subst > d_subst).
% 32.60/5.94 thf(func_def_634, type, sK492: subst).
% 32.60/5.94 thf(func_def_635, type, sK493: term > $o).
% 32.60/5.94 thf(func_def_636, type, sK494: term).
% 32.60/5.94 thf(func_def_637, type, sK495: (term > $o) > term).
% 32.60/5.94 thf(func_def_638, type, sK496: term > (term > $o) > subst > term > $o).
% 32.60/5.94 thf(func_def_639, type, sK497: term).
% 32.60/5.94 thf(func_def_640, type, sK498: term).
% 32.60/5.94 thf(func_def_641, type, sK499: term).
% 32.60/5.94 thf(func_def_642, type, sK500: term).
% 32.60/5.94 thf(func_def_643, type, sK501: term).
% 32.60/5.94 thf(func_def_644, type, sK502: term).
% 32.60/5.94 thf(func_def_645, type, sK503: term).
% 32.60/5.94 thf(func_def_646, type, sK504: term).
% 32.60/5.94 thf(func_def_647, type, sK505: term).
% 32.60/5.94 thf(func_def_648, type, sK506: (term > $o) > term).
% 32.60/5.94 thf(func_def_649, type, sK507: (term > $o) > term).
% 32.60/5.94 thf(func_def_650, type, sK508: term > $o).
% 32.60/5.94 thf(func_def_651, type, sK509: term).
% 32.60/5.94 thf(func_def_652, type, sK510: subst).
% 32.60/5.94 thf(func_def_653, type, sK511: subst).
% 32.60/5.94 thf(func_def_654, type, sK512: term).
% 32.60/5.94 thf(func_def_655, type, sK513: term > subst > term > term).
% 32.60/5.94 thf(func_def_656, type, sK514: term).
% 32.60/5.94 thf(func_def_657, type, sK515: term).
% 32.60/5.94 thf(func_def_658, type, sK516: term).
% 32.60/5.94 thf(func_def_659, type, sK517: term).
% 32.60/5.94 thf(func_def_660, type, sK518: term > $o).
% 32.60/5.94 thf(func_def_661, type, sK519: term).
% 32.60/5.94 thf(func_def_662, type, sK520: subst).
% 32.60/5.94 thf(func_def_663, type, sK521: (term > $o) > term).
% 32.60/5.94 thf(func_def_664, type, sK522: subst > term > (term > $o) > term > $o).
% 32.60/5.94 thf(func_def_665, type, sK523: term).
% 32.60/5.94 thf(func_def_666, type, sK524: term).
% 32.60/5.94 thf(func_def_667, type, sK525: subst).
% 32.60/5.94 thf(func_def_668, type, sK526: subst).
% 32.60/5.94 thf(func_def_669, type, sK527: subst).
% 32.60/5.94 thf(func_def_670, type, sK528: subst).
% 32.60/5.94 thf(func_def_671, type, sK529: term > $o).
% 32.60/5.94 thf(func_def_672, type, sK530: subst).
% 32.60/5.94 thf(func_def_673, type, sK531: term > $o).
% 32.60/5.94 thf(func_def_674, type, sK532: term).
% 32.60/5.94 thf(func_def_675, type, sK533: term).
% 32.60/5.94 thf(func_def_676, type, sK534: term).
% 32.60/5.94 thf(func_def_677, type, sK535: term).
% 32.60/5.94 thf(func_def_678, type, sK536: term).
% 32.60/5.94 thf(func_def_679, type, sK537: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_680, type, sK538: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_681, type, sK539: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_682, type, sK540: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_683, type, sK541: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_684, type, sK542: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_685, type, sK543: subst > term > term).
% 32.60/5.94 thf(func_def_686, type, sK544: subst).
% 32.60/5.94 thf(func_def_687, type, sK545: subst > term > term).
% 32.60/5.94 thf(func_def_688, type, sK546: term).
% 32.60/5.94 thf(func_def_689, type, sK547: subst).
% 32.60/5.94 thf(func_def_690, type, sK548: subst > term > term).
% 32.60/5.94 thf(func_def_691, type, sK549: term).
% 32.60/5.94 thf(func_def_692, type, sK550: term).
% 32.60/5.94 thf(func_def_693, type, sK551: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_694, type, sK552: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_695, type, sK553: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_696, type, sK554: term).
% 32.60/5.94 thf(func_def_697, type, sK555: term).
% 32.60/5.94 thf(func_def_698, type, sK556: term).
% 32.60/5.94 thf(func_def_699, type, sK557: term).
% 32.60/5.94 thf(func_def_700, type, sK558: term > subst > (term > $o) > (term > $o) > term).
% 32.60/5.94 thf(func_def_701, type, sK559: term > $o).
% 32.60/5.94 thf(func_def_702, type, sK560: term > $o).
% 32.60/5.94 thf(func_def_703, type, sK561: subst).
% 32.60/5.94 thf(func_def_704, type, sK562: term).
% 32.60/5.94 thf(func_def_705, type, sK563: subst).
% 32.60/5.94 thf(func_def_706, type, sK564: term).
% 32.60/5.94 thf(func_def_707, type, sK565: term > $o).
% 32.60/5.94 thf(func_def_708, type, sK566: term > $o).
% 32.60/5.94 thf(func_def_709, type, sK567: subst).
% 32.60/5.94 thf(func_def_710, type, sK568: term).
% 32.60/5.94 thf(func_def_711, type, sK569: term).
% 32.60/5.94 thf(func_def_712, type, sK570: subst).
% 32.60/5.94 thf(func_def_713, type, sK571: subst).
% 32.60/5.94 thf(func_def_714, type, sK572: term).
% 32.60/5.94 thf(func_def_715, type, sK573: (subst > term > subst > $o) > term > $o).
% 32.60/5.94 thf(func_def_716, type, sK574: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_717, type, sK575: (term > $o) > term).
% 32.60/5.94 thf(func_def_718, type, sK576: subst).
% 32.60/5.94 thf(func_def_719, type, sK577: term).
% 32.60/5.94 thf(func_def_720, type, sK578: subst).
% 32.60/5.94 thf(func_def_721, type, sK579: term).
% 32.60/5.94 thf(func_def_722, type, sK580: subst).
% 32.60/5.94 thf(func_def_723, type, sK581: term).
% 32.60/5.94 thf(func_def_724, type, sK582: (term > $o) > (term > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_725, type, sK583: term).
% 32.60/5.94 thf(func_def_726, type, sK584: subst).
% 32.60/5.94 thf(func_def_727, type, sK585: term > $o).
% 32.60/5.94 thf(func_def_728, type, sK586: term > $o).
% 32.60/5.94 thf(func_def_729, type, sK587: term).
% 32.60/5.94 thf(func_def_730, type, sK588: term).
% 32.60/5.94 thf(func_def_731, type, sK589: term).
% 32.60/5.94 thf(func_def_732, type, sK590: term).
% 32.60/5.94 thf(func_def_734, type, sK592: term > $o).
% 32.60/5.94 thf(func_def_735, type, sK593: subst > term > subst > $o).
% 32.60/5.94 thf(func_def_736, type, sK594: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_737, type, sK595: (subst > term > term) > term).
% 32.60/5.94 thf(func_def_738, type, sK596: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_739, type, sK597: (subst > term > term) > subst).
% 32.60/5.94 thf(func_def_740, type, sK598: term).
% 32.60/5.94 thf(func_def_741, type, sK599: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_742, type, sK600: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_743, type, sK601: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_744, type, sK602: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_745, type, sK603: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_746, type, sK604: (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_747, type, sK605: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_748, type, sK606: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_749, type, sK607: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_750, type, sK608: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_751, type, sK609: (term > $o) > term > term).
% 32.60/5.94 thf(func_def_752, type, sK610: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_753, type, sK611: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_754, type, sK612: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_755, type, sK613: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_756, type, sK614: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_757, type, sK615: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_758, type, sK616: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_759, type, sK617: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_760, type, sK618: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_761, type, sK619: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_762, type, sK620: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_763, type, sK621: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_764, type, sK622: (term > $o) > (subst > term > subst > $o) > term).
% 32.60/5.94 thf(func_def_765, type, sK623: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_766, type, sK624: (subst > term > subst > $o) > subst).
% 32.60/5.94 thf(func_def_767, type, sK625: term > (term > $o) > term).
% 32.60/5.94 thf(func_def_768, type, sK626: (subst > term > subst > $o) > subst > term > term).
% 32.60/5.94 thf(func_def_770, type, ph627: !>[X0: $tType]:(X0)).
% 32.60/5.94 thf(f12740,plain,(
% 32.60/5.94 $false),
% 32.60/5.94 inference(avatar_sat_refutation,[status(thm)],[f3220,f3834,f3842,f3858,f4559,f4613,f4848,f5545,f7223,f7333,f7414,f12736,f12738])).
% 32.60/5.94 thf(f12738,plain,(
% 32.60/5.94 spl591_545 | spl591_255 | ~spl591_515 | ~spl591_517),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f12672,f4611,f4597,f3217,f4845])).
% 32.60/5.94 thf(f4845,definition,(
% 32.60/5.94 spl591_545 <=> ((sP57 @ sK59) = $true)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_545])],[avatar_definition])).
% 32.60/5.94 thf(f3217,definition,(
% 32.60/5.94 spl591_255 <=> ($true = (sK60 @ (lam @ sK61)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_255])],[avatar_definition])).
% 32.60/5.94 thf(f4597,definition,(
% 32.60/5.94 spl591_515 <=> ! [X9 : term,X10 : term] : (X9 = X10)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_515])],[avatar_definition])).
% 32.60/5.94 thf(f4611,definition,(
% 32.60/5.94 spl591_517 <=> ! [X11 : term] : (((sK60 @ X11) = $true) | ($false = (sK59 @ (d2subst @ d_id) @ X11 @ (d2subst @ d_id))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_517])],[avatar_definition])).
% 32.60/5.94 thf(f12672,plain,(
% 32.60/5.94 ((sP57 @ sK59) = $true) | (spl591_255 | ~spl591_515 | ~spl591_517)),
% 32.60/5.94 inference(trivial_inequality_removal,[status(thm)],[f12636])).
% 32.60/5.94 thf(f12636,plain,(
% 32.60/5.94 ((sP57 @ sK59) = $true) | ($false = $true) | (spl591_255 | ~spl591_515 | ~spl591_517)),
% 32.60/5.94 inference(superposition,[status(thm)],[f7678,f4237])).
% 32.60/5.94 thf(f4237,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP57 @ X0) = $true)) )),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f4236,f4138])).
% 32.60/5.94 thf(f4138,plain,(
% 32.60/5.94 ( ! [X55 : term] : (((d2term @ d_one) = X55)) )),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f1217,f1180])).
% 32.60/5.94 thf(f1180,plain,(
% 32.60/5.94 ( ! [X113 : d_term] : ((d_one = X113)) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f545,plain,(
% 32.60/5.94 ((hoasinduction_lem3v2_f_lthm = $true) | ! [X1 : subst > term > term] : ((X1 @ (sK455 @ X1) @ (sK456 @ X1)) != (sub @ sK454 @ (push @ (sK456 @ X1) @ (sK455 @ X1))))) & (! [X4 : term] : ! [X6 : subst,X7 : term] : ((sK457 @ X4 @ X6 @ X7) = (sub @ X4 @ (push @ X7 @ X6))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (! [X8 : term,X9 : term,X10 : term,X11 : term] : (((ap @ X9 @ X8) != (ap @ X10 @ X11)) | (X9 = X10)) | (apinj1 != $true)) & ((apinj1 = $true) | (((ap @ sK459 @ sK458) = (ap @ sK460 @ sK461)) & (sK460 != sK459))) & (hoasinduction_lem2_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP58 != $true)) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) | (! [X16 : term,X17 : term,X18 : term,X19 : term] : (((ap @ X19 @ X17) != (ap @ X16 @ X18)) | (X17 = X18)) & (((ap @ (sub @ sK465 @ id) @ sK462) = (ap @ (sub @ sK464 @ id) @ sK463)) & (sK462 != sK463)))) & ((((ap @ sK469 @ sK467) = (ap @ sK466 @ sK468)) & (sK468 != sK467)) | ! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ (sub @ X30 @ id) @ X29) != (ap @ (sub @ X31 @ id) @ X28)) | (X28 = X29)) | (hoasapinj2_lthm != $true)) & (axapp = $true) & (induction2_gthm = $true) & ! [X32 : d_subst] : (d_id = X32) & ((termmset_lthm = $true) | (((sub @ sK470 @ id) != sK470) & ! [X34 : term] : ((sub @ X34 @ id) = X34))) & (! [X35 : term] : ((sub @ X35 @ id) = X35) | ((sub @ sK471 @ id) != sK471) | (termmset_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X38 : subst > term > term] : ((sub @ sK472 @ (push @ (sK474 @ X38) @ (sK473 @ X38))) != (X38 @ (sK473 @ X38) @ (sK474 @ X38)))) & (! [X41 : term] : ! [X43 : subst,X44 : term] : ((sub @ X41 @ (push @ X44 @ X43)) = (sK475 @ X41 @ X43 @ X44)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (ulamvarind = $true) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X46 : term > $o] : ((sK476 @ id @ (sK477 @ X46) @ id) != (X46 @ (sK477 @ X46)))) & (! [X48 : subst > term > subst > $o] : ! [X50 : term] : ((sK478 @ X48 @ X50) = (X48 @ id @ X50 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X52 : subst > term > term] : ((sub @ sK479 @ (push @ one @ sh)) != (X52 @ sh @ one))) & (! [X53 : term] : ((sK480 @ X53 @ sh @ one) = (sub @ X53 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP53)) & (($true = sP53) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X55 : term] : ((d2term @ (sK481 @ X55)) = X55) & (hoasapinj2_gthm = $true) & (! [X57 : subst,X58 : term] : ((sub @ one @ (push @ X58 @ X57)) = X58) | (axvarcons != $true)) & ((axvarcons = $true) | (sK483 != (sub @ one @ (push @ sK483 @ sK482)))) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((induction2_lthm = $true) | ($true != sP46)) & (($true = sP46) | (induction2_lthm != $true)) & (! [X61 : term,X62 : subst > term > subst > $o] : ((! [X64 : subst,X65 : term,X66 : subst] : ((sK484 @ X62 @ (comp @ X64 @ X66) @ (sub @ X65 @ X66)) = (sub @ (sK484 @ X62 @ X64 @ X65) @ X66)) & ! [X67 : term] : (($true = (X62 @ id @ (sK484 @ X62 @ id @ X67) @ id)) | ((X62 @ id @ X67 @ id) != $true)) & ((X62 @ id @ (lam @ (sK484 @ X62 @ sh @ one)) @ id) != $true)) | ((X62 @ id @ X61 @ id) = $true) | ((sP42 @ X62) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X70 : subst > term > term] : (((X70 @ (comp @ (sK487 @ X70) @ (sK489 @ X70)) @ (sub @ (sK488 @ X70) @ (sK489 @ X70))) != (sub @ (X70 @ (sK487 @ X70) @ (sK488 @ X70)) @ (sK489 @ X70))) | (($true != (sK486 @ id @ (X70 @ id @ (sK490 @ X70)) @ id)) & ((sK486 @ id @ (sK490 @ X70) @ id) = $true)) | ($true = (sK486 @ id @ (lam @ (X70 @ sh @ one)) @ id))) & ((sK486 @ id @ sK485 @ id) != $true) & ((sP42 @ sK486) != $true))) & ! [X75 : subst] : ((d2subst @ (sK491 @ X75)) = X75) & ((pushprop_lem0 = $true) | ! [X80 : term > $o] : ((sK493 @ (sub @ (sK495 @ X80) @ (push @ sK494 @ sK492))) != (X80 @ (sK495 @ X80)))) & (! [X82 : subst,X83 : term > $o,X84 : term] : ! [X86 : term] : ((X83 @ (sub @ X86 @ (push @ X84 @ X82))) = (sK496 @ X84 @ X83 @ X82 @ X86)) | (pushprop_lem0 != $true)) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & (! [X87 : term,X88 : term,X89 : term,X90 : term] : (((ap @ (sub @ X90 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)) | (X87 = X90)) | (sK497 != (sub @ sK497 @ id)) | ((sK500 != sK501) & ((ap @ sK501 @ sK499) = (ap @ sK500 @ sK498))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ((((ap @ (sub @ sK502 @ id) @ sK503) = (ap @ (sub @ sK505 @ id) @ sK504)) & (sK505 != sK502)) & ! [X100 : term] : ((sub @ X100 @ id) = X100) & ! [X101 : term,X102 : term,X103 : term,X104 : term] : ((X103 = X104) | ((ap @ X104 @ X102) != (ap @ X103 @ X101))))) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & (! [X105 : term > $o,X106 : term] : ((($true != (X105 @ (sK506 @ X105))) & ((var @ (sK506 @ X105)) = $true)) | ((sP39 @ X105) = $true) | ((X105 @ X106) = $true) | (((X105 @ (sK507 @ X105)) = $true) & ((X105 @ (lam @ (sK507 @ X105))) != $true))) | (induction != $true)) & ((induction = $true) | (! [X111 : term] : (((sK508 @ X111) = $true) | ((var @ X111) != $true)) & ((sP39 @ sK508) != $true) & ((sK508 @ sK509) != $true) & ! [X112 : term] : (((sK508 @ X112) != $true) | ((sK508 @ (lam @ X112)) = $true)))) & (hoasinduction_gthm = $true) & ! [X113 : d_term] : (d_one = X113) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction != $true)) & ((! [X114 : subst] : ((comp @ id @ X114) = X114) & ! [X115 : subst] : ((comp @ X115 @ id) = X115)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK510 != (comp @ id @ sK510)) | (sK511 != (comp @ sK511 @ id))) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3b = $true) | ! [X119 : subst > term > term] : ((X119 @ sh @ one) != (sub @ sK512 @ (push @ one @ sh)))) & (! [X120 : term] : ((sub @ X120 @ (push @ one @ sh)) = (sK513 @ X120 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj1 = $true) | ((sK514 != sK517) & ((ap @ (sub @ sK514 @ id) @ sK515) = (ap @ (sub @ sK517 @ id) @ sK516)))) & (! [X126 : term,X127 : term,X128 : term,X129 : term] : ((X126 = X129) | ((ap @ (sub @ X126 @ id) @ X127) != (ap @ (sub @ X129 @ id) @ X128))) | (hoasapinj1 != $true)) & ((pushprop_lem0_lthm = $true) | ! [X133 : term > $o] : ((sK518 @ (sub @ (sK521 @ X133) @ (push @ sK519 @ sK520))) != (X133 @ (sK521 @ X133)))) & (! [X135 : term > $o,X136 : term,X137 : subst] : ! [X139 : term] : ((sK522 @ X137 @ X136 @ X135 @ X139) = (X135 @ (sub @ X139 @ (push @ X136 @ X137)))) | (pushprop_lem0_lthm != $true)) & (ulamvarsh = $true) & ((laminj = $true) | (((lam @ sK523) = (lam @ sK524)) & (sK523 != sK524))) & (! [X142 : term,X143 : term] : (((lam @ X142) != (lam @ X143)) | (X142 = X143)) | (laminj != $true)) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X144 : d_term,X145 : d_term] : ((X144 = X145) | ((d2term @ X144) != (d2term @ X145))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3v2a = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2a != $true)) & (((comp @ id @ sK525) != sK525) | (sK526 != (comp @ sK526 @ id)) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X149 : subst] : ((comp @ X149 @ id) = X149)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X150 : subst] : ((comp @ id @ X150) = X150) & ! [X151 : subst] : ((comp @ X151 @ id) = X151) & ((sK527 != (comp @ id @ sK527)) | (sK528 != (comp @ sK528 @ id))))) & (($true = sP32) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP32)) & (! [X154 : term > $o,X155 : subst,X156 : term > $o,X157 : term,X158 : term] : (((X156 @ (sub @ X158 @ (push @ X157 @ X155))) = $true) | ($true != (X154 @ X158))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (((sK531 @ (sub @ sK533 @ (push @ sK532 @ sK530))) != $true) & ((sK529 @ sK533) = $true))) & (pushprop_lem2v2_gthm = $true) & ((sP31 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP31 != $true)) & ((hoaslaminj_lthm = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar = $true) & ((shinj = $true) | (((sub @ sK535 @ sh) = (sub @ sK534 @ sh)) & (sK534 != sK535))) & (! [X166 : term,X167 : term] : (((sub @ X167 @ sh) != (sub @ X166 @ sh)) | (X166 = X167)) | (shinj != $true)) & (! [X168 : term] : ((sub @ X168 @ id) = X168) | (termmset != $true)) & ((termmset = $true) | ((sub @ sK536 @ id) != sK536)) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X170 : subst > term > term,X171 : subst,X172 : subst > term > term,X173 : term] : (((lam @ (X172 @ sh @ one)) != (lam @ (X170 @ sh @ one))) | ((X172 @ X171 @ X173) = (X170 @ X171 @ X173)) | ((X170 @ (comp @ (sK538 @ X170) @ (sK539 @ X170)) @ (sub @ (sK537 @ X170) @ (sK539 @ X170))) != (sub @ (X170 @ (sK538 @ X170) @ (sK537 @ X170)) @ (sK539 @ X170))) | ((X172 @ (comp @ (sK540 @ X172) @ (sK542 @ X172)) @ (sub @ (sK541 @ X172) @ (sK542 @ X172))) != (sub @ (X172 @ (sK540 @ X172) @ (sK541 @ X172)) @ (sK542 @ X172)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (((lam @ (sK543 @ sh @ one)) = (lam @ (sK545 @ sh @ one))) & ((sK543 @ sK544 @ sK546) != (sK545 @ sK544 @ sK546)) & ! [X184 : term,X185 : subst,X186 : subst] : ((sK543 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)) = (sub @ (sK543 @ X185 @ X184) @ X186)) & ! [X187 : subst,X188 : term,X189 : subst] : ((sub @ (sK545 @ X187 @ X188) @ X189) = (sK545 @ (comp @ X187 @ X189) @ (sub @ X188 @ X189))))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X190 : subst] : ((push @ (sub @ one @ X190) @ (comp @ sh @ X190)) = X190) | (axscons != $true)) & ((axscons = $true) | ((push @ (sub @ one @ sK547) @ (comp @ sh @ sK547)) != sK547)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) | (! [X195 : subst,X196 : term,X197 : subst] : ((sK548 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195)) = (sub @ (sK548 @ X197 @ X196) @ X195)) & ((ap @ (sub @ sK549 @ id) @ sK550) = (lam @ (sK548 @ sh @ one))))) & (! [X198 : subst > term > term,X199 : term,X200 : term] : (((X198 @ (comp @ (sK553 @ X198) @ (sK551 @ X198)) @ (sub @ (sK552 @ X198) @ (sK551 @ X198))) != (sub @ (X198 @ (sK553 @ X198) @ (sK552 @ X198)) @ (sK551 @ X198))) | ((ap @ (sub @ X199 @ id) @ X200) != (lam @ (X198 @ sh @ one)))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & (($true = sP16) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP16)) & ((sP15 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP15 != $true)) & (! [X204 : term,X205 : term,X206 : term,X207 : term] : (((ap @ (sub @ X204 @ id) @ X205) != (ap @ (sub @ X207 @ id) @ X206)) | (X205 = X206)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | (((ap @ (sub @ sK554 @ id) @ sK555) = (ap @ (sub @ sK557 @ id) @ sK556)) & (sK555 != sK556))) & ((hoasinduction_lem3a_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lem3a_lthm != $true)) & (! [X212 : term > $o,X213 : term > $o,X214 : subst,X215 : term] : (((X213 @ (sub @ (sK558 @ X215 @ X214 @ X213 @ X212) @ (push @ X215 @ X214))) != (X212 @ (sK558 @ X215 @ X214 @ X213 @ X212))) | ((X212 @ one) = $true) | ((X213 @ X215) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X221 : term] : ((sK560 @ (sub @ X221 @ (push @ sK562 @ sK561))) = (sK559 @ X221)) & ((sK559 @ one) != $true) & ($true = (sK560 @ sK562)))) & ((axidr = $true) | (sK563 != (comp @ sK563 @ id))) & (! [X223 : subst] : ((comp @ X223 @ id) = X223) | (axidr != $true)) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) | (! [X224 : term,X225 : subst] : ((sub @ one @ (push @ X224 @ X225)) = X224) & ! [X226 : subst,X227 : term] : ((comp @ sh @ (push @ X227 @ X226)) = X226) & (((sK565 @ sK568) = $true) & ((sK566 @ (sub @ sK568 @ (push @ sK564 @ sK567))) != $true)))) & ((sK569 != (sub @ one @ (push @ sK569 @ sK570))) | (sK571 != (comp @ sh @ (push @ sK572 @ sK571))) | ! [X237 : term,X238 : term > $o,X239 : term > $o,X240 : subst,X241 : term] : (((X238 @ X241) != $true) | ((X239 @ (sub @ X241 @ (push @ X237 @ X240))) = $true)) | (pushprop_lem1_lthm != $true)) & (! [X242 : subst > term > subst > $o] : ! [X244 : term] : ((sK573 @ X242 @ X244) = (X242 @ id @ X244 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X246 : term > $o] : ((X246 @ (sK575 @ X246)) != (sK574 @ id @ (sK575 @ X246) @ id))) & ((sP11 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP11 != $true)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK577 @ sK576)) != sK576)) & (! [X250 : subst,X251 : term] : ((comp @ sh @ (push @ X251 @ X250)) = X250) | (axshiftcons != $true)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X252 : d_subst,X253 : d_subst] : ((X252 = X253) | ((d2subst @ X253) != (d2subst @ X252))) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((axidl = $true) | ((comp @ id @ sK578) != sK578)) & (! [X255 : subst] : ((comp @ id @ X255) = X255) | (axidl != $true)) & (! [X256 : term] : ((sub @ X256 @ id) = X256) | (axvarid != $true)) & ((axvarid = $true) | ((sub @ sK579 @ id) != sK579)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & ((sK581 != (sub @ one @ (push @ sK581 @ sK580))) | ! [X260 : term,X261 : subst,X262 : term > $o,X263 : term > $o] : (((X263 @ (sub @ (sK582 @ X263 @ X262 @ X261 @ X260) @ (push @ X260 @ X261))) != (X262 @ (sK582 @ X263 @ X262 @ X261 @ X260))) | ((X262 @ one) = $true) | ((X263 @ X260) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X265 : subst,X266 : term] : ((sub @ one @ (push @ X266 @ X265)) = X266) & (! [X271 : term] : ((sK585 @ X271) = (sK586 @ (sub @ X271 @ (push @ sK583 @ sK584)))) & ($true != (sK585 @ one)) & ((sK586 @ sK583) = $true)))) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X272 : term,X273 : term,X274 : term,X275 : term] : (((ap @ X273 @ X275) != (ap @ X272 @ X274)) | (X274 = X275)) | (apinj2 != $true)) & ((apinj2 = $true) | (((ap @ sK587 @ sK589) = (ap @ sK588 @ sK590)) & (sK590 != sK589))) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474])).
% 32.60/5.94 thf(f474,plain,(
% 32.60/5.94 ? [X0 : term] : ! [X1 : subst > term > term] : ? [X2 : subst,X3 : term] : ((sub @ X0 @ (push @ X3 @ X2)) != (X1 @ X2 @ X3)) => ! [X1 : subst > term > term] : ? [X3 : term,X2 : subst] : ((X1 @ X2 @ X3) != (sub @ sK454 @ (push @ X3 @ X2)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f475,plain,(
% 32.60/5.94 ! [X1 : subst > term > term] : (? [X3 : term,X2 : subst] : ((X1 @ X2 @ X3) != (sub @ sK454 @ (push @ X3 @ X2))) => ((X1 @ (sK455 @ X1) @ (sK456 @ X1)) != (sub @ sK454 @ (push @ (sK456 @ X1) @ (sK455 @ X1)))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f476,plain,(
% 32.60/5.94 ! [X4 : term] : (? [X5 : subst > term > term] : ! [X6 : subst,X7 : term] : ((X5 @ X6 @ X7) = (sub @ X4 @ (push @ X7 @ X6))) => ! [X7 : term,X6 : subst] : ((sK457 @ X4 @ X6 @ X7) = (sub @ X4 @ (push @ X7 @ X6))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f477,plain,(
% 32.60/5.94 ? [X12 : term,X13 : term,X14 : term,X15 : term] : (((ap @ X14 @ X15) = (ap @ X13 @ X12)) & (X13 != X14)) => (((ap @ sK459 @ sK458) = (ap @ sK460 @ sK461)) & (sK460 != sK459))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f478,plain,(
% 32.60/5.94 ? [X20 : term,X21 : term,X22 : term,X23 : term] : (((ap @ (sub @ X23 @ id) @ X20) = (ap @ (sub @ X22 @ id) @ X21)) & (X20 != X21)) => (((ap @ (sub @ sK465 @ id) @ sK462) = (ap @ (sub @ sK464 @ id) @ sK463)) & (sK462 != sK463))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f479,plain,(
% 32.60/5.94 ? [X24 : term,X25 : term,X26 : term,X27 : term] : (((ap @ X27 @ X25) = (ap @ X24 @ X26)) & (X25 != X26)) => (((ap @ sK469 @ sK467) = (ap @ sK466 @ sK468)) & (sK468 != sK467))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f480,plain,(
% 32.60/5.94 ? [X33 : term] : ((sub @ X33 @ id) != X33) => ((sub @ sK470 @ id) != sK470)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f481,plain,(
% 32.60/5.94 ? [X36 : term] : ((sub @ X36 @ id) != X36) => ((sub @ sK471 @ id) != sK471)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f482,plain,(
% 32.60/5.94 ? [X37 : term] : ! [X38 : subst > term > term] : ? [X39 : subst,X40 : term] : ((X38 @ X39 @ X40) != (sub @ X37 @ (push @ X40 @ X39))) => ! [X38 : subst > term > term] : ? [X40 : term,X39 : subst] : ((X38 @ X39 @ X40) != (sub @ sK472 @ (push @ X40 @ X39)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f483,plain,(
% 32.60/5.94 ! [X38 : subst > term > term] : (? [X40 : term,X39 : subst] : ((X38 @ X39 @ X40) != (sub @ sK472 @ (push @ X40 @ X39))) => ((sub @ sK472 @ (push @ (sK474 @ X38) @ (sK473 @ X38))) != (X38 @ (sK473 @ X38) @ (sK474 @ X38))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f484,plain,(
% 32.60/5.94 ! [X41 : term] : (? [X42 : subst > term > term] : ! [X43 : subst,X44 : term] : ((X42 @ X43 @ X44) = (sub @ X41 @ (push @ X44 @ X43))) => ! [X44 : term,X43 : subst] : ((sub @ X41 @ (push @ X44 @ X43)) = (sK475 @ X41 @ X43 @ X44)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f485,plain,(
% 32.60/5.94 ? [X45 : subst > term > subst > $o] : ! [X46 : term > $o] : ? [X47 : term] : ((X45 @ id @ X47 @ id) != (X46 @ X47)) => ! [X46 : term > $o] : ? [X47 : term] : ((sK476 @ id @ X47 @ id) != (X46 @ X47))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f486,plain,(
% 32.60/5.94 ! [X46 : term > $o] : (? [X47 : term] : ((sK476 @ id @ X47 @ id) != (X46 @ X47)) => ((sK476 @ id @ (sK477 @ X46) @ id) != (X46 @ (sK477 @ X46))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f487,plain,(
% 32.60/5.94 ! [X48 : subst > term > subst > $o] : (? [X49 : term > $o] : ! [X50 : term] : ((X48 @ id @ X50 @ id) = (X49 @ X50)) => ! [X50 : term] : ((sK478 @ X48 @ X50) = (X48 @ id @ X50 @ id)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f488,plain,(
% 32.60/5.94 ? [X51 : term] : ! [X52 : subst > term > term] : ((X52 @ sh @ one) != (sub @ X51 @ (push @ one @ sh))) => ! [X52 : subst > term > term] : ((sub @ sK479 @ (push @ one @ sh)) != (X52 @ sh @ one))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f489,plain,(
% 32.60/5.94 ! [X53 : term] : (? [X54 : subst > term > term] : ((sub @ X53 @ (push @ one @ sh)) = (X54 @ sh @ one)) => ((sK480 @ X53 @ sh @ one) = (sub @ X53 @ (push @ one @ sh))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f490,plain,(
% 32.60/5.94 ! [X55 : term] : (? [X56 : d_term] : ((d2term @ X56) = X55) => ((d2term @ (sK481 @ X55)) = X55))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f491,plain,(
% 32.60/5.94 ? [X59 : subst,X60 : term] : ((sub @ one @ (push @ X60 @ X59)) != X60) => (sK483 != (sub @ one @ (push @ sK483 @ sK482)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f492,plain,(
% 32.60/5.94 ! [X62 : subst > term > subst > $o] : (? [X63 : subst > term > term] : (! [X64 : subst,X65 : term,X66 : subst] : ((sub @ (X63 @ X64 @ X65) @ X66) = (X63 @ (comp @ X64 @ X66) @ (sub @ X65 @ X66))) & ! [X67 : term] : (((X62 @ id @ (X63 @ id @ X67) @ id) = $true) | ((X62 @ id @ X67 @ id) != $true)) & ((X62 @ id @ (lam @ (X63 @ sh @ one)) @ id) != $true)) => (! [X66 : subst,X65 : term,X64 : subst] : ((sK484 @ X62 @ (comp @ X64 @ X66) @ (sub @ X65 @ X66)) = (sub @ (sK484 @ X62 @ X64 @ X65) @ X66)) & ! [X67 : term] : (($true = (X62 @ id @ (sK484 @ X62 @ id @ X67) @ id)) | ((X62 @ id @ X67 @ id) != $true)) & ((X62 @ id @ (lam @ (sK484 @ X62 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f493,plain,(
% 32.60/5.94 ? [X68 : term,X69 : subst > term > subst > $o] : (! [X70 : subst > term > term] : (? [X71 : subst,X72 : term,X73 : subst] : ((sub @ (X70 @ X71 @ X72) @ X73) != (X70 @ (comp @ X71 @ X73) @ (sub @ X72 @ X73))) | ? [X74 : term] : (((X69 @ id @ (X70 @ id @ X74) @ id) != $true) & ((X69 @ id @ X74 @ id) = $true)) | ((X69 @ id @ (lam @ (X70 @ sh @ one)) @ id) = $true)) & ((X69 @ id @ X68 @ id) != $true) & ((sP42 @ X69) != $true)) => (! [X70 : subst > term > term] : (? [X71 : subst,X72 : term,X73 : subst] : ((sub @ (X70 @ X71 @ X72) @ X73) != (X70 @ (comp @ X71 @ X73) @ (sub @ X72 @ X73))) | ? [X74 : term] : (((sK486 @ id @ (X70 @ id @ X74) @ id) != $true) & ((sK486 @ id @ X74 @ id) = $true)) | ($true = (sK486 @ id @ (lam @ (X70 @ sh @ one)) @ id))) & ((sK486 @ id @ sK485 @ id) != $true) & ((sP42 @ sK486) != $true))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f494,plain,(
% 32.60/5.94 ! [X70 : subst > term > term] : (? [X71 : subst,X72 : term,X73 : subst] : ((sub @ (X70 @ X71 @ X72) @ X73) != (X70 @ (comp @ X71 @ X73) @ (sub @ X72 @ X73))) => ((X70 @ (comp @ (sK487 @ X70) @ (sK489 @ X70)) @ (sub @ (sK488 @ X70) @ (sK489 @ X70))) != (sub @ (X70 @ (sK487 @ X70) @ (sK488 @ X70)) @ (sK489 @ X70))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f495,plain,(
% 32.60/5.94 ! [X70 : subst > term > term] : (? [X74 : term] : (((sK486 @ id @ (X70 @ id @ X74) @ id) != $true) & ((sK486 @ id @ X74 @ id) = $true)) => (($true != (sK486 @ id @ (X70 @ id @ (sK490 @ X70)) @ id)) & ((sK486 @ id @ (sK490 @ X70) @ id) = $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f496,plain,(
% 32.60/5.94 ! [X75 : subst] : (? [X76 : d_subst] : ((d2subst @ X76) = X75) => ((d2subst @ (sK491 @ X75)) = X75))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f497,plain,(
% 32.60/5.94 ? [X77 : subst,X78 : term > $o,X79 : term] : ! [X80 : term > $o] : ? [X81 : term] : ((X80 @ X81) != (X78 @ (sub @ X81 @ (push @ X79 @ X77)))) => ! [X80 : term > $o] : ? [X81 : term] : ((sK493 @ (sub @ X81 @ (push @ sK494 @ sK492))) != (X80 @ X81))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f498,plain,(
% 32.60/5.94 ! [X80 : term > $o] : (? [X81 : term] : ((sK493 @ (sub @ X81 @ (push @ sK494 @ sK492))) != (X80 @ X81)) => ((sK493 @ (sub @ (sK495 @ X80) @ (push @ sK494 @ sK492))) != (X80 @ (sK495 @ X80))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f499,plain,(
% 32.60/5.94 ! [X82 : subst,X83 : term > $o,X84 : term] : (? [X85 : term > $o] : ! [X86 : term] : ((X83 @ (sub @ X86 @ (push @ X84 @ X82))) = (X85 @ X86)) => ! [X86 : term] : ((X83 @ (sub @ X86 @ (push @ X84 @ X82))) = (sK496 @ X84 @ X83 @ X82 @ X86)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f500,plain,(
% 32.60/5.94 ? [X91 : term] : ((sub @ X91 @ id) != X91) => (sK497 != (sub @ sK497 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f501,plain,(
% 32.60/5.94 ? [X92 : term,X93 : term,X94 : term,X95 : term] : ((X94 != X95) & ((ap @ X94 @ X92) = (ap @ X95 @ X93))) => ((sK500 != sK501) & ((ap @ sK501 @ sK499) = (ap @ sK500 @ sK498)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f502,plain,(
% 32.60/5.94 ? [X96 : term,X97 : term,X98 : term,X99 : term] : (((ap @ (sub @ X96 @ id) @ X97) = (ap @ (sub @ X99 @ id) @ X98)) & (X96 != X99)) => (((ap @ (sub @ sK502 @ id) @ sK503) = (ap @ (sub @ sK505 @ id) @ sK504)) & (sK505 != sK502))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f503,plain,(
% 32.60/5.94 ! [X105 : term > $o] : (? [X107 : term] : (((X105 @ X107) != $true) & ((var @ X107) = $true)) => (($true != (X105 @ (sK506 @ X105))) & ((var @ (sK506 @ X105)) = $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f504,plain,(
% 32.60/5.94 ! [X105 : term > $o] : (? [X108 : term] : (((X105 @ X108) = $true) & ((X105 @ (lam @ X108)) != $true)) => (((X105 @ (sK507 @ X105)) = $true) & ((X105 @ (lam @ (sK507 @ X105))) != $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f505,plain,(
% 32.60/5.94 ? [X109 : term > $o,X110 : term] : (! [X111 : term] : (((X109 @ X111) = $true) | ((var @ X111) != $true)) & ((sP39 @ X109) != $true) & ((X109 @ X110) != $true) & ! [X112 : term] : (((X109 @ X112) != $true) | ((X109 @ (lam @ X112)) = $true))) => (! [X111 : term] : (((sK508 @ X111) = $true) | ((var @ X111) != $true)) & ((sP39 @ sK508) != $true) & ((sK508 @ sK509) != $true) & ! [X112 : term] : (((sK508 @ X112) != $true) | ((sK508 @ (lam @ X112)) = $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f506,plain,(
% 32.60/5.94 ? [X116 : subst] : ((comp @ id @ X116) != X116) => (sK510 != (comp @ id @ sK510))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f507,plain,(
% 32.60/5.94 ? [X117 : subst] : ((comp @ X117 @ id) != X117) => (sK511 != (comp @ sK511 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f508,plain,(
% 32.60/5.94 ? [X118 : term] : ! [X119 : subst > term > term] : ((X119 @ sh @ one) != (sub @ X118 @ (push @ one @ sh))) => ! [X119 : subst > term > term] : ((X119 @ sh @ one) != (sub @ sK512 @ (push @ one @ sh)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f509,plain,(
% 32.60/5.94 ! [X120 : term] : (? [X121 : subst > term > term] : ((sub @ X120 @ (push @ one @ sh)) = (X121 @ sh @ one)) => ((sub @ X120 @ (push @ one @ sh)) = (sK513 @ X120 @ sh @ one)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f510,plain,(
% 32.60/5.94 ? [X122 : term,X123 : term,X124 : term,X125 : term] : ((X122 != X125) & ((ap @ (sub @ X125 @ id) @ X124) = (ap @ (sub @ X122 @ id) @ X123))) => ((sK514 != sK517) & ((ap @ (sub @ sK514 @ id) @ sK515) = (ap @ (sub @ sK517 @ id) @ sK516)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f511,plain,(
% 32.60/5.94 ? [X130 : term > $o,X131 : term,X132 : subst] : ! [X133 : term > $o] : ? [X134 : term] : ((X133 @ X134) != (X130 @ (sub @ X134 @ (push @ X131 @ X132)))) => ! [X133 : term > $o] : ? [X134 : term] : ((X133 @ X134) != (sK518 @ (sub @ X134 @ (push @ sK519 @ sK520))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f512,plain,(
% 32.60/5.94 ! [X133 : term > $o] : (? [X134 : term] : ((X133 @ X134) != (sK518 @ (sub @ X134 @ (push @ sK519 @ sK520)))) => ((sK518 @ (sub @ (sK521 @ X133) @ (push @ sK519 @ sK520))) != (X133 @ (sK521 @ X133))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f513,plain,(
% 32.60/5.94 ! [X135 : term > $o,X136 : term,X137 : subst] : (? [X138 : term > $o] : ! [X139 : term] : ((X138 @ X139) = (X135 @ (sub @ X139 @ (push @ X136 @ X137)))) => ! [X139 : term] : ((sK522 @ X137 @ X136 @ X135 @ X139) = (X135 @ (sub @ X139 @ (push @ X136 @ X137)))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f514,plain,(
% 32.60/5.94 ? [X140 : term,X141 : term] : (((lam @ X141) = (lam @ X140)) & (X140 != X141)) => (((lam @ sK523) = (lam @ sK524)) & (sK523 != sK524))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f515,plain,(
% 32.60/5.94 ? [X146 : subst] : ((comp @ id @ X146) != X146) => ((comp @ id @ sK525) != sK525)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f516,plain,(
% 32.60/5.94 ? [X147 : subst] : ((comp @ X147 @ id) != X147) => (sK526 != (comp @ sK526 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f517,plain,(
% 32.60/5.94 ? [X152 : subst] : ((comp @ id @ X152) != X152) => (sK527 != (comp @ id @ sK527))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f518,plain,(
% 32.60/5.94 ? [X153 : subst] : ((comp @ X153 @ id) != X153) => (sK528 != (comp @ sK528 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f519,plain,(
% 32.60/5.94 ? [X159 : term > $o,X160 : subst,X161 : term > $o,X162 : term,X163 : term] : (((X161 @ (sub @ X163 @ (push @ X162 @ X160))) != $true) & ($true = (X159 @ X163))) => (((sK531 @ (sub @ sK533 @ (push @ sK532 @ sK530))) != $true) & ((sK529 @ sK533) = $true))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f520,plain,(
% 32.60/5.94 ? [X164 : term,X165 : term] : (((sub @ X164 @ sh) = (sub @ X165 @ sh)) & (X164 != X165)) => (((sub @ sK535 @ sh) = (sub @ sK534 @ sh)) & (sK534 != sK535))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f521,plain,(
% 32.60/5.94 ? [X169 : term] : ((sub @ X169 @ id) != X169) => ((sub @ sK536 @ id) != sK536)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f522,plain,(
% 32.60/5.94 ! [X170 : subst > term > term] : (? [X174 : term,X175 : subst,X176 : subst] : ((sub @ (X170 @ X175 @ X174) @ X176) != (X170 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) => ((X170 @ (comp @ (sK538 @ X170) @ (sK539 @ X170)) @ (sub @ (sK537 @ X170) @ (sK539 @ X170))) != (sub @ (X170 @ (sK538 @ X170) @ (sK537 @ X170)) @ (sK539 @ X170))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f523,plain,(
% 32.60/5.94 ! [X172 : subst > term > term] : (? [X177 : subst,X178 : term,X179 : subst] : ((X172 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179)) != (sub @ (X172 @ X177 @ X178) @ X179)) => ((X172 @ (comp @ (sK540 @ X172) @ (sK542 @ X172)) @ (sub @ (sK541 @ X172) @ (sK542 @ X172))) != (sub @ (X172 @ (sK540 @ X172) @ (sK541 @ X172)) @ (sK542 @ X172))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f524,plain,(
% 32.60/5.94 ? [X180 : subst > term > term,X181 : subst,X182 : subst > term > term,X183 : term] : (((lam @ (X182 @ sh @ one)) = (lam @ (X180 @ sh @ one))) & ((X182 @ X181 @ X183) != (X180 @ X181 @ X183)) & ! [X184 : term,X185 : subst,X186 : subst] : ((sub @ (X180 @ X185 @ X184) @ X186) = (X180 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186))) & ! [X187 : subst,X188 : term,X189 : subst] : ((X182 @ (comp @ X187 @ X189) @ (sub @ X188 @ X189)) = (sub @ (X182 @ X187 @ X188) @ X189))) => (((lam @ (sK543 @ sh @ one)) = (lam @ (sK545 @ sh @ one))) & ((sK543 @ sK544 @ sK546) != (sK545 @ sK544 @ sK546)) & ! [X186 : subst,X185 : subst,X184 : term] : ((sK543 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)) = (sub @ (sK543 @ X185 @ X184) @ X186)) & ! [X189 : subst,X188 : term,X187 : subst] : ((sub @ (sK545 @ X187 @ X188) @ X189) = (sK545 @ (comp @ X187 @ X189) @ (sub @ X188 @ X189))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f525,plain,(
% 32.60/5.94 ? [X191 : subst] : ((push @ (sub @ one @ X191) @ (comp @ sh @ X191)) != X191) => ((push @ (sub @ one @ sK547) @ (comp @ sh @ sK547)) != sK547)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f526,plain,(
% 32.60/5.94 ? [X192 : subst > term > term,X193 : term,X194 : term] : (! [X195 : subst,X196 : term,X197 : subst] : ((sub @ (X192 @ X197 @ X196) @ X195) = (X192 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195))) & ((ap @ (sub @ X193 @ id) @ X194) = (lam @ (X192 @ sh @ one)))) => (! [X197 : subst,X196 : term,X195 : subst] : ((sK548 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195)) = (sub @ (sK548 @ X197 @ X196) @ X195)) & ((ap @ (sub @ sK549 @ id) @ sK550) = (lam @ (sK548 @ sh @ one))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f527,plain,(
% 32.60/5.94 ! [X198 : subst > term > term] : (? [X201 : subst,X202 : term,X203 : subst] : ((sub @ (X198 @ X203 @ X202) @ X201) != (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) => ((X198 @ (comp @ (sK553 @ X198) @ (sK551 @ X198)) @ (sub @ (sK552 @ X198) @ (sK551 @ X198))) != (sub @ (X198 @ (sK553 @ X198) @ (sK552 @ X198)) @ (sK551 @ X198))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f528,plain,(
% 32.60/5.94 ? [X208 : term,X209 : term,X210 : term,X211 : term] : (((ap @ (sub @ X208 @ id) @ X209) = (ap @ (sub @ X211 @ id) @ X210)) & (X209 != X210)) => (((ap @ (sub @ sK554 @ id) @ sK555) = (ap @ (sub @ sK557 @ id) @ sK556)) & (sK555 != sK556))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f529,plain,(
% 32.60/5.94 ! [X212 : term > $o,X213 : term > $o,X214 : subst,X215 : term] : (? [X216 : term] : ((X213 @ (sub @ X216 @ (push @ X215 @ X214))) != (X212 @ X216)) => ((X213 @ (sub @ (sK558 @ X215 @ X214 @ X213 @ X212) @ (push @ X215 @ X214))) != (X212 @ (sK558 @ X215 @ X214 @ X213 @ X212))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f530,plain,(
% 32.60/5.94 ? [X217 : term > $o,X218 : term > $o,X219 : subst,X220 : term] : (! [X221 : term] : ((X217 @ X221) = (X218 @ (sub @ X221 @ (push @ X220 @ X219)))) & ((X217 @ one) != $true) & ((X218 @ X220) = $true)) => (! [X221 : term] : ((sK560 @ (sub @ X221 @ (push @ sK562 @ sK561))) = (sK559 @ X221)) & ((sK559 @ one) != $true) & ($true = (sK560 @ sK562)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f531,plain,(
% 32.60/5.94 ? [X222 : subst] : ((comp @ X222 @ id) != X222) => (sK563 != (comp @ sK563 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f532,plain,(
% 32.60/5.94 ? [X228 : term,X229 : term > $o,X230 : term > $o,X231 : subst,X232 : term] : (((X229 @ X232) = $true) & ($true != (X230 @ (sub @ X232 @ (push @ X228 @ X231))))) => (((sK565 @ sK568) = $true) & ((sK566 @ (sub @ sK568 @ (push @ sK564 @ sK567))) != $true))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f533,plain,(
% 32.60/5.94 ? [X233 : term,X234 : subst] : ((sub @ one @ (push @ X233 @ X234)) != X233) => (sK569 != (sub @ one @ (push @ sK569 @ sK570)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f534,plain,(
% 32.60/5.94 ? [X235 : subst,X236 : term] : ((comp @ sh @ (push @ X236 @ X235)) != X235) => (sK571 != (comp @ sh @ (push @ sK572 @ sK571)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f535,plain,(
% 32.60/5.94 ! [X242 : subst > term > subst > $o] : (? [X243 : term > $o] : ! [X244 : term] : ((X243 @ X244) = (X242 @ id @ X244 @ id)) => ! [X244 : term] : ((sK573 @ X242 @ X244) = (X242 @ id @ X244 @ id)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f536,plain,(
% 32.60/5.94 ? [X245 : subst > term > subst > $o] : ! [X246 : term > $o] : ? [X247 : term] : ((X246 @ X247) != (X245 @ id @ X247 @ id)) => ! [X246 : term > $o] : ? [X247 : term] : ((X246 @ X247) != (sK574 @ id @ X247 @ id))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f537,plain,(
% 32.60/5.94 ! [X246 : term > $o] : (? [X247 : term] : ((X246 @ X247) != (sK574 @ id @ X247 @ id)) => ((X246 @ (sK575 @ X246)) != (sK574 @ id @ (sK575 @ X246) @ id)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f538,plain,(
% 32.60/5.94 ? [X248 : subst,X249 : term] : ((comp @ sh @ (push @ X249 @ X248)) != X248) => ((comp @ sh @ (push @ sK577 @ sK576)) != sK576)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f539,plain,(
% 32.60/5.94 ? [X254 : subst] : ((comp @ id @ X254) != X254) => ((comp @ id @ sK578) != sK578)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f540,plain,(
% 32.60/5.94 ? [X257 : term] : ((sub @ X257 @ id) != X257) => ((sub @ sK579 @ id) != sK579)),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f541,plain,(
% 32.60/5.94 ? [X258 : subst,X259 : term] : ((sub @ one @ (push @ X259 @ X258)) != X259) => (sK581 != (sub @ one @ (push @ sK581 @ sK580)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f542,plain,(
% 32.60/5.94 ! [X260 : term,X261 : subst,X262 : term > $o,X263 : term > $o] : (? [X264 : term] : ((X262 @ X264) != (X263 @ (sub @ X264 @ (push @ X260 @ X261)))) => ((X263 @ (sub @ (sK582 @ X263 @ X262 @ X261 @ X260) @ (push @ X260 @ X261))) != (X262 @ (sK582 @ X263 @ X262 @ X261 @ X260))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f543,plain,(
% 32.60/5.94 ? [X267 : term,X268 : subst,X269 : term > $o,X270 : term > $o] : (! [X271 : term] : ((X269 @ X271) = (X270 @ (sub @ X271 @ (push @ X267 @ X268)))) & ((X269 @ one) != $true) & ((X270 @ X267) = $true)) => (! [X271 : term] : ((sK585 @ X271) = (sK586 @ (sub @ X271 @ (push @ sK583 @ sK584)))) & ($true != (sK585 @ one)) & ((sK586 @ sK583) = $true))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f544,plain,(
% 32.60/5.94 ? [X276 : term,X277 : term,X278 : term,X279 : term] : (((ap @ X277 @ X279) = (ap @ X276 @ X278)) & (X278 != X279)) => (((ap @ sK587 @ sK589) = (ap @ sK588 @ sK590)) & (sK590 != sK589))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f473,plain,(
% 32.60/5.94 ((hoasinduction_lem3v2_f_lthm = $true) | ? [X0 : term] : ! [X1 : subst > term > term] : ? [X2 : subst,X3 : term] : ((sub @ X0 @ (push @ X3 @ X2)) != (X1 @ X2 @ X3))) & (! [X4 : term] : ? [X5 : subst > term > term] : ! [X6 : subst,X7 : term] : ((X5 @ X6 @ X7) = (sub @ X4 @ (push @ X7 @ X6))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (! [X8 : term,X9 : term,X10 : term,X11 : term] : (((ap @ X9 @ X8) != (ap @ X10 @ X11)) | (X9 = X10)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X12 : term,X13 : term,X14 : term,X15 : term] : (((ap @ X14 @ X15) = (ap @ X13 @ X12)) & (X13 != X14))) & (hoasinduction_lem2_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP58 != $true)) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) | (! [X16 : term,X17 : term,X18 : term,X19 : term] : (((ap @ X19 @ X17) != (ap @ X16 @ X18)) | (X17 = X18)) & ? [X20 : term,X21 : term,X22 : term,X23 : term] : (((ap @ (sub @ X23 @ id) @ X20) = (ap @ (sub @ X22 @ id) @ X21)) & (X20 != X21)))) & (? [X24 : term,X25 : term,X26 : term,X27 : term] : (((ap @ X27 @ X25) = (ap @ X24 @ X26)) & (X25 != X26)) | ! [X28 : term,X29 : term,X30 : term,X31 : term] : (((ap @ (sub @ X30 @ id) @ X29) != (ap @ (sub @ X31 @ id) @ X28)) | (X28 = X29)) | (hoasapinj2_lthm != $true)) & (axapp = $true) & (induction2_gthm = $true) & ! [X32 : d_subst] : (d_id = X32) & ((termmset_lthm = $true) | (? [X33 : term] : ((sub @ X33 @ id) != X33) & ! [X34 : term] : ((sub @ X34 @ id) = X34))) & (! [X35 : term] : ((sub @ X35 @ id) = X35) | ? [X36 : term] : ((sub @ X36 @ id) != X36) | (termmset_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X37 : term] : ! [X38 : subst > term > term] : ? [X39 : subst,X40 : term] : ((X38 @ X39 @ X40) != (sub @ X37 @ (push @ X40 @ X39)))) & (! [X41 : term] : ? [X42 : subst > term > term] : ! [X43 : subst,X44 : term] : ((X42 @ X43 @ X44) = (sub @ X41 @ (push @ X44 @ X43))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (ulamvarind = $true) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X45 : subst > term > subst > $o] : ! [X46 : term > $o] : ? [X47 : term] : ((X45 @ id @ X47 @ id) != (X46 @ X47))) & (! [X48 : subst > term > subst > $o] : ? [X49 : term > $o] : ! [X50 : term] : ((X48 @ id @ X50 @ id) = (X49 @ X50)) | (hoasinduction_lem0_lthm != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X51 : term] : ! [X52 : subst > term > term] : ((X52 @ sh @ one) != (sub @ X51 @ (push @ one @ sh)))) & (! [X53 : term] : ? [X54 : subst > term > term] : ((sub @ X53 @ (push @ one @ sh)) = (X54 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP53)) & (($true = sP53) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X55 : term] : ? [X56 : d_term] : ((d2term @ X56) = X55) & (hoasapinj2_gthm = $true) & (! [X57 : subst,X58 : term] : ((sub @ one @ (push @ X58 @ X57)) = X58) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X59 : subst,X60 : term] : ((sub @ one @ (push @ X60 @ X59)) != X60)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((induction2_lthm = $true) | ($true != sP46)) & (($true = sP46) | (induction2_lthm != $true)) & (! [X61 : term,X62 : subst > term > subst > $o] : (? [X63 : subst > term > term] : (! [X64 : subst,X65 : term,X66 : subst] : ((sub @ (X63 @ X64 @ X65) @ X66) = (X63 @ (comp @ X64 @ X66) @ (sub @ X65 @ X66))) & ! [X67 : term] : (((X62 @ id @ (X63 @ id @ X67) @ id) = $true) | ((X62 @ id @ X67 @ id) != $true)) & ((X62 @ id @ (lam @ (X63 @ sh @ one)) @ id) != $true)) | ((X62 @ id @ X61 @ id) = $true) | ((sP42 @ X62) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X68 : term,X69 : subst > term > subst > $o] : (! [X70 : subst > term > term] : (? [X71 : subst,X72 : term,X73 : subst] : ((sub @ (X70 @ X71 @ X72) @ X73) != (X70 @ (comp @ X71 @ X73) @ (sub @ X72 @ X73))) | ? [X74 : term] : (((X69 @ id @ (X70 @ id @ X74) @ id) != $true) & ((X69 @ id @ X74 @ id) = $true)) | ((X69 @ id @ (lam @ (X70 @ sh @ one)) @ id) = $true)) & ((X69 @ id @ X68 @ id) != $true) & ((sP42 @ X69) != $true))) & ! [X75 : subst] : ? [X76 : d_subst] : ((d2subst @ X76) = X75) & ((pushprop_lem0 = $true) | ? [X77 : subst,X78 : term > $o,X79 : term] : ! [X80 : term > $o] : ? [X81 : term] : ((X80 @ X81) != (X78 @ (sub @ X81 @ (push @ X79 @ X77))))) & (! [X82 : subst,X83 : term > $o,X84 : term] : ? [X85 : term > $o] : ! [X86 : term] : ((X83 @ (sub @ X86 @ (push @ X84 @ X82))) = (X85 @ X86)) | (pushprop_lem0 != $true)) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & (! [X87 : term,X88 : term,X89 : term,X90 : term] : (((ap @ (sub @ X90 @ id) @ X89) != (ap @ (sub @ X87 @ id) @ X88)) | (X87 = X90)) | ? [X91 : term] : ((sub @ X91 @ id) != X91) | ? [X92 : term,X93 : term,X94 : term,X95 : term] : ((X94 != X95) & ((ap @ X94 @ X92) = (ap @ X95 @ X93))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X96 : term,X97 : term,X98 : term,X99 : term] : (((ap @ (sub @ X96 @ id) @ X97) = (ap @ (sub @ X99 @ id) @ X98)) & (X96 != X99)) & ! [X100 : term] : ((sub @ X100 @ id) = X100) & ! [X101 : term,X102 : term,X103 : term,X104 : term] : ((X103 = X104) | ((ap @ X104 @ X102) != (ap @ X103 @ X101))))) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & (! [X105 : term > $o,X106 : term] : (? [X107 : term] : (((X105 @ X107) != $true) & ((var @ X107) = $true)) | ((sP39 @ X105) = $true) | ((X105 @ X106) = $true) | ? [X108 : term] : (((X105 @ X108) = $true) & ((X105 @ (lam @ X108)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X109 : term > $o,X110 : term] : (! [X111 : term] : (((X109 @ X111) = $true) | ((var @ X111) != $true)) & ((sP39 @ X109) != $true) & ((X109 @ X110) != $true) & ! [X112 : term] : (((X109 @ X112) != $true) | ((X109 @ (lam @ X112)) = $true)))) & (hoasinduction_gthm = $true) & ! [X113 : d_term] : (d_one = X113) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction != $true)) & ((! [X114 : subst] : ((comp @ id @ X114) = X114) & ! [X115 : subst] : ((comp @ X115 @ id) = X115)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X116 : subst] : ((comp @ id @ X116) != X116) | ? [X117 : subst] : ((comp @ X117 @ id) != X117)) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3b = $true) | ? [X118 : term] : ! [X119 : subst > term > term] : ((X119 @ sh @ one) != (sub @ X118 @ (push @ one @ sh)))) & (! [X120 : term] : ? [X121 : subst > term > term] : ((sub @ X120 @ (push @ one @ sh)) = (X121 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj1 = $true) | ? [X122 : term,X123 : term,X124 : term,X125 : term] : ((X122 != X125) & ((ap @ (sub @ X125 @ id) @ X124) = (ap @ (sub @ X122 @ id) @ X123)))) & (! [X126 : term,X127 : term,X128 : term,X129 : term] : ((X126 = X129) | ((ap @ (sub @ X126 @ id) @ X127) != (ap @ (sub @ X129 @ id) @ X128))) | (hoasapinj1 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X130 : term > $o,X131 : term,X132 : subst] : ! [X133 : term > $o] : ? [X134 : term] : ((X133 @ X134) != (X130 @ (sub @ X134 @ (push @ X131 @ X132))))) & (! [X135 : term > $o,X136 : term,X137 : subst] : ? [X138 : term > $o] : ! [X139 : term] : ((X138 @ X139) = (X135 @ (sub @ X139 @ (push @ X136 @ X137)))) | (pushprop_lem0_lthm != $true)) & (ulamvarsh = $true) & ((laminj = $true) | ? [X140 : term,X141 : term] : (((lam @ X141) = (lam @ X140)) & (X140 != X141))) & (! [X142 : term,X143 : term] : (((lam @ X142) != (lam @ X143)) | (X142 = X143)) | (laminj != $true)) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X144 : d_term,X145 : d_term] : ((X144 = X145) | ((d2term @ X144) != (d2term @ X145))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3v2a = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2a != $true)) & (? [X146 : subst] : ((comp @ id @ X146) != X146) | ? [X147 : subst] : ((comp @ X147 @ id) != X147) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X149 : subst] : ((comp @ X149 @ id) = X149)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X150 : subst] : ((comp @ id @ X150) = X150) & ! [X151 : subst] : ((comp @ X151 @ id) = X151) & (? [X152 : subst] : ((comp @ id @ X152) != X152) | ? [X153 : subst] : ((comp @ X153 @ id) != X153)))) & (($true = sP32) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP32)) & (! [X154 : term > $o,X155 : subst,X156 : term > $o,X157 : term,X158 : term] : (((X156 @ (sub @ X158 @ (push @ X157 @ X155))) = $true) | ($true != (X154 @ X158))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X159 : term > $o,X160 : subst,X161 : term > $o,X162 : term,X163 : term] : (((X161 @ (sub @ X163 @ (push @ X162 @ X160))) != $true) & ($true = (X159 @ X163)))) & (pushprop_lem2v2_gthm = $true) & ((sP31 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP31 != $true)) & ((hoaslaminj_lthm = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar = $true) & ((shinj = $true) | ? [X164 : term,X165 : term] : (((sub @ X164 @ sh) = (sub @ X165 @ sh)) & (X164 != X165))) & (! [X166 : term,X167 : term] : (((sub @ X167 @ sh) != (sub @ X166 @ sh)) | (X166 = X167)) | (shinj != $true)) & (! [X168 : term] : ((sub @ X168 @ id) = X168) | (termmset != $true)) & ((termmset = $true) | ? [X169 : term] : ((sub @ X169 @ id) != X169)) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X170 : subst > term > term,X171 : subst,X172 : subst > term > term,X173 : term] : (((lam @ (X172 @ sh @ one)) != (lam @ (X170 @ sh @ one))) | ((X172 @ X171 @ X173) = (X170 @ X171 @ X173)) | ? [X174 : term,X175 : subst,X176 : subst] : ((sub @ (X170 @ X175 @ X174) @ X176) != (X170 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) | ? [X177 : subst,X178 : term,X179 : subst] : ((X172 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179)) != (sub @ (X172 @ X177 @ X178) @ X179))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X180 : subst > term > term,X181 : subst,X182 : subst > term > term,X183 : term] : (((lam @ (X182 @ sh @ one)) = (lam @ (X180 @ sh @ one))) & ((X182 @ X181 @ X183) != (X180 @ X181 @ X183)) & ! [X184 : term,X185 : subst,X186 : subst] : ((sub @ (X180 @ X185 @ X184) @ X186) = (X180 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186))) & ! [X187 : subst,X188 : term,X189 : subst] : ((X182 @ (comp @ X187 @ X189) @ (sub @ X188 @ X189)) = (sub @ (X182 @ X187 @ X188) @ X189)))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X190 : subst] : ((push @ (sub @ one @ X190) @ (comp @ sh @ X190)) = X190) | (axscons != $true)) & ((axscons = $true) | ? [X191 : subst] : ((push @ (sub @ one @ X191) @ (comp @ sh @ X191)) != X191)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X192 : subst > term > term,X193 : term,X194 : term] : (! [X195 : subst,X196 : term,X197 : subst] : ((sub @ (X192 @ X197 @ X196) @ X195) = (X192 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195))) & ((ap @ (sub @ X193 @ id) @ X194) = (lam @ (X192 @ sh @ one))))) & (! [X198 : subst > term > term,X199 : term,X200 : term] : (? [X201 : subst,X202 : term,X203 : subst] : ((sub @ (X198 @ X203 @ X202) @ X201) != (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) | ((ap @ (sub @ X199 @ id) @ X200) != (lam @ (X198 @ sh @ one)))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & (($true = sP16) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP16)) & ((sP15 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP15 != $true)) & (! [X204 : term,X205 : term,X206 : term,X207 : term] : (((ap @ (sub @ X204 @ id) @ X205) != (ap @ (sub @ X207 @ id) @ X206)) | (X205 = X206)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X208 : term,X209 : term,X210 : term,X211 : term] : (((ap @ (sub @ X208 @ id) @ X209) = (ap @ (sub @ X211 @ id) @ X210)) & (X209 != X210))) & ((hoasinduction_lem3a_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lem3a_lthm != $true)) & (! [X212 : term > $o,X213 : term > $o,X214 : subst,X215 : term] : (? [X216 : term] : ((X213 @ (sub @ X216 @ (push @ X215 @ X214))) != (X212 @ X216)) | ((X212 @ one) = $true) | ((X213 @ X215) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X217 : term > $o,X218 : term > $o,X219 : subst,X220 : term] : (! [X221 : term] : ((X217 @ X221) = (X218 @ (sub @ X221 @ (push @ X220 @ X219)))) & ((X217 @ one) != $true) & ((X218 @ X220) = $true))) & ((axidr = $true) | ? [X222 : subst] : ((comp @ X222 @ id) != X222)) & (! [X223 : subst] : ((comp @ X223 @ id) = X223) | (axidr != $true)) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) | (! [X224 : term,X225 : subst] : ((sub @ one @ (push @ X224 @ X225)) = X224) & ! [X226 : subst,X227 : term] : ((comp @ sh @ (push @ X227 @ X226)) = X226) & ? [X228 : term,X229 : term > $o,X230 : term > $o,X231 : subst,X232 : term] : (((X229 @ X232) = $true) & ($true != (X230 @ (sub @ X232 @ (push @ X228 @ X231))))))) & (? [X233 : term,X234 : subst] : ((sub @ one @ (push @ X233 @ X234)) != X233) | ? [X235 : subst,X236 : term] : ((comp @ sh @ (push @ X236 @ X235)) != X235) | ! [X237 : term,X238 : term > $o,X239 : term > $o,X240 : subst,X241 : term] : (((X238 @ X241) != $true) | ((X239 @ (sub @ X241 @ (push @ X237 @ X240))) = $true)) | (pushprop_lem1_lthm != $true)) & (! [X242 : subst > term > subst > $o] : ? [X243 : term > $o] : ! [X244 : term] : ((X243 @ X244) = (X242 @ id @ X244 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X245 : subst > term > subst > $o] : ! [X246 : term > $o] : ? [X247 : term] : ((X246 @ X247) != (X245 @ id @ X247 @ id))) & ((sP11 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP11 != $true)) & ((axshiftcons = $true) | ? [X248 : subst,X249 : term] : ((comp @ sh @ (push @ X249 @ X248)) != X248)) & (! [X250 : subst,X251 : term] : ((comp @ sh @ (push @ X251 @ X250)) = X250) | (axshiftcons != $true)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X252 : d_subst,X253 : d_subst] : ((X252 = X253) | ((d2subst @ X253) != (d2subst @ X252))) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((axidl = $true) | ? [X254 : subst] : ((comp @ id @ X254) != X254)) & (! [X255 : subst] : ((comp @ id @ X255) = X255) | (axidl != $true)) & (! [X256 : term] : ((sub @ X256 @ id) = X256) | (axvarid != $true)) & ((axvarid = $true) | ? [X257 : term] : ((sub @ X257 @ id) != X257)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & (? [X258 : subst,X259 : term] : ((sub @ one @ (push @ X259 @ X258)) != X259) | ! [X260 : term,X261 : subst,X262 : term > $o,X263 : term > $o] : (? [X264 : term] : ((X262 @ X264) != (X263 @ (sub @ X264 @ (push @ X260 @ X261)))) | ((X262 @ one) = $true) | ((X263 @ X260) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X265 : subst,X266 : term] : ((sub @ one @ (push @ X266 @ X265)) = X266) & ? [X267 : term,X268 : subst,X269 : term > $o,X270 : term > $o] : (! [X271 : term] : ((X269 @ X271) = (X270 @ (sub @ X271 @ (push @ X267 @ X268)))) & ((X269 @ one) != $true) & ((X270 @ X267) = $true)))) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X272 : term,X273 : term,X274 : term,X275 : term] : (((ap @ X273 @ X275) != (ap @ X272 @ X274)) | (X274 = X275)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X276 : term,X277 : term,X278 : term,X279 : term] : (((ap @ X277 @ X279) = (ap @ X276 @ X278)) & (X278 != X279))) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(rectify,[status(thm)],[f472])).
% 32.60/5.94 thf(f472,plain,(
% 32.60/5.94 ((hoasinduction_lem3v2_f_lthm = $true) | ? [X34 : term] : ! [X35 : subst > term > term] : ? [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) != (sub @ X34 @ (push @ X37 @ X36)))) & (! [X34 : term] : ? [X35 : subst > term > term] : ! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) = (ap @ X413 @ X414)) & (X412 != X413))) & (hoasinduction_lem2_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP58 != $true)) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) | (! [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) != (ap @ X59 @ X57)) | (X57 = X58)) & ? [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) = (ap @ (sub @ X62 @ id) @ X61)) & (X60 != X61)))) & (? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) = (ap @ X59 @ X57)) & (X57 != X58)) | ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61)) | (hoasapinj2_lthm != $true)) & (axapp = $true) & (induction2_gthm = $true) & ! [X209 : d_subst] : (d_id = X209) & ((termmset_lthm = $true) | (? [X418 : term] : ((sub @ X418 @ id) != X418) & ! [X417 : term] : ((sub @ X417 @ id) = X417))) & (! [X418 : term] : ((sub @ X418 @ id) = X418) | ? [X417 : term] : ((sub @ X417 @ id) != X417) | (termmset_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X483 : term] : ! [X484 : subst > term > term] : ? [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) != (X484 @ X485 @ X486))) & (! [X483 : term] : ? [X484 : subst > term > term] : ! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (ulamvarind = $true) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X311 : subst > term > subst > $o] : ! [X312 : term > $o] : ? [X313 : term] : ((X311 @ id @ X313 @ id) != (X312 @ X313))) & (! [X311 : subst > term > subst > $o] : ? [X312 : term > $o] : ! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313)) | (hoasinduction_lem0_lthm != $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X28 : term] : ! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one))) & (! [X28 : term] : ? [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) = (X29 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP53)) & (($true = sP53) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasapinj2_gthm = $true) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) != X156)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((induction2_lthm = $true) | ($true != sP46)) & (($true = sP46) | (induction2_lthm != $true)) & (! [X487 : term,X488 : subst > term > subst > $o] : (? [X491 : subst > term > term] : (! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) & ! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) != $true)) | ((X488 @ id @ X487 @ id) = $true) | ((sP42 @ X488) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X487 : term,X488 : subst > term > subst > $o] : (! [X491 : subst > term > term] : (? [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) != (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) | ? [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) != $true) & ((X488 @ id @ X495 @ id) = $true)) | ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) = $true)) & ((X488 @ id @ X487 @ id) != $true) & ((sP42 @ X488) != $true))) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & ((pushprop_lem0 = $true) | ? [X456 : subst,X457 : term > $o,X458 : term] : ! [X459 : term > $o] : ? [X460 : term] : ((X459 @ X460) != (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & (! [X456 : subst,X457 : term > $o,X458 : term] : ? [X459 : term > $o] : ! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456)))) | (pushprop_lem0 != $true)) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & (! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)) | ? [X5 : term] : ((sub @ X5 @ id) != X5) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 != X9) & ((ap @ X8 @ X6) = (ap @ X9 @ X7))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) = (ap @ (sub @ X10 @ id) @ X11)) & (X10 != X13)) & ! [X5 : term] : ((sub @ X5 @ id) = X5) & ! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7))))) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & (! [X149 : term > $o,X150 : term] : (? [X154 : term] : (((X149 @ X154) != $true) & ((var @ X154) = $true)) | ((sP39 @ X149) = $true) | ((X149 @ X150) = $true) | ? [X153 : term] : (((X149 @ X153) = $true) & ((X149 @ (lam @ X153)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X149 : term > $o,X150 : term] : (! [X154 : term] : (((X149 @ X154) = $true) | ((var @ X154) != $true)) & ((sP39 @ X149) != $true) & ((X149 @ X150) != $true) & ! [X153 : term] : (((X149 @ X153) != $true) | ((X149 @ (lam @ X153)) = $true)))) & (hoasinduction_gthm = $true) & ! [X410 : d_term] : (d_one = X410) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction != $true)) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X408 : subst] : ((comp @ id @ X408) != X408) | ? [X407 : subst] : ((comp @ X407 @ id) != X407)) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3b = $true) | ? [X415 : term] : ! [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) != (X416 @ sh @ one))) & (! [X415 : term] : ? [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) = (X416 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj1 = $true) | ? [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 != X33) & ((ap @ (sub @ X30 @ id) @ X31) = (ap @ (sub @ X33 @ id) @ X32)))) & (! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32))) | (hoasapinj1 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X14 : term > $o,X15 : term,X16 : subst] : ! [X17 : term > $o] : ? [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) != (X17 @ X18))) & (! [X14 : term > $o,X15 : term,X16 : subst] : ? [X17 : term > $o] : ! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18)) | (pushprop_lem0_lthm != $true)) & (ulamvarsh = $true) & ((laminj = $true) | ? [X461 : term,X462 : term] : (((lam @ X461) = (lam @ X462)) & (X461 != X462))) & (! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462)) | (laminj != $true)) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X199 : d_term,X200 : d_term] : ((X199 = X200) | ((d2term @ X200) != (d2term @ X199))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3v2a = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2a != $true)) & (? [X145 : subst] : ((comp @ id @ X145) != X145) | ? [X146 : subst] : ((comp @ X146 @ id) != X146) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X145 : subst] : ((comp @ id @ X145) = X145) & ! [X146 : subst] : ((comp @ X146 @ id) = X146) & (? [X148 : subst] : ((comp @ id @ X148) != X148) | ? [X147 : subst] : ((comp @ X147 @ id) != X147)))) & (($true = sP32) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP32)) & (! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) != $true) & ((X204 @ X208) = $true))) & (pushprop_lem2v2_gthm = $true) & ((sP31 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP31 != $true)) & ((hoaslaminj_lthm = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar = $true) & ((shinj = $true) | ? [X197 : term,X198 : term] : (((sub @ X197 @ sh) = (sub @ X198 @ sh)) & (X197 != X198))) & (! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198)) | (shinj != $true)) & (! [X383 : term] : ((sub @ X383 @ id) = X383) | (termmset != $true)) & ((termmset = $true) | ? [X383 : term] : ((sub @ X383 @ id) != X383)) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ? [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) != (sub @ (X522 @ X530 @ X529) @ X531)) | ? [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) != (sub @ (X524 @ X526 @ X527) @ X528))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) = (lam @ (X524 @ sh @ one))) & ((X524 @ X523 @ X525) != (X522 @ X523 @ X525)) & ! [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) = (sub @ (X522 @ X530 @ X529) @ X531)) & ! [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) = (sub @ (X524 @ X526 @ X527) @ X528)))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) | (axscons != $true)) & ((axscons = $true) | ? [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) != X196)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X314 : subst > term > term,X315 : term,X316 : term] : (! [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) = (sub @ (X314 @ X319 @ X318) @ X317)) & ((ap @ (sub @ X315 @ id) @ X316) = (lam @ (X314 @ sh @ one))))) & (! [X314 : subst > term > term,X315 : term,X316 : term] : (? [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) != (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one)))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & (($true = sP16) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP16)) & ((sP15 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP15 != $true)) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) = (ap @ (sub @ X452 @ id) @ X453)) & (X453 != X454))) & ((hoasinduction_lem3a_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lem3a_lthm != $true)) & (! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (? [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) != (X0 @ X4)) | ((X0 @ one) = $true) | ((X1 @ X3) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4)) & ((X0 @ one) != $true) & ((X1 @ X3) = $true))) & ((axidr = $true) | ? [X172 : subst] : ((comp @ X172 @ id) != X172)) & (! [X172 : subst] : ((comp @ X172 @ id) = X172) | (axidr != $true)) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) | (! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) & ! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) & ? [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) = $true) & ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) != $true)))) & (? [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) != X19) | ? [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) != X21) | ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true)) | (pushprop_lem1_lthm != $true)) & (! [X201 : subst > term > subst > $o] : ? [X202 : term > $o] : ! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X201 : subst > term > subst > $o] : ! [X202 : term > $o] : ? [X203 : term] : ((X202 @ X203) != (X201 @ id @ X203 @ id))) & ((sP11 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP11 != $true)) & ((axshiftcons = $true) | ? [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) != X463)) & (! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463) | (axshiftcons != $true)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X54 : d_subst,X55 : d_subst] : ((X54 = X55) | ((d2subst @ X55) != (d2subst @ X54))) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((axidl = $true) | ? [X409 : subst] : ((comp @ id @ X409) != X409)) & (! [X409 : subst] : ((comp @ id @ X409) = X409) | (axidl != $true)) & (! [X374 : term] : ((sub @ X374 @ id) = X374) | (axvarid != $true)) & ((axvarid = $true) | ? [X374 : term] : ((sub @ X374 @ id) != X374)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & (? [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) != X211) | ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (? [X216 : term] : ((X214 @ X216) != (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) | ($true = (X214 @ one)) | ((X215 @ X212) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) = X211) & ? [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (! [X216 : term] : ((X214 @ X216) = (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) & ($true != (X214 @ one)) & ((X215 @ X212) = $true)))) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) = (ap @ X174 @ X176)) & (X175 != X176))) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(flattening,[status(thm)],[f471])).
% 32.60/5.94 thf(f471,plain,(
% 32.60/5.94 (((hoasinduction_lem3v2_f_lthm = $true) | ? [X34 : term] : ! [X35 : subst > term > term] : ? [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) != (sub @ X34 @ (push @ X37 @ X36)))) & (! [X34 : term] : ? [X35 : subst > term > term] : ! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36))) | (hoasinduction_lem3v2_f_lthm != $true))) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & ((! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) = (ap @ X413 @ X414)) & (X412 != X413)))) & (hoasinduction_lem2_gthm = $true) & (((sP58 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP58 != $true))) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasapinj2_lthm = $true) | (! [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) != (ap @ X59 @ X57)) | (X57 = X58)) & ? [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) = (ap @ (sub @ X62 @ id) @ X61)) & (X60 != X61)))) & ((? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) = (ap @ X59 @ X57)) & (X57 != X58)) | ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61))) | (hoasapinj2_lthm != $true))) & (axapp = $true) & (induction2_gthm = $true) & ! [X209 : d_subst] : (d_id = X209) & (((termmset_lthm = $true) | (? [X418 : term] : ((sub @ X418 @ id) != X418) & ! [X417 : term] : ((sub @ X417 @ id) = X417))) & ((! [X418 : term] : ((sub @ X418 @ id) = X418) | ? [X417 : term] : ((sub @ X417 @ id) != X417)) | (termmset_lthm != $true))) & (((hoasinduction_lem3v2_f = $true) | ? [X483 : term] : ! [X484 : subst > term > term] : ? [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) != (X484 @ X485 @ X486))) & (! [X483 : term] : ? [X484 : subst > term > term] : ! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486)) | (hoasinduction_lem3v2_f != $true))) & (((hoasinduction_lem3v2_lthm = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2_lthm != $true))) & (ulamvarind = $true) & (((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true))) & (hoaslamnotvar_gthm = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X311 : subst > term > subst > $o] : ! [X312 : term > $o] : ? [X313 : term] : ((X311 @ id @ X313 @ id) != (X312 @ X313))) & (! [X311 : subst > term > subst > $o] : ? [X312 : term > $o] : ! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313)) | (hoasinduction_lem0_lthm != $true))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X28 : term] : ! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one))) & (! [X28 : term] : ? [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) = (X29 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true))) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP53)) & (($true = sP53) | (hoasinduction_lem3a != $true))) & (hoasinduction_lem3v2_gthm = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasapinj2_gthm = $true) & ((! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) != X156))) & (((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true))) & (((induction2_lthm = $true) | ($true != sP46)) & (($true = sP46) | (induction2_lthm != $true))) & ((! [X487 : term,X488 : subst > term > subst > $o] : (? [X491 : subst > term > term] : (! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) & ! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) != $true)) | ((X488 @ id @ X487 @ id) = $true) | ((sP42 @ X488) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X487 : term,X488 : subst > term > subst > $o] : (! [X491 : subst > term > term] : (? [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) != (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) | ? [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) != $true) & ((X488 @ id @ X495 @ id) = $true)) | ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) = $true)) & ((X488 @ id @ X487 @ id) != $true) & ((sP42 @ X488) != $true)))) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & (((pushprop_lem0 = $true) | ? [X456 : subst,X457 : term > $o,X458 : term] : ! [X459 : term > $o] : ? [X460 : term] : ((X459 @ X460) != (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & (! [X456 : subst,X457 : term > $o,X458 : term] : ? [X459 : term > $o] : ! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456)))) | (pushprop_lem0 != $true))) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & (((! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)) | ? [X5 : term] : ((sub @ X5 @ id) != X5) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 != X9) & ((ap @ X8 @ X6) = (ap @ X9 @ X7)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) = (ap @ (sub @ X10 @ id) @ X11)) & (X10 != X13)) & ! [X5 : term] : ((sub @ X5 @ id) = X5) & ! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7)))))) & (((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((sP41 = $true) | (hoasinduction_lem3 != $true))) & ((! [X149 : term > $o,X150 : term] : (? [X154 : term] : (((X149 @ X154) != $true) & ((var @ X154) = $true)) | ((sP39 @ X149) = $true) | ((X149 @ X150) = $true) | ? [X153 : term] : (((X149 @ X153) = $true) & ((X149 @ (lam @ X153)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X149 : term > $o,X150 : term] : (! [X154 : term] : (((X149 @ X154) = $true) | ((var @ X154) != $true)) & ((sP39 @ X149) != $true) & ((X149 @ X150) != $true) & ! [X153 : term] : (((X149 @ X153) != $true) | ((X149 @ (lam @ X153)) = $true))))) & (hoasinduction_gthm = $true) & ! [X410 : d_term] : (d_one = X410) & (hoasinduction_lem1 = $true) & (((hoasinduction = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction != $true))) & (((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X408 : subst] : ((comp @ id @ X408) != X408) | ? [X407 : subst] : ((comp @ X407 @ id) != X407)))) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (((hoasinduction_lem3b = $true) | ? [X415 : term] : ! [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) != (X416 @ sh @ one))) & (! [X415 : term] : ? [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) = (X416 @ sh @ one)) | (hoasinduction_lem3b != $true))) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((hoasapinj1 = $true) | ? [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 != X33) & ((ap @ (sub @ X30 @ id) @ X31) = (ap @ (sub @ X33 @ id) @ X32)))) & (! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32))) | (hoasapinj1 != $true))) & (((pushprop_lem0_lthm = $true) | ? [X14 : term > $o,X15 : term,X16 : subst] : ! [X17 : term > $o] : ? [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) != (X17 @ X18))) & (! [X14 : term > $o,X15 : term,X16 : subst] : ? [X17 : term > $o] : ! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18)) | (pushprop_lem0_lthm != $true))) & (ulamvarsh = $true) & (((laminj = $true) | ? [X461 : term,X462 : term] : (((lam @ X461) = (lam @ X462)) & (X461 != X462))) & (! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462)) | (laminj != $true))) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X199 : d_term,X200 : d_term] : ((X199 = X200) | ((d2term @ X200) != (d2term @ X199))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (((hoasinduction_lem3v2a = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2a != $true))) & (((? [X145 : subst] : ((comp @ id @ X145) != X145) | ? [X146 : subst] : ((comp @ X146 @ id) != X146) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X145 : subst] : ((comp @ id @ X145) = X145) & ! [X146 : subst] : ((comp @ X146 @ id) = X146) & (? [X148 : subst] : ((comp @ id @ X148) != X148) | ? [X147 : subst] : ((comp @ X147 @ id) != X147))))) & ((($true = sP32) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP32))) & ((! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) != $true) & ((X204 @ X208) = $true)))) & (pushprop_lem2v2_gthm = $true) & (((sP31 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP31 != $true))) & (((hoaslaminj_lthm = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoaslaminj_lthm != $true))) & (hoaslamnotvar = $true) & (((shinj = $true) | ? [X197 : term,X198 : term] : (((sub @ X197 @ sh) = (sub @ X198 @ sh)) & (X197 != X198))) & (! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198)) | (shinj != $true))) & ((! [X383 : term] : ((sub @ X383 @ id) = X383) | (termmset != $true)) & ((termmset = $true) | ? [X383 : term] : ((sub @ X383 @ id) != X383))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ? [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) != (sub @ (X522 @ X530 @ X529) @ X531)) | ? [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) != (sub @ (X524 @ X526 @ X527) @ X528))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) = (lam @ (X524 @ sh @ one))) & ((X524 @ X523 @ X525) != (X522 @ X523 @ X525)) & ! [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) = (sub @ (X522 @ X530 @ X529) @ X531)) & ! [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) = (sub @ (X524 @ X526 @ X527) @ X528))))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & (((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) | (axscons != $true)) & ((axscons = $true) | ? [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) != X196))) & (termmset_gthm = $true) & (((hoasinduction_lem3_lthm = $true) | (sP19 != $true)) & ((sP19 = $true) | (hoasinduction_lem3_lthm != $true))) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & (((hoaslamnotap = $true) | ? [X314 : subst > term > term,X315 : term,X316 : term] : (! [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) = (sub @ (X314 @ X319 @ X318) @ X317)) & ((ap @ (sub @ X315 @ id) @ X316) = (lam @ (X314 @ sh @ one))))) & (! [X314 : subst > term > term,X315 : term,X316 : term] : (? [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) != (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one)))) | (hoaslamnotap != $true))) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & ((($true = sP16) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP16))) & (((sP15 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP15 != $true))) & ((! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) = (ap @ (sub @ X452 @ id) @ X453)) & (X453 != X454)))) & (((hoasinduction_lem3a_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lem3a_lthm != $true))) & ((! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (? [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) != (X0 @ X4)) | ((X0 @ one) = $true) | ((X1 @ X3) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4)) & ((X0 @ one) != $true) & ((X1 @ X3) = $true)))) & (((axidr = $true) | ? [X172 : subst] : ((comp @ X172 @ id) != X172)) & (! [X172 : subst] : ((comp @ X172 @ id) = X172) | (axidr != $true))) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & (((pushprop_lem1_lthm = $true) | (! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) & ! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) & ? [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) = $true) & ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) != $true)))) & ((? [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) != X19) | ? [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) != X21) | ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true))) | (pushprop_lem1_lthm != $true))) & ((! [X201 : subst > term > subst > $o] : ? [X202 : term > $o] : ! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X201 : subst > term > subst > $o] : ! [X202 : term > $o] : ? [X203 : term] : ((X202 @ X203) != (X201 @ id @ X203 @ id)))) & (((sP11 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP11 != $true))) & (((axshiftcons = $true) | ? [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) != X463)) & (! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463) | (axshiftcons != $true))) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X54 : d_subst,X55 : d_subst] : ((X54 = X55) | ((d2subst @ X55) != (d2subst @ X54))) & (((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP6 != $true))) & (((axidl = $true) | ? [X409 : subst] : ((comp @ id @ X409) != X409)) & (! [X409 : subst] : ((comp @ id @ X409) = X409) | (axidl != $true))) & ((! [X374 : term] : ((sub @ X374 @ id) = X374) | (axvarid != $true)) & ((axvarid = $true) | ? [X374 : term] : ((sub @ X374 @ id) != X374))) & (hoasinduction_lem1_lthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3v2a_lthm != $true))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & (((? [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) != X211) | ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (? [X216 : term] : ((X214 @ X216) != (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) | ($true = (X214 @ one)) | ((X215 @ X212) != $true))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) = X211) & ? [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (! [X216 : term] : ((X214 @ X216) = (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) & ($true != (X214 @ one)) & ((X215 @ X212) = $true))))) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & ((! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) = (ap @ X174 @ X176)) & (X175 != X176)))) & (hoasapnotvar_lthm = $true) & (((induction2lem_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2lem_lthm != $true))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(nnf_transformation,[status(thm)],[f73])).
% 32.60/5.94 thf(f73,plain,(
% 32.60/5.94 ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X34 : term] : ? [X35 : subst > term > term] : ! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36)))) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & ((sP58 = $true) <=> (hoasinduction_lem3v2 = $true)) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) <=> (? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) = (ap @ X59 @ X57)) & (X57 != X58)) | ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61)))) & (axapp = $true) & (induction2_gthm = $true) & ! [X209 : d_subst] : (d_id = X209) & ((termmset_lthm = $true) <=> (! [X418 : term] : ((sub @ X418 @ id) = X418) | ? [X417 : term] : ((sub @ X417 @ id) != X417))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X483 : term] : ? [X484 : subst > term > term] : ! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486))) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP56 = $true)) & (ulamvarind = $true) & ((sP54 = $true) <=> (hoasinduction_lem3aa = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X311 : subst > term > subst > $o] : ? [X312 : term > $o] : ! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ? [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) = (X29 @ sh @ one))) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP53)) & (hoasinduction_lem3v2_gthm = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasapinj2_gthm = $true) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) <=> (axvarcons = $true)) & ((hoasinduction_lthm_3 = $true) <=> (sP52 = $true)) & ((induction2_lthm = $true) <=> ($true = sP46)) & (! [X487 : term,X488 : subst > term > subst > $o] : (? [X491 : subst > term > term] : (! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) & ! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) != $true)) | ((X488 @ id @ X487 @ id) = $true) | ((sP42 @ X488) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & ((pushprop_lem0 = $true) <=> ! [X456 : subst,X457 : term > $o,X458 : term] : ? [X459 : term > $o] : ! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & ((! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)) | ? [X5 : term] : ((sub @ X5 @ id) != X5) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 != X9) & ((ap @ X8 @ X6) = (ap @ X9 @ X7)))) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> (sP41 = $true)) & (! [X149 : term > $o,X150 : term] : (? [X154 : term] : (((X149 @ X154) != $true) & ((var @ X154) = $true)) | ((sP39 @ X149) = $true) | ((X149 @ X150) = $true) | ? [X153 : term] : (((X149 @ X153) = $true) & ((X149 @ (lam @ X153)) != $true))) <=> (induction = $true)) & (hoasinduction_gthm = $true) & ! [X410 : d_term] : (d_one = X410) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) <=> (sP38 = $true)) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) <=> (substmonoid = $true)) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3b = $true) <=> ! [X415 : term] : ? [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) = (X416 @ sh @ one))) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & ((pushprop_lem0_lthm = $true) <=> ! [X14 : term > $o,X15 : term,X16 : subst] : ? [X17 : term > $o] : ! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18))) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462))) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X199 : d_term,X200 : d_term] : ((X199 = X200) | ((d2term @ X200) != (d2term @ X199))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP35 = $true) <=> (hoasinduction_lem2v2 = $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3v2a = $true) <=> (sP33 = $true)) & ((? [X145 : subst] : ((comp @ id @ X145) != X145) | ? [X146 : subst] : ((comp @ X146 @ id) != X146) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147))) <=> (substmonoid_lthm = $true)) & (($true = sP32) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2_gthm = $true) & ((sP31 = $true) <=> (hoasinduction_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> (sP22 = $true)) & (hoaslamnotvar = $true) & ((shinj = $true) <=> ! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198))) & (! [X383 : term] : ((sub @ X383 @ id) = X383) <=> (termmset = $true)) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ? [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) != (sub @ (X522 @ X530 @ X529) @ X531)) | ? [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) != (sub @ (X524 @ X526 @ X527) @ X528))) <=> (hoaslaminj = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & ((induction2 = $true) <=> (sP21 = $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) <=> (axscons = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (sP19 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X314 : subst > term > term,X315 : term,X316 : term] : (? [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) != (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one))))) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & (($true = sP16) <=> (hoasinduction_lem3aaa = $true)) & ((sP15 = $true) <=> (induction2lem = $true)) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) <=> (hoasapinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP13 = $true)) & (! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (? [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) != (X0 @ X4)) | ((X0 @ one) = $true) | ((X1 @ X3) != $true)) <=> (pushprop_lem1v2 = $true)) & ((axidr = $true) <=> ! [X172 : subst] : ((comp @ X172 @ id) = X172)) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) <=> (? [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) != X19) | ? [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) != X21) | ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true)))) & (! [X201 : subst > term > subst > $o] : ? [X202 : term > $o] : ! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id)) <=> (hoasinduction_lem0 = $true)) & ((sP11 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axshiftcons = $true) <=> ! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X54 : d_subst,X55 : d_subst] : ((X54 = X55) | ((d2subst @ X55) != (d2subst @ X54))) & ((sP6 = $true) <=> (hoasinduction_lem2 = $true)) & ((axidl = $true) <=> ! [X409 : subst] : ((comp @ id @ X409) = X409)) & (! [X374 : term] : ((sub @ X374 @ id) = X374) <=> (axvarid = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (sP4 = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & ((? [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) != X211) | ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (? [X216 : term] : ((X214 @ X216) != (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) | ($true = (X214 @ one)) | ((X215 @ X212) != $true))) <=> (pushprop_lem1v2_lthm = $true)) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) <=> (apinj2 = $true)) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (sP3 = $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 32.60/5.94 thf(f14,plain,(
% 32.60/5.94 ! [X342 : term > $o] : (((sP0 @ X342) = $true) <=> ! [X344 : term,X345 : term] : (((X342 @ (ap @ X345 @ X344)) = $true) | ((X342 @ X344) != $true) | ((X342 @ X345) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f15,plain,(
% 32.60/5.94 ! [X348 : term > $o] : (((sP1 @ X348) = $true) <=> ? [X351 : term,X352 : term] : (((X348 @ X351) = $true) & ((X348 @ (ap @ X352 @ X351)) != $true) & ((X348 @ X352) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f16,plain,(
% 32.60/5.94 ($true = sP2) <=> ! [X348 : term > $o,X349 : term,X350 : subst] : (((X348 @ (sub @ X349 @ X350)) = $true) | ((sP1 @ X348) = $true) | ? [X353 : term] : (! [X354 : term] : (($true = (X348 @ (sub @ X353 @ (push @ X354 @ id)))) | ((X348 @ X354) != $true)) & ((X348 @ (lam @ X353)) != $true)) | ? [X355 : term] : (($true != (X348 @ (sub @ X355 @ X350))) & ((var @ X355) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f17,plain,(
% 32.60/5.94 (sP3 = $true) <=> (($true = sP2) | ? [X341 : subst] : ((comp @ X341 @ id) != X341) | ? [X342 : term > $o,X343 : term] : (((X342 @ X343) != $true) & ! [X346 : term] : (((X342 @ X346) != $true) | ((X342 @ (lam @ X346)) = $true)) & ((sP0 @ X342) = $true) & ! [X347 : term] : (($true != (var @ X347)) | ((X342 @ X347) = $true))) | ? [X339 : term,X340 : subst] : ((comp @ sh @ (push @ X339 @ X340)) != X340) | ? [X337 : subst,X338 : term] : ((sub @ one @ (push @ X338 @ X337)) != X338))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f18,plain,(
% 32.60/5.94 (sP4 = $true) <=> (? [X161 : term] : ((sub @ X161 @ id) != X161) | ? [X157 : term] : ! [X158 : subst > term > term] : ? [X159 : term,X160 : subst] : ((X158 @ X160 @ X159) != (sub @ X157 @ (push @ X159 @ X160))) | ! [X162 : subst > term > subst > $o,X163 : term > $o,X164 : term] : (((X163 @ (lam @ X164)) = $true) | ? [X171 : term] : ((X163 @ X171) != (X162 @ id @ X171 @ id)) | ? [X165 : term] : (((X163 @ (sub @ X164 @ (push @ X165 @ id))) != $true) & ((X163 @ X165) = $true)) | ? [X166 : subst > term > term] : (((X162 @ id @ (lam @ (X166 @ sh @ one)) @ id) != $true) & ! [X167 : term] : (((X162 @ id @ X167 @ id) != $true) | ((X162 @ id @ (X166 @ id @ X167) @ id) = $true)) & ! [X168 : subst,X169 : subst,X170 : term] : ((sub @ (X166 @ X168 @ X170) @ X169) = (X166 @ (comp @ X168 @ X169) @ (sub @ X170 @ X169))))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f19,plain,(
% 32.60/5.94 ! [X431 : subst > term > subst > $o] : (($true = (sP5 @ X431)) <=> ? [X432 : term,X433 : term] : (((X431 @ id @ X433 @ id) = $true) & ((X431 @ id @ X432 @ id) = $true) & ((X431 @ id @ (ap @ (sub @ X432 @ id) @ X433) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f20,plain,(
% 32.60/5.94 (sP6 = $true) <=> ! [X429 : term,X430 : term,X431 : subst > term > subst > $o] : (? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X431 @ X436 @ X434 @ (comp @ X435 @ X437)) = $true) & ((X431 @ (comp @ X436 @ X435) @ (sub @ X434 @ X435) @ X437) != $true)) | ? [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (((X431 @ X438 @ X439 @ (comp @ X441 @ X440)) != $true) & ((X431 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440) = $true)) | ((X431 @ id @ X429 @ id) != $true) | ($true = (sP5 @ X431)) | ((X431 @ id @ (ap @ X430 @ X429) @ id) = $true) | ($true != (X431 @ id @ X430 @ id)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f21,plain,(
% 32.60/5.94 ! [X119 : term > $o] : (($true = (sP7 @ X119)) <=> ! [X120 : term,X121 : term] : (((X119 @ (ap @ X120 @ X121)) = $true) | ((X119 @ X121) != $true) | ((X119 @ X120) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f22,plain,(
% 32.60/5.94 ! [X136 : subst > term > subst > $o] : (((sP8 @ X136) = $true) <=> ? [X138 : subst > term > term] : (! [X139 : term] : (((X136 @ id @ (X138 @ id @ X139) @ id) = $true) | ((X136 @ id @ X139 @ id) != $true)) & ((X136 @ id @ (lam @ (X138 @ sh @ one)) @ id) != $true) & ! [X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)) = (sub @ (X138 @ X142 @ X140) @ X141))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f23,plain,(
% 32.60/5.94 ($true = sP9) <=> ? [X126 : subst > term > subst > $o,X127 : term,X128 : term > $o] : (! [X130 : term] : ((X126 @ id @ X130 @ id) = (X128 @ X130)) & ! [X131 : subst > term > term] : (((X126 @ id @ (lam @ (X131 @ sh @ one)) @ id) = $true) | ? [X132 : term] : (($true = (X126 @ id @ X132 @ id)) & ((X126 @ id @ (X131 @ id @ X132) @ id) != $true)) | ? [X133 : subst,X134 : term,X135 : subst] : ((X131 @ (comp @ X133 @ X135) @ (sub @ X134 @ X135)) != (sub @ (X131 @ X133 @ X134) @ X135))) & ((X128 @ (lam @ X127)) != $true) & ! [X129 : term] : (((X128 @ (sub @ X127 @ (push @ X129 @ id))) = $true) | ((X128 @ X129) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f24,plain,(
% 32.60/5.94 (sP10 = $true) <=> ? [X118 : term,X119 : term > $o] : (! [X122 : term] : (((var @ X122) != $true) | ((X119 @ X122) = $true)) & ! [X123 : term] : (? [X124 : term] : (((X119 @ X124) = $true) & ((X119 @ (sub @ X123 @ (push @ X124 @ id))) != $true)) | ((X119 @ (lam @ X123)) = $true)) & ($true != (X119 @ X118)) & ($true = (sP7 @ X119)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f25,plain,(
% 32.60/5.94 (sP11 = $true) <=> (! [X136 : subst > term > subst > $o,X137 : term] : (? [X143 : term,X144 : term] : (((X136 @ id @ (ap @ (sub @ X144 @ id) @ X143) @ id) != $true) & ((X136 @ id @ X143 @ id) = $true) & ((X136 @ id @ X144 @ id) = $true)) | ((sP8 @ X136) = $true) | ((X136 @ id @ X137 @ id) = $true)) | ? [X115 : subst > term > subst > $o] : ! [X116 : term > $o] : ? [X117 : term] : ((X116 @ X117) != (X115 @ id @ X117 @ id)) | ($true = sP9) | ? [X125 : term] : ((sub @ X125 @ id) != X125) | (sP10 = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f26,plain,(
% 32.60/5.94 (sP12 = $true) <=> ? [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ (lam @ (sub @ X322 @ (push @ one @ sh))) @ id) != $true) & ! [X323 : term] : (((X321 @ id @ (sub @ X322 @ (push @ X323 @ id)) @ id) = $true) | ($true != (X321 @ id @ X323 @ id))) & ! [X324 : subst > term > term] : (? [X328 : term] : (($true != (X321 @ id @ (X324 @ id @ X328) @ id)) & ((X321 @ id @ X328 @ id) = $true)) | ((X321 @ id @ (lam @ (X324 @ sh @ one)) @ id) = $true) | ? [X325 : subst,X326 : subst,X327 : term] : ((X324 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)) != (sub @ (X324 @ X325 @ X327) @ X326))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f27,plain,(
% 32.60/5.94 (sP13 = $true) <=> ((sP12 = $true) | ! [X329 : subst > term > subst > $o,X330 : term] : (? [X331 : term] : (($true != (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ((X329 @ id @ (lam @ X330) @ id) = $true) | ? [X332 : subst > term > term] : (! [X336 : term] : (($true != (X329 @ id @ X336 @ id)) | ((X329 @ id @ (X332 @ id @ X336) @ id) = $true)) & ((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) != $true) & ! [X333 : subst,X334 : term,X335 : subst] : ((X332 @ (comp @ X333 @ X335) @ (sub @ X334 @ X335)) = (sub @ (X332 @ X333 @ X334) @ X335)))) | ? [X320 : term] : ((sub @ X320 @ id) != X320))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f28,plain,(
% 32.60/5.94 ! [X534 : term > $o] : (((sP14 @ X534) = $true) <=> ? [X538 : term,X539 : term] : (((X534 @ X538) = $true) & ((X534 @ X539) = $true) & ((X534 @ (ap @ X538 @ X539)) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f29,plain,(
% 32.60/5.94 (sP15 = $true) <=> ! [X532 : term,X533 : subst,X534 : term > $o] : (((X534 @ (sub @ X532 @ X533)) = $true) | ? [X537 : term] : (((X534 @ (sub @ X537 @ X533)) != $true) & ((var @ X537) = $true)) | ? [X535 : term] : (! [X536 : term] : (((X534 @ X536) != $true) | ((X534 @ (sub @ X535 @ (push @ X536 @ id))) = $true)) & ((X534 @ (lam @ X535)) != $true)) | ((sP14 @ X534) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f30,plain,(
% 32.60/5.94 ($true = sP16) <=> ! [X64 : term,X65 : subst > term > subst > $o] : (? [X67 : subst > term > term,X68 : term] : (! [X72 : subst,X73 : term,X74 : subst] : ((X67 @ (comp @ X72 @ X74) @ (sub @ X73 @ X74)) = (sub @ X68 @ (push @ (sub @ X73 @ X74) @ (comp @ X72 @ X74)))) & ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) != $true) & ! [X69 : subst,X70 : subst,X71 : term] : ((sub @ (sub @ X68 @ (push @ X71 @ X69)) @ X70) = (sub @ (X67 @ X69 @ X71) @ X70)) & ! [X75 : term] : (((X65 @ id @ X75 @ id) != $true) | ((X65 @ id @ (X67 @ id @ X75) @ id) = $true))) | ((X65 @ id @ (lam @ (sub @ X64 @ (push @ one @ sh))) @ id) = $true) | ? [X66 : term] : (((X65 @ id @ (sub @ X64 @ (push @ X66 @ id)) @ id) != $true) & ((X65 @ id @ X66 @ id) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f31,plain,(
% 32.60/5.94 ! [X295 : subst > term > subst > $o] : (((sP17 @ X295) = $true) <=> ? [X301 : subst > term > term] : (! [X302 : subst,X303 : subst,X304 : term] : ((X301 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302)) = (sub @ (X301 @ X303 @ X304) @ X302)) & ($true != (X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)) & ! [X305 : term] : (((X295 @ id @ (X301 @ id @ X305) @ id) = $true) | ((X295 @ id @ X305 @ id) != $true))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f32,plain,(
% 32.60/5.94 (sP18 = $true) <=> ? [X287 : term,X288 : subst > term > subst > $o] : (! [X294 : term] : (((X288 @ id @ X294 @ id) != $true) | ($true = (X288 @ id @ (sub @ X287 @ (push @ X294 @ id)) @ id))) & ! [X289 : subst > term > term] : (? [X290 : term] : (($true = (X288 @ id @ X290 @ id)) & ((X288 @ id @ (X289 @ id @ X290) @ id) != $true)) | ($true = (X288 @ id @ (lam @ (X289 @ sh @ one)) @ id)) | ? [X291 : term,X292 : subst,X293 : subst] : ((sub @ (X289 @ X292 @ X291) @ X293) != (X289 @ (comp @ X292 @ X293) @ (sub @ X291 @ X293)))) & ((X288 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id) != $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f33,plain,(
% 32.60/5.94 (sP19 = $true) <=> ((sP18 = $true) | ? [X286 : term] : ((sub @ X286 @ id) != X286) | ! [X295 : subst > term > subst > $o,X296 : term] : (? [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (((X295 @ X307 @ X310 @ (comp @ X308 @ X309)) = $true) & ((X295 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309) != $true)) | ((sP17 @ X295) = $true) | ? [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (($true = (X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299)) & ((X295 @ X297 @ X300 @ (comp @ X298 @ X299)) != $true)) | ? [X306 : term] : (((X295 @ id @ X306 @ id) = $true) & ((X295 @ id @ (sub @ X296 @ (push @ X306 @ id)) @ id) != $true)) | ((X295 @ id @ (lam @ X296) @ id) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f34,plain,(
% 32.60/5.94 ! [X400 : term > $o] : (((sP20 @ X400) = $true) <=> ? [X402 : term,X403 : term] : (((X400 @ X403) = $true) & ($true != (X400 @ (ap @ X403 @ X402))) & ((X400 @ X402) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f35,plain,(
% 32.60/5.94 (sP21 = $true) <=> ! [X400 : term > $o,X401 : term] : (? [X404 : term] : (((var @ X404) = $true) & ((X400 @ X404) != $true)) | ? [X405 : term] : (((X400 @ (lam @ X405)) != $true) & ! [X406 : term] : (((X400 @ (sub @ X405 @ (push @ X406 @ id))) = $true) | ((X400 @ X406) != $true))) | ((sP20 @ X400) = $true) | ((X400 @ X401) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f36,plain,(
% 32.60/5.94 (sP22 = $true) <=> (! [X390 : subst,X391 : subst > term > term,X392 : term,X393 : subst > term > term] : (? [X394 : subst,X395 : term,X396 : subst] : ((X393 @ (comp @ X396 @ X394) @ (sub @ X395 @ X394)) != (sub @ (X393 @ X396 @ X395) @ X394)) | ((lam @ (X391 @ sh @ one)) != (lam @ (X393 @ sh @ one))) | ((X391 @ X390 @ X392) = (X393 @ X390 @ X392)) | ? [X397 : subst,X398 : term,X399 : subst] : ((X391 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399)) != (sub @ (X391 @ X397 @ X398) @ X399))) | ? [X386 : subst,X387 : term] : ((comp @ sh @ (push @ X387 @ X386)) != X386) | ? [X384 : term,X385 : subst] : ((sub @ one @ (push @ X384 @ X385)) != X384) | ? [X388 : term,X389 : term] : (((lam @ X389) = (lam @ X388)) & (X388 != X389)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f37,plain,(
% 32.60/5.94 ! [X217 : term > $o] : (((sP23 @ X217) = $true) <=> ! [X222 : term,X223 : term] : (((X217 @ (ap @ X222 @ X223)) = $true) | ((X217 @ X222) != $true) | ((X217 @ X223) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f38,plain,(
% 32.60/5.94 ! [X238 : subst > term > subst > $o] : (($true = (sP24 @ X238)) <=> ! [X247 : subst > term > term] : (((X238 @ id @ (lam @ (X247 @ sh @ one)) @ id) = $true) | ? [X248 : term] : (((X238 @ id @ (X247 @ id @ X248) @ id) != $true) & ($true = (X238 @ id @ X248 @ id))) | ? [X249 : subst,X250 : subst,X251 : term] : ((X247 @ (comp @ X249 @ X250) @ (sub @ X251 @ X250)) != (sub @ (X247 @ X249 @ X251) @ X250))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f39,plain,(
% 32.60/5.94 ! [X224 : subst > term > subst > $o] : (((sP25 @ X224) = $true) <=> ! [X227 : term,X228 : term] : (((X224 @ id @ X228 @ id) != $true) | ((X224 @ id @ (ap @ (sub @ X227 @ id) @ X228) @ id) = $true) | ((X224 @ id @ X227 @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f40,plain,(
% 32.60/5.94 ! [X253 : subst > term > subst > $o] : (((sP26 @ X253) = $true) <=> ? [X261 : subst > term > term] : (((X253 @ id @ (lam @ (X261 @ sh @ one)) @ id) != $true) & ! [X262 : term] : (($true != (X253 @ id @ X262 @ id)) | ($true = (X253 @ id @ (X261 @ id @ X262) @ id))) & ! [X263 : term,X264 : subst,X265 : subst] : ((X261 @ (comp @ X265 @ X264) @ (sub @ X263 @ X264)) = (sub @ (X261 @ X265 @ X263) @ X264))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f41,plain,(
% 32.60/5.94 ! [X253 : subst > term > subst > $o] : (((sP27 @ X253) = $true) <=> ? [X259 : term,X260 : term] : (($true != (X253 @ id @ (ap @ (sub @ X259 @ id) @ X260) @ id)) & ((X253 @ id @ X260 @ id) = $true) & ((X253 @ id @ X259 @ id) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f42,plain,(
% 32.60/5.94 (sP28 = $true) <=> ? [X237 : term,X238 : subst > term > subst > $o] : (((X238 @ id @ (lam @ X237) @ id) != $true) & ($true = (sP24 @ X238)) & ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) = $true) | ((X238 @ X244 @ X245 @ (comp @ X243 @ X246)) != $true)) & ! [X252 : term] : (((X238 @ id @ (sub @ X237 @ (push @ X252 @ id)) @ id) = $true) | ((X238 @ id @ X252 @ id) != $true)) & ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (((X238 @ (comp @ X241 @ X242) @ (sub @ X240 @ X242) @ X239) != $true) | ((X238 @ X241 @ X240 @ (comp @ X242 @ X239)) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f43,plain,(
% 32.60/5.94 (sP29 = $true) <=> ! [X253 : subst > term > subst > $o,X254 : term] : (((sP27 @ X253) = $true) | ? [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (((X253 @ X267 @ X268 @ (comp @ X269 @ X266)) != $true) & ((X253 @ (comp @ X267 @ X269) @ (sub @ X268 @ X269) @ X266) = $true)) | ((X253 @ id @ X254 @ id) = $true) | ? [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (((X253 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257) @ X255) != $true) & ($true = (X253 @ X258 @ X256 @ (comp @ X257 @ X255)))) | ? [X270 : term] : (($true = (var @ (sub @ X270 @ id))) & ((X253 @ id @ X270 @ id) != $true)) | ((sP26 @ X253) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f44,plain,(
% 32.60/5.94 (sP30 = $true) <=> ? [X217 : term > $o,X218 : term] : (((sP23 @ X217) = $true) & ! [X219 : term] : (((X217 @ X219) = $true) | ((var @ X219) != $true)) & ! [X220 : term] : (((X217 @ (lam @ X220)) = $true) | ? [X221 : term] : (((X217 @ (sub @ X220 @ (push @ X221 @ id))) != $true) & ((X217 @ X221) = $true))) & ((X217 @ X218) != $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f45,plain,(
% 32.60/5.94 (sP31 = $true) <=> ((sP29 = $true) | ? [X224 : subst > term > subst > $o,X225 : term,X226 : term] : (! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : (((X224 @ X235 @ X234 @ (comp @ X233 @ X236)) != $true) | ((X224 @ (comp @ X235 @ X233) @ (sub @ X234 @ X233) @ X236) = $true)) & ! [X229 : term,X230 : subst,X231 : subst,X232 : subst] : (((X224 @ X230 @ X229 @ (comp @ X231 @ X232)) = $true) | ((X224 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231) @ X232) != $true)) & ((X224 @ id @ X226 @ id) = $true) & ((X224 @ id @ X225 @ id) = $true) & ((sP25 @ X224) = $true) & ($true != (X224 @ id @ (ap @ X225 @ X226) @ id))) | (sP28 = $true) | (sP30 = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f46,plain,(
% 32.60/5.94 ($true = sP32) <=> ! [X442 : term,X443 : subst > term > subst > $o] : (((X443 @ id @ (lam @ (sub @ X442 @ (push @ one @ sh))) @ id) = $true) | ? [X444 : term] : (((X443 @ id @ (sub @ X442 @ (push @ X444 @ id)) @ id) != $true) & ((X443 @ id @ X444 @ id) = $true)) | ? [X445 : subst > term > term] : (! [X446 : subst,X447 : term,X448 : subst] : ((sub @ (X445 @ X446 @ X447) @ X448) = (X445 @ (comp @ X446 @ X448) @ (sub @ X447 @ X448))) & ! [X449 : term] : (((X443 @ id @ X449 @ id) != $true) | ((X443 @ id @ (X445 @ id @ X449) @ id) = $true)) & ((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f47,plain,(
% 32.60/5.94 (sP33 = $true) <=> ! [X512 : subst > term > subst > $o,X513 : term > $o,X514 : term] : (? [X515 : term] : ((X513 @ X515) != (X512 @ id @ X515 @ id)) | ? [X516 : subst > term > term] : (((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id) != $true) & ! [X517 : subst,X518 : subst,X519 : term] : ((sub @ (X516 @ X518 @ X519) @ X517) = (X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) & ! [X520 : term] : (((X512 @ id @ X520 @ id) != $true) | ((X512 @ id @ (X516 @ id @ X520) @ id) = $true))) | ($true = (X513 @ (lam @ X514))) | ? [X521 : term] : (((X513 @ (sub @ X514 @ (push @ X521 @ id))) != $true) & ((X513 @ X521) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f48,plain,(
% 32.60/5.94 ! [X273 : subst > term > subst > $o] : (($true = (sP34 @ X273)) <=> ? [X280 : term,X281 : term] : (((X273 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id) != $true) & ((X273 @ id @ X281 @ id) = $true) & ((X273 @ id @ X280 @ id) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f49,plain,(
% 32.60/5.94 (sP35 = $true) <=> ! [X271 : term,X272 : term > $o,X273 : subst > term > subst > $o,X274 : term] : (? [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (((X273 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) = $true) & ((X273 @ X285 @ X283 @ (comp @ X282 @ X284)) != $true)) | ($true = (sP34 @ X273)) | ($true != (X272 @ X274)) | ((X272 @ X271) != $true) | ((X272 @ (ap @ X274 @ X271)) = $true) | ? [X275 : term] : ((X272 @ X275) != (X273 @ id @ X275 @ id)) | ? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (((X273 @ (comp @ X276 @ X278) @ (sub @ X279 @ X278) @ X277) != $true) & ((X273 @ X276 @ X279 @ (comp @ X278 @ X277)) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f50,plain,(
% 32.60/5.94 ! [X466 : subst > term > subst > $o] : (((sP36 @ X466) = $true) <=> ? [X481 : term,X482 : term] : (((X466 @ id @ X481 @ id) = $true) & ($true = (X466 @ id @ X482 @ id)) & ((X466 @ id @ (ap @ (sub @ X482 @ id) @ X481) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f51,plain,(
% 32.60/5.94 ! [X466 : subst > term > subst > $o] : (((sP37 @ X466) = $true) <=> ? [X472 : subst > term > term] : (! [X476 : term] : (((X466 @ id @ X476 @ id) != $true) | ((X466 @ id @ (X472 @ id @ X476) @ id) = $true)) & ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) != $true) & ! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f52,plain,(
% 32.60/5.94 (sP38 = $true) <=> ! [X465 : term,X466 : subst > term > subst > $o] : (((X466 @ id @ X465 @ id) = $true) | ((sP37 @ X466) = $true) | ? [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (((X466 @ X470 @ X468 @ (comp @ X471 @ X469)) = $true) & ((X466 @ (comp @ X470 @ X471) @ (sub @ X468 @ X471) @ X469) != $true)) | ((sP36 @ X466) = $true) | ? [X467 : term] : (($true != (X466 @ id @ X467 @ id)) & ((var @ (sub @ X467 @ id)) = $true)) | ? [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = (X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477)) & ($true != (X466 @ X479 @ X480 @ (comp @ X478 @ X477)))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f53,plain,(
% 32.60/5.94 ! [X149 : term > $o] : (((sP39 @ X149) = $true) <=> ? [X151 : term,X152 : term] : (((X149 @ (ap @ X152 @ X151)) != $true) & ($true = (X149 @ X151)) & ((X149 @ X152) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f54,plain,(
% 32.60/5.94 ! [X38 : subst > term > subst > $o] : (((sP40 @ X38) = $true) <=> ? [X49 : subst > term > term] : (! [X53 : term] : (((X38 @ id @ X53 @ id) != $true) | ((X38 @ id @ (X49 @ id @ X53) @ id) = $true)) & ! [X50 : subst,X51 : subst,X52 : term] : ((X49 @ (comp @ X50 @ X51) @ (sub @ X52 @ X51)) = (sub @ (X49 @ X50 @ X52) @ X51)) & ((X38 @ id @ (lam @ (X49 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f55,plain,(
% 32.60/5.94 (sP41 = $true) <=> ! [X38 : subst > term > subst > $o,X39 : term] : (((X38 @ id @ (lam @ X39) @ id) = $true) | ? [X44 : subst,X45 : subst,X46 : subst,X47 : term] : (((X38 @ (comp @ X44 @ X46) @ (sub @ X47 @ X46) @ X45) = $true) & ((X38 @ X44 @ X47 @ (comp @ X46 @ X45)) != $true)) | ((sP40 @ X38) = $true) | ? [X40 : term,X41 : subst,X42 : subst,X43 : subst] : (($true != (X38 @ (comp @ X42 @ X43) @ (sub @ X40 @ X43) @ X41)) & ((X38 @ X42 @ X40 @ (comp @ X43 @ X41)) = $true)) | ? [X48 : term] : (((X38 @ id @ (sub @ X39 @ (push @ X48 @ id)) @ id) != $true) & ($true = (X38 @ id @ X48 @ id))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f56,plain,(
% 32.60/5.94 ! [X488 : subst > term > subst > $o] : (((sP42 @ X488) = $true) <=> ? [X489 : term,X490 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (ap @ (sub @ X489 @ id) @ X490) @ id) != $true) & ((X488 @ id @ X490 @ id) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f57,plain,(
% 32.60/5.94 ! [X497 : term > $o] : (((sP43 @ X497) = $true) <=> ! [X500 : term,X501 : term] : (((X497 @ X501) != $true) | ((X497 @ X500) != $true) | ((X497 @ (ap @ X500 @ X501)) = $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f58,plain,(
% 32.60/5.94 ! [X505 : term > $o] : (($true = (sP44 @ X505)) <=> ? [X509 : term,X510 : term] : (((X505 @ X510) = $true) & ((X505 @ X509) = $true) & ((X505 @ (ap @ X509 @ X510)) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f59,plain,(
% 32.60/5.94 (sP45 = $true) <=> ! [X505 : term > $o,X506 : term] : (? [X507 : term] : (! [X508 : term] : (((X505 @ X508) != $true) | ((X505 @ (sub @ X507 @ (push @ X508 @ id))) = $true)) & ($true != (X505 @ (lam @ X507)))) | ? [X511 : term] : (((var @ X511) = $true) & ((X505 @ X511) != $true)) | ($true = (sP44 @ X505)) | ($true = (X505 @ X506)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f60,plain,(
% 32.60/5.94 ($true = sP46) <=> (? [X496 : term] : ((sub @ X496 @ id) != X496) | (sP45 = $true) | ? [X497 : term > $o,X498 : subst,X499 : term] : (! [X502 : term] : (((X497 @ (lam @ X502)) = $true) | ? [X503 : term] : (((X497 @ X503) = $true) & ((X497 @ (sub @ X502 @ (push @ X503 @ id))) != $true))) & ((sP43 @ X497) = $true) & ((X497 @ (sub @ X499 @ X498)) != $true) & ! [X504 : term] : (($true = (X497 @ (sub @ X504 @ X498))) | ((var @ X504) != $true))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f61,plain,(
% 32.60/5.94 ! [X79 : term > $o] : (((sP47 @ X79) = $true) <=> ! [X81 : term,X82 : term] : (($true != (X79 @ X82)) | ((X79 @ (ap @ X82 @ X81)) = $true) | ((X79 @ X81) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f62,plain,(
% 32.60/5.94 ! [X97 : subst > term > subst > $o] : (((sP48 @ X97) = $true) <=> ? [X110 : subst > term > term] : (! [X111 : subst,X112 : term,X113 : subst] : ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)) = (sub @ (X110 @ X113 @ X112) @ X111)) & ! [X114 : term] : (((X97 @ id @ (X110 @ id @ X114) @ id) = $true) | ((X97 @ id @ X114 @ id) != $true)) & ((X97 @ id @ (lam @ (X110 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f63,plain,(
% 32.60/5.94 ! [X97 : subst > term > subst > $o] : (((sP49 @ X97) = $true) <=> ? [X107 : term,X108 : term] : (((X97 @ id @ X107 @ id) = $true) & ((X97 @ id @ X108 @ id) = $true) & ((X97 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f64,plain,(
% 32.60/5.94 (sP50 = $true) <=> ? [X87 : subst > term > subst > $o,X88 : term > $o,X89 : term] : (! [X90 : term] : ((X87 @ id @ X90 @ id) = (X88 @ X90)) & ! [X91 : subst > term > term] : (((X87 @ id @ (lam @ (X91 @ sh @ one)) @ id) = $true) | ? [X92 : term] : (($true != (X87 @ id @ (X91 @ id @ X92) @ id)) & ((X87 @ id @ X92 @ id) = $true)) | ? [X93 : subst,X94 : term,X95 : subst] : ((X91 @ (comp @ X95 @ X93) @ (sub @ X94 @ X93)) != (sub @ (X91 @ X95 @ X94) @ X93))) & ! [X96 : term] : (((X88 @ (sub @ X89 @ (push @ X96 @ id))) = $true) | ((X88 @ X96) != $true)) & ((X88 @ (lam @ X89)) != $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f65,plain,(
% 32.60/5.94 (sP51 = $true) <=> ! [X97 : subst > term > subst > $o,X98 : term] : (? [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (((X97 @ (comp @ X103 @ X104) @ (sub @ X106 @ X104) @ X105) = $true) & ((X97 @ X103 @ X106 @ (comp @ X104 @ X105)) != $true)) | ((sP49 @ X97) = $true) | ? [X99 : subst,X100 : subst,X101 : term,X102 : subst] : (((X97 @ X99 @ X101 @ (comp @ X102 @ X100)) = $true) & ((X97 @ (comp @ X99 @ X102) @ (sub @ X101 @ X102) @ X100) != $true)) | ((sP48 @ X97) = $true) | ? [X109 : term] : (((var @ (sub @ X109 @ id)) = $true) & ($true != (X97 @ id @ X109 @ id))) | ((X97 @ id @ X98 @ id) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f66,plain,(
% 32.60/5.94 (sP52 = $true) <=> (? [X76 : subst > term > subst > $o] : ! [X77 : term > $o] : ? [X78 : term] : ((X76 @ id @ X78 @ id) != (X77 @ X78)) | (sP51 = $true) | ? [X86 : term] : ((sub @ X86 @ id) != X86) | (sP50 = $true) | ? [X79 : term > $o,X80 : term] : (! [X84 : term] : (((X79 @ (lam @ X84)) = $true) | ? [X85 : term] : (((X79 @ (sub @ X84 @ (push @ X85 @ id))) != $true) & ((X79 @ X85) = $true))) & ((sP47 @ X79) = $true) & ! [X83 : term] : (((var @ X83) != $true) | ((X79 @ X83) = $true)) & ((X79 @ X80) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f67,plain,(
% 32.60/5.94 ($true = sP53) <=> ! [X375 : subst > term > subst > $o,X376 : term] : (((X375 @ id @ (lam @ X376) @ id) = $true) | ? [X377 : term] : (($true = (X375 @ id @ X377 @ id)) & ((X375 @ id @ (sub @ X376 @ (push @ X377 @ id)) @ id) != $true)) | ? [X378 : subst > term > term] : (! [X380 : subst,X381 : subst,X382 : term] : ((sub @ (X378 @ X380 @ X382) @ X381) = (X378 @ (comp @ X380 @ X381) @ (sub @ X382 @ X381))) & ((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id) != $true) & ! [X379 : term] : (((X375 @ id @ X379 @ id) != $true) | ((X375 @ id @ (X378 @ id @ X379) @ id) = $true))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f68,plain,(
% 32.60/5.94 (sP54 = $true) <=> ! [X421 : subst > term > subst > $o,X422 : term] : (? [X428 : term] : (((X421 @ id @ (sub @ X422 @ (push @ X428 @ id)) @ id) != $true) & ((X421 @ id @ X428 @ id) = $true)) | ? [X423 : subst > term > term] : (! [X424 : term] : (((X421 @ id @ X424 @ id) != $true) | ((X421 @ id @ (X423 @ id @ X424) @ id) = $true)) & ! [X425 : term,X426 : subst,X427 : subst] : ((sub @ (X423 @ X427 @ X425) @ X426) = (X423 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426))) & ((X421 @ id @ (lam @ (X423 @ sh @ one)) @ id) != $true)) | ((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f69,plain,(
% 32.60/5.94 ! [X178 : subst > term > subst > $o] : (((sP55 @ X178) = $true) <=> ? [X186 : subst > term > term] : (((X178 @ id @ (lam @ (X186 @ sh @ one)) @ id) != $true) & ! [X188 : term,X189 : subst,X190 : subst] : ((X186 @ (comp @ X189 @ X190) @ (sub @ X188 @ X190)) = (sub @ (X186 @ X189 @ X188) @ X190)) & ! [X187 : term] : (((X178 @ id @ (X186 @ id @ X187) @ id) = $true) | ((X178 @ id @ X187 @ id) != $true))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f70,plain,(
% 32.60/5.94 (sP56 = $true) <=> (! [X178 : subst > term > subst > $o,X179 : term,X180 : term > $o] : (((sP55 @ X178) = $true) | ((X180 @ (lam @ X179)) = $true) | ? [X195 : term] : ((X180 @ X195) != (X178 @ id @ X195 @ id)) | ? [X191 : subst,X192 : term,X193 : subst,X194 : subst] : (($true != (X178 @ X191 @ X192 @ (comp @ X193 @ X194))) & ((X178 @ (comp @ X191 @ X193) @ (sub @ X192 @ X193) @ X194) = $true)) | ? [X181 : subst,X182 : subst,X183 : subst,X184 : term] : (((X178 @ X183 @ X184 @ (comp @ X182 @ X181)) = $true) & ((X178 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182) @ X181) != $true)) | ? [X185 : term] : (((X180 @ X185) = $true) & ((X180 @ (sub @ X179 @ (push @ X185 @ id))) != $true))) | ? [X177 : term] : ((sub @ X177 @ id) != X177))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f71,plain,(
% 32.60/5.94 ! [X356 : subst > term > subst > $o] : (((sP57 @ X356) = $true) <=> ? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373)) & ! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ((X356 @ id @ X370 @ id) != $true)) & ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f72,plain,(
% 32.60/5.94 (sP58 = $true) <=> ! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (? [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) != $true) & ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) = $true)) | ((X357 @ (lam @ X358)) = $true) | ((sP57 @ X356) = $true) | ? [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) = $true) & ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) != $true)) | ? [X359 : term] : ((X357 @ X359) != (X356 @ id @ X359 @ id)) | ? [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) != $true) & ($true = (X357 @ X364))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.60/5.94 thf(f13,plain,(
% 32.60/5.94 ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X34 : term] : ? [X35 : subst > term > term] : ! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36)))) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (? [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) != $true) & ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) = $true)) | ((X357 @ (lam @ X358)) = $true) | ? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373)) & ! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ((X356 @ id @ X370 @ id) != $true)) & ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) != $true)) | ? [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) = $true) & ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) != $true)) | ? [X359 : term] : ((X357 @ X359) != (X356 @ id @ X359 @ id)) | ? [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) != $true) & ($true = (X357 @ X364)))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslaminj_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) <=> (? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) = (ap @ X59 @ X57)) & (X57 != X58)) | ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61)))) & (axapp = $true) & (induction2_gthm = $true) & ! [X209 : d_subst] : (d_id = X209) & ((termmset_lthm = $true) <=> (! [X418 : term] : ((sub @ X418 @ id) = X418) | ? [X417 : term] : ((sub @ X417 @ id) != X417))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X483 : term] : ? [X484 : subst > term > term] : ! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X178 : subst > term > subst > $o,X179 : term,X180 : term > $o] : (? [X186 : subst > term > term] : (((X178 @ id @ (lam @ (X186 @ sh @ one)) @ id) != $true) & ! [X188 : term,X189 : subst,X190 : subst] : ((X186 @ (comp @ X189 @ X190) @ (sub @ X188 @ X190)) = (sub @ (X186 @ X189 @ X188) @ X190)) & ! [X187 : term] : (((X178 @ id @ (X186 @ id @ X187) @ id) = $true) | ((X178 @ id @ X187 @ id) != $true))) | ((X180 @ (lam @ X179)) = $true) | ? [X195 : term] : ((X180 @ X195) != (X178 @ id @ X195 @ id)) | ? [X191 : subst,X192 : term,X193 : subst,X194 : subst] : (($true != (X178 @ X191 @ X192 @ (comp @ X193 @ X194))) & ((X178 @ (comp @ X191 @ X193) @ (sub @ X192 @ X193) @ X194) = $true)) | ? [X181 : subst,X182 : subst,X183 : subst,X184 : term] : (((X178 @ X183 @ X184 @ (comp @ X182 @ X181)) = $true) & ((X178 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182) @ X181) != $true)) | ? [X185 : term] : (((X180 @ X185) = $true) & ((X180 @ (sub @ X179 @ (push @ X185 @ id))) != $true))) | ? [X177 : term] : ((sub @ X177 @ id) != X177))) & (ulamvarind = $true) & (! [X421 : subst > term > subst > $o,X422 : term] : (? [X428 : term] : (((X421 @ id @ (sub @ X422 @ (push @ X428 @ id)) @ id) != $true) & ((X421 @ id @ X428 @ id) = $true)) | ? [X423 : subst > term > term] : (! [X424 : term] : (((X421 @ id @ X424 @ id) != $true) | ((X421 @ id @ (X423 @ id @ X424) @ id) = $true)) & ! [X425 : term,X426 : subst,X427 : subst] : ((sub @ (X423 @ X427 @ X425) @ X426) = (X423 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426))) & ((X421 @ id @ (lam @ (X423 @ sh @ one)) @ id) != $true)) | ((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X311 : subst > term > subst > $o] : ? [X312 : term > $o] : ! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ? [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) = (X29 @ sh @ one))) & (pushprop_lem3v2 = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X375 : subst > term > subst > $o,X376 : term] : (((X375 @ id @ (lam @ X376) @ id) = $true) | ? [X377 : term] : (($true = (X375 @ id @ X377 @ id)) & ((X375 @ id @ (sub @ X376 @ (push @ X377 @ id)) @ id) != $true)) | ? [X378 : subst > term > term] : (! [X380 : subst,X381 : subst,X382 : term] : ((sub @ (X378 @ X380 @ X382) @ X381) = (X378 @ (comp @ X380 @ X381) @ (sub @ X382 @ X381))) & ((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id) != $true) & ! [X379 : term] : (((X375 @ id @ X379 @ id) != $true) | ((X375 @ id @ (X378 @ id @ X379) @ id) = $true))))) & (hoasinduction_lem3v2_gthm = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasapinj2_gthm = $true) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) <=> (axvarcons = $true)) & ((hoasinduction_lthm_3 = $true) <=> (? [X76 : subst > term > subst > $o] : ! [X77 : term > $o] : ? [X78 : term] : ((X76 @ id @ X78 @ id) != (X77 @ X78)) | ! [X97 : subst > term > subst > $o,X98 : term] : (? [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (((X97 @ (comp @ X103 @ X104) @ (sub @ X106 @ X104) @ X105) = $true) & ((X97 @ X103 @ X106 @ (comp @ X104 @ X105)) != $true)) | ? [X107 : term,X108 : term] : (((X97 @ id @ X107 @ id) = $true) & ((X97 @ id @ X108 @ id) = $true) & ((X97 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id) != $true)) | ? [X99 : subst,X100 : subst,X101 : term,X102 : subst] : (((X97 @ X99 @ X101 @ (comp @ X102 @ X100)) = $true) & ((X97 @ (comp @ X99 @ X102) @ (sub @ X101 @ X102) @ X100) != $true)) | ? [X110 : subst > term > term] : (! [X111 : subst,X112 : term,X113 : subst] : ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)) = (sub @ (X110 @ X113 @ X112) @ X111)) & ! [X114 : term] : (((X97 @ id @ (X110 @ id @ X114) @ id) = $true) | ((X97 @ id @ X114 @ id) != $true)) & ((X97 @ id @ (lam @ (X110 @ sh @ one)) @ id) != $true)) | ? [X109 : term] : (((var @ (sub @ X109 @ id)) = $true) & ($true != (X97 @ id @ X109 @ id))) | ((X97 @ id @ X98 @ id) = $true)) | ? [X86 : term] : ((sub @ X86 @ id) != X86) | ? [X87 : subst > term > subst > $o,X88 : term > $o,X89 : term] : (! [X90 : term] : ((X87 @ id @ X90 @ id) = (X88 @ X90)) & ! [X91 : subst > term > term] : (((X87 @ id @ (lam @ (X91 @ sh @ one)) @ id) = $true) | ? [X92 : term] : (($true != (X87 @ id @ (X91 @ id @ X92) @ id)) & ((X87 @ id @ X92 @ id) = $true)) | ? [X93 : subst,X94 : term,X95 : subst] : ((X91 @ (comp @ X95 @ X93) @ (sub @ X94 @ X93)) != (sub @ (X91 @ X95 @ X94) @ X93))) & ! [X96 : term] : (((X88 @ (sub @ X89 @ (push @ X96 @ id))) = $true) | ((X88 @ X96) != $true)) & ((X88 @ (lam @ X89)) != $true)) | ? [X79 : term > $o,X80 : term] : (! [X84 : term] : (((X79 @ (lam @ X84)) = $true) | ? [X85 : term] : (((X79 @ (sub @ X84 @ (push @ X85 @ id))) != $true) & ((X79 @ X85) = $true))) & ! [X81 : term,X82 : term] : (($true != (X79 @ X82)) | ((X79 @ (ap @ X82 @ X81)) = $true) | ((X79 @ X81) != $true)) & ! [X83 : term] : (((var @ X83) != $true) | ((X79 @ X83) = $true)) & ((X79 @ X80) != $true)))) & ((induction2_lthm = $true) <=> (? [X496 : term] : ((sub @ X496 @ id) != X496) | ! [X505 : term > $o,X506 : term] : (? [X507 : term] : (! [X508 : term] : (((X505 @ X508) != $true) | ((X505 @ (sub @ X507 @ (push @ X508 @ id))) = $true)) & ($true != (X505 @ (lam @ X507)))) | ? [X511 : term] : (((var @ X511) = $true) & ((X505 @ X511) != $true)) | ? [X509 : term,X510 : term] : (((X505 @ X510) = $true) & ((X505 @ X509) = $true) & ((X505 @ (ap @ X509 @ X510)) != $true)) | ($true = (X505 @ X506))) | ? [X497 : term > $o,X498 : subst,X499 : term] : (! [X502 : term] : (((X497 @ (lam @ X502)) = $true) | ? [X503 : term] : (((X497 @ X503) = $true) & ((X497 @ (sub @ X502 @ (push @ X503 @ id))) != $true))) & ! [X500 : term,X501 : term] : (((X497 @ X501) != $true) | ((X497 @ X500) != $true) | ((X497 @ (ap @ X500 @ X501)) = $true)) & ((X497 @ (sub @ X499 @ X498)) != $true) & ! [X504 : term] : (($true = (X497 @ (sub @ X504 @ X498))) | ((var @ X504) != $true))))) & (! [X487 : term,X488 : subst > term > subst > $o] : (? [X491 : subst > term > term] : (! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) & ! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) != $true)) | ((X488 @ id @ X487 @ id) = $true) | ? [X489 : term,X490 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (ap @ (sub @ X489 @ id) @ X490) @ id) != $true) & ((X488 @ id @ X490 @ id) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & ((pushprop_lem0 = $true) <=> ! [X456 : subst,X457 : term > $o,X458 : term] : ? [X459 : term > $o] : ! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & ((var @ (d2term @ d_one)) != $true) & (pushprop = $true) & ((! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)) | ? [X5 : term] : ((sub @ X5 @ id) != X5) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 != X9) & ((ap @ X8 @ X6) = (ap @ X9 @ X7)))) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X38 : subst > term > subst > $o,X39 : term] : (((X38 @ id @ (lam @ X39) @ id) = $true) | ? [X44 : subst,X45 : subst,X46 : subst,X47 : term] : (((X38 @ (comp @ X44 @ X46) @ (sub @ X47 @ X46) @ X45) = $true) & ((X38 @ X44 @ X47 @ (comp @ X46 @ X45)) != $true)) | ? [X49 : subst > term > term] : (! [X53 : term] : (((X38 @ id @ X53 @ id) != $true) | ((X38 @ id @ (X49 @ id @ X53) @ id) = $true)) & ! [X50 : subst,X51 : subst,X52 : term] : ((X49 @ (comp @ X50 @ X51) @ (sub @ X52 @ X51)) = (sub @ (X49 @ X50 @ X52) @ X51)) & ((X38 @ id @ (lam @ (X49 @ sh @ one)) @ id) != $true)) | ? [X40 : term,X41 : subst,X42 : subst,X43 : subst] : (($true != (X38 @ (comp @ X42 @ X43) @ (sub @ X40 @ X43) @ X41)) & ((X38 @ X42 @ X40 @ (comp @ X43 @ X41)) = $true)) | ? [X48 : term] : (((X38 @ id @ (sub @ X39 @ (push @ X48 @ id)) @ id) != $true) & ($true = (X38 @ id @ X48 @ id))))) & (! [X149 : term > $o,X150 : term] : (? [X154 : term] : (((X149 @ X154) != $true) & ((var @ X154) = $true)) | ? [X151 : term,X152 : term] : (((X149 @ (ap @ X152 @ X151)) != $true) & ($true = (X149 @ X151)) & ((X149 @ X152) = $true)) | ((X149 @ X150) = $true) | ? [X153 : term] : (((X149 @ X153) = $true) & ((X149 @ (lam @ X153)) != $true))) <=> (induction = $true)) & (hoasinduction_gthm = $true) & ! [X410 : d_term] : (d_one = X410) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) <=> ! [X465 : term,X466 : subst > term > subst > $o] : (((X466 @ id @ X465 @ id) = $true) | ? [X472 : subst > term > term] : (! [X476 : term] : (((X466 @ id @ X476 @ id) != $true) | ((X466 @ id @ (X472 @ id @ X476) @ id) = $true)) & ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) != $true) & ! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473))) | ? [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (((X466 @ X470 @ X468 @ (comp @ X471 @ X469)) = $true) & ((X466 @ (comp @ X470 @ X471) @ (sub @ X468 @ X471) @ X469) != $true)) | ? [X481 : term,X482 : term] : (((X466 @ id @ X481 @ id) = $true) & ($true = (X466 @ id @ X482 @ id)) & ((X466 @ id @ (ap @ (sub @ X482 @ id) @ X481) @ id) != $true)) | ? [X467 : term] : (($true != (X466 @ id @ X467 @ id)) & ((var @ (sub @ X467 @ id)) = $true)) | ? [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = (X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477)) & ($true != (X466 @ X479 @ X480 @ (comp @ X478 @ X477)))))) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) <=> (substmonoid = $true)) & (axclos = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3b = $true) <=> ! [X415 : term] : ? [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) = (X416 @ sh @ one))) & (ulamvar1 != $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & ((pushprop_lem0_lthm = $true) <=> ! [X14 : term > $o,X15 : term,X16 : subst] : ? [X17 : term > $o] : ! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18))) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462))) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X199 : d_term,X200 : d_term] : ((X199 = X200) | ((d2term @ X200) != (d2term @ X199))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X271 : term,X272 : term > $o,X273 : subst > term > subst > $o,X274 : term] : (? [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (((X273 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) = $true) & ((X273 @ X285 @ X283 @ (comp @ X282 @ X284)) != $true)) | ? [X280 : term,X281 : term] : (((X273 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id) != $true) & ((X273 @ id @ X281 @ id) = $true) & ((X273 @ id @ X280 @ id) = $true)) | ($true != (X272 @ X274)) | ((X272 @ X271) != $true) | ((X272 @ (ap @ X274 @ X271)) = $true) | ? [X275 : term] : ((X272 @ X275) != (X273 @ id @ X275 @ id)) | ? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (((X273 @ (comp @ X276 @ X278) @ (sub @ X279 @ X278) @ X277) != $true) & ((X273 @ X276 @ X279 @ (comp @ X278 @ X277)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3v2a = $true) <=> ! [X512 : subst > term > subst > $o,X513 : term > $o,X514 : term] : (? [X515 : term] : ((X513 @ X515) != (X512 @ id @ X515 @ id)) | ? [X516 : subst > term > term] : (((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id) != $true) & ! [X517 : subst,X518 : subst,X519 : term] : ((sub @ (X516 @ X518 @ X519) @ X517) = (X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) & ! [X520 : term] : (((X512 @ id @ X520 @ id) != $true) | ((X512 @ id @ (X516 @ id @ X520) @ id) = $true))) | ($true = (X513 @ (lam @ X514))) | ? [X521 : term] : (((X513 @ (sub @ X514 @ (push @ X521 @ id))) != $true) & ((X513 @ X521) = $true)))) & ((? [X145 : subst] : ((comp @ id @ X145) != X145) | ? [X146 : subst] : ((comp @ X146 @ id) != X146) | (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147))) <=> (substmonoid_lthm = $true)) & (! [X442 : term,X443 : subst > term > subst > $o] : (((X443 @ id @ (lam @ (sub @ X442 @ (push @ one @ sh))) @ id) = $true) | ? [X444 : term] : (((X443 @ id @ (sub @ X442 @ (push @ X444 @ id)) @ id) != $true) & ((X443 @ id @ X444 @ id) = $true)) | ? [X445 : subst > term > term] : (! [X446 : subst,X447 : term,X448 : subst] : ((sub @ (X445 @ X446 @ X447) @ X448) = (X445 @ (comp @ X446 @ X448) @ (sub @ X447 @ X448))) & ! [X449 : term] : (((X443 @ id @ X449 @ id) != $true) | ((X443 @ id @ (X445 @ id @ X449) @ id) = $true)) & ((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2_gthm = $true) & ((! [X253 : subst > term > subst > $o,X254 : term] : (? [X259 : term,X260 : term] : (($true != (X253 @ id @ (ap @ (sub @ X259 @ id) @ X260) @ id)) & ((X253 @ id @ X260 @ id) = $true) & ((X253 @ id @ X259 @ id) = $true)) | ? [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (((X253 @ X267 @ X268 @ (comp @ X269 @ X266)) != $true) & ((X253 @ (comp @ X267 @ X269) @ (sub @ X268 @ X269) @ X266) = $true)) | ((X253 @ id @ X254 @ id) = $true) | ? [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (((X253 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257) @ X255) != $true) & ($true = (X253 @ X258 @ X256 @ (comp @ X257 @ X255)))) | ? [X270 : term] : (($true = (var @ (sub @ X270 @ id))) & ((X253 @ id @ X270 @ id) != $true)) | ? [X261 : subst > term > term] : (((X253 @ id @ (lam @ (X261 @ sh @ one)) @ id) != $true) & ! [X262 : term] : (($true != (X253 @ id @ X262 @ id)) | ($true = (X253 @ id @ (X261 @ id @ X262) @ id))) & ! [X263 : term,X264 : subst,X265 : subst] : ((X261 @ (comp @ X265 @ X264) @ (sub @ X263 @ X264)) = (sub @ (X261 @ X265 @ X263) @ X264)))) | ? [X224 : subst > term > subst > $o,X225 : term,X226 : term] : (! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : (((X224 @ X235 @ X234 @ (comp @ X233 @ X236)) != $true) | ((X224 @ (comp @ X235 @ X233) @ (sub @ X234 @ X233) @ X236) = $true)) & ! [X229 : term,X230 : subst,X231 : subst,X232 : subst] : (((X224 @ X230 @ X229 @ (comp @ X231 @ X232)) = $true) | ((X224 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231) @ X232) != $true)) & ((X224 @ id @ X226 @ id) = $true) & ((X224 @ id @ X225 @ id) = $true) & ! [X227 : term,X228 : term] : (((X224 @ id @ X228 @ id) != $true) | ((X224 @ id @ (ap @ (sub @ X227 @ id) @ X228) @ id) = $true) | ((X224 @ id @ X227 @ id) != $true)) & ($true != (X224 @ id @ (ap @ X225 @ X226) @ id))) | ? [X237 : term,X238 : subst > term > subst > $o] : (((X238 @ id @ (lam @ X237) @ id) != $true) & ! [X247 : subst > term > term] : (((X238 @ id @ (lam @ (X247 @ sh @ one)) @ id) = $true) | ? [X248 : term] : (((X238 @ id @ (X247 @ id @ X248) @ id) != $true) & ($true = (X238 @ id @ X248 @ id))) | ? [X249 : subst,X250 : subst,X251 : term] : ((X247 @ (comp @ X249 @ X250) @ (sub @ X251 @ X250)) != (sub @ (X247 @ X249 @ X251) @ X250))) & ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) = $true) | ((X238 @ X244 @ X245 @ (comp @ X243 @ X246)) != $true)) & ! [X252 : term] : (((X238 @ id @ (sub @ X237 @ (push @ X252 @ id)) @ id) = $true) | ((X238 @ id @ X252 @ id) != $true)) & ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (((X238 @ (comp @ X241 @ X242) @ (sub @ X240 @ X242) @ X239) != $true) | ((X238 @ X241 @ X240 @ (comp @ X242 @ X239)) = $true))) | ? [X217 : term > $o,X218 : term] : (! [X222 : term,X223 : term] : (((X217 @ (ap @ X222 @ X223)) = $true) | ((X217 @ X222) != $true) | ((X217 @ X223) != $true)) & ! [X219 : term] : (((X217 @ X219) = $true) | ((var @ X219) != $true)) & ! [X220 : term] : (((X217 @ (lam @ X220)) = $true) | ? [X221 : term] : (((X217 @ (sub @ X220 @ (push @ X221 @ id))) != $true) & ((X217 @ X221) = $true))) & ((X217 @ X218) != $true))) <=> (hoasinduction_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X390 : subst,X391 : subst > term > term,X392 : term,X393 : subst > term > term] : (? [X394 : subst,X395 : term,X396 : subst] : ((X393 @ (comp @ X396 @ X394) @ (sub @ X395 @ X394)) != (sub @ (X393 @ X396 @ X395) @ X394)) | ((lam @ (X391 @ sh @ one)) != (lam @ (X393 @ sh @ one))) | ((X391 @ X390 @ X392) = (X393 @ X390 @ X392)) | ? [X397 : subst,X398 : term,X399 : subst] : ((X391 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399)) != (sub @ (X391 @ X397 @ X398) @ X399))) | ? [X386 : subst,X387 : term] : ((comp @ sh @ (push @ X387 @ X386)) != X386) | ? [X384 : term,X385 : subst] : ((sub @ one @ (push @ X384 @ X385)) != X384) | ? [X388 : term,X389 : term] : (((lam @ X389) = (lam @ X388)) & (X388 != X389)))) & (hoaslamnotvar = $true) & ((shinj = $true) <=> ! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198))) & (! [X383 : term] : ((sub @ X383 @ id) = X383) <=> (termmset = $true)) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ? [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) != (sub @ (X522 @ X530 @ X529) @ X531)) | ? [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) != (sub @ (X524 @ X526 @ X527) @ X528))) <=> (hoaslaminj = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((d2subst @ d_id) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & ((induction2 = $true) <=> ! [X400 : term > $o,X401 : term] : (? [X404 : term] : (((var @ X404) = $true) & ((X400 @ X404) != $true)) | ? [X405 : term] : (((X400 @ (lam @ X405)) != $true) & ! [X406 : term] : (((X400 @ (sub @ X405 @ (push @ X406 @ id))) = $true) | ((X400 @ X406) != $true))) | ? [X402 : term,X403 : term] : (((X400 @ X403) = $true) & ($true != (X400 @ (ap @ X403 @ X402))) & ((X400 @ X402) = $true)) | ((X400 @ X401) = $true))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) <=> (axscons = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (? [X287 : term,X288 : subst > term > subst > $o] : (! [X294 : term] : (((X288 @ id @ X294 @ id) != $true) | ($true = (X288 @ id @ (sub @ X287 @ (push @ X294 @ id)) @ id))) & ! [X289 : subst > term > term] : (? [X290 : term] : (($true = (X288 @ id @ X290 @ id)) & ((X288 @ id @ (X289 @ id @ X290) @ id) != $true)) | ($true = (X288 @ id @ (lam @ (X289 @ sh @ one)) @ id)) | ? [X291 : term,X292 : subst,X293 : subst] : ((sub @ (X289 @ X292 @ X291) @ X293) != (X289 @ (comp @ X292 @ X293) @ (sub @ X291 @ X293)))) & ((X288 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id) != $true)) | ? [X286 : term] : ((sub @ X286 @ id) != X286) | ! [X295 : subst > term > subst > $o,X296 : term] : (? [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (((X295 @ X307 @ X310 @ (comp @ X308 @ X309)) = $true) & ((X295 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309) != $true)) | ? [X301 : subst > term > term] : (! [X302 : subst,X303 : subst,X304 : term] : ((X301 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302)) = (sub @ (X301 @ X303 @ X304) @ X302)) & ($true != (X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)) & ! [X305 : term] : (((X295 @ id @ (X301 @ id @ X305) @ id) = $true) | ((X295 @ id @ X305 @ id) != $true))) | ? [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (($true = (X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299)) & ((X295 @ X297 @ X300 @ (comp @ X298 @ X299)) != $true)) | ? [X306 : term] : (((X295 @ id @ X306 @ id) = $true) & ((X295 @ id @ (sub @ X296 @ (push @ X306 @ id)) @ id) != $true)) | ((X295 @ id @ (lam @ X296) @ id) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X314 : subst > term > term,X315 : term,X316 : term] : (? [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) != (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one))))) & (hoasinduction_lem1v2 = $true) & (pushprop_gthm = $true) & (! [X64 : term,X65 : subst > term > subst > $o] : (? [X67 : subst > term > term,X68 : term] : (! [X72 : subst,X73 : term,X74 : subst] : ((X67 @ (comp @ X72 @ X74) @ (sub @ X73 @ X74)) = (sub @ X68 @ (push @ (sub @ X73 @ X74) @ (comp @ X72 @ X74)))) & ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) != $true) & ! [X69 : subst,X70 : subst,X71 : term] : ((sub @ (sub @ X68 @ (push @ X71 @ X69)) @ X70) = (sub @ (X67 @ X69 @ X71) @ X70)) & ! [X75 : term] : (((X65 @ id @ X75 @ id) != $true) | ((X65 @ id @ (X67 @ id @ X75) @ id) = $true))) | ((X65 @ id @ (lam @ (sub @ X64 @ (push @ one @ sh))) @ id) = $true) | ? [X66 : term] : (((X65 @ id @ (sub @ X64 @ (push @ X66 @ id)) @ id) != $true) & ((X65 @ id @ X66 @ id) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X532 : term,X533 : subst,X534 : term > $o] : (((X534 @ (sub @ X532 @ X533)) = $true) | ? [X537 : term] : (((X534 @ (sub @ X537 @ X533)) != $true) & ((var @ X537) = $true)) | ? [X535 : term] : (! [X536 : term] : (((X534 @ X536) != $true) | ((X534 @ (sub @ X535 @ (push @ X536 @ id))) = $true)) & ((X534 @ (lam @ X535)) != $true)) | ? [X538 : term,X539 : term] : (((X534 @ X538) = $true) & ((X534 @ X539) = $true) & ((X534 @ (ap @ X538 @ X539)) != $true))) <=> (induction2lem = $true)) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) <=> (hoasapinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ (lam @ (sub @ X322 @ (push @ one @ sh))) @ id) != $true) & ! [X323 : term] : (((X321 @ id @ (sub @ X322 @ (push @ X323 @ id)) @ id) = $true) | ($true != (X321 @ id @ X323 @ id))) & ! [X324 : subst > term > term] : (? [X328 : term] : (($true != (X321 @ id @ (X324 @ id @ X328) @ id)) & ((X321 @ id @ X328 @ id) = $true)) | ((X321 @ id @ (lam @ (X324 @ sh @ one)) @ id) = $true) | ? [X325 : subst,X326 : subst,X327 : term] : ((X324 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)) != (sub @ (X324 @ X325 @ X327) @ X326)))) | ! [X329 : subst > term > subst > $o,X330 : term] : (? [X331 : term] : (($true != (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ((X329 @ id @ (lam @ X330) @ id) = $true) | ? [X332 : subst > term > term] : (! [X336 : term] : (($true != (X329 @ id @ X336 @ id)) | ((X329 @ id @ (X332 @ id @ X336) @ id) = $true)) & ((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) != $true) & ! [X333 : subst,X334 : term,X335 : subst] : ((X332 @ (comp @ X333 @ X335) @ (sub @ X334 @ X335)) = (sub @ (X332 @ X333 @ X334) @ X335)))) | ? [X320 : term] : ((sub @ X320 @ id) != X320))) & (! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (? [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) != (X0 @ X4)) | ((X0 @ one) = $true) | ((X1 @ X3) != $true)) <=> (pushprop_lem1v2 = $true)) & ((axidr = $true) <=> ! [X172 : subst] : ((comp @ X172 @ id) = X172)) & (pushprop_lthm_orig = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) <=> (? [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) != X19) | ? [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) != X21) | ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true)))) & (! [X201 : subst > term > subst > $o] : ? [X202 : term > $o] : ! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id)) <=> (hoasinduction_lem0 = $true)) & ((! [X136 : subst > term > subst > $o,X137 : term] : (? [X143 : term,X144 : term] : (((X136 @ id @ (ap @ (sub @ X144 @ id) @ X143) @ id) != $true) & ((X136 @ id @ X143 @ id) = $true) & ((X136 @ id @ X144 @ id) = $true)) | ? [X138 : subst > term > term] : (! [X139 : term] : (((X136 @ id @ (X138 @ id @ X139) @ id) = $true) | ((X136 @ id @ X139 @ id) != $true)) & ((X136 @ id @ (lam @ (X138 @ sh @ one)) @ id) != $true) & ! [X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)) = (sub @ (X138 @ X142 @ X140) @ X141))) | ((X136 @ id @ X137 @ id) = $true)) | ? [X115 : subst > term > subst > $o] : ! [X116 : term > $o] : ? [X117 : term] : ((X116 @ X117) != (X115 @ id @ X117 @ id)) | ? [X126 : subst > term > subst > $o,X127 : term,X128 : term > $o] : (! [X130 : term] : ((X126 @ id @ X130 @ id) = (X128 @ X130)) & ! [X131 : subst > term > term] : (((X126 @ id @ (lam @ (X131 @ sh @ one)) @ id) = $true) | ? [X132 : term] : (($true = (X126 @ id @ X132 @ id)) & ((X126 @ id @ (X131 @ id @ X132) @ id) != $true)) | ? [X133 : subst,X134 : term,X135 : subst] : ((X131 @ (comp @ X133 @ X135) @ (sub @ X134 @ X135)) != (sub @ (X131 @ X133 @ X134) @ X135))) & ((X128 @ (lam @ X127)) != $true) & ! [X129 : term] : (((X128 @ (sub @ X127 @ (push @ X129 @ id))) = $true) | ((X128 @ X129) != $true))) | ? [X125 : term] : ((sub @ X125 @ id) != X125) | ? [X118 : term,X119 : term > $o] : (! [X122 : term] : (((var @ X122) != $true) | ((X119 @ X122) = $true)) & ! [X123 : term] : (? [X124 : term] : (((X119 @ X124) = $true) & ((X119 @ (sub @ X123 @ (push @ X124 @ id))) != $true)) | ((X119 @ (lam @ X123)) = $true)) & ($true != (X119 @ X118)) & ! [X120 : term,X121 : term] : (((X119 @ (ap @ X120 @ X121)) = $true) | ((X119 @ X121) != $true) | ((X119 @ X120) != $true)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axshiftcons = $true) <=> ! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & ! [X54 : d_subst,X55 : d_subst] : ((X54 = X55) | ((d2subst @ X55) != (d2subst @ X54))) & (! [X429 : term,X430 : term,X431 : subst > term > subst > $o] : (? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X431 @ X436 @ X434 @ (comp @ X435 @ X437)) = $true) & ((X431 @ (comp @ X436 @ X435) @ (sub @ X434 @ X435) @ X437) != $true)) | ? [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (((X431 @ X438 @ X439 @ (comp @ X441 @ X440)) != $true) & ((X431 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440) = $true)) | ((X431 @ id @ X429 @ id) != $true) | ? [X432 : term,X433 : term] : (((X431 @ id @ X433 @ id) = $true) & ((X431 @ id @ X432 @ id) = $true) & ((X431 @ id @ (ap @ (sub @ X432 @ id) @ X433) @ id) != $true)) | ((X431 @ id @ (ap @ X430 @ X429) @ id) = $true) | ($true != (X431 @ id @ X430 @ id))) <=> (hoasinduction_lem2 = $true)) & ((axidl = $true) <=> ! [X409 : subst] : ((comp @ id @ X409) = X409)) & (! [X374 : term] : ((sub @ X374 @ id) = X374) <=> (axvarid = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X161 : term] : ((sub @ X161 @ id) != X161) | ? [X157 : term] : ! [X158 : subst > term > term] : ? [X159 : term,X160 : subst] : ((X158 @ X160 @ X159) != (sub @ X157 @ (push @ X159 @ X160))) | ! [X162 : subst > term > subst > $o,X163 : term > $o,X164 : term] : (((X163 @ (lam @ X164)) = $true) | ? [X171 : term] : ((X163 @ X171) != (X162 @ id @ X171 @ id)) | ? [X165 : term] : (((X163 @ (sub @ X164 @ (push @ X165 @ id))) != $true) & ((X163 @ X165) = $true)) | ? [X166 : subst > term > term] : (((X162 @ id @ (lam @ (X166 @ sh @ one)) @ id) != $true) & ! [X167 : term] : (((X162 @ id @ X167 @ id) != $true) | ((X162 @ id @ (X166 @ id @ X167) @ id) = $true)) & ! [X168 : subst,X169 : subst,X170 : term] : ((sub @ (X166 @ X168 @ X170) @ X169) = (X166 @ (comp @ X168 @ X169) @ (sub @ X170 @ X169))))))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axvarshift = $true) & ((? [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) != X211) | ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (? [X216 : term] : ((X214 @ X216) != (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) | ($true = (X214 @ one)) | ((X215 @ X212) != $true))) <=> (pushprop_lem1v2_lthm = $true)) & (lamnotvar = $true) & ((d2subst @ d_id) = id) & (substmonoid_gthm = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) <=> (apinj2 = $true)) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X348 : term > $o,X349 : term,X350 : subst] : (((X348 @ (sub @ X349 @ X350)) = $true) | ? [X351 : term,X352 : term] : (((X348 @ X351) = $true) & ((X348 @ (ap @ X352 @ X351)) != $true) & ((X348 @ X352) = $true)) | ? [X353 : term] : (! [X354 : term] : (($true = (X348 @ (sub @ X353 @ (push @ X354 @ id)))) | ((X348 @ X354) != $true)) & ((X348 @ (lam @ X353)) != $true)) | ? [X355 : term] : (($true != (X348 @ (sub @ X355 @ X350))) & ((var @ X355) = $true))) | ? [X341 : subst] : ((comp @ X341 @ id) != X341) | ? [X342 : term > $o,X343 : term] : (((X342 @ X343) != $true) & ! [X346 : term] : (((X342 @ X346) != $true) | ((X342 @ (lam @ X346)) = $true)) & ! [X344 : term,X345 : term] : (((X342 @ (ap @ X345 @ X344)) = $true) | ((X342 @ X344) != $true) | ((X342 @ X345) != $true)) & ! [X347 : term] : (($true != (var @ X347)) | ((X342 @ X347) = $true))) | ? [X339 : term,X340 : subst] : ((comp @ sh @ (push @ X339 @ X340)) != X340) | ? [X337 : subst,X338 : term] : ((sub @ one @ (push @ X338 @ X337)) != X338))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lthm = $true)),
% 32.60/5.94 inference(flattening,[status(thm)],[f12])).
% 32.60/5.94 thf(f12,plain,(
% 32.60/5.94 (((! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true)) | ? [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) != X21)) | ? [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) != X19)) <=> (pushprop_lem1_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X314 : subst > term > term,X315 : term,X316 : term] : (? [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) != (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one))))) & ((hoasapinj2_lthm = $true) <=> (? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ X56 @ X58) = (ap @ X59 @ X57)) & (X57 != X58)) | ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61)))) & (hoasinduction_lem3b_gthm = $true) & (((! [X162 : subst > term > subst > $o,X163 : term > $o,X164 : term] : (((X163 @ (lam @ X164)) = $true) | ? [X171 : term] : ((X163 @ X171) != (X162 @ id @ X171 @ id)) | ? [X165 : term] : (((X163 @ (sub @ X164 @ (push @ X165 @ id))) != $true) & ((X163 @ X165) = $true)) | ? [X166 : subst > term > term] : (((X162 @ id @ (lam @ (X166 @ sh @ one)) @ id) != $true) & ! [X167 : term] : (((X162 @ id @ X167 @ id) != $true) | ((X162 @ id @ (X166 @ id @ X167) @ id) = $true)) & ! [X168 : subst,X169 : subst,X170 : term] : ((sub @ (X166 @ X168 @ X170) @ X169) = (X166 @ (comp @ X168 @ X169) @ (sub @ X170 @ X169))))) | ? [X161 : term] : ((sub @ X161 @ id) != X161)) | ? [X157 : term] : ! [X158 : subst > term > term] : ? [X159 : term,X160 : subst] : ((X158 @ X160 @ X159) != (sub @ X157 @ (push @ X159 @ X160)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((? [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) != X211) | ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (? [X216 : term] : ((X214 @ X216) != (X215 @ (sub @ X216 @ (push @ X212 @ X213)))) | ($true = (X214 @ one)) | ((X215 @ X212) != $true))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lthm = $true) <=> (((! [X253 : subst > term > subst > $o,X254 : term] : (? [X259 : term,X260 : term] : (($true != (X253 @ id @ (ap @ (sub @ X259 @ id) @ X260) @ id)) & ((X253 @ id @ X260 @ id) = $true) & ((X253 @ id @ X259 @ id) = $true)) | ? [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (((X253 @ X267 @ X268 @ (comp @ X269 @ X266)) != $true) & ((X253 @ (comp @ X267 @ X269) @ (sub @ X268 @ X269) @ X266) = $true)) | ((X253 @ id @ X254 @ id) = $true) | ? [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (((X253 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257) @ X255) != $true) & ($true = (X253 @ X258 @ X256 @ (comp @ X257 @ X255)))) | ? [X270 : term] : (($true = (var @ (sub @ X270 @ id))) & ((X253 @ id @ X270 @ id) != $true)) | ? [X261 : subst > term > term] : (((X253 @ id @ (lam @ (X261 @ sh @ one)) @ id) != $true) & ! [X262 : term] : (($true != (X253 @ id @ X262 @ id)) | ($true = (X253 @ id @ (X261 @ id @ X262) @ id))) & ! [X263 : term,X264 : subst,X265 : subst] : ((X261 @ (comp @ X265 @ X264) @ (sub @ X263 @ X264)) = (sub @ (X261 @ X265 @ X263) @ X264)))) | ? [X237 : term,X238 : subst > term > subst > $o] : (((X238 @ id @ (lam @ X237) @ id) != $true) & ! [X247 : subst > term > term] : (((X238 @ id @ (lam @ (X247 @ sh @ one)) @ id) = $true) | ? [X248 : term] : (((X238 @ id @ (X247 @ id @ X248) @ id) != $true) & ($true = (X238 @ id @ X248 @ id))) | ? [X249 : subst,X250 : subst,X251 : term] : ((X247 @ (comp @ X249 @ X250) @ (sub @ X251 @ X250)) != (sub @ (X247 @ X249 @ X251) @ X250))) & ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) = $true) | ((X238 @ X244 @ X245 @ (comp @ X243 @ X246)) != $true)) & ! [X252 : term] : (((X238 @ id @ (sub @ X237 @ (push @ X252 @ id)) @ id) = $true) | ((X238 @ id @ X252 @ id) != $true)) & ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (((X238 @ (comp @ X241 @ X242) @ (sub @ X240 @ X242) @ X239) != $true) | ((X238 @ X241 @ X240 @ (comp @ X242 @ X239)) = $true)))) | ? [X224 : subst > term > subst > $o,X225 : term,X226 : term] : (! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : (((X224 @ X235 @ X234 @ (comp @ X233 @ X236)) != $true) | ((X224 @ (comp @ X235 @ X233) @ (sub @ X234 @ X233) @ X236) = $true)) & ! [X229 : term,X230 : subst,X231 : subst,X232 : subst] : (((X224 @ X230 @ X229 @ (comp @ X231 @ X232)) = $true) | ((X224 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231) @ X232) != $true)) & ((X224 @ id @ X226 @ id) = $true) & ((X224 @ id @ X225 @ id) = $true) & ! [X227 : term,X228 : term] : (((X224 @ id @ X228 @ id) != $true) | ((X224 @ id @ (ap @ (sub @ X227 @ id) @ X228) @ id) = $true) | ((X224 @ id @ X227 @ id) != $true)) & ($true != (X224 @ id @ (ap @ X225 @ X226) @ id)))) | ? [X217 : term > $o,X218 : term] : (! [X222 : term,X223 : term] : (((X217 @ (ap @ X222 @ X223)) = $true) | ((X217 @ X222) != $true) | ((X217 @ X223) != $true)) & ! [X219 : term] : (((X217 @ X219) = $true) | ((var @ X219) != $true)) & ! [X220 : term] : (((X217 @ (lam @ X220)) = $true) | ? [X221 : term] : (((X217 @ (sub @ X220 @ (push @ X221 @ id))) != $true) & ((X217 @ X221) = $true))) & ((X217 @ X218) != $true)))) & (pushprop_gthm = $true) & (((((! [X97 : subst > term > subst > $o,X98 : term] : (? [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (((X97 @ (comp @ X103 @ X104) @ (sub @ X106 @ X104) @ X105) = $true) & ((X97 @ X103 @ X106 @ (comp @ X104 @ X105)) != $true)) | ? [X107 : term,X108 : term] : (((X97 @ id @ X107 @ id) = $true) & ((X97 @ id @ X108 @ id) = $true) & ((X97 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id) != $true)) | ? [X99 : subst,X100 : subst,X101 : term,X102 : subst] : (((X97 @ X99 @ X101 @ (comp @ X102 @ X100)) = $true) & ((X97 @ (comp @ X99 @ X102) @ (sub @ X101 @ X102) @ X100) != $true)) | ? [X110 : subst > term > term] : (! [X111 : subst,X112 : term,X113 : subst] : ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)) = (sub @ (X110 @ X113 @ X112) @ X111)) & ! [X114 : term] : (((X97 @ id @ (X110 @ id @ X114) @ id) = $true) | ((X97 @ id @ X114 @ id) != $true)) & ((X97 @ id @ (lam @ (X110 @ sh @ one)) @ id) != $true)) | ? [X109 : term] : (((var @ (sub @ X109 @ id)) = $true) & ($true != (X97 @ id @ X109 @ id))) | ((X97 @ id @ X98 @ id) = $true)) | ? [X87 : subst > term > subst > $o,X88 : term > $o,X89 : term] : (! [X90 : term] : ((X87 @ id @ X90 @ id) = (X88 @ X90)) & ! [X91 : subst > term > term] : (((X87 @ id @ (lam @ (X91 @ sh @ one)) @ id) = $true) | ? [X92 : term] : (($true != (X87 @ id @ (X91 @ id @ X92) @ id)) & ((X87 @ id @ X92 @ id) = $true)) | ? [X93 : subst,X94 : term,X95 : subst] : ((X91 @ (comp @ X95 @ X93) @ (sub @ X94 @ X93)) != (sub @ (X91 @ X95 @ X94) @ X93))) & ! [X96 : term] : (((X88 @ (sub @ X89 @ (push @ X96 @ id))) = $true) | ((X88 @ X96) != $true)) & ((X88 @ (lam @ X89)) != $true))) | ? [X86 : term] : ((sub @ X86 @ id) != X86)) | ? [X79 : term > $o,X80 : term] : (! [X84 : term] : (((X79 @ (lam @ X84)) = $true) | ? [X85 : term] : (((X79 @ (sub @ X84 @ (push @ X85 @ id))) != $true) & ((X79 @ X85) = $true))) & ! [X81 : term,X82 : term] : (($true != (X79 @ X82)) | ((X79 @ (ap @ X82 @ X81)) = $true) | ((X79 @ X81) != $true)) & ! [X83 : term] : (((var @ X83) != $true) | ((X79 @ X83) = $true)) & ((X79 @ X80) != $true))) | ? [X76 : subst > term > subst > $o] : ! [X77 : term > $o] : ? [X78 : term] : ((X76 @ id @ X78 @ id) != (X77 @ X78))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2_lthm = $true) & (one = (d2term @ d_one)) & (! [X201 : subst > term > subst > $o] : ? [X202 : term > $o] : ! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id)) <=> (hoasinduction_lem0 = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X38 : subst > term > subst > $o,X39 : term] : (((X38 @ id @ (lam @ X39) @ id) = $true) | ? [X44 : subst,X45 : subst,X46 : subst,X47 : term] : (((X38 @ (comp @ X44 @ X46) @ (sub @ X47 @ X46) @ X45) = $true) & ((X38 @ X44 @ X47 @ (comp @ X46 @ X45)) != $true)) | ? [X49 : subst > term > term] : (! [X53 : term] : (((X38 @ id @ X53 @ id) != $true) | ((X38 @ id @ (X49 @ id @ X53) @ id) = $true)) & ! [X50 : subst,X51 : subst,X52 : term] : ((X49 @ (comp @ X50 @ X51) @ (sub @ X52 @ X51)) = (sub @ (X49 @ X50 @ X52) @ X51)) & ((X38 @ id @ (lam @ (X49 @ sh @ one)) @ id) != $true)) | ? [X40 : term,X41 : subst,X42 : subst,X43 : subst] : (($true != (X38 @ (comp @ X42 @ X43) @ (sub @ X40 @ X43) @ X41)) & ((X38 @ X42 @ X40 @ (comp @ X43 @ X41)) = $true)) | ? [X48 : term] : (((X38 @ id @ (sub @ X39 @ (push @ X48 @ id)) @ id) != $true) & ($true = (X38 @ id @ X48 @ id))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X512 : subst > term > subst > $o,X513 : term > $o,X514 : term] : (? [X515 : term] : ((X513 @ X515) != (X512 @ id @ X515 @ id)) | ? [X516 : subst > term > term] : (((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id) != $true) & ! [X517 : subst,X518 : subst,X519 : term] : ((sub @ (X516 @ X518 @ X519) @ X517) = (X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) & ! [X520 : term] : (((X512 @ id @ X520 @ id) != $true) | ((X512 @ id @ (X516 @ id @ X520) @ id) = $true))) | ($true = (X513 @ (lam @ X514))) | ? [X521 : term] : (((X513 @ (sub @ X514 @ (push @ X521 @ id))) != $true) & ((X513 @ X521) = $true)))) & (hoasinduction_lem3a_gthm = $true) & ! [X54 : d_subst,X55 : d_subst] : ((X54 = X55) | ((d2subst @ X55) != (d2subst @ X54))) & ! [X209 : d_subst] : (d_id = X209) & (((((! [X136 : subst > term > subst > $o,X137 : term] : (? [X143 : term,X144 : term] : (((X136 @ id @ (ap @ (sub @ X144 @ id) @ X143) @ id) != $true) & ((X136 @ id @ X143 @ id) = $true) & ((X136 @ id @ X144 @ id) = $true)) | ? [X138 : subst > term > term] : (! [X139 : term] : (((X136 @ id @ (X138 @ id @ X139) @ id) = $true) | ((X136 @ id @ X139 @ id) != $true)) & ((X136 @ id @ (lam @ (X138 @ sh @ one)) @ id) != $true) & ! [X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)) = (sub @ (X138 @ X142 @ X140) @ X141))) | ((X136 @ id @ X137 @ id) = $true)) | ? [X126 : subst > term > subst > $o,X127 : term,X128 : term > $o] : (! [X130 : term] : ((X126 @ id @ X130 @ id) = (X128 @ X130)) & ! [X131 : subst > term > term] : (((X126 @ id @ (lam @ (X131 @ sh @ one)) @ id) = $true) | ? [X132 : term] : (($true = (X126 @ id @ X132 @ id)) & ((X126 @ id @ (X131 @ id @ X132) @ id) != $true)) | ? [X133 : subst,X134 : term,X135 : subst] : ((X131 @ (comp @ X133 @ X135) @ (sub @ X134 @ X135)) != (sub @ (X131 @ X133 @ X134) @ X135))) & ((X128 @ (lam @ X127)) != $true) & ! [X129 : term] : (((X128 @ (sub @ X127 @ (push @ X129 @ id))) = $true) | ((X128 @ X129) != $true)))) | ? [X125 : term] : ((sub @ X125 @ id) != X125)) | ? [X118 : term,X119 : term > $o] : (! [X122 : term] : (((var @ X122) != $true) | ((X119 @ X122) = $true)) & ! [X123 : term] : (? [X124 : term] : (((X119 @ X124) = $true) & ((X119 @ (sub @ X123 @ (push @ X124 @ id))) != $true)) | ((X119 @ (lam @ X123)) = $true)) & ($true != (X119 @ X118)) & ! [X120 : term,X121 : term] : (((X119 @ (ap @ X120 @ X121)) = $true) | ((X119 @ X121) != $true) | ((X119 @ X120) != $true)))) | ? [X115 : subst > term > subst > $o] : ! [X116 : term > $o] : ? [X117 : term] : ((X116 @ X117) != (X115 @ id @ X117 @ id))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axidr = $true) <=> ! [X172 : subst] : ((comp @ X172 @ id) = X172)) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) <=> (apinj2 = $true)) & (! [X532 : term,X533 : subst,X534 : term > $o] : (((X534 @ (sub @ X532 @ X533)) = $true) | ? [X537 : term] : (((X534 @ (sub @ X537 @ X533)) != $true) & ((var @ X537) = $true)) | ? [X535 : term] : (! [X536 : term] : (((X534 @ X536) != $true) | ((X534 @ (sub @ X535 @ (push @ X536 @ id))) = $true)) & ((X534 @ (lam @ X535)) != $true)) | ? [X538 : term,X539 : term] : (((X534 @ X538) = $true) & ((X534 @ X539) = $true) & ((X534 @ (ap @ X538 @ X539)) != $true))) <=> (induction2lem = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X311 : subst > term > subst > $o] : ? [X312 : term > $o] : ! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313))) & ((induction2 = $true) <=> ! [X400 : term > $o,X401 : term] : (? [X404 : term] : (((var @ X404) = $true) & ((X400 @ X404) != $true)) | ? [X405 : term] : (((X400 @ (lam @ X405)) != $true) & ! [X406 : term] : (((X400 @ (sub @ X405 @ (push @ X406 @ id))) = $true) | ((X400 @ X406) != $true))) | ? [X402 : term,X403 : term] : (((X400 @ X403) = $true) & ($true != (X400 @ (ap @ X403 @ X402))) & ((X400 @ X402) = $true)) | ((X400 @ X401) = $true))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapinj2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (? [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) != $true) & ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) = $true)) | ((X357 @ (lam @ X358)) = $true) | ? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373)) & ! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ((X356 @ id @ X370 @ id) != $true)) & ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) != $true)) | ? [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) = $true) & ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) != $true)) | ? [X359 : term] : ((X357 @ X359) != (X356 @ id @ X359 @ id)) | ? [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) != $true) & ($true = (X357 @ X364)))) <=> (hoasinduction_lem3v2 = $true)) & (! [X442 : term,X443 : subst > term > subst > $o] : (((X443 @ id @ (lam @ (sub @ X442 @ (push @ one @ sh))) @ id) = $true) | ? [X444 : term] : (((X443 @ id @ (sub @ X442 @ (push @ X444 @ id)) @ id) != $true) & ((X443 @ id @ X444 @ id) = $true)) | ? [X445 : subst > term > term] : (! [X446 : subst,X447 : term,X448 : subst] : ((sub @ (X445 @ X446 @ X447) @ X448) = (X445 @ (comp @ X446 @ X448) @ (sub @ X447 @ X448))) & ! [X449 : term] : (((X443 @ id @ X449 @ id) != $true) | ((X443 @ id @ (X445 @ id @ X449) @ id) = $true)) & ((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X295 : subst > term > subst > $o,X296 : term] : (? [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (((X295 @ X307 @ X310 @ (comp @ X308 @ X309)) = $true) & ((X295 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309) != $true)) | ? [X301 : subst > term > term] : (! [X302 : subst,X303 : subst,X304 : term] : ((X301 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302)) = (sub @ (X301 @ X303 @ X304) @ X302)) & ($true != (X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)) & ! [X305 : term] : (((X295 @ id @ (X301 @ id @ X305) @ id) = $true) | ((X295 @ id @ X305 @ id) != $true))) | ? [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (($true = (X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299)) & ((X295 @ X297 @ X300 @ (comp @ X298 @ X299)) != $true)) | ? [X306 : term] : (((X295 @ id @ X306 @ id) = $true) & ((X295 @ id @ (sub @ X296 @ (push @ X306 @ id)) @ id) != $true)) | ((X295 @ id @ (lam @ X296) @ id) = $true)) | ? [X287 : term,X288 : subst > term > subst > $o] : (! [X294 : term] : (((X288 @ id @ X294 @ id) != $true) | ($true = (X288 @ id @ (sub @ X287 @ (push @ X294 @ id)) @ id))) & ! [X289 : subst > term > term] : (? [X290 : term] : (($true = (X288 @ id @ X290 @ id)) & ((X288 @ id @ (X289 @ id @ X290) @ id) != $true)) | ($true = (X288 @ id @ (lam @ (X289 @ sh @ one)) @ id)) | ? [X291 : term,X292 : subst,X293 : subst] : ((sub @ (X289 @ X292 @ X291) @ X293) != (X289 @ (comp @ X292 @ X293) @ (sub @ X291 @ X293)))) & ((X288 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id) != $true))) | ? [X286 : term] : ((sub @ X286 @ id) != X286))) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) <=> (apinj1 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvar1 != $true) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lem1_lthm = $true) & (ulamvarsh = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X329 : subst > term > subst > $o,X330 : term] : (? [X331 : term] : (($true != (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ((X329 @ id @ (lam @ X330) @ id) = $true) | ? [X332 : subst > term > term] : (! [X336 : term] : (($true != (X329 @ id @ X336 @ id)) | ((X329 @ id @ (X332 @ id @ X336) @ id) = $true)) & ((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) != $true) & ! [X333 : subst,X334 : term,X335 : subst] : ((X332 @ (comp @ X333 @ X335) @ (sub @ X334 @ X335)) = (sub @ (X332 @ X333 @ X334) @ X335)))) | ? [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ (lam @ (sub @ X322 @ (push @ one @ sh))) @ id) != $true) & ! [X323 : term] : (((X321 @ id @ (sub @ X322 @ (push @ X323 @ id)) @ id) = $true) | ($true != (X321 @ id @ X323 @ id))) & ! [X324 : subst > term > term] : (? [X328 : term] : (($true != (X321 @ id @ (X324 @ id @ X328) @ id)) & ((X321 @ id @ X328 @ id) = $true)) | ((X321 @ id @ (lam @ (X324 @ sh @ one)) @ id) = $true) | ? [X325 : subst,X326 : subst,X327 : term] : ((X324 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)) != (sub @ (X324 @ X325 @ X327) @ X326))))) | ? [X320 : term] : ((sub @ X320 @ id) != X320))) & (hoasapinj1_gthm = $true) & (((((! [X348 : term > $o,X349 : term,X350 : subst] : (((X348 @ (sub @ X349 @ X350)) = $true) | ? [X351 : term,X352 : term] : (((X348 @ X351) = $true) & ((X348 @ (ap @ X352 @ X351)) != $true) & ((X348 @ X352) = $true)) | ? [X353 : term] : (! [X354 : term] : (($true = (X348 @ (sub @ X353 @ (push @ X354 @ id)))) | ((X348 @ X354) != $true)) & ((X348 @ (lam @ X353)) != $true)) | ? [X355 : term] : (($true != (X348 @ (sub @ X355 @ X350))) & ((var @ X355) = $true))) | ? [X342 : term > $o,X343 : term] : (((X342 @ X343) != $true) & ! [X346 : term] : (((X342 @ X346) != $true) | ((X342 @ (lam @ X346)) = $true)) & ! [X344 : term,X345 : term] : (((X342 @ (ap @ X345 @ X344)) = $true) | ((X342 @ X344) != $true) | ((X342 @ X345) != $true)) & ! [X347 : term] : (($true != (var @ X347)) | ((X342 @ X347) = $true)))) | ? [X341 : subst] : ((comp @ X341 @ id) != X341)) | ? [X339 : term,X340 : subst] : ((comp @ sh @ (push @ X339 @ X340)) != X340)) | ? [X337 : subst,X338 : term] : ((sub @ one @ (push @ X338 @ X337)) != X338)) <=> (induction2lem_lthm = $true)) & (lamnotvar = $true) & ((((! [X390 : subst,X391 : subst > term > term,X392 : term,X393 : subst > term > term] : (? [X394 : subst,X395 : term,X396 : subst] : ((X393 @ (comp @ X396 @ X394) @ (sub @ X395 @ X394)) != (sub @ (X393 @ X396 @ X395) @ X394)) | ((lam @ (X391 @ sh @ one)) != (lam @ (X393 @ sh @ one))) | ((X391 @ X390 @ X392) = (X393 @ X390 @ X392)) | ? [X397 : subst,X398 : term,X399 : subst] : ((X391 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399)) != (sub @ (X391 @ X397 @ X398) @ X399))) | ? [X388 : term,X389 : term] : (((lam @ X389) = (lam @ X388)) & (X388 != X389))) | ? [X386 : subst,X387 : term] : ((comp @ sh @ (push @ X387 @ X386)) != X386)) | ? [X384 : term,X385 : subst] : ((sub @ one @ (push @ X384 @ X385)) != X384)) <=> (hoaslaminj_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ? [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) = (X29 @ sh @ one))) & (! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ? [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) != (sub @ (X522 @ X530 @ X529) @ X531)) | ? [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) != (sub @ (X524 @ X526 @ X527) @ X528))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X415 : term] : ? [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) = (X416 @ sh @ one))) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & (axvarshift = $true) & (! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) <=> (pushprop_lem1 = $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (axmap = $true) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X483 : term] : ? [X484 : subst > term > term] : ! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486))) & (lamnotap != $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X34 : term] : ? [X35 : subst > term > term] : ! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36)))) & ! [X199 : d_term,X200 : d_term] : ((X199 = X200) | ((d2term @ X200) != (d2term @ X199))) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463)) & (hoasinduction_lem2v2_gthm = $true) & ((termmset_lthm = $true) <=> (! [X418 : term] : ((sub @ X418 @ id) = X418) | ? [X417 : term] : ((sub @ X417 @ id) != X417))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((pushprop_lem0_lthm = $true) <=> ! [X14 : term > $o,X15 : term,X16 : subst] : ? [X17 : term > $o] : ! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18))) & ((pushprop_lem0 = $true) <=> ! [X456 : subst,X457 : term > $o,X458 : term] : ? [X459 : term > $o] : ! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & (! [X421 : subst > term > subst > $o,X422 : term] : (? [X428 : term] : (((X421 @ id @ (sub @ X422 @ (push @ X428 @ id)) @ id) != $true) & ((X421 @ id @ X428 @ id) = $true)) | ? [X423 : subst > term > term] : (! [X424 : term] : (((X421 @ id @ X424 @ id) != $true) | ((X421 @ id @ (X423 @ id @ X424) @ id) = $true)) & ! [X425 : term,X426 : subst,X427 : subst] : ((sub @ (X423 @ X427 @ X425) @ X426) = (X423 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426))) & ((X421 @ id @ (lam @ (X423 @ sh @ one)) @ id) != $true)) | ((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa = $true)) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (((! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 != X9) & ((ap @ X8 @ X6) = (ap @ X9 @ X7)))) | ? [X5 : term] : ((sub @ X5 @ id) != X5)) <=> (hoasapinj1_lthm = $true)) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) <=> (axscons = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X178 : subst > term > subst > $o,X179 : term,X180 : term > $o] : (? [X186 : subst > term > term] : (((X178 @ id @ (lam @ (X186 @ sh @ one)) @ id) != $true) & ! [X188 : term,X189 : subst,X190 : subst] : ((X186 @ (comp @ X189 @ X190) @ (sub @ X188 @ X190)) = (sub @ (X186 @ X189 @ X188) @ X190)) & ! [X187 : term] : (((X178 @ id @ (X186 @ id @ X187) @ id) = $true) | ((X178 @ id @ X187 @ id) != $true))) | ((X180 @ (lam @ X179)) = $true) | ? [X195 : term] : ((X180 @ X195) != (X178 @ id @ X195 @ id)) | ? [X191 : subst,X192 : term,X193 : subst,X194 : subst] : (($true != (X178 @ X191 @ X192 @ (comp @ X193 @ X194))) & ((X178 @ (comp @ X191 @ X193) @ (sub @ X192 @ X193) @ X194) = $true)) | ? [X181 : subst,X182 : subst,X183 : subst,X184 : term] : (((X178 @ X183 @ X184 @ (comp @ X182 @ X181)) = $true) & ((X178 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182) @ X181) != $true)) | ? [X185 : term] : (((X180 @ X185) = $true) & ((X180 @ (sub @ X179 @ (push @ X185 @ id))) != $true))) | ? [X177 : term] : ((sub @ X177 @ id) != X177))) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (substmonoid_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ! [X410 : d_term] : (d_one = X410) & ((shinj = $true) <=> ! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198))) & (induction2lem_gthm = $true) & (hoasapnotvar = $true) & (ulamvarind = $true) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & (((! [X505 : term > $o,X506 : term] : (? [X507 : term] : (! [X508 : term] : (((X505 @ X508) != $true) | ((X505 @ (sub @ X507 @ (push @ X508 @ id))) = $true)) & ($true != (X505 @ (lam @ X507)))) | ? [X511 : term] : (((var @ X511) = $true) & ((X505 @ X511) != $true)) | ? [X509 : term,X510 : term] : (((X505 @ X510) = $true) & ((X505 @ X509) = $true) & ((X505 @ (ap @ X509 @ X510)) != $true)) | ($true = (X505 @ X506))) | ? [X497 : term > $o,X498 : subst,X499 : term] : (! [X502 : term] : (((X497 @ (lam @ X502)) = $true) | ? [X503 : term] : (((X497 @ X503) = $true) & ((X497 @ (sub @ X502 @ (push @ X503 @ id))) != $true))) & ! [X500 : term,X501 : term] : (((X497 @ X501) != $true) | ((X497 @ X500) != $true) | ((X497 @ (ap @ X500 @ X501)) = $true)) & ((X497 @ (sub @ X499 @ X498)) != $true) & ! [X504 : term] : (($true = (X497 @ (sub @ X504 @ X498))) | ((var @ X504) != $true)))) | ? [X496 : term] : ((sub @ X496 @ id) != X496)) <=> (induction2_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X487 : term,X488 : subst > term > subst > $o] : (? [X491 : subst > term > term] : (! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) & ! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) & ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) != $true)) | ((X488 @ id @ X487 @ id) = $true) | ? [X489 : term,X490 : term] : (($true = (X488 @ id @ X489 @ id)) & ((X488 @ id @ (ap @ (sub @ X489 @ id) @ X490) @ id) != $true) & ((X488 @ id @ X490 @ id) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X375 : subst > term > subst > $o,X376 : term] : (((X375 @ id @ (lam @ X376) @ id) = $true) | ? [X377 : term] : (($true = (X375 @ id @ X377 @ id)) & ((X375 @ id @ (sub @ X376 @ (push @ X377 @ id)) @ id) != $true)) | ? [X378 : subst > term > term] : (! [X380 : subst,X381 : subst,X382 : term] : ((sub @ (X378 @ X380 @ X382) @ X381) = (X378 @ (comp @ X380 @ X381) @ (sub @ X382 @ X381))) & ((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id) != $true) & ! [X379 : term] : (((X375 @ id @ X379 @ id) != $true) | ((X375 @ id @ (X378 @ id @ X379) @ id) = $true))))) & (axapp = $true) & (! [X429 : term,X430 : term,X431 : subst > term > subst > $o] : (? [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X431 @ X436 @ X434 @ (comp @ X435 @ X437)) = $true) & ((X431 @ (comp @ X436 @ X435) @ (sub @ X434 @ X435) @ X437) != $true)) | ? [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (((X431 @ X438 @ X439 @ (comp @ X441 @ X440)) != $true) & ((X431 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440) = $true)) | ((X431 @ id @ X429 @ id) != $true) | ? [X432 : term,X433 : term] : (((X431 @ id @ X433 @ id) = $true) & ((X431 @ id @ X432 @ id) = $true) & ((X431 @ id @ (ap @ (sub @ X432 @ id) @ X433) @ id) != $true)) | ((X431 @ id @ (ap @ X430 @ X429) @ id) = $true) | ($true != (X431 @ id @ X430 @ id))) <=> (hoasinduction_lem2 = $true)) & ((laminj = $true) <=> ! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462))) & (apnotvar = $true) & (! [X383 : term] : ((sub @ X383 @ id) = X383) <=> (termmset = $true)) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) <=> (substmonoid = $true)) & (hoaslaminj_gthm = $true) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) <=> (hoasapinj2 = $true)) & (axabs = $true) & (pushprop_lthm = $true) & (! [X64 : term,X65 : subst > term > subst > $o] : (? [X67 : subst > term > term,X68 : term] : (! [X72 : subst,X73 : term,X74 : subst] : ((X67 @ (comp @ X72 @ X74) @ (sub @ X73 @ X74)) = (sub @ X68 @ (push @ (sub @ X73 @ X74) @ (comp @ X72 @ X74)))) & ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) != $true) & ! [X69 : subst,X70 : subst,X71 : term] : ((sub @ (sub @ X68 @ (push @ X71 @ X69)) @ X70) = (sub @ (X67 @ X69 @ X71) @ X70)) & ! [X75 : term] : (((X65 @ id @ X75 @ id) != $true) | ((X65 @ id @ (X67 @ id @ X75) @ id) = $true))) | ((X65 @ id @ (lam @ (sub @ X64 @ (push @ one @ sh))) @ id) = $true) | ? [X66 : term] : (((X65 @ id @ (sub @ X64 @ (push @ X66 @ id)) @ id) != $true) & ((X65 @ id @ X66 @ id) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X149 : term > $o,X150 : term] : (? [X154 : term] : (((X149 @ X154) != $true) & ((var @ X154) = $true)) | ? [X151 : term,X152 : term] : (((X149 @ (ap @ X152 @ X151)) != $true) & ($true = (X149 @ X151)) & ((X149 @ X152) = $true)) | ((X149 @ X150) = $true) | ? [X153 : term] : (((X149 @ X153) = $true) & ((X149 @ (lam @ X153)) != $true))) <=> (induction = $true)) & (! [X271 : term,X272 : term > $o,X273 : subst > term > subst > $o,X274 : term] : (? [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (((X273 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) = $true) & ((X273 @ X285 @ X283 @ (comp @ X282 @ X284)) != $true)) | ? [X280 : term,X281 : term] : (((X273 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id) != $true) & ((X273 @ id @ X281 @ id) = $true) & ((X273 @ id @ X280 @ id) = $true)) | ($true != (X272 @ X274)) | ((X272 @ X271) != $true) | ((X272 @ (ap @ X274 @ X271)) = $true) | ? [X275 : term] : ((X272 @ X275) != (X273 @ id @ X275 @ id)) | ? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (((X273 @ (comp @ X276 @ X278) @ (sub @ X279 @ X278) @ X277) != $true) & ((X273 @ X276 @ X279 @ (comp @ X278 @ X277)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lthm_orig = $true) & (! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (? [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) != (X0 @ X4)) | ((X0 @ one) = $true) | ((X1 @ X3) != $true)) <=> (pushprop_lem1v2 = $true)) & (induction2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X374 : term] : ((sub @ X374 @ id) = X374) <=> (axvarid = $true)) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = id) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (axassoc = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasinduction_gthm = $true) & (pushprop_lem2v2 = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((substmonoid_lthm = $true) <=> (((! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147)) | ? [X146 : subst] : ((comp @ X146 @ id) != X146)) | ? [X145 : subst] : ((comp @ id @ X145) != X145))) & ((axidl = $true) <=> ! [X409 : subst] : ((comp @ id @ X409) = X409)) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) <=> ! [X465 : term,X466 : subst > term > subst > $o] : (((X466 @ id @ X465 @ id) = $true) | ? [X472 : subst > term > term] : (! [X476 : term] : (((X466 @ id @ X476 @ id) != $true) | ((X466 @ id @ (X472 @ id @ X476) @ id) = $true)) & ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) != $true) & ! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473))) | ? [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (((X466 @ X470 @ X468 @ (comp @ X471 @ X469)) = $true) & ((X466 @ (comp @ X470 @ X471) @ (sub @ X468 @ X471) @ X469) != $true)) | ? [X481 : term,X482 : term] : (((X466 @ id @ X481 @ id) = $true) & ($true = (X466 @ id @ X482 @ id)) & ((X466 @ id @ (ap @ (sub @ X482 @ id) @ X481) @ id) != $true)) | ? [X467 : term] : (($true != (X466 @ id @ X467 @ id)) & ((var @ (sub @ X467 @ id)) = $true)) | ? [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = (X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477)) & ($true != (X466 @ X479 @ X480 @ (comp @ X478 @ X477)))))) & (hoasinduction_lem2_lthm = $true)),
% 32.60/5.94 inference(ennf_transformation,[status(thm)],[f11])).
% 32.60/5.94 thf(f11,plain,(
% 32.60/5.94 ((! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) => (! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) => ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X24 @ X27) != $true) | ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X314 : subst > term > term,X315 : term,X316 : term] : (~! [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) = (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one))))) & ((! [X56 : term,X57 : term,X58 : term,X59 : term] : ((X57 = X58) | ((ap @ X56 @ X58) != (ap @ X59 @ X57))) => ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((! [X157 : term] : ~! [X158 : subst > term > term] : ~! [X159 : term,X160 : subst] : ((X158 @ X160 @ X159) = (sub @ X157 @ (push @ X159 @ X160))) => (! [X161 : term] : ((sub @ X161 @ id) = X161) => ! [X162 : subst > term > subst > $o,X163 : term > $o,X164 : term] : (~! [X166 : subst > term > term] : (((X162 @ id @ (lam @ (X166 @ sh @ one)) @ id) = $true) | ~! [X167 : term] : (((X162 @ id @ X167 @ id) != $true) | ((X162 @ id @ (X166 @ id @ X167) @ id) = $true)) | ~! [X168 : subst,X169 : subst,X170 : term] : ((sub @ (X166 @ X168 @ X170) @ X169) = (X166 @ (comp @ X168 @ X169) @ (sub @ X170 @ X169)))) | ~! [X171 : term] : ((X163 @ X171) = (X162 @ id @ X171 @ id)) | ~! [X165 : term] : (((X163 @ X165) != $true) | ((X163 @ (sub @ X164 @ (push @ X165 @ id))) = $true)) | ((X163 @ (lam @ X164)) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) = X211) => ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (($true = (X214 @ one)) | ((X215 @ X212) != $true) | ~! [X216 : term] : ((X214 @ X216) = (X215 @ (sub @ X216 @ (push @ X212 @ X213))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lthm = $true) <=> (! [X217 : term > $o,X218 : term] : (~! [X220 : term] : (~! [X221 : term] : (((X217 @ (sub @ X220 @ (push @ X221 @ id))) = $true) | ((X217 @ X221) != $true)) | ((X217 @ (lam @ X220)) = $true)) | ~! [X222 : term,X223 : term] : (((X217 @ (ap @ X222 @ X223)) = $true) | ((X217 @ X222) != $true) | ((X217 @ X223) != $true)) | ((X217 @ X218) = $true) | ~! [X219 : term] : (((X217 @ X219) = $true) | ((var @ X219) != $true))) => (! [X224 : subst > term > subst > $o,X225 : term,X226 : term] : (((X224 @ id @ X226 @ id) != $true) | ~! [X229 : term,X230 : subst,X231 : subst,X232 : subst] : (((X224 @ X230 @ X229 @ (comp @ X231 @ X232)) = $true) | ((X224 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231) @ X232) != $true)) | ~! [X227 : term,X228 : term] : (((X224 @ id @ X228 @ id) != $true) | ((X224 @ id @ (ap @ (sub @ X227 @ id) @ X228) @ id) = $true) | ((X224 @ id @ X227 @ id) != $true)) | ($true = (X224 @ id @ (ap @ X225 @ X226) @ id)) | ((X224 @ id @ X225 @ id) != $true) | ~! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : (((X224 @ X235 @ X234 @ (comp @ X233 @ X236)) != $true) | ((X224 @ (comp @ X235 @ X233) @ (sub @ X234 @ X233) @ X236) = $true))) => (! [X237 : term,X238 : subst > term > subst > $o] : (~! [X247 : subst > term > term] : (~! [X249 : subst,X250 : subst,X251 : term] : ((X247 @ (comp @ X249 @ X250) @ (sub @ X251 @ X250)) = (sub @ (X247 @ X249 @ X251) @ X250)) | ~! [X248 : term] : (((X238 @ id @ (X247 @ id @ X248) @ id) = $true) | ($true != (X238 @ id @ X248 @ id))) | ((X238 @ id @ (lam @ (X247 @ sh @ one)) @ id) = $true)) | ~! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) = $true) | ((X238 @ X244 @ X245 @ (comp @ X243 @ X246)) != $true)) | ~! [X252 : term] : (((X238 @ id @ (sub @ X237 @ (push @ X252 @ id)) @ id) = $true) | ((X238 @ id @ X252 @ id) != $true)) | ((X238 @ id @ (lam @ X237) @ id) = $true) | ~! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (((X238 @ (comp @ X241 @ X242) @ (sub @ X240 @ X242) @ X239) != $true) | ((X238 @ X241 @ X240 @ (comp @ X242 @ X239)) = $true))) => ! [X253 : subst > term > subst > $o,X254 : term] : (~! [X270 : term] : (($true != (var @ (sub @ X270 @ id))) | ((X253 @ id @ X270 @ id) = $true)) | ~! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (($true != (X253 @ X258 @ X256 @ (comp @ X257 @ X255))) | ((X253 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257) @ X255) = $true)) | ~! [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (((X253 @ X267 @ X268 @ (comp @ X269 @ X266)) = $true) | ((X253 @ (comp @ X267 @ X269) @ (sub @ X268 @ X269) @ X266) != $true)) | ~! [X261 : subst > term > term] : (((X253 @ id @ (lam @ (X261 @ sh @ one)) @ id) = $true) | ~! [X262 : term] : (($true != (X253 @ id @ X262 @ id)) | ($true = (X253 @ id @ (X261 @ id @ X262) @ id))) | ~! [X263 : term,X264 : subst,X265 : subst] : ((X261 @ (comp @ X265 @ X264) @ (sub @ X263 @ X264)) = (sub @ (X261 @ X265 @ X263) @ X264))) | ((X253 @ id @ X254 @ id) = $true) | ~! [X259 : term,X260 : term] : (((X253 @ id @ X260 @ id) != $true) | ((X253 @ id @ X259 @ id) != $true) | ($true = (X253 @ id @ (ap @ (sub @ X259 @ id) @ X260) @ id)))))))) & (pushprop_gthm = $true) & ((! [X76 : subst > term > subst > $o] : ~! [X77 : term > $o] : ~! [X78 : term] : ((X76 @ id @ X78 @ id) = (X77 @ X78)) => (! [X79 : term > $o,X80 : term] : (((X79 @ X80) = $true) | ~! [X81 : term,X82 : term] : (($true != (X79 @ X82)) | ((X79 @ (ap @ X82 @ X81)) = $true) | ((X79 @ X81) != $true)) | ~! [X84 : term] : (((X79 @ (lam @ X84)) = $true) | ~! [X85 : term] : (((X79 @ (sub @ X84 @ (push @ X85 @ id))) = $true) | ((X79 @ X85) != $true))) | ~! [X83 : term] : (((var @ X83) != $true) | ((X79 @ X83) = $true))) => (! [X86 : term] : ((sub @ X86 @ id) = X86) => (! [X87 : subst > term > subst > $o,X88 : term > $o,X89 : term] : (~! [X96 : term] : (((X88 @ (sub @ X89 @ (push @ X96 @ id))) = $true) | ((X88 @ X96) != $true)) | ((X88 @ (lam @ X89)) = $true) | ~! [X90 : term] : ((X87 @ id @ X90 @ id) = (X88 @ X90)) | ~! [X91 : subst > term > term] : (~! [X93 : subst,X94 : term,X95 : subst] : ((X91 @ (comp @ X95 @ X93) @ (sub @ X94 @ X93)) = (sub @ (X91 @ X95 @ X94) @ X93)) | ~! [X92 : term] : (($true = (X87 @ id @ (X91 @ id @ X92) @ id)) | ((X87 @ id @ X92 @ id) != $true)) | ((X87 @ id @ (lam @ (X91 @ sh @ one)) @ id) = $true))) => ! [X97 : subst > term > subst > $o,X98 : term] : (~! [X109 : term] : (((var @ (sub @ X109 @ id)) != $true) | ($true = (X97 @ id @ X109 @ id))) | ~! [X107 : term,X108 : term] : (((X97 @ id @ X108 @ id) != $true) | ((X97 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id) = $true) | ((X97 @ id @ X107 @ id) != $true)) | ~! [X110 : subst > term > term] : (~! [X114 : term] : (((X97 @ id @ (X110 @ id @ X114) @ id) = $true) | ((X97 @ id @ X114 @ id) != $true)) | ((X97 @ id @ (lam @ (X110 @ sh @ one)) @ id) = $true) | ~! [X111 : subst,X112 : term,X113 : subst] : ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)) = (sub @ (X110 @ X113 @ X112) @ X111))) | ~! [X99 : subst,X100 : subst,X101 : term,X102 : subst] : (((X97 @ (comp @ X99 @ X102) @ (sub @ X101 @ X102) @ X100) = $true) | ((X97 @ X99 @ X101 @ (comp @ X102 @ X100)) != $true)) | ~! [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (((X97 @ X103 @ X106 @ (comp @ X104 @ X105)) = $true) | ((X97 @ (comp @ X103 @ X104) @ (sub @ X106 @ X104) @ X105) != $true)) | ((X97 @ id @ X98 @ id) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2_lthm = $true) & (one = (d2term @ d_one)) & ((hoasinduction_lem0 = $true) <=> ! [X201 : subst > term > subst > $o] : ~! [X202 : term > $o] : ~! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id))) & (termmset_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X38 : subst > term > subst > $o,X39 : term] : (~! [X49 : subst > term > term] : (((X38 @ id @ (lam @ (X49 @ sh @ one)) @ id) = $true) | ~! [X53 : term] : (((X38 @ id @ X53 @ id) != $true) | ((X38 @ id @ (X49 @ id @ X53) @ id) = $true)) | ~! [X50 : subst,X51 : subst,X52 : term] : ((X49 @ (comp @ X50 @ X51) @ (sub @ X52 @ X51)) = (sub @ (X49 @ X50 @ X52) @ X51))) | ~! [X48 : term] : (((X38 @ id @ (sub @ X39 @ (push @ X48 @ id)) @ id) = $true) | ($true != (X38 @ id @ X48 @ id))) | ~! [X40 : term,X41 : subst,X42 : subst,X43 : subst] : (($true = (X38 @ (comp @ X42 @ X43) @ (sub @ X40 @ X43) @ X41)) | ((X38 @ X42 @ X40 @ (comp @ X43 @ X41)) != $true)) | ((X38 @ id @ (lam @ X39) @ id) = $true) | ~! [X44 : subst,X45 : subst,X46 : subst,X47 : term] : (((X38 @ (comp @ X44 @ X46) @ (sub @ X47 @ X46) @ X45) != $true) | ((X38 @ X44 @ X47 @ (comp @ X46 @ X45)) = $true)))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & (! [X512 : subst > term > subst > $o,X513 : term > $o,X514 : term] : (~! [X515 : term] : ((X513 @ X515) = (X512 @ id @ X515 @ id)) | ($true = (X513 @ (lam @ X514))) | ~! [X516 : subst > term > term] : (~! [X520 : term] : (((X512 @ id @ X520 @ id) != $true) | ((X512 @ id @ (X516 @ id @ X520) @ id) = $true)) | ((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id) = $true) | ~! [X517 : subst,X518 : subst,X519 : term] : ((sub @ (X516 @ X518 @ X519) @ X517) = (X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517)))) | ~! [X521 : term] : (((X513 @ X521) != $true) | ((X513 @ (sub @ X514 @ (push @ X521 @ id))) = $true))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X54 : d_subst,X55 : d_subst] : (((d2subst @ X55) = (d2subst @ X54)) => (X54 = X55)) & ! [X209 : d_subst] : (d_id = X209) & ((! [X115 : subst > term > subst > $o] : ~! [X116 : term > $o] : ~! [X117 : term] : ((X116 @ X117) = (X115 @ id @ X117 @ id)) => (! [X118 : term,X119 : term > $o] : (($true = (X119 @ X118)) | ~! [X123 : term] : (~! [X124 : term] : (((X119 @ (sub @ X123 @ (push @ X124 @ id))) = $true) | ((X119 @ X124) != $true)) | ((X119 @ (lam @ X123)) = $true)) | ~! [X122 : term] : (((var @ X122) != $true) | ((X119 @ X122) = $true)) | ~! [X120 : term,X121 : term] : (((X119 @ (ap @ X120 @ X121)) = $true) | ((X119 @ X121) != $true) | ((X119 @ X120) != $true))) => (! [X125 : term] : ((sub @ X125 @ id) = X125) => (! [X126 : subst > term > subst > $o,X127 : term,X128 : term > $o] : (((X128 @ (lam @ X127)) = $true) | ~! [X131 : subst > term > term] : (~! [X133 : subst,X134 : term,X135 : subst] : ((X131 @ (comp @ X133 @ X135) @ (sub @ X134 @ X135)) = (sub @ (X131 @ X133 @ X134) @ X135)) | ((X126 @ id @ (lam @ (X131 @ sh @ one)) @ id) = $true) | ~! [X132 : term] : (((X126 @ id @ (X131 @ id @ X132) @ id) = $true) | ($true != (X126 @ id @ X132 @ id)))) | ~! [X130 : term] : ((X126 @ id @ X130 @ id) = (X128 @ X130)) | ~! [X129 : term] : (((X128 @ (sub @ X127 @ (push @ X129 @ id))) = $true) | ((X128 @ X129) != $true))) => ! [X136 : subst > term > subst > $o,X137 : term] : (~! [X138 : subst > term > term] : (~! [X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)) = (sub @ (X138 @ X142 @ X140) @ X141)) | ((X136 @ id @ (lam @ (X138 @ sh @ one)) @ id) = $true) | ~! [X139 : term] : (((X136 @ id @ (X138 @ id @ X139) @ id) = $true) | ((X136 @ id @ X139 @ id) != $true))) | ~! [X143 : term,X144 : term] : (((X136 @ id @ (ap @ (sub @ X144 @ id) @ X143) @ id) = $true) | ((X136 @ id @ X143 @ id) != $true) | ((X136 @ id @ X144 @ id) != $true)) | ((X136 @ id @ X137 @ id) = $true)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axidr = $true) <=> ! [X172 : subst] : ((comp @ X172 @ id) = X172)) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) <=> (apinj2 = $true)) & ((induction2lem = $true) <=> ! [X532 : term,X533 : subst,X534 : term > $o] : (~! [X537 : term] : (((X534 @ (sub @ X537 @ X533)) = $true) | ((var @ X537) != $true)) | ~! [X538 : term,X539 : term] : (((X534 @ X538) != $true) | ((X534 @ (ap @ X538 @ X539)) = $true) | ((X534 @ X539) != $true)) | ((X534 @ (sub @ X532 @ X533)) = $true) | ~! [X535 : term] : (~! [X536 : term] : (((X534 @ X536) != $true) | ((X534 @ (sub @ X535 @ (push @ X536 @ id))) = $true)) | ((X534 @ (lam @ X535)) = $true)))) & (! [X311 : subst > term > subst > $o] : ~! [X312 : term > $o] : ~! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313)) <=> (hoasinduction_lem0_lthm = $true)) & ((induction2 = $true) <=> ! [X400 : term > $o,X401 : term] : (~! [X404 : term] : (((var @ X404) != $true) | ((X400 @ X404) = $true)) | ((X400 @ X401) = $true) | ~! [X402 : term,X403 : term] : (((X400 @ X403) != $true) | ($true = (X400 @ (ap @ X403 @ X402))) | ((X400 @ X402) != $true)) | ~! [X405 : term] : (((X400 @ (lam @ X405)) = $true) | ~! [X406 : term] : (((X400 @ (sub @ X405 @ (push @ X406 @ id))) = $true) | ((X400 @ X406) != $true))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapinj2_gthm = $true) & (axclos = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (~! [X359 : term] : ((X357 @ X359) = (X356 @ id @ X359 @ id)) | ~! [X369 : subst > term > term] : (~! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373)) | ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) = $true) | ~! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ((X356 @ id @ X370 @ id) != $true))) | ((X357 @ (lam @ X358)) = $true) | ~! [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) != $true) | ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) = $true)) | ~! [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) = $true) | ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) != $true)) | ~! [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) = $true) | ($true != (X357 @ X364)))) <=> (hoasinduction_lem3v2 = $true)) & (! [X442 : term,X443 : subst > term > subst > $o] : (((X443 @ id @ (lam @ (sub @ X442 @ (push @ one @ sh))) @ id) = $true) | ~! [X444 : term] : (((X443 @ id @ X444 @ id) != $true) | ((X443 @ id @ (sub @ X442 @ (push @ X444 @ id)) @ id) = $true)) | ~! [X445 : subst > term > term] : (((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) = $true) | ~! [X446 : subst,X447 : term,X448 : subst] : ((sub @ (X445 @ X446 @ X447) @ X448) = (X445 @ (comp @ X446 @ X448) @ (sub @ X447 @ X448))) | ~! [X449 : term] : (((X443 @ id @ X449 @ id) != $true) | ((X443 @ id @ (X445 @ id @ X449) @ id) = $true)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X286 : term] : ((sub @ X286 @ id) = X286) => (! [X287 : term,X288 : subst > term > subst > $o] : (~! [X289 : subst > term > term] : (~! [X290 : term] : (($true != (X288 @ id @ X290 @ id)) | ((X288 @ id @ (X289 @ id @ X290) @ id) = $true)) | ($true = (X288 @ id @ (lam @ (X289 @ sh @ one)) @ id)) | ~! [X291 : term,X292 : subst,X293 : subst] : ((sub @ (X289 @ X292 @ X291) @ X293) = (X289 @ (comp @ X292 @ X293) @ (sub @ X291 @ X293)))) | ((X288 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id) = $true) | ~! [X294 : term] : (((X288 @ id @ X294 @ id) != $true) | ($true = (X288 @ id @ (sub @ X287 @ (push @ X294 @ id)) @ id)))) => ! [X295 : subst > term > subst > $o,X296 : term] : (~! [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (((X295 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309) = $true) | ((X295 @ X307 @ X310 @ (comp @ X308 @ X309)) != $true)) | ~! [X301 : subst > term > term] : (($true = (X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)) | ~! [X305 : term] : (((X295 @ id @ (X301 @ id @ X305) @ id) = $true) | ((X295 @ id @ X305 @ id) != $true)) | ~! [X302 : subst,X303 : subst,X304 : term] : ((X301 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302)) = (sub @ (X301 @ X303 @ X304) @ X302))) | ~! [X306 : term] : (((X295 @ id @ X306 @ id) != $true) | ((X295 @ id @ (sub @ X296 @ (push @ X306 @ id)) @ id) = $true)) | ((X295 @ id @ (lam @ X296) @ id) = $true) | ~! [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (($true != (X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299)) | ((X295 @ X297 @ X300 @ (comp @ X298 @ X299)) = $true)))))) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) <=> (apinj1 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (ulamvar1 != $true) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lem1_lthm = $true) & (ulamvarsh = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X320 : term] : ((sub @ X320 @ id) = X320) => (! [X321 : subst > term > subst > $o,X322 : term] : (((X321 @ id @ (lam @ (sub @ X322 @ (push @ one @ sh))) @ id) = $true) | ~! [X324 : subst > term > term] : (((X321 @ id @ (lam @ (X324 @ sh @ one)) @ id) = $true) | ~! [X325 : subst,X326 : subst,X327 : term] : ((X324 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)) = (sub @ (X324 @ X325 @ X327) @ X326)) | ~! [X328 : term] : (((X321 @ id @ X328 @ id) != $true) | ($true = (X321 @ id @ (X324 @ id @ X328) @ id)))) | ~! [X323 : term] : (((X321 @ id @ (sub @ X322 @ (push @ X323 @ id)) @ id) = $true) | ($true != (X321 @ id @ X323 @ id)))) => ! [X329 : subst > term > subst > $o,X330 : term] : (~! [X332 : subst > term > term] : (((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) = $true) | ~! [X336 : term] : (($true != (X329 @ id @ X336 @ id)) | ((X329 @ id @ (X332 @ id @ X336) @ id) = $true)) | ~! [X333 : subst,X334 : term,X335 : subst] : ((X332 @ (comp @ X333 @ X335) @ (sub @ X334 @ X335)) = (sub @ (X332 @ X333 @ X334) @ X335))) | ~! [X331 : term] : (((X329 @ id @ X331 @ id) != $true) | ($true = (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id))) | ((X329 @ id @ (lam @ X330) @ id) = $true))))) & (hoasapinj1_gthm = $true) & ((! [X337 : subst,X338 : term] : ((sub @ one @ (push @ X338 @ X337)) = X338) => (! [X339 : term,X340 : subst] : ((comp @ sh @ (push @ X339 @ X340)) = X340) => (! [X341 : subst] : ((comp @ X341 @ id) = X341) => (! [X342 : term > $o,X343 : term] : (((X342 @ X343) = $true) | ~! [X344 : term,X345 : term] : (((X342 @ (ap @ X345 @ X344)) = $true) | ((X342 @ X344) != $true) | ((X342 @ X345) != $true)) | ~! [X347 : term] : (($true != (var @ X347)) | ((X342 @ X347) = $true)) | ~! [X346 : term] : (((X342 @ X346) != $true) | ((X342 @ (lam @ X346)) = $true))) => ! [X348 : term > $o,X349 : term,X350 : subst] : (~! [X355 : term] : (((var @ X355) != $true) | ($true = (X348 @ (sub @ X355 @ X350)))) | ~! [X353 : term] : (((X348 @ (lam @ X353)) = $true) | ~! [X354 : term] : (($true = (X348 @ (sub @ X353 @ (push @ X354 @ id)))) | ((X348 @ X354) != $true))) | ((X348 @ (sub @ X349 @ X350)) = $true) | ~! [X351 : term,X352 : term] : (((X348 @ X352) != $true) | ((X348 @ (ap @ X352 @ X351)) = $true) | ((X348 @ X351) != $true))))))) <=> (induction2lem_lthm = $true)) & (lamnotvar = $true) & ((! [X384 : term,X385 : subst] : ((sub @ one @ (push @ X384 @ X385)) = X384) => (! [X386 : subst,X387 : term] : ((comp @ sh @ (push @ X387 @ X386)) = X386) => (! [X388 : term,X389 : term] : (((lam @ X389) != (lam @ X388)) | (X388 = X389)) => ! [X390 : subst,X391 : subst > term > term,X392 : term,X393 : subst > term > term] : (((X391 @ X390 @ X392) = (X393 @ X390 @ X392)) | ~! [X394 : subst,X395 : term,X396 : subst] : ((X393 @ (comp @ X396 @ X394) @ (sub @ X395 @ X394)) = (sub @ (X393 @ X396 @ X395) @ X394)) | ((lam @ (X391 @ sh @ one)) != (lam @ (X393 @ sh @ one))) | ~! [X397 : subst,X398 : term,X399 : subst] : ((X391 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399)) = (sub @ (X391 @ X397 @ X398) @ X399)))))) <=> (hoaslaminj_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ~! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one))) & ((hoaslaminj = $true) <=> ! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ~! [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) = (sub @ (X524 @ X526 @ X527) @ X528)) | ~! [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) = (sub @ (X522 @ X530 @ X529) @ X531)))) & (! [X415 : term] : ~! [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) != (X416 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & (axvarshift = $true) & (! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ((X204 @ X208) != $true)) <=> (pushprop_lem1 = $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (axmap = $true) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) <=> (axvarcons = $true)) & (! [X483 : term] : ~! [X484 : subst > term > term] : ~! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486)) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotap != $true) & (! [X34 : term] : ~! [X35 : subst > term > term] : ~! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X199 : d_term,X200 : d_term] : (((d2term @ X200) = (d2term @ X199)) => (X199 = X200)) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463)) & (hoasinduction_lem2v2_gthm = $true) & ((! [X417 : term] : ((sub @ X417 @ id) = X417) => ! [X418 : term] : ((sub @ X418 @ id) = X418)) <=> (termmset_lthm = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X14 : term > $o,X15 : term,X16 : subst] : ~! [X17 : term > $o] : ~! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18)) <=> (pushprop_lem0_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X456 : subst,X457 : term > $o,X458 : term] : ~! [X459 : term > $o] : ~! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & ((hoasinduction_lem3aa = $true) <=> ! [X421 : subst > term > subst > $o,X422 : term] : (~! [X423 : subst > term > term] : (~! [X424 : term] : (((X421 @ id @ X424 @ id) != $true) | ((X421 @ id @ (X423 @ id @ X424) @ id) = $true)) | ~! [X425 : term,X426 : subst,X427 : subst] : ((sub @ (X423 @ X427 @ X425) @ X426) = (X423 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426))) | ((X421 @ id @ (lam @ (X423 @ sh @ one)) @ id) = $true)) | ((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id) = $true) | ~! [X428 : term] : (((X421 @ id @ X428 @ id) != $true) | ((X421 @ id @ (sub @ X422 @ (push @ X428 @ id)) @ id) = $true)))) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & ((! [X5 : term] : ((sub @ X5 @ id) = X5) => (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7))) => ! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)))) <=> (hoasapinj1_lthm = $true)) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) <=> (axscons = $true)) & ((! [X177 : term] : ((sub @ X177 @ id) = X177) => ! [X178 : subst > term > subst > $o,X179 : term,X180 : term > $o] : (~! [X191 : subst,X192 : term,X193 : subst,X194 : subst] : (((X178 @ (comp @ X191 @ X193) @ (sub @ X192 @ X193) @ X194) != $true) | ($true = (X178 @ X191 @ X192 @ (comp @ X193 @ X194)))) | ~! [X185 : term] : (((X180 @ X185) != $true) | ((X180 @ (sub @ X179 @ (push @ X185 @ id))) = $true)) | ~! [X195 : term] : ((X180 @ X195) = (X178 @ id @ X195 @ id)) | ((X180 @ (lam @ X179)) = $true) | ~! [X186 : subst > term > term] : (~! [X188 : term,X189 : subst,X190 : subst] : ((X186 @ (comp @ X189 @ X190) @ (sub @ X188 @ X190)) = (sub @ (X186 @ X189 @ X188) @ X190)) | ((X178 @ id @ (lam @ (X186 @ sh @ one)) @ id) = $true) | ~! [X187 : term] : (((X178 @ id @ (X186 @ id @ X187) @ id) = $true) | ((X178 @ id @ X187 @ id) != $true))) | ~! [X181 : subst,X182 : subst,X183 : subst,X184 : term] : (((X178 @ X183 @ X184 @ (comp @ X182 @ X181)) != $true) | ((X178 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182) @ X181) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (substmonoid_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ! [X410 : d_term] : (d_one = X410) & ((shinj = $true) <=> ! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198))) & (induction2lem_gthm = $true) & (hoasapnotvar = $true) & (ulamvarind = $true) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & ((! [X496 : term] : ((sub @ X496 @ id) = X496) => (! [X497 : term > $o,X498 : subst,X499 : term] : (~! [X504 : term] : (($true = (X497 @ (sub @ X504 @ X498))) | ((var @ X504) != $true)) | ~! [X502 : term] : (((X497 @ (lam @ X502)) = $true) | ~! [X503 : term] : (((X497 @ X503) != $true) | ((X497 @ (sub @ X502 @ (push @ X503 @ id))) = $true))) | ((X497 @ (sub @ X499 @ X498)) = $true) | ~! [X500 : term,X501 : term] : (((X497 @ X501) != $true) | ((X497 @ X500) != $true) | ((X497 @ (ap @ X500 @ X501)) = $true))) => ! [X505 : term > $o,X506 : term] : (~! [X507 : term] : (($true = (X505 @ (lam @ X507))) | ~! [X508 : term] : (((X505 @ X508) != $true) | ((X505 @ (sub @ X507 @ (push @ X508 @ id))) = $true))) | ~! [X509 : term,X510 : term] : (((X505 @ X510) != $true) | ((X505 @ (ap @ X509 @ X510)) = $true) | ((X505 @ X509) != $true)) | ~! [X511 : term] : (((var @ X511) != $true) | ((X505 @ X511) = $true)) | ($true = (X505 @ X506))))) <=> (induction2_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X487 : term,X488 : subst > term > subst > $o] : (~! [X491 : subst > term > term] : (~! [X495 : term] : (((X488 @ id @ (X491 @ id @ X495) @ id) = $true) | ((X488 @ id @ X495 @ id) != $true)) | ~! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) | ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) = $true)) | ~! [X489 : term,X490 : term] : (((X488 @ id @ X490 @ id) != $true) | ((X488 @ id @ (ap @ (sub @ X489 @ id) @ X490) @ id) = $true) | ($true != (X488 @ id @ X489 @ id))) | ((X488 @ id @ X487 @ id) = $true))) & (! [X375 : subst > term > subst > $o,X376 : term] : (~! [X377 : term] : (($true != (X375 @ id @ X377 @ id)) | ((X375 @ id @ (sub @ X376 @ (push @ X377 @ id)) @ id) = $true)) | ((X375 @ id @ (lam @ X376) @ id) = $true) | ~! [X378 : subst > term > term] : (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id) = $true) | ~! [X380 : subst,X381 : subst,X382 : term] : ((sub @ (X378 @ X380 @ X382) @ X381) = (X378 @ (comp @ X380 @ X381) @ (sub @ X382 @ X381))) | ~! [X379 : term] : (((X375 @ id @ X379 @ id) != $true) | ((X375 @ id @ (X378 @ id @ X379) @ id) = $true)))) <=> (hoasinduction_lem3a = $true)) & (axapp = $true) & (! [X429 : term,X430 : term,X431 : subst > term > subst > $o] : (((X431 @ id @ (ap @ X430 @ X429) @ id) = $true) | ($true != (X431 @ id @ X430 @ id)) | ((X431 @ id @ X429 @ id) != $true) | ~! [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X431 @ (comp @ X436 @ X435) @ (sub @ X434 @ X435) @ X437) = $true) | ((X431 @ X436 @ X434 @ (comp @ X435 @ X437)) != $true)) | ~! [X432 : term,X433 : term] : (((X431 @ id @ (ap @ (sub @ X432 @ id) @ X433) @ id) = $true) | ((X431 @ id @ X433 @ id) != $true) | ((X431 @ id @ X432 @ id) != $true)) | ~! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (((X431 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440) != $true) | ((X431 @ X438 @ X439 @ (comp @ X441 @ X440)) = $true))) <=> (hoasinduction_lem2 = $true)) & ((laminj = $true) <=> ! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462))) & (apnotvar = $true) & (! [X383 : term] : ((sub @ X383 @ id) = X383) <=> (termmset = $true)) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) <=> (substmonoid = $true)) & (hoaslaminj_gthm = $true) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) <=> (hoasapinj2 = $true)) & (axabs = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X64 : term,X65 : subst > term > subst > $o] : (~! [X67 : subst > term > term,X68 : term] : (~! [X75 : term] : (((X65 @ id @ X75 @ id) != $true) | ((X65 @ id @ (X67 @ id @ X75) @ id) = $true)) | ~! [X69 : subst,X70 : subst,X71 : term] : ((sub @ (sub @ X68 @ (push @ X71 @ X69)) @ X70) = (sub @ (X67 @ X69 @ X71) @ X70)) | ~! [X72 : subst,X73 : term,X74 : subst] : ((X67 @ (comp @ X72 @ X74) @ (sub @ X73 @ X74)) = (sub @ X68 @ (push @ (sub @ X73 @ X74) @ (comp @ X72 @ X74)))) | ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) = $true)) | ~! [X66 : term] : (((X65 @ id @ X66 @ id) != $true) | ((X65 @ id @ (sub @ X64 @ (push @ X66 @ id)) @ id) = $true)) | ((X65 @ id @ (lam @ (sub @ X64 @ (push @ one @ sh))) @ id) = $true))) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1_gthm = $true) & ((induction = $true) <=> ! [X149 : term > $o,X150 : term] : (~! [X154 : term] : (((X149 @ X154) = $true) | ((var @ X154) != $true)) | ((X149 @ X150) = $true) | ~! [X153 : term] : (((X149 @ X153) != $true) | ((X149 @ (lam @ X153)) = $true)) | ~! [X151 : term,X152 : term] : (((X149 @ (ap @ X152 @ X151)) = $true) | ($true != (X149 @ X151)) | ((X149 @ X152) != $true)))) & (! [X271 : term,X272 : term > $o,X273 : subst > term > subst > $o,X274 : term] : (((X272 @ X271) != $true) | ($true != (X272 @ X274)) | ~! [X280 : term,X281 : term] : (((X273 @ id @ X280 @ id) != $true) | ((X273 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id) = $true) | ((X273 @ id @ X281 @ id) != $true)) | ~! [X275 : term] : ((X272 @ X275) = (X273 @ id @ X275 @ id)) | ~! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (((X273 @ (comp @ X276 @ X278) @ (sub @ X279 @ X278) @ X277) = $true) | ((X273 @ X276 @ X279 @ (comp @ X278 @ X277)) != $true)) | ~! [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (((X273 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) != $true) | ((X273 @ X285 @ X283 @ (comp @ X282 @ X284)) = $true)) | ((X272 @ (ap @ X274 @ X271)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lthm_orig = $true) & (! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (((X1 @ X3) != $true) | ((X0 @ one) = $true) | ~! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4))) <=> (pushprop_lem1v2 = $true)) & (induction2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X374 : term] : ((sub @ X374 @ id) = X374) <=> (axvarid = $true)) & ((var @ (d2term @ d_one)) != $true) & ((d2subst @ d_id) = id) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (axassoc = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoasinduction_gthm = $true) & (pushprop_lem2v2 = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((substmonoid_lthm = $true) <=> (! [X145 : subst] : ((comp @ id @ X145) = X145) => (! [X146 : subst] : ((comp @ X146 @ id) = X146) => (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147))))) & ((axidl = $true) <=> ! [X409 : subst] : ((comp @ id @ X409) = X409)) & (pushprop_lem3v2 = $true) & (! [X465 : term,X466 : subst > term > subst > $o] : (((X466 @ id @ X465 @ id) = $true) | ~! [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (((X466 @ X470 @ X468 @ (comp @ X471 @ X469)) != $true) | ((X466 @ (comp @ X470 @ X471) @ (sub @ X468 @ X471) @ X469) = $true)) | ~! [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = (X466 @ X479 @ X480 @ (comp @ X478 @ X477))) | ($true != (X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477))) | ~! [X467 : term] : (((var @ (sub @ X467 @ id)) != $true) | ($true = (X466 @ id @ X467 @ id))) | ~! [X472 : subst > term > term] : (((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) = $true) | ~! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473)) | ~! [X476 : term] : (((X466 @ id @ X476 @ id) != $true) | ((X466 @ id @ (X472 @ id @ X476) @ id) = $true))) | ~! [X481 : term,X482 : term] : (((X466 @ id @ X481 @ id) != $true) | ((X466 @ id @ (ap @ (sub @ X482 @ id) @ X481) @ id) = $true) | ($true != (X466 @ id @ X482 @ id)))) <=> (hoasinduction = $true)) & (hoasinduction_lem2_lthm = $true)),
% 32.60/5.94 inference(flattening,[status(thm)],[f10])).
% 32.60/5.94 thf(f10,plain,(
% 32.60/5.94 (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (~! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4)) | ~((X1 @ X3) = $true) | ((X0 @ one) = $true))) & ((! [X5 : term] : ((sub @ X5 @ id) = X5) => (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7))) => ! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lthm = $true) & (! [X14 : term > $o,X15 : term,X16 : subst] : ~! [X17 : term > $o] : ~! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18)) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotvar = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) <=> (! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) => (! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) => ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true) | ~((X24 @ X27) = $true))))) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ~! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one))) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & (hoasapinj1_gthm = $true) & (axabs = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X34 : term] : ~! [X35 : subst > term > term] : ~! [X36 : subst,X37 : term] : ((X35 @ X36 @ X37) = (sub @ X34 @ (push @ X37 @ X36))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X38 : subst > term > subst > $o,X39 : term] : (~! [X40 : term,X41 : subst,X42 : subst,X43 : subst] : (($true = (X38 @ (comp @ X42 @ X43) @ (sub @ X40 @ X43) @ X41)) | ~((X38 @ X42 @ X40 @ (comp @ X43 @ X41)) = $true)) | ~! [X44 : subst,X45 : subst,X46 : subst,X47 : term] : (~((X38 @ (comp @ X44 @ X46) @ (sub @ X47 @ X46) @ X45) = $true) | ((X38 @ X44 @ X47 @ (comp @ X46 @ X45)) = $true)) | ~! [X48 : term] : (~($true = (X38 @ id @ X48 @ id)) | ((X38 @ id @ (sub @ X39 @ (push @ X48 @ id)) @ id) = $true)) | ((X38 @ id @ (lam @ X39) @ id) = $true) | ~! [X49 : subst > term > term] : (~! [X50 : subst,X51 : subst,X52 : term] : ((X49 @ (comp @ X50 @ X51) @ (sub @ X52 @ X51)) = (sub @ (X49 @ X50 @ X52) @ X51)) | ~! [X53 : term] : (((X38 @ id @ (X49 @ id @ X53) @ id) = $true) | ~((X38 @ id @ X53 @ id) = $true)) | ((X38 @ id @ (lam @ (X49 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & ! [X54 : d_subst,X55 : d_subst] : (((d2subst @ X55) = (d2subst @ X54)) => (X54 = X55)) & ((! [X56 : term,X57 : term,X58 : term,X59 : term] : ((X57 = X58) | ((ap @ X56 @ X58) != (ap @ X59 @ X57))) => ! [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ (sub @ X63 @ id) @ X60) != (ap @ (sub @ X62 @ id) @ X61)) | (X60 = X61))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X64 : term,X65 : subst > term > subst > $o] : (((X65 @ id @ (lam @ (sub @ X64 @ (push @ one @ sh))) @ id) = $true) | ~! [X66 : term] : (((X65 @ id @ (sub @ X64 @ (push @ X66 @ id)) @ id) = $true) | ~((X65 @ id @ X66 @ id) = $true)) | ~! [X67 : subst > term > term,X68 : term] : (~! [X69 : subst,X70 : subst,X71 : term] : ((sub @ (sub @ X68 @ (push @ X71 @ X69)) @ X70) = (sub @ (X67 @ X69 @ X71) @ X70)) | ~! [X72 : subst,X73 : term,X74 : subst] : ((X67 @ (comp @ X72 @ X74) @ (sub @ X73 @ X74)) = (sub @ X68 @ (push @ (sub @ X73 @ X74) @ (comp @ X72 @ X74)))) | ~! [X75 : term] : (~((X65 @ id @ X75 @ id) = $true) | ((X65 @ id @ (X67 @ id @ X75) @ id) = $true)) | ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id) = $true)))) & (apnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lthm_3 = $true) <=> (! [X76 : subst > term > subst > $o] : ~! [X77 : term > $o] : ~! [X78 : term] : ((X76 @ id @ X78 @ id) = (X77 @ X78)) => (! [X79 : term > $o,X80 : term] : (((X79 @ X80) = $true) | ~! [X81 : term,X82 : term] : (~($true = (X79 @ X82)) | ((X79 @ (ap @ X82 @ X81)) = $true) | ~((X79 @ X81) = $true)) | ~! [X83 : term] : (~((var @ X83) = $true) | ((X79 @ X83) = $true)) | ~! [X84 : term] : (((X79 @ (lam @ X84)) = $true) | ~! [X85 : term] : (((X79 @ (sub @ X84 @ (push @ X85 @ id))) = $true) | ~((X79 @ X85) = $true)))) => (! [X86 : term] : ((sub @ X86 @ id) = X86) => (! [X87 : subst > term > subst > $o,X88 : term > $o,X89 : term] : (((X88 @ (lam @ X89)) = $true) | ~! [X90 : term] : ((X87 @ id @ X90 @ id) = (X88 @ X90)) | ~! [X91 : subst > term > term] : (((X87 @ id @ (lam @ (X91 @ sh @ one)) @ id) = $true) | ~! [X92 : term] : (~((X87 @ id @ X92 @ id) = $true) | ($true = (X87 @ id @ (X91 @ id @ X92) @ id))) | ~! [X93 : subst,X94 : term,X95 : subst] : ((X91 @ (comp @ X95 @ X93) @ (sub @ X94 @ X93)) = (sub @ (X91 @ X95 @ X94) @ X93))) | ~! [X96 : term] : (((X88 @ (sub @ X89 @ (push @ X96 @ id))) = $true) | ~((X88 @ X96) = $true))) => ! [X97 : subst > term > subst > $o,X98 : term] : (~! [X99 : subst,X100 : subst,X101 : term,X102 : subst] : (((X97 @ (comp @ X99 @ X102) @ (sub @ X101 @ X102) @ X100) = $true) | ~((X97 @ X99 @ X101 @ (comp @ X102 @ X100)) = $true)) | ~! [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (((X97 @ X103 @ X106 @ (comp @ X104 @ X105)) = $true) | ~((X97 @ (comp @ X103 @ X104) @ (sub @ X106 @ X104) @ X105) = $true)) | ~! [X107 : term,X108 : term] : (~((X97 @ id @ X107 @ id) = $true) | ~((X97 @ id @ X108 @ id) = $true) | ((X97 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id) = $true)) | ~! [X109 : term] : (($true = (X97 @ id @ X109 @ id)) | ~((var @ (sub @ X109 @ id)) = $true)) | ((X97 @ id @ X98 @ id) = $true) | ~! [X110 : subst > term > term] : (~! [X111 : subst,X112 : term,X113 : subst] : ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)) = (sub @ (X110 @ X113 @ X112) @ X111)) | ~! [X114 : term] : (~((X97 @ id @ X114 @ id) = $true) | ((X97 @ id @ (X110 @ id @ X114) @ id) = $true)) | ((X97 @ id @ (lam @ (X110 @ sh @ one)) @ id) = $true)))))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X115 : subst > term > subst > $o] : ~! [X116 : term > $o] : ~! [X117 : term] : ((X116 @ X117) = (X115 @ id @ X117 @ id)) => (! [X118 : term,X119 : term > $o] : (~! [X120 : term,X121 : term] : (~((X119 @ X121) = $true) | ((X119 @ (ap @ X120 @ X121)) = $true) | ~((X119 @ X120) = $true)) | ~! [X122 : term] : (((X119 @ X122) = $true) | ~((var @ X122) = $true)) | ~! [X123 : term] : (((X119 @ (lam @ X123)) = $true) | ~! [X124 : term] : (~((X119 @ X124) = $true) | ((X119 @ (sub @ X123 @ (push @ X124 @ id))) = $true))) | ($true = (X119 @ X118))) => (! [X125 : term] : ((sub @ X125 @ id) = X125) => (! [X126 : subst > term > subst > $o,X127 : term,X128 : term > $o] : (((X128 @ (lam @ X127)) = $true) | ~! [X129 : term] : (~((X128 @ X129) = $true) | ((X128 @ (sub @ X127 @ (push @ X129 @ id))) = $true)) | ~! [X130 : term] : ((X126 @ id @ X130 @ id) = (X128 @ X130)) | ~! [X131 : subst > term > term] : (((X126 @ id @ (lam @ (X131 @ sh @ one)) @ id) = $true) | ~! [X132 : term] : (~($true = (X126 @ id @ X132 @ id)) | ((X126 @ id @ (X131 @ id @ X132) @ id) = $true)) | ~! [X133 : subst,X134 : term,X135 : subst] : ((X131 @ (comp @ X133 @ X135) @ (sub @ X134 @ X135)) = (sub @ (X131 @ X133 @ X134) @ X135)))) => ! [X136 : subst > term > subst > $o,X137 : term] : (((X136 @ id @ X137 @ id) = $true) | ~! [X138 : subst > term > term] : (~! [X139 : term] : (~((X136 @ id @ X139 @ id) = $true) | ((X136 @ id @ (X138 @ id @ X139) @ id) = $true)) | ((X136 @ id @ (lam @ (X138 @ sh @ one)) @ id) = $true) | ~! [X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)) = (sub @ (X138 @ X142 @ X140) @ X141))) | ~! [X143 : term,X144 : term] : (~((X136 @ id @ X144 @ id) = $true) | ~((X136 @ id @ X143 @ id) = $true) | ((X136 @ id @ (ap @ (sub @ X144 @ id) @ X143) @ id) = $true)))))))) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & ~(ulamvar1 = $true) & (hoasinduction_lem1 = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((substmonoid_lthm = $true) <=> (! [X145 : subst] : ((comp @ id @ X145) = X145) => (! [X146 : subst] : ((comp @ X146 @ id) = X146) => (! [X148 : subst] : ((comp @ id @ X148) = X148) & ! [X147 : subst] : ((comp @ X147 @ id) = X147))))) & (! [X149 : term > $o,X150 : term] : (~! [X151 : term,X152 : term] : (((X149 @ (ap @ X152 @ X151)) = $true) | ~((X149 @ X152) = $true) | ~($true = (X149 @ X151))) | ~! [X153 : term] : (~((X149 @ X153) = $true) | ((X149 @ (lam @ X153)) = $true)) | ((X149 @ X150) = $true) | ~! [X154 : term] : (((X149 @ X154) = $true) | ~((var @ X154) = $true))) <=> (induction = $true)) & (! [X155 : subst,X156 : term] : ((sub @ one @ (push @ X156 @ X155)) = X156) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X157 : term] : ~! [X158 : subst > term > term] : ~! [X159 : term,X160 : subst] : ((X158 @ X160 @ X159) = (sub @ X157 @ (push @ X159 @ X160))) => (! [X161 : term] : ((sub @ X161 @ id) = X161) => ! [X162 : subst > term > subst > $o,X163 : term > $o,X164 : term] : (~! [X165 : term] : (((X163 @ (sub @ X164 @ (push @ X165 @ id))) = $true) | ~((X163 @ X165) = $true)) | ~! [X166 : subst > term > term] : (~! [X167 : term] : (~((X162 @ id @ X167 @ id) = $true) | ((X162 @ id @ (X166 @ id @ X167) @ id) = $true)) | ~! [X168 : subst,X169 : subst,X170 : term] : ((sub @ (X166 @ X168 @ X170) @ X169) = (X166 @ (comp @ X168 @ X169) @ (sub @ X170 @ X169))) | ((X162 @ id @ (lam @ (X166 @ sh @ one)) @ id) = $true)) | ((X163 @ (lam @ X164)) = $true) | ~! [X171 : term] : ((X163 @ X171) = (X162 @ id @ X171 @ id)))))) & ((axidr = $true) <=> ! [X172 : subst] : ((comp @ X172 @ id) = X172)) & (! [X173 : term,X174 : term,X175 : term,X176 : term] : (((ap @ X173 @ X175) != (ap @ X174 @ X176)) | (X175 = X176)) <=> (apinj2 = $true)) & (hoasinduction_lem3_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X177 : term] : ((sub @ X177 @ id) = X177) => ! [X178 : subst > term > subst > $o,X179 : term,X180 : term > $o] : (((X180 @ (lam @ X179)) = $true) | ~! [X181 : subst,X182 : subst,X183 : subst,X184 : term] : (((X178 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182) @ X181) = $true) | ~((X178 @ X183 @ X184 @ (comp @ X182 @ X181)) = $true)) | ~! [X185 : term] : (((X180 @ (sub @ X179 @ (push @ X185 @ id))) = $true) | ~((X180 @ X185) = $true)) | ~! [X186 : subst > term > term] : (((X178 @ id @ (lam @ (X186 @ sh @ one)) @ id) = $true) | ~! [X187 : term] : (((X178 @ id @ (X186 @ id @ X187) @ id) = $true) | ~((X178 @ id @ X187 @ id) = $true)) | ~! [X188 : term,X189 : subst,X190 : subst] : ((X186 @ (comp @ X189 @ X190) @ (sub @ X188 @ X190)) = (sub @ (X186 @ X189 @ X188) @ X190))) | ~! [X191 : subst,X192 : term,X193 : subst,X194 : subst] : (~((X178 @ (comp @ X191 @ X193) @ (sub @ X192 @ X193) @ X194) = $true) | ($true = (X178 @ X191 @ X192 @ (comp @ X193 @ X194)))) | ~! [X195 : term] : ((X180 @ X195) = (X178 @ id @ X195 @ id))))) & (axassoc = $true) & (hoasapinj2_gthm = $true) & (termmset_gthm = $true) & (! [X196 : subst] : ((push @ (sub @ one @ X196) @ (comp @ sh @ X196)) = X196) <=> (axscons = $true)) & ((shinj = $true) <=> ! [X197 : term,X198 : term] : (((sub @ X197 @ sh) != (sub @ X198 @ sh)) | (X197 = X198))) & ! [X199 : d_term,X200 : d_term] : (((d2term @ X200) = (d2term @ X199)) => (X199 = X200)) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarind = $true) & ((hoasinduction_lem0 = $true) <=> ! [X201 : subst > term > subst > $o] : ~! [X202 : term > $o] : ~! [X203 : term] : ((X202 @ X203) = (X201 @ id @ X203 @ id))) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X204 : term > $o,X205 : subst,X206 : term > $o,X207 : term,X208 : term] : (((X206 @ (sub @ X208 @ (push @ X207 @ X205))) = $true) | ~((X204 @ X208) = $true))) & ! [X209 : d_subst] : (d_id = X209) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X210 : subst,X211 : term] : ((sub @ one @ (push @ X211 @ X210)) = X211) => ! [X212 : term,X213 : subst,X214 : term > $o,X215 : term > $o] : (~((X215 @ X212) = $true) | ($true = (X214 @ one)) | ~! [X216 : term] : ((X214 @ X216) = (X215 @ (sub @ X216 @ (push @ X212 @ X213))))))) & (hoaslaminj_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X217 : term > $o,X218 : term] : (((X217 @ X218) = $true) | ~! [X219 : term] : (~((var @ X219) = $true) | ((X217 @ X219) = $true)) | ~! [X220 : term] : (((X217 @ (lam @ X220)) = $true) | ~! [X221 : term] : (~((X217 @ X221) = $true) | ((X217 @ (sub @ X220 @ (push @ X221 @ id))) = $true))) | ~! [X222 : term,X223 : term] : (~((X217 @ X222) = $true) | ((X217 @ (ap @ X222 @ X223)) = $true) | ~((X217 @ X223) = $true))) => (! [X224 : subst > term > subst > $o,X225 : term,X226 : term] : (~! [X227 : term,X228 : term] : (~((X224 @ id @ X228 @ id) = $true) | ((X224 @ id @ (ap @ (sub @ X227 @ id) @ X228) @ id) = $true) | ~((X224 @ id @ X227 @ id) = $true)) | ~((X224 @ id @ X226 @ id) = $true) | ($true = (X224 @ id @ (ap @ X225 @ X226) @ id)) | ~((X224 @ id @ X225 @ id) = $true) | ~! [X229 : term,X230 : subst,X231 : subst,X232 : subst] : (((X224 @ X230 @ X229 @ (comp @ X231 @ X232)) = $true) | ~((X224 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231) @ X232) = $true)) | ~! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : (~((X224 @ X235 @ X234 @ (comp @ X233 @ X236)) = $true) | ((X224 @ (comp @ X235 @ X233) @ (sub @ X234 @ X233) @ X236) = $true))) => (! [X237 : term,X238 : subst > term > subst > $o] : (~! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (((X238 @ X241 @ X240 @ (comp @ X242 @ X239)) = $true) | ~((X238 @ (comp @ X241 @ X242) @ (sub @ X240 @ X242) @ X239) = $true)) | ~! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (~((X238 @ X244 @ X245 @ (comp @ X243 @ X246)) = $true) | ((X238 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) = $true)) | ~! [X247 : subst > term > term] : (~! [X248 : term] : (~($true = (X238 @ id @ X248 @ id)) | ((X238 @ id @ (X247 @ id @ X248) @ id) = $true)) | ~! [X249 : subst,X250 : subst,X251 : term] : ((X247 @ (comp @ X249 @ X250) @ (sub @ X251 @ X250)) = (sub @ (X247 @ X249 @ X251) @ X250)) | ((X238 @ id @ (lam @ (X247 @ sh @ one)) @ id) = $true)) | ((X238 @ id @ (lam @ X237) @ id) = $true) | ~! [X252 : term] : (~((X238 @ id @ X252 @ id) = $true) | ((X238 @ id @ (sub @ X237 @ (push @ X252 @ id)) @ id) = $true))) => ! [X253 : subst > term > subst > $o,X254 : term] : (~! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (((X253 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257) @ X255) = $true) | ~($true = (X253 @ X258 @ X256 @ (comp @ X257 @ X255)))) | ~! [X259 : term,X260 : term] : (~((X253 @ id @ X259 @ id) = $true) | ($true = (X253 @ id @ (ap @ (sub @ X259 @ id) @ X260) @ id)) | ~((X253 @ id @ X260 @ id) = $true)) | ~! [X261 : subst > term > term] : (~! [X262 : term] : (~($true = (X253 @ id @ X262 @ id)) | ($true = (X253 @ id @ (X261 @ id @ X262) @ id))) | ((X253 @ id @ (lam @ (X261 @ sh @ one)) @ id) = $true) | ~! [X263 : term,X264 : subst,X265 : subst] : ((X261 @ (comp @ X265 @ X264) @ (sub @ X263 @ X264)) = (sub @ (X261 @ X265 @ X263) @ X264))) | ~! [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (((X253 @ X267 @ X268 @ (comp @ X269 @ X266)) = $true) | ~((X253 @ (comp @ X267 @ X269) @ (sub @ X268 @ X269) @ X266) = $true)) | ~! [X270 : term] : (((X253 @ id @ X270 @ id) = $true) | ~($true = (var @ (sub @ X270 @ id)))) | ((X253 @ id @ X254 @ id) = $true)))))) & (! [X271 : term,X272 : term > $o,X273 : subst > term > subst > $o,X274 : term] : (~($true = (X272 @ X274)) | ~! [X275 : term] : ((X272 @ X275) = (X273 @ id @ X275 @ id)) | ~! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (~((X273 @ X276 @ X279 @ (comp @ X278 @ X277)) = $true) | ((X273 @ (comp @ X276 @ X278) @ (sub @ X279 @ X278) @ X277) = $true)) | ~! [X280 : term,X281 : term] : (((X273 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id) = $true) | ~((X273 @ id @ X280 @ id) = $true) | ~((X273 @ id @ X281 @ id) = $true)) | ~! [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (~((X273 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) = $true) | ((X273 @ X285 @ X283 @ (comp @ X282 @ X284)) = $true)) | ~((X272 @ X271) = $true) | ((X272 @ (ap @ X274 @ X271)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X286 : term] : ((sub @ X286 @ id) = X286) => (! [X287 : term,X288 : subst > term > subst > $o] : (~! [X289 : subst > term > term] : (~! [X290 : term] : (((X288 @ id @ (X289 @ id @ X290) @ id) = $true) | ~($true = (X288 @ id @ X290 @ id))) | ~! [X291 : term,X292 : subst,X293 : subst] : ((sub @ (X289 @ X292 @ X291) @ X293) = (X289 @ (comp @ X292 @ X293) @ (sub @ X291 @ X293))) | ($true = (X288 @ id @ (lam @ (X289 @ sh @ one)) @ id))) | ~! [X294 : term] : (($true = (X288 @ id @ (sub @ X287 @ (push @ X294 @ id)) @ id)) | ~((X288 @ id @ X294 @ id) = $true)) | ((X288 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id) = $true)) => ! [X295 : subst > term > subst > $o,X296 : term] : (((X295 @ id @ (lam @ X296) @ id) = $true) | ~! [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (~($true = (X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299)) | ((X295 @ X297 @ X300 @ (comp @ X298 @ X299)) = $true)) | ~! [X301 : subst > term > term] : (~! [X302 : subst,X303 : subst,X304 : term] : ((X301 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302)) = (sub @ (X301 @ X303 @ X304) @ X302)) | ~! [X305 : term] : (~((X295 @ id @ X305 @ id) = $true) | ((X295 @ id @ (X301 @ id @ X305) @ id) = $true)) | ($true = (X295 @ id @ (lam @ (X301 @ sh @ one)) @ id))) | ~! [X306 : term] : (~((X295 @ id @ X306 @ id) = $true) | ((X295 @ id @ (sub @ X296 @ (push @ X306 @ id)) @ id) = $true)) | ~! [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (((X295 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309) = $true) | ~((X295 @ X307 @ X310 @ (comp @ X308 @ X309)) = $true)))))) & (! [X311 : subst > term > subst > $o] : ~! [X312 : term > $o] : ~! [X313 : term] : ((X311 @ id @ X313 @ id) = (X312 @ X313)) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X314 : subst > term > term,X315 : term,X316 : term] : (~! [X317 : subst,X318 : term,X319 : subst] : ((X314 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317)) = (sub @ (X314 @ X319 @ X318) @ X317)) | ((ap @ (sub @ X315 @ id) @ X316) != (lam @ (X314 @ sh @ one))))) & (lamnotvar = $true) & ((! [X320 : term] : ((sub @ X320 @ id) = X320) => (! [X321 : subst > term > subst > $o,X322 : term] : (~! [X323 : term] : (((X321 @ id @ (sub @ X322 @ (push @ X323 @ id)) @ id) = $true) | ~($true = (X321 @ id @ X323 @ id))) | ((X321 @ id @ (lam @ (sub @ X322 @ (push @ one @ sh))) @ id) = $true) | ~! [X324 : subst > term > term] : (~! [X325 : subst,X326 : subst,X327 : term] : ((X324 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)) = (sub @ (X324 @ X325 @ X327) @ X326)) | ((X321 @ id @ (lam @ (X324 @ sh @ one)) @ id) = $true) | ~! [X328 : term] : (($true = (X321 @ id @ (X324 @ id @ X328) @ id)) | ~((X321 @ id @ X328 @ id) = $true)))) => ! [X329 : subst > term > subst > $o,X330 : term] : (~! [X331 : term] : (($true = (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)) | ~((X329 @ id @ X331 @ id) = $true)) | ~! [X332 : subst > term > term] : (~! [X333 : subst,X334 : term,X335 : subst] : ((X332 @ (comp @ X333 @ X335) @ (sub @ X334 @ X335)) = (sub @ (X332 @ X333 @ X334) @ X335)) | ((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) = $true) | ~! [X336 : term] : (((X329 @ id @ (X332 @ id @ X336) @ id) = $true) | ~($true = (X329 @ id @ X336 @ id)))) | ((X329 @ id @ (lam @ X330) @ id) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X337 : subst,X338 : term] : ((sub @ one @ (push @ X338 @ X337)) = X338) => (! [X339 : term,X340 : subst] : ((comp @ sh @ (push @ X339 @ X340)) = X340) => (! [X341 : subst] : ((comp @ X341 @ id) = X341) => (! [X342 : term > $o,X343 : term] : (~! [X344 : term,X345 : term] : (((X342 @ (ap @ X345 @ X344)) = $true) | ~((X342 @ X345) = $true) | ~((X342 @ X344) = $true)) | ~! [X346 : term] : (((X342 @ (lam @ X346)) = $true) | ~((X342 @ X346) = $true)) | ~! [X347 : term] : (~($true = (var @ X347)) | ((X342 @ X347) = $true)) | ((X342 @ X343) = $true)) => ! [X348 : term > $o,X349 : term,X350 : subst] : (~! [X351 : term,X352 : term] : (((X348 @ (ap @ X352 @ X351)) = $true) | ~((X348 @ X351) = $true) | ~((X348 @ X352) = $true)) | ~! [X353 : term] : (~! [X354 : term] : (($true = (X348 @ (sub @ X353 @ (push @ X354 @ id)))) | ~((X348 @ X354) = $true)) | ((X348 @ (lam @ X353)) = $true)) | ~! [X355 : term] : (~((var @ X355) = $true) | ($true = (X348 @ (sub @ X355 @ X350)))) | ((X348 @ (sub @ X349 @ X350)) = $true))))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (~! [X359 : term] : ((X357 @ X359) = (X356 @ id @ X359 @ id)) | ((X357 @ (lam @ X358)) = $true) | ~! [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (~((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) = $true) | ((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) = $true)) | ~! [X364 : term] : (~($true = (X357 @ X364)) | ((X357 @ (sub @ X358 @ (push @ X364 @ id))) = $true)) | ~! [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (~((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) = $true) | ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) = $true)) | ~! [X369 : subst > term > term] : (~! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ~((X356 @ id @ X370 @ id) = $true)) | ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) = $true) | ~! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X374 : term] : ((sub @ X374 @ id) = X374) <=> (axvarid = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X375 : subst > term > subst > $o,X376 : term] : (((X375 @ id @ (lam @ X376) @ id) = $true) | ~! [X377 : term] : (((X375 @ id @ (sub @ X376 @ (push @ X377 @ id)) @ id) = $true) | ~($true = (X375 @ id @ X377 @ id))) | ~! [X378 : subst > term > term] : (~! [X379 : term] : (((X375 @ id @ (X378 @ id @ X379) @ id) = $true) | ~((X375 @ id @ X379 @ id) = $true)) | ((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id) = $true) | ~! [X380 : subst,X381 : subst,X382 : term] : ((sub @ (X378 @ X380 @ X382) @ X381) = (X378 @ (comp @ X380 @ X381) @ (sub @ X382 @ X381)))))) & (! [X383 : term] : ((sub @ X383 @ id) = X383) <=> (termmset = $true)) & ((! [X384 : term,X385 : subst] : ((sub @ one @ (push @ X384 @ X385)) = X384) => (! [X386 : subst,X387 : term] : ((comp @ sh @ (push @ X387 @ X386)) = X386) => (! [X388 : term,X389 : term] : (((lam @ X389) != (lam @ X388)) | (X388 = X389)) => ! [X390 : subst,X391 : subst > term > term,X392 : term,X393 : subst > term > term] : (((X391 @ X390 @ X392) = (X393 @ X390 @ X392)) | ~! [X394 : subst,X395 : term,X396 : subst] : ((X393 @ (comp @ X396 @ X394) @ (sub @ X395 @ X394)) = (sub @ (X393 @ X396 @ X395) @ X394)) | ((lam @ (X391 @ sh @ one)) != (lam @ (X393 @ sh @ one))) | ~! [X397 : subst,X398 : term,X399 : subst] : ((X391 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399)) = (sub @ (X391 @ X397 @ X398) @ X399)))))) <=> (hoaslaminj_lthm = $true)) & ((induction2 = $true) <=> ! [X400 : term > $o,X401 : term] : (~! [X402 : term,X403 : term] : (($true = (X400 @ (ap @ X403 @ X402))) | ~((X400 @ X402) = $true) | ~((X400 @ X403) = $true)) | ((X400 @ X401) = $true) | ~! [X404 : term] : (~((var @ X404) = $true) | ((X400 @ X404) = $true)) | ~! [X405 : term] : (~! [X406 : term] : (~((X400 @ X406) = $true) | ((X400 @ (sub @ X405 @ (push @ X406 @ id))) = $true)) | ((X400 @ (lam @ X405)) = $true)))) & ((! [X408 : subst] : ((comp @ id @ X408) = X408) & ! [X407 : subst] : ((comp @ X407 @ id) = X407)) <=> (substmonoid = $true)) & ((axidl = $true) <=> ! [X409 : subst] : ((comp @ id @ X409) = X409)) & ! [X410 : d_term] : (d_one = X410) & (pushprop_lthm_orig = $true) & (! [X411 : term,X412 : term,X413 : term,X414 : term] : (((ap @ X412 @ X411) != (ap @ X413 @ X414)) | (X412 = X413)) <=> (apinj1 = $true)) & (pushprop_lem2v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop = $true) & (axvarshift = $true) & (pushprop_lem1v2_gthm = $true) & ~((var @ (d2term @ d_one)) = $true) & (! [X415 : term] : ~! [X416 : subst > term > term] : ((sub @ X415 @ (push @ one @ sh)) != (X416 @ sh @ one)) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem1_gthm = $true) & ((! [X417 : term] : ((sub @ X417 @ id) = X417) => ! [X418 : term] : ((sub @ X418 @ id) = X418)) <=> (termmset_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (axmap = $true) & ! [X419 : subst] : ? [X420 : d_subst] : ((d2subst @ X420) = X419) & ~(lamnotap = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X421 : subst > term > subst > $o,X422 : term] : (~! [X423 : subst > term > term] : (~! [X424 : term] : (((X421 @ id @ (X423 @ id @ X424) @ id) = $true) | ~((X421 @ id @ X424 @ id) = $true)) | ~! [X425 : term,X426 : subst,X427 : subst] : ((sub @ (X423 @ X427 @ X425) @ X426) = (X423 @ (comp @ X427 @ X426) @ (sub @ X425 @ X426))) | ((X421 @ id @ (lam @ (X423 @ sh @ one)) @ id) = $true)) | ((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id) = $true) | ~! [X428 : term] : (((X421 @ id @ (sub @ X422 @ (push @ X428 @ id)) @ id) = $true) | ~((X421 @ id @ X428 @ id) = $true)))) & (ulamvarsh = $true) & (! [X429 : term,X430 : term,X431 : subst > term > subst > $o] : (~((X431 @ id @ X429 @ id) = $true) | ~! [X432 : term,X433 : term] : (~((X431 @ id @ X432 @ id) = $true) | ((X431 @ id @ (ap @ (sub @ X432 @ id) @ X433) @ id) = $true) | ~((X431 @ id @ X433 @ id) = $true)) | ((X431 @ id @ (ap @ X430 @ X429) @ id) = $true) | ~! [X434 : term,X435 : subst,X436 : subst,X437 : subst] : (((X431 @ (comp @ X436 @ X435) @ (sub @ X434 @ X435) @ X437) = $true) | ~((X431 @ X436 @ X434 @ (comp @ X435 @ X437)) = $true)) | ~! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (((X431 @ X438 @ X439 @ (comp @ X441 @ X440)) = $true) | ~((X431 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440) = $true)) | ~($true = (X431 @ id @ X430 @ id))) <=> (hoasinduction_lem2 = $true)) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X442 : term,X443 : subst > term > subst > $o] : (~! [X444 : term] : (((X443 @ id @ (sub @ X442 @ (push @ X444 @ id)) @ id) = $true) | ~((X443 @ id @ X444 @ id) = $true)) | ~! [X445 : subst > term > term] : (~! [X446 : subst,X447 : term,X448 : subst] : ((sub @ (X445 @ X446 @ X447) @ X448) = (X445 @ (comp @ X446 @ X448) @ (sub @ X447 @ X448))) | ~! [X449 : term] : (~((X443 @ id @ X449 @ id) = $true) | ((X443 @ id @ (X445 @ id @ X449) @ id) = $true)) | ((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) = $true)) | ((X443 @ id @ (lam @ (sub @ X442 @ (push @ one @ sh))) @ id) = $true))) & (hoaslamnotap_gthm = $true) & ! [X450 : term] : ? [X451 : d_term] : ((d2term @ X451) = X450) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X452 : term,X453 : term,X454 : term,X455 : term] : (((ap @ (sub @ X455 @ id) @ X454) != (ap @ (sub @ X452 @ id) @ X453)) | (X453 = X454)) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X456 : subst,X457 : term > $o,X458 : term] : ~! [X459 : term > $o] : ~! [X460 : term] : ((X459 @ X460) = (X457 @ (sub @ X460 @ (push @ X458 @ X456))))) & ((laminj = $true) <=> ! [X461 : term,X462 : term] : (((lam @ X461) != (lam @ X462)) | (X461 = X462))) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((axshiftcons = $true) <=> ! [X463 : subst,X464 : term] : ((comp @ sh @ (push @ X464 @ X463)) = X463)) & (induction2lem_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((hoasinduction = $true) <=> ! [X465 : term,X466 : subst > term > subst > $o] : (~! [X467 : term] : (($true = (X466 @ id @ X467 @ id)) | ~((var @ (sub @ X467 @ id)) = $true)) | ~! [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (~((X466 @ X470 @ X468 @ (comp @ X471 @ X469)) = $true) | ((X466 @ (comp @ X470 @ X471) @ (sub @ X468 @ X471) @ X469) = $true)) | ~! [X472 : subst > term > term] : (~! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473)) | ~! [X476 : term] : (((X466 @ id @ (X472 @ id @ X476) @ id) = $true) | ~((X466 @ id @ X476 @ id) = $true)) | ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) = $true)) | ((X466 @ id @ X465 @ id) = $true) | ~! [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = (X466 @ X479 @ X480 @ (comp @ X478 @ X477))) | ~($true = (X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477))) | ~! [X481 : term,X482 : term] : (((X466 @ id @ (ap @ (sub @ X482 @ id) @ X481) @ id) = $true) | ~((X466 @ id @ X481 @ id) = $true) | ~($true = (X466 @ id @ X482 @ id))))) & (! [X483 : term] : ~! [X484 : subst > term > term] : ~! [X485 : subst,X486 : term] : ((sub @ X483 @ (push @ X486 @ X485)) = (X484 @ X485 @ X486)) <=> (hoasinduction_lem3v2_f = $true)) & (! [X487 : term,X488 : subst > term > subst > $o] : (~! [X489 : term,X490 : term] : (~((X488 @ id @ X490 @ id) = $true) | ((X488 @ id @ (ap @ (sub @ X489 @ id) @ X490) @ id) = $true) | ~($true = (X488 @ id @ X489 @ id))) | ~! [X491 : subst > term > term] : (~! [X492 : subst,X493 : term,X494 : subst] : ((sub @ (X491 @ X492 @ X493) @ X494) = (X491 @ (comp @ X492 @ X494) @ (sub @ X493 @ X494))) | ((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id) = $true) | ~! [X495 : term] : (~((X488 @ id @ X495 @ id) = $true) | ((X488 @ id @ (X491 @ id @ X495) @ id) = $true))) | ((X488 @ id @ X487 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X496 : term] : ((sub @ X496 @ id) = X496) => (! [X497 : term > $o,X498 : subst,X499 : term] : (((X497 @ (sub @ X499 @ X498)) = $true) | ~! [X500 : term,X501 : term] : (~((X497 @ X500) = $true) | ((X497 @ (ap @ X500 @ X501)) = $true) | ~((X497 @ X501) = $true)) | ~! [X502 : term] : (((X497 @ (lam @ X502)) = $true) | ~! [X503 : term] : (~((X497 @ X503) = $true) | ((X497 @ (sub @ X502 @ (push @ X503 @ id))) = $true))) | ~! [X504 : term] : (~((var @ X504) = $true) | ($true = (X497 @ (sub @ X504 @ X498))))) => ! [X505 : term > $o,X506 : term] : (($true = (X505 @ X506)) | ~! [X507 : term] : (~! [X508 : term] : (~((X505 @ X508) = $true) | ((X505 @ (sub @ X507 @ (push @ X508 @ id))) = $true)) | ($true = (X505 @ (lam @ X507)))) | ~! [X509 : term,X510 : term] : (((X505 @ (ap @ X509 @ X510)) = $true) | ~((X505 @ X509) = $true) | ~((X505 @ X510) = $true)) | ~! [X511 : term] : (~((var @ X511) = $true) | ((X505 @ X511) = $true))))) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X512 : subst > term > subst > $o,X513 : term > $o,X514 : term] : (~! [X515 : term] : ((X513 @ X515) = (X512 @ id @ X515 @ id)) | ($true = (X513 @ (lam @ X514))) | ~! [X516 : subst > term > term] : (~! [X517 : subst,X518 : subst,X519 : term] : ((sub @ (X516 @ X518 @ X519) @ X517) = (X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) | ((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id) = $true) | ~! [X520 : term] : (((X512 @ id @ (X516 @ id @ X520) @ id) = $true) | ~((X512 @ id @ X520 @ id) = $true))) | ~! [X521 : term] : (((X513 @ (sub @ X514 @ (push @ X521 @ id))) = $true) | ~((X513 @ X521) = $true)))) & ((hoaslaminj = $true) <=> ! [X522 : subst > term > term,X523 : subst,X524 : subst > term > term,X525 : term] : (((lam @ (X522 @ sh @ one)) != (lam @ (X524 @ sh @ one))) | ((X524 @ X523 @ X525) = (X522 @ X523 @ X525)) | ~! [X526 : subst,X527 : term,X528 : subst] : ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)) = (sub @ (X524 @ X526 @ X527) @ X528)) | ~! [X529 : term,X530 : subst,X531 : subst] : ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)) = (sub @ (X522 @ X530 @ X529) @ X531)))) & (pushprop_gthm = $true) & ((induction2lem = $true) <=> ! [X532 : term,X533 : subst,X534 : term > $o] : (~! [X535 : term] : (((X534 @ (lam @ X535)) = $true) | ~! [X536 : term] : (((X534 @ (sub @ X535 @ (push @ X536 @ id))) = $true) | ~((X534 @ X536) = $true))) | ((X534 @ (sub @ X532 @ X533)) = $true) | ~! [X537 : term] : (~((var @ X537) = $true) | ((X534 @ (sub @ X537 @ X533)) = $true)) | ~! [X538 : term,X539 : term] : (~((X534 @ X539) = $true) | ~((X534 @ X538) = $true) | ((X534 @ (ap @ X538 @ X539)) = $true)))) & (hoasapnotvar_gthm = $true)),
% 32.60/5.94 inference(rectify,[status(thm)],[f8])).
% 32.60/5.94 thf(f8,plain,(
% 32.60/5.94 (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (~! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4)) | ~((X1 @ X3) = $true) | ((X0 @ one) = $true))) & ((! [X5 : term] : ((sub @ X5 @ id) = X5) => (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7))) => ! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lthm = $true) & (! [X14 : term > $o,X15 : term,X16 : subst] : ~! [X17 : term > $o] : ~! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18)) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotvar = $true) & (one = (d2term @ d_one)) & ((pushprop_lem1_lthm = $true) <=> (! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) => (! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) => ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : (((X25 @ (sub @ X27 @ (push @ X23 @ X26))) = $true) | ~((X24 @ X27) = $true))))) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X28 : term] : ~! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one))) & ((hoasapinj1 = $true) <=> ! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X33) | ((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)))) & (hoasapinj1_gthm = $true) & (axabs = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X39 : term] : ~! [X40 : subst > term > term] : ~! [X41 : subst,X42 : term] : ((sub @ X39 @ (push @ X42 @ X41)) = (X40 @ X41 @ X42)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X43 : subst > term > subst > $o,X44 : term] : (~! [X45 : term,X46 : subst,X47 : subst,X48 : subst] : (((X43 @ (comp @ X47 @ X48) @ (sub @ X45 @ X48) @ X46) = $true) | ~((X43 @ X47 @ X45 @ (comp @ X48 @ X46)) = $true)) | ~! [X49 : subst,X50 : subst,X51 : subst,X52 : term] : (~((X43 @ (comp @ X49 @ X51) @ (sub @ X52 @ X51) @ X50) = $true) | ($true = (X43 @ X49 @ X52 @ (comp @ X51 @ X50)))) | ~! [X53 : term] : (~($true = (X43 @ id @ X53 @ id)) | ((X43 @ id @ (sub @ X44 @ (push @ X53 @ id)) @ id) = $true)) | ((X43 @ id @ (lam @ X44) @ id) = $true) | ~! [X54 : subst > term > term] : (~! [X55 : subst,X56 : subst,X57 : term] : ((sub @ (X54 @ X55 @ X57) @ X56) = (X54 @ (comp @ X55 @ X56) @ (sub @ X57 @ X56))) | ~! [X58 : term] : (((X43 @ id @ (X54 @ id @ X58) @ id) = $true) | ~((X43 @ id @ X58 @ id) = $true)) | ((X43 @ id @ (lam @ (X54 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & ! [X59 : d_subst,X60 : d_subst] : (((d2subst @ X59) = (d2subst @ X60)) => (X59 = X60)) & ((hoasapinj2_lthm = $true) <=> (! [X61 : term,X62 : term,X63 : term,X64 : term] : ((X62 = X63) | ((ap @ X61 @ X63) != (ap @ X64 @ X62))) => ! [X65 : term,X66 : term,X67 : term,X68 : term] : (((ap @ (sub @ X68 @ id) @ X65) != (ap @ (sub @ X67 @ id) @ X66)) | (X65 = X66)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X69 : term,X70 : subst > term > subst > $o] : (((X70 @ id @ (lam @ (sub @ X69 @ (push @ one @ sh))) @ id) = $true) | ~! [X71 : term] : (($true = (X70 @ id @ (sub @ X69 @ (push @ X71 @ id)) @ id)) | ~((X70 @ id @ X71 @ id) = $true)) | ~! [X72 : subst > term > term,X73 : term] : (~! [X74 : subst,X75 : subst,X76 : term] : ((sub @ (X72 @ X74 @ X76) @ X75) = (sub @ (sub @ X73 @ (push @ X76 @ X74)) @ X75)) | ~! [X77 : subst,X78 : term,X79 : subst] : ((sub @ X73 @ (push @ (sub @ X78 @ X79) @ (comp @ X77 @ X79))) = (X72 @ (comp @ X77 @ X79) @ (sub @ X78 @ X79))) | ~! [X80 : term] : (~((X70 @ id @ X80 @ id) = $true) | ($true = (X70 @ id @ (X72 @ id @ X80) @ id))) | ((X70 @ id @ (lam @ (X72 @ sh @ one)) @ id) = $true)))) & (apnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lthm_3 = $true) <=> (! [X81 : subst > term > subst > $o] : ~! [X82 : term > $o] : ~! [X83 : term] : ((X81 @ id @ X83 @ id) = (X82 @ X83)) => (! [X84 : term > $o,X85 : term] : (($true = (X84 @ X85)) | ~! [X86 : term,X87 : term] : (~((X84 @ X87) = $true) | ((X84 @ (ap @ X87 @ X86)) = $true) | ~((X84 @ X86) = $true)) | ~! [X88 : term] : (~((var @ X88) = $true) | ((X84 @ X88) = $true)) | ~! [X89 : term] : (((X84 @ (lam @ X89)) = $true) | ~! [X90 : term] : (((X84 @ (sub @ X89 @ (push @ X90 @ id))) = $true) | ~((X84 @ X90) = $true)))) => (! [X91 : term] : ((sub @ X91 @ id) = X91) => (! [X92 : subst > term > subst > $o,X93 : term > $o,X94 : term] : (($true = (X93 @ (lam @ X94))) | ~! [X95 : term] : ((X93 @ X95) = (X92 @ id @ X95 @ id)) | ~! [X96 : subst > term > term] : (($true = (X92 @ id @ (lam @ (X96 @ sh @ one)) @ id)) | ~! [X97 : term] : (~((X92 @ id @ X97 @ id) = $true) | ((X92 @ id @ (X96 @ id @ X97) @ id) = $true)) | ~! [X98 : subst,X99 : term,X100 : subst] : ((X96 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98)) = (sub @ (X96 @ X100 @ X99) @ X98))) | ~! [X101 : term] : (((X93 @ (sub @ X94 @ (push @ X101 @ id))) = $true) | ~((X93 @ X101) = $true))) => ! [X102 : subst > term > subst > $o,X103 : term] : (~! [X104 : subst,X105 : subst,X106 : term,X107 : subst] : (($true = (X102 @ (comp @ X104 @ X107) @ (sub @ X106 @ X107) @ X105)) | ~((X102 @ X104 @ X106 @ (comp @ X107 @ X105)) = $true)) | ~! [X108 : subst,X109 : subst,X110 : subst,X111 : term] : (((X102 @ X108 @ X111 @ (comp @ X109 @ X110)) = $true) | ~((X102 @ (comp @ X108 @ X109) @ (sub @ X111 @ X109) @ X110) = $true)) | ~! [X112 : term,X113 : term] : (~((X102 @ id @ X112 @ id) = $true) | ~((X102 @ id @ X113 @ id) = $true) | ((X102 @ id @ (ap @ (sub @ X113 @ id) @ X112) @ id) = $true)) | ~! [X114 : term] : (((X102 @ id @ X114 @ id) = $true) | ~((var @ (sub @ X114 @ id)) = $true)) | ((X102 @ id @ X103 @ id) = $true) | ~! [X115 : subst > term > term] : (~! [X116 : subst,X117 : term,X118 : subst] : ((sub @ (X115 @ X118 @ X117) @ X116) = (X115 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116))) | ~! [X119 : term] : (~((X102 @ id @ X119 @ id) = $true) | ((X102 @ id @ (X115 @ id @ X119) @ id) = $true)) | ($true = (X102 @ id @ (lam @ (X115 @ sh @ one)) @ id))))))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X120 : subst > term > subst > $o] : ~! [X121 : term > $o] : ~! [X122 : term] : ((X121 @ X122) = (X120 @ id @ X122 @ id)) => (! [X123 : term,X124 : term > $o] : (~! [X125 : term,X126 : term] : (~($true = (X124 @ X126)) | ((X124 @ (ap @ X125 @ X126)) = $true) | ~((X124 @ X125) = $true)) | ~! [X127 : term] : (($true = (X124 @ X127)) | ~((var @ X127) = $true)) | ~! [X128 : term] : (((X124 @ (lam @ X128)) = $true) | ~! [X129 : term] : (~((X124 @ X129) = $true) | ((X124 @ (sub @ X128 @ (push @ X129 @ id))) = $true))) | ((X124 @ X123) = $true)) => (! [X130 : term] : ((sub @ X130 @ id) = X130) => (! [X131 : subst > term > subst > $o,X132 : term,X133 : term > $o] : (($true = (X133 @ (lam @ X132))) | ~! [X134 : term] : (~((X133 @ X134) = $true) | ((X133 @ (sub @ X132 @ (push @ X134 @ id))) = $true)) | ~! [X135 : term] : ((X131 @ id @ X135 @ id) = (X133 @ X135)) | ~! [X136 : subst > term > term] : (((X131 @ id @ (lam @ (X136 @ sh @ one)) @ id) = $true) | ~! [X137 : term] : (~((X131 @ id @ X137 @ id) = $true) | ((X131 @ id @ (X136 @ id @ X137) @ id) = $true)) | ~! [X138 : subst,X139 : term,X140 : subst] : ((sub @ (X136 @ X138 @ X139) @ X140) = (X136 @ (comp @ X138 @ X140) @ (sub @ X139 @ X140))))) => ! [X141 : subst > term > subst > $o,X142 : term] : (((X141 @ id @ X142 @ id) = $true) | ~! [X143 : subst > term > term] : (~! [X144 : term] : (~($true = (X141 @ id @ X144 @ id)) | ((X141 @ id @ (X143 @ id @ X144) @ id) = $true)) | ((X141 @ id @ (lam @ (X143 @ sh @ one)) @ id) = $true) | ~! [X145 : term,X146 : subst,X147 : subst] : ((X143 @ (comp @ X147 @ X146) @ (sub @ X145 @ X146)) = (sub @ (X143 @ X147 @ X145) @ X146))) | ~! [X148 : term,X149 : term] : (~((X141 @ id @ X149 @ id) = $true) | ~((X141 @ id @ X148 @ id) = $true) | ((X141 @ id @ (ap @ (sub @ X149 @ id) @ X148) @ id) = $true)))))))) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & ~(ulamvar1 = $true) & (hoasinduction_lem1 = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X150 : subst] : ((comp @ id @ X150) = X150) => (! [X151 : subst] : ((comp @ X151 @ id) = X151) => (! [X152 : subst] : ((comp @ X152 @ id) = X152) & ! [X153 : subst] : ((comp @ id @ X153) = X153)))) <=> (substmonoid_lthm = $true)) & (! [X154 : term > $o,X155 : term] : (~! [X156 : term,X157 : term] : (((X154 @ (ap @ X157 @ X156)) = $true) | ~((X154 @ X157) = $true) | ~((X154 @ X156) = $true)) | ~! [X158 : term] : (~($true = (X154 @ X158)) | ((X154 @ (lam @ X158)) = $true)) | ((X154 @ X155) = $true) | ~! [X159 : term] : (($true = (X154 @ X159)) | ~($true = (var @ X159)))) <=> (induction = $true)) & ((axvarcons = $true) <=> ! [X160 : subst,X161 : term] : ((sub @ one @ (push @ X161 @ X160)) = X161)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X162 : term] : ~! [X163 : subst > term > term] : ~! [X164 : term,X165 : subst] : ((X163 @ X165 @ X164) = (sub @ X162 @ (push @ X164 @ X165))) => (! [X166 : term] : ((sub @ X166 @ id) = X166) => ! [X167 : subst > term > subst > $o,X168 : term > $o,X169 : term] : (~! [X170 : term] : (($true = (X168 @ (sub @ X169 @ (push @ X170 @ id)))) | ~($true = (X168 @ X170))) | ~! [X171 : subst > term > term] : (~! [X172 : term] : (~((X167 @ id @ X172 @ id) = $true) | ((X167 @ id @ (X171 @ id @ X172) @ id) = $true)) | ~! [X173 : subst,X174 : subst,X175 : term] : ((sub @ (X171 @ X173 @ X175) @ X174) = (X171 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174))) | ($true = (X167 @ id @ (lam @ (X171 @ sh @ one)) @ id))) | ((X168 @ (lam @ X169)) = $true) | ~! [X176 : term] : ((X168 @ X176) = (X167 @ id @ X176 @ id)))))) & (! [X177 : subst] : ((comp @ X177 @ id) = X177) <=> (axidr = $true)) & (! [X178 : term,X179 : term,X180 : term,X181 : term] : (((ap @ X178 @ X180) != (ap @ X179 @ X181)) | (X180 = X181)) <=> (apinj2 = $true)) & (hoasinduction_lem3_gthm = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X182 : term] : ((sub @ X182 @ id) = X182) => ! [X183 : subst > term > subst > $o,X184 : term,X185 : term > $o] : (($true = (X185 @ (lam @ X184))) | ~! [X186 : subst,X187 : subst,X188 : subst,X189 : term] : (((X183 @ (comp @ X188 @ X187) @ (sub @ X189 @ X187) @ X186) = $true) | ~((X183 @ X188 @ X189 @ (comp @ X187 @ X186)) = $true)) | ~! [X190 : term] : (((X185 @ (sub @ X184 @ (push @ X190 @ id))) = $true) | ~((X185 @ X190) = $true)) | ~! [X191 : subst > term > term] : (($true = (X183 @ id @ (lam @ (X191 @ sh @ one)) @ id)) | ~! [X192 : term] : (((X183 @ id @ (X191 @ id @ X192) @ id) = $true) | ~($true = (X183 @ id @ X192 @ id))) | ~! [X193 : term,X194 : subst,X195 : subst] : ((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195)) = (sub @ (X191 @ X194 @ X193) @ X195))) | ~! [X196 : subst,X197 : term,X198 : subst,X199 : subst] : (~($true = (X183 @ (comp @ X196 @ X198) @ (sub @ X197 @ X198) @ X199)) | ((X183 @ X196 @ X197 @ (comp @ X198 @ X199)) = $true)) | ~! [X200 : term] : ((X183 @ id @ X200 @ id) = (X185 @ X200))))) & (axassoc = $true) & (hoasapinj2_gthm = $true) & (termmset_gthm = $true) & (! [X201 : subst] : ((push @ (sub @ one @ X201) @ (comp @ sh @ X201)) = X201) <=> (axscons = $true)) & (! [X202 : term,X203 : term] : ((X202 = X203) | ((sub @ X202 @ sh) != (sub @ X203 @ sh))) <=> (shinj = $true)) & ! [X204 : d_term,X205 : d_term] : (((d2term @ X205) = (d2term @ X204)) => (X204 = X205)) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarind = $true) & ((hoasinduction_lem0 = $true) <=> ! [X206 : subst > term > subst > $o] : ~! [X207 : term > $o] : ~! [X208 : term] : ((X206 @ id @ X208 @ id) = (X207 @ X208))) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X209 : term > $o,X210 : subst,X211 : term > $o,X212 : term,X213 : term] : (((X211 @ (sub @ X213 @ (push @ X212 @ X210))) = $true) | ~((X209 @ X213) = $true))) & ! [X214 : d_subst] : (d_id = X214) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X215 : subst,X216 : term] : ((sub @ one @ (push @ X216 @ X215)) = X216) => ! [X217 : term,X218 : subst,X219 : term > $o,X220 : term > $o] : (~((X220 @ X217) = $true) | ((X219 @ one) = $true) | ~! [X221 : term] : ((X219 @ X221) = (X220 @ (sub @ X221 @ (push @ X217 @ X218))))))) & (hoaslaminj_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X222 : term > $o,X223 : term] : (((X222 @ X223) = $true) | ~! [X224 : term] : (~((var @ X224) = $true) | ((X222 @ X224) = $true)) | ~! [X225 : term] : (((X222 @ (lam @ X225)) = $true) | ~! [X226 : term] : (~((X222 @ X226) = $true) | ((X222 @ (sub @ X225 @ (push @ X226 @ id))) = $true))) | ~! [X227 : term,X228 : term] : (~($true = (X222 @ X227)) | ((X222 @ (ap @ X227 @ X228)) = $true) | ~((X222 @ X228) = $true))) => (! [X229 : subst > term > subst > $o,X230 : term,X231 : term] : (~! [X232 : term,X233 : term] : (~((X229 @ id @ X233 @ id) = $true) | ((X229 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id) = $true) | ~((X229 @ id @ X232 @ id) = $true)) | ~((X229 @ id @ X231 @ id) = $true) | ((X229 @ id @ (ap @ X230 @ X231) @ id) = $true) | ~((X229 @ id @ X230 @ id) = $true) | ~! [X234 : term,X235 : subst,X236 : subst,X237 : subst] : (((X229 @ X235 @ X234 @ (comp @ X236 @ X237)) = $true) | ~((X229 @ (comp @ X235 @ X236) @ (sub @ X234 @ X236) @ X237) = $true)) | ~! [X238 : subst,X239 : term,X240 : subst,X241 : subst] : (~((X229 @ X240 @ X239 @ (comp @ X238 @ X241)) = $true) | ((X229 @ (comp @ X240 @ X238) @ (sub @ X239 @ X238) @ X241) = $true))) => (! [X242 : term,X243 : subst > term > subst > $o] : (~! [X244 : subst,X245 : term,X246 : subst,X247 : subst] : (((X243 @ X246 @ X245 @ (comp @ X247 @ X244)) = $true) | ~((X243 @ (comp @ X246 @ X247) @ (sub @ X245 @ X247) @ X244) = $true)) | ~! [X248 : subst,X249 : subst,X250 : term,X251 : subst] : (~((X243 @ X249 @ X250 @ (comp @ X248 @ X251)) = $true) | ((X243 @ (comp @ X249 @ X248) @ (sub @ X250 @ X248) @ X251) = $true)) | ~! [X252 : subst > term > term] : (~! [X253 : term] : (~((X243 @ id @ X253 @ id) = $true) | ((X243 @ id @ (X252 @ id @ X253) @ id) = $true)) | ~! [X254 : subst,X255 : subst,X256 : term] : ((X252 @ (comp @ X254 @ X255) @ (sub @ X256 @ X255)) = (sub @ (X252 @ X254 @ X256) @ X255)) | ((X243 @ id @ (lam @ (X252 @ sh @ one)) @ id) = $true)) | ((X243 @ id @ (lam @ X242) @ id) = $true) | ~! [X257 : term] : (~((X243 @ id @ X257 @ id) = $true) | ((X243 @ id @ (sub @ X242 @ (push @ X257 @ id)) @ id) = $true))) => ! [X258 : subst > term > subst > $o,X259 : term] : (~! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (((X258 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262) @ X260) = $true) | ~($true = (X258 @ X263 @ X261 @ (comp @ X262 @ X260)))) | ~! [X264 : term,X265 : term] : (~((X258 @ id @ X264 @ id) = $true) | ($true = (X258 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) | ~((X258 @ id @ X265 @ id) = $true)) | ~! [X266 : subst > term > term] : (~! [X267 : term] : (~((X258 @ id @ X267 @ id) = $true) | ((X258 @ id @ (X266 @ id @ X267) @ id) = $true)) | ((X258 @ id @ (lam @ (X266 @ sh @ one)) @ id) = $true) | ~! [X268 : term,X269 : subst,X270 : subst] : ((X266 @ (comp @ X270 @ X269) @ (sub @ X268 @ X269)) = (sub @ (X266 @ X270 @ X268) @ X269))) | ~! [X271 : subst,X272 : subst,X273 : term,X274 : subst] : (((X258 @ X272 @ X273 @ (comp @ X274 @ X271)) = $true) | ~((X258 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271) = $true)) | ~! [X275 : term] : (((X258 @ id @ X275 @ id) = $true) | ~((var @ (sub @ X275 @ id)) = $true)) | ((X258 @ id @ X259 @ id) = $true)))))) & (! [X276 : term,X277 : term > $o,X278 : subst > term > subst > $o,X279 : term] : (~($true = (X277 @ X279)) | ~! [X280 : term] : ((X278 @ id @ X280 @ id) = (X277 @ X280)) | ~! [X281 : subst,X282 : subst,X283 : subst,X284 : term] : (~((X278 @ X281 @ X284 @ (comp @ X283 @ X282)) = $true) | ((X278 @ (comp @ X281 @ X283) @ (sub @ X284 @ X283) @ X282) = $true)) | ~! [X285 : term,X286 : term] : (((X278 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id) = $true) | ~((X278 @ id @ X285 @ id) = $true) | ~((X278 @ id @ X286 @ id) = $true)) | ~! [X287 : subst,X288 : term,X289 : subst,X290 : subst] : (~((X278 @ (comp @ X290 @ X287) @ (sub @ X288 @ X287) @ X289) = $true) | ((X278 @ X290 @ X288 @ (comp @ X287 @ X289)) = $true)) | ~($true = (X277 @ X276)) | ((X277 @ (ap @ X279 @ X276)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X291 : term] : ((sub @ X291 @ id) = X291) => (! [X292 : term,X293 : subst > term > subst > $o] : (~! [X294 : subst > term > term] : (~! [X295 : term] : (($true = (X293 @ id @ (X294 @ id @ X295) @ id)) | ~($true = (X293 @ id @ X295 @ id))) | ~! [X296 : term,X297 : subst,X298 : subst] : ((sub @ (X294 @ X297 @ X296) @ X298) = (X294 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298))) | ((X293 @ id @ (lam @ (X294 @ sh @ one)) @ id) = $true)) | ~! [X299 : term] : (((X293 @ id @ (sub @ X292 @ (push @ X299 @ id)) @ id) = $true) | ~((X293 @ id @ X299 @ id) = $true)) | ((X293 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id) = $true)) => ! [X300 : subst > term > subst > $o,X301 : term] : (((X300 @ id @ (lam @ X301) @ id) = $true) | ~! [X302 : subst,X303 : subst,X304 : subst,X305 : term] : (~((X300 @ (comp @ X302 @ X303) @ (sub @ X305 @ X303) @ X304) = $true) | ((X300 @ X302 @ X305 @ (comp @ X303 @ X304)) = $true)) | ~! [X306 : subst > term > term] : (~! [X307 : subst,X308 : subst,X309 : term] : ((X306 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307)) = (sub @ (X306 @ X308 @ X309) @ X307)) | ~! [X310 : term] : (~($true = (X300 @ id @ X310 @ id)) | ($true = (X300 @ id @ (X306 @ id @ X310) @ id))) | ((X300 @ id @ (lam @ (X306 @ sh @ one)) @ id) = $true)) | ~! [X311 : term] : (~((X300 @ id @ X311 @ id) = $true) | ((X300 @ id @ (sub @ X301 @ (push @ X311 @ id)) @ id) = $true)) | ~! [X312 : subst,X313 : subst,X314 : subst,X315 : term] : (((X300 @ (comp @ X312 @ X313) @ (sub @ X315 @ X313) @ X314) = $true) | ~((X300 @ X312 @ X315 @ (comp @ X313 @ X314)) = $true)))))) & (! [X316 : subst > term > subst > $o] : ~! [X317 : term > $o] : ~! [X318 : term] : ((X316 @ id @ X318 @ id) = (X317 @ X318)) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X319 : subst > term > term,X320 : term,X321 : term] : (((ap @ (sub @ X320 @ id) @ X321) != (lam @ (X319 @ sh @ one))) | ~! [X322 : subst,X323 : term,X324 : subst] : ((sub @ (X319 @ X324 @ X323) @ X322) = (X319 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))))) & (lamnotvar = $true) & ((! [X325 : term] : ((sub @ X325 @ id) = X325) => (! [X326 : subst > term > subst > $o,X327 : term] : (~! [X328 : term] : (($true = (X326 @ id @ (sub @ X327 @ (push @ X328 @ id)) @ id)) | ~((X326 @ id @ X328 @ id) = $true)) | ((X326 @ id @ (lam @ (sub @ X327 @ (push @ one @ sh))) @ id) = $true) | ~! [X329 : subst > term > term] : (~! [X330 : subst,X331 : subst,X332 : term] : ((sub @ (X329 @ X330 @ X332) @ X331) = (X329 @ (comp @ X330 @ X331) @ (sub @ X332 @ X331))) | ((X326 @ id @ (lam @ (X329 @ sh @ one)) @ id) = $true) | ~! [X333 : term] : (((X326 @ id @ (X329 @ id @ X333) @ id) = $true) | ~((X326 @ id @ X333 @ id) = $true)))) => ! [X334 : subst > term > subst > $o,X335 : term] : (~! [X336 : term] : (((X334 @ id @ (sub @ X335 @ (push @ X336 @ id)) @ id) = $true) | ~((X334 @ id @ X336 @ id) = $true)) | ~! [X337 : subst > term > term] : (~! [X338 : subst,X339 : term,X340 : subst] : ((X337 @ (comp @ X338 @ X340) @ (sub @ X339 @ X340)) = (sub @ (X337 @ X338 @ X339) @ X340)) | ($true = (X334 @ id @ (lam @ (X337 @ sh @ one)) @ id)) | ~! [X341 : term] : (((X334 @ id @ (X337 @ id @ X341) @ id) = $true) | ~((X334 @ id @ X341 @ id) = $true))) | ((X334 @ id @ (lam @ X335) @ id) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X342 : subst,X343 : term] : ((sub @ one @ (push @ X343 @ X342)) = X343) => (! [X344 : term,X345 : subst] : ((comp @ sh @ (push @ X344 @ X345)) = X345) => (! [X346 : subst] : ((comp @ X346 @ id) = X346) => (! [X347 : term > $o,X348 : term] : (~! [X349 : term,X350 : term] : (((X347 @ (ap @ X350 @ X349)) = $true) | ~((X347 @ X350) = $true) | ~((X347 @ X349) = $true)) | ~! [X351 : term] : (((X347 @ (lam @ X351)) = $true) | ~((X347 @ X351) = $true)) | ~! [X352 : term] : (~((var @ X352) = $true) | ((X347 @ X352) = $true)) | ((X347 @ X348) = $true)) => ! [X353 : term > $o,X354 : term,X355 : subst] : (~! [X356 : term,X357 : term] : (((X353 @ (ap @ X357 @ X356)) = $true) | ~((X353 @ X356) = $true) | ~((X353 @ X357) = $true)) | ~! [X358 : term] : (~! [X359 : term] : (((X353 @ (sub @ X358 @ (push @ X359 @ id))) = $true) | ~((X353 @ X359) = $true)) | ((X353 @ (lam @ X358)) = $true)) | ~! [X360 : term] : (~((var @ X360) = $true) | ($true = (X353 @ (sub @ X360 @ X355)))) | ((X353 @ (sub @ X354 @ X355)) = $true))))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X361 : subst > term > subst > $o,X362 : term > $o,X363 : term] : (~! [X364 : term] : ((X361 @ id @ X364 @ id) = (X362 @ X364)) | ((X362 @ (lam @ X363)) = $true) | ~! [X365 : term,X366 : subst,X367 : subst,X368 : subst] : (~((X361 @ X366 @ X365 @ (comp @ X367 @ X368)) = $true) | ((X361 @ (comp @ X366 @ X367) @ (sub @ X365 @ X367) @ X368) = $true)) | ~! [X369 : term] : (~((X362 @ X369) = $true) | ((X362 @ (sub @ X363 @ (push @ X369 @ id))) = $true)) | ~! [X370 : subst,X371 : subst,X372 : subst,X373 : term] : (~((X361 @ (comp @ X372 @ X370) @ (sub @ X373 @ X370) @ X371) = $true) | ((X361 @ X372 @ X373 @ (comp @ X370 @ X371)) = $true)) | ~! [X374 : subst > term > term] : (~! [X375 : term] : (((X361 @ id @ (X374 @ id @ X375) @ id) = $true) | ~((X361 @ id @ X375 @ id) = $true)) | ($true = (X361 @ id @ (lam @ (X374 @ sh @ one)) @ id)) | ~! [X376 : term,X377 : subst,X378 : subst] : ((X374 @ (comp @ X377 @ X378) @ (sub @ X376 @ X378)) = (sub @ (X374 @ X377 @ X376) @ X378))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X382 : term] : ((sub @ X382 @ id) = X382) <=> (axvarid = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X383 : subst > term > subst > $o,X384 : term] : (((X383 @ id @ (lam @ X384) @ id) = $true) | ~! [X385 : term] : (((X383 @ id @ (sub @ X384 @ (push @ X385 @ id)) @ id) = $true) | ~((X383 @ id @ X385 @ id) = $true)) | ~! [X386 : subst > term > term] : (~! [X387 : term] : (((X383 @ id @ (X386 @ id @ X387) @ id) = $true) | ~((X383 @ id @ X387 @ id) = $true)) | ($true = (X383 @ id @ (lam @ (X386 @ sh @ one)) @ id)) | ~! [X388 : subst,X389 : subst,X390 : term] : ((sub @ (X386 @ X388 @ X390) @ X389) = (X386 @ (comp @ X388 @ X389) @ (sub @ X390 @ X389)))))) & (! [X391 : term] : ((sub @ X391 @ id) = X391) <=> (termmset = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X392 : term,X393 : subst] : ((sub @ one @ (push @ X392 @ X393)) = X392) => (! [X394 : subst,X395 : term] : ((comp @ sh @ (push @ X395 @ X394)) = X394) => (! [X396 : term,X397 : term] : ((X396 = X397) | ((lam @ X396) != (lam @ X397))) => ! [X398 : subst,X399 : subst > term > term,X400 : term,X401 : subst > term > term] : (~! [X402 : subst,X403 : term,X404 : subst] : ((sub @ (X401 @ X404 @ X403) @ X402) = (X401 @ (comp @ X404 @ X402) @ (sub @ X403 @ X402))) | ~! [X405 : subst,X406 : term,X407 : subst] : ((X399 @ (comp @ X405 @ X407) @ (sub @ X406 @ X407)) = (sub @ (X399 @ X405 @ X406) @ X407)) | ((X399 @ X398 @ X400) = (X401 @ X398 @ X400)) | ((lam @ (X399 @ sh @ one)) != (lam @ (X401 @ sh @ one)))))))) & ((induction2 = $true) <=> ! [X408 : term > $o,X409 : term] : (~! [X410 : term,X411 : term] : (((X408 @ (ap @ X411 @ X410)) = $true) | ~((X408 @ X410) = $true) | ~((X408 @ X411) = $true)) | ($true = (X408 @ X409)) | ~! [X412 : term] : (~((var @ X412) = $true) | ($true = (X408 @ X412))) | ~! [X413 : term] : (~! [X414 : term] : (~((X408 @ X414) = $true) | ((X408 @ (sub @ X413 @ (push @ X414 @ id))) = $true)) | ((X408 @ (lam @ X413)) = $true)))) & ((! [X415 : subst] : ((comp @ X415 @ id) = X415) & ! [X416 : subst] : ((comp @ id @ X416) = X416)) <=> (substmonoid = $true)) & ((axidl = $true) <=> ! [X417 : subst] : ((comp @ id @ X417) = X417)) & ! [X418 : d_term] : (d_one = X418) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) <=> ! [X419 : term,X420 : term,X421 : term,X422 : term] : ((X420 = X421) | ((ap @ X421 @ X422) != (ap @ X420 @ X419)))) & (pushprop_lem2v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop = $true) & (axvarshift = $true) & (pushprop_lem1v2_gthm = $true) & ~((var @ (d2term @ d_one)) = $true) & (! [X423 : term] : ~! [X424 : subst > term > term] : ((X424 @ sh @ one) != (sub @ X423 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem1_gthm = $true) & ((termmset_lthm = $true) <=> (! [X425 : term] : ((sub @ X425 @ id) = X425) => ! [X426 : term] : ((sub @ X426 @ id) = X426))) & (pushprop_lem2v2_lthm = $true) & (axmap = $true) & ! [X427 : subst] : ? [X428 : d_subst] : ((d2subst @ X428) = X427) & ~(lamnotap = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X429 : subst > term > subst > $o,X430 : term] : (~! [X431 : subst > term > term] : (~! [X432 : term] : (((X429 @ id @ (X431 @ id @ X432) @ id) = $true) | ~((X429 @ id @ X432 @ id) = $true)) | ~! [X433 : term,X434 : subst,X435 : subst] : ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434)) = (sub @ (X431 @ X435 @ X433) @ X434)) | ((X429 @ id @ (lam @ (X431 @ sh @ one)) @ id) = $true)) | ($true = (X429 @ id @ (lam @ (sub @ X430 @ (push @ one @ sh))) @ id)) | ~! [X436 : term] : (((X429 @ id @ (sub @ X430 @ (push @ X436 @ id)) @ id) = $true) | ~((X429 @ id @ X436 @ id) = $true)))) & (ulamvarsh = $true) & (! [X437 : term,X438 : term,X439 : subst > term > subst > $o] : (~((X439 @ id @ X437 @ id) = $true) | ~! [X440 : term,X441 : term] : (~((X439 @ id @ X440 @ id) = $true) | ((X439 @ id @ (ap @ (sub @ X440 @ id) @ X441) @ id) = $true) | ~((X439 @ id @ X441 @ id) = $true)) | ((X439 @ id @ (ap @ X438 @ X437) @ id) = $true) | ~! [X442 : term,X443 : subst,X444 : subst,X445 : subst] : (((X439 @ (comp @ X444 @ X443) @ (sub @ X442 @ X443) @ X445) = $true) | ~((X439 @ X444 @ X442 @ (comp @ X443 @ X445)) = $true)) | ~! [X446 : subst,X447 : term,X448 : subst,X449 : subst] : (($true = (X439 @ X446 @ X447 @ (comp @ X449 @ X448))) | ~((X439 @ (comp @ X446 @ X449) @ (sub @ X447 @ X449) @ X448) = $true)) | ~((X439 @ id @ X438 @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X450 : term,X451 : subst > term > subst > $o] : (~! [X452 : term] : (((X451 @ id @ (sub @ X450 @ (push @ X452 @ id)) @ id) = $true) | ~((X451 @ id @ X452 @ id) = $true)) | ~! [X453 : subst > term > term] : (~! [X454 : subst,X455 : term,X456 : subst] : ((sub @ (X453 @ X454 @ X455) @ X456) = (X453 @ (comp @ X454 @ X456) @ (sub @ X455 @ X456))) | ~! [X457 : term] : (~($true = (X451 @ id @ X457 @ id)) | ((X451 @ id @ (X453 @ id @ X457) @ id) = $true)) | ($true = (X451 @ id @ (lam @ (X453 @ sh @ one)) @ id))) | ((X451 @ id @ (lam @ (sub @ X450 @ (push @ one @ sh))) @ id) = $true))) & (hoaslamnotap_gthm = $true) & ! [X458 : term] : ? [X459 : d_term] : ((d2term @ X459) = X458) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X462 : term,X463 : term,X464 : term,X465 : term] : (((ap @ (sub @ X465 @ id) @ X464) != (ap @ (sub @ X462 @ id) @ X463)) | (X463 = X464)) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X466 : subst,X467 : term > $o,X468 : term] : ~! [X469 : term > $o] : ~! [X470 : term] : ((X467 @ (sub @ X470 @ (push @ X468 @ X466))) = (X469 @ X470)) <=> (pushprop_lem0 = $true)) & ((laminj = $true) <=> ! [X471 : term,X472 : term] : (((lam @ X472) != (lam @ X471)) | (X471 = X472))) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & (! [X473 : subst,X474 : term] : ((comp @ sh @ (push @ X474 @ X473)) = X473) <=> (axshiftcons = $true)) & (induction2lem_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((hoasinduction = $true) <=> ! [X475 : term,X476 : subst > term > subst > $o] : (~! [X477 : term] : (((X476 @ id @ X477 @ id) = $true) | ~((var @ (sub @ X477 @ id)) = $true)) | ~! [X478 : term,X479 : subst,X480 : subst,X481 : subst] : (~((X476 @ X480 @ X478 @ (comp @ X481 @ X479)) = $true) | ($true = (X476 @ (comp @ X480 @ X481) @ (sub @ X478 @ X481) @ X479))) | ~! [X482 : subst > term > term] : (~! [X483 : subst,X484 : term,X485 : subst] : ((sub @ (X482 @ X485 @ X484) @ X483) = (X482 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) | ~! [X486 : term] : (((X476 @ id @ (X482 @ id @ X486) @ id) = $true) | ~($true = (X476 @ id @ X486 @ id))) | ((X476 @ id @ (lam @ (X482 @ sh @ one)) @ id) = $true)) | ((X476 @ id @ X475 @ id) = $true) | ~! [X487 : subst,X488 : subst,X489 : subst,X490 : term] : (((X476 @ X489 @ X490 @ (comp @ X488 @ X487)) = $true) | ~($true = (X476 @ (comp @ X489 @ X488) @ (sub @ X490 @ X488) @ X487))) | ~! [X491 : term,X492 : term] : (((X476 @ id @ (ap @ (sub @ X492 @ id) @ X491) @ id) = $true) | ~((X476 @ id @ X491 @ id) = $true) | ~((X476 @ id @ X492 @ id) = $true)))) & (! [X493 : term] : ~! [X494 : subst > term > term] : ~! [X495 : subst,X496 : term] : ((sub @ X493 @ (push @ X496 @ X495)) = (X494 @ X495 @ X496)) <=> (hoasinduction_lem3v2_f = $true)) & (! [X497 : term,X498 : subst > term > subst > $o] : (~! [X499 : term,X500 : term] : (~((X498 @ id @ X500 @ id) = $true) | ((X498 @ id @ (ap @ (sub @ X499 @ id) @ X500) @ id) = $true) | ~((X498 @ id @ X499 @ id) = $true)) | ~! [X501 : subst > term > term] : (~! [X502 : subst,X503 : term,X504 : subst] : ((sub @ (X501 @ X502 @ X503) @ X504) = (X501 @ (comp @ X502 @ X504) @ (sub @ X503 @ X504))) | ((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id) = $true) | ~! [X505 : term] : (~((X498 @ id @ X505 @ id) = $true) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id)))) | ((X498 @ id @ X497 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X506 : term] : ((sub @ X506 @ id) = X506) => (! [X507 : term > $o,X508 : subst,X509 : term] : (((X507 @ (sub @ X509 @ X508)) = $true) | ~! [X510 : term,X511 : term] : (~((X507 @ X510) = $true) | ((X507 @ (ap @ X510 @ X511)) = $true) | ~((X507 @ X511) = $true)) | ~! [X512 : term] : (((X507 @ (lam @ X512)) = $true) | ~! [X513 : term] : (~((X507 @ X513) = $true) | ((X507 @ (sub @ X512 @ (push @ X513 @ id))) = $true))) | ~! [X514 : term] : (~($true = (var @ X514)) | ($true = (X507 @ (sub @ X514 @ X508))))) => ! [X515 : term > $o,X516 : term] : (((X515 @ X516) = $true) | ~! [X517 : term] : (~! [X518 : term] : (~((X515 @ X518) = $true) | ((X515 @ (sub @ X517 @ (push @ X518 @ id))) = $true)) | ((X515 @ (lam @ X517)) = $true)) | ~! [X519 : term,X520 : term] : (($true = (X515 @ (ap @ X519 @ X520))) | ~((X515 @ X519) = $true) | ~($true = (X515 @ X520))) | ~! [X521 : term] : (~($true = (var @ X521)) | ((X515 @ X521) = $true))))) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X522 : subst > term > subst > $o,X523 : term > $o,X524 : term] : (~! [X525 : term] : ((X523 @ X525) = (X522 @ id @ X525 @ id)) | ((X523 @ (lam @ X524)) = $true) | ~! [X526 : subst > term > term] : (~! [X527 : subst,X528 : subst,X529 : term] : ((sub @ (X526 @ X528 @ X529) @ X527) = (X526 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527))) | ((X522 @ id @ (lam @ (X526 @ sh @ one)) @ id) = $true) | ~! [X530 : term] : (($true = (X522 @ id @ (X526 @ id @ X530) @ id)) | ~((X522 @ id @ X530 @ id) = $true))) | ~! [X531 : term] : (((X523 @ (sub @ X524 @ (push @ X531 @ id))) = $true) | ~((X523 @ X531) = $true)))) & ((hoaslaminj = $true) <=> ! [X532 : subst > term > term,X533 : subst,X534 : subst > term > term,X535 : term] : (((X532 @ X533 @ X535) = (X534 @ X533 @ X535)) | ~! [X536 : subst,X537 : term,X538 : subst] : ((X534 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538)) = (sub @ (X534 @ X536 @ X537) @ X538)) | ~! [X539 : term,X540 : subst,X541 : subst] : ((sub @ (X532 @ X540 @ X539) @ X541) = (X532 @ (comp @ X540 @ X541) @ (sub @ X539 @ X541))) | ((lam @ (X534 @ sh @ one)) != (lam @ (X532 @ sh @ one))))) & (pushprop_gthm = $true) & ((induction2lem = $true) <=> ! [X542 : term,X543 : subst,X544 : term > $o] : (~! [X545 : term] : (((X544 @ (lam @ X545)) = $true) | ~! [X546 : term] : (((X544 @ (sub @ X545 @ (push @ X546 @ id))) = $true) | ~((X544 @ X546) = $true))) | ($true = (X544 @ (sub @ X542 @ X543))) | ~! [X547 : term] : (~($true = (var @ X547)) | ($true = (X544 @ (sub @ X547 @ X543)))) | ~! [X548 : term,X549 : term] : (~((X544 @ X549) = $true) | ~((X544 @ X548) = $true) | ((X544 @ (ap @ X548 @ X549)) = $true)))) & (hoasapnotvar_gthm = $true)),
% 32.60/5.94 inference(fool_elimination,[status(thm)],[f7])).
% 32.60/5.94 thf(f7,plain,(
% 32.60/5.94 hoasinduction_lem1v2 & (pushprop_lem1v2 <=> ! [X0 : term > $o,X1 : term > $o,X2 : subst,X3 : term] : (~! [X4 : term] : ((X1 @ (sub @ X4 @ (push @ X3 @ X2))) = (X0 @ X4)) | ~(X1 @ X3) | (X0 @ one))) & ((! [X5 : term] : ((sub @ X5 @ id) = X5) => (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | ((ap @ X8 @ X6) != (ap @ X9 @ X7))) => ! [X10 : term,X11 : term,X12 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X12) != (ap @ (sub @ X10 @ id) @ X11)) | (X10 = X13)))) <=> hoasapinj1_lthm) & pushprop_lthm & (pushprop_lem0_lthm <=> ! [X14 : term > $o,X15 : term,X16 : subst] : ~! [X17 : term > $o] : ~! [X18 : term] : ((X14 @ (sub @ X18 @ (push @ X15 @ X16))) = (X17 @ X18))) & hoaslamnotvar & (one = (d2term @ d_one)) & (pushprop_lem1_lthm <=> (! [X19 : term,X20 : subst] : ((sub @ one @ (push @ X19 @ X20)) = X19) => (! [X21 : subst,X22 : term] : ((comp @ sh @ (push @ X22 @ X21)) = X21) => ! [X23 : term,X24 : term > $o,X25 : term > $o,X26 : subst,X27 : term] : ((X25 @ (sub @ X27 @ (push @ X23 @ X26))) | ~(X24 @ X27))))) & hoasapnotvar & hoasinduction_lem1_lthm & (! [X28 : term] : ~! [X29 : subst > term > term] : ((sub @ X28 @ (push @ one @ sh)) != (X29 @ sh @ one)) <=> hoasinduction_lem3b_lthm) & (! [X30 : term,X31 : term,X32 : term,X33 : term] : (((ap @ (sub @ X30 @ id) @ X31) != (ap @ (sub @ X33 @ id) @ X32)) | (X30 = X33)) <=> hoasapinj1) & hoasapinj1_gthm & axabs & (pushprop_p_and_p_prime = (^[X34 : term, X35 : subst, X36 : term > $o, X37 : term > $o] : (! [X38 : term] : ((X36 @ (sub @ X38 @ (push @ X34 @ X35))) = (X37 @ X38))))) & (! [X39 : term] : ~! [X40 : subst > term > term] : ~! [X41 : subst,X42 : term] : ((sub @ X39 @ (push @ X42 @ X41)) = (X40 @ X41 @ X42)) <=> hoasinduction_lem3v2_f_lthm) & pushprop_lem3v2 & hoasinduction_lem3a_gthm & hoaslamnotvar_gthm & ((d2subst @ d_id) = sh) & hoasinduction_lem3v2_gthm & pushprop_lem2v2 & (! [X43 : subst > term > subst > $o,X44 : term] : (~! [X45 : term,X46 : subst,X47 : subst,X48 : subst] : ((X43 @ (comp @ X47 @ X48) @ (sub @ X45 @ X48) @ X46) | ~(X43 @ X47 @ X45 @ (comp @ X48 @ X46))) | ~! [X49 : subst,X50 : subst,X51 : subst,X52 : term] : (~(X43 @ (comp @ X49 @ X51) @ (sub @ X52 @ X51) @ X50) | (X43 @ X49 @ X52 @ (comp @ X51 @ X50))) | ~! [X53 : term] : (~(X43 @ id @ X53 @ id) | (X43 @ id @ (sub @ X44 @ (push @ X53 @ id)) @ id)) | (X43 @ id @ (lam @ X44) @ id) | ~! [X54 : subst > term > term] : (~! [X55 : subst,X56 : subst,X57 : term] : ((sub @ (X54 @ X55 @ X57) @ X56) = (X54 @ (comp @ X55 @ X56) @ (sub @ X57 @ X56))) | ~! [X58 : term] : ((X43 @ id @ (X54 @ id @ X58) @ id) | ~(X43 @ id @ X58 @ id)) | (X43 @ id @ (lam @ (X54 @ sh @ one)) @ id))) <=> hoasinduction_lem3) & ! [X59 : d_subst,X60 : d_subst] : (((d2subst @ X59) = (d2subst @ X60)) => (X59 = X60)) & (hoasapinj2_lthm <=> (! [X61 : term,X62 : term,X63 : term,X64 : term] : ((X62 = X63) | ((ap @ X61 @ X63) != (ap @ X64 @ X62))) => ! [X65 : term,X66 : term,X67 : term,X68 : term] : (((ap @ (sub @ X68 @ id) @ X65) != (ap @ (sub @ X67 @ id) @ X66)) | (X65 = X66)))) & (hoasinduction_lem3aaa <=> ! [X69 : term,X70 : subst > term > subst > $o] : ((X70 @ id @ (lam @ (sub @ X69 @ (push @ one @ sh))) @ id) | ~! [X71 : term] : ((X70 @ id @ (sub @ X69 @ (push @ X71 @ id)) @ id) | ~(X70 @ id @ X71 @ id)) | ~! [X72 : subst > term > term,X73 : term] : (~! [X74 : subst,X75 : subst,X76 : term] : ((sub @ (X72 @ X74 @ X76) @ X75) = (sub @ (sub @ X73 @ (push @ X76 @ X74)) @ X75)) | ~! [X77 : subst,X78 : term,X79 : subst] : ((sub @ X73 @ (push @ (sub @ X78 @ X79) @ (comp @ X77 @ X79))) = (X72 @ (comp @ X77 @ X79) @ (sub @ X78 @ X79))) | ~! [X80 : term] : (~(X70 @ id @ X80 @ id) | (X70 @ id @ (X72 @ id @ X80) @ id)) | (X70 @ id @ (lam @ (X72 @ sh @ one)) @ id)))) & apnotvar & hoasinduction_lem2v2_gthm & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lthm_3 <=> (! [X81 : subst > term > subst > $o] : ~! [X82 : term > $o] : ~! [X83 : term] : ((X81 @ id @ X83 @ id) = (X82 @ X83)) => (! [X84 : term > $o,X85 : term] : ((X84 @ X85) | ~! [X86 : term,X87 : term] : (~(X84 @ X87) | (X84 @ (ap @ X87 @ X86)) | ~(X84 @ X86)) | ~! [X88 : term] : (~(var @ X88) | (X84 @ X88)) | ~! [X89 : term] : ((X84 @ (lam @ X89)) | ~! [X90 : term] : ((X84 @ (sub @ X89 @ (push @ X90 @ id))) | ~(X84 @ X90)))) => (! [X91 : term] : ((sub @ X91 @ id) = X91) => (! [X92 : subst > term > subst > $o,X93 : term > $o,X94 : term] : ((X93 @ (lam @ X94)) | ~! [X95 : term] : ((X93 @ X95) = (X92 @ id @ X95 @ id)) | ~! [X96 : subst > term > term] : ((X92 @ id @ (lam @ (X96 @ sh @ one)) @ id) | ~! [X97 : term] : (~(X92 @ id @ X97 @ id) | (X92 @ id @ (X96 @ id @ X97) @ id)) | ~! [X98 : subst,X99 : term,X100 : subst] : ((X96 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98)) = (sub @ (X96 @ X100 @ X99) @ X98))) | ~! [X101 : term] : ((X93 @ (sub @ X94 @ (push @ X101 @ id))) | ~(X93 @ X101))) => ! [X102 : subst > term > subst > $o,X103 : term] : (~! [X104 : subst,X105 : subst,X106 : term,X107 : subst] : ((X102 @ (comp @ X104 @ X107) @ (sub @ X106 @ X107) @ X105) | ~(X102 @ X104 @ X106 @ (comp @ X107 @ X105))) | ~! [X108 : subst,X109 : subst,X110 : subst,X111 : term] : ((X102 @ X108 @ X111 @ (comp @ X109 @ X110)) | ~(X102 @ (comp @ X108 @ X109) @ (sub @ X111 @ X109) @ X110)) | ~! [X112 : term,X113 : term] : (~(X102 @ id @ X112 @ id) | ~(X102 @ id @ X113 @ id) | (X102 @ id @ (ap @ (sub @ X113 @ id) @ X112) @ id)) | ~! [X114 : term] : ((X102 @ id @ X114 @ id) | ~(var @ (sub @ X114 @ id))) | (X102 @ id @ X103 @ id) | ~! [X115 : subst > term > term] : (~! [X116 : subst,X117 : term,X118 : subst] : ((sub @ (X115 @ X118 @ X117) @ X116) = (X115 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116))) | ~! [X119 : term] : (~(X102 @ id @ X119 @ id) | (X102 @ id @ (X115 @ id @ X119) @ id)) | (X102 @ id @ (lam @ (X115 @ sh @ one)) @ id)))))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X120 : subst > term > subst > $o] : ~! [X121 : term > $o] : ~! [X122 : term] : ((X121 @ X122) = (X120 @ id @ X122 @ id)) => (! [X123 : term,X124 : term > $o] : (~! [X125 : term,X126 : term] : (~(X124 @ X126) | (X124 @ (ap @ X125 @ X126)) | ~(X124 @ X125)) | ~! [X127 : term] : ((X124 @ X127) | ~(var @ X127)) | ~! [X128 : term] : ((X124 @ (lam @ X128)) | ~! [X129 : term] : (~(X124 @ X129) | (X124 @ (sub @ X128 @ (push @ X129 @ id))))) | (X124 @ X123)) => (! [X130 : term] : ((sub @ X130 @ id) = X130) => (! [X131 : subst > term > subst > $o,X132 : term,X133 : term > $o] : ((X133 @ (lam @ X132)) | ~! [X134 : term] : (~(X133 @ X134) | (X133 @ (sub @ X132 @ (push @ X134 @ id)))) | ~! [X135 : term] : ((X131 @ id @ X135 @ id) = (X133 @ X135)) | ~! [X136 : subst > term > term] : ((X131 @ id @ (lam @ (X136 @ sh @ one)) @ id) | ~! [X137 : term] : (~(X131 @ id @ X137 @ id) | (X131 @ id @ (X136 @ id @ X137) @ id)) | ~! [X138 : subst,X139 : term,X140 : subst] : ((sub @ (X136 @ X138 @ X139) @ X140) = (X136 @ (comp @ X138 @ X140) @ (sub @ X139 @ X140))))) => ! [X141 : subst > term > subst > $o,X142 : term] : ((X141 @ id @ X142 @ id) | ~! [X143 : subst > term > term] : (~! [X144 : term] : (~(X141 @ id @ X144 @ id) | (X141 @ id @ (X143 @ id @ X144) @ id)) | (X141 @ id @ (lam @ (X143 @ sh @ one)) @ id) | ~! [X145 : term,X146 : subst,X147 : subst] : ((X143 @ (comp @ X147 @ X146) @ (sub @ X145 @ X146)) = (sub @ (X143 @ X147 @ X145) @ X146))) | ~! [X148 : term,X149 : term] : (~(X141 @ id @ X149 @ id) | ~(X141 @ id @ X148 @ id) | (X141 @ id @ (ap @ (sub @ X149 @ id) @ X148) @ id)))))))) & axapp & hoasinduction_lem2_gthm & ~ulamvar1 & hoasinduction_lem1 & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X150 : subst] : ((comp @ id @ X150) = X150) => (! [X151 : subst] : ((comp @ X151 @ id) = X151) => (! [X152 : subst] : ((comp @ X152 @ id) = X152) & ! [X153 : subst] : ((comp @ id @ X153) = X153)))) <=> substmonoid_lthm) & (! [X154 : term > $o,X155 : term] : (~! [X156 : term,X157 : term] : ((X154 @ (ap @ X157 @ X156)) | ~(X154 @ X157) | ~(X154 @ X156)) | ~! [X158 : term] : (~(X154 @ X158) | (X154 @ (lam @ X158))) | (X154 @ X155) | ~! [X159 : term] : ((X154 @ X159) | ~(var @ X159))) <=> induction) & (axvarcons <=> ! [X160 : subst,X161 : term] : ((sub @ one @ (push @ X161 @ X160)) = X161)) & (hoasinduction_lem3v2a_lthm <=> (! [X162 : term] : ~! [X163 : subst > term > term] : ~! [X164 : term,X165 : subst] : ((X163 @ X165 @ X164) = (sub @ X162 @ (push @ X164 @ X165))) => (! [X166 : term] : ((sub @ X166 @ id) = X166) => ! [X167 : subst > term > subst > $o,X168 : term > $o,X169 : term] : (~! [X170 : term] : ((X168 @ (sub @ X169 @ (push @ X170 @ id))) | ~(X168 @ X170)) | ~! [X171 : subst > term > term] : (~! [X172 : term] : (~(X167 @ id @ X172 @ id) | (X167 @ id @ (X171 @ id @ X172) @ id)) | ~! [X173 : subst,X174 : subst,X175 : term] : ((sub @ (X171 @ X173 @ X175) @ X174) = (X171 @ (comp @ X173 @ X174) @ (sub @ X175 @ X174))) | (X167 @ id @ (lam @ (X171 @ sh @ one)) @ id)) | (X168 @ (lam @ X169)) | ~! [X176 : term] : ((X168 @ X176) = (X167 @ id @ X176 @ id)))))) & (! [X177 : subst] : ((comp @ X177 @ id) = X177) <=> axidr) & (! [X178 : term,X179 : term,X180 : term,X181 : term] : (((ap @ X178 @ X180) != (ap @ X179 @ X181)) | (X180 = X181)) <=> apinj2) & hoasinduction_lem3_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_gthm & (hoasinduction_lem3v2_lthm <=> (! [X182 : term] : ((sub @ X182 @ id) = X182) => ! [X183 : subst > term > subst > $o,X184 : term,X185 : term > $o] : ((X185 @ (lam @ X184)) | ~! [X186 : subst,X187 : subst,X188 : subst,X189 : term] : ((X183 @ (comp @ X188 @ X187) @ (sub @ X189 @ X187) @ X186) | ~(X183 @ X188 @ X189 @ (comp @ X187 @ X186))) | ~! [X190 : term] : ((X185 @ (sub @ X184 @ (push @ X190 @ id))) | ~(X185 @ X190)) | ~! [X191 : subst > term > term] : ((X183 @ id @ (lam @ (X191 @ sh @ one)) @ id) | ~! [X192 : term] : ((X183 @ id @ (X191 @ id @ X192) @ id) | ~(X183 @ id @ X192 @ id)) | ~! [X193 : term,X194 : subst,X195 : subst] : ((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195)) = (sub @ (X191 @ X194 @ X193) @ X195))) | ~! [X196 : subst,X197 : term,X198 : subst,X199 : subst] : (~(X183 @ (comp @ X196 @ X198) @ (sub @ X197 @ X198) @ X199) | (X183 @ X196 @ X197 @ (comp @ X198 @ X199))) | ~! [X200 : term] : ((X183 @ id @ X200 @ id) = (X185 @ X200))))) & axassoc & hoasapinj2_gthm & termmset_gthm & (! [X201 : subst] : ((push @ (sub @ one @ X201) @ (comp @ sh @ X201)) = X201) <=> axscons) & (! [X202 : term,X203 : term] : ((X202 = X203) | ((sub @ X202 @ sh) != (sub @ X203 @ sh))) <=> shinj) & ! [X204 : d_term,X205 : d_term] : (((d2term @ X205) = (d2term @ X204)) => (X204 = X205)) & pushprop_lem0_gthm & axclos & hoasinduction_lem3b_gthm & ulamvarind & (hoasinduction_lem0 <=> ! [X206 : subst > term > subst > $o] : ~! [X207 : term > $o] : ~! [X208 : term] : ((X206 @ id @ X208 @ id) = (X207 @ X208))) & hoasinduction_lem1v2_gthm & (pushprop_lem1 <=> ! [X209 : term > $o,X210 : subst,X211 : term > $o,X212 : term,X213 : term] : ((X211 @ (sub @ X213 @ (push @ X212 @ X210))) | ~(X209 @ X213))) & ! [X214 : d_subst] : (d_id = X214) & hoaslamnotap_lthm & (pushprop_lem1v2_lthm <=> (! [X215 : subst,X216 : term] : ((sub @ one @ (push @ X216 @ X215)) = X216) => ! [X217 : term,X218 : subst,X219 : term > $o,X220 : term > $o] : (~(X220 @ X217) | (X219 @ one) | ~! [X221 : term] : ((X219 @ X221) = (X220 @ (sub @ X221 @ (push @ X217 @ X218))))))) & hoaslaminj_gthm & (hoasinduction_lthm <=> (! [X222 : term > $o,X223 : term] : ((X222 @ X223) | ~! [X224 : term] : (~(var @ X224) | (X222 @ X224)) | ~! [X225 : term] : ((X222 @ (lam @ X225)) | ~! [X226 : term] : (~(X222 @ X226) | (X222 @ (sub @ X225 @ (push @ X226 @ id))))) | ~! [X227 : term,X228 : term] : (~(X222 @ X227) | (X222 @ (ap @ X227 @ X228)) | ~(X222 @ X228))) => (! [X229 : subst > term > subst > $o,X230 : term,X231 : term] : (~! [X232 : term,X233 : term] : (~(X229 @ id @ X233 @ id) | (X229 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id) | ~(X229 @ id @ X232 @ id)) | ~(X229 @ id @ X231 @ id) | (X229 @ id @ (ap @ X230 @ X231) @ id) | ~(X229 @ id @ X230 @ id) | ~! [X234 : term,X235 : subst,X236 : subst,X237 : subst] : ((X229 @ X235 @ X234 @ (comp @ X236 @ X237)) | ~(X229 @ (comp @ X235 @ X236) @ (sub @ X234 @ X236) @ X237)) | ~! [X238 : subst,X239 : term,X240 : subst,X241 : subst] : (~(X229 @ X240 @ X239 @ (comp @ X238 @ X241)) | (X229 @ (comp @ X240 @ X238) @ (sub @ X239 @ X238) @ X241))) => (! [X242 : term,X243 : subst > term > subst > $o] : (~! [X244 : subst,X245 : term,X246 : subst,X247 : subst] : ((X243 @ X246 @ X245 @ (comp @ X247 @ X244)) | ~(X243 @ (comp @ X246 @ X247) @ (sub @ X245 @ X247) @ X244)) | ~! [X248 : subst,X249 : subst,X250 : term,X251 : subst] : (~(X243 @ X249 @ X250 @ (comp @ X248 @ X251)) | (X243 @ (comp @ X249 @ X248) @ (sub @ X250 @ X248) @ X251)) | ~! [X252 : subst > term > term] : (~! [X253 : term] : (~(X243 @ id @ X253 @ id) | (X243 @ id @ (X252 @ id @ X253) @ id)) | ~! [X254 : subst,X255 : subst,X256 : term] : ((X252 @ (comp @ X254 @ X255) @ (sub @ X256 @ X255)) = (sub @ (X252 @ X254 @ X256) @ X255)) | (X243 @ id @ (lam @ (X252 @ sh @ one)) @ id)) | (X243 @ id @ (lam @ X242) @ id) | ~! [X257 : term] : (~(X243 @ id @ X257 @ id) | (X243 @ id @ (sub @ X242 @ (push @ X257 @ id)) @ id))) => ! [X258 : subst > term > subst > $o,X259 : term] : (~! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : ((X258 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262) @ X260) | ~(X258 @ X263 @ X261 @ (comp @ X262 @ X260))) | ~! [X264 : term,X265 : term] : (~(X258 @ id @ X264 @ id) | (X258 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id) | ~(X258 @ id @ X265 @ id)) | ~! [X266 : subst > term > term] : (~! [X267 : term] : (~(X258 @ id @ X267 @ id) | (X258 @ id @ (X266 @ id @ X267) @ id)) | (X258 @ id @ (lam @ (X266 @ sh @ one)) @ id) | ~! [X268 : term,X269 : subst,X270 : subst] : ((X266 @ (comp @ X270 @ X269) @ (sub @ X268 @ X269)) = (sub @ (X266 @ X270 @ X268) @ X269))) | ~! [X271 : subst,X272 : subst,X273 : term,X274 : subst] : ((X258 @ X272 @ X273 @ (comp @ X274 @ X271)) | ~(X258 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271)) | ~! [X275 : term] : ((X258 @ id @ X275 @ id) | ~(var @ (sub @ X275 @ id))) | (X258 @ id @ X259 @ id)))))) & (! [X276 : term,X277 : term > $o,X278 : subst > term > subst > $o,X279 : term] : (~(X277 @ X279) | ~! [X280 : term] : ((X278 @ id @ X280 @ id) = (X277 @ X280)) | ~! [X281 : subst,X282 : subst,X283 : subst,X284 : term] : (~(X278 @ X281 @ X284 @ (comp @ X283 @ X282)) | (X278 @ (comp @ X281 @ X283) @ (sub @ X284 @ X283) @ X282)) | ~! [X285 : term,X286 : term] : ((X278 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id) | ~(X278 @ id @ X285 @ id) | ~(X278 @ id @ X286 @ id)) | ~! [X287 : subst,X288 : term,X289 : subst,X290 : subst] : (~(X278 @ (comp @ X290 @ X287) @ (sub @ X288 @ X287) @ X289) | (X278 @ X290 @ X288 @ (comp @ X287 @ X289))) | ~(X277 @ X276) | (X277 @ (ap @ X279 @ X276))) <=> hoasinduction_lem2v2) & hoasapnotvar_lthm & (hoasinduction_lem3_lthm <=> (! [X291 : term] : ((sub @ X291 @ id) = X291) => (! [X292 : term,X293 : subst > term > subst > $o] : (~! [X294 : subst > term > term] : (~! [X295 : term] : ((X293 @ id @ (X294 @ id @ X295) @ id) | ~(X293 @ id @ X295 @ id)) | ~! [X296 : term,X297 : subst,X298 : subst] : ((sub @ (X294 @ X297 @ X296) @ X298) = (X294 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298))) | (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id)) | ~! [X299 : term] : ((X293 @ id @ (sub @ X292 @ (push @ X299 @ id)) @ id) | ~(X293 @ id @ X299 @ id)) | (X293 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) => ! [X300 : subst > term > subst > $o,X301 : term] : ((X300 @ id @ (lam @ X301) @ id) | ~! [X302 : subst,X303 : subst,X304 : subst,X305 : term] : (~(X300 @ (comp @ X302 @ X303) @ (sub @ X305 @ X303) @ X304) | (X300 @ X302 @ X305 @ (comp @ X303 @ X304))) | ~! [X306 : subst > term > term] : (~! [X307 : subst,X308 : subst,X309 : term] : ((X306 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307)) = (sub @ (X306 @ X308 @ X309) @ X307)) | ~! [X310 : term] : (~(X300 @ id @ X310 @ id) | (X300 @ id @ (X306 @ id @ X310) @ id)) | (X300 @ id @ (lam @ (X306 @ sh @ one)) @ id)) | ~! [X311 : term] : (~(X300 @ id @ X311 @ id) | (X300 @ id @ (sub @ X301 @ (push @ X311 @ id)) @ id)) | ~! [X312 : subst,X313 : subst,X314 : subst,X315 : term] : ((X300 @ (comp @ X312 @ X313) @ (sub @ X315 @ X313) @ X314) | ~(X300 @ X312 @ X315 @ (comp @ X313 @ X314))))))) & (! [X316 : subst > term > subst > $o] : ~! [X317 : term > $o] : ~! [X318 : term] : ((X316 @ id @ X318 @ id) = (X317 @ X318)) <=> hoasinduction_lem0_lthm) & hoaslamnotvar_lthm & pushprop_lem1_gthm & (hoaslamnotap <=> ! [X319 : subst > term > term,X320 : term,X321 : term] : (((ap @ (sub @ X320 @ id) @ X321) != (lam @ (X319 @ sh @ one))) | ~! [X322 : subst,X323 : term,X324 : subst] : ((sub @ (X319 @ X324 @ X323) @ X322) = (X319 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))))) & lamnotvar & ((! [X325 : term] : ((sub @ X325 @ id) = X325) => (! [X326 : subst > term > subst > $o,X327 : term] : (~! [X328 : term] : ((X326 @ id @ (sub @ X327 @ (push @ X328 @ id)) @ id) | ~(X326 @ id @ X328 @ id)) | (X326 @ id @ (lam @ (sub @ X327 @ (push @ one @ sh))) @ id) | ~! [X329 : subst > term > term] : (~! [X330 : subst,X331 : subst,X332 : term] : ((sub @ (X329 @ X330 @ X332) @ X331) = (X329 @ (comp @ X330 @ X331) @ (sub @ X332 @ X331))) | (X326 @ id @ (lam @ (X329 @ sh @ one)) @ id) | ~! [X333 : term] : ((X326 @ id @ (X329 @ id @ X333) @ id) | ~(X326 @ id @ X333 @ id)))) => ! [X334 : subst > term > subst > $o,X335 : term] : (~! [X336 : term] : ((X334 @ id @ (sub @ X335 @ (push @ X336 @ id)) @ id) | ~(X334 @ id @ X336 @ id)) | ~! [X337 : subst > term > term] : (~! [X338 : subst,X339 : term,X340 : subst] : ((X337 @ (comp @ X338 @ X340) @ (sub @ X339 @ X340)) = (sub @ (X337 @ X338 @ X339) @ X340)) | (X334 @ id @ (lam @ (X337 @ sh @ one)) @ id) | ~! [X341 : term] : ((X334 @ id @ (X337 @ id @ X341) @ id) | ~(X334 @ id @ X341 @ id))) | (X334 @ id @ (lam @ X335) @ id)))) <=> hoasinduction_lem3a_lthm) & (induction2lem_lthm <=> (! [X342 : subst,X343 : term] : ((sub @ one @ (push @ X343 @ X342)) = X343) => (! [X344 : term,X345 : subst] : ((comp @ sh @ (push @ X344 @ X345)) = X345) => (! [X346 : subst] : ((comp @ X346 @ id) = X346) => (! [X347 : term > $o,X348 : term] : (~! [X349 : term,X350 : term] : ((X347 @ (ap @ X350 @ X349)) | ~(X347 @ X350) | ~(X347 @ X349)) | ~! [X351 : term] : ((X347 @ (lam @ X351)) | ~(X347 @ X351)) | ~! [X352 : term] : (~(var @ X352) | (X347 @ X352)) | (X347 @ X348)) => ! [X353 : term > $o,X354 : term,X355 : subst] : (~! [X356 : term,X357 : term] : ((X353 @ (ap @ X357 @ X356)) | ~(X353 @ X356) | ~(X353 @ X357)) | ~! [X358 : term] : (~! [X359 : term] : ((X353 @ (sub @ X358 @ (push @ X359 @ id))) | ~(X353 @ X359)) | (X353 @ (lam @ X358))) | ~! [X360 : term] : (~(var @ X360) | (X353 @ (sub @ X360 @ X355))) | (X353 @ (sub @ X354 @ X355)))))))) & (hoasinduction_lem3v2 <=> ! [X361 : subst > term > subst > $o,X362 : term > $o,X363 : term] : (~! [X364 : term] : ((X361 @ id @ X364 @ id) = (X362 @ X364)) | (X362 @ (lam @ X363)) | ~! [X365 : term,X366 : subst,X367 : subst,X368 : subst] : (~(X361 @ X366 @ X365 @ (comp @ X367 @ X368)) | (X361 @ (comp @ X366 @ X367) @ (sub @ X365 @ X367) @ X368)) | ~! [X369 : term] : (~(X362 @ X369) | (X362 @ (sub @ X363 @ (push @ X369 @ id)))) | ~! [X370 : subst,X371 : subst,X372 : subst,X373 : term] : (~(X361 @ (comp @ X372 @ X370) @ (sub @ X373 @ X370) @ X371) | (X361 @ X372 @ X373 @ (comp @ X370 @ X371))) | ~! [X374 : subst > term > term] : (~! [X375 : term] : ((X361 @ id @ (X374 @ id @ X375) @ id) | ~(X361 @ id @ X375 @ id)) | (X361 @ id @ (lam @ (X374 @ sh @ one)) @ id) | ~! [X376 : term,X377 : subst,X378 : subst] : ((X374 @ (comp @ X377 @ X378) @ (sub @ X376 @ X378)) = (sub @ (X374 @ X377 @ X376) @ X378))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[X379 : subst > term > subst > $o, X380 : term > $o] : (! [X381 : term] : ((X380 @ X381) = (X379 @ id @ X381 @ id))))) & (! [X382 : term] : ((sub @ X382 @ id) = X382) <=> axvarid) & (hoasinduction_lem3a <=> ! [X383 : subst > term > subst > $o,X384 : term] : ((X383 @ id @ (lam @ X384) @ id) | ~! [X385 : term] : ((X383 @ id @ (sub @ X384 @ (push @ X385 @ id)) @ id) | ~(X383 @ id @ X385 @ id)) | ~! [X386 : subst > term > term] : (~! [X387 : term] : ((X383 @ id @ (X386 @ id @ X387) @ id) | ~(X383 @ id @ X387 @ id)) | (X383 @ id @ (lam @ (X386 @ sh @ one)) @ id) | ~! [X388 : subst,X389 : subst,X390 : term] : ((sub @ (X386 @ X388 @ X390) @ X389) = (X386 @ (comp @ X388 @ X389) @ (sub @ X390 @ X389)))))) & (! [X391 : term] : ((sub @ X391 @ id) = X391) <=> termmset) & (hoaslaminj_lthm <=> (! [X392 : term,X393 : subst] : ((sub @ one @ (push @ X392 @ X393)) = X392) => (! [X394 : subst,X395 : term] : ((comp @ sh @ (push @ X395 @ X394)) = X394) => (! [X396 : term,X397 : term] : ((X396 = X397) | ((lam @ X396) != (lam @ X397))) => ! [X398 : subst,X399 : subst > term > term,X400 : term,X401 : subst > term > term] : (~! [X402 : subst,X403 : term,X404 : subst] : ((sub @ (X401 @ X404 @ X403) @ X402) = (X401 @ (comp @ X404 @ X402) @ (sub @ X403 @ X402))) | ~! [X405 : subst,X406 : term,X407 : subst] : ((X399 @ (comp @ X405 @ X407) @ (sub @ X406 @ X407)) = (sub @ (X399 @ X405 @ X406) @ X407)) | ((X399 @ X398 @ X400) = (X401 @ X398 @ X400)) | ((lam @ (X399 @ sh @ one)) != (lam @ (X401 @ sh @ one)))))))) & (induction2 <=> ! [X408 : term > $o,X409 : term] : (~! [X410 : term,X411 : term] : ((X408 @ (ap @ X411 @ X410)) | ~(X408 @ X410) | ~(X408 @ X411)) | (X408 @ X409) | ~! [X412 : term] : (~(var @ X412) | (X408 @ X412)) | ~! [X413 : term] : (~! [X414 : term] : (~(X408 @ X414) | (X408 @ (sub @ X413 @ (push @ X414 @ id)))) | (X408 @ (lam @ X413))))) & ((! [X415 : subst] : ((comp @ X415 @ id) = X415) & ! [X416 : subst] : ((comp @ id @ X416) = X416)) <=> substmonoid) & (axidl <=> ! [X417 : subst] : ((comp @ id @ X417) = X417)) & ! [X418 : d_term] : (d_one = X418) & pushprop_lthm_orig & (apinj1 <=> ! [X419 : term,X420 : term,X421 : term,X422 : term] : ((X420 = X421) | ((ap @ X421 @ X422) != (ap @ X420 @ X419)))) & pushprop_lem2v2_gthm & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop & axvarshift & pushprop_lem1v2_gthm & ~(var @ (d2term @ d_one)) & (! [X423 : term] : ~! [X424 : subst > term > term] : ((X424 @ sh @ one) != (sub @ X423 @ (push @ one @ sh))) <=> hoasinduction_lem3b) & hoasinduction_lem1_gthm & (termmset_lthm <=> (! [X425 : term] : ((sub @ X425 @ id) = X425) => ! [X426 : term] : ((sub @ X426 @ id) = X426))) & pushprop_lem2v2_lthm & axmap & ! [X427 : subst] : ? [X428 : d_subst] : ((d2subst @ X428) = X427) & ~lamnotap & (hoasinduction_lem3aa <=> ! [X429 : subst > term > subst > $o,X430 : term] : (~! [X431 : subst > term > term] : (~! [X432 : term] : ((X429 @ id @ (X431 @ id @ X432) @ id) | ~(X429 @ id @ X432 @ id)) | ~! [X433 : term,X434 : subst,X435 : subst] : ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434)) = (sub @ (X431 @ X435 @ X433) @ X434)) | (X429 @ id @ (lam @ (X431 @ sh @ one)) @ id)) | (X429 @ id @ (lam @ (sub @ X430 @ (push @ one @ sh))) @ id) | ~! [X436 : term] : ((X429 @ id @ (sub @ X430 @ (push @ X436 @ id)) @ id) | ~(X429 @ id @ X436 @ id)))) & ulamvarsh & (! [X437 : term,X438 : term,X439 : subst > term > subst > $o] : (~(X439 @ id @ X437 @ id) | ~! [X440 : term,X441 : term] : (~(X439 @ id @ X440 @ id) | (X439 @ id @ (ap @ (sub @ X440 @ id) @ X441) @ id) | ~(X439 @ id @ X441 @ id)) | (X439 @ id @ (ap @ X438 @ X437) @ id) | ~! [X442 : term,X443 : subst,X444 : subst,X445 : subst] : ((X439 @ (comp @ X444 @ X443) @ (sub @ X442 @ X443) @ X445) | ~(X439 @ X444 @ X442 @ (comp @ X443 @ X445))) | ~! [X446 : subst,X447 : term,X448 : subst,X449 : subst] : ((X439 @ X446 @ X447 @ (comp @ X449 @ X448)) | ~(X439 @ (comp @ X446 @ X449) @ (sub @ X447 @ X449) @ X448)) | ~(X439 @ id @ X438 @ id)) <=> hoasinduction_lem2) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem3aa_lthm <=> ! [X450 : term,X451 : subst > term > subst > $o] : (~! [X452 : term] : ((X451 @ id @ (sub @ X450 @ (push @ X452 @ id)) @ id) | ~(X451 @ id @ X452 @ id)) | ~! [X453 : subst > term > term] : (~! [X454 : subst,X455 : term,X456 : subst] : ((sub @ (X453 @ X454 @ X455) @ X456) = (X453 @ (comp @ X454 @ X456) @ (sub @ X455 @ X456))) | ~! [X457 : term] : (~(X451 @ id @ X457 @ id) | (X451 @ id @ (X453 @ id @ X457) @ id)) | (X451 @ id @ (lam @ (X453 @ sh @ one)) @ id)) | (X451 @ id @ (lam @ (sub @ X450 @ (push @ one @ sh))) @ id))) & hoaslamnotap_gthm & ! [X458 : term] : ? [X459 : d_term] : ((d2term @ X459) = X458) & (hoaslam = (^[X460 : subst, X461 : subst > term > term] : (d2term @ d_one))) & (! [X462 : term,X463 : term,X464 : term,X465 : term] : (((ap @ (sub @ X465 @ id) @ X464) != (ap @ (sub @ X462 @ id) @ X463)) | (X463 = X464)) <=> hoasapinj2) & pushprop_lem3v2_lthm & (! [X466 : subst,X467 : term > $o,X468 : term] : ~! [X469 : term > $o] : ~! [X470 : term] : ((X467 @ (sub @ X470 @ (push @ X468 @ X466))) = (X469 @ X470)) <=> pushprop_lem0) & (laminj <=> ! [X471 : term,X472 : term] : (((lam @ X472) != (lam @ X471)) | (X471 = X472))) & induction2_gthm & substmonoid_gthm & (! [X473 : subst,X474 : term] : ((comp @ sh @ (push @ X474 @ X473)) = X473) <=> axshiftcons) & induction2lem_gthm & hoasinduction_lem2_lthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction <=> ! [X475 : term,X476 : subst > term > subst > $o] : (~! [X477 : term] : ((X476 @ id @ X477 @ id) | ~(var @ (sub @ X477 @ id))) | ~! [X478 : term,X479 : subst,X480 : subst,X481 : subst] : (~(X476 @ X480 @ X478 @ (comp @ X481 @ X479)) | (X476 @ (comp @ X480 @ X481) @ (sub @ X478 @ X481) @ X479)) | ~! [X482 : subst > term > term] : (~! [X483 : subst,X484 : term,X485 : subst] : ((sub @ (X482 @ X485 @ X484) @ X483) = (X482 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) | ~! [X486 : term] : ((X476 @ id @ (X482 @ id @ X486) @ id) | ~(X476 @ id @ X486 @ id)) | (X476 @ id @ (lam @ (X482 @ sh @ one)) @ id)) | (X476 @ id @ X475 @ id) | ~! [X487 : subst,X488 : subst,X489 : subst,X490 : term] : ((X476 @ X489 @ X490 @ (comp @ X488 @ X487)) | ~(X476 @ (comp @ X489 @ X488) @ (sub @ X490 @ X488) @ X487)) | ~! [X491 : term,X492 : term] : ((X476 @ id @ (ap @ (sub @ X492 @ id) @ X491) @ id) | ~(X476 @ id @ X491 @ id) | ~(X476 @ id @ X492 @ id)))) & (! [X493 : term] : ~! [X494 : subst > term > term] : ~! [X495 : subst,X496 : term] : ((sub @ X493 @ (push @ X496 @ X495)) = (X494 @ X495 @ X496)) <=> hoasinduction_lem3v2_f) & (! [X497 : term,X498 : subst > term > subst > $o] : (~! [X499 : term,X500 : term] : (~(X498 @ id @ X500 @ id) | (X498 @ id @ (ap @ (sub @ X499 @ id) @ X500) @ id) | ~(X498 @ id @ X499 @ id)) | ~! [X501 : subst > term > term] : (~! [X502 : subst,X503 : term,X504 : subst] : ((sub @ (X501 @ X502 @ X503) @ X504) = (X501 @ (comp @ X502 @ X504) @ (sub @ X503 @ X504))) | (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id) | ~! [X505 : term] : (~(X498 @ id @ X505 @ id) | (X498 @ id @ (X501 @ id @ X505) @ id))) | (X498 @ id @ X497 @ id)) <=> hoasinduction_no_psi_cond) & ((! [X506 : term] : ((sub @ X506 @ id) = X506) => (! [X507 : term > $o,X508 : subst,X509 : term] : ((X507 @ (sub @ X509 @ X508)) | ~! [X510 : term,X511 : term] : (~(X507 @ X510) | (X507 @ (ap @ X510 @ X511)) | ~(X507 @ X511)) | ~! [X512 : term] : ((X507 @ (lam @ X512)) | ~! [X513 : term] : (~(X507 @ X513) | (X507 @ (sub @ X512 @ (push @ X513 @ id))))) | ~! [X514 : term] : (~(var @ X514) | (X507 @ (sub @ X514 @ X508)))) => ! [X515 : term > $o,X516 : term] : ((X515 @ X516) | ~! [X517 : term] : (~! [X518 : term] : (~(X515 @ X518) | (X515 @ (sub @ X517 @ (push @ X518 @ id)))) | (X515 @ (lam @ X517))) | ~! [X519 : term,X520 : term] : ((X515 @ (ap @ X519 @ X520)) | ~(X515 @ X519) | ~(X515 @ X520)) | ~! [X521 : term] : (~(var @ X521) | (X515 @ X521))))) <=> induction2_lthm) & (hoasinduction_lem3v2a <=> ! [X522 : subst > term > subst > $o,X523 : term > $o,X524 : term] : (~! [X525 : term] : ((X523 @ X525) = (X522 @ id @ X525 @ id)) | (X523 @ (lam @ X524)) | ~! [X526 : subst > term > term] : (~! [X527 : subst,X528 : subst,X529 : term] : ((sub @ (X526 @ X528 @ X529) @ X527) = (X526 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527))) | (X522 @ id @ (lam @ (X526 @ sh @ one)) @ id) | ~! [X530 : term] : ((X522 @ id @ (X526 @ id @ X530) @ id) | ~(X522 @ id @ X530 @ id))) | ~! [X531 : term] : ((X523 @ (sub @ X524 @ (push @ X531 @ id))) | ~(X523 @ X531)))) & (hoaslaminj <=> ! [X532 : subst > term > term,X533 : subst,X534 : subst > term > term,X535 : term] : (((X532 @ X533 @ X535) = (X534 @ X533 @ X535)) | ~! [X536 : subst,X537 : term,X538 : subst] : ((X534 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538)) = (sub @ (X534 @ X536 @ X537) @ X538)) | ~! [X539 : term,X540 : subst,X541 : subst] : ((sub @ (X532 @ X540 @ X539) @ X541) = (X532 @ (comp @ X540 @ X541) @ (sub @ X539 @ X541))) | ((lam @ (X534 @ sh @ one)) != (lam @ (X532 @ sh @ one))))) & pushprop_gthm & (induction2lem <=> ! [X542 : term,X543 : subst,X544 : term > $o] : (~! [X545 : term] : ((X544 @ (lam @ X545)) | ~! [X546 : term] : ((X544 @ (sub @ X545 @ (push @ X546 @ id))) | ~(X544 @ X546))) | (X544 @ (sub @ X542 @ X543)) | ~! [X547 : term] : (~(var @ X547) | (X544 @ (sub @ X547 @ X543))) | ~! [X548 : term,X549 : term] : (~(X544 @ X549) | ~(X544 @ X548) | (X544 @ (ap @ X548 @ X549))))) & hoasapnotvar_gthm),
% 32.60/5.94 inference(rectify,[status(thm)],[f1])).
% 32.60/5.94 thf(f1,axiom,(
% 32.60/5.94 hoasinduction_lem1v2 & (pushprop_lem1v2 <=> ! [X11 : term > $o,X10 : term > $o,X14 : subst,X13 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | ~(X10 @ X13) | (X11 @ one))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X15 : term,X20 : term,X19 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)))) <=> hoasapinj1_lthm) & pushprop_lthm & (pushprop_lem0_lthm <=> ! [X10 : term > $o,X13 : term,X14 : subst] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & hoaslamnotvar & (one = (d2term @ d_one)) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X15 : term,X10 : term > $o,X26 : term > $o,X14 : subst,X13 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & hoasapnotvar & hoasinduction_lem1_lthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & (! [X15 : term,X20 : term,X19 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)) <=> hoasapinj1) & hoasapinj1_gthm & axabs & (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))))))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f_lthm) & pushprop_lem3v2 & hoasinduction_lem3a_gthm & hoaslamnotvar_gthm & ((d2subst @ d_id) = sh) & hoasinduction_lem3v2_gthm & pushprop_lem2v2 & (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X14 : subst,X25 : subst,X26 : 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)) | (X10 @ id @ (lam @ X27) @ 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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3) & ! [X6 : d_subst,X7 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & (hoasapinj2_lthm <=> (! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X19 = X20) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X19 : term,X20 : term,X15 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20)))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term,X35 : term] : (~! [X36 : subst,X38 : subst,X37 : term] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | ~! [X39 : subst,X40 : term,X41 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))) & apnotvar & hoasinduction_lem2v2_gthm & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_lthm_3 <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X11 : term > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))))) & (hoasinduction_no_psi_cond_lthm <=> (! [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 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : ((X11 @ (lam @ X29)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) => ! [X10 : subst > term > subst > $o,X30 : term] : ((X10 @ id @ X30 @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))))))) & axapp & hoasinduction_lem2_gthm & ~ulamvar1 & hoasinduction_lem1 & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X14 : subst] : ((comp @ id @ X14) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14)))) <=> substmonoid_lthm) & (! [X10 : term > $o,X21 : term] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) <=> induction) & (axvarcons <=> ! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13)) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X11 : term > $o,X29 : term] : (~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))))) & (! [X14 : subst] : ((comp @ X14 @ id) = X14) <=> axidr) & (! [X13 : term,X15 : term,X19 : term,X20 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) <=> apinj2) & hoasinduction_lem3_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_gthm & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X48 : term,X11 : term > $o] : ((X11 @ (lam @ X48)) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))))) & axassoc & hoasapinj2_gthm & termmset_gthm & (! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14) <=> axscons) & (! [X15 : term,X13 : term] : ((X13 = X15) | ((sub @ X13 @ sh) != (sub @ X15 @ sh))) <=> shinj) & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & pushprop_lem0_gthm & axclos & hoasinduction_lem3b_gthm & ulamvarind & (hoasinduction_lem0 <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & hoasinduction_lem1v2_gthm & (pushprop_lem1 <=> ! [X10 : term > $o,X14 : subst,X26 : term > $o,X15 : term,X13 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))) & ! [X5 : d_subst] : (d_id = X5) & hoaslamnotap_lthm & (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X13 : term,X14 : subst,X11 : term > $o,X10 : term > $o] : (~(X10 @ X13) | (X11 @ one) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & hoaslaminj_gthm & (hoasinduction_lthm <=> (! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) => (! [X10 : subst > term > subst > $o,X23 : term,X24 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X24 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X27 : term,X10 : subst > term > subst > $o] : (~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : 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)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id))) => ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X25 : subst,X13 : term,X26 : subst,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)) | ~! [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)))) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id)))))) & (! [X45 : term,X11 : term > $o,X10 : subst > term > subst > $o,X44 : term] : (~(X11 @ X44) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45))) <=> hoasinduction_lem2v2) & hoasapnotvar_lthm & (hoasinduction_lem3_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : subst > term > subst > $o,X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0_lthm) & hoaslamnotvar_lthm & pushprop_lem1_gthm & (hoaslamnotap <=> ! [X18 : subst > term > term,X46 : term,X47 : 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))))) & lamnotvar & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) => ! [X10 : subst > term > subst > $o,X43 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X10 : term > $o,X21 : term] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X21)) => ! [X10 : term > $o,X16 : term,X17 : subst] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)))))))) & (hoasinduction_lem3v2 <=> ! [X10 : subst > term > subst > $o,X11 : term > $o,X48 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X48)) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & (hoasinduction_lem3a <=> ! [X10 : subst > term > subst > $o,X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X13 : term,X15 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15))) => ! [X32 : subst,X18 : subst > term > term,X33 : term,X31 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X14 : subst,X13 : term,X25 : 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)))))))) & (induction2 <=> ! [X10 : term > $o,X22 : term] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))))) & ((! [X14 : subst] : ((comp @ X14 @ id) = X14) & ! [X14 : subst] : ((comp @ id @ X14) = X14)) <=> substmonoid) & (axidl <=> ! [X14 : subst] : ((comp @ id @ X14) = X14)) & ! [X1 : d_term] : (d_one = X1) & pushprop_lthm_orig & (apinj1 <=> ! [X20 : term,X15 : term,X13 : term,X19 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20)))) & pushprop_lem2v2_gthm & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop & axvarshift & pushprop_lem1v2_gthm & ~(var @ (d2term @ d_one)) & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b) & hoasinduction_lem1_gthm & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & pushprop_lem2v2_lthm & axmap & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & ~lamnotap & (hoasinduction_lem3aa <=> ! [X10 : subst > term > subst > $o,X42 : term] : (~! [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)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & ulamvarsh & (! [X24 : term,X23 : term,X10 : subst > term > subst > $o] : (~(X10 @ id @ X24 @ id) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id)) <=> hoasinduction_lem2) & ((d2subst @ d_id) = id) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem3aa_lthm <=> ! [X42 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & hoaslamnotap_gthm & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & (hoaslam = (^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one))) & (! [X15 : term,X20 : term,X19 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20)) <=> hoasapinj2) & pushprop_lem3v2_lthm & (! [X14 : subst,X10 : term > $o,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0) & (laminj <=> ! [X13 : term,X15 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15))) & induction2_gthm & substmonoid_gthm & (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) <=> axshiftcons) & induction2lem_gthm & hoasinduction_lem2_lthm & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (hoasinduction <=> ! [X28 : term,X10 : subst > term > subst > $o] : (~! [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] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & (! [X30 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : term > $o,X17 : subst,X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))) => ! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))))) <=> induction2_lthm) & (hoasinduction_lem3v2a <=> ! [X10 : subst > term > subst > $o,X11 : term > $o,X29 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))) & (hoaslaminj <=> ! [X18 : subst > term > term,X32 : subst,X31 : subst > term > term,X33 : term] : (((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))))) & pushprop_gthm & (induction2lem <=> ! [X16 : term,X17 : subst,X10 : term > $o] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))))) & hoasapnotvar_gthm),
% 32.60/5.94 file('/export/starexec/sandbox/tmp/tmp.SwuThMpGUN/DTF2THF_19838.p',alg444_1)).
% 32.60/5.94 thf(f1217,plain,(
% 32.60/5.94 ( ! [X55 : term] : (((d2term @ (sK481 @ X55)) = X55)) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f4236,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((d2term @ d_one) != (X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1)))) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP57 @ X0) = $true)) )),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f4235,f4138])).
% 32.60/5.94 thf(f4235,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) | ((sP57 @ X0) = $true)) )),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f4140,f4232])).
% 32.60/5.94 thf(f4232,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X7 : term] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ X7 @ (d2subst @ d_id)) != $true)) )),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f4181,f4213])).
% 32.60/5.94 thf(f4213,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP37 @ X0) = $true)) )),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f4212,f4138])).
% 32.60/5.94 thf(f4212,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((d2term @ d_one) != (sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1))) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP37 @ X0) = $true)) )),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f4211,f4138])).
% 32.60/5.94 thf(f4211,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1)))) | ((sP37 @ X0) = $true)) )),
% 32.60/5.94 inference(duplicate_literal_removal,[status(thm)],[f4210])).
% 32.60/5.94 thf(f4210,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP37 @ X0) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1))))) )),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f4145,f4138])).
% 32.60/5.94 thf(f4145,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (sK198 @ X1 @ X0) @ (d2subst @ d_id))) | ((sP37 @ X0) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1))))) )),
% 32.60/5.94 inference(backward_demodulation,[status(thm)],[f1388,f4138])).
% 32.60/5.94 thf(f1388,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (sK198 @ X1 @ X0) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sP37 @ X0) = $true) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1))))) )),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f729,f1046,f1046,f1046,f1116,f1078,f1046])).
% 32.60/5.94 thf(f1078,plain,(
% 32.60/5.94 (one = (d2term @ d_one))),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f1116,plain,(
% 32.60/5.94 ((d2subst @ d_id) = sh)),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f1046,plain,(
% 32.60/5.94 ((d2subst @ d_id) = id)),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f729,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP37 @ X0) = $true) | ((X0 @ id @ (sK198 @ X1 @ X0) @ id) = $true) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1))))) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f219])).
% 32.60/5.94 thf(f219,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : ((((sP37 @ X0) = $true) | ! [X1 : subst > term > term] : ((((X0 @ id @ (sK198 @ X1 @ X0) @ id) = $true) & ((X0 @ id @ (X1 @ id @ (sK198 @ X1 @ X0)) @ id) != $true)) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true) | ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1)))))) & ((! [X7 : term] : (((X0 @ id @ X7 @ id) != $true) | ($true = (X0 @ id @ (sK202 @ X0 @ id @ X7) @ id))) & ((X0 @ id @ (lam @ (sK202 @ X0 @ sh @ one)) @ id) != $true) & ! [X8 : subst,X9 : term,X10 : subst] : ((sK202 @ X0 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8)) = (sub @ (sK202 @ X0 @ X10 @ X9) @ X8))) | ((sP37 @ X0) != $true)))),
% 32.60/5.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199,sK200,sK201,sK202])],[f215,f218,f217,f216])).
% 32.60/5.94 thf(f216,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X2 : term] : (((X0 @ id @ X2 @ id) = $true) & ($true != (X0 @ id @ (X1 @ id @ X2) @ id))) => (((X0 @ id @ (sK198 @ X1 @ X0) @ id) = $true) & ((X0 @ id @ (X1 @ id @ (sK198 @ X1 @ X0)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f217,plain,(
% 32.60/5.94 ! [X1 : subst > term > term] : (? [X3 : subst,X4 : term,X5 : subst] : ((X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3)) != (sub @ (X1 @ X5 @ X4) @ X3)) => ((sub @ (X1 @ (sK201 @ X1) @ (sK200 @ X1)) @ (sK199 @ X1)) != (X1 @ (comp @ (sK201 @ X1) @ (sK199 @ X1)) @ (sub @ (sK200 @ X1) @ (sK199 @ X1)))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f218,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (! [X7 : term] : (((X0 @ id @ X7 @ id) != $true) | ((X0 @ id @ (X6 @ id @ X7) @ id) = $true)) & ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X8 : subst,X9 : term,X10 : subst] : ((sub @ (X6 @ X10 @ X9) @ X8) = (X6 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8)))) => (! [X7 : term] : (((X0 @ id @ X7 @ id) != $true) | ($true = (X0 @ id @ (sK202 @ X0 @ id @ X7) @ id))) & ((X0 @ id @ (lam @ (sK202 @ X0 @ sh @ one)) @ id) != $true) & ! [X10 : subst,X9 : term,X8 : subst] : ((sK202 @ X0 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8)) = (sub @ (sK202 @ X0 @ X10 @ X9) @ X8))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f215,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : ((((sP37 @ X0) = $true) | ! [X1 : subst > term > term] : (? [X2 : term] : (((X0 @ id @ X2 @ id) = $true) & ($true != (X0 @ id @ (X1 @ id @ X2) @ id))) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true) | ? [X3 : subst,X4 : term,X5 : subst] : ((X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3)) != (sub @ (X1 @ X5 @ X4) @ X3)))) & (? [X6 : subst > term > term] : (! [X7 : term] : (((X0 @ id @ X7 @ id) != $true) | ((X0 @ id @ (X6 @ id @ X7) @ id) = $true)) & ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X8 : subst,X9 : term,X10 : subst] : ((sub @ (X6 @ X10 @ X9) @ X8) = (X6 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8)))) | ((sP37 @ X0) != $true)))),
% 32.60/5.94 inference(rectify,[status(thm)],[f214])).
% 32.60/5.94 thf(f214,plain,(
% 32.60/5.94 ! [X466 : subst > term > subst > $o] : ((((sP37 @ X466) = $true) | ! [X472 : subst > term > term] : (? [X476 : term] : (((X466 @ id @ X476 @ id) = $true) & ((X466 @ id @ (X472 @ id @ X476) @ id) != $true)) | ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) = $true) | ? [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) != (sub @ (X472 @ X475 @ X474) @ X473)))) & (? [X472 : subst > term > term] : (! [X476 : term] : (((X466 @ id @ X476 @ id) != $true) | ((X466 @ id @ (X472 @ id @ X476) @ id) = $true)) & ((X466 @ id @ (lam @ (X472 @ sh @ one)) @ id) != $true) & ! [X473 : subst,X474 : term,X475 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473)) = (sub @ (X472 @ X475 @ X474) @ X473))) | ((sP37 @ X466) != $true)))),
% 32.60/5.94 inference(nnf_transformation,[status(thm)],[f51])).
% 32.60/5.94 thf(f4181,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X7 : term] : (((X0 @ (d2subst @ d_id) @ X7 @ (d2subst @ d_id)) != $true) | ((sP37 @ X0) != $true) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.60/5.94 inference(backward_demodulation,[status(thm)],[f1390,f4138])).
% 32.60/5.94 thf(f1390,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X7 : term] : (((X0 @ (d2subst @ d_id) @ (sK202 @ X0 @ (d2subst @ d_id) @ X7) @ (d2subst @ d_id)) = $true) | ((sP37 @ X0) != $true) | ((X0 @ (d2subst @ d_id) @ X7 @ (d2subst @ d_id)) != $true)) )),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f727,f1046,f1046,f1046,f1046,f1046])).
% 32.60/5.94 thf(f727,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X7 : term] : (((X0 @ id @ X7 @ id) != $true) | ($true = (X0 @ id @ (sK202 @ X0 @ id @ X7) @ id)) | ((sP37 @ X0) != $true)) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f219])).
% 32.60/5.94 thf(f4140,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP57 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (sK75 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1)))) )),
% 32.60/5.94 inference(backward_demodulation,[status(thm)],[f1274,f4138])).
% 32.60/5.94 thf(f1274,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((X0 @ (d2subst @ d_id) @ (sK75 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) | ((sP57 @ X0) = $true)) )),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f564,f1046,f1046,f1046,f1116,f1078,f1046])).
% 32.60/5.94 thf(f564,plain,(
% 32.60/5.94 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP57 @ X0) = $true) | ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) | ((X0 @ id @ (sK75 @ X1 @ X0) @ id) = $true) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true)) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f87])).
% 32.60/5.94 thf(f87,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : ((((sP57 @ X0) = $true) | ! [X1 : subst > term > term] : (((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) | (((X0 @ id @ (X1 @ id @ (sK75 @ X1 @ X0)) @ id) != $true) & ((X0 @ id @ (sK75 @ X1 @ X0) @ id) = $true)) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true))) & ((! [X7 : term,X8 : subst,X9 : subst] : ((sub @ (sK76 @ X0 @ X8 @ X7) @ X9) = (sK76 @ X0 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9))) & ! [X10 : term] : (((X0 @ id @ (sK76 @ X0 @ id @ X10) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ((X0 @ id @ (lam @ (sK76 @ X0 @ sh @ one)) @ id) != $true)) | ((sP57 @ X0) != $true)))),
% 32.60/5.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74,sK75,sK76])],[f83,f86,f85,f84])).
% 32.60/5.94 thf(f84,plain,(
% 32.60/5.94 ! [X1 : subst > term > term] : (? [X2 : term,X3 : subst,X4 : subst] : ((X1 @ (comp @ X3 @ X4) @ (sub @ X2 @ X4)) != (sub @ (X1 @ X3 @ X2) @ X4)) => ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))) != (sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f85,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X5 : term] : (((X0 @ id @ (X1 @ id @ X5) @ id) != $true) & ($true = (X0 @ id @ X5 @ id))) => (((X0 @ id @ (X1 @ id @ (sK75 @ X1 @ X0)) @ id) != $true) & ((X0 @ id @ (sK75 @ X1 @ X0) @ id) = $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f86,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (! [X7 : term,X8 : subst,X9 : subst] : ((X6 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9)) = (sub @ (X6 @ X8 @ X7) @ X9)) & ! [X10 : term] : (((X0 @ id @ (X6 @ id @ X10) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true)) => (! [X9 : subst,X8 : subst,X7 : term] : ((sub @ (sK76 @ X0 @ X8 @ X7) @ X9) = (sK76 @ X0 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9))) & ! [X10 : term] : (((X0 @ id @ (sK76 @ X0 @ id @ X10) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ((X0 @ id @ (lam @ (sK76 @ X0 @ sh @ one)) @ id) != $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f83,plain,(
% 32.60/5.94 ! [X0 : subst > term > subst > $o] : ((((sP57 @ X0) = $true) | ! [X1 : subst > term > term] : (? [X2 : term,X3 : subst,X4 : subst] : ((X1 @ (comp @ X3 @ X4) @ (sub @ X2 @ X4)) != (sub @ (X1 @ X3 @ X2) @ X4)) | ? [X5 : term] : (((X0 @ id @ (X1 @ id @ X5) @ id) != $true) & ($true = (X0 @ id @ X5 @ id))) | ((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) = $true))) & (? [X6 : subst > term > term] : (! [X7 : term,X8 : subst,X9 : subst] : ((X6 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9)) = (sub @ (X6 @ X8 @ X7) @ X9)) & ! [X10 : term] : (((X0 @ id @ (X6 @ id @ X10) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true)) | ((sP57 @ X0) != $true)))),
% 32.60/5.94 inference(rectify,[status(thm)],[f82])).
% 32.60/5.94 thf(f82,plain,(
% 32.60/5.94 ! [X356 : subst > term > subst > $o] : ((((sP57 @ X356) = $true) | ! [X369 : subst > term > term] : (? [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) != (sub @ (X369 @ X372 @ X371) @ X373)) | ? [X370 : term] : (($true != (X356 @ id @ (X369 @ id @ X370) @ id)) & ((X356 @ id @ X370 @ id) = $true)) | ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) = $true))) & (? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((X369 @ (comp @ X372 @ X373) @ (sub @ X371 @ X373)) = (sub @ (X369 @ X372 @ X371) @ X373)) & ! [X370 : term] : (($true = (X356 @ id @ (X369 @ id @ X370) @ id)) | ((X356 @ id @ X370 @ id) != $true)) & ((X356 @ id @ (lam @ (X369 @ sh @ one)) @ id) != $true)) | ((sP57 @ X356) != $true)))),
% 32.60/5.94 inference(nnf_transformation,[status(thm)],[f71])).
% 32.60/5.94 thf(f7678,plain,(
% 32.60/5.94 ( ! [X11 : term] : (($false = (sK59 @ (d2subst @ d_id) @ X11 @ (d2subst @ d_id)))) ) | (spl591_255 | ~spl591_515 | ~spl591_517)),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f4612,f7546])).
% 32.60/5.94 thf(f7546,plain,(
% 32.60/5.94 ( ! [X0 : term] : (($true != (sK60 @ X0))) ) | (spl591_255 | ~spl591_515)),
% 32.60/5.94 inference(superposition,[status(thm)],[f3219,f4598])).
% 32.60/5.94 thf(f4598,plain,(
% 32.60/5.94 ( ! [X10 : term,X9 : term] : ((X9 = X10)) ) | ~spl591_515),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f4597])).
% 32.60/5.94 thf(f3219,plain,(
% 32.60/5.94 ($true != (sK60 @ (lam @ sK61))) | spl591_255),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3217])).
% 32.60/5.94 thf(f4612,plain,(
% 32.60/5.94 ( ! [X11 : term] : (((sK60 @ X11) = $true) | ($false = (sK59 @ (d2subst @ d_id) @ X11 @ (d2subst @ d_id)))) ) | ~spl591_517),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f4611])).
% 32.60/5.94 thf(f12736,plain,(
% 32.60/5.94 spl591_633 | ~spl591_401 | ~spl591_515),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f7436,f4597,f3827,f6777])).
% 32.60/5.94 thf(f6777,definition,(
% 32.60/5.94 spl591_633 <=> ! [X1 : term] : ($false = (sK592 @ X1))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_633])],[avatar_definition])).
% 32.60/5.94 thf(f3827,definition,(
% 32.60/5.94 spl591_401 <=> ($false = (sK592 @ (lam @ sK598)))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_401])],[avatar_definition])).
% 32.60/5.94 thf(f7436,plain,(
% 32.60/5.94 ( ! [X0 : term] : (($false = (sK592 @ X0))) ) | (~spl591_401 | ~spl591_515)),
% 32.60/5.94 inference(superposition,[status(thm)],[f3829,f4598])).
% 32.60/5.94 thf(f3829,plain,(
% 32.60/5.94 ($false = (sK592 @ (lam @ sK598))) | ~spl591_401),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3827])).
% 32.60/5.94 thf(f7414,plain,(
% 32.60/5.94 spl591_515),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f7410,f4597])).
% 32.60/5.94 thf(f7410,plain,(
% 32.60/5.94 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 32.60/5.94 inference(superposition,[status(thm)],[f4138,f4138])).
% 32.60/5.94 thf(f7333,plain,(
% 32.60/5.94 ~spl591_404 | ~spl591_406 | ~spl591_633),
% 32.60/5.94 inference(avatar_contradiction_clause,[status(thm)],[f7332])).
% 32.60/5.94 thf(f7332,plain,(
% 32.60/5.94 $false | (~spl591_404 | ~spl591_406 | ~spl591_633)),
% 32.60/5.94 inference(trivial_inequality_removal,[status(thm)],[f7331])).
% 32.60/5.94 thf(f7331,plain,(
% 32.60/5.94 ($false = $true) | (~spl591_404 | ~spl591_406 | ~spl591_633)),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f3850,f7217])).
% 32.60/5.94 thf(f7217,plain,(
% 32.60/5.94 ( ! [X1 : term] : (($false = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id)))) ) | (~spl591_404 | ~spl591_633)),
% 32.60/5.94 inference(trivial_inequality_removal,[status(thm)],[f7216])).
% 32.60/5.94 thf(f7216,plain,(
% 32.60/5.94 ( ! [X1 : term] : (($false = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | ($false = $true)) ) | (~spl591_404 | ~spl591_633)),
% 32.60/5.94 inference(backward_demodulation,[status(thm)],[f3841,f6778])).
% 32.60/5.94 thf(f6778,plain,(
% 32.60/5.94 ( ! [X1 : term] : (($false = (sK592 @ X1))) ) | ~spl591_633),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f6777])).
% 32.60/5.94 thf(f3841,plain,(
% 32.60/5.94 ( ! [X1 : term] : (($false = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | ((sK592 @ X1) = $true)) ) | ~spl591_404),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3840])).
% 32.60/5.94 thf(f3840,definition,(
% 32.60/5.94 spl591_404 <=> ! [X1 : term] : (($false = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | ((sK592 @ X1) = $true))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_404])],[avatar_definition])).
% 32.60/5.94 thf(f3850,plain,(
% 32.60/5.94 ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ~spl591_406),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3848])).
% 32.60/5.94 thf(f3848,definition,(
% 32.60/5.94 spl591_406 <=> ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_406])],[avatar_definition])).
% 32.60/5.94 thf(f7223,plain,(
% 32.60/5.94 ~spl591_404 | ~spl591_408 | ~spl591_633),
% 32.60/5.94 inference(avatar_contradiction_clause,[status(thm)],[f7222])).
% 32.60/5.94 thf(f7222,plain,(
% 32.60/5.94 $false | (~spl591_404 | ~spl591_408 | ~spl591_633)),
% 32.60/5.94 inference(subsumption_resolution,[status(thm)],[f7221,f4138])).
% 32.60/5.94 thf(f7221,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (((d2term @ d_one) != (sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)))) ) | (~spl591_404 | ~spl591_408 | ~spl591_633)),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f7220,f4138])).
% 32.60/5.94 thf(f7220,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))))) ) | (~spl591_404 | ~spl591_408 | ~spl591_633)),
% 32.60/5.94 inference(trivial_inequality_removal,[status(thm)],[f7219])).
% 32.60/5.94 thf(f7219,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = $true) | ((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))))) ) | (~spl591_404 | ~spl591_408 | ~spl591_633)),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f3857,f7217])).
% 32.60/5.94 thf(f3857,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($true = (sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id))) | ((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))))) ) | ~spl591_408),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3856])).
% 32.60/5.94 thf(f3856,definition,(
% 32.60/5.94 spl591_408 <=> ! [X1 : subst > term > term] : (($true = (sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id))) | ((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1)))))),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_408])],[avatar_definition])).
% 32.60/5.94 thf(f5545,plain,(
% 32.60/5.94 ~spl591_197 | ~spl591_402),
% 32.60/5.94 inference(avatar_contradiction_clause,[status(thm)],[f5544])).
% 32.60/5.94 thf(f5544,plain,(
% 32.60/5.94 $false | (~spl591_197 | ~spl591_402)),
% 32.60/5.94 inference(trivial_inequality_removal,[status(thm)],[f5543])).
% 32.60/5.94 thf(f5543,plain,(
% 32.60/5.94 ($false = $true) | (~spl591_197 | ~spl591_402)),
% 32.60/5.94 inference(forward_demodulation,[status(thm)],[f2966,f3833])).
% 32.60/5.94 thf(f3833,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ~spl591_402),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f3831])).
% 32.60/5.94 thf(f3831,definition,(
% 32.60/5.94 spl591_402 <=> (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_402])],[avatar_definition])).
% 32.60/5.94 thf(f2966,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $true) | ~spl591_197),
% 32.60/5.94 inference(avatar_component_clause,[status(thm)],[f2965])).
% 32.60/5.94 thf(f2965,definition,(
% 32.60/5.94 spl591_197 <=> (hoasinduction_lem3v2 = $true)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_197])],[avatar_definition])).
% 32.60/5.94 thf(f4848,plain,(
% 32.60/5.94 spl591_191 | ~spl591_545),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f558,f4845,f2940])).
% 32.60/5.94 thf(f2940,definition,(
% 32.60/5.94 spl591_191 <=> (sP58 = $true)),
% 32.60/5.94 introduced(definition,[new_symbols(naming,[spl591_191])],[avatar_definition])).
% 32.60/5.94 thf(f558,plain,(
% 32.60/5.94 ((sP57 @ sK59) != $true) | (sP58 = $true)),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f81])).
% 32.60/5.94 thf(f81,plain,(
% 32.60/5.94 ((sP58 = $true) | (! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (((sK59 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5) @ X6) = $true) | ((sK59 @ X4 @ X3 @ (comp @ X5 @ X6)) != $true)) & ($true != (sK60 @ (lam @ sK61))) & ((sP57 @ sK59) != $true) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (((sK59 @ (comp @ X9 @ X7) @ (sub @ X10 @ X7) @ X8) != $true) | ((sK59 @ X9 @ X10 @ (comp @ X7 @ X8)) = $true)) & ! [X11 : term] : ((sK59 @ id @ X11 @ id) = (sK60 @ X11)) & ! [X12 : term] : (($true = (sK60 @ (sub @ sK61 @ (push @ X12 @ id)))) | ((sK60 @ X12) != $true)))) & (! [X13 : subst > term > subst > $o,X14 : term > $o,X15 : term] : ((((X13 @ (comp @ (sK63 @ X13) @ (sK64 @ X13)) @ (sub @ (sK62 @ X13) @ (sK64 @ X13)) @ (sK65 @ X13)) != $true) & ((X13 @ (sK63 @ X13) @ (sK62 @ X13) @ (comp @ (sK64 @ X13) @ (sK65 @ X13))) = $true)) | ((X14 @ (lam @ X15)) = $true) | ((sP57 @ X13) = $true) | (((X13 @ (comp @ (sK68 @ X13) @ (sK66 @ X13)) @ (sub @ (sK69 @ X13) @ (sK66 @ X13)) @ (sK67 @ X13)) = $true) & ($true != (X13 @ (sK68 @ X13) @ (sK69 @ X13) @ (comp @ (sK66 @ X13) @ (sK67 @ X13))))) | ((X13 @ id @ (sK70 @ X14 @ X13) @ id) != (X14 @ (sK70 @ X14 @ X13))) | (((X14 @ (sub @ X15 @ (push @ (sK71 @ X15 @ X14) @ id))) != $true) & ($true = (X14 @ (sK71 @ X15 @ X14))))) | (sP58 != $true))),
% 32.60/5.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63,sK64,sK65,sK66,sK67,sK68,sK69,sK70,sK71])],[f75,f80,f79,f78,f77,f76])).
% 32.60/5.94 thf(f76,plain,(
% 32.60/5.94 ? [X0 : subst > term > subst > $o,X1 : term > $o,X2 : term] : (! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (((X0 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5) @ X6) = $true) | ((X0 @ X4 @ X3 @ (comp @ X5 @ X6)) != $true)) & ((X1 @ (lam @ X2)) != $true) & ((sP57 @ X0) != $true) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X0 @ (comp @ X9 @ X7) @ (sub @ X10 @ X7) @ X8)) | ((X0 @ X9 @ X10 @ (comp @ X7 @ X8)) = $true)) & ! [X11 : term] : ((X0 @ id @ X11 @ id) = (X1 @ X11)) & ! [X12 : term] : (((X1 @ (sub @ X2 @ (push @ X12 @ id))) = $true) | ((X1 @ X12) != $true))) => (! [X6 : subst,X5 : subst,X4 : subst,X3 : term] : (((sK59 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5) @ X6) = $true) | ((sK59 @ X4 @ X3 @ (comp @ X5 @ X6)) != $true)) & ($true != (sK60 @ (lam @ sK61))) & ((sP57 @ sK59) != $true) & ! [X10 : term,X9 : subst,X8 : subst,X7 : subst] : (((sK59 @ (comp @ X9 @ X7) @ (sub @ X10 @ X7) @ X8) != $true) | ((sK59 @ X9 @ X10 @ (comp @ X7 @ X8)) = $true)) & ! [X11 : term] : ((sK59 @ id @ X11 @ id) = (sK60 @ X11)) & ! [X12 : term] : (($true = (sK60 @ (sub @ sK61 @ (push @ X12 @ id)))) | ((sK60 @ X12) != $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f77,plain,(
% 32.60/5.94 ! [X13 : subst > term > subst > $o] : (? [X16 : term,X17 : subst,X18 : subst,X19 : subst] : (((X13 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18) @ X19) != $true) & ($true = (X13 @ X17 @ X16 @ (comp @ X18 @ X19)))) => (((X13 @ (comp @ (sK63 @ X13) @ (sK64 @ X13)) @ (sub @ (sK62 @ X13) @ (sK64 @ X13)) @ (sK65 @ X13)) != $true) & ((X13 @ (sK63 @ X13) @ (sK62 @ X13) @ (comp @ (sK64 @ X13) @ (sK65 @ X13))) = $true)))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f78,plain,(
% 32.60/5.94 ! [X13 : subst > term > subst > $o] : (? [X20 : subst,X21 : subst,X22 : subst,X23 : term] : (((X13 @ (comp @ X22 @ X20) @ (sub @ X23 @ X20) @ X21) = $true) & ($true != (X13 @ X22 @ X23 @ (comp @ X20 @ X21)))) => (((X13 @ (comp @ (sK68 @ X13) @ (sK66 @ X13)) @ (sub @ (sK69 @ X13) @ (sK66 @ X13)) @ (sK67 @ X13)) = $true) & ($true != (X13 @ (sK68 @ X13) @ (sK69 @ X13) @ (comp @ (sK66 @ X13) @ (sK67 @ X13))))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f79,plain,(
% 32.60/5.94 ! [X13 : subst > term > subst > $o,X14 : term > $o] : (? [X24 : term] : ((X14 @ X24) != (X13 @ id @ X24 @ id)) => ((X13 @ id @ (sK70 @ X14 @ X13) @ id) != (X14 @ (sK70 @ X14 @ X13))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f80,plain,(
% 32.60/5.94 ! [X14 : term > $o,X15 : term] : (? [X25 : term] : (((X14 @ (sub @ X15 @ (push @ X25 @ id))) != $true) & ((X14 @ X25) = $true)) => (((X14 @ (sub @ X15 @ (push @ (sK71 @ X15 @ X14) @ id))) != $true) & ($true = (X14 @ (sK71 @ X15 @ X14)))))),
% 32.60/5.94 introduced(definition,[],[choice_axiom])).
% 32.60/5.94 thf(f75,plain,(
% 32.60/5.94 ((sP58 = $true) | ? [X0 : subst > term > subst > $o,X1 : term > $o,X2 : term] : (! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (((X0 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5) @ X6) = $true) | ((X0 @ X4 @ X3 @ (comp @ X5 @ X6)) != $true)) & ((X1 @ (lam @ X2)) != $true) & ((sP57 @ X0) != $true) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X0 @ (comp @ X9 @ X7) @ (sub @ X10 @ X7) @ X8)) | ((X0 @ X9 @ X10 @ (comp @ X7 @ X8)) = $true)) & ! [X11 : term] : ((X0 @ id @ X11 @ id) = (X1 @ X11)) & ! [X12 : term] : (((X1 @ (sub @ X2 @ (push @ X12 @ id))) = $true) | ((X1 @ X12) != $true)))) & (! [X13 : subst > term > subst > $o,X14 : term > $o,X15 : term] : (? [X16 : term,X17 : subst,X18 : subst,X19 : subst] : (((X13 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18) @ X19) != $true) & ($true = (X13 @ X17 @ X16 @ (comp @ X18 @ X19)))) | ((X14 @ (lam @ X15)) = $true) | ((sP57 @ X13) = $true) | ? [X20 : subst,X21 : subst,X22 : subst,X23 : term] : (((X13 @ (comp @ X22 @ X20) @ (sub @ X23 @ X20) @ X21) = $true) & ($true != (X13 @ X22 @ X23 @ (comp @ X20 @ X21)))) | ? [X24 : term] : ((X14 @ X24) != (X13 @ id @ X24 @ id)) | ? [X25 : term] : (((X14 @ (sub @ X15 @ (push @ X25 @ id))) != $true) & ((X14 @ X25) = $true))) | (sP58 != $true))),
% 32.60/5.94 inference(rectify,[status(thm)],[f74])).
% 32.60/5.94 thf(f74,plain,(
% 32.60/5.94 ((sP58 = $true) | ? [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (! [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) = $true) | ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) != $true)) & ((X357 @ (lam @ X358)) != $true) & ((sP57 @ X356) != $true) & ! [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) != $true) | ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) = $true)) & ! [X359 : term] : ((X357 @ X359) = (X356 @ id @ X359 @ id)) & ! [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) = $true) | ($true != (X357 @ X364))))) & (! [X356 : subst > term > subst > $o,X357 : term > $o,X358 : term] : (? [X360 : term,X361 : subst,X362 : subst,X363 : subst] : (((X356 @ (comp @ X361 @ X362) @ (sub @ X360 @ X362) @ X363) != $true) & ((X356 @ X361 @ X360 @ (comp @ X362 @ X363)) = $true)) | ((X357 @ (lam @ X358)) = $true) | ((sP57 @ X356) = $true) | ? [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (((X356 @ (comp @ X367 @ X365) @ (sub @ X368 @ X365) @ X366) = $true) & ((X356 @ X367 @ X368 @ (comp @ X365 @ X366)) != $true)) | ? [X359 : term] : ((X357 @ X359) != (X356 @ id @ X359 @ id)) | ? [X364 : term] : (((X357 @ (sub @ X358 @ (push @ X364 @ id))) != $true) & ($true = (X357 @ X364)))) | (sP58 != $true))),
% 32.60/5.94 inference(nnf_transformation,[status(thm)],[f72])).
% 32.60/5.94 thf(f4613,plain,(
% 32.60/5.94 spl591_517 | spl591_191),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f1702,f2940,f4611])).
% 32.60/5.94 thf(f1702,plain,(
% 32.60/5.94 ( ! [X11 : term] : ((sP58 = $true) | ((sK60 @ X11) = $true) | ($false = (sK59 @ (d2subst @ d_id) @ X11 @ (d2subst @ d_id)))) )),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1263])).
% 32.60/5.94 thf(f1263,plain,(
% 32.60/5.94 ( ! [X11 : term] : (((sK60 @ X11) = (sK59 @ (d2subst @ d_id) @ X11 @ (d2subst @ d_id))) | (sP58 = $true)) )),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f556,f1046,f1046])).
% 32.60/5.94 thf(f556,plain,(
% 32.60/5.94 ( ! [X11 : term] : ((sP58 = $true) | ((sK59 @ id @ X11 @ id) = (sK60 @ X11))) )),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f81])).
% 32.60/5.94 thf(f4559,plain,(
% 32.60/5.94 ~spl591_191 | spl591_197),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f1251,f2965,f2940])).
% 32.60/5.94 thf(f1251,plain,(
% 32.60/5.94 (sP58 != $true) | (hoasinduction_lem3v2 = $true)),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f3858,plain,(
% 32.60/5.94 spl591_406 | spl591_408 | spl591_402),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f1785,f3831,f3856,f3848])).
% 32.60/5.94 thf(f1785,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($true = (sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id))) | (hoasinduction_lem3v2 = $false) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))))) )),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1783])).
% 32.60/5.94 thf(f1783,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)) != (X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1)))) | (hoasinduction_lem3v2 = $false) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id))))) )),
% 32.60/5.94 inference(equality_proxy_clausification,[status(thm)],[f1782])).
% 32.60/5.94 thf(f1782,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = ((X1 @ (comp @ (sK596 @ X1) @ (sK597 @ X1)) @ (sub @ (sK595 @ X1) @ (sK597 @ X1))) = (sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK597 @ X1)))) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1781])).
% 32.60/5.94 thf(f1781,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2 = $false) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | ($false = ((^[Y0 : subst]: ((X1 @ (comp @ (sK596 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ Y0))) @ (sK597 @ X1)))) )),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1780])).
% 32.60/5.94 thf(f1780,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = (!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK596 @ X1) @ Y0) @ (sub @ (sK595 @ X1) @ Y0)) = (sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ Y0))))) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1779])).
% 32.60/5.94 thf(f1779,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | (hoasinduction_lem3v2 = $false) | ($false = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK595 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK595 @ X1)) @ Y1))))) @ (sK596 @ X1))) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1778])).
% 32.60/5.94 thf(f1778,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK595 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK595 @ X1)) @ Y1))))))) | (hoasinduction_lem3v2 = $false) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id))))) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1777])).
% 32.60/5.94 thf(f1777,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))) @ (sK595 @ X1))) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1776])).
% 32.60/5.94 thf(f1776,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) | ($false = ((sK593 @ (d2subst @ d_id) @ (sK594 @ X1) @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK594 @ X1)) @ (d2subst @ d_id)))) | (hoasinduction_lem3v2 = $false) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1775])).
% 32.60/5.94 thf(f1775,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : (($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) | (((^[Y0 : term]: ((sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id)))) @ (sK594 @ X1)) = $false) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1774])).
% 32.60/5.94 thf(f1774,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3v2 = $false) | ((!! @ term @ (^[Y0 : term]: ((sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) | ((sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)) )),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1773])).
% 32.60/5.94 thf(f1773,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : ((((!! @ term @ (^[Y0 : term]: ((sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) | (hoasinduction_lem3v2 = $false) | ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2)))))))))) )),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1772])).
% 32.60/5.94 thf(f1772,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3v2 = $false) | (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) = $true)) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1771])).
% 32.60/5.94 thf(f1771,plain,(
% 32.60/5.94 ( ! [X1 : subst > term > term] : ((((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) @ X1) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(pi_clausification,[status(thm)],[f1770])).
% 32.60/5.94 thf(f1770,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) = $true)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1758])).
% 32.60/5.94 thf(f1758,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ($false = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0))))))))),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1747])).
% 32.60/5.94 thf(f1747,plain,(
% 32.60/5.94 ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK593 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0) @ Y3) => (sK593 @ Y2 @ Y1 @ (comp @ Y0 @ Y3))))))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0))))))))) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1746])).
% 32.60/5.94 thf(f1746,plain,(
% 32.60/5.94 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK593 @ Y0 @ Y1 @ (comp @ Y3 @ Y2)) => (sK593 @ (comp @ Y0 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK593 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0) @ Y3) => (sK593 @ Y2 @ Y1 @ (comp @ Y0 @ Y3))))))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK593 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK593 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0))))))))) = $false) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1745])).
% 32.60/5.94 thf(f1745,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ($false = ((^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y1 @ Y2 @ (comp @ Y4 @ Y3)) => (Y0 @ (comp @ Y1 @ Y4) @ (sub @ Y2 @ Y4) @ Y3)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) = (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((sK592 @ Y2) => (sK592 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y1)))))))))) @ sK593))),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1744])).
% 32.60/5.94 thf(f1744,plain,(
% 32.60/5.94 ($false = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y1 @ Y2 @ (comp @ Y4 @ Y3)) => (Y0 @ (comp @ Y1 @ Y4) @ (sub @ Y2 @ Y4) @ Y3)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) = (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((sK592 @ Y2) => (sK592 @ (sub @ Y1 @ (push @ Y2 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y1)))))))))))) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1743])).
% 32.60/5.94 thf(f1743,plain,(
% 32.60/5.94 (((^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y1 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (Y1 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y2)))))))))))) @ sK592) = $false) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1742])).
% 32.60/5.94 thf(f1742,plain,(
% 32.60/5.94 ($false = (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y1 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (Y1 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y2)))))))))))))) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1740])).
% 32.60/5.94 thf(f1740,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 != (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y1 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y1 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (Y1 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y2))))))))))))))),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1262])).
% 32.60/5.94 thf(f1262,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 != (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ (d2subst @ d_id) @ Y3 @ (d2subst @ d_id)) => (Y1 @ (d2subst @ d_id) @ (Y2 @ (d2subst @ d_id) @ Y3) @ (d2subst @ d_id))))) => (Y1 @ (d2subst @ d_id) @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ (d2subst @ d_id) @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ (d2subst @ d_id)))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (d2subst @ d_id) @ Y4 @ (d2subst @ d_id)))))))) @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ (d2subst @ d_id))))))) => (Y0 @ (lam @ Y2))))))))))))))),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f546,f1046,f1046,f1046,f1046,f1046,f1046,f1115,f1046,f1046,f1261,f1046])).
% 32.60/5.94 thf(f1261,plain,(
% 32.60/5.94 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)))))))))),
% 32.60/5.94 inference(definition_unfolding,[status(thm)],[f1108,f1046,f1046])).
% 32.60/5.94 thf(f1108,plain,(
% 32.60/5.94 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id))))))))),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f1115,plain,(
% 32.60/5.94 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f545])).
% 32.60/5.94 thf(f546,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 != (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2))))))))))))))),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f9])).
% 32.60/5.94 thf(f9,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 != (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2))))))))))))))),
% 32.60/5.94 inference(flattening,[status(thm)],[f6])).
% 32.60/5.94 thf(f6,plain,(
% 32.60/5.94 ~(hoasinduction_lem3v2 = (!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ Y2 @ Y3 @ (comp @ Y5 @ Y4)) => (Y1 @ (comp @ Y2 @ Y5) @ (sub @ Y3 @ Y5) @ Y4)))))))))) => ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2) @ Y5) => (Y1 @ Y4 @ Y3 @ (comp @ Y2 @ Y5))))))))))) => ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5)) = (sub @ (Y2 @ Y4 @ Y3) @ Y5)))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2))))))))))))))),
% 32.60/5.94 inference(fool_elimination,[status(thm)],[f5])).
% 32.60/5.94 thf(f5,plain,(
% 32.60/5.94 ~(! [X0 : subst > term > subst > $o,X1 : term > $o] : (! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((X0 @ X5 @ X4 @ (comp @ X2 @ X3)) => (X0 @ (comp @ X5 @ X2) @ (sub @ X4 @ X2) @ X3)) => (! [X6 : subst,X7 : subst,X8 : term,X9 : subst] : ((X0 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9) @ X6) => (X0 @ X7 @ X8 @ (comp @ X9 @ X6))) => (! [X10 : subst > term > term] : (! [X11 : subst,X12 : subst,X13 : term] : ((X10 @ (comp @ X12 @ X11) @ (sub @ X13 @ X11)) = (sub @ (X10 @ X12 @ X13) @ X11)) => (! [X14 : term] : ((X0 @ id @ X14 @ id) => (X0 @ id @ (X10 @ id @ X14) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X15 : subst, X16 : term] : (X10 @ X15 @ X16))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X17 : term] : (! [X18 : term] : ((X1 @ X18) => (X1 @ (sub @ X17 @ (push @ X18 @ id)))) => (X1 @ (lam @ X17))))))) = hoasinduction_lem3v2)),
% 32.60/5.94 inference(rectify,[status(thm)],[f3])).
% 32.60/5.94 thf(f3,negated_conjecture,(
% 32.60/5.94 ~(! [X10 : subst > term > subst > $o,X11 : term > $o] : (! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) => (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) => (! [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 @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ((hoasinduction_p_and_p_prime @ X10 @ X11) => ! [X13 : term] : (! [X15 : term] : ((X11 @ X15) => (X11 @ (sub @ X13 @ (push @ X15 @ id)))) => (X11 @ (lam @ X13))))))) = hoasinduction_lem3v2)),
% 32.60/5.94 inference(negated_conjecture,[status(cth)],[f2])).
% 32.60/5.94 thf(f2,conjecture,(
% 32.60/5.94 (! [X10 : subst > term > subst > $o,X11 : term > $o] : (! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) => (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) => (! [X18 : subst > term > term] : (! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ((hoasinduction_p_and_p_prime @ X10 @ X11) => ! [X13 : term] : (! [X15 : term] : ((X11 @ X15) => (X11 @ (sub @ X13 @ (push @ X15 @ id)))) => (X11 @ (lam @ X13))))))) = hoasinduction_lem3v2)),
% 32.60/5.94 file('/export/starexec/sandbox/tmp/tmp.SwuThMpGUN/DTF2THF_19838.p',hoasinduction_lem3v2)).
% 32.60/5.94 thf(f3842,plain,(
% 32.60/5.94 spl591_404 | spl591_402),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f1791,f3831,f3840])).
% 32.60/5.94 thf(f1791,plain,(
% 32.60/5.94 ( ! [X1 : term] : (($false = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | ((sK592 @ X1) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1790])).
% 32.60/5.94 thf(f1790,plain,(
% 32.60/5.94 ( ! [X1 : term] : (((sK592 @ X1) = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(equality_proxy_clausification,[status(thm)],[f1789])).
% 32.60/5.94 thf(f1789,plain,(
% 32.60/5.94 ( ! [X1 : term] : ((hoasinduction_lem3v2 = $false) | (((sK592 @ X1) = (sK593 @ (d2subst @ d_id) @ X1 @ (d2subst @ d_id))) = $true)) )),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1788])).
% 32.60/5.94 thf(f1788,plain,(
% 32.60/5.94 ( ! [X1 : term] : ((((^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))) @ X1) = $true) | (hoasinduction_lem3v2 = $false)) )),
% 32.60/5.94 inference(pi_clausification,[status(thm)],[f1787])).
% 32.60/5.94 thf(f1787,plain,(
% 32.60/5.94 ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) = $true) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1769])).
% 32.60/5.94 thf(f1769,plain,(
% 32.60/5.94 ($false = ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) = (sK593 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0))))))) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1758])).
% 32.60/5.94 thf(f3834,plain,(
% 32.60/5.94 spl591_401 | spl591_402),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f1795,f3831,f3827])).
% 32.60/5.94 thf(f1795,plain,(
% 32.60/5.94 ($false = (sK592 @ (lam @ sK598))) | (hoasinduction_lem3v2 = $false)),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1794])).
% 32.60/5.94 thf(f1794,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) => (sK592 @ (sub @ sK598 @ (push @ Y0 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ sK598))))),
% 32.60/5.94 inference(beta_eta_normalization,[status(thm)],[f1793])).
% 32.60/5.94 thf(f1793,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ($false = ((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0)))) @ sK598))),
% 32.60/5.94 inference(sigma_clausification,[status(thm)],[f1786])).
% 32.60/5.94 thf(f1786,plain,(
% 32.60/5.94 (hoasinduction_lem3v2 = $false) | ($false = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => (sK592 @ (sub @ Y0 @ (push @ Y1 @ (d2subst @ d_id))))))) => (sK592 @ (lam @ Y0))))))),
% 32.60/5.94 inference(binary_proxy_clausification,[status(thm)],[f1769])).
% 32.60/5.94 thf(f3220,plain,(
% 32.60/5.94 ~spl591_255 | spl591_191),
% 32.60/5.94 inference(avatar_split_clause,[status(thm)],[f559,f2940,f3217])).
% 32.60/5.94 thf(f559,plain,(
% 32.60/5.94 ($true != (sK60 @ (lam @ sK61))) | (sP58 = $true)),
% 32.60/5.94 inference(cnf_transformation,[status(thm)],[f81])).
% 32.60/5.94 % SZS output end Proof for DTF2THF_19838
% 32.60/5.94 % (20337)------------------------------
% 32.60/5.94 % (20337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.60/5.94 % (20337)Termination reason: Refutation
% 32.60/5.94
% 32.60/5.94 % (20337)Memory used [KB]: 15863
% 32.60/5.94 % (20337)Time elapsed: 0.981 s
% 32.60/5.94 % (20337)Instructions burned: 3004 (million)
% 32.60/5.94 % (20337)------------------------------
% 32.60/5.94 % (20337)------------------------------
% 32.60/5.94 % (20171)Success in time 4.423 s
%------------------------------------------------------------------------------