%------------------------------------------------------------------------------
% 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 : n001.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 06:58:52 PM UTC 2026
% Result : Theorem 15.37s 3.55s
% Output : Refutation 15.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 168
% Syntax : Number of formulae : 387 ( 20 unt; 0 typ; 23 def)
% Number of atoms : 13153 (6004 equ; 0 cnn)
% Maximal formula atoms : 530 ( 33 avg)
% Number of connectives : 31374 (3383 ~;3214 |;2547 &;21073 @)
% ( 530 <=>; 426 =>; 0 <=; 0 <~>)
% Maximal formula depth : 192 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2333 (2333 >; 0 *; 0 +; 0 <<)
% Number of symbols : 776 ( 772 usr; 316 con; 0-4 aty)
% ( 201 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 6477 ( 320 ^;4707 !;1450 ?;6477 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(type_def_8,type,
d_term: $tType ).
thf(type_def_9,type,
d_subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_124,type,
d_term: $tType ).
thf(func_def_125,type,
d_subst: $tType ).
thf(func_def_126,type,
d2term: d_term > term ).
thf(func_def_127,type,
d2subst: d_subst > subst ).
thf(func_def_128,type,
d_one: d_term ).
thf(func_def_129,type,
d_id: d_subst ).
thf(func_def_143,type,
sP1: ( subst > term > subst > $o ) > $o ).
thf(func_def_147,type,
sP5: ( subst > term > subst > $o ) > $o ).
thf(func_def_148,type,
sP6: ( subst > term > subst > $o ) > $o ).
thf(func_def_151,type,
sP9: ( subst > term > subst > $o ) > $o ).
thf(func_def_152,type,
sP10: ( subst > term > subst > $o ) > $o ).
thf(func_def_154,type,
sP12: ( subst > term > subst > $o ) > $o ).
thf(func_def_157,type,
sP15: ( subst > term > subst > $o ) > $o ).
thf(func_def_158,type,
sP16: ( subst > term > subst > $o ) > $o ).
thf(func_def_159,type,
sP17: ( subst > term > subst > $o ) > $o ).
thf(func_def_160,type,
sP18: ( term > $o ) > $o ).
thf(func_def_161,type,
sP19: ( subst > term > subst > $o ) > $o ).
thf(func_def_166,type,
sP24: ( term > $o ) > $o ).
thf(func_def_169,type,
sP27: ( subst > term > subst > $o ) > $o ).
thf(func_def_171,type,
sP29: ( subst > term > subst > $o ) > $o ).
thf(func_def_174,type,
sP32: ( subst > term > subst > $o ) > $o ).
thf(func_def_175,type,
sP33: ( term > $o ) > $o ).
thf(func_def_181,type,
sP39: ( term > $o ) > $o ).
thf(func_def_182,type,
sP40: ( term > $o ) > $o ).
thf(func_def_185,type,
sP43: ( term > $o ) > $o ).
thf(func_def_187,type,
sP45: ( subst > term > subst > $o ) > $o ).
thf(func_def_189,type,
sP47: ( subst > term > subst > $o ) > $o ).
thf(func_def_190,type,
sP48: ( subst > term > subst > $o ) > $o ).
thf(func_def_191,type,
sP49: ( term > $o ) > $o ).
thf(func_def_195,type,
sP53: ( term > $o ) > $o ).
thf(func_def_196,type,
sP54: ( term > $o ) > $o ).
thf(func_def_199,type,
sP57: ( term > $o ) > $o ).
thf(func_def_201,type,
sK59: term > $o ).
thf(func_def_202,type,
sK60: subst ).
thf(func_def_203,type,
sK61: term ).
thf(func_def_204,type,
sK62: term > term ).
thf(func_def_205,type,
sK63: subst > ( term > $o ) > term ).
thf(func_def_206,type,
sK64: ( term > $o ) > term ).
thf(func_def_207,type,
sK65: ( term > $o ) > term ).
thf(func_def_208,type,
sK66: ( term > $o ) > term ).
thf(func_def_209,type,
sK67: ( term > $o ) > term ).
thf(func_def_210,type,
sK68: ( term > $o ) > term ).
thf(func_def_211,type,
sK69: subst ).
thf(func_def_212,type,
sK70: term ).
thf(func_def_213,type,
sK71: subst ).
thf(func_def_214,type,
sK72: term ).
thf(func_def_215,type,
sK73: subst ).
thf(func_def_216,type,
sK74: term > $o ).
thf(func_def_217,type,
sK75: term ).
thf(func_def_218,type,
sK76: term ).
thf(func_def_219,type,
sK77: subst ).
thf(func_def_220,type,
sK78: term > $o ).
thf(func_def_221,type,
sK79: term > term ).
thf(func_def_222,type,
sK80: ( term > $o ) > term ).
thf(func_def_223,type,
sK81: ( term > $o ) > subst > term ).
thf(func_def_224,type,
sK82: ( term > $o ) > term ).
thf(func_def_225,type,
sK83: ( term > $o ) > term ).
thf(func_def_226,type,
sK84: ( term > $o ) > term ).
thf(func_def_227,type,
sK85: ( term > $o ) > term ).
thf(func_def_228,type,
sK86: ( term > $o ) > term ).
thf(func_def_229,type,
sK87: ( term > $o ) > term ).
thf(func_def_230,type,
sK88: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_231,type,
sK89: term ).
thf(func_def_232,type,
sK90: term ).
thf(func_def_233,type,
sK91: term > $o ).
thf(func_def_234,type,
sK92: term > term ).
thf(func_def_235,type,
sK93: subst > term > subst > $o ).
thf(func_def_236,type,
sK94: ( term > $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 ) > ( term > $o ) > term ).
thf(func_def_239,type,
sK97: term > ( term > $o ) > term ).
thf(func_def_240,type,
sK98: term > $o ).
thf(func_def_241,type,
sK99: subst > term > subst > $o ).
thf(func_def_242,type,
sK100: term ).
thf(func_def_243,type,
sK101: ( subst > term > term ) > term ).
thf(func_def_244,type,
sK102: ( subst > term > term ) > term ).
thf(func_def_245,type,
sK103: ( subst > term > term ) > subst ).
thf(func_def_246,type,
sK104: ( subst > term > term ) > subst ).
thf(func_def_247,type,
sK105: term ).
thf(func_def_248,type,
sK106: subst > term > subst > $o ).
thf(func_def_249,type,
sK107: ( subst > term > subst > $o ) > subst ).
thf(func_def_250,type,
sK108: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK109: ( subst > term > subst > $o ) > subst ).
thf(func_def_252,type,
sK110: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK111: ( subst > term > subst > $o ) > term ).
thf(func_def_254,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_255,type,
sK113: ( subst > term > subst > $o ) > subst ).
thf(func_def_256,type,
sK114: ( subst > term > subst > $o ) > term ).
thf(func_def_257,type,
sK115: ( subst > term > subst > $o ) > subst ).
thf(func_def_258,type,
sK116: ( term > $o ) > term ).
thf(func_def_259,type,
sK117: ( term > $o ) > term ).
thf(func_def_260,type,
sK118: ( subst > term > subst > $o ) > term ).
thf(func_def_261,type,
sK119: ( subst > term > subst > $o ) > term ).
thf(func_def_262,type,
sK120: ( subst > term > term ) > subst ).
thf(func_def_263,type,
sK121: ( subst > term > term ) > subst ).
thf(func_def_264,type,
sK122: ( subst > term > term ) > term ).
thf(func_def_265,type,
sK123: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_266,type,
sK124: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_267,type,
sK125: term ).
thf(func_def_268,type,
sK126: term > $o ).
thf(func_def_269,type,
sK127: subst > term > subst > $o ).
thf(func_def_270,type,
sK128: ( term > $o ) > term > term ).
thf(func_def_271,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK131: ( subst > term > subst > $o ) > subst ).
thf(func_def_274,type,
sK132: ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK133: ( subst > term > subst > $o ) > subst ).
thf(func_def_276,type,
sK134: ( subst > term > subst > $o ) > term ).
thf(func_def_277,type,
sK135: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK136: ( subst > term > subst > $o ) > subst ).
thf(func_def_279,type,
sK137: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_280,type,
sK138: term ).
thf(func_def_281,type,
sK139: ( subst > term > term ) > term ).
thf(func_def_282,type,
sK140: ( subst > term > term ) > subst ).
thf(func_def_283,type,
sK141: ( subst > term > term ) > subst ).
thf(func_def_284,type,
sK142: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_285,type,
sK143: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_286,type,
sK144: term ).
thf(func_def_287,type,
sK145: subst > term > subst > $o ).
thf(func_def_288,type,
sK146: ( subst > term > term ) > subst ).
thf(func_def_289,type,
sK147: ( subst > term > term ) > term ).
thf(func_def_290,type,
sK148: ( subst > term > term ) > subst ).
thf(func_def_291,type,
sK149: ( subst > term > term ) > term ).
thf(func_def_292,type,
sK150: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_293,type,
sK151: ( subst > term > subst > $o ) > term > term ).
thf(func_def_294,type,
sK152: ( term > $o ) > term ).
thf(func_def_295,type,
sK153: ( term > $o ) > term ).
thf(func_def_296,type,
sK154: ( term > $o ) > term ).
thf(func_def_297,type,
sK155: ( term > $o ) > subst > term ).
thf(func_def_298,type,
sK156: term ).
thf(func_def_299,type,
sK157: subst ).
thf(func_def_300,type,
sK158: term ).
thf(func_def_301,type,
sK159: term > $o ).
thf(func_def_302,type,
sK160: term > term ).
thf(func_def_303,type,
sK161: term ).
thf(func_def_304,type,
sK162: term > $o ).
thf(func_def_305,type,
sK163: term > 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: ( term > $o ) > term ).
thf(func_def_310,type,
sK168: ( term > $o ) > term ).
thf(func_def_311,type,
sK169: ( term > $o ) > term ).
thf(func_def_312,type,
sK170: subst > term > subst > $o ).
thf(func_def_313,type,
sK171: term ).
thf(func_def_314,type,
sK172: term > ( subst > term > term ) > subst ).
thf(func_def_315,type,
sK173: term > ( subst > term > term ) > term ).
thf(func_def_316,type,
sK174: term > ( subst > term > term ) > subst ).
thf(func_def_317,type,
sK175: term > ( subst > term > term ) > subst ).
thf(func_def_318,type,
sK176: term > ( subst > term > term ) > term ).
thf(func_def_319,type,
sK177: term > ( subst > term > term ) > subst ).
thf(func_def_320,type,
sK178: ( subst > term > term ) > term ).
thf(func_def_321,type,
sK179: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_322,type,
sK180: ( subst > term > subst > $o ) > term ).
thf(func_def_323,type,
sK181: term > ( subst > term > subst > $o ) > term ).
thf(func_def_324,type,
sK182: subst > term > term ).
thf(func_def_325,type,
sK183: term ).
thf(func_def_326,type,
sK184: subst ).
thf(func_def_327,type,
sK185: subst > term > term ).
thf(func_def_328,type,
sK186: term ).
thf(func_def_329,type,
sK187: subst ).
thf(func_def_330,type,
sK188: term ).
thf(func_def_331,type,
sK189: subst ).
thf(func_def_332,type,
sK190: ( subst > term > term ) > subst ).
thf(func_def_333,type,
sK191: ( subst > term > term ) > subst ).
thf(func_def_334,type,
sK192: ( subst > term > term ) > term ).
thf(func_def_335,type,
sK193: ( subst > term > term ) > subst ).
thf(func_def_336,type,
sK194: ( subst > term > term ) > subst ).
thf(func_def_337,type,
sK195: ( subst > term > term ) > term ).
thf(func_def_338,type,
sK196: term ).
thf(func_def_339,type,
sK197: term ).
thf(func_def_340,type,
sK198: ( term > $o ) > term ).
thf(func_def_341,type,
sK199: ( term > $o ) > term ).
thf(func_def_342,type,
sK200: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_343,type,
sK201: term > $o ).
thf(func_def_344,type,
sK202: term ).
thf(func_def_345,type,
sK203: term > term ).
thf(func_def_346,type,
sK204: subst > term > subst > $o ).
thf(func_def_347,type,
sK205: ( term > $o ) > term ).
thf(func_def_348,type,
sK206: term ).
thf(func_def_349,type,
sK207: term ).
thf(func_def_350,type,
sK208: subst > term > subst > $o ).
thf(func_def_351,type,
sK209: ( subst > term > term ) > term ).
thf(func_def_352,type,
sK210: ( subst > term > term ) > term ).
thf(func_def_353,type,
sK211: ( subst > term > term ) > subst ).
thf(func_def_354,type,
sK212: ( subst > term > term ) > subst ).
thf(func_def_355,type,
sK213: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_356,type,
sK214: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_357,type,
sK215: term > ( term > $o ) > term ).
thf(func_def_358,type,
sK216: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_359,type,
sK217: term > $o ).
thf(func_def_360,type,
sK218: subst > term > subst > $o ).
thf(func_def_361,type,
sK219: term ).
thf(func_def_362,type,
sK220: ( subst > term > term ) > term ).
thf(func_def_363,type,
sK221: ( subst > term > term ) > subst ).
thf(func_def_364,type,
sK222: ( subst > term > term ) > subst ).
thf(func_def_365,type,
sK223: ( subst > term > term ) > term ).
thf(func_def_366,type,
sK224: ( term > $o ) > term ).
thf(func_def_367,type,
sK225: ( term > $o ) > term ).
thf(func_def_368,type,
sK226: ( subst > term > subst > $o ) > term ).
thf(func_def_369,type,
sK227: ( subst > term > subst > $o ) > term ).
thf(func_def_370,type,
sK228: term > $o ).
thf(func_def_371,type,
sK229: subst > term > subst > $o ).
thf(func_def_372,type,
sK230: term ).
thf(func_def_373,type,
sK231: ( subst > term > term ) > term ).
thf(func_def_374,type,
sK232: ( subst > term > term ) > subst ).
thf(func_def_375,type,
sK233: ( subst > term > term ) > subst ).
thf(func_def_376,type,
sK234: ( subst > term > term ) > term ).
thf(func_def_377,type,
sK235: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_378,type,
sK236: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_379,type,
sK237: term > ( term > $o ) > term ).
thf(func_def_380,type,
sK238: term ).
thf(func_def_381,type,
sK239: term ).
thf(func_def_382,type,
sK240: term > $o ).
thf(func_def_383,type,
sK241: subst > term > subst > $o ).
thf(func_def_384,type,
sK242: ( subst > term > subst > $o ) > subst ).
thf(func_def_385,type,
sK243: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_389,type,
sK247: ( subst > term > subst > $o ) > term ).
thf(func_def_390,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK249: ( subst > term > subst > $o ) > subst ).
thf(func_def_392,type,
sK250: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_393,type,
sK251: ( subst > term > subst > $o ) > term ).
thf(func_def_394,type,
sK252: ( subst > term > subst > $o ) > term ).
thf(func_def_395,type,
sK253: subst > term > subst > $o ).
thf(func_def_396,type,
sK254: term ).
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 ) > subst ).
thf(func_def_401,type,
sK259: ( subst > term > subst > $o ) > term ).
thf(func_def_402,type,
sK260: ( subst > term > subst > $o ) > term ).
thf(func_def_403,type,
sK261: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_408,type,
sK266: term > subst > term > term ).
thf(func_def_409,type,
sK267: term ).
thf(func_def_410,type,
sK268: term > $o ).
thf(func_def_411,type,
sK269: subst > term > subst > $o ).
thf(func_def_412,type,
sK270: ( subst > term > term ) > term ).
thf(func_def_413,type,
sK271: ( subst > term > term ) > subst ).
thf(func_def_414,type,
sK272: ( subst > term > term ) > subst ).
thf(func_def_415,type,
sK273: ( subst > term > term ) > term ).
thf(func_def_416,type,
sK274: term ).
thf(func_def_417,type,
sK275: term ).
thf(func_def_418,type,
sK276: ( subst > term > term ) > term ).
thf(func_def_419,type,
sK277: ( subst > term > term ) > subst ).
thf(func_def_420,type,
sK278: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_421,type,
sK279: ( term > $o ) > term > term ).
thf(func_def_422,type,
sK280: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_423,type,
sK281: term > $o ).
thf(func_def_424,type,
sK282: term ).
thf(func_def_425,type,
sK283: term > term ).
thf(func_def_426,type,
sK284: ( term > $o ) > term ).
thf(func_def_427,type,
sK285: ( term > $o ) > term ).
thf(func_def_428,type,
sK286: ( term > $o ) > term ).
thf(func_def_429,type,
sK287: ( term > $o ) > term ).
thf(func_def_430,type,
sK288: ( subst > term > subst > $o ) > term ).
thf(func_def_431,type,
sK289: ( subst > term > subst > $o ) > subst ).
thf(func_def_432,type,
sK290: ( subst > term > subst > $o ) > subst ).
thf(func_def_433,type,
sK291: ( subst > term > subst > $o ) > subst ).
thf(func_def_434,type,
sK292: ( subst > term > subst > $o ) > subst ).
thf(func_def_435,type,
sK293: ( subst > term > subst > $o ) > term ).
thf(func_def_436,type,
sK294: ( subst > term > subst > $o ) > subst ).
thf(func_def_437,type,
sK295: ( subst > term > subst > $o ) > subst ).
thf(func_def_438,type,
sK296: subst > term > subst > $o ).
thf(func_def_439,type,
sK297: term ).
thf(func_def_440,type,
sK298: term ).
thf(func_def_441,type,
sK299: ( term > $o ) > term ).
thf(func_def_442,type,
sK300: ( term > $o ) > term ).
thf(func_def_443,type,
sK301: term > $o ).
thf(func_def_444,type,
sK302: term ).
thf(func_def_445,type,
sK303: term > term ).
thf(func_def_446,type,
sK304: term ).
thf(func_def_447,type,
sK305: subst > term > subst > $o ).
thf(func_def_448,type,
sK306: ( subst > term > subst > $o ) > term ).
thf(func_def_449,type,
sK307: ( subst > term > subst > $o ) > subst ).
thf(func_def_450,type,
sK308: ( subst > term > subst > $o ) > subst ).
thf(func_def_451,type,
sK309: ( subst > term > subst > $o ) > subst ).
thf(func_def_452,type,
sK310: ( subst > term > subst > $o ) > subst ).
thf(func_def_453,type,
sK311: ( subst > term > subst > $o ) > subst ).
thf(func_def_454,type,
sK312: ( subst > term > subst > $o ) > subst ).
thf(func_def_455,type,
sK313: ( subst > term > subst > $o ) > term ).
thf(func_def_456,type,
sK314: ( subst > term > subst > $o ) > term ).
thf(func_def_457,type,
sK315: ( subst > term > subst > $o ) > subst ).
thf(func_def_458,type,
sK316: ( subst > term > subst > $o ) > subst ).
thf(func_def_459,type,
sK317: ( subst > term > subst > $o ) > term ).
thf(func_def_460,type,
sK318: ( subst > term > subst > $o ) > subst ).
thf(func_def_461,type,
sK319: term > ( subst > term > subst > $o ) > term ).
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 ).
thf(func_def_467,type,
sK325: term ).
thf(func_def_468,type,
sK326: ( subst > term > subst > $o ) > term ).
thf(func_def_469,type,
sK327: ( subst > term > subst > $o ) > term ).
thf(func_def_470,type,
sK328: ( term > $o ) > term ).
thf(func_def_471,type,
sK329: ( term > $o ) > term ).
thf(func_def_472,type,
sK330: ( subst > term > term ) > subst ).
thf(func_def_473,type,
sK331: ( subst > term > term ) > term ).
thf(func_def_474,type,
sK332: ( subst > term > term ) > subst ).
thf(func_def_475,type,
sK333: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_476,type,
sK334: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_477,type,
sK335: ( subst > term > subst > $o ) > term ).
thf(func_def_478,type,
sK336: ( subst > term > subst > $o ) > term ).
thf(func_def_479,type,
sK337: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_480,type,
sK338: ( subst > term > term ) > subst ).
thf(func_def_481,type,
sK339: ( subst > term > term ) > subst ).
thf(func_def_482,type,
sK340: ( subst > term > term ) > term ).
thf(func_def_483,type,
sK341: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_484,type,
sK342: term ).
thf(func_def_485,type,
sK343: subst > term > subst > $o ).
thf(func_def_486,type,
sK344: ( subst > term > term ) > term ).
thf(func_def_487,type,
sK345: ( subst > term > term ) > subst ).
thf(func_def_488,type,
sK346: ( subst > term > term ) > subst ).
thf(func_def_489,type,
sK347: ( subst > term > term ) > term ).
thf(func_def_490,type,
sK348: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_491,type,
sK349: ( subst > term > subst > $o ) > term > term ).
thf(func_def_492,type,
sK350: subst > term > subst > $o ).
thf(func_def_493,type,
sK351: term ).
thf(func_def_494,type,
sK352: ( subst > term > subst > $o ) > subst ).
thf(func_def_495,type,
sK353: ( subst > term > subst > $o ) > subst ).
thf(func_def_496,type,
sK354: ( subst > term > subst > $o ) > term ).
thf(func_def_497,type,
sK355: ( subst > term > subst > $o ) > subst ).
thf(func_def_498,type,
sK356: ( subst > term > subst > $o ) > subst ).
thf(func_def_499,type,
sK357: ( subst > term > subst > $o ) > subst ).
thf(func_def_500,type,
sK358: ( subst > term > subst > $o ) > term ).
thf(func_def_501,type,
sK359: ( subst > term > subst > $o ) > subst ).
thf(func_def_502,type,
sK360: term > ( subst > term > subst > $o ) > term ).
thf(func_def_503,type,
sK361: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_504,type,
sK362: ( subst > term > term ) > subst ).
thf(func_def_505,type,
sK363: ( subst > term > term ) > term ).
thf(func_def_506,type,
sK364: ( subst > term > term ) > subst ).
thf(func_def_507,type,
sK365: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_508,type,
sK366: term ).
thf(func_def_509,type,
sK367: subst > term > subst > $o ).
thf(func_def_510,type,
sK368: ( subst > term > subst > $o ) > subst ).
thf(func_def_511,type,
sK369: ( subst > term > subst > $o ) > term ).
thf(func_def_512,type,
sK370: ( subst > term > subst > $o ) > subst ).
thf(func_def_513,type,
sK371: ( subst > term > subst > $o ) > subst ).
thf(func_def_514,type,
sK372: ( subst > term > subst > $o ) > subst ).
thf(func_def_515,type,
sK373: ( subst > term > subst > $o ) > subst ).
thf(func_def_516,type,
sK374: ( subst > term > subst > $o ) > subst ).
thf(func_def_517,type,
sK375: ( subst > term > subst > $o ) > term ).
thf(func_def_518,type,
sK376: ( subst > term > subst > $o ) > term ).
thf(func_def_519,type,
sK377: ( subst > term > subst > $o ) > term ).
thf(func_def_520,type,
sK378: ( subst > term > subst > $o ) > term ).
thf(func_def_521,type,
sK379: ( subst > term > term ) > term ).
thf(func_def_522,type,
sK380: ( subst > term > term ) > subst ).
thf(func_def_523,type,
sK381: ( subst > term > term ) > subst ).
thf(func_def_524,type,
sK382: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_525,type,
sK383: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_526,type,
sK384: term ).
thf(func_def_527,type,
sK385: subst > term > subst > $o ).
thf(func_def_528,type,
sK386: term ).
thf(func_def_529,type,
sK387: ( subst > term > subst > $o ) > subst ).
thf(func_def_530,type,
sK388: ( subst > term > subst > $o ) > subst ).
thf(func_def_531,type,
sK389: ( subst > term > subst > $o ) > subst ).
thf(func_def_532,type,
sK390: ( subst > term > subst > $o ) > term ).
thf(func_def_533,type,
sK391: ( subst > term > subst > $o ) > term > term ).
thf(func_def_534,type,
sK392: ( subst > term > subst > $o ) > subst ).
thf(func_def_535,type,
sK393: ( subst > term > subst > $o ) > subst ).
thf(func_def_536,type,
sK394: ( subst > term > subst > $o ) > subst ).
thf(func_def_537,type,
sK395: ( subst > term > subst > $o ) > term ).
thf(func_def_538,type,
sK396: term > ( subst > term > subst > $o ) > term ).
thf(func_def_539,type,
sK397: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_540,type,
sK398: subst > term > subst > $o ).
thf(func_def_541,type,
sK399: term ).
thf(func_def_542,type,
sK400: ( subst > term > term ) > subst ).
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 ) > term ).
thf(func_def_546,type,
sK404: ( subst > term > term ) > subst ).
thf(func_def_547,type,
sK405: ( subst > term > term ) > term ).
thf(func_def_548,type,
sK406: ( subst > term > term ) > subst ).
thf(func_def_549,type,
sK407: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_550,type,
sK408: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_551,type,
sK409: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_552,type,
sK410: ( subst > term > term ) > subst ).
thf(func_def_553,type,
sK411: ( subst > term > term ) > subst ).
thf(func_def_554,type,
sK412: ( subst > term > term ) > term ).
thf(func_def_555,type,
sK413: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_556,type,
sK414: subst > term > subst > $o ).
thf(func_def_557,type,
sK415: term ).
thf(func_def_558,type,
sK416: ( subst > term > term ) > term ).
thf(func_def_559,type,
sK417: ( subst > term > term ) > term ).
thf(func_def_560,type,
sK418: ( subst > term > term ) > subst ).
thf(func_def_561,type,
sK419: ( subst > term > term ) > subst ).
thf(func_def_562,type,
sK420: term ).
thf(func_def_563,type,
sK421: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_564,type,
sK422: term > ( subst > term > subst > $o ) > term ).
thf(func_def_565,type,
sK423: term > ( subst > term > subst > $o ) > term ).
thf(func_def_566,type,
sK424: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_567,type,
sK425: subst > term > subst > $o ).
thf(func_def_568,type,
sK426: term ).
thf(func_def_569,type,
sK427: ( subst > term > term ) > term ).
thf(func_def_570,type,
sK428: ( subst > term > term ) > subst ).
thf(func_def_571,type,
sK429: ( subst > term > term ) > term ).
thf(func_def_572,type,
sK430: ( subst > term > term ) > subst ).
thf(func_def_573,type,
sK431: term ).
thf(func_def_574,type,
sK432: term > $o ).
thf(func_def_575,type,
sK433: subst > term > subst > $o ).
thf(func_def_576,type,
sK434: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_577,type,
sK435: ( subst > term > subst > $o ) > term ).
thf(func_def_578,type,
sK436: ( subst > term > subst > $o ) > subst ).
thf(func_def_579,type,
sK437: ( subst > term > subst > $o ) > subst ).
thf(func_def_580,type,
sK438: ( subst > term > subst > $o ) > subst ).
thf(func_def_581,type,
sK439: ( term > $o ) > term > term ).
thf(func_def_582,type,
sK440: ( subst > term > subst > $o ) > subst ).
thf(func_def_583,type,
sK441: ( subst > term > subst > $o ) > subst ).
thf(func_def_584,type,
sK442: ( subst > term > subst > $o ) > term ).
thf(func_def_585,type,
sK443: ( subst > term > subst > $o ) > subst ).
thf(func_def_586,type,
sK444: ( subst > term > term ) > term ).
thf(func_def_587,type,
sK445: ( subst > term > term ) > subst ).
thf(func_def_588,type,
sK446: ( subst > term > term ) > subst ).
thf(func_def_589,type,
sK447: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_590,type,
sK448: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_591,type,
sK449: subst > term > subst > $o ).
thf(func_def_592,type,
sK450: term ).
thf(func_def_593,type,
sK451: ( subst > term > term ) > subst ).
thf(func_def_594,type,
sK452: ( subst > term > term ) > term ).
thf(func_def_595,type,
sK453: ( subst > term > term ) > subst ).
thf(func_def_596,type,
sK454: ( subst > term > term ) > term ).
thf(func_def_597,type,
sK455: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_598,type,
sK456: term > ( subst > term > subst > $o ) > term ).
thf(func_def_599,type,
sK457: term > d_term ).
thf(func_def_600,type,
sK458: subst ).
thf(func_def_601,type,
sK459: term > subst > ( term > $o ) > ( term > $o ) > term ).
thf(func_def_602,type,
sK460: term > $o ).
thf(func_def_603,type,
sK461: term > $o ).
thf(func_def_604,type,
sK462: subst ).
thf(func_def_605,type,
sK463: term ).
thf(func_def_606,type,
sK464: term ).
thf(func_def_607,type,
sK465: term ).
thf(func_def_608,type,
sK466: term ).
thf(func_def_609,type,
sK467: subst ).
thf(func_def_610,type,
sK468: term > subst > term > term ).
thf(func_def_611,type,
sK469: term ).
thf(func_def_612,type,
sK470: ( subst > term > term ) > term ).
thf(func_def_613,type,
sK471: ( subst > term > term ) > subst ).
thf(func_def_614,type,
sK472: term ).
thf(func_def_615,type,
sK473: subst ).
thf(func_def_616,type,
sK474: subst ).
thf(func_def_617,type,
sK475: subst ).
thf(func_def_618,type,
sK476: subst ).
thf(func_def_619,type,
sK477: subst ).
thf(func_def_620,type,
sK478: term > subst > term > term ).
thf(func_def_621,type,
sK479: term ).
thf(func_def_622,type,
sK480: ( subst > term > term ) > term ).
thf(func_def_623,type,
sK481: ( subst > term > term ) > subst ).
thf(func_def_624,type,
sK482: term ).
thf(func_def_625,type,
sK483: term ).
thf(func_def_626,type,
sK484: term ).
thf(func_def_627,type,
sK485: term ).
thf(func_def_628,type,
sK486: term ).
thf(func_def_629,type,
sK487: term ).
thf(func_def_630,type,
sK488: term ).
thf(func_def_631,type,
sK489: term ).
thf(func_def_632,type,
sK490: term ).
thf(func_def_633,type,
sK491: term ).
thf(func_def_634,type,
sK492: term ).
thf(func_def_635,type,
sK493: term ).
thf(func_def_636,type,
sK494: ( term > $o ) > term ).
thf(func_def_637,type,
sK495: ( term > $o ) > term ).
thf(func_def_638,type,
sK496: 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 > $o ).
thf(func_def_645,type,
sK503: term > $o ).
thf(func_def_646,type,
sK504: term ).
thf(func_def_647,type,
sK505: subst ).
thf(func_def_648,type,
sK506: term ).
thf(func_def_649,type,
sK507: subst ).
thf(func_def_650,type,
sK508: term ).
thf(func_def_651,type,
sK509: subst ).
thf(func_def_652,type,
sK510: term ).
thf(func_def_653,type,
sK511: term ).
thf(func_def_654,type,
sK512: term ).
thf(func_def_655,type,
sK513: subst ).
thf(func_def_656,type,
sK514: subst ).
thf(func_def_657,type,
sK515: term ).
thf(func_def_658,type,
sK516: term > subst > term > term ).
thf(func_def_659,type,
sK517: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_660,type,
sK518: subst > term > subst > $o ).
thf(func_def_661,type,
sK519: ( term > $o ) > term ).
thf(func_def_662,type,
sK520: term > $o ).
thf(func_def_663,type,
sK521: term ).
thf(func_def_664,type,
sK522: subst ).
thf(func_def_665,type,
sK523: ( term > $o ) > term ).
thf(func_def_666,type,
sK524: subst > term > ( term > $o ) > term > $o ).
thf(func_def_667,type,
sK525: ( subst > term > term ) > subst ).
thf(func_def_668,type,
sK526: ( subst > term > term ) > term ).
thf(func_def_669,type,
sK527: ( subst > term > term ) > subst ).
thf(func_def_670,type,
sK528: term ).
thf(func_def_671,type,
sK529: term ).
thf(func_def_672,type,
sK530: subst > term > term ).
thf(func_def_673,type,
sK531: term > $o ).
thf(func_def_674,type,
sK532: subst ).
thf(func_def_675,type,
sK533: term ).
thf(func_def_676,type,
sK534: term > $o ).
thf(func_def_677,type,
sK535: ( term > $o ) > term > subst > ( term > $o ) > term ).
thf(func_def_678,type,
sK536: subst ).
thf(func_def_679,type,
sK537: term ).
thf(func_def_680,type,
sK538: term ).
thf(func_def_681,type,
sK539: term ).
thf(func_def_682,type,
sK540: term ).
thf(func_def_683,type,
sK541: term ).
thf(func_def_684,type,
sK542: term ).
thf(func_def_685,type,
sK543: term ).
thf(func_def_686,type,
sK544: term ).
thf(func_def_687,type,
sK545: term ).
thf(func_def_688,type,
sK546: term ).
thf(func_def_689,type,
sK547: term ).
thf(func_def_690,type,
sK548: term ).
thf(func_def_691,type,
sK549: term ).
thf(func_def_692,type,
sK550: subst ).
thf(func_def_693,type,
sK551: subst ).
thf(func_def_694,type,
sK552: subst > term > subst > $o ).
thf(func_def_695,type,
sK553: ( term > $o ) > term ).
thf(func_def_696,type,
sK554: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_697,type,
sK555: subst > d_subst ).
thf(func_def_698,type,
sK556: ( subst > term > subst > $o ) > term ).
thf(func_def_699,type,
sK557: ( subst > term > subst > $o ) > term ).
thf(func_def_700,type,
sK558: subst > term > subst > $o ).
thf(func_def_701,type,
sK559: term ).
thf(func_def_702,type,
sK560: term ).
thf(func_def_703,type,
sK561: term ).
thf(func_def_704,type,
sK562: term ).
thf(func_def_705,type,
sK563: term ).
thf(func_def_706,type,
sK564: term ).
thf(func_def_707,type,
sK565: term ).
thf(func_def_708,type,
sK566: term > subst > term > term ).
thf(func_def_709,type,
sK567: term > ( term > $o ) > subst > term > $o ).
thf(func_def_710,type,
sK568: subst ).
thf(func_def_711,type,
sK569: term > $o ).
thf(func_def_712,type,
sK570: term ).
thf(func_def_713,type,
sK571: ( term > $o ) > term ).
thf(func_def_714,type,
sK572: term ).
thf(func_def_715,type,
sK573: term ).
thf(func_def_716,type,
sK574: term ).
thf(func_def_717,type,
sK575: term ).
thf(func_def_718,type,
sK576: ( subst > term > term ) > subst ).
thf(func_def_719,type,
sK577: ( subst > term > term ) > term ).
thf(func_def_720,type,
sK578: ( subst > term > term ) > subst ).
thf(func_def_721,type,
sK579: ( subst > term > term ) > subst ).
thf(func_def_722,type,
sK580: ( subst > term > term ) > term ).
thf(func_def_723,type,
sK581: ( subst > term > term ) > subst ).
thf(func_def_724,type,
sK582: subst > term > term ).
thf(func_def_725,type,
sK583: subst > term > term ).
thf(func_def_726,type,
sK584: term ).
thf(func_def_727,type,
sK585: subst ).
thf(func_def_728,type,
sK586: subst ).
thf(func_def_729,type,
sK587: term > $o ).
thf(func_def_730,type,
sK588: term ).
thf(func_def_731,type,
sK589: term ).
thf(func_def_732,type,
sK590: term > $o ).
thf(func_def_734,type,
sK592: subst > term > subst > $o ).
thf(func_def_735,type,
sK593: ( subst > term > term ) > term ).
thf(func_def_736,type,
sK594: ( subst > term > term ) > subst ).
thf(func_def_737,type,
sK595: ( subst > term > term ) > subst ).
thf(func_def_738,type,
sK596: ( subst > term > term ) > term ).
thf(func_def_739,type,
sK597: term ).
thf(func_def_740,type,
sK598: ( subst > term > subst > $o ) > term ).
thf(func_def_741,type,
sK599: ( subst > term > subst > $o ) > subst ).
thf(func_def_742,type,
sK600: ( subst > term > subst > $o ) > subst ).
thf(func_def_743,type,
sK601: ( subst > term > subst > $o ) > subst ).
thf(func_def_744,type,
sK602: ( subst > term > subst > $o ) > term ).
thf(func_def_745,type,
sK603: ( subst > term > subst > $o ) > term > term ).
thf(func_def_746,type,
sK604: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_747,type,
sK605: ( subst > term > subst > $o ) > subst ).
thf(func_def_748,type,
sK606: ( subst > term > subst > $o ) > subst ).
thf(func_def_749,type,
sK607: ( subst > term > subst > $o ) > subst ).
thf(func_def_750,type,
sK608: ( subst > term > subst > $o ) > subst ).
thf(func_def_751,type,
sK609: ( subst > term > subst > $o ) > subst ).
thf(func_def_752,type,
sK610: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_753,type,
sK611: ( subst > term > subst > $o ) > term > term ).
thf(func_def_754,type,
sK612: ( subst > term > subst > $o ) > subst ).
thf(func_def_755,type,
sK613: ( subst > term > subst > $o ) > subst ).
thf(func_def_756,type,
sK614: ( subst > term > subst > $o ) > subst ).
thf(func_def_757,type,
sK615: ( subst > term > subst > $o ) > subst ).
thf(func_def_758,type,
sK616: ( subst > term > subst > $o ) > subst ).
thf(func_def_759,type,
sK617: ( subst > term > subst > $o ) > subst ).
thf(func_def_760,type,
sK618: ( subst > term > subst > $o ) > subst ).
thf(func_def_761,type,
sK619: ( subst > term > subst > $o ) > subst ).
thf(func_def_762,type,
sK620: ( subst > term > subst > $o ) > subst ).
thf(func_def_763,type,
sK621: ( subst > term > subst > $o ) > subst ).
thf(func_def_764,type,
sK622: ( subst > term > subst > $o ) > subst ).
thf(func_def_766,type,
ph623:
!>[X0: $tType] : X0 ).
thf(f10598,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2053,f2113,f2252,f2308,f2520,f2532,f2540,f2628,f3159,f3792,f3819,f3880,f6949,f7010,f8591,f8623,f8645,f8677,f9350,f9472,f9825,f9872,f10345,f10597]) ).
thf(f10597,plain,
( ~ spl591_214
| spl591_705 ),
inference(avatar_contradiction_clause,[status(thm)],[f10596]) ).
thf(f10596,plain,
( $false
| ~ spl591_214
| spl591_705 ),
inference(subsumption_resolution,[status(thm)],[f2515,f10348]) ).
thf(f10348,plain,
( ! [X0: term] :
( $false
!= ( sK592 @ id @ X0 @ id ) )
| spl591_705 ),
inference(superposition,[status(thm)],[f8657,f4484]) ).
thf(f4484,plain,
! [X0: term,X1: term] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f4480,f4480]) ).
thf(f4480,plain,
! [X0: term] :
( ( d2term @ d_one )
= X0 ),
inference(forward_demodulation,[status(thm)],[f1258,f1186]) ).
thf(f1186,plain,
! [X84: d_term] : ( d_one = X84 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( hoasinduction_lem1 = $true )
& ! [X0: term] :
( ( d2term @ ( sK457 @ X0 ) )
= X0 )
& ( ( $true = sP58 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP58 ) )
& ( ( axscons = $true )
| ( ( push @ ( sub @ one @ sK458 ) @ ( comp @ sh @ sK458 ) )
!= sK458 ) )
& ( ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 )
| ( axscons != $true ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
| ( $true != sP56 ) )
& ( ( $true = sP56 )
| ( induction2lem_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X4: term > $o,X5: term > $o,X6: subst,X7: term] :
( ( $true
= ( X5 @ one ) )
| ( $true
!= ( X4 @ X7 ) )
| ( ( X5 @ ( sK459 @ X7 @ X6 @ X5 @ X4 ) )
!= ( X4 @ ( sub @ ( sK459 @ X7 @ X6 @ X5 @ X4 ) @ ( push @ X7 @ X6 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ( $true
!= ( sK461 @ one ) )
& ( $true
= ( sK460 @ sK463 ) )
& ! [X13: term] :
( ( sK461 @ X13 )
= ( sK460 @ ( sub @ X13 @ ( push @ sK463 @ sK462 ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ( sK464
!= ( sub @ sK464 @ id ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
| ( ( sK465 != sK466 )
& ( ( lam @ sK465 )
= ( lam @ sK466 ) ) ) )
& ( ! [X18: term,X19: term] :
( ( X18 = X19 )
| ( ( lam @ X19 )
!= ( lam @ X18 ) ) )
| ( laminj != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( $true = sP46 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP46 ) )
& ! [X20: d_subst,X21: d_subst] :
( ( ( d2subst @ X21 )
!= ( d2subst @ X20 ) )
| ( X20 = X21 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
| ( sK467
!= ( comp @ sK467 @ id ) ) )
& ( ! [X23: subst] :
( ( comp @ X23 @ id )
= X23 )
| ( axidr != $true ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ( $true = sP44 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP44 ) )
& ( ! [X24: term,X26: term,X27: subst] :
( ( sK468 @ X24 @ X27 @ X26 )
= ( sub @ X24 @ ( push @ X26 @ X27 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X29: subst > term > term] :
( ( X29 @ ( sK471 @ X29 ) @ ( sK470 @ X29 ) )
!= ( sub @ sK469 @ ( push @ ( sK470 @ X29 ) @ ( sK471 @ X29 ) ) ) ) )
& ( ( axvarcons = $true )
| ( ( sub @ one @ ( push @ sK472 @ sK473 ) )
!= sK472 ) )
& ( ! [X34: term,X35: subst] :
( ( sub @ one @ ( push @ X34 @ X35 ) )
= X34 )
| ( axvarcons != $true ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( sK474
!= ( comp @ id @ sK474 ) )
| ( ( comp @ sK475 @ id )
!= sK475 )
| ( ! [X38: subst] :
( ( comp @ id @ X38 )
= X38 )
& ! [X39: subst] :
( ( comp @ X39 @ id )
= X39 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X40: subst] :
( ( comp @ id @ X40 )
= X40 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 )
& ( ( sK476
!= ( comp @ id @ sK476 ) )
| ( ( comp @ sK477 @ id )
!= sK477 ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X44: term,X46: term,X47: subst] :
( ( sK478 @ X44 @ X47 @ X46 )
= ( sub @ X44 @ ( push @ X46 @ X47 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X49: subst > term > term] :
( ( X49 @ ( sK481 @ X49 ) @ ( sK480 @ X49 ) )
!= ( sub @ sK479 @ ( push @ ( sK480 @ X49 ) @ ( sK481 @ X49 ) ) ) ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X52: term,X53: term,X54: term,X55: term] :
( ( ( ap @ X55 @ X52 )
!= ( ap @ X54 @ X53 ) )
| ( X52 = X53 ) )
& ( ( ap @ ( sub @ sK483 @ id ) @ sK482 )
= ( ap @ ( sub @ sK485 @ id ) @ sK484 ) )
& ( sK482 != sK484 ) ) )
& ( ( ( ( ap @ sK488 @ sK487 )
= ( ap @ sK489 @ sK486 ) )
& ( sK487 != sK486 ) )
| ! [X64: term,X65: term,X66: term,X67: term] :
( ( ( ap @ ( sub @ X67 @ id ) @ X66 )
!= ( ap @ ( sub @ X65 @ id ) @ X64 ) )
| ( X64 = X66 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( sK493 != sK491 )
& ( ( ap @ ( sub @ sK493 @ id ) @ sK492 )
= ( ap @ ( sub @ sK491 @ id ) @ sK490 ) ) ) )
& ( ! [X72: term,X73: term,X74: term,X75: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X72 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) )
| ( hoasapinj1 != $true ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X76: term > $o,X77: term] :
( ( $true
= ( sP43 @ X76 ) )
| ( ( ( X76 @ ( sK494 @ X76 ) )
= $true )
& ( $true
!= ( X76 @ ( lam @ ( sK494 @ X76 ) ) ) ) )
| ( ( ( var @ ( sK495 @ X76 ) )
= $true )
& ( $true
!= ( X76 @ ( sK495 @ X76 ) ) ) )
| ( ( X76 @ X77 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ( ( $true
!= ( sP43 @ sK496 ) )
& ! [X82: term] :
( ( $true
!= ( sK496 @ X82 ) )
| ( $true
= ( sK496 @ ( lam @ X82 ) ) ) )
& ! [X83: term] :
( ( $true
!= ( var @ X83 ) )
| ( ( sK496 @ X83 )
= $true ) )
& ( $true
!= ( sK496 @ sK497 ) ) ) )
& ( ( induction2_lthm = $true )
| ( $true != sP42 ) )
& ( ( $true = sP42 )
| ( induction2_lthm != $true ) )
& ! [X84: d_term] : ( d_one = X84 )
& ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( ( ap @ X85 @ X88 )
!= ( ap @ X86 @ X87 ) )
| ( X85 = X86 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ( ( ( ap @ sK498 @ sK501 )
= ( ap @ sK499 @ sK500 ) )
& ( sK499 != sK498 ) ) )
& ( ( sP38 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP38 != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( $true = sP37 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP37 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X93: subst,X94: term] :
( ( comp @ sh @ ( push @ X94 @ X93 ) )
= X93 )
& ( $true
!= ( sK503 @ ( sub @ sK506 @ ( push @ sK504 @ sK505 ) ) ) )
& ( $true
= ( sK502 @ sK506 ) )
& ! [X100: subst,X101: term] :
( ( sub @ one @ ( push @ X101 @ X100 ) )
= X101 ) ) )
& ( ( ( comp @ sh @ ( push @ sK508 @ sK507 ) )
!= sK507 )
| ! [X104: term > $o,X105: term > $o,X106: term,X107: subst,X108: term] :
( ( $true
= ( X105 @ ( sub @ X108 @ ( push @ X106 @ X107 ) ) ) )
| ( $true
!= ( X104 @ X108 ) ) )
| ( ( sub @ one @ ( push @ sK510 @ sK509 ) )
!= sK510 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X111: term] :
( ( sub @ X111 @ id )
= X111 )
& ( sK511
!= ( sub @ sK511 @ id ) ) ) )
& ( ( sK512
!= ( sub @ sK512 @ id ) )
| ! [X114: term] :
( ( sub @ X114 @ id )
= X114 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP36 ) )
& ( ( $true = sP36 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP31 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP31 ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
| ( sK513
!= ( comp @ sK513 @ id ) )
| ( sK514
!= ( comp @ id @ sK514 ) ) )
& ( ( ! [X117: subst] :
( ( comp @ X117 @ id )
= X117 )
& ! [X118: subst] :
( ( comp @ id @ X118 )
= X118 ) )
| ( substmonoid != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( $true = sP28 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP26 ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ sK515 @ ( push @ one @ sh ) ) ) )
& ( ! [X121: term] :
( ( sub @ X121 @ ( push @ one @ sh ) )
= ( sK516 @ X121 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ! [X123: subst > term > subst > $o,X125: term] :
( ( X123 @ id @ X125 @ id )
= ( sK517 @ X123 @ X125 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X127: term > $o] :
( ( X127 @ ( sK519 @ X127 ) )
!= ( sK518 @ id @ ( sK519 @ X127 ) @ id ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X132: term > $o] :
( ( X132 @ ( sK523 @ X132 ) )
!= ( sK520 @ ( sub @ ( sK523 @ X132 ) @ ( push @ sK521 @ sK522 ) ) ) ) )
& ( ! [X134: term > $o,X135: term,X136: subst,X138: term] :
( ( sK524 @ X136 @ X135 @ X134 @ X138 )
= ( X134 @ ( sub @ X138 @ ( push @ X135 @ X136 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP25 )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP25 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X139: term,X140: term,X141: subst > term > term] :
( ( ( ap @ ( sub @ X140 @ id ) @ X139 )
!= ( lam @ ( X141 @ sh @ one ) ) )
| ( ( X141 @ ( comp @ ( sK525 @ X141 ) @ ( sK527 @ X141 ) ) @ ( sub @ ( sK526 @ X141 ) @ ( sK527 @ X141 ) ) )
!= ( sub @ ( X141 @ ( sK525 @ X141 ) @ ( sK526 @ X141 ) ) @ ( sK527 @ X141 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ( ( ( ap @ ( sub @ sK529 @ id ) @ sK528 )
= ( lam @ ( sK530 @ sh @ one ) ) )
& ! [X148: subst,X149: term,X150: subst] :
( ( sub @ ( sK530 @ X148 @ X149 ) @ X150 )
= ( sK530 @ ( comp @ X148 @ X150 ) @ ( sub @ X149 @ X150 ) ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ( $true
= ( sK531 @ sK533 ) )
& ! [X155: term] :
( ( sK531 @ ( sub @ X155 @ ( push @ sK533 @ sK532 ) ) )
= ( sK534 @ X155 ) )
& ( ( sK534 @ one )
!= $true )
& ! [X156: subst,X157: term] :
( ( sub @ one @ ( push @ X157 @ X156 ) )
= X157 ) ) )
& ( ! [X158: term > $o,X159: subst,X160: term,X161: term > $o] :
( ( $true
!= ( X158 @ X160 ) )
| ( ( X161 @ ( sK535 @ X161 @ X160 @ X159 @ X158 ) )
!= ( X158 @ ( sub @ ( sK535 @ X161 @ X160 @ X159 @ X158 ) @ ( push @ X160 @ X159 ) ) ) )
| ( $true
= ( X161 @ one ) ) )
| ( sK537
!= ( sub @ one @ ( push @ sK537 @ sK536 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP23 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP23 ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X165: d_term,X166: d_term] :
( ( X165 = X166 )
| ( ( d2term @ X165 )
!= ( d2term @ X166 ) ) )
& ( ( shinj = $true )
| ( ( sK538 != sK539 )
& ( ( sub @ sK538 @ sh )
= ( sub @ sK539 @ sh ) ) ) )
& ( ! [X169: term,X170: term] :
( ( X169 = X170 )
| ( ( sub @ X169 @ sh )
!= ( sub @ X170 @ sh ) ) )
| ( shinj != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
& ( sK540 != sK541 )
& ( ( ap @ ( sub @ sK540 @ id ) @ sK543 )
= ( ap @ ( sub @ sK541 @ id ) @ sK542 ) )
& ! [X176: term,X177: term,X178: term,X179: term] :
( ( ( ap @ X178 @ X177 )
!= ( ap @ X176 @ X179 ) )
| ( X176 = X178 ) ) ) )
& ( ( sK544
!= ( sub @ sK544 @ id ) )
| ! [X181: term,X182: term,X183: term,X184: term] :
( ( X181 = X182 )
| ( ( ap @ ( sub @ X181 @ id ) @ X184 )
!= ( ap @ ( sub @ X182 @ id ) @ X183 ) ) )
| ( ( ( ap @ sK545 @ sK548 )
= ( ap @ sK547 @ sK546 ) )
& ( sK547 != sK545 ) )
| ( hoasapinj1_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP14 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP13 ) )
& ( ( $true = sP13 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
| ( $true != sP11 ) )
& ( ( $true = sP11 )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK549 @ sK550 ) )
!= sK550 ) )
& ( ! [X191: term,X192: subst] :
( ( comp @ sh @ ( push @ X191 @ X192 ) )
= X192 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
| ( ( comp @ id @ sK551 )
!= sK551 ) )
& ( ! [X194: subst] :
( ( comp @ id @ X194 )
= X194 )
| ( axidl != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP8 ) )
& ( ( $true = sP8 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ! [X196: term > $o] :
( ( sK552 @ id @ ( sK553 @ X196 ) @ id )
!= ( X196 @ ( sK553 @ X196 ) ) ) )
& ( ! [X198: subst > term > subst > $o,X200: term] :
( ( X198 @ id @ X200 @ id )
= ( sK554 @ X198 @ X200 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X201: subst] :
( ( d2subst @ ( sK555 @ X201 ) )
= X201 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ( ( $true
= ( X203 @ id @ ( sK557 @ X203 ) @ id ) )
& ( $true
= ( X203 @ id @ ( sK556 @ X203 ) @ id ) )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ ( sK557 @ X203 ) @ id ) @ ( sK556 @ X203 ) ) @ id ) ) )
| ( ( X203 @ id @ X204 @ id )
= $true )
| ( $true
= ( sP5 @ X203 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X209: term,X210: term] :
( ( $true
!= ( sK558 @ id @ X210 @ id ) )
| ( $true
!= ( sK558 @ id @ X209 @ id ) )
| ( $true
= ( sK558 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id ) ) )
& ( ( sK558 @ id @ sK559 @ id )
!= $true )
& ( $true
!= ( sP5 @ sK558 ) ) ) )
& ( lamnotvar = $true )
& ( ! [X211: term,X212: term,X213: term,X214: term] :
( ( X213 = X214 )
| ( ( ap @ ( sub @ X212 @ id ) @ X213 )
!= ( ap @ ( sub @ X211 @ id ) @ X214 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( sK563 != sK562 )
& ( ( ap @ ( sub @ sK561 @ id ) @ sK562 )
= ( ap @ ( sub @ sK560 @ id ) @ sK563 ) ) ) )
& ( axvarshift = $true )
& ( ! [X219: term] :
( ( sub @ X219 @ id )
= X219 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ( ( sub @ sK564 @ id )
!= sK564 ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X222: subst > term > term] :
( ( sub @ sK565 @ ( push @ one @ sh ) )
!= ( X222 @ sh @ one ) ) )
& ( ! [X223: term] :
( ( sK566 @ X223 @ sh @ one )
= ( sub @ X223 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ! [X225: subst,X226: term > $o,X227: term,X229: term] :
( ( X226 @ ( sub @ X229 @ ( push @ X227 @ X225 ) ) )
= ( sK567 @ X227 @ X226 @ X225 @ X229 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ! [X233: term > $o] :
( ( X233 @ ( sK571 @ X233 ) )
!= ( sK569 @ ( sub @ ( sK571 @ X233 ) @ ( push @ sK570 @ sK568 ) ) ) ) )
& ( ! [X235: term,X236: term,X237: term,X238: term] :
( ( ( ap @ X236 @ X235 )
!= ( ap @ X238 @ X237 ) )
| ( X235 = X237 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( ( ap @ sK573 @ sK572 )
= ( ap @ sK575 @ sK574 ) )
& ( sK572 != sK574 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP2 ) )
& ( ( $true = sP2 )
| ( hoasinduction_lem3v2 != $true ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X243: subst > term > term,X244: subst > term > term,X245: term,X246: subst] :
( ( ( lam @ ( X244 @ sh @ one ) )
!= ( lam @ ( X243 @ sh @ one ) ) )
| ( ( sub @ ( X244 @ ( sK576 @ X244 ) @ ( sK577 @ X244 ) ) @ ( sK578 @ X244 ) )
!= ( X244 @ ( comp @ ( sK576 @ X244 ) @ ( sK578 @ X244 ) ) @ ( sub @ ( sK577 @ X244 ) @ ( sK578 @ X244 ) ) ) )
| ( ( X243 @ ( comp @ ( sK581 @ X243 ) @ ( sK579 @ X243 ) ) @ ( sub @ ( sK580 @ X243 ) @ ( sK579 @ X243 ) ) )
!= ( sub @ ( X243 @ ( sK581 @ X243 ) @ ( sK580 @ X243 ) ) @ ( sK579 @ X243 ) ) )
| ( ( X244 @ X246 @ X245 )
= ( X243 @ X246 @ X245 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ( ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK582 @ sh @ one ) ) )
& ! [X257: subst,X258: term,X259: subst] :
( ( sK583 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( sK583 @ X257 @ X258 ) @ X259 ) )
& ! [X260: subst,X261: term,X262: subst] :
( ( sK582 @ ( comp @ X262 @ X260 ) @ ( sub @ X261 @ X260 ) )
= ( sub @ ( sK582 @ X262 @ X261 ) @ X260 ) )
& ( ( sK583 @ sK585 @ sK584 )
!= ( sK582 @ sK585 @ sK584 ) ) ) )
& ! [X263: d_subst] : ( d_id = X263 )
& ( ( pushprop_lem1 = $true )
| ( ( $true
= ( sK587 @ sK589 ) )
& ( $true
!= ( sK590 @ ( sub @ sK589 @ ( push @ sK588 @ sK586 ) ) ) ) ) )
& ( ! [X269: subst,X270: term > $o,X271: term,X272: term,X273: term > $o] :
( ( $true
!= ( X270 @ X272 ) )
| ( ( X273 @ ( sub @ X272 @ ( push @ X271 @ X269 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( hoasinduction_lem1_gthm = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f475,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476]) ).
thf(f476,plain,
! [X0: term] :
( ? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
=> ( ( d2term @ ( sK457 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
( ? [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
!= X2 )
=> ( ( push @ ( sub @ one @ sK458 ) @ ( comp @ sh @ sK458 ) )
!= sK458 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
! [X4: term > $o,X5: term > $o,X6: subst,X7: term] :
( ? [X8: term] :
( ( X4 @ ( sub @ X8 @ ( push @ X7 @ X6 ) ) )
!= ( X5 @ X8 ) )
=> ( ( X5 @ ( sK459 @ X7 @ X6 @ X5 @ X4 ) )
!= ( X4 @ ( sub @ ( sK459 @ X7 @ X6 @ X5 @ X4 ) @ ( push @ X7 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X9: term > $o,X10: term > $o,X11: subst,X12: term] :
( ( ( X10 @ one )
!= $true )
& ( $true
= ( X9 @ X12 ) )
& ! [X13: term] :
( ( X10 @ X13 )
= ( X9 @ ( sub @ X13 @ ( push @ X12 @ X11 ) ) ) ) )
=> ( ( $true
!= ( sK461 @ one ) )
& ( $true
= ( sK460 @ sK463 ) )
& ! [X13: term] :
( ( sK461 @ X13 )
= ( sK460 @ ( sub @ X13 @ ( push @ sK463 @ sK462 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
( ? [X15: term] :
( ( sub @ X15 @ id )
!= X15 )
=> ( sK464
!= ( sub @ sK464 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
( ? [X16: term,X17: term] :
( ( X16 != X17 )
& ( ( lam @ X16 )
= ( lam @ X17 ) ) )
=> ( ( sK465 != sK466 )
& ( ( lam @ sK465 )
= ( lam @ sK466 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ? [X22: subst] :
( ( comp @ X22 @ id )
!= X22 )
=> ( sK467
!= ( comp @ sK467 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
! [X24: term] :
( ? [X25: subst > term > term] :
! [X26: term,X27: subst] :
( ( sub @ X24 @ ( push @ X26 @ X27 ) )
= ( X25 @ X27 @ X26 ) )
=> ! [X27: subst,X26: term] :
( ( sK468 @ X24 @ X27 @ X26 )
= ( sub @ X24 @ ( push @ X26 @ X27 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
( ? [X28: term] :
! [X29: subst > term > term] :
? [X30: term,X31: subst] :
( ( sub @ X28 @ ( push @ X30 @ X31 ) )
!= ( X29 @ X31 @ X30 ) )
=> ! [X29: subst > term > term] :
? [X31: subst,X30: term] :
( ( sub @ sK469 @ ( push @ X30 @ X31 ) )
!= ( X29 @ X31 @ X30 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
! [X29: subst > term > term] :
( ? [X31: subst,X30: term] :
( ( sub @ sK469 @ ( push @ X30 @ X31 ) )
!= ( X29 @ X31 @ X30 ) )
=> ( ( X29 @ ( sK471 @ X29 ) @ ( sK470 @ X29 ) )
!= ( sub @ sK469 @ ( push @ ( sK470 @ X29 ) @ ( sK471 @ X29 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
( ? [X32: term,X33: subst] :
( ( sub @ one @ ( push @ X32 @ X33 ) )
!= X32 )
=> ( ( sub @ one @ ( push @ sK472 @ sK473 ) )
!= sK472 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
( ? [X36: subst] :
( ( comp @ id @ X36 )
!= X36 )
=> ( sK474
!= ( comp @ id @ sK474 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
( ? [X37: subst] :
( ( comp @ X37 @ id )
!= X37 )
=> ( ( comp @ sK475 @ id )
!= sK475 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
( ? [X42: subst] :
( ( comp @ id @ X42 )
!= X42 )
=> ( sK476
!= ( comp @ id @ sK476 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
( ? [X43: subst] :
( ( comp @ X43 @ id )
!= X43 )
=> ( ( comp @ sK477 @ id )
!= sK477 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
! [X44: term] :
( ? [X45: subst > term > term] :
! [X46: term,X47: subst] :
( ( sub @ X44 @ ( push @ X46 @ X47 ) )
= ( X45 @ X47 @ X46 ) )
=> ! [X47: subst,X46: term] :
( ( sK478 @ X44 @ X47 @ X46 )
= ( sub @ X44 @ ( push @ X46 @ X47 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
( ? [X48: term] :
! [X49: subst > term > term] :
? [X50: term,X51: subst] :
( ( X49 @ X51 @ X50 )
!= ( sub @ X48 @ ( push @ X50 @ X51 ) ) )
=> ! [X49: subst > term > term] :
? [X51: subst,X50: term] :
( ( sub @ sK479 @ ( push @ X50 @ X51 ) )
!= ( X49 @ X51 @ X50 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
! [X49: subst > term > term] :
( ? [X51: subst,X50: term] :
( ( sub @ sK479 @ ( push @ X50 @ X51 ) )
!= ( X49 @ X51 @ X50 ) )
=> ( ( X49 @ ( sK481 @ X49 ) @ ( sK480 @ X49 ) )
!= ( sub @ sK479 @ ( push @ ( sK480 @ X49 ) @ ( sK481 @ X49 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
( ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ ( sub @ X59 @ id ) @ X58 )
= ( ap @ ( sub @ X57 @ id ) @ X56 ) )
& ( X56 != X58 ) )
=> ( ( ( ap @ ( sub @ sK483 @ id ) @ sK482 )
= ( ap @ ( sub @ sK485 @ id ) @ sK484 ) )
& ( sK482 != sK484 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
( ? [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ X63 @ X60 )
= ( ap @ X62 @ X61 ) )
& ( X60 != X61 ) )
=> ( ( ( ap @ sK488 @ sK487 )
= ( ap @ sK489 @ sK486 ) )
& ( sK487 != sK486 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
( ? [X68: term,X69: term,X70: term,X71: term] :
( ( X69 != X71 )
& ( ( ap @ ( sub @ X71 @ id ) @ X70 )
= ( ap @ ( sub @ X69 @ id ) @ X68 ) ) )
=> ( ( sK493 != sK491 )
& ( ( ap @ ( sub @ sK493 @ id ) @ sK492 )
= ( ap @ ( sub @ sK491 @ id ) @ sK490 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
! [X76: term > $o] :
( ? [X78: term] :
( ( $true
= ( X76 @ X78 ) )
& ( $true
!= ( X76 @ ( lam @ X78 ) ) ) )
=> ( ( ( X76 @ ( sK494 @ X76 ) )
= $true )
& ( $true
!= ( X76 @ ( lam @ ( sK494 @ X76 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
! [X76: term > $o] :
( ? [X79: term] :
( ( $true
= ( var @ X79 ) )
& ( $true
!= ( X76 @ X79 ) ) )
=> ( ( ( var @ ( sK495 @ X76 ) )
= $true )
& ( $true
!= ( X76 @ ( sK495 @ X76 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
( ? [X80: term > $o,X81: term] :
( ( $true
!= ( sP43 @ X80 ) )
& ! [X82: term] :
( ( $true
!= ( X80 @ X82 ) )
| ( $true
= ( X80 @ ( lam @ X82 ) ) ) )
& ! [X83: term] :
( ( $true
!= ( var @ X83 ) )
| ( $true
= ( X80 @ X83 ) ) )
& ( $true
!= ( X80 @ X81 ) ) )
=> ( ( $true
!= ( sP43 @ sK496 ) )
& ! [X82: term] :
( ( $true
!= ( sK496 @ X82 ) )
| ( $true
= ( sK496 @ ( lam @ X82 ) ) ) )
& ! [X83: term] :
( ( $true
!= ( var @ X83 ) )
| ( ( sK496 @ X83 )
= $true ) )
& ( $true
!= ( sK496 @ sK497 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
( ? [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ X89 @ X92 )
= ( ap @ X90 @ X91 ) )
& ( X89 != X90 ) )
=> ( ( ( ap @ sK498 @ sK501 )
= ( ap @ sK499 @ sK500 ) )
& ( sK499 != sK498 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
( ? [X95: term > $o,X96: term > $o,X97: term,X98: subst,X99: term] :
( ( ( X96 @ ( sub @ X99 @ ( push @ X97 @ X98 ) ) )
!= $true )
& ( $true
= ( X95 @ X99 ) ) )
=> ( ( $true
!= ( sK503 @ ( sub @ sK506 @ ( push @ sK504 @ sK505 ) ) ) )
& ( $true
= ( sK502 @ sK506 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
( ? [X102: subst,X103: term] :
( ( comp @ sh @ ( push @ X103 @ X102 ) )
!= X102 )
=> ( ( comp @ sh @ ( push @ sK508 @ sK507 ) )
!= sK507 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
( ? [X109: subst,X110: term] :
( ( sub @ one @ ( push @ X110 @ X109 ) )
!= X110 )
=> ( ( sub @ one @ ( push @ sK510 @ sK509 ) )
!= sK510 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
( ? [X112: term] :
( ( sub @ X112 @ id )
!= X112 )
=> ( sK511
!= ( sub @ sK511 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
( ? [X113: term] :
( ( sub @ X113 @ id )
!= X113 )
=> ( sK512
!= ( sub @ sK512 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
( ? [X115: subst] :
( ( comp @ X115 @ id )
!= X115 )
=> ( sK513
!= ( comp @ sK513 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
( ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 )
=> ( sK514
!= ( comp @ id @ sK514 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X119: term] :
! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ X119 @ ( push @ one @ sh ) ) )
=> ! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ sK515 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
! [X121: term] :
( ? [X122: subst > term > term] :
( ( X122 @ sh @ one )
= ( sub @ X121 @ ( push @ one @ sh ) ) )
=> ( ( sub @ X121 @ ( push @ one @ sh ) )
= ( sK516 @ X121 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
! [X123: subst > term > subst > $o] :
( ? [X124: term > $o] :
! [X125: term] :
( ( X123 @ id @ X125 @ id )
= ( X124 @ X125 ) )
=> ! [X125: term] :
( ( X123 @ id @ X125 @ id )
= ( sK517 @ X123 @ X125 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
( ? [X126: subst > term > subst > $o] :
! [X127: term > $o] :
? [X128: term] :
( ( X127 @ X128 )
!= ( X126 @ id @ X128 @ id ) )
=> ! [X127: term > $o] :
? [X128: term] :
( ( X127 @ X128 )
!= ( sK518 @ id @ X128 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
! [X127: term > $o] :
( ? [X128: term] :
( ( X127 @ X128 )
!= ( sK518 @ id @ X128 @ id ) )
=> ( ( X127 @ ( sK519 @ X127 ) )
!= ( sK518 @ id @ ( sK519 @ X127 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
( ? [X129: term > $o,X130: term,X131: subst] :
! [X132: term > $o] :
? [X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X130 @ X131 ) ) )
!= ( X132 @ X133 ) )
=> ! [X132: term > $o] :
? [X133: term] :
( ( sK520 @ ( sub @ X133 @ ( push @ sK521 @ sK522 ) ) )
!= ( X132 @ X133 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
! [X132: term > $o] :
( ? [X133: term] :
( ( sK520 @ ( sub @ X133 @ ( push @ sK521 @ sK522 ) ) )
!= ( X132 @ X133 ) )
=> ( ( X132 @ ( sK523 @ X132 ) )
!= ( sK520 @ ( sub @ ( sK523 @ X132 ) @ ( push @ sK521 @ sK522 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
! [X134: term > $o,X135: term,X136: subst] :
( ? [X137: term > $o] :
! [X138: term] :
( ( X137 @ X138 )
= ( X134 @ ( sub @ X138 @ ( push @ X135 @ X136 ) ) ) )
=> ! [X138: term] :
( ( sK524 @ X136 @ X135 @ X134 @ X138 )
= ( X134 @ ( sub @ X138 @ ( push @ X135 @ X136 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
! [X141: subst > term > term] :
( ? [X142: subst,X143: term,X144: subst] :
( ( sub @ ( X141 @ X142 @ X143 ) @ X144 )
!= ( X141 @ ( comp @ X142 @ X144 ) @ ( sub @ X143 @ X144 ) ) )
=> ( ( X141 @ ( comp @ ( sK525 @ X141 ) @ ( sK527 @ X141 ) ) @ ( sub @ ( sK526 @ X141 ) @ ( sK527 @ X141 ) ) )
!= ( sub @ ( X141 @ ( sK525 @ X141 ) @ ( sK526 @ X141 ) ) @ ( sK527 @ X141 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
( ? [X145: term,X146: term,X147: subst > term > term] :
( ( ( ap @ ( sub @ X146 @ id ) @ X145 )
= ( lam @ ( X147 @ sh @ one ) ) )
& ! [X148: subst,X149: term,X150: subst] :
( ( sub @ ( X147 @ X148 @ X149 ) @ X150 )
= ( X147 @ ( comp @ X148 @ X150 ) @ ( sub @ X149 @ X150 ) ) ) )
=> ( ( ( ap @ ( sub @ sK529 @ id ) @ sK528 )
= ( lam @ ( sK530 @ sh @ one ) ) )
& ! [X150: subst,X149: term,X148: subst] :
( ( sub @ ( sK530 @ X148 @ X149 ) @ X150 )
= ( sK530 @ ( comp @ X148 @ X150 ) @ ( sub @ X149 @ X150 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
( ? [X151: term > $o,X152: subst,X153: term,X154: term > $o] :
( ( $true
= ( X151 @ X153 ) )
& ! [X155: term] :
( ( X151 @ ( sub @ X155 @ ( push @ X153 @ X152 ) ) )
= ( X154 @ X155 ) )
& ( $true
!= ( X154 @ one ) ) )
=> ( ( $true
= ( sK531 @ sK533 ) )
& ! [X155: term] :
( ( sK531 @ ( sub @ X155 @ ( push @ sK533 @ sK532 ) ) )
= ( sK534 @ X155 ) )
& ( ( sK534 @ one )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
! [X158: term > $o,X159: subst,X160: term,X161: term > $o] :
( ? [X162: term] :
( ( X158 @ ( sub @ X162 @ ( push @ X160 @ X159 ) ) )
!= ( X161 @ X162 ) )
=> ( ( X161 @ ( sK535 @ X161 @ X160 @ X159 @ X158 ) )
!= ( X158 @ ( sub @ ( sK535 @ X161 @ X160 @ X159 @ X158 ) @ ( push @ X160 @ X159 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
( ? [X163: subst,X164: term] :
( ( sub @ one @ ( push @ X164 @ X163 ) )
!= X164 )
=> ( sK537
!= ( sub @ one @ ( push @ sK537 @ sK536 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X167: term,X168: term] :
( ( X167 != X168 )
& ( ( sub @ X167 @ sh )
= ( sub @ X168 @ sh ) ) )
=> ( ( sK538 != sK539 )
& ( ( sub @ sK538 @ sh )
= ( sub @ sK539 @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
( ? [X172: term,X173: term,X174: term,X175: term] :
( ( X172 != X173 )
& ( ( ap @ ( sub @ X172 @ id ) @ X175 )
= ( ap @ ( sub @ X173 @ id ) @ X174 ) ) )
=> ( ( sK540 != sK541 )
& ( ( ap @ ( sub @ sK540 @ id ) @ sK543 )
= ( ap @ ( sub @ sK541 @ id ) @ sK542 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
( ? [X180: term] :
( ( sub @ X180 @ id )
!= X180 )
=> ( sK544
!= ( sub @ sK544 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
( ? [X185: term,X186: term,X187: term,X188: term] :
( ( ( ap @ X185 @ X188 )
= ( ap @ X187 @ X186 ) )
& ( X185 != X187 ) )
=> ( ( ( ap @ sK545 @ sK548 )
= ( ap @ sK547 @ sK546 ) )
& ( sK547 != sK545 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
( ? [X189: term,X190: subst] :
( ( comp @ sh @ ( push @ X189 @ X190 ) )
!= X190 )
=> ( ( comp @ sh @ ( push @ sK549 @ sK550 ) )
!= sK550 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
( ? [X193: subst] :
( ( comp @ id @ X193 )
!= X193 )
=> ( ( comp @ id @ sK551 )
!= sK551 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
( ? [X195: subst > term > subst > $o] :
! [X196: term > $o] :
? [X197: term] :
( ( X196 @ X197 )
!= ( X195 @ id @ X197 @ id ) )
=> ! [X196: term > $o] :
? [X197: term] :
( ( sK552 @ id @ X197 @ id )
!= ( X196 @ X197 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
! [X196: term > $o] :
( ? [X197: term] :
( ( sK552 @ id @ X197 @ id )
!= ( X196 @ X197 ) )
=> ( ( sK552 @ id @ ( sK553 @ X196 ) @ id )
!= ( X196 @ ( sK553 @ X196 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
! [X198: subst > term > subst > $o] :
( ? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ id @ X200 @ id ) )
=> ! [X200: term] :
( ( X198 @ id @ X200 @ id )
= ( sK554 @ X198 @ X200 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
! [X201: subst] :
( ? [X202: d_subst] :
( ( d2subst @ X202 )
= X201 )
=> ( ( d2subst @ ( sK555 @ X201 ) )
= X201 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
! [X203: subst > term > subst > $o] :
( ? [X205: term,X206: term] :
( ( $true
= ( X203 @ id @ X206 @ id ) )
& ( $true
= ( X203 @ id @ X205 @ id ) )
& ( ( X203 @ id @ ( ap @ ( sub @ X206 @ id ) @ X205 ) @ id )
!= $true ) )
=> ( ( $true
= ( X203 @ id @ ( sK557 @ X203 ) @ id ) )
& ( $true
= ( X203 @ id @ ( sK556 @ X203 ) @ id ) )
& ( $true
!= ( X203 @ id @ ( ap @ ( sub @ ( sK557 @ X203 ) @ id ) @ ( sK556 @ X203 ) ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X207: subst > term > subst > $o,X208: term] :
( ! [X209: term,X210: term] :
( ( $true
!= ( X207 @ id @ X210 @ id ) )
| ( $true
!= ( X207 @ id @ X209 @ id ) )
| ( $true
= ( X207 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id ) ) )
& ( $true
!= ( X207 @ id @ X208 @ id ) )
& ( $true
!= ( sP5 @ X207 ) ) )
=> ( ! [X210: term,X209: term] :
( ( $true
!= ( sK558 @ id @ X210 @ id ) )
| ( $true
!= ( sK558 @ id @ X209 @ id ) )
| ( $true
= ( sK558 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id ) ) )
& ( ( sK558 @ id @ sK559 @ id )
!= $true )
& ( $true
!= ( sP5 @ sK558 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
( ? [X215: term,X216: term,X217: term,X218: term] :
( ( X217 != X218 )
& ( ( ap @ ( sub @ X216 @ id ) @ X217 )
= ( ap @ ( sub @ X215 @ id ) @ X218 ) ) )
=> ( ( sK563 != sK562 )
& ( ( ap @ ( sub @ sK561 @ id ) @ sK562 )
= ( ap @ ( sub @ sK560 @ id ) @ sK563 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
( ? [X220: term] :
( ( sub @ X220 @ id )
!= X220 )
=> ( ( sub @ sK564 @ id )
!= sK564 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
( ? [X221: term] :
! [X222: subst > term > term] :
( ( X222 @ sh @ one )
!= ( sub @ X221 @ ( push @ one @ sh ) ) )
=> ! [X222: subst > term > term] :
( ( sub @ sK565 @ ( push @ one @ sh ) )
!= ( X222 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
! [X223: term] :
( ? [X224: subst > term > term] :
( ( X224 @ sh @ one )
= ( sub @ X223 @ ( push @ one @ sh ) ) )
=> ( ( sK566 @ X223 @ sh @ one )
= ( sub @ X223 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
! [X225: subst,X226: term > $o,X227: term] :
( ? [X228: term > $o] :
! [X229: term] :
( ( X226 @ ( sub @ X229 @ ( push @ X227 @ X225 ) ) )
= ( X228 @ X229 ) )
=> ! [X229: term] :
( ( X226 @ ( sub @ X229 @ ( push @ X227 @ X225 ) ) )
= ( sK567 @ X227 @ X226 @ X225 @ X229 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
( ? [X230: subst,X231: term > $o,X232: term] :
! [X233: term > $o] :
? [X234: term] :
( ( X233 @ X234 )
!= ( X231 @ ( sub @ X234 @ ( push @ X232 @ X230 ) ) ) )
=> ! [X233: term > $o] :
? [X234: term] :
( ( X233 @ X234 )
!= ( sK569 @ ( sub @ X234 @ ( push @ sK570 @ sK568 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
! [X233: term > $o] :
( ? [X234: term] :
( ( X233 @ X234 )
!= ( sK569 @ ( sub @ X234 @ ( push @ sK570 @ sK568 ) ) ) )
=> ( ( X233 @ ( sK571 @ X233 ) )
!= ( sK569 @ ( sub @ ( sK571 @ X233 ) @ ( push @ sK570 @ sK568 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
( ? [X239: term,X240: term,X241: term,X242: term] :
( ( ( ap @ X242 @ X241 )
= ( ap @ X240 @ X239 ) )
& ( X239 != X241 ) )
=> ( ( ( ap @ sK573 @ sK572 )
= ( ap @ sK575 @ sK574 ) )
& ( sK572 != sK574 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
! [X244: subst > term > term] :
( ? [X247: subst,X248: term,X249: subst] :
( ( sub @ ( X244 @ X247 @ X248 ) @ X249 )
!= ( X244 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) ) )
=> ( ( sub @ ( X244 @ ( sK576 @ X244 ) @ ( sK577 @ X244 ) ) @ ( sK578 @ X244 ) )
!= ( X244 @ ( comp @ ( sK576 @ X244 ) @ ( sK578 @ X244 ) ) @ ( sub @ ( sK577 @ X244 ) @ ( sK578 @ X244 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
! [X243: subst > term > term] :
( ? [X250: subst,X251: term,X252: subst] :
( ( X243 @ ( comp @ X252 @ X250 ) @ ( sub @ X251 @ X250 ) )
!= ( sub @ ( X243 @ X252 @ X251 ) @ X250 ) )
=> ( ( X243 @ ( comp @ ( sK581 @ X243 ) @ ( sK579 @ X243 ) ) @ ( sub @ ( sK580 @ X243 ) @ ( sK579 @ X243 ) ) )
!= ( sub @ ( X243 @ ( sK581 @ X243 ) @ ( sK580 @ X243 ) ) @ ( sK579 @ X243 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
( ? [X253: subst > term > term,X254: subst > term > term,X255: term,X256: subst] :
( ( ( lam @ ( X253 @ sh @ one ) )
= ( lam @ ( X254 @ sh @ one ) ) )
& ! [X257: subst,X258: term,X259: subst] :
( ( X254 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X254 @ X257 @ X258 ) @ X259 ) )
& ! [X260: subst,X261: term,X262: subst] :
( ( sub @ ( X253 @ X262 @ X261 ) @ X260 )
= ( X253 @ ( comp @ X262 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
& ( ( X254 @ X256 @ X255 )
!= ( X253 @ X256 @ X255 ) ) )
=> ( ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK582 @ sh @ one ) ) )
& ! [X259: subst,X258: term,X257: subst] :
( ( sK583 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( sK583 @ X257 @ X258 ) @ X259 ) )
& ! [X262: subst,X261: term,X260: subst] :
( ( sK582 @ ( comp @ X262 @ X260 ) @ ( sub @ X261 @ X260 ) )
= ( sub @ ( sK582 @ X262 @ X261 ) @ X260 ) )
& ( ( sK583 @ sK585 @ sK584 )
!= ( sK582 @ sK585 @ sK584 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
( ? [X264: subst,X265: term > $o,X266: term,X267: term,X268: term > $o] :
( ( $true
= ( X265 @ X267 ) )
& ( $true
!= ( X268 @ ( sub @ X267 @ ( push @ X266 @ X264 ) ) ) ) )
=> ( ( $true
= ( sK587 @ sK589 ) )
& ( $true
!= ( sK590 @ ( sub @ sK589 @ ( push @ sK588 @ sK586 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
( ( hoasinduction_lem1 = $true )
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( ( $true = sP58 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP58 ) )
& ( ( axscons = $true )
| ? [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
!= X2 ) )
& ( ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 )
| ( axscons != $true ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
| ( $true != sP56 ) )
& ( ( $true = sP56 )
| ( induction2lem_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X4: term > $o,X5: term > $o,X6: subst,X7: term] :
( ( $true
= ( X5 @ one ) )
| ( $true
!= ( X4 @ X7 ) )
| ? [X8: term] :
( ( X4 @ ( sub @ X8 @ ( push @ X7 @ X6 ) ) )
!= ( X5 @ X8 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X9: term > $o,X10: term > $o,X11: subst,X12: term] :
( ( ( X10 @ one )
!= $true )
& ( $true
= ( X9 @ X12 ) )
& ! [X13: term] :
( ( X10 @ X13 )
= ( X9 @ ( sub @ X13 @ ( push @ X12 @ X11 ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X15: term] :
( ( sub @ X15 @ id )
!= X15 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
| ? [X16: term,X17: term] :
( ( X16 != X17 )
& ( ( lam @ X16 )
= ( lam @ X17 ) ) ) )
& ( ! [X18: term,X19: term] :
( ( X18 = X19 )
| ( ( lam @ X19 )
!= ( lam @ X18 ) ) )
| ( laminj != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( $true = sP46 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP46 ) )
& ! [X20: d_subst,X21: d_subst] :
( ( ( d2subst @ X21 )
!= ( d2subst @ X20 ) )
| ( X20 = X21 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
| ? [X22: subst] :
( ( comp @ X22 @ id )
!= X22 ) )
& ( ! [X23: subst] :
( ( comp @ X23 @ id )
= X23 )
| ( axidr != $true ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ( $true = sP44 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP44 ) )
& ( ! [X24: term] :
? [X25: subst > term > term] :
! [X26: term,X27: subst] :
( ( sub @ X24 @ ( push @ X26 @ X27 ) )
= ( X25 @ X27 @ X26 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X28: term] :
! [X29: subst > term > term] :
? [X30: term,X31: subst] :
( ( sub @ X28 @ ( push @ X30 @ X31 ) )
!= ( X29 @ X31 @ X30 ) ) )
& ( ( axvarcons = $true )
| ? [X32: term,X33: subst] :
( ( sub @ one @ ( push @ X32 @ X33 ) )
!= X32 ) )
& ( ! [X34: term,X35: subst] :
( ( sub @ one @ ( push @ X34 @ X35 ) )
= X34 )
| ( axvarcons != $true ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ? [X36: subst] :
( ( comp @ id @ X36 )
!= X36 )
| ? [X37: subst] :
( ( comp @ X37 @ id )
!= X37 )
| ( ! [X38: subst] :
( ( comp @ id @ X38 )
= X38 )
& ! [X39: subst] :
( ( comp @ X39 @ id )
= X39 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X40: subst] :
( ( comp @ id @ X40 )
= X40 )
& ! [X41: subst] :
( ( comp @ X41 @ id )
= X41 )
& ( ? [X42: subst] :
( ( comp @ id @ X42 )
!= X42 )
| ? [X43: subst] :
( ( comp @ X43 @ id )
!= X43 ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X44: term] :
? [X45: subst > term > term] :
! [X46: term,X47: subst] :
( ( sub @ X44 @ ( push @ X46 @ X47 ) )
= ( X45 @ X47 @ X46 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X48: term] :
! [X49: subst > term > term] :
? [X50: term,X51: subst] :
( ( X49 @ X51 @ X50 )
!= ( sub @ X48 @ ( push @ X50 @ X51 ) ) ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X52: term,X53: term,X54: term,X55: term] :
( ( ( ap @ X55 @ X52 )
!= ( ap @ X54 @ X53 ) )
| ( X52 = X53 ) )
& ? [X56: term,X57: term,X58: term,X59: term] :
( ( ( ap @ ( sub @ X59 @ id ) @ X58 )
= ( ap @ ( sub @ X57 @ id ) @ X56 ) )
& ( X56 != X58 ) ) ) )
& ( ? [X60: term,X61: term,X62: term,X63: term] :
( ( ( ap @ X63 @ X60 )
= ( ap @ X62 @ X61 ) )
& ( X60 != X61 ) )
| ! [X64: term,X65: term,X66: term,X67: term] :
( ( ( ap @ ( sub @ X67 @ id ) @ X66 )
!= ( ap @ ( sub @ X65 @ id ) @ X64 ) )
| ( X64 = X66 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X68: term,X69: term,X70: term,X71: term] :
( ( X69 != X71 )
& ( ( ap @ ( sub @ X71 @ id ) @ X70 )
= ( ap @ ( sub @ X69 @ id ) @ X68 ) ) ) )
& ( ! [X72: term,X73: term,X74: term,X75: term] :
( ( X73 = X75 )
| ( ( ap @ ( sub @ X73 @ id ) @ X72 )
!= ( ap @ ( sub @ X75 @ id ) @ X74 ) ) )
| ( hoasapinj1 != $true ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X76: term > $o,X77: term] :
( ( $true
= ( sP43 @ X76 ) )
| ? [X78: term] :
( ( $true
= ( X76 @ X78 ) )
& ( $true
!= ( X76 @ ( lam @ X78 ) ) ) )
| ? [X79: term] :
( ( $true
= ( var @ X79 ) )
& ( $true
!= ( X76 @ X79 ) ) )
| ( ( X76 @ X77 )
= $true ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X80: term > $o,X81: term] :
( ( $true
!= ( sP43 @ X80 ) )
& ! [X82: term] :
( ( $true
!= ( X80 @ X82 ) )
| ( $true
= ( X80 @ ( lam @ X82 ) ) ) )
& ! [X83: term] :
( ( $true
!= ( var @ X83 ) )
| ( $true
= ( X80 @ X83 ) ) )
& ( $true
!= ( X80 @ X81 ) ) ) )
& ( ( induction2_lthm = $true )
| ( $true != sP42 ) )
& ( ( $true = sP42 )
| ( induction2_lthm != $true ) )
& ! [X84: d_term] : ( d_one = X84 )
& ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( ( ap @ X85 @ X88 )
!= ( ap @ X86 @ X87 ) )
| ( X85 = X86 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ X89 @ X92 )
= ( ap @ X90 @ X91 ) )
& ( X89 != X90 ) ) )
& ( ( sP38 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP38 != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( $true = sP37 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP37 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X93: subst,X94: term] :
( ( comp @ sh @ ( push @ X94 @ X93 ) )
= X93 )
& ? [X95: term > $o,X96: term > $o,X97: term,X98: subst,X99: term] :
( ( ( X96 @ ( sub @ X99 @ ( push @ X97 @ X98 ) ) )
!= $true )
& ( $true
= ( X95 @ X99 ) ) )
& ! [X100: subst,X101: term] :
( ( sub @ one @ ( push @ X101 @ X100 ) )
= X101 ) ) )
& ( ? [X102: subst,X103: term] :
( ( comp @ sh @ ( push @ X103 @ X102 ) )
!= X102 )
| ! [X104: term > $o,X105: term > $o,X106: term,X107: subst,X108: term] :
( ( $true
= ( X105 @ ( sub @ X108 @ ( push @ X106 @ X107 ) ) ) )
| ( $true
!= ( X104 @ X108 ) ) )
| ? [X109: subst,X110: term] :
( ( sub @ one @ ( push @ X110 @ X109 ) )
!= X110 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X111: term] :
( ( sub @ X111 @ id )
= X111 )
& ? [X112: term] :
( ( sub @ X112 @ id )
!= X112 ) ) )
& ( ? [X113: term] :
( ( sub @ X113 @ id )
!= X113 )
| ! [X114: term] :
( ( sub @ X114 @ id )
= X114 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP36 ) )
& ( ( $true = sP36 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP31 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP31 ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
| ? [X115: subst] :
( ( comp @ X115 @ id )
!= X115 )
| ? [X116: subst] :
( ( comp @ id @ X116 )
!= X116 ) )
& ( ( ! [X117: subst] :
( ( comp @ X117 @ id )
= X117 )
& ! [X118: subst] :
( ( comp @ id @ X118 )
= X118 ) )
| ( substmonoid != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( $true = sP28 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP26 ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X119: term] :
! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ X119 @ ( push @ one @ sh ) ) ) )
& ( ! [X121: term] :
? [X122: subst > term > term] :
( ( X122 @ sh @ one )
= ( sub @ X121 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ! [X123: subst > term > subst > $o] :
? [X124: term > $o] :
! [X125: term] :
( ( X123 @ id @ X125 @ id )
= ( X124 @ X125 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X126: subst > term > subst > $o] :
! [X127: term > $o] :
? [X128: term] :
( ( X127 @ X128 )
!= ( X126 @ id @ X128 @ id ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X129: term > $o,X130: term,X131: subst] :
! [X132: term > $o] :
? [X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X130 @ X131 ) ) )
!= ( X132 @ X133 ) ) )
& ( ! [X134: term > $o,X135: term,X136: subst] :
? [X137: term > $o] :
! [X138: term] :
( ( X137 @ X138 )
= ( X134 @ ( sub @ X138 @ ( push @ X135 @ X136 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP25 )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP25 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X139: term,X140: term,X141: subst > term > term] :
( ( ( ap @ ( sub @ X140 @ id ) @ X139 )
!= ( lam @ ( X141 @ sh @ one ) ) )
| ? [X142: subst,X143: term,X144: subst] :
( ( sub @ ( X141 @ X142 @ X143 ) @ X144 )
!= ( X141 @ ( comp @ X142 @ X144 ) @ ( sub @ X143 @ X144 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X145: term,X146: term,X147: subst > term > term] :
( ( ( ap @ ( sub @ X146 @ id ) @ X145 )
= ( lam @ ( X147 @ sh @ one ) ) )
& ! [X148: subst,X149: term,X150: subst] :
( ( sub @ ( X147 @ X148 @ X149 ) @ X150 )
= ( X147 @ ( comp @ X148 @ X150 ) @ ( sub @ X149 @ X150 ) ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X151: term > $o,X152: subst,X153: term,X154: term > $o] :
( ( $true
= ( X151 @ X153 ) )
& ! [X155: term] :
( ( X151 @ ( sub @ X155 @ ( push @ X153 @ X152 ) ) )
= ( X154 @ X155 ) )
& ( $true
!= ( X154 @ one ) ) )
& ! [X156: subst,X157: term] :
( ( sub @ one @ ( push @ X157 @ X156 ) )
= X157 ) ) )
& ( ! [X158: term > $o,X159: subst,X160: term,X161: term > $o] :
( ( $true
!= ( X158 @ X160 ) )
| ? [X162: term] :
( ( X158 @ ( sub @ X162 @ ( push @ X160 @ X159 ) ) )
!= ( X161 @ X162 ) )
| ( $true
= ( X161 @ one ) ) )
| ? [X163: subst,X164: term] :
( ( sub @ one @ ( push @ X164 @ X163 ) )
!= X164 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP23 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP23 ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X165: d_term,X166: d_term] :
( ( X165 = X166 )
| ( ( d2term @ X165 )
!= ( d2term @ X166 ) ) )
& ( ( shinj = $true )
| ? [X167: term,X168: term] :
( ( X167 != X168 )
& ( ( sub @ X167 @ sh )
= ( sub @ X168 @ sh ) ) ) )
& ( ! [X169: term,X170: term] :
( ( X169 = X170 )
| ( ( sub @ X169 @ sh )
!= ( sub @ X170 @ sh ) ) )
| ( shinj != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X171: term] :
( ( sub @ X171 @ id )
= X171 )
& ? [X172: term,X173: term,X174: term,X175: term] :
( ( X172 != X173 )
& ( ( ap @ ( sub @ X172 @ id ) @ X175 )
= ( ap @ ( sub @ X173 @ id ) @ X174 ) ) )
& ! [X176: term,X177: term,X178: term,X179: term] :
( ( ( ap @ X178 @ X177 )
!= ( ap @ X176 @ X179 ) )
| ( X176 = X178 ) ) ) )
& ( ? [X180: term] :
( ( sub @ X180 @ id )
!= X180 )
| ! [X181: term,X182: term,X183: term,X184: term] :
( ( X181 = X182 )
| ( ( ap @ ( sub @ X181 @ id ) @ X184 )
!= ( ap @ ( sub @ X182 @ id ) @ X183 ) ) )
| ? [X185: term,X186: term,X187: term,X188: term] :
( ( ( ap @ X185 @ X188 )
= ( ap @ X187 @ X186 ) )
& ( X185 != X187 ) )
| ( hoasapinj1_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP14 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP13 ) )
& ( ( $true = sP13 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
| ( $true != sP11 ) )
& ( ( $true = sP11 )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X189: term,X190: subst] :
( ( comp @ sh @ ( push @ X189 @ X190 ) )
!= X190 ) )
& ( ! [X191: term,X192: subst] :
( ( comp @ sh @ ( push @ X191 @ X192 ) )
= X192 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
| ? [X193: subst] :
( ( comp @ id @ X193 )
!= X193 ) )
& ( ! [X194: subst] :
( ( comp @ id @ X194 )
= X194 )
| ( axidl != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP8 ) )
& ( ( $true = sP8 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X195: subst > term > subst > $o] :
! [X196: term > $o] :
? [X197: term] :
( ( X196 @ X197 )
!= ( X195 @ id @ X197 @ id ) ) )
& ( ! [X198: subst > term > subst > $o] :
? [X199: term > $o] :
! [X200: term] :
( ( X199 @ X200 )
= ( X198 @ id @ X200 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X201: subst] :
? [X202: d_subst] :
( ( d2subst @ X202 )
= X201 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X203: subst > term > subst > $o,X204: term] :
( ? [X205: term,X206: term] :
( ( $true
= ( X203 @ id @ X206 @ id ) )
& ( $true
= ( X203 @ id @ X205 @ id ) )
& ( ( X203 @ id @ ( ap @ ( sub @ X206 @ id ) @ X205 ) @ id )
!= $true ) )
| ( ( X203 @ id @ X204 @ id )
= $true )
| ( $true
= ( sP5 @ X203 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X207: subst > term > subst > $o,X208: term] :
( ! [X209: term,X210: term] :
( ( $true
!= ( X207 @ id @ X210 @ id ) )
| ( $true
!= ( X207 @ id @ X209 @ id ) )
| ( $true
= ( X207 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id ) ) )
& ( $true
!= ( X207 @ id @ X208 @ id ) )
& ( $true
!= ( sP5 @ X207 ) ) ) )
& ( lamnotvar = $true )
& ( ! [X211: term,X212: term,X213: term,X214: term] :
( ( X213 = X214 )
| ( ( ap @ ( sub @ X212 @ id ) @ X213 )
!= ( ap @ ( sub @ X211 @ id ) @ X214 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X215: term,X216: term,X217: term,X218: term] :
( ( X217 != X218 )
& ( ( ap @ ( sub @ X216 @ id ) @ X217 )
= ( ap @ ( sub @ X215 @ id ) @ X218 ) ) ) )
& ( axvarshift = $true )
& ( ! [X219: term] :
( ( sub @ X219 @ id )
= X219 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X220: term] :
( ( sub @ X220 @ id )
!= X220 ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X221: term] :
! [X222: subst > term > term] :
( ( X222 @ sh @ one )
!= ( sub @ X221 @ ( push @ one @ sh ) ) ) )
& ( ! [X223: term] :
? [X224: subst > term > term] :
( ( X224 @ sh @ one )
= ( sub @ X223 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ! [X225: subst,X226: term > $o,X227: term] :
? [X228: term > $o] :
! [X229: term] :
( ( X226 @ ( sub @ X229 @ ( push @ X227 @ X225 ) ) )
= ( X228 @ X229 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X230: subst,X231: term > $o,X232: term] :
! [X233: term > $o] :
? [X234: term] :
( ( X233 @ X234 )
!= ( X231 @ ( sub @ X234 @ ( push @ X232 @ X230 ) ) ) ) )
& ( ! [X235: term,X236: term,X237: term,X238: term] :
( ( ( ap @ X236 @ X235 )
!= ( ap @ X238 @ X237 ) )
| ( X235 = X237 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X239: term,X240: term,X241: term,X242: term] :
( ( ( ap @ X242 @ X241 )
= ( ap @ X240 @ X239 ) )
& ( X239 != X241 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP2 ) )
& ( ( $true = sP2 )
| ( hoasinduction_lem3v2 != $true ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X243: subst > term > term,X244: subst > term > term,X245: term,X246: subst] :
( ( ( lam @ ( X244 @ sh @ one ) )
!= ( lam @ ( X243 @ sh @ one ) ) )
| ? [X247: subst,X248: term,X249: subst] :
( ( sub @ ( X244 @ X247 @ X248 ) @ X249 )
!= ( X244 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) ) )
| ? [X250: subst,X251: term,X252: subst] :
( ( X243 @ ( comp @ X252 @ X250 ) @ ( sub @ X251 @ X250 ) )
!= ( sub @ ( X243 @ X252 @ X251 ) @ X250 ) )
| ( ( X244 @ X246 @ X245 )
= ( X243 @ X246 @ X245 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X253: subst > term > term,X254: subst > term > term,X255: term,X256: subst] :
( ( ( lam @ ( X253 @ sh @ one ) )
= ( lam @ ( X254 @ sh @ one ) ) )
& ! [X257: subst,X258: term,X259: subst] :
( ( X254 @ ( comp @ X257 @ X259 ) @ ( sub @ X258 @ X259 ) )
= ( sub @ ( X254 @ X257 @ X258 ) @ X259 ) )
& ! [X260: subst,X261: term,X262: subst] :
( ( sub @ ( X253 @ X262 @ X261 ) @ X260 )
= ( X253 @ ( comp @ X262 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
& ( ( X254 @ X256 @ X255 )
!= ( X253 @ X256 @ X255 ) ) ) )
& ! [X263: d_subst] : ( d_id = X263 )
& ( ( pushprop_lem1 = $true )
| ? [X264: subst,X265: term > $o,X266: term,X267: term,X268: term > $o] :
( ( $true
= ( X265 @ X267 ) )
& ( $true
!= ( X268 @ ( sub @ X267 @ ( push @ X266 @ X264 ) ) ) ) ) )
& ( ! [X269: subst,X270: term > $o,X271: term,X272: term,X273: term > $o] :
( ( $true
!= ( X270 @ X272 ) )
| ( ( X273 @ ( sub @ X272 @ ( push @ X271 @ X269 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( hoasinduction_lem1_gthm = $true ) ),
inference(rectify,[status(thm)],[f474]) ).
thf(f474,plain,
( ( hoasinduction_lem1 = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( ( $true = sP58 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP58 ) )
& ( ( axscons = $true )
| ? [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
!= X157 ) )
& ( ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 )
| ( axscons != $true ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
| ( $true != sP56 ) )
& ( ( $true = sP56 )
| ( induction2lem_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ? [X156: term] :
( ( X153 @ X156 )
!= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
!= ( X153 @ one ) )
& ( $true
= ( X152 @ X155 ) )
& ! [X156: term] :
( ( X153 @ X156 )
= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X26: term] :
( ( sub @ X26 @ id )
!= X26 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
| ? [X417: term,X418: term] :
( ( X417 != X418 )
& ( ( lam @ X418 )
= ( lam @ X417 ) ) ) )
& ( ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) )
| ( laminj != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( $true = sP46 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP46 ) )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
!= ( d2subst @ X291 ) )
| ( X290 = X291 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
| ? [X196: subst] :
( ( comp @ X196 @ id )
!= X196 ) )
& ( ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 )
| ( axidr != $true ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ( $true = sP44 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP44 ) )
& ( ! [X434: term] :
? [X435: subst > term > term] :
! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X434: term] :
! [X435: subst > term > term] :
? [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
!= ( sub @ X434 @ ( push @ X436 @ X437 ) ) ) )
& ( ( axvarcons = $true )
| ? [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
!= X470 ) )
& ( ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 )
| ( axvarcons != $true ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ? [X456: subst] :
( ( comp @ id @ X456 )
!= X456 )
| ? [X457: subst] :
( ( comp @ X457 @ id )
!= X457 )
| ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X456: subst] :
( ( comp @ id @ X456 )
= X456 )
& ! [X457: subst] :
( ( comp @ X457 @ id )
= X457 )
& ( ? [X459: subst] :
( ( comp @ id @ X459 )
!= X459 )
| ? [X458: subst] :
( ( comp @ X458 @ id )
!= X458 ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X536: term] :
? [X537: subst > term > term] :
! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X536: term] :
! [X537: subst > term > term] :
? [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
!= ( X537 @ X539 @ X538 ) ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
!= ( ap @ X411 @ X410 ) )
| ( X409 = X410 ) )
& ? [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
& ( X413 != X415 ) ) ) )
& ( ? [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
= ( ap @ X411 @ X410 ) )
& ( X409 != X410 ) )
| ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X353: term,X354: term,X355: term,X356: term] :
( ( X354 != X356 )
& ( ( ap @ ( sub @ X356 @ id ) @ X355 )
= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) )
| ( hoasapinj1 != $true ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X28: term > $o,X29: term] :
( ( $true
= ( sP43 @ X28 ) )
| ? [X33: term] :
( ( ( X28 @ X33 )
= $true )
& ( ( X28 @ ( lam @ X33 ) )
!= $true ) )
| ? [X30: term] :
( ( $true
= ( var @ X30 ) )
& ( ( X28 @ X30 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X28: term > $o,X29: term] :
( ( $true
!= ( sP43 @ X28 ) )
& ! [X33: term] :
( ( ( X28 @ X33 )
!= $true )
| ( ( X28 @ ( lam @ X33 ) )
= $true ) )
& ! [X30: term] :
( ( $true
!= ( var @ X30 ) )
| ( ( X28 @ X30 )
= $true ) )
& ( $true
!= ( X28 @ X29 ) ) ) )
& ( ( induction2_lthm = $true )
| ( $true != sP42 ) )
& ( ( $true = sP42 )
| ( induction2_lthm != $true ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
= ( ap @ X60 @ X61 ) )
& ( X59 != X60 ) ) )
& ( ( sP38 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP38 != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( $true = sP37 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP37 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
= X474 )
& ? [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
!= $true )
& ( $true
= ( X476 @ X480 ) ) )
& ! [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
= X473 ) ) )
& ( ? [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
!= X474 )
| ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) )
| ? [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
!= X473 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X251: term] :
( ( sub @ X251 @ id )
= X251 )
& ? [X252: term] :
( ( sub @ X252 @ id )
!= X252 ) ) )
& ( ? [X251: term] :
( ( sub @ X251 @ id )
!= X251 )
| ! [X252: term] :
( ( sub @ X252 @ id )
= X252 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP36 ) )
& ( ( $true = sP36 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP31 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP31 ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
| ? [X358: subst] :
( ( comp @ X358 @ id )
!= X358 )
| ? [X357: subst] :
( ( comp @ id @ X357 )
!= X357 ) )
& ( ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) )
| ( substmonoid != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( $true = sP28 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP26 ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X454: term] :
! [X455: subst > term > term] :
( ( X455 @ sh @ one )
!= ( sub @ X454 @ ( push @ one @ sh ) ) ) )
& ( ! [X454: term] :
? [X455: subst > term > term] :
( ( X455 @ sh @ one )
= ( sub @ X454 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ! [X34: subst > term > subst > $o] :
? [X35: term > $o] :
! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X34: subst > term > subst > $o] :
! [X35: term > $o] :
? [X36: term] :
( ( X34 @ id @ X36 @ id )
!= ( X35 @ X36 ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X112: term > $o,X113: term,X114: subst] :
! [X115: term > $o] :
? [X116: term] :
( ( X115 @ X116 )
!= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( ! [X112: term > $o,X113: term,X114: subst] :
? [X115: term > $o] :
! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP25 )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP25 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) )
| ? [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
!= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
= ( lam @ ( X348 @ sh @ one ) ) )
& ! [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
= $true )
& ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) )
& ( $true
!= ( X5 @ one ) ) )
& ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) )
& ( ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ? [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
!= ( X5 @ X6 ) )
| ( $true
= ( X5 @ one ) ) )
| ? [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
!= X1 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP23 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP23 ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X7: d_term,X8: d_term] :
( ( X7 = X8 )
| ( ( d2term @ X7 )
!= ( d2term @ X8 ) ) )
& ( ( shinj = $true )
| ? [X379: term,X380: term] :
( ( X379 != X380 )
& ( ( sub @ X379 @ sh )
= ( sub @ X380 @ sh ) ) ) )
& ( ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) )
| ( shinj != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
& ? [X42: term,X43: term,X44: term,X45: term] :
( ( X42 != X43 )
& ( ( ap @ ( sub @ X42 @ id ) @ X45 )
= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
& ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) ) ) )
& ( ? [X37: term] :
( ( sub @ X37 @ id )
!= X37 )
| ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
| ? [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
= ( ap @ X40 @ X39 ) )
& ( X38 != X40 ) )
| ( hoasapinj1_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP14 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP13 ) )
& ( ( $true = sP13 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
| ( $true != sP11 ) )
& ( ( $true = sP11 )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
!= X275 ) )
& ( ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
| ? [X197: subst] :
( ( comp @ id @ X197 )
!= X197 ) )
& ( ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 )
| ( axidl != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP8 ) )
& ( ( $true = sP8 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X102: subst > term > subst > $o] :
! [X103: term > $o] :
? [X104: term] :
( ( X102 @ id @ X104 @ id )
!= ( X103 @ X104 ) ) )
& ( ! [X102: subst > term > subst > $o] :
? [X103: term > $o] :
! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X125: subst > term > subst > $o,X126: term] :
( ? [X132: term,X133: term] :
( ( $true
= ( X125 @ id @ X133 @ id ) )
& ( $true
= ( X125 @ id @ X132 @ id ) )
& ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
!= $true ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ( $true
= ( sP5 @ X125 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X125: subst > term > subst > $o,X126: term] :
( ! [X132: term,X133: term] :
( ( $true
!= ( X125 @ id @ X133 @ id ) )
| ( $true
!= ( X125 @ id @ X132 @ id ) )
| ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
= $true ) )
& ( $true
!= ( X125 @ id @ X126 @ id ) )
& ( $true
!= ( sP5 @ X125 ) ) ) )
& ( lamnotvar = $true )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X286: term,X287: term,X288: term,X289: term] :
( ( X288 != X289 )
& ( ( ap @ ( sub @ X286 @ id ) @ X289 )
= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) ) )
& ( axvarshift = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X352: term] :
( ( sub @ X352 @ id )
!= X352 ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X253: term] :
! [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
!= ( X254 @ sh @ one ) ) )
& ( ! [X253: term] :
? [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
= ( X254 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ! [X374: subst,X375: term > $o,X376: term] :
? [X377: term > $o] :
! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X374: subst,X375: term > $o,X376: term] :
! [X377: term > $o] :
? [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
!= ( X377 @ X378 ) ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
= ( ap @ X392 @ X391 ) )
& ( X389 != X391 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP2 ) )
& ( ( $true = sP2 )
| ( hoasinduction_lem3v2 != $true ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ? [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
!= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
| ? [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
!= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
= ( lam @ ( X443 @ sh @ one ) ) )
& ! [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
& ! [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
& ( ( X444 @ X446 @ X445 )
!= ( X443 @ X446 @ X445 ) ) ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( pushprop_lem1 = $true )
| ? [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
= ( X439 @ X441 ) )
& ( $true
!= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ( ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) )
| ( pushprop_lem1 != $true ) )
& ( hoasinduction_lem1_gthm = $true ) ),
inference(flattening,[status(thm)],[f473]) ).
thf(f473,plain,
( ( hoasinduction_lem1 = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( ( $true = sP58 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP58 ) )
& ( ( axscons = $true )
| ? [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
!= X157 ) )
& ( ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 )
| ( axscons != $true ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
| ( $true != sP56 ) )
& ( ( $true = sP56 )
| ( induction2lem_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ? [X156: term] :
( ( X153 @ X156 )
!= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
!= ( X153 @ one ) )
& ( $true
= ( X152 @ X155 ) )
& ! [X156: term] :
( ( X153 @ X156 )
= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
| ( termmset != $true ) )
& ( ( termmset = $true )
| ? [X26: term] :
( ( sub @ X26 @ id )
!= X26 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
| ? [X417: term,X418: term] :
( ( X417 != X418 )
& ( ( lam @ X418 )
= ( lam @ X417 ) ) ) )
& ( ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) )
| ( laminj != $true ) )
& ( ( sP52 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( sP52 != $true ) )
& ( ( $true = sP46 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP46 ) )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
!= ( d2subst @ X291 ) )
| ( X290 = X291 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
| ? [X196: subst] :
( ( comp @ X196 @ id )
!= X196 ) )
& ( ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 )
| ( axidr != $true ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ( $true = sP44 )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( $true != sP44 ) )
& ( ! [X434: term] :
? [X435: subst > term > term] :
! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X434: term] :
! [X435: subst > term > term] :
? [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
!= ( sub @ X434 @ ( push @ X436 @ X437 ) ) ) )
& ( ( axvarcons = $true )
| ? [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
!= X470 ) )
& ( ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 )
| ( axvarcons != $true ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ? [X456: subst] :
( ( comp @ id @ X456 )
!= X456 )
| ? [X457: subst] :
( ( comp @ X457 @ id )
!= X457 )
| ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) )
| ( substmonoid_lthm != $true ) )
& ( ( substmonoid_lthm = $true )
| ( ! [X456: subst] :
( ( comp @ id @ X456 )
= X456 )
& ! [X457: subst] :
( ( comp @ X457 @ id )
= X457 )
& ( ? [X459: subst] :
( ( comp @ id @ X459 )
!= X459 )
| ? [X458: subst] :
( ( comp @ X458 @ id )
!= X458 ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X536: term] :
? [X537: subst > term > term] :
! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X536: term] :
! [X537: subst > term > term] :
? [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
!= ( X537 @ X539 @ X538 ) ) )
& ( ( hoasapinj2_lthm = $true )
| ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
!= ( ap @ X411 @ X410 ) )
| ( X409 = X410 ) )
& ? [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
& ( X413 != X415 ) ) ) )
& ( ? [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
= ( ap @ X411 @ X410 ) )
& ( X409 != X410 ) )
| ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X353: term,X354: term,X355: term,X356: term] :
( ( X354 != X356 )
& ( ( ap @ ( sub @ X356 @ id ) @ X355 )
= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) )
| ( hoasapinj1 != $true ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X28: term > $o,X29: term] :
( ( $true
= ( sP43 @ X28 ) )
| ? [X33: term] :
( ( ( X28 @ X33 )
= $true )
& ( ( X28 @ ( lam @ X33 ) )
!= $true ) )
| ? [X30: term] :
( ( $true
= ( var @ X30 ) )
& ( ( X28 @ X30 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) ) )
| ( induction != $true ) )
& ( ( induction = $true )
| ? [X28: term > $o,X29: term] :
( ( $true
!= ( sP43 @ X28 ) )
& ! [X33: term] :
( ( ( X28 @ X33 )
!= $true )
| ( ( X28 @ ( lam @ X33 ) )
= $true ) )
& ! [X30: term] :
( ( $true
!= ( var @ X30 ) )
| ( ( X28 @ X30 )
= $true ) )
& ( $true
!= ( X28 @ X29 ) ) ) )
& ( ( induction2_lthm = $true )
| ( $true != sP42 ) )
& ( ( $true = sP42 )
| ( induction2_lthm != $true ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
| ( apinj1 != $true ) )
& ( ( apinj1 = $true )
| ? [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
= ( ap @ X60 @ X61 ) )
& ( X59 != X60 ) ) )
& ( ( sP38 = $true )
| ( hoasinduction_lem3aaa != $true ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( sP38 != $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( $true = sP37 )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP37 ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
= X474 )
& ? [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
!= $true )
& ( $true
= ( X476 @ X480 ) ) )
& ! [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
= X473 ) ) )
& ( ? [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
!= X474 )
| ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) )
| ? [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
!= X473 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X251: term] :
( ( sub @ X251 @ id )
= X251 )
& ? [X252: term] :
( ( sub @ X252 @ id )
!= X252 ) ) )
& ( ? [X251: term] :
( ( sub @ X251 @ id )
!= X251 )
| ! [X252: term] :
( ( sub @ X252 @ id )
= X252 )
| ( termmset_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP36 ) )
& ( ( $true = sP36 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP31 )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( $true != sP31 ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
| ? [X358: subst] :
( ( comp @ X358 @ id )
!= X358 )
| ? [X357: subst] :
( ( comp @ id @ X357 )
!= X357 ) )
& ( ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) )
| ( substmonoid != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP30 ) )
& ( ( $true = sP30 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( $true = sP28 )
| ( hoasinduction_lem2 != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP28 ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP26 ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X454: term] :
! [X455: subst > term > term] :
( ( X455 @ sh @ one )
!= ( sub @ X454 @ ( push @ one @ sh ) ) ) )
& ( ! [X454: term] :
? [X455: subst > term > term] :
( ( X455 @ sh @ one )
= ( sub @ X454 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ! [X34: subst > term > subst > $o] :
? [X35: term > $o] :
! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X34: subst > term > subst > $o] :
! [X35: term > $o] :
? [X36: term] :
( ( X34 @ id @ X36 @ id )
!= ( X35 @ X36 ) ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X112: term > $o,X113: term,X114: subst] :
! [X115: term > $o] :
? [X116: term] :
( ( X115 @ X116 )
!= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( ! [X112: term > $o,X113: term,X114: subst] :
? [X115: term > $o] :
! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP25 )
| ( induction2 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP25 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) )
| ? [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
!= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
= ( lam @ ( X348 @ sh @ one ) ) )
& ! [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
= $true )
& ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) )
& ( $true
!= ( X5 @ one ) ) )
& ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) )
& ( ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ? [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
!= ( X5 @ X6 ) )
| ( $true
= ( X5 @ one ) ) )
| ? [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
!= X1 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( ( $true = sP23 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP23 ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X7: d_term,X8: d_term] :
( ( X7 = X8 )
| ( ( d2term @ X7 )
!= ( d2term @ X8 ) ) )
& ( ( shinj = $true )
| ? [X379: term,X380: term] :
( ( X379 != X380 )
& ( ( sub @ X379 @ sh )
= ( sub @ X380 @ sh ) ) ) )
& ( ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) )
| ( shinj != $true ) )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
& ? [X42: term,X43: term,X44: term,X45: term] :
( ( X42 != X43 )
& ( ( ap @ ( sub @ X42 @ id ) @ X45 )
= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
& ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) ) ) )
& ( ? [X37: term] :
( ( sub @ X37 @ id )
!= X37 )
| ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
| ? [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
= ( ap @ X40 @ X39 ) )
& ( X38 != X40 ) )
| ( hoasapinj1_lthm != $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP14 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP14 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP13 ) )
& ( ( $true = sP13 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
| ( $true != sP11 ) )
& ( ( $true = sP11 )
| ( hoasinduction != $true ) )
& ( ( axshiftcons = $true )
| ? [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
!= X275 ) )
& ( ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 )
| ( axshiftcons != $true ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
| ? [X197: subst] :
( ( comp @ id @ X197 )
!= X197 ) )
& ( ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 )
| ( axidl != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP8 ) )
& ( ( $true = sP8 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X102: subst > term > subst > $o] :
! [X103: term > $o] :
? [X104: term] :
( ( X102 @ id @ X104 @ id )
!= ( X103 @ X104 ) ) )
& ( ! [X102: subst > term > subst > $o] :
? [X103: term > $o] :
! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X125: subst > term > subst > $o,X126: term] :
( ? [X132: term,X133: term] :
( ( $true
= ( X125 @ id @ X133 @ id ) )
& ( $true
= ( X125 @ id @ X132 @ id ) )
& ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
!= $true ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ( $true
= ( sP5 @ X125 ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X125: subst > term > subst > $o,X126: term] :
( ! [X132: term,X133: term] :
( ( $true
!= ( X125 @ id @ X133 @ id ) )
| ( $true
!= ( X125 @ id @ X132 @ id ) )
| ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
= $true ) )
& ( $true
!= ( X125 @ id @ X126 @ id ) )
& ( $true
!= ( sP5 @ X125 ) ) ) )
& ( lamnotvar = $true )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X286: term,X287: term,X288: term,X289: term] :
( ( X288 != X289 )
& ( ( ap @ ( sub @ X286 @ id ) @ X289 )
= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) ) )
& ( axvarshift = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X352: term] :
( ( sub @ X352 @ id )
!= X352 ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X253: term] :
! [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
!= ( X254 @ sh @ one ) ) )
& ( ! [X253: term] :
? [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
= ( X254 @ sh @ one ) )
| ( hoasinduction_lem3b != $true ) )
& ( ! [X374: subst,X375: term > $o,X376: term] :
? [X377: term > $o] :
! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X374: subst,X375: term > $o,X376: term] :
! [X377: term > $o] :
? [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
!= ( X377 @ X378 ) ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
= ( ap @ X392 @ X391 ) )
& ( X389 != X391 ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP2 ) )
& ( ( $true = sP2 )
| ( hoasinduction_lem3v2 != $true ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ? [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
!= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
| ? [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
!= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
= ( lam @ ( X443 @ sh @ one ) ) )
& ! [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
& ! [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
& ( ( X444 @ X446 @ X445 )
!= ( X443 @ X446 @ X445 ) ) ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( pushprop_lem1 = $true )
| ? [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
= ( X439 @ X441 ) )
& ( $true
!= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ( ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) )
| ( pushprop_lem1 != $true ) )
& ( hoasinduction_lem1_gthm = $true ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( hoasinduction_lem1 = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( ( $true = sP58 )
<=> ( induction2lem = $true ) )
& ( ( axscons = $true )
<=> ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
<=> ( $true = sP56 ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ? [X156: term] :
( ( X153 @ X156 )
!= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
<=> ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) ) )
& ( ( sP52 = $true )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( $true = sP46 )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
!= ( d2subst @ X291 ) )
| ( X290 = X291 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
<=> ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ( $true = sP44 )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X434: term] :
? [X435: subst > term > term] :
! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( axvarcons = $true )
<=> ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ? [X456: subst] :
( ( comp @ id @ X456 )
!= X456 )
| ? [X457: subst] :
( ( comp @ X457 @ id )
!= X457 )
| ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ulamvarsh = $true )
& ( ! [X536: term] :
? [X537: subst > term > term] :
! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
= ( ap @ X411 @ X410 ) )
& ( X409 != X410 ) )
| ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X28: term > $o,X29: term] :
( ( $true
= ( sP43 @ X28 ) )
| ? [X33: term] :
( ( ( X28 @ X33 )
= $true )
& ( ( X28 @ ( lam @ X33 ) )
!= $true ) )
| ? [X30: term] :
( ( $true
= ( var @ X30 ) )
& ( ( X28 @ X30 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) ) )
<=> ( induction = $true ) )
& ( ( induction2_lthm = $true )
<=> ( $true = sP42 ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ( sP38 = $true )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( $true = sP37 )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ? [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
!= X474 )
| ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) )
| ? [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
!= X473 ) ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X251: term] :
( ( sub @ X251 @ id )
!= X251 )
| ! [X252: term] :
( ( sub @ X252 @ id )
= X252 ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( $true = sP36 ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( $true = sP31 )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
<=> ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ( $true = sP30 ) )
& ( ( $true = sP28 )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( $true = sP26 )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X454: term] :
? [X455: subst > term > term] :
( ( X455 @ sh @ one )
= ( sub @ X454 @ ( push @ one @ sh ) ) ) )
& ( ! [X34: subst > term > subst > $o] :
? [X35: term > $o] :
! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X112: term > $o,X113: term,X114: subst] :
? [X115: term > $o] :
! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ( $true = sP25 )
<=> ( induction2 = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) )
| ? [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
!= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ? [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
!= ( X5 @ X6 ) )
| ( $true
= ( X5 @ one ) ) )
| ? [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
!= X1 ) ) )
& ( ( $true = sP23 )
<=> ( hoasinduction_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X7: d_term,X8: d_term] :
( ( X7 = X8 )
| ( ( d2term @ X7 )
!= ( d2term @ X8 ) ) )
& ( ( shinj = $true )
<=> ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ? [X37: term] :
( ( sub @ X37 @ id )
!= X37 )
| ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
| ? [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
= ( ap @ X40 @ X39 ) )
& ( X38 != X40 ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP14 = $true )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ( $true = sP13 ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
<=> ( $true = sP11 ) )
& ( ( axshiftcons = $true )
<=> ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
<=> ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( $true = sP8 ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X102: subst > term > subst > $o] :
? [X103: term > $o] :
! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X125: subst > term > subst > $o,X126: term] :
( ? [X132: term,X133: term] :
( ( $true
= ( X125 @ id @ X133 @ id ) )
& ( $true
= ( X125 @ id @ X132 @ id ) )
& ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
!= $true ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ( $true
= ( sP5 @ X125 ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( lamnotvar = $true )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
<=> ( hoasapinj2 = $true ) )
& ( axvarshift = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X253: term] :
? [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
= ( X254 @ sh @ one ) ) )
& ( ! [X374: subst,X375: term > $o,X376: term] :
? [X377: term > $o] :
! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) )
<=> ( pushprop_lem0 = $true ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
<=> ( apinj2 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( $true = sP4 ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ( $true = sP2 ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ( $true = sP0 ) )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ? [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
!= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
| ? [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
!= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) ) )
<=> ( hoaslaminj = $true ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( pushprop_lem1 = $true )
<=> ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ( hoasinduction_lem1_gthm = $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,
( ( $true = sP0 )
<=> ! [X276: subst > term > subst > $o,X277: term] :
( ? [X279: subst > term > term] :
( ! [X281: subst,X282: term,X283: subst] :
( ( X279 @ ( comp @ X283 @ X281 ) @ ( sub @ X282 @ X281 ) )
= ( sub @ ( X279 @ X283 @ X282 ) @ X281 ) )
& ! [X280: term] :
( ( $true
= ( X276 @ id @ ( X279 @ id @ X280 ) @ id ) )
| ( $true
!= ( X276 @ id @ X280 @ id ) ) )
& ( $true
!= ( X276 @ id @ ( lam @ ( X279 @ sh @ one ) ) @ id ) ) )
| ? [X278: term] :
( ( $true
= ( X276 @ id @ X278 @ id ) )
& ( $true
!= ( X276 @ id @ ( sub @ X277 @ ( push @ X278 @ id ) ) @ id ) ) )
| ( $true
= ( X276 @ id @ ( lam @ X277 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
! [X216: subst > term > subst > $o] :
( ( ( sP1 @ X216 )
= $true )
<=> ? [X217: subst > term > term] :
( ( $true
!= ( X216 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id ) )
& ! [X218: term,X219: subst,X220: subst] :
( ( sub @ ( X217 @ X220 @ X218 ) @ X219 )
= ( X217 @ ( comp @ X220 @ X219 ) @ ( sub @ X218 @ X219 ) ) )
& ! [X221: term] :
( ( $true
!= ( X216 @ id @ X221 @ id ) )
| ( $true
= ( X216 @ id @ ( X217 @ id @ X221 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( $true = sP2 )
<=> ! [X214: term,X215: term > $o,X216: subst > term > subst > $o] :
( ( ( sP1 @ X216 )
= $true )
| ? [X231: term] :
( ( X215 @ X231 )
!= ( X216 @ id @ X231 @ id ) )
| ? [X227: term,X228: subst,X229: subst,X230: subst] :
( ( $true
!= ( X216 @ X228 @ X227 @ ( comp @ X230 @ X229 ) ) )
& ( $true
= ( X216 @ ( comp @ X228 @ X230 ) @ ( sub @ X227 @ X230 ) @ X229 ) ) )
| ? [X222: term] :
( ( $true
!= ( X215 @ ( sub @ X214 @ ( push @ X222 @ id ) ) ) )
& ( ( X215 @ X222 )
= $true ) )
| ? [X223: subst,X224: subst,X225: term,X226: subst] :
( ( $true
= ( X216 @ X224 @ X225 @ ( comp @ X223 @ X226 ) ) )
& ( $true
!= ( X216 @ ( comp @ X224 @ X223 ) @ ( sub @ X225 @ X223 ) @ X226 ) ) )
| ( $true
= ( X215 @ ( lam @ X214 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( $true = sP3 )
<=> ? [X10: subst > term > subst > $o,X11: term] :
( ! [X17: term] :
( ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) )
| ( $true
!= ( X10 @ id @ X17 @ id ) ) )
& ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X12: subst > term > term] :
( ? [X16: term] :
( ( $true
!= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
& ( ( X10 @ id @ X16 @ id )
= $true ) )
| ? [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
!= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
( ( $true = sP4 )
<=> ( ( $true = sP3 )
| ? [X9: term] :
( ( sub @ X9 @ id )
!= X9 )
| ! [X18: subst > term > subst > $o,X19: term] :
( ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) )
| ? [X21: subst > term > term] :
( ( $true
!= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) )
& ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
& ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) ) )
| ? [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
!= $true )
& ( $true
= ( X18 @ id @ X20 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X125: subst > term > subst > $o] :
( ( $true
= ( sP5 @ X125 ) )
<=> ? [X127: subst > term > term] :
( ( $true
!= ( X125 @ id @ ( lam @ ( X127 @ sh @ one ) ) @ id ) )
& ! [X128: term] :
( ( $true
!= ( X125 @ id @ X128 @ id ) )
| ( $true
= ( X125 @ id @ ( X127 @ id @ X128 ) @ id ) ) )
& ! [X129: subst,X130: subst,X131: term] :
( ( X127 @ ( comp @ X129 @ X130 ) @ ( sub @ X131 @ X130 ) )
= ( sub @ ( X127 @ X129 @ X131 ) @ X130 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
! [X491: subst > term > subst > $o] :
( ( $true
= ( sP6 @ X491 ) )
<=> ? [X492: subst > term > term] :
( ( $true
!= ( X491 @ id @ ( lam @ ( X492 @ sh @ one ) ) @ id ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X492 @ X494 @ X495 ) @ X496 )
= ( X492 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) )
& ! [X493: term] :
( ( $true
!= ( X491 @ id @ X493 @ id ) )
| ( ( X491 @ id @ ( X492 @ id @ X493 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
( ( $true = sP7 )
<=> ? [X482: subst > term > subst > $o,X483: term] :
( ! [X489: term] :
( ( $true
!= ( X482 @ id @ X489 @ id ) )
| ( $true
= ( X482 @ id @ ( sub @ X483 @ ( push @ X489 @ id ) ) @ id ) ) )
& ( ( X482 @ id @ ( lam @ ( sub @ X483 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X484: subst > term > term] :
( ? [X485: subst,X486: term,X487: subst] :
( ( X484 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) )
!= ( sub @ ( X484 @ X485 @ X486 ) @ X487 ) )
| ? [X488: term] :
( ( $true
= ( X482 @ id @ X488 @ id ) )
& ( $true
!= ( X482 @ id @ ( X484 @ id @ X488 ) @ id ) ) )
| ( $true
= ( X482 @ id @ ( lam @ ( X484 @ sh @ one ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
( ( $true = sP8 )
<=> ( ? [X481: term] :
( ( sub @ X481 @ id )
!= X481 )
| ! [X490: term,X491: subst > term > subst > $o] :
( ? [X498: subst,X499: subst,X500: subst,X501: term] :
( ( $true
= ( X491 @ X499 @ X501 @ ( comp @ X500 @ X498 ) ) )
& ( $true
!= ( X491 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) @ X498 ) ) )
| ( $true
= ( sP6 @ X491 ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) )
| ? [X497: term] :
( ( $true
= ( X491 @ id @ X497 @ id ) )
& ( $true
!= ( X491 @ id @ ( sub @ X490 @ ( push @ X497 @ id ) ) @ id ) ) )
| ? [X502: subst,X503: subst,X504: subst,X505: term] :
( ( $true
= ( X491 @ ( comp @ X503 @ X502 ) @ ( sub @ X505 @ X502 ) @ X504 ) )
& ( $true
!= ( X491 @ X503 @ X505 @ ( comp @ X502 @ X504 ) ) ) ) )
| ( $true = sP7 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
! [X135: subst > term > subst > $o] :
( ( $true
= ( sP9 @ X135 ) )
<=> ? [X140: subst > term > term] :
( ! [X141: term,X142: subst,X143: subst] :
( ( X140 @ ( comp @ X143 @ X142 ) @ ( sub @ X141 @ X142 ) )
= ( sub @ ( X140 @ X143 @ X141 ) @ X142 ) )
& ! [X144: term] :
( ( $true
!= ( X135 @ id @ X144 @ id ) )
| ( $true
= ( X135 @ id @ ( X140 @ id @ X144 ) @ id ) ) )
& ( $true
!= ( X135 @ id @ ( lam @ ( X140 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
! [X135: subst > term > subst > $o] :
( ( $true
= ( sP10 @ X135 ) )
<=> ? [X146: term,X147: term] :
( ( $true
!= ( X135 @ id @ ( ap @ ( sub @ X147 @ id ) @ X146 ) @ id ) )
& ( $true
= ( X135 @ id @ X147 @ id ) )
& ( ( X135 @ id @ X146 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( $true = sP11 )
<=> ! [X134: term,X135: subst > term > subst > $o] :
( ? [X136: subst,X137: term,X138: subst,X139: subst] :
( ( ( X135 @ X136 @ X137 @ ( comp @ X138 @ X139 ) )
= $true )
& ( $true
!= ( X135 @ ( comp @ X136 @ X138 ) @ ( sub @ X137 @ X138 ) @ X139 ) ) )
| ( ( X135 @ id @ X134 @ id )
= $true )
| ( $true
= ( sP10 @ X135 ) )
| ( $true
= ( sP9 @ X135 ) )
| ? [X148: subst,X149: subst,X150: subst,X151: term] :
( ( $true
!= ( X135 @ X148 @ X151 @ ( comp @ X149 @ X150 ) ) )
& ( $true
= ( X135 @ ( comp @ X148 @ X149 ) @ ( sub @ X151 @ X149 ) @ X150 ) ) )
| ? [X145: term] :
( ( $true
!= ( X135 @ id @ X145 @ id ) )
& ( $true
= ( var @ ( sub @ X145 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
! [X198: subst > term > subst > $o] :
( ( $true
= ( sP12 @ X198 ) )
<=> ? [X204: subst > term > term] :
( ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
!= $true )
& ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
& ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( $true = sP13 )
<=> ! [X198: subst > term > subst > $o,X199: term] :
( ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) )
| ? [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
!= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
& ( $true
= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
| ? [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
& ( $true
!= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ? [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
!= $true )
& ( $true
= ( X198 @ id @ X213 @ id ) ) )
| ( $true
= ( sP12 @ X198 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
( ( sP14 = $true )
<=> ! [X117: term,X118: subst > term > subst > $o] :
( ( $true
= ( X118 @ id @ ( lam @ ( sub @ X117 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X120: subst > term > term] :
( ! [X121: term] :
( ( $true
= ( X118 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ( $true
!= ( X118 @ id @ X121 @ id ) ) )
& ( $true
!= ( X118 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id ) )
& ! [X122: subst,X123: subst,X124: term] :
( ( sub @ ( X120 @ X122 @ X124 ) @ X123 )
= ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) ) ) )
| ? [X119: term] :
( ( $true
!= ( X118 @ id @ ( sub @ X117 @ ( push @ X119 @ id ) ) @ id ) )
& ( $true
= ( X118 @ id @ X119 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
! [X312: subst > term > subst > $o] :
( ( $true
= ( sP15 @ X312 ) )
<=> ! [X315: subst > term > term] :
( ( $true
= ( X312 @ id @ ( lam @ ( X315 @ sh @ one ) ) @ id ) )
| ? [X317: subst,X318: subst,X319: term] :
( ( sub @ ( X315 @ X318 @ X319 ) @ X317 )
!= ( X315 @ ( comp @ X318 @ X317 ) @ ( sub @ X319 @ X317 ) ) )
| ? [X316: term] :
( ( ( X312 @ id @ X316 @ id )
= $true )
& ( $true
!= ( X312 @ id @ ( X315 @ id @ X316 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
! [X329: subst > term > subst > $o] :
( ( $true
= ( sP16 @ X329 ) )
<=> ? [X330: term,X331: term] :
( ( ( X329 @ id @ X330 @ id )
= $true )
& ( $true
!= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
! [X329: subst > term > subst > $o] :
( ( $true
= ( sP17 @ X329 ) )
<=> ? [X337: subst > term > term] :
( ( $true
!= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
& ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) )
& ! [X338: term] :
( ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X329 @ id @ X338 @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
! [X292: term > $o] :
( ( $true
= ( sP18 @ X292 ) )
<=> ! [X297: term,X298: term] :
( ( $true
= ( X292 @ ( ap @ X298 @ X297 ) ) )
| ( ( X292 @ X298 )
!= $true )
| ( $true
!= ( X292 @ X297 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
! [X299: subst > term > subst > $o] :
( ( ( sP19 @ X299 )
= $true )
<=> ! [X306: term,X307: term] :
( ( ( X299 @ id @ X307 @ id )
!= $true )
| ( $true
= ( X299 @ id @ ( ap @ ( sub @ X306 @ id ) @ X307 ) @ id ) )
| ( $true
!= ( X299 @ id @ X306 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
( ( $true = sP20 )
<=> ? [X312: subst > term > subst > $o,X313: term] :
( ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( $true
= ( X312 @ ( comp @ X325 @ X324 ) @ ( sub @ X326 @ X324 ) @ X327 ) )
| ( $true
!= ( X312 @ X325 @ X326 @ ( comp @ X324 @ X327 ) ) ) )
& ! [X314: term] :
( ( $true
= ( X312 @ id @ ( sub @ X313 @ ( push @ X314 @ id ) ) @ id ) )
| ( ( X312 @ id @ X314 @ id )
!= $true ) )
& ( $true
!= ( X312 @ id @ ( lam @ X313 ) @ id ) )
& ( $true
= ( sP15 @ X312 ) )
& ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X312 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ( $true
= ( X312 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
( ( $true = sP21 )
<=> ! [X328: term,X329: subst > term > subst > $o] :
( ? [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
& ( $true
!= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
| ? [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
& ( $true
!= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
| ? [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
& ( ( var @ ( sub @ X336 @ id ) )
= $true ) )
| ( $true
= ( sP17 @ X329 ) )
| ( $true
= ( sP16 @ X329 ) )
| ( $true
= ( X329 @ id @ X328 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( $true = sP22 )
<=> ? [X292: term > $o,X293: term] :
( ( $true
= ( sP18 @ X292 ) )
& ! [X294: term] :
( ? [X295: term] :
( ( ( X292 @ X295 )
= $true )
& ( $true
!= ( X292 @ ( sub @ X294 @ ( push @ X295 @ id ) ) ) ) )
| ( $true
= ( X292 @ ( lam @ X294 ) ) ) )
& ( $true
!= ( X292 @ X293 ) )
& ! [X296: term] :
( ( $true
= ( X292 @ X296 ) )
| ( $true
!= ( var @ X296 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
( ( $true = sP23 )
<=> ( ? [X299: subst > term > subst > $o,X300: term,X301: term] :
( ( ( sP19 @ X299 )
= $true )
& ! [X308: term,X309: subst,X310: subst,X311: subst] :
( ( $true
= ( X299 @ ( comp @ X311 @ X309 ) @ ( sub @ X308 @ X309 ) @ X310 ) )
| ( $true
!= ( X299 @ X311 @ X308 @ ( comp @ X309 @ X310 ) ) ) )
& ! [X302: subst,X303: term,X304: subst,X305: subst] :
( ( $true
= ( X299 @ X305 @ X303 @ ( comp @ X302 @ X304 ) ) )
| ( $true
!= ( X299 @ ( comp @ X305 @ X302 ) @ ( sub @ X303 @ X302 ) @ X304 ) ) )
& ( ( X299 @ id @ X300 @ id )
= $true )
& ( $true
= ( X299 @ id @ X301 @ id ) )
& ( $true
!= ( X299 @ id @ ( ap @ X300 @ X301 ) @ id ) ) )
| ( $true = sP22 )
| ( $true = sP21 )
| ( $true = sP20 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
! [X105: term > $o] :
( ( $true
= ( sP24 @ X105 ) )
<=> ? [X108: term,X109: term] :
( ( $true
= ( X105 @ X108 ) )
& ( $true
= ( X105 @ X109 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X108 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
( ( $true = sP25 )
<=> ! [X105: term > $o,X106: term] :
( ? [X110: term] :
( ( ( X105 @ ( lam @ X110 ) )
!= $true )
& ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) ) )
| ( $true
= ( X105 @ X106 ) )
| ? [X107: term] :
( ( $true
= ( var @ X107 ) )
& ( ( X105 @ X107 )
!= $true ) )
| ( $true
= ( sP24 @ X105 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
( ( $true = sP26 )
<=> ( ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 )
| ? [X359: term] :
! [X360: subst > term > term] :
? [X361: term,X362: subst] :
( ( X360 @ X362 @ X361 )
!= ( sub @ X359 @ ( push @ X361 @ X362 ) ) )
| ! [X364: term,X365: term > $o,X366: subst > term > subst > $o] :
( ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X369 @ X373 @ X371 ) @ X372 )
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ! [X370: term] :
( ( ( X366 @ id @ ( X369 @ id @ X370 ) @ id )
= $true )
| ( $true
!= ( X366 @ id @ X370 @ id ) ) )
& ( $true
!= ( X366 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id ) ) )
| ? [X368: term] :
( ( $true
!= ( X365 @ ( sub @ X364 @ ( push @ X368 @ id ) ) ) )
& ( $true
= ( X365 @ X368 ) ) )
| ( $true
= ( X365 @ ( lam @ X364 ) ) )
| ? [X367: term] :
( ( X366 @ id @ X367 @ id )
!= ( X365 @ X367 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
! [X46: subst > term > subst > $o] :
( ( $true
= ( sP27 @ X46 ) )
<=> ? [X49: term,X50: term] :
( ( ( X46 @ id @ X49 @ id )
= $true )
& ( ( X46 @ id @ X50 @ id )
= $true )
& ( $true
!= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
( ( $true = sP28 )
<=> ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ( $true
!= ( X46 @ id @ X47 @ id ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) )
| ? [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) )
& ( $true
!= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) ) )
| ? [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) )
& ( $true
!= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ( $true
= ( sP27 @ X46 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
! [X422: subst > term > subst > $o] :
( ( $true
= ( sP29 @ X422 ) )
<=> ? [X432: term,X433: term] :
( ( $true
= ( X422 @ id @ X433 @ id ) )
& ( $true
!= ( X422 @ id @ ( ap @ ( sub @ X433 @ id ) @ X432 ) @ id ) )
& ( ( X422 @ id @ X432 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( $true = sP30 )
<=> ! [X419: term,X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ? [X428: subst,X429: term,X430: subst,X431: subst] :
( ( ( X422 @ X431 @ X429 @ ( comp @ X430 @ X428 ) )
= $true )
& ( $true
!= ( X422 @ ( comp @ X431 @ X430 ) @ ( sub @ X429 @ X430 ) @ X428 ) ) )
| ? [X423: subst,X424: term,X425: subst,X426: subst] :
( ( $true
= ( X422 @ ( comp @ X425 @ X426 ) @ ( sub @ X424 @ X426 ) @ X423 ) )
& ( $true
!= ( X422 @ X425 @ X424 @ ( comp @ X426 @ X423 ) ) ) )
| ( $true
= ( sP29 @ X422 ) )
| ? [X427: term] :
( ( X422 @ id @ X427 @ id )
!= ( X421 @ X427 ) )
| ( $true
= ( X421 @ ( ap @ X420 @ X419 ) ) )
| ( $true
!= ( X421 @ X419 ) )
| ( $true
!= ( X421 @ X420 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
( ( $true = sP31 )
<=> ! [X460: term > $o,X461: subst > term > subst > $o,X462: term] :
( ? [X463: term] :
( ( X461 @ id @ X463 @ id )
!= ( X460 @ X463 ) )
| ? [X465: subst > term > term] :
( ( $true
!= ( X461 @ id @ ( lam @ ( X465 @ sh @ one ) ) @ id ) )
& ! [X466: term,X467: subst,X468: subst] :
( ( sub @ ( X465 @ X467 @ X466 ) @ X468 )
= ( X465 @ ( comp @ X467 @ X468 ) @ ( sub @ X466 @ X468 ) ) )
& ! [X469: term] :
( ( $true
!= ( X461 @ id @ X469 @ id ) )
| ( $true
= ( X461 @ id @ ( X465 @ id @ X469 ) @ id ) ) ) )
| ? [X464: term] :
( ( $true
= ( X460 @ X464 ) )
& ( $true
!= ( X460 @ ( sub @ X462 @ ( push @ X464 @ id ) ) ) ) )
| ( $true
= ( X460 @ ( lam @ X462 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
! [X528: subst > term > subst > $o] :
( ( $true
= ( sP32 @ X528 ) )
<=> ? [X529: term,X530: term] :
( ( $true
!= ( X528 @ id @ ( ap @ ( sub @ X529 @ id ) @ X530 ) @ id ) )
& ( $true
= ( X528 @ id @ X529 @ id ) )
& ( $true
= ( X528 @ id @ X530 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
! [X509: term > $o] :
( ( $true
= ( sP33 @ X509 ) )
<=> ! [X511: term,X512: term] :
( ( ( X509 @ X511 )
!= $true )
| ( $true
= ( X509 @ ( ap @ X512 @ X511 ) ) )
| ( $true
!= ( X509 @ X512 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
( ( $true = sP34 )
<=> ? [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ! [X522: subst > term > term] :
( ( $true
= ( X518 @ id @ ( lam @ ( X522 @ sh @ one ) ) @ id ) )
| ? [X524: term,X525: subst,X526: subst] :
( ( X522 @ ( comp @ X525 @ X526 ) @ ( sub @ X524 @ X526 ) )
!= ( sub @ ( X522 @ X525 @ X524 ) @ X526 ) )
| ? [X523: term] :
( ( $true
!= ( X518 @ id @ ( X522 @ id @ X523 ) @ id ) )
& ( ( X518 @ id @ X523 @ id )
= $true ) ) )
& ( $true
!= ( X517 @ ( lam @ X519 ) ) )
& ! [X521: term] :
( ( ( X517 @ ( sub @ X519 @ ( push @ X521 @ id ) ) )
= $true )
| ( $true
!= ( X517 @ X521 ) ) )
& ! [X520: term] :
( ( X517 @ X520 )
= ( X518 @ id @ X520 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
( ( $true = sP35 )
<=> ! [X527: term,X528: subst > term > subst > $o] :
( ( $true
= ( X528 @ id @ X527 @ id ) )
| ? [X531: subst > term > term] :
( ! [X532: term] :
( ( $true
!= ( X528 @ id @ X532 @ id ) )
| ( $true
= ( X528 @ id @ ( X531 @ id @ X532 ) @ id ) ) )
& ( $true
!= ( X528 @ id @ ( lam @ ( X531 @ sh @ one ) ) @ id ) )
& ! [X533: term,X534: subst,X535: subst] :
( ( sub @ ( X531 @ X534 @ X533 ) @ X535 )
= ( X531 @ ( comp @ X534 @ X535 ) @ ( sub @ X533 @ X535 ) ) ) )
| ( $true
= ( sP32 @ X528 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
( ( $true = sP36 )
<=> ( ( $true = sP34 )
| ? [X509: term > $o,X510: term] :
( ! [X515: term] :
( ( $true
!= ( var @ X515 ) )
| ( $true
= ( X509 @ X515 ) ) )
& ( $true
!= ( X509 @ X510 ) )
& ( $true
= ( sP33 @ X509 ) )
& ! [X513: term] :
( ? [X514: term] :
( ( $true
!= ( X509 @ ( sub @ X513 @ ( push @ X514 @ id ) ) ) )
& ( $true
= ( X509 @ X514 ) ) )
| ( $true
= ( X509 @ ( lam @ X513 ) ) ) ) )
| ? [X506: subst > term > subst > $o] :
! [X507: term > $o] :
? [X508: term] :
( ( X506 @ id @ X508 @ id )
!= ( X507 @ X508 ) )
| ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 )
| ( $true = sP35 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
( ( $true = sP37 )
<=> ( ? [X168: term,X169: subst] :
( ( sub @ one @ ( push @ X168 @ X169 ) )
!= X168 )
| ? [X170: term,X171: subst] :
( ( comp @ sh @ ( push @ X170 @ X171 ) )
!= X171 )
| ! [X174: subst > term > term,X175: term,X176: subst,X177: subst > term > term] :
( ( ( X174 @ X176 @ X175 )
= ( X177 @ X176 @ X175 ) )
| ( ( lam @ ( X177 @ sh @ one ) )
!= ( lam @ ( X174 @ sh @ one ) ) )
| ? [X181: subst,X182: subst,X183: term] :
( ( sub @ ( X177 @ X182 @ X183 ) @ X181 )
!= ( X177 @ ( comp @ X182 @ X181 ) @ ( sub @ X183 @ X181 ) ) )
| ? [X178: subst,X179: subst,X180: term] :
( ( sub @ ( X174 @ X178 @ X180 ) @ X179 )
!= ( X174 @ ( comp @ X178 @ X179 ) @ ( sub @ X180 @ X179 ) ) ) )
| ? [X172: term,X173: term] :
( ( ( lam @ X173 )
= ( lam @ X172 ) )
& ( X172 != X173 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
( ( sP38 = $true )
<=> ! [X184: subst > term > subst > $o,X185: term] :
( ? [X187: subst > term > term,X188: term] :
( ! [X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X191 @ X189 ) @ ( sub @ X190 @ X189 ) )
= ( sub @ X188 @ ( push @ ( sub @ X190 @ X189 ) @ ( comp @ X191 @ X189 ) ) ) )
& ! [X192: subst,X193: term,X194: subst] :
( ( sub @ ( sub @ X188 @ ( push @ X193 @ X194 ) ) @ X192 )
= ( sub @ ( X187 @ X194 @ X193 ) @ X192 ) )
& ! [X195: term] :
( ( $true
!= ( X184 @ id @ X195 @ id ) )
| ( $true
= ( X184 @ id @ ( X187 @ id @ X195 ) @ id ) ) )
& ( $true
!= ( X184 @ id @ ( lam @ ( X187 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X184 @ id @ ( lam @ ( sub @ X185 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X186: term] :
( ( $true
= ( X184 @ id @ X186 @ id ) )
& ( $true
!= ( X184 @ id @ ( sub @ X185 @ ( push @ X186 @ id ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
! [X396: term > $o] :
( ( $true
= ( sP39 @ X396 ) )
<=> ! [X398: term,X399: term] :
( ( $true
!= ( X396 @ X399 ) )
| ( $true
!= ( X396 @ X398 ) )
| ( $true
= ( X396 @ ( ap @ X398 @ X399 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X403: term > $o] :
( ( ( sP40 @ X403 )
= $true )
<=> ? [X407: term,X408: term] :
( ( $true
!= ( X403 @ ( ap @ X407 @ X408 ) ) )
& ( ( X403 @ X408 )
= $true )
& ( $true
= ( X403 @ X407 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( $true = sP41 )
<=> ! [X402: term,X403: term > $o] :
( ? [X405: term] :
( ! [X406: term] :
( ( $true
!= ( X403 @ X406 ) )
| ( $true
= ( X403 @ ( sub @ X405 @ ( push @ X406 @ id ) ) ) ) )
& ( $true
!= ( X403 @ ( lam @ X405 ) ) ) )
| ( ( sP40 @ X403 )
= $true )
| ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( $true
!= ( X403 @ X404 ) ) )
| ( $true
= ( X403 @ X402 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
( ( $true = sP42 )
<=> ( ( $true = sP41 )
| ? [X393: term] :
( ( sub @ X393 @ id )
!= X393 )
| ? [X394: subst,X395: term,X396: term > $o] :
( ( $true
!= ( X396 @ ( sub @ X395 @ X394 ) ) )
& ! [X400: term] :
( ? [X401: term] :
( ( $true
= ( X396 @ X401 ) )
& ( ( X396 @ ( sub @ X400 @ ( push @ X401 @ id ) ) )
!= $true ) )
| ( $true
= ( X396 @ ( lam @ X400 ) ) ) )
& ( $true
= ( sP39 @ X396 ) )
& ! [X397: term] :
( ( $true
= ( X396 @ ( sub @ X397 @ X394 ) ) )
| ( $true
!= ( var @ X397 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
! [X28: term > $o] :
( ( $true
= ( sP43 @ X28 ) )
<=> ? [X31: term,X32: term] :
( ( $true
= ( X28 @ X31 ) )
& ( ( X28 @ X32 )
= $true )
& ( $true
!= ( X28 @ ( ap @ X32 @ X31 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
( ( $true = sP44 )
<=> ! [X160: term,X161: subst > term > subst > $o] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X161 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X162 @ X165 @ X164 ) @ X163 )
= ( X162 @ ( comp @ X165 @ X163 ) @ ( sub @ X164 @ X163 ) ) )
& ! [X166: term] :
( ( $true
= ( X161 @ id @ ( X162 @ id @ X166 ) @ id ) )
| ( $true
!= ( X161 @ id @ X166 @ id ) ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X167: term] :
( ( $true
!= ( X161 @ id @ ( sub @ X160 @ ( push @ X167 @ id ) ) @ id ) )
& ( $true
= ( X161 @ id @ X167 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
! [X235: subst > term > subst > $o] :
( ( $true
= ( sP45 @ X235 ) )
<=> ? [X241: subst > term > term] :
( ( $true
!= ( X235 @ id @ ( lam @ ( X241 @ sh @ one ) ) @ id ) )
& ! [X242: term,X243: subst,X244: subst] :
( ( X241 @ ( comp @ X244 @ X243 ) @ ( sub @ X242 @ X243 ) )
= ( sub @ ( X241 @ X244 @ X242 ) @ X243 ) )
& ! [X245: term] :
( ( $true
!= ( X235 @ id @ X245 @ id ) )
| ( $true
= ( X235 @ id @ ( X241 @ id @ X245 ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
( ( $true = sP46 )
<=> ( ! [X233: term,X234: term > $o,X235: subst > term > subst > $o] :
( ? [X240: term] :
( ( ( X234 @ X240 )
= $true )
& ( ( X234 @ ( sub @ X233 @ ( push @ X240 @ id ) ) )
!= $true ) )
| ? [X236: subst,X237: subst,X238: subst,X239: term] :
( ( $true
= ( X235 @ ( comp @ X238 @ X237 ) @ ( sub @ X239 @ X237 ) @ X236 ) )
& ( ( X235 @ X238 @ X239 @ ( comp @ X237 @ X236 ) )
!= $true ) )
| ? [X247: subst,X248: term,X249: subst,X250: subst] :
( ( $true
= ( X235 @ X247 @ X248 @ ( comp @ X249 @ X250 ) ) )
& ( $true
!= ( X235 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) @ X250 ) ) )
| ( ( X234 @ ( lam @ X233 ) )
= $true )
| ? [X246: term] :
( ( X234 @ X246 )
!= ( X235 @ id @ X246 @ id ) )
| ( $true
= ( sP45 @ X235 ) ) )
| ? [X232: term] :
( ( sub @ X232 @ id )
!= X232 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
! [X85: subst > term > subst > $o] :
( ( $true
= ( sP47 @ X85 ) )
<=> ? [X97: subst > term > term] :
( ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) )
& ! [X98: term] :
( ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) )
| ( ( X85 @ id @ X98 @ id )
!= $true ) )
& ( $true
!= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
! [X85: subst > term > subst > $o] :
( ( ( sP48 @ X85 )
= $true )
<=> ? [X86: term,X87: term] :
( ( $true
= ( X85 @ id @ X87 @ id ) )
& ( $true
= ( X85 @ id @ X86 @ id ) )
& ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
! [X67: term > $o] :
( ( $true
= ( sP49 @ X67 ) )
<=> ! [X69: term,X70: term] :
( ( ( X67 @ X70 )
!= $true )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( $true
!= ( X67 @ X69 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
( ( sP50 = $true )
<=> ! [X84: term,X85: subst > term > subst > $o] :
( ? [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
!= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) )
& ( $true
= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) ) )
| ( ( sP48 @ X85 )
= $true )
| ? [X88: term] :
( ( $true
= ( var @ ( sub @ X88 @ id ) ) )
& ( $true
!= ( X85 @ id @ X88 @ id ) ) )
| ( $true
= ( sP47 @ X85 ) )
| ( $true
= ( X85 @ id @ X84 @ id ) )
| ? [X89: subst,X90: subst,X91: term,X92: subst] :
( ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
= $true )
& ( $true
!= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
( ( sP51 = $true )
<=> ? [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ! [X78: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ? [X82: term] :
( ( $true
!= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) )
& ( $true
= ( X75 @ id @ X82 @ id ) ) )
| ? [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
!= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) ) )
& ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
& ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) )
& ( $true
!= ( X74 @ ( lam @ X76 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( sP52 = $true )
<=> ( ? [X73: term] :
( ( sub @ X73 @ id )
!= X73 )
| ( sP51 = $true )
| ? [X66: term,X67: term > $o] :
( ( $true
= ( sP49 @ X67 ) )
& ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ? [X72: term] :
( ( ( X67 @ X72 )
= $true )
& ( $true
!= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) ) ) )
& ( $true
!= ( X67 @ X66 ) )
& ! [X68: term] :
( ( $true
= ( X67 @ X68 ) )
| ( $true
!= ( var @ X68 ) ) ) )
| ( sP50 = $true )
| ? [X63: subst > term > subst > $o] :
! [X64: term > $o] :
? [X65: term] :
( ( X64 @ X65 )
!= ( X63 @ id @ X65 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
! [X268: term > $o] :
( ( $true
= ( sP53 @ X268 ) )
<=> ? [X269: term,X270: term] :
( ( $true
= ( X268 @ X270 ) )
& ( $true
!= ( X268 @ ( ap @ X270 @ X269 ) ) )
& ( $true
= ( X268 @ X269 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X260: term > $o] :
( ( ( sP54 @ X260 )
= $true )
<=> ! [X263: term,X264: term] :
( ( $true
!= ( X260 @ X264 ) )
| ( $true
!= ( X260 @ X263 ) )
| ( $true
= ( X260 @ ( ap @ X264 @ X263 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
( ( $true = sP55 )
<=> ! [X266: term,X267: subst,X268: term > $o] :
( ? [X271: term] :
( ( $true
!= ( X268 @ ( lam @ X271 ) ) )
& ! [X272: term] :
( ( $true
= ( X268 @ ( sub @ X271 @ ( push @ X272 @ id ) ) ) )
| ( $true
!= ( X268 @ X272 ) ) ) )
| ? [X273: term] :
( ( $true
!= ( X268 @ ( sub @ X273 @ X267 ) ) )
& ( $true
= ( var @ X273 ) ) )
| ( $true
= ( sP53 @ X268 ) )
| ( $true
= ( X268 @ ( sub @ X266 @ X267 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( $true = sP56 )
<=> ( ? [X259: subst] :
( ( comp @ X259 @ id )
!= X259 )
| ? [X255: term,X256: subst] :
( ( sub @ one @ ( push @ X255 @ X256 ) )
!= X255 )
| ? [X257: term,X258: subst] :
( ( comp @ sh @ ( push @ X257 @ X258 ) )
!= X258 )
| ? [X260: term > $o,X261: term] :
( ! [X265: term] :
( ( $true
= ( X260 @ X265 ) )
| ( $true
!= ( var @ X265 ) ) )
& ( ( sP54 @ X260 )
= $true )
& ! [X262: term] :
( ( $true
!= ( X260 @ X262 ) )
| ( $true
= ( X260 @ ( lam @ X262 ) ) ) )
& ( $true
!= ( X260 @ X261 ) ) )
| ( $true = sP55 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
! [X381: term > $o] :
( ( $true
= ( sP57 @ X381 ) )
<=> ? [X387: term,X388: term] :
( ( $true
= ( X381 @ X387 ) )
& ( $true
!= ( X381 @ ( ap @ X388 @ X387 ) ) )
& ( $true
= ( X381 @ X388 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( $true = sP58 )
<=> ! [X381: term > $o,X382: subst,X383: term] :
( ? [X386: term] :
( ( $true
= ( var @ X386 ) )
& ( $true
!= ( X381 @ ( sub @ X386 @ X382 ) ) ) )
| ( $true
= ( X381 @ ( sub @ X383 @ X382 ) ) )
| ( $true
= ( sP57 @ X381 ) )
| ? [X384: term] :
( ( $true
!= ( X381 @ ( lam @ X384 ) ) )
& ! [X385: term] :
( ( $true
= ( X381 @ ( sub @ X384 @ ( push @ X385 @ id ) ) ) )
| ( $true
!= ( X381 @ X385 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( hoasinduction_lem1 = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( ! [X381: term > $o,X382: subst,X383: term] :
( ? [X386: term] :
( ( $true
= ( var @ X386 ) )
& ( $true
!= ( X381 @ ( sub @ X386 @ X382 ) ) ) )
| ( $true
= ( X381 @ ( sub @ X383 @ X382 ) ) )
| ? [X387: term,X388: term] :
( ( $true
= ( X381 @ X387 ) )
& ( $true
!= ( X381 @ ( ap @ X388 @ X387 ) ) )
& ( $true
= ( X381 @ X388 ) ) )
| ? [X384: term] :
( ( $true
!= ( X381 @ ( lam @ X384 ) ) )
& ! [X385: term] :
( ( $true
= ( X381 @ ( sub @ X384 @ ( push @ X385 @ id ) ) ) )
| ( $true
!= ( X381 @ X385 ) ) ) ) )
<=> ( induction2lem = $true ) )
& ( ( axscons = $true )
<=> ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 ) )
& ( ulamvar1 != $true )
& ( ( induction2lem_lthm = $true )
<=> ( ? [X259: subst] :
( ( comp @ X259 @ id )
!= X259 )
| ? [X255: term,X256: subst] :
( ( sub @ one @ ( push @ X255 @ X256 ) )
!= X255 )
| ? [X257: term,X258: subst] :
( ( comp @ sh @ ( push @ X257 @ X258 ) )
!= X258 )
| ? [X260: term > $o,X261: term] :
( ! [X265: term] :
( ( $true
= ( X260 @ X265 ) )
| ( $true
!= ( var @ X265 ) ) )
& ! [X263: term,X264: term] :
( ( $true
!= ( X260 @ X264 ) )
| ( $true
!= ( X260 @ X263 ) )
| ( $true
= ( X260 @ ( ap @ X264 @ X263 ) ) ) )
& ! [X262: term] :
( ( $true
!= ( X260 @ X262 ) )
| ( $true
= ( X260 @ ( lam @ X262 ) ) ) )
& ( $true
!= ( X260 @ X261 ) ) )
| ! [X266: term,X267: subst,X268: term > $o] :
( ? [X271: term] :
( ( $true
!= ( X268 @ ( lam @ X271 ) ) )
& ! [X272: term] :
( ( $true
= ( X268 @ ( sub @ X271 @ ( push @ X272 @ id ) ) ) )
| ( $true
!= ( X268 @ X272 ) ) ) )
| ? [X273: term] :
( ( $true
!= ( X268 @ ( sub @ X273 @ X267 ) ) )
& ( $true
= ( var @ X273 ) ) )
| ? [X269: term,X270: term] :
( ( $true
= ( X268 @ X270 ) )
& ( $true
!= ( X268 @ ( ap @ X270 @ X269 ) ) )
& ( $true
= ( X268 @ X269 ) ) )
| ( $true
= ( X268 @ ( sub @ X266 @ X267 ) ) ) ) ) )
& ( hoasapinj1_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ? [X156: term] :
( ( X153 @ X156 )
!= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_lthm_orig = $true )
& ( ( laminj = $true )
<=> ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) ) )
& ( ( ? [X73: term] :
( ( sub @ X73 @ id )
!= X73 )
| ? [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ! [X78: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ? [X82: term] :
( ( $true
!= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) )
& ( $true
= ( X75 @ id @ X82 @ id ) ) )
| ? [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
!= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) ) )
& ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
& ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) )
& ( $true
!= ( X74 @ ( lam @ X76 ) ) ) )
| ? [X66: term,X67: term > $o] :
( ! [X69: term,X70: term] :
( ( ( X67 @ X70 )
!= $true )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( $true
!= ( X67 @ X69 ) ) )
& ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ? [X72: term] :
( ( ( X67 @ X72 )
= $true )
& ( $true
!= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) ) ) )
& ( $true
!= ( X67 @ X66 ) )
& ! [X68: term] :
( ( $true
= ( X67 @ X68 ) )
| ( $true
!= ( var @ X68 ) ) ) )
| ! [X84: term,X85: subst > term > subst > $o] :
( ? [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
!= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) )
& ( $true
= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) ) )
| ? [X86: term,X87: term] :
( ( $true
= ( X85 @ id @ X87 @ id ) )
& ( $true
= ( X85 @ id @ X86 @ id ) )
& ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
!= $true ) )
| ? [X88: term] :
( ( $true
= ( var @ ( sub @ X88 @ id ) ) )
& ( $true
!= ( X85 @ id @ X88 @ id ) ) )
| ? [X97: subst > term > term] :
( ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) )
& ! [X98: term] :
( ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) )
| ( ( X85 @ id @ X98 @ id )
!= $true ) )
& ( $true
!= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X85 @ id @ X84 @ id ) )
| ? [X89: subst,X90: subst,X91: term,X92: subst] :
( ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
= $true )
& ( $true
!= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) ) ) )
| ? [X63: subst > term > subst > $o] :
! [X64: term > $o] :
? [X65: term] :
( ( X64 @ X65 )
!= ( X63 @ id @ X65 @ id ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( ! [X233: term,X234: term > $o,X235: subst > term > subst > $o] :
( ? [X240: term] :
( ( ( X234 @ X240 )
= $true )
& ( ( X234 @ ( sub @ X233 @ ( push @ X240 @ id ) ) )
!= $true ) )
| ? [X236: subst,X237: subst,X238: subst,X239: term] :
( ( $true
= ( X235 @ ( comp @ X238 @ X237 ) @ ( sub @ X239 @ X237 ) @ X236 ) )
& ( ( X235 @ X238 @ X239 @ ( comp @ X237 @ X236 ) )
!= $true ) )
| ? [X247: subst,X248: term,X249: subst,X250: subst] :
( ( $true
= ( X235 @ X247 @ X248 @ ( comp @ X249 @ X250 ) ) )
& ( $true
!= ( X235 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) @ X250 ) ) )
| ( ( X234 @ ( lam @ X233 ) )
= $true )
| ? [X246: term] :
( ( X234 @ X246 )
!= ( X235 @ id @ X246 @ id ) )
| ? [X241: subst > term > term] :
( ( $true
!= ( X235 @ id @ ( lam @ ( X241 @ sh @ one ) ) @ id ) )
& ! [X242: term,X243: subst,X244: subst] :
( ( X241 @ ( comp @ X244 @ X243 ) @ ( sub @ X242 @ X243 ) )
= ( sub @ ( X241 @ X244 @ X242 ) @ X243 ) )
& ! [X245: term] :
( ( $true
!= ( X235 @ id @ X245 @ id ) )
| ( $true
= ( X235 @ id @ ( X241 @ id @ X245 ) @ id ) ) ) ) )
| ? [X232: term] :
( ( sub @ X232 @ id )
!= X232 ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
!= ( d2subst @ X291 ) )
| ( X290 = X291 ) )
& ( hoasinduction_lem1v2 = $true )
& ( ( axidr = $true )
<=> ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 ) )
& ( hoasapnotvar = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ! [X160: term,X161: subst > term > subst > $o] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X161 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X162 @ X165 @ X164 ) @ X163 )
= ( X162 @ ( comp @ X165 @ X163 ) @ ( sub @ X164 @ X163 ) ) )
& ! [X166: term] :
( ( $true
= ( X161 @ id @ ( X162 @ id @ X166 ) @ id ) )
| ( $true
!= ( X161 @ id @ X166 @ id ) ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X167: term] :
( ( $true
!= ( X161 @ id @ ( sub @ X160 @ ( push @ X167 @ id ) ) @ id ) )
& ( $true
= ( X161 @ id @ X167 @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X434: term] :
? [X435: subst > term > term] :
! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( axvarcons = $true )
<=> ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 ) )
& ( pushprop = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ? [X456: subst] :
( ( comp @ id @ X456 )
!= X456 )
| ? [X457: subst] :
( ( comp @ X457 @ id )
!= X457 )
| ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ulamvarsh = $true )
& ( ! [X536: term] :
? [X537: subst > term > term] :
! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
= ( ap @ X411 @ X410 ) )
& ( X409 != X410 ) )
| ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( axmap = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X28: term > $o,X29: term] :
( ? [X31: term,X32: term] :
( ( $true
= ( X28 @ X31 ) )
& ( ( X28 @ X32 )
= $true )
& ( $true
!= ( X28 @ ( ap @ X32 @ X31 ) ) ) )
| ? [X33: term] :
( ( ( X28 @ X33 )
= $true )
& ( ( X28 @ ( lam @ X33 ) )
!= $true ) )
| ? [X30: term] :
( ( $true
= ( var @ X30 ) )
& ( ( X28 @ X30 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) ) )
<=> ( induction = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X402: term,X403: term > $o] :
( ? [X405: term] :
( ! [X406: term] :
( ( $true
!= ( X403 @ X406 ) )
| ( $true
= ( X403 @ ( sub @ X405 @ ( push @ X406 @ id ) ) ) ) )
& ( $true
!= ( X403 @ ( lam @ X405 ) ) ) )
| ? [X407: term,X408: term] :
( ( $true
!= ( X403 @ ( ap @ X407 @ X408 ) ) )
& ( ( X403 @ X408 )
= $true )
& ( $true
= ( X403 @ X407 ) ) )
| ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( $true
!= ( X403 @ X404 ) ) )
| ( $true
= ( X403 @ X402 ) ) )
| ? [X393: term] :
( ( sub @ X393 @ id )
!= X393 )
| ? [X394: subst,X395: term,X396: term > $o] :
( ( $true
!= ( X396 @ ( sub @ X395 @ X394 ) ) )
& ! [X400: term] :
( ? [X401: term] :
( ( $true
= ( X396 @ X401 ) )
& ( ( X396 @ ( sub @ X400 @ ( push @ X401 @ id ) ) )
!= $true ) )
| ( $true
= ( X396 @ ( lam @ X400 ) ) ) )
& ! [X398: term,X399: term] :
( ( $true
!= ( X396 @ X399 ) )
| ( $true
!= ( X396 @ X398 ) )
| ( $true
= ( X396 @ ( ap @ X398 @ X399 ) ) ) )
& ! [X397: term] :
( ( $true
= ( X396 @ ( sub @ X397 @ X394 ) ) )
| ( $true
!= ( var @ X397 ) ) ) ) ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ! [X184: subst > term > subst > $o,X185: term] :
( ? [X187: subst > term > term,X188: term] :
( ! [X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X191 @ X189 ) @ ( sub @ X190 @ X189 ) )
= ( sub @ X188 @ ( push @ ( sub @ X190 @ X189 ) @ ( comp @ X191 @ X189 ) ) ) )
& ! [X192: subst,X193: term,X194: subst] :
( ( sub @ ( sub @ X188 @ ( push @ X193 @ X194 ) ) @ X192 )
= ( sub @ ( X187 @ X194 @ X193 ) @ X192 ) )
& ! [X195: term] :
( ( $true
!= ( X184 @ id @ X195 @ id ) )
| ( $true
= ( X184 @ id @ ( X187 @ id @ X195 ) @ id ) ) )
& ( $true
!= ( X184 @ id @ ( lam @ ( X187 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X184 @ id @ ( lam @ ( sub @ X185 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X186: term] :
( ( $true
= ( X184 @ id @ X186 @ id ) )
& ( $true
!= ( X184 @ id @ ( sub @ X185 @ ( push @ X186 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( ? [X168: term,X169: subst] :
( ( sub @ one @ ( push @ X168 @ X169 ) )
!= X168 )
| ? [X170: term,X171: subst] :
( ( comp @ sh @ ( push @ X170 @ X171 ) )
!= X171 )
| ! [X174: subst > term > term,X175: term,X176: subst,X177: subst > term > term] :
( ( ( X174 @ X176 @ X175 )
= ( X177 @ X176 @ X175 ) )
| ( ( lam @ ( X177 @ sh @ one ) )
!= ( lam @ ( X174 @ sh @ one ) ) )
| ? [X181: subst,X182: subst,X183: term] :
( ( sub @ ( X177 @ X182 @ X183 ) @ X181 )
!= ( X177 @ ( comp @ X182 @ X181 ) @ ( sub @ X183 @ X181 ) ) )
| ? [X178: subst,X179: subst,X180: term] :
( ( sub @ ( X174 @ X178 @ X180 ) @ X179 )
!= ( X174 @ ( comp @ X178 @ X179 ) @ ( sub @ X180 @ X179 ) ) ) )
| ? [X172: term,X173: term] :
( ( ( lam @ X173 )
= ( lam @ X172 ) )
& ( X172 != X173 ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ? [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
!= X474 )
| ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) )
| ? [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
!= X473 ) ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X251: term] :
( ( sub @ X251 @ id )
!= X251 )
| ! [X252: term] :
( ( sub @ X252 @ id )
= X252 ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ? [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ! [X522: subst > term > term] :
( ( $true
= ( X518 @ id @ ( lam @ ( X522 @ sh @ one ) ) @ id ) )
| ? [X524: term,X525: subst,X526: subst] :
( ( X522 @ ( comp @ X525 @ X526 ) @ ( sub @ X524 @ X526 ) )
!= ( sub @ ( X522 @ X525 @ X524 ) @ X526 ) )
| ? [X523: term] :
( ( $true
!= ( X518 @ id @ ( X522 @ id @ X523 ) @ id ) )
& ( ( X518 @ id @ X523 @ id )
= $true ) ) )
& ( $true
!= ( X517 @ ( lam @ X519 ) ) )
& ! [X521: term] :
( ( ( X517 @ ( sub @ X519 @ ( push @ X521 @ id ) ) )
= $true )
| ( $true
!= ( X517 @ X521 ) ) )
& ! [X520: term] :
( ( X517 @ X520 )
= ( X518 @ id @ X520 @ id ) ) )
| ? [X509: term > $o,X510: term] :
( ! [X515: term] :
( ( $true
!= ( var @ X515 ) )
| ( $true
= ( X509 @ X515 ) ) )
& ( $true
!= ( X509 @ X510 ) )
& ! [X511: term,X512: term] :
( ( ( X509 @ X511 )
!= $true )
| ( $true
= ( X509 @ ( ap @ X512 @ X511 ) ) )
| ( $true
!= ( X509 @ X512 ) ) )
& ! [X513: term] :
( ? [X514: term] :
( ( $true
!= ( X509 @ ( sub @ X513 @ ( push @ X514 @ id ) ) ) )
& ( $true
= ( X509 @ X514 ) ) )
| ( $true
= ( X509 @ ( lam @ X513 ) ) ) ) )
| ? [X506: subst > term > subst > $o] :
! [X507: term > $o] :
? [X508: term] :
( ( X506 @ id @ X508 @ id )
!= ( X507 @ X508 ) )
| ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 )
| ! [X527: term,X528: subst > term > subst > $o] :
( ( $true
= ( X528 @ id @ X527 @ id ) )
| ? [X531: subst > term > term] :
( ! [X532: term] :
( ( $true
!= ( X528 @ id @ X532 @ id ) )
| ( $true
= ( X528 @ id @ ( X531 @ id @ X532 ) @ id ) ) )
& ( $true
!= ( X528 @ id @ ( lam @ ( X531 @ sh @ one ) ) @ id ) )
& ! [X533: term,X534: subst,X535: subst] :
( ( sub @ ( X531 @ X534 @ X533 ) @ X535 )
= ( X531 @ ( comp @ X534 @ X535 ) @ ( sub @ X533 @ X535 ) ) ) )
| ? [X529: term,X530: term] :
( ( $true
!= ( X528 @ id @ ( ap @ ( sub @ X529 @ id ) @ X530 ) @ id ) )
& ( $true
= ( X528 @ id @ X529 @ id ) )
& ( $true
= ( X528 @ id @ X530 @ id ) ) ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ! [X460: term > $o,X461: subst > term > subst > $o,X462: term] :
( ? [X463: term] :
( ( X461 @ id @ X463 @ id )
!= ( X460 @ X463 ) )
| ? [X465: subst > term > term] :
( ( $true
!= ( X461 @ id @ ( lam @ ( X465 @ sh @ one ) ) @ id ) )
& ! [X466: term,X467: subst,X468: subst] :
( ( sub @ ( X465 @ X467 @ X466 ) @ X468 )
= ( X465 @ ( comp @ X467 @ X468 ) @ ( sub @ X466 @ X468 ) ) )
& ! [X469: term] :
( ( $true
!= ( X461 @ id @ X469 @ id ) )
| ( $true
= ( X461 @ id @ ( X465 @ id @ X469 ) @ id ) ) ) )
| ? [X464: term] :
( ( $true
= ( X460 @ X464 ) )
& ( $true
!= ( X460 @ ( sub @ X462 @ ( push @ X464 @ id ) ) ) ) )
| ( $true
= ( X460 @ ( lam @ X462 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ( substmonoid = $true )
<=> ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X419: term,X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ? [X428: subst,X429: term,X430: subst,X431: subst] :
( ( ( X422 @ X431 @ X429 @ ( comp @ X430 @ X428 ) )
= $true )
& ( $true
!= ( X422 @ ( comp @ X431 @ X430 ) @ ( sub @ X429 @ X430 ) @ X428 ) ) )
| ? [X423: subst,X424: term,X425: subst,X426: subst] :
( ( $true
= ( X422 @ ( comp @ X425 @ X426 ) @ ( sub @ X424 @ X426 ) @ X423 ) )
& ( $true
!= ( X422 @ X425 @ X424 @ ( comp @ X426 @ X423 ) ) ) )
| ? [X432: term,X433: term] :
( ( $true
= ( X422 @ id @ X433 @ id ) )
& ( $true
!= ( X422 @ id @ ( ap @ ( sub @ X433 @ id ) @ X432 ) @ id ) )
& ( ( X422 @ id @ X432 @ id )
= $true ) )
| ? [X427: term] :
( ( X422 @ id @ X427 @ id )
!= ( X421 @ X427 ) )
| ( $true
= ( X421 @ ( ap @ X420 @ X419 ) ) )
| ( $true
!= ( X421 @ X419 ) )
| ( $true
!= ( X421 @ X420 ) ) ) )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ( $true
!= ( X46 @ id @ X47 @ id ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) )
| ? [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) )
& ( $true
!= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) ) )
| ? [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) )
& ( $true
!= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ? [X49: term,X50: term] :
( ( ( X46 @ id @ X49 @ id )
= $true )
& ( ( X46 @ id @ X50 @ id )
= $true )
& ( $true
!= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 )
| ? [X359: term] :
! [X360: subst > term > term] :
? [X361: term,X362: subst] :
( ( X360 @ X362 @ X361 )
!= ( sub @ X359 @ ( push @ X361 @ X362 ) ) )
| ! [X364: term,X365: term > $o,X366: subst > term > subst > $o] :
( ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X369 @ X373 @ X371 ) @ X372 )
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ! [X370: term] :
( ( ( X366 @ id @ ( X369 @ id @ X370 ) @ id )
= $true )
| ( $true
!= ( X366 @ id @ X370 @ id ) ) )
& ( $true
!= ( X366 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id ) ) )
| ? [X368: term] :
( ( $true
!= ( X365 @ ( sub @ X364 @ ( push @ X368 @ id ) ) ) )
& ( $true
= ( X365 @ X368 ) ) )
| ( $true
= ( X365 @ ( lam @ X364 ) ) )
| ? [X367: term] :
( ( X366 @ id @ X367 @ id )
!= ( X365 @ X367 ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X454: term] :
? [X455: subst > term > term] :
( ( X455 @ sh @ one )
= ( sub @ X454 @ ( push @ one @ sh ) ) ) )
& ( ! [X34: subst > term > subst > $o] :
? [X35: term > $o] :
! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X112: term > $o,X113: term,X114: subst] :
? [X115: term > $o] :
! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoaslaminj_gthm = $true )
& ( ! [X105: term > $o,X106: term] :
( ? [X110: term] :
( ( ( X105 @ ( lam @ X110 ) )
!= $true )
& ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) ) )
| ( $true
= ( X105 @ X106 ) )
| ? [X107: term] :
( ( $true
= ( var @ X107 ) )
& ( ( X105 @ X107 )
!= $true ) )
| ? [X108: term,X109: term] :
( ( $true
= ( X105 @ X108 ) )
& ( $true
= ( X105 @ X109 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X108 ) ) ) ) )
<=> ( induction2 = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axclos = $true )
& ( ! [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) )
| ? [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
!= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ? [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
!= ( X5 @ X6 ) )
| ( $true
= ( X5 @ one ) ) )
| ? [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
!= X1 ) ) )
& ( ( ? [X299: subst > term > subst > $o,X300: term,X301: term] :
( ! [X306: term,X307: term] :
( ( ( X299 @ id @ X307 @ id )
!= $true )
| ( $true
= ( X299 @ id @ ( ap @ ( sub @ X306 @ id ) @ X307 ) @ id ) )
| ( $true
!= ( X299 @ id @ X306 @ id ) ) )
& ! [X308: term,X309: subst,X310: subst,X311: subst] :
( ( $true
= ( X299 @ ( comp @ X311 @ X309 ) @ ( sub @ X308 @ X309 ) @ X310 ) )
| ( $true
!= ( X299 @ X311 @ X308 @ ( comp @ X309 @ X310 ) ) ) )
& ! [X302: subst,X303: term,X304: subst,X305: subst] :
( ( $true
= ( X299 @ X305 @ X303 @ ( comp @ X302 @ X304 ) ) )
| ( $true
!= ( X299 @ ( comp @ X305 @ X302 ) @ ( sub @ X303 @ X302 ) @ X304 ) ) )
& ( ( X299 @ id @ X300 @ id )
= $true )
& ( $true
= ( X299 @ id @ X301 @ id ) )
& ( $true
!= ( X299 @ id @ ( ap @ X300 @ X301 ) @ id ) ) )
| ? [X292: term > $o,X293: term] :
( ! [X297: term,X298: term] :
( ( $true
= ( X292 @ ( ap @ X298 @ X297 ) ) )
| ( ( X292 @ X298 )
!= $true )
| ( $true
!= ( X292 @ X297 ) ) )
& ! [X294: term] :
( ? [X295: term] :
( ( ( X292 @ X295 )
= $true )
& ( $true
!= ( X292 @ ( sub @ X294 @ ( push @ X295 @ id ) ) ) ) )
| ( $true
= ( X292 @ ( lam @ X294 ) ) ) )
& ( $true
!= ( X292 @ X293 ) )
& ! [X296: term] :
( ( $true
= ( X292 @ X296 ) )
| ( $true
!= ( var @ X296 ) ) ) )
| ! [X328: term,X329: subst > term > subst > $o] :
( ? [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
& ( $true
!= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
| ? [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
& ( $true
!= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
| ? [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
& ( ( var @ ( sub @ X336 @ id ) )
= $true ) )
| ? [X337: subst > term > term] :
( ( $true
!= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
& ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) )
& ! [X338: term] :
( ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X329 @ id @ X338 @ id )
!= $true ) ) )
| ? [X330: term,X331: term] :
( ( ( X329 @ id @ X330 @ id )
= $true )
& ( $true
!= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( $true
= ( X329 @ id @ X328 @ id ) ) )
| ? [X312: subst > term > subst > $o,X313: term] :
( ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( $true
= ( X312 @ ( comp @ X325 @ X324 ) @ ( sub @ X326 @ X324 ) @ X327 ) )
| ( $true
!= ( X312 @ X325 @ X326 @ ( comp @ X324 @ X327 ) ) ) )
& ! [X314: term] :
( ( $true
= ( X312 @ id @ ( sub @ X313 @ ( push @ X314 @ id ) ) @ id ) )
| ( ( X312 @ id @ X314 @ id )
!= $true ) )
& ( $true
!= ( X312 @ id @ ( lam @ X313 ) @ id ) )
& ! [X315: subst > term > term] :
( ( $true
= ( X312 @ id @ ( lam @ ( X315 @ sh @ one ) ) @ id ) )
| ? [X317: subst,X318: subst,X319: term] :
( ( sub @ ( X315 @ X318 @ X319 ) @ X317 )
!= ( X315 @ ( comp @ X318 @ X317 ) @ ( sub @ X319 @ X317 ) ) )
| ? [X316: term] :
( ( ( X312 @ id @ X316 @ id )
= $true )
& ( $true
!= ( X312 @ id @ ( X315 @ id @ X316 ) @ id ) ) ) )
& ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X312 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ( $true
= ( X312 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X7: d_term,X8: d_term] :
( ( X7 = X8 )
| ( ( d2term @ X7 )
!= ( d2term @ X8 ) ) )
& ( ( shinj = $true )
<=> ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) ) )
& ( ( hoasapinj1_lthm = $true )
<=> ( ? [X37: term] :
( ( sub @ X37 @ id )
!= X37 )
| ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
| ? [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
= ( ap @ X40 @ X39 ) )
& ( X38 != X40 ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X117: term,X118: subst > term > subst > $o] :
( ( $true
= ( X118 @ id @ ( lam @ ( sub @ X117 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X120: subst > term > term] :
( ! [X121: term] :
( ( $true
= ( X118 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ( $true
!= ( X118 @ id @ X121 @ id ) ) )
& ( $true
!= ( X118 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id ) )
& ! [X122: subst,X123: subst,X124: term] :
( ( sub @ ( X120 @ X122 @ X124 ) @ X123 )
= ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) ) ) )
| ? [X119: term] :
( ( $true
!= ( X118 @ id @ ( sub @ X117 @ ( push @ X119 @ id ) ) @ id ) )
& ( $true
= ( X118 @ id @ X119 @ id ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X198: subst > term > subst > $o,X199: term] :
( ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) )
| ? [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
!= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
& ( $true
= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
| ? [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
& ( $true
!= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ? [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
!= $true )
& ( $true
= ( X198 @ id @ X213 @ id ) ) )
| ? [X204: subst > term > term] :
( ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
!= $true )
& ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
& ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( axassoc = $true )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction = $true )
<=> ! [X134: term,X135: subst > term > subst > $o] :
( ? [X136: subst,X137: term,X138: subst,X139: subst] :
( ( ( X135 @ X136 @ X137 @ ( comp @ X138 @ X139 ) )
= $true )
& ( $true
!= ( X135 @ ( comp @ X136 @ X138 ) @ ( sub @ X137 @ X138 ) @ X139 ) ) )
| ( ( X135 @ id @ X134 @ id )
= $true )
| ? [X146: term,X147: term] :
( ( $true
!= ( X135 @ id @ ( ap @ ( sub @ X147 @ id ) @ X146 ) @ id ) )
& ( $true
= ( X135 @ id @ X147 @ id ) )
& ( ( X135 @ id @ X146 @ id )
= $true ) )
| ? [X140: subst > term > term] :
( ! [X141: term,X142: subst,X143: subst] :
( ( X140 @ ( comp @ X143 @ X142 ) @ ( sub @ X141 @ X142 ) )
= ( sub @ ( X140 @ X143 @ X141 ) @ X142 ) )
& ! [X144: term] :
( ( $true
!= ( X135 @ id @ X144 @ id ) )
| ( $true
= ( X135 @ id @ ( X140 @ id @ X144 ) @ id ) ) )
& ( $true
!= ( X135 @ id @ ( lam @ ( X140 @ sh @ one ) ) @ id ) ) )
| ? [X148: subst,X149: subst,X150: subst,X151: term] :
( ( $true
!= ( X135 @ X148 @ X151 @ ( comp @ X149 @ X150 ) ) )
& ( $true
= ( X135 @ ( comp @ X148 @ X149 ) @ ( sub @ X151 @ X149 ) @ X150 ) ) )
| ? [X145: term] :
( ( $true
!= ( X135 @ id @ X145 @ id ) )
& ( $true
= ( var @ ( sub @ X145 @ id ) ) ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 ) )
& ( hoaslamnotvar = $true )
& ( induction2_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( axidl = $true )
<=> ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ? [X481: term] :
( ( sub @ X481 @ id )
!= X481 )
| ! [X490: term,X491: subst > term > subst > $o] :
( ? [X498: subst,X499: subst,X500: subst,X501: term] :
( ( $true
= ( X491 @ X499 @ X501 @ ( comp @ X500 @ X498 ) ) )
& ( $true
!= ( X491 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) @ X498 ) ) )
| ? [X492: subst > term > term] :
( ( $true
!= ( X491 @ id @ ( lam @ ( X492 @ sh @ one ) ) @ id ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X492 @ X494 @ X495 ) @ X496 )
= ( X492 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) )
& ! [X493: term] :
( ( $true
!= ( X491 @ id @ X493 @ id ) )
| ( ( X491 @ id @ ( X492 @ id @ X493 ) @ id )
= $true ) ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) )
| ? [X497: term] :
( ( $true
= ( X491 @ id @ X497 @ id ) )
& ( $true
!= ( X491 @ id @ ( sub @ X490 @ ( push @ X497 @ id ) ) @ id ) ) )
| ? [X502: subst,X503: subst,X504: subst,X505: term] :
( ( $true
= ( X491 @ ( comp @ X503 @ X502 ) @ ( sub @ X505 @ X502 ) @ X504 ) )
& ( $true
!= ( X491 @ X503 @ X505 @ ( comp @ X502 @ X504 ) ) ) ) )
| ? [X482: subst > term > subst > $o,X483: term] :
( ! [X489: term] :
( ( $true
!= ( X482 @ id @ X489 @ id ) )
| ( $true
= ( X482 @ id @ ( sub @ X483 @ ( push @ X489 @ id ) ) @ id ) ) )
& ( ( X482 @ id @ ( lam @ ( sub @ X483 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X484: subst > term > term] :
( ? [X485: subst,X486: term,X487: subst] :
( ( X484 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) )
!= ( sub @ ( X484 @ X485 @ X486 ) @ X487 ) )
| ? [X488: term] :
( ( $true
= ( X482 @ id @ X488 @ id ) )
& ( $true
!= ( X482 @ id @ ( X484 @ id @ X488 ) @ id ) ) )
| ( $true
= ( X482 @ id @ ( lam @ ( X484 @ sh @ one ) ) @ id ) ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( substmonoid_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X102: subst > term > subst > $o] :
? [X103: term > $o] :
! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasapnotvar_lthm = $true )
& ( apnotvar = $true )
& ( ! [X125: subst > term > subst > $o,X126: term] :
( ? [X132: term,X133: term] :
( ( $true
= ( X125 @ id @ X133 @ id ) )
& ( $true
= ( X125 @ id @ X132 @ id ) )
& ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
!= $true ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ? [X127: subst > term > term] :
( ( $true
!= ( X125 @ id @ ( lam @ ( X127 @ sh @ one ) ) @ id ) )
& ! [X128: term] :
( ( $true
!= ( X125 @ id @ X128 @ id ) )
| ( $true
= ( X125 @ id @ ( X127 @ id @ X128 ) @ id ) ) )
& ! [X129: subst,X130: subst,X131: term] :
( ( X127 @ ( comp @ X129 @ X130 ) @ ( sub @ X131 @ X130 ) )
= ( sub @ ( X127 @ X129 @ X131 ) @ X130 ) ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( lamnotvar = $true )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
<=> ( hoasapinj2 = $true ) )
& ( axvarshift = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
<=> ( axvarid = $true ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X253: term] :
? [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
= ( X254 @ sh @ one ) ) )
& ( ! [X374: subst,X375: term > $o,X376: term] :
? [X377: term > $o] :
! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) )
<=> ( pushprop_lem0 = $true ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
<=> ( apinj2 = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ? [X10: subst > term > subst > $o,X11: term] :
( ! [X17: term] :
( ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) )
| ( $true
!= ( X10 @ id @ X17 @ id ) ) )
& ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X12: subst > term > term] :
( ? [X16: term] :
( ( $true
!= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
& ( ( X10 @ id @ X16 @ id )
= $true ) )
| ? [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
!= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) )
| ? [X9: term] :
( ( sub @ X9 @ id )
!= X9 )
| ! [X18: subst > term > subst > $o,X19: term] :
( ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) )
| ? [X21: subst > term > term] :
( ( $true
!= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) )
& ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
& ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) ) )
| ? [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
!= $true )
& ( $true
= ( X18 @ id @ X20 @ id ) ) ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( induction2lem_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( axabs = $true )
& ( termmset_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X214: term,X215: term > $o,X216: subst > term > subst > $o] :
( ? [X217: subst > term > term] :
( ( $true
!= ( X216 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id ) )
& ! [X218: term,X219: subst,X220: subst] :
( ( sub @ ( X217 @ X220 @ X218 ) @ X219 )
= ( X217 @ ( comp @ X220 @ X219 ) @ ( sub @ X218 @ X219 ) ) )
& ! [X221: term] :
( ( $true
!= ( X216 @ id @ X221 @ id ) )
| ( $true
= ( X216 @ id @ ( X217 @ id @ X221 ) @ id ) ) ) )
| ? [X231: term] :
( ( X215 @ X231 )
!= ( X216 @ id @ X231 @ id ) )
| ? [X227: term,X228: subst,X229: subst,X230: subst] :
( ( $true
!= ( X216 @ X228 @ X227 @ ( comp @ X230 @ X229 ) ) )
& ( $true
= ( X216 @ ( comp @ X228 @ X230 ) @ ( sub @ X227 @ X230 ) @ X229 ) ) )
| ? [X222: term] :
( ( $true
!= ( X215 @ ( sub @ X214 @ ( push @ X222 @ id ) ) ) )
& ( ( X215 @ X222 )
= $true ) )
| ? [X223: subst,X224: subst,X225: term,X226: subst] :
( ( $true
= ( X216 @ X224 @ X225 @ ( comp @ X223 @ X226 ) ) )
& ( $true
!= ( X216 @ ( comp @ X224 @ X223 ) @ ( sub @ X225 @ X223 ) @ X226 ) ) )
| ( $true
= ( X215 @ ( lam @ X214 ) ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotap != $true )
& ( ulamvarind = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X276: subst > term > subst > $o,X277: term] :
( ? [X279: subst > term > term] :
( ! [X281: subst,X282: term,X283: subst] :
( ( X279 @ ( comp @ X283 @ X281 ) @ ( sub @ X282 @ X281 ) )
= ( sub @ ( X279 @ X283 @ X282 ) @ X281 ) )
& ! [X280: term] :
( ( $true
= ( X276 @ id @ ( X279 @ id @ X280 ) @ id ) )
| ( $true
!= ( X276 @ id @ X280 @ id ) ) )
& ( $true
!= ( X276 @ id @ ( lam @ ( X279 @ sh @ one ) ) @ id ) ) )
| ? [X278: term] :
( ( $true
= ( X276 @ id @ X278 @ id ) )
& ( $true
!= ( X276 @ id @ ( sub @ X277 @ ( push @ X278 @ id ) ) @ id ) ) )
| ( $true
= ( X276 @ id @ ( lam @ X277 ) @ id ) ) ) )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ? [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
!= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
| ? [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
!= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) ) )
<=> ( hoaslaminj = $true ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( pushprop_lem1 = $true )
<=> ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ( hoasinduction_lem1_gthm = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X364: term,X365: term > $o,X366: subst > term > subst > $o] :
( ? [X369: subst > term > term] :
( ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X369 @ X373 @ X371 ) @ X372 )
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ! [X370: term] :
( ( ( X366 @ id @ ( X369 @ id @ X370 ) @ id )
= $true )
| ( $true
!= ( X366 @ id @ X370 @ id ) ) )
& ( $true
!= ( X366 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id ) ) )
| ? [X368: term] :
( ( $true
!= ( X365 @ ( sub @ X364 @ ( push @ X368 @ id ) ) ) )
& ( $true
= ( X365 @ X368 ) ) )
| ( $true
= ( X365 @ ( lam @ X364 ) ) )
| ? [X367: term] :
( ( X366 @ id @ X367 @ id )
!= ( X365 @ X367 ) ) )
| ? [X363: term] :
( ( sub @ X363 @ id )
!= X363 )
| ? [X359: term] :
! [X360: subst > term > term] :
? [X361: term,X362: subst] :
( ( X360 @ X362 @ X361 )
!= ( sub @ X359 @ ( push @ X361 @ X362 ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( ! [X174: subst > term > term,X175: term,X176: subst,X177: subst > term > term] :
( ( ( X174 @ X176 @ X175 )
= ( X177 @ X176 @ X175 ) )
| ( ( lam @ ( X177 @ sh @ one ) )
!= ( lam @ ( X174 @ sh @ one ) ) )
| ? [X181: subst,X182: subst,X183: term] :
( ( sub @ ( X177 @ X182 @ X183 ) @ X181 )
!= ( X177 @ ( comp @ X182 @ X181 ) @ ( sub @ X183 @ X181 ) ) )
| ? [X178: subst,X179: subst,X180: term] :
( ( sub @ ( X174 @ X178 @ X180 ) @ X179 )
!= ( X174 @ ( comp @ X178 @ X179 ) @ ( sub @ X180 @ X179 ) ) ) )
| ? [X172: term,X173: term] :
( ( ( lam @ X173 )
= ( lam @ X172 ) )
& ( X172 != X173 ) )
| ? [X170: term,X171: subst] :
( ( comp @ sh @ ( push @ X170 @ X171 ) )
!= X171 )
| ? [X168: term,X169: subst] :
( ( sub @ one @ ( push @ X168 @ X169 ) )
!= X168 ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoasinduction = $true )
<=> ! [X134: term,X135: subst > term > subst > $o] :
( ? [X136: subst,X137: term,X138: subst,X139: subst] :
( ( ( X135 @ X136 @ X137 @ ( comp @ X138 @ X139 ) )
= $true )
& ( $true
!= ( X135 @ ( comp @ X136 @ X138 ) @ ( sub @ X137 @ X138 ) @ X139 ) ) )
| ( ( X135 @ id @ X134 @ id )
= $true )
| ? [X146: term,X147: term] :
( ( $true
!= ( X135 @ id @ ( ap @ ( sub @ X147 @ id ) @ X146 ) @ id ) )
& ( $true
= ( X135 @ id @ X147 @ id ) )
& ( ( X135 @ id @ X146 @ id )
= $true ) )
| ? [X140: subst > term > term] :
( ! [X141: term,X142: subst,X143: subst] :
( ( X140 @ ( comp @ X143 @ X142 ) @ ( sub @ X141 @ X142 ) )
= ( sub @ ( X140 @ X143 @ X141 ) @ X142 ) )
& ! [X144: term] :
( ( $true
!= ( X135 @ id @ X144 @ id ) )
| ( $true
= ( X135 @ id @ ( X140 @ id @ X144 ) @ id ) ) )
& ( $true
!= ( X135 @ id @ ( lam @ ( X140 @ sh @ one ) ) @ id ) ) )
| ? [X148: subst,X149: subst,X150: subst,X151: term] :
( ( $true
!= ( X135 @ X148 @ X151 @ ( comp @ X149 @ X150 ) ) )
& ( $true
= ( X135 @ ( comp @ X148 @ X149 ) @ ( sub @ X151 @ X149 ) @ X150 ) ) )
| ? [X145: term] :
( ( $true
!= ( X135 @ id @ X145 @ id ) )
& ( $true
= ( var @ ( sub @ X145 @ id ) ) ) ) ) )
& ( ( axvarcons = $true )
<=> ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 ) )
& ( 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 ) ) ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( ! [X381: term > $o,X382: subst,X383: term] :
( ? [X386: term] :
( ( $true
= ( var @ X386 ) )
& ( $true
!= ( X381 @ ( sub @ X386 @ X382 ) ) ) )
| ( $true
= ( X381 @ ( sub @ X383 @ X382 ) ) )
| ? [X387: term,X388: term] :
( ( $true
= ( X381 @ X387 ) )
& ( $true
!= ( X381 @ ( ap @ X388 @ X387 ) ) )
& ( $true
= ( X381 @ X388 ) ) )
| ? [X384: term] :
( ( $true
!= ( X381 @ ( lam @ X384 ) ) )
& ! [X385: term] :
( ( $true
= ( X381 @ ( sub @ X384 @ ( push @ X385 @ id ) ) ) )
| ( $true
!= ( X381 @ X385 ) ) ) ) )
<=> ( induction2lem = $true ) )
& ( axclos = $true )
& ( ulamvar1 != $true )
& ( ! [X160: term,X161: subst > term > subst > $o] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X161 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X162 @ X165 @ X164 ) @ X163 )
= ( X162 @ ( comp @ X165 @ X163 ) @ ( sub @ X164 @ X163 ) ) )
& ! [X166: term] :
( ( $true
= ( X161 @ id @ ( X162 @ id @ X166 ) @ id ) )
| ( $true
!= ( X161 @ id @ X166 @ id ) ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X167: term] :
( ( $true
!= ( X161 @ id @ ( sub @ X160 @ ( push @ X167 @ id ) ) @ id ) )
& ( $true
= ( X161 @ id @ X167 @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 ) )
& ( lamnotvar = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( axassoc = $true )
& ( ! [X105: term > $o,X106: term] :
( ? [X110: term] :
( ( ( X105 @ ( lam @ X110 ) )
!= $true )
& ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) ) )
| ( $true
= ( X105 @ X106 ) )
| ? [X107: term] :
( ( $true
= ( var @ X107 ) )
& ( ( X105 @ X107 )
!= $true ) )
| ? [X108: term,X109: term] :
( ( $true
= ( X105 @ X108 ) )
& ( $true
= ( X105 @ X109 ) )
& ( $true
!= ( X105 @ ( ap @ X109 @ X108 ) ) ) ) )
<=> ( induction2 = $true ) )
& ( ( ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) )
| ? [X457: subst] :
( ( comp @ X457 @ id )
!= X457 )
| ? [X456: subst] :
( ( comp @ id @ X456 )
!= X456 ) )
<=> ( substmonoid_lthm = $true ) )
& ( ! [X346: term,X347: term,X348: subst > term > term] :
( ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) )
| ? [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
!= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj2_gthm = $true )
& ! [X7: d_term,X8: d_term] :
( ( X7 = X8 )
| ( ( d2term @ X7 )
!= ( d2term @ X8 ) ) )
& ( ( termmset_lthm = $true )
<=> ( ? [X251: term] :
( ( sub @ X251 @ id )
!= X251 )
| ! [X252: term] :
( ( sub @ X252 @ id )
= X252 ) ) )
& ( ( ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) )
| ? [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
!= X474 )
| ? [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
!= X473 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasinduction_lem1_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ulamvarind = $true )
& ( axvarshift = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X102: subst > term > subst > $o] :
? [X103: term > $o] :
! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) ) )
& ( termmset_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X18: subst > term > subst > $o,X19: term] :
( ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) )
| ? [X21: subst > term > term] :
( ( $true
!= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) )
& ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
& ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) ) )
| ? [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
!= $true )
& ( $true
= ( X18 @ id @ X20 @ id ) ) ) )
| ? [X10: subst > term > subst > $o,X11: term] :
( ! [X17: term] :
( ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) )
| ( $true
!= ( X10 @ id @ X17 @ id ) ) )
& ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X12: subst > term > term] :
( ? [X16: term] :
( ( $true
!= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
& ( ( X10 @ id @ X16 @ id )
= $true ) )
| ? [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
!= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) )
| ? [X9: term] :
( ( sub @ X9 @ id )
!= X9 ) ) )
& ( ( ! [X527: term,X528: subst > term > subst > $o] :
( ( $true
= ( X528 @ id @ X527 @ id ) )
| ? [X531: subst > term > term] :
( ! [X532: term] :
( ( $true
!= ( X528 @ id @ X532 @ id ) )
| ( $true
= ( X528 @ id @ ( X531 @ id @ X532 ) @ id ) ) )
& ( $true
!= ( X528 @ id @ ( lam @ ( X531 @ sh @ one ) ) @ id ) )
& ! [X533: term,X534: subst,X535: subst] :
( ( sub @ ( X531 @ X534 @ X533 ) @ X535 )
= ( X531 @ ( comp @ X534 @ X535 ) @ ( sub @ X533 @ X535 ) ) ) )
| ? [X529: term,X530: term] :
( ( $true
!= ( X528 @ id @ ( ap @ ( sub @ X529 @ id ) @ X530 ) @ id ) )
& ( $true
= ( X528 @ id @ X529 @ id ) )
& ( $true
= ( X528 @ id @ X530 @ id ) ) ) )
| ? [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ! [X522: subst > term > term] :
( ( $true
= ( X518 @ id @ ( lam @ ( X522 @ sh @ one ) ) @ id ) )
| ? [X524: term,X525: subst,X526: subst] :
( ( X522 @ ( comp @ X525 @ X526 ) @ ( sub @ X524 @ X526 ) )
!= ( sub @ ( X522 @ X525 @ X524 ) @ X526 ) )
| ? [X523: term] :
( ( $true
!= ( X518 @ id @ ( X522 @ id @ X523 ) @ id ) )
& ( ( X518 @ id @ X523 @ id )
= $true ) ) )
& ( $true
!= ( X517 @ ( lam @ X519 ) ) )
& ! [X521: term] :
( ( ( X517 @ ( sub @ X519 @ ( push @ X521 @ id ) ) )
= $true )
| ( $true
!= ( X517 @ X521 ) ) )
& ! [X520: term] :
( ( X517 @ X520 )
= ( X518 @ id @ X520 @ id ) ) )
| ? [X516: term] :
( ( sub @ X516 @ id )
!= X516 )
| ? [X509: term > $o,X510: term] :
( ! [X515: term] :
( ( $true
!= ( var @ X515 ) )
| ( $true
= ( X509 @ X515 ) ) )
& ( $true
!= ( X509 @ X510 ) )
& ! [X511: term,X512: term] :
( ( ( X509 @ X511 )
!= $true )
| ( $true
= ( X509 @ ( ap @ X512 @ X511 ) ) )
| ( $true
!= ( X509 @ X512 ) ) )
& ! [X513: term] :
( ? [X514: term] :
( ( $true
!= ( X509 @ ( sub @ X513 @ ( push @ X514 @ id ) ) ) )
& ( $true
= ( X509 @ X514 ) ) )
| ( $true
= ( X509 @ ( lam @ X513 ) ) ) ) )
| ? [X506: subst > term > subst > $o] :
! [X507: term > $o] :
? [X508: term] :
( ( X506 @ id @ X508 @ id )
!= ( X507 @ X508 ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axidr = $true )
<=> ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 ) )
& ( pushprop_lthm_orig = $true )
& ( ! [X434: term] :
? [X435: subst > term > term] :
! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( ! [X184: subst > term > subst > $o,X185: term] :
( ? [X187: subst > term > term,X188: term] :
( ! [X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X191 @ X189 ) @ ( sub @ X190 @ X189 ) )
= ( sub @ X188 @ ( push @ ( sub @ X190 @ X189 ) @ ( comp @ X191 @ X189 ) ) ) )
& ! [X192: subst,X193: term,X194: subst] :
( ( sub @ ( sub @ X188 @ ( push @ X193 @ X194 ) ) @ X192 )
= ( sub @ ( X187 @ X194 @ X193 ) @ X192 ) )
& ! [X195: term] :
( ( $true
!= ( X184 @ id @ X195 @ id ) )
| ( $true
= ( X184 @ id @ ( X187 @ id @ X195 ) @ id ) ) )
& ( $true
!= ( X184 @ id @ ( lam @ ( X187 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X184 @ id @ ( lam @ ( sub @ X185 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X186: term] :
( ( $true
= ( X184 @ id @ X186 @ id ) )
& ( $true
!= ( X184 @ id @ ( sub @ X185 @ ( push @ X186 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 ) )
& ( ! [X117: term,X118: subst > term > subst > $o] :
( ( $true
= ( X118 @ id @ ( lam @ ( sub @ X117 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X120: subst > term > term] :
( ! [X121: term] :
( ( $true
= ( X118 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ( $true
!= ( X118 @ id @ X121 @ id ) ) )
& ( $true
!= ( X118 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id ) )
& ! [X122: subst,X123: subst,X124: term] :
( ( sub @ ( X120 @ X122 @ X124 ) @ X123 )
= ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) ) ) )
| ? [X119: term] :
( ( $true
!= ( X118 @ id @ ( sub @ X117 @ ( push @ X119 @ id ) ) @ id ) )
& ( $true
= ( X118 @ id @ X119 @ id ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X490: term,X491: subst > term > subst > $o] :
( ? [X498: subst,X499: subst,X500: subst,X501: term] :
( ( $true
= ( X491 @ X499 @ X501 @ ( comp @ X500 @ X498 ) ) )
& ( $true
!= ( X491 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) @ X498 ) ) )
| ? [X492: subst > term > term] :
( ( $true
!= ( X491 @ id @ ( lam @ ( X492 @ sh @ one ) ) @ id ) )
& ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X492 @ X494 @ X495 ) @ X496 )
= ( X492 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) )
& ! [X493: term] :
( ( $true
!= ( X491 @ id @ X493 @ id ) )
| ( ( X491 @ id @ ( X492 @ id @ X493 ) @ id )
= $true ) ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) )
| ? [X497: term] :
( ( $true
= ( X491 @ id @ X497 @ id ) )
& ( $true
!= ( X491 @ id @ ( sub @ X490 @ ( push @ X497 @ id ) ) @ id ) ) )
| ? [X502: subst,X503: subst,X504: subst,X505: term] :
( ( $true
= ( X491 @ ( comp @ X503 @ X502 ) @ ( sub @ X505 @ X502 ) @ X504 ) )
& ( $true
!= ( X491 @ X503 @ X505 @ ( comp @ X502 @ X504 ) ) ) ) )
| ? [X482: subst > term > subst > $o,X483: term] :
( ! [X489: term] :
( ( $true
!= ( X482 @ id @ X489 @ id ) )
| ( $true
= ( X482 @ id @ ( sub @ X483 @ ( push @ X489 @ id ) ) @ id ) ) )
& ( ( X482 @ id @ ( lam @ ( sub @ X483 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X484: subst > term > term] :
( ? [X485: subst,X486: term,X487: subst] :
( ( X484 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) )
!= ( sub @ ( X484 @ X485 @ X486 ) @ X487 ) )
| ? [X488: term] :
( ( $true
= ( X482 @ id @ X488 @ id ) )
& ( $true
!= ( X482 @ id @ ( X484 @ id @ X488 ) @ id ) ) )
| ( $true
= ( X482 @ id @ ( lam @ ( X484 @ sh @ one ) ) @ id ) ) ) )
| ? [X481: term] :
( ( sub @ X481 @ id )
!= X481 ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ( shinj = $true )
<=> ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X454: term] :
? [X455: subst > term > term] :
( ( X455 @ sh @ one )
= ( sub @ X454 @ ( push @ one @ sh ) ) ) )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ? [X156: term] :
( ( X153 @ X156 )
!= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( ! [X328: term,X329: subst > term > subst > $o] :
( ? [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
& ( $true
!= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
| ? [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
& ( $true
!= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
| ? [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
& ( ( var @ ( sub @ X336 @ id ) )
= $true ) )
| ? [X337: subst > term > term] :
( ( $true
!= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
& ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) )
& ! [X338: term] :
( ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X329 @ id @ X338 @ id )
!= $true ) ) )
| ? [X330: term,X331: term] :
( ( ( X329 @ id @ X330 @ id )
= $true )
& ( $true
!= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( $true
= ( X329 @ id @ X328 @ id ) ) )
| ? [X312: subst > term > subst > $o,X313: term] :
( ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( $true
= ( X312 @ ( comp @ X325 @ X324 ) @ ( sub @ X326 @ X324 ) @ X327 ) )
| ( $true
!= ( X312 @ X325 @ X326 @ ( comp @ X324 @ X327 ) ) ) )
& ! [X314: term] :
( ( $true
= ( X312 @ id @ ( sub @ X313 @ ( push @ X314 @ id ) ) @ id ) )
| ( ( X312 @ id @ X314 @ id )
!= $true ) )
& ( $true
!= ( X312 @ id @ ( lam @ X313 ) @ id ) )
& ! [X315: subst > term > term] :
( ( $true
= ( X312 @ id @ ( lam @ ( X315 @ sh @ one ) ) @ id ) )
| ? [X317: subst,X318: subst,X319: term] :
( ( sub @ ( X315 @ X318 @ X319 ) @ X317 )
!= ( X315 @ ( comp @ X318 @ X317 ) @ ( sub @ X319 @ X317 ) ) )
| ? [X316: term] :
( ( ( X312 @ id @ X316 @ id )
= $true )
& ( $true
!= ( X312 @ id @ ( X315 @ id @ X316 ) @ id ) ) ) )
& ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X312 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ( $true
= ( X312 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) ) ) )
| ? [X299: subst > term > subst > $o,X300: term,X301: term] :
( ! [X306: term,X307: term] :
( ( ( X299 @ id @ X307 @ id )
!= $true )
| ( $true
= ( X299 @ id @ ( ap @ ( sub @ X306 @ id ) @ X307 ) @ id ) )
| ( $true
!= ( X299 @ id @ X306 @ id ) ) )
& ! [X308: term,X309: subst,X310: subst,X311: subst] :
( ( $true
= ( X299 @ ( comp @ X311 @ X309 ) @ ( sub @ X308 @ X309 ) @ X310 ) )
| ( $true
!= ( X299 @ X311 @ X308 @ ( comp @ X309 @ X310 ) ) ) )
& ! [X302: subst,X303: term,X304: subst,X305: subst] :
( ( $true
= ( X299 @ X305 @ X303 @ ( comp @ X302 @ X304 ) ) )
| ( $true
!= ( X299 @ ( comp @ X305 @ X302 ) @ ( sub @ X303 @ X302 ) @ X304 ) ) )
& ( ( X299 @ id @ X300 @ id )
= $true )
& ( $true
= ( X299 @ id @ X301 @ id ) )
& ( $true
!= ( X299 @ id @ ( ap @ X300 @ X301 ) @ id ) ) )
| ? [X292: term > $o,X293: term] :
( ! [X297: term,X298: term] :
( ( $true
= ( X292 @ ( ap @ X298 @ X297 ) ) )
| ( ( X292 @ X298 )
!= $true )
| ( $true
!= ( X292 @ X297 ) ) )
& ! [X294: term] :
( ? [X295: term] :
( ( ( X292 @ X295 )
= $true )
& ( $true
!= ( X292 @ ( sub @ X294 @ ( push @ X295 @ id ) ) ) ) )
| ( $true
= ( X292 @ ( lam @ X294 ) ) ) )
& ( $true
!= ( X292 @ X293 ) )
& ! [X296: term] :
( ( $true
= ( X292 @ X296 ) )
| ( $true
!= ( var @ X296 ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ( $true
!= ( X46 @ id @ X47 @ id ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) )
| ? [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) )
& ( $true
!= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) ) )
| ? [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) )
& ( $true
!= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ? [X49: term,X50: term] :
( ( ( X46 @ id @ X49 @ id )
= $true )
& ( ( X46 @ id @ X50 @ id )
= $true )
& ( $true
!= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X266: term,X267: subst,X268: term > $o] :
( ? [X271: term] :
( ( $true
!= ( X268 @ ( lam @ X271 ) ) )
& ! [X272: term] :
( ( $true
= ( X268 @ ( sub @ X271 @ ( push @ X272 @ id ) ) ) )
| ( $true
!= ( X268 @ X272 ) ) ) )
| ? [X273: term] :
( ( $true
!= ( X268 @ ( sub @ X273 @ X267 ) ) )
& ( $true
= ( var @ X273 ) ) )
| ? [X269: term,X270: term] :
( ( $true
= ( X268 @ X270 ) )
& ( $true
!= ( X268 @ ( ap @ X270 @ X269 ) ) )
& ( $true
= ( X268 @ X269 ) ) )
| ( $true
= ( X268 @ ( sub @ X266 @ X267 ) ) ) )
| ? [X260: term > $o,X261: term] :
( ! [X265: term] :
( ( $true
= ( X260 @ X265 ) )
| ( $true
!= ( var @ X265 ) ) )
& ! [X263: term,X264: term] :
( ( $true
!= ( X260 @ X264 ) )
| ( $true
!= ( X260 @ X263 ) )
| ( $true
= ( X260 @ ( ap @ X264 @ X263 ) ) ) )
& ! [X262: term] :
( ( $true
!= ( X260 @ X262 ) )
| ( $true
= ( X260 @ ( lam @ X262 ) ) ) )
& ( $true
!= ( X260 @ X261 ) ) )
| ? [X259: subst] :
( ( comp @ X259 @ id )
!= X259 )
| ? [X257: term,X258: subst] :
( ( comp @ sh @ ( push @ X257 @ X258 ) )
!= X258 )
| ? [X255: term,X256: subst] :
( ( sub @ one @ ( push @ X255 @ X256 ) )
!= X255 ) ) )
& ( hoasapnotvar_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X198: subst > term > subst > $o,X199: term] :
( ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) )
| ? [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
!= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
& ( $true
= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
| ? [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
& ( $true
!= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ? [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
!= $true )
& ( $true
= ( X198 @ id @ X213 @ id ) ) )
| ? [X204: subst > term > term] :
( ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
!= $true )
& ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
& ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) ) ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
<=> ( apinj2 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( one
= ( d2term @ d_one ) )
& ( substmonoid_gthm = $true )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ( axidl = $true )
<=> ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X253: term] :
? [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
= ( X254 @ sh @ one ) ) )
& ( pushprop_lthm = $true )
& ( ulamvarsh = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X276: subst > term > subst > $o,X277: term] :
( ? [X279: subst > term > term] :
( ! [X281: subst,X282: term,X283: subst] :
( ( X279 @ ( comp @ X283 @ X281 ) @ ( sub @ X282 @ X281 ) )
= ( sub @ ( X279 @ X283 @ X282 ) @ X281 ) )
& ! [X280: term] :
( ( $true
= ( X276 @ id @ ( X279 @ id @ X280 ) @ id ) )
| ( $true
!= ( X276 @ id @ X280 @ id ) ) )
& ( $true
!= ( X276 @ id @ ( lam @ ( X279 @ sh @ one ) ) @ id ) ) )
| ? [X278: term] :
( ( $true
= ( X276 @ id @ X278 @ id ) )
& ( $true
!= ( X276 @ id @ ( sub @ X277 @ ( push @ X278 @ id ) ) @ id ) ) )
| ( $true
= ( X276 @ id @ ( lam @ X277 ) @ id ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X536: term] :
? [X537: subst > term > term] :
! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X125: subst > term > subst > $o,X126: term] :
( ? [X132: term,X133: term] :
( ( $true
= ( X125 @ id @ X133 @ id ) )
& ( $true
= ( X125 @ id @ X132 @ id ) )
& ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
!= $true ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ? [X127: subst > term > term] :
( ( $true
!= ( X125 @ id @ ( lam @ ( X127 @ sh @ one ) ) @ id ) )
& ! [X128: term] :
( ( $true
!= ( X125 @ id @ X128 @ id ) )
| ( $true
= ( X125 @ id @ ( X127 @ id @ X128 ) @ id ) ) )
& ! [X129: subst,X130: subst,X131: term] :
( ( X127 @ ( comp @ X129 @ X130 ) @ ( sub @ X131 @ X130 ) )
= ( sub @ ( X127 @ X129 @ X131 ) @ X130 ) ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( lamnotap != $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X112: term > $o,X113: term,X114: subst] :
? [X115: term > $o] :
! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ! [X28: term > $o,X29: term] :
( ? [X31: term,X32: term] :
( ( $true
= ( X28 @ X31 ) )
& ( ( X28 @ X32 )
= $true )
& ( $true
!= ( X28 @ ( ap @ X32 @ X31 ) ) ) )
| ? [X33: term] :
( ( ( X28 @ X33 )
= $true )
& ( ( X28 @ ( lam @ X33 ) )
!= $true ) )
| ? [X30: term] :
( ( $true
= ( var @ X30 ) )
& ( ( X28 @ X30 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) ) )
<=> ( induction = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X419: term,X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ? [X428: subst,X429: term,X430: subst,X431: subst] :
( ( ( X422 @ X431 @ X429 @ ( comp @ X430 @ X428 ) )
= $true )
& ( $true
!= ( X422 @ ( comp @ X431 @ X430 ) @ ( sub @ X429 @ X430 ) @ X428 ) ) )
| ? [X423: subst,X424: term,X425: subst,X426: subst] :
( ( $true
= ( X422 @ ( comp @ X425 @ X426 ) @ ( sub @ X424 @ X426 ) @ X423 ) )
& ( $true
!= ( X422 @ X425 @ X424 @ ( comp @ X426 @ X423 ) ) ) )
| ? [X432: term,X433: term] :
( ( $true
= ( X422 @ id @ X433 @ id ) )
& ( $true
!= ( X422 @ id @ ( ap @ ( sub @ X433 @ id ) @ X432 ) @ id ) )
& ( ( X422 @ id @ X432 @ id )
= $true ) )
| ? [X427: term] :
( ( X422 @ id @ X427 @ id )
!= ( X421 @ X427 ) )
| ( $true
= ( X421 @ ( ap @ X420 @ X419 ) ) )
| ( $true
!= ( X421 @ X419 ) )
| ( $true
!= ( X421 @ X420 ) ) ) )
& ( hoasapnotvar_lthm = $true )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
!= ( d2subst @ X291 ) )
| ( X290 = X291 ) )
& ( ( laminj = $true )
<=> ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) ) )
& ( axapp = $true )
& ( ! [X460: term > $o,X461: subst > term > subst > $o,X462: term] :
( ? [X463: term] :
( ( X461 @ id @ X463 @ id )
!= ( X460 @ X463 ) )
| ? [X465: subst > term > term] :
( ( $true
!= ( X461 @ id @ ( lam @ ( X465 @ sh @ one ) ) @ id ) )
& ! [X466: term,X467: subst,X468: subst] :
( ( sub @ ( X465 @ X467 @ X466 ) @ X468 )
= ( X465 @ ( comp @ X467 @ X468 ) @ ( sub @ X466 @ X468 ) ) )
& ! [X469: term] :
( ( $true
!= ( X461 @ id @ X469 @ id ) )
| ( $true
= ( X461 @ id @ ( X465 @ id @ X469 ) @ id ) ) ) )
| ? [X464: term] :
( ( $true
= ( X460 @ X464 ) )
& ( $true
!= ( X460 @ ( sub @ X462 @ ( push @ X464 @ id ) ) ) ) )
| ( $true
= ( X460 @ ( lam @ X462 ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ! [X34: subst > term > subst > $o] :
? [X35: term > $o] :
! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X214: term,X215: term > $o,X216: subst > term > subst > $o] :
( ? [X217: subst > term > term] :
( ( $true
!= ( X216 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id ) )
& ! [X218: term,X219: subst,X220: subst] :
( ( sub @ ( X217 @ X220 @ X218 ) @ X219 )
= ( X217 @ ( comp @ X220 @ X219 ) @ ( sub @ X218 @ X219 ) ) )
& ! [X221: term] :
( ( $true
!= ( X216 @ id @ X221 @ id ) )
| ( $true
= ( X216 @ id @ ( X217 @ id @ X221 ) @ id ) ) ) )
| ? [X231: term] :
( ( X215 @ X231 )
!= ( X216 @ id @ X231 @ id ) )
| ? [X227: term,X228: subst,X229: subst,X230: subst] :
( ( $true
!= ( X216 @ X228 @ X227 @ ( comp @ X230 @ X229 ) ) )
& ( $true
= ( X216 @ ( comp @ X228 @ X230 ) @ ( sub @ X227 @ X230 ) @ X229 ) ) )
| ? [X222: term] :
( ( $true
!= ( X215 @ ( sub @ X214 @ ( push @ X222 @ id ) ) ) )
& ( ( X215 @ X222 )
= $true ) )
| ? [X223: subst,X224: subst,X225: term,X226: subst] :
( ( $true
= ( X216 @ X224 @ X225 @ ( comp @ X223 @ X226 ) ) )
& ( $true
!= ( X216 @ ( comp @ X224 @ X223 ) @ ( sub @ X225 @ X223 ) @ X226 ) ) )
| ( $true
= ( X215 @ ( lam @ X214 ) ) ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) )
| ? [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
= ( ap @ X40 @ X39 ) )
& ( X38 != X40 ) )
| ? [X37: term] :
( ( sub @ X37 @ id )
!= X37 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( apnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( hoasapinj2_lthm = $true )
<=> ( ? [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
= ( ap @ X411 @ X410 ) )
& ( X409 != X410 ) )
| ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ! [X374: subst,X375: term > $o,X376: term] :
? [X377: term > $o] :
! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) )
<=> ( pushprop_lem0 = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X84: term,X85: subst > term > subst > $o] :
( ? [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
!= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) )
& ( $true
= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) ) )
| ? [X86: term,X87: term] :
( ( $true
= ( X85 @ id @ X87 @ id ) )
& ( $true
= ( X85 @ id @ X86 @ id ) )
& ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
!= $true ) )
| ? [X88: term] :
( ( $true
= ( var @ ( sub @ X88 @ id ) ) )
& ( $true
!= ( X85 @ id @ X88 @ id ) ) )
| ? [X97: subst > term > term] :
( ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) )
& ! [X98: term] :
( ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) )
| ( ( X85 @ id @ X98 @ id )
!= $true ) )
& ( $true
!= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X85 @ id @ X84 @ id ) )
| ? [X89: subst,X90: subst,X91: term,X92: subst] :
( ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
= $true )
& ( $true
!= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) ) ) )
| ? [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ! [X78: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ? [X82: term] :
( ( $true
!= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) )
& ( $true
= ( X75 @ id @ X82 @ id ) ) )
| ? [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
!= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) ) )
& ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
& ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) )
& ( $true
!= ( X74 @ ( lam @ X76 ) ) ) )
| ? [X73: term] :
( ( sub @ X73 @ id )
!= X73 )
| ? [X66: term,X67: term > $o] :
( ! [X69: term,X70: term] :
( ( ( X67 @ X70 )
!= $true )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( $true
!= ( X67 @ X69 ) ) )
& ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ? [X72: term] :
( ( ( X67 @ X72 )
= $true )
& ( $true
!= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) ) ) )
& ( $true
!= ( X67 @ X66 ) )
& ! [X68: term] :
( ( $true
= ( X67 @ X68 ) )
| ( $true
!= ( var @ X68 ) ) ) )
| ? [X63: subst > term > subst > $o] :
! [X64: term > $o] :
? [X65: term] :
( ( X64 @ X65 )
!= ( X63 @ id @ X65 @ id ) ) ) )
& ( ( ! [X233: term,X234: term > $o,X235: subst > term > subst > $o] :
( ? [X240: term] :
( ( ( X234 @ X240 )
= $true )
& ( ( X234 @ ( sub @ X233 @ ( push @ X240 @ id ) ) )
!= $true ) )
| ? [X236: subst,X237: subst,X238: subst,X239: term] :
( ( $true
= ( X235 @ ( comp @ X238 @ X237 ) @ ( sub @ X239 @ X237 ) @ X236 ) )
& ( ( X235 @ X238 @ X239 @ ( comp @ X237 @ X236 ) )
!= $true ) )
| ? [X247: subst,X248: term,X249: subst,X250: subst] :
( ( $true
= ( X235 @ X247 @ X248 @ ( comp @ X249 @ X250 ) ) )
& ( $true
!= ( X235 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) @ X250 ) ) )
| ( ( X234 @ ( lam @ X233 ) )
= $true )
| ? [X246: term] :
( ( X234 @ X246 )
!= ( X235 @ id @ X246 @ id ) )
| ? [X241: subst > term > term] :
( ( $true
!= ( X235 @ id @ ( lam @ ( X241 @ sh @ one ) ) @ id ) )
& ! [X242: term,X243: subst,X244: subst] :
( ( X241 @ ( comp @ X244 @ X243 ) @ ( sub @ X242 @ X243 ) )
= ( sub @ ( X241 @ X244 @ X242 ) @ X243 ) )
& ! [X245: term] :
( ( $true
!= ( X235 @ id @ X245 @ id ) )
| ( $true
= ( X235 @ id @ ( X241 @ id @ X245 ) @ id ) ) ) ) )
| ? [X232: term] :
( ( sub @ X232 @ id )
!= X232 ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
<=> ( hoasapinj2 = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ? [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
!= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) )
| ? [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
!= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) ) )
<=> ( hoaslaminj = $true ) )
& ( pushprop = $true )
& ( ( substmonoid = $true )
<=> ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axmap = $true )
& ( induction2lem_gthm = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
<=> ( axvarid = $true ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ? [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
!= ( X5 @ X6 ) )
| ( $true
= ( X5 @ one ) ) )
| ? [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
!= X1 ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X402: term,X403: term > $o] :
( ? [X405: term] :
( ! [X406: term] :
( ( $true
!= ( X403 @ X406 ) )
| ( $true
= ( X403 @ ( sub @ X405 @ ( push @ X406 @ id ) ) ) ) )
& ( $true
!= ( X403 @ ( lam @ X405 ) ) ) )
| ? [X407: term,X408: term] :
( ( $true
!= ( X403 @ ( ap @ X407 @ X408 ) ) )
& ( ( X403 @ X408 )
= $true )
& ( $true
= ( X403 @ X407 ) ) )
| ? [X404: term] :
( ( ( var @ X404 )
= $true )
& ( $true
!= ( X403 @ X404 ) ) )
| ( $true
= ( X403 @ X402 ) ) )
| ? [X394: subst,X395: term,X396: term > $o] :
( ( $true
!= ( X396 @ ( sub @ X395 @ X394 ) ) )
& ! [X400: term] :
( ? [X401: term] :
( ( $true
= ( X396 @ X401 ) )
& ( ( X396 @ ( sub @ X400 @ ( push @ X401 @ id ) ) )
!= $true ) )
| ( $true
= ( X396 @ ( lam @ X400 ) ) ) )
& ! [X398: term,X399: term] :
( ( $true
!= ( X396 @ X399 ) )
| ( $true
!= ( X396 @ X398 ) )
| ( $true
= ( X396 @ ( ap @ X398 @ X399 ) ) ) )
& ! [X397: term] :
( ( $true
= ( X396 @ ( sub @ X397 @ X394 ) ) )
| ( $true
!= ( var @ X397 ) ) ) )
| ? [X393: term] :
( ( sub @ X393 @ id )
!= X393 ) )
<=> ( induction2_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( induction2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( hoaslamnotap_lthm = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( axabs = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X359: term] :
~ ! [X360: subst > term > term] :
~ ! [X361: term,X362: subst] :
( ( X360 @ X362 @ X361 )
= ( sub @ X359 @ ( push @ X361 @ X362 ) ) )
=> ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
=> ! [X364: term,X365: term > $o,X366: subst > term > subst > $o] :
( ~ ! [X367: term] :
( ( X366 @ id @ X367 @ id )
= ( X365 @ X367 ) )
| ( $true
= ( X365 @ ( lam @ X364 ) ) )
| ~ ! [X369: subst > term > term] :
( ~ ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X369 @ X373 @ X371 ) @ X372 )
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
| ( $true
= ( X366 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id ) )
| ~ ! [X370: term] :
( ( ( X366 @ id @ ( X369 @ id @ X370 ) @ id )
= $true )
| ( $true
!= ( X366 @ id @ X370 @ id ) ) ) )
| ~ ! [X368: term] :
( ( $true
= ( X365 @ ( sub @ X364 @ ( push @ X368 @ id ) ) ) )
| ( $true
!= ( X365 @ X368 ) ) ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( ! [X168: term,X169: subst] :
( ( sub @ one @ ( push @ X168 @ X169 ) )
= X168 )
=> ( ! [X170: term,X171: subst] :
( ( comp @ sh @ ( push @ X170 @ X171 ) )
= X171 )
=> ( ! [X172: term,X173: term] :
( ( X172 = X173 )
| ( ( lam @ X173 )
!= ( lam @ X172 ) ) )
=> ! [X174: subst > term > term,X175: term,X176: subst,X177: subst > term > term] :
( ( ( X174 @ X176 @ X175 )
= ( X177 @ X176 @ X175 ) )
| ~ ! [X181: subst,X182: subst,X183: term] :
( ( sub @ ( X177 @ X182 @ X183 ) @ X181 )
= ( X177 @ ( comp @ X182 @ X181 ) @ ( sub @ X183 @ X181 ) ) )
| ~ ! [X178: subst,X179: subst,X180: term] :
( ( sub @ ( X174 @ X178 @ X180 ) @ X179 )
= ( X174 @ ( comp @ X178 @ X179 ) @ ( sub @ X180 @ X179 ) ) )
| ( ( lam @ ( X177 @ sh @ one ) )
!= ( lam @ ( X174 @ sh @ one ) ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ( hoasinduction = $true )
<=> ! [X134: term,X135: subst > term > subst > $o] :
( ~ ! [X140: subst > term > term] :
( ( $true
= ( X135 @ id @ ( lam @ ( X140 @ sh @ one ) ) @ id ) )
| ~ ! [X141: term,X142: subst,X143: subst] :
( ( X140 @ ( comp @ X143 @ X142 ) @ ( sub @ X141 @ X142 ) )
= ( sub @ ( X140 @ X143 @ X141 ) @ X142 ) )
| ~ ! [X144: term] :
( ( $true
!= ( X135 @ id @ X144 @ id ) )
| ( $true
= ( X135 @ id @ ( X140 @ id @ X144 ) @ id ) ) ) )
| ~ ! [X146: term,X147: term] :
( ( ( X135 @ id @ X146 @ id )
!= $true )
| ( $true
!= ( X135 @ id @ X147 @ id ) )
| ( $true
= ( X135 @ id @ ( ap @ ( sub @ X147 @ id ) @ X146 ) @ id ) ) )
| ~ ! [X148: subst,X149: subst,X150: subst,X151: term] :
( ( $true
!= ( X135 @ ( comp @ X148 @ X149 ) @ ( sub @ X151 @ X149 ) @ X150 ) )
| ( $true
= ( X135 @ X148 @ X151 @ ( comp @ X149 @ X150 ) ) ) )
| ( ( X135 @ id @ X134 @ id )
= $true )
| ~ ! [X145: term] :
( ( $true
!= ( var @ ( sub @ X145 @ id ) ) )
| ( $true
= ( X135 @ id @ X145 @ id ) ) )
| ~ ! [X136: subst,X137: term,X138: subst,X139: subst] :
( ( ( X135 @ X136 @ X137 @ ( comp @ X138 @ X139 ) )
!= $true )
| ( $true
= ( X135 @ ( comp @ X136 @ X138 ) @ ( sub @ X137 @ X138 ) @ X139 ) ) ) ) )
& ( ( axvarcons = $true )
<=> ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 ) )
& ( 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 ) ) ) ) )
& ( ( hoasapinj1 = $true )
<=> ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X381: term > $o,X382: subst,X383: term] :
( ( $true
= ( X381 @ ( sub @ X383 @ X382 ) ) )
| ~ ! [X384: term] :
( ~ ! [X385: term] :
( ( $true
= ( X381 @ ( sub @ X384 @ ( push @ X385 @ id ) ) ) )
| ( $true
!= ( X381 @ X385 ) ) )
| ( $true
= ( X381 @ ( lam @ X384 ) ) ) )
| ~ ! [X387: term,X388: term] :
( ( $true
= ( X381 @ ( ap @ X388 @ X387 ) ) )
| ( $true
!= ( X381 @ X387 ) )
| ( $true
!= ( X381 @ X388 ) ) )
| ~ ! [X386: term] :
( ( $true
!= ( var @ X386 ) )
| ( $true
= ( X381 @ ( sub @ X386 @ X382 ) ) ) ) ) )
& ( axclos = $true )
& ( ulamvar1 != $true )
& ( ! [X160: term,X161: subst > term > subst > $o] :
( ( $true
= ( X161 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X167: term] :
( ( $true
!= ( X161 @ id @ X167 @ id ) )
| ( $true
= ( X161 @ id @ ( sub @ X160 @ ( push @ X167 @ id ) ) @ id ) ) )
| ~ ! [X162: subst > term > term] :
( ~ ! [X166: term] :
( ( $true
= ( X161 @ id @ ( X162 @ id @ X166 ) @ id ) )
| ( $true
!= ( X161 @ id @ X166 @ id ) ) )
| ~ ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X162 @ X165 @ X164 ) @ X163 )
= ( X162 @ ( comp @ X165 @ X163 ) @ ( sub @ X164 @ X163 ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 ) )
& ( lamnotvar = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasapnotvar = $true )
& ( axassoc = $true )
& ( ( induction2 = $true )
<=> ! [X105: term > $o,X106: term] :
( ~ ! [X110: term] :
( ~ ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) )
| ( ( X105 @ ( lam @ X110 ) )
= $true ) )
| ~ ! [X108: term,X109: term] :
( ( $true
!= ( X105 @ X108 ) )
| ( $true
= ( X105 @ ( ap @ X109 @ X108 ) ) )
| ( $true
!= ( X105 @ X109 ) ) )
| ( $true
= ( X105 @ X106 ) )
| ~ ! [X107: term] :
( ( $true
!= ( var @ X107 ) )
| ( ( X105 @ X107 )
= $true ) ) ) )
& ( ( ! [X456: subst] :
( ( comp @ id @ X456 )
= X456 )
=> ( ! [X457: subst] :
( ( comp @ X457 @ id )
= X457 )
=> ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X346: term,X347: term,X348: subst > term > term] :
( ~ ! [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) )
| ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ! [X7: d_term,X8: d_term] :
( ( ( d2term @ X7 )
= ( d2term @ X8 ) )
=> ( X7 = X8 ) )
& ( ( ! [X251: term] :
( ( sub @ X251 @ id )
= X251 )
=> ! [X252: term] :
( ( sub @ X252 @ id )
= X252 ) )
<=> ( termmset_lthm = $true ) )
& ( ( ! [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
= X473 )
=> ( ! [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
= X474 )
=> ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( hoasinduction_lem1_lthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ulamvarind = $true )
& ( axvarshift = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ! [X102: subst > term > subst > $o] :
~ ! [X103: term > $o] :
~ ! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( termmset_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X9: term] :
( ( sub @ X9 @ id )
= X9 )
=> ( ! [X10: subst > term > subst > $o,X11: term] :
( ~ ! [X17: term] :
( ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) )
| ( $true
!= ( X10 @ id @ X17 @ id ) ) )
| ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X12: subst > term > term] :
( ~ ! [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) )
| ~ ! [X16: term] :
( ( $true
= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
| ( ( X10 @ id @ X16 @ id )
!= $true ) ) ) )
=> ! [X18: subst > term > subst > $o,X19: term] :
( ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) )
| ~ ! [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
= $true )
| ( $true
!= ( X18 @ id @ X20 @ id ) ) )
| ~ ! [X21: subst > term > term] :
( ( $true
= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) )
| ~ ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
| ~ ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) ) ) ) ) ) )
& ( ( ! [X506: subst > term > subst > $o] :
~ ! [X507: term > $o] :
~ ! [X508: term] :
( ( X506 @ id @ X508 @ id )
= ( X507 @ X508 ) )
=> ( ! [X509: term > $o,X510: term] :
( ~ ! [X513: term] :
( ( $true
= ( X509 @ ( lam @ X513 ) ) )
| ~ ! [X514: term] :
( ( $true
= ( X509 @ ( sub @ X513 @ ( push @ X514 @ id ) ) ) )
| ( $true
!= ( X509 @ X514 ) ) ) )
| ( $true
= ( X509 @ X510 ) )
| ~ ! [X511: term,X512: term] :
( ( ( X509 @ X511 )
!= $true )
| ( $true
= ( X509 @ ( ap @ X512 @ X511 ) ) )
| ( $true
!= ( X509 @ X512 ) ) )
| ~ ! [X515: term] :
( ( $true
!= ( var @ X515 ) )
| ( $true
= ( X509 @ X515 ) ) ) )
=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ( ! [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ( $true
= ( X517 @ ( lam @ X519 ) ) )
| ~ ! [X521: term] :
( ( ( X517 @ ( sub @ X519 @ ( push @ X521 @ id ) ) )
= $true )
| ( $true
!= ( X517 @ X521 ) ) )
| ~ ! [X522: subst > term > term] :
( ( $true
= ( X518 @ id @ ( lam @ ( X522 @ sh @ one ) ) @ id ) )
| ~ ! [X524: term,X525: subst,X526: subst] :
( ( X522 @ ( comp @ X525 @ X526 ) @ ( sub @ X524 @ X526 ) )
= ( sub @ ( X522 @ X525 @ X524 ) @ X526 ) )
| ~ ! [X523: term] :
( ( $true
= ( X518 @ id @ ( X522 @ id @ X523 ) @ id ) )
| ( ( X518 @ id @ X523 @ id )
!= $true ) ) )
| ~ ! [X520: term] :
( ( X517 @ X520 )
= ( X518 @ id @ X520 @ id ) ) )
=> ! [X527: term,X528: subst > term > subst > $o] :
( ~ ! [X531: subst > term > term] :
( ~ ! [X533: term,X534: subst,X535: subst] :
( ( sub @ ( X531 @ X534 @ X533 ) @ X535 )
= ( X531 @ ( comp @ X534 @ X535 ) @ ( sub @ X533 @ X535 ) ) )
| ~ ! [X532: term] :
( ( $true
!= ( X528 @ id @ X532 @ id ) )
| ( $true
= ( X528 @ id @ ( X531 @ id @ X532 ) @ id ) ) )
| ( $true
= ( X528 @ id @ ( lam @ ( X531 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X528 @ id @ X527 @ id ) )
| ~ ! [X529: term,X530: term] :
( ( $true
!= ( X528 @ id @ X529 @ id ) )
| ( $true
= ( X528 @ id @ ( ap @ ( sub @ X529 @ id ) @ X530 ) @ id ) )
| ( $true
!= ( X528 @ id @ X530 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( ( axidr = $true )
<=> ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 ) )
& ( pushprop_lthm_orig = $true )
& ( ! [X434: term] :
~ ! [X435: subst > term > term] :
~ ! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( pushprop_gthm = $true )
& ( ! [X184: subst > term > subst > $o,X185: term] :
( ( $true
= ( X184 @ id @ ( lam @ ( sub @ X185 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X186: term] :
( ( $true
= ( X184 @ id @ ( sub @ X185 @ ( push @ X186 @ id ) ) @ id ) )
| ( $true
!= ( X184 @ id @ X186 @ id ) ) )
| ~ ! [X187: subst > term > term,X188: term] :
( ~ ! [X195: term] :
( ( $true
!= ( X184 @ id @ X195 @ id ) )
| ( $true
= ( X184 @ id @ ( X187 @ id @ X195 ) @ id ) ) )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( sub @ ( sub @ X188 @ ( push @ X193 @ X194 ) ) @ X192 )
= ( sub @ ( X187 @ X194 @ X193 ) @ X192 ) )
| ( $true
= ( X184 @ id @ ( lam @ ( X187 @ sh @ one ) ) @ id ) )
| ~ ! [X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X191 @ X189 ) @ ( sub @ X190 @ X189 ) )
= ( sub @ X188 @ ( push @ ( sub @ X190 @ X189 ) @ ( comp @ X191 @ X189 ) ) ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 ) )
& ( ! [X117: term,X118: subst > term > subst > $o] :
( ~ ! [X119: term] :
( ( $true
= ( X118 @ id @ ( sub @ X117 @ ( push @ X119 @ id ) ) @ id ) )
| ( $true
!= ( X118 @ id @ X119 @ id ) ) )
| ~ ! [X120: subst > term > term] :
( ( $true
= ( X118 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id ) )
| ~ ! [X122: subst,X123: subst,X124: term] :
( ( sub @ ( X120 @ X122 @ X124 ) @ X123 )
= ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) ) )
| ~ ! [X121: term] :
( ( $true
= ( X118 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ( $true
!= ( X118 @ id @ X121 @ id ) ) ) )
| ( $true
= ( X118 @ id @ ( lam @ ( sub @ X117 @ ( push @ one @ sh ) ) ) @ id ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( ! [X481: term] :
( ( sub @ X481 @ id )
= X481 )
=> ( ! [X482: subst > term > subst > $o,X483: term] :
( ~ ! [X484: subst > term > term] :
( ( $true
= ( X482 @ id @ ( lam @ ( X484 @ sh @ one ) ) @ id ) )
| ~ ! [X488: term] :
( ( $true
= ( X482 @ id @ ( X484 @ id @ X488 ) @ id ) )
| ( $true
!= ( X482 @ id @ X488 @ id ) ) )
| ~ ! [X485: subst,X486: term,X487: subst] :
( ( X484 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) )
= ( sub @ ( X484 @ X485 @ X486 ) @ X487 ) ) )
| ~ ! [X489: term] :
( ( $true
!= ( X482 @ id @ X489 @ id ) )
| ( $true
= ( X482 @ id @ ( sub @ X483 @ ( push @ X489 @ id ) ) @ id ) ) )
| ( ( X482 @ id @ ( lam @ ( sub @ X483 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
=> ! [X490: term,X491: subst > term > subst > $o] :
( ~ ! [X492: subst > term > term] :
( ~ ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X492 @ X494 @ X495 ) @ X496 )
= ( X492 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) )
| ( $true
= ( X491 @ id @ ( lam @ ( X492 @ sh @ one ) ) @ id ) )
| ~ ! [X493: term] :
( ( $true
!= ( X491 @ id @ X493 @ id ) )
| ( ( X491 @ id @ ( X492 @ id @ X493 ) @ id )
= $true ) ) )
| ~ ! [X498: subst,X499: subst,X500: subst,X501: term] :
( ( $true
= ( X491 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) @ X498 ) )
| ( $true
!= ( X491 @ X499 @ X501 @ ( comp @ X500 @ X498 ) ) ) )
| ~ ! [X497: term] :
( ( $true
!= ( X491 @ id @ X497 @ id ) )
| ( $true
= ( X491 @ id @ ( sub @ X490 @ ( push @ X497 @ id ) ) @ id ) ) )
| ~ ! [X502: subst,X503: subst,X504: subst,X505: term] :
( ( $true
= ( X491 @ X503 @ X505 @ ( comp @ X502 @ X504 ) ) )
| ( $true
!= ( X491 @ ( comp @ X503 @ X502 ) @ ( sub @ X505 @ X502 ) @ X504 ) ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ( shinj = $true )
<=> ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) ) )
& ( ! [X454: term] :
~ ! [X455: subst > term > term] :
( ( X455 @ sh @ one )
!= ( sub @ X454 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ( $true
!= ( X152 @ X155 ) )
| ~ ! [X156: term] :
( ( X153 @ X156 )
= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( ! [X292: term > $o,X293: term] :
( ~ ! [X296: term] :
( ( $true
= ( X292 @ X296 ) )
| ( $true
!= ( var @ X296 ) ) )
| ~ ! [X297: term,X298: term] :
( ( $true
= ( X292 @ ( ap @ X298 @ X297 ) ) )
| ( ( X292 @ X298 )
!= $true )
| ( $true
!= ( X292 @ X297 ) ) )
| ~ ! [X294: term] :
( ~ ! [X295: term] :
( ( ( X292 @ X295 )
!= $true )
| ( $true
= ( X292 @ ( sub @ X294 @ ( push @ X295 @ id ) ) ) ) )
| ( $true
= ( X292 @ ( lam @ X294 ) ) ) )
| ( $true
= ( X292 @ X293 ) ) )
=> ( ! [X299: subst > term > subst > $o,X300: term,X301: term] :
( ~ ! [X306: term,X307: term] :
( ( ( X299 @ id @ X307 @ id )
!= $true )
| ( $true
= ( X299 @ id @ ( ap @ ( sub @ X306 @ id ) @ X307 ) @ id ) )
| ( $true
!= ( X299 @ id @ X306 @ id ) ) )
| ( $true
= ( X299 @ id @ ( ap @ X300 @ X301 ) @ id ) )
| ~ ! [X308: term,X309: subst,X310: subst,X311: subst] :
( ( $true
= ( X299 @ ( comp @ X311 @ X309 ) @ ( sub @ X308 @ X309 ) @ X310 ) )
| ( $true
!= ( X299 @ X311 @ X308 @ ( comp @ X309 @ X310 ) ) ) )
| ( $true
!= ( X299 @ id @ X301 @ id ) )
| ( ( X299 @ id @ X300 @ id )
!= $true )
| ~ ! [X302: subst,X303: term,X304: subst,X305: subst] :
( ( $true
= ( X299 @ X305 @ X303 @ ( comp @ X302 @ X304 ) ) )
| ( $true
!= ( X299 @ ( comp @ X305 @ X302 ) @ ( sub @ X303 @ X302 ) @ X304 ) ) ) )
=> ( ! [X312: subst > term > subst > $o,X313: term] :
( ~ ! [X314: term] :
( ( $true
= ( X312 @ id @ ( sub @ X313 @ ( push @ X314 @ id ) ) @ id ) )
| ( ( X312 @ id @ X314 @ id )
!= $true ) )
| ( $true
= ( X312 @ id @ ( lam @ X313 ) @ id ) )
| ~ ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( $true
= ( X312 @ ( comp @ X325 @ X324 ) @ ( sub @ X326 @ X324 ) @ X327 ) )
| ( $true
!= ( X312 @ X325 @ X326 @ ( comp @ X324 @ X327 ) ) ) )
| ~ ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X312 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ( $true
= ( X312 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) ) )
| ~ ! [X315: subst > term > term] :
( ~ ! [X316: term] :
( ( $true
= ( X312 @ id @ ( X315 @ id @ X316 ) @ id ) )
| ( ( X312 @ id @ X316 @ id )
!= $true ) )
| ~ ! [X317: subst,X318: subst,X319: term] :
( ( sub @ ( X315 @ X318 @ X319 ) @ X317 )
= ( X315 @ ( comp @ X318 @ X317 ) @ ( sub @ X319 @ X317 ) ) )
| ( $true
= ( X312 @ id @ ( lam @ ( X315 @ sh @ one ) ) @ id ) ) ) )
=> ! [X328: term,X329: subst > term > subst > $o] :
( ~ ! [X337: subst > term > term] :
( ( $true
= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
| ~ ! [X338: term] :
( ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X329 @ id @ X338 @ id )
!= $true ) )
| ~ ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) ) )
| ~ ! [X330: term,X331: term] :
( ( $true
= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
| ( ( X329 @ id @ X330 @ id )
!= $true )
| ( ( X329 @ id @ X331 @ id )
!= $true ) )
| ~ ! [X336: term] :
( ( $true
= ( X329 @ id @ X336 @ id ) )
| ( ( var @ ( sub @ X336 @ id ) )
!= $true ) )
| ( $true
= ( X329 @ id @ X328 @ id ) )
| ~ ! [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
!= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
| ( $true
= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
| ~ ! [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
!= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
| ( $true
= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ~ ! [X49: term,X50: term] :
( ( ( X46 @ id @ X49 @ id )
!= $true )
| ( ( X46 @ id @ X50 @ id )
!= $true )
| ( $true
= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) )
| ( $true
!= ( X46 @ id @ X47 @ id ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ~ ! [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) )
| ( $true
!= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) ) )
| ~ ! [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) )
| ( $true
!= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X255: term,X256: subst] :
( ( sub @ one @ ( push @ X255 @ X256 ) )
= X255 )
=> ( ! [X257: term,X258: subst] :
( ( comp @ sh @ ( push @ X257 @ X258 ) )
= X258 )
=> ( ! [X259: subst] :
( ( comp @ X259 @ id )
= X259 )
=> ( ! [X260: term > $o,X261: term] :
( ( $true
= ( X260 @ X261 ) )
| ~ ! [X263: term,X264: term] :
( ( $true
!= ( X260 @ X264 ) )
| ( $true
!= ( X260 @ X263 ) )
| ( $true
= ( X260 @ ( ap @ X264 @ X263 ) ) ) )
| ~ ! [X262: term] :
( ( $true
!= ( X260 @ X262 ) )
| ( $true
= ( X260 @ ( lam @ X262 ) ) ) )
| ~ ! [X265: term] :
( ( $true
= ( X260 @ X265 ) )
| ( $true
!= ( var @ X265 ) ) ) )
=> ! [X266: term,X267: subst,X268: term > $o] :
( ~ ! [X273: term] :
( ( $true
= ( X268 @ ( sub @ X273 @ X267 ) ) )
| ( $true
!= ( var @ X273 ) ) )
| ~ ! [X269: term,X270: term] :
( ( $true
!= ( X268 @ X269 ) )
| ( $true
!= ( X268 @ X270 ) )
| ( $true
= ( X268 @ ( ap @ X270 @ X269 ) ) ) )
| ~ ! [X271: term] :
( ( $true
= ( X268 @ ( lam @ X271 ) ) )
| ~ ! [X272: term] :
( ( $true
= ( X268 @ ( sub @ X271 @ ( push @ X272 @ id ) ) ) )
| ( $true
!= ( X268 @ X272 ) ) ) )
| ( $true
= ( X268 @ ( sub @ X266 @ X267 ) ) ) ) ) ) ) ) )
& ( hoasapnotvar_gthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X198: subst > term > subst > $o,X199: term] :
( ~ ! [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
!= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
| ( $true
= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ~ ! [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
| ( $true
!= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
| ~ ! [X204: subst > term > term] :
( ~ ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) )
| ~ ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
| ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X213 @ id ) ) )
| ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) ) ) )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
<=> ( apinj2 = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( one
= ( d2term @ d_one ) )
& ( substmonoid_gthm = $true )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ( axidl = $true )
<=> ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X253: term] :
~ ! [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
!= ( X254 @ sh @ one ) ) )
& ( pushprop_lthm = $true )
& ( ulamvarsh = $true )
& ( ! [X276: subst > term > subst > $o,X277: term] :
( ~ ! [X279: subst > term > term] :
( ~ ! [X281: subst,X282: term,X283: subst] :
( ( X279 @ ( comp @ X283 @ X281 ) @ ( sub @ X282 @ X281 ) )
= ( sub @ ( X279 @ X283 @ X282 ) @ X281 ) )
| ( $true
= ( X276 @ id @ ( lam @ ( X279 @ sh @ one ) ) @ id ) )
| ~ ! [X280: term] :
( ( $true
= ( X276 @ id @ ( X279 @ id @ X280 ) @ id ) )
| ( $true
!= ( X276 @ id @ X280 @ id ) ) ) )
| ~ ! [X278: term] :
( ( $true
= ( X276 @ id @ ( sub @ X277 @ ( push @ X278 @ id ) ) @ id ) )
| ( $true
!= ( X276 @ id @ X278 @ id ) ) )
| ( $true
= ( X276 @ id @ ( lam @ X277 ) @ id ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X536: term] :
~ ! [X537: subst > term > term] :
~ ! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X125: subst > term > subst > $o,X126: term] :
( ~ ! [X132: term,X133: term] :
( ( $true
!= ( X125 @ id @ X132 @ id ) )
| ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
= $true )
| ( $true
!= ( X125 @ id @ X133 @ id ) ) )
| ( $true
= ( X125 @ id @ X126 @ id ) )
| ~ ! [X127: subst > term > term] :
( ( $true
= ( X125 @ id @ ( lam @ ( X127 @ sh @ one ) ) @ id ) )
| ~ ! [X129: subst,X130: subst,X131: term] :
( ( X127 @ ( comp @ X129 @ X130 ) @ ( sub @ X131 @ X130 ) )
= ( sub @ ( X127 @ X129 @ X131 ) @ X130 ) )
| ~ ! [X128: term] :
( ( $true
!= ( X125 @ id @ X128 @ id ) )
| ( $true
= ( X125 @ id @ ( X127 @ id @ X128 ) @ id ) ) ) ) ) )
& ( lamnotap != $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X112: term > $o,X113: term,X114: subst] :
~ ! [X115: term > $o] :
~ ! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ! [X28: term > $o,X29: term] :
( ~ ! [X33: term] :
( ( ( X28 @ ( lam @ X33 ) )
= $true )
| ( ( X28 @ X33 )
!= $true ) )
| ( $true
= ( X28 @ X29 ) )
| ~ ! [X31: term,X32: term] :
( ( ( X28 @ X32 )
!= $true )
| ( $true
!= ( X28 @ X31 ) )
| ( $true
= ( X28 @ ( ap @ X32 @ X31 ) ) ) )
| ~ ! [X30: term] :
( ( ( X28 @ X30 )
= $true )
| ( $true
!= ( var @ X30 ) ) ) )
<=> ( induction = $true ) )
& ( ! [X419: term,X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ~ ! [X428: subst,X429: term,X430: subst,X431: subst] :
( ( ( X422 @ X431 @ X429 @ ( comp @ X430 @ X428 ) )
!= $true )
| ( $true
= ( X422 @ ( comp @ X431 @ X430 ) @ ( sub @ X429 @ X430 ) @ X428 ) ) )
| ( $true
!= ( X421 @ X419 ) )
| ~ ! [X427: term] :
( ( X422 @ id @ X427 @ id )
= ( X421 @ X427 ) )
| ~ ! [X423: subst,X424: term,X425: subst,X426: subst] :
( ( $true
= ( X422 @ X425 @ X424 @ ( comp @ X426 @ X423 ) ) )
| ( $true
!= ( X422 @ ( comp @ X425 @ X426 ) @ ( sub @ X424 @ X426 ) @ X423 ) ) )
| ( $true
= ( X421 @ ( ap @ X420 @ X419 ) ) )
| ( $true
!= ( X421 @ X420 ) )
| ~ ! [X432: term,X433: term] :
( ( $true
!= ( X422 @ id @ X433 @ id ) )
| ( ( X422 @ id @ X432 @ id )
!= $true )
| ( $true
= ( X422 @ id @ ( ap @ ( sub @ X433 @ id ) @ X432 ) @ id ) ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasapnotvar_lthm = $true )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
= ( d2subst @ X291 ) )
=> ( X290 = X291 ) )
& ( ( laminj = $true )
<=> ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) ) )
& ( axapp = $true )
& ( ! [X460: term > $o,X461: subst > term > subst > $o,X462: term] :
( ~ ! [X463: term] :
( ( X461 @ id @ X463 @ id )
= ( X460 @ X463 ) )
| ~ ! [X465: subst > term > term] :
( ~ ! [X466: term,X467: subst,X468: subst] :
( ( sub @ ( X465 @ X467 @ X466 ) @ X468 )
= ( X465 @ ( comp @ X467 @ X468 ) @ ( sub @ X466 @ X468 ) ) )
| ~ ! [X469: term] :
( ( $true
!= ( X461 @ id @ X469 @ id ) )
| ( $true
= ( X461 @ id @ ( X465 @ id @ X469 ) @ id ) ) )
| ( $true
= ( X461 @ id @ ( lam @ ( X465 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X460 @ ( lam @ X462 ) ) )
| ~ ! [X464: term] :
( ( $true
!= ( X460 @ X464 ) )
| ( $true
= ( X460 @ ( sub @ X462 @ ( push @ X464 @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X34: subst > term > subst > $o] :
~ ! [X35: term > $o] :
~ ! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) ) )
& ( ! [X214: term,X215: term > $o,X216: subst > term > subst > $o] :
( ~ ! [X227: term,X228: subst,X229: subst,X230: subst] :
( ( $true
= ( X216 @ X228 @ X227 @ ( comp @ X230 @ X229 ) ) )
| ( $true
!= ( X216 @ ( comp @ X228 @ X230 ) @ ( sub @ X227 @ X230 ) @ X229 ) ) )
| ~ ! [X223: subst,X224: subst,X225: term,X226: subst] :
( ( $true
!= ( X216 @ X224 @ X225 @ ( comp @ X223 @ X226 ) ) )
| ( $true
= ( X216 @ ( comp @ X224 @ X223 ) @ ( sub @ X225 @ X223 ) @ X226 ) ) )
| ~ ! [X231: term] :
( ( X215 @ X231 )
= ( X216 @ id @ X231 @ id ) )
| ( $true
= ( X215 @ ( lam @ X214 ) ) )
| ~ ! [X222: term] :
( ( $true
= ( X215 @ ( sub @ X214 @ ( push @ X222 @ id ) ) ) )
| ( ( X215 @ X222 )
!= $true ) )
| ~ ! [X217: subst > term > term] :
( ~ ! [X218: term,X219: subst,X220: subst] :
( ( sub @ ( X217 @ X220 @ X218 ) @ X219 )
= ( X217 @ ( comp @ X220 @ X219 ) @ ( sub @ X218 @ X219 ) ) )
| ( $true
= ( X216 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id ) )
| ~ ! [X221: term] :
( ( $true
!= ( X216 @ id @ X221 @ id ) )
| ( $true
= ( X216 @ id @ ( X217 @ id @ X221 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
=> ( ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) )
=> ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( apnotvar = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
!= ( ap @ X411 @ X410 ) )
| ( X409 = X410 ) )
=> ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X374: subst,X375: term > $o,X376: term] :
~ ! [X377: term > $o] :
~ ! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X63: subst > term > subst > $o] :
~ ! [X64: term > $o] :
~ ! [X65: term] :
( ( X64 @ X65 )
= ( X63 @ id @ X65 @ id ) )
=> ( ! [X66: term,X67: term > $o] :
( ~ ! [X68: term] :
( ( $true
= ( X67 @ X68 ) )
| ( $true
!= ( var @ X68 ) ) )
| ~ ! [X69: term,X70: term] :
( ( ( X67 @ X70 )
!= $true )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( $true
!= ( X67 @ X69 ) ) )
| ~ ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ~ ! [X72: term] :
( ( ( X67 @ X72 )
!= $true )
| ( $true
= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) ) ) )
| ( $true
= ( X67 @ X66 ) ) )
=> ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
=> ( ! [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ( $true
= ( X74 @ ( lam @ X76 ) ) )
| ~ ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
| ~ ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) )
| ~ ! [X78: subst > term > term] :
( ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X82: term] :
( ( $true
!= ( X75 @ id @ X82 @ id ) )
| ( $true
= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) ) )
| ~ ! [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) ) ) )
=> ! [X84: term,X85: subst > term > subst > $o] :
( ( $true
= ( X85 @ id @ X84 @ id ) )
| ~ ! [X97: subst > term > term] :
( ~ ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) )
| ( $true
= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) )
| ~ ! [X98: term] :
( ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) )
| ( ( X85 @ id @ X98 @ id )
!= $true ) ) )
| ~ ! [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) )
| ( $true
!= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) ) )
| ~ ! [X88: term] :
( ( $true
!= ( var @ ( sub @ X88 @ id ) ) )
| ( $true
= ( X85 @ id @ X88 @ id ) ) )
| ~ ! [X89: subst,X90: subst,X91: term,X92: subst] :
( ( $true
= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) )
| ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
!= $true ) )
| ~ ! [X86: term,X87: term] :
( ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
= $true )
| ( $true
!= ( X85 @ id @ X86 @ id ) )
| ( $true
!= ( X85 @ id @ X87 @ id ) ) ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X232: term] :
( ( sub @ X232 @ id )
= X232 )
=> ! [X233: term,X234: term > $o,X235: subst > term > subst > $o] :
( ~ ! [X241: subst > term > term] :
( ~ ! [X242: term,X243: subst,X244: subst] :
( ( X241 @ ( comp @ X244 @ X243 ) @ ( sub @ X242 @ X243 ) )
= ( sub @ ( X241 @ X244 @ X242 ) @ X243 ) )
| ( $true
= ( X235 @ id @ ( lam @ ( X241 @ sh @ one ) ) @ id ) )
| ~ ! [X245: term] :
( ( $true
!= ( X235 @ id @ X245 @ id ) )
| ( $true
= ( X235 @ id @ ( X241 @ id @ X245 ) @ id ) ) ) )
| ~ ! [X246: term] :
( ( X234 @ X246 )
= ( X235 @ id @ X246 @ id ) )
| ~ ! [X240: term] :
( ( ( X234 @ X240 )
!= $true )
| ( ( X234 @ ( sub @ X233 @ ( push @ X240 @ id ) ) )
= $true ) )
| ~ ! [X247: subst,X248: term,X249: subst,X250: subst] :
( ( $true
!= ( X235 @ X247 @ X248 @ ( comp @ X249 @ X250 ) ) )
| ( $true
= ( X235 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) @ X250 ) ) )
| ~ ! [X236: subst,X237: subst,X238: subst,X239: term] :
( ( ( X235 @ X238 @ X239 @ ( comp @ X237 @ X236 ) )
= $true )
| ( $true
!= ( X235 @ ( comp @ X238 @ X237 ) @ ( sub @ X239 @ X237 ) @ X236 ) ) )
| ( ( X234 @ ( lam @ X233 ) )
= $true ) ) ) )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
<=> ( hoasapinj2 = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ~ ! [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) )
| ~ ! [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( pushprop = $true )
& ( ( substmonoid = $true )
<=> ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axmap = $true )
& ( induction2lem_gthm = $true )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
<=> ( axvarid = $true ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
=> ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( ( X2 @ X4 )
!= $true )
| ( $true
= ( X5 @ one ) )
| ~ ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X393: term] :
( ( sub @ X393 @ id )
= X393 )
=> ( ! [X394: subst,X395: term,X396: term > $o] :
( ~ ! [X400: term] :
( ~ ! [X401: term] :
( ( ( X396 @ ( sub @ X400 @ ( push @ X401 @ id ) ) )
= $true )
| ( $true
!= ( X396 @ X401 ) ) )
| ( $true
= ( X396 @ ( lam @ X400 ) ) ) )
| ~ ! [X398: term,X399: term] :
( ( $true
!= ( X396 @ X399 ) )
| ( $true
!= ( X396 @ X398 ) )
| ( $true
= ( X396 @ ( ap @ X398 @ X399 ) ) ) )
| ~ ! [X397: term] :
( ( $true
= ( X396 @ ( sub @ X397 @ X394 ) ) )
| ( $true
!= ( var @ X397 ) ) )
| ( $true
= ( X396 @ ( sub @ X395 @ X394 ) ) ) )
=> ! [X402: term,X403: term > $o] :
( ~ ! [X405: term] :
( ~ ! [X406: term] :
( ( $true
!= ( X403 @ X406 ) )
| ( $true
= ( X403 @ ( sub @ X405 @ ( push @ X406 @ id ) ) ) ) )
| ( $true
= ( X403 @ ( lam @ X405 ) ) ) )
| ~ ! [X407: term,X408: term] :
( ( $true
= ( X403 @ ( ap @ X407 @ X408 ) ) )
| ( $true
!= ( X403 @ X407 ) )
| ( ( X403 @ X408 )
!= $true ) )
| ~ ! [X404: term] :
( ( ( var @ X404 )
!= $true )
| ( $true
= ( X403 @ X404 ) ) )
| ( $true
= ( X403 @ X402 ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( hoaslamnotvar = $true )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( induction2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( hoaslamnotap_lthm = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
=> ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( $true
= ( X5 @ one ) )
| ( ( X2 @ X4 )
!= $true )
| ~ ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ulamvarind = $true )
& ! [X7: d_term,X8: d_term] :
( ( ( d2term @ X7 )
= ( d2term @ X8 ) )
=> ( X7 = X8 ) )
& ( ( ! [X9: term] :
( ( sub @ X9 @ id )
= X9 )
=> ( ! [X10: subst > term > subst > $o,X11: term] :
( ~ ! [X12: subst > term > term] :
( ~ ! [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) )
| ~ ! [X16: term] :
( ( $true
= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
| ( ( X10 @ id @ X16 @ id )
!= $true ) ) )
| ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X17: term] :
( ( $true
!= ( X10 @ id @ X17 @ id ) )
| ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) ) ) )
=> ! [X18: subst > term > subst > $o,X19: term] :
( ~ ! [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
= $true )
| ( $true
!= ( X18 @ id @ X20 @ id ) ) )
| ~ ! [X21: subst > term > term] :
( ~ ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
| ~ ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) )
| ( $true
= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction = $true )
<=> ! [X28: term > $o,X29: term] :
( ( $true
= ( X28 @ X29 ) )
| ~ ! [X30: term] :
( ( ( X28 @ X30 )
= $true )
| ( $true
!= ( var @ X30 ) ) )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X28 @ ( ap @ X32 @ X31 ) ) )
| ( ( X28 @ X32 )
!= $true )
| ( $true
!= ( X28 @ X31 ) ) )
| ~ ! [X33: term] :
( ( ( X28 @ ( lam @ X33 ) )
= $true )
| ( ( X28 @ X33 )
!= $true ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X34: subst > term > subst > $o] :
~ ! [X35: term > $o] :
~ ! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) ) )
& ( ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
=> ( ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) )
=> ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ~ ! [X49: term,X50: term] :
( ( ( X46 @ id @ X50 @ id )
!= $true )
| ( ( X46 @ id @ X49 @ id )
!= $true )
| ( $true
= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) )
| ~ ! [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
!= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) )
| ( $true
= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) ) )
| ~ ! [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
!= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) )
| ( $true
= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ( $true
!= ( X46 @ id @ X47 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X63: subst > term > subst > $o] :
~ ! [X64: term > $o] :
~ ! [X65: term] :
( ( X64 @ X65 )
= ( X63 @ id @ X65 @ id ) )
=> ( ! [X66: term,X67: term > $o] :
( ( $true
= ( X67 @ X66 ) )
| ~ ! [X68: term] :
( ( $true
!= ( var @ X68 ) )
| ( $true
= ( X67 @ X68 ) ) )
| ~ ! [X69: term,X70: term] :
( ( $true
!= ( X67 @ X69 ) )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( ( X67 @ X70 )
!= $true ) )
| ~ ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ~ ! [X72: term] :
( ( $true
= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) )
| ( ( X67 @ X72 )
!= $true ) ) ) )
=> ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
=> ( ! [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ( $true
= ( X74 @ ( lam @ X76 ) ) )
| ~ ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
| ~ ! [X78: subst > term > term] :
( ~ ! [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) )
| ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X82: term] :
( ( $true
= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) )
| ( $true
!= ( X75 @ id @ X82 @ id ) ) ) )
| ~ ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) ) )
=> ! [X84: term,X85: subst > term > subst > $o] :
( ~ ! [X86: term,X87: term] :
( ( $true
!= ( X85 @ id @ X87 @ id ) )
| ( $true
!= ( X85 @ id @ X86 @ id ) )
| ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
= $true ) )
| ~ ! [X88: term] :
( ( $true
!= ( var @ ( sub @ X88 @ id ) ) )
| ( $true
= ( X85 @ id @ X88 @ id ) ) )
| ~ ! [X89: subst,X90: subst,X91: term,X92: subst] :
( ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
!= $true )
| ( $true
= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) ) )
| ~ ! [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
!= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) )
| ( $true
= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) ) )
| ~ ! [X97: subst > term > term] :
( ( $true
= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) )
| ~ ! [X98: term] :
( ( ( X85 @ id @ X98 @ id )
!= $true )
| ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) ) )
| ~ ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) ) )
| ( $true
= ( X85 @ id @ X84 @ id ) ) ) ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X102: subst > term > subst > $o] :
~ ! [X103: term > $o] :
~ ! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( induction2 = $true )
<=> ! [X105: term > $o,X106: term] :
( ~ ! [X107: term] :
( ( $true
!= ( var @ X107 ) )
| ( ( X105 @ X107 )
= $true ) )
| ~ ! [X108: term,X109: term] :
( ( $true
= ( X105 @ ( ap @ X109 @ X108 ) ) )
| ( $true
!= ( X105 @ X108 ) )
| ( $true
!= ( X105 @ X109 ) ) )
| ( $true
= ( X105 @ X106 ) )
| ~ ! [X110: term] :
( ~ ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) )
| ( ( X105 @ ( lam @ X110 ) )
= $true ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X112: term > $o,X113: term,X114: subst] :
~ ! [X115: term > $o] :
~ ! [X116: term] :
( ( X115 @ X116 )
= ( X112 @ ( sub @ X116 @ ( push @ X113 @ X114 ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X117: term,X118: subst > term > subst > $o] :
( ( $true
= ( X118 @ id @ ( lam @ ( sub @ X117 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X119: term] :
( ( $true
!= ( X118 @ id @ X119 @ id ) )
| ( $true
= ( X118 @ id @ ( sub @ X117 @ ( push @ X119 @ id ) ) @ id ) ) )
| ~ ! [X120: subst > term > term] :
( ( $true
= ( X118 @ id @ ( lam @ ( X120 @ sh @ one ) ) @ id ) )
| ~ ! [X121: term] :
( ( $true
= ( X118 @ id @ ( X120 @ id @ X121 ) @ id ) )
| ( $true
!= ( X118 @ id @ X121 @ id ) ) )
| ~ ! [X122: subst,X123: subst,X124: term] :
( ( sub @ ( X120 @ X122 @ X124 ) @ X123 )
= ( X120 @ ( comp @ X122 @ X123 ) @ ( sub @ X124 @ X123 ) ) ) ) ) )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X125: subst > term > subst > $o,X126: term] :
( ( $true
= ( X125 @ id @ X126 @ id ) )
| ~ ! [X127: subst > term > term] :
( ~ ! [X128: term] :
( ( $true
!= ( X125 @ id @ X128 @ id ) )
| ( $true
= ( X125 @ id @ ( X127 @ id @ X128 ) @ id ) ) )
| ~ ! [X129: subst,X130: subst,X131: term] :
( ( X127 @ ( comp @ X129 @ X130 ) @ ( sub @ X131 @ X130 ) )
= ( sub @ ( X127 @ X129 @ X131 ) @ X130 ) )
| ( $true
= ( X125 @ id @ ( lam @ ( X127 @ sh @ one ) ) @ id ) ) )
| ~ ! [X132: term,X133: term] :
( ( ( X125 @ id @ ( ap @ ( sub @ X133 @ id ) @ X132 ) @ id )
= $true )
| ( $true
!= ( X125 @ id @ X132 @ id ) )
| ( $true
!= ( X125 @ id @ X133 @ id ) ) ) ) )
& ( ! [X134: term,X135: subst > term > subst > $o] :
( ( ( X135 @ id @ X134 @ id )
= $true )
| ~ ! [X136: subst,X137: term,X138: subst,X139: subst] :
( ( $true
= ( X135 @ ( comp @ X136 @ X138 ) @ ( sub @ X137 @ X138 ) @ X139 ) )
| ( ( X135 @ X136 @ X137 @ ( comp @ X138 @ X139 ) )
!= $true ) )
| ~ ! [X140: subst > term > term] :
( ~ ! [X141: term,X142: subst,X143: subst] :
( ( X140 @ ( comp @ X143 @ X142 ) @ ( sub @ X141 @ X142 ) )
= ( sub @ ( X140 @ X143 @ X141 ) @ X142 ) )
| ~ ! [X144: term] :
( ( $true
!= ( X135 @ id @ X144 @ id ) )
| ( $true
= ( X135 @ id @ ( X140 @ id @ X144 ) @ id ) ) )
| ( $true
= ( X135 @ id @ ( lam @ ( X140 @ sh @ one ) ) @ id ) ) )
| ~ ! [X145: term] :
( ( $true
= ( X135 @ id @ X145 @ id ) )
| ( $true
!= ( var @ ( sub @ X145 @ id ) ) ) )
| ~ ! [X146: term,X147: term] :
( ( ( X135 @ id @ X146 @ id )
!= $true )
| ( $true
!= ( X135 @ id @ X147 @ id ) )
| ( $true
= ( X135 @ id @ ( ap @ ( sub @ X147 @ id ) @ X146 ) @ id ) ) )
| ~ ! [X148: subst,X149: subst,X150: subst,X151: term] :
( ( $true
= ( X135 @ X148 @ X151 @ ( comp @ X149 @ X150 ) ) )
| ( $true
!= ( X135 @ ( comp @ X148 @ X149 ) @ ( sub @ X151 @ X149 ) @ X150 ) ) ) )
<=> ( hoasinduction = $true ) )
& ( ! [X152: term > $o,X153: term > $o,X154: subst,X155: term] :
( ( $true
= ( X153 @ one ) )
| ~ ! [X156: term] :
( ( X153 @ X156 )
= ( X152 @ ( sub @ X156 @ ( push @ X155 @ X154 ) ) ) )
| ( $true
!= ( X152 @ X155 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axscons = $true )
<=> ! [X157: subst] :
( ( push @ ( sub @ one @ X157 ) @ ( comp @ sh @ X157 ) )
= X157 ) )
& ( ( d2subst @ d_id )
= sh )
& ( substmonoid_gthm = $true )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( induction2_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X158: term] :
? [X159: d_term] :
( ( d2term @ X159 )
= X158 )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X160: term,X161: subst > term > subst > $o] :
( ~ ! [X162: subst > term > term] :
( ~ ! [X163: subst,X164: term,X165: subst] :
( ( sub @ ( X162 @ X165 @ X164 ) @ X163 )
= ( X162 @ ( comp @ X165 @ X163 ) @ ( sub @ X164 @ X163 ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
| ~ ! [X166: term] :
( ( $true
= ( X161 @ id @ ( X162 @ id @ X166 ) @ id ) )
| ( $true
!= ( X161 @ id @ X166 @ id ) ) ) )
| ( $true
= ( X161 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X167: term] :
( ( $true
= ( X161 @ id @ ( sub @ X160 @ ( push @ X167 @ id ) ) @ id ) )
| ( $true
!= ( X161 @ id @ X167 @ id ) ) ) ) )
& ( ( ! [X168: term,X169: subst] :
( ( sub @ one @ ( push @ X168 @ X169 ) )
= X168 )
=> ( ! [X170: term,X171: subst] :
( ( comp @ sh @ ( push @ X170 @ X171 ) )
= X171 )
=> ( ! [X172: term,X173: term] :
( ( X172 = X173 )
| ( ( lam @ X173 )
!= ( lam @ X172 ) ) )
=> ! [X174: subst > term > term,X175: term,X176: subst,X177: subst > term > term] :
( ( ( X174 @ X176 @ X175 )
= ( X177 @ X176 @ X175 ) )
| ~ ! [X181: subst,X182: subst,X183: term] :
( ( sub @ ( X177 @ X182 @ X183 ) @ X181 )
= ( X177 @ ( comp @ X182 @ X181 ) @ ( sub @ X183 @ X181 ) ) )
| ~ ! [X178: subst,X179: subst,X180: term] :
( ( sub @ ( X174 @ X178 @ X180 ) @ X179 )
= ( X174 @ ( comp @ X178 @ X179 ) @ ( sub @ X180 @ X179 ) ) )
| ( ( lam @ ( X177 @ sh @ one ) )
!= ( lam @ ( X174 @ sh @ one ) ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( axapp = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem3v2 = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X184: subst > term > subst > $o,X185: term] :
( ( $true
= ( X184 @ id @ ( lam @ ( sub @ X185 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X186: term] :
( ( $true
!= ( X184 @ id @ X186 @ id ) )
| ( $true
= ( X184 @ id @ ( sub @ X185 @ ( push @ X186 @ id ) ) @ id ) ) )
| ~ ! [X187: subst > term > term,X188: term] :
( ~ ! [X189: subst,X190: term,X191: subst] :
( ( X187 @ ( comp @ X191 @ X189 ) @ ( sub @ X190 @ X189 ) )
= ( sub @ X188 @ ( push @ ( sub @ X190 @ X189 ) @ ( comp @ X191 @ X189 ) ) ) )
| ( $true
= ( X184 @ id @ ( lam @ ( X187 @ sh @ one ) ) @ id ) )
| ~ ! [X192: subst,X193: term,X194: subst] :
( ( sub @ ( sub @ X188 @ ( push @ X193 @ X194 ) ) @ X192 )
= ( sub @ ( X187 @ X194 @ X193 ) @ X192 ) )
| ~ ! [X195: term] :
( ( $true
!= ( X184 @ id @ X195 @ id ) )
| ( $true
= ( X184 @ id @ ( X187 @ id @ X195 ) @ id ) ) ) ) ) )
& ( axmap = $true )
& ( ( axidr = $true )
<=> ! [X196: subst] :
( ( comp @ X196 @ id )
= X196 ) )
& ( ( axidl = $true )
<=> ! [X197: subst] :
( ( comp @ id @ X197 )
= X197 ) )
& ( termmset_gthm = $true )
& ( ! [X198: subst > term > subst > $o,X199: term] :
( ~ ! [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
!= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) )
| ( $true
= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) ) )
| ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) )
| ~ ! [X204: subst > term > term] :
( ~ ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
| ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) )
| ~ ! [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
!= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
| ( $true
= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ~ ! [X213: term] :
( ( $true
!= ( X198 @ id @ X213 @ id ) )
| ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( hoasapinj2_gthm = $true )
& ( lamnotvar = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X214: term,X215: term > $o,X216: subst > term > subst > $o] :
( ~ ! [X217: subst > term > term] :
( ( $true
= ( X216 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id ) )
| ~ ! [X218: term,X219: subst,X220: subst] :
( ( sub @ ( X217 @ X220 @ X218 ) @ X219 )
= ( X217 @ ( comp @ X220 @ X219 ) @ ( sub @ X218 @ X219 ) ) )
| ~ ! [X221: term] :
( ( $true
!= ( X216 @ id @ X221 @ id ) )
| ( $true
= ( X216 @ id @ ( X217 @ id @ X221 ) @ id ) ) ) )
| ~ ! [X222: term] :
( ( ( X215 @ X222 )
!= $true )
| ( $true
= ( X215 @ ( sub @ X214 @ ( push @ X222 @ id ) ) ) ) )
| ~ ! [X223: subst,X224: subst,X225: term,X226: subst] :
( ( $true
= ( X216 @ ( comp @ X224 @ X223 ) @ ( sub @ X225 @ X223 ) @ X226 ) )
| ( $true
!= ( X216 @ X224 @ X225 @ ( comp @ X223 @ X226 ) ) ) )
| ~ ! [X227: term,X228: subst,X229: subst,X230: subst] :
( ( $true
= ( X216 @ X228 @ X227 @ ( comp @ X230 @ X229 ) ) )
| ( $true
!= ( X216 @ ( comp @ X228 @ X230 ) @ ( sub @ X227 @ X230 ) @ X229 ) ) )
| ( $true
= ( X215 @ ( lam @ X214 ) ) )
| ~ ! [X231: term] :
( ( X215 @ X231 )
= ( X216 @ id @ X231 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( ! [X232: term] :
( ( sub @ X232 @ id )
= X232 )
=> ! [X233: term,X234: term > $o,X235: subst > term > subst > $o] :
( ~ ! [X236: subst,X237: subst,X238: subst,X239: term] :
( ( ( X235 @ X238 @ X239 @ ( comp @ X237 @ X236 ) )
= $true )
| ( $true
!= ( X235 @ ( comp @ X238 @ X237 ) @ ( sub @ X239 @ X237 ) @ X236 ) ) )
| ~ ! [X240: term] :
( ( ( X234 @ X240 )
!= $true )
| ( ( X234 @ ( sub @ X233 @ ( push @ X240 @ id ) ) )
= $true ) )
| ~ ! [X241: subst > term > term] :
( ~ ! [X242: term,X243: subst,X244: subst] :
( ( X241 @ ( comp @ X244 @ X243 ) @ ( sub @ X242 @ X243 ) )
= ( sub @ ( X241 @ X244 @ X242 ) @ X243 ) )
| ~ ! [X245: term] :
( ( $true
= ( X235 @ id @ ( X241 @ id @ X245 ) @ id ) )
| ( $true
!= ( X235 @ id @ X245 @ id ) ) )
| ( $true
= ( X235 @ id @ ( lam @ ( X241 @ sh @ one ) ) @ id ) ) )
| ~ ! [X246: term] :
( ( X234 @ X246 )
= ( X235 @ id @ X246 @ id ) )
| ~ ! [X247: subst,X248: term,X249: subst,X250: subst] :
( ( $true
!= ( X235 @ X247 @ X248 @ ( comp @ X249 @ X250 ) ) )
| ( $true
= ( X235 @ ( comp @ X247 @ X249 ) @ ( sub @ X248 @ X249 ) @ X250 ) ) )
| ( ( X234 @ ( lam @ X233 ) )
= $true ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( ! [X251: term] :
( ( sub @ X251 @ id )
= X251 )
=> ! [X252: term] :
( ( sub @ X252 @ id )
= X252 ) )
<=> ( termmset_lthm = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X253: term] :
~ ! [X254: subst > term > term] :
( ( sub @ X253 @ ( push @ one @ sh ) )
!= ( X254 @ sh @ one ) ) )
& ( apnotvar = $true )
& ( ( ! [X255: term,X256: subst] :
( ( sub @ one @ ( push @ X255 @ X256 ) )
= X255 )
=> ( ! [X257: term,X258: subst] :
( ( comp @ sh @ ( push @ X257 @ X258 ) )
= X258 )
=> ( ! [X259: subst] :
( ( comp @ X259 @ id )
= X259 )
=> ( ! [X260: term > $o,X261: term] :
( ~ ! [X262: term] :
( ( $true
= ( X260 @ ( lam @ X262 ) ) )
| ( $true
!= ( X260 @ X262 ) ) )
| ~ ! [X263: term,X264: term] :
( ( $true
!= ( X260 @ X263 ) )
| ( $true
!= ( X260 @ X264 ) )
| ( $true
= ( X260 @ ( ap @ X264 @ X263 ) ) ) )
| ~ ! [X265: term] :
( ( $true
!= ( var @ X265 ) )
| ( $true
= ( X260 @ X265 ) ) )
| ( $true
= ( X260 @ X261 ) ) )
=> ! [X266: term,X267: subst,X268: term > $o] :
( ~ ! [X269: term,X270: term] :
( ( $true
= ( X268 @ ( ap @ X270 @ X269 ) ) )
| ( $true
!= ( X268 @ X269 ) )
| ( $true
!= ( X268 @ X270 ) ) )
| ~ ! [X271: term] :
( ~ ! [X272: term] :
( ( $true
!= ( X268 @ X272 ) )
| ( $true
= ( X268 @ ( sub @ X271 @ ( push @ X272 @ id ) ) ) ) )
| ( $true
= ( X268 @ ( lam @ X271 ) ) ) )
| ( $true
= ( X268 @ ( sub @ X266 @ X267 ) ) )
| ~ ! [X273: term] :
( ( $true
= ( X268 @ ( sub @ X273 @ X267 ) ) )
| ( $true
!= ( var @ X273 ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ulamvar1 != $true )
& ( ( axshiftcons = $true )
<=> ! [X274: term,X275: subst] :
( ( comp @ sh @ ( push @ X274 @ X275 ) )
= X275 ) )
& ( ! [X276: subst > term > subst > $o,X277: term] :
( ~ ! [X278: term] :
( ( $true
!= ( X276 @ id @ X278 @ id ) )
| ( $true
= ( X276 @ id @ ( sub @ X277 @ ( push @ X278 @ id ) ) @ id ) ) )
| ( $true
= ( X276 @ id @ ( lam @ X277 ) @ id ) )
| ~ ! [X279: subst > term > term] :
( ~ ! [X280: term] :
( ( $true
!= ( X276 @ id @ X280 @ id ) )
| ( $true
= ( X276 @ id @ ( X279 @ id @ X280 ) @ id ) ) )
| ~ ! [X281: subst,X282: term,X283: subst] :
( ( X279 @ ( comp @ X283 @ X281 ) @ ( sub @ X282 @ X281 ) )
= ( sub @ ( X279 @ X283 @ X282 ) @ X281 ) )
| ( $true
= ( X276 @ id @ ( lam @ ( X279 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ! [X284: subst] :
? [X285: d_subst] :
( ( d2subst @ X285 )
= X284 )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X286: term,X287: term,X288: term,X289: term] :
( ( X288 = X289 )
| ( ( ap @ ( sub @ X286 @ id ) @ X289 )
!= ( ap @ ( sub @ X287 @ id ) @ X288 ) ) )
<=> ( hoasapinj2 = $true ) )
& ! [X290: d_subst,X291: d_subst] :
( ( ( d2subst @ X290 )
= ( d2subst @ X291 ) )
=> ( X290 = X291 ) )
& ( ( ! [X292: term > $o,X293: term] :
( ~ ! [X294: term] :
( ( $true
= ( X292 @ ( lam @ X294 ) ) )
| ~ ! [X295: term] :
( ( $true
= ( X292 @ ( sub @ X294 @ ( push @ X295 @ id ) ) ) )
| ( ( X292 @ X295 )
!= $true ) ) )
| ~ ! [X296: term] :
( ( $true
= ( X292 @ X296 ) )
| ( $true
!= ( var @ X296 ) ) )
| ( $true
= ( X292 @ X293 ) )
| ~ ! [X297: term,X298: term] :
( ( ( X292 @ X298 )
!= $true )
| ( $true
= ( X292 @ ( ap @ X298 @ X297 ) ) )
| ( $true
!= ( X292 @ X297 ) ) ) )
=> ( ! [X299: subst > term > subst > $o,X300: term,X301: term] :
( ( $true
= ( X299 @ id @ ( ap @ X300 @ X301 ) @ id ) )
| ~ ! [X302: subst,X303: term,X304: subst,X305: subst] :
( ( $true
!= ( X299 @ ( comp @ X305 @ X302 ) @ ( sub @ X303 @ X302 ) @ X304 ) )
| ( $true
= ( X299 @ X305 @ X303 @ ( comp @ X302 @ X304 ) ) ) )
| ~ ! [X306: term,X307: term] :
( ( $true
!= ( X299 @ id @ X306 @ id ) )
| ( $true
= ( X299 @ id @ ( ap @ ( sub @ X306 @ id ) @ X307 ) @ id ) )
| ( ( X299 @ id @ X307 @ id )
!= $true ) )
| ( $true
!= ( X299 @ id @ X301 @ id ) )
| ( ( X299 @ id @ X300 @ id )
!= $true )
| ~ ! [X308: term,X309: subst,X310: subst,X311: subst] :
( ( $true
= ( X299 @ ( comp @ X311 @ X309 ) @ ( sub @ X308 @ X309 ) @ X310 ) )
| ( $true
!= ( X299 @ X311 @ X308 @ ( comp @ X309 @ X310 ) ) ) ) )
=> ( ! [X312: subst > term > subst > $o,X313: term] :
( ~ ! [X314: term] :
( ( $true
= ( X312 @ id @ ( sub @ X313 @ ( push @ X314 @ id ) ) @ id ) )
| ( ( X312 @ id @ X314 @ id )
!= $true ) )
| ( $true
= ( X312 @ id @ ( lam @ X313 ) @ id ) )
| ~ ! [X315: subst > term > term] :
( ~ ! [X316: term] :
( ( ( X312 @ id @ X316 @ id )
!= $true )
| ( $true
= ( X312 @ id @ ( X315 @ id @ X316 ) @ id ) ) )
| ( $true
= ( X312 @ id @ ( lam @ ( X315 @ sh @ one ) ) @ id ) )
| ~ ! [X317: subst,X318: subst,X319: term] :
( ( sub @ ( X315 @ X318 @ X319 ) @ X317 )
= ( X315 @ ( comp @ X318 @ X317 ) @ ( sub @ X319 @ X317 ) ) ) )
| ~ ! [X320: subst,X321: term,X322: subst,X323: subst] :
( ( $true
!= ( X312 @ ( comp @ X322 @ X323 ) @ ( sub @ X321 @ X323 ) @ X320 ) )
| ( $true
= ( X312 @ X322 @ X321 @ ( comp @ X323 @ X320 ) ) ) )
| ~ ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( $true
= ( X312 @ ( comp @ X325 @ X324 ) @ ( sub @ X326 @ X324 ) @ X327 ) )
| ( $true
!= ( X312 @ X325 @ X326 @ ( comp @ X324 @ X327 ) ) ) ) )
=> ! [X328: term,X329: subst > term > subst > $o] :
( ~ ! [X330: term,X331: term] :
( ( $true
= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
| ( ( X329 @ id @ X330 @ id )
!= $true )
| ( ( X329 @ id @ X331 @ id )
!= $true ) )
| ( $true
= ( X329 @ id @ X328 @ id ) )
| ~ ! [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
!= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
| ( $true
= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
| ~ ! [X336: term] :
( ( $true
= ( X329 @ id @ X336 @ id ) )
| ( ( var @ ( sub @ X336 @ id ) )
!= $true ) )
| ~ ! [X337: subst > term > term] :
( ( $true
= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
| ~ ! [X338: term] :
( ( ( X329 @ id @ X338 @ id )
!= $true )
| ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) ) )
| ~ ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) ) )
| ~ ! [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
!= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
| ( $true
= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X346: term,X347: term,X348: subst > term > term] :
( ~ ! [X349: subst,X350: term,X351: subst] :
( ( X348 @ ( comp @ X349 @ X351 ) @ ( sub @ X350 @ X351 ) )
= ( sub @ ( X348 @ X349 @ X350 ) @ X351 ) )
| ( ( ap @ ( sub @ X347 @ id ) @ X346 )
!= ( lam @ ( X348 @ sh @ one ) ) ) ) )
& ( ! [X352: term] :
( ( sub @ X352 @ id )
= X352 )
<=> ( axvarid = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X353: term,X354: term,X355: term,X356: term] :
( ( X354 = X356 )
| ( ( ap @ ( sub @ X356 @ id ) @ X355 )
!= ( ap @ ( sub @ X354 @ id ) @ X353 ) ) ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( substmonoid = $true )
<=> ( ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 )
& ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X359: term] :
~ ! [X360: subst > term > term] :
~ ! [X361: term,X362: subst] :
( ( X360 @ X362 @ X361 )
= ( sub @ X359 @ ( push @ X361 @ X362 ) ) )
=> ( ! [X363: term] :
( ( sub @ X363 @ id )
= X363 )
=> ! [X364: term,X365: term > $o,X366: subst > term > subst > $o] :
( ~ ! [X367: term] :
( ( X366 @ id @ X367 @ id )
= ( X365 @ X367 ) )
| ~ ! [X368: term] :
( ( $true
= ( X365 @ ( sub @ X364 @ ( push @ X368 @ id ) ) ) )
| ( $true
!= ( X365 @ X368 ) ) )
| ~ ! [X369: subst > term > term] :
( ~ ! [X370: term] :
( ( $true
!= ( X366 @ id @ X370 @ id ) )
| ( ( X366 @ id @ ( X369 @ id @ X370 ) @ id )
= $true ) )
| ( $true
= ( X366 @ id @ ( lam @ ( X369 @ sh @ one ) ) @ id ) )
| ~ ! [X371: term,X372: subst,X373: subst] :
( ( sub @ ( X369 @ X373 @ X371 ) @ X372 )
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X371 @ X372 ) ) ) )
| ( $true
= ( X365 @ ( lam @ X364 ) ) ) ) ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X374: subst,X375: term > $o,X376: term] :
~ ! [X377: term > $o] :
~ ! [X378: term] :
( ( X375 @ ( sub @ X378 @ ( push @ X376 @ X374 ) ) )
= ( X377 @ X378 ) ) )
& ( hoasinduction_gthm = $true )
& ( ( shinj = $true )
<=> ! [X379: term,X380: term] :
( ( X379 = X380 )
| ( ( sub @ X379 @ sh )
!= ( sub @ X380 @ sh ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X381: term > $o,X382: subst,X383: term] :
( ( $true
= ( X381 @ ( sub @ X383 @ X382 ) ) )
| ~ ! [X384: term] :
( ~ ! [X385: term] :
( ( $true
!= ( X381 @ X385 ) )
| ( $true
= ( X381 @ ( sub @ X384 @ ( push @ X385 @ id ) ) ) ) )
| ( $true
= ( X381 @ ( lam @ X384 ) ) ) )
| ~ ! [X386: term] :
( ( $true
= ( X381 @ ( sub @ X386 @ X382 ) ) )
| ( $true
!= ( var @ X386 ) ) )
| ~ ! [X387: term,X388: term] :
( ( $true
= ( X381 @ ( ap @ X388 @ X387 ) ) )
| ( $true
!= ( X381 @ X388 ) )
| ( $true
!= ( X381 @ X387 ) ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X389: term,X390: term,X391: term,X392: term] :
( ( ( ap @ X390 @ X389 )
!= ( ap @ X392 @ X391 ) )
| ( X389 = X391 ) )
<=> ( apinj2 = $true ) )
& ( ( ! [X393: term] :
( ( sub @ X393 @ id )
= X393 )
=> ( ! [X394: subst,X395: term,X396: term > $o] :
( ~ ! [X397: term] :
( ( $true
= ( X396 @ ( sub @ X397 @ X394 ) ) )
| ( $true
!= ( var @ X397 ) ) )
| ~ ! [X398: term,X399: term] :
( ( $true
= ( X396 @ ( ap @ X398 @ X399 ) ) )
| ( $true
!= ( X396 @ X399 ) )
| ( $true
!= ( X396 @ X398 ) ) )
| ~ ! [X400: term] :
( ~ ! [X401: term] :
( ( $true
!= ( X396 @ X401 ) )
| ( ( X396 @ ( sub @ X400 @ ( push @ X401 @ id ) ) )
= $true ) )
| ( $true
= ( X396 @ ( lam @ X400 ) ) ) )
| ( $true
= ( X396 @ ( sub @ X395 @ X394 ) ) ) )
=> ! [X402: term,X403: term > $o] :
( ~ ! [X404: term] :
( ( ( var @ X404 )
!= $true )
| ( $true
= ( X403 @ X404 ) ) )
| ( $true
= ( X403 @ X402 ) )
| ~ ! [X405: term] :
( ~ ! [X406: term] :
( ( $true
!= ( X403 @ X406 ) )
| ( $true
= ( X403 @ ( sub @ X405 @ ( push @ X406 @ id ) ) ) ) )
| ( $true
= ( X403 @ ( lam @ X405 ) ) ) )
| ~ ! [X407: term,X408: term] :
( ( $true
= ( X403 @ ( ap @ X407 @ X408 ) ) )
| ( $true
!= ( X403 @ X407 ) )
| ( ( X403 @ X408 )
!= $true ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X409: term,X410: term,X411: term,X412: term] :
( ( ( ap @ X412 @ X409 )
!= ( ap @ X411 @ X410 ) )
| ( X409 = X410 ) )
=> ! [X413: term,X414: term,X415: term,X416: term] :
( ( ( ap @ ( sub @ X414 @ id ) @ X413 )
!= ( ap @ ( sub @ X416 @ id ) @ X415 ) )
| ( X413 = X415 ) ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( axassoc = $true )
& ( ( laminj = $true )
<=> ! [X417: term,X418: term] :
( ( X417 = X418 )
| ( ( lam @ X418 )
!= ( lam @ X417 ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X419: term,X420: term,X421: term > $o,X422: subst > term > subst > $o] :
( ~ ! [X423: subst,X424: term,X425: subst,X426: subst] :
( ( $true
= ( X422 @ X425 @ X424 @ ( comp @ X426 @ X423 ) ) )
| ( $true
!= ( X422 @ ( comp @ X425 @ X426 ) @ ( sub @ X424 @ X426 ) @ X423 ) ) )
| ~ ! [X427: term] :
( ( X422 @ id @ X427 @ id )
= ( X421 @ X427 ) )
| ~ ! [X428: subst,X429: term,X430: subst,X431: subst] :
( ( $true
= ( X422 @ ( comp @ X431 @ X430 ) @ ( sub @ X429 @ X430 ) @ X428 ) )
| ( ( X422 @ X431 @ X429 @ ( comp @ X430 @ X428 ) )
!= $true ) )
| ( $true
!= ( X421 @ X420 ) )
| ( $true
!= ( X421 @ X419 ) )
| ( $true
= ( X421 @ ( ap @ X420 @ X419 ) ) )
| ~ ! [X432: term,X433: term] :
( ( $true
= ( X422 @ id @ ( ap @ ( sub @ X433 @ id ) @ X432 ) @ id ) )
| ( $true
!= ( X422 @ id @ X433 @ id ) )
| ( ( X422 @ id @ X432 @ id )
!= $true ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X434: term] :
~ ! [X435: subst > term > term] :
~ ! [X436: term,X437: subst] :
( ( X435 @ X437 @ X436 )
= ( sub @ X434 @ ( push @ X436 @ X437 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X438: subst,X439: term > $o,X440: term,X441: term,X442: term > $o] :
( ( $true
!= ( X439 @ X441 ) )
| ( $true
= ( X442 @ ( sub @ X441 @ ( push @ X440 @ X438 ) ) ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ! [X443: subst > term > term,X444: subst > term > term,X445: term,X446: subst] :
( ~ ! [X450: subst,X451: term,X452: subst] :
( ( sub @ ( X443 @ X452 @ X451 ) @ X450 )
= ( X443 @ ( comp @ X452 @ X450 ) @ ( sub @ X451 @ X450 ) ) )
| ( ( lam @ ( X444 @ sh @ one ) )
!= ( lam @ ( X443 @ sh @ one ) ) )
| ( ( X444 @ X446 @ X445 )
= ( X443 @ X446 @ X445 ) )
| ~ ! [X447: subst,X448: term,X449: subst] :
( ( sub @ ( X444 @ X447 @ X448 ) @ X449 )
= ( X444 @ ( comp @ X447 @ X449 ) @ ( sub @ X448 @ X449 ) ) ) )
<=> ( hoaslaminj = $true ) )
& ! [X453: d_term] : ( d_one = X453 )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop = $true )
& ( ! [X454: term] :
~ ! [X455: subst > term > term] :
( ( X455 @ sh @ one )
!= ( sub @ X454 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axvarshift = $true )
& ( pushprop_gthm = $true )
& ( ( ! [X456: subst] :
( ( comp @ id @ X456 )
= X456 )
=> ( ! [X457: subst] :
( ( comp @ X457 @ id )
= X457 )
=> ( ! [X459: subst] :
( ( comp @ id @ X459 )
= X459 )
& ! [X458: subst] :
( ( comp @ X458 @ id )
= X458 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X460: term > $o,X461: subst > term > subst > $o,X462: term] :
( ( $true
= ( X460 @ ( lam @ X462 ) ) )
| ~ ! [X463: term] :
( ( X461 @ id @ X463 @ id )
= ( X460 @ X463 ) )
| ~ ! [X464: term] :
( ( $true
= ( X460 @ ( sub @ X462 @ ( push @ X464 @ id ) ) ) )
| ( $true
!= ( X460 @ X464 ) ) )
| ~ ! [X465: subst > term > term] :
( ( $true
= ( X461 @ id @ ( lam @ ( X465 @ sh @ one ) ) @ id ) )
| ~ ! [X466: term,X467: subst,X468: subst] :
( ( sub @ ( X465 @ X467 @ X466 ) @ X468 )
= ( X465 @ ( comp @ X467 @ X468 ) @ ( sub @ X466 @ X468 ) ) )
| ~ ! [X469: term] :
( ( $true
!= ( X461 @ id @ X469 @ id ) )
| ( $true
= ( X461 @ id @ ( X465 @ id @ X469 ) @ id ) ) ) ) ) )
& ( ( axvarcons = $true )
<=> ! [X470: term,X471: subst] :
( ( sub @ one @ ( push @ X470 @ X471 ) )
= X470 ) )
& ( axabs = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X472: subst,X473: term] :
( ( sub @ one @ ( push @ X473 @ X472 ) )
= X473 )
=> ( ! [X474: subst,X475: term] :
( ( comp @ sh @ ( push @ X475 @ X474 ) )
= X474 )
=> ! [X476: term > $o,X477: term > $o,X478: term,X479: subst,X480: term] :
( ( ( X477 @ ( sub @ X480 @ ( push @ X478 @ X479 ) ) )
= $true )
| ( $true
!= ( X476 @ X480 ) ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X481: term] :
( ( sub @ X481 @ id )
= X481 )
=> ( ! [X482: subst > term > subst > $o,X483: term] :
( ~ ! [X484: subst > term > term] :
( ~ ! [X485: subst,X486: term,X487: subst] :
( ( X484 @ ( comp @ X485 @ X487 ) @ ( sub @ X486 @ X487 ) )
= ( sub @ ( X484 @ X485 @ X486 ) @ X487 ) )
| ( $true
= ( X482 @ id @ ( lam @ ( X484 @ sh @ one ) ) @ id ) )
| ~ ! [X488: term] :
( ( $true
= ( X482 @ id @ ( X484 @ id @ X488 ) @ id ) )
| ( $true
!= ( X482 @ id @ X488 @ id ) ) ) )
| ( ( X482 @ id @ ( lam @ ( sub @ X483 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X489: term] :
( ( $true
!= ( X482 @ id @ X489 @ id ) )
| ( $true
= ( X482 @ id @ ( sub @ X483 @ ( push @ X489 @ id ) ) @ id ) ) ) )
=> ! [X490: term,X491: subst > term > subst > $o] :
( ~ ! [X492: subst > term > term] :
( ~ ! [X493: term] :
( ( $true
!= ( X491 @ id @ X493 @ id ) )
| ( ( X491 @ id @ ( X492 @ id @ X493 ) @ id )
= $true ) )
| ~ ! [X494: subst,X495: term,X496: subst] :
( ( sub @ ( X492 @ X494 @ X495 ) @ X496 )
= ( X492 @ ( comp @ X494 @ X496 ) @ ( sub @ X495 @ X496 ) ) )
| ( $true
= ( X491 @ id @ ( lam @ ( X492 @ sh @ one ) ) @ id ) ) )
| ~ ! [X497: term] :
( ( $true
= ( X491 @ id @ ( sub @ X490 @ ( push @ X497 @ id ) ) @ id ) )
| ( $true
!= ( X491 @ id @ X497 @ id ) ) )
| ~ ! [X498: subst,X499: subst,X500: subst,X501: term] :
( ( $true
!= ( X491 @ X499 @ X501 @ ( comp @ X500 @ X498 ) ) )
| ( $true
= ( X491 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) @ X498 ) ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) )
| ~ ! [X502: subst,X503: subst,X504: subst,X505: term] :
( ( $true
!= ( X491 @ ( comp @ X503 @ X502 ) @ ( sub @ X505 @ X502 ) @ X504 ) )
| ( $true
= ( X491 @ X503 @ X505 @ ( comp @ X502 @ X504 ) ) ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ( ! [X506: subst > term > subst > $o] :
~ ! [X507: term > $o] :
~ ! [X508: term] :
( ( X506 @ id @ X508 @ id )
= ( X507 @ X508 ) )
=> ( ! [X509: term > $o,X510: term] :
( ~ ! [X511: term,X512: term] :
( ( ( X509 @ X511 )
!= $true )
| ( $true
= ( X509 @ ( ap @ X512 @ X511 ) ) )
| ( $true
!= ( X509 @ X512 ) ) )
| ( $true
= ( X509 @ X510 ) )
| ~ ! [X513: term] :
( ~ ! [X514: term] :
( ( $true
!= ( X509 @ X514 ) )
| ( $true
= ( X509 @ ( sub @ X513 @ ( push @ X514 @ id ) ) ) ) )
| ( $true
= ( X509 @ ( lam @ X513 ) ) ) )
| ~ ! [X515: term] :
( ( $true
!= ( var @ X515 ) )
| ( $true
= ( X509 @ X515 ) ) ) )
=> ( ! [X516: term] :
( ( sub @ X516 @ id )
= X516 )
=> ( ! [X517: term > $o,X518: subst > term > subst > $o,X519: term] :
( ~ ! [X520: term] :
( ( X517 @ X520 )
= ( X518 @ id @ X520 @ id ) )
| ( $true
= ( X517 @ ( lam @ X519 ) ) )
| ~ ! [X521: term] :
( ( ( X517 @ ( sub @ X519 @ ( push @ X521 @ id ) ) )
= $true )
| ( $true
!= ( X517 @ X521 ) ) )
| ~ ! [X522: subst > term > term] :
( ~ ! [X523: term] :
( ( ( X518 @ id @ X523 @ id )
!= $true )
| ( $true
= ( X518 @ id @ ( X522 @ id @ X523 ) @ id ) ) )
| ~ ! [X524: term,X525: subst,X526: subst] :
( ( X522 @ ( comp @ X525 @ X526 ) @ ( sub @ X524 @ X526 ) )
= ( sub @ ( X522 @ X525 @ X524 ) @ X526 ) )
| ( $true
= ( X518 @ id @ ( lam @ ( X522 @ sh @ one ) ) @ id ) ) ) )
=> ! [X527: term,X528: subst > term > subst > $o] :
( ~ ! [X529: term,X530: term] :
( ( $true
!= ( X528 @ id @ X529 @ id ) )
| ( $true
!= ( X528 @ id @ X530 @ id ) )
| ( $true
= ( X528 @ id @ ( ap @ ( sub @ X529 @ id ) @ X530 ) @ id ) ) )
| ~ ! [X531: subst > term > term] :
( ~ ! [X532: term] :
( ( $true
= ( X528 @ id @ ( X531 @ id @ X532 ) @ id ) )
| ( $true
!= ( X528 @ id @ X532 @ id ) ) )
| ( $true
= ( X528 @ id @ ( lam @ ( X531 @ sh @ one ) ) @ id ) )
| ~ ! [X533: term,X534: subst,X535: subst] :
( ( sub @ ( X531 @ X534 @ X533 ) @ X535 )
= ( X531 @ ( comp @ X534 @ X535 ) @ ( sub @ X533 @ X535 ) ) ) )
| ( $true
= ( X528 @ id @ X527 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( axclos = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X536: term] :
~ ! [X537: subst > term > term] :
~ ! [X538: term,X539: subst] :
( ( sub @ X536 @ ( push @ X538 @ X539 ) )
= ( X537 @ X539 @ X538 ) ) )
& ( lamnotap != $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
=> ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( $true
= ( X5 @ one ) )
| ( ( X2 @ X4 )
!= $true )
| ~ ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) ) ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ulamvarind = $true )
& ! [X7: d_term,X8: d_term] :
( ( ( d2term @ X7 )
= ( d2term @ X8 ) )
=> ( X7 = X8 ) )
& ( ( ! [X9: term] :
( ( sub @ X9 @ id )
= X9 )
=> ( ! [X10: subst > term > subst > $o,X11: term] :
( ~ ! [X12: subst > term > term] :
( ~ ! [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( $true
= ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) )
| ~ ! [X16: term] :
( ( $true
= ( X10 @ id @ ( X12 @ id @ X16 ) @ id ) )
| ( ( X10 @ id @ X16 @ id )
!= $true ) ) )
| ( ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X17: term] :
( ( $true
!= ( X10 @ id @ X17 @ id ) )
| ( $true
= ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) ) ) )
=> ! [X18: subst > term > subst > $o,X19: term] :
( ~ ! [X20: term] :
( ( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
= $true )
| ( $true
!= ( X18 @ id @ X20 @ id ) ) )
| ~ ! [X21: subst > term > term] :
( ~ ! [X22: term] :
( ( $true
= ( X18 @ id @ ( X21 @ id @ X22 ) @ id ) )
| ( $true
!= ( X18 @ id @ X22 @ id ) ) )
| ~ ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) )
| ( $true
= ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X18 @ id @ ( lam @ X19 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> ( termmset = $true ) )
& ! [X27: d_subst] : ( d_id = X27 )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( induction = $true )
<=> ! [X28: term > $o,X29: term] :
( ( $true
= ( X28 @ X29 ) )
| ~ ! [X30: term] :
( ( ( X28 @ X30 )
= $true )
| ( $true
!= ( var @ X30 ) ) )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X28 @ ( ap @ X32 @ X31 ) ) )
| ( ( X28 @ X32 )
!= $true )
| ( $true
!= ( X28 @ X31 ) ) )
| ~ ! [X33: term] :
( ( ( X28 @ ( lam @ X33 ) )
= $true )
| ( ( X28 @ X33 )
!= $true ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X34: subst > term > subst > $o] :
~ ! [X35: term > $o] :
~ ! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) ) )
& ( ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
=> ( ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) )
=> ! [X42: term,X43: term,X44: term,X45: term] :
( ( X42 = X43 )
| ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ~ ! [X49: term,X50: term] :
( ( ( X46 @ id @ X50 @ id )
!= $true )
| ( ( X46 @ id @ X49 @ id )
!= $true )
| ( $true
= ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) ) )
| ~ ! [X51: subst,X52: subst,X53: subst,X54: term] :
( ( $true
!= ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) ) )
| ( $true
= ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) ) )
| ~ ! [X55: term,X56: subst,X57: subst,X58: subst] :
( ( $true
!= ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 ) )
| ( $true
= ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) ) )
| ( $true
!= ( X46 @ id @ X48 @ id ) )
| ( $true
= ( X46 @ id @ ( ap @ X48 @ X47 ) @ id ) )
| ( $true
!= ( X46 @ id @ X47 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) )
| ( X59 = X60 ) )
<=> ( apinj1 = $true ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X63: subst > term > subst > $o] :
~ ! [X64: term > $o] :
~ ! [X65: term] :
( ( X64 @ X65 )
= ( X63 @ id @ X65 @ id ) )
=> ( ! [X66: term,X67: term > $o] :
( ( $true
= ( X67 @ X66 ) )
| ~ ! [X68: term] :
( ( $true
!= ( var @ X68 ) )
| ( $true
= ( X67 @ X68 ) ) )
| ~ ! [X69: term,X70: term] :
( ( $true
!= ( X67 @ X69 ) )
| ( ( X67 @ ( ap @ X70 @ X69 ) )
= $true )
| ( ( X67 @ X70 )
!= $true ) )
| ~ ! [X71: term] :
( ( ( X67 @ ( lam @ X71 ) )
= $true )
| ~ ! [X72: term] :
( ( $true
= ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) ) )
| ( ( X67 @ X72 )
!= $true ) ) ) )
=> ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
=> ( ! [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ( $true
= ( X74 @ ( lam @ X76 ) ) )
| ~ ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
| ~ ! [X78: subst > term > term] :
( ~ ! [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) )
| ( ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X82: term] :
( ( $true
= ( X75 @ id @ ( X78 @ id @ X82 ) @ id ) )
| ( $true
!= ( X75 @ id @ X82 @ id ) ) ) )
| ~ ! [X83: term] :
( ( $true
!= ( X74 @ X83 ) )
| ( $true
= ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) ) )
=> ! [X84: term,X85: subst > term > subst > $o] :
( ~ ! [X86: term,X87: term] :
( ( $true
!= ( X85 @ id @ X87 @ id ) )
| ( $true
!= ( X85 @ id @ X86 @ id ) )
| ( ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id )
= $true ) )
| ~ ! [X88: term] :
( ( $true
!= ( var @ ( sub @ X88 @ id ) ) )
| ( $true
= ( X85 @ id @ X88 @ id ) ) )
| ~ ! [X89: subst,X90: subst,X91: term,X92: subst] :
( ( ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
!= $true )
| ( $true
= ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) ) )
| ~ ! [X93: subst,X94: term,X95: subst,X96: subst] :
( ( $true
!= ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) ) )
| ( $true
= ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) ) )
| ~ ! [X97: subst > term > term] :
( ( $true
= ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id ) )
| ~ ! [X98: term] :
( ( ( X85 @ id @ X98 @ id )
!= $true )
| ( $true
= ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) ) )
| ~ ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) ) )
| ( $true
= ( X85 @ id @ X84 @ id ) ) ) ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X102: subst > term > subst > $o] :
~ ! [X103: term > $o] :
~ ! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ( induction2 = $true )
<=> ! [X105: term > $o,X106: term] :
( ~ ! [X107: term] :
( ( $true
!= ( var @ X107 ) )
| ( ( X105 @ X107 )
= $true ) )
| ~ ! [X108: term,X109: term] :
( ( $true
= ( X105 @ ( ap @ X109 @ X108 ) ) )
| ( $true
!= ( X105 @ X108 ) )
| ( $true
!= ( X105 @ X109 ) ) )
| ( $true
= ( X105 @ X106 ) )
| ~ ! [X110: term] :
( ~ ! [X111: term] :
( ( $true
= ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) ) )
| ( $true
!= ( X105 @ X111 ) ) )
| ( ( X105 @ ( lam @ X110 ) )
= $true ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X115: term > $o,X116: term,X117: subst] :
~ ! [X118: term > $o] :
~ ! [X119: term] :
( ( X118 @ X119 )
= ( X115 @ ( sub @ X119 @ ( push @ X116 @ X117 ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X120: term,X121: subst > term > subst > $o] :
( ( $true
= ( X121 @ id @ ( lam @ ( sub @ X120 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X122: term] :
( ( $true
!= ( X121 @ id @ X122 @ id ) )
| ( ( X121 @ id @ ( sub @ X120 @ ( push @ X122 @ id ) ) @ id )
= $true ) )
| ~ ! [X123: subst > term > term] :
( ( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X124: term] :
( ( $true
= ( X121 @ id @ ( X123 @ id @ X124 ) @ id ) )
| ( $true
!= ( X121 @ id @ X124 @ id ) ) )
| ~ ! [X125: subst,X126: subst,X127: term] :
( ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X123 @ X125 @ X127 ) @ X126 ) ) ) ) )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X128: subst > term > subst > $o,X129: term] :
( ( $true
= ( X128 @ id @ X129 @ id ) )
| ~ ! [X130: subst > term > term] :
( ~ ! [X131: term] :
( ( $true
!= ( X128 @ id @ X131 @ id ) )
| ( $true
= ( X128 @ id @ ( X130 @ id @ X131 ) @ id ) ) )
| ~ ! [X132: subst,X133: subst,X134: term] :
( ( sub @ ( X130 @ X132 @ X134 ) @ X133 )
= ( X130 @ ( comp @ X132 @ X133 ) @ ( sub @ X134 @ X133 ) ) )
| ( $true
= ( X128 @ id @ ( lam @ ( X130 @ sh @ one ) ) @ id ) ) )
| ~ ! [X135: term,X136: term] :
( ( ( X128 @ id @ ( ap @ ( sub @ X136 @ id ) @ X135 ) @ id )
= $true )
| ( $true
!= ( X128 @ id @ X135 @ id ) )
| ( $true
!= ( X128 @ id @ X136 @ id ) ) ) ) )
& ( ! [X137: term,X138: subst > term > subst > $o] :
( ( $true
= ( X138 @ id @ X137 @ id ) )
| ~ ! [X139: subst,X140: term,X141: subst,X142: subst] :
( ( $true
= ( X138 @ ( comp @ X139 @ X141 ) @ ( sub @ X140 @ X141 ) @ X142 ) )
| ( $true
!= ( X138 @ X139 @ X140 @ ( comp @ X141 @ X142 ) ) ) )
| ~ ! [X143: subst > term > term] :
( ~ ! [X144: term,X145: subst,X146: subst] :
( ( X143 @ ( comp @ X146 @ X145 ) @ ( sub @ X144 @ X145 ) )
= ( sub @ ( X143 @ X146 @ X144 ) @ X145 ) )
| ~ ! [X147: term] :
( ( $true
!= ( X138 @ id @ X147 @ id ) )
| ( $true
= ( X138 @ id @ ( X143 @ id @ X147 ) @ id ) ) )
| ( $true
= ( X138 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) ) )
| ~ ! [X148: term] :
( ( $true
= ( X138 @ id @ X148 @ id ) )
| ( ( var @ ( sub @ X148 @ id ) )
!= $true ) )
| ~ ! [X149: term,X150: term] :
( ( $true
!= ( X138 @ id @ X149 @ id ) )
| ( $true
!= ( X138 @ id @ X150 @ id ) )
| ( $true
= ( X138 @ id @ ( ap @ ( sub @ X150 @ id ) @ X149 ) @ id ) ) )
| ~ ! [X151: subst,X152: subst,X153: subst,X154: term] :
( ( ( X138 @ X151 @ X154 @ ( comp @ X152 @ X153 ) )
= $true )
| ( $true
!= ( X138 @ ( comp @ X151 @ X152 ) @ ( sub @ X154 @ X152 ) @ X153 ) ) ) )
<=> ( hoasinduction = $true ) )
& ( ! [X155: term > $o,X156: term > $o,X157: subst,X158: term] :
( ( $true
= ( X156 @ one ) )
| ~ ! [X159: term] :
( ( X156 @ X159 )
= ( X155 @ ( sub @ X159 @ ( push @ X158 @ X157 ) ) ) )
| ( $true
!= ( X155 @ X158 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ( axscons = $true )
<=> ! [X160: subst] :
( ( push @ ( sub @ one @ X160 ) @ ( comp @ sh @ X160 ) )
= X160 ) )
& ( ( d2subst @ d_id )
= sh )
& ( substmonoid_gthm = $true )
& ( hoasapnotvar = $true )
& ( hoasapinj1_gthm = $true )
& ( pushprop_lem2v2_gthm = $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 ) ) ) ) )
& ( induction2_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X166: term] :
? [X167: d_term] :
( ( d2term @ X167 )
= X166 )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X168: term,X169: subst > term > subst > $o] :
( ~ ! [X170: subst > term > term] :
( ~ ! [X171: subst,X172: term,X173: subst] :
( ( X170 @ ( comp @ X173 @ X171 ) @ ( sub @ X172 @ X171 ) )
= ( sub @ ( X170 @ X173 @ X172 ) @ X171 ) )
| ( $true
= ( X169 @ id @ ( lam @ ( X170 @ sh @ one ) ) @ id ) )
| ~ ! [X174: term] :
( ( ( X169 @ id @ ( X170 @ id @ X174 ) @ id )
= $true )
| ( $true
!= ( X169 @ id @ X174 @ id ) ) ) )
| ( $true
= ( X169 @ id @ ( lam @ ( sub @ X168 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X175: term] :
( ( $true
= ( X169 @ id @ ( sub @ X168 @ ( push @ X175 @ id ) ) @ id ) )
| ( $true
!= ( X169 @ id @ X175 @ id ) ) ) ) )
& ( ( ! [X176: term,X177: subst] :
( ( sub @ one @ ( push @ X176 @ X177 ) )
= X176 )
=> ( ! [X178: term,X179: subst] :
( ( comp @ sh @ ( push @ X178 @ X179 ) )
= X179 )
=> ( ! [X180: term,X181: term] :
( ( X180 = X181 )
| ( ( lam @ X181 )
!= ( lam @ X180 ) ) )
=> ! [X182: subst > term > term,X183: term,X184: subst,X185: subst > term > term] :
( ~ ! [X186: subst,X187: subst,X188: term] :
( ( sub @ ( X182 @ X186 @ X188 ) @ X187 )
= ( X182 @ ( comp @ X186 @ X187 ) @ ( sub @ X188 @ X187 ) ) )
| ~ ! [X189: subst,X190: subst,X191: term] :
( ( sub @ ( X185 @ X190 @ X191 ) @ X189 )
= ( X185 @ ( comp @ X190 @ X189 ) @ ( sub @ X191 @ X189 ) ) )
| ( ( lam @ ( X185 @ sh @ one ) )
!= ( lam @ ( X182 @ sh @ one ) ) )
| ( ( X182 @ X184 @ X183 )
= ( X185 @ X184 @ X183 ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( axapp = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( pushprop_lem3v2 = $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X192: subst > term > subst > $o,X193: term] :
( ( $true
= ( X192 @ id @ ( lam @ ( sub @ X193 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X194: term] :
( ( ( X192 @ id @ X194 @ id )
!= $true )
| ( $true
= ( X192 @ id @ ( sub @ X193 @ ( push @ X194 @ id ) ) @ id ) ) )
| ~ ! [X195: subst > term > term,X196: term] :
( ~ ! [X197: subst,X198: term,X199: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X198 @ X197 ) @ ( comp @ X199 @ X197 ) ) )
= ( X195 @ ( comp @ X199 @ X197 ) @ ( sub @ X198 @ X197 ) ) )
| ( $true
= ( X192 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id ) )
| ~ ! [X200: subst,X201: term,X202: subst] :
( ( sub @ ( X195 @ X202 @ X201 ) @ X200 )
= ( sub @ ( sub @ X196 @ ( push @ X201 @ X202 ) ) @ X200 ) )
| ~ ! [X203: term] :
( ( $true
!= ( X192 @ id @ X203 @ id ) )
| ( $true
= ( X192 @ id @ ( X195 @ id @ X203 ) @ id ) ) ) ) ) )
& ( axmap = $true )
& ( ( axidr = $true )
<=> ! [X204: subst] :
( ( comp @ X204 @ id )
= X204 ) )
& ( ( axidl = $true )
<=> ! [X205: subst] :
( ( comp @ id @ X205 )
= X205 ) )
& ( termmset_gthm = $true )
& ( ! [X206: subst > term > subst > $o,X207: term] :
( ~ ! [X208: subst,X209: subst,X210: term,X211: subst] :
( ( $true
!= ( X206 @ ( comp @ X211 @ X209 ) @ ( sub @ X210 @ X209 ) @ X208 ) )
| ( ( X206 @ X211 @ X210 @ ( comp @ X209 @ X208 ) )
= $true ) )
| ( $true
= ( X206 @ id @ ( lam @ X207 ) @ id ) )
| ~ ! [X212: subst > term > term] :
( ~ ! [X213: term] :
( ( $true
= ( X206 @ id @ ( X212 @ id @ X213 ) @ id ) )
| ( $true
!= ( X206 @ id @ X213 @ id ) ) )
| ( ( X206 @ id @ ( lam @ ( X212 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X214: subst,X215: term,X216: subst] :
( ( sub @ ( X212 @ X214 @ X215 ) @ X216 )
= ( X212 @ ( comp @ X214 @ X216 ) @ ( sub @ X215 @ X216 ) ) ) )
| ~ ! [X217: subst,X218: subst,X219: term,X220: subst] :
( ( $true
!= ( X206 @ X218 @ X219 @ ( comp @ X217 @ X220 ) ) )
| ( $true
= ( X206 @ ( comp @ X218 @ X217 ) @ ( sub @ X219 @ X217 ) @ X220 ) ) )
| ~ ! [X221: term] :
( ( $true
!= ( X206 @ id @ X221 @ id ) )
| ( $true
= ( X206 @ id @ ( sub @ X207 @ ( push @ X221 @ id ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( hoasapinj2_gthm = $true )
& ( lamnotvar = $true )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X222: term,X223: term > $o,X224: subst > term > subst > $o] :
( ~ ! [X225: subst > term > term] :
( ( $true
= ( X224 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id ) )
| ~ ! [X226: term,X227: subst,X228: subst] :
( ( sub @ ( X225 @ X228 @ X226 ) @ X227 )
= ( X225 @ ( comp @ X228 @ X227 ) @ ( sub @ X226 @ X227 ) ) )
| ~ ! [X229: term] :
( ( ( X224 @ id @ X229 @ id )
!= $true )
| ( $true
= ( X224 @ id @ ( X225 @ id @ X229 ) @ id ) ) ) )
| ~ ! [X230: term] :
( ( $true
!= ( X223 @ X230 ) )
| ( $true
= ( X223 @ ( sub @ X222 @ ( push @ X230 @ id ) ) ) ) )
| ~ ! [X231: subst,X232: subst,X233: term,X234: subst] :
( ( ( X224 @ ( comp @ X232 @ X231 ) @ ( sub @ X233 @ X231 ) @ X234 )
= $true )
| ( ( X224 @ X232 @ X233 @ ( comp @ X231 @ X234 ) )
!= $true ) )
| ~ ! [X235: term,X236: subst,X237: subst,X238: subst] :
( ( $true
= ( X224 @ X236 @ X235 @ ( comp @ X238 @ X237 ) ) )
| ( $true
!= ( X224 @ ( comp @ X236 @ X238 ) @ ( sub @ X235 @ X238 ) @ X237 ) ) )
| ( ( X223 @ ( lam @ X222 ) )
= $true )
| ~ ! [X239: term] :
( ( X223 @ X239 )
= ( X224 @ id @ X239 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( ! [X240: term] :
( ( sub @ X240 @ id )
= X240 )
=> ! [X241: term,X242: term > $o,X243: subst > term > subst > $o] :
( ~ ! [X244: subst,X245: subst,X246: subst,X247: term] :
( ( $true
= ( X243 @ X246 @ X247 @ ( comp @ X245 @ X244 ) ) )
| ( $true
!= ( X243 @ ( comp @ X246 @ X245 ) @ ( sub @ X247 @ X245 ) @ X244 ) ) )
| ~ ! [X248: term] :
( ( $true
!= ( X242 @ X248 ) )
| ( $true
= ( X242 @ ( sub @ X241 @ ( push @ X248 @ id ) ) ) ) )
| ~ ! [X249: subst > term > term] :
( ~ ! [X250: term,X251: subst,X252: subst] :
( ( X249 @ ( comp @ X252 @ X251 ) @ ( sub @ X250 @ X251 ) )
= ( sub @ ( X249 @ X252 @ X250 ) @ X251 ) )
| ~ ! [X253: term] :
( ( ( X243 @ id @ ( X249 @ id @ X253 ) @ id )
= $true )
| ( $true
!= ( X243 @ id @ X253 @ id ) ) )
| ( $true
= ( X243 @ id @ ( lam @ ( X249 @ sh @ one ) ) @ id ) ) )
| ~ ! [X254: term] :
( ( X242 @ X254 )
= ( X243 @ id @ X254 @ id ) )
| ~ ! [X255: subst,X256: term,X257: subst,X258: subst] :
( ( $true
!= ( X243 @ X255 @ X256 @ ( comp @ X257 @ X258 ) ) )
| ( $true
= ( X243 @ ( comp @ X255 @ X257 ) @ ( sub @ X256 @ X257 ) @ X258 ) ) )
| ( $true
= ( X242 @ ( lam @ X241 ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( termmset_lthm = $true )
<=> ( ! [X259: term] :
( ( sub @ X259 @ id )
= X259 )
=> ! [X260: term] :
( ( sub @ X260 @ id )
= X260 ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X261: term] :
~ ! [X262: subst > term > term] :
( ( X262 @ sh @ one )
!= ( sub @ X261 @ ( push @ one @ sh ) ) ) )
& ( apnotvar = $true )
& ( ( ! [X263: term,X264: subst] :
( ( sub @ one @ ( push @ X263 @ X264 ) )
= X263 )
=> ( ! [X265: term,X266: subst] :
( ( comp @ sh @ ( push @ X265 @ X266 ) )
= X266 )
=> ( ! [X267: subst] :
( ( comp @ X267 @ id )
= X267 )
=> ( ! [X268: term > $o,X269: term] :
( ~ ! [X270: term] :
( ( $true
= ( X268 @ ( lam @ X270 ) ) )
| ( $true
!= ( X268 @ X270 ) ) )
| ~ ! [X271: term,X272: term] :
( ( $true
!= ( X268 @ X271 ) )
| ( $true
!= ( X268 @ X272 ) )
| ( $true
= ( X268 @ ( ap @ X272 @ X271 ) ) ) )
| ~ ! [X273: term] :
( ( $true
!= ( var @ X273 ) )
| ( $true
= ( X268 @ X273 ) ) )
| ( $true
= ( X268 @ X269 ) ) )
=> ! [X274: term,X275: subst,X276: term > $o] :
( ~ ! [X277: term,X278: term] :
( ( $true
= ( X276 @ ( ap @ X278 @ X277 ) ) )
| ( $true
!= ( X276 @ X277 ) )
| ( $true
!= ( X276 @ X278 ) ) )
| ~ ! [X279: term] :
( ~ ! [X280: term] :
( ( $true
!= ( X276 @ X280 ) )
| ( $true
= ( X276 @ ( sub @ X279 @ ( push @ X280 @ id ) ) ) ) )
| ( $true
= ( X276 @ ( lam @ X279 ) ) ) )
| ( $true
= ( X276 @ ( sub @ X274 @ X275 ) ) )
| ~ ! [X281: term] :
( ( $true
= ( X276 @ ( sub @ X281 @ X275 ) ) )
| ( $true
!= ( var @ X281 ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ulamvar1 != $true )
& ( ! [X282: term,X283: subst] :
( ( comp @ sh @ ( push @ X282 @ X283 ) )
= X283 )
<=> ( axshiftcons = $true ) )
& ( ! [X284: subst > term > subst > $o,X285: term] :
( ~ ! [X286: term] :
( ( $true
!= ( X284 @ id @ X286 @ id ) )
| ( ( X284 @ id @ ( sub @ X285 @ ( push @ X286 @ id ) ) @ id )
= $true ) )
| ( ( X284 @ id @ ( lam @ X285 ) @ id )
= $true )
| ~ ! [X287: subst > term > term] :
( ~ ! [X288: term] :
( ( $true
!= ( X284 @ id @ X288 @ id ) )
| ( $true
= ( X284 @ id @ ( X287 @ id @ X288 ) @ id ) ) )
| ~ ! [X289: subst,X290: term,X291: subst] :
( ( X287 @ ( comp @ X291 @ X289 ) @ ( sub @ X290 @ X289 ) )
= ( sub @ ( X287 @ X291 @ X290 ) @ X289 ) )
| ( $true
= ( X284 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ! [X292: subst] :
? [X293: d_subst] :
( ( d2subst @ X293 )
= X292 )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X294: term,X295: term,X296: term,X297: term] :
( ( X296 = X297 )
| ( ( ap @ ( sub @ X295 @ id ) @ X296 )
!= ( ap @ ( sub @ X294 @ id ) @ X297 ) ) )
<=> ( hoasapinj2 = $true ) )
& ! [X298: d_subst,X299: d_subst] :
( ( ( d2subst @ X298 )
= ( d2subst @ X299 ) )
=> ( X298 = X299 ) )
& ( ( ! [X300: term > $o,X301: term] :
( ~ ! [X302: term] :
( ( $true
= ( X300 @ ( lam @ X302 ) ) )
| ~ ! [X303: term] :
( ( ( X300 @ ( sub @ X302 @ ( push @ X303 @ id ) ) )
= $true )
| ( $true
!= ( X300 @ X303 ) ) ) )
| ~ ! [X304: term] :
( ( $true
= ( X300 @ X304 ) )
| ( $true
!= ( var @ X304 ) ) )
| ( ( X300 @ X301 )
= $true )
| ~ ! [X305: term,X306: term] :
( ( $true
!= ( X300 @ X306 ) )
| ( $true
= ( X300 @ ( ap @ X306 @ X305 ) ) )
| ( $true
!= ( X300 @ X305 ) ) ) )
=> ( ! [X307: subst > term > subst > $o,X308: term,X309: term] :
( ( ( X307 @ id @ ( ap @ X308 @ X309 ) @ id )
= $true )
| ~ ! [X310: subst,X311: term,X312: subst,X313: subst] :
( ( $true
!= ( X307 @ ( comp @ X313 @ X310 ) @ ( sub @ X311 @ X310 ) @ X312 ) )
| ( $true
= ( X307 @ X313 @ X311 @ ( comp @ X310 @ X312 ) ) ) )
| ~ ! [X314: term,X315: term] :
( ( $true
!= ( X307 @ id @ X314 @ id ) )
| ( $true
= ( X307 @ id @ ( ap @ ( sub @ X314 @ id ) @ X315 ) @ id ) )
| ( $true
!= ( X307 @ id @ X315 @ id ) ) )
| ( $true
!= ( X307 @ id @ X309 @ id ) )
| ( $true
!= ( X307 @ id @ X308 @ id ) )
| ~ ! [X316: term,X317: subst,X318: subst,X319: subst] :
( ( $true
= ( X307 @ ( comp @ X319 @ X317 ) @ ( sub @ X316 @ X317 ) @ X318 ) )
| ( $true
!= ( X307 @ X319 @ X316 @ ( comp @ X317 @ X318 ) ) ) ) )
=> ( ! [X320: subst > term > subst > $o,X321: term] :
( ~ ! [X322: term] :
( ( $true
= ( X320 @ id @ ( sub @ X321 @ ( push @ X322 @ id ) ) @ id ) )
| ( $true
!= ( X320 @ id @ X322 @ id ) ) )
| ( ( X320 @ id @ ( lam @ X321 ) @ id )
= $true )
| ~ ! [X323: subst > term > term] :
( ~ ! [X324: term] :
( ( $true
!= ( X320 @ id @ X324 @ id ) )
| ( $true
= ( X320 @ id @ ( X323 @ id @ X324 ) @ id ) ) )
| ( $true
= ( X320 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id ) )
| ~ ! [X325: subst,X326: subst,X327: term] :
( ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) )
= ( sub @ ( X323 @ X326 @ X327 ) @ X325 ) ) )
| ~ ! [X328: subst,X329: term,X330: subst,X331: subst] :
( ( $true
!= ( X320 @ ( comp @ X330 @ X331 ) @ ( sub @ X329 @ X331 ) @ X328 ) )
| ( $true
= ( X320 @ X330 @ X329 @ ( comp @ X331 @ X328 ) ) ) )
| ~ ! [X332: subst,X333: subst,X334: term,X335: subst] :
( ( $true
= ( X320 @ ( comp @ X333 @ X332 ) @ ( sub @ X334 @ X332 ) @ X335 ) )
| ( $true
!= ( X320 @ X333 @ X334 @ ( comp @ X332 @ X335 ) ) ) ) )
=> ! [X336: term,X337: subst > term > subst > $o] :
( ~ ! [X338: term,X339: term] :
( ( $true
= ( X337 @ id @ ( ap @ ( sub @ X338 @ id ) @ X339 ) @ id ) )
| ( $true
!= ( X337 @ id @ X338 @ id ) )
| ( $true
!= ( X337 @ id @ X339 @ id ) ) )
| ( $true
= ( X337 @ id @ X336 @ id ) )
| ~ ! [X340: term,X341: subst,X342: subst,X343: subst] :
( ( $true
!= ( X337 @ ( comp @ X342 @ X341 ) @ ( sub @ X340 @ X341 ) @ X343 ) )
| ( ( X337 @ X342 @ X340 @ ( comp @ X341 @ X343 ) )
= $true ) )
| ~ ! [X344: term] :
( ( $true
= ( X337 @ id @ X344 @ id ) )
| ( $true
!= ( var @ ( sub @ X344 @ id ) ) ) )
| ~ ! [X345: subst > term > term] :
( ( ( X337 @ id @ ( lam @ ( X345 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X346: term] :
( ( $true
!= ( X337 @ id @ X346 @ id ) )
| ( $true
= ( X337 @ id @ ( X345 @ id @ X346 ) @ id ) ) )
| ~ ! [X347: subst,X348: term,X349: subst] :
( ( sub @ ( X345 @ X347 @ X348 ) @ X349 )
= ( X345 @ ( comp @ X347 @ X349 ) @ ( sub @ X348 @ X349 ) ) ) )
| ~ ! [X350: subst,X351: subst,X352: subst,X353: term] :
( ( $true
!= ( X337 @ X350 @ X353 @ ( comp @ X351 @ X352 ) ) )
| ( $true
= ( X337 @ ( comp @ X350 @ X351 ) @ ( sub @ X353 @ X351 ) @ X352 ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ! [X354: term,X355: term,X356: subst > term > term] :
( ~ ! [X357: subst,X358: term,X359: subst] :
( ( X356 @ ( comp @ X357 @ X359 ) @ ( sub @ X358 @ X359 ) )
= ( sub @ ( X356 @ X357 @ X358 ) @ X359 ) )
| ( ( lam @ ( X356 @ sh @ one ) )
!= ( ap @ ( sub @ X355 @ id ) @ X354 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( ( axvarid = $true )
<=> ! [X360: term] :
( ( sub @ X360 @ id )
= X360 ) )
& ( ! [X361: term,X362: term,X363: term,X364: term] :
( ( ( ap @ ( sub @ X364 @ id ) @ X363 )
!= ( ap @ ( sub @ X362 @ id ) @ X361 ) )
| ( X362 = X364 ) )
<=> ( hoasapinj1 = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ! [X365: subst] :
( ( comp @ id @ X365 )
= X365 )
& ! [X366: subst] :
( ( comp @ X366 @ id )
= X366 ) )
<=> ( substmonoid = $true ) )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction_lem2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lthm = $true )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X367: term] :
~ ! [X368: subst > term > term] :
~ ! [X369: term,X370: subst] :
( ( sub @ X367 @ ( push @ X369 @ X370 ) )
= ( X368 @ X370 @ X369 ) )
=> ( ! [X371: term] :
( ( sub @ X371 @ id )
= X371 )
=> ! [X372: term,X373: term > $o,X374: subst > term > subst > $o] :
( ~ ! [X375: term] :
( ( X373 @ X375 )
= ( X374 @ id @ X375 @ id ) )
| ~ ! [X376: term] :
( ( ( X373 @ ( sub @ X372 @ ( push @ X376 @ id ) ) )
= $true )
| ( $true
!= ( X373 @ X376 ) ) )
| ~ ! [X377: subst > term > term] :
( ~ ! [X378: term] :
( ( $true
!= ( X374 @ id @ X378 @ id ) )
| ( $true
= ( X374 @ id @ ( X377 @ id @ X378 ) @ id ) ) )
| ( $true
= ( X374 @ id @ ( lam @ ( X377 @ sh @ one ) ) @ id ) )
| ~ ! [X379: term,X380: subst,X381: subst] :
( ( sub @ ( X377 @ X381 @ X379 ) @ X380 )
= ( X377 @ ( comp @ X381 @ X380 ) @ ( sub @ X379 @ X380 ) ) ) )
| ( $true
= ( X373 @ ( lam @ X372 ) ) ) ) ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X382: subst,X383: term > $o,X384: term] :
~ ! [X385: term > $o] :
~ ! [X386: term] :
( ( X383 @ ( sub @ X386 @ ( push @ X384 @ X382 ) ) )
= ( X385 @ X386 ) ) )
& ( hoasinduction_gthm = $true )
& ( ! [X387: term,X388: term] :
( ( ( sub @ X387 @ sh )
!= ( sub @ X388 @ sh ) )
| ( X387 = X388 ) )
<=> ( shinj = $true ) )
& ( ( induction2lem = $true )
<=> ! [X389: term > $o,X390: subst,X391: term] :
( ( $true
= ( X389 @ ( sub @ X391 @ X390 ) ) )
| ~ ! [X392: term] :
( ~ ! [X393: term] :
( ( $true
!= ( X389 @ X393 ) )
| ( $true
= ( X389 @ ( sub @ X392 @ ( push @ X393 @ id ) ) ) ) )
| ( ( X389 @ ( lam @ X392 ) )
= $true ) )
| ~ ! [X394: term] :
( ( $true
= ( X389 @ ( sub @ X394 @ X390 ) ) )
| ( $true
!= ( var @ X394 ) ) )
| ~ ! [X395: term,X396: term] :
( ( $true
= ( X389 @ ( ap @ X396 @ X395 ) ) )
| ( $true
!= ( X389 @ X396 ) )
| ( $true
!= ( X389 @ X395 ) ) ) ) )
& ( ulamvarsh = $true )
& ( ! [X397: term,X398: term,X399: term,X400: term] :
( ( ( ap @ X400 @ X399 )
!= ( ap @ X398 @ X397 ) )
| ( X397 = X399 ) )
<=> ( apinj2 = $true ) )
& ( ( ! [X401: term] :
( ( sub @ X401 @ id )
= X401 )
=> ( ! [X402: subst,X403: term,X404: term > $o] :
( ~ ! [X405: term] :
( ( $true
= ( X404 @ ( sub @ X405 @ X402 ) ) )
| ( $true
!= ( var @ X405 ) ) )
| ~ ! [X406: term,X407: term] :
( ( $true
= ( X404 @ ( ap @ X406 @ X407 ) ) )
| ( $true
!= ( X404 @ X407 ) )
| ( $true
!= ( X404 @ X406 ) ) )
| ~ ! [X408: term] :
( ~ ! [X409: term] :
( ( $true
!= ( X404 @ X409 ) )
| ( $true
= ( X404 @ ( sub @ X408 @ ( push @ X409 @ id ) ) ) ) )
| ( $true
= ( X404 @ ( lam @ X408 ) ) ) )
| ( ( X404 @ ( sub @ X403 @ X402 ) )
= $true ) )
=> ! [X410: term,X411: term > $o] :
( ~ ! [X412: term] :
( ( $true
!= ( var @ X412 ) )
| ( $true
= ( X411 @ X412 ) ) )
| ( $true
= ( X411 @ X410 ) )
| ~ ! [X413: term] :
( ~ ! [X414: term] :
( ( ( X411 @ X414 )
!= $true )
| ( ( X411 @ ( sub @ X413 @ ( push @ X414 @ id ) ) )
= $true ) )
| ( $true
= ( X411 @ ( lam @ X413 ) ) ) )
| ~ ! [X415: term,X416: term] :
( ( $true
= ( X411 @ ( ap @ X415 @ X416 ) ) )
| ( ( X411 @ X415 )
!= $true )
| ( $true
!= ( X411 @ X416 ) ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( ( ! [X417: term,X418: term,X419: term,X420: term] :
( ( ( ap @ X419 @ X418 )
!= ( ap @ X420 @ X417 ) )
| ( X417 = X418 ) )
=> ! [X421: term,X422: term,X423: term,X424: term] :
( ( ( ap @ ( sub @ X422 @ id ) @ X421 )
!= ( ap @ ( sub @ X424 @ id ) @ X423 ) )
| ( X421 = X423 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( axassoc = $true )
& ( ( laminj = $true )
<=> ! [X427: term,X428: term] :
( ( ( lam @ X428 )
!= ( lam @ X427 ) )
| ( X427 = X428 ) ) )
& ( pushprop_lem0_gthm = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( ! [X429: term,X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ~ ! [X433: subst,X434: term,X435: subst,X436: subst] :
( ( $true
= ( X432 @ X435 @ X434 @ ( comp @ X436 @ X433 ) ) )
| ( $true
!= ( X432 @ ( comp @ X435 @ X436 ) @ ( sub @ X434 @ X436 ) @ X433 ) ) )
| ~ ! [X437: term] :
( ( X431 @ X437 )
= ( X432 @ id @ X437 @ id ) )
| ~ ! [X438: subst,X439: term,X440: subst,X441: subst] :
( ( $true
= ( X432 @ ( comp @ X441 @ X440 ) @ ( sub @ X439 @ X440 ) @ X438 ) )
| ( $true
!= ( X432 @ X441 @ X439 @ ( comp @ X440 @ X438 ) ) ) )
| ( $true
!= ( X431 @ X430 ) )
| ( $true
!= ( X431 @ X429 ) )
| ( $true
= ( X431 @ ( ap @ X430 @ X429 ) ) )
| ~ ! [X442: term,X443: term] :
( ( $true
= ( X432 @ id @ ( ap @ ( sub @ X443 @ id ) @ X442 ) @ id ) )
| ( ( X432 @ id @ X443 @ id )
!= $true )
| ( $true
!= ( X432 @ id @ X442 @ id ) ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X444: term] :
~ ! [X445: subst > term > term] :
~ ! [X446: term,X447: subst] :
( ( sub @ X444 @ ( push @ X446 @ X447 ) )
= ( X445 @ X447 @ X446 ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X448: subst,X449: term > $o,X450: term,X451: term,X452: term > $o] :
( ( ( X449 @ X451 )
!= $true )
| ( ( X452 @ ( sub @ X451 @ ( push @ X450 @ X448 ) ) )
= $true ) ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ! [X453: subst > term > term,X454: subst > term > term,X455: term,X456: subst] :
( ~ ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( X454 @ X457 @ X458 ) @ X459 )
= ( X454 @ ( comp @ X457 @ X459 ) @ ( sub @ X458 @ X459 ) ) )
| ( ( X453 @ X456 @ X455 )
= ( X454 @ X456 @ X455 ) )
| ~ ! [X460: subst,X461: term,X462: subst] :
( ( sub @ ( X453 @ X462 @ X461 ) @ X460 )
= ( X453 @ ( comp @ X462 @ X460 ) @ ( sub @ X461 @ X460 ) ) )
| ( ( lam @ ( X454 @ sh @ one ) )
!= ( lam @ ( X453 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ! [X463: d_term] : ( d_one = X463 )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop = $true )
& ( ! [X464: term] :
~ ! [X465: subst > term > term] :
( ( X465 @ sh @ one )
!= ( sub @ X464 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( axvarshift = $true )
& ( pushprop_gthm = $true )
& ( ( ! [X466: subst] :
( ( comp @ id @ X466 )
= X466 )
=> ( ! [X467: subst] :
( ( comp @ X467 @ id )
= X467 )
=> ( ! [X468: subst] :
( ( comp @ X468 @ id )
= X468 )
& ! [X469: subst] :
( ( comp @ id @ X469 )
= X469 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X470: term > $o,X471: subst > term > subst > $o,X472: term] :
( ( $true
= ( X470 @ ( lam @ X472 ) ) )
| ~ ! [X473: term] :
( ( X471 @ id @ X473 @ id )
= ( X470 @ X473 ) )
| ~ ! [X474: term] :
( ( $true
= ( X470 @ ( sub @ X472 @ ( push @ X474 @ id ) ) ) )
| ( $true
!= ( X470 @ X474 ) ) )
| ~ ! [X475: subst > term > term] :
( ( $true
= ( X471 @ id @ ( lam @ ( X475 @ sh @ one ) ) @ id ) )
| ~ ! [X476: term,X477: subst,X478: subst] :
( ( sub @ ( X475 @ X477 @ X476 ) @ X478 )
= ( X475 @ ( comp @ X477 @ X478 ) @ ( sub @ X476 @ X478 ) ) )
| ~ ! [X479: term] :
( ( $true
!= ( X471 @ id @ X479 @ id ) )
| ( $true
= ( X471 @ id @ ( X475 @ id @ X479 ) @ id ) ) ) ) ) )
& ( ! [X480: term,X481: subst] :
( ( sub @ one @ ( push @ X480 @ X481 ) )
= X480 )
<=> ( axvarcons = $true ) )
& ( axabs = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X482: subst,X483: term] :
( ( sub @ one @ ( push @ X483 @ X482 ) )
= X483 )
=> ( ! [X484: subst,X485: term] :
( ( comp @ sh @ ( push @ X485 @ X484 ) )
= X484 )
=> ! [X486: term > $o,X487: term > $o,X488: term,X489: subst,X490: term] :
( ( $true
= ( X487 @ ( sub @ X490 @ ( push @ X488 @ X489 ) ) ) )
| ( $true
!= ( X486 @ X490 ) ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X491: term] :
( ( sub @ X491 @ id )
= X491 )
=> ( ! [X492: subst > term > subst > $o,X493: term] :
( ~ ! [X494: subst > term > term] :
( ~ ! [X495: subst,X496: term,X497: subst] :
( ( X494 @ ( comp @ X495 @ X497 ) @ ( sub @ X496 @ X497 ) )
= ( sub @ ( X494 @ X495 @ X496 ) @ X497 ) )
| ( $true
= ( X492 @ id @ ( lam @ ( X494 @ sh @ one ) ) @ id ) )
| ~ ! [X498: term] :
( ( $true
= ( X492 @ id @ ( X494 @ id @ X498 ) @ id ) )
| ( $true
!= ( X492 @ id @ X498 @ id ) ) ) )
| ( $true
= ( X492 @ id @ ( lam @ ( sub @ X493 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X499: term] :
( ( $true
!= ( X492 @ id @ X499 @ id ) )
| ( $true
= ( X492 @ id @ ( sub @ X493 @ ( push @ X499 @ id ) ) @ id ) ) ) )
=> ! [X500: term,X501: subst > term > subst > $o] :
( ~ ! [X502: subst > term > term] :
( ~ ! [X503: term] :
( ( $true
!= ( X501 @ id @ X503 @ id ) )
| ( $true
= ( X501 @ id @ ( X502 @ id @ X503 ) @ id ) ) )
| ~ ! [X504: subst,X505: term,X506: subst] :
( ( sub @ ( X502 @ X504 @ X505 ) @ X506 )
= ( X502 @ ( comp @ X504 @ X506 ) @ ( sub @ X505 @ X506 ) ) )
| ( ( X501 @ id @ ( lam @ ( X502 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X507: term] :
( ( $true
= ( X501 @ id @ ( sub @ X500 @ ( push @ X507 @ id ) ) @ id ) )
| ( $true
!= ( X501 @ id @ X507 @ id ) ) )
| ~ ! [X508: subst,X509: subst,X510: subst,X511: term] :
( ( $true
!= ( X501 @ X509 @ X511 @ ( comp @ X510 @ X508 ) ) )
| ( $true
= ( X501 @ ( comp @ X509 @ X510 ) @ ( sub @ X511 @ X510 ) @ X508 ) ) )
| ( $true
= ( X501 @ id @ ( lam @ X500 ) @ id ) )
| ~ ! [X512: subst,X513: subst,X514: subst,X515: term] :
( ( ( X501 @ ( comp @ X513 @ X512 ) @ ( sub @ X515 @ X512 ) @ X514 )
!= $true )
| ( $true
= ( X501 @ X513 @ X515 @ ( comp @ X512 @ X514 ) ) ) ) ) ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ( ! [X516: subst > term > subst > $o] :
~ ! [X517: term > $o] :
~ ! [X518: term] :
( ( X517 @ X518 )
= ( X516 @ id @ X518 @ id ) )
=> ( ! [X519: term > $o,X520: term] :
( ~ ! [X521: term,X522: term] :
( ( $true
!= ( X519 @ X521 ) )
| ( $true
= ( X519 @ ( ap @ X522 @ X521 ) ) )
| ( ( X519 @ X522 )
!= $true ) )
| ( $true
= ( X519 @ X520 ) )
| ~ ! [X523: term] :
( ~ ! [X524: term] :
( ( $true
!= ( X519 @ X524 ) )
| ( $true
= ( X519 @ ( sub @ X523 @ ( push @ X524 @ id ) ) ) ) )
| ( $true
= ( X519 @ ( lam @ X523 ) ) ) )
| ~ ! [X525: term] :
( ( ( var @ X525 )
!= $true )
| ( $true
= ( X519 @ X525 ) ) ) )
=> ( ! [X526: term] :
( ( sub @ X526 @ id )
= X526 )
=> ( ! [X527: term > $o,X528: subst > term > subst > $o,X529: term] :
( ~ ! [X530: term] :
( ( X527 @ X530 )
= ( X528 @ id @ X530 @ id ) )
| ( $true
= ( X527 @ ( lam @ X529 ) ) )
| ~ ! [X531: term] :
( ( $true
= ( X527 @ ( sub @ X529 @ ( push @ X531 @ id ) ) ) )
| ( $true
!= ( X527 @ X531 ) ) )
| ~ ! [X532: subst > term > term] :
( ~ ! [X533: term] :
( ( $true
!= ( X528 @ id @ X533 @ id ) )
| ( $true
= ( X528 @ id @ ( X532 @ id @ X533 ) @ id ) ) )
| ~ ! [X534: term,X535: subst,X536: subst] :
( ( X532 @ ( comp @ X535 @ X536 ) @ ( sub @ X534 @ X536 ) )
= ( sub @ ( X532 @ X535 @ X534 ) @ X536 ) )
| ( $true
= ( X528 @ id @ ( lam @ ( X532 @ sh @ one ) ) @ id ) ) ) )
=> ! [X537: term,X538: subst > term > subst > $o] :
( ~ ! [X539: term,X540: term] :
( ( $true
!= ( X538 @ id @ X539 @ id ) )
| ( $true
!= ( X538 @ id @ X540 @ id ) )
| ( $true
= ( X538 @ id @ ( ap @ ( sub @ X539 @ id ) @ X540 ) @ id ) ) )
| ~ ! [X541: subst > term > term] :
( ~ ! [X542: term] :
( ( $true
= ( X538 @ id @ ( X541 @ id @ X542 ) @ id ) )
| ( $true
!= ( X538 @ id @ X542 @ id ) ) )
| ( $true
= ( X538 @ id @ ( lam @ ( X541 @ sh @ one ) ) @ id ) )
| ~ ! [X543: term,X544: subst,X545: subst] :
( ( X541 @ ( comp @ X544 @ X545 ) @ ( sub @ X543 @ X545 ) )
= ( sub @ ( X541 @ X544 @ X543 ) @ X545 ) ) )
| ( $true
= ( X538 @ id @ X537 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( axclos = $true )
& ( ! [X546: term] :
~ ! [X547: subst > term > term] :
~ ! [X548: term,X549: subst] :
( ( sub @ X546 @ ( push @ X548 @ X549 ) )
= ( X547 @ X549 @ X548 ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( lamnotap != $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( pushprop_lem1v2_lthm
<=> ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
=> ! [X2: term > $o,X3: subst,X4: term,X5: term > $o] :
( ( X5 @ one )
| ~ ( X2 @ X4 )
| ~ ! [X6: term] :
( ( X2 @ ( sub @ X6 @ ( push @ X4 @ X3 ) ) )
= ( X5 @ X6 ) ) ) ) )
& hoasinduction_lem1v2
& hoasinduction_lem1_lthm
& ulamvarind
& ! [X7: d_term,X8: d_term] :
( ( ( d2term @ X7 )
= ( d2term @ X8 ) )
=> ( X7 = X8 ) )
& ( ( ! [X9: term] :
( ( sub @ X9 @ id )
= X9 )
=> ( ! [X10: subst > term > subst > $o,X11: term] :
( ~ ! [X12: subst > term > term] :
( ~ ! [X13: subst,X14: term,X15: subst] :
( ( X12 @ ( comp @ X13 @ X15 ) @ ( sub @ X14 @ X15 ) )
= ( sub @ ( X12 @ X13 @ X14 ) @ X15 ) )
| ( X10 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id )
| ~ ! [X16: term] :
( ( X10 @ id @ ( X12 @ id @ X16 ) @ id )
| ~ ( X10 @ id @ X16 @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X11 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X17: term] :
( ~ ( X10 @ id @ X17 @ id )
| ( X10 @ id @ ( sub @ X11 @ ( push @ X17 @ id ) ) @ id ) ) )
=> ! [X18: subst > term > subst > $o,X19: term] :
( ~ ! [X20: term] :
( ( X18 @ id @ ( sub @ X19 @ ( push @ X20 @ id ) ) @ id )
| ~ ( X18 @ id @ X20 @ id ) )
| ~ ! [X21: subst > term > term] :
( ~ ! [X22: term] :
( ( X18 @ id @ ( X21 @ id @ X22 ) @ id )
| ~ ( X18 @ id @ X22 @ id ) )
| ~ ! [X23: term,X24: subst,X25: subst] :
( ( X21 @ ( comp @ X24 @ X25 ) @ ( sub @ X23 @ X25 ) )
= ( sub @ ( X21 @ X24 @ X23 ) @ X25 ) )
| ( X18 @ id @ ( lam @ ( X21 @ sh @ one ) ) @ id ) )
| ( X18 @ id @ ( lam @ X19 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X26: term] :
( ( sub @ X26 @ id )
= X26 )
<=> termmset )
& ! [X27: d_subst] : ( d_id = X27 )
& ~ ( var @ ( d2term @ d_one ) )
& ( induction
<=> ! [X28: term > $o,X29: term] :
( ( X28 @ X29 )
| ~ ! [X30: term] :
( ( X28 @ X30 )
| ~ ( var @ X30 ) )
| ~ ! [X31: term,X32: term] :
( ( X28 @ ( ap @ X32 @ X31 ) )
| ~ ( X28 @ X32 )
| ~ ( X28 @ X31 ) )
| ~ ! [X33: term] :
( ( X28 @ ( lam @ X33 ) )
| ~ ( X28 @ X33 ) ) ) )
& pushprop_lthm_orig
& ( hoasinduction_lem0_lthm
<=> ! [X34: subst > term > subst > $o] :
~ ! [X35: term > $o] :
~ ! [X36: term] :
( ( X34 @ id @ X36 @ id )
= ( X35 @ X36 ) ) )
& ( ( ! [X37: term] :
( ( sub @ X37 @ id )
= X37 )
=> ( ! [X38: term,X39: term,X40: term,X41: term] :
( ( ( ap @ X38 @ X41 )
!= ( ap @ X40 @ X39 ) )
| ( X38 = X40 ) )
=> ! [X42: term,X43: term,X44: term,X45: term] :
( ( ( ap @ ( sub @ X42 @ id ) @ X45 )
!= ( ap @ ( sub @ X43 @ id ) @ X44 ) )
| ( X42 = X43 ) ) ) )
<=> hoasapinj1_lthm )
& ( ! [X46: subst > term > subst > $o,X47: term,X48: term] :
( ~ ! [X49: term,X50: term] :
( ~ ( X46 @ id @ X50 @ id )
| ~ ( X46 @ id @ X49 @ id )
| ( X46 @ id @ ( ap @ ( sub @ X50 @ id ) @ X49 ) @ id ) )
| ~ ! [X51: subst,X52: subst,X53: subst,X54: term] :
( ~ ( X46 @ X52 @ X54 @ ( comp @ X51 @ X53 ) )
| ( X46 @ ( comp @ X52 @ X51 ) @ ( sub @ X54 @ X51 ) @ X53 ) )
| ~ ! [X55: term,X56: subst,X57: subst,X58: subst] :
( ~ ( X46 @ ( comp @ X58 @ X56 ) @ ( sub @ X55 @ X56 ) @ X57 )
| ( X46 @ X58 @ X55 @ ( comp @ X56 @ X57 ) ) )
| ~ ( X46 @ id @ X48 @ id )
| ( X46 @ id @ ( ap @ X48 @ X47 ) @ id )
| ~ ( X46 @ id @ X47 @ id ) )
<=> hoasinduction_lem2 )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( X59 = X60 )
| ( ( ap @ X59 @ X62 )
!= ( ap @ X60 @ X61 ) ) )
<=> apinj1 )
& ( hoasinduction_lthm_3
<=> ( ! [X63: subst > term > subst > $o] :
~ ! [X64: term > $o] :
~ ! [X65: term] :
( ( X64 @ X65 )
= ( X63 @ id @ X65 @ id ) )
=> ( ! [X66: term,X67: term > $o] :
( ( X67 @ X66 )
| ~ ! [X68: term] :
( ~ ( var @ X68 )
| ( X67 @ X68 ) )
| ~ ! [X69: term,X70: term] :
( ~ ( X67 @ X69 )
| ( X67 @ ( ap @ X70 @ X69 ) )
| ~ ( X67 @ X70 ) )
| ~ ! [X71: term] :
( ( X67 @ ( lam @ X71 ) )
| ~ ! [X72: term] :
( ( X67 @ ( sub @ X71 @ ( push @ X72 @ id ) ) )
| ~ ( X67 @ X72 ) ) ) )
=> ( ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
=> ( ! [X74: term > $o,X75: subst > term > subst > $o,X76: term] :
( ( X74 @ ( lam @ X76 ) )
| ~ ! [X77: term] :
( ( X74 @ X77 )
= ( X75 @ id @ X77 @ id ) )
| ~ ! [X78: subst > term > term] :
( ~ ! [X79: term,X80: subst,X81: subst] :
( ( X78 @ ( comp @ X81 @ X80 ) @ ( sub @ X79 @ X80 ) )
= ( sub @ ( X78 @ X81 @ X79 ) @ X80 ) )
| ( X75 @ id @ ( lam @ ( X78 @ sh @ one ) ) @ id )
| ~ ! [X82: term] :
( ( X75 @ id @ ( X78 @ id @ X82 ) @ id )
| ~ ( X75 @ id @ X82 @ id ) ) )
| ~ ! [X83: term] :
( ~ ( X74 @ X83 )
| ( X74 @ ( sub @ X76 @ ( push @ X83 @ id ) ) ) ) )
=> ! [X84: term,X85: subst > term > subst > $o] :
( ~ ! [X86: term,X87: term] :
( ~ ( X85 @ id @ X87 @ id )
| ~ ( X85 @ id @ X86 @ id )
| ( X85 @ id @ ( ap @ ( sub @ X87 @ id ) @ X86 ) @ id ) )
| ~ ! [X88: term] :
( ~ ( var @ ( sub @ X88 @ id ) )
| ( X85 @ id @ X88 @ id ) )
| ~ ! [X89: subst,X90: subst,X91: term,X92: subst] :
( ~ ( X85 @ ( comp @ X90 @ X92 ) @ ( sub @ X91 @ X92 ) @ X89 )
| ( X85 @ X90 @ X91 @ ( comp @ X92 @ X89 ) ) )
| ~ ! [X93: subst,X94: term,X95: subst,X96: subst] :
( ~ ( X85 @ X96 @ X94 @ ( comp @ X93 @ X95 ) )
| ( X85 @ ( comp @ X96 @ X93 ) @ ( sub @ X94 @ X93 ) @ X95 ) )
| ~ ! [X97: subst > term > term] :
( ( X85 @ id @ ( lam @ ( X97 @ sh @ one ) ) @ id )
| ~ ! [X98: term] :
( ~ ( X85 @ id @ X98 @ id )
| ( X85 @ id @ ( X97 @ id @ X98 ) @ id ) )
| ~ ! [X99: subst,X100: subst,X101: term] :
( ( X97 @ ( comp @ X99 @ X100 ) @ ( sub @ X101 @ X100 ) )
= ( sub @ ( X97 @ X99 @ X101 ) @ X100 ) ) )
| ( X85 @ id @ X84 @ id ) ) ) ) ) ) )
& hoaslamnotvar_lthm
& ( ! [X102: subst > term > subst > $o] :
~ ! [X103: term > $o] :
~ ! [X104: term] :
( ( X102 @ id @ X104 @ id )
= ( X103 @ X104 ) )
<=> hoasinduction_lem0 )
& ( induction2
<=> ! [X105: term > $o,X106: term] :
( ~ ! [X107: term] :
( ~ ( var @ X107 )
| ( X105 @ X107 ) )
| ~ ! [X108: term,X109: term] :
( ( X105 @ ( ap @ X109 @ X108 ) )
| ~ ( X105 @ X108 )
| ~ ( X105 @ X109 ) )
| ( X105 @ X106 )
| ~ ! [X110: term] :
( ~ ! [X111: term] :
( ( X105 @ ( sub @ X110 @ ( push @ X111 @ id ) ) )
| ~ ( X105 @ X111 ) )
| ( X105 @ ( lam @ X110 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [X112: subst > term > subst > $o,X113: term > $o] :
! [X114: term] :
( ( X112 @ id @ X114 @ id )
= ( X113 @ X114 ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X115: term > $o,X116: term,X117: subst] :
~ ! [X118: term > $o] :
~ ! [X119: term] :
( ( X118 @ X119 )
= ( X115 @ ( sub @ X119 @ ( push @ X116 @ X117 ) ) ) ) )
& ( hoasinduction_lem3aa
<=> ! [X120: term,X121: subst > term > subst > $o] :
( ( X121 @ id @ ( lam @ ( sub @ X120 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X122: term] :
( ~ ( X121 @ id @ X122 @ id )
| ( X121 @ id @ ( sub @ X120 @ ( push @ X122 @ id ) ) @ id ) )
| ~ ! [X123: subst > term > term] :
( ( X121 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id )
| ~ ! [X124: term] :
( ( X121 @ id @ ( X123 @ id @ X124 ) @ id )
| ~ ( X121 @ id @ X124 @ id ) )
| ~ ! [X125: subst,X126: subst,X127: term] :
( ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) )
= ( sub @ ( X123 @ X125 @ X127 ) @ X126 ) ) ) ) )
& ( hoasinduction_no_psi_cond
<=> ! [X128: subst > term > subst > $o,X129: term] :
( ( X128 @ id @ X129 @ id )
| ~ ! [X130: subst > term > term] :
( ~ ! [X131: term] :
( ~ ( X128 @ id @ X131 @ id )
| ( X128 @ id @ ( X130 @ id @ X131 ) @ id ) )
| ~ ! [X132: subst,X133: subst,X134: term] :
( ( sub @ ( X130 @ X132 @ X134 ) @ X133 )
= ( X130 @ ( comp @ X132 @ X133 ) @ ( sub @ X134 @ X133 ) ) )
| ( X128 @ id @ ( lam @ ( X130 @ sh @ one ) ) @ id ) )
| ~ ! [X135: term,X136: term] :
( ( X128 @ id @ ( ap @ ( sub @ X136 @ id ) @ X135 ) @ id )
| ~ ( X128 @ id @ X135 @ id )
| ~ ( X128 @ id @ X136 @ id ) ) ) )
& ( ! [X137: term,X138: subst > term > subst > $o] :
( ( X138 @ id @ X137 @ id )
| ~ ! [X139: subst,X140: term,X141: subst,X142: subst] :
( ( X138 @ ( comp @ X139 @ X141 ) @ ( sub @ X140 @ X141 ) @ X142 )
| ~ ( X138 @ X139 @ X140 @ ( comp @ X141 @ X142 ) ) )
| ~ ! [X143: subst > term > term] :
( ~ ! [X144: term,X145: subst,X146: subst] :
( ( X143 @ ( comp @ X146 @ X145 ) @ ( sub @ X144 @ X145 ) )
= ( sub @ ( X143 @ X146 @ X144 ) @ X145 ) )
| ~ ! [X147: term] :
( ~ ( X138 @ id @ X147 @ id )
| ( X138 @ id @ ( X143 @ id @ X147 ) @ id ) )
| ( X138 @ id @ ( lam @ ( X143 @ sh @ one ) ) @ id ) )
| ~ ! [X148: term] :
( ( X138 @ id @ X148 @ id )
| ~ ( var @ ( sub @ X148 @ id ) ) )
| ~ ! [X149: term,X150: term] :
( ~ ( X138 @ id @ X149 @ id )
| ~ ( X138 @ id @ X150 @ id )
| ( X138 @ id @ ( ap @ ( sub @ X150 @ id ) @ X149 ) @ id ) )
| ~ ! [X151: subst,X152: subst,X153: subst,X154: term] :
( ( X138 @ X151 @ X154 @ ( comp @ X152 @ X153 ) )
| ~ ( X138 @ ( comp @ X151 @ X152 ) @ ( sub @ X154 @ X152 ) @ X153 ) ) )
<=> hoasinduction )
& ( ! [X155: term > $o,X156: term > $o,X157: subst,X158: term] :
( ( X156 @ one )
| ~ ! [X159: term] :
( ( X156 @ X159 )
= ( X155 @ ( sub @ X159 @ ( push @ X158 @ X157 ) ) ) )
| ~ ( X155 @ X158 ) )
<=> pushprop_lem1v2 )
& hoasapnotvar_gthm
& ( axscons
<=> ! [X160: subst] :
( ( push @ ( sub @ one @ X160 ) @ ( comp @ sh @ X160 ) )
= X160 ) )
& ( ( d2subst @ d_id )
= sh )
& substmonoid_gthm
& hoasapnotvar
& hoasapinj1_gthm
& pushprop_lem2v2_gthm
& ( pushprop_p_and_p_prime
= ( ^ [X161: term,X162: subst,X163: term > $o,X164: term > $o] :
! [X165: term] :
( ( X163 @ ( sub @ X165 @ ( push @ X161 @ X162 ) ) )
= ( X164 @ X165 ) ) ) )
& induction2_gthm
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X166: term] :
? [X167: d_term] :
( ( d2term @ X167 )
= X166 )
& ( hoasinduction_lem3aa_lthm
<=> ! [X168: term,X169: subst > term > subst > $o] :
( ~ ! [X170: subst > term > term] :
( ~ ! [X171: subst,X172: term,X173: subst] :
( ( X170 @ ( comp @ X173 @ X171 ) @ ( sub @ X172 @ X171 ) )
= ( sub @ ( X170 @ X173 @ X172 ) @ X171 ) )
| ( X169 @ id @ ( lam @ ( X170 @ sh @ one ) ) @ id )
| ~ ! [X174: term] :
( ( X169 @ id @ ( X170 @ id @ X174 ) @ id )
| ~ ( X169 @ id @ X174 @ id ) ) )
| ( X169 @ id @ ( lam @ ( sub @ X168 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X175: term] :
( ( X169 @ id @ ( sub @ X168 @ ( push @ X175 @ id ) ) @ id )
| ~ ( X169 @ id @ X175 @ id ) ) ) )
& ( ( ! [X176: term,X177: subst] :
( ( sub @ one @ ( push @ X176 @ X177 ) )
= X176 )
=> ( ! [X178: term,X179: subst] :
( ( comp @ sh @ ( push @ X178 @ X179 ) )
= X179 )
=> ( ! [X180: term,X181: term] :
( ( X180 = X181 )
| ( ( lam @ X181 )
!= ( lam @ X180 ) ) )
=> ! [X182: subst > term > term,X183: term,X184: subst,X185: subst > term > term] :
( ~ ! [X186: subst,X187: subst,X188: term] :
( ( sub @ ( X182 @ X186 @ X188 ) @ X187 )
= ( X182 @ ( comp @ X186 @ X187 ) @ ( sub @ X188 @ X187 ) ) )
| ~ ! [X189: subst,X190: subst,X191: term] :
( ( sub @ ( X185 @ X190 @ X191 ) @ X189 )
= ( X185 @ ( comp @ X190 @ X189 ) @ ( sub @ X191 @ X189 ) ) )
| ( ( lam @ ( X185 @ sh @ one ) )
!= ( lam @ ( X182 @ sh @ one ) ) )
| ( ( X182 @ X184 @ X183 )
= ( X185 @ X184 @ X183 ) ) ) ) ) )
<=> hoaslaminj_lthm )
& axapp
& hoasinduction_lem2v2_gthm
& ( one
= ( d2term @ d_one ) )
& pushprop_lem3v2
& ( hoasinduction_lem3aaa
<=> ! [X192: subst > term > subst > $o,X193: term] :
( ( X192 @ id @ ( lam @ ( sub @ X193 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X194: term] :
( ~ ( X192 @ id @ X194 @ id )
| ( X192 @ id @ ( sub @ X193 @ ( push @ X194 @ id ) ) @ id ) )
| ~ ! [X195: subst > term > term,X196: term] :
( ~ ! [X197: subst,X198: term,X199: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X198 @ X197 ) @ ( comp @ X199 @ X197 ) ) )
= ( X195 @ ( comp @ X199 @ X197 ) @ ( sub @ X198 @ X197 ) ) )
| ( X192 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
| ~ ! [X200: subst,X201: term,X202: subst] :
( ( sub @ ( X195 @ X202 @ X201 ) @ X200 )
= ( sub @ ( sub @ X196 @ ( push @ X201 @ X202 ) ) @ X200 ) )
| ~ ! [X203: term] :
( ~ ( X192 @ id @ X203 @ id )
| ( X192 @ id @ ( X195 @ id @ X203 ) @ id ) ) ) ) )
& axmap
& ( axidr
<=> ! [X204: subst] :
( ( comp @ X204 @ id )
= X204 ) )
& ( axidl
<=> ! [X205: subst] :
( ( comp @ id @ X205 )
= X205 ) )
& termmset_gthm
& ( ! [X206: subst > term > subst > $o,X207: term] :
( ~ ! [X208: subst,X209: subst,X210: term,X211: subst] :
( ~ ( X206 @ ( comp @ X211 @ X209 ) @ ( sub @ X210 @ X209 ) @ X208 )
| ( X206 @ X211 @ X210 @ ( comp @ X209 @ X208 ) ) )
| ( X206 @ id @ ( lam @ X207 ) @ id )
| ~ ! [X212: subst > term > term] :
( ~ ! [X213: term] :
( ( X206 @ id @ ( X212 @ id @ X213 ) @ id )
| ~ ( X206 @ id @ X213 @ id ) )
| ( X206 @ id @ ( lam @ ( X212 @ sh @ one ) ) @ id )
| ~ ! [X214: subst,X215: term,X216: subst] :
( ( sub @ ( X212 @ X214 @ X215 ) @ X216 )
= ( X212 @ ( comp @ X214 @ X216 ) @ ( sub @ X215 @ X216 ) ) ) )
| ~ ! [X217: subst,X218: subst,X219: term,X220: subst] :
( ~ ( X206 @ X218 @ X219 @ ( comp @ X217 @ X220 ) )
| ( X206 @ ( comp @ X218 @ X217 ) @ ( sub @ X219 @ X217 ) @ X220 ) )
| ~ ! [X221: term] :
( ~ ( X206 @ id @ X221 @ id )
| ( X206 @ id @ ( sub @ X207 @ ( push @ X221 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3 )
& hoasapinj2_gthm
& lamnotvar
& hoaslamnotvar
& hoasinduction_lem3_gthm
& ( ! [X222: term,X223: term > $o,X224: subst > term > subst > $o] :
( ~ ! [X225: subst > term > term] :
( ( X224 @ id @ ( lam @ ( X225 @ sh @ one ) ) @ id )
| ~ ! [X226: term,X227: subst,X228: subst] :
( ( sub @ ( X225 @ X228 @ X226 ) @ X227 )
= ( X225 @ ( comp @ X228 @ X227 ) @ ( sub @ X226 @ X227 ) ) )
| ~ ! [X229: term] :
( ~ ( X224 @ id @ X229 @ id )
| ( X224 @ id @ ( X225 @ id @ X229 ) @ id ) ) )
| ~ ! [X230: term] :
( ~ ( X223 @ X230 )
| ( X223 @ ( sub @ X222 @ ( push @ X230 @ id ) ) ) )
| ~ ! [X231: subst,X232: subst,X233: term,X234: subst] :
( ( X224 @ ( comp @ X232 @ X231 ) @ ( sub @ X233 @ X231 ) @ X234 )
| ~ ( X224 @ X232 @ X233 @ ( comp @ X231 @ X234 ) ) )
| ~ ! [X235: term,X236: subst,X237: subst,X238: subst] :
( ( X224 @ X236 @ X235 @ ( comp @ X238 @ X237 ) )
| ~ ( X224 @ ( comp @ X236 @ X238 ) @ ( sub @ X235 @ X238 ) @ X237 ) )
| ( X223 @ ( lam @ X222 ) )
| ~ ! [X239: term] :
( ( X223 @ X239 )
= ( X224 @ id @ X239 @ id ) ) )
<=> hoasinduction_lem3v2 )
& ( ( ! [X240: term] :
( ( sub @ X240 @ id )
= X240 )
=> ! [X241: term,X242: term > $o,X243: subst > term > subst > $o] :
( ~ ! [X244: subst,X245: subst,X246: subst,X247: term] :
( ( X243 @ X246 @ X247 @ ( comp @ X245 @ X244 ) )
| ~ ( X243 @ ( comp @ X246 @ X245 ) @ ( sub @ X247 @ X245 ) @ X244 ) )
| ~ ! [X248: term] :
( ~ ( X242 @ X248 )
| ( X242 @ ( sub @ X241 @ ( push @ X248 @ id ) ) ) )
| ~ ! [X249: subst > term > term] :
( ~ ! [X250: term,X251: subst,X252: subst] :
( ( X249 @ ( comp @ X252 @ X251 ) @ ( sub @ X250 @ X251 ) )
= ( sub @ ( X249 @ X252 @ X250 ) @ X251 ) )
| ~ ! [X253: term] :
( ( X243 @ id @ ( X249 @ id @ X253 ) @ id )
| ~ ( X243 @ id @ X253 @ id ) )
| ( X243 @ id @ ( lam @ ( X249 @ sh @ one ) ) @ id ) )
| ~ ! [X254: term] :
( ( X242 @ X254 )
= ( X243 @ id @ X254 @ id ) )
| ~ ! [X255: subst,X256: term,X257: subst,X258: subst] :
( ~ ( X243 @ X255 @ X256 @ ( comp @ X257 @ X258 ) )
| ( X243 @ ( comp @ X255 @ X257 ) @ ( sub @ X256 @ X257 ) @ X258 ) )
| ( X242 @ ( lam @ X241 ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& ( termmset_lthm
<=> ( ! [X259: term] :
( ( sub @ X259 @ id )
= X259 )
=> ! [X260: term] :
( ( sub @ X260 @ id )
= X260 ) ) )
& hoaslaminj_gthm
& ( hoasinduction_lem3b
<=> ! [X261: term] :
~ ! [X262: subst > term > term] :
( ( X262 @ sh @ one )
!= ( sub @ X261 @ ( push @ one @ sh ) ) ) )
& apnotvar
& ( ( ! [X263: term,X264: subst] :
( ( sub @ one @ ( push @ X263 @ X264 ) )
= X263 )
=> ( ! [X265: term,X266: subst] :
( ( comp @ sh @ ( push @ X265 @ X266 ) )
= X266 )
=> ( ! [X267: subst] :
( ( comp @ X267 @ id )
= X267 )
=> ( ! [X268: term > $o,X269: term] :
( ~ ! [X270: term] :
( ( X268 @ ( lam @ X270 ) )
| ~ ( X268 @ X270 ) )
| ~ ! [X271: term,X272: term] :
( ~ ( X268 @ X271 )
| ~ ( X268 @ X272 )
| ( X268 @ ( ap @ X272 @ X271 ) ) )
| ~ ! [X273: term] :
( ~ ( var @ X273 )
| ( X268 @ X273 ) )
| ( X268 @ X269 ) )
=> ! [X274: term,X275: subst,X276: term > $o] :
( ~ ! [X277: term,X278: term] :
( ( X276 @ ( ap @ X278 @ X277 ) )
| ~ ( X276 @ X277 )
| ~ ( X276 @ X278 ) )
| ~ ! [X279: term] :
( ~ ! [X280: term] :
( ~ ( X276 @ X280 )
| ( X276 @ ( sub @ X279 @ ( push @ X280 @ id ) ) ) )
| ( X276 @ ( lam @ X279 ) ) )
| ( X276 @ ( sub @ X274 @ X275 ) )
| ~ ! [X281: term] :
( ( X276 @ ( sub @ X281 @ X275 ) )
| ~ ( var @ X281 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop_lem3v2_lthm
& hoasinduction_lem2_lthm
& ~ ulamvar1
& ( ! [X282: term,X283: subst] :
( ( comp @ sh @ ( push @ X282 @ X283 ) )
= X283 )
<=> axshiftcons )
& ( ! [X284: subst > term > subst > $o,X285: term] :
( ~ ! [X286: term] :
( ~ ( X284 @ id @ X286 @ id )
| ( X284 @ id @ ( sub @ X285 @ ( push @ X286 @ id ) ) @ id ) )
| ( X284 @ id @ ( lam @ X285 ) @ id )
| ~ ! [X287: subst > term > term] :
( ~ ! [X288: term] :
( ~ ( X284 @ id @ X288 @ id )
| ( X284 @ id @ ( X287 @ id @ X288 ) @ id ) )
| ~ ! [X289: subst,X290: term,X291: subst] :
( ( X287 @ ( comp @ X291 @ X289 ) @ ( sub @ X290 @ X289 ) )
= ( sub @ ( X287 @ X291 @ X290 ) @ X289 ) )
| ( X284 @ id @ ( lam @ ( X287 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3a )
& ! [X292: subst] :
? [X293: d_subst] :
( ( d2subst @ X293 )
= X292 )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X294: term,X295: term,X296: term,X297: term] :
( ( X296 = X297 )
| ( ( ap @ ( sub @ X295 @ id ) @ X296 )
!= ( ap @ ( sub @ X294 @ id ) @ X297 ) ) )
<=> hoasapinj2 )
& ! [X298: d_subst,X299: d_subst] :
( ( ( d2subst @ X298 )
= ( d2subst @ X299 ) )
=> ( X298 = X299 ) )
& ( ( ! [X300: term > $o,X301: term] :
( ~ ! [X302: term] :
( ( X300 @ ( lam @ X302 ) )
| ~ ! [X303: term] :
( ( X300 @ ( sub @ X302 @ ( push @ X303 @ id ) ) )
| ~ ( X300 @ X303 ) ) )
| ~ ! [X304: term] :
( ( X300 @ X304 )
| ~ ( var @ X304 ) )
| ( X300 @ X301 )
| ~ ! [X305: term,X306: term] :
( ~ ( X300 @ X306 )
| ( X300 @ ( ap @ X306 @ X305 ) )
| ~ ( X300 @ X305 ) ) )
=> ( ! [X307: subst > term > subst > $o,X308: term,X309: term] :
( ( X307 @ id @ ( ap @ X308 @ X309 ) @ id )
| ~ ! [X310: subst,X311: term,X312: subst,X313: subst] :
( ~ ( X307 @ ( comp @ X313 @ X310 ) @ ( sub @ X311 @ X310 ) @ X312 )
| ( X307 @ X313 @ X311 @ ( comp @ X310 @ X312 ) ) )
| ~ ! [X314: term,X315: term] :
( ~ ( X307 @ id @ X314 @ id )
| ( X307 @ id @ ( ap @ ( sub @ X314 @ id ) @ X315 ) @ id )
| ~ ( X307 @ id @ X315 @ id ) )
| ~ ( X307 @ id @ X309 @ id )
| ~ ( X307 @ id @ X308 @ id )
| ~ ! [X316: term,X317: subst,X318: subst,X319: subst] :
( ( X307 @ ( comp @ X319 @ X317 ) @ ( sub @ X316 @ X317 ) @ X318 )
| ~ ( X307 @ X319 @ X316 @ ( comp @ X317 @ X318 ) ) ) )
=> ( ! [X320: subst > term > subst > $o,X321: term] :
( ~ ! [X322: term] :
( ( X320 @ id @ ( sub @ X321 @ ( push @ X322 @ id ) ) @ id )
| ~ ( X320 @ id @ X322 @ id ) )
| ( X320 @ id @ ( lam @ X321 ) @ id )
| ~ ! [X323: subst > term > term] :
( ~ ! [X324: term] :
( ~ ( X320 @ id @ X324 @ id )
| ( X320 @ id @ ( X323 @ id @ X324 ) @ id ) )
| ( X320 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
| ~ ! [X325: subst,X326: subst,X327: term] :
( ( X323 @ ( comp @ X326 @ X325 ) @ ( sub @ X327 @ X325 ) )
= ( sub @ ( X323 @ X326 @ X327 ) @ X325 ) ) )
| ~ ! [X328: subst,X329: term,X330: subst,X331: subst] :
( ~ ( X320 @ ( comp @ X330 @ X331 ) @ ( sub @ X329 @ X331 ) @ X328 )
| ( X320 @ X330 @ X329 @ ( comp @ X331 @ X328 ) ) )
| ~ ! [X332: subst,X333: subst,X334: term,X335: subst] :
( ( X320 @ ( comp @ X333 @ X332 ) @ ( sub @ X334 @ X332 ) @ X335 )
| ~ ( X320 @ X333 @ X334 @ ( comp @ X332 @ X335 ) ) ) )
=> ! [X336: term,X337: subst > term > subst > $o] :
( ~ ! [X338: term,X339: term] :
( ( X337 @ id @ ( ap @ ( sub @ X338 @ id ) @ X339 ) @ id )
| ~ ( X337 @ id @ X338 @ id )
| ~ ( X337 @ id @ X339 @ id ) )
| ( X337 @ id @ X336 @ id )
| ~ ! [X340: term,X341: subst,X342: subst,X343: subst] :
( ~ ( X337 @ ( comp @ X342 @ X341 ) @ ( sub @ X340 @ X341 ) @ X343 )
| ( X337 @ X342 @ X340 @ ( comp @ X341 @ X343 ) ) )
| ~ ! [X344: term] :
( ( X337 @ id @ X344 @ id )
| ~ ( var @ ( sub @ X344 @ id ) ) )
| ~ ! [X345: subst > term > term] :
( ( X337 @ id @ ( lam @ ( X345 @ sh @ one ) ) @ id )
| ~ ! [X346: term] :
( ~ ( X337 @ id @ X346 @ id )
| ( X337 @ id @ ( X345 @ id @ X346 ) @ id ) )
| ~ ! [X347: subst,X348: term,X349: subst] :
( ( sub @ ( X345 @ X347 @ X348 ) @ X349 )
= ( X345 @ ( comp @ X347 @ X349 ) @ ( sub @ X348 @ X349 ) ) ) )
| ~ ! [X350: subst,X351: subst,X352: subst,X353: term] :
( ~ ( X337 @ X350 @ X353 @ ( comp @ X351 @ X352 ) )
| ( X337 @ ( comp @ X350 @ X351 ) @ ( sub @ X353 @ X351 ) @ X352 ) ) ) ) ) )
<=> hoasinduction_lthm )
& hoaslamnotap_gthm
& ( ! [X354: term,X355: term,X356: subst > term > term] :
( ~ ! [X357: subst,X358: term,X359: subst] :
( ( X356 @ ( comp @ X357 @ X359 ) @ ( sub @ X358 @ X359 ) )
= ( sub @ ( X356 @ X357 @ X358 ) @ X359 ) )
| ( ( lam @ ( X356 @ sh @ one ) )
!= ( ap @ ( sub @ X355 @ id ) @ X354 ) ) )
<=> hoaslamnotap )
& ( axvarid
<=> ! [X360: term] :
( ( sub @ X360 @ id )
= X360 ) )
& ( ! [X361: term,X362: term,X363: term,X364: term] :
( ( ( ap @ ( sub @ X364 @ id ) @ X363 )
!= ( ap @ ( sub @ X362 @ id ) @ X361 ) )
| ( X362 = X364 ) )
<=> hoasapinj1 )
& hoasinduction_lem3a_gthm
& ( ( ! [X365: subst] :
( ( comp @ id @ X365 )
= X365 )
& ! [X366: subst] :
( ( comp @ X366 @ id )
= X366 ) )
<=> substmonoid )
& ( ( d2subst @ d_id )
= id )
& hoasinduction_lem2_gthm
& hoasinduction_lem1
& pushprop_lthm
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X367: term] :
~ ! [X368: subst > term > term] :
~ ! [X369: term,X370: subst] :
( ( sub @ X367 @ ( push @ X369 @ X370 ) )
= ( X368 @ X370 @ X369 ) )
=> ( ! [X371: term] :
( ( sub @ X371 @ id )
= X371 )
=> ! [X372: term,X373: term > $o,X374: subst > term > subst > $o] :
( ~ ! [X375: term] :
( ( X373 @ X375 )
= ( X374 @ id @ X375 @ id ) )
| ~ ! [X376: term] :
( ( X373 @ ( sub @ X372 @ ( push @ X376 @ id ) ) )
| ~ ( X373 @ X376 ) )
| ~ ! [X377: subst > term > term] :
( ~ ! [X378: term] :
( ~ ( X374 @ id @ X378 @ id )
| ( X374 @ id @ ( X377 @ id @ X378 ) @ id ) )
| ( X374 @ id @ ( lam @ ( X377 @ sh @ one ) ) @ id )
| ~ ! [X379: term,X380: subst,X381: subst] :
( ( sub @ ( X377 @ X381 @ X379 ) @ X380 )
= ( X377 @ ( comp @ X381 @ X380 ) @ ( sub @ X379 @ X380 ) ) ) )
| ( X373 @ ( lam @ X372 ) ) ) ) ) )
& ( pushprop_lem0
<=> ! [X382: subst,X383: term > $o,X384: term] :
~ ! [X385: term > $o] :
~ ! [X386: term] :
( ( X383 @ ( sub @ X386 @ ( push @ X384 @ X382 ) ) )
= ( X385 @ X386 ) ) )
& hoasinduction_gthm
& ( ! [X387: term,X388: term] :
( ( ( sub @ X387 @ sh )
!= ( sub @ X388 @ sh ) )
| ( X387 = X388 ) )
<=> shinj )
& ( induction2lem
<=> ! [X389: term > $o,X390: subst,X391: term] :
( ( X389 @ ( sub @ X391 @ X390 ) )
| ~ ! [X392: term] :
( ~ ! [X393: term] :
( ~ ( X389 @ X393 )
| ( X389 @ ( sub @ X392 @ ( push @ X393 @ id ) ) ) )
| ( X389 @ ( lam @ X392 ) ) )
| ~ ! [X394: term] :
( ( X389 @ ( sub @ X394 @ X390 ) )
| ~ ( var @ X394 ) )
| ~ ! [X395: term,X396: term] :
( ( X389 @ ( ap @ X396 @ X395 ) )
| ~ ( X389 @ X396 )
| ~ ( X389 @ X395 ) ) ) )
& ulamvarsh
& ( ! [X397: term,X398: term,X399: term,X400: term] :
( ( ( ap @ X400 @ X399 )
!= ( ap @ X398 @ X397 ) )
| ( X397 = X399 ) )
<=> apinj2 )
& ( ( ! [X401: term] :
( ( sub @ X401 @ id )
= X401 )
=> ( ! [X402: subst,X403: term,X404: term > $o] :
( ~ ! [X405: term] :
( ( X404 @ ( sub @ X405 @ X402 ) )
| ~ ( var @ X405 ) )
| ~ ! [X406: term,X407: term] :
( ( X404 @ ( ap @ X406 @ X407 ) )
| ~ ( X404 @ X407 )
| ~ ( X404 @ X406 ) )
| ~ ! [X408: term] :
( ~ ! [X409: term] :
( ~ ( X404 @ X409 )
| ( X404 @ ( sub @ X408 @ ( push @ X409 @ id ) ) ) )
| ( X404 @ ( lam @ X408 ) ) )
| ( X404 @ ( sub @ X403 @ X402 ) ) )
=> ! [X410: term,X411: term > $o] :
( ~ ! [X412: term] :
( ~ ( var @ X412 )
| ( X411 @ X412 ) )
| ( X411 @ X410 )
| ~ ! [X413: term] :
( ~ ! [X414: term] :
( ~ ( X411 @ X414 )
| ( X411 @ ( sub @ X413 @ ( push @ X414 @ id ) ) ) )
| ( X411 @ ( lam @ X413 ) ) )
| ~ ! [X415: term,X416: term] :
( ( X411 @ ( ap @ X415 @ X416 ) )
| ~ ( X411 @ X415 )
| ~ ( X411 @ X416 ) ) ) ) )
<=> induction2_lthm )
& ( ( ! [X417: term,X418: term,X419: term,X420: term] :
( ( ( ap @ X419 @ X418 )
!= ( ap @ X420 @ X417 ) )
| ( X417 = X418 ) )
=> ! [X421: term,X422: term,X423: term,X424: term] :
( ( ( ap @ ( sub @ X422 @ id ) @ X421 )
!= ( ap @ ( sub @ X424 @ id ) @ X423 ) )
| ( X421 = X423 ) ) )
<=> hoasapinj2_lthm )
& pushprop_lem1v2_gthm
& ( ( ^ [X425: subst,X426: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& axassoc
& ( laminj
<=> ! [X427: term,X428: term] :
( ( ( lam @ X428 )
!= ( lam @ X427 ) )
| ( X427 = X428 ) ) )
& pushprop_lem0_gthm
& hoasinduction_lem3b_gthm
& ( ! [X429: term,X430: term,X431: term > $o,X432: subst > term > subst > $o] :
( ~ ! [X433: subst,X434: term,X435: subst,X436: subst] :
( ( X432 @ X435 @ X434 @ ( comp @ X436 @ X433 ) )
| ~ ( X432 @ ( comp @ X435 @ X436 ) @ ( sub @ X434 @ X436 ) @ X433 ) )
| ~ ! [X437: term] :
( ( X431 @ X437 )
= ( X432 @ id @ X437 @ id ) )
| ~ ! [X438: subst,X439: term,X440: subst,X441: subst] :
( ( X432 @ ( comp @ X441 @ X440 ) @ ( sub @ X439 @ X440 ) @ X438 )
| ~ ( X432 @ X441 @ X439 @ ( comp @ X440 @ X438 ) ) )
| ~ ( X431 @ X430 )
| ~ ( X431 @ X429 )
| ( X431 @ ( ap @ X430 @ X429 ) )
| ~ ! [X442: term,X443: term] :
( ( X432 @ id @ ( ap @ ( sub @ X443 @ id ) @ X442 ) @ id )
| ~ ( X432 @ id @ X443 @ id )
| ~ ( X432 @ id @ X442 @ id ) ) )
<=> hoasinduction_lem2v2 )
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_gthm
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X444: term] :
~ ! [X445: subst > term > term] :
~ ! [X446: term,X447: subst] :
( ( sub @ X444 @ ( push @ X446 @ X447 ) )
= ( X445 @ X447 @ X446 ) ) )
& hoasinduction_lem1_gthm
& ( pushprop_lem1
<=> ! [X448: subst,X449: term > $o,X450: term,X451: term,X452: term > $o] :
( ~ ( X449 @ X451 )
| ( X452 @ ( sub @ X451 @ ( push @ X450 @ X448 ) ) ) ) )
& hoaslamnotap_lthm
& hoasapnotvar_lthm
& ( ! [X453: subst > term > term,X454: subst > term > term,X455: term,X456: subst] :
( ~ ! [X457: subst,X458: term,X459: subst] :
( ( sub @ ( X454 @ X457 @ X458 ) @ X459 )
= ( X454 @ ( comp @ X457 @ X459 ) @ ( sub @ X458 @ X459 ) ) )
| ( ( X453 @ X456 @ X455 )
= ( X454 @ X456 @ X455 ) )
| ~ ! [X460: subst,X461: term,X462: subst] :
( ( sub @ ( X453 @ X462 @ X461 ) @ X460 )
= ( X453 @ ( comp @ X462 @ X460 ) @ ( sub @ X461 @ X460 ) ) )
| ( ( lam @ ( X454 @ sh @ one ) )
!= ( lam @ ( X453 @ sh @ one ) ) ) )
<=> hoaslaminj )
& ! [X463: d_term] : ( d_one = X463 )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& pushprop
& ( ! [X464: term] :
~ ! [X465: subst > term > term] :
( ( X465 @ sh @ one )
!= ( sub @ X464 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& pushprop_lem2v2
& hoasinduction_lem3v2_gthm
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop_lem2v2_lthm
& axvarshift
& pushprop_gthm
& ( ( ! [X466: subst] :
( ( comp @ id @ X466 )
= X466 )
=> ( ! [X467: subst] :
( ( comp @ X467 @ id )
= X467 )
=> ( ! [X468: subst] :
( ( comp @ X468 @ id )
= X468 )
& ! [X469: subst] :
( ( comp @ id @ X469 )
= X469 ) ) ) )
<=> substmonoid_lthm )
& ( hoasinduction_lem3v2a
<=> ! [X470: term > $o,X471: subst > term > subst > $o,X472: term] :
( ( X470 @ ( lam @ X472 ) )
| ~ ! [X473: term] :
( ( X471 @ id @ X473 @ id )
= ( X470 @ X473 ) )
| ~ ! [X474: term] :
( ( X470 @ ( sub @ X472 @ ( push @ X474 @ id ) ) )
| ~ ( X470 @ X474 ) )
| ~ ! [X475: subst > term > term] :
( ( X471 @ id @ ( lam @ ( X475 @ sh @ one ) ) @ id )
| ~ ! [X476: term,X477: subst,X478: subst] :
( ( sub @ ( X475 @ X477 @ X476 ) @ X478 )
= ( X475 @ ( comp @ X477 @ X478 ) @ ( sub @ X476 @ X478 ) ) )
| ~ ! [X479: term] :
( ~ ( X471 @ id @ X479 @ id )
| ( X471 @ id @ ( X475 @ id @ X479 ) @ id ) ) ) ) )
& ( ! [X480: term,X481: subst] :
( ( sub @ one @ ( push @ X480 @ X481 ) )
= X480 )
<=> axvarcons )
& axabs
& ( pushprop_lem1_lthm
<=> ( ! [X482: subst,X483: term] :
( ( sub @ one @ ( push @ X483 @ X482 ) )
= X483 )
=> ( ! [X484: subst,X485: term] :
( ( comp @ sh @ ( push @ X485 @ X484 ) )
= X484 )
=> ! [X486: term > $o,X487: term > $o,X488: term,X489: subst,X490: term] :
( ( X487 @ ( sub @ X490 @ ( push @ X488 @ X489 ) ) )
| ~ ( X486 @ X490 ) ) ) ) )
& induction2lem_gthm
& pushprop_lem1_gthm
& ( ( ! [X491: term] :
( ( sub @ X491 @ id )
= X491 )
=> ( ! [X492: subst > term > subst > $o,X493: term] :
( ~ ! [X494: subst > term > term] :
( ~ ! [X495: subst,X496: term,X497: subst] :
( ( X494 @ ( comp @ X495 @ X497 ) @ ( sub @ X496 @ X497 ) )
= ( sub @ ( X494 @ X495 @ X496 ) @ X497 ) )
| ( X492 @ id @ ( lam @ ( X494 @ sh @ one ) ) @ id )
| ~ ! [X498: term] :
( ( X492 @ id @ ( X494 @ id @ X498 ) @ id )
| ~ ( X492 @ id @ X498 @ id ) ) )
| ( X492 @ id @ ( lam @ ( sub @ X493 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X499: term] :
( ~ ( X492 @ id @ X499 @ id )
| ( X492 @ id @ ( sub @ X493 @ ( push @ X499 @ id ) ) @ id ) ) )
=> ! [X500: term,X501: subst > term > subst > $o] :
( ~ ! [X502: subst > term > term] :
( ~ ! [X503: term] :
( ~ ( X501 @ id @ X503 @ id )
| ( X501 @ id @ ( X502 @ id @ X503 ) @ id ) )
| ~ ! [X504: subst,X505: term,X506: subst] :
( ( sub @ ( X502 @ X504 @ X505 ) @ X506 )
= ( X502 @ ( comp @ X504 @ X506 ) @ ( sub @ X505 @ X506 ) ) )
| ( X501 @ id @ ( lam @ ( X502 @ sh @ one ) ) @ id ) )
| ~ ! [X507: term] :
( ( X501 @ id @ ( sub @ X500 @ ( push @ X507 @ id ) ) @ id )
| ~ ( X501 @ id @ X507 @ id ) )
| ~ ! [X508: subst,X509: subst,X510: subst,X511: term] :
( ~ ( X501 @ X509 @ X511 @ ( comp @ X510 @ X508 ) )
| ( X501 @ ( comp @ X509 @ X510 ) @ ( sub @ X511 @ X510 ) @ X508 ) )
| ( X501 @ id @ ( lam @ X500 ) @ id )
| ~ ! [X512: subst,X513: subst,X514: subst,X515: term] :
( ~ ( X501 @ ( comp @ X513 @ X512 ) @ ( sub @ X515 @ X512 ) @ X514 )
| ( X501 @ X513 @ X515 @ ( comp @ X512 @ X514 ) ) ) ) ) )
<=> hoasinduction_lem3_lthm )
& ( ( ! [X516: subst > term > subst > $o] :
~ ! [X517: term > $o] :
~ ! [X518: term] :
( ( X517 @ X518 )
= ( X516 @ id @ X518 @ id ) )
=> ( ! [X519: term > $o,X520: term] :
( ~ ! [X521: term,X522: term] :
( ~ ( X519 @ X521 )
| ( X519 @ ( ap @ X522 @ X521 ) )
| ~ ( X519 @ X522 ) )
| ( X519 @ X520 )
| ~ ! [X523: term] :
( ~ ! [X524: term] :
( ~ ( X519 @ X524 )
| ( X519 @ ( sub @ X523 @ ( push @ X524 @ id ) ) ) )
| ( X519 @ ( lam @ X523 ) ) )
| ~ ! [X525: term] :
( ~ ( var @ X525 )
| ( X519 @ X525 ) ) )
=> ( ! [X526: term] :
( ( sub @ X526 @ id )
= X526 )
=> ( ! [X527: term > $o,X528: subst > term > subst > $o,X529: term] :
( ~ ! [X530: term] :
( ( X527 @ X530 )
= ( X528 @ id @ X530 @ id ) )
| ( X527 @ ( lam @ X529 ) )
| ~ ! [X531: term] :
( ( X527 @ ( sub @ X529 @ ( push @ X531 @ id ) ) )
| ~ ( X527 @ X531 ) )
| ~ ! [X532: subst > term > term] :
( ~ ! [X533: term] :
( ~ ( X528 @ id @ X533 @ id )
| ( X528 @ id @ ( X532 @ id @ X533 ) @ id ) )
| ~ ! [X534: term,X535: subst,X536: subst] :
( ( X532 @ ( comp @ X535 @ X536 ) @ ( sub @ X534 @ X536 ) )
= ( sub @ ( X532 @ X535 @ X534 ) @ X536 ) )
| ( X528 @ id @ ( lam @ ( X532 @ sh @ one ) ) @ id ) ) )
=> ! [X537: term,X538: subst > term > subst > $o] :
( ~ ! [X539: term,X540: term] :
( ~ ( X538 @ id @ X539 @ id )
| ~ ( X538 @ id @ X540 @ id )
| ( X538 @ id @ ( ap @ ( sub @ X539 @ id ) @ X540 ) @ id ) )
| ~ ! [X541: subst > term > term] :
( ~ ! [X542: term] :
( ( X538 @ id @ ( X541 @ id @ X542 ) @ id )
| ~ ( X538 @ id @ X542 @ id ) )
| ( X538 @ id @ ( lam @ ( X541 @ sh @ one ) ) @ id )
| ~ ! [X543: term,X544: subst,X545: subst] :
( ( X541 @ ( comp @ X544 @ X545 ) @ ( sub @ X543 @ X545 ) )
= ( sub @ ( X541 @ X544 @ X543 ) @ X545 ) ) )
| ( X538 @ id @ X537 @ id ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& axclos
& ( ! [X546: term] :
~ ! [X547: subst > term > term] :
~ ! [X548: term,X549: subst] :
( ( sub @ X546 @ ( push @ X548 @ X549 ) )
= ( X547 @ X549 @ X548 ) )
<=> hoasinduction_lem3v2_f )
& ~ lamnotap
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( pushprop_lem1v2_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X10: term > $o,X14: subst,X13: term,X11: term > $o] :
( ( X11 @ one )
| ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) ) )
& hoasinduction_lem1v2
& hoasinduction_lem1_lthm
& ulamvarind
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [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 @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X10: subst > term > subst > $o,X43: term] :
( ~ ! [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 ) )
| ~ ! [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 ) )
| ( X10 @ id @ ( lam @ X43 ) @ id ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& ! [X5: d_subst] : ( d_id = X5 )
& ~ ( var @ ( d2term @ d_one ) )
& ( induction
<=> ! [X10: term > $o,X21: term] :
( ( X10 @ X21 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) ) ) )
& pushprop_lthm_orig
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X13: term,X20: term,X15: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
=> ! [X15: term,X13: term,X19: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) ) )
<=> hoasapinj1_lthm )
& ( ! [X10: subst > term > subst > $o,X24: term,X23: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X26: subst,X14: subst,X25: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X26: subst,X25: subst,X14: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X10 @ id @ X23 @ id )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ( X10 @ id @ X24 @ id ) )
<=> hoasinduction_lem2 )
& ( ! [X15: term,X13: term,X19: term,X20: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
<=> apinj1 )
& ( hoasinduction_lthm_3
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) ) )
& hoaslamnotvar_lthm
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0 )
& ( induction2
<=> ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X10: term > $o,X13: term,X14: subst] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& ( hoasinduction_lem3aa
<=> ! [X42: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) )
& ( hoasinduction_no_psi_cond
<=> ! [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 ) )
| ~ ! [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 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
& ( ! [X28: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ X28 @ id )
| ~ ! [X14: subst,X13: term,X26: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) )
<=> hoasinduction )
& ( ! [X10: term > $o,X11: term > $o,X14: subst,X13: term] :
( ( X11 @ one )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ~ ( X10 @ X13 ) )
<=> pushprop_lem1v2 )
& hoasapnotvar_gthm
& ( axscons
<=> ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 ) )
& ( ( d2subst @ d_id )
= sh )
& substmonoid_gthm
& hoasapnotvar
& hoasapinj1_gthm
& pushprop_lem2v2_gthm
& ( pushprop_p_and_p_prime
= ( ^ [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) )
& induction2_gthm
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( hoasinduction_lem3aa_lthm
<=> ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X13: term,X15: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) )
=> ! [X31: subst > term > term,X33: term,X32: subst,X18: subst > term > term] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) ) ) ) ) )
<=> hoaslaminj_lthm )
& axapp
& hoasinduction_lem2v2_gthm
& ( one
= ( d2term @ d_one ) )
& pushprop_lem3v2
& ( hoasinduction_lem3aaa
<=> ! [X10: subst > term > subst > $o,X34: term] :
( ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term,X35: term] :
( ~ ! [X41: subst,X40: term,X39: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X38: subst,X37: term,X36: subst] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) ) ) )
& axmap
& ( axidr
<=> ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
& ( axidl
<=> ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 ) )
& termmset_gthm
& ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X25: subst,X26: subst,X13: term,X14: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( lam @ X27 ) @ 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,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) ) )
<=> hoasinduction_lem3 )
& hoasapinj2_gthm
& lamnotvar
& hoaslamnotvar
& hoasinduction_lem3_gthm
& ( ! [X48: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X14: subst,X25: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
<=> hoasinduction_lem3v2 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X48: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X14: subst,X13: term,X26: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X11 @ ( lam @ X48 ) ) ) )
<=> hoasinduction_lem3v2_lthm )
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& hoaslaminj_gthm
& ( hoasinduction_lem3b
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& apnotvar
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X10: term > $o,X21: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( X10 @ X21 ) )
=> ! [X16: term,X17: subst,X10: term > $o] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop_lem3v2_lthm
& hoasinduction_lem2_lthm
& ~ ulamvar1
& ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
<=> axshiftcons )
& ( ! [X10: subst > term > subst > $o,X43: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3a )
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ! [X13: term,X15: term,X20: term,X19: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) )
<=> hoasapinj2 )
& ! [X7: d_subst,X6: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) ) )
=> ( ! [X10: subst > term > subst > $o,X23: term,X24: term] :
( ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X26: subst,X13: term,X25: 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 ) )
| ~ ( X10 @ id @ X24 @ id )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X26: subst,X25: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) )
=> ( ! [X10: subst > term > subst > $o,X27: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [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 ) ) ) )
| ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) ) ) ) )
<=> hoasinduction_lthm )
& hoaslamnotap_gthm
& ( ! [X47: term,X46: term,X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) ) )
<=> hoaslamnotap )
& ( axvarid
<=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) )
& ( ! [X19: term,X13: term,X20: term,X15: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) )
<=> hoasapinj1 )
& hoasinduction_lem3a_gthm
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
<=> substmonoid )
& ( ( d2subst @ d_id )
= id )
& hoasinduction_lem2_gthm
& hoasinduction_lem1
& pushprop_lthm
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X29: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [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 ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X11 @ ( lam @ X29 ) ) ) ) ) )
& ( pushprop_lem0
<=> ! [X14: subst,X10: term > $o,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& hoasinduction_gthm
& ( ! [X13: term,X15: term] :
( ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) )
| ( X13 = X15 ) )
<=> shinj )
& ( induction2lem
<=> ! [X10: term > $o,X17: subst,X16: term] :
( ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) ) ) )
& ulamvarsh
& ( ! [X19: term,X13: term,X20: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
<=> apinj2 )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X17: subst,X16: term,X10: term > $o] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( 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 ) ) ) ) )
<=> induction2_lthm )
& ( ( ! [X20: term,X19: term,X13: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
=> ! [X20: term,X15: term,X19: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
<=> hoasapinj2_lthm )
& pushprop_lem1v2_gthm
& ( ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& axassoc
& ( laminj
<=> ! [X15: term,X13: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) ) )
& pushprop_lem0_gthm
& hoasinduction_lem3b_gthm
& ( ! [X45: term,X44: term,X11: term > $o,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 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X11 @ X44 )
| ~ ( X11 @ X45 )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_lem2v2 )
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_gthm
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) ) )
& hoasinduction_lem1_gthm
& ( pushprop_lem1
<=> ! [X14: subst,X10: term > $o,X15: term,X13: term,X26: term > $o] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) )
& hoaslamnotap_lthm
& hoasapnotvar_lthm
& ( ! [X18: subst > term > term,X31: subst > term > term,X33: term,X32: subst] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) ) )
<=> hoaslaminj )
& ! [X1: d_term] : ( d_one = X1 )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& pushprop
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& pushprop_lem2v2
& hoasinduction_lem3v2_gthm
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& pushprop_lem2v2_lthm
& axvarshift
& pushprop_gthm
& ( ( ! [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 )
& ( hoasinduction_lem3v2a
<=> ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) ) ) )
& ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& axabs
& ( pushprop_lem1_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X10: term > $o,X26: term > $o,X15: term,X14: subst,X13: term] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) ) ) ) )
& induction2lem_gthm
& pushprop_lem1_gthm
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [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 @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X26: subst,X14: subst,X25: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) ) )
<=> hoasinduction_lem3_lthm )
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
=> ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ 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 )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ X30 @ id ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& axclos
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& ~ lamnotap
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZKaewZbi7/DTF2THF_21668.p',alg444_1) ).
thf(f1258,plain,
! [X0: term] :
( ( d2term @ ( sK457 @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f8657,plain,
( ( $false
!= ( sK592 @ id @ one @ id ) )
| spl591_705 ),
inference(avatar_component_clause,[status(thm)],[f8656]) ).
thf(f8656,definition,
( spl591_705
<=> ( $false
= ( sK592 @ id @ one @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_705])],[avatar_definition]) ).
thf(f2515,plain,
( ( $false
= ( sK592 @ id @ ( lam @ sK597 ) @ id ) )
| ~ spl591_214 ),
inference(avatar_component_clause,[status(thm)],[f2513]) ).
thf(f2513,definition,
( spl591_214
<=> ( $false
= ( sK592 @ id @ ( lam @ sK597 ) @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_214])],[avatar_definition]) ).
thf(f10345,plain,
( ~ spl591_702
| ~ spl591_705 ),
inference(avatar_contradiction_clause,[status(thm)],[f10344]) ).
thf(f10344,plain,
( $false
| ~ spl591_702
| ~ spl591_705 ),
inference(subsumption_resolution,[status(thm)],[f10279,f9527]) ).
thf(f9527,plain,
( ( $true
!= ( sP12 @ sK592 ) )
| ~ spl591_702 ),
inference(trivial_inequality_removal,[status(thm)],[f9514]) ).
thf(f9514,plain,
( ( $true != $true )
| ( $true
!= ( sP12 @ sK592 ) )
| ~ spl591_702 ),
inference(superposition,[status(thm)],[f6120,f8641]) ).
thf(f8641,plain,
( ! [X4: subst] :
( $true
= ( sK592 @ id @ one @ X4 ) )
| ~ spl591_702 ),
inference(avatar_component_clause,[status(thm)],[f8640]) ).
thf(f8640,definition,
( spl591_702
<=> ! [X4: subst] :
( $true
= ( sK592 @ id @ one @ X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_702])],[avatar_definition]) ).
thf(f6120,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( X0 @ id @ one @ id ) )
| ( $true
!= ( sP12 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f6119,f1061]) ).
thf(f1061,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f6119,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( sP12 @ X0 ) )
| ( $true
!= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f923,f4480]) ).
thf(f923,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( sP12 @ X0 ) )
| ( $true
!= ( X0 @ id @ ( lam @ ( sK365 @ X0 @ sh @ one ) ) @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
thf(f386,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP12 @ X0 ) )
| ! [X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK361 @ X1 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK361 @ X1 @ X0 ) @ id ) ) )
| ( ( sub @ ( X1 @ ( sK362 @ X1 ) @ ( sK363 @ X1 ) ) @ ( sK364 @ X1 ) )
!= ( X1 @ ( comp @ ( sK362 @ X1 ) @ ( sK364 @ X1 ) ) @ ( sub @ ( sK363 @ X1 ) @ ( sK364 @ X1 ) ) ) ) ) )
& ( ( ( $true
!= ( X0 @ id @ ( lam @ ( sK365 @ X0 @ sh @ one ) ) @ id ) )
& ! [X7: term] :
( ( ( X0 @ id @ ( sK365 @ X0 @ id @ X7 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X7 @ id ) ) )
& ! [X8: subst,X9: term,X10: subst] :
( ( sK365 @ X0 @ ( comp @ X8 @ X10 ) @ ( sub @ X9 @ X10 ) )
= ( sub @ ( sK365 @ X0 @ X8 @ X9 ) @ X10 ) ) )
| ( $true
!= ( sP12 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK361,sK362,sK363,sK364,sK365])],[f382,f385,f384,f383]) ).
thf(f383,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ X2 @ id ) ) )
=> ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK361 @ X1 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK361 @ X1 @ X0 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f384,plain,
! [X1: subst > term > term] :
( ? [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X1 @ X3 @ X4 ) @ X5 )
!= ( X1 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ( sub @ ( X1 @ ( sK362 @ X1 ) @ ( sK363 @ X1 ) ) @ ( sK364 @ X1 ) )
!= ( X1 @ ( comp @ ( sK362 @ X1 ) @ ( sK364 @ X1 ) ) @ ( sub @ ( sK363 @ X1 ) @ ( sK364 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f385,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X7: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X7 ) @ id ) )
| ( $true
!= ( X0 @ id @ X7 @ id ) ) )
& ! [X8: subst,X9: term,X10: subst] :
( ( sub @ ( X6 @ X8 @ X9 ) @ X10 )
= ( X6 @ ( comp @ X8 @ X10 ) @ ( sub @ X9 @ X10 ) ) ) )
=> ( ( $true
!= ( X0 @ id @ ( lam @ ( sK365 @ X0 @ sh @ one ) ) @ id ) )
& ! [X7: term] :
( ( ( X0 @ id @ ( sK365 @ X0 @ id @ X7 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X7 @ id ) ) )
& ! [X10: subst,X9: term,X8: subst] :
( ( sK365 @ X0 @ ( comp @ X8 @ X10 ) @ ( sub @ X9 @ X10 ) )
= ( sub @ ( sK365 @ X0 @ X8 @ X9 ) @ X10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f382,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP12 @ X0 ) )
| ! [X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ? [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ X2 @ id ) ) )
| ? [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X1 @ X3 @ X4 ) @ X5 )
!= ( X1 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) ) ) )
& ( ? [X6: subst > term > term] :
( ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X7: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X7 ) @ id ) )
| ( $true
!= ( X0 @ id @ X7 @ id ) ) )
& ! [X8: subst,X9: term,X10: subst] :
( ( sub @ ( X6 @ X8 @ X9 ) @ X10 )
= ( X6 @ ( comp @ X8 @ X10 ) @ ( sub @ X9 @ X10 ) ) ) )
| ( $true
!= ( sP12 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f381]) ).
thf(f381,plain,
! [X198: subst > term > subst > $o] :
( ( ( $true
= ( sP12 @ X198 ) )
| ! [X204: subst > term > term] :
( ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
= $true )
| ? [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
!= $true )
& ( $true
= ( X198 @ id @ X205 @ id ) ) )
| ? [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
!= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) ) )
& ( ? [X204: subst > term > term] :
( ( ( X198 @ id @ ( lam @ ( X204 @ sh @ one ) ) @ id )
!= $true )
& ! [X205: term] :
( ( ( X198 @ id @ ( X204 @ id @ X205 ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X205 @ id ) ) )
& ! [X206: subst,X207: term,X208: subst] :
( ( sub @ ( X204 @ X206 @ X207 ) @ X208 )
= ( X204 @ ( comp @ X206 @ X208 ) @ ( sub @ X207 @ X208 ) ) ) )
| ( $true
!= ( sP12 @ X198 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f10279,plain,
( ( $true
= ( sP12 @ sK592 ) )
| ~ spl591_705 ),
inference(trivial_inequality_removal,[status(thm)],[f10270]) ).
thf(f10270,plain,
( ( $true
= ( sP12 @ sK592 ) )
| ( $true = $false )
| ~ spl591_705 ),
inference(superposition,[status(thm)],[f8524,f8658]) ).
thf(f8658,plain,
( ( $false
= ( sK592 @ id @ one @ id ) )
| ~ spl591_705 ),
inference(avatar_component_clause,[status(thm)],[f8656]) ).
thf(f8524,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ one @ id ) )
| ( $true
= ( sP12 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f8523,f1061]) ).
thf(f8523,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) )
| ( $true
= ( sP12 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f8522]) ).
thf(f8522,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP12 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f8521,f4480]) ).
thf(f8521,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( $true
= ( sP12 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f8520,f4480]) ).
thf(f8520,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( sP12 @ X0 ) )
| ( $true
= ( X0 @ id @ ( sK361 @ X1 @ X0 ) @ id ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
inference(subsumption_resolution,[status(thm)],[f924,f4484]) ).
thf(f924,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( sK361 @ X1 @ X0 ) @ id ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( $true
= ( sP12 @ X0 ) )
| ( ( sub @ ( X1 @ ( sK362 @ X1 ) @ ( sK363 @ X1 ) ) @ ( sK364 @ X1 ) )
!= ( X1 @ ( comp @ ( sK362 @ X1 ) @ ( sK364 @ X1 ) ) @ ( sub @ ( sK363 @ X1 ) @ ( sK364 @ X1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
thf(f9872,plain,
( spl591_104
| ~ spl591_716 ),
inference(avatar_split_clause,[status(thm)],[f9869,f9467,f2050]) ).
thf(f2050,definition,
( spl591_104
<=> ( $true
= ( sP17 @ sK305 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_104])],[avatar_definition]) ).
thf(f9467,definition,
( spl591_716
<=> ! [X5: subst] :
( $true
!= ( sK305 @ id @ one @ X5 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_716])],[avatar_definition]) ).
thf(f9869,plain,
( ( $true
= ( sP17 @ sK305 ) )
| ~ spl591_716 ),
inference(trivial_inequality_removal,[status(thm)],[f9861]) ).
thf(f9861,plain,
( ( $true
= ( sP17 @ sK305 ) )
| ( $true != $true )
| ~ spl591_716 ),
inference(superposition,[status(thm)],[f9468,f8440]) ).
thf(f8440,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ one @ id ) )
| ( $true
= ( sP17 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f8439,f1061]) ).
thf(f8439,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP17 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f8438]) ).
thf(f8438,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) )
| ( $true
= ( sP17 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f8437,f4480]) ).
thf(f8437,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( sK333 @ X1 @ X0 ) @ id ) )
| ( $true
= ( sP17 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f8436,f4480]) ).
thf(f8436,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( $true
= ( X0 @ id @ ( sK333 @ X1 @ X0 ) @ id ) )
| ( $true
= ( sP17 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f887,f4484]) ).
thf(f887,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK330 @ X1 ) @ ( sK331 @ X1 ) ) @ ( sK332 @ X1 ) )
!= ( X1 @ ( comp @ ( sK330 @ X1 ) @ ( sK332 @ X1 ) ) @ ( sub @ ( sK331 @ X1 ) @ ( sK332 @ X1 ) ) ) )
| ( $true
= ( X0 @ id @ ( sK333 @ X1 @ X0 ) @ id ) )
| ( $true
= ( sP17 @ X0 ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
thf(f355,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP17 @ X0 ) )
| ! [X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( ( sub @ ( X1 @ ( sK330 @ X1 ) @ ( sK331 @ X1 ) ) @ ( sK332 @ X1 ) )
!= ( X1 @ ( comp @ ( sK330 @ X1 ) @ ( sK332 @ X1 ) ) @ ( sub @ ( sK331 @ X1 ) @ ( sK332 @ X1 ) ) ) )
| ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK333 @ X1 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK333 @ X1 @ X0 ) @ id ) ) ) ) )
& ( ( ( $true
!= ( X0 @ id @ ( lam @ ( sK334 @ X0 @ sh @ one ) ) @ id ) )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( sK334 @ X0 @ X7 @ X8 ) @ X9 )
= ( sK334 @ X0 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( sK334 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
| ( $true
!= ( sP17 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK330,sK331,sK332,sK333,sK334])],[f351,f354,f353,f352]) ).
thf(f352,plain,
! [X1: subst > term > term] :
( ? [X2: subst,X3: term,X4: subst] :
( ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) )
!= ( sub @ ( X1 @ X2 @ X3 ) @ X4 ) )
=> ( ( sub @ ( X1 @ ( sK330 @ X1 ) @ ( sK331 @ X1 ) ) @ ( sK332 @ X1 ) )
!= ( X1 @ ( comp @ ( sK330 @ X1 ) @ ( sK332 @ X1 ) ) @ ( sub @ ( sK331 @ X1 ) @ ( sK332 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f353,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X5: term] :
( ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
& ( ( X0 @ id @ X5 @ id )
= $true ) )
=> ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK333 @ X1 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK333 @ X1 @ X0 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f354,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( X6 @ X7 @ X8 ) @ X9 )
= ( X6 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
=> ( ( $true
!= ( X0 @ id @ ( lam @ ( sK334 @ X0 @ sh @ one ) ) @ id ) )
& ! [X9: subst,X8: term,X7: subst] :
( ( sub @ ( sK334 @ X0 @ X7 @ X8 ) @ X9 )
= ( sK334 @ X0 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( sK334 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f351,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP17 @ X0 ) )
| ! [X1: subst > term > term] :
( ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ? [X2: subst,X3: term,X4: subst] :
( ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) )
!= ( sub @ ( X1 @ X2 @ X3 ) @ X4 ) )
| ? [X5: term] :
( ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
& ( ( X0 @ id @ X5 @ id )
= $true ) ) ) )
& ( ? [X6: subst > term > term] :
( ( ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id )
!= $true )
& ! [X7: subst,X8: term,X9: subst] :
( ( sub @ ( X6 @ X7 @ X8 ) @ X9 )
= ( X6 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
| ( $true
!= ( sP17 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f350]) ).
thf(f350,plain,
! [X329: subst > term > subst > $o] :
( ( ( $true
= ( sP17 @ X329 ) )
| ! [X337: subst > term > term] :
( ( $true
= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
| ? [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
!= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) )
| ? [X338: term] :
( ( $true
!= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
& ( ( X329 @ id @ X338 @ id )
= $true ) ) ) )
& ( ? [X337: subst > term > term] :
( ( $true
!= ( X329 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id ) )
& ! [X339: subst,X340: term,X341: subst] :
( ( sub @ ( X337 @ X339 @ X340 ) @ X341 )
= ( X337 @ ( comp @ X339 @ X341 ) @ ( sub @ X340 @ X341 ) ) )
& ! [X338: term] :
( ( $true
= ( X329 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X329 @ id @ X338 @ id )
!= $true ) ) )
| ( $true
!= ( sP17 @ X329 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f9468,plain,
( ! [X5: subst] :
( $true
!= ( sK305 @ id @ one @ X5 ) )
| ~ spl591_716 ),
inference(avatar_component_clause,[status(thm)],[f9467]) ).
thf(f9825,plain,
( spl591_362
| ~ spl591_717 ),
inference(avatar_contradiction_clause,[status(thm)],[f9824]) ).
thf(f9824,plain,
( $false
| spl591_362
| ~ spl591_717 ),
inference(trivial_inequality_removal,[status(thm)],[f9807]) ).
thf(f9807,plain,
( ( $true != $true )
| spl591_362
| ~ spl591_717 ),
inference(superposition,[status(thm)],[f3158,f9471]) ).
thf(f9471,plain,
( ! [X2: term,X4: subst] :
( $true
= ( sK305 @ X4 @ X2 @ id ) )
| ~ spl591_717 ),
inference(avatar_component_clause,[status(thm)],[f9470]) ).
thf(f9470,definition,
( spl591_717
<=> ! [X2: term,X4: subst] :
( $true
= ( sK305 @ X4 @ X2 @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_717])],[avatar_definition]) ).
thf(f3158,plain,
( ( $true
!= ( sK305 @ id @ sK304 @ id ) )
| spl591_362 ),
inference(avatar_component_clause,[status(thm)],[f3156]) ).
thf(f3156,definition,
( spl591_362
<=> ( $true
= ( sK305 @ id @ sK304 @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_362])],[avatar_definition]) ).
thf(f9472,plain,
( spl591_716
| spl591_717
| ~ spl591_151 ),
inference(avatar_split_clause,[status(thm)],[f9465,f2250,f9470,f9467]) ).
thf(f2250,definition,
( spl591_151
<=> ! [X3: subst,X4: subst,X5: subst,X2: term] :
( ( ( sK305 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 )
!= $true )
| ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_151])],[avatar_definition]) ).
thf(f9465,plain,
( ! [X2: term,X4: subst,X5: subst] :
( ( $true
= ( sK305 @ X4 @ X2 @ id ) )
| ( $true
!= ( sK305 @ id @ one @ X5 ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f9464,f1061]) ).
thf(f9464,plain,
( ! [X2: term,X4: subst,X5: subst] :
( ( $true
= ( sK305 @ X4 @ X2 @ id ) )
| ( $true
!= ( sK305 @ id @ ( d2term @ d_one ) @ X5 ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f9463,f4480]) ).
thf(f9463,plain,
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
!= ( sK305 @ id @ ( sub @ X2 @ X3 ) @ X5 ) )
| ( $true
= ( sK305 @ X4 @ X2 @ id ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f9462,f1226]) ).
thf(f1226,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f9462,plain,
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
= ( sK305 @ X4 @ X2 @ id ) )
| ( $true
!= ( sK305 @ ( d2subst @ d_id ) @ ( sub @ X2 @ X3 ) @ X5 ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f9461,f1226]) ).
thf(f9461,plain,
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
= ( sK305 @ X4 @ X2 @ ( d2subst @ d_id ) ) )
| ( $true
!= ( sK305 @ ( d2subst @ d_id ) @ ( sub @ X2 @ X3 ) @ X5 ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f9460,f4466]) ).
thf(f4466,plain,
! [X201: subst] :
( ( d2subst @ d_id )
= X201 ),
inference(forward_demodulation,[status(thm)],[f1086,f1039]) ).
thf(f1039,plain,
! [X263: d_subst] : ( d_id = X263 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1086,plain,
! [X201: subst] :
( ( d2subst @ ( sK555 @ X201 ) )
= X201 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f9460,plain,
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) )
| ( $true
!= ( sK305 @ ( d2subst @ d_id ) @ ( sub @ X2 @ X3 ) @ X5 ) ) )
| ~ spl591_151 ),
inference(forward_demodulation,[status(thm)],[f2251,f4466]) ).
thf(f2251,plain,
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( ( sK305 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 )
!= $true )
| ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) ) )
| ~ spl591_151 ),
inference(avatar_component_clause,[status(thm)],[f2250]) ).
thf(f9350,plain,
( ~ spl591_703
| ~ spl591_704 ),
inference(avatar_contradiction_clause,[status(thm)],[f9349]) ).
thf(f9349,plain,
( $false
| ~ spl591_703
| ~ spl591_704 ),
inference(trivial_inequality_removal,[status(thm)],[f9348]) ).
thf(f9348,plain,
( ( $true = $false )
| ~ spl591_703
| ~ spl591_704 ),
inference(forward_demodulation,[status(thm)],[f8654,f8644]) ).
thf(f8644,plain,
( ! [X2: subst,X1: term] :
( ( sK592 @ X2 @ X1 @ id )
= $false )
| ~ spl591_703 ),
inference(avatar_component_clause,[status(thm)],[f8643]) ).
thf(f8643,definition,
( spl591_703
<=> ! [X2: subst,X1: term] :
( ( sK592 @ X2 @ X1 @ id )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl591_703])],[avatar_definition]) ).
thf(f8654,plain,
( ( $true
= ( sK592 @ id @ one @ id ) )
| ~ spl591_704 ),
inference(avatar_component_clause,[status(thm)],[f8652]) ).
thf(f8652,definition,
( spl591_704
<=> ( $true
= ( sK592 @ id @ one @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_704])],[avatar_definition]) ).
thf(f8677,plain,
( spl591_704
| ~ spl591_218
| ~ spl591_513 ),
inference(avatar_split_clause,[status(thm)],[f8676,f3817,f2530,f8652]) ).
thf(f2530,definition,
( spl591_218
<=> ! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_218])],[avatar_definition]) ).
thf(f3817,definition,
( spl591_513
<=> ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( var @ ( sub @ ( sK314 @ X12 ) @ id ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( sP16 @ X12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_513])],[avatar_definition]) ).
thf(f8676,plain,
( ( $true
= ( sK592 @ id @ one @ id ) )
| ~ spl591_218
| ~ spl591_513 ),
inference(subsumption_resolution,[status(thm)],[f8675,f7255]) ).
thf(f7255,plain,
( ! [X10: term,X0: subst > term > subst > $o] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
= ( X0 @ id @ one @ id ) ) )
| ~ spl591_513 ),
inference(subsumption_resolution,[status(thm)],[f7254,f6699]) ).
thf(f6699,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( X12 @ id @ one @ id )
= $true )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) ) )
| ~ spl591_513 ),
inference(subsumption_resolution,[status(thm)],[f4864,f5799]) ).
thf(f5799,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( sP16 @ X0 ) )
| ( $true
= ( X0 @ id @ one @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f5798,f1061]) ).
thf(f5798,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( sP16 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f889,f4480]) ).
thf(f889,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( sK336 @ X0 ) @ id ) )
| ( $true
!= ( sP16 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f359]) ).
thf(f359,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP16 @ X0 ) )
| ! [X1: term,X2: term] :
( ( $true
!= ( X0 @ id @ X1 @ id ) )
| ( $true
= ( X0 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) )
| ( $true
!= ( X0 @ id @ X2 @ id ) ) ) )
& ( ( ( ( X0 @ id @ ( sK335 @ X0 ) @ id )
= $true )
& ( $true
!= ( X0 @ id @ ( ap @ ( sub @ ( sK335 @ X0 ) @ id ) @ ( sK336 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK336 @ X0 ) @ id ) ) )
| ( $true
!= ( sP16 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK335,sK336])],[f357,f358]) ).
thf(f358,plain,
! [X0: subst > term > subst > $o] :
( ? [X3: term,X4: term] :
( ( $true
= ( X0 @ id @ X3 @ id ) )
& ( $true
!= ( X0 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
& ( $true
= ( X0 @ id @ X4 @ id ) ) )
=> ( ( ( X0 @ id @ ( sK335 @ X0 ) @ id )
= $true )
& ( $true
!= ( X0 @ id @ ( ap @ ( sub @ ( sK335 @ X0 ) @ id ) @ ( sK336 @ X0 ) ) @ id ) )
& ( $true
= ( X0 @ id @ ( sK336 @ X0 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f357,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP16 @ X0 ) )
| ! [X1: term,X2: term] :
( ( $true
!= ( X0 @ id @ X1 @ id ) )
| ( $true
= ( X0 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) )
| ( $true
!= ( X0 @ id @ X2 @ id ) ) ) )
& ( ? [X3: term,X4: term] :
( ( $true
= ( X0 @ id @ X3 @ id ) )
& ( $true
!= ( X0 @ id @ ( ap @ ( sub @ X3 @ id ) @ X4 ) @ id ) )
& ( $true
= ( X0 @ id @ X4 @ id ) ) )
| ( $true
!= ( sP16 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,plain,
! [X329: subst > term > subst > $o] :
( ( ( $true
= ( sP16 @ X329 ) )
| ! [X330: term,X331: term] :
( ( ( X329 @ id @ X330 @ id )
!= $true )
| ( $true
= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
| ( ( X329 @ id @ X331 @ id )
!= $true ) ) )
& ( ? [X330: term,X331: term] :
( ( ( X329 @ id @ X330 @ id )
= $true )
& ( $true
!= ( X329 @ id @ ( ap @ ( sub @ X330 @ id ) @ X331 ) @ id ) )
& ( ( X329 @ id @ X331 @ id )
= $true ) )
| ( $true
!= ( sP16 @ X329 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f4864,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( X12 @ id @ one @ id )
= $true )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(duplicate_literal_removal,[status(thm)],[f4863]) ).
thf(f4863,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( X12 @ id @ one @ id )
= $true )
| ( ( X12 @ id @ one @ id )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( ( sP17 @ X12 )
= $true ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4862,f1226]) ).
thf(f4862,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( X12 @ id @ one @ ( d2subst @ d_id ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( ( X12 @ id @ one @ id )
= $true ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4861,f4466]) ).
thf(f4861,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ one @ ( sK309 @ X12 ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP16 @ X12 ) )
| ( ( X12 @ id @ one @ id )
= $true ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4860,f1061]) ).
thf(f4860,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ ( d2term @ d_one ) @ ( sK309 @ X12 ) ) )
| ( ( X12 @ id @ one @ id )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4859,f1226]) ).
thf(f4859,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ one @ ( d2subst @ d_id ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( X12 @ id @ ( d2term @ d_one ) @ ( sK309 @ X12 ) ) )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4858,f4480]) ).
thf(f4858,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( X12 @ id @ one @ ( d2subst @ d_id ) ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4857,f1226]) ).
thf(f4857,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ ( d2subst @ d_id ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) ) )
| ( $true
= ( X12 @ id @ one @ ( d2subst @ d_id ) ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4856,f4466]) ).
thf(f4856,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( X12 @ id @ one @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( $true
= ( X12 @ ( d2subst @ d_id ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4855,f4466]) ).
thf(f4855,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ one @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4854,f1061]) ).
thf(f4854,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ ( d2term @ d_one ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( sP17 @ X12 )
= $true ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4853,f4480]) ).
thf(f4853,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4852,f1226]) ).
thf(f4852,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ ( d2subst @ d_id ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(forward_demodulation,[status(thm)],[f4851,f4466]) ).
thf(f4851,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( sP17 @ X12 )
= $true )
| ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP16 @ X12 ) ) )
| ~ spl591_513 ),
inference(subsumption_resolution,[status(thm)],[f3818,f4487]) ).
thf(f4487,plain,
! [X0: term] :
( $true
!= ( var @ X0 ) ),
inference(superposition,[status(thm)],[f4473,f4484]) ).
thf(f4473,plain,
( $true
!= ( var @ one ) ),
inference(forward_demodulation,[status(thm)],[f1142,f1061]) ).
thf(f1142,plain,
( ( var @ ( d2term @ d_one ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3818,plain,
( ! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( $true
= ( var @ ( sub @ ( sK314 @ X12 ) @ id ) ) ) )
| ~ spl591_513 ),
inference(avatar_component_clause,[status(thm)],[f3817]) ).
thf(f7254,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
!= ( sP17 @ X0 ) )
| ( $true
= ( X0 @ id @ one @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f7253,f1061]) ).
thf(f7253,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
!= ( sP17 @ X0 ) )
| ( $true
= ( X0 @ id @ ( d2term @ d_one ) @ id ) ) ),
inference(forward_demodulation,[status(thm)],[f884,f4480]) ).
thf(f884,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( sK334 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
!= ( sP17 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
thf(f8675,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK592 @ id @ one @ id ) )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) ) )
| ~ spl591_218 ),
inference(forward_demodulation,[status(thm)],[f8674,f1061]) ).
thf(f8674,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK592 @ id @ ( d2term @ d_one ) @ id ) )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) ) )
| ~ spl591_218 ),
inference(forward_demodulation,[status(thm)],[f8673,f4480]) ).
thf(f8673,plain,
( ! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) ) )
| ~ spl591_218 ),
inference(subsumption_resolution,[status(thm)],[f2531,f4484]) ).
thf(f2531,plain,
( ! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) ) )
| ~ spl591_218 ),
inference(avatar_component_clause,[status(thm)],[f2530]) ).
thf(f8645,plain,
( spl591_702
| spl591_703
| ~ spl591_220 ),
inference(avatar_split_clause,[status(thm)],[f8638,f2538,f8643,f8640]) ).
thf(f2538,definition,
( spl591_220
<=> ! [X4: subst,X3: subst,X2: subst,X1: term] :
( ( $false
= ( sK592 @ X2 @ X1 @ ( comp @ X3 @ X4 ) ) )
| ( $true
= ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_220])],[avatar_definition]) ).
thf(f8638,plain,
( ! [X2: subst,X1: term,X4: subst] :
( ( ( sK592 @ X2 @ X1 @ id )
= $false )
| ( $true
= ( sK592 @ id @ one @ X4 ) ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f8637,f1061]) ).
thf(f8637,plain,
( ! [X2: subst,X1: term,X4: subst] :
( ( ( sK592 @ X2 @ X1 @ id )
= $false )
| ( ( sK592 @ id @ ( d2term @ d_one ) @ X4 )
= $true ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f8636,f1226]) ).
thf(f8636,plain,
( ! [X2: subst,X1: term,X4: subst] :
( ( $false
= ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) ) )
| ( ( sK592 @ id @ ( d2term @ d_one ) @ X4 )
= $true ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f8635,f4480]) ).
thf(f8635,plain,
( ! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $true
= ( sK592 @ id @ ( sub @ X1 @ X3 ) @ X4 ) )
| ( $false
= ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f8634,f1226]) ).
thf(f8634,plain,
( ! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X3 ) @ X4 ) )
| ( $false
= ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f8633,f4466]) ).
thf(f8633,plain,
( ! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $false
= ( sK592 @ X2 @ X1 @ ( comp @ X3 @ X4 ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X3 ) @ X4 ) ) )
| ~ spl591_220 ),
inference(forward_demodulation,[status(thm)],[f2539,f4466]) ).
thf(f2539,plain,
( ! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $true
= ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ X4 ) )
| ( $false
= ( sK592 @ X2 @ X1 @ ( comp @ X3 @ X4 ) ) ) )
| ~ spl591_220 ),
inference(avatar_component_clause,[status(thm)],[f2538]) ).
thf(f8623,plain,
( ~ spl591_189
| ~ spl591_215 ),
inference(avatar_contradiction_clause,[status(thm)],[f8622]) ).
thf(f8622,plain,
( $false
| ~ spl591_189
| ~ spl591_215 ),
inference(trivial_inequality_removal,[status(thm)],[f8621]) ).
thf(f8621,plain,
( ( $true = $false )
| ~ spl591_189
| ~ spl591_215 ),
inference(forward_demodulation,[status(thm)],[f2415,f2519]) ).
thf(f2519,plain,
( ( hoasinduction_lem3 = $false )
| ~ spl591_215 ),
inference(avatar_component_clause,[status(thm)],[f2517]) ).
thf(f2517,definition,
( spl591_215
<=> ( hoasinduction_lem3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl591_215])],[avatar_definition]) ).
thf(f2415,plain,
( ( hoasinduction_lem3 = $true )
| ~ spl591_189 ),
inference(avatar_component_clause,[status(thm)],[f2413]) ).
thf(f2413,definition,
( spl591_189
<=> ( hoasinduction_lem3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_189])],[avatar_definition]) ).
thf(f8591,plain,
( spl591_118
| ~ spl591_681 ),
inference(avatar_contradiction_clause,[status(thm)],[f8590]) ).
thf(f8590,plain,
( $false
| spl591_118
| ~ spl591_681 ),
inference(subsumption_resolution,[status(thm)],[f8564,f2112]) ).
thf(f2112,plain,
( ( $true
!= ( sP12 @ sK350 ) )
| spl591_118 ),
inference(avatar_component_clause,[status(thm)],[f2110]) ).
thf(f2110,definition,
( spl591_118
<=> ( $true
= ( sP12 @ sK350 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_118])],[avatar_definition]) ).
thf(f8564,plain,
( ( $true
= ( sP12 @ sK350 ) )
| ~ spl591_681 ),
inference(trivial_inequality_removal,[status(thm)],[f8556]) ).
thf(f8556,plain,
( ( $true
= ( sP12 @ sK350 ) )
| ( $true != $true )
| ~ spl591_681 ),
inference(superposition,[status(thm)],[f6948,f8524]) ).
thf(f6948,plain,
( ! [X8: term,X7: subst] :
( $true
!= ( sK350 @ X7 @ X8 @ id ) )
| ~ spl591_681 ),
inference(avatar_component_clause,[status(thm)],[f6947]) ).
thf(f6947,definition,
( spl591_681
<=> ! [X8: term,X7: subst] :
( $true
!= ( sK350 @ X7 @ X8 @ id ) ) ),
introduced(definition,[new_symbols(naming,[spl591_681])],[avatar_definition]) ).
thf(f7010,plain,
( ~ spl591_241
| spl591_507
| ~ spl591_680 ),
inference(avatar_contradiction_clause,[status(thm)],[f7009]) ).
thf(f7009,plain,
( $false
| ~ spl591_241
| spl591_507
| ~ spl591_680 ),
inference(trivial_inequality_removal,[status(thm)],[f6997]) ).
thf(f6997,plain,
( ( $true != $true )
| ~ spl591_241
| spl591_507
| ~ spl591_680 ),
inference(superposition,[status(thm)],[f3791,f6994]) ).
thf(f6994,plain,
( ! [X4: term,X5: subst] :
( $true
= ( sK350 @ X5 @ X4 @ id ) )
| ~ spl591_241
| ~ spl591_680 ),
inference(subsumption_resolution,[status(thm)],[f6993,f6945]) ).
thf(f6945,plain,
( ! [X9: subst] :
( $true
= ( sK350 @ id @ one @ X9 ) )
| ~ spl591_680 ),
inference(avatar_component_clause,[status(thm)],[f6944]) ).
thf(f6944,definition,
( spl591_680
<=> ! [X9: subst] :
( $true
= ( sK350 @ id @ one @ X9 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_680])],[avatar_definition]) ).
thf(f6993,plain,
( ! [X2: subst,X4: term,X5: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ id ) )
| ( ( sK350 @ id @ one @ X2 )
!= $true ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f6992,f1061]) ).
thf(f6992,plain,
( ! [X2: subst,X4: term,X5: subst] :
( ( $true
!= ( sK350 @ id @ ( d2term @ d_one ) @ X2 ) )
| ( $true
= ( sK350 @ X5 @ X4 @ id ) ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f6991,f1226]) ).
thf(f6991,plain,
( ! [X2: subst,X4: term,X5: subst] :
( ( ( sK350 @ X5 @ X4 @ ( d2subst @ d_id ) )
= $true )
| ( $true
!= ( sK350 @ id @ ( d2term @ d_one ) @ X2 ) ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f6990,f4480]) ).
thf(f6990,plain,
( ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
!= ( sK350 @ id @ ( sub @ X4 @ X3 ) @ X2 ) )
| ( ( sK350 @ X5 @ X4 @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f6989,f1226]) ).
thf(f6989,plain,
( ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( ( sK350 @ ( d2subst @ d_id ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true )
| ( ( sK350 @ X5 @ X4 @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f6988,f4466]) ).
thf(f6988,plain,
( ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true )
| ( ( sK350 @ X5 @ X4 @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_241 ),
inference(forward_demodulation,[status(thm)],[f2627,f4466]) ).
thf(f2627,plain,
( ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) )
| ~ spl591_241 ),
inference(avatar_component_clause,[status(thm)],[f2626]) ).
thf(f2626,definition,
( spl591_241
<=> ! [X3: subst,X4: term,X5: subst,X2: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl591_241])],[avatar_definition]) ).
thf(f3791,plain,
( ( ( sK350 @ id @ ( lam @ sK351 ) @ id )
!= $true )
| spl591_507 ),
inference(avatar_component_clause,[status(thm)],[f3789]) ).
thf(f3789,definition,
( spl591_507
<=> ( ( sK350 @ id @ ( lam @ sK351 ) @ id )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_507])],[avatar_definition]) ).
thf(f6949,plain,
( spl591_680
| spl591_681
| ~ spl591_164 ),
inference(avatar_split_clause,[status(thm)],[f6942,f2306,f6947,f6944]) ).
thf(f2306,definition,
( spl591_164
<=> ! [X9: subst,X7: subst,X6: subst,X8: term] :
( ( $true
= ( sK350 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_164])],[avatar_definition]) ).
thf(f6942,plain,
( ! [X8: term,X9: subst,X7: subst] :
( ( $true
!= ( sK350 @ X7 @ X8 @ id ) )
| ( $true
= ( sK350 @ id @ one @ X9 ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f6941,f1226]) ).
thf(f6941,plain,
( ! [X8: term,X9: subst,X7: subst] :
( ( $true
!= ( sK350 @ X7 @ X8 @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK350 @ id @ one @ X9 ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f6940,f1061]) ).
thf(f6940,plain,
( ! [X8: term,X9: subst,X7: subst] :
( ( ( sK350 @ id @ ( d2term @ d_one ) @ X9 )
= $true )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f6939,f4480]) ).
thf(f6939,plain,
( ! [X8: term,X6: subst,X9: subst,X7: subst] :
( ( $true
= ( sK350 @ id @ ( sub @ X8 @ X6 ) @ X9 ) )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( d2subst @ d_id ) ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f6938,f4466]) ).
thf(f6938,plain,
( ! [X8: term,X6: subst,X9: subst,X7: subst] :
( ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
| ( $true
= ( sK350 @ id @ ( sub @ X8 @ X6 ) @ X9 ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f6937,f1226]) ).
thf(f6937,plain,
( ! [X8: term,X6: subst,X9: subst,X7: subst] :
( ( $true
= ( sK350 @ ( d2subst @ d_id ) @ ( sub @ X8 @ X6 ) @ X9 ) )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) ) )
| ~ spl591_164 ),
inference(forward_demodulation,[status(thm)],[f2307,f4466]) ).
thf(f2307,plain,
( ! [X8: term,X6: subst,X9: subst,X7: subst] :
( ( $true
= ( sK350 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) ) )
| ~ spl591_164 ),
inference(avatar_component_clause,[status(thm)],[f2306]) ).
thf(f3880,plain,
( spl591_189
| ~ spl591_5 ),
inference(avatar_split_clause,[status(thm)],[f1113,f1641,f2413]) ).
thf(f1641,definition,
( spl591_5
<=> ( $true = sP13 ) ),
introduced(definition,[new_symbols(naming,[spl591_5])],[avatar_definition]) ).
thf(f1113,plain,
( ( $true != sP13 )
| ( hoasinduction_lem3 = $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f3819,plain,
( spl591_513
| ~ spl591_28 ),
inference(avatar_split_clause,[status(thm)],[f855,f1734,f3817]) ).
thf(f1734,definition,
( spl591_28
<=> ( $true = sP21 ) ),
introduced(definition,[new_symbols(naming,[spl591_28])],[avatar_definition]) ).
thf(f855,plain,
! [X11: term,X12: subst > term > subst > $o] :
( ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
| ( $true
= ( sP16 @ X12 ) )
| ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( var @ ( sub @ ( sK314 @ X12 ) @ id ) ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true != sP21 ) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
thf(f334,plain,
( ( ( $true = sP21 )
| ( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( ( sK305 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 )
!= $true )
| ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) ) )
& ! [X6: subst,X7: subst,X8: subst,X9: term] :
( ( $true
!= ( sK305 @ X6 @ X9 @ ( comp @ X7 @ X8 ) ) )
| ( ( sK305 @ ( comp @ X6 @ X7 ) @ ( sub @ X9 @ X7 ) @ X8 )
= $true ) )
& ! [X10: term] :
( ( $true
= ( sK305 @ id @ X10 @ id ) )
| ( $true
!= ( var @ ( sub @ X10 @ id ) ) ) )
& ( $true
!= ( sP17 @ sK305 ) )
& ( $true
!= ( sP16 @ sK305 ) )
& ( $true
!= ( sK305 @ id @ sK304 @ id ) ) ) )
& ( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
& ( $true
!= ( X12 @ ( sK308 @ X12 ) @ ( sK306 @ X12 ) @ ( comp @ ( sK307 @ X12 ) @ ( sK309 @ X12 ) ) ) ) )
| ( ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
& ( ( X12 @ ( comp @ ( sK310 @ X12 ) @ ( sK311 @ X12 ) ) @ ( sub @ ( sK313 @ X12 ) @ ( sK311 @ X12 ) ) @ ( sK312 @ X12 ) )
!= $true ) )
| ( ( $true
!= ( X12 @ id @ ( sK314 @ X12 ) @ id ) )
& ( $true
= ( var @ ( sub @ ( sK314 @ X12 ) @ id ) ) ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ X11 @ id ) ) )
| ( $true != sP21 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK304,sK305,sK306,sK307,sK308,sK309,sK310,sK311,sK312,sK313,sK314])],[f329,f333,f332,f331,f330]) ).
thf(f330,plain,
( ? [X0: term,X1: subst > term > subst > $o] :
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
!= ( X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 ) )
| ( ( X1 @ X4 @ X2 @ ( comp @ X3 @ X5 ) )
= $true ) )
& ! [X6: subst,X7: subst,X8: subst,X9: term] :
( ( $true
!= ( X1 @ X6 @ X9 @ ( comp @ X7 @ X8 ) ) )
| ( ( X1 @ ( comp @ X6 @ X7 ) @ ( sub @ X9 @ X7 ) @ X8 )
= $true ) )
& ! [X10: term] :
( ( $true
= ( X1 @ id @ X10 @ id ) )
| ( $true
!= ( var @ ( sub @ X10 @ id ) ) ) )
& ( $true
!= ( sP17 @ X1 ) )
& ( $true
!= ( sP16 @ X1 ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) ) )
=> ( ! [X5: subst,X4: subst,X3: subst,X2: term] :
( ( ( sK305 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 )
!= $true )
| ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) ) )
& ! [X9: term,X8: subst,X7: subst,X6: subst] :
( ( $true
!= ( sK305 @ X6 @ X9 @ ( comp @ X7 @ X8 ) ) )
| ( ( sK305 @ ( comp @ X6 @ X7 ) @ ( sub @ X9 @ X7 ) @ X8 )
= $true ) )
& ! [X10: term] :
( ( $true
= ( sK305 @ id @ X10 @ id ) )
| ( $true
!= ( var @ ( sub @ X10 @ id ) ) ) )
& ( $true
!= ( sP17 @ sK305 ) )
& ( $true
!= ( sP16 @ sK305 ) )
& ( $true
!= ( sK305 @ id @ sK304 @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f331,plain,
! [X12: subst > term > subst > $o] :
( ? [X13: term,X14: subst,X15: subst,X16: subst] :
( ( $true
= ( X12 @ ( comp @ X15 @ X14 ) @ ( sub @ X13 @ X14 ) @ X16 ) )
& ( $true
!= ( X12 @ X15 @ X13 @ ( comp @ X14 @ X16 ) ) ) )
=> ( ( ( X12 @ ( comp @ ( sK308 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sub @ ( sK306 @ X12 ) @ ( sK307 @ X12 ) ) @ ( sK309 @ X12 ) )
= $true )
& ( $true
!= ( X12 @ ( sK308 @ X12 ) @ ( sK306 @ X12 ) @ ( comp @ ( sK307 @ X12 ) @ ( sK309 @ X12 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f332,plain,
! [X12: subst > term > subst > $o] :
( ? [X17: subst,X18: subst,X19: subst,X20: term] :
( ( $true
= ( X12 @ X17 @ X20 @ ( comp @ X18 @ X19 ) ) )
& ( $true
!= ( X12 @ ( comp @ X17 @ X18 ) @ ( sub @ X20 @ X18 ) @ X19 ) ) )
=> ( ( $true
= ( X12 @ ( sK310 @ X12 ) @ ( sK313 @ X12 ) @ ( comp @ ( sK311 @ X12 ) @ ( sK312 @ X12 ) ) ) )
& ( ( X12 @ ( comp @ ( sK310 @ X12 ) @ ( sK311 @ X12 ) ) @ ( sub @ ( sK313 @ X12 ) @ ( sK311 @ X12 ) ) @ ( sK312 @ X12 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f333,plain,
! [X12: subst > term > subst > $o] :
( ? [X21: term] :
( ( ( X12 @ id @ X21 @ id )
!= $true )
& ( ( var @ ( sub @ X21 @ id ) )
= $true ) )
=> ( ( $true
!= ( X12 @ id @ ( sK314 @ X12 ) @ id ) )
& ( $true
= ( var @ ( sub @ ( sK314 @ X12 ) @ id ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f329,plain,
( ( ( $true = sP21 )
| ? [X0: term,X1: subst > term > subst > $o] :
( ! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( $true
!= ( X1 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 ) )
| ( ( X1 @ X4 @ X2 @ ( comp @ X3 @ X5 ) )
= $true ) )
& ! [X6: subst,X7: subst,X8: subst,X9: term] :
( ( $true
!= ( X1 @ X6 @ X9 @ ( comp @ X7 @ X8 ) ) )
| ( ( X1 @ ( comp @ X6 @ X7 ) @ ( sub @ X9 @ X7 ) @ X8 )
= $true ) )
& ! [X10: term] :
( ( $true
= ( X1 @ id @ X10 @ id ) )
| ( $true
!= ( var @ ( sub @ X10 @ id ) ) ) )
& ( $true
!= ( sP17 @ X1 ) )
& ( $true
!= ( sP16 @ X1 ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) ) ) )
& ( ! [X11: term,X12: subst > term > subst > $o] :
( ? [X13: term,X14: subst,X15: subst,X16: subst] :
( ( $true
= ( X12 @ ( comp @ X15 @ X14 ) @ ( sub @ X13 @ X14 ) @ X16 ) )
& ( $true
!= ( X12 @ X15 @ X13 @ ( comp @ X14 @ X16 ) ) ) )
| ? [X17: subst,X18: subst,X19: subst,X20: term] :
( ( $true
= ( X12 @ X17 @ X20 @ ( comp @ X18 @ X19 ) ) )
& ( $true
!= ( X12 @ ( comp @ X17 @ X18 ) @ ( sub @ X20 @ X18 ) @ X19 ) ) )
| ? [X21: term] :
( ( ( X12 @ id @ X21 @ id )
!= $true )
& ( ( var @ ( sub @ X21 @ id ) )
= $true ) )
| ( ( sP17 @ X12 )
= $true )
| ( $true
= ( sP16 @ X12 ) )
| ( $true
= ( X12 @ id @ X11 @ id ) ) )
| ( $true != sP21 ) ) ),
inference(rectify,[status(thm)],[f328]) ).
thf(f328,plain,
( ( ( $true = sP21 )
| ? [X328: term,X329: subst > term > subst > $o] :
( ! [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
!= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
| ( $true
= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
& ! [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
!= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
| ( $true
= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
& ! [X336: term] :
( ( $true
= ( X329 @ id @ X336 @ id ) )
| ( ( var @ ( sub @ X336 @ id ) )
!= $true ) )
& ( $true
!= ( sP17 @ X329 ) )
& ( $true
!= ( sP16 @ X329 ) )
& ( $true
!= ( X329 @ id @ X328 @ id ) ) ) )
& ( ! [X328: term,X329: subst > term > subst > $o] :
( ? [X332: term,X333: subst,X334: subst,X335: subst] :
( ( $true
= ( X329 @ ( comp @ X334 @ X333 ) @ ( sub @ X332 @ X333 ) @ X335 ) )
& ( $true
!= ( X329 @ X334 @ X332 @ ( comp @ X333 @ X335 ) ) ) )
| ? [X342: subst,X343: subst,X344: subst,X345: term] :
( ( $true
= ( X329 @ X342 @ X345 @ ( comp @ X343 @ X344 ) ) )
& ( $true
!= ( X329 @ ( comp @ X342 @ X343 ) @ ( sub @ X345 @ X343 ) @ X344 ) ) )
| ? [X336: term] :
( ( $true
!= ( X329 @ id @ X336 @ id ) )
& ( ( var @ ( sub @ X336 @ id ) )
= $true ) )
| ( $true
= ( sP17 @ X329 ) )
| ( $true
= ( sP16 @ X329 ) )
| ( $true
= ( X329 @ id @ X328 @ id ) ) )
| ( $true != sP21 ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f3792,plain,
( spl591_5
| ~ spl591_507 ),
inference(avatar_split_clause,[status(thm)],[f920,f3789,f1641]) ).
thf(f920,plain,
( ( $true = sP13 )
| ( ( sK350 @ id @ ( lam @ sK351 ) @ id )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f380]) ).
thf(f380,plain,
( ( ( $true = sP13 )
| ( ( ( sK350 @ id @ ( lam @ sK351 ) @ id )
!= $true )
& ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) )
& ! [X6: subst,X7: subst,X8: term,X9: subst] :
( ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
| ( $true
= ( sK350 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( sK350 @ id @ ( sub @ sK351 @ ( push @ X10 @ id ) ) @ id ) )
| ( $true
!= ( sK350 @ id @ X10 @ id ) ) )
& ( $true
!= ( sP12 @ sK350 ) ) ) )
& ( ! [X11: subst > term > subst > $o,X12: term] :
( ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ( ( ( X11 @ ( sK355 @ X11 ) @ ( sK354 @ X11 ) @ ( comp @ ( sK353 @ X11 ) @ ( sK352 @ X11 ) ) )
!= $true )
& ( $true
= ( X11 @ ( comp @ ( sK355 @ X11 ) @ ( sK353 @ X11 ) ) @ ( sub @ ( sK354 @ X11 ) @ ( sK353 @ X11 ) ) @ ( sK352 @ X11 ) ) ) )
| ( ( $true
= ( X11 @ ( sK357 @ X11 ) @ ( sK358 @ X11 ) @ ( comp @ ( sK356 @ X11 ) @ ( sK359 @ X11 ) ) ) )
& ( $true
!= ( X11 @ ( comp @ ( sK357 @ X11 ) @ ( sK356 @ X11 ) ) @ ( sub @ ( sK358 @ X11 ) @ ( sK356 @ X11 ) ) @ ( sK359 @ X11 ) ) ) )
| ( ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ ( sK360 @ X12 @ X11 ) @ id ) ) @ id ) )
& ( $true
= ( X11 @ id @ ( sK360 @ X12 @ X11 ) @ id ) ) )
| ( ( sP12 @ X11 )
= $true ) )
| ( $true != sP13 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK350,sK351,sK352,sK353,sK354,sK355,sK356,sK357,sK358,sK359,sK360])],[f375,f379,f378,f377,f376]) ).
thf(f376,plain,
( ? [X0: subst > term > subst > $o,X1: term] :
( ( $true
!= ( X0 @ id @ ( lam @ X1 ) @ id ) )
& ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
= ( X0 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( X0 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) )
& ! [X6: subst,X7: subst,X8: term,X9: subst] :
( ( $true
!= ( X0 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
| ( $true
= ( X0 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( sub @ X1 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( $true
!= ( sP12 @ X0 ) ) )
=> ( ( ( sK350 @ id @ ( lam @ sK351 ) @ id )
!= $true )
& ! [X5: subst,X4: term,X3: subst,X2: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) )
& ! [X9: subst,X8: term,X7: subst,X6: subst] :
( ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
| ( $true
= ( sK350 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) ) )
& ! [X10: term] :
( ( $true
= ( sK350 @ id @ ( sub @ sK351 @ ( push @ X10 @ id ) ) @ id ) )
| ( $true
!= ( sK350 @ id @ X10 @ id ) ) )
& ( $true
!= ( sP12 @ sK350 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f377,plain,
! [X11: subst > term > subst > $o] :
( ? [X13: subst,X14: subst,X15: term,X16: subst] :
( ( $true
!= ( X11 @ X16 @ X15 @ ( comp @ X14 @ X13 ) ) )
& ( ( X11 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) @ X13 )
= $true ) )
=> ( ( ( X11 @ ( sK355 @ X11 ) @ ( sK354 @ X11 ) @ ( comp @ ( sK353 @ X11 ) @ ( sK352 @ X11 ) ) )
!= $true )
& ( $true
= ( X11 @ ( comp @ ( sK355 @ X11 ) @ ( sK353 @ X11 ) ) @ ( sub @ ( sK354 @ X11 ) @ ( sK353 @ X11 ) ) @ ( sK352 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f378,plain,
! [X11: subst > term > subst > $o] :
( ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X11 @ X18 @ X19 @ ( comp @ X17 @ X20 ) ) )
& ( $true
!= ( X11 @ ( comp @ X18 @ X17 ) @ ( sub @ X19 @ X17 ) @ X20 ) ) )
=> ( ( $true
= ( X11 @ ( sK357 @ X11 ) @ ( sK358 @ X11 ) @ ( comp @ ( sK356 @ X11 ) @ ( sK359 @ X11 ) ) ) )
& ( $true
!= ( X11 @ ( comp @ ( sK357 @ X11 ) @ ( sK356 @ X11 ) ) @ ( sub @ ( sK358 @ X11 ) @ ( sK356 @ X11 ) ) @ ( sK359 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f379,plain,
! [X11: subst > term > subst > $o,X12: term] :
( ? [X21: term] :
( ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ X21 @ id ) ) @ id ) )
& ( $true
= ( X11 @ id @ X21 @ id ) ) )
=> ( ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ ( sK360 @ X12 @ X11 ) @ id ) ) @ id ) )
& ( $true
= ( X11 @ id @ ( sK360 @ X12 @ X11 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f375,plain,
( ( ( $true = sP13 )
| ? [X0: subst > term > subst > $o,X1: term] :
( ( $true
!= ( X0 @ id @ ( lam @ X1 ) @ id ) )
& ! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
= ( X0 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( X0 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true ) )
& ! [X6: subst,X7: subst,X8: term,X9: subst] :
( ( $true
!= ( X0 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
| ( $true
= ( X0 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) ) )
& ! [X10: term] :
( ( ( X0 @ id @ ( sub @ X1 @ ( push @ X10 @ id ) ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) )
& ( $true
!= ( sP12 @ X0 ) ) ) )
& ( ! [X11: subst > term > subst > $o,X12: term] :
( ( $true
= ( X11 @ id @ ( lam @ X12 ) @ id ) )
| ? [X13: subst,X14: subst,X15: term,X16: subst] :
( ( $true
!= ( X11 @ X16 @ X15 @ ( comp @ X14 @ X13 ) ) )
& ( ( X11 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) @ X13 )
= $true ) )
| ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X11 @ X18 @ X19 @ ( comp @ X17 @ X20 ) ) )
& ( $true
!= ( X11 @ ( comp @ X18 @ X17 ) @ ( sub @ X19 @ X17 ) @ X20 ) ) )
| ? [X21: term] :
( ( $true
!= ( X11 @ id @ ( sub @ X12 @ ( push @ X21 @ id ) ) @ id ) )
& ( $true
= ( X11 @ id @ X21 @ id ) ) )
| ( ( sP12 @ X11 )
= $true ) )
| ( $true != sP13 ) ) ),
inference(rectify,[status(thm)],[f374]) ).
thf(f374,plain,
( ( ( $true = sP13 )
| ? [X198: subst > term > subst > $o,X199: term] :
( ( $true
!= ( X198 @ id @ ( lam @ X199 ) @ id ) )
& ! [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
| ( $true
!= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
& ! [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
!= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
| ( $true
= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
& ! [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
= $true )
| ( $true
!= ( X198 @ id @ X213 @ id ) ) )
& ( $true
!= ( sP12 @ X198 ) ) ) )
& ( ! [X198: subst > term > subst > $o,X199: term] :
( ( $true
= ( X198 @ id @ ( lam @ X199 ) @ id ) )
| ? [X200: subst,X201: subst,X202: term,X203: subst] :
( ( $true
!= ( X198 @ X203 @ X202 @ ( comp @ X201 @ X200 ) ) )
& ( $true
= ( X198 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) @ X200 ) ) )
| ? [X209: subst,X210: subst,X211: term,X212: subst] :
( ( $true
= ( X198 @ X210 @ X211 @ ( comp @ X209 @ X212 ) ) )
& ( $true
!= ( X198 @ ( comp @ X210 @ X209 ) @ ( sub @ X211 @ X209 ) @ X212 ) ) )
| ? [X213: term] :
( ( ( X198 @ id @ ( sub @ X199 @ ( push @ X213 @ id ) ) @ id )
!= $true )
& ( $true
= ( X198 @ id @ X213 @ id ) ) )
| ( $true
= ( sP12 @ X198 ) ) )
| ( $true != sP13 ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f3159,plain,
( spl591_28
| ~ spl591_362 ),
inference(avatar_split_clause,[status(thm)],[f857,f3156,f1734]) ).
thf(f857,plain,
( ( $true = sP21 )
| ( $true
!= ( sK305 @ id @ sK304 @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
thf(f2628,plain,
( spl591_241
| spl591_5 ),
inference(avatar_split_clause,[status(thm)],[f919,f1641,f2626]) ).
thf(f919,plain,
! [X2: subst,X3: subst,X4: term,X5: subst] :
( ( $true
= ( sK350 @ X5 @ X4 @ ( comp @ X3 @ X2 ) ) )
| ( ( sK350 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) @ X2 )
!= $true )
| ( $true = sP13 ) ),
inference(cnf_transformation,[status(thm)],[f380]) ).
thf(f2540,plain,
( spl591_220
| spl591_215 ),
inference(avatar_split_clause,[status(thm)],[f1396,f2517,f2538]) ).
thf(f1396,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( hoasinduction_lem3 = $false )
| ( $false
= ( sK592 @ X2 @ X1 @ ( comp @ X3 @ X4 ) ) )
| ( $true
= ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1395]) ).
thf(f1395,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( hoasinduction_lem3 = $false )
| ( $true
= ( ( sK592 @ X2 @ X1 @ ( comp @ X3 @ X4 ) )
=> ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1394]) ).
thf(f1394,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $true
= ( ^ [Y0: subst] :
( ( sK592 @ X2 @ X1 @ ( comp @ X3 @ Y0 ) )
=> ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ Y0 ) )
@ X4 ) )
| ( hoasinduction_lem3 = $false ) ),
inference(pi_clausification,[status(thm)],[f1393]) ).
thf(f1393,plain,
! [X2: subst,X3: subst,X1: term] :
( ( hoasinduction_lem3 = $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK592 @ X2 @ X1 @ ( comp @ X3 @ Y0 ) )
=> ( sK592 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1392]) ).
thf(f1392,plain,
! [X2: subst,X3: subst,X1: term] :
( ( hoasinduction_lem3 = $false )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK592 @ X2 @ X1 @ ( comp @ Y0 @ Y1 ) )
=> ( sK592 @ ( comp @ X2 @ Y0 ) @ ( sub @ X1 @ Y0 ) @ Y1 ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1391]) ).
thf(f1391,plain,
! [X2: subst,X1: term] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK592 @ X2 @ X1 @ ( comp @ Y0 @ Y1 ) )
=> ( sK592 @ ( comp @ X2 @ Y0 ) @ ( sub @ X1 @ Y0 ) @ Y1 ) ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1390]) ).
thf(f1390,plain,
! [X2: subst,X1: term] :
( ( hoasinduction_lem3 = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK592 @ Y0 @ X1 @ ( comp @ Y1 @ Y2 ) )
=> ( sK592 @ ( comp @ Y0 @ Y1 ) @ ( sub @ X1 @ Y1 ) @ Y2 ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1389]) ).
thf(f1389,plain,
! [X1: term] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK592 @ Y0 @ X1 @ ( comp @ Y1 @ Y2 ) )
=> ( sK592 @ ( comp @ Y0 @ Y1 ) @ ( sub @ X1 @ Y1 ) @ Y2 ) ) ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1388]) ).
thf(f1388,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ Y1 @ Y0 @ ( comp @ Y2 @ Y3 ) )
=> ( sK592 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) @ Y3 ) ) ) ) )
@ X1 )
= $true )
| ( hoasinduction_lem3 = $false ) ),
inference(pi_clausification,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( hoasinduction_lem3 = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ Y1 @ Y0 @ ( comp @ Y2 @ Y3 ) )
=> ( sK592 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) @ Y3 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1385]) ).
thf(f1385,plain,
( ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ Y1 @ Y0 @ ( comp @ Y2 @ Y3 ) )
=> ( sK592 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK592 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK592 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1384]) ).
thf(f1384,plain,
( ( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) )
@ sK592 ) )
| ( hoasinduction_lem3 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1383]) ).
thf(f1383,plain,
( ( hoasinduction_lem3 = $false )
| ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1381]) ).
thf(f1381,plain,
( hoasinduction_lem3
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( hoaslam @ id @ Y1 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1260]) ).
thf(f1260,plain,
( hoasinduction_lem3
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( hoasinduction_lem3
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( hoasinduction_lem3
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y3 @ Y4 ) )
=> ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: subst > term > subst > $o] :
( ( ! [X1: subst,X2: subst,X3: subst,X4: term] :
( ( X0 @ X3 @ X4 @ ( comp @ X2 @ X1 ) )
=> ( X0 @ ( comp @ X3 @ X2 ) @ ( sub @ X4 @ X2 ) @ X1 ) )
=> ( ! [X5: term,X6: subst,X7: subst,X8: subst] :
( ( X0 @ ( comp @ X6 @ X7 ) @ ( sub @ X5 @ X7 ) @ X8 )
=> ( X0 @ X6 @ X5 @ ( comp @ X7 @ X8 ) ) )
=> ( ! [X9: subst > term > term] :
( ! [X10: subst,X11: subst,X12: term] :
( ( X9 @ ( comp @ X11 @ X10 ) @ ( sub @ X12 @ X10 ) )
= ( sub @ ( X9 @ X11 @ X12 ) @ X10 ) )
=> ( ! [X13: term] :
( ( X0 @ id @ X13 @ id )
=> ( X0 @ id @ ( X9 @ id @ X13 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X15: term] : ( X9 @ X14 @ X15 ) )
@ id ) ) )
=> ! [X16: term] :
( ! [X17: term] :
( ( X0 @ id @ X17 @ id )
=> ( X0 @ id @ ( sub @ X16 @ ( push @ X17 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X16 ) @ id ) ) ) ) )
= hoasinduction_lem3 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X10: subst > term > subst > $o] :
( ( ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X13: term,X14: subst,X26: subst,X25: 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 ) ) )
=> ! [X13: term] :
( ! [X15: term] :
( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( sub @ X13 @ ( push @ X15 @ id ) ) @ id ) )
=> ( X10 @ id @ ( lam @ X13 ) @ id ) ) ) ) )
= hoasinduction_lem3 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X10: subst > term > subst > $o] :
( ( ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X13: term,X14: subst,X26: subst,X25: 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 ) ) )
=> ! [X13: term] :
( ! [X15: term] :
( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( sub @ X13 @ ( push @ X15 @ id ) ) @ id ) )
=> ( X10 @ id @ ( lam @ X13 ) @ id ) ) ) ) )
= hoasinduction_lem3 ),
file('/export/starexec/sandbox/tmp/tmp.OZKaewZbi7/DTF2THF_21668.p',hoasinduction_lem3) ).
thf(f2532,plain,
( spl591_218
| spl591_215 ),
inference(avatar_split_clause,[status(thm)],[f1424,f2517,f2530]) ).
thf(f1424,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( hoasinduction_lem3 = $false )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) )
| ( $true
= ( sK592 @ id @ ( sK596 @ X1 ) @ id ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1422]) ).
thf(f1422,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( ( sK592 @ id @ ( sK596 @ X1 ) @ id )
=> ( sK592 @ id @ ( X1 @ id @ ( sK596 @ X1 ) ) @ id ) )
= $false )
| ( hoasinduction_lem3 = $false )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1421]) ).
thf(f1421,plain,
! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK596 @ X1 ) ) )
| ( hoasinduction_lem3 = $false )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1420]) ).
thf(f1420,plain,
! [X1: subst > term > term] :
( ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) )
| ( ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) )
!= ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f1419]) ).
thf(f1419,plain,
! [X1: subst > term > term] :
( ( $false
= ( ( X1 @ ( comp @ ( sK594 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sub @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ ( sK595 @ X1 ) ) ) )
| ( hoasinduction_lem3 = $false )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1418]) ).
thf(f1418,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3 = $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( ( ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK593 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ Y0 ) )
@ ( sK595 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1417]) ).
thf(f1417,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( X1 @ ( comp @ ( sK594 @ X1 ) @ Y0 ) @ ( sub @ ( sK593 @ X1 ) @ Y0 ) )
= ( sub @ ( X1 @ ( sK594 @ X1 ) @ ( sK593 @ X1 ) ) @ Y0 ) ) ) )
| ( hoasinduction_lem3 = $false )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1416]) ).
thf(f1416,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( hoasinduction_lem3 = $false )
| ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ ( sK593 @ X1 ) @ Y1 ) )
= ( sub @ ( X1 @ Y0 @ ( sK593 @ X1 ) ) @ Y1 ) ) )
@ ( sK594 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1415]) ).
thf(f1415,plain,
! [X1: subst > term > term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ ( sK593 @ X1 ) @ Y1 ) )
= ( sub @ ( X1 @ Y0 @ ( sK593 @ X1 ) ) @ Y1 ) ) ) )
= $false )
| ( ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1414]) ).
thf(f1414,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3 = $false )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ ( sK593 @ X1 ) @ Y1 ) )
= ( sub @ ( X1 @ Y0 @ ( sK593 @ X1 ) ) @ Y1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1413]) ).
thf(f1413,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 ) ) ) )
@ ( sK593 @ X1 ) ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1412]) ).
thf(f1412,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 ) ) ) ) ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1411]) ).
thf(f1411,plain,
! [X1: subst > term > term] :
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( X1 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( X1 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ X1 ) @ id ) ) ) )
| ( hoasinduction_lem3 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1410]) ).
thf(f1410,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3 = $false )
| ( $true
= ( ^ [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] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f1409]) ).
thf(f1409,plain,
( ( hoasinduction_lem3 = $false )
| ( $true
= ( !! @ ( 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] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1397]) ).
thf(f1397,plain,
( ( hoasinduction_lem3 = $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] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1386]) ).
thf(f1386,plain,
( ( hoasinduction_lem3 = $false )
| ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK592 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK592 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK592 @ id @ ( hoaslam @ id @ Y0 ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1385]) ).
thf(f2520,plain,
( spl591_214
| spl591_215 ),
inference(avatar_split_clause,[status(thm)],[f1427,f2517,f2513]) ).
thf(f1427,plain,
( ( hoasinduction_lem3 = $false )
| ( $false
= ( sK592 @ id @ ( lam @ sK597 ) @ id ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1426]) ).
thf(f1426,plain,
( ( hoasinduction_lem3 = $false )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ id @ Y0 @ id )
=> ( sK592 @ id @ ( sub @ sK597 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ sK597 ) @ id ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1425]) ).
thf(f1425,plain,
( ( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ Y0 ) @ id ) )
@ sK597 ) )
| ( hoasinduction_lem3 = $false ) ),
inference(sigma_clausification,[status(thm)],[f1408]) ).
thf(f1408,plain,
( ( hoasinduction_lem3 = $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ id @ Y1 @ id )
=> ( sK592 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK592 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1397]) ).
thf(f2308,plain,
( spl591_5
| spl591_164 ),
inference(avatar_split_clause,[status(thm)],[f918,f2306,f1641]) ).
thf(f918,plain,
! [X8: term,X6: subst,X9: subst,X7: subst] :
( ( $true = sP13 )
| ( $true
= ( sK350 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 ) )
| ( $true
!= ( sK350 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f380]) ).
thf(f2252,plain,
( spl591_28
| spl591_151 ),
inference(avatar_split_clause,[status(thm)],[f862,f2250,f1734]) ).
thf(f862,plain,
! [X2: term,X3: subst,X4: subst,X5: subst] :
( ( ( sK305 @ ( comp @ X4 @ X3 ) @ ( sub @ X2 @ X3 ) @ X5 )
!= $true )
| ( $true
= ( sK305 @ X4 @ X2 @ ( comp @ X3 @ X5 ) ) )
| ( $true = sP21 ) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
thf(f2113,plain,
( ~ spl591_118
| spl591_5 ),
inference(avatar_split_clause,[status(thm)],[f916,f1641,f2110]) ).
thf(f916,plain,
( ( $true
!= ( sP12 @ sK350 ) )
| ( $true = sP13 ) ),
inference(cnf_transformation,[status(thm)],[f380]) ).
thf(f2053,plain,
( spl591_28
| ~ spl591_104 ),
inference(avatar_split_clause,[status(thm)],[f859,f2050,f1734]) ).
thf(f859,plain,
( ( $true
!= ( sP17 @ sK305 ) )
| ( $true = sP21 ) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.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 09:12:33 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.30/0.46 % Domain : Software Verification
% 0.30/0.46 % Problem : Benchmark: ALG444^1, Active target: hoasinduction_lem3
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Kon26]
% 0.30/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : ? v9.3.0
% 0.30/0.46 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.30/0.46 % Number of atoms : 255 ( 129 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 248 ( 127 avg)
% 0.30/0.46 % Number of connectives : 2642 ( 333 ~; 306 |; 129 &;1770 @)
% 0.30/0.46 % ( 56 <=>; 48 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 151 ( 76 avg)
% 0.30/0.46 % Number of types : 5 ( 4 usr)
% 0.30/0.46 % Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.30/0.46 % Number of variables : 568 ( 10 ^; 556 !; 2 ?; 568 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(term_type,type,
% 0.30/0.46 term: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(subst_type,type,
% 0.30/0.46 subst: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(one_decl,type,
% 0.30/0.46 one: term ).
% 0.30/0.46
% 0.30/0.46 thf(ap_decl,type,
% 0.30/0.46 ap: term > term > term ).
% 0.30/0.46
% 0.30/0.46 thf(lam_decl,type,
% 0.30/0.46 lam: term > term ).
% 0.30/0.46
% 0.30/0.46 thf(sub_decl,type,
% 0.30/0.46 sub: term > subst > term ).
% 0.30/0.46
% 0.30/0.46 thf(id_decl,type,
% 0.30/0.46 id: subst ).
% 0.30/0.46
% 0.30/0.46 thf(sh_decl,type,
% 0.30/0.46 sh: subst ).
% 0.30/0.46
% 0.30/0.46 thf(push_decl,type,
% 0.30/0.46 push: term > subst > subst ).
% 0.30/0.46
% 0.30/0.46 thf(comp_decl,type,
% 0.30/0.46 comp: subst > subst > subst ).
% 0.30/0.46
% 0.30/0.46 thf(var_decl,type,
% 0.30/0.46 var: term > $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1v2_decl,type,
% 0.30/0.46 pushprop_lem1v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1_gthm_decl,type,
% 0.30/0.46 pushprop_lem1_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axmap_decl,type,
% 0.30/0.46 axmap: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem0_gthm_decl,type,
% 0.30/0.46 pushprop_lem0_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(shinj_decl,type,
% 0.30/0.46 shinj: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem1v2_decl,type,
% 0.30/0.46 hoasinduction_lem1v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem1v2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasap_decl,type,
% 0.30/0.46 hoasap: subst > term > subst > term > term ).
% 0.30/0.46
% 0.30/0.46 thf(induction2lem_decl,type,
% 0.30/0.46 induction2lem: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2_f_decl,type,
% 0.30/0.46 hoasinduction_lem3v2_f: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axvarshift_decl,type,
% 0.30/0.46 axvarshift: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj2_decl,type,
% 0.30/0.46 hoasapinj2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapnotvar_gthm_decl,type,
% 0.30/0.46 hoasapnotvar_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj1_decl,type,
% 0.30/0.46 hoasapinj1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ulamvar1_decl,type,
% 0.30/0.46 ulamvar1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction2lem_lthm_decl,type,
% 0.30/0.46 induction2lem_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem3v2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(apnotvar_decl,type,
% 0.30/0.46 apnotvar: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lthm_orig_decl,type,
% 0.30/0.46 pushprop_lthm_orig: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3v2_f_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lthm_decl,type,
% 0.30/0.46 hoasinduction_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.30/0.46 hoasinduction_no_psi_cond_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslaminj_decl,type,
% 0.30/0.46 hoaslaminj: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3aaa_decl,type,
% 0.30/0.46 hoasinduction_lem3aaa: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction2lem_gthm_decl,type,
% 0.30/0.46 induction2lem_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3aa_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3_decl,type,
% 0.30/0.46 hoasinduction_lem3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem2_decl,type,
% 0.30/0.46 hoasinduction_lem2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(termmset_lthm_decl,type,
% 0.30/0.46 termmset_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem1_decl,type,
% 0.30/0.46 hoasinduction_lem1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotap_lthm_decl,type,
% 0.30/0.46 hoaslamnotap_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1v2_lthm_decl,type,
% 0.30/0.46 pushprop_lem1v2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapnotvar_decl,type,
% 0.30/0.46 hoasapnotvar: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem0_decl,type,
% 0.30/0.46 hoasinduction_lem0: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_decl,type,
% 0.30/0.46 hoasinduction: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_gthm_decl,type,
% 0.30/0.46 hoasinduction_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axapp_decl,type,
% 0.30/0.46 axapp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotvar_lthm_decl,type,
% 0.30/0.46 hoaslamnotvar_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem3v2_lthm_decl,type,
% 0.30/0.46 pushprop_lem3v2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3b_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ulamvarind_decl,type,
% 0.30/0.46 ulamvarind: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction_decl,type,
% 0.30/0.46 induction: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3a_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(termmset_gthm_decl,type,
% 0.30/0.46 termmset_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3aa_decl,type,
% 0.30/0.46 hoasinduction_lem3aa: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1v2_gthm_decl,type,
% 0.30/0.46 pushprop_lem1v2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotap_gthm_decl,type,
% 0.30/0.46 hoaslamnotap_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotvar_gthm_decl,type,
% 0.30/0.46 hoaslamnotvar_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem3b_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem2v2_decl,type,
% 0.30/0.46 pushprop_lem2v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem3a_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axclos_decl,type,
% 0.30/0.46 axclos: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axassoc_decl,type,
% 0.30/0.46 axassoc: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem2v2_decl,type,
% 0.30/0.46 hoasinduction_lem2v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lthm_decl,type,
% 0.30/0.46 pushprop_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(apinj2_decl,type,
% 0.30/0.46 apinj2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(apinj1_decl,type,
% 0.30/0.46 apinj1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj2_lthm_decl,type,
% 0.30/0.46 hoasapinj2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2a_decl,type,
% 0.30/0.46 hoasinduction_lem3v2a: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj1_lthm_decl,type,
% 0.30/0.46 hoasapinj1_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslaminj_lthm_decl,type,
% 0.30/0.46 hoaslaminj_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axvarcons_decl,type,
% 0.30/0.46 axvarcons: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslam_decl,type,
% 0.30/0.46 hoaslam: subst > ( subst > term > term ) > term ).
% 0.30/0.46
% 0.30/0.46 thf(axscons_decl,type,
% 0.30/0.46 axscons: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem2v2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axidr_decl,type,
% 0.30/0.46 axidr: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1_decl,type,
% 0.30/0.46 pushprop_lem1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(laminj_decl,type,
% 0.30/0.46 laminj: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem0_decl,type,
% 0.30/0.46 pushprop_lem0: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_gthm_decl,type,
% 0.30/0.46 pushprop_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axabs_decl,type,
% 0.30/0.46 axabs: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3v2a_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem2_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj2_gthm_decl,type,
% 0.30/0.46 hoasapinj2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.30/0.46 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem1_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem1_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(lamnotap_decl,type,
% 0.30/0.46 lamnotap: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapinj1_gthm_decl,type,
% 0.30/0.46 hoasapinj1_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotvar_decl,type,
% 0.30/0.46 hoaslamnotvar: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axidl_decl,type,
% 0.30/0.46 axidl: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslaminj_gthm_decl,type,
% 0.30/0.46 hoaslaminj_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction2_lthm_decl,type,
% 0.30/0.46 induction2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem0_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem0_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(substmonoid_lthm_decl,type,
% 0.30/0.46 substmonoid_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_decl,type,
% 0.30/0.46 pushprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem3_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem2_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3b_decl,type,
% 0.30/0.46 hoasinduction_lem3b: $o ).
% 0.30/0.46
% 0.30/0.46 thf(substmonoid_decl,type,
% 0.30/0.46 substmonoid: $o ).
% 0.30/0.46
% 0.30/0.46 thf(lamnotvar_decl,type,
% 0.30/0.46 lamnotvar: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3a_decl,type,
% 0.30/0.46 hoasinduction_lem3a: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem1_gthm_decl,type,
% 0.30/0.46 hoasinduction_lem1_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_no_psi_cond_decl,type,
% 0.30/0.46 hoasinduction_no_psi_cond: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction2_gthm_decl,type,
% 0.30/0.46 induction2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem2v2_lthm_decl,type,
% 0.30/0.46 pushprop_lem2v2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasvar_decl,type,
% 0.30/0.46 hoasvar: subst > term > subst > $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoaslamnotap_decl,type,
% 0.30/0.46 hoaslamnotap: $o ).
% 0.30/0.46
% 0.30/0.46 thf(substmonoid_gthm_decl,type,
% 0.30/0.46 substmonoid_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ulamvarsh_decl,type,
% 0.30/0.46 ulamvarsh: $o ).
% 0.30/0.46
% 0.30/0.46 thf(induction2_decl,type,
% 0.30/0.46 induction2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem3v2_decl,type,
% 0.30/0.46 pushprop_lem3v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem2v2_gthm_decl,type,
% 0.30/0.46 pushprop_lem2v2_gthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem1_lthm_decl,type,
% 0.30/0.46 pushprop_lem1_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2_decl,type,
% 0.30/0.46 hoasinduction_lem3v2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(axshiftcons_decl,type,
% 0.30/0.46 axshiftcons: $o ).
% 0.30/0.46
% 0.30/0.46 thf(termmset_decl,type,
% 0.30/0.46 termmset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_lem0_lthm_decl,type,
% 0.30/0.46 pushprop_lem0_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasapnotvar_lthm_decl,type,
% 0.30/0.46 hoasapnotvar_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.30/0.46 hoasinduction_lem3v2_lthm: $o ).
% 0.30/0.46
% 0.30/0.46 thf(pushprop_p_and_p_prime_decl,type,
% 0.30/0.46 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(axvarid_decl,type,
% 0.30/0.46 axvarid: $o ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lthm_3_decl,type,
% 0.30/0.46 hoasinduction_lthm_3: $o ).
% 0.30/0.46
% 0.30/0.46 %----Types of the domains
% 0.30/0.46 thf(d_term_type,type,
% 0.30/0.46 d_term: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(d_subst_type,type,
% 0.30/0.46 d_subst: $tType ).
% 0.30/0.46
% 0.30/0.46 %----Types of the promotion functions
% 0.30/0.46 thf(d2term_decl,type,
% 0.30/0.46 d2term: d_term > term ).
% 0.30/0.46
% 0.30/0.46 thf(d2subst_decl,type,
% 0.30/0.46 d2subst: d_subst > subst ).
% 0.30/0.46
% 0.30/0.46 %----Types of the domain elements
% 0.30/0.46 thf(d_one_decl,type,
% 0.30/0.46 d_one: d_term ).
% 0.30/0.46
% 0.30/0.46 thf(d_id_decl,type,
% 0.30/0.46 d_id: d_subst ).
% 0.30/0.46
% 0.30/0.46 thf(alg444_1,axiom,
% 0.30/0.46 ( ! [T: term] :
% 0.30/0.46 ? [DT: d_term] :
% 0.30/0.46 ( T
% 0.30/0.46 = ( d2term @ DT ) )
% 0.30/0.46 & ! [DT: d_term] : ( DT = d_one )
% 0.30/0.46 & ! [DT1: d_term,DT2: d_term] :
% 0.30/0.46 ( ( ( d2term @ DT1 )
% 0.30/0.46 = ( d2term @ DT2 ) )
% 0.30/0.46 => ( DT1 = DT2 ) )
% 0.30/0.46 & ! [S: subst] :
% 0.30/0.46 ? [DS: d_subst] :
% 0.30/0.46 ( S
% 0.30/0.46 = ( d2subst @ DS ) )
% 0.30/0.46 & ! [DS: d_subst] : ( DS = d_id )
% 0.30/0.46 & ! [DS1: d_subst,DS2: d_subst] :
% 0.30/0.46 ( ( ( d2subst @ DS1 )
% 0.30/0.46 = ( d2subst @ DS2 ) )
% 0.30/0.46 => ( DS1 = DS2 ) )
% 0.30/0.46 & ( one
% 0.30/0.46 = ( d2term @ d_one ) )
% 0.30/0.46 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.30/0.46 = ( d2term @ d_one ) )
% 0.30/0.46 & ( ( lam @ ( d2term @ d_one ) )
% 0.30/0.46 = ( d2term @ d_one ) )
% 0.30/0.46 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.46 = ( d2term @ d_one ) )
% 0.30/0.46 & ( id
% 0.30/0.46 = ( d2subst @ d_id ) )
% 0.30/0.46 & ( sh
% 0.30/0.46 = ( d2subst @ d_id ) )
% 0.30/0.46 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.46 = ( d2subst @ d_id ) )
% 0.30/0.46 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.30/0.46 = ( d2subst @ d_id ) )
% 0.30/0.46 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.30/0.46 = ( d2term @ d_one ) )
% 0.30/0.46 & ( hoaslam
% 0.30/0.46 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.30/0.46 & ( hoasinduction_p_and_p_prime
% 0.30/0.46 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.30/0.46 ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) ) ) )
% 0.30/0.46 & ( pushprop_p_and_p_prime
% 0.30/0.46 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.30/0.46 ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.30/0.46 & ~ ( var @ ( d2term @ d_one ) )
% 0.30/0.46 & ( pushprop_lem1v2
% 0.30/0.46 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.30/0.46 | ( Q @ one ) ) )
% 0.30/0.46 & pushprop_lem1_gthm
% 0.30/0.46 & axmap
% 0.30/0.46 & pushprop_lem0_gthm
% 0.30/0.46 & ( shinj
% 0.30/0.46 <=> ! [A: term,B: term] :
% 0.30/0.46 ( ( ( sub @ A @ sh )
% 0.30/0.46 != ( sub @ B @ sh ) )
% 0.30/0.46 | ( A = B ) ) )
% 0.30/0.46 & hoasinduction_lem1v2
% 0.30/0.46 & hoasinduction_lem1v2_gthm
% 0.30/0.46 & ( induction2lem
% 0.30/0.46 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( var @ B )
% 0.30/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3v2_f
% 0.30/0.46 <=> ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ~ ! [A: term,M: subst] :
% 0.30/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.46 = ( F @ M @ A ) ) )
% 0.30/0.46 & axvarshift
% 0.30/0.46 & ( hoasapinj2
% 0.30/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( C = D ) ) )
% 0.30/0.46 & hoasapnotvar_gthm
% 0.30/0.46 & ( hoasapinj1
% 0.30/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( A = B ) ) )
% 0.30/0.46 & ~ ulamvar1
% 0.30/0.46 & ( induction2lem_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2140 ) )
% 0.30/0.46 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( var @ B )
% 0.30/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.30/0.46 & hoasinduction_lem3v2_gthm
% 0.30/0.46 & apnotvar
% 0.30/0.46 & pushprop_lthm_orig
% 0.30/0.46 & ( hoasinduction_lem3v2_f_lthm
% 0.30/0.46 <=> ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ~ ! [A: term,M: subst] :
% 0.30/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.46 = ( F @ M @ A ) ) )
% 0.30/0.46 & ( hoasinduction_lthm
% 0.30/0.46 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.30/0.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.46 | ( P @ id @ A @ id ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.30/0.46 & ( hoasinduction_no_psi_cond_lthm
% 0.30/0.46 <=> ( ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.30/0.46 & ( hoaslaminj
% 0.30/0.46 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.30/0.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.30/0.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.30/0.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3aaa
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.30/0.46 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.30/0.46 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.30/0.46 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.30/0.46 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.30/0.46 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.30/0.46 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.46 & induction2lem_gthm
% 0.30/0.46 & ( hoasinduction_lem3aa_lthm
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.46 & ( hoasinduction_lem3
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.30/0.46 & ( hoasinduction_lem2
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.30/0.46 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.30/0.46 & ( termmset_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) ) ) )
% 0.30/0.46 & hoasinduction_lem1
% 0.30/0.46 & hoaslamnotap_lthm
% 0.30/0.46 & ( pushprop_lem1v2_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.30/0.46 | ( Q @ one ) ) ) )
% 0.30/0.46 & hoasapnotvar
% 0.30/0.46 & ( hoasinduction_lem0
% 0.30/0.46 <=> ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) ) )
% 0.30/0.46 & ( hoasinduction
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.46 | ( P @ id @ A @ id ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.30/0.46 & hoasinduction_gthm
% 0.30/0.46 & axapp
% 0.30/0.46 & hoaslamnotvar_lthm
% 0.30/0.46 & pushprop_lem3v2_lthm
% 0.30/0.46 & ( hoasinduction_lem3b_lthm
% 0.30/0.46 <=> ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ( F @ sh @ one )
% 0.30/0.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.30/0.46 & ulamvarind
% 0.30/0.46 & ( induction
% 0.30/0.46 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2140 ) ) )
% 0.30/0.46 & ( hoasinduction_lem3a_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.30/0.46 & termmset_gthm
% 0.30/0.46 & ( hoasinduction_lem3aa
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.46 & pushprop_lem1v2_gthm
% 0.30/0.46 & hoaslamnotap_gthm
% 0.30/0.46 & hoaslamnotvar_gthm
% 0.30/0.46 & hoasinduction_lem3b_gthm
% 0.30/0.46 & pushprop_lem2v2
% 0.30/0.46 & hoasinduction_lem3a_gthm
% 0.30/0.46 & axclos
% 0.30/0.46 & axassoc
% 0.30/0.46 & ( hoasinduction_lem2v2
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ( Q @ Bound_variable_2820 )
% 0.30/0.46 | ~ ( Q @ Bound_variable_2822 )
% 0.30/0.46 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.30/0.46 & pushprop_lthm
% 0.30/0.46 & ( apinj2
% 0.30/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( C = D ) ) )
% 0.30/0.46 & ( apinj1
% 0.30/0.46 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( A = B ) ) )
% 0.30/0.46 & ( hoasapinj2_lthm
% 0.30/0.46 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( C = D ) )
% 0.30/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( C = D ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3v2a
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.30/0.46 & ( hoasapinj1_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( A = B ) )
% 0.30/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( A = B ) ) ) ) )
% 0.30/0.46 & ( hoaslaminj_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,B: term] :
% 0.30/0.46 ( ( ( lam @ A )
% 0.30/0.46 != ( lam @ B ) )
% 0.30/0.46 | ( A = B ) )
% 0.30/0.46 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.30/0.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.30/0.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.30/0.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.30/0.46 & ( axvarcons
% 0.30/0.46 <=> ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.30/0.46 & ( axscons
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.30/0.46 & hoasinduction_lem2v2_gthm
% 0.30/0.46 & ( axidr
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) )
% 0.30/0.46 & ( pushprop_lem1
% 0.30/0.46 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.30/0.46 & ( laminj
% 0.30/0.46 <=> ! [A: term,B: term] :
% 0.30/0.46 ( ( ( lam @ A )
% 0.30/0.46 != ( lam @ B ) )
% 0.30/0.46 | ( A = B ) ) )
% 0.30/0.46 & ( hoasinduction_lem3_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.30/0.46 & ( pushprop_lem0
% 0.30/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.30/0.46 & pushprop_gthm
% 0.30/0.46 & axabs
% 0.30/0.46 & ( hoasinduction_lem3v2a_lthm
% 0.30/0.46 <=> ( ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ~ ! [A: term,M: subst] :
% 0.30/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.46 = ( F @ M @ A ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.30/0.46 & hoasinduction_lem2_lthm
% 0.30/0.46 & hoasapinj2_gthm
% 0.30/0.46 & hoasinduction_lem1_lthm
% 0.30/0.46 & ~ lamnotap
% 0.30/0.46 & hoasapinj1_gthm
% 0.30/0.46 & hoaslamnotvar
% 0.30/0.46 & ( axidl
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) ) )
% 0.30/0.46 & hoaslaminj_gthm
% 0.30/0.46 & ( induction2_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( var @ B )
% 0.30/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.30/0.46 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem0_lthm
% 0.30/0.46 <=> ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) ) )
% 0.30/0.46 & ( substmonoid_lthm
% 0.30/0.46 <=> ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 => ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) )
% 0.30/0.46 => ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 & ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) ) ) ) )
% 0.30/0.46 & pushprop
% 0.30/0.46 & hoasinduction_lem3_gthm
% 0.30/0.46 & hoasinduction_lem2_gthm
% 0.30/0.46 & ( hoasinduction_lem3b
% 0.30/0.46 <=> ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ( F @ sh @ one )
% 0.30/0.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.30/0.46 & ( substmonoid
% 0.30/0.46 <=> ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 & ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) ) )
% 0.30/0.46 & lamnotvar
% 0.30/0.46 & ( hoasinduction_lem3a
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.30/0.46 & hoasinduction_lem1_gthm
% 0.30/0.46 & ( hoasinduction_no_psi_cond
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.30/0.46 & induction2_gthm
% 0.30/0.46 & pushprop_lem2v2_lthm
% 0.30/0.46 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.46 & ( hoaslamnotap
% 0.30/0.46 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.46 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.30/0.46 & substmonoid_gthm
% 0.30/0.46 & ulamvarsh
% 0.30/0.46 & ( induction2
% 0.30/0.46 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) ) )
% 0.30/0.46 & pushprop_lem3v2
% 0.30/0.46 & pushprop_lem2v2_gthm
% 0.30/0.46 & ( pushprop_lem1_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.46 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3v2
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.30/0.46 & ( axshiftcons
% 0.30/0.46 <=> ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.30/0.46 & ( termmset
% 0.30/0.46 <=> ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) ) )
% 0.30/0.46 & ( pushprop_lem0_lthm
% 0.30/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.30/0.46 & hoasapnotvar_lthm
% 0.30/0.46 & ( hoasinduction_lem3v2_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.30/0.46 & ( axvarid
% 0.30/0.46 <=> ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) ) )
% 0.30/0.46 & ( hoasinduction_lthm_3
% 0.30/0.46 <=> ( ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.46 | ( P @ id @ A @ id ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3,conjecture,
% 0.30/0.46 ( hoasinduction_lem3
% 0.30/0.46 = ( ! [P: subst > term > subst > $o] :
% 0.30/0.46 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 => ( ! [F: subst > term > term] :
% 0.30/0.46 ( ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( ( P @ id @ A @ id )
% 0.30/0.46 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 => ( P @ id
% 0.30/0.46 @ ( hoaslam @ id
% 0.30/0.46 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.30/0.46 @ id ) ) )
% 0.30/0.46 => ! [A: term] :
% 0.30/0.46 ( ! [B: term] :
% 0.30/0.46 ( ( P @ id @ B @ id )
% 0.30/0.46 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.28/1.46 ---- Embedded in THF ---
% 2.28/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.28/1.46 %%% Generated on Tue May 05 09:12:34 EDT 2026
% 2.28/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.28/1.46 %%% Logic specification used:
% 2.28/1.46 %%% thf(spec, logic, $$dhol).
% 2.28/1.46
% 2.28/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OZKaewZbi7/DTF2DTF21668.p
% See solution above
% 2.28/1.46 ------------------------
% 2.28/1.49 ---- Cleaned THF ---
% 2.28/1.50 thf(term_type,type,
% 2.28/1.50 term: $tType ).
% 2.28/1.50
% 2.28/1.50 thf(subst_type,type,
% 2.28/1.50 subst: $tType ).
% 2.28/1.50
% 2.28/1.50 thf(one_decl,type,
% 2.28/1.50 one: term ).
% 2.28/1.50
% 2.28/1.50 thf(ap_decl,type,
% 2.28/1.50 ap: term > term > term ).
% 2.28/1.50
% 2.28/1.50 thf(lam_decl,type,
% 2.28/1.50 lam: term > term ).
% 2.28/1.50
% 2.28/1.50 thf(sub_decl,type,
% 2.28/1.50 sub: term > subst > term ).
% 2.28/1.50
% 2.28/1.50 thf(id_decl,type,
% 2.28/1.50 id: subst ).
% 2.28/1.50
% 2.28/1.50 thf(sh_decl,type,
% 2.28/1.50 sh: subst ).
% 2.28/1.50
% 2.28/1.50 thf(push_decl,type,
% 2.28/1.50 push: term > subst > subst ).
% 2.28/1.50
% 2.28/1.50 thf(comp_decl,type,
% 2.28/1.50 comp: subst > subst > subst ).
% 2.28/1.50
% 2.28/1.50 thf(var_decl,type,
% 2.28/1.50 var: term > $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem1v2_decl,type,
% 2.28/1.50 pushprop_lem1v2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem1_gthm_decl,type,
% 2.28/1.50 pushprop_lem1_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axmap_decl,type,
% 2.28/1.50 axmap: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem0_gthm_decl,type,
% 2.28/1.50 pushprop_lem0_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(shinj_decl,type,
% 2.28/1.50 shinj: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem1v2_decl,type,
% 2.28/1.50 hoasinduction_lem1v2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem1v2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasap_decl,type,
% 2.28/1.50 hoasap: subst > term > subst > term > term ).
% 2.28/1.50
% 2.28/1.50 thf(induction2lem_decl,type,
% 2.28/1.50 induction2lem: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3v2_f_decl,type,
% 2.28/1.50 hoasinduction_lem3v2_f: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axvarshift_decl,type,
% 2.28/1.50 axvarshift: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj2_decl,type,
% 2.28/1.50 hoasapinj2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapnotvar_gthm_decl,type,
% 2.28/1.50 hoasapnotvar_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj1_decl,type,
% 2.28/1.50 hoasapinj1: $o ).
% 2.28/1.50
% 2.28/1.50 thf(ulamvar1_decl,type,
% 2.28/1.50 ulamvar1: $o ).
% 2.28/1.50
% 2.28/1.50 thf(induction2lem_lthm_decl,type,
% 2.28/1.50 induction2lem_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem3v2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(apnotvar_decl,type,
% 2.28/1.50 apnotvar: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lthm_orig_decl,type,
% 2.28/1.50 pushprop_lthm_orig: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3v2_f_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lthm_decl,type,
% 2.28/1.50 hoasinduction_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.28/1.50 hoasinduction_no_psi_cond_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslaminj_decl,type,
% 2.28/1.50 hoaslaminj: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3aaa_decl,type,
% 2.28/1.50 hoasinduction_lem3aaa: $o ).
% 2.28/1.50
% 2.28/1.50 thf(induction2lem_gthm_decl,type,
% 2.28/1.50 induction2lem_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3aa_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3_decl,type,
% 2.28/1.50 hoasinduction_lem3: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem2_decl,type,
% 2.28/1.50 hoasinduction_lem2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(termmset_lthm_decl,type,
% 2.28/1.50 termmset_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem1_decl,type,
% 2.28/1.50 hoasinduction_lem1: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslamnotap_lthm_decl,type,
% 2.28/1.50 hoaslamnotap_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem1v2_lthm_decl,type,
% 2.28/1.50 pushprop_lem1v2_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapnotvar_decl,type,
% 2.28/1.50 hoasapnotvar: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem0_decl,type,
% 2.28/1.50 hoasinduction_lem0: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_decl,type,
% 2.28/1.50 hoasinduction: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_gthm_decl,type,
% 2.28/1.50 hoasinduction_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axapp_decl,type,
% 2.28/1.50 axapp: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslamnotvar_lthm_decl,type,
% 2.28/1.50 hoaslamnotvar_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem3v2_lthm_decl,type,
% 2.28/1.50 pushprop_lem3v2_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3b_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(ulamvarind_decl,type,
% 2.28/1.50 ulamvarind: $o ).
% 2.28/1.50
% 2.28/1.50 thf(induction_decl,type,
% 2.28/1.50 induction: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3a_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(termmset_gthm_decl,type,
% 2.28/1.50 termmset_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3aa_decl,type,
% 2.28/1.50 hoasinduction_lem3aa: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem1v2_gthm_decl,type,
% 2.28/1.50 pushprop_lem1v2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslamnotap_gthm_decl,type,
% 2.28/1.50 hoaslamnotap_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslamnotvar_gthm_decl,type,
% 2.28/1.50 hoaslamnotvar_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem3b_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem2v2_decl,type,
% 2.28/1.50 pushprop_lem2v2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem3a_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axclos_decl,type,
% 2.28/1.50 axclos: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axassoc_decl,type,
% 2.28/1.50 axassoc: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem2v2_decl,type,
% 2.28/1.50 hoasinduction_lem2v2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lthm_decl,type,
% 2.28/1.50 pushprop_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(apinj2_decl,type,
% 2.28/1.50 apinj2: $o ).
% 2.28/1.50
% 2.28/1.50 thf(apinj1_decl,type,
% 2.28/1.50 apinj1: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj2_lthm_decl,type,
% 2.28/1.50 hoasapinj2_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3v2a_decl,type,
% 2.28/1.50 hoasinduction_lem3v2a: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj1_lthm_decl,type,
% 2.28/1.50 hoasapinj1_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslaminj_lthm_decl,type,
% 2.28/1.50 hoaslaminj_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axvarcons_decl,type,
% 2.28/1.50 axvarcons: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslam_decl,type,
% 2.28/1.50 hoaslam: subst > ( subst > term > term ) > term ).
% 2.28/1.50
% 2.28/1.50 thf(axscons_decl,type,
% 2.28/1.50 axscons: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem2v2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axidr_decl,type,
% 2.28/1.50 axidr: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem1_decl,type,
% 2.28/1.50 pushprop_lem1: $o ).
% 2.28/1.50
% 2.28/1.50 thf(laminj_decl,type,
% 2.28/1.50 laminj: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_lem0_decl,type,
% 2.28/1.50 pushprop_lem0: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_gthm_decl,type,
% 2.28/1.50 pushprop_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axabs_decl,type,
% 2.28/1.50 axabs: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem3v2a_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem2_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem2_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj2_gthm_decl,type,
% 2.28/1.50 hoasapinj2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.28/1.50 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem1_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem1_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(lamnotap_decl,type,
% 2.28/1.50 lamnotap: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasapinj1_gthm_decl,type,
% 2.28/1.50 hoasapinj1_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslamnotvar_decl,type,
% 2.28/1.50 hoaslamnotvar: $o ).
% 2.28/1.50
% 2.28/1.50 thf(axidl_decl,type,
% 2.28/1.50 axidl: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoaslaminj_gthm_decl,type,
% 2.28/1.50 hoaslaminj_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(induction2_lthm_decl,type,
% 2.28/1.50 induction2_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem0_lthm_decl,type,
% 2.28/1.50 hoasinduction_lem0_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(substmonoid_lthm_decl,type,
% 2.28/1.50 substmonoid_lthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(pushprop_decl,type,
% 2.28/1.50 pushprop: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem3_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem2_gthm_decl,type,
% 2.28/1.50 hoasinduction_lem2_gthm: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3b_decl,type,
% 2.28/1.50 hoasinduction_lem3b: $o ).
% 2.28/1.50
% 2.28/1.50 thf(substmonoid_decl,type,
% 2.28/1.50 substmonoid: $o ).
% 2.28/1.50
% 2.28/1.50 thf(lamnotvar_decl,type,
% 2.28/1.50 lamnotvar: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem3a_decl,type,
% 2.28/1.50 hoasinduction_lem3a: $o ).
% 2.28/1.50
% 2.28/1.50 thf(hoasinduction_lem1_gthm_decl,type,
% 2.53/1.50 hoasinduction_lem1_gthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasinduction_no_psi_cond_decl,type,
% 2.53/1.50 hoasinduction_no_psi_cond: $o ).
% 2.53/1.50
% 2.53/1.50 thf(induction2_gthm_decl,type,
% 2.53/1.50 induction2_gthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_lem2v2_lthm_decl,type,
% 2.53/1.50 pushprop_lem2v2_lthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasvar_decl,type,
% 2.53/1.50 hoasvar: subst > term > subst > $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoaslamnotap_decl,type,
% 2.53/1.50 hoaslamnotap: $o ).
% 2.53/1.50
% 2.53/1.50 thf(substmonoid_gthm_decl,type,
% 2.53/1.50 substmonoid_gthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ulamvarsh_decl,type,
% 2.53/1.50 ulamvarsh: $o ).
% 2.53/1.50
% 2.53/1.50 thf(induction2_decl,type,
% 2.53/1.50 induction2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_lem3v2_decl,type,
% 2.53/1.50 pushprop_lem3v2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_lem2v2_gthm_decl,type,
% 2.53/1.50 pushprop_lem2v2_gthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_lem1_lthm_decl,type,
% 2.53/1.50 pushprop_lem1_lthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasinduction_lem3v2_decl,type,
% 2.53/1.50 hoasinduction_lem3v2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(axshiftcons_decl,type,
% 2.53/1.50 axshiftcons: $o ).
% 2.53/1.50
% 2.53/1.50 thf(termmset_decl,type,
% 2.53/1.50 termmset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_lem0_lthm_decl,type,
% 2.53/1.50 pushprop_lem0_lthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasapnotvar_lthm_decl,type,
% 2.53/1.50 hoasapnotvar_lthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.53/1.50 hoasinduction_lem3v2_lthm: $o ).
% 2.53/1.50
% 2.53/1.50 thf(pushprop_p_and_p_prime_decl,type,
% 2.53/1.50 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.53/1.50
% 2.53/1.50 thf(axvarid_decl,type,
% 2.53/1.50 axvarid: $o ).
% 2.53/1.50
% 2.53/1.50 thf(hoasinduction_lthm_3_decl,type,
% 2.53/1.50 hoasinduction_lthm_3: $o ).
% 2.53/1.50
% 2.53/1.50 thf(d_term_type,type,
% 2.53/1.50 d_term: $tType ).
% 2.53/1.50
% 2.53/1.50 thf(d_subst_type,type,
% 2.53/1.50 d_subst: $tType ).
% 2.53/1.50
% 2.53/1.50 thf(d2term_decl,type,
% 2.53/1.50 d2term: d_term > term ).
% 2.53/1.50
% 2.53/1.50 thf(d2subst_decl,type,
% 2.53/1.50 d2subst: d_subst > subst ).
% 2.53/1.50
% 2.53/1.50 thf(d_one_decl,type,
% 2.53/1.50 d_one: d_term ).
% 2.53/1.50
% 2.53/1.50 thf(d_id_decl,type,
% 2.53/1.50 d_id: d_subst ).
% 2.53/1.50
% 2.53/1.50 thf(alg444_1,axiom,
% 2.53/1.50 ( ! [T: term] :
% 2.53/1.50 ? [DT: d_term] :
% 2.53/1.50 ( T
% 2.53/1.50 = ( d2term @ DT ) )
% 2.53/1.50 & ! [DT: d_term] : ( DT = d_one )
% 2.53/1.50 & ! [DT1: d_term,DT2: d_term] :
% 2.53/1.50 ( ( ( d2term @ DT1 )
% 2.53/1.50 = ( d2term @ DT2 ) )
% 2.53/1.50 => ( DT1 = DT2 ) )
% 2.53/1.50 & ! [S: subst] :
% 2.53/1.50 ? [DS: d_subst] :
% 2.53/1.50 ( S
% 2.53/1.50 = ( d2subst @ DS ) )
% 2.53/1.50 & ! [DS: d_subst] : ( DS = d_id )
% 2.53/1.50 & ! [DS1: d_subst,DS2: d_subst] :
% 2.53/1.50 ( ( ( d2subst @ DS1 )
% 2.53/1.50 = ( d2subst @ DS2 ) )
% 2.53/1.50 => ( DS1 = DS2 ) )
% 2.53/1.50 & ( one
% 2.53/1.50 = ( d2term @ d_one ) )
% 2.53/1.50 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.53/1.50 = ( d2term @ d_one ) )
% 2.53/1.50 & ( ( lam @ ( d2term @ d_one ) )
% 2.53/1.50 = ( d2term @ d_one ) )
% 2.53/1.50 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.53/1.50 = ( d2term @ d_one ) )
% 2.53/1.50 & ( id
% 2.53/1.50 = ( d2subst @ d_id ) )
% 2.53/1.50 & ( sh
% 2.53/1.50 = ( d2subst @ d_id ) )
% 2.53/1.50 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.53/1.50 = ( d2subst @ d_id ) )
% 2.53/1.50 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.53/1.50 = ( d2subst @ d_id ) )
% 2.53/1.50 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.53/1.50 = ( d2term @ d_one ) )
% 2.53/1.50 & ( hoaslam
% 2.53/1.50 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.53/1.50 & ( hoasinduction_p_and_p_prime
% 2.53/1.50 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.53/1.50 ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) ) ) )
% 2.53/1.50 & ( pushprop_p_and_p_prime
% 2.53/1.50 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.53/1.50 ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.53/1.50 & ~ ( var @ ( d2term @ d_one ) )
% 2.53/1.50 & ( pushprop_lem1v2
% 2.53/1.50 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.53/1.50 | ( Q @ one ) ) )
% 2.53/1.50 & pushprop_lem1_gthm
% 2.53/1.50 & axmap
% 2.53/1.50 & pushprop_lem0_gthm
% 2.53/1.50 & ( shinj
% 2.53/1.50 <=> ! [A: term,B: term] :
% 2.53/1.50 ( ( ( sub @ A @ sh )
% 2.53/1.50 != ( sub @ B @ sh ) )
% 2.53/1.50 | ( A = B ) ) )
% 2.53/1.50 & hoasinduction_lem1v2
% 2.53/1.50 & hoasinduction_lem1v2_gthm
% 2.53/1.50 & ( induction2lem
% 2.53/1.50 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.53/1.50 ( ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( var @ B )
% 2.53/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.53/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.53/1.50 & ( hoasinduction_lem3v2_f
% 2.53/1.50 <=> ! [B: term] :
% 2.53/1.50 ~ ! [F: subst > term > term] :
% 2.53/1.50 ~ ! [A: term,M: subst] :
% 2.53/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.53/1.50 = ( F @ M @ A ) ) )
% 2.53/1.50 & axvarshift
% 2.53/1.50 & ( hoasapinj2
% 2.53/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.53/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.53/1.50 | ( C = D ) ) )
% 2.53/1.50 & hoasapnotvar_gthm
% 2.53/1.50 & ( hoasapinj1
% 2.53/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.53/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.53/1.50 | ( A = B ) ) )
% 2.53/1.50 & ~ ulamvar1
% 2.53/1.50 & ( induction2lem_lthm
% 2.53/1.50 <=> ( ! [A: term,M: subst] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.53/1.50 => ( ! [A: term,M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.53/1.50 => ( ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ M @ id ) )
% 2.53/1.50 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2140 ) )
% 2.53/1.50 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.53/1.50 ( ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( var @ B )
% 2.53/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.53/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.53/1.50 & hoasinduction_lem3v2_gthm
% 2.53/1.50 & apnotvar
% 2.53/1.50 & pushprop_lthm_orig
% 2.53/1.50 & ( hoasinduction_lem3v2_f_lthm
% 2.53/1.50 <=> ! [B: term] :
% 2.53/1.50 ~ ! [F: subst > term > term] :
% 2.53/1.50 ~ ! [A: term,M: subst] :
% 2.53/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.53/1.50 = ( F @ M @ A ) ) )
% 2.53/1.50 & ( hoasinduction_lthm
% 2.53/1.50 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2367 ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.53/1.50 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.53/1.50 | ( P @ id @ A @ id ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.53/1.50 & ( hoasinduction_no_psi_cond_lthm
% 2.53/1.50 <=> ( ! [P: subst > term > subst > $o] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2367 ) )
% 2.53/1.50 => ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.53/1.50 ( ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.53/1.50 & ( hoaslaminj
% 2.53/1.50 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.53/1.50 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.53/1.50 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.53/1.50 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.53/1.50 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.53/1.50 & ( hoasinduction_lem3aaa
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.53/1.50 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.53/1.50 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.53/1.50 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.53/1.50 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.53/1.50 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.53/1.50 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.53/1.50 & induction2lem_gthm
% 2.53/1.50 & ( hoasinduction_lem3aa_lthm
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.53/1.50 & ( hoasinduction_lem3
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 2.53/1.50 & ( hoasinduction_lem2
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.53/1.50 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 2.53/1.50 & ( termmset_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) ) ) )
% 2.53/1.50 & hoasinduction_lem1
% 2.53/1.50 & hoaslamnotap_lthm
% 2.53/1.50 & ( pushprop_lem1v2_lthm
% 2.53/1.50 <=> ( ! [A: term,M: subst] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.53/1.50 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.53/1.50 | ( Q @ one ) ) ) )
% 2.53/1.50 & hoasapnotvar
% 2.53/1.50 & ( hoasinduction_lem0
% 2.53/1.50 <=> ! [P: subst > term > subst > $o] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) ) )
% 2.53/1.50 & ( hoasinduction
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.53/1.50 | ( P @ id @ A @ id ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 2.53/1.50 & hoasinduction_gthm
% 2.53/1.50 & axapp
% 2.53/1.50 & hoaslamnotvar_lthm
% 2.53/1.50 & pushprop_lem3v2_lthm
% 2.53/1.50 & ( hoasinduction_lem3b_lthm
% 2.53/1.50 <=> ! [B: term] :
% 2.53/1.50 ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ( F @ sh @ one )
% 2.53/1.50 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.53/1.50 & ulamvarind
% 2.53/1.50 & ( induction
% 2.53/1.50 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2140 ) ) )
% 2.53/1.50 & ( hoasinduction_lem3a_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 2.53/1.50 & termmset_gthm
% 2.53/1.50 & ( hoasinduction_lem3aa
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.53/1.50 & pushprop_lem1v2_gthm
% 2.53/1.50 & hoaslamnotap_gthm
% 2.53/1.50 & hoaslamnotvar_gthm
% 2.53/1.50 & hoasinduction_lem3b_gthm
% 2.53/1.50 & pushprop_lem2v2
% 2.53/1.50 & hoasinduction_lem3a_gthm
% 2.53/1.50 & axclos
% 2.53/1.50 & axassoc
% 2.53/1.50 & ( hoasinduction_lem2v2
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ( Q @ Bound_variable_2820 )
% 2.53/1.50 | ~ ( Q @ Bound_variable_2822 )
% 2.53/1.50 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 2.53/1.50 & pushprop_lthm
% 2.53/1.50 & ( apinj2
% 2.53/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ A @ C )
% 2.53/1.50 != ( ap @ B @ D ) )
% 2.53/1.50 | ( C = D ) ) )
% 2.53/1.50 & ( apinj1
% 2.53/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ A @ C )
% 2.53/1.50 != ( ap @ B @ D ) )
% 2.53/1.50 | ( A = B ) ) )
% 2.53/1.50 & ( hoasapinj2_lthm
% 2.53/1.50 <=> ( ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ A @ C )
% 2.53/1.50 != ( ap @ B @ D ) )
% 2.53/1.50 | ( C = D ) )
% 2.53/1.50 => ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.53/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.53/1.50 | ( C = D ) ) ) )
% 2.53/1.50 & ( hoasinduction_lem3v2a
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 2.53/1.50 & ( hoasapinj1_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ A @ C )
% 2.53/1.50 != ( ap @ B @ D ) )
% 2.53/1.50 | ( A = B ) )
% 2.53/1.50 => ! [A: term,B: term,C: term,D: term] :
% 2.53/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.53/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.53/1.50 | ( A = B ) ) ) ) )
% 2.53/1.50 & ( hoaslaminj_lthm
% 2.53/1.50 <=> ( ! [A: term,M: subst] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.53/1.50 => ( ! [A: term,M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.53/1.50 => ( ! [A: term,B: term] :
% 2.53/1.50 ( ( ( lam @ A )
% 2.53/1.50 != ( lam @ B ) )
% 2.53/1.50 | ( A = B ) )
% 2.53/1.50 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.53/1.50 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.53/1.50 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.53/1.50 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.53/1.50 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 2.53/1.50 & ( axvarcons
% 2.53/1.50 <=> ! [A: term,M: subst] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 2.53/1.50 & ( axscons
% 2.53/1.50 <=> ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 2.53/1.50 & hoasinduction_lem2v2_gthm
% 2.53/1.50 & ( axidr
% 2.53/1.50 <=> ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ M @ id ) ) )
% 2.53/1.50 & ( pushprop_lem1
% 2.53/1.50 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 2.53/1.50 & ( laminj
% 2.53/1.50 <=> ! [A: term,B: term] :
% 2.53/1.50 ( ( ( lam @ A )
% 2.53/1.50 != ( lam @ B ) )
% 2.53/1.50 | ( A = B ) ) )
% 2.53/1.50 & ( hoasinduction_lem3_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 2.53/1.50 & ( pushprop_lem0
% 2.53/1.50 <=> ! [P: term > $o,A: term,M: subst] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.53/1.50 & pushprop_gthm
% 2.53/1.50 & axabs
% 2.53/1.50 & ( hoasinduction_lem3v2a_lthm
% 2.53/1.50 <=> ( ! [B: term] :
% 2.53/1.50 ~ ! [F: subst > term > term] :
% 2.53/1.50 ~ ! [A: term,M: subst] :
% 2.53/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.53/1.50 = ( F @ M @ A ) )
% 2.53/1.50 => ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 2.53/1.50 & hoasinduction_lem2_lthm
% 2.53/1.50 & hoasapinj2_gthm
% 2.53/1.50 & hoasinduction_lem1_lthm
% 2.53/1.50 & ~ lamnotap
% 2.53/1.50 & hoasapinj1_gthm
% 2.53/1.50 & hoaslamnotvar
% 2.53/1.50 & ( axidl
% 2.53/1.50 <=> ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ id @ M ) ) )
% 2.53/1.50 & hoaslaminj_gthm
% 2.53/1.50 & ( induction2_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.53/1.50 ( ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( var @ B )
% 2.53/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.53/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 2.53/1.50 => ! [P: term > $o,Bound_variable_2367: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2367 ) ) ) ) )
% 2.53/1.50 & ( hoasinduction_lem0_lthm
% 2.53/1.50 <=> ! [P: subst > term > subst > $o] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) ) )
% 2.53/1.50 & ( substmonoid_lthm
% 2.53/1.50 <=> ( ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ id @ M ) )
% 2.53/1.50 => ( ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ M @ id ) )
% 2.53/1.50 => ( ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ id @ M ) )
% 2.53/1.50 & ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ M @ id ) ) ) ) ) )
% 2.53/1.50 & pushprop
% 2.53/1.50 & hoasinduction_lem3_gthm
% 2.53/1.50 & hoasinduction_lem2_gthm
% 2.53/1.50 & ( hoasinduction_lem3b
% 2.53/1.50 <=> ! [B: term] :
% 2.53/1.50 ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ( F @ sh @ one )
% 2.53/1.50 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.53/1.50 & ( substmonoid
% 2.53/1.50 <=> ( ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ id @ M ) )
% 2.53/1.50 & ! [M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ M @ id ) ) ) )
% 2.53/1.50 & lamnotvar
% 2.53/1.50 & ( hoasinduction_lem3a
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 2.53/1.50 & hoasinduction_lem1_gthm
% 2.53/1.50 & ( hoasinduction_no_psi_cond
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.53/1.50 ( ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 2.53/1.50 & induction2_gthm
% 2.53/1.50 & pushprop_lem2v2_lthm
% 2.53/1.50 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.53/1.50 & ( hoaslamnotap
% 2.53/1.50 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.53/1.50 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 2.53/1.50 & substmonoid_gthm
% 2.53/1.50 & ulamvarsh
% 2.53/1.50 & ( induction2
% 2.53/1.50 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2367 ) ) )
% 2.53/1.50 & pushprop_lem3v2
% 2.53/1.50 & pushprop_lem2v2_gthm
% 2.53/1.50 & ( pushprop_lem1_lthm
% 2.53/1.50 <=> ( ! [A: term,M: subst] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.53/1.50 => ( ! [A: term,M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.53/1.50 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 2.53/1.50 & ( hoasinduction_lem3v2
% 2.53/1.50 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 2.53/1.50 & ( axshiftcons
% 2.53/1.50 <=> ! [A: term,M: subst] :
% 2.53/1.50 ( M
% 2.53/1.50 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 2.53/1.50 & ( termmset
% 2.53/1.50 <=> ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) ) )
% 2.53/1.50 & ( pushprop_lem0_lthm
% 2.53/1.50 <=> ! [P: term > $o,A: term,M: subst] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.53/1.50 & hoasapnotvar_lthm
% 2.53/1.50 & ( hoasinduction_lem3v2_lthm
% 2.53/1.50 <=> ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 2.53/1.50 & ( axvarid
% 2.53/1.50 <=> ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) ) )
% 2.53/1.50 & ( hoasinduction_lthm_3
% 2.53/1.50 <=> ( ! [P: subst > term > subst > $o] :
% 2.53/1.50 ~ ! [Q: term > $o] :
% 2.53/1.50 ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.53/1.50 ( ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ A )
% 2.53/1.50 | ( P @ A ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ A )
% 2.53/1.50 | ~ ( P @ B )
% 2.53/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ! [B: term] :
% 2.53/1.50 ( ~ ( P @ B )
% 2.53/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( P @ ( lam @ A ) ) )
% 2.53/1.50 | ( P @ Bound_variable_2367 ) )
% 2.53/1.50 => ( ! [A: term] :
% 2.53/1.50 ( A
% 2.53/1.50 = ( sub @ A @ id ) )
% 2.53/1.50 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.53/1.50 ( ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ~ ! [X: term] :
% 2.53/1.50 ( ( Q @ X )
% 2.53/1.50 = ( P @ id @ X @ id ) )
% 2.53/1.50 | ~ ! [B: term] :
% 2.53/1.50 ( ~ ( Q @ B )
% 2.53/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.53/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.53/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.53/1.50 | ( P @ id @ A @ id ) )
% 2.53/1.50 | ~ ! [A: term,B: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ~ ( P @ id @ B @ id )
% 2.53/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.53/1.50 | ~ ! [F: subst > term > term] :
% 2.53/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 | ~ ! [A: term] :
% 2.53/1.50 ( ~ ( P @ id @ A @ id )
% 2.53/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.53/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(hoasinduction_lem3,conjecture,
% 2.53/1.50 ( hoasinduction_lem3
% 2.53/1.50 = ( ! [P: subst > term > subst > $o] :
% 2.53/1.50 ( ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 2.53/1.50 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.53/1.50 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 2.53/1.50 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.53/1.50 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.53/1.50 => ( ! [F: subst > term > term] :
% 2.53/1.50 ( ! [M: subst,A: term,N: subst] :
% 2.53/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.53/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.53/1.50 => ( ! [A: term] :
% 2.53/1.50 ( ( P @ id @ A @ id )
% 2.53/1.50 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.53/1.50 => ( P @ id
% 2.53/1.50 @ ( hoaslam @ id
% 2.53/1.50 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 2.53/1.50 @ id ) ) )
% 2.53/1.50 => ! [A: term] :
% 2.53/1.50 ( ! [B: term] :
% 2.53/1.50 ( ( P @ id @ B @ id )
% 2.53/1.50 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 2.53/1.50 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ) ).
% 2.53/1.50 ------------------------
% 2.53/1.52 % (21773)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_21668 for (2999ds/275Mi)
% 2.53/1.52 % (21774)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/18Mi)
% 2.53/1.52 % (21771)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/2Mi)
% 2.53/1.52 % (21771)Instruction limit reached!
% 2.53/1.52 % (21771)------------------------------
% 2.53/1.52 % (21771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.52 % (21771)Termination reason: Unknown
% 2.53/1.52 % (21771)Termination phase: shuffling
% 2.53/1.52
% 2.53/1.52 % (21771)Memory used [KB]: 1279
% 2.53/1.52 % (21771)Time elapsed: 0.003 s
% 2.53/1.52 % (21771)Instructions burned: 4 (million)
% 2.53/1.52 % (21771)------------------------------
% 2.53/1.52 % (21771)------------------------------
% 2.53/1.52 % (21772)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_21668 for (2999ds/2Mi)
% 2.53/1.52 % (21774)Instruction limit reached!
% 2.53/1.52 % (21774)------------------------------
% 2.53/1.52 % (21774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.52 % (21774)Termination reason: Unknown
% 2.53/1.52 % (21774)Termination phase: shuffling
% 2.53/1.52
% 2.53/1.52 % (21774)Memory used [KB]: 2046
% 2.53/1.52 % (21774)Time elapsed: 0.007 s
% 2.53/1.52 % (21774)Instructions burned: 19 (million)
% 2.53/1.52 % (21774)------------------------------
% 2.53/1.52 % (21774)------------------------------
% 2.53/1.52 % (21772)Instruction limit reached!
% 2.53/1.52 % (21772)------------------------------
% 2.53/1.52 % (21772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.52 % (21772)Termination reason: Unknown
% 2.53/1.52 % (21772)Termination phase: shuffling
% 2.53/1.52
% 2.53/1.52 % (21772)Memory used [KB]: 1151
% 2.53/1.52 % (21772)Time elapsed: 0.003 s
% 2.53/1.52 % (21772)Instructions burned: 2 (million)
% 2.53/1.52 % (21772)------------------------------
% 2.53/1.52 % (21772)------------------------------
% 2.53/1.52 % (21769)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_21668 for (2999ds/4Mi)
% 2.53/1.52 % (21768)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/183Mi)
% 2.53/1.52 % (21770)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_21668 for (2999ds/27Mi)
% 2.53/1.53 % (21769)Instruction limit reached!
% 2.53/1.53 % (21769)------------------------------
% 2.53/1.53 % (21769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (21769)Termination reason: Unknown
% 2.53/1.53 % (21769)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (21769)Memory used [KB]: 1279
% 2.53/1.53 % (21769)Time elapsed: 0.005 s
% 2.53/1.53 % (21769)Instructions burned: 5 (million)
% 2.53/1.53 % (21769)------------------------------
% 2.53/1.53 % (21769)------------------------------
% 2.53/1.53 % (21773)Refutation not found, incomplete strategy
% 2.53/1.53 % (21773)------------------------------
% 2.53/1.53 % (21773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (21773)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.53
% 2.53/1.53
% 2.53/1.53 % (21773)Memory used [KB]: 6780
% 2.53/1.53 % (21773)Time elapsed: 0.015 s
% 2.53/1.53 % (21773)Instructions burned: 43 (million)
% 2.53/1.53 % (21773)------------------------------
% 2.53/1.53 % (21773)------------------------------
% 2.53/1.53 % (21776)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/3Mi)
% 2.53/1.53 % (21776)Instruction limit reached!
% 2.53/1.53 % (21776)------------------------------
% 2.53/1.53 % (21776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (21776)Termination reason: Unknown
% 2.53/1.53 % (21776)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (21776)Memory used [KB]: 1279
% 2.53/1.53 % (21776)Time elapsed: 0.003 s
% 2.53/1.53 % (21776)Instructions burned: 4 (million)
% 2.53/1.53 % (21776)------------------------------
% 2.53/1.53 % (21776)------------------------------
% 2.53/1.53 % (21777)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_21668 for (2999ds/37Mi)
% 2.53/1.54 % (21778)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_21668 for (2999ds/15Mi)
% 2.53/1.54 % (21780)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_21668 for (2999ds/1041Mi)
% 2.53/1.54 % (21770)Instruction limit reached!
% 2.53/1.54 % (21770)------------------------------
% 2.53/1.54 % (21770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (21770)Termination reason: Unknown
% 2.53/1.54 % (21770)Termination phase: Property scanning
% 2.53/1.54
% 2.53/1.54 % (21770)Memory used [KB]: 2174
% 2.53/1.54 % (21770)Time elapsed: 0.018 s
% 2.53/1.54 % (21770)Instructions burned: 27 (million)
% 2.53/1.54 % (21770)------------------------------
% 2.53/1.54 % (21770)------------------------------
% 2.53/1.54 % (21781)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/7Mi)
% 2.53/1.54 % (21777)Instruction limit reached!
% 2.53/1.54 % (21777)------------------------------
% 2.53/1.54 % (21777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (21777)Termination reason: Unknown
% 2.53/1.54 % (21777)Termination phase: Property scanning
% 2.53/1.54
% 2.53/1.54 % (21777)Memory used [KB]: 1918
% 2.53/1.54 % (21777)Time elapsed: 0.011 s
% 2.53/1.54 % (21777)Instructions burned: 39 (million)
% 2.53/1.54 % (21777)------------------------------
% 2.53/1.54 % (21777)------------------------------
% 2.53/1.54 % (21781)Instruction limit reached!
% 2.53/1.54 % (21781)------------------------------
% 2.53/1.54 % (21781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (21781)Termination reason: Unknown
% 2.53/1.54 % (21781)Termination phase: shuffling
% 2.53/1.54
% 2.53/1.54 % (21781)Memory used [KB]: 1407
% 2.53/1.54 % (21781)Time elapsed: 0.003 s
% 2.53/1.54 % (21781)Instructions burned: 7 (million)
% 2.53/1.54 % (21781)------------------------------
% 2.53/1.54 % (21781)------------------------------
% 2.53/1.54 % (21778)Instruction limit reached!
% 2.53/1.54 % (21778)------------------------------
% 2.53/1.54 % (21778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (21778)Termination reason: Unknown
% 2.53/1.54 % (21778)Termination phase: shuffling
% 2.53/1.54
% 2.53/1.54 % (21778)Memory used [KB]: 1791
% 2.53/1.54 % (21778)Time elapsed: 0.007 s
% 2.53/1.54 % (21778)Instructions burned: 15 (million)
% 2.53/1.54 % (21778)------------------------------
% 2.53/1.54 % (21778)------------------------------
% 2.53/1.54 % (21779)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_21668 for (2999ds/3Mi)
% 2.53/1.55 % (21779)Instruction limit reached!
% 2.53/1.55 % (21779)------------------------------
% 2.53/1.55 % (21779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (21779)Termination reason: Unknown
% 2.53/1.55 % (21779)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.55 % (21779)Memory used [KB]: 1279
% 2.53/1.55 % (21779)Time elapsed: 0.004 s
% 2.53/1.55 % (21779)Instructions burned: 4 (million)
% 2.53/1.55 % (21779)------------------------------
% 2.53/1.55 % (21779)------------------------------
% 2.53/1.55 % (21783)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_21668 for (2999ds/3Mi)
% 2.53/1.55 % (21783)Instruction limit reached!
% 2.53/1.55 % (21783)------------------------------
% 2.53/1.55 % (21783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (21783)Termination reason: Unknown
% 2.53/1.55 % (21783)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.55 % (21783)Memory used [KB]: 1279
% 2.53/1.55 % (21783)Time elapsed: 0.002 s
% 2.53/1.55 % (21783)Instructions burned: 4 (million)
% 2.53/1.55 % (21783)------------------------------
% 2.53/1.55 % (21783)------------------------------
% 2.53/1.55 % (21784)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_21668 for (2999ds/3Mi)
% 2.53/1.55 % (21785)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/7Mi)
% 2.53/1.55 % (21784)Instruction limit reached!
% 2.53/1.55 % (21784)------------------------------
% 2.53/1.55 % (21784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (21784)Termination reason: Unknown
% 2.53/1.55 % (21784)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.55 % (21784)Memory used [KB]: 1279
% 2.53/1.55 % (21784)Time elapsed: 0.003 s
% 2.53/1.55 % (21784)Instructions burned: 4 (million)
% 2.53/1.55 % (21784)------------------------------
% 2.53/1.55 % (21784)------------------------------
% 2.53/1.56 % (21785)Instruction limit reached!
% 2.53/1.56 % (21785)------------------------------
% 2.53/1.56 % (21785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (21785)Termination reason: Unknown
% 2.53/1.56 % (21785)Termination phase: shuffling
% 2.53/1.56
% 2.53/1.56 % (21785)Memory used [KB]: 1407
% 2.53/1.56 % (21785)Time elapsed: 0.004 s
% 2.53/1.56 % (21785)Instructions burned: 8 (million)
% 2.53/1.56 % (21785)------------------------------
% 2.53/1.56 % (21785)------------------------------
% 2.53/1.56 % (21782)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/16Mi)
% 2.53/1.56 % (21787)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/4Mi)
% 2.53/1.56 % (21787)Instruction limit reached!
% 2.53/1.56 % (21787)------------------------------
% 2.53/1.56 % (21787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (21787)Termination reason: Unknown
% 2.53/1.56 % (21787)Termination phase: shuffling
% 2.53/1.56
% 2.53/1.56 % (21787)Memory used [KB]: 1279
% 2.53/1.56 % (21787)Time elapsed: 0.002 s
% 2.53/1.56 % (21787)Instructions burned: 4 (million)
% 2.53/1.56 % (21787)------------------------------
% 2.53/1.56 % (21787)------------------------------
% 2.53/1.56 % (21786)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/3Mi)
% 2.53/1.56 % (21788)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/18Mi)
% 2.53/1.56 % (21782)Instruction limit reached!
% 2.53/1.56 % (21782)------------------------------
% 2.53/1.56 % (21782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (21782)Termination reason: Unknown
% 2.53/1.57 % (21782)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (21782)Memory used [KB]: 2046
% 2.53/1.57 % (21782)Time elapsed: 0.010 s
% 2.53/1.57 % (21782)Instructions burned: 17 (million)
% 2.53/1.57 % (21782)------------------------------
% 2.53/1.57 % (21782)------------------------------
% 2.53/1.57 % (21786)Instruction limit reached!
% 2.53/1.57 % (21786)------------------------------
% 2.53/1.57 % (21786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (21786)Termination reason: Unknown
% 2.53/1.57 % (21786)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (21786)Memory used [KB]: 1279
% 2.53/1.57 % (21786)Time elapsed: 0.004 s
% 2.53/1.57 % (21786)Instructions burned: 4 (million)
% 2.53/1.57 % (21786)------------------------------
% 2.53/1.57 % (21786)------------------------------
% 2.53/1.57 % (21789)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/710Mi)
% 2.53/1.57 % (21788)Instruction limit reached!
% 2.53/1.57 % (21788)------------------------------
% 2.53/1.57 % (21788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (21788)Termination reason: Unknown
% 2.53/1.57 % (21788)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (21788)Memory used [KB]: 2046
% 2.53/1.57 % (21788)Time elapsed: 0.008 s
% 2.53/1.57 % (21788)Instructions burned: 19 (million)
% 2.53/1.57 % (21788)------------------------------
% 2.53/1.57 % (21788)------------------------------
% 2.53/1.57 % (21790)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/6Mi)
% 2.53/1.57 % (21790)Instruction limit reached!
% 2.53/1.57 % (21790)------------------------------
% 2.53/1.57 % (21790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (21790)Termination reason: Unknown
% 2.53/1.57 % (21790)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (21790)Memory used [KB]: 1407
% 2.53/1.57 % (21790)Time elapsed: 0.003 s
% 2.53/1.57 % (21790)Instructions burned: 8 (million)
% 2.53/1.57 % (21790)------------------------------
% 2.53/1.57 % (21790)------------------------------
% 2.53/1.58 % (21791)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_21668 for (2999ds/902Mi)
% 2.53/1.58 % (21793)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/5Mi)
% 2.53/1.58 % (21792)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_21668 for (2999ds/21Mi)
% 2.53/1.58 % (21793)Instruction limit reached!
% 2.53/1.58 % (21793)------------------------------
% 2.53/1.58 % (21793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (21794)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_21668 for (2999ds/6Mi)
% 2.53/1.58 % (21793)Termination reason: Unknown
% 2.53/1.58 % (21793)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (21793)Memory used [KB]: 1407
% 2.53/1.58 % (21793)Time elapsed: 0.004 s
% 2.53/1.58 % (21793)Instructions burned: 7 (million)
% 2.53/1.58 % (21793)------------------------------
% 2.53/1.58 % (21793)------------------------------
% 2.53/1.59 % (21794)Instruction limit reached!
% 2.53/1.59 % (21794)------------------------------
% 2.53/1.59 % (21794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (21794)Termination reason: Unknown
% 2.53/1.59 % (21794)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (21794)Memory used [KB]: 1407
% 2.53/1.59 % (21794)Time elapsed: 0.003 s
% 2.53/1.59 % (21794)Instructions burned: 7 (million)
% 2.53/1.59 % (21794)------------------------------
% 2.53/1.59 % (21794)------------------------------
% 2.53/1.59 % (21795)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21668 for (2999ds/377Mi)
% 2.53/1.59 % (21792)Instruction limit reached!
% 2.53/1.59 % (21792)------------------------------
% 2.53/1.59 % (21792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (21792)Termination reason: Unknown
% 2.53/1.59 % (21792)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (21792)Memory used [KB]: 2046
% 2.53/1.59 % (21792)Time elapsed: 0.013 s
% 2.53/1.59 % (21792)Instructions burned: 21 (million)
% 2.53/1.59 % (21792)------------------------------
% 2.53/1.59 % (21792)------------------------------
% 2.53/1.59 % (21796)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_21668 for (2999ds/779Mi)
% 2.53/1.61 % (21797)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_21668 for (2999ds/19Mi)
% 2.53/1.61 % (21797)Instruction limit reached!
% 2.53/1.61 % (21797)------------------------------
% 2.53/1.61 % (21797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (21797)Termination reason: Unknown
% 2.53/1.61 % (21797)Termination phase: shuffling
% 2.53/1.61
% 2.53/1.61 % (21797)Memory used [KB]: 1535
% 2.53/1.61 % (21797)Time elapsed: 0.007 s
% 2.53/1.61 % (21797)Instructions burned: 19 (million)
% 2.53/1.61 % (21797)------------------------------
% 2.53/1.61 % (21797)------------------------------
% 2.53/1.61 % (21768)Instruction limit reached!
% 2.53/1.61 % (21768)------------------------------
% 2.53/1.61 % (21768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (21768)Termination reason: Unknown
% 2.53/1.61 % (21768)Termination phase: Property scanning
% 2.53/1.61
% 2.53/1.61 % (21768)Memory used [KB]: 4477
% 2.53/1.61 % (21768)Time elapsed: 0.091 s
% 2.53/1.61 % (21768)Instructions burned: 186 (million)
% 2.53/1.61 % (21768)------------------------------
% 2.53/1.61 % (21768)------------------------------
% 2.53/1.62 % (21798)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/879Mi)
% 2.53/1.62 % (21799)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/17Mi)
% 2.53/1.63 % (21799)Instruction limit reached!
% 2.53/1.63 % (21799)------------------------------
% 2.53/1.63 % (21799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.63 % (21799)Termination reason: Unknown
% 2.53/1.63 % (21799)Termination phase: shuffling
% 2.53/1.63
% 2.53/1.63 % (21799)Memory used [KB]: 1918
% 2.53/1.63 % (21799)Time elapsed: 0.007 s
% 2.53/1.63 % (21799)Instructions burned: 18 (million)
% 2.53/1.63 % (21799)------------------------------
% 2.53/1.63 % (21799)------------------------------
% 2.53/1.64 % (21800)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/3Mi)
% 2.53/1.64 % (21791)Refutation not found, incomplete strategy
% 2.53/1.64 % (21791)------------------------------
% 2.53/1.64 % (21791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.64 % (21791)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.64
% 2.53/1.64
% 2.53/1.64 % (21791)Memory used [KB]: 9338
% 2.53/1.64 % (21800)Instruction limit reached!
% 2.53/1.64 % (21800)------------------------------
% 2.53/1.64 % (21800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.64 % (21800)Termination reason: Unknown
% 2.53/1.64 % (21800)Termination phase: shuffling
% 2.53/1.64
% 2.53/1.64 % (21800)Memory used [KB]: 1279
% 2.53/1.64 % (21800)Time elapsed: 0.003 s
% 2.53/1.64 % (21800)Instructions burned: 4 (million)
% 2.53/1.64 % (21800)------------------------------
% 2.53/1.64 % (21800)------------------------------
% 2.53/1.64 % (21791)Time elapsed: 0.064 s
% 2.53/1.64 % (21791)Instructions burned: 208 (million)
% 2.53/1.64 % (21791)------------------------------
% 2.53/1.64 % (21791)------------------------------
% 2.53/1.65 % (21801)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/30Mi)
% 2.53/1.65 % (21802)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/127Mi)
% 2.53/1.66 % (21801)Instruction limit reached!
% 2.53/1.66 % (21801)------------------------------
% 2.53/1.66 % (21801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.66 % (21801)Termination reason: Unknown
% 2.53/1.66 % (21801)Termination phase: Property scanning
% 2.53/1.66
% 2.53/1.66 % (21801)Memory used [KB]: 2174
% 2.53/1.66 % (21801)Time elapsed: 0.012 s
% 2.53/1.66 % (21801)Instructions burned: 32 (million)
% 2.53/1.66 % (21801)------------------------------
% 2.53/1.66 % (21801)------------------------------
% 2.53/1.67 % (21803)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21668 for (2998ds/100Mi)
% 2.53/1.69 % (21802)Instruction limit reached!
% 2.53/1.69 % (21802)------------------------------
% 2.53/1.69 % (21802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.69 % (21802)Termination reason: Unknown
% 2.53/1.69 % (21802)Termination phase: Property scanning
% 2.53/1.69
% 2.53/1.69 % (21802)Memory used [KB]: 4093
% 2.53/1.69 % (21802)Time elapsed: 0.039 s
% 2.53/1.69 % (21802)Instructions burned: 128 (million)
% 2.53/1.69 % (21802)------------------------------
% 2.53/1.69 % (21802)------------------------------
% 2.53/1.70 % (21803)Instruction limit reached!
% 2.53/1.70 % (21803)------------------------------
% 2.53/1.70 % (21803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.70 % (21803)Termination reason: Unknown
% 2.53/1.70 % (21803)Termination phase: Saturation
% 2.53/1.70
% 2.53/1.70 % (21803)Memory used [KB]: 6524
% 2.53/1.70 % (21803)Time elapsed: 0.029 s
% 2.53/1.70 % (21803)Instructions burned: 103 (million)
% 2.53/1.70 % (21803)------------------------------
% 2.53/1.70 % (21803)------------------------------
% 2.53/1.70 % (21804)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_21668 for (2998ds/3Mi)
% 2.53/1.70 % (21804)Instruction limit reached!
% 2.53/1.70 % (21804)------------------------------
% 2.53/1.70 % (21804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.70 % (21804)Termination reason: Unknown
% 2.53/1.70 % (21804)Termination phase: shuffling
% 2.53/1.70
% 2.53/1.70 % (21804)Memory used [KB]: 1151
% 2.53/1.70 % (21804)Time elapsed: 0.002 s
% 2.53/1.70 % (21804)Instructions burned: 3 (million)
% 2.53/1.70 % (21804)------------------------------
% 2.53/1.70 % (21804)------------------------------
% 2.53/1.71 % (21805)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_21668 for (2998ds/20Mi)
% 2.53/1.71 % (21795)Instruction limit reached!
% 2.53/1.71 % (21795)------------------------------
% 2.53/1.71 % (21795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.71 % (21795)Termination reason: Unknown
% 2.53/1.71 % (21795)Termination phase: Saturation
% 2.53/1.71
% 2.53/1.71 % (21795)Memory used [KB]: 10362
% 2.53/1.71 % (21795)Time elapsed: 0.118 s
% 2.53/1.71 % (21795)Instructions burned: 379 (million)
% 2.53/1.71 % (21795)------------------------------
% 2.53/1.71 % (21795)------------------------------
% 2.53/1.71 % (21806)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_21668 for (2998ds/86Mi)
% 2.53/1.72 % (21805)Instruction limit reached!
% 2.53/1.72 % (21805)------------------------------
% 2.53/1.72 % (21805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.72 % (21805)Termination reason: Unknown
% 2.53/1.72 % (21805)Termination phase: shuffling
% 2.53/1.72
% 2.53/1.72 % (21805)Memory used [KB]: 2046
% 2.53/1.72 % (21805)Time elapsed: 0.009 s
% 2.53/1.72 % (21805)Instructions burned: 21 (million)
% 2.53/1.72 % (21805)------------------------------
% 2.53/1.72 % (21805)------------------------------
% 2.53/1.72 % (21807)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_21668 for (2997ds/107Mi)
% 2.53/1.73 % (21808)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_21668 for (2997ds/39Mi)
% 2.53/1.74 % (21808)Instruction limit reached!
% 2.53/1.74 % (21808)------------------------------
% 2.53/1.74 % (21808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.74 % (21808)Termination reason: Unknown
% 2.53/1.74 % (21808)Termination phase: Property scanning
% 2.53/1.74
% 2.53/1.74 % (21808)Memory used [KB]: 1918
% 2.53/1.74 % (21808)Time elapsed: 0.013 s
% 2.53/1.74 % (21808)Instructions burned: 39 (million)
% 2.53/1.74 % (21808)------------------------------
% 2.53/1.74 % (21808)------------------------------
% 2.53/1.74 % (21806)Instruction limit reached!
% 2.53/1.74 % (21806)------------------------------
% 2.53/1.74 % (21806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.74 % (21806)Termination reason: Unknown
% 2.53/1.74 % (21806)Termination phase: Preprocessing 3
% 2.53/1.74
% 2.53/1.74 % (21806)Memory used [KB]: 3965
% 2.53/1.74 % (21806)Time elapsed: 0.029 s
% 2.53/1.74 % (21806)Instructions burned: 87 (million)
% 2.53/1.74 % (21806)------------------------------
% 2.53/1.74 % (21806)------------------------------
% 2.53/1.75 % (21809)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_21668 for (2997ds/448Mi)
% 2.53/1.75 % (21810)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_21668 for (2997ds/46Mi)
% 2.53/1.75 % (21807)Instruction limit reached!
% 2.53/1.75 % (21807)------------------------------
% 2.53/1.75 % (21807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.75 % (21807)Termination reason: Unknown
% 2.53/1.75 % (21807)Termination phase: Property scanning
% 2.53/1.75
% 2.53/1.75 % (21807)Memory used [KB]: 4477
% 2.53/1.75 % (21807)Time elapsed: 0.034 s
% 2.53/1.75 % (21807)Instructions burned: 107 (million)
% 2.53/1.75 % (21807)------------------------------
% 2.53/1.75 % (21807)------------------------------
% 2.53/1.76 % (21811)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_21668 for (2997ds/98Mi)
% 2.53/1.76 % (21810)Instruction limit reached!
% 2.53/1.76 % (21810)------------------------------
% 2.53/1.76 % (21810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.76 % (21810)Termination reason: Unknown
% 2.53/1.76 % (21810)Termination phase: Preprocessing 2
% 2.53/1.76
% 2.53/1.76 % (21810)Memory used [KB]: 2430
% 2.53/1.76 % (21810)Time elapsed: 0.016 s
% 2.53/1.76 % (21810)Instructions burned: 49 (million)
% 2.53/1.76 % (21810)------------------------------
% 2.53/1.76 % (21810)------------------------------
% 2.53/1.77 % (21789)Instruction limit reached!
% 2.53/1.77 % (21789)------------------------------
% 2.53/1.77 % (21789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.77 % (21789)Termination reason: Unknown
% 2.53/1.77 % (21789)Termination phase: Saturation
% 2.53/1.77 % (21812)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_21668 for (2997ds/507Mi)
% 2.53/1.77
% 2.53/1.77 % (21789)Memory used [KB]: 11769
% 2.53/1.77 % (21789)Time elapsed: 0.210 s
% 2.53/1.77 % (21789)Instructions burned: 711 (million)
% 2.53/1.77 % (21789)------------------------------
% 2.53/1.77 % (21789)------------------------------
% 2.53/1.78 % (21796)Instruction limit reached!
% 2.53/1.78 % (21796)------------------------------
% 2.53/1.78 % (21796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.78 % (21796)Termination reason: Unknown
% 2.53/1.78 % (21796)Termination phase: Saturation
% 2.53/1.78
% 2.53/1.78 % (21796)Memory used [KB]: 6780
% 2.53/1.78 % (21796)Time elapsed: 0.189 s
% 2.53/1.78 % (21796)Instructions burned: 782 (million)
% 2.53/1.78 % (21796)------------------------------
% 2.53/1.78 % (21796)------------------------------
% 2.53/1.78 % (21813)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_21668 for (2997ds/149Mi)
% 2.53/1.79 % (21811)Instruction limit reached!
% 2.53/1.79 % (21811)------------------------------
% 2.53/1.79 % (21811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.79 % (21811)Termination reason: Unknown
% 2.53/1.79 % (21811)Termination phase: Saturation
% 2.53/1.79
% 2.53/1.79 % (21811)Memory used [KB]: 2046
% 2.53/1.79 % (21811)Time elapsed: 0.028 s
% 2.53/1.79 % (21811)Instructions burned: 100 (million)
% 2.53/1.79 % (21811)------------------------------
% 2.53/1.79 % (21811)------------------------------
% 2.53/1.79 % (21780)Instruction limit reached!
% 2.53/1.79 % (21780)------------------------------
% 2.53/1.79 % (21780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.79 % (21780)Termination reason: Unknown
% 2.53/1.79 % (21780)Termination phase: Saturation
% 2.53/1.79
% 2.53/1.79 % (21780)Memory used [KB]: 7803
% 2.53/1.79 % (21780)Time elapsed: 0.275 s
% 2.53/1.79 % (21780)Instructions burned: 1041 (million)
% 2.53/1.79 % (21780)------------------------------
% 2.53/1.79 % (21780)------------------------------
% 2.53/1.79 % (21814)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21668 for (2997ds/39Mi)
% 2.53/1.80 % (21815)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_21668 for (2997ds/6Mi)
% 2.53/1.80 % (21816)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_21668 for (2997ds/1087Mi)
% 2.53/1.80 % (21815)Instruction limit reached!
% 2.53/1.80 % (21815)------------------------------
% 2.53/1.80 % (21815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.80 % (21815)Termination reason: Unknown
% 2.53/1.80 % (21815)Termination phase: shuffling
% 2.53/1.80
% 2.53/1.80 % (21815)Memory used [KB]: 1407
% 2.53/1.80 % (21815)Time elapsed: 0.004 s
% 2.53/1.80 % (21815)Instructions burned: 7 (million)
% 2.53/1.80 % (21815)------------------------------
% 2.53/1.80 % (21815)------------------------------
% 2.53/1.80 % (21814)Instruction limit reached!
% 2.53/1.80 % (21814)------------------------------
% 2.53/1.80 % (21814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.80 % (21814)Termination reason: Unknown
% 2.53/1.80 % (21814)Termination phase: Preprocessing 1
% 2.53/1.80
% 2.53/1.80 % (21814)Memory used [KB]: 2302
% 2.53/1.80 % (21814)Time elapsed: 0.013 s
% 2.53/1.80 % (21814)Instructions burned: 41 (million)
% 2.53/1.80 % (21814)------------------------------
% 2.53/1.80 % (21814)------------------------------
% 2.53/1.81 % (21818)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_21668 for (2997ds/44Mi)
% 2.53/1.81 % (21817)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21668 for (2997ds/47Mi)
% 2.53/1.83 % (21818)Instruction limit reached!
% 2.53/1.83 % (21818)------------------------------
% 2.53/1.83 % (21818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (21818)Termination reason: Unknown
% 2.53/1.83 % (21818)Termination phase: Property scanning
% 2.53/1.83
% 2.53/1.83 % (21818)Memory used [KB]: 1918
% 2.53/1.83 % (21818)Time elapsed: 0.013 s
% 2.53/1.83 % (21818)Instructions burned: 46 (million)
% 2.53/1.83 % (21818)------------------------------
% 2.53/1.83 % (21818)------------------------------
% 2.53/1.83 % (21813)Instruction limit reached!
% 2.53/1.83 % (21813)------------------------------
% 2.53/1.83 % (21813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (21813)Termination reason: Unknown
% 2.53/1.83 % (21813)Termination phase: Property scanning
% 2.53/1.83
% 2.53/1.83 % (21813)Memory used [KB]: 7931
% 2.53/1.83 % (21813)Time elapsed: 0.043 s
% 2.53/1.83 % (21813)Instructions burned: 152 (million)
% 2.53/1.83 % (21813)------------------------------
% 2.53/1.83 % (21813)------------------------------
% 2.53/1.83 % (21817)Instruction limit reached!
% 2.53/1.83 % (21817)------------------------------
% 2.53/1.83 % (21817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (21817)Termination reason: Unknown
% 2.53/1.83 % (21817)Termination phase: Naming
% 2.53/1.83
% 2.53/1.83 % (21817)Memory used [KB]: 2686
% 2.53/1.83 % (21817)Time elapsed: 0.017 s
% 2.53/1.83 % (21817)Instructions burned: 48 (million)
% 2.53/1.83 % (21817)------------------------------
% 2.53/1.83 % (21817)------------------------------
% 2.53/1.84 % (21819)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_21668 for (2996ds/432Mi)
% 2.53/1.84 % (21820)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21668 for (2996ds/62Mi)
% 2.53/1.84 % (21821)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_21668 for (2996ds/31Mi)
% 2.53/1.85 % (21821)Instruction limit reached!
% 2.53/1.85 % (21821)------------------------------
% 2.53/1.85 % (21821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (21821)Termination reason: Unknown
% 2.53/1.85 % (21821)Termination phase: Property scanning
% 2.53/1.85
% 2.53/1.85 % (21821)Memory used [KB]: 2174
% 2.53/1.85 % (21821)Time elapsed: 0.011 s
% 2.53/1.85 % (21821)Instructions burned: 34 (million)
% 2.53/1.85 % (21821)------------------------------
% 2.53/1.85 % (21821)------------------------------
% 2.53/1.85 % (21820)Instruction limit reached!
% 2.53/1.85 % (21820)------------------------------
% 2.53/1.85 % (21820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (21820)Termination reason: Unknown
% 2.53/1.85 % (21820)Termination phase: Property scanning
% 2.53/1.85
% 2.53/1.85 % (21820)Memory used [KB]: 2046
% 2.53/1.85 % (21820)Time elapsed: 0.017 s
% 2.53/1.85 % (21820)Instructions burned: 64 (million)
% 2.53/1.85 % (21820)------------------------------
% 2.53/1.85 % (21820)------------------------------
% 2.53/1.86 % (21822)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_21668 for (2996ds/96Mi)
% 2.53/1.86 % (21812)Refutation not found, incomplete strategy
% 2.53/1.86 % (21812)------------------------------
% 2.53/1.86 % (21812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.86 % (21812)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.86
% 2.53/1.86
% 2.53/1.86 % (21812)Memory used [KB]: 9978
% 2.53/1.86 % (21812)Time elapsed: 0.087 s
% 2.53/1.86 % (21812)Instructions burned: 282 (million)
% 2.53/1.86 % (21812)------------------------------
% 2.53/1.86 % (21812)------------------------------
% 2.53/1.86 % (21823)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_21668 for (2996ds/453Mi)
% 2.53/1.87 % (21824)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_21668 for (2996ds/71Mi)
% 2.53/1.88 % (21809)Instruction limit reached!
% 2.53/1.88 % (21809)------------------------------
% 2.53/1.88 % (21809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.88 % (21809)Termination reason: Unknown
% 2.53/1.88 % (21809)Termination phase: Saturation
% 2.53/1.88
% 2.53/1.88 % (21809)Memory used [KB]: 7419
% 2.53/1.88 % (21809)Time elapsed: 0.132 s
% 2.53/1.88 % (21809)Instructions burned: 449 (million)
% 2.53/1.88 % (21809)------------------------------
% 2.53/1.88 % (21809)------------------------------
% 2.53/1.89 % (21822)Instruction limit reached!
% 2.53/1.89 % (21822)------------------------------
% 2.53/1.89 % (21822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (21822)Termination reason: Unknown
% 2.53/1.89 % (21822)Termination phase: Property scanning
% 2.53/1.89
% 2.53/1.89 % (21822)Memory used [KB]: 4349
% 2.53/1.89 % (21822)Time elapsed: 0.029 s
% 2.53/1.89 % (21822)Instructions burned: 98 (million)
% 2.53/1.89 % (21822)------------------------------
% 2.53/1.89 % (21822)------------------------------
% 2.53/1.89 % (21825)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_21668 for (2996ds/83Mi)
% 2.53/1.89 % (21824)Instruction limit reached!
% 2.53/1.89 % (21824)------------------------------
% 2.53/1.89 % (21824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (21824)Termination reason: Unknown
% 2.53/1.89 % (21824)Termination phase: Preprocessing 3
% 2.53/1.89
% 2.53/1.89 % (21824)Memory used [KB]: 3326
% 2.53/1.89 % (21824)Time elapsed: 0.023 s
% 2.53/1.89 % (21824)Instructions burned: 71 (million)
% 2.53/1.89 % (21824)------------------------------
% 2.53/1.89 % (21824)------------------------------
% 2.53/1.90 % (21826)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_21668 for (2996ds/11Mi)
% 2.53/1.90 % (21826)Instruction limit reached!
% 2.53/1.90 % (21826)------------------------------
% 2.53/1.90 % (21826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.90 % (21826)Termination reason: Unknown
% 2.53/1.90 % (21826)Termination phase: shuffling
% 2.53/1.90
% 2.53/1.90 % (21826)Memory used [KB]: 1535
% 2.53/1.90 % (21826)Time elapsed: 0.004 s
% 2.53/1.90 % (21826)Instructions burned: 11 (million)
% 2.53/1.90 % (21826)------------------------------
% 2.53/1.90 % (21826)------------------------------
% 2.53/1.90 % (21827)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_21668 for (2995ds/41Mi)
% 2.53/1.90 % (21798)Instruction limit reached!
% 2.53/1.90 % (21798)------------------------------
% 2.53/1.90 % (21798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.90 % (21798)Termination reason: Unknown
% 2.53/1.90 % (21798)Termination phase: Saturation
% 2.53/1.90
% 2.53/1.90 % (21798)Memory used [KB]: 11641
% 2.53/1.90 % (21798)Time elapsed: 0.284 s
% 2.53/1.90 % (21798)Instructions burned: 879 (million)
% 2.53/1.90 % (21798)------------------------------
% 2.53/1.90 % (21798)------------------------------
% 2.53/1.91 % (21828)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21668 for (2995ds/6Mi)
% 2.53/1.91 % (21828)Instruction limit reached!
% 2.53/1.91 % (21828)------------------------------
% 2.53/1.91 % (21828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.91 % (21828)Termination reason: Unknown
% 2.53/1.91 % (21828)Termination phase: shuffling
% 2.53/1.91
% 2.53/1.91 % (21828)Memory used [KB]: 1407
% 2.53/1.91 % (21828)Time elapsed: 0.003 s
% 2.53/1.91 % (21828)Instructions burned: 7 (million)
% 2.53/1.91 % (21828)------------------------------
% 2.53/1.91 % (21828)------------------------------
% 2.53/1.92 % (21829)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_21668 for (2995ds/150Mi)
% 2.53/1.92 % (21825)Instruction limit reached!
% 2.53/1.92 % (21825)------------------------------
% 2.53/1.92 % (21825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (21825)Termination reason: Unknown
% 2.53/1.92 % (21825)Termination phase: Saturation
% 2.53/1.92
% 2.53/1.92 % (21825)Memory used [KB]: 7036
% 2.53/1.92 % (21825)Time elapsed: 0.027 s
% 2.53/1.92 % (21825)Instructions burned: 85 (million)
% 2.53/1.92 % (21825)------------------------------
% 2.53/1.92 % (21825)------------------------------
% 2.53/1.92 % (21827)Instruction limit reached!
% 2.53/1.92 % (21827)------------------------------
% 2.53/1.92 % (21827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (21827)Termination reason: Unknown
% 2.53/1.92 % (21827)Termination phase: Property scanning
% 2.53/1.92
% 2.53/1.92 % (21827)Memory used [KB]: 1918
% 2.53/1.92 % (21827)Time elapsed: 0.014 s
% 2.53/1.92 % (21827)Instructions burned: 44 (million)
% 2.53/1.92 % (21827)------------------------------
% 2.53/1.92 % (21827)------------------------------
% 2.53/1.92 % (21830)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_21668 for (2995ds/343Mi)
% 2.53/1.93 % (21831)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_21668 for (2995ds/109Mi)
% 2.53/1.93 % (21832)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_21668 for (2995ds/253Mi)
% 2.53/1.94 % (21819)Instruction limit reached!
% 2.53/1.94 % (21819)------------------------------
% 2.53/1.94 % (21819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.94 % (21819)Termination reason: Unknown
% 2.53/1.94 % (21819)Termination phase: Saturation
% 2.53/1.94
% 2.53/1.94 % (21819)Memory used [KB]: 2558
% 2.53/1.94 % (21819)Time elapsed: 0.109 s
% 2.53/1.94 % (21819)Instructions burned: 434 (million)
% 2.53/1.94 % (21819)------------------------------
% 2.53/1.94 % (21819)------------------------------
% 2.53/1.95 % (21833)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_21668 for (2995ds/140Mi)
% 2.53/1.96 % (21829)Instruction limit reached!
% 2.53/1.96 % (21829)------------------------------
% 2.53/1.96 % (21829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.96 % (21829)Termination reason: Unknown
% 2.53/1.96 % (21829)Termination phase: Property scanning
% 2.53/1.96
% 2.53/1.96 % (21829)Memory used [KB]: 4349
% 2.53/1.96 % (21829)Time elapsed: 0.045 s
% 2.53/1.96 % (21829)Instructions burned: 153 (million)
% 2.53/1.96 % (21829)------------------------------
% 2.53/1.96 % (21829)------------------------------
% 2.53/1.96 % (21831)Instruction limit reached!
% 2.53/1.96 % (21831)------------------------------
% 2.53/1.96 % (21831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.96 % (21831)Termination reason: Unknown
% 2.53/1.96 % (21831)Termination phase: Property scanning
% 2.53/1.96
% 2.53/1.96 % (21831)Memory used [KB]: 4221
% 2.53/1.96 % (21831)Time elapsed: 0.036 s
% 2.53/1.96 % (21831)Instructions burned: 112 (million)
% 2.53/1.96 % (21831)------------------------------
% 2.53/1.96 % (21831)------------------------------
% 2.53/1.97 % (21834)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_21668 for (2995ds/614Mi)
% 2.53/1.97 % (21835)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_21668 for (2995ds/202Mi)
% 2.53/1.97 % (21823)Instruction limit reached!
% 2.53/1.97 % (21823)------------------------------
% 2.53/1.97 % (21823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.97 % (21823)Termination reason: Unknown
% 2.53/1.97 % (21823)Termination phase: Saturation
% 2.53/1.97
% 2.53/1.97 % (21823)Memory used [KB]: 6652
% 2.53/1.97 % (21823)Time elapsed: 0.110 s
% 2.53/1.97 % (21823)Instructions burned: 456 (million)
% 2.53/1.97 % (21823)------------------------------
% 2.53/1.97 % (21823)------------------------------
% 2.53/1.98 % (21836)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_21668 for (2995ds/339Mi)
% 2.53/1.99 % (21833)Instruction limit reached!
% 2.53/1.99 % (21833)------------------------------
% 2.53/1.99 % (21833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.99 % (21833)Termination reason: Unknown
% 2.53/1.99 % (21833)Termination phase: Property scanning
% 2.53/1.99
% 2.53/1.99 % (21833)Memory used [KB]: 4349
% 2.53/1.99 % (21833)Time elapsed: 0.039 s
% 2.53/1.99 % (21833)Instructions burned: 140 (million)
% 2.53/1.99 % (21833)------------------------------
% 2.53/1.99 % (21833)------------------------------
% 2.53/2.00 % (21837)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_21668 for (2995ds/283Mi)
% 2.53/2.00 % (21832)Instruction limit reached!
% 2.53/2.00 % (21832)------------------------------
% 2.53/2.00 % (21832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/2.00 % (21832)Termination reason: Unknown
% 2.53/2.00 % (21832)Termination phase: Saturation
% 2.53/2.00
% 2.53/2.00 % (21832)Memory used [KB]: 7419
% 2.53/2.00 % (21832)Time elapsed: 0.079 s
% 2.53/2.00 % (21832)Instructions burned: 254 (million)
% 2.53/2.00 % (21832)------------------------------
% 2.53/2.00 % (21832)------------------------------
% 2.53/2.01 % (21838)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_21668 for (2994ds/134Mi)
% 2.53/2.02 % (21830)Instruction limit reached!
% 2.53/2.02 % (21830)------------------------------
% 2.53/2.02 % (21830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/2.02 % (21830)Termination reason: Unknown
% 2.53/2.02 % (21830)Termination phase: Saturation
% 2.53/2.02
% 2.53/2.02 % (21830)Memory used [KB]: 7931
% 2.53/2.02 % (21830)Time elapsed: 0.099 s
% 2.53/2.02 % (21830)Instructions burned: 345 (million)
% 2.53/2.02 % (21830)------------------------------
% 2.53/2.02 % (21830)------------------------------
% 2.53/2.02 % (21835)Instruction limit reached!
% 2.53/2.02 % (21835)------------------------------
% 2.53/2.02 % (21835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/2.02 % (21835)Termination reason: Unknown
% 2.53/2.02 % (21835)Termination phase: Saturation
% 2.53/2.02
% 2.53/2.02 % (21835)Memory used [KB]: 4477
% 2.53/2.02 % (21835)Time elapsed: 0.055 s
% 2.53/2.02 % (21835)Instructions burned: 203 (million)
% 2.53/2.02 % (21835)------------------------------
% 2.53/2.02 % (21835)------------------------------
% 2.53/2.03 % (21839)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_21668 for (2994ds/298Mi)
% 6.08/2.03 % (21840)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_21668 for (2994ds/192Mi)
% 6.08/2.05 % (21838)Instruction limit reached!
% 6.08/2.05 % (21838)------------------------------
% 6.08/2.05 % (21838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.05 % (21838)Termination reason: Unknown
% 6.08/2.05 % (21838)Termination phase: Property scanning
% 6.08/2.05
% 6.08/2.05 % (21838)Memory used [KB]: 4221
% 6.08/2.05 % (21838)Time elapsed: 0.038 s
% 6.08/2.05 % (21838)Instructions burned: 136 (million)
% 6.08/2.05 % (21838)------------------------------
% 6.08/2.05 % (21838)------------------------------
% 6.08/2.06 % (21841)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_21668 for (2994ds/258Mi)
% 6.08/2.07 % (21836)Instruction limit reached!
% 6.08/2.07 % (21836)------------------------------
% 6.08/2.07 % (21836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.07 % (21836)Termination reason: Unknown
% 6.08/2.07 % (21836)Termination phase: Saturation
% 6.08/2.07
% 6.08/2.07 % (21837)Instruction limit reached!
% 6.08/2.07 % (21837)------------------------------
% 6.08/2.07 % (21837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.07 % (21837)Termination reason: Unknown
% 6.08/2.07 % (21837)Termination phase: Saturation
% 6.08/2.07
% 6.08/2.07 % (21837)Memory used [KB]: 7547
% 6.08/2.07 % (21837)Time elapsed: 0.071 s
% 6.08/2.07 % (21837)Instructions burned: 283 (million)
% 6.08/2.07 % (21837)------------------------------
% 6.08/2.07 % (21837)------------------------------
% 6.08/2.07 % (21836)Memory used [KB]: 9466
% 6.08/2.07 % (21836)Time elapsed: 0.091 s
% 6.08/2.07 % (21836)Instructions burned: 340 (million)
% 6.08/2.07 % (21836)------------------------------
% 6.08/2.07 % (21836)------------------------------
% 6.08/2.08 % (21842)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_21668 for (2994ds/90Mi)
% 6.08/2.08 % (21843)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_21668 for (2994ds/231Mi)
% 6.08/2.09 % (21840)Instruction limit reached!
% 6.08/2.09 % (21840)------------------------------
% 6.08/2.09 % (21840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.09 % (21840)Termination reason: Unknown
% 6.08/2.09 % (21840)Termination phase: Property scanning
% 6.08/2.09
% 6.08/2.09 % (21840)Memory used [KB]: 4477
% 6.08/2.09 % (21840)Time elapsed: 0.052 s
% 6.08/2.09 % (21840)Instructions burned: 194 (million)
% 6.08/2.09 % (21840)------------------------------
% 6.08/2.09 % (21840)------------------------------
% 6.08/2.10 % (21844)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_21668 for (2994ds/458Mi)
% 6.08/2.10 % (21839)Instruction limit reached!
% 6.08/2.10 % (21839)------------------------------
% 6.08/2.10 % (21839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.10 % (21839)Termination reason: Unknown
% 6.08/2.10 % (21839)Termination phase: Saturation
% 6.08/2.10
% 6.08/2.10 % (21839)Memory used [KB]: 6780
% 6.08/2.10 % (21839)Time elapsed: 0.076 s
% 6.08/2.10 % (21839)Instructions burned: 300 (million)
% 6.08/2.10 % (21839)------------------------------
% 6.08/2.10 % (21839)------------------------------
% 6.08/2.11 % (21842)Instruction limit reached!
% 6.08/2.11 % (21842)------------------------------
% 6.08/2.11 % (21842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.11 % (21842)Termination reason: Unknown
% 6.08/2.11 % (21842)Termination phase: Preprocessing 3
% 6.08/2.11
% 6.08/2.11 % (21842)Memory used [KB]: 4093
% 6.08/2.11 % (21842)Time elapsed: 0.027 s
% 6.08/2.11 % (21842)Instructions burned: 91 (million)
% 6.08/2.11 % (21842)------------------------------
% 6.08/2.11 % (21842)------------------------------
% 6.08/2.11 % (21845)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_21668 for (2994ds/31Mi)
% 6.08/2.12 % (21846)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_21668 for (2993ds/297Mi)
% 6.08/2.12 % (21845)Instruction limit reached!
% 6.08/2.12 % (21845)------------------------------
% 6.08/2.12 % (21845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.12 % (21845)Termination reason: Unknown
% 6.08/2.12 % (21845)Termination phase: Property scanning
% 6.08/2.12
% 6.08/2.12 % (21845)Memory used [KB]: 2174
% 6.08/2.12 % (21845)Time elapsed: 0.011 s
% 6.08/2.12 % (21845)Instructions burned: 34 (million)
% 6.08/2.12 % (21845)------------------------------
% 6.08/2.12 % (21845)------------------------------
% 6.08/2.13 % (21841)Instruction limit reached!
% 6.08/2.13 % (21841)------------------------------
% 6.08/2.13 % (21841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (21841)Termination reason: Unknown
% 6.08/2.13 % (21841)Termination phase: Property scanning
% 6.08/2.13
% 6.08/2.13 % (21841)Memory used [KB]: 7931
% 6.08/2.13 % (21841)Time elapsed: 0.068 s
% 6.08/2.13 % (21841)Instructions burned: 258 (million)
% 6.08/2.13 % (21841)------------------------------
% 6.08/2.13 % (21841)------------------------------
% 6.70/2.13 % (21847)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_21668 for (2993ds/987Mi)
% 6.70/2.14 % (21843)Instruction limit reached!
% 6.70/2.14 % (21843)------------------------------
% 6.70/2.14 % (21843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.14 % (21843)Termination reason: Unknown
% 6.70/2.14 % (21848)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_21668 for (2993ds/182Mi)
% 6.70/2.14 % (21843)Termination phase: Saturation
% 6.70/2.14
% 6.70/2.14 % (21843)Memory used [KB]: 7164
% 6.70/2.14 % (21843)Time elapsed: 0.058 s
% 6.70/2.14 % (21843)Instructions burned: 232 (million)
% 6.70/2.14 % (21843)------------------------------
% 6.70/2.14 % (21843)------------------------------
% 6.70/2.14 % (21834)Instruction limit reached!
% 6.70/2.14 % (21834)------------------------------
% 6.70/2.14 % (21834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.14 % (21834)Termination reason: Unknown
% 6.70/2.14 % (21834)Termination phase: Saturation
% 6.70/2.14
% 6.70/2.14 % (21834)Memory used [KB]: 12409
% 6.70/2.14 % (21834)Time elapsed: 0.176 s
% 6.70/2.14 % (21834)Instructions burned: 615 (million)
% 6.70/2.14 % (21834)------------------------------
% 6.70/2.14 % (21834)------------------------------
% 6.70/2.15 % (21849)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_21668 for (2993ds/182Mi)
% 6.70/2.15 % (21850)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_21668 for (2993ds/154Mi)
% 6.70/2.16 % (21816)Instruction limit reached!
% 6.70/2.16 % (21816)------------------------------
% 6.70/2.16 % (21816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.16 % (21816)Termination reason: Unknown
% 6.70/2.16 % (21816)Termination phase: Saturation
% 6.70/2.16
% 6.70/2.16 % (21816)Memory used [KB]: 12281
% 6.70/2.16 % (21816)Time elapsed: 0.370 s
% 6.70/2.16 % (21816)Instructions burned: 1090 (million)
% 6.70/2.16 % (21816)------------------------------
% 6.70/2.16 % (21816)------------------------------
% 6.70/2.17 % (21851)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_21668 for (2993ds/79Mi)
% 6.70/2.19 % (21848)Instruction limit reached!
% 6.70/2.19 % (21848)------------------------------
% 6.70/2.19 % (21848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.19 % (21848)Termination reason: Unknown
% 6.70/2.19 % (21848)Termination phase: Property scanning
% 6.70/2.19
% 6.70/2.19 % (21848)Memory used [KB]: 7675
% 6.70/2.19 % (21848)Time elapsed: 0.050 s
% 6.70/2.19 % (21848)Instructions burned: 183 (million)
% 6.70/2.19 % (21848)------------------------------
% 6.70/2.19 % (21848)------------------------------
% 6.70/2.19 % (21850)Instruction limit reached!
% 6.70/2.19 % (21850)------------------------------
% 6.70/2.19 % (21850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.19 % (21850)Termination reason: Unknown
% 6.70/2.19 % (21850)Termination phase: Saturation
% 6.70/2.19
% 6.70/2.19 % (21850)Memory used [KB]: 2686
% 6.70/2.19 % (21850)Time elapsed: 0.040 s
% 6.70/2.19 % (21850)Instructions burned: 156 (million)
% 6.70/2.19 % (21850)------------------------------
% 6.70/2.19 % (21850)------------------------------
% 6.70/2.19 % (21851)Instruction limit reached!
% 6.70/2.19 % (21851)------------------------------
% 6.70/2.19 % (21851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.19 % (21851)Termination reason: Unknown
% 6.70/2.19 % (21851)Termination phase: Preprocessing 3
% 6.70/2.19
% 6.70/2.19 % (21851)Memory used [KB]: 3837
% 6.70/2.19 % (21851)Time elapsed: 0.025 s
% 6.70/2.19 % (21851)Instructions burned: 81 (million)
% 6.70/2.19 % (21851)------------------------------
% 6.70/2.19 % (21851)------------------------------
% 6.70/2.20 % (21846)Instruction limit reached!
% 6.70/2.20 % (21846)------------------------------
% 6.70/2.20 % (21846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.20 % (21846)Termination reason: Unknown
% 6.70/2.20 % (21846)Termination phase: Saturation
% 6.70/2.20
% 6.70/2.20 % (21846)Memory used [KB]: 7164
% 6.70/2.20 % (21846)Time elapsed: 0.081 s
% 6.70/2.20 % (21846)Instructions burned: 298 (million)
% 6.70/2.20 % (21846)------------------------------
% 6.70/2.20 % (21846)------------------------------
% 6.98/2.20 % (21852)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_21668 for (2993ds/216Mi)
% 6.98/2.20 % (21849)Instruction limit reached!
% 6.98/2.20 % (21849)------------------------------
% 6.98/2.20 % (21849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.20 % (21849)Termination reason: Unknown
% 6.98/2.20 % (21849)Termination phase: Saturation
% 6.98/2.20
% 6.98/2.20 % (21849)Memory used [KB]: 9083
% 6.98/2.20 % (21849)Time elapsed: 0.051 s
% 6.98/2.20 % (21849)Instructions burned: 183 (million)
% 6.98/2.20 % (21849)------------------------------
% 6.98/2.20 % (21849)------------------------------
% 6.98/2.20 % (21853)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_21668 for (2993ds/114Mi)
% 6.98/2.20 % (21854)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_21668 for (2993ds/922Mi)
% 6.98/2.21 % (21855)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_21668 for (2993ds/182Mi)
% 6.98/2.21 % (21856)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_21668 for (2993ds/164Mi)
% 6.98/2.23 % (21844)Instruction limit reached!
% 6.98/2.23 % (21844)------------------------------
% 6.98/2.23 % (21844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.23 % (21844)Termination reason: Unknown
% 6.98/2.23 % (21844)Termination phase: Saturation
% 6.98/2.23
% 6.98/2.23 % (21844)Memory used [KB]: 10362
% 6.98/2.23 % (21844)Time elapsed: 0.132 s
% 6.98/2.23 % (21844)Instructions burned: 460 (million)
% 6.98/2.23 % (21844)------------------------------
% 6.98/2.23 % (21844)------------------------------
% 6.98/2.23 % (21853)Instruction limit reached!
% 6.98/2.23 % (21853)------------------------------
% 6.98/2.23 % (21853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.23 % (21853)Termination reason: Unknown
% 6.98/2.23 % (21853)Termination phase: Property scanning
% 6.98/2.23
% 6.98/2.23 % (21853)Memory used [KB]: 4221
% 6.98/2.23 % (21853)Time elapsed: 0.033 s
% 6.98/2.23 % (21853)Instructions burned: 116 (million)
% 6.98/2.23 % (21853)------------------------------
% 6.98/2.23 % (21853)------------------------------
% 6.98/2.24 % (21857)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_21668 for (2992ds/50Mi)
% 6.98/2.24 % (21858)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_21668 for (2992ds/368Mi)
% 6.98/2.25 % (21857)Instruction limit reached!
% 6.98/2.25 % (21857)------------------------------
% 6.98/2.25 % (21857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.25 % (21857)Termination reason: Unknown
% 6.98/2.25 % (21857)Termination phase: Property scanning
% 6.98/2.25
% 6.98/2.25 % (21857)Memory used [KB]: 1918
% 6.98/2.25 % (21857)Time elapsed: 0.014 s
% 6.98/2.25 % (21857)Instructions burned: 51 (million)
% 6.98/2.25 % (21857)------------------------------
% 6.98/2.25 % (21857)------------------------------
% 6.98/2.25 % (21855)Instruction limit reached!
% 6.98/2.25 % (21855)------------------------------
% 6.98/2.25 % (21855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.25 % (21855)Termination reason: Unknown
% 6.98/2.25 % (21855)Termination phase: Saturation
% 6.98/2.25
% 6.98/2.25 % (21855)Memory used [KB]: 6524
% 6.98/2.25 % (21855)Time elapsed: 0.046 s
% 6.98/2.25 % (21855)Instructions burned: 182 (million)
% 6.98/2.25 % (21855)------------------------------
% 6.98/2.25 % (21855)------------------------------
% 6.98/2.25 % (21856)Instruction limit reached!
% 6.98/2.25 % (21856)------------------------------
% 6.98/2.25 % (21856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.25 % (21856)Termination reason: Unknown
% 6.98/2.25 % (21856)Termination phase: Saturation
% 6.98/2.25
% 6.98/2.25 % (21856)Memory used [KB]: 2174
% 6.98/2.25 % (21856)Time elapsed: 0.045 s
% 6.98/2.25 % (21856)Instructions burned: 165 (million)
% 6.98/2.25 % (21856)------------------------------
% 6.98/2.25 % (21856)------------------------------
% 6.98/2.26 % (21852)Instruction limit reached!
% 6.98/2.26 % (21852)------------------------------
% 6.98/2.26 % (21852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.26 % (21852)Termination reason: Unknown
% 6.98/2.26 % (21852)Termination phase: Saturation
% 6.98/2.26
% 6.98/2.26 % (21852)Memory used [KB]: 6780
% 6.98/2.26 % (21852)Time elapsed: 0.061 s
% 6.98/2.26 % (21852)Instructions burned: 218 (million)
% 6.98/2.26 % (21852)------------------------------
% 6.98/2.26 % (21852)------------------------------
% 6.98/2.26 % (21859)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_21668 for (2992ds/1021Mi)
% 6.98/2.26 % (21860)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_21668 for (2992ds/267Mi)
% 6.98/2.26 % (21861)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_21668 for (2992ds/204Mi)
% 6.98/2.27 % (21862)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_21668 for (2992ds/26Mi)
% 6.98/2.27 % (21862)Instruction limit reached!
% 6.98/2.27 % (21862)------------------------------
% 6.98/2.27 % (21862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.27 % (21862)Termination reason: Unknown
% 6.98/2.27 % (21862)Termination phase: shuffling
% 6.98/2.27
% 6.98/2.27 % (21862)Memory used [KB]: 1791
% 6.98/2.27 % (21862)Time elapsed: 0.008 s
% 6.98/2.27 % (21862)Instructions burned: 26 (million)
% 6.98/2.27 % (21862)------------------------------
% 6.98/2.27 % (21862)------------------------------
% 6.98/2.28 % (21863)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_21668 for (2992ds/53Mi)
% 7.52/2.30 % (21863)Instruction limit reached!
% 7.52/2.30 % (21863)------------------------------
% 7.52/2.30 % (21863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.30 % (21863)Termination reason: Unknown
% 7.52/2.30 % (21863)Termination phase: Property scanning
% 7.52/2.30
% 7.52/2.30 % (21863)Memory used [KB]: 1918
% 7.52/2.30 % (21863)Time elapsed: 0.015 s
% 7.52/2.30 % (21863)Instructions burned: 55 (million)
% 7.52/2.30 % (21863)------------------------------
% 7.52/2.30 % (21863)------------------------------
% 7.52/2.31 % (21864)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_21668 for (2991ds/4436Mi)
% 7.52/2.31 % (21861)Instruction limit reached!
% 7.52/2.31 % (21861)------------------------------
% 7.52/2.31 % (21861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.31 % (21861)Termination reason: Unknown
% 7.52/2.31 % (21861)Termination phase: Property scanning
% 7.52/2.31
% 7.52/2.31 % (21861)Memory used [KB]: 4605
% 7.52/2.31 % (21861)Time elapsed: 0.054 s
% 7.52/2.31 % (21861)Instructions burned: 204 (million)
% 7.52/2.31 % (21861)------------------------------
% 7.52/2.31 % (21861)------------------------------
% 7.52/2.32 % (21865)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_21668 for (2991ds/1539Mi)
% 7.52/2.33 % (21860)Instruction limit reached!
% 7.52/2.33 % (21860)------------------------------
% 7.52/2.33 % (21860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.33 % (21860)Termination reason: Unknown
% 7.52/2.33 % (21860)Termination phase: Saturation
% 7.52/2.33
% 7.52/2.33 % (21860)Memory used [KB]: 6652
% 7.52/2.33 % (21860)Time elapsed: 0.067 s
% 7.52/2.33 % (21860)Instructions burned: 268 (million)
% 7.52/2.33 % (21860)------------------------------
% 7.52/2.33 % (21860)------------------------------
% 7.52/2.34 % (21866)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_21668 for (2991ds/408Mi)
% 7.52/2.35 % (21858)Instruction limit reached!
% 7.52/2.35 % (21858)------------------------------
% 7.52/2.35 % (21858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.35 % (21858)Termination reason: Unknown
% 7.52/2.35 % (21858)Termination phase: Saturation
% 7.52/2.35
% 7.52/2.35 % (21858)Memory used [KB]: 11513
% 7.52/2.35 % (21858)Time elapsed: 0.103 s
% 7.52/2.35 % (21858)Instructions burned: 370 (million)
% 7.52/2.35 % (21858)------------------------------
% 7.52/2.35 % (21858)------------------------------
% 7.52/2.36 % (21867)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_21668 for (2991ds/5205Mi)
% 7.52/2.37 % (21847)Instruction limit reached!
% 7.52/2.37 % (21847)------------------------------
% 7.52/2.37 % (21847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.52/2.37 % (21847)Termination reason: Unknown
% 7.52/2.37 % (21847)Termination phase: Saturation
% 7.52/2.37
% 7.52/2.37 % (21847)Memory used [KB]: 7675
% 7.52/2.37 % (21847)Time elapsed: 0.236 s
% 7.52/2.37 % (21847)Instructions burned: 987 (million)
% 7.52/2.37 % (21847)------------------------------
% 7.52/2.37 % (21847)------------------------------
% 7.52/2.38 % (21868)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_21668 for (2991ds/1913Mi)
% 8.05/2.45 % (21866)Instruction limit reached!
% 8.05/2.45 % (21866)------------------------------
% 8.05/2.45 % (21866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.45 % (21866)Termination reason: Unknown
% 8.05/2.45 % (21866)Termination phase: Saturation
% 8.05/2.45
% 8.05/2.45 % (21866)Memory used [KB]: 11001
% 8.05/2.45 % (21866)Time elapsed: 0.118 s
% 8.05/2.45 % (21866)Instructions burned: 408 (million)
% 8.05/2.45 % (21866)------------------------------
% 8.05/2.45 % (21866)------------------------------
% 8.05/2.46 % (21869)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_21668 for (2990ds/4350Mi)
% 8.05/2.48 % (21854)Instruction limit reached!
% 8.05/2.48 % (21854)------------------------------
% 8.05/2.48 % (21854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.48 % (21854)Termination reason: Unknown
% 8.05/2.48 % (21854)Termination phase: Saturation
% 8.05/2.48
% 8.05/2.48 % (21854)Memory used [KB]: 13432
% 8.05/2.48 % (21854)Time elapsed: 0.280 s
% 8.05/2.48 % (21854)Instructions burned: 922 (million)
% 8.05/2.48 % (21854)------------------------------
% 8.05/2.48 % (21854)------------------------------
% 8.05/2.49 % (21870)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_21668 for (2990ds/68Mi)
% 8.46/2.51 % (21870)Instruction limit reached!
% 8.46/2.51 % (21870)------------------------------
% 8.46/2.51 % (21870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.51 % (21870)Termination reason: Unknown
% 8.46/2.51 % (21870)Termination phase: Preprocessing 3
% 8.46/2.51
% 8.46/2.51 % (21870)Memory used [KB]: 3198
% 8.46/2.51 % (21870)Time elapsed: 0.022 s
% 8.46/2.51 % (21870)Instructions burned: 70 (million)
% 8.46/2.51 % (21870)------------------------------
% 8.46/2.51 % (21870)------------------------------
% 8.46/2.52 % (21871)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_21668 for (2989ds/358Mi)
% 8.46/2.56 % (21859)Instruction limit reached!
% 8.46/2.56 % (21859)------------------------------
% 8.46/2.56 % (21859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.56 % (21859)Termination reason: Unknown
% 8.46/2.56 % (21859)Termination phase: Saturation
% 8.46/2.56
% 8.46/2.56 % (21859)Memory used [KB]: 12409
% 8.46/2.56 % (21859)Time elapsed: 0.327 s
% 8.46/2.56 % (21859)Instructions burned: 1023 (million)
% 8.46/2.56 % (21859)------------------------------
% 8.46/2.56 % (21859)------------------------------
% 8.46/2.57 % (21872)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_21668 for (2989ds/31Mi)
% 8.46/2.58 % (21872)Instruction limit reached!
% 8.46/2.58 % (21872)------------------------------
% 8.46/2.58 % (21872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.58 % (21872)Termination reason: Unknown
% 8.46/2.58 % (21872)Termination phase: Property scanning
% 8.46/2.58
% 8.46/2.58 % (21872)Memory used [KB]: 2174
% 8.46/2.58 % (21872)Time elapsed: 0.011 s
% 8.46/2.58 % (21872)Instructions burned: 32 (million)
% 8.46/2.58 % (21872)------------------------------
% 8.46/2.58 % (21872)------------------------------
% 8.46/2.59 % (21873)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_21668 for (2989ds/279Mi)
% 8.82/2.63 % (21871)Instruction limit reached!
% 8.82/2.63 % (21871)------------------------------
% 8.82/2.63 % (21871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.63 % (21871)Termination reason: Unknown
% 8.82/2.63 % (21871)Termination phase: Saturation
% 8.82/2.63
% 8.82/2.63 % (21871)Memory used [KB]: 9594
% 8.82/2.63 % (21871)Time elapsed: 0.102 s
% 8.82/2.63 % (21871)Instructions burned: 359 (million)
% 8.82/2.63 % (21871)------------------------------
% 8.82/2.63 % (21871)------------------------------
% 8.82/2.64 % (21874)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_21668 for (2988ds/258Mi)
% 8.82/2.66 % (21873)Instruction limit reached!
% 8.82/2.66 % (21873)------------------------------
% 8.82/2.66 % (21873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.66 % (21873)Termination reason: Unknown
% 8.82/2.66 % (21873)Termination phase: Saturation
% 8.82/2.66
% 8.82/2.66 % (21873)Memory used [KB]: 7675
% 8.82/2.66 % (21873)Time elapsed: 0.073 s
% 8.82/2.66 % (21873)Instructions burned: 281 (million)
% 8.82/2.66 % (21873)------------------------------
% 8.82/2.66 % (21873)------------------------------
% 8.82/2.67 % (21875)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_21668 for (2988ds/26Mi)
% 8.82/2.68 % (21875)Instruction limit reached!
% 8.82/2.68 % (21875)------------------------------
% 8.82/2.68 % (21875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.82/2.68 % (21875)Termination reason: Unknown
% 8.82/2.68 % (21875)Termination phase: shuffling
% 8.82/2.68
% 8.82/2.68 % (21875)Memory used [KB]: 1791
% 8.82/2.68 % (21875)Time elapsed: 0.008 s
% 8.82/2.68 % (21875)Instructions burned: 26 (million)
% 8.82/2.68 % (21875)------------------------------
% 8.82/2.68 % (21875)------------------------------
% 8.82/2.69 % (21876)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_21668 for (2988ds/995Mi)
% 9.03/2.71 % (21874)Instruction limit reached!
% 9.03/2.71 % (21874)------------------------------
% 9.03/2.71 % (21874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.71 % (21874)Termination reason: Unknown
% 9.03/2.71 % (21874)Termination phase: Saturation
% 9.03/2.71
% 9.03/2.71 % (21874)Memory used [KB]: 9466
% 9.03/2.71 % (21874)Time elapsed: 0.075 s
% 9.03/2.71 % (21874)Instructions burned: 259 (million)
% 9.03/2.71 % (21874)------------------------------
% 9.03/2.71 % (21874)------------------------------
% 9.03/2.72 % (21877)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_21668 for (2987ds/373Mi)
% 9.03/2.75 % (21865)Instruction limit reached!
% 9.03/2.75 % (21865)------------------------------
% 9.03/2.75 % (21865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.75 % (21865)Termination reason: Unknown
% 9.03/2.75 % (21865)Termination phase: Saturation
% 9.03/2.75
% 9.03/2.75 % (21865)Memory used [KB]: 12281
% 9.03/2.75 % (21865)Time elapsed: 0.432 s
% 9.03/2.75 % (21865)Instructions burned: 1542 (million)
% 9.03/2.75 % (21865)------------------------------
% 9.03/2.75 % (21865)------------------------------
% 9.03/2.76 % (21878)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_21668 for (2987ds/253Mi)
% 9.55/2.83 % (21878)Instruction limit reached!
% 9.55/2.83 % (21878)------------------------------
% 9.55/2.83 % (21878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.83 % (21878)Termination reason: Unknown
% 9.55/2.83 % (21877)Instruction limit reached!
% 9.55/2.83 % (21877)------------------------------
% 9.55/2.83 % (21877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.83 % (21877)Termination reason: Unknown
% 9.55/2.83 % (21877)Termination phase: Saturation
% 9.55/2.83
% 9.55/2.83 % (21877)Memory used [KB]: 10234
% 9.55/2.83 % (21877)Time elapsed: 0.108 s
% 9.55/2.83 % (21877)Instructions burned: 373 (million)
% 9.55/2.83 % (21877)------------------------------
% 9.55/2.83 % (21877)------------------------------
% 9.55/2.83 % (21878)Termination phase: Saturation
% 9.55/2.83
% 9.55/2.83 % (21878)Memory used [KB]: 6780
% 9.55/2.83 % (21878)Time elapsed: 0.063 s
% 9.55/2.83 % (21878)Instructions burned: 253 (million)
% 9.55/2.83 % (21878)------------------------------
% 9.55/2.83 % (21878)------------------------------
% 9.55/2.84 % (21880)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_21668 for (2986ds/832Mi)
% 9.55/2.84 % (21881)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_21668 for (2986ds/668Mi)
% 9.74/2.91 % (21880)Refutation not found, incomplete strategy
% 9.74/2.91 % (21880)------------------------------
% 9.74/2.91 % (21880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.91 % (21880)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.91
% 9.74/2.91
% 9.74/2.91 % (21880)Memory used [KB]: 9594
% 9.74/2.91 % (21880)Time elapsed: 0.075 s
% 9.74/2.91 % (21880)Instructions burned: 268 (million)
% 9.74/2.91 % (21880)------------------------------
% 9.74/2.91 % (21880)------------------------------
% 9.74/2.92 % (21882)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_21668 for (2985ds/40Mi)
% 9.74/2.93 % (21876)Instruction limit reached!
% 9.74/2.93 % (21876)------------------------------
% 9.74/2.93 % (21876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.93 % (21876)Termination reason: Unknown
% 9.74/2.93 % (21876)Termination phase: Saturation
% 9.74/2.93
% 9.74/2.93 % (21876)Memory used [KB]: 6652
% 9.74/2.93 % (21876)Time elapsed: 0.240 s
% 9.74/2.93 % (21876)Instructions burned: 997 (million)
% 9.74/2.93 % (21876)------------------------------
% 9.74/2.93 % (21876)------------------------------
% 9.74/2.93 % (21882)Instruction limit reached!
% 9.74/2.93 % (21882)------------------------------
% 9.74/2.93 % (21882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.93 % (21882)Termination reason: Unknown
% 9.74/2.93 % (21882)Termination phase: Property scanning
% 9.74/2.93
% 9.74/2.93 % (21882)Memory used [KB]: 1918
% 9.74/2.93 % (21882)Time elapsed: 0.012 s
% 9.74/2.93 % (21882)Instructions burned: 42 (million)
% 9.74/2.93 % (21882)------------------------------
% 9.74/2.93 % (21882)------------------------------
% 9.74/2.94 % (21883)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_21668 for (2985ds/294Mi)
% 9.74/2.94 % (21884)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_21668 for (2985ds/187Mi)
% 9.74/2.95 % (21868)Instruction limit reached!
% 9.74/2.95 % (21868)------------------------------
% 9.74/2.95 % (21868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.95 % (21868)Termination reason: Unknown
% 9.74/2.95 % (21868)Termination phase: Saturation
% 9.74/2.95
% 9.74/2.95 % (21868)Memory used [KB]: 6524
% 9.74/2.95 % (21868)Time elapsed: 0.576 s
% 9.74/2.95 % (21868)Instructions burned: 1914 (million)
% 9.74/2.95 % (21868)------------------------------
% 9.74/2.95 % (21868)------------------------------
% 9.74/2.96 % (21885)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_21668 for (2985ds/371Mi)
% 9.74/2.99 % (21884)Instruction limit reached!
% 9.74/2.99 % (21884)------------------------------
% 9.74/2.99 % (21884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.99 % (21884)Termination reason: Unknown
% 9.74/2.99 % (21884)Termination phase: Property scanning
% 9.74/2.99
% 9.74/2.99 % (21884)Memory used [KB]: 4605
% 9.74/2.99 % (21884)Time elapsed: 0.051 s
% 9.74/2.99 % (21884)Instructions burned: 188 (million)
% 9.74/2.99 % (21884)------------------------------
% 9.74/2.99 % (21884)------------------------------
% 9.74/3.00 % (21886)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_21668 for (2985ds/1827Mi)
% 9.74/3.01 % (21883)Instruction limit reached!
% 9.74/3.01 % (21883)------------------------------
% 9.74/3.01 % (21883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/3.01 % (21883)Termination reason: Unknown
% 9.74/3.01 % (21883)Termination phase: Saturation
% 9.74/3.01
% 9.74/3.01 % (21883)Memory used [KB]: 7547
% 9.74/3.01 % (21883)Time elapsed: 0.072 s
% 9.74/3.01 % (21883)Instructions burned: 294 (million)
% 9.74/3.01 % (21883)------------------------------
% 9.74/3.01 % (21883)------------------------------
% 9.74/3.02 % (21887)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_21668 for (2984ds/70Mi)
% 9.74/3.02 % (21881)Instruction limit reached!
% 9.74/3.02 % (21881)------------------------------
% 9.74/3.02 % (21881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/3.02 % (21881)Termination reason: Unknown
% 9.74/3.02 % (21881)Termination phase: Saturation
% 9.74/3.02
% 9.74/3.02 % (21881)Memory used [KB]: 11129
% 9.74/3.02 % (21881)Time elapsed: 0.169 s
% 9.74/3.02 % (21881)Instructions burned: 669 (million)
% 9.74/3.02 % (21881)------------------------------
% 9.74/3.02 % (21881)------------------------------
% 13.04/3.03 % (21888)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_21668 for (2984ds/316Mi)
% 13.04/3.04 % (21887)Instruction limit reached!
% 13.04/3.04 % (21887)------------------------------
% 13.04/3.04 % (21887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.04/3.04 % (21887)Termination reason: Unknown
% 13.04/3.04 % (21887)Termination phase: Property scanning
% 13.04/3.04
% 13.04/3.04 % (21887)Memory used [KB]: 2046
% 13.04/3.04 % (21887)Time elapsed: 0.019 s
% 13.04/3.04 % (21887)Instructions burned: 70 (million)
% 13.04/3.04 % (21887)------------------------------
% 13.04/3.04 % (21887)------------------------------
% 13.04/3.05 % (21889)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_21668 for (2984ds/932Mi)
% 13.04/3.07 % (21885)Instruction limit reached!
% 13.04/3.07 % (21885)------------------------------
% 13.04/3.07 % (21885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.04/3.07 % (21885)Termination reason: Unknown
% 13.04/3.07 % (21885)Termination phase: Saturation
% 13.04/3.07
% 13.04/3.07 % (21885)Memory used [KB]: 8059
% 13.04/3.07 % (21885)Time elapsed: 0.107 s
% 13.04/3.07 % (21885)Instructions burned: 371 (million)
% 13.04/3.07 % (21885)------------------------------
% 13.04/3.07 % (21885)------------------------------
% 13.04/3.08 % (21890)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_21668 for (2984ds/4714Mi)
% 13.53/3.14 % (21888)Instruction limit reached!
% 13.53/3.14 % (21888)------------------------------
% 13.53/3.14 % (21888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.53/3.14 % (21888)Termination reason: Unknown
% 13.53/3.14 % (21888)Termination phase: Saturation
% 13.53/3.14
% 13.53/3.14 % (21888)Memory used [KB]: 7291
% 13.53/3.14 % (21888)Time elapsed: 0.103 s
% 13.53/3.14 % (21888)Instructions burned: 316 (million)
% 13.53/3.14 % (21888)------------------------------
% 13.53/3.14 % (21888)------------------------------
% 13.53/3.15 % (21891)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_21668 for (2983ds/8250Mi)
% 13.92/3.28 % (21889)Instruction limit reached!
% 13.92/3.28 % (21889)------------------------------
% 13.92/3.28 % (21889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.28 % (21889)Termination reason: Unknown
% 13.92/3.28 % (21889)Termination phase: Saturation
% 13.92/3.28
% 13.92/3.28 % (21889)Memory used [KB]: 8315
% 13.92/3.28 % (21889)Time elapsed: 0.231 s
% 13.92/3.28 % (21889)Instructions burned: 933 (million)
% 13.92/3.28 % (21889)------------------------------
% 13.92/3.28 % (21889)------------------------------
% 13.92/3.29 % (21892)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_21668 for (2982ds/770Mi)
% 14.56/3.30 % (21892)Refutation not found, incomplete strategy
% 14.56/3.30 % (21892)------------------------------
% 14.56/3.30 % (21892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.56/3.30 % (21892)Termination reason: Refutation not found, incomplete strategy
% 14.56/3.30
% 14.56/3.30
% 14.56/3.30 % (21892)Memory used [KB]: 6652
% 14.56/3.30 % (21892)Time elapsed: 0.015 s
% 14.56/3.30 % (21892)Instructions burned: 42 (million)
% 14.56/3.30 % (21892)------------------------------
% 14.56/3.30 % (21892)------------------------------
% 14.56/3.31 % (21893)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_21668 for (2982ds/794Mi)
% 15.37/3.51 % (21886)First to succeed.
% 15.37/3.55 % (21886)Refutation found. Thanks to Tanya!
% 15.37/3.55 % SZS status Theorem for DTF2THF_21668
% 15.37/3.55 % SZS output start Proof for DTF2THF_21668
% 15.37/3.55 thf(type_def_5, type, term: $tType).
% 15.37/3.55 thf(type_def_7, type, subst: $tType).
% 15.37/3.55 thf(type_def_8, type, d_term: $tType).
% 15.37/3.55 thf(type_def_9, type, d_subst: $tType).
% 15.37/3.55 thf(func_def_0, type, term: $tType).
% 15.37/3.55 thf(func_def_1, type, subst: $tType).
% 15.37/3.55 thf(func_def_2, type, one: term).
% 15.37/3.55 thf(func_def_3, type, ap: term > term > term).
% 15.37/3.55 thf(func_def_4, type, lam: term > term).
% 15.37/3.55 thf(func_def_5, type, sub: term > subst > term).
% 15.37/3.55 thf(func_def_6, type, id: subst).
% 15.37/3.55 thf(func_def_7, type, sh: subst).
% 15.37/3.55 thf(func_def_8, type, push: term > subst > subst).
% 15.37/3.55 thf(func_def_9, type, comp: subst > subst > subst).
% 15.37/3.55 thf(func_def_10, type, var: term > $o).
% 15.37/3.55 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 15.37/3.55 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 15.37/3.55 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 15.37/3.55 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 15.37/3.55 thf(func_def_124, type, d_term: $tType).
% 15.37/3.55 thf(func_def_125, type, d_subst: $tType).
% 15.37/3.55 thf(func_def_126, type, d2term: d_term > term).
% 15.37/3.55 thf(func_def_127, type, d2subst: d_subst > subst).
% 15.37/3.55 thf(func_def_128, type, d_one: d_term).
% 15.37/3.55 thf(func_def_129, type, d_id: d_subst).
% 15.37/3.55 thf(func_def_143, type, sP1: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_147, type, sP5: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_148, type, sP6: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_151, type, sP9: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_152, type, sP10: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_154, type, sP12: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_157, type, sP15: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_158, type, sP16: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_159, type, sP17: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_160, type, sP18: (term > $o) > $o).
% 15.37/3.55 thf(func_def_161, type, sP19: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_166, type, sP24: (term > $o) > $o).
% 15.37/3.55 thf(func_def_169, type, sP27: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_171, type, sP29: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_174, type, sP32: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_175, type, sP33: (term > $o) > $o).
% 15.37/3.55 thf(func_def_181, type, sP39: (term > $o) > $o).
% 15.37/3.55 thf(func_def_182, type, sP40: (term > $o) > $o).
% 15.37/3.55 thf(func_def_185, type, sP43: (term > $o) > $o).
% 15.37/3.55 thf(func_def_187, type, sP45: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_189, type, sP47: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_190, type, sP48: (subst > term > subst > $o) > $o).
% 15.37/3.55 thf(func_def_191, type, sP49: (term > $o) > $o).
% 15.37/3.55 thf(func_def_195, type, sP53: (term > $o) > $o).
% 15.37/3.55 thf(func_def_196, type, sP54: (term > $o) > $o).
% 15.37/3.55 thf(func_def_199, type, sP57: (term > $o) > $o).
% 15.37/3.55 thf(func_def_201, type, sK59: term > $o).
% 15.37/3.55 thf(func_def_202, type, sK60: subst).
% 15.37/3.55 thf(func_def_203, type, sK61: term).
% 15.37/3.55 thf(func_def_204, type, sK62: term > term).
% 15.37/3.55 thf(func_def_205, type, sK63: subst > (term > $o) > term).
% 15.37/3.55 thf(func_def_206, type, sK64: (term > $o) > term).
% 15.37/3.55 thf(func_def_207, type, sK65: (term > $o) > term).
% 15.37/3.55 thf(func_def_208, type, sK66: (term > $o) > term).
% 15.37/3.55 thf(func_def_209, type, sK67: (term > $o) > term).
% 15.37/3.55 thf(func_def_210, type, sK68: (term > $o) > term).
% 15.37/3.55 thf(func_def_211, type, sK69: subst).
% 15.37/3.55 thf(func_def_212, type, sK70: term).
% 15.37/3.55 thf(func_def_213, type, sK71: subst).
% 15.37/3.55 thf(func_def_214, type, sK72: term).
% 15.37/3.55 thf(func_def_215, type, sK73: subst).
% 15.37/3.55 thf(func_def_216, type, sK74: term > $o).
% 15.37/3.55 thf(func_def_217, type, sK75: term).
% 15.37/3.55 thf(func_def_218, type, sK76: term).
% 15.37/3.55 thf(func_def_219, type, sK77: subst).
% 15.37/3.55 thf(func_def_220, type, sK78: term > $o).
% 15.37/3.55 thf(func_def_221, type, sK79: term > term).
% 15.37/3.55 thf(func_def_222, type, sK80: (term > $o) > term).
% 15.37/3.55 thf(func_def_223, type, sK81: (term > $o) > subst > term).
% 15.37/3.55 thf(func_def_224, type, sK82: (term > $o) > term).
% 15.37/3.55 thf(func_def_225, type, sK83: (term > $o) > term).
% 15.37/3.55 thf(func_def_226, type, sK84: (term > $o) > term).
% 15.37/3.55 thf(func_def_227, type, sK85: (term > $o) > term).
% 15.37/3.55 thf(func_def_228, type, sK86: (term > $o) > term).
% 15.37/3.55 thf(func_def_229, type, sK87: (term > $o) > term).
% 15.37/3.55 thf(func_def_230, type, sK88: (subst > term > subst > $o) > term > $o).
% 15.37/3.55 thf(func_def_231, type, sK89: term).
% 15.37/3.55 thf(func_def_232, type, sK90: term).
% 15.37/3.55 thf(func_def_233, type, sK91: term > $o).
% 15.37/3.55 thf(func_def_234, type, sK92: term > term).
% 15.37/3.55 thf(func_def_235, type, sK93: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_236, type, sK94: (term > $o) > term).
% 15.37/3.55 thf(func_def_237, type, sK95: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_238, type, sK96: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_239, type, sK97: term > (term > $o) > term).
% 15.37/3.55 thf(func_def_240, type, sK98: term > $o).
% 15.37/3.55 thf(func_def_241, type, sK99: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_242, type, sK100: term).
% 15.37/3.55 thf(func_def_243, type, sK101: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_244, type, sK102: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_245, type, sK103: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_246, type, sK104: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_247, type, sK105: term).
% 15.37/3.55 thf(func_def_248, type, sK106: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_249, type, sK107: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_250, type, sK108: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_251, type, sK109: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_252, type, sK110: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_253, type, sK111: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_254, type, sK112: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_255, type, sK113: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_256, type, sK114: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_257, type, sK115: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_258, type, sK116: (term > $o) > term).
% 15.37/3.55 thf(func_def_259, type, sK117: (term > $o) > term).
% 15.37/3.55 thf(func_def_260, type, sK118: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_261, type, sK119: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_262, type, sK120: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_263, type, sK121: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_264, type, sK122: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_265, type, sK123: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_266, type, sK124: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_267, type, sK125: term).
% 15.37/3.55 thf(func_def_268, type, sK126: term > $o).
% 15.37/3.55 thf(func_def_269, type, sK127: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_270, type, sK128: (term > $o) > term > term).
% 15.37/3.55 thf(func_def_271, type, sK129: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_272, type, sK130: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_273, type, sK131: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_274, type, sK132: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_275, type, sK133: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_276, type, sK134: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_277, type, sK135: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_278, type, sK136: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_279, type, sK137: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_280, type, sK138: term).
% 15.37/3.55 thf(func_def_281, type, sK139: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_282, type, sK140: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_283, type, sK141: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_284, type, sK142: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_285, type, sK143: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_286, type, sK144: term).
% 15.37/3.55 thf(func_def_287, type, sK145: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_288, type, sK146: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_289, type, sK147: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_290, type, sK148: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_291, type, sK149: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_292, type, sK150: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_293, type, sK151: (subst > term > subst > $o) > term > term).
% 15.37/3.55 thf(func_def_294, type, sK152: (term > $o) > term).
% 15.37/3.55 thf(func_def_295, type, sK153: (term > $o) > term).
% 15.37/3.55 thf(func_def_296, type, sK154: (term > $o) > term).
% 15.37/3.55 thf(func_def_297, type, sK155: (term > $o) > subst > term).
% 15.37/3.55 thf(func_def_298, type, sK156: term).
% 15.37/3.55 thf(func_def_299, type, sK157: subst).
% 15.37/3.55 thf(func_def_300, type, sK158: term).
% 15.37/3.55 thf(func_def_301, type, sK159: term > $o).
% 15.37/3.55 thf(func_def_302, type, sK160: term > term).
% 15.37/3.55 thf(func_def_303, type, sK161: term).
% 15.37/3.55 thf(func_def_304, type, sK162: term > $o).
% 15.37/3.55 thf(func_def_305, type, sK163: term > term).
% 15.37/3.55 thf(func_def_306, type, sK164: (term > $o) > term).
% 15.37/3.55 thf(func_def_307, type, sK165: (term > $o) > term).
% 15.37/3.55 thf(func_def_308, type, sK166: (term > $o) > term).
% 15.37/3.55 thf(func_def_309, type, sK167: (term > $o) > term).
% 15.37/3.55 thf(func_def_310, type, sK168: (term > $o) > term).
% 15.37/3.55 thf(func_def_311, type, sK169: (term > $o) > term).
% 15.37/3.55 thf(func_def_312, type, sK170: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_313, type, sK171: term).
% 15.37/3.55 thf(func_def_314, type, sK172: term > (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_315, type, sK173: term > (subst > term > term) > term).
% 15.37/3.55 thf(func_def_316, type, sK174: term > (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_317, type, sK175: term > (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_318, type, sK176: term > (subst > term > term) > term).
% 15.37/3.55 thf(func_def_319, type, sK177: term > (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_320, type, sK178: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_321, type, sK179: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_322, type, sK180: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_323, type, sK181: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_324, type, sK182: subst > term > term).
% 15.37/3.55 thf(func_def_325, type, sK183: term).
% 15.37/3.55 thf(func_def_326, type, sK184: subst).
% 15.37/3.55 thf(func_def_327, type, sK185: subst > term > term).
% 15.37/3.55 thf(func_def_328, type, sK186: term).
% 15.37/3.55 thf(func_def_329, type, sK187: subst).
% 15.37/3.55 thf(func_def_330, type, sK188: term).
% 15.37/3.55 thf(func_def_331, type, sK189: subst).
% 15.37/3.55 thf(func_def_332, type, sK190: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_333, type, sK191: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_334, type, sK192: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_335, type, sK193: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_336, type, sK194: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_337, type, sK195: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_338, type, sK196: term).
% 15.37/3.55 thf(func_def_339, type, sK197: term).
% 15.37/3.55 thf(func_def_340, type, sK198: (term > $o) > term).
% 15.37/3.55 thf(func_def_341, type, sK199: (term > $o) > term).
% 15.37/3.55 thf(func_def_342, type, sK200: (subst > term > subst > $o) > term > $o).
% 15.37/3.55 thf(func_def_343, type, sK201: term > $o).
% 15.37/3.55 thf(func_def_344, type, sK202: term).
% 15.37/3.55 thf(func_def_345, type, sK203: term > term).
% 15.37/3.55 thf(func_def_346, type, sK204: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_347, type, sK205: (term > $o) > term).
% 15.37/3.55 thf(func_def_348, type, sK206: term).
% 15.37/3.55 thf(func_def_349, type, sK207: term).
% 15.37/3.55 thf(func_def_350, type, sK208: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_351, type, sK209: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_352, type, sK210: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_353, type, sK211: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_354, type, sK212: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_355, type, sK213: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_356, type, sK214: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_357, type, sK215: term > (term > $o) > term).
% 15.37/3.55 thf(func_def_358, type, sK216: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_359, type, sK217: term > $o).
% 15.37/3.55 thf(func_def_360, type, sK218: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_361, type, sK219: term).
% 15.37/3.55 thf(func_def_362, type, sK220: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_363, type, sK221: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_364, type, sK222: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_365, type, sK223: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_366, type, sK224: (term > $o) > term).
% 15.37/3.55 thf(func_def_367, type, sK225: (term > $o) > term).
% 15.37/3.55 thf(func_def_368, type, sK226: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_369, type, sK227: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_370, type, sK228: term > $o).
% 15.37/3.55 thf(func_def_371, type, sK229: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_372, type, sK230: term).
% 15.37/3.55 thf(func_def_373, type, sK231: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_374, type, sK232: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_375, type, sK233: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_376, type, sK234: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_377, type, sK235: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_378, type, sK236: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_379, type, sK237: term > (term > $o) > term).
% 15.37/3.55 thf(func_def_380, type, sK238: term).
% 15.37/3.55 thf(func_def_381, type, sK239: term).
% 15.37/3.55 thf(func_def_382, type, sK240: term > $o).
% 15.37/3.55 thf(func_def_383, type, sK241: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_384, type, sK242: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_385, type, sK243: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_386, type, sK244: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_387, type, sK245: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_388, type, sK246: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_389, type, sK247: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_390, type, sK248: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_391, type, sK249: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_392, type, sK250: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_393, type, sK251: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_394, type, sK252: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_395, type, sK253: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_396, type, sK254: term).
% 15.37/3.55 thf(func_def_397, type, sK255: term).
% 15.37/3.55 thf(func_def_398, type, sK256: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_399, type, sK257: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_400, type, sK258: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_401, type, sK259: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_402, type, sK260: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_403, type, sK261: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_404, type, sK262: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_405, type, sK263: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_406, type, sK264: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_407, type, sK265: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_408, type, sK266: term > subst > term > term).
% 15.37/3.55 thf(func_def_409, type, sK267: term).
% 15.37/3.55 thf(func_def_410, type, sK268: term > $o).
% 15.37/3.55 thf(func_def_411, type, sK269: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_412, type, sK270: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_413, type, sK271: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_414, type, sK272: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_415, type, sK273: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_416, type, sK274: term).
% 15.37/3.55 thf(func_def_417, type, sK275: term).
% 15.37/3.55 thf(func_def_418, type, sK276: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_419, type, sK277: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_420, type, sK278: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_421, type, sK279: (term > $o) > term > term).
% 15.37/3.55 thf(func_def_422, type, sK280: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_423, type, sK281: term > $o).
% 15.37/3.55 thf(func_def_424, type, sK282: term).
% 15.37/3.55 thf(func_def_425, type, sK283: term > term).
% 15.37/3.55 thf(func_def_426, type, sK284: (term > $o) > term).
% 15.37/3.55 thf(func_def_427, type, sK285: (term > $o) > term).
% 15.37/3.55 thf(func_def_428, type, sK286: (term > $o) > term).
% 15.37/3.55 thf(func_def_429, type, sK287: (term > $o) > term).
% 15.37/3.55 thf(func_def_430, type, sK288: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_431, type, sK289: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_432, type, sK290: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_433, type, sK291: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_434, type, sK292: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_435, type, sK293: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_436, type, sK294: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_437, type, sK295: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_438, type, sK296: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_439, type, sK297: term).
% 15.37/3.55 thf(func_def_440, type, sK298: term).
% 15.37/3.55 thf(func_def_441, type, sK299: (term > $o) > term).
% 15.37/3.55 thf(func_def_442, type, sK300: (term > $o) > term).
% 15.37/3.55 thf(func_def_443, type, sK301: term > $o).
% 15.37/3.55 thf(func_def_444, type, sK302: term).
% 15.37/3.55 thf(func_def_445, type, sK303: term > term).
% 15.37/3.55 thf(func_def_446, type, sK304: term).
% 15.37/3.55 thf(func_def_447, type, sK305: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_448, type, sK306: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_449, type, sK307: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_450, type, sK308: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_451, type, sK309: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_452, type, sK310: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_453, type, sK311: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_454, type, sK312: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_455, type, sK313: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_456, type, sK314: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_457, type, sK315: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_458, type, sK316: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_459, type, sK317: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_460, type, sK318: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_461, type, sK319: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_462, type, sK320: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_463, type, sK321: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_464, type, sK322: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_465, type, sK323: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_466, type, sK324: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_467, type, sK325: term).
% 15.37/3.55 thf(func_def_468, type, sK326: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_469, type, sK327: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_470, type, sK328: (term > $o) > term).
% 15.37/3.55 thf(func_def_471, type, sK329: (term > $o) > term).
% 15.37/3.55 thf(func_def_472, type, sK330: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_473, type, sK331: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_474, type, sK332: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_475, type, sK333: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_476, type, sK334: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_477, type, sK335: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_478, type, sK336: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_479, type, sK337: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_480, type, sK338: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_481, type, sK339: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_482, type, sK340: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_483, type, sK341: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_484, type, sK342: term).
% 15.37/3.55 thf(func_def_485, type, sK343: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_486, type, sK344: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_487, type, sK345: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_488, type, sK346: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_489, type, sK347: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_490, type, sK348: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_491, type, sK349: (subst > term > subst > $o) > term > term).
% 15.37/3.55 thf(func_def_492, type, sK350: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_493, type, sK351: term).
% 15.37/3.55 thf(func_def_494, type, sK352: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_495, type, sK353: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_496, type, sK354: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_497, type, sK355: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_498, type, sK356: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_499, type, sK357: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_500, type, sK358: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_501, type, sK359: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_502, type, sK360: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_503, type, sK361: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_504, type, sK362: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_505, type, sK363: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_506, type, sK364: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_507, type, sK365: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_508, type, sK366: term).
% 15.37/3.55 thf(func_def_509, type, sK367: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_510, type, sK368: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_511, type, sK369: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_512, type, sK370: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_513, type, sK371: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_514, type, sK372: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_515, type, sK373: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_516, type, sK374: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_517, type, sK375: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_518, type, sK376: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_519, type, sK377: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_520, type, sK378: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_521, type, sK379: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_522, type, sK380: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_523, type, sK381: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_524, type, sK382: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_525, type, sK383: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_526, type, sK384: term).
% 15.37/3.55 thf(func_def_527, type, sK385: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_528, type, sK386: term).
% 15.37/3.55 thf(func_def_529, type, sK387: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_530, type, sK388: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_531, type, sK389: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_532, type, sK390: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_533, type, sK391: (subst > term > subst > $o) > term > term).
% 15.37/3.55 thf(func_def_534, type, sK392: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_535, type, sK393: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_536, type, sK394: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_537, type, sK395: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_538, type, sK396: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_539, type, sK397: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_540, type, sK398: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_541, type, sK399: term).
% 15.37/3.55 thf(func_def_542, type, sK400: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_543, type, sK401: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_544, type, sK402: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_545, type, sK403: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_546, type, sK404: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_547, type, sK405: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_548, type, sK406: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_549, type, sK407: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_550, type, sK408: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_551, type, sK409: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_552, type, sK410: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_553, type, sK411: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_554, type, sK412: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_555, type, sK413: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_556, type, sK414: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_557, type, sK415: term).
% 15.37/3.55 thf(func_def_558, type, sK416: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_559, type, sK417: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_560, type, sK418: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_561, type, sK419: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_562, type, sK420: term).
% 15.37/3.55 thf(func_def_563, type, sK421: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_564, type, sK422: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_565, type, sK423: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_566, type, sK424: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_567, type, sK425: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_568, type, sK426: term).
% 15.37/3.55 thf(func_def_569, type, sK427: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_570, type, sK428: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_571, type, sK429: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_572, type, sK430: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_573, type, sK431: term).
% 15.37/3.55 thf(func_def_574, type, sK432: term > $o).
% 15.37/3.55 thf(func_def_575, type, sK433: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_576, type, sK434: (subst > term > subst > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_577, type, sK435: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_578, type, sK436: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_579, type, sK437: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_580, type, sK438: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_581, type, sK439: (term > $o) > term > term).
% 15.37/3.55 thf(func_def_582, type, sK440: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_583, type, sK441: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_584, type, sK442: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_585, type, sK443: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_586, type, sK444: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_587, type, sK445: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_588, type, sK446: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_589, type, sK447: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_590, type, sK448: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_591, type, sK449: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_592, type, sK450: term).
% 15.37/3.55 thf(func_def_593, type, sK451: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_594, type, sK452: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_595, type, sK453: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_596, type, sK454: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_597, type, sK455: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_598, type, sK456: term > (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_599, type, sK457: term > d_term).
% 15.37/3.55 thf(func_def_600, type, sK458: subst).
% 15.37/3.55 thf(func_def_601, type, sK459: term > subst > (term > $o) > (term > $o) > term).
% 15.37/3.55 thf(func_def_602, type, sK460: term > $o).
% 15.37/3.55 thf(func_def_603, type, sK461: term > $o).
% 15.37/3.55 thf(func_def_604, type, sK462: subst).
% 15.37/3.55 thf(func_def_605, type, sK463: term).
% 15.37/3.55 thf(func_def_606, type, sK464: term).
% 15.37/3.55 thf(func_def_607, type, sK465: term).
% 15.37/3.55 thf(func_def_608, type, sK466: term).
% 15.37/3.55 thf(func_def_609, type, sK467: subst).
% 15.37/3.55 thf(func_def_610, type, sK468: term > subst > term > term).
% 15.37/3.55 thf(func_def_611, type, sK469: term).
% 15.37/3.55 thf(func_def_612, type, sK470: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_613, type, sK471: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_614, type, sK472: term).
% 15.37/3.55 thf(func_def_615, type, sK473: subst).
% 15.37/3.55 thf(func_def_616, type, sK474: subst).
% 15.37/3.55 thf(func_def_617, type, sK475: subst).
% 15.37/3.55 thf(func_def_618, type, sK476: subst).
% 15.37/3.55 thf(func_def_619, type, sK477: subst).
% 15.37/3.55 thf(func_def_620, type, sK478: term > subst > term > term).
% 15.37/3.55 thf(func_def_621, type, sK479: term).
% 15.37/3.55 thf(func_def_622, type, sK480: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_623, type, sK481: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_624, type, sK482: term).
% 15.37/3.55 thf(func_def_625, type, sK483: term).
% 15.37/3.55 thf(func_def_626, type, sK484: term).
% 15.37/3.55 thf(func_def_627, type, sK485: term).
% 15.37/3.55 thf(func_def_628, type, sK486: term).
% 15.37/3.55 thf(func_def_629, type, sK487: term).
% 15.37/3.55 thf(func_def_630, type, sK488: term).
% 15.37/3.55 thf(func_def_631, type, sK489: term).
% 15.37/3.55 thf(func_def_632, type, sK490: term).
% 15.37/3.55 thf(func_def_633, type, sK491: term).
% 15.37/3.55 thf(func_def_634, type, sK492: term).
% 15.37/3.55 thf(func_def_635, type, sK493: term).
% 15.37/3.55 thf(func_def_636, type, sK494: (term > $o) > term).
% 15.37/3.55 thf(func_def_637, type, sK495: (term > $o) > term).
% 15.37/3.55 thf(func_def_638, type, sK496: term > $o).
% 15.37/3.55 thf(func_def_639, type, sK497: term).
% 15.37/3.55 thf(func_def_640, type, sK498: term).
% 15.37/3.55 thf(func_def_641, type, sK499: term).
% 15.37/3.55 thf(func_def_642, type, sK500: term).
% 15.37/3.55 thf(func_def_643, type, sK501: term).
% 15.37/3.55 thf(func_def_644, type, sK502: term > $o).
% 15.37/3.55 thf(func_def_645, type, sK503: term > $o).
% 15.37/3.55 thf(func_def_646, type, sK504: term).
% 15.37/3.55 thf(func_def_647, type, sK505: subst).
% 15.37/3.55 thf(func_def_648, type, sK506: term).
% 15.37/3.55 thf(func_def_649, type, sK507: subst).
% 15.37/3.55 thf(func_def_650, type, sK508: term).
% 15.37/3.55 thf(func_def_651, type, sK509: subst).
% 15.37/3.55 thf(func_def_652, type, sK510: term).
% 15.37/3.55 thf(func_def_653, type, sK511: term).
% 15.37/3.55 thf(func_def_654, type, sK512: term).
% 15.37/3.55 thf(func_def_655, type, sK513: subst).
% 15.37/3.55 thf(func_def_656, type, sK514: subst).
% 15.37/3.55 thf(func_def_657, type, sK515: term).
% 15.37/3.55 thf(func_def_658, type, sK516: term > subst > term > term).
% 15.37/3.55 thf(func_def_659, type, sK517: (subst > term > subst > $o) > term > $o).
% 15.37/3.55 thf(func_def_660, type, sK518: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_661, type, sK519: (term > $o) > term).
% 15.37/3.55 thf(func_def_662, type, sK520: term > $o).
% 15.37/3.55 thf(func_def_663, type, sK521: term).
% 15.37/3.55 thf(func_def_664, type, sK522: subst).
% 15.37/3.55 thf(func_def_665, type, sK523: (term > $o) > term).
% 15.37/3.55 thf(func_def_666, type, sK524: subst > term > (term > $o) > term > $o).
% 15.37/3.55 thf(func_def_667, type, sK525: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_668, type, sK526: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_669, type, sK527: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_670, type, sK528: term).
% 15.37/3.55 thf(func_def_671, type, sK529: term).
% 15.37/3.55 thf(func_def_672, type, sK530: subst > term > term).
% 15.37/3.55 thf(func_def_673, type, sK531: term > $o).
% 15.37/3.55 thf(func_def_674, type, sK532: subst).
% 15.37/3.55 thf(func_def_675, type, sK533: term).
% 15.37/3.55 thf(func_def_676, type, sK534: term > $o).
% 15.37/3.55 thf(func_def_677, type, sK535: (term > $o) > term > subst > (term > $o) > term).
% 15.37/3.55 thf(func_def_678, type, sK536: subst).
% 15.37/3.55 thf(func_def_679, type, sK537: term).
% 15.37/3.55 thf(func_def_680, type, sK538: term).
% 15.37/3.55 thf(func_def_681, type, sK539: term).
% 15.37/3.55 thf(func_def_682, type, sK540: term).
% 15.37/3.55 thf(func_def_683, type, sK541: term).
% 15.37/3.55 thf(func_def_684, type, sK542: term).
% 15.37/3.55 thf(func_def_685, type, sK543: term).
% 15.37/3.55 thf(func_def_686, type, sK544: term).
% 15.37/3.55 thf(func_def_687, type, sK545: term).
% 15.37/3.55 thf(func_def_688, type, sK546: term).
% 15.37/3.55 thf(func_def_689, type, sK547: term).
% 15.37/3.55 thf(func_def_690, type, sK548: term).
% 15.37/3.55 thf(func_def_691, type, sK549: term).
% 15.37/3.55 thf(func_def_692, type, sK550: subst).
% 15.37/3.55 thf(func_def_693, type, sK551: subst).
% 15.37/3.55 thf(func_def_694, type, sK552: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_695, type, sK553: (term > $o) > term).
% 15.37/3.55 thf(func_def_696, type, sK554: (subst > term > subst > $o) > term > $o).
% 15.37/3.55 thf(func_def_697, type, sK555: subst > d_subst).
% 15.37/3.55 thf(func_def_698, type, sK556: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_699, type, sK557: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_700, type, sK558: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_701, type, sK559: term).
% 15.37/3.55 thf(func_def_702, type, sK560: term).
% 15.37/3.55 thf(func_def_703, type, sK561: term).
% 15.37/3.55 thf(func_def_704, type, sK562: term).
% 15.37/3.55 thf(func_def_705, type, sK563: term).
% 15.37/3.55 thf(func_def_706, type, sK564: term).
% 15.37/3.55 thf(func_def_707, type, sK565: term).
% 15.37/3.55 thf(func_def_708, type, sK566: term > subst > term > term).
% 15.37/3.55 thf(func_def_709, type, sK567: term > (term > $o) > subst > term > $o).
% 15.37/3.55 thf(func_def_710, type, sK568: subst).
% 15.37/3.55 thf(func_def_711, type, sK569: term > $o).
% 15.37/3.55 thf(func_def_712, type, sK570: term).
% 15.37/3.55 thf(func_def_713, type, sK571: (term > $o) > term).
% 15.37/3.55 thf(func_def_714, type, sK572: term).
% 15.37/3.55 thf(func_def_715, type, sK573: term).
% 15.37/3.55 thf(func_def_716, type, sK574: term).
% 15.37/3.55 thf(func_def_717, type, sK575: term).
% 15.37/3.55 thf(func_def_718, type, sK576: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_719, type, sK577: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_720, type, sK578: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_721, type, sK579: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_722, type, sK580: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_723, type, sK581: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_724, type, sK582: subst > term > term).
% 15.37/3.55 thf(func_def_725, type, sK583: subst > term > term).
% 15.37/3.55 thf(func_def_726, type, sK584: term).
% 15.37/3.55 thf(func_def_727, type, sK585: subst).
% 15.37/3.55 thf(func_def_728, type, sK586: subst).
% 15.37/3.55 thf(func_def_729, type, sK587: term > $o).
% 15.37/3.55 thf(func_def_730, type, sK588: term).
% 15.37/3.55 thf(func_def_731, type, sK589: term).
% 15.37/3.55 thf(func_def_732, type, sK590: term > $o).
% 15.37/3.55 thf(func_def_734, type, sK592: subst > term > subst > $o).
% 15.37/3.55 thf(func_def_735, type, sK593: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_736, type, sK594: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_737, type, sK595: (subst > term > term) > subst).
% 15.37/3.55 thf(func_def_738, type, sK596: (subst > term > term) > term).
% 15.37/3.55 thf(func_def_739, type, sK597: term).
% 15.37/3.55 thf(func_def_740, type, sK598: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_741, type, sK599: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_742, type, sK600: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_743, type, sK601: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_744, type, sK602: (subst > term > subst > $o) > term).
% 15.37/3.55 thf(func_def_745, type, sK603: (subst > term > subst > $o) > term > term).
% 15.37/3.55 thf(func_def_746, type, sK604: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_747, type, sK605: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_748, type, sK606: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_749, type, sK607: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_750, type, sK608: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_751, type, sK609: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_752, type, sK610: (subst > term > subst > $o) > subst > term > term).
% 15.37/3.55 thf(func_def_753, type, sK611: (subst > term > subst > $o) > term > term).
% 15.37/3.55 thf(func_def_754, type, sK612: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_755, type, sK613: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_756, type, sK614: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_757, type, sK615: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_758, type, sK616: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_759, type, sK617: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_760, type, sK618: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_761, type, sK619: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_762, type, sK620: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_763, type, sK621: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_764, type, sK622: (subst > term > subst > $o) > subst).
% 15.37/3.55 thf(func_def_766, type, ph623: !>[X0: $tType]:(X0)).
% 15.37/3.55 thf(f10598,plain,(
% 15.37/3.55 $false),
% 15.37/3.55 inference(avatar_sat_refutation,[status(thm)],[f2053,f2113,f2252,f2308,f2520,f2532,f2540,f2628,f3159,f3792,f3819,f3880,f6949,f7010,f8591,f8623,f8645,f8677,f9350,f9472,f9825,f9872,f10345,f10597])).
% 15.37/3.55 thf(f10597,plain,(
% 15.37/3.55 ~spl591_214 | spl591_705),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f10596])).
% 15.37/3.55 thf(f10596,plain,(
% 15.37/3.55 $false | (~spl591_214 | spl591_705)),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f2515,f10348])).
% 15.37/3.55 thf(f10348,plain,(
% 15.37/3.55 ( ! [X0 : term] : (($false != (sK592 @ id @ X0 @ id))) ) | spl591_705),
% 15.37/3.55 inference(superposition,[status(thm)],[f8657,f4484])).
% 15.37/3.55 thf(f4484,plain,(
% 15.37/3.55 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 15.37/3.55 inference(superposition,[status(thm)],[f4480,f4480])).
% 15.37/3.55 thf(f4480,plain,(
% 15.37/3.55 ( ! [X0 : term] : (((d2term @ d_one) = X0)) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f1258,f1186])).
% 15.37/3.55 thf(f1186,plain,(
% 15.37/3.55 ( ! [X84 : d_term] : ((d_one = X84)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f545,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X0 : term] : ((d2term @ (sK457 @ X0)) = X0) & (($true = sP58) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP58)) & ((axscons = $true) | ((push @ (sub @ one @ sK458) @ (comp @ sh @ sK458)) != sK458)) & (! [X3 : subst] : ((push @ (sub @ one @ X3) @ (comp @ sh @ X3)) = X3) | (axscons != $true)) & (ulamvar1 != $true) & ((induction2lem_lthm = $true) | ($true != sP56)) & (($true = sP56) | (induction2lem_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X4 : term > $o,X5 : term > $o,X6 : subst,X7 : term] : (($true = (X5 @ one)) | ($true != (X4 @ X7)) | ((X5 @ (sK459 @ X7 @ X6 @ X5 @ X4)) != (X4 @ (sub @ (sK459 @ X7 @ X6 @ X5 @ X4) @ (push @ X7 @ X6))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true != (sK461 @ one)) & ($true = (sK460 @ sK463)) & ! [X13 : term] : ((sK461 @ X13) = (sK460 @ (sub @ X13 @ (push @ sK463 @ sK462)))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X14 : term] : ((sub @ X14 @ id) = X14) | (termmset != $true)) & ((termmset = $true) | (sK464 != (sub @ sK464 @ id))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ((sK465 != sK466) & ((lam @ sK465) = (lam @ sK466)))) & (! [X18 : term,X19 : term] : ((X18 = X19) | ((lam @ X19) != (lam @ X18))) | (laminj != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (($true = sP46) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP46)) & ! [X20 : d_subst,X21 : d_subst] : (((d2subst @ X21) != (d2subst @ X20)) | (X20 = X21)) & (hoasinduction_lem1v2 = $true) & ((axidr = $true) | (sK467 != (comp @ sK467 @ id))) & (! [X23 : subst] : ((comp @ X23 @ id) = X23) | (axidr != $true)) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & (($true = sP44) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP44)) & (! [X24 : term] : ! [X26 : term,X27 : subst] : ((sK468 @ X24 @ X27 @ X26) = (sub @ X24 @ (push @ X26 @ X27))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X29 : subst > term > term] : ((X29 @ (sK471 @ X29) @ (sK470 @ X29)) != (sub @ sK469 @ (push @ (sK470 @ X29) @ (sK471 @ X29))))) & ((axvarcons = $true) | ((sub @ one @ (push @ sK472 @ sK473)) != sK472)) & (! [X34 : term,X35 : subst] : ((sub @ one @ (push @ X34 @ X35)) = X34) | (axvarcons != $true)) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sK474 != (comp @ id @ sK474)) | ((comp @ sK475 @ id) != sK475) | (! [X38 : subst] : ((comp @ id @ X38) = X38) & ! [X39 : subst] : ((comp @ X39 @ id) = X39)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X40 : subst] : ((comp @ id @ X40) = X40) & ! [X41 : subst] : ((comp @ X41 @ id) = X41) & ((sK476 != (comp @ id @ sK476)) | ((comp @ sK477 @ id) != sK477)))) & (ulamvarsh = $true) & (! [X44 : term] : ! [X46 : term,X47 : subst] : ((sK478 @ X44 @ X47 @ X46) = (sub @ X44 @ (push @ X46 @ X47))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X49 : subst > term > term] : ((X49 @ (sK481 @ X49) @ (sK480 @ X49)) != (sub @ sK479 @ (push @ (sK480 @ X49) @ (sK481 @ X49))))) & ((hoasapinj2_lthm = $true) | (! [X52 : term,X53 : term,X54 : term,X55 : term] : (((ap @ X55 @ X52) != (ap @ X54 @ X53)) | (X52 = X53)) & (((ap @ (sub @ sK483 @ id) @ sK482) = (ap @ (sub @ sK485 @ id) @ sK484)) & (sK482 != sK484)))) & ((((ap @ sK488 @ sK487) = (ap @ sK489 @ sK486)) & (sK487 != sK486)) | ! [X64 : term,X65 : term,X66 : term,X67 : term] : (((ap @ (sub @ X67 @ id) @ X66) != (ap @ (sub @ X65 @ id) @ X64)) | (X64 = X66)) | (hoasapinj2_lthm != $true)) & ((hoasapinj1 = $true) | ((sK493 != sK491) & ((ap @ (sub @ sK493 @ id) @ sK492) = (ap @ (sub @ sK491 @ id) @ sK490)))) & (! [X72 : term,X73 : term,X74 : term,X75 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X72) != (ap @ (sub @ X75 @ id) @ X74))) | (hoasapinj1 != $true)) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X76 : term > $o,X77 : term] : (($true = (sP43 @ X76)) | (((X76 @ (sK494 @ X76)) = $true) & ($true != (X76 @ (lam @ (sK494 @ X76))))) | (((var @ (sK495 @ X76)) = $true) & ($true != (X76 @ (sK495 @ X76)))) | ((X76 @ X77) = $true)) | (induction != $true)) & ((induction = $true) | (($true != (sP43 @ sK496)) & ! [X82 : term] : (($true != (sK496 @ X82)) | ($true = (sK496 @ (lam @ X82)))) & ! [X83 : term] : (($true != (var @ X83)) | ((sK496 @ X83) = $true)) & ($true != (sK496 @ sK497)))) & ((induction2_lthm = $true) | ($true != sP42)) & (($true = sP42) | (induction2_lthm != $true)) & ! [X84 : d_term] : (d_one = X84) & (! [X85 : term,X86 : term,X87 : term,X88 : term] : (((ap @ X85 @ X88) != (ap @ X86 @ X87)) | (X85 = X86)) | (apinj1 != $true)) & ((apinj1 = $true) | (((ap @ sK498 @ sK501) = (ap @ sK499 @ sK500)) & (sK499 != sK498))) & ((sP38 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP38 != $true)) & (hoasapnotvar_gthm = $true) & (($true = sP37) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP37)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem1_lthm = $true) | (! [X93 : subst,X94 : term] : ((comp @ sh @ (push @ X94 @ X93)) = X93) & (($true != (sK503 @ (sub @ sK506 @ (push @ sK504 @ sK505)))) & ($true = (sK502 @ sK506))) & ! [X100 : subst,X101 : term] : ((sub @ one @ (push @ X101 @ X100)) = X101))) & (((comp @ sh @ (push @ sK508 @ sK507)) != sK507) | ! [X104 : term > $o,X105 : term > $o,X106 : term,X107 : subst,X108 : term] : (($true = (X105 @ (sub @ X108 @ (push @ X106 @ X107)))) | ($true != (X104 @ X108))) | ((sub @ one @ (push @ sK510 @ sK509)) != sK510) | (pushprop_lem1_lthm != $true)) & ((termmset_lthm = $true) | (! [X111 : term] : ((sub @ X111 @ id) = X111) & (sK511 != (sub @ sK511 @ id)))) & ((sK512 != (sub @ sK512 @ id)) | ! [X114 : term] : ((sub @ X114 @ id) = X114) | (termmset_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_no_psi_cond_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP31) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP31)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | (sK513 != (comp @ sK513 @ id)) | (sK514 != (comp @ id @ sK514))) & ((! [X117 : subst] : ((comp @ X117 @ id) = X117) & ! [X118 : subst] : ((comp @ id @ X118) = X118)) | (substmonoid != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2v2 != $true)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP26)) & ((hoasinduction_lem3b_lthm = $true) | ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ sK515 @ (push @ one @ sh)))) & (! [X121 : term] : ((sub @ X121 @ (push @ one @ sh)) = (sK516 @ X121 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & (! [X123 : subst > term > subst > $o] : ! [X125 : term] : ((X123 @ id @ X125 @ id) = (sK517 @ X123 @ X125)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X127 : term > $o] : ((X127 @ (sK519 @ X127)) != (sK518 @ id @ (sK519 @ X127) @ id))) & ((pushprop_lem0_lthm = $true) | ! [X132 : term > $o] : ((X132 @ (sK523 @ X132)) != (sK520 @ (sub @ (sK523 @ X132) @ (push @ sK521 @ sK522))))) & (! [X134 : term > $o,X135 : term,X136 : subst] : ! [X138 : term] : ((sK524 @ X136 @ X135 @ X134 @ X138) = (X134 @ (sub @ X138 @ (push @ X135 @ X136)))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP25) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP25)) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & (! [X139 : term,X140 : term,X141 : subst > term > term] : (((ap @ (sub @ X140 @ id) @ X139) != (lam @ (X141 @ sh @ one))) | ((X141 @ (comp @ (sK525 @ X141) @ (sK527 @ X141)) @ (sub @ (sK526 @ X141) @ (sK527 @ X141))) != (sub @ (X141 @ (sK525 @ X141) @ (sK526 @ X141)) @ (sK527 @ X141)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (((ap @ (sub @ sK529 @ id) @ sK528) = (lam @ (sK530 @ sh @ one))) & ! [X148 : subst,X149 : term,X150 : subst] : ((sub @ (sK530 @ X148 @ X149) @ X150) = (sK530 @ (comp @ X148 @ X150) @ (sub @ X149 @ X150))))) & ((pushprop_lem1v2_lthm = $true) | ((($true = (sK531 @ sK533)) & ! [X155 : term] : ((sK531 @ (sub @ X155 @ (push @ sK533 @ sK532))) = (sK534 @ X155)) & ((sK534 @ one) != $true)) & ! [X156 : subst,X157 : term] : ((sub @ one @ (push @ X157 @ X156)) = X157))) & (! [X158 : term > $o,X159 : subst,X160 : term,X161 : term > $o] : (($true != (X158 @ X160)) | ((X161 @ (sK535 @ X161 @ X160 @ X159 @ X158)) != (X158 @ (sub @ (sK535 @ X161 @ X160 @ X159 @ X158) @ (push @ X160 @ X159)))) | ($true = (X161 @ one))) | (sK537 != (sub @ one @ (push @ sK537 @ sK536))) | (pushprop_lem1v2_lthm != $true)) & (($true = sP23) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP23)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X165 : d_term,X166 : d_term] : ((X165 = X166) | ((d2term @ X165) != (d2term @ X166))) & ((shinj = $true) | ((sK538 != sK539) & ((sub @ sK538 @ sh) = (sub @ sK539 @ sh)))) & (! [X169 : term,X170 : term] : ((X169 = X170) | ((sub @ X169 @ sh) != (sub @ X170 @ sh))) | (shinj != $true)) & ((hoasapinj1_lthm = $true) | (! [X171 : term] : ((sub @ X171 @ id) = X171) & ((sK540 != sK541) & ((ap @ (sub @ sK540 @ id) @ sK543) = (ap @ (sub @ sK541 @ id) @ sK542))) & ! [X176 : term,X177 : term,X178 : term,X179 : term] : (((ap @ X178 @ X177) != (ap @ X176 @ X179)) | (X176 = X178)))) & ((sK544 != (sub @ sK544 @ id)) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X181 = X182) | ((ap @ (sub @ X181 @ id) @ X184) != (ap @ (sub @ X182 @ id) @ X183))) | (((ap @ sK545 @ sK548) = (ap @ sK547 @ sK546)) & (sK547 != sK545)) | (hoasapinj1_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((sP14 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP14 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP13)) & (($true = sP13) | (hoasinduction_lem3 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction != $true)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK549 @ sK550)) != sK550)) & (! [X191 : term,X192 : subst] : ((comp @ sh @ (push @ X191 @ X192)) = X192) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((axidl = $true) | ((comp @ id @ sK551) != sK551)) & (! [X194 : subst] : ((comp @ id @ X194) = X194) | (axidl != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem3_lthm != $true)) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem0 = $true) | ! [X196 : term > $o] : ((sK552 @ id @ (sK553 @ X196) @ id) != (X196 @ (sK553 @ X196)))) & (! [X198 : subst > term > subst > $o] : ! [X200 : term] : ((X198 @ id @ X200 @ id) = (sK554 @ X198 @ X200)) | (hoasinduction_lem0 != $true)) & ! [X201 : subst] : ((d2subst @ (sK555 @ X201)) = X201) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : ((($true = (X203 @ id @ (sK557 @ X203) @ id)) & ($true = (X203 @ id @ (sK556 @ X203) @ id)) & ($true != (X203 @ id @ (ap @ (sub @ (sK557 @ X203) @ id) @ (sK556 @ X203)) @ id))) | ((X203 @ id @ X204 @ id) = $true) | ($true = (sP5 @ X203))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X209 : term,X210 : term] : (($true != (sK558 @ id @ X210 @ id)) | ($true != (sK558 @ id @ X209 @ id)) | ($true = (sK558 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id))) & ((sK558 @ id @ sK559 @ id) != $true) & ($true != (sP5 @ sK558)))) & (lamnotvar = $true) & (! [X211 : term,X212 : term,X213 : term,X214 : term] : ((X213 = X214) | ((ap @ (sub @ X212 @ id) @ X213) != (ap @ (sub @ X211 @ id) @ X214))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((sK563 != sK562) & ((ap @ (sub @ sK561 @ id) @ sK562) = (ap @ (sub @ sK560 @ id) @ sK563)))) & (axvarshift = $true) & (! [X219 : term] : ((sub @ X219 @ id) = X219) | (axvarid != $true)) & ((axvarid = $true) | ((sub @ sK564 @ id) != sK564)) & ((hoasinduction_lem3b = $true) | ! [X222 : subst > term > term] : ((sub @ sK565 @ (push @ one @ sh)) != (X222 @ sh @ one))) & (! [X223 : term] : ((sK566 @ X223 @ sh @ one) = (sub @ X223 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & (! [X225 : subst,X226 : term > $o,X227 : term] : ! [X229 : term] : ((X226 @ (sub @ X229 @ (push @ X227 @ X225))) = (sK567 @ X227 @ X226 @ X225 @ X229)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X233 : term > $o] : ((X233 @ (sK571 @ X233)) != (sK569 @ (sub @ (sK571 @ X233) @ (push @ sK570 @ sK568))))) & (! [X235 : term,X236 : term,X237 : term,X238 : term] : (((ap @ X236 @ X235) != (ap @ X238 @ X237)) | (X235 = X237)) | (apinj2 != $true)) & ((apinj2 = $true) | (((ap @ sK573 @ sK572) = (ap @ sK575 @ sK574)) & (sK572 != sK574))) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3v2 != $true)) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & (($true = sP0) | (hoasinduction_lem3a != $true)) & (! [X243 : subst > term > term,X244 : subst > term > term,X245 : term,X246 : subst] : (((lam @ (X244 @ sh @ one)) != (lam @ (X243 @ sh @ one))) | ((sub @ (X244 @ (sK576 @ X244) @ (sK577 @ X244)) @ (sK578 @ X244)) != (X244 @ (comp @ (sK576 @ X244) @ (sK578 @ X244)) @ (sub @ (sK577 @ X244) @ (sK578 @ X244)))) | ((X243 @ (comp @ (sK581 @ X243) @ (sK579 @ X243)) @ (sub @ (sK580 @ X243) @ (sK579 @ X243))) != (sub @ (X243 @ (sK581 @ X243) @ (sK580 @ X243)) @ (sK579 @ X243))) | ((X244 @ X246 @ X245) = (X243 @ X246 @ X245))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (((lam @ (sK583 @ sh @ one)) = (lam @ (sK582 @ sh @ one))) & ! [X257 : subst,X258 : term,X259 : subst] : ((sK583 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (sK583 @ X257 @ X258) @ X259)) & ! [X260 : subst,X261 : term,X262 : subst] : ((sK582 @ (comp @ X262 @ X260) @ (sub @ X261 @ X260)) = (sub @ (sK582 @ X262 @ X261) @ X260)) & ((sK583 @ sK585 @ sK584) != (sK582 @ sK585 @ sK584)))) & ! [X263 : d_subst] : (d_id = X263) & ((pushprop_lem1 = $true) | (($true = (sK587 @ sK589)) & ($true != (sK590 @ (sub @ sK589 @ (push @ sK588 @ sK586)))))) & (! [X269 : subst,X270 : term > $o,X271 : term,X272 : term,X273 : term > $o] : (($true != (X270 @ X272)) | ((X273 @ (sub @ X272 @ (push @ X271 @ X269))) = $true)) | (pushprop_lem1 != $true)) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f475,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476])).
% 15.37/3.55 thf(f476,plain,(
% 15.37/3.55 ! [X0 : term] : (? [X1 : d_term] : ((d2term @ X1) = X0) => ((d2term @ (sK457 @ X0)) = X0))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f477,plain,(
% 15.37/3.55 ? [X2 : subst] : ((push @ (sub @ one @ X2) @ (comp @ sh @ X2)) != X2) => ((push @ (sub @ one @ sK458) @ (comp @ sh @ sK458)) != sK458)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f478,plain,(
% 15.37/3.55 ! [X4 : term > $o,X5 : term > $o,X6 : subst,X7 : term] : (? [X8 : term] : ((X4 @ (sub @ X8 @ (push @ X7 @ X6))) != (X5 @ X8)) => ((X5 @ (sK459 @ X7 @ X6 @ X5 @ X4)) != (X4 @ (sub @ (sK459 @ X7 @ X6 @ X5 @ X4) @ (push @ X7 @ X6)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f479,plain,(
% 15.37/3.55 ? [X9 : term > $o,X10 : term > $o,X11 : subst,X12 : term] : (((X10 @ one) != $true) & ($true = (X9 @ X12)) & ! [X13 : term] : ((X10 @ X13) = (X9 @ (sub @ X13 @ (push @ X12 @ X11))))) => (($true != (sK461 @ one)) & ($true = (sK460 @ sK463)) & ! [X13 : term] : ((sK461 @ X13) = (sK460 @ (sub @ X13 @ (push @ sK463 @ sK462)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f480,plain,(
% 15.37/3.55 ? [X15 : term] : ((sub @ X15 @ id) != X15) => (sK464 != (sub @ sK464 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f481,plain,(
% 15.37/3.55 ? [X16 : term,X17 : term] : ((X16 != X17) & ((lam @ X16) = (lam @ X17))) => ((sK465 != sK466) & ((lam @ sK465) = (lam @ sK466)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f482,plain,(
% 15.37/3.55 ? [X22 : subst] : ((comp @ X22 @ id) != X22) => (sK467 != (comp @ sK467 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f483,plain,(
% 15.37/3.55 ! [X24 : term] : (? [X25 : subst > term > term] : ! [X26 : term,X27 : subst] : ((sub @ X24 @ (push @ X26 @ X27)) = (X25 @ X27 @ X26)) => ! [X27 : subst,X26 : term] : ((sK468 @ X24 @ X27 @ X26) = (sub @ X24 @ (push @ X26 @ X27))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f484,plain,(
% 15.37/3.55 ? [X28 : term] : ! [X29 : subst > term > term] : ? [X30 : term,X31 : subst] : ((sub @ X28 @ (push @ X30 @ X31)) != (X29 @ X31 @ X30)) => ! [X29 : subst > term > term] : ? [X31 : subst,X30 : term] : ((sub @ sK469 @ (push @ X30 @ X31)) != (X29 @ X31 @ X30))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f485,plain,(
% 15.37/3.55 ! [X29 : subst > term > term] : (? [X31 : subst,X30 : term] : ((sub @ sK469 @ (push @ X30 @ X31)) != (X29 @ X31 @ X30)) => ((X29 @ (sK471 @ X29) @ (sK470 @ X29)) != (sub @ sK469 @ (push @ (sK470 @ X29) @ (sK471 @ X29)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f486,plain,(
% 15.37/3.55 ? [X32 : term,X33 : subst] : ((sub @ one @ (push @ X32 @ X33)) != X32) => ((sub @ one @ (push @ sK472 @ sK473)) != sK472)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f487,plain,(
% 15.37/3.55 ? [X36 : subst] : ((comp @ id @ X36) != X36) => (sK474 != (comp @ id @ sK474))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f488,plain,(
% 15.37/3.55 ? [X37 : subst] : ((comp @ X37 @ id) != X37) => ((comp @ sK475 @ id) != sK475)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f489,plain,(
% 15.37/3.55 ? [X42 : subst] : ((comp @ id @ X42) != X42) => (sK476 != (comp @ id @ sK476))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f490,plain,(
% 15.37/3.55 ? [X43 : subst] : ((comp @ X43 @ id) != X43) => ((comp @ sK477 @ id) != sK477)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f491,plain,(
% 15.37/3.55 ! [X44 : term] : (? [X45 : subst > term > term] : ! [X46 : term,X47 : subst] : ((sub @ X44 @ (push @ X46 @ X47)) = (X45 @ X47 @ X46)) => ! [X47 : subst,X46 : term] : ((sK478 @ X44 @ X47 @ X46) = (sub @ X44 @ (push @ X46 @ X47))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f492,plain,(
% 15.37/3.55 ? [X48 : term] : ! [X49 : subst > term > term] : ? [X50 : term,X51 : subst] : ((X49 @ X51 @ X50) != (sub @ X48 @ (push @ X50 @ X51))) => ! [X49 : subst > term > term] : ? [X51 : subst,X50 : term] : ((sub @ sK479 @ (push @ X50 @ X51)) != (X49 @ X51 @ X50))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f493,plain,(
% 15.37/3.55 ! [X49 : subst > term > term] : (? [X51 : subst,X50 : term] : ((sub @ sK479 @ (push @ X50 @ X51)) != (X49 @ X51 @ X50)) => ((X49 @ (sK481 @ X49) @ (sK480 @ X49)) != (sub @ sK479 @ (push @ (sK480 @ X49) @ (sK481 @ X49)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f494,plain,(
% 15.37/3.55 ? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ (sub @ X59 @ id) @ X58) = (ap @ (sub @ X57 @ id) @ X56)) & (X56 != X58)) => (((ap @ (sub @ sK483 @ id) @ sK482) = (ap @ (sub @ sK485 @ id) @ sK484)) & (sK482 != sK484))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f495,plain,(
% 15.37/3.55 ? [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ X63 @ X60) = (ap @ X62 @ X61)) & (X60 != X61)) => (((ap @ sK488 @ sK487) = (ap @ sK489 @ sK486)) & (sK487 != sK486))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f496,plain,(
% 15.37/3.55 ? [X68 : term,X69 : term,X70 : term,X71 : term] : ((X69 != X71) & ((ap @ (sub @ X71 @ id) @ X70) = (ap @ (sub @ X69 @ id) @ X68))) => ((sK493 != sK491) & ((ap @ (sub @ sK493 @ id) @ sK492) = (ap @ (sub @ sK491 @ id) @ sK490)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f497,plain,(
% 15.37/3.55 ! [X76 : term > $o] : (? [X78 : term] : (($true = (X76 @ X78)) & ($true != (X76 @ (lam @ X78)))) => (((X76 @ (sK494 @ X76)) = $true) & ($true != (X76 @ (lam @ (sK494 @ X76))))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f498,plain,(
% 15.37/3.55 ! [X76 : term > $o] : (? [X79 : term] : (($true = (var @ X79)) & ($true != (X76 @ X79))) => (((var @ (sK495 @ X76)) = $true) & ($true != (X76 @ (sK495 @ X76)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f499,plain,(
% 15.37/3.55 ? [X80 : term > $o,X81 : term] : (($true != (sP43 @ X80)) & ! [X82 : term] : (($true != (X80 @ X82)) | ($true = (X80 @ (lam @ X82)))) & ! [X83 : term] : (($true != (var @ X83)) | ($true = (X80 @ X83))) & ($true != (X80 @ X81))) => (($true != (sP43 @ sK496)) & ! [X82 : term] : (($true != (sK496 @ X82)) | ($true = (sK496 @ (lam @ X82)))) & ! [X83 : term] : (($true != (var @ X83)) | ((sK496 @ X83) = $true)) & ($true != (sK496 @ sK497)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f500,plain,(
% 15.37/3.55 ? [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ X89 @ X92) = (ap @ X90 @ X91)) & (X89 != X90)) => (((ap @ sK498 @ sK501) = (ap @ sK499 @ sK500)) & (sK499 != sK498))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f501,plain,(
% 15.37/3.55 ? [X95 : term > $o,X96 : term > $o,X97 : term,X98 : subst,X99 : term] : (((X96 @ (sub @ X99 @ (push @ X97 @ X98))) != $true) & ($true = (X95 @ X99))) => (($true != (sK503 @ (sub @ sK506 @ (push @ sK504 @ sK505)))) & ($true = (sK502 @ sK506)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f502,plain,(
% 15.37/3.55 ? [X102 : subst,X103 : term] : ((comp @ sh @ (push @ X103 @ X102)) != X102) => ((comp @ sh @ (push @ sK508 @ sK507)) != sK507)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f503,plain,(
% 15.37/3.55 ? [X109 : subst,X110 : term] : ((sub @ one @ (push @ X110 @ X109)) != X110) => ((sub @ one @ (push @ sK510 @ sK509)) != sK510)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f504,plain,(
% 15.37/3.55 ? [X112 : term] : ((sub @ X112 @ id) != X112) => (sK511 != (sub @ sK511 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f505,plain,(
% 15.37/3.55 ? [X113 : term] : ((sub @ X113 @ id) != X113) => (sK512 != (sub @ sK512 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f506,plain,(
% 15.37/3.55 ? [X115 : subst] : ((comp @ X115 @ id) != X115) => (sK513 != (comp @ sK513 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f507,plain,(
% 15.37/3.55 ? [X116 : subst] : ((comp @ id @ X116) != X116) => (sK514 != (comp @ id @ sK514))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f508,plain,(
% 15.37/3.55 ? [X119 : term] : ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ X119 @ (push @ one @ sh))) => ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ sK515 @ (push @ one @ sh)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f509,plain,(
% 15.37/3.55 ! [X121 : term] : (? [X122 : subst > term > term] : ((X122 @ sh @ one) = (sub @ X121 @ (push @ one @ sh))) => ((sub @ X121 @ (push @ one @ sh)) = (sK516 @ X121 @ sh @ one)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f510,plain,(
% 15.37/3.55 ! [X123 : subst > term > subst > $o] : (? [X124 : term > $o] : ! [X125 : term] : ((X123 @ id @ X125 @ id) = (X124 @ X125)) => ! [X125 : term] : ((X123 @ id @ X125 @ id) = (sK517 @ X123 @ X125)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f511,plain,(
% 15.37/3.55 ? [X126 : subst > term > subst > $o] : ! [X127 : term > $o] : ? [X128 : term] : ((X127 @ X128) != (X126 @ id @ X128 @ id)) => ! [X127 : term > $o] : ? [X128 : term] : ((X127 @ X128) != (sK518 @ id @ X128 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f512,plain,(
% 15.37/3.55 ! [X127 : term > $o] : (? [X128 : term] : ((X127 @ X128) != (sK518 @ id @ X128 @ id)) => ((X127 @ (sK519 @ X127)) != (sK518 @ id @ (sK519 @ X127) @ id)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f513,plain,(
% 15.37/3.55 ? [X129 : term > $o,X130 : term,X131 : subst] : ! [X132 : term > $o] : ? [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X130 @ X131))) != (X132 @ X133)) => ! [X132 : term > $o] : ? [X133 : term] : ((sK520 @ (sub @ X133 @ (push @ sK521 @ sK522))) != (X132 @ X133))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f514,plain,(
% 15.37/3.55 ! [X132 : term > $o] : (? [X133 : term] : ((sK520 @ (sub @ X133 @ (push @ sK521 @ sK522))) != (X132 @ X133)) => ((X132 @ (sK523 @ X132)) != (sK520 @ (sub @ (sK523 @ X132) @ (push @ sK521 @ sK522)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f515,plain,(
% 15.37/3.55 ! [X134 : term > $o,X135 : term,X136 : subst] : (? [X137 : term > $o] : ! [X138 : term] : ((X137 @ X138) = (X134 @ (sub @ X138 @ (push @ X135 @ X136)))) => ! [X138 : term] : ((sK524 @ X136 @ X135 @ X134 @ X138) = (X134 @ (sub @ X138 @ (push @ X135 @ X136)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f516,plain,(
% 15.37/3.55 ! [X141 : subst > term > term] : (? [X142 : subst,X143 : term,X144 : subst] : ((sub @ (X141 @ X142 @ X143) @ X144) != (X141 @ (comp @ X142 @ X144) @ (sub @ X143 @ X144))) => ((X141 @ (comp @ (sK525 @ X141) @ (sK527 @ X141)) @ (sub @ (sK526 @ X141) @ (sK527 @ X141))) != (sub @ (X141 @ (sK525 @ X141) @ (sK526 @ X141)) @ (sK527 @ X141))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f517,plain,(
% 15.37/3.55 ? [X145 : term,X146 : term,X147 : subst > term > term] : (((ap @ (sub @ X146 @ id) @ X145) = (lam @ (X147 @ sh @ one))) & ! [X148 : subst,X149 : term,X150 : subst] : ((sub @ (X147 @ X148 @ X149) @ X150) = (X147 @ (comp @ X148 @ X150) @ (sub @ X149 @ X150)))) => (((ap @ (sub @ sK529 @ id) @ sK528) = (lam @ (sK530 @ sh @ one))) & ! [X150 : subst,X149 : term,X148 : subst] : ((sub @ (sK530 @ X148 @ X149) @ X150) = (sK530 @ (comp @ X148 @ X150) @ (sub @ X149 @ X150))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f518,plain,(
% 15.37/3.55 ? [X151 : term > $o,X152 : subst,X153 : term,X154 : term > $o] : (($true = (X151 @ X153)) & ! [X155 : term] : ((X151 @ (sub @ X155 @ (push @ X153 @ X152))) = (X154 @ X155)) & ($true != (X154 @ one))) => (($true = (sK531 @ sK533)) & ! [X155 : term] : ((sK531 @ (sub @ X155 @ (push @ sK533 @ sK532))) = (sK534 @ X155)) & ((sK534 @ one) != $true))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f519,plain,(
% 15.37/3.55 ! [X158 : term > $o,X159 : subst,X160 : term,X161 : term > $o] : (? [X162 : term] : ((X158 @ (sub @ X162 @ (push @ X160 @ X159))) != (X161 @ X162)) => ((X161 @ (sK535 @ X161 @ X160 @ X159 @ X158)) != (X158 @ (sub @ (sK535 @ X161 @ X160 @ X159 @ X158) @ (push @ X160 @ X159)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f520,plain,(
% 15.37/3.55 ? [X163 : subst,X164 : term] : ((sub @ one @ (push @ X164 @ X163)) != X164) => (sK537 != (sub @ one @ (push @ sK537 @ sK536)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f521,plain,(
% 15.37/3.55 ? [X167 : term,X168 : term] : ((X167 != X168) & ((sub @ X167 @ sh) = (sub @ X168 @ sh))) => ((sK538 != sK539) & ((sub @ sK538 @ sh) = (sub @ sK539 @ sh)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f522,plain,(
% 15.37/3.55 ? [X172 : term,X173 : term,X174 : term,X175 : term] : ((X172 != X173) & ((ap @ (sub @ X172 @ id) @ X175) = (ap @ (sub @ X173 @ id) @ X174))) => ((sK540 != sK541) & ((ap @ (sub @ sK540 @ id) @ sK543) = (ap @ (sub @ sK541 @ id) @ sK542)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f523,plain,(
% 15.37/3.55 ? [X180 : term] : ((sub @ X180 @ id) != X180) => (sK544 != (sub @ sK544 @ id))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f524,plain,(
% 15.37/3.55 ? [X185 : term,X186 : term,X187 : term,X188 : term] : (((ap @ X185 @ X188) = (ap @ X187 @ X186)) & (X185 != X187)) => (((ap @ sK545 @ sK548) = (ap @ sK547 @ sK546)) & (sK547 != sK545))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f525,plain,(
% 15.37/3.55 ? [X189 : term,X190 : subst] : ((comp @ sh @ (push @ X189 @ X190)) != X190) => ((comp @ sh @ (push @ sK549 @ sK550)) != sK550)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f526,plain,(
% 15.37/3.55 ? [X193 : subst] : ((comp @ id @ X193) != X193) => ((comp @ id @ sK551) != sK551)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f527,plain,(
% 15.37/3.55 ? [X195 : subst > term > subst > $o] : ! [X196 : term > $o] : ? [X197 : term] : ((X196 @ X197) != (X195 @ id @ X197 @ id)) => ! [X196 : term > $o] : ? [X197 : term] : ((sK552 @ id @ X197 @ id) != (X196 @ X197))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f528,plain,(
% 15.37/3.55 ! [X196 : term > $o] : (? [X197 : term] : ((sK552 @ id @ X197 @ id) != (X196 @ X197)) => ((sK552 @ id @ (sK553 @ X196) @ id) != (X196 @ (sK553 @ X196))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f529,plain,(
% 15.37/3.55 ! [X198 : subst > term > subst > $o] : (? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ id @ X200 @ id)) => ! [X200 : term] : ((X198 @ id @ X200 @ id) = (sK554 @ X198 @ X200)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f530,plain,(
% 15.37/3.55 ! [X201 : subst] : (? [X202 : d_subst] : ((d2subst @ X202) = X201) => ((d2subst @ (sK555 @ X201)) = X201))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f531,plain,(
% 15.37/3.55 ! [X203 : subst > term > subst > $o] : (? [X205 : term,X206 : term] : (($true = (X203 @ id @ X206 @ id)) & ($true = (X203 @ id @ X205 @ id)) & ((X203 @ id @ (ap @ (sub @ X206 @ id) @ X205) @ id) != $true)) => (($true = (X203 @ id @ (sK557 @ X203) @ id)) & ($true = (X203 @ id @ (sK556 @ X203) @ id)) & ($true != (X203 @ id @ (ap @ (sub @ (sK557 @ X203) @ id) @ (sK556 @ X203)) @ id))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f532,plain,(
% 15.37/3.55 ? [X207 : subst > term > subst > $o,X208 : term] : (! [X209 : term,X210 : term] : (($true != (X207 @ id @ X210 @ id)) | ($true != (X207 @ id @ X209 @ id)) | ($true = (X207 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id))) & ($true != (X207 @ id @ X208 @ id)) & ($true != (sP5 @ X207))) => (! [X210 : term,X209 : term] : (($true != (sK558 @ id @ X210 @ id)) | ($true != (sK558 @ id @ X209 @ id)) | ($true = (sK558 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id))) & ((sK558 @ id @ sK559 @ id) != $true) & ($true != (sP5 @ sK558)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f533,plain,(
% 15.37/3.55 ? [X215 : term,X216 : term,X217 : term,X218 : term] : ((X217 != X218) & ((ap @ (sub @ X216 @ id) @ X217) = (ap @ (sub @ X215 @ id) @ X218))) => ((sK563 != sK562) & ((ap @ (sub @ sK561 @ id) @ sK562) = (ap @ (sub @ sK560 @ id) @ sK563)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f534,plain,(
% 15.37/3.55 ? [X220 : term] : ((sub @ X220 @ id) != X220) => ((sub @ sK564 @ id) != sK564)),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f535,plain,(
% 15.37/3.55 ? [X221 : term] : ! [X222 : subst > term > term] : ((X222 @ sh @ one) != (sub @ X221 @ (push @ one @ sh))) => ! [X222 : subst > term > term] : ((sub @ sK565 @ (push @ one @ sh)) != (X222 @ sh @ one))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f536,plain,(
% 15.37/3.55 ! [X223 : term] : (? [X224 : subst > term > term] : ((X224 @ sh @ one) = (sub @ X223 @ (push @ one @ sh))) => ((sK566 @ X223 @ sh @ one) = (sub @ X223 @ (push @ one @ sh))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f537,plain,(
% 15.37/3.55 ! [X225 : subst,X226 : term > $o,X227 : term] : (? [X228 : term > $o] : ! [X229 : term] : ((X226 @ (sub @ X229 @ (push @ X227 @ X225))) = (X228 @ X229)) => ! [X229 : term] : ((X226 @ (sub @ X229 @ (push @ X227 @ X225))) = (sK567 @ X227 @ X226 @ X225 @ X229)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f538,plain,(
% 15.37/3.55 ? [X230 : subst,X231 : term > $o,X232 : term] : ! [X233 : term > $o] : ? [X234 : term] : ((X233 @ X234) != (X231 @ (sub @ X234 @ (push @ X232 @ X230)))) => ! [X233 : term > $o] : ? [X234 : term] : ((X233 @ X234) != (sK569 @ (sub @ X234 @ (push @ sK570 @ sK568))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f539,plain,(
% 15.37/3.55 ! [X233 : term > $o] : (? [X234 : term] : ((X233 @ X234) != (sK569 @ (sub @ X234 @ (push @ sK570 @ sK568)))) => ((X233 @ (sK571 @ X233)) != (sK569 @ (sub @ (sK571 @ X233) @ (push @ sK570 @ sK568)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f540,plain,(
% 15.37/3.55 ? [X239 : term,X240 : term,X241 : term,X242 : term] : (((ap @ X242 @ X241) = (ap @ X240 @ X239)) & (X239 != X241)) => (((ap @ sK573 @ sK572) = (ap @ sK575 @ sK574)) & (sK572 != sK574))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f541,plain,(
% 15.37/3.55 ! [X244 : subst > term > term] : (? [X247 : subst,X248 : term,X249 : subst] : ((sub @ (X244 @ X247 @ X248) @ X249) != (X244 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249))) => ((sub @ (X244 @ (sK576 @ X244) @ (sK577 @ X244)) @ (sK578 @ X244)) != (X244 @ (comp @ (sK576 @ X244) @ (sK578 @ X244)) @ (sub @ (sK577 @ X244) @ (sK578 @ X244)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f542,plain,(
% 15.37/3.55 ! [X243 : subst > term > term] : (? [X250 : subst,X251 : term,X252 : subst] : ((X243 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250)) != (sub @ (X243 @ X252 @ X251) @ X250)) => ((X243 @ (comp @ (sK581 @ X243) @ (sK579 @ X243)) @ (sub @ (sK580 @ X243) @ (sK579 @ X243))) != (sub @ (X243 @ (sK581 @ X243) @ (sK580 @ X243)) @ (sK579 @ X243))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f543,plain,(
% 15.37/3.55 ? [X253 : subst > term > term,X254 : subst > term > term,X255 : term,X256 : subst] : (((lam @ (X253 @ sh @ one)) = (lam @ (X254 @ sh @ one))) & ! [X257 : subst,X258 : term,X259 : subst] : ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X254 @ X257 @ X258) @ X259)) & ! [X260 : subst,X261 : term,X262 : subst] : ((sub @ (X253 @ X262 @ X261) @ X260) = (X253 @ (comp @ X262 @ X260) @ (sub @ X261 @ X260))) & ((X254 @ X256 @ X255) != (X253 @ X256 @ X255))) => (((lam @ (sK583 @ sh @ one)) = (lam @ (sK582 @ sh @ one))) & ! [X259 : subst,X258 : term,X257 : subst] : ((sK583 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (sK583 @ X257 @ X258) @ X259)) & ! [X262 : subst,X261 : term,X260 : subst] : ((sK582 @ (comp @ X262 @ X260) @ (sub @ X261 @ X260)) = (sub @ (sK582 @ X262 @ X261) @ X260)) & ((sK583 @ sK585 @ sK584) != (sK582 @ sK585 @ sK584)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f544,plain,(
% 15.37/3.55 ? [X264 : subst,X265 : term > $o,X266 : term,X267 : term,X268 : term > $o] : (($true = (X265 @ X267)) & ($true != (X268 @ (sub @ X267 @ (push @ X266 @ X264))))) => (($true = (sK587 @ sK589)) & ($true != (sK590 @ (sub @ sK589 @ (push @ sK588 @ sK586)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f475,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & (($true = sP58) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP58)) & ((axscons = $true) | ? [X2 : subst] : ((push @ (sub @ one @ X2) @ (comp @ sh @ X2)) != X2)) & (! [X3 : subst] : ((push @ (sub @ one @ X3) @ (comp @ sh @ X3)) = X3) | (axscons != $true)) & (ulamvar1 != $true) & ((induction2lem_lthm = $true) | ($true != sP56)) & (($true = sP56) | (induction2lem_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X4 : term > $o,X5 : term > $o,X6 : subst,X7 : term] : (($true = (X5 @ one)) | ($true != (X4 @ X7)) | ? [X8 : term] : ((X4 @ (sub @ X8 @ (push @ X7 @ X6))) != (X5 @ X8))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X9 : term > $o,X10 : term > $o,X11 : subst,X12 : term] : (((X10 @ one) != $true) & ($true = (X9 @ X12)) & ! [X13 : term] : ((X10 @ X13) = (X9 @ (sub @ X13 @ (push @ X12 @ X11)))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X14 : term] : ((sub @ X14 @ id) = X14) | (termmset != $true)) & ((termmset = $true) | ? [X15 : term] : ((sub @ X15 @ id) != X15)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ? [X16 : term,X17 : term] : ((X16 != X17) & ((lam @ X16) = (lam @ X17)))) & (! [X18 : term,X19 : term] : ((X18 = X19) | ((lam @ X19) != (lam @ X18))) | (laminj != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (($true = sP46) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP46)) & ! [X20 : d_subst,X21 : d_subst] : (((d2subst @ X21) != (d2subst @ X20)) | (X20 = X21)) & (hoasinduction_lem1v2 = $true) & ((axidr = $true) | ? [X22 : subst] : ((comp @ X22 @ id) != X22)) & (! [X23 : subst] : ((comp @ X23 @ id) = X23) | (axidr != $true)) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & (($true = sP44) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP44)) & (! [X24 : term] : ? [X25 : subst > term > term] : ! [X26 : term,X27 : subst] : ((sub @ X24 @ (push @ X26 @ X27)) = (X25 @ X27 @ X26)) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X28 : term] : ! [X29 : subst > term > term] : ? [X30 : term,X31 : subst] : ((sub @ X28 @ (push @ X30 @ X31)) != (X29 @ X31 @ X30))) & ((axvarcons = $true) | ? [X32 : term,X33 : subst] : ((sub @ one @ (push @ X32 @ X33)) != X32)) & (! [X34 : term,X35 : subst] : ((sub @ one @ (push @ X34 @ X35)) = X34) | (axvarcons != $true)) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & (? [X36 : subst] : ((comp @ id @ X36) != X36) | ? [X37 : subst] : ((comp @ X37 @ id) != X37) | (! [X38 : subst] : ((comp @ id @ X38) = X38) & ! [X39 : subst] : ((comp @ X39 @ id) = X39)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X40 : subst] : ((comp @ id @ X40) = X40) & ! [X41 : subst] : ((comp @ X41 @ id) = X41) & (? [X42 : subst] : ((comp @ id @ X42) != X42) | ? [X43 : subst] : ((comp @ X43 @ id) != X43)))) & (ulamvarsh = $true) & (! [X44 : term] : ? [X45 : subst > term > term] : ! [X46 : term,X47 : subst] : ((sub @ X44 @ (push @ X46 @ X47)) = (X45 @ X47 @ X46)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X48 : term] : ! [X49 : subst > term > term] : ? [X50 : term,X51 : subst] : ((X49 @ X51 @ X50) != (sub @ X48 @ (push @ X50 @ X51)))) & ((hoasapinj2_lthm = $true) | (! [X52 : term,X53 : term,X54 : term,X55 : term] : (((ap @ X55 @ X52) != (ap @ X54 @ X53)) | (X52 = X53)) & ? [X56 : term,X57 : term,X58 : term,X59 : term] : (((ap @ (sub @ X59 @ id) @ X58) = (ap @ (sub @ X57 @ id) @ X56)) & (X56 != X58)))) & (? [X60 : term,X61 : term,X62 : term,X63 : term] : (((ap @ X63 @ X60) = (ap @ X62 @ X61)) & (X60 != X61)) | ! [X64 : term,X65 : term,X66 : term,X67 : term] : (((ap @ (sub @ X67 @ id) @ X66) != (ap @ (sub @ X65 @ id) @ X64)) | (X64 = X66)) | (hoasapinj2_lthm != $true)) & ((hoasapinj1 = $true) | ? [X68 : term,X69 : term,X70 : term,X71 : term] : ((X69 != X71) & ((ap @ (sub @ X71 @ id) @ X70) = (ap @ (sub @ X69 @ id) @ X68)))) & (! [X72 : term,X73 : term,X74 : term,X75 : term] : ((X73 = X75) | ((ap @ (sub @ X73 @ id) @ X72) != (ap @ (sub @ X75 @ id) @ X74))) | (hoasapinj1 != $true)) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X76 : term > $o,X77 : term] : (($true = (sP43 @ X76)) | ? [X78 : term] : (($true = (X76 @ X78)) & ($true != (X76 @ (lam @ X78)))) | ? [X79 : term] : (($true = (var @ X79)) & ($true != (X76 @ X79))) | ((X76 @ X77) = $true)) | (induction != $true)) & ((induction = $true) | ? [X80 : term > $o,X81 : term] : (($true != (sP43 @ X80)) & ! [X82 : term] : (($true != (X80 @ X82)) | ($true = (X80 @ (lam @ X82)))) & ! [X83 : term] : (($true != (var @ X83)) | ($true = (X80 @ X83))) & ($true != (X80 @ X81)))) & ((induction2_lthm = $true) | ($true != sP42)) & (($true = sP42) | (induction2_lthm != $true)) & ! [X84 : d_term] : (d_one = X84) & (! [X85 : term,X86 : term,X87 : term,X88 : term] : (((ap @ X85 @ X88) != (ap @ X86 @ X87)) | (X85 = X86)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ X89 @ X92) = (ap @ X90 @ X91)) & (X89 != X90))) & ((sP38 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP38 != $true)) & (hoasapnotvar_gthm = $true) & (($true = sP37) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP37)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem1_lthm = $true) | (! [X93 : subst,X94 : term] : ((comp @ sh @ (push @ X94 @ X93)) = X93) & ? [X95 : term > $o,X96 : term > $o,X97 : term,X98 : subst,X99 : term] : (((X96 @ (sub @ X99 @ (push @ X97 @ X98))) != $true) & ($true = (X95 @ X99))) & ! [X100 : subst,X101 : term] : ((sub @ one @ (push @ X101 @ X100)) = X101))) & (? [X102 : subst,X103 : term] : ((comp @ sh @ (push @ X103 @ X102)) != X102) | ! [X104 : term > $o,X105 : term > $o,X106 : term,X107 : subst,X108 : term] : (($true = (X105 @ (sub @ X108 @ (push @ X106 @ X107)))) | ($true != (X104 @ X108))) | ? [X109 : subst,X110 : term] : ((sub @ one @ (push @ X110 @ X109)) != X110) | (pushprop_lem1_lthm != $true)) & ((termmset_lthm = $true) | (! [X111 : term] : ((sub @ X111 @ id) = X111) & ? [X112 : term] : ((sub @ X112 @ id) != X112))) & (? [X113 : term] : ((sub @ X113 @ id) != X113) | ! [X114 : term] : ((sub @ X114 @ id) = X114) | (termmset_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_no_psi_cond_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP31) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP31)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | ? [X115 : subst] : ((comp @ X115 @ id) != X115) | ? [X116 : subst] : ((comp @ id @ X116) != X116)) & ((! [X117 : subst] : ((comp @ X117 @ id) = X117) & ! [X118 : subst] : ((comp @ id @ X118) = X118)) | (substmonoid != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2v2 != $true)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP26)) & ((hoasinduction_lem3b_lthm = $true) | ? [X119 : term] : ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ X119 @ (push @ one @ sh)))) & (! [X121 : term] : ? [X122 : subst > term > term] : ((X122 @ sh @ one) = (sub @ X121 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & (! [X123 : subst > term > subst > $o] : ? [X124 : term > $o] : ! [X125 : term] : ((X123 @ id @ X125 @ id) = (X124 @ X125)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X126 : subst > term > subst > $o] : ! [X127 : term > $o] : ? [X128 : term] : ((X127 @ X128) != (X126 @ id @ X128 @ id))) & ((pushprop_lem0_lthm = $true) | ? [X129 : term > $o,X130 : term,X131 : subst] : ! [X132 : term > $o] : ? [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X130 @ X131))) != (X132 @ X133))) & (! [X134 : term > $o,X135 : term,X136 : subst] : ? [X137 : term > $o] : ! [X138 : term] : ((X137 @ X138) = (X134 @ (sub @ X138 @ (push @ X135 @ X136)))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP25) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP25)) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & (! [X139 : term,X140 : term,X141 : subst > term > term] : (((ap @ (sub @ X140 @ id) @ X139) != (lam @ (X141 @ sh @ one))) | ? [X142 : subst,X143 : term,X144 : subst] : ((sub @ (X141 @ X142 @ X143) @ X144) != (X141 @ (comp @ X142 @ X144) @ (sub @ X143 @ X144)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X145 : term,X146 : term,X147 : subst > term > term] : (((ap @ (sub @ X146 @ id) @ X145) = (lam @ (X147 @ sh @ one))) & ! [X148 : subst,X149 : term,X150 : subst] : ((sub @ (X147 @ X148 @ X149) @ X150) = (X147 @ (comp @ X148 @ X150) @ (sub @ X149 @ X150))))) & ((pushprop_lem1v2_lthm = $true) | (? [X151 : term > $o,X152 : subst,X153 : term,X154 : term > $o] : (($true = (X151 @ X153)) & ! [X155 : term] : ((X151 @ (sub @ X155 @ (push @ X153 @ X152))) = (X154 @ X155)) & ($true != (X154 @ one))) & ! [X156 : subst,X157 : term] : ((sub @ one @ (push @ X157 @ X156)) = X157))) & (! [X158 : term > $o,X159 : subst,X160 : term,X161 : term > $o] : (($true != (X158 @ X160)) | ? [X162 : term] : ((X158 @ (sub @ X162 @ (push @ X160 @ X159))) != (X161 @ X162)) | ($true = (X161 @ one))) | ? [X163 : subst,X164 : term] : ((sub @ one @ (push @ X164 @ X163)) != X164) | (pushprop_lem1v2_lthm != $true)) & (($true = sP23) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP23)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X165 : d_term,X166 : d_term] : ((X165 = X166) | ((d2term @ X165) != (d2term @ X166))) & ((shinj = $true) | ? [X167 : term,X168 : term] : ((X167 != X168) & ((sub @ X167 @ sh) = (sub @ X168 @ sh)))) & (! [X169 : term,X170 : term] : ((X169 = X170) | ((sub @ X169 @ sh) != (sub @ X170 @ sh))) | (shinj != $true)) & ((hoasapinj1_lthm = $true) | (! [X171 : term] : ((sub @ X171 @ id) = X171) & ? [X172 : term,X173 : term,X174 : term,X175 : term] : ((X172 != X173) & ((ap @ (sub @ X172 @ id) @ X175) = (ap @ (sub @ X173 @ id) @ X174))) & ! [X176 : term,X177 : term,X178 : term,X179 : term] : (((ap @ X178 @ X177) != (ap @ X176 @ X179)) | (X176 = X178)))) & (? [X180 : term] : ((sub @ X180 @ id) != X180) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X181 = X182) | ((ap @ (sub @ X181 @ id) @ X184) != (ap @ (sub @ X182 @ id) @ X183))) | ? [X185 : term,X186 : term,X187 : term,X188 : term] : (((ap @ X185 @ X188) = (ap @ X187 @ X186)) & (X185 != X187)) | (hoasapinj1_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((sP14 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP14 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP13)) & (($true = sP13) | (hoasinduction_lem3 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X189 : term,X190 : subst] : ((comp @ sh @ (push @ X189 @ X190)) != X190)) & (! [X191 : term,X192 : subst] : ((comp @ sh @ (push @ X191 @ X192)) = X192) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((axidl = $true) | ? [X193 : subst] : ((comp @ id @ X193) != X193)) & (! [X194 : subst] : ((comp @ id @ X194) = X194) | (axidl != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem3_lthm != $true)) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem0 = $true) | ? [X195 : subst > term > subst > $o] : ! [X196 : term > $o] : ? [X197 : term] : ((X196 @ X197) != (X195 @ id @ X197 @ id))) & (! [X198 : subst > term > subst > $o] : ? [X199 : term > $o] : ! [X200 : term] : ((X199 @ X200) = (X198 @ id @ X200 @ id)) | (hoasinduction_lem0 != $true)) & ! [X201 : subst] : ? [X202 : d_subst] : ((d2subst @ X202) = X201) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & (! [X203 : subst > term > subst > $o,X204 : term] : (? [X205 : term,X206 : term] : (($true = (X203 @ id @ X206 @ id)) & ($true = (X203 @ id @ X205 @ id)) & ((X203 @ id @ (ap @ (sub @ X206 @ id) @ X205) @ id) != $true)) | ((X203 @ id @ X204 @ id) = $true) | ($true = (sP5 @ X203))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X207 : subst > term > subst > $o,X208 : term] : (! [X209 : term,X210 : term] : (($true != (X207 @ id @ X210 @ id)) | ($true != (X207 @ id @ X209 @ id)) | ($true = (X207 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id))) & ($true != (X207 @ id @ X208 @ id)) & ($true != (sP5 @ X207)))) & (lamnotvar = $true) & (! [X211 : term,X212 : term,X213 : term,X214 : term] : ((X213 = X214) | ((ap @ (sub @ X212 @ id) @ X213) != (ap @ (sub @ X211 @ id) @ X214))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X215 : term,X216 : term,X217 : term,X218 : term] : ((X217 != X218) & ((ap @ (sub @ X216 @ id) @ X217) = (ap @ (sub @ X215 @ id) @ X218)))) & (axvarshift = $true) & (! [X219 : term] : ((sub @ X219 @ id) = X219) | (axvarid != $true)) & ((axvarid = $true) | ? [X220 : term] : ((sub @ X220 @ id) != X220)) & ((hoasinduction_lem3b = $true) | ? [X221 : term] : ! [X222 : subst > term > term] : ((X222 @ sh @ one) != (sub @ X221 @ (push @ one @ sh)))) & (! [X223 : term] : ? [X224 : subst > term > term] : ((X224 @ sh @ one) = (sub @ X223 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & (! [X225 : subst,X226 : term > $o,X227 : term] : ? [X228 : term > $o] : ! [X229 : term] : ((X226 @ (sub @ X229 @ (push @ X227 @ X225))) = (X228 @ X229)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X230 : subst,X231 : term > $o,X232 : term] : ! [X233 : term > $o] : ? [X234 : term] : ((X233 @ X234) != (X231 @ (sub @ X234 @ (push @ X232 @ X230))))) & (! [X235 : term,X236 : term,X237 : term,X238 : term] : (((ap @ X236 @ X235) != (ap @ X238 @ X237)) | (X235 = X237)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X239 : term,X240 : term,X241 : term,X242 : term] : (((ap @ X242 @ X241) = (ap @ X240 @ X239)) & (X239 != X241))) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3v2 != $true)) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & (($true = sP0) | (hoasinduction_lem3a != $true)) & (! [X243 : subst > term > term,X244 : subst > term > term,X245 : term,X246 : subst] : (((lam @ (X244 @ sh @ one)) != (lam @ (X243 @ sh @ one))) | ? [X247 : subst,X248 : term,X249 : subst] : ((sub @ (X244 @ X247 @ X248) @ X249) != (X244 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249))) | ? [X250 : subst,X251 : term,X252 : subst] : ((X243 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250)) != (sub @ (X243 @ X252 @ X251) @ X250)) | ((X244 @ X246 @ X245) = (X243 @ X246 @ X245))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X253 : subst > term > term,X254 : subst > term > term,X255 : term,X256 : subst] : (((lam @ (X253 @ sh @ one)) = (lam @ (X254 @ sh @ one))) & ! [X257 : subst,X258 : term,X259 : subst] : ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259)) = (sub @ (X254 @ X257 @ X258) @ X259)) & ! [X260 : subst,X261 : term,X262 : subst] : ((sub @ (X253 @ X262 @ X261) @ X260) = (X253 @ (comp @ X262 @ X260) @ (sub @ X261 @ X260))) & ((X254 @ X256 @ X255) != (X253 @ X256 @ X255)))) & ! [X263 : d_subst] : (d_id = X263) & ((pushprop_lem1 = $true) | ? [X264 : subst,X265 : term > $o,X266 : term,X267 : term,X268 : term > $o] : (($true = (X265 @ X267)) & ($true != (X268 @ (sub @ X267 @ (push @ X266 @ X264)))))) & (! [X269 : subst,X270 : term > $o,X271 : term,X272 : term,X273 : term > $o] : (($true != (X270 @ X272)) | ((X273 @ (sub @ X272 @ (push @ X271 @ X269))) = $true)) | (pushprop_lem1 != $true)) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(rectify,[status(thm)],[f474])).
% 15.37/3.55 thf(f474,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & (($true = sP58) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP58)) & ((axscons = $true) | ? [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) != X157)) & (! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157) | (axscons != $true)) & (ulamvar1 != $true) & ((induction2lem_lthm = $true) | ($true != sP56)) & (($true = sP56) | (induction2lem_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ? [X156 : term] : ((X153 @ X156) != (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true != (X153 @ one)) & ($true = (X152 @ X155)) & ! [X156 : term] : ((X153 @ X156) = (X152 @ (sub @ X156 @ (push @ X155 @ X154)))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) | (termmset != $true)) & ((termmset = $true) | ? [X26 : term] : ((sub @ X26 @ id) != X26)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ? [X417 : term,X418 : term] : ((X417 != X418) & ((lam @ X418) = (lam @ X417)))) & (! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417))) | (laminj != $true)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (($true = sP46) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP46)) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) != (d2subst @ X291)) | (X290 = X291)) & (hoasinduction_lem1v2 = $true) & ((axidr = $true) | ? [X196 : subst] : ((comp @ X196 @ id) != X196)) & (! [X196 : subst] : ((comp @ X196 @ id) = X196) | (axidr != $true)) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & (($true = sP44) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP44)) & (! [X434 : term] : ? [X435 : subst > term > term] : ! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X434 : term] : ! [X435 : subst > term > term] : ? [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) != (sub @ X434 @ (push @ X436 @ X437)))) & ((axvarcons = $true) | ? [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) != X470)) & (! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470) | (axvarcons != $true)) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & (? [X456 : subst] : ((comp @ id @ X456) != X456) | ? [X457 : subst] : ((comp @ X457 @ id) != X457) | (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X456 : subst] : ((comp @ id @ X456) = X456) & ! [X457 : subst] : ((comp @ X457 @ id) = X457) & (? [X459 : subst] : ((comp @ id @ X459) != X459) | ? [X458 : subst] : ((comp @ X458 @ id) != X458)))) & (ulamvarsh = $true) & (! [X536 : term] : ? [X537 : subst > term > term] : ! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X536 : term] : ! [X537 : subst > term > term] : ? [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) != (X537 @ X539 @ X538))) & ((hoasapinj2_lthm = $true) | (! [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) != (ap @ X411 @ X410)) | (X409 = X410)) & ? [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) = (ap @ (sub @ X416 @ id) @ X415)) & (X413 != X415)))) & (? [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) = (ap @ X411 @ X410)) & (X409 != X410)) | ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)) | (hoasapinj2_lthm != $true)) & ((hoasapinj1 = $true) | ? [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 != X356) & ((ap @ (sub @ X356 @ id) @ X355) = (ap @ (sub @ X354 @ id) @ X353)))) & (! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353))) | (hoasapinj1 != $true)) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X28 : term > $o,X29 : term] : (($true = (sP43 @ X28)) | ? [X33 : term] : (((X28 @ X33) = $true) & ((X28 @ (lam @ X33)) != $true)) | ? [X30 : term] : (($true = (var @ X30)) & ((X28 @ X30) != $true)) | ($true = (X28 @ X29))) | (induction != $true)) & ((induction = $true) | ? [X28 : term > $o,X29 : term] : (($true != (sP43 @ X28)) & ! [X33 : term] : (((X28 @ X33) != $true) | ((X28 @ (lam @ X33)) = $true)) & ! [X30 : term] : (($true != (var @ X30)) | ((X28 @ X30) = $true)) & ($true != (X28 @ X29)))) & ((induction2_lthm = $true) | ($true != sP42)) & (($true = sP42) | (induction2_lthm != $true)) & ! [X453 : d_term] : (d_one = X453) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) = (ap @ X60 @ X61)) & (X59 != X60))) & ((sP38 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP38 != $true)) & (hoasapnotvar_gthm = $true) & (($true = sP37) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP37)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem1_lthm = $true) | (! [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) = X474) & ? [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) != $true) & ($true = (X476 @ X480))) & ! [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) = X473))) & (? [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) != X474) | ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))) | ? [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) != X473) | (pushprop_lem1_lthm != $true)) & ((termmset_lthm = $true) | (! [X251 : term] : ((sub @ X251 @ id) = X251) & ? [X252 : term] : ((sub @ X252 @ id) != X252))) & (? [X251 : term] : ((sub @ X251 @ id) != X251) | ! [X252 : term] : ((sub @ X252 @ id) = X252) | (termmset_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_no_psi_cond_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP31) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP31)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | ? [X358 : subst] : ((comp @ X358 @ id) != X358) | ? [X357 : subst] : ((comp @ id @ X357) != X357)) & ((! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357)) | (substmonoid != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2v2 != $true)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP26)) & ((hoasinduction_lem3b_lthm = $true) | ? [X454 : term] : ! [X455 : subst > term > term] : ((X455 @ sh @ one) != (sub @ X454 @ (push @ one @ sh)))) & (! [X454 : term] : ? [X455 : subst > term > term] : ((X455 @ sh @ one) = (sub @ X454 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & (! [X34 : subst > term > subst > $o] : ? [X35 : term > $o] : ! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X34 : subst > term > subst > $o] : ! [X35 : term > $o] : ? [X36 : term] : ((X34 @ id @ X36 @ id) != (X35 @ X36))) & ((pushprop_lem0_lthm = $true) | ? [X112 : term > $o,X113 : term,X114 : subst] : ! [X115 : term > $o] : ? [X116 : term] : ((X115 @ X116) != (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (! [X112 : term > $o,X113 : term,X114 : subst] : ? [X115 : term > $o] : ! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114)))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP25) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP25)) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & (! [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))) | ? [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) != (sub @ (X348 @ X349 @ X350) @ X351))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) = (lam @ (X348 @ sh @ one))) & ! [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) = (sub @ (X348 @ X349 @ X350) @ X351)))) & ((pushprop_lem1v2_lthm = $true) | (? [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) = $true) & ! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6)) & ($true != (X5 @ one))) & ! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1))) & (! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ? [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) != (X5 @ X6)) | ($true = (X5 @ one))) | ? [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) != X1) | (pushprop_lem1v2_lthm != $true)) & (($true = sP23) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP23)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X7 : d_term,X8 : d_term] : ((X7 = X8) | ((d2term @ X7) != (d2term @ X8))) & ((shinj = $true) | ? [X379 : term,X380 : term] : ((X379 != X380) & ((sub @ X379 @ sh) = (sub @ X380 @ sh)))) & (! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh))) | (shinj != $true)) & ((hoasapinj1_lthm = $true) | (! [X37 : term] : ((sub @ X37 @ id) = X37) & ? [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 != X43) & ((ap @ (sub @ X42 @ id) @ X45) = (ap @ (sub @ X43 @ id) @ X44))) & ! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)))) & (? [X37 : term] : ((sub @ X37 @ id) != X37) | ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) = (ap @ X40 @ X39)) & (X38 != X40)) | (hoasapinj1_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & ((sP14 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP14 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP13)) & (($true = sP13) | (hoasinduction_lem3 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) != X275)) & (! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275) | (axshiftcons != $true)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((axidl = $true) | ? [X197 : subst] : ((comp @ id @ X197) != X197)) & (! [X197 : subst] : ((comp @ id @ X197) = X197) | (axidl != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem3_lthm != $true)) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem0 = $true) | ? [X102 : subst > term > subst > $o] : ! [X103 : term > $o] : ? [X104 : term] : ((X102 @ id @ X104 @ id) != (X103 @ X104))) & (! [X102 : subst > term > subst > $o] : ? [X103 : term > $o] : ! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) | (hoasinduction_lem0 != $true)) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & (! [X125 : subst > term > subst > $o,X126 : term] : (? [X132 : term,X133 : term] : (($true = (X125 @ id @ X133 @ id)) & ($true = (X125 @ id @ X132 @ id)) & ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) != $true)) | ($true = (X125 @ id @ X126 @ id)) | ($true = (sP5 @ X125))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X125 : subst > term > subst > $o,X126 : term] : (! [X132 : term,X133 : term] : (($true != (X125 @ id @ X133 @ id)) | ($true != (X125 @ id @ X132 @ id)) | ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) = $true)) & ($true != (X125 @ id @ X126 @ id)) & ($true != (sP5 @ X125)))) & (lamnotvar = $true) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 != X289) & ((ap @ (sub @ X286 @ id) @ X289) = (ap @ (sub @ X287 @ id) @ X288)))) & (axvarshift = $true) & (! [X352 : term] : ((sub @ X352 @ id) = X352) | (axvarid != $true)) & ((axvarid = $true) | ? [X352 : term] : ((sub @ X352 @ id) != X352)) & ((hoasinduction_lem3b = $true) | ? [X253 : term] : ! [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) != (X254 @ sh @ one))) & (! [X253 : term] : ? [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) = (X254 @ sh @ one)) | (hoasinduction_lem3b != $true)) & (! [X374 : subst,X375 : term > $o,X376 : term] : ? [X377 : term > $o] : ! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X374 : subst,X375 : term > $o,X376 : term] : ! [X377 : term > $o] : ? [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) != (X377 @ X378))) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) = (ap @ X392 @ X391)) & (X389 != X391))) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3v2 != $true)) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & (($true = sP0) | (hoasinduction_lem3a != $true)) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ? [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) != (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) | ? [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) != (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) = (lam @ (X443 @ sh @ one))) & ! [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) = (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) & ! [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) = (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) & ((X444 @ X446 @ X445) != (X443 @ X446 @ X445)))) & ! [X27 : d_subst] : (d_id = X27) & ((pushprop_lem1 = $true) | ? [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true = (X439 @ X441)) & ($true != (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & (! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438))))) | (pushprop_lem1 != $true)) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(flattening,[status(thm)],[f473])).
% 15.37/3.55 thf(f473,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & ((($true = sP58) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP58))) & (((axscons = $true) | ? [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) != X157)) & (! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157) | (axscons != $true))) & (ulamvar1 != $true) & (((induction2lem_lthm = $true) | ($true != sP56)) & (($true = sP56) | (induction2lem_lthm != $true))) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & ((! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ? [X156 : term] : ((X153 @ X156) != (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true != (X153 @ one)) & ($true = (X152 @ X155)) & ! [X156 : term] : ((X153 @ X156) = (X152 @ (sub @ X156 @ (push @ X155 @ X154))))))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((! [X26 : term] : ((sub @ X26 @ id) = X26) | (termmset != $true)) & ((termmset = $true) | ? [X26 : term] : ((sub @ X26 @ id) != X26))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & (((laminj = $true) | ? [X417 : term,X418 : term] : ((X417 != X418) & ((lam @ X418) = (lam @ X417)))) & (! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417))) | (laminj != $true))) & (((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true))) & ((($true = sP46) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP46))) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) != (d2subst @ X291)) | (X290 = X291)) & (hoasinduction_lem1v2 = $true) & (((axidr = $true) | ? [X196 : subst] : ((comp @ X196 @ id) != X196)) & (! [X196 : subst] : ((comp @ X196 @ id) = X196) | (axidr != $true))) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & ((($true = sP44) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP44))) & ((! [X434 : term] : ? [X435 : subst > term > term] : ! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X434 : term] : ! [X435 : subst > term > term] : ? [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) != (sub @ X434 @ (push @ X436 @ X437))))) & (((axvarcons = $true) | ? [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) != X470)) & (! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470) | (axvarcons != $true))) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & (((? [X456 : subst] : ((comp @ id @ X456) != X456) | ? [X457 : subst] : ((comp @ X457 @ id) != X457) | (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X456 : subst] : ((comp @ id @ X456) = X456) & ! [X457 : subst] : ((comp @ X457 @ id) = X457) & (? [X459 : subst] : ((comp @ id @ X459) != X459) | ? [X458 : subst] : ((comp @ X458 @ id) != X458))))) & (ulamvarsh = $true) & ((! [X536 : term] : ? [X537 : subst > term > term] : ! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538)) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X536 : term] : ! [X537 : subst > term > term] : ? [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) != (X537 @ X539 @ X538)))) & (((hoasapinj2_lthm = $true) | (! [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) != (ap @ X411 @ X410)) | (X409 = X410)) & ? [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) = (ap @ (sub @ X416 @ id) @ X415)) & (X413 != X415)))) & ((? [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) = (ap @ X411 @ X410)) & (X409 != X410)) | ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415))) | (hoasapinj2_lthm != $true))) & (((hoasapinj1 = $true) | ? [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 != X356) & ((ap @ (sub @ X356 @ id) @ X355) = (ap @ (sub @ X354 @ id) @ X353)))) & (! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353))) | (hoasapinj1 != $true))) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X28 : term > $o,X29 : term] : (($true = (sP43 @ X28)) | ? [X33 : term] : (((X28 @ X33) = $true) & ((X28 @ (lam @ X33)) != $true)) | ? [X30 : term] : (($true = (var @ X30)) & ((X28 @ X30) != $true)) | ($true = (X28 @ X29))) | (induction != $true)) & ((induction = $true) | ? [X28 : term > $o,X29 : term] : (($true != (sP43 @ X28)) & ! [X33 : term] : (((X28 @ X33) != $true) | ((X28 @ (lam @ X33)) = $true)) & ! [X30 : term] : (($true != (var @ X30)) | ((X28 @ X30) = $true)) & ($true != (X28 @ X29))))) & (((induction2_lthm = $true) | ($true != sP42)) & (($true = sP42) | (induction2_lthm != $true))) & ! [X453 : d_term] : (d_one = X453) & ((! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) = (ap @ X60 @ X61)) & (X59 != X60)))) & (((sP38 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP38 != $true))) & (hoasapnotvar_gthm = $true) & ((($true = sP37) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP37))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (((pushprop_lem1_lthm = $true) | (! [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) = X474) & ? [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) != $true) & ($true = (X476 @ X480))) & ! [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) = X473))) & ((? [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) != X474) | ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))) | ? [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) != X473)) | (pushprop_lem1_lthm != $true))) & (((termmset_lthm = $true) | (! [X251 : term] : ((sub @ X251 @ id) = X251) & ? [X252 : term] : ((sub @ X252 @ id) != X252))) & ((? [X251 : term] : ((sub @ X251 @ id) != X251) | ! [X252 : term] : ((sub @ X252 @ id) = X252)) | (termmset_lthm != $true))) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_no_psi_cond_lthm != $true))) & (hoasinduction_lem3a_gthm = $true) & ((($true = sP31) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP31))) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & (((substmonoid = $true) | (? [X358 : subst] : ((comp @ X358 @ id) != X358) | ? [X357 : subst] : ((comp @ id @ X357) != X357))) & ((! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357)) | (substmonoid != $true))) & (((hoasinduction_lem2v2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2v2 != $true))) & ((($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28))) & ((($true = sP26) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP26))) & (((hoasinduction_lem3b_lthm = $true) | ? [X454 : term] : ! [X455 : subst > term > term] : ((X455 @ sh @ one) != (sub @ X454 @ (push @ one @ sh)))) & (! [X454 : term] : ? [X455 : subst > term > term] : ((X455 @ sh @ one) = (sub @ X454 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true))) & ((! [X34 : subst > term > subst > $o] : ? [X35 : term > $o] : ! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X34 : subst > term > subst > $o] : ! [X35 : term > $o] : ? [X36 : term] : ((X34 @ id @ X36 @ id) != (X35 @ X36)))) & (((pushprop_lem0_lthm = $true) | ? [X112 : term > $o,X113 : term,X114 : subst] : ! [X115 : term > $o] : ? [X116 : term] : ((X115 @ X116) != (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (! [X112 : term > $o,X113 : term,X114 : subst] : ? [X115 : term > $o] : ! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114)))) | (pushprop_lem0_lthm != $true))) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & ((($true = sP25) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP25))) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & ((! [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))) | ? [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) != (sub @ (X348 @ X349 @ X350) @ X351))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) = (lam @ (X348 @ sh @ one))) & ! [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) = (sub @ (X348 @ X349 @ X350) @ X351))))) & (((pushprop_lem1v2_lthm = $true) | (? [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) = $true) & ! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6)) & ($true != (X5 @ one))) & ! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1))) & ((! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ? [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) != (X5 @ X6)) | ($true = (X5 @ one))) | ? [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) != X1)) | (pushprop_lem1v2_lthm != $true))) & ((($true = sP23) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP23))) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X7 : d_term,X8 : d_term] : ((X7 = X8) | ((d2term @ X7) != (d2term @ X8))) & (((shinj = $true) | ? [X379 : term,X380 : term] : ((X379 != X380) & ((sub @ X379 @ sh) = (sub @ X380 @ sh)))) & (! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh))) | (shinj != $true))) & (((hoasapinj1_lthm = $true) | (! [X37 : term] : ((sub @ X37 @ id) = X37) & ? [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 != X43) & ((ap @ (sub @ X42 @ id) @ X45) = (ap @ (sub @ X43 @ id) @ X44))) & ! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)))) & ((? [X37 : term] : ((sub @ X37 @ id) != X37) | ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) = (ap @ X40 @ X39)) & (X38 != X40))) | (hoasapinj1_lthm != $true))) & (hoasinduction_lem1_lthm = $true) & (((sP14 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP14 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP13)) & (($true = sP13) | (hoasinduction_lem3 != $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & (((hoasinduction = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction != $true))) & (((axshiftcons = $true) | ? [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) != X275)) & (! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275) | (axshiftcons != $true))) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((axidl = $true) | ? [X197 : subst] : ((comp @ id @ X197) != X197)) & (! [X197 : subst] : ((comp @ id @ X197) = X197) | (axidl != $true))) & (((hoasinduction_lem3_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem3_lthm != $true))) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & (((hoasinduction_lem0 = $true) | ? [X102 : subst > term > subst > $o] : ! [X103 : term > $o] : ? [X104 : term] : ((X102 @ id @ X104 @ id) != (X103 @ X104))) & (! [X102 : subst > term > subst > $o] : ? [X103 : term > $o] : ! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) | (hoasinduction_lem0 != $true))) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & ((! [X125 : subst > term > subst > $o,X126 : term] : (? [X132 : term,X133 : term] : (($true = (X125 @ id @ X133 @ id)) & ($true = (X125 @ id @ X132 @ id)) & ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) != $true)) | ($true = (X125 @ id @ X126 @ id)) | ($true = (sP5 @ X125))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X125 : subst > term > subst > $o,X126 : term] : (! [X132 : term,X133 : term] : (($true != (X125 @ id @ X133 @ id)) | ($true != (X125 @ id @ X132 @ id)) | ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) = $true)) & ($true != (X125 @ id @ X126 @ id)) & ($true != (sP5 @ X125))))) & (lamnotvar = $true) & ((! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 != X289) & ((ap @ (sub @ X286 @ id) @ X289) = (ap @ (sub @ X287 @ id) @ X288))))) & (axvarshift = $true) & ((! [X352 : term] : ((sub @ X352 @ id) = X352) | (axvarid != $true)) & ((axvarid = $true) | ? [X352 : term] : ((sub @ X352 @ id) != X352))) & (((hoasinduction_lem3b = $true) | ? [X253 : term] : ! [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) != (X254 @ sh @ one))) & (! [X253 : term] : ? [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) = (X254 @ sh @ one)) | (hoasinduction_lem3b != $true))) & ((! [X374 : subst,X375 : term > $o,X376 : term] : ? [X377 : term > $o] : ! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X374 : subst,X375 : term > $o,X376 : term] : ! [X377 : term > $o] : ? [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) != (X377 @ X378)))) & ((! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) = (ap @ X392 @ X391)) & (X389 != X391)))) & (((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true))) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & (((hoasinduction_lem3v2 = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3v2 != $true))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((hoasinduction_lem3a = $true) | ($true != sP0)) & (($true = sP0) | (hoasinduction_lem3a != $true))) & ((! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ? [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) != (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) | ? [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) != (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) = (lam @ (X443 @ sh @ one))) & ! [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) = (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) & ! [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) = (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) & ((X444 @ X446 @ X445) != (X443 @ X446 @ X445))))) & ! [X27 : d_subst] : (d_id = X27) & (((pushprop_lem1 = $true) | ? [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true = (X439 @ X441)) & ($true != (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & (! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438))))) | (pushprop_lem1 != $true))) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f73])).
% 15.37/3.55 thf(f73,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & (($true = sP58) <=> (induction2lem = $true)) & ((axscons = $true) <=> ! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157)) & (ulamvar1 != $true) & ((induction2lem_lthm = $true) <=> ($true = sP56)) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ? [X156 : term] : ((X153 @ X156) != (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) <=> (pushprop_lem1v2 = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) <=> ! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417)))) & ((sP52 = $true) <=> (hoasinduction_lthm_3 = $true)) & (($true = sP46) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) != (d2subst @ X291)) | (X290 = X291)) & (hoasinduction_lem1v2 = $true) & ((axidr = $true) <=> ! [X196 : subst] : ((comp @ X196 @ id) = X196)) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & (($true = sP44) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X434 : term] : ? [X435 : subst > term > term] : ! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((axvarcons = $true) <=> ! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470)) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & ((? [X456 : subst] : ((comp @ id @ X456) != X456) | ? [X457 : subst] : ((comp @ X457 @ id) != X457) | (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458))) <=> (substmonoid_lthm = $true)) & (ulamvarsh = $true) & (! [X536 : term] : ? [X537 : subst > term > term] : ! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538)) <=> (hoasinduction_lem3v2_f = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) = (ap @ X411 @ X410)) & (X409 != X410)) | ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)))) & ((hoasapinj1 = $true) <=> ! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353)))) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X28 : term > $o,X29 : term] : (($true = (sP43 @ X28)) | ? [X33 : term] : (((X28 @ X33) = $true) & ((X28 @ (lam @ X33)) != $true)) | ? [X30 : term] : (($true = (var @ X30)) & ((X28 @ X30) != $true)) | ($true = (X28 @ X29))) <=> (induction = $true)) & ((induction2_lthm = $true) <=> ($true = sP42)) & ! [X453 : d_term] : (d_one = X453) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & ((sP38 = $true) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar_gthm = $true) & (($true = sP37) <=> (hoaslaminj_lthm = $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem1_lthm = $true) <=> (? [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) != X474) | ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))) | ? [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) != X473))) & ((termmset_lthm = $true) <=> (? [X251 : term] : ((sub @ X251 @ id) != X251) | ! [X252 : term] : ((sub @ X252 @ id) = X252))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP36)) & (hoasinduction_lem3a_gthm = $true) & (($true = sP31) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) <=> (! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357))) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP30)) & (($true = sP28) <=> (hoasinduction_lem2 = $true)) & (($true = sP26) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X454 : term] : ? [X455 : subst > term > term] : ((X455 @ sh @ one) = (sub @ X454 @ (push @ one @ sh)))) & (! [X34 : subst > term > subst > $o] : ? [X35 : term > $o] : ! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36)) <=> (hoasinduction_lem0_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X112 : term > $o,X113 : term,X114 : subst] : ? [X115 : term > $o] : ! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & (($true = sP25) <=> (induction2 = $true)) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & (! [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))) | ? [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) != (sub @ (X348 @ X349 @ X350) @ X351))) <=> (hoaslamnotap = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ? [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) != (X5 @ X6)) | ($true = (X5 @ one))) | ? [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) != X1))) & (($true = sP23) <=> (hoasinduction_lthm = $true)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X7 : d_term,X8 : d_term] : ((X7 = X8) | ((d2term @ X7) != (d2term @ X8))) & ((shinj = $true) <=> ! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh)))) & ((hoasapinj1_lthm = $true) <=> (? [X37 : term] : ((sub @ X37 @ id) != X37) | ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) = (ap @ X40 @ X39)) & (X38 != X40)))) & (hoasinduction_lem1_lthm = $true) & ((sP14 = $true) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3 = $true) <=> ($true = sP13)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction = $true) <=> ($true = sP11)) & ((axshiftcons = $true) <=> ! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((axidl = $true) <=> ! [X197 : subst] : ((comp @ id @ X197) = X197)) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP8)) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X102 : subst > term > subst > $o] : ? [X103 : term > $o] : ! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104))) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & (! [X125 : subst > term > subst > $o,X126 : term] : (? [X132 : term,X133 : term] : (($true = (X125 @ id @ X133 @ id)) & ($true = (X125 @ id @ X132 @ id)) & ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) != $true)) | ($true = (X125 @ id @ X126 @ id)) | ($true = (sP5 @ X125))) <=> (hoasinduction_no_psi_cond = $true)) & (lamnotvar = $true) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) <=> (hoasapinj2 = $true)) & (axvarshift = $true) & (! [X352 : term] : ((sub @ X352 @ id) = X352) <=> (axvarid = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X253 : term] : ? [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) = (X254 @ sh @ one))) & (! [X374 : subst,X375 : term > $o,X376 : term] : ? [X377 : term > $o] : ! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378)) <=> (pushprop_lem0 = $true)) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> ($true = sP4)) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP2)) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3a = $true) <=> ($true = sP0)) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ? [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) != (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) | ? [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) != (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445))) <=> (hoaslaminj = $true)) & ! [X27 : d_subst] : (d_id = X27) & ((pushprop_lem1 = $true) <=> ! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 15.37/3.55 thf(f14,plain,(
% 15.37/3.55 ($true = sP0) <=> ! [X276 : subst > term > subst > $o,X277 : term] : (? [X279 : subst > term > term] : (! [X281 : subst,X282 : term,X283 : subst] : ((X279 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281)) = (sub @ (X279 @ X283 @ X282) @ X281)) & ! [X280 : term] : (($true = (X276 @ id @ (X279 @ id @ X280) @ id)) | ($true != (X276 @ id @ X280 @ id))) & ($true != (X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X278 : term] : (($true = (X276 @ id @ X278 @ id)) & ($true != (X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id))) | ($true = (X276 @ id @ (lam @ X277) @ id)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f15,plain,(
% 15.37/3.55 ! [X216 : subst > term > subst > $o] : (((sP1 @ X216) = $true) <=> ? [X217 : subst > term > term] : (($true != (X216 @ id @ (lam @ (X217 @ sh @ one)) @ id)) & ! [X218 : term,X219 : subst,X220 : subst] : ((sub @ (X217 @ X220 @ X218) @ X219) = (X217 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) & ! [X221 : term] : (($true != (X216 @ id @ X221 @ id)) | ($true = (X216 @ id @ (X217 @ id @ X221) @ id)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f16,plain,(
% 15.37/3.55 ($true = sP2) <=> ! [X214 : term,X215 : term > $o,X216 : subst > term > subst > $o] : (((sP1 @ X216) = $true) | ? [X231 : term] : ((X215 @ X231) != (X216 @ id @ X231 @ id)) | ? [X227 : term,X228 : subst,X229 : subst,X230 : subst] : (($true != (X216 @ X228 @ X227 @ (comp @ X230 @ X229))) & ($true = (X216 @ (comp @ X228 @ X230) @ (sub @ X227 @ X230) @ X229))) | ? [X222 : term] : (($true != (X215 @ (sub @ X214 @ (push @ X222 @ id)))) & ((X215 @ X222) = $true)) | ? [X223 : subst,X224 : subst,X225 : term,X226 : subst] : (($true = (X216 @ X224 @ X225 @ (comp @ X223 @ X226))) & ($true != (X216 @ (comp @ X224 @ X223) @ (sub @ X225 @ X223) @ X226))) | ($true = (X215 @ (lam @ X214))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f17,plain,(
% 15.37/3.55 ($true = sP3) <=> ? [X10 : subst > term > subst > $o,X11 : term] : (! [X17 : term] : (($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) | ($true != (X10 @ id @ X17 @ id))) & ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) != $true) & ! [X12 : subst > term > term] : (? [X16 : term] : (($true != (X10 @ id @ (X12 @ id @ X16) @ id)) & ((X10 @ id @ X16 @ id) = $true)) | ? [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) != (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f18,plain,(
% 15.37/3.55 ($true = sP4) <=> (($true = sP3) | ? [X9 : term] : ((sub @ X9 @ id) != X9) | ! [X18 : subst > term > subst > $o,X19 : term] : (($true = (X18 @ id @ (lam @ X19) @ id)) | ? [X21 : subst > term > term] : (($true != (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id)) & ! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ($true != (X18 @ id @ X22 @ id))) & ! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25))) | ? [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) != $true) & ($true = (X18 @ id @ X20 @ id)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f19,plain,(
% 15.37/3.55 ! [X125 : subst > term > subst > $o] : (($true = (sP5 @ X125)) <=> ? [X127 : subst > term > term] : (($true != (X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) & ! [X128 : term] : (($true != (X125 @ id @ X128 @ id)) | ($true = (X125 @ id @ (X127 @ id @ X128) @ id))) & ! [X129 : subst,X130 : subst,X131 : term] : ((X127 @ (comp @ X129 @ X130) @ (sub @ X131 @ X130)) = (sub @ (X127 @ X129 @ X131) @ X130))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f20,plain,(
% 15.37/3.55 ! [X491 : subst > term > subst > $o] : (($true = (sP6 @ X491)) <=> ? [X492 : subst > term > term] : (($true != (X491 @ id @ (lam @ (X492 @ sh @ one)) @ id)) & ! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X492 @ X494 @ X495) @ X496) = (X492 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496))) & ! [X493 : term] : (($true != (X491 @ id @ X493 @ id)) | ((X491 @ id @ (X492 @ id @ X493) @ id) = $true))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f21,plain,(
% 15.37/3.55 ($true = sP7) <=> ? [X482 : subst > term > subst > $o,X483 : term] : (! [X489 : term] : (($true != (X482 @ id @ X489 @ id)) | ($true = (X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id))) & ((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id) != $true) & ! [X484 : subst > term > term] : (? [X485 : subst,X486 : term,X487 : subst] : ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)) != (sub @ (X484 @ X485 @ X486) @ X487)) | ? [X488 : term] : (($true = (X482 @ id @ X488 @ id)) & ($true != (X482 @ id @ (X484 @ id @ X488) @ id))) | ($true = (X482 @ id @ (lam @ (X484 @ sh @ one)) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f22,plain,(
% 15.37/3.55 ($true = sP8) <=> (? [X481 : term] : ((sub @ X481 @ id) != X481) | ! [X490 : term,X491 : subst > term > subst > $o] : (? [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (($true = (X491 @ X499 @ X501 @ (comp @ X500 @ X498))) & ($true != (X491 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500) @ X498))) | ($true = (sP6 @ X491)) | ($true = (X491 @ id @ (lam @ X490) @ id)) | ? [X497 : term] : (($true = (X491 @ id @ X497 @ id)) & ($true != (X491 @ id @ (sub @ X490 @ (push @ X497 @ id)) @ id))) | ? [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (($true = (X491 @ (comp @ X503 @ X502) @ (sub @ X505 @ X502) @ X504)) & ($true != (X491 @ X503 @ X505 @ (comp @ X502 @ X504))))) | ($true = sP7))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f23,plain,(
% 15.37/3.55 ! [X135 : subst > term > subst > $o] : (($true = (sP9 @ X135)) <=> ? [X140 : subst > term > term] : (! [X141 : term,X142 : subst,X143 : subst] : ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)) = (sub @ (X140 @ X143 @ X141) @ X142)) & ! [X144 : term] : (($true != (X135 @ id @ X144 @ id)) | ($true = (X135 @ id @ (X140 @ id @ X144) @ id))) & ($true != (X135 @ id @ (lam @ (X140 @ sh @ one)) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f24,plain,(
% 15.37/3.55 ! [X135 : subst > term > subst > $o] : (($true = (sP10 @ X135)) <=> ? [X146 : term,X147 : term] : (($true != (X135 @ id @ (ap @ (sub @ X147 @ id) @ X146) @ id)) & ($true = (X135 @ id @ X147 @ id)) & ((X135 @ id @ X146 @ id) = $true)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f25,plain,(
% 15.37/3.55 ($true = sP11) <=> ! [X134 : term,X135 : subst > term > subst > $o] : (? [X136 : subst,X137 : term,X138 : subst,X139 : subst] : (((X135 @ X136 @ X137 @ (comp @ X138 @ X139)) = $true) & ($true != (X135 @ (comp @ X136 @ X138) @ (sub @ X137 @ X138) @ X139))) | ((X135 @ id @ X134 @ id) = $true) | ($true = (sP10 @ X135)) | ($true = (sP9 @ X135)) | ? [X148 : subst,X149 : subst,X150 : subst,X151 : term] : (($true != (X135 @ X148 @ X151 @ (comp @ X149 @ X150))) & ($true = (X135 @ (comp @ X148 @ X149) @ (sub @ X151 @ X149) @ X150))) | ? [X145 : term] : (($true != (X135 @ id @ X145 @ id)) & ($true = (var @ (sub @ X145 @ id)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f26,plain,(
% 15.37/3.55 ! [X198 : subst > term > subst > $o] : (($true = (sP12 @ X198)) <=> ? [X204 : subst > term > term] : (((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) != $true) & ! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ($true != (X198 @ id @ X205 @ id))) & ! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f27,plain,(
% 15.37/3.55 ($true = sP13) <=> ! [X198 : subst > term > subst > $o,X199 : term] : (($true = (X198 @ id @ (lam @ X199) @ id)) | ? [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true != (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) & ($true = (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) | ? [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true = (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) & ($true != (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ? [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) != $true) & ($true = (X198 @ id @ X213 @ id))) | ($true = (sP12 @ X198)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f28,plain,(
% 15.37/3.55 (sP14 = $true) <=> ! [X117 : term,X118 : subst > term > subst > $o] : (($true = (X118 @ id @ (lam @ (sub @ X117 @ (push @ one @ sh))) @ id)) | ? [X120 : subst > term > term] : (! [X121 : term] : (($true = (X118 @ id @ (X120 @ id @ X121) @ id)) | ($true != (X118 @ id @ X121 @ id))) & ($true != (X118 @ id @ (lam @ (X120 @ sh @ one)) @ id)) & ! [X122 : subst,X123 : subst,X124 : term] : ((sub @ (X120 @ X122 @ X124) @ X123) = (X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)))) | ? [X119 : term] : (($true != (X118 @ id @ (sub @ X117 @ (push @ X119 @ id)) @ id)) & ($true = (X118 @ id @ X119 @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f29,plain,(
% 15.37/3.55 ! [X312 : subst > term > subst > $o] : (($true = (sP15 @ X312)) <=> ! [X315 : subst > term > term] : (($true = (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) | ? [X317 : subst,X318 : subst,X319 : term] : ((sub @ (X315 @ X318 @ X319) @ X317) != (X315 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) | ? [X316 : term] : (((X312 @ id @ X316 @ id) = $true) & ($true != (X312 @ id @ (X315 @ id @ X316) @ id)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f30,plain,(
% 15.37/3.55 ! [X329 : subst > term > subst > $o] : (($true = (sP16 @ X329)) <=> ? [X330 : term,X331 : term] : (((X329 @ id @ X330 @ id) = $true) & ($true != (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) & ((X329 @ id @ X331 @ id) = $true)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f31,plain,(
% 15.37/3.55 ! [X329 : subst > term > subst > $o] : (($true = (sP17 @ X329)) <=> ? [X337 : subst > term > term] : (($true != (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) & ! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341))) & ! [X338 : term] : (($true = (X329 @ id @ (X337 @ id @ X338) @ id)) | ((X329 @ id @ X338 @ id) != $true))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f32,plain,(
% 15.37/3.55 ! [X292 : term > $o] : (($true = (sP18 @ X292)) <=> ! [X297 : term,X298 : term] : (($true = (X292 @ (ap @ X298 @ X297))) | ((X292 @ X298) != $true) | ($true != (X292 @ X297))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f33,plain,(
% 15.37/3.55 ! [X299 : subst > term > subst > $o] : (((sP19 @ X299) = $true) <=> ! [X306 : term,X307 : term] : (((X299 @ id @ X307 @ id) != $true) | ($true = (X299 @ id @ (ap @ (sub @ X306 @ id) @ X307) @ id)) | ($true != (X299 @ id @ X306 @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f34,plain,(
% 15.37/3.55 ($true = sP20) <=> ? [X312 : subst > term > subst > $o,X313 : term] : (! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = (X312 @ (comp @ X325 @ X324) @ (sub @ X326 @ X324) @ X327)) | ($true != (X312 @ X325 @ X326 @ (comp @ X324 @ X327)))) & ! [X314 : term] : (($true = (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | ((X312 @ id @ X314 @ id) != $true)) & ($true != (X312 @ id @ (lam @ X313) @ id)) & ($true = (sP15 @ X312)) & ! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (($true != (X312 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ($true = (X312 @ X322 @ X321 @ (comp @ X323 @ X320)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f35,plain,(
% 15.37/3.55 ($true = sP21) <=> ! [X328 : term,X329 : subst > term > subst > $o] : (? [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true = (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) & ($true != (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) | ? [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true = (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) & ($true != (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) | ? [X336 : term] : (($true != (X329 @ id @ X336 @ id)) & ((var @ (sub @ X336 @ id)) = $true)) | ($true = (sP17 @ X329)) | ($true = (sP16 @ X329)) | ($true = (X329 @ id @ X328 @ id)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f36,plain,(
% 15.37/3.55 ($true = sP22) <=> ? [X292 : term > $o,X293 : term] : (($true = (sP18 @ X292)) & ! [X294 : term] : (? [X295 : term] : (((X292 @ X295) = $true) & ($true != (X292 @ (sub @ X294 @ (push @ X295 @ id))))) | ($true = (X292 @ (lam @ X294)))) & ($true != (X292 @ X293)) & ! [X296 : term] : (($true = (X292 @ X296)) | ($true != (var @ X296))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f37,plain,(
% 15.37/3.55 ($true = sP23) <=> (? [X299 : subst > term > subst > $o,X300 : term,X301 : term] : (((sP19 @ X299) = $true) & ! [X308 : term,X309 : subst,X310 : subst,X311 : subst] : (($true = (X299 @ (comp @ X311 @ X309) @ (sub @ X308 @ X309) @ X310)) | ($true != (X299 @ X311 @ X308 @ (comp @ X309 @ X310)))) & ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (($true = (X299 @ X305 @ X303 @ (comp @ X302 @ X304))) | ($true != (X299 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304))) & ((X299 @ id @ X300 @ id) = $true) & ($true = (X299 @ id @ X301 @ id)) & ($true != (X299 @ id @ (ap @ X300 @ X301) @ id))) | ($true = sP22) | ($true = sP21) | ($true = sP20))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f38,plain,(
% 15.37/3.55 ! [X105 : term > $o] : (($true = (sP24 @ X105)) <=> ? [X108 : term,X109 : term] : (($true = (X105 @ X108)) & ($true = (X105 @ X109)) & ($true != (X105 @ (ap @ X109 @ X108)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f39,plain,(
% 15.37/3.55 ($true = sP25) <=> ! [X105 : term > $o,X106 : term] : (? [X110 : term] : (((X105 @ (lam @ X110)) != $true) & ! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ($true != (X105 @ X111)))) | ($true = (X105 @ X106)) | ? [X107 : term] : (($true = (var @ X107)) & ((X105 @ X107) != $true)) | ($true = (sP24 @ X105)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f40,plain,(
% 15.37/3.55 ($true = sP26) <=> (? [X363 : term] : ((sub @ X363 @ id) != X363) | ? [X359 : term] : ! [X360 : subst > term > term] : ? [X361 : term,X362 : subst] : ((X360 @ X362 @ X361) != (sub @ X359 @ (push @ X361 @ X362))) | ! [X364 : term,X365 : term > $o,X366 : subst > term > subst > $o] : (? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X369 @ X373 @ X371) @ X372) = (X369 @ (comp @ X373 @ X372) @ (sub @ X371 @ X372))) & ! [X370 : term] : (((X366 @ id @ (X369 @ id @ X370) @ id) = $true) | ($true != (X366 @ id @ X370 @ id))) & ($true != (X366 @ id @ (lam @ (X369 @ sh @ one)) @ id))) | ? [X368 : term] : (($true != (X365 @ (sub @ X364 @ (push @ X368 @ id)))) & ($true = (X365 @ X368))) | ($true = (X365 @ (lam @ X364))) | ? [X367 : term] : ((X366 @ id @ X367 @ id) != (X365 @ X367))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f41,plain,(
% 15.37/3.55 ! [X46 : subst > term > subst > $o] : (($true = (sP27 @ X46)) <=> ? [X49 : term,X50 : term] : (((X46 @ id @ X49 @ id) = $true) & ((X46 @ id @ X50 @ id) = $true) & ($true != (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f42,plain,(
% 15.37/3.55 ($true = sP28) <=> ! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (($true != (X46 @ id @ X47 @ id)) | ($true != (X46 @ id @ X48 @ id)) | ? [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (($true = (X46 @ X52 @ X54 @ (comp @ X51 @ X53))) & ($true != (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53))) | ? [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57)) & ($true != (X46 @ X58 @ X55 @ (comp @ X56 @ X57)))) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ($true = (sP27 @ X46)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f43,plain,(
% 15.37/3.55 ! [X422 : subst > term > subst > $o] : (($true = (sP29 @ X422)) <=> ? [X432 : term,X433 : term] : (($true = (X422 @ id @ X433 @ id)) & ($true != (X422 @ id @ (ap @ (sub @ X433 @ id) @ X432) @ id)) & ((X422 @ id @ X432 @ id) = $true)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f44,plain,(
% 15.37/3.55 ($true = sP30) <=> ! [X419 : term,X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (? [X428 : subst,X429 : term,X430 : subst,X431 : subst] : (((X422 @ X431 @ X429 @ (comp @ X430 @ X428)) = $true) & ($true != (X422 @ (comp @ X431 @ X430) @ (sub @ X429 @ X430) @ X428))) | ? [X423 : subst,X424 : term,X425 : subst,X426 : subst] : (($true = (X422 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426) @ X423)) & ($true != (X422 @ X425 @ X424 @ (comp @ X426 @ X423)))) | ($true = (sP29 @ X422)) | ? [X427 : term] : ((X422 @ id @ X427 @ id) != (X421 @ X427)) | ($true = (X421 @ (ap @ X420 @ X419))) | ($true != (X421 @ X419)) | ($true != (X421 @ X420)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f45,plain,(
% 15.37/3.55 ($true = sP31) <=> ! [X460 : term > $o,X461 : subst > term > subst > $o,X462 : term] : (? [X463 : term] : ((X461 @ id @ X463 @ id) != (X460 @ X463)) | ? [X465 : subst > term > term] : (($true != (X461 @ id @ (lam @ (X465 @ sh @ one)) @ id)) & ! [X466 : term,X467 : subst,X468 : subst] : ((sub @ (X465 @ X467 @ X466) @ X468) = (X465 @ (comp @ X467 @ X468) @ (sub @ X466 @ X468))) & ! [X469 : term] : (($true != (X461 @ id @ X469 @ id)) | ($true = (X461 @ id @ (X465 @ id @ X469) @ id)))) | ? [X464 : term] : (($true = (X460 @ X464)) & ($true != (X460 @ (sub @ X462 @ (push @ X464 @ id))))) | ($true = (X460 @ (lam @ X462))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f46,plain,(
% 15.37/3.55 ! [X528 : subst > term > subst > $o] : (($true = (sP32 @ X528)) <=> ? [X529 : term,X530 : term] : (($true != (X528 @ id @ (ap @ (sub @ X529 @ id) @ X530) @ id)) & ($true = (X528 @ id @ X529 @ id)) & ($true = (X528 @ id @ X530 @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f47,plain,(
% 15.37/3.55 ! [X509 : term > $o] : (($true = (sP33 @ X509)) <=> ! [X511 : term,X512 : term] : (((X509 @ X511) != $true) | ($true = (X509 @ (ap @ X512 @ X511))) | ($true != (X509 @ X512))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f48,plain,(
% 15.37/3.55 ($true = sP34) <=> ? [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (! [X522 : subst > term > term] : (($true = (X518 @ id @ (lam @ (X522 @ sh @ one)) @ id)) | ? [X524 : term,X525 : subst,X526 : subst] : ((X522 @ (comp @ X525 @ X526) @ (sub @ X524 @ X526)) != (sub @ (X522 @ X525 @ X524) @ X526)) | ? [X523 : term] : (($true != (X518 @ id @ (X522 @ id @ X523) @ id)) & ((X518 @ id @ X523 @ id) = $true))) & ($true != (X517 @ (lam @ X519))) & ! [X521 : term] : (((X517 @ (sub @ X519 @ (push @ X521 @ id))) = $true) | ($true != (X517 @ X521))) & ! [X520 : term] : ((X517 @ X520) = (X518 @ id @ X520 @ id)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f49,plain,(
% 15.37/3.55 ($true = sP35) <=> ! [X527 : term,X528 : subst > term > subst > $o] : (($true = (X528 @ id @ X527 @ id)) | ? [X531 : subst > term > term] : (! [X532 : term] : (($true != (X528 @ id @ X532 @ id)) | ($true = (X528 @ id @ (X531 @ id @ X532) @ id))) & ($true != (X528 @ id @ (lam @ (X531 @ sh @ one)) @ id)) & ! [X533 : term,X534 : subst,X535 : subst] : ((sub @ (X531 @ X534 @ X533) @ X535) = (X531 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | ($true = (sP32 @ X528)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f50,plain,(
% 15.37/3.55 ($true = sP36) <=> (($true = sP34) | ? [X509 : term > $o,X510 : term] : (! [X515 : term] : (($true != (var @ X515)) | ($true = (X509 @ X515))) & ($true != (X509 @ X510)) & ($true = (sP33 @ X509)) & ! [X513 : term] : (? [X514 : term] : (($true != (X509 @ (sub @ X513 @ (push @ X514 @ id)))) & ($true = (X509 @ X514))) | ($true = (X509 @ (lam @ X513))))) | ? [X506 : subst > term > subst > $o] : ! [X507 : term > $o] : ? [X508 : term] : ((X506 @ id @ X508 @ id) != (X507 @ X508)) | ? [X516 : term] : ((sub @ X516 @ id) != X516) | ($true = sP35))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f51,plain,(
% 15.37/3.55 ($true = sP37) <=> (? [X168 : term,X169 : subst] : ((sub @ one @ (push @ X168 @ X169)) != X168) | ? [X170 : term,X171 : subst] : ((comp @ sh @ (push @ X170 @ X171)) != X171) | ! [X174 : subst > term > term,X175 : term,X176 : subst,X177 : subst > term > term] : (((X174 @ X176 @ X175) = (X177 @ X176 @ X175)) | ((lam @ (X177 @ sh @ one)) != (lam @ (X174 @ sh @ one))) | ? [X181 : subst,X182 : subst,X183 : term] : ((sub @ (X177 @ X182 @ X183) @ X181) != (X177 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) | ? [X178 : subst,X179 : subst,X180 : term] : ((sub @ (X174 @ X178 @ X180) @ X179) != (X174 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179)))) | ? [X172 : term,X173 : term] : (((lam @ X173) = (lam @ X172)) & (X172 != X173)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f52,plain,(
% 15.37/3.55 (sP38 = $true) <=> ! [X184 : subst > term > subst > $o,X185 : term] : (? [X187 : subst > term > term,X188 : term] : (! [X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189)) = (sub @ X188 @ (push @ (sub @ X190 @ X189) @ (comp @ X191 @ X189)))) & ! [X192 : subst,X193 : term,X194 : subst] : ((sub @ (sub @ X188 @ (push @ X193 @ X194)) @ X192) = (sub @ (X187 @ X194 @ X193) @ X192)) & ! [X195 : term] : (($true != (X184 @ id @ X195 @ id)) | ($true = (X184 @ id @ (X187 @ id @ X195) @ id))) & ($true != (X184 @ id @ (lam @ (X187 @ sh @ one)) @ id))) | ($true = (X184 @ id @ (lam @ (sub @ X185 @ (push @ one @ sh))) @ id)) | ? [X186 : term] : (($true = (X184 @ id @ X186 @ id)) & ($true != (X184 @ id @ (sub @ X185 @ (push @ X186 @ id)) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f53,plain,(
% 15.37/3.55 ! [X396 : term > $o] : (($true = (sP39 @ X396)) <=> ! [X398 : term,X399 : term] : (($true != (X396 @ X399)) | ($true != (X396 @ X398)) | ($true = (X396 @ (ap @ X398 @ X399)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f54,plain,(
% 15.37/3.55 ! [X403 : term > $o] : (((sP40 @ X403) = $true) <=> ? [X407 : term,X408 : term] : (($true != (X403 @ (ap @ X407 @ X408))) & ((X403 @ X408) = $true) & ($true = (X403 @ X407))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f55,plain,(
% 15.37/3.55 ($true = sP41) <=> ! [X402 : term,X403 : term > $o] : (? [X405 : term] : (! [X406 : term] : (($true != (X403 @ X406)) | ($true = (X403 @ (sub @ X405 @ (push @ X406 @ id))))) & ($true != (X403 @ (lam @ X405)))) | ((sP40 @ X403) = $true) | ? [X404 : term] : (((var @ X404) = $true) & ($true != (X403 @ X404))) | ($true = (X403 @ X402)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f56,plain,(
% 15.37/3.55 ($true = sP42) <=> (($true = sP41) | ? [X393 : term] : ((sub @ X393 @ id) != X393) | ? [X394 : subst,X395 : term,X396 : term > $o] : (($true != (X396 @ (sub @ X395 @ X394))) & ! [X400 : term] : (? [X401 : term] : (($true = (X396 @ X401)) & ((X396 @ (sub @ X400 @ (push @ X401 @ id))) != $true)) | ($true = (X396 @ (lam @ X400)))) & ($true = (sP39 @ X396)) & ! [X397 : term] : (($true = (X396 @ (sub @ X397 @ X394))) | ($true != (var @ X397)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f57,plain,(
% 15.37/3.55 ! [X28 : term > $o] : (($true = (sP43 @ X28)) <=> ? [X31 : term,X32 : term] : (($true = (X28 @ X31)) & ((X28 @ X32) = $true) & ($true != (X28 @ (ap @ X32 @ X31)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f58,plain,(
% 15.37/3.55 ($true = sP44) <=> ! [X160 : term,X161 : subst > term > subst > $o] : (? [X162 : subst > term > term] : (($true != (X161 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X162 @ X165 @ X164) @ X163) = (X162 @ (comp @ X165 @ X163) @ (sub @ X164 @ X163))) & ! [X166 : term] : (($true = (X161 @ id @ (X162 @ id @ X166) @ id)) | ($true != (X161 @ id @ X166 @ id)))) | ($true = (X161 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) | ? [X167 : term] : (($true != (X161 @ id @ (sub @ X160 @ (push @ X167 @ id)) @ id)) & ($true = (X161 @ id @ X167 @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f59,plain,(
% 15.37/3.55 ! [X235 : subst > term > subst > $o] : (($true = (sP45 @ X235)) <=> ? [X241 : subst > term > term] : (($true != (X235 @ id @ (lam @ (X241 @ sh @ one)) @ id)) & ! [X242 : term,X243 : subst,X244 : subst] : ((X241 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243)) = (sub @ (X241 @ X244 @ X242) @ X243)) & ! [X245 : term] : (($true != (X235 @ id @ X245 @ id)) | ($true = (X235 @ id @ (X241 @ id @ X245) @ id)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f60,plain,(
% 15.37/3.55 ($true = sP46) <=> (! [X233 : term,X234 : term > $o,X235 : subst > term > subst > $o] : (? [X240 : term] : (((X234 @ X240) = $true) & ((X234 @ (sub @ X233 @ (push @ X240 @ id))) != $true)) | ? [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (($true = (X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237) @ X236)) & ((X235 @ X238 @ X239 @ (comp @ X237 @ X236)) != $true)) | ? [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (($true = (X235 @ X247 @ X248 @ (comp @ X249 @ X250))) & ($true != (X235 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249) @ X250))) | ((X234 @ (lam @ X233)) = $true) | ? [X246 : term] : ((X234 @ X246) != (X235 @ id @ X246 @ id)) | ($true = (sP45 @ X235))) | ? [X232 : term] : ((sub @ X232 @ id) != X232))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f61,plain,(
% 15.37/3.55 ! [X85 : subst > term > subst > $o] : (($true = (sP47 @ X85)) <=> ? [X97 : subst > term > term] : (! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100)) & ! [X98 : term] : (($true = (X85 @ id @ (X97 @ id @ X98) @ id)) | ((X85 @ id @ X98 @ id) != $true)) & ($true != (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f62,plain,(
% 15.37/3.55 ! [X85 : subst > term > subst > $o] : (((sP48 @ X85) = $true) <=> ? [X86 : term,X87 : term] : (($true = (X85 @ id @ X87 @ id)) & ($true = (X85 @ id @ X86 @ id)) & ((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) != $true)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f63,plain,(
% 15.37/3.55 ! [X67 : term > $o] : (($true = (sP49 @ X67)) <=> ! [X69 : term,X70 : term] : (((X67 @ X70) != $true) | ((X67 @ (ap @ X70 @ X69)) = $true) | ($true != (X67 @ X69))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f64,plain,(
% 15.37/3.55 (sP50 = $true) <=> ! [X84 : term,X85 : subst > term > subst > $o] : (? [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (($true != (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95)) & ($true = (X85 @ X96 @ X94 @ (comp @ X93 @ X95)))) | ((sP48 @ X85) = $true) | ? [X88 : term] : (($true = (var @ (sub @ X88 @ id))) & ($true != (X85 @ id @ X88 @ id))) | ($true = (sP47 @ X85)) | ($true = (X85 @ id @ X84 @ id)) | ? [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) = $true) & ($true != (X85 @ X90 @ X91 @ (comp @ X92 @ X89)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f65,plain,(
% 15.37/3.55 (sP51 = $true) <=> ? [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (! [X78 : subst > term > term] : (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ? [X82 : term] : (($true != (X75 @ id @ (X78 @ id @ X82) @ id)) & ($true = (X75 @ id @ X82 @ id))) | ? [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) != (sub @ (X78 @ X81 @ X79) @ X80))) & ! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) & ! [X83 : term] : (($true != (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id))))) & ($true != (X74 @ (lam @ X76))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f66,plain,(
% 15.37/3.55 (sP52 = $true) <=> (? [X73 : term] : ((sub @ X73 @ id) != X73) | (sP51 = $true) | ? [X66 : term,X67 : term > $o] : (($true = (sP49 @ X67)) & ! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ? [X72 : term] : (((X67 @ X72) = $true) & ($true != (X67 @ (sub @ X71 @ (push @ X72 @ id)))))) & ($true != (X67 @ X66)) & ! [X68 : term] : (($true = (X67 @ X68)) | ($true != (var @ X68)))) | (sP50 = $true) | ? [X63 : subst > term > subst > $o] : ! [X64 : term > $o] : ? [X65 : term] : ((X64 @ X65) != (X63 @ id @ X65 @ id)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f67,plain,(
% 15.37/3.55 ! [X268 : term > $o] : (($true = (sP53 @ X268)) <=> ? [X269 : term,X270 : term] : (($true = (X268 @ X270)) & ($true != (X268 @ (ap @ X270 @ X269))) & ($true = (X268 @ X269))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f68,plain,(
% 15.37/3.55 ! [X260 : term > $o] : (((sP54 @ X260) = $true) <=> ! [X263 : term,X264 : term] : (($true != (X260 @ X264)) | ($true != (X260 @ X263)) | ($true = (X260 @ (ap @ X264 @ X263)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f69,plain,(
% 15.37/3.55 ($true = sP55) <=> ! [X266 : term,X267 : subst,X268 : term > $o] : (? [X271 : term] : (($true != (X268 @ (lam @ X271))) & ! [X272 : term] : (($true = (X268 @ (sub @ X271 @ (push @ X272 @ id)))) | ($true != (X268 @ X272)))) | ? [X273 : term] : (($true != (X268 @ (sub @ X273 @ X267))) & ($true = (var @ X273))) | ($true = (sP53 @ X268)) | ($true = (X268 @ (sub @ X266 @ X267))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f70,plain,(
% 15.37/3.55 ($true = sP56) <=> (? [X259 : subst] : ((comp @ X259 @ id) != X259) | ? [X255 : term,X256 : subst] : ((sub @ one @ (push @ X255 @ X256)) != X255) | ? [X257 : term,X258 : subst] : ((comp @ sh @ (push @ X257 @ X258)) != X258) | ? [X260 : term > $o,X261 : term] : (! [X265 : term] : (($true = (X260 @ X265)) | ($true != (var @ X265))) & ((sP54 @ X260) = $true) & ! [X262 : term] : (($true != (X260 @ X262)) | ($true = (X260 @ (lam @ X262)))) & ($true != (X260 @ X261))) | ($true = sP55))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f71,plain,(
% 15.37/3.55 ! [X381 : term > $o] : (($true = (sP57 @ X381)) <=> ? [X387 : term,X388 : term] : (($true = (X381 @ X387)) & ($true != (X381 @ (ap @ X388 @ X387))) & ($true = (X381 @ X388))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f72,plain,(
% 15.37/3.55 ($true = sP58) <=> ! [X381 : term > $o,X382 : subst,X383 : term] : (? [X386 : term] : (($true = (var @ X386)) & ($true != (X381 @ (sub @ X386 @ X382)))) | ($true = (X381 @ (sub @ X383 @ X382))) | ($true = (sP57 @ X381)) | ? [X384 : term] : (($true != (X381 @ (lam @ X384))) & ! [X385 : term] : (($true = (X381 @ (sub @ X384 @ (push @ X385 @ id)))) | ($true != (X381 @ X385)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.37/3.55 thf(f13,plain,(
% 15.37/3.55 (hoasinduction_lem1 = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & (! [X381 : term > $o,X382 : subst,X383 : term] : (? [X386 : term] : (($true = (var @ X386)) & ($true != (X381 @ (sub @ X386 @ X382)))) | ($true = (X381 @ (sub @ X383 @ X382))) | ? [X387 : term,X388 : term] : (($true = (X381 @ X387)) & ($true != (X381 @ (ap @ X388 @ X387))) & ($true = (X381 @ X388))) | ? [X384 : term] : (($true != (X381 @ (lam @ X384))) & ! [X385 : term] : (($true = (X381 @ (sub @ X384 @ (push @ X385 @ id)))) | ($true != (X381 @ X385))))) <=> (induction2lem = $true)) & ((axscons = $true) <=> ! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157)) & (ulamvar1 != $true) & ((induction2lem_lthm = $true) <=> (? [X259 : subst] : ((comp @ X259 @ id) != X259) | ? [X255 : term,X256 : subst] : ((sub @ one @ (push @ X255 @ X256)) != X255) | ? [X257 : term,X258 : subst] : ((comp @ sh @ (push @ X257 @ X258)) != X258) | ? [X260 : term > $o,X261 : term] : (! [X265 : term] : (($true = (X260 @ X265)) | ($true != (var @ X265))) & ! [X263 : term,X264 : term] : (($true != (X260 @ X264)) | ($true != (X260 @ X263)) | ($true = (X260 @ (ap @ X264 @ X263)))) & ! [X262 : term] : (($true != (X260 @ X262)) | ($true = (X260 @ (lam @ X262)))) & ($true != (X260 @ X261))) | ! [X266 : term,X267 : subst,X268 : term > $o] : (? [X271 : term] : (($true != (X268 @ (lam @ X271))) & ! [X272 : term] : (($true = (X268 @ (sub @ X271 @ (push @ X272 @ id)))) | ($true != (X268 @ X272)))) | ? [X273 : term] : (($true != (X268 @ (sub @ X273 @ X267))) & ($true = (var @ X273))) | ? [X269 : term,X270 : term] : (($true = (X268 @ X270)) & ($true != (X268 @ (ap @ X270 @ X269))) & ($true = (X268 @ X269))) | ($true = (X268 @ (sub @ X266 @ X267)))))) & (hoasapinj1_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ? [X156 : term] : ((X153 @ X156) != (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) <=> (pushprop_lem1v2 = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) <=> ! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417)))) & ((? [X73 : term] : ((sub @ X73 @ id) != X73) | ? [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (! [X78 : subst > term > term] : (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ? [X82 : term] : (($true != (X75 @ id @ (X78 @ id @ X82) @ id)) & ($true = (X75 @ id @ X82 @ id))) | ? [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) != (sub @ (X78 @ X81 @ X79) @ X80))) & ! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) & ! [X83 : term] : (($true != (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id))))) & ($true != (X74 @ (lam @ X76)))) | ? [X66 : term,X67 : term > $o] : (! [X69 : term,X70 : term] : (((X67 @ X70) != $true) | ((X67 @ (ap @ X70 @ X69)) = $true) | ($true != (X67 @ X69))) & ! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ? [X72 : term] : (((X67 @ X72) = $true) & ($true != (X67 @ (sub @ X71 @ (push @ X72 @ id)))))) & ($true != (X67 @ X66)) & ! [X68 : term] : (($true = (X67 @ X68)) | ($true != (var @ X68)))) | ! [X84 : term,X85 : subst > term > subst > $o] : (? [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (($true != (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95)) & ($true = (X85 @ X96 @ X94 @ (comp @ X93 @ X95)))) | ? [X86 : term,X87 : term] : (($true = (X85 @ id @ X87 @ id)) & ($true = (X85 @ id @ X86 @ id)) & ((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) != $true)) | ? [X88 : term] : (($true = (var @ (sub @ X88 @ id))) & ($true != (X85 @ id @ X88 @ id))) | ? [X97 : subst > term > term] : (! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100)) & ! [X98 : term] : (($true = (X85 @ id @ (X97 @ id @ X98) @ id)) | ((X85 @ id @ X98 @ id) != $true)) & ($true != (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id))) | ($true = (X85 @ id @ X84 @ id)) | ? [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) = $true) & ($true != (X85 @ X90 @ X91 @ (comp @ X92 @ X89))))) | ? [X63 : subst > term > subst > $o] : ! [X64 : term > $o] : ? [X65 : term] : ((X64 @ X65) != (X63 @ id @ X65 @ id))) <=> (hoasinduction_lthm_3 = $true)) & ((! [X233 : term,X234 : term > $o,X235 : subst > term > subst > $o] : (? [X240 : term] : (((X234 @ X240) = $true) & ((X234 @ (sub @ X233 @ (push @ X240 @ id))) != $true)) | ? [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (($true = (X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237) @ X236)) & ((X235 @ X238 @ X239 @ (comp @ X237 @ X236)) != $true)) | ? [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (($true = (X235 @ X247 @ X248 @ (comp @ X249 @ X250))) & ($true != (X235 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249) @ X250))) | ((X234 @ (lam @ X233)) = $true) | ? [X246 : term] : ((X234 @ X246) != (X235 @ id @ X246 @ id)) | ? [X241 : subst > term > term] : (($true != (X235 @ id @ (lam @ (X241 @ sh @ one)) @ id)) & ! [X242 : term,X243 : subst,X244 : subst] : ((X241 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243)) = (sub @ (X241 @ X244 @ X242) @ X243)) & ! [X245 : term] : (($true != (X235 @ id @ X245 @ id)) | ($true = (X235 @ id @ (X241 @ id @ X245) @ id))))) | ? [X232 : term] : ((sub @ X232 @ id) != X232)) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) != (d2subst @ X291)) | (X290 = X291)) & (hoasinduction_lem1v2 = $true) & ((axidr = $true) <=> ! [X196 : subst] : ((comp @ X196 @ id) = X196)) & (hoasapnotvar = $true) & (pushprop_lem1v2_gthm = $true) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem3v2 = $true) & (! [X160 : term,X161 : subst > term > subst > $o] : (? [X162 : subst > term > term] : (($true != (X161 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X162 @ X165 @ X164) @ X163) = (X162 @ (comp @ X165 @ X163) @ (sub @ X164 @ X163))) & ! [X166 : term] : (($true = (X161 @ id @ (X162 @ id @ X166) @ id)) | ($true != (X161 @ id @ X166 @ id)))) | ($true = (X161 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) | ? [X167 : term] : (($true != (X161 @ id @ (sub @ X160 @ (push @ X167 @ id)) @ id)) & ($true = (X161 @ id @ X167 @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X434 : term] : ? [X435 : subst > term > term] : ! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((axvarcons = $true) <=> ! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470)) & (pushprop = $true) & (hoasinduction_lem3v2_gthm = $true) & ((? [X456 : subst] : ((comp @ id @ X456) != X456) | ? [X457 : subst] : ((comp @ X457 @ id) != X457) | (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458))) <=> (substmonoid_lthm = $true)) & (ulamvarsh = $true) & (! [X536 : term] : ? [X537 : subst > term > term] : ! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538)) <=> (hoasinduction_lem3v2_f = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) = (ap @ X411 @ X410)) & (X409 != X410)) | ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)))) & ((hoasapinj1 = $true) <=> ! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353)))) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X28 : term > $o,X29 : term] : (? [X31 : term,X32 : term] : (($true = (X28 @ X31)) & ((X28 @ X32) = $true) & ($true != (X28 @ (ap @ X32 @ X31)))) | ? [X33 : term] : (((X28 @ X33) = $true) & ((X28 @ (lam @ X33)) != $true)) | ? [X30 : term] : (($true = (var @ X30)) & ((X28 @ X30) != $true)) | ($true = (X28 @ X29))) <=> (induction = $true)) & ((induction2_lthm = $true) <=> (! [X402 : term,X403 : term > $o] : (? [X405 : term] : (! [X406 : term] : (($true != (X403 @ X406)) | ($true = (X403 @ (sub @ X405 @ (push @ X406 @ id))))) & ($true != (X403 @ (lam @ X405)))) | ? [X407 : term,X408 : term] : (($true != (X403 @ (ap @ X407 @ X408))) & ((X403 @ X408) = $true) & ($true = (X403 @ X407))) | ? [X404 : term] : (((var @ X404) = $true) & ($true != (X403 @ X404))) | ($true = (X403 @ X402))) | ? [X393 : term] : ((sub @ X393 @ id) != X393) | ? [X394 : subst,X395 : term,X396 : term > $o] : (($true != (X396 @ (sub @ X395 @ X394))) & ! [X400 : term] : (? [X401 : term] : (($true = (X396 @ X401)) & ((X396 @ (sub @ X400 @ (push @ X401 @ id))) != $true)) | ($true = (X396 @ (lam @ X400)))) & ! [X398 : term,X399 : term] : (($true != (X396 @ X399)) | ($true != (X396 @ X398)) | ($true = (X396 @ (ap @ X398 @ X399)))) & ! [X397 : term] : (($true = (X396 @ (sub @ X397 @ X394))) | ($true != (var @ X397)))))) & ! [X453 : d_term] : (d_one = X453) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & (! [X184 : subst > term > subst > $o,X185 : term] : (? [X187 : subst > term > term,X188 : term] : (! [X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189)) = (sub @ X188 @ (push @ (sub @ X190 @ X189) @ (comp @ X191 @ X189)))) & ! [X192 : subst,X193 : term,X194 : subst] : ((sub @ (sub @ X188 @ (push @ X193 @ X194)) @ X192) = (sub @ (X187 @ X194 @ X193) @ X192)) & ! [X195 : term] : (($true != (X184 @ id @ X195 @ id)) | ($true = (X184 @ id @ (X187 @ id @ X195) @ id))) & ($true != (X184 @ id @ (lam @ (X187 @ sh @ one)) @ id))) | ($true = (X184 @ id @ (lam @ (sub @ X185 @ (push @ one @ sh))) @ id)) | ? [X186 : term] : (($true = (X184 @ id @ X186 @ id)) & ($true != (X184 @ id @ (sub @ X185 @ (push @ X186 @ id)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar_gthm = $true) & ((? [X168 : term,X169 : subst] : ((sub @ one @ (push @ X168 @ X169)) != X168) | ? [X170 : term,X171 : subst] : ((comp @ sh @ (push @ X170 @ X171)) != X171) | ! [X174 : subst > term > term,X175 : term,X176 : subst,X177 : subst > term > term] : (((X174 @ X176 @ X175) = (X177 @ X176 @ X175)) | ((lam @ (X177 @ sh @ one)) != (lam @ (X174 @ sh @ one))) | ? [X181 : subst,X182 : subst,X183 : term] : ((sub @ (X177 @ X182 @ X183) @ X181) != (X177 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) | ? [X178 : subst,X179 : subst,X180 : term] : ((sub @ (X174 @ X178 @ X180) @ X179) != (X174 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179)))) | ? [X172 : term,X173 : term] : (((lam @ X173) = (lam @ X172)) & (X172 != X173))) <=> (hoaslaminj_lthm = $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((pushprop_lem1_lthm = $true) <=> (? [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) != X474) | ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))) | ? [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) != X473))) & ((termmset_lthm = $true) <=> (? [X251 : term] : ((sub @ X251 @ id) != X251) | ! [X252 : term] : ((sub @ X252 @ id) = X252))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (! [X522 : subst > term > term] : (($true = (X518 @ id @ (lam @ (X522 @ sh @ one)) @ id)) | ? [X524 : term,X525 : subst,X526 : subst] : ((X522 @ (comp @ X525 @ X526) @ (sub @ X524 @ X526)) != (sub @ (X522 @ X525 @ X524) @ X526)) | ? [X523 : term] : (($true != (X518 @ id @ (X522 @ id @ X523) @ id)) & ((X518 @ id @ X523 @ id) = $true))) & ($true != (X517 @ (lam @ X519))) & ! [X521 : term] : (((X517 @ (sub @ X519 @ (push @ X521 @ id))) = $true) | ($true != (X517 @ X521))) & ! [X520 : term] : ((X517 @ X520) = (X518 @ id @ X520 @ id))) | ? [X509 : term > $o,X510 : term] : (! [X515 : term] : (($true != (var @ X515)) | ($true = (X509 @ X515))) & ($true != (X509 @ X510)) & ! [X511 : term,X512 : term] : (((X509 @ X511) != $true) | ($true = (X509 @ (ap @ X512 @ X511))) | ($true != (X509 @ X512))) & ! [X513 : term] : (? [X514 : term] : (($true != (X509 @ (sub @ X513 @ (push @ X514 @ id)))) & ($true = (X509 @ X514))) | ($true = (X509 @ (lam @ X513))))) | ? [X506 : subst > term > subst > $o] : ! [X507 : term > $o] : ? [X508 : term] : ((X506 @ id @ X508 @ id) != (X507 @ X508)) | ? [X516 : term] : ((sub @ X516 @ id) != X516) | ! [X527 : term,X528 : subst > term > subst > $o] : (($true = (X528 @ id @ X527 @ id)) | ? [X531 : subst > term > term] : (! [X532 : term] : (($true != (X528 @ id @ X532 @ id)) | ($true = (X528 @ id @ (X531 @ id @ X532) @ id))) & ($true != (X528 @ id @ (lam @ (X531 @ sh @ one)) @ id)) & ! [X533 : term,X534 : subst,X535 : subst] : ((sub @ (X531 @ X534 @ X533) @ X535) = (X531 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | ? [X529 : term,X530 : term] : (($true != (X528 @ id @ (ap @ (sub @ X529 @ id) @ X530) @ id)) & ($true = (X528 @ id @ X529 @ id)) & ($true = (X528 @ id @ X530 @ id)))))) & (hoasinduction_lem3a_gthm = $true) & (! [X460 : term > $o,X461 : subst > term > subst > $o,X462 : term] : (? [X463 : term] : ((X461 @ id @ X463 @ id) != (X460 @ X463)) | ? [X465 : subst > term > term] : (($true != (X461 @ id @ (lam @ (X465 @ sh @ one)) @ id)) & ! [X466 : term,X467 : subst,X468 : subst] : ((sub @ (X465 @ X467 @ X466) @ X468) = (X465 @ (comp @ X467 @ X468) @ (sub @ X466 @ X468))) & ! [X469 : term] : (($true != (X461 @ id @ X469 @ id)) | ($true = (X461 @ id @ (X465 @ id @ X469) @ id)))) | ? [X464 : term] : (($true = (X460 @ X464)) & ($true != (X460 @ (sub @ X462 @ (push @ X464 @ id))))) | ($true = (X460 @ (lam @ X462)))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) <=> (! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357))) & ((hoasinduction_lem2v2 = $true) <=> ! [X419 : term,X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (? [X428 : subst,X429 : term,X430 : subst,X431 : subst] : (((X422 @ X431 @ X429 @ (comp @ X430 @ X428)) = $true) & ($true != (X422 @ (comp @ X431 @ X430) @ (sub @ X429 @ X430) @ X428))) | ? [X423 : subst,X424 : term,X425 : subst,X426 : subst] : (($true = (X422 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426) @ X423)) & ($true != (X422 @ X425 @ X424 @ (comp @ X426 @ X423)))) | ? [X432 : term,X433 : term] : (($true = (X422 @ id @ X433 @ id)) & ($true != (X422 @ id @ (ap @ (sub @ X433 @ id) @ X432) @ id)) & ((X422 @ id @ X432 @ id) = $true)) | ? [X427 : term] : ((X422 @ id @ X427 @ id) != (X421 @ X427)) | ($true = (X421 @ (ap @ X420 @ X419))) | ($true != (X421 @ X419)) | ($true != (X421 @ X420)))) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (($true != (X46 @ id @ X47 @ id)) | ($true != (X46 @ id @ X48 @ id)) | ? [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (($true = (X46 @ X52 @ X54 @ (comp @ X51 @ X53))) & ($true != (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53))) | ? [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57)) & ($true != (X46 @ X58 @ X55 @ (comp @ X56 @ X57)))) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ? [X49 : term,X50 : term] : (((X46 @ id @ X49 @ id) = $true) & ((X46 @ id @ X50 @ id) = $true) & ($true != (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id)))) <=> (hoasinduction_lem2 = $true)) & ((? [X363 : term] : ((sub @ X363 @ id) != X363) | ? [X359 : term] : ! [X360 : subst > term > term] : ? [X361 : term,X362 : subst] : ((X360 @ X362 @ X361) != (sub @ X359 @ (push @ X361 @ X362))) | ! [X364 : term,X365 : term > $o,X366 : subst > term > subst > $o] : (? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X369 @ X373 @ X371) @ X372) = (X369 @ (comp @ X373 @ X372) @ (sub @ X371 @ X372))) & ! [X370 : term] : (((X366 @ id @ (X369 @ id @ X370) @ id) = $true) | ($true != (X366 @ id @ X370 @ id))) & ($true != (X366 @ id @ (lam @ (X369 @ sh @ one)) @ id))) | ? [X368 : term] : (($true != (X365 @ (sub @ X364 @ (push @ X368 @ id)))) & ($true = (X365 @ X368))) | ($true = (X365 @ (lam @ X364))) | ? [X367 : term] : ((X366 @ id @ X367 @ id) != (X365 @ X367)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X454 : term] : ? [X455 : subst > term > term] : ((X455 @ sh @ one) = (sub @ X454 @ (push @ one @ sh)))) & (! [X34 : subst > term > subst > $o] : ? [X35 : term > $o] : ! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36)) <=> (hoasinduction_lem0_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X112 : term > $o,X113 : term,X114 : subst] : ? [X115 : term > $o] : ! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (pushprop_lem1_gthm = $true) & (hoaslaminj_gthm = $true) & (! [X105 : term > $o,X106 : term] : (? [X110 : term] : (((X105 @ (lam @ X110)) != $true) & ! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ($true != (X105 @ X111)))) | ($true = (X105 @ X106)) | ? [X107 : term] : (($true = (var @ X107)) & ((X105 @ X107) != $true)) | ? [X108 : term,X109 : term] : (($true = (X105 @ X108)) & ($true = (X105 @ X109)) & ($true != (X105 @ (ap @ X109 @ X108))))) <=> (induction2 = $true)) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem3b_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axclos = $true) & (! [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))) | ? [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) != (sub @ (X348 @ X349 @ X350) @ X351))) <=> (hoaslamnotap = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ? [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) != (X5 @ X6)) | ($true = (X5 @ one))) | ? [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) != X1))) & ((? [X299 : subst > term > subst > $o,X300 : term,X301 : term] : (! [X306 : term,X307 : term] : (((X299 @ id @ X307 @ id) != $true) | ($true = (X299 @ id @ (ap @ (sub @ X306 @ id) @ X307) @ id)) | ($true != (X299 @ id @ X306 @ id))) & ! [X308 : term,X309 : subst,X310 : subst,X311 : subst] : (($true = (X299 @ (comp @ X311 @ X309) @ (sub @ X308 @ X309) @ X310)) | ($true != (X299 @ X311 @ X308 @ (comp @ X309 @ X310)))) & ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (($true = (X299 @ X305 @ X303 @ (comp @ X302 @ X304))) | ($true != (X299 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304))) & ((X299 @ id @ X300 @ id) = $true) & ($true = (X299 @ id @ X301 @ id)) & ($true != (X299 @ id @ (ap @ X300 @ X301) @ id))) | ? [X292 : term > $o,X293 : term] : (! [X297 : term,X298 : term] : (($true = (X292 @ (ap @ X298 @ X297))) | ((X292 @ X298) != $true) | ($true != (X292 @ X297))) & ! [X294 : term] : (? [X295 : term] : (((X292 @ X295) = $true) & ($true != (X292 @ (sub @ X294 @ (push @ X295 @ id))))) | ($true = (X292 @ (lam @ X294)))) & ($true != (X292 @ X293)) & ! [X296 : term] : (($true = (X292 @ X296)) | ($true != (var @ X296)))) | ! [X328 : term,X329 : subst > term > subst > $o] : (? [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true = (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) & ($true != (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) | ? [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true = (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) & ($true != (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) | ? [X336 : term] : (($true != (X329 @ id @ X336 @ id)) & ((var @ (sub @ X336 @ id)) = $true)) | ? [X337 : subst > term > term] : (($true != (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) & ! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341))) & ! [X338 : term] : (($true = (X329 @ id @ (X337 @ id @ X338) @ id)) | ((X329 @ id @ X338 @ id) != $true))) | ? [X330 : term,X331 : term] : (((X329 @ id @ X330 @ id) = $true) & ($true != (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ($true = (X329 @ id @ X328 @ id))) | ? [X312 : subst > term > subst > $o,X313 : term] : (! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = (X312 @ (comp @ X325 @ X324) @ (sub @ X326 @ X324) @ X327)) | ($true != (X312 @ X325 @ X326 @ (comp @ X324 @ X327)))) & ! [X314 : term] : (($true = (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | ((X312 @ id @ X314 @ id) != $true)) & ($true != (X312 @ id @ (lam @ X313) @ id)) & ! [X315 : subst > term > term] : (($true = (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) | ? [X317 : subst,X318 : subst,X319 : term] : ((sub @ (X315 @ X318 @ X319) @ X317) != (X315 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) | ? [X316 : term] : (((X312 @ id @ X316 @ id) = $true) & ($true != (X312 @ id @ (X315 @ id @ X316) @ id)))) & ! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (($true != (X312 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ($true = (X312 @ X322 @ X321 @ (comp @ X323 @ X320)))))) <=> (hoasinduction_lthm = $true)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X7 : d_term,X8 : d_term] : ((X7 = X8) | ((d2term @ X7) != (d2term @ X8))) & ((shinj = $true) <=> ! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh)))) & ((hoasapinj1_lthm = $true) <=> (? [X37 : term] : ((sub @ X37 @ id) != X37) | ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) = (ap @ X40 @ X39)) & (X38 != X40)))) & (hoasinduction_lem1_lthm = $true) & (! [X117 : term,X118 : subst > term > subst > $o] : (($true = (X118 @ id @ (lam @ (sub @ X117 @ (push @ one @ sh))) @ id)) | ? [X120 : subst > term > term] : (! [X121 : term] : (($true = (X118 @ id @ (X120 @ id @ X121) @ id)) | ($true != (X118 @ id @ X121 @ id))) & ($true != (X118 @ id @ (lam @ (X120 @ sh @ one)) @ id)) & ! [X122 : subst,X123 : subst,X124 : term] : ((sub @ (X120 @ X122 @ X124) @ X123) = (X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)))) | ? [X119 : term] : (($true != (X118 @ id @ (sub @ X117 @ (push @ X119 @ id)) @ id)) & ($true = (X118 @ id @ X119 @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X198 : subst > term > subst > $o,X199 : term] : (($true = (X198 @ id @ (lam @ X199) @ id)) | ? [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true != (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) & ($true = (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) | ? [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true = (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) & ($true != (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ? [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) != $true) & ($true = (X198 @ id @ X213 @ id))) | ? [X204 : subst > term > term] : (((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) != $true) & ! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ($true != (X198 @ id @ X205 @ id))) & ! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208)))))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_gthm = $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)))))))))))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (axassoc = $true) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction = $true) <=> ! [X134 : term,X135 : subst > term > subst > $o] : (? [X136 : subst,X137 : term,X138 : subst,X139 : subst] : (((X135 @ X136 @ X137 @ (comp @ X138 @ X139)) = $true) & ($true != (X135 @ (comp @ X136 @ X138) @ (sub @ X137 @ X138) @ X139))) | ((X135 @ id @ X134 @ id) = $true) | ? [X146 : term,X147 : term] : (($true != (X135 @ id @ (ap @ (sub @ X147 @ id) @ X146) @ id)) & ($true = (X135 @ id @ X147 @ id)) & ((X135 @ id @ X146 @ id) = $true)) | ? [X140 : subst > term > term] : (! [X141 : term,X142 : subst,X143 : subst] : ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)) = (sub @ (X140 @ X143 @ X141) @ X142)) & ! [X144 : term] : (($true != (X135 @ id @ X144 @ id)) | ($true = (X135 @ id @ (X140 @ id @ X144) @ id))) & ($true != (X135 @ id @ (lam @ (X140 @ sh @ one)) @ id))) | ? [X148 : subst,X149 : subst,X150 : subst,X151 : term] : (($true != (X135 @ X148 @ X151 @ (comp @ X149 @ X150))) & ($true = (X135 @ (comp @ X148 @ X149) @ (sub @ X151 @ X149) @ X150))) | ? [X145 : term] : (($true != (X135 @ id @ X145 @ id)) & ($true = (var @ (sub @ X145 @ id)))))) & ((axshiftcons = $true) <=> ! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((axidl = $true) <=> ! [X197 : subst] : ((comp @ id @ X197) = X197)) & ((hoasinduction_lem3_lthm = $true) <=> (? [X481 : term] : ((sub @ X481 @ id) != X481) | ! [X490 : term,X491 : subst > term > subst > $o] : (? [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (($true = (X491 @ X499 @ X501 @ (comp @ X500 @ X498))) & ($true != (X491 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500) @ X498))) | ? [X492 : subst > term > term] : (($true != (X491 @ id @ (lam @ (X492 @ sh @ one)) @ id)) & ! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X492 @ X494 @ X495) @ X496) = (X492 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496))) & ! [X493 : term] : (($true != (X491 @ id @ X493 @ id)) | ((X491 @ id @ (X492 @ id @ X493) @ id) = $true))) | ($true = (X491 @ id @ (lam @ X490) @ id)) | ? [X497 : term] : (($true = (X491 @ id @ X497 @ id)) & ($true != (X491 @ id @ (sub @ X490 @ (push @ X497 @ id)) @ id))) | ? [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (($true = (X491 @ (comp @ X503 @ X502) @ (sub @ X505 @ X502) @ X504)) & ($true != (X491 @ X503 @ X505 @ (comp @ X502 @ X504))))) | ? [X482 : subst > term > subst > $o,X483 : term] : (! [X489 : term] : (($true != (X482 @ id @ X489 @ id)) | ($true = (X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id))) & ((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id) != $true) & ! [X484 : subst > term > term] : (? [X485 : subst,X486 : term,X487 : subst] : ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)) != (sub @ (X484 @ X485 @ X486) @ X487)) | ? [X488 : term] : (($true = (X482 @ id @ X488 @ id)) & ($true != (X482 @ id @ (X484 @ id @ X488) @ id))) | ($true = (X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)))))) & (hoaslamnotap_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X102 : subst > term > subst > $o] : ? [X103 : term > $o] : ! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104))) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasapnotvar_lthm = $true) & (apnotvar = $true) & (! [X125 : subst > term > subst > $o,X126 : term] : (? [X132 : term,X133 : term] : (($true = (X125 @ id @ X133 @ id)) & ($true = (X125 @ id @ X132 @ id)) & ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) != $true)) | ($true = (X125 @ id @ X126 @ id)) | ? [X127 : subst > term > term] : (($true != (X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) & ! [X128 : term] : (($true != (X125 @ id @ X128 @ id)) | ($true = (X125 @ id @ (X127 @ id @ X128) @ id))) & ! [X129 : subst,X130 : subst,X131 : term] : ((X127 @ (comp @ X129 @ X130) @ (sub @ X131 @ X130)) = (sub @ (X127 @ X129 @ X131) @ X130)))) <=> (hoasinduction_no_psi_cond = $true)) & (lamnotvar = $true) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) <=> (hoasapinj2 = $true)) & (axvarshift = $true) & (! [X352 : term] : ((sub @ X352 @ id) = X352) <=> (axvarid = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X253 : term] : ? [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) = (X254 @ sh @ one))) & (! [X374 : subst,X375 : term > $o,X376 : term] : ? [X377 : term > $o] : ! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378)) <=> (pushprop_lem0 = $true)) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X10 : subst > term > subst > $o,X11 : term] : (! [X17 : term] : (($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) | ($true != (X10 @ id @ X17 @ id))) & ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) != $true) & ! [X12 : subst > term > term] : (? [X16 : term] : (($true != (X10 @ id @ (X12 @ id @ X16) @ id)) & ((X10 @ id @ X16 @ id) = $true)) | ? [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) != (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)))) | ? [X9 : term] : ((sub @ X9 @ id) != X9) | ! [X18 : subst > term > subst > $o,X19 : term] : (($true = (X18 @ id @ (lam @ X19) @ id)) | ? [X21 : subst > term > term] : (($true != (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id)) & ! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ($true != (X18 @ id @ X22 @ id))) & ! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25))) | ? [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) != $true) & ($true = (X18 @ id @ X20 @ id)))))) & (one = (d2term @ d_one)) & (induction2lem_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((d2subst @ d_id) = sh) & (axabs = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X214 : term,X215 : term > $o,X216 : subst > term > subst > $o] : (? [X217 : subst > term > term] : (($true != (X216 @ id @ (lam @ (X217 @ sh @ one)) @ id)) & ! [X218 : term,X219 : subst,X220 : subst] : ((sub @ (X217 @ X220 @ X218) @ X219) = (X217 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) & ! [X221 : term] : (($true != (X216 @ id @ X221 @ id)) | ($true = (X216 @ id @ (X217 @ id @ X221) @ id)))) | ? [X231 : term] : ((X215 @ X231) != (X216 @ id @ X231 @ id)) | ? [X227 : term,X228 : subst,X229 : subst,X230 : subst] : (($true != (X216 @ X228 @ X227 @ (comp @ X230 @ X229))) & ($true = (X216 @ (comp @ X228 @ X230) @ (sub @ X227 @ X230) @ X229))) | ? [X222 : term] : (($true != (X215 @ (sub @ X214 @ (push @ X222 @ id)))) & ((X215 @ X222) = $true)) | ? [X223 : subst,X224 : subst,X225 : term,X226 : subst] : (($true = (X216 @ X224 @ X225 @ (comp @ X223 @ X226))) & ($true != (X216 @ (comp @ X224 @ X223) @ (sub @ X225 @ X223) @ X226))) | ($true = (X215 @ (lam @ X214))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotap != $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3a = $true) <=> ! [X276 : subst > term > subst > $o,X277 : term] : (? [X279 : subst > term > term] : (! [X281 : subst,X282 : term,X283 : subst] : ((X279 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281)) = (sub @ (X279 @ X283 @ X282) @ X281)) & ! [X280 : term] : (($true = (X276 @ id @ (X279 @ id @ X280) @ id)) | ($true != (X276 @ id @ X280 @ id))) & ($true != (X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X278 : term] : (($true = (X276 @ id @ X278 @ id)) & ($true != (X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id))) | ($true = (X276 @ id @ (lam @ X277) @ id)))) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ? [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) != (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) | ? [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) != (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445))) <=> (hoaslaminj = $true)) & ! [X27 : d_subst] : (d_id = X27) & ((pushprop_lem1 = $true) <=> ! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & (hoasinduction_lem1_gthm = $true)),
% 15.37/3.55 inference(flattening,[status(thm)],[f12])).
% 15.37/3.55 thf(f12,plain,(
% 15.37/3.55 (axabs = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X364 : term,X365 : term > $o,X366 : subst > term > subst > $o] : (? [X369 : subst > term > term] : (! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X369 @ X373 @ X371) @ X372) = (X369 @ (comp @ X373 @ X372) @ (sub @ X371 @ X372))) & ! [X370 : term] : (((X366 @ id @ (X369 @ id @ X370) @ id) = $true) | ($true != (X366 @ id @ X370 @ id))) & ($true != (X366 @ id @ (lam @ (X369 @ sh @ one)) @ id))) | ? [X368 : term] : (($true != (X365 @ (sub @ X364 @ (push @ X368 @ id)))) & ($true = (X365 @ X368))) | ($true = (X365 @ (lam @ X364))) | ? [X367 : term] : ((X366 @ id @ X367 @ id) != (X365 @ X367))) | ? [X363 : term] : ((sub @ X363 @ id) != X363)) | ? [X359 : term] : ! [X360 : subst > term > term] : ? [X361 : term,X362 : subst] : ((X360 @ X362 @ X361) != (sub @ X359 @ (push @ X361 @ X362))))) & (hoaslaminj_gthm = $true) & ((((! [X174 : subst > term > term,X175 : term,X176 : subst,X177 : subst > term > term] : (((X174 @ X176 @ X175) = (X177 @ X176 @ X175)) | ((lam @ (X177 @ sh @ one)) != (lam @ (X174 @ sh @ one))) | ? [X181 : subst,X182 : subst,X183 : term] : ((sub @ (X177 @ X182 @ X183) @ X181) != (X177 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) | ? [X178 : subst,X179 : subst,X180 : term] : ((sub @ (X174 @ X178 @ X180) @ X179) != (X174 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179)))) | ? [X172 : term,X173 : term] : (((lam @ X173) = (lam @ X172)) & (X172 != X173))) | ? [X170 : term,X171 : subst] : ((comp @ sh @ (push @ X170 @ X171)) != X171)) | ? [X168 : term,X169 : subst] : ((sub @ one @ (push @ X168 @ X169)) != X168)) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction = $true) <=> ! [X134 : term,X135 : subst > term > subst > $o] : (? [X136 : subst,X137 : term,X138 : subst,X139 : subst] : (((X135 @ X136 @ X137 @ (comp @ X138 @ X139)) = $true) & ($true != (X135 @ (comp @ X136 @ X138) @ (sub @ X137 @ X138) @ X139))) | ((X135 @ id @ X134 @ id) = $true) | ? [X146 : term,X147 : term] : (($true != (X135 @ id @ (ap @ (sub @ X147 @ id) @ X146) @ id)) & ($true = (X135 @ id @ X147 @ id)) & ((X135 @ id @ X146 @ id) = $true)) | ? [X140 : subst > term > term] : (! [X141 : term,X142 : subst,X143 : subst] : ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)) = (sub @ (X140 @ X143 @ X141) @ X142)) & ! [X144 : term] : (($true != (X135 @ id @ X144 @ id)) | ($true = (X135 @ id @ (X140 @ id @ X144) @ id))) & ($true != (X135 @ id @ (lam @ (X140 @ sh @ one)) @ id))) | ? [X148 : subst,X149 : subst,X150 : subst,X151 : term] : (($true != (X135 @ X148 @ X151 @ (comp @ X149 @ X150))) & ($true = (X135 @ (comp @ X148 @ X149) @ (sub @ X151 @ X149) @ X150))) | ? [X145 : term] : (($true != (X135 @ id @ X145 @ id)) & ($true = (var @ (sub @ X145 @ id)))))) & ((axvarcons = $true) <=> ! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470)) & (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)))))))))))) & ((hoasapinj1 = $true) <=> ! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353)))) & (! [X381 : term > $o,X382 : subst,X383 : term] : (? [X386 : term] : (($true = (var @ X386)) & ($true != (X381 @ (sub @ X386 @ X382)))) | ($true = (X381 @ (sub @ X383 @ X382))) | ? [X387 : term,X388 : term] : (($true = (X381 @ X387)) & ($true != (X381 @ (ap @ X388 @ X387))) & ($true = (X381 @ X388))) | ? [X384 : term] : (($true != (X381 @ (lam @ X384))) & ! [X385 : term] : (($true = (X381 @ (sub @ X384 @ (push @ X385 @ id)))) | ($true != (X381 @ X385))))) <=> (induction2lem = $true)) & (axclos = $true) & (ulamvar1 != $true) & (! [X160 : term,X161 : subst > term > subst > $o] : (? [X162 : subst > term > term] : (($true != (X161 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X162 @ X165 @ X164) @ X163) = (X162 @ (comp @ X165 @ X163) @ (sub @ X164 @ X163))) & ! [X166 : term] : (($true = (X161 @ id @ (X162 @ id @ X166) @ id)) | ($true != (X161 @ id @ X166 @ id)))) | ($true = (X161 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) | ? [X167 : term] : (($true != (X161 @ id @ (sub @ X160 @ (push @ X167 @ id)) @ id)) & ($true = (X161 @ id @ X167 @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axscons = $true) <=> ! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157)) & (lamnotvar = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (axassoc = $true) & (! [X105 : term > $o,X106 : term] : (? [X110 : term] : (((X105 @ (lam @ X110)) != $true) & ! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ($true != (X105 @ X111)))) | ($true = (X105 @ X106)) | ? [X107 : term] : (($true = (var @ X107)) & ((X105 @ X107) != $true)) | ? [X108 : term,X109 : term] : (($true = (X105 @ X108)) & ($true = (X105 @ X109)) & ($true != (X105 @ (ap @ X109 @ X108))))) <=> (induction2 = $true)) & ((((! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458)) | ? [X457 : subst] : ((comp @ X457 @ id) != X457)) | ? [X456 : subst] : ((comp @ id @ X456) != X456)) <=> (substmonoid_lthm = $true)) & (! [X346 : term,X347 : term,X348 : subst > term > term] : (((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))) | ? [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) != (sub @ (X348 @ X349 @ X350) @ X351))) <=> (hoaslamnotap = $true)) & (hoasapinj2_gthm = $true) & ! [X7 : d_term,X8 : d_term] : ((X7 = X8) | ((d2term @ X7) != (d2term @ X8))) & ((termmset_lthm = $true) <=> (? [X251 : term] : ((sub @ X251 @ id) != X251) | ! [X252 : term] : ((sub @ X252 @ id) = X252))) & (((! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))) | ? [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) != X474)) | ? [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) != X473)) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem3v2 = $true) & (ulamvarind = $true) & (axvarshift = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem0 = $true) <=> ! [X102 : subst > term > subst > $o] : ? [X103 : term > $o] : ! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104))) & (termmset_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X18 : subst > term > subst > $o,X19 : term] : (($true = (X18 @ id @ (lam @ X19) @ id)) | ? [X21 : subst > term > term] : (($true != (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id)) & ! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ($true != (X18 @ id @ X22 @ id))) & ! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25))) | ? [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) != $true) & ($true = (X18 @ id @ X20 @ id)))) | ? [X10 : subst > term > subst > $o,X11 : term] : (! [X17 : term] : (($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) | ($true != (X10 @ id @ X17 @ id))) & ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) != $true) & ! [X12 : subst > term > term] : (? [X16 : term] : (($true != (X10 @ id @ (X12 @ id @ X16) @ id)) & ((X10 @ id @ X16 @ id) = $true)) | ? [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) != (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id))))) | ? [X9 : term] : ((sub @ X9 @ id) != X9))) & (((((! [X527 : term,X528 : subst > term > subst > $o] : (($true = (X528 @ id @ X527 @ id)) | ? [X531 : subst > term > term] : (! [X532 : term] : (($true != (X528 @ id @ X532 @ id)) | ($true = (X528 @ id @ (X531 @ id @ X532) @ id))) & ($true != (X528 @ id @ (lam @ (X531 @ sh @ one)) @ id)) & ! [X533 : term,X534 : subst,X535 : subst] : ((sub @ (X531 @ X534 @ X533) @ X535) = (X531 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | ? [X529 : term,X530 : term] : (($true != (X528 @ id @ (ap @ (sub @ X529 @ id) @ X530) @ id)) & ($true = (X528 @ id @ X529 @ id)) & ($true = (X528 @ id @ X530 @ id)))) | ? [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (! [X522 : subst > term > term] : (($true = (X518 @ id @ (lam @ (X522 @ sh @ one)) @ id)) | ? [X524 : term,X525 : subst,X526 : subst] : ((X522 @ (comp @ X525 @ X526) @ (sub @ X524 @ X526)) != (sub @ (X522 @ X525 @ X524) @ X526)) | ? [X523 : term] : (($true != (X518 @ id @ (X522 @ id @ X523) @ id)) & ((X518 @ id @ X523 @ id) = $true))) & ($true != (X517 @ (lam @ X519))) & ! [X521 : term] : (((X517 @ (sub @ X519 @ (push @ X521 @ id))) = $true) | ($true != (X517 @ X521))) & ! [X520 : term] : ((X517 @ X520) = (X518 @ id @ X520 @ id)))) | ? [X516 : term] : ((sub @ X516 @ id) != X516)) | ? [X509 : term > $o,X510 : term] : (! [X515 : term] : (($true != (var @ X515)) | ($true = (X509 @ X515))) & ($true != (X509 @ X510)) & ! [X511 : term,X512 : term] : (((X509 @ X511) != $true) | ($true = (X509 @ (ap @ X512 @ X511))) | ($true != (X509 @ X512))) & ! [X513 : term] : (? [X514 : term] : (($true != (X509 @ (sub @ X513 @ (push @ X514 @ id)))) & ($true = (X509 @ X514))) | ($true = (X509 @ (lam @ X513)))))) | ? [X506 : subst > term > subst > $o] : ! [X507 : term > $o] : ? [X508 : term] : ((X506 @ id @ X508 @ id) != (X507 @ X508))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axidr = $true) <=> ! [X196 : subst] : ((comp @ X196 @ id) = X196)) & (pushprop_lthm_orig = $true) & (! [X434 : term] : ? [X435 : subst > term > term] : ! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_gthm = $true) & (! [X184 : subst > term > subst > $o,X185 : term] : (? [X187 : subst > term > term,X188 : term] : (! [X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189)) = (sub @ X188 @ (push @ (sub @ X190 @ X189) @ (comp @ X191 @ X189)))) & ! [X192 : subst,X193 : term,X194 : subst] : ((sub @ (sub @ X188 @ (push @ X193 @ X194)) @ X192) = (sub @ (X187 @ X194 @ X193) @ X192)) & ! [X195 : term] : (($true != (X184 @ id @ X195 @ id)) | ($true = (X184 @ id @ (X187 @ id @ X195) @ id))) & ($true != (X184 @ id @ (lam @ (X187 @ sh @ one)) @ id))) | ($true = (X184 @ id @ (lam @ (sub @ X185 @ (push @ one @ sh))) @ id)) | ? [X186 : term] : (($true = (X184 @ id @ X186 @ id)) & ($true != (X184 @ id @ (sub @ X185 @ (push @ X186 @ id)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ((axshiftcons = $true) <=> ! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275)) & (! [X117 : term,X118 : subst > term > subst > $o] : (($true = (X118 @ id @ (lam @ (sub @ X117 @ (push @ one @ sh))) @ id)) | ? [X120 : subst > term > term] : (! [X121 : term] : (($true = (X118 @ id @ (X120 @ id @ X121) @ id)) | ($true != (X118 @ id @ X121 @ id))) & ($true != (X118 @ id @ (lam @ (X120 @ sh @ one)) @ id)) & ! [X122 : subst,X123 : subst,X124 : term] : ((sub @ (X120 @ X122 @ X124) @ X123) = (X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)))) | ? [X119 : term] : (($true != (X118 @ id @ (sub @ X117 @ (push @ X119 @ id)) @ id)) & ($true = (X118 @ id @ X119 @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3b_gthm = $true) & (((! [X490 : term,X491 : subst > term > subst > $o] : (? [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (($true = (X491 @ X499 @ X501 @ (comp @ X500 @ X498))) & ($true != (X491 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500) @ X498))) | ? [X492 : subst > term > term] : (($true != (X491 @ id @ (lam @ (X492 @ sh @ one)) @ id)) & ! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X492 @ X494 @ X495) @ X496) = (X492 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496))) & ! [X493 : term] : (($true != (X491 @ id @ X493 @ id)) | ((X491 @ id @ (X492 @ id @ X493) @ id) = $true))) | ($true = (X491 @ id @ (lam @ X490) @ id)) | ? [X497 : term] : (($true = (X491 @ id @ X497 @ id)) & ($true != (X491 @ id @ (sub @ X490 @ (push @ X497 @ id)) @ id))) | ? [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (($true = (X491 @ (comp @ X503 @ X502) @ (sub @ X505 @ X502) @ X504)) & ($true != (X491 @ X503 @ X505 @ (comp @ X502 @ X504))))) | ? [X482 : subst > term > subst > $o,X483 : term] : (! [X489 : term] : (($true != (X482 @ id @ X489 @ id)) | ($true = (X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id))) & ((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id) != $true) & ! [X484 : subst > term > term] : (? [X485 : subst,X486 : term,X487 : subst] : ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)) != (sub @ (X484 @ X485 @ X486) @ X487)) | ? [X488 : term] : (($true = (X482 @ id @ X488 @ id)) & ($true != (X482 @ id @ (X484 @ id @ X488) @ id))) | ($true = (X482 @ id @ (lam @ (X484 @ sh @ one)) @ id))))) | ? [X481 : term] : ((sub @ X481 @ id) != X481)) <=> (hoasinduction_lem3_lthm = $true)) & ((shinj = $true) <=> ! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X454 : term] : ? [X455 : subst > term > term] : ((X455 @ sh @ one) = (sub @ X454 @ (push @ one @ sh)))) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ? [X156 : term] : ((X153 @ X156) != (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) <=> (pushprop_lem1v2 = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((((! [X328 : term,X329 : subst > term > subst > $o] : (? [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true = (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) & ($true != (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) | ? [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true = (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) & ($true != (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) | ? [X336 : term] : (($true != (X329 @ id @ X336 @ id)) & ((var @ (sub @ X336 @ id)) = $true)) | ? [X337 : subst > term > term] : (($true != (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) & ! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341))) & ! [X338 : term] : (($true = (X329 @ id @ (X337 @ id @ X338) @ id)) | ((X329 @ id @ X338 @ id) != $true))) | ? [X330 : term,X331 : term] : (((X329 @ id @ X330 @ id) = $true) & ($true != (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ($true = (X329 @ id @ X328 @ id))) | ? [X312 : subst > term > subst > $o,X313 : term] : (! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = (X312 @ (comp @ X325 @ X324) @ (sub @ X326 @ X324) @ X327)) | ($true != (X312 @ X325 @ X326 @ (comp @ X324 @ X327)))) & ! [X314 : term] : (($true = (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | ((X312 @ id @ X314 @ id) != $true)) & ($true != (X312 @ id @ (lam @ X313) @ id)) & ! [X315 : subst > term > term] : (($true = (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) | ? [X317 : subst,X318 : subst,X319 : term] : ((sub @ (X315 @ X318 @ X319) @ X317) != (X315 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) | ? [X316 : term] : (((X312 @ id @ X316 @ id) = $true) & ($true != (X312 @ id @ (X315 @ id @ X316) @ id)))) & ! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (($true != (X312 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ($true = (X312 @ X322 @ X321 @ (comp @ X323 @ X320)))))) | ? [X299 : subst > term > subst > $o,X300 : term,X301 : term] : (! [X306 : term,X307 : term] : (((X299 @ id @ X307 @ id) != $true) | ($true = (X299 @ id @ (ap @ (sub @ X306 @ id) @ X307) @ id)) | ($true != (X299 @ id @ X306 @ id))) & ! [X308 : term,X309 : subst,X310 : subst,X311 : subst] : (($true = (X299 @ (comp @ X311 @ X309) @ (sub @ X308 @ X309) @ X310)) | ($true != (X299 @ X311 @ X308 @ (comp @ X309 @ X310)))) & ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (($true = (X299 @ X305 @ X303 @ (comp @ X302 @ X304))) | ($true != (X299 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304))) & ((X299 @ id @ X300 @ id) = $true) & ($true = (X299 @ id @ X301 @ id)) & ($true != (X299 @ id @ (ap @ X300 @ X301) @ id)))) | ? [X292 : term > $o,X293 : term] : (! [X297 : term,X298 : term] : (($true = (X292 @ (ap @ X298 @ X297))) | ((X292 @ X298) != $true) | ($true != (X292 @ X297))) & ! [X294 : term] : (? [X295 : term] : (((X292 @ X295) = $true) & ($true != (X292 @ (sub @ X294 @ (push @ X295 @ id))))) | ($true = (X292 @ (lam @ X294)))) & ($true != (X292 @ X293)) & ! [X296 : term] : (($true = (X292 @ X296)) | ($true != (var @ X296))))) <=> (hoasinduction_lthm = $true)) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (($true != (X46 @ id @ X47 @ id)) | ($true != (X46 @ id @ X48 @ id)) | ? [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (($true = (X46 @ X52 @ X54 @ (comp @ X51 @ X53))) & ($true != (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53))) | ? [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57)) & ($true != (X46 @ X58 @ X55 @ (comp @ X56 @ X57)))) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ? [X49 : term,X50 : term] : (((X46 @ id @ X49 @ id) = $true) & ((X46 @ id @ X50 @ id) = $true) & ($true != (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id)))) <=> (hoasinduction_lem2 = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X266 : term,X267 : subst,X268 : term > $o] : (? [X271 : term] : (($true != (X268 @ (lam @ X271))) & ! [X272 : term] : (($true = (X268 @ (sub @ X271 @ (push @ X272 @ id)))) | ($true != (X268 @ X272)))) | ? [X273 : term] : (($true != (X268 @ (sub @ X273 @ X267))) & ($true = (var @ X273))) | ? [X269 : term,X270 : term] : (($true = (X268 @ X270)) & ($true != (X268 @ (ap @ X270 @ X269))) & ($true = (X268 @ X269))) | ($true = (X268 @ (sub @ X266 @ X267)))) | ? [X260 : term > $o,X261 : term] : (! [X265 : term] : (($true = (X260 @ X265)) | ($true != (var @ X265))) & ! [X263 : term,X264 : term] : (($true != (X260 @ X264)) | ($true != (X260 @ X263)) | ($true = (X260 @ (ap @ X264 @ X263)))) & ! [X262 : term] : (($true != (X260 @ X262)) | ($true = (X260 @ (lam @ X262)))) & ($true != (X260 @ X261)))) | ? [X259 : subst] : ((comp @ X259 @ id) != X259)) | ? [X257 : term,X258 : subst] : ((comp @ sh @ (push @ X257 @ X258)) != X258)) | ? [X255 : term,X256 : subst] : ((sub @ one @ (push @ X255 @ X256)) != X255))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X198 : subst > term > subst > $o,X199 : term] : (($true = (X198 @ id @ (lam @ X199) @ id)) | ? [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true != (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) & ($true = (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) | ? [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true = (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) & ($true != (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ? [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) != $true) & ($true = (X198 @ id @ X213 @ id))) | ? [X204 : subst > term > term] : (((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) != $true) & ! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ($true != (X198 @ id @ X205 @ id))) & ! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208)))))) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) <=> (apinj2 = $true)) & ((d2subst @ d_id) = id) & (one = (d2term @ d_one)) & (substmonoid_gthm = $true) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & ((axidl = $true) <=> ! [X197 : subst] : ((comp @ id @ X197) = X197)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((hoasinduction_lem3b = $true) <=> ! [X253 : term] : ? [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) = (X254 @ sh @ one))) & (pushprop_lthm = $true) & (ulamvarsh = $true) & ((hoasinduction_lem3a = $true) <=> ! [X276 : subst > term > subst > $o,X277 : term] : (? [X279 : subst > term > term] : (! [X281 : subst,X282 : term,X283 : subst] : ((X279 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281)) = (sub @ (X279 @ X283 @ X282) @ X281)) & ! [X280 : term] : (($true = (X276 @ id @ (X279 @ id @ X280) @ id)) | ($true != (X276 @ id @ X280 @ id))) & ($true != (X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X278 : term] : (($true = (X276 @ id @ X278 @ id)) & ($true != (X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id))) | ($true = (X276 @ id @ (lam @ X277) @ id)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem1v2_gthm = $true) & (! [X536 : term] : ? [X537 : subst > term > term] : ! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538)) <=> (hoasinduction_lem3v2_f = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X125 : subst > term > subst > $o,X126 : term] : (? [X132 : term,X133 : term] : (($true = (X125 @ id @ X133 @ id)) & ($true = (X125 @ id @ X132 @ id)) & ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) != $true)) | ($true = (X125 @ id @ X126 @ id)) | ? [X127 : subst > term > term] : (($true != (X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) & ! [X128 : term] : (($true != (X125 @ id @ X128 @ id)) | ($true = (X125 @ id @ (X127 @ id @ X128) @ id))) & ! [X129 : subst,X130 : subst,X131 : term] : ((X127 @ (comp @ X129 @ X130) @ (sub @ X131 @ X130)) = (sub @ (X127 @ X129 @ X131) @ X130)))) <=> (hoasinduction_no_psi_cond = $true)) & (lamnotap != $true) & ((pushprop_lem0_lthm = $true) <=> ! [X112 : term > $o,X113 : term,X114 : subst] : ? [X115 : term > $o] : ! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X28 : term > $o,X29 : term] : (? [X31 : term,X32 : term] : (($true = (X28 @ X31)) & ((X28 @ X32) = $true) & ($true != (X28 @ (ap @ X32 @ X31)))) | ? [X33 : term] : (((X28 @ X33) = $true) & ((X28 @ (lam @ X33)) != $true)) | ? [X30 : term] : (($true = (var @ X30)) & ((X28 @ X30) != $true)) | ($true = (X28 @ X29))) <=> (induction = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X419 : term,X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (? [X428 : subst,X429 : term,X430 : subst,X431 : subst] : (((X422 @ X431 @ X429 @ (comp @ X430 @ X428)) = $true) & ($true != (X422 @ (comp @ X431 @ X430) @ (sub @ X429 @ X430) @ X428))) | ? [X423 : subst,X424 : term,X425 : subst,X426 : subst] : (($true = (X422 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426) @ X423)) & ($true != (X422 @ X425 @ X424 @ (comp @ X426 @ X423)))) | ? [X432 : term,X433 : term] : (($true = (X422 @ id @ X433 @ id)) & ($true != (X422 @ id @ (ap @ (sub @ X433 @ id) @ X432) @ id)) & ((X422 @ id @ X432 @ id) = $true)) | ? [X427 : term] : ((X422 @ id @ X427 @ id) != (X421 @ X427)) | ($true = (X421 @ (ap @ X420 @ X419))) | ($true != (X421 @ X419)) | ($true != (X421 @ X420)))) & (hoasapnotvar_lthm = $true) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) != (d2subst @ X291)) | (X290 = X291)) & ((laminj = $true) <=> ! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417)))) & (axapp = $true) & (! [X460 : term > $o,X461 : subst > term > subst > $o,X462 : term] : (? [X463 : term] : ((X461 @ id @ X463 @ id) != (X460 @ X463)) | ? [X465 : subst > term > term] : (($true != (X461 @ id @ (lam @ (X465 @ sh @ one)) @ id)) & ! [X466 : term,X467 : subst,X468 : subst] : ((sub @ (X465 @ X467 @ X466) @ X468) = (X465 @ (comp @ X467 @ X468) @ (sub @ X466 @ X468))) & ! [X469 : term] : (($true != (X461 @ id @ X469 @ id)) | ($true = (X461 @ id @ (X465 @ id @ X469) @ id)))) | ? [X464 : term] : (($true = (X460 @ X464)) & ($true != (X460 @ (sub @ X462 @ (push @ X464 @ id))))) | ($true = (X460 @ (lam @ X462)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem1v2_gthm = $true) & (! [X34 : subst > term > subst > $o] : ? [X35 : term > $o] : ! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36)) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X214 : term,X215 : term > $o,X216 : subst > term > subst > $o] : (? [X217 : subst > term > term] : (($true != (X216 @ id @ (lam @ (X217 @ sh @ one)) @ id)) & ! [X218 : term,X219 : subst,X220 : subst] : ((sub @ (X217 @ X220 @ X218) @ X219) = (X217 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) & ! [X221 : term] : (($true != (X216 @ id @ X221 @ id)) | ($true = (X216 @ id @ (X217 @ id @ X221) @ id)))) | ? [X231 : term] : ((X215 @ X231) != (X216 @ id @ X231 @ id)) | ? [X227 : term,X228 : subst,X229 : subst,X230 : subst] : (($true != (X216 @ X228 @ X227 @ (comp @ X230 @ X229))) & ($true = (X216 @ (comp @ X228 @ X230) @ (sub @ X227 @ X230) @ X229))) | ? [X222 : term] : (($true != (X215 @ (sub @ X214 @ (push @ X222 @ id)))) & ((X215 @ X222) = $true)) | ? [X223 : subst,X224 : subst,X225 : term,X226 : subst] : (($true = (X216 @ X224 @ X225 @ (comp @ X223 @ X226))) & ($true != (X216 @ (comp @ X224 @ X223) @ (sub @ X225 @ X223) @ X226))) | ($true = (X215 @ (lam @ X214))))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (((! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) = (ap @ X40 @ X39)) & (X38 != X40))) | ? [X37 : term] : ((sub @ X37 @ id) != X37)) <=> (hoasapinj1_lthm = $true)) & (apnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & ! [X27 : d_subst] : (d_id = X27) & ((hoasapinj2_lthm = $true) <=> (? [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) = (ap @ X411 @ X410)) & (X409 != X410)) | ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)))) & (hoaslamnotap_gthm = $true) & (! [X374 : subst,X375 : term > $o,X376 : term] : ? [X377 : term > $o] : ! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378)) <=> (pushprop_lem0 = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X84 : term,X85 : subst > term > subst > $o] : (? [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (($true != (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95)) & ($true = (X85 @ X96 @ X94 @ (comp @ X93 @ X95)))) | ? [X86 : term,X87 : term] : (($true = (X85 @ id @ X87 @ id)) & ($true = (X85 @ id @ X86 @ id)) & ((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) != $true)) | ? [X88 : term] : (($true = (var @ (sub @ X88 @ id))) & ($true != (X85 @ id @ X88 @ id))) | ? [X97 : subst > term > term] : (! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100)) & ! [X98 : term] : (($true = (X85 @ id @ (X97 @ id @ X98) @ id)) | ((X85 @ id @ X98 @ id) != $true)) & ($true != (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id))) | ($true = (X85 @ id @ X84 @ id)) | ? [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) = $true) & ($true != (X85 @ X90 @ X91 @ (comp @ X92 @ X89))))) | ? [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (! [X78 : subst > term > term] : (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ? [X82 : term] : (($true != (X75 @ id @ (X78 @ id @ X82) @ id)) & ($true = (X75 @ id @ X82 @ id))) | ? [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) != (sub @ (X78 @ X81 @ X79) @ X80))) & ! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) & ! [X83 : term] : (($true != (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id))))) & ($true != (X74 @ (lam @ X76))))) | ? [X73 : term] : ((sub @ X73 @ id) != X73)) | ? [X66 : term,X67 : term > $o] : (! [X69 : term,X70 : term] : (((X67 @ X70) != $true) | ((X67 @ (ap @ X70 @ X69)) = $true) | ($true != (X67 @ X69))) & ! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ? [X72 : term] : (((X67 @ X72) = $true) & ($true != (X67 @ (sub @ X71 @ (push @ X72 @ id)))))) & ($true != (X67 @ X66)) & ! [X68 : term] : (($true = (X67 @ X68)) | ($true != (var @ X68))))) | ? [X63 : subst > term > subst > $o] : ! [X64 : term > $o] : ? [X65 : term] : ((X64 @ X65) != (X63 @ id @ X65 @ id)))) & ((! [X233 : term,X234 : term > $o,X235 : subst > term > subst > $o] : (? [X240 : term] : (((X234 @ X240) = $true) & ((X234 @ (sub @ X233 @ (push @ X240 @ id))) != $true)) | ? [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (($true = (X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237) @ X236)) & ((X235 @ X238 @ X239 @ (comp @ X237 @ X236)) != $true)) | ? [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (($true = (X235 @ X247 @ X248 @ (comp @ X249 @ X250))) & ($true != (X235 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249) @ X250))) | ((X234 @ (lam @ X233)) = $true) | ? [X246 : term] : ((X234 @ X246) != (X235 @ id @ X246 @ id)) | ? [X241 : subst > term > term] : (($true != (X235 @ id @ (lam @ (X241 @ sh @ one)) @ id)) & ! [X242 : term,X243 : subst,X244 : subst] : ((X241 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243)) = (sub @ (X241 @ X244 @ X242) @ X243)) & ! [X245 : term] : (($true != (X235 @ id @ X245 @ id)) | ($true = (X235 @ id @ (X241 @ id @ X245) @ id))))) | ? [X232 : term] : ((sub @ X232 @ id) != X232)) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) <=> (hoasapinj2 = $true)) & (hoasinduction_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ? [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) != (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) | ? [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) != (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445))) <=> (hoaslaminj = $true)) & (pushprop = $true) & ((substmonoid = $true) <=> (! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357))) & ((var @ (d2term @ d_one)) != $true) & (axmap = $true) & (induction2lem_gthm = $true) & (! [X352 : term] : ((sub @ X352 @ id) = X352) <=> (axvarid = $true)) & ! [X453 : d_term] : (d_one = X453) & ((pushprop_lem1v2_lthm = $true) <=> (! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ? [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) != (X5 @ X6)) | ($true = (X5 @ one))) | ? [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) != X1))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (((! [X402 : term,X403 : term > $o] : (? [X405 : term] : (! [X406 : term] : (($true != (X403 @ X406)) | ($true = (X403 @ (sub @ X405 @ (push @ X406 @ id))))) & ($true != (X403 @ (lam @ X405)))) | ? [X407 : term,X408 : term] : (($true != (X403 @ (ap @ X407 @ X408))) & ((X403 @ X408) = $true) & ($true = (X403 @ X407))) | ? [X404 : term] : (((var @ X404) = $true) & ($true != (X403 @ X404))) | ($true = (X403 @ X402))) | ? [X394 : subst,X395 : term,X396 : term > $o] : (($true != (X396 @ (sub @ X395 @ X394))) & ! [X400 : term] : (? [X401 : term] : (($true = (X396 @ X401)) & ((X396 @ (sub @ X400 @ (push @ X401 @ id))) != $true)) | ($true = (X396 @ (lam @ X400)))) & ! [X398 : term,X399 : term] : (($true != (X396 @ X399)) | ($true != (X396 @ X398)) | ($true = (X396 @ (ap @ X398 @ X399)))) & ! [X397 : term] : (($true = (X396 @ (sub @ X397 @ X394))) | ($true != (var @ X397))))) | ? [X393 : term] : ((sub @ X393 @ id) != X393)) <=> (induction2_lthm = $true)) & (hoaslamnotvar = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & (induction2_gthm = $true) & (pushprop_lem2v2 = $true) & (hoaslamnotap_lthm = $true)),
% 15.37/3.55 inference(ennf_transformation,[status(thm)],[f10])).
% 15.37/3.55 thf(f10,plain,(
% 15.37/3.55 (axabs = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X359 : term] : ~! [X360 : subst > term > term] : ~! [X361 : term,X362 : subst] : ((X360 @ X362 @ X361) = (sub @ X359 @ (push @ X361 @ X362))) => (! [X363 : term] : ((sub @ X363 @ id) = X363) => ! [X364 : term,X365 : term > $o,X366 : subst > term > subst > $o] : (~! [X367 : term] : ((X366 @ id @ X367 @ id) = (X365 @ X367)) | ($true = (X365 @ (lam @ X364))) | ~! [X369 : subst > term > term] : (~! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X369 @ X373 @ X371) @ X372) = (X369 @ (comp @ X373 @ X372) @ (sub @ X371 @ X372))) | ($true = (X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) | ~! [X370 : term] : (((X366 @ id @ (X369 @ id @ X370) @ id) = $true) | ($true != (X366 @ id @ X370 @ id)))) | ~! [X368 : term] : (($true = (X365 @ (sub @ X364 @ (push @ X368 @ id)))) | ($true != (X365 @ X368))))))) & (hoaslaminj_gthm = $true) & ((! [X168 : term,X169 : subst] : ((sub @ one @ (push @ X168 @ X169)) = X168) => (! [X170 : term,X171 : subst] : ((comp @ sh @ (push @ X170 @ X171)) = X171) => (! [X172 : term,X173 : term] : ((X172 = X173) | ((lam @ X173) != (lam @ X172))) => ! [X174 : subst > term > term,X175 : term,X176 : subst,X177 : subst > term > term] : (((X174 @ X176 @ X175) = (X177 @ X176 @ X175)) | ~! [X181 : subst,X182 : subst,X183 : term] : ((sub @ (X177 @ X182 @ X183) @ X181) = (X177 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) | ~! [X178 : subst,X179 : subst,X180 : term] : ((sub @ (X174 @ X178 @ X180) @ X179) = (X174 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) | ((lam @ (X177 @ sh @ one)) != (lam @ (X174 @ sh @ one))))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction = $true) <=> ! [X134 : term,X135 : subst > term > subst > $o] : (~! [X140 : subst > term > term] : (($true = (X135 @ id @ (lam @ (X140 @ sh @ one)) @ id)) | ~! [X141 : term,X142 : subst,X143 : subst] : ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)) = (sub @ (X140 @ X143 @ X141) @ X142)) | ~! [X144 : term] : (($true != (X135 @ id @ X144 @ id)) | ($true = (X135 @ id @ (X140 @ id @ X144) @ id)))) | ~! [X146 : term,X147 : term] : (((X135 @ id @ X146 @ id) != $true) | ($true != (X135 @ id @ X147 @ id)) | ($true = (X135 @ id @ (ap @ (sub @ X147 @ id) @ X146) @ id))) | ~! [X148 : subst,X149 : subst,X150 : subst,X151 : term] : (($true != (X135 @ (comp @ X148 @ X149) @ (sub @ X151 @ X149) @ X150)) | ($true = (X135 @ X148 @ X151 @ (comp @ X149 @ X150)))) | ((X135 @ id @ X134 @ id) = $true) | ~! [X145 : term] : (($true != (var @ (sub @ X145 @ id))) | ($true = (X135 @ id @ X145 @ id))) | ~! [X136 : subst,X137 : term,X138 : subst,X139 : subst] : (((X135 @ X136 @ X137 @ (comp @ X138 @ X139)) != $true) | ($true = (X135 @ (comp @ X136 @ X138) @ (sub @ X137 @ X138) @ X139))))) & ((axvarcons = $true) <=> ! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470)) & (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)))))))))))) & ((hoasapinj1 = $true) <=> ! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353)))) & ((induction2lem = $true) <=> ! [X381 : term > $o,X382 : subst,X383 : term] : (($true = (X381 @ (sub @ X383 @ X382))) | ~! [X384 : term] : (~! [X385 : term] : (($true = (X381 @ (sub @ X384 @ (push @ X385 @ id)))) | ($true != (X381 @ X385))) | ($true = (X381 @ (lam @ X384)))) | ~! [X387 : term,X388 : term] : (($true = (X381 @ (ap @ X388 @ X387))) | ($true != (X381 @ X387)) | ($true != (X381 @ X388))) | ~! [X386 : term] : (($true != (var @ X386)) | ($true = (X381 @ (sub @ X386 @ X382)))))) & (axclos = $true) & (ulamvar1 != $true) & (! [X160 : term,X161 : subst > term > subst > $o] : (($true = (X161 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) | ~! [X167 : term] : (($true != (X161 @ id @ X167 @ id)) | ($true = (X161 @ id @ (sub @ X160 @ (push @ X167 @ id)) @ id))) | ~! [X162 : subst > term > term] : (~! [X166 : term] : (($true = (X161 @ id @ (X162 @ id @ X166) @ id)) | ($true != (X161 @ id @ X166 @ id))) | ~! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X162 @ X165 @ X164) @ X163) = (X162 @ (comp @ X165 @ X163) @ (sub @ X164 @ X163))) | ($true = (X161 @ id @ (lam @ (X162 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axscons = $true) <=> ! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157)) & (lamnotvar = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & (axassoc = $true) & ((induction2 = $true) <=> ! [X105 : term > $o,X106 : term] : (~! [X110 : term] : (~! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ($true != (X105 @ X111))) | ((X105 @ (lam @ X110)) = $true)) | ~! [X108 : term,X109 : term] : (($true != (X105 @ X108)) | ($true = (X105 @ (ap @ X109 @ X108))) | ($true != (X105 @ X109))) | ($true = (X105 @ X106)) | ~! [X107 : term] : (($true != (var @ X107)) | ((X105 @ X107) = $true)))) & ((! [X456 : subst] : ((comp @ id @ X456) = X456) => (! [X457 : subst] : ((comp @ X457 @ id) = X457) => (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458)))) <=> (substmonoid_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X346 : term,X347 : term,X348 : subst > term > term] : (~! [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) = (sub @ (X348 @ X349 @ X350) @ X351)) | ((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))))) & (hoasapinj2_gthm = $true) & ! [X7 : d_term,X8 : d_term] : (((d2term @ X7) = (d2term @ X8)) => (X7 = X8)) & ((! [X251 : term] : ((sub @ X251 @ id) = X251) => ! [X252 : term] : ((sub @ X252 @ id) = X252)) <=> (termmset_lthm = $true)) & ((! [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) = X473) => (! [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) = X474) => ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ($true != (X476 @ X480))))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (($true != (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem3v2 = $true) & (ulamvarind = $true) & (axvarshift = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X102 : subst > term > subst > $o] : ~! [X103 : term > $o] : ~! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) <=> (hoasinduction_lem0 = $true)) & (termmset_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X9 : term] : ((sub @ X9 @ id) = X9) => (! [X10 : subst > term > subst > $o,X11 : term] : (~! [X17 : term] : (($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) | ($true != (X10 @ id @ X17 @ id))) | ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) = $true) | ~! [X12 : subst > term > term] : (~! [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) = (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) | ~! [X16 : term] : (($true = (X10 @ id @ (X12 @ id @ X16) @ id)) | ((X10 @ id @ X16 @ id) != $true)))) => ! [X18 : subst > term > subst > $o,X19 : term] : (($true = (X18 @ id @ (lam @ X19) @ id)) | ~! [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) = $true) | ($true != (X18 @ id @ X20 @ id))) | ~! [X21 : subst > term > term] : (($true = (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | ~! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ($true != (X18 @ id @ X22 @ id))) | ~! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25))))))) & ((! [X506 : subst > term > subst > $o] : ~! [X507 : term > $o] : ~! [X508 : term] : ((X506 @ id @ X508 @ id) = (X507 @ X508)) => (! [X509 : term > $o,X510 : term] : (~! [X513 : term] : (($true = (X509 @ (lam @ X513))) | ~! [X514 : term] : (($true = (X509 @ (sub @ X513 @ (push @ X514 @ id)))) | ($true != (X509 @ X514)))) | ($true = (X509 @ X510)) | ~! [X511 : term,X512 : term] : (((X509 @ X511) != $true) | ($true = (X509 @ (ap @ X512 @ X511))) | ($true != (X509 @ X512))) | ~! [X515 : term] : (($true != (var @ X515)) | ($true = (X509 @ X515)))) => (! [X516 : term] : ((sub @ X516 @ id) = X516) => (! [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (($true = (X517 @ (lam @ X519))) | ~! [X521 : term] : (((X517 @ (sub @ X519 @ (push @ X521 @ id))) = $true) | ($true != (X517 @ X521))) | ~! [X522 : subst > term > term] : (($true = (X518 @ id @ (lam @ (X522 @ sh @ one)) @ id)) | ~! [X524 : term,X525 : subst,X526 : subst] : ((X522 @ (comp @ X525 @ X526) @ (sub @ X524 @ X526)) = (sub @ (X522 @ X525 @ X524) @ X526)) | ~! [X523 : term] : (($true = (X518 @ id @ (X522 @ id @ X523) @ id)) | ((X518 @ id @ X523 @ id) != $true))) | ~! [X520 : term] : ((X517 @ X520) = (X518 @ id @ X520 @ id))) => ! [X527 : term,X528 : subst > term > subst > $o] : (~! [X531 : subst > term > term] : (~! [X533 : term,X534 : subst,X535 : subst] : ((sub @ (X531 @ X534 @ X533) @ X535) = (X531 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535))) | ~! [X532 : term] : (($true != (X528 @ id @ X532 @ id)) | ($true = (X528 @ id @ (X531 @ id @ X532) @ id))) | ($true = (X528 @ id @ (lam @ (X531 @ sh @ one)) @ id))) | ($true = (X528 @ id @ X527 @ id)) | ~! [X529 : term,X530 : term] : (($true != (X528 @ id @ X529 @ id)) | ($true = (X528 @ id @ (ap @ (sub @ X529 @ id) @ X530) @ id)) | ($true != (X528 @ id @ X530 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axidr = $true) <=> ! [X196 : subst] : ((comp @ X196 @ id) = X196)) & (pushprop_lthm_orig = $true) & (! [X434 : term] : ~! [X435 : subst > term > term] : ~! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_gthm = $true) & (! [X184 : subst > term > subst > $o,X185 : term] : (($true = (X184 @ id @ (lam @ (sub @ X185 @ (push @ one @ sh))) @ id)) | ~! [X186 : term] : (($true = (X184 @ id @ (sub @ X185 @ (push @ X186 @ id)) @ id)) | ($true != (X184 @ id @ X186 @ id))) | ~! [X187 : subst > term > term,X188 : term] : (~! [X195 : term] : (($true != (X184 @ id @ X195 @ id)) | ($true = (X184 @ id @ (X187 @ id @ X195) @ id))) | ~! [X192 : subst,X193 : term,X194 : subst] : ((sub @ (sub @ X188 @ (push @ X193 @ X194)) @ X192) = (sub @ (X187 @ X194 @ X193) @ X192)) | ($true = (X184 @ id @ (lam @ (X187 @ sh @ one)) @ id)) | ~! [X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189)) = (sub @ X188 @ (push @ (sub @ X190 @ X189) @ (comp @ X191 @ X189)))))) <=> (hoasinduction_lem3aaa = $true)) & ((axshiftcons = $true) <=> ! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275)) & (! [X117 : term,X118 : subst > term > subst > $o] : (~! [X119 : term] : (($true = (X118 @ id @ (sub @ X117 @ (push @ X119 @ id)) @ id)) | ($true != (X118 @ id @ X119 @ id))) | ~! [X120 : subst > term > term] : (($true = (X118 @ id @ (lam @ (X120 @ sh @ one)) @ id)) | ~! [X122 : subst,X123 : subst,X124 : term] : ((sub @ (X120 @ X122 @ X124) @ X123) = (X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) | ~! [X121 : term] : (($true = (X118 @ id @ (X120 @ id @ X121) @ id)) | ($true != (X118 @ id @ X121 @ id)))) | ($true = (X118 @ id @ (lam @ (sub @ X117 @ (push @ one @ sh))) @ id))) <=> (hoasinduction_lem3aa = $true)) & ((d2subst @ d_id) = sh) & (hoasinduction_lem3b_gthm = $true) & ((! [X481 : term] : ((sub @ X481 @ id) = X481) => (! [X482 : subst > term > subst > $o,X483 : term] : (~! [X484 : subst > term > term] : (($true = (X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) | ~! [X488 : term] : (($true = (X482 @ id @ (X484 @ id @ X488) @ id)) | ($true != (X482 @ id @ X488 @ id))) | ~! [X485 : subst,X486 : term,X487 : subst] : ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)) = (sub @ (X484 @ X485 @ X486) @ X487))) | ~! [X489 : term] : (($true != (X482 @ id @ X489 @ id)) | ($true = (X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id))) | ((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id) = $true)) => ! [X490 : term,X491 : subst > term > subst > $o] : (~! [X492 : subst > term > term] : (~! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X492 @ X494 @ X495) @ X496) = (X492 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496))) | ($true = (X491 @ id @ (lam @ (X492 @ sh @ one)) @ id)) | ~! [X493 : term] : (($true != (X491 @ id @ X493 @ id)) | ((X491 @ id @ (X492 @ id @ X493) @ id) = $true))) | ~! [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (($true = (X491 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500) @ X498)) | ($true != (X491 @ X499 @ X501 @ (comp @ X500 @ X498)))) | ~! [X497 : term] : (($true != (X491 @ id @ X497 @ id)) | ($true = (X491 @ id @ (sub @ X490 @ (push @ X497 @ id)) @ id))) | ~! [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (($true = (X491 @ X503 @ X505 @ (comp @ X502 @ X504))) | ($true != (X491 @ (comp @ X503 @ X502) @ (sub @ X505 @ X502) @ X504))) | ($true = (X491 @ id @ (lam @ X490) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & ((shinj = $true) <=> ! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh)))) & (! [X454 : term] : ~! [X455 : subst > term > term] : ((X455 @ sh @ one) != (sub @ X454 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ($true != (X152 @ X155)) | ~! [X156 : term] : ((X153 @ X156) = (X152 @ (sub @ X156 @ (push @ X155 @ X154))))) <=> (pushprop_lem1v2 = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((! [X292 : term > $o,X293 : term] : (~! [X296 : term] : (($true = (X292 @ X296)) | ($true != (var @ X296))) | ~! [X297 : term,X298 : term] : (($true = (X292 @ (ap @ X298 @ X297))) | ((X292 @ X298) != $true) | ($true != (X292 @ X297))) | ~! [X294 : term] : (~! [X295 : term] : (((X292 @ X295) != $true) | ($true = (X292 @ (sub @ X294 @ (push @ X295 @ id))))) | ($true = (X292 @ (lam @ X294)))) | ($true = (X292 @ X293))) => (! [X299 : subst > term > subst > $o,X300 : term,X301 : term] : (~! [X306 : term,X307 : term] : (((X299 @ id @ X307 @ id) != $true) | ($true = (X299 @ id @ (ap @ (sub @ X306 @ id) @ X307) @ id)) | ($true != (X299 @ id @ X306 @ id))) | ($true = (X299 @ id @ (ap @ X300 @ X301) @ id)) | ~! [X308 : term,X309 : subst,X310 : subst,X311 : subst] : (($true = (X299 @ (comp @ X311 @ X309) @ (sub @ X308 @ X309) @ X310)) | ($true != (X299 @ X311 @ X308 @ (comp @ X309 @ X310)))) | ($true != (X299 @ id @ X301 @ id)) | ((X299 @ id @ X300 @ id) != $true) | ~! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (($true = (X299 @ X305 @ X303 @ (comp @ X302 @ X304))) | ($true != (X299 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304)))) => (! [X312 : subst > term > subst > $o,X313 : term] : (~! [X314 : term] : (($true = (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | ((X312 @ id @ X314 @ id) != $true)) | ($true = (X312 @ id @ (lam @ X313) @ id)) | ~! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = (X312 @ (comp @ X325 @ X324) @ (sub @ X326 @ X324) @ X327)) | ($true != (X312 @ X325 @ X326 @ (comp @ X324 @ X327)))) | ~! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (($true != (X312 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ($true = (X312 @ X322 @ X321 @ (comp @ X323 @ X320)))) | ~! [X315 : subst > term > term] : (~! [X316 : term] : (($true = (X312 @ id @ (X315 @ id @ X316) @ id)) | ((X312 @ id @ X316 @ id) != $true)) | ~! [X317 : subst,X318 : subst,X319 : term] : ((sub @ (X315 @ X318 @ X319) @ X317) = (X315 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) | ($true = (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)))) => ! [X328 : term,X329 : subst > term > subst > $o] : (~! [X337 : subst > term > term] : (($true = (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) | ~! [X338 : term] : (($true = (X329 @ id @ (X337 @ id @ X338) @ id)) | ((X329 @ id @ X338 @ id) != $true)) | ~! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341)))) | ~! [X330 : term,X331 : term] : (($true = (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) | ((X329 @ id @ X330 @ id) != $true) | ((X329 @ id @ X331 @ id) != $true)) | ~! [X336 : term] : (($true = (X329 @ id @ X336 @ id)) | ((var @ (sub @ X336 @ id)) != $true)) | ($true = (X329 @ id @ X328 @ id)) | ~! [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true != (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) | ($true = (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) | ~! [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true != (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) | ($true = (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))))))) <=> (hoasinduction_lthm = $true)) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (~! [X49 : term,X50 : term] : (((X46 @ id @ X49 @ id) != $true) | ((X46 @ id @ X50 @ id) != $true) | ($true = (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id))) | ($true != (X46 @ id @ X47 @ id)) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ~! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (($true = (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53)) | ($true != (X46 @ X52 @ X54 @ (comp @ X51 @ X53)))) | ~! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = (X46 @ X58 @ X55 @ (comp @ X56 @ X57))) | ($true != (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57))) | ($true != (X46 @ id @ X48 @ id))) <=> (hoasinduction_lem2 = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X255 : term,X256 : subst] : ((sub @ one @ (push @ X255 @ X256)) = X255) => (! [X257 : term,X258 : subst] : ((comp @ sh @ (push @ X257 @ X258)) = X258) => (! [X259 : subst] : ((comp @ X259 @ id) = X259) => (! [X260 : term > $o,X261 : term] : (($true = (X260 @ X261)) | ~! [X263 : term,X264 : term] : (($true != (X260 @ X264)) | ($true != (X260 @ X263)) | ($true = (X260 @ (ap @ X264 @ X263)))) | ~! [X262 : term] : (($true != (X260 @ X262)) | ($true = (X260 @ (lam @ X262)))) | ~! [X265 : term] : (($true = (X260 @ X265)) | ($true != (var @ X265)))) => ! [X266 : term,X267 : subst,X268 : term > $o] : (~! [X273 : term] : (($true = (X268 @ (sub @ X273 @ X267))) | ($true != (var @ X273))) | ~! [X269 : term,X270 : term] : (($true != (X268 @ X269)) | ($true != (X268 @ X270)) | ($true = (X268 @ (ap @ X270 @ X269)))) | ~! [X271 : term] : (($true = (X268 @ (lam @ X271))) | ~! [X272 : term] : (($true = (X268 @ (sub @ X271 @ (push @ X272 @ id)))) | ($true != (X268 @ X272)))) | ($true = (X268 @ (sub @ X266 @ X267))))))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X198 : subst > term > subst > $o,X199 : term] : (~! [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true != (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) | ($true = (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ~! [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true = (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) | ($true != (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) | ~! [X204 : subst > term > term] : (~! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208))) | ~! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ($true != (X198 @ id @ X205 @ id))) | ((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) = $true)) | ~! [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) = $true) | ($true != (X198 @ id @ X213 @ id))) | ($true = (X198 @ id @ (lam @ X199) @ id)))) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) <=> (apinj2 = $true)) & ((d2subst @ d_id) = id) & (one = (d2term @ d_one)) & (substmonoid_gthm = $true) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & ((axidl = $true) <=> ! [X197 : subst] : ((comp @ id @ X197) = X197)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((hoasinduction_lem3b = $true) <=> ! [X253 : term] : ~! [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) != (X254 @ sh @ one))) & (pushprop_lthm = $true) & (ulamvarsh = $true) & (! [X276 : subst > term > subst > $o,X277 : term] : (~! [X279 : subst > term > term] : (~! [X281 : subst,X282 : term,X283 : subst] : ((X279 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281)) = (sub @ (X279 @ X283 @ X282) @ X281)) | ($true = (X276 @ id @ (lam @ (X279 @ sh @ one)) @ id)) | ~! [X280 : term] : (($true = (X276 @ id @ (X279 @ id @ X280) @ id)) | ($true != (X276 @ id @ X280 @ id)))) | ~! [X278 : term] : (($true = (X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) | ($true != (X276 @ id @ X278 @ id))) | ($true = (X276 @ id @ (lam @ X277) @ id))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X536 : term] : ~! [X537 : subst > term > term] : ~! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X125 : subst > term > subst > $o,X126 : term] : (~! [X132 : term,X133 : term] : (($true != (X125 @ id @ X132 @ id)) | ((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) = $true) | ($true != (X125 @ id @ X133 @ id))) | ($true = (X125 @ id @ X126 @ id)) | ~! [X127 : subst > term > term] : (($true = (X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) | ~! [X129 : subst,X130 : subst,X131 : term] : ((X127 @ (comp @ X129 @ X130) @ (sub @ X131 @ X130)) = (sub @ (X127 @ X129 @ X131) @ X130)) | ~! [X128 : term] : (($true != (X125 @ id @ X128 @ id)) | ($true = (X125 @ id @ (X127 @ id @ X128) @ id)))))) & (lamnotap != $true) & ((pushprop_lem0_lthm = $true) <=> ! [X112 : term > $o,X113 : term,X114 : subst] : ~! [X115 : term > $o] : ~! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X28 : term > $o,X29 : term] : (~! [X33 : term] : (((X28 @ (lam @ X33)) = $true) | ((X28 @ X33) != $true)) | ($true = (X28 @ X29)) | ~! [X31 : term,X32 : term] : (((X28 @ X32) != $true) | ($true != (X28 @ X31)) | ($true = (X28 @ (ap @ X32 @ X31)))) | ~! [X30 : term] : (((X28 @ X30) = $true) | ($true != (var @ X30)))) <=> (induction = $true)) & (! [X419 : term,X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (~! [X428 : subst,X429 : term,X430 : subst,X431 : subst] : (((X422 @ X431 @ X429 @ (comp @ X430 @ X428)) != $true) | ($true = (X422 @ (comp @ X431 @ X430) @ (sub @ X429 @ X430) @ X428))) | ($true != (X421 @ X419)) | ~! [X427 : term] : ((X422 @ id @ X427 @ id) = (X421 @ X427)) | ~! [X423 : subst,X424 : term,X425 : subst,X426 : subst] : (($true = (X422 @ X425 @ X424 @ (comp @ X426 @ X423))) | ($true != (X422 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426) @ X423))) | ($true = (X421 @ (ap @ X420 @ X419))) | ($true != (X421 @ X420)) | ~! [X432 : term,X433 : term] : (($true != (X422 @ id @ X433 @ id)) | ((X422 @ id @ X432 @ id) != $true) | ($true = (X422 @ id @ (ap @ (sub @ X433 @ id) @ X432) @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_lthm = $true) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) = (d2subst @ X291)) => (X290 = X291)) & ((laminj = $true) <=> ! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417)))) & (axapp = $true) & (! [X460 : term > $o,X461 : subst > term > subst > $o,X462 : term] : (~! [X463 : term] : ((X461 @ id @ X463 @ id) = (X460 @ X463)) | ~! [X465 : subst > term > term] : (~! [X466 : term,X467 : subst,X468 : subst] : ((sub @ (X465 @ X467 @ X466) @ X468) = (X465 @ (comp @ X467 @ X468) @ (sub @ X466 @ X468))) | ~! [X469 : term] : (($true != (X461 @ id @ X469 @ id)) | ($true = (X461 @ id @ (X465 @ id @ X469) @ id))) | ($true = (X461 @ id @ (lam @ (X465 @ sh @ one)) @ id))) | ($true = (X460 @ (lam @ X462))) | ~! [X464 : term] : (($true != (X460 @ X464)) | ($true = (X460 @ (sub @ X462 @ (push @ X464 @ id)))))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X34 : subst > term > subst > $o] : ~! [X35 : term > $o] : ~! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36))) & (! [X214 : term,X215 : term > $o,X216 : subst > term > subst > $o] : (~! [X227 : term,X228 : subst,X229 : subst,X230 : subst] : (($true = (X216 @ X228 @ X227 @ (comp @ X230 @ X229))) | ($true != (X216 @ (comp @ X228 @ X230) @ (sub @ X227 @ X230) @ X229))) | ~! [X223 : subst,X224 : subst,X225 : term,X226 : subst] : (($true != (X216 @ X224 @ X225 @ (comp @ X223 @ X226))) | ($true = (X216 @ (comp @ X224 @ X223) @ (sub @ X225 @ X223) @ X226))) | ~! [X231 : term] : ((X215 @ X231) = (X216 @ id @ X231 @ id)) | ($true = (X215 @ (lam @ X214))) | ~! [X222 : term] : (($true = (X215 @ (sub @ X214 @ (push @ X222 @ id)))) | ((X215 @ X222) != $true)) | ~! [X217 : subst > term > term] : (~! [X218 : term,X219 : subst,X220 : subst] : ((sub @ (X217 @ X220 @ X218) @ X219) = (X217 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) | ($true = (X216 @ id @ (lam @ (X217 @ sh @ one)) @ id)) | ~! [X221 : term] : (($true != (X216 @ id @ X221 @ id)) | ($true = (X216 @ id @ (X217 @ id @ X221) @ id))))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((! [X37 : term] : ((sub @ X37 @ id) = X37) => (! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)) => ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))))) <=> (hoasapinj1_lthm = $true)) & (apnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & ! [X27 : d_subst] : (d_id = X27) & ((hoasapinj2_lthm = $true) <=> (! [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) != (ap @ X411 @ X410)) | (X409 = X410)) => ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)))) & (hoaslamnotap_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X374 : subst,X375 : term > $o,X376 : term] : ~! [X377 : term > $o] : ~! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378))) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X63 : subst > term > subst > $o] : ~! [X64 : term > $o] : ~! [X65 : term] : ((X64 @ X65) = (X63 @ id @ X65 @ id)) => (! [X66 : term,X67 : term > $o] : (~! [X68 : term] : (($true = (X67 @ X68)) | ($true != (var @ X68))) | ~! [X69 : term,X70 : term] : (((X67 @ X70) != $true) | ((X67 @ (ap @ X70 @ X69)) = $true) | ($true != (X67 @ X69))) | ~! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ~! [X72 : term] : (((X67 @ X72) != $true) | ($true = (X67 @ (sub @ X71 @ (push @ X72 @ id)))))) | ($true = (X67 @ X66))) => (! [X73 : term] : ((sub @ X73 @ id) = X73) => (! [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (($true = (X74 @ (lam @ X76))) | ~! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) | ~! [X83 : term] : (($true != (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id))))) | ~! [X78 : subst > term > term] : (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ~! [X82 : term] : (($true != (X75 @ id @ X82 @ id)) | ($true = (X75 @ id @ (X78 @ id @ X82) @ id))) | ~! [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X78 @ X81 @ X79) @ X80)))) => ! [X84 : term,X85 : subst > term > subst > $o] : (($true = (X85 @ id @ X84 @ id)) | ~! [X97 : subst > term > term] : (~! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100)) | ($true = (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id)) | ~! [X98 : term] : (($true = (X85 @ id @ (X97 @ id @ X98) @ id)) | ((X85 @ id @ X98 @ id) != $true))) | ~! [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (($true = (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95)) | ($true != (X85 @ X96 @ X94 @ (comp @ X93 @ X95)))) | ~! [X88 : term] : (($true != (var @ (sub @ X88 @ id))) | ($true = (X85 @ id @ X88 @ id))) | ~! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (($true = (X85 @ X90 @ X91 @ (comp @ X92 @ X89))) | ((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) != $true)) | ~! [X86 : term,X87 : term] : (((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) = $true) | ($true != (X85 @ id @ X86 @ id)) | ($true != (X85 @ id @ X87 @ id))))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X232 : term] : ((sub @ X232 @ id) = X232) => ! [X233 : term,X234 : term > $o,X235 : subst > term > subst > $o] : (~! [X241 : subst > term > term] : (~! [X242 : term,X243 : subst,X244 : subst] : ((X241 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243)) = (sub @ (X241 @ X244 @ X242) @ X243)) | ($true = (X235 @ id @ (lam @ (X241 @ sh @ one)) @ id)) | ~! [X245 : term] : (($true != (X235 @ id @ X245 @ id)) | ($true = (X235 @ id @ (X241 @ id @ X245) @ id)))) | ~! [X246 : term] : ((X234 @ X246) = (X235 @ id @ X246 @ id)) | ~! [X240 : term] : (((X234 @ X240) != $true) | ((X234 @ (sub @ X233 @ (push @ X240 @ id))) = $true)) | ~! [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (($true != (X235 @ X247 @ X248 @ (comp @ X249 @ X250))) | ($true = (X235 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249) @ X250))) | ~! [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (((X235 @ X238 @ X239 @ (comp @ X237 @ X236)) = $true) | ($true != (X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237) @ X236))) | ((X234 @ (lam @ X233)) = $true)))) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) <=> (hoasapinj2 = $true)) & (hoasinduction_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (~! [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) = (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445)) | ~! [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) = (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) <=> (hoaslaminj = $true)) & (pushprop = $true) & ((substmonoid = $true) <=> (! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357))) & ((var @ (d2term @ d_one)) != $true) & (axmap = $true) & (induction2lem_gthm = $true) & (! [X352 : term] : ((sub @ X352 @ id) = X352) <=> (axvarid = $true)) & ! [X453 : d_term] : (d_one = X453) & ((pushprop_lem1v2_lthm = $true) <=> (! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1) => ! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (((X2 @ X4) != $true) | ($true = (X5 @ one)) | ~! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6))))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((! [X393 : term] : ((sub @ X393 @ id) = X393) => (! [X394 : subst,X395 : term,X396 : term > $o] : (~! [X400 : term] : (~! [X401 : term] : (((X396 @ (sub @ X400 @ (push @ X401 @ id))) = $true) | ($true != (X396 @ X401))) | ($true = (X396 @ (lam @ X400)))) | ~! [X398 : term,X399 : term] : (($true != (X396 @ X399)) | ($true != (X396 @ X398)) | ($true = (X396 @ (ap @ X398 @ X399)))) | ~! [X397 : term] : (($true = (X396 @ (sub @ X397 @ X394))) | ($true != (var @ X397))) | ($true = (X396 @ (sub @ X395 @ X394)))) => ! [X402 : term,X403 : term > $o] : (~! [X405 : term] : (~! [X406 : term] : (($true != (X403 @ X406)) | ($true = (X403 @ (sub @ X405 @ (push @ X406 @ id))))) | ($true = (X403 @ (lam @ X405)))) | ~! [X407 : term,X408 : term] : (($true = (X403 @ (ap @ X407 @ X408))) | ($true != (X403 @ X407)) | ((X403 @ X408) != $true)) | ~! [X404 : term] : (((var @ X404) != $true) | ($true = (X403 @ X404))) | ($true = (X403 @ X402))))) <=> (induction2_lthm = $true)) & (hoaslamnotvar = $true) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & (induction2_gthm = $true) & (pushprop_lem2v2 = $true) & (hoaslamnotap_lthm = $true)),
% 15.37/3.55 inference(flattening,[status(thm)],[f9])).
% 15.37/3.55 thf(f9,plain,(
% 15.37/3.55 ((pushprop_lem1v2_lthm = $true) <=> (! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1) => ! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (($true = (X5 @ one)) | ~((X2 @ X4) = $true) | ~! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvarind = $true) & ! [X7 : d_term,X8 : d_term] : (((d2term @ X7) = (d2term @ X8)) => (X7 = X8)) & ((! [X9 : term] : ((sub @ X9 @ id) = X9) => (! [X10 : subst > term > subst > $o,X11 : term] : (~! [X12 : subst > term > term] : (~! [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) = (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) | ~! [X16 : term] : (($true = (X10 @ id @ (X12 @ id @ X16) @ id)) | ~((X10 @ id @ X16 @ id) = $true))) | ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) = $true) | ~! [X17 : term] : (~($true = (X10 @ id @ X17 @ id)) | ($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)))) => ! [X18 : subst > term > subst > $o,X19 : term] : (~! [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) = $true) | ~($true = (X18 @ id @ X20 @ id))) | ~! [X21 : subst > term > term] : (~! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ~($true = (X18 @ id @ X22 @ id))) | ~! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25)) | ($true = (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id))) | ($true = (X18 @ id @ (lam @ X19) @ id))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & ! [X27 : d_subst] : (d_id = X27) & ~((var @ (d2term @ d_one)) = $true) & ((induction = $true) <=> ! [X28 : term > $o,X29 : term] : (($true = (X28 @ X29)) | ~! [X30 : term] : (((X28 @ X30) = $true) | ~($true = (var @ X30))) | ~! [X31 : term,X32 : term] : (($true = (X28 @ (ap @ X32 @ X31))) | ~((X28 @ X32) = $true) | ~($true = (X28 @ X31))) | ~! [X33 : term] : (((X28 @ (lam @ X33)) = $true) | ~((X28 @ X33) = $true)))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X34 : subst > term > subst > $o] : ~! [X35 : term > $o] : ~! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36))) & ((! [X37 : term] : ((sub @ X37 @ id) = X37) => (! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)) => ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))))) <=> (hoasapinj1_lthm = $true)) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (~! [X49 : term,X50 : term] : (~((X46 @ id @ X50 @ id) = $true) | ~((X46 @ id @ X49 @ id) = $true) | ($true = (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id))) | ~! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (~($true = (X46 @ X52 @ X54 @ (comp @ X51 @ X53))) | ($true = (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53))) | ~! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (~($true = (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57)) | ($true = (X46 @ X58 @ X55 @ (comp @ X56 @ X57)))) | ~($true = (X46 @ id @ X48 @ id)) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ~($true = (X46 @ id @ X47 @ id))) <=> (hoasinduction_lem2 = $true)) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X63 : subst > term > subst > $o] : ~! [X64 : term > $o] : ~! [X65 : term] : ((X64 @ X65) = (X63 @ id @ X65 @ id)) => (! [X66 : term,X67 : term > $o] : (($true = (X67 @ X66)) | ~! [X68 : term] : (~($true = (var @ X68)) | ($true = (X67 @ X68))) | ~! [X69 : term,X70 : term] : (~($true = (X67 @ X69)) | ((X67 @ (ap @ X70 @ X69)) = $true) | ~((X67 @ X70) = $true)) | ~! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ~! [X72 : term] : (($true = (X67 @ (sub @ X71 @ (push @ X72 @ id)))) | ~((X67 @ X72) = $true)))) => (! [X73 : term] : ((sub @ X73 @ id) = X73) => (! [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (($true = (X74 @ (lam @ X76))) | ~! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) | ~! [X78 : subst > term > term] : (~! [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X78 @ X81 @ X79) @ X80)) | ((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ~! [X82 : term] : (($true = (X75 @ id @ (X78 @ id @ X82) @ id)) | ~($true = (X75 @ id @ X82 @ id)))) | ~! [X83 : term] : (~($true = (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id)))))) => ! [X84 : term,X85 : subst > term > subst > $o] : (~! [X86 : term,X87 : term] : (~($true = (X85 @ id @ X87 @ id)) | ~($true = (X85 @ id @ X86 @ id)) | ((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) = $true)) | ~! [X88 : term] : (~($true = (var @ (sub @ X88 @ id))) | ($true = (X85 @ id @ X88 @ id))) | ~! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (~((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) = $true) | ($true = (X85 @ X90 @ X91 @ (comp @ X92 @ X89)))) | ~! [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (~($true = (X85 @ X96 @ X94 @ (comp @ X93 @ X95))) | ($true = (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95))) | ~! [X97 : subst > term > term] : (($true = (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id)) | ~! [X98 : term] : (~((X85 @ id @ X98 @ id) = $true) | ($true = (X85 @ id @ (X97 @ id @ X98) @ id))) | ~! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100))) | ($true = (X85 @ id @ X84 @ id)))))))) & (hoaslamnotvar_lthm = $true) & (! [X102 : subst > term > subst > $o] : ~! [X103 : term > $o] : ~! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) <=> (hoasinduction_lem0 = $true)) & ((induction2 = $true) <=> ! [X105 : term > $o,X106 : term] : (~! [X107 : term] : (~($true = (var @ X107)) | ((X105 @ X107) = $true)) | ~! [X108 : term,X109 : term] : (($true = (X105 @ (ap @ X109 @ X108))) | ~($true = (X105 @ X108)) | ~($true = (X105 @ X109))) | ($true = (X105 @ X106)) | ~! [X110 : term] : (~! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ~($true = (X105 @ X111))) | ((X105 @ (lam @ X110)) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X112 : term > $o,X113 : term,X114 : subst] : ~! [X115 : term > $o] : ~! [X116 : term] : ((X115 @ X116) = (X112 @ (sub @ X116 @ (push @ X113 @ X114))))) & ((hoasinduction_lem3aa = $true) <=> ! [X117 : term,X118 : subst > term > subst > $o] : (($true = (X118 @ id @ (lam @ (sub @ X117 @ (push @ one @ sh))) @ id)) | ~! [X119 : term] : (~($true = (X118 @ id @ X119 @ id)) | ($true = (X118 @ id @ (sub @ X117 @ (push @ X119 @ id)) @ id))) | ~! [X120 : subst > term > term] : (($true = (X118 @ id @ (lam @ (X120 @ sh @ one)) @ id)) | ~! [X121 : term] : (($true = (X118 @ id @ (X120 @ id @ X121) @ id)) | ~($true = (X118 @ id @ X121 @ id))) | ~! [X122 : subst,X123 : subst,X124 : term] : ((sub @ (X120 @ X122 @ X124) @ X123) = (X120 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123)))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X125 : subst > term > subst > $o,X126 : term] : (($true = (X125 @ id @ X126 @ id)) | ~! [X127 : subst > term > term] : (~! [X128 : term] : (~($true = (X125 @ id @ X128 @ id)) | ($true = (X125 @ id @ (X127 @ id @ X128) @ id))) | ~! [X129 : subst,X130 : subst,X131 : term] : ((X127 @ (comp @ X129 @ X130) @ (sub @ X131 @ X130)) = (sub @ (X127 @ X129 @ X131) @ X130)) | ($true = (X125 @ id @ (lam @ (X127 @ sh @ one)) @ id))) | ~! [X132 : term,X133 : term] : (((X125 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id) = $true) | ~($true = (X125 @ id @ X132 @ id)) | ~($true = (X125 @ id @ X133 @ id))))) & (! [X134 : term,X135 : subst > term > subst > $o] : (((X135 @ id @ X134 @ id) = $true) | ~! [X136 : subst,X137 : term,X138 : subst,X139 : subst] : (($true = (X135 @ (comp @ X136 @ X138) @ (sub @ X137 @ X138) @ X139)) | ~((X135 @ X136 @ X137 @ (comp @ X138 @ X139)) = $true)) | ~! [X140 : subst > term > term] : (~! [X141 : term,X142 : subst,X143 : subst] : ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)) = (sub @ (X140 @ X143 @ X141) @ X142)) | ~! [X144 : term] : (~($true = (X135 @ id @ X144 @ id)) | ($true = (X135 @ id @ (X140 @ id @ X144) @ id))) | ($true = (X135 @ id @ (lam @ (X140 @ sh @ one)) @ id))) | ~! [X145 : term] : (($true = (X135 @ id @ X145 @ id)) | ~($true = (var @ (sub @ X145 @ id)))) | ~! [X146 : term,X147 : term] : (~((X135 @ id @ X146 @ id) = $true) | ~($true = (X135 @ id @ X147 @ id)) | ($true = (X135 @ id @ (ap @ (sub @ X147 @ id) @ X146) @ id))) | ~! [X148 : subst,X149 : subst,X150 : subst,X151 : term] : (($true = (X135 @ X148 @ X151 @ (comp @ X149 @ X150))) | ~($true = (X135 @ (comp @ X148 @ X149) @ (sub @ X151 @ X149) @ X150)))) <=> (hoasinduction = $true)) & (! [X152 : term > $o,X153 : term > $o,X154 : subst,X155 : term] : (($true = (X153 @ one)) | ~! [X156 : term] : ((X153 @ X156) = (X152 @ (sub @ X156 @ (push @ X155 @ X154)))) | ~($true = (X152 @ X155))) <=> (pushprop_lem1v2 = $true)) & (hoasapnotvar_gthm = $true) & ((axscons = $true) <=> ! [X157 : subst] : ((push @ (sub @ one @ X157) @ (comp @ sh @ X157)) = X157)) & ((d2subst @ d_id) = sh) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $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)))))))))))) & (induction2_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X158 : term] : ? [X159 : d_term] : ((d2term @ X159) = X158) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X160 : term,X161 : subst > term > subst > $o] : (~! [X162 : subst > term > term] : (~! [X163 : subst,X164 : term,X165 : subst] : ((sub @ (X162 @ X165 @ X164) @ X163) = (X162 @ (comp @ X165 @ X163) @ (sub @ X164 @ X163))) | ($true = (X161 @ id @ (lam @ (X162 @ sh @ one)) @ id)) | ~! [X166 : term] : (($true = (X161 @ id @ (X162 @ id @ X166) @ id)) | ~($true = (X161 @ id @ X166 @ id)))) | ($true = (X161 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id)) | ~! [X167 : term] : (($true = (X161 @ id @ (sub @ X160 @ (push @ X167 @ id)) @ id)) | ~($true = (X161 @ id @ X167 @ id))))) & ((! [X168 : term,X169 : subst] : ((sub @ one @ (push @ X168 @ X169)) = X168) => (! [X170 : term,X171 : subst] : ((comp @ sh @ (push @ X170 @ X171)) = X171) => (! [X172 : term,X173 : term] : ((X172 = X173) | ((lam @ X173) != (lam @ X172))) => ! [X174 : subst > term > term,X175 : term,X176 : subst,X177 : subst > term > term] : (((X174 @ X176 @ X175) = (X177 @ X176 @ X175)) | ~! [X181 : subst,X182 : subst,X183 : term] : ((sub @ (X177 @ X182 @ X183) @ X181) = (X177 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) | ~! [X178 : subst,X179 : subst,X180 : term] : ((sub @ (X174 @ X178 @ X180) @ X179) = (X174 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) | ((lam @ (X177 @ sh @ one)) != (lam @ (X174 @ sh @ one))))))) <=> (hoaslaminj_lthm = $true)) & (axapp = $true) & (hoasinduction_lem2v2_gthm = $true) & (one = (d2term @ d_one)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X184 : subst > term > subst > $o,X185 : term] : (($true = (X184 @ id @ (lam @ (sub @ X185 @ (push @ one @ sh))) @ id)) | ~! [X186 : term] : (~($true = (X184 @ id @ X186 @ id)) | ($true = (X184 @ id @ (sub @ X185 @ (push @ X186 @ id)) @ id))) | ~! [X187 : subst > term > term,X188 : term] : (~! [X189 : subst,X190 : term,X191 : subst] : ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189)) = (sub @ X188 @ (push @ (sub @ X190 @ X189) @ (comp @ X191 @ X189)))) | ($true = (X184 @ id @ (lam @ (X187 @ sh @ one)) @ id)) | ~! [X192 : subst,X193 : term,X194 : subst] : ((sub @ (sub @ X188 @ (push @ X193 @ X194)) @ X192) = (sub @ (X187 @ X194 @ X193) @ X192)) | ~! [X195 : term] : (~($true = (X184 @ id @ X195 @ id)) | ($true = (X184 @ id @ (X187 @ id @ X195) @ id)))))) & (axmap = $true) & ((axidr = $true) <=> ! [X196 : subst] : ((comp @ X196 @ id) = X196)) & ((axidl = $true) <=> ! [X197 : subst] : ((comp @ id @ X197) = X197)) & (termmset_gthm = $true) & (! [X198 : subst > term > subst > $o,X199 : term] : (~! [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (~($true = (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200)) | ($true = (X198 @ X203 @ X202 @ (comp @ X201 @ X200)))) | ($true = (X198 @ id @ (lam @ X199) @ id)) | ~! [X204 : subst > term > term] : (~! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ~($true = (X198 @ id @ X205 @ id))) | ((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) = $true) | ~! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208)))) | ~! [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (~($true = (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) | ($true = (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ~! [X213 : term] : (~($true = (X198 @ id @ X213 @ id)) | ((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) = $true))) <=> (hoasinduction_lem3 = $true)) & (hoasapinj2_gthm = $true) & (lamnotvar = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (! [X214 : term,X215 : term > $o,X216 : subst > term > subst > $o] : (~! [X217 : subst > term > term] : (($true = (X216 @ id @ (lam @ (X217 @ sh @ one)) @ id)) | ~! [X218 : term,X219 : subst,X220 : subst] : ((sub @ (X217 @ X220 @ X218) @ X219) = (X217 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) | ~! [X221 : term] : (~($true = (X216 @ id @ X221 @ id)) | ($true = (X216 @ id @ (X217 @ id @ X221) @ id)))) | ~! [X222 : term] : (~((X215 @ X222) = $true) | ($true = (X215 @ (sub @ X214 @ (push @ X222 @ id))))) | ~! [X223 : subst,X224 : subst,X225 : term,X226 : subst] : (($true = (X216 @ (comp @ X224 @ X223) @ (sub @ X225 @ X223) @ X226)) | ~($true = (X216 @ X224 @ X225 @ (comp @ X223 @ X226)))) | ~! [X227 : term,X228 : subst,X229 : subst,X230 : subst] : (($true = (X216 @ X228 @ X227 @ (comp @ X230 @ X229))) | ~($true = (X216 @ (comp @ X228 @ X230) @ (sub @ X227 @ X230) @ X229))) | ($true = (X215 @ (lam @ X214))) | ~! [X231 : term] : ((X215 @ X231) = (X216 @ id @ X231 @ id))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X232 : term] : ((sub @ X232 @ id) = X232) => ! [X233 : term,X234 : term > $o,X235 : subst > term > subst > $o] : (~! [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (((X235 @ X238 @ X239 @ (comp @ X237 @ X236)) = $true) | ~($true = (X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237) @ X236))) | ~! [X240 : term] : (~((X234 @ X240) = $true) | ((X234 @ (sub @ X233 @ (push @ X240 @ id))) = $true)) | ~! [X241 : subst > term > term] : (~! [X242 : term,X243 : subst,X244 : subst] : ((X241 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243)) = (sub @ (X241 @ X244 @ X242) @ X243)) | ~! [X245 : term] : (($true = (X235 @ id @ (X241 @ id @ X245) @ id)) | ~($true = (X235 @ id @ X245 @ id))) | ($true = (X235 @ id @ (lam @ (X241 @ sh @ one)) @ id))) | ~! [X246 : term] : ((X234 @ X246) = (X235 @ id @ X246 @ id)) | ~! [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (~($true = (X235 @ X247 @ X248 @ (comp @ X249 @ X250))) | ($true = (X235 @ (comp @ X247 @ X249) @ (sub @ X248 @ X249) @ X250))) | ((X234 @ (lam @ X233)) = $true))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((! [X251 : term] : ((sub @ X251 @ id) = X251) => ! [X252 : term] : ((sub @ X252 @ id) = X252)) <=> (termmset_lthm = $true)) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X253 : term] : ~! [X254 : subst > term > term] : ((sub @ X253 @ (push @ one @ sh)) != (X254 @ sh @ one))) & (apnotvar = $true) & ((! [X255 : term,X256 : subst] : ((sub @ one @ (push @ X255 @ X256)) = X255) => (! [X257 : term,X258 : subst] : ((comp @ sh @ (push @ X257 @ X258)) = X258) => (! [X259 : subst] : ((comp @ X259 @ id) = X259) => (! [X260 : term > $o,X261 : term] : (~! [X262 : term] : (($true = (X260 @ (lam @ X262))) | ~($true = (X260 @ X262))) | ~! [X263 : term,X264 : term] : (~($true = (X260 @ X263)) | ~($true = (X260 @ X264)) | ($true = (X260 @ (ap @ X264 @ X263)))) | ~! [X265 : term] : (~($true = (var @ X265)) | ($true = (X260 @ X265))) | ($true = (X260 @ X261))) => ! [X266 : term,X267 : subst,X268 : term > $o] : (~! [X269 : term,X270 : term] : (($true = (X268 @ (ap @ X270 @ X269))) | ~($true = (X268 @ X269)) | ~($true = (X268 @ X270))) | ~! [X271 : term] : (~! [X272 : term] : (~($true = (X268 @ X272)) | ($true = (X268 @ (sub @ X271 @ (push @ X272 @ id))))) | ($true = (X268 @ (lam @ X271)))) | ($true = (X268 @ (sub @ X266 @ X267))) | ~! [X273 : term] : (($true = (X268 @ (sub @ X273 @ X267))) | ~($true = (var @ X273)))))))) <=> (induction2lem_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & ~(ulamvar1 = $true) & ((axshiftcons = $true) <=> ! [X274 : term,X275 : subst] : ((comp @ sh @ (push @ X274 @ X275)) = X275)) & (! [X276 : subst > term > subst > $o,X277 : term] : (~! [X278 : term] : (~($true = (X276 @ id @ X278 @ id)) | ($true = (X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id))) | ($true = (X276 @ id @ (lam @ X277) @ id)) | ~! [X279 : subst > term > term] : (~! [X280 : term] : (~($true = (X276 @ id @ X280 @ id)) | ($true = (X276 @ id @ (X279 @ id @ X280) @ id))) | ~! [X281 : subst,X282 : term,X283 : subst] : ((X279 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281)) = (sub @ (X279 @ X283 @ X282) @ X281)) | ($true = (X276 @ id @ (lam @ (X279 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3a = $true)) & ! [X284 : subst] : ? [X285 : d_subst] : ((d2subst @ X285) = X284) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X286 : term,X287 : term,X288 : term,X289 : term] : ((X288 = X289) | ((ap @ (sub @ X286 @ id) @ X289) != (ap @ (sub @ X287 @ id) @ X288))) <=> (hoasapinj2 = $true)) & ! [X290 : d_subst,X291 : d_subst] : (((d2subst @ X290) = (d2subst @ X291)) => (X290 = X291)) & ((! [X292 : term > $o,X293 : term] : (~! [X294 : term] : (($true = (X292 @ (lam @ X294))) | ~! [X295 : term] : (($true = (X292 @ (sub @ X294 @ (push @ X295 @ id)))) | ~((X292 @ X295) = $true))) | ~! [X296 : term] : (($true = (X292 @ X296)) | ~($true = (var @ X296))) | ($true = (X292 @ X293)) | ~! [X297 : term,X298 : term] : (~((X292 @ X298) = $true) | ($true = (X292 @ (ap @ X298 @ X297))) | ~($true = (X292 @ X297)))) => (! [X299 : subst > term > subst > $o,X300 : term,X301 : term] : (($true = (X299 @ id @ (ap @ X300 @ X301) @ id)) | ~! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~($true = (X299 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304)) | ($true = (X299 @ X305 @ X303 @ (comp @ X302 @ X304)))) | ~! [X306 : term,X307 : term] : (~($true = (X299 @ id @ X306 @ id)) | ($true = (X299 @ id @ (ap @ (sub @ X306 @ id) @ X307) @ id)) | ~((X299 @ id @ X307 @ id) = $true)) | ~($true = (X299 @ id @ X301 @ id)) | ~((X299 @ id @ X300 @ id) = $true) | ~! [X308 : term,X309 : subst,X310 : subst,X311 : subst] : (($true = (X299 @ (comp @ X311 @ X309) @ (sub @ X308 @ X309) @ X310)) | ~($true = (X299 @ X311 @ X308 @ (comp @ X309 @ X310))))) => (! [X312 : subst > term > subst > $o,X313 : term] : (~! [X314 : term] : (($true = (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | ~((X312 @ id @ X314 @ id) = $true)) | ($true = (X312 @ id @ (lam @ X313) @ id)) | ~! [X315 : subst > term > term] : (~! [X316 : term] : (~((X312 @ id @ X316 @ id) = $true) | ($true = (X312 @ id @ (X315 @ id @ X316) @ id))) | ($true = (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) | ~! [X317 : subst,X318 : subst,X319 : term] : ((sub @ (X315 @ X318 @ X319) @ X317) = (X315 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317)))) | ~! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (~($true = (X312 @ (comp @ X322 @ X323) @ (sub @ X321 @ X323) @ X320)) | ($true = (X312 @ X322 @ X321 @ (comp @ X323 @ X320)))) | ~! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = (X312 @ (comp @ X325 @ X324) @ (sub @ X326 @ X324) @ X327)) | ~($true = (X312 @ X325 @ X326 @ (comp @ X324 @ X327))))) => ! [X328 : term,X329 : subst > term > subst > $o] : (~! [X330 : term,X331 : term] : (($true = (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) | ~((X329 @ id @ X330 @ id) = $true) | ~((X329 @ id @ X331 @ id) = $true)) | ($true = (X329 @ id @ X328 @ id)) | ~! [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (~($true = (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) | ($true = (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) | ~! [X336 : term] : (($true = (X329 @ id @ X336 @ id)) | ~((var @ (sub @ X336 @ id)) = $true)) | ~! [X337 : subst > term > term] : (($true = (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) | ~! [X338 : term] : (~((X329 @ id @ X338 @ id) = $true) | ($true = (X329 @ id @ (X337 @ id @ X338) @ id))) | ~! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341)))) | ~! [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (~($true = (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) | ($true = (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X346 : term,X347 : term,X348 : subst > term > term] : (~! [X349 : subst,X350 : term,X351 : subst] : ((X348 @ (comp @ X349 @ X351) @ (sub @ X350 @ X351)) = (sub @ (X348 @ X349 @ X350) @ X351)) | ((ap @ (sub @ X347 @ id) @ X346) != (lam @ (X348 @ sh @ one))))) & (! [X352 : term] : ((sub @ X352 @ id) = X352) <=> (axvarid = $true)) & ((hoasapinj1 = $true) <=> ! [X353 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X356) | ((ap @ (sub @ X356 @ id) @ X355) != (ap @ (sub @ X354 @ id) @ X353)))) & (hoasinduction_lem3a_gthm = $true) & ((substmonoid = $true) <=> (! [X358 : subst] : ((comp @ X358 @ id) = X358) & ! [X357 : subst] : ((comp @ id @ X357) = X357))) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X359 : term] : ~! [X360 : subst > term > term] : ~! [X361 : term,X362 : subst] : ((X360 @ X362 @ X361) = (sub @ X359 @ (push @ X361 @ X362))) => (! [X363 : term] : ((sub @ X363 @ id) = X363) => ! [X364 : term,X365 : term > $o,X366 : subst > term > subst > $o] : (~! [X367 : term] : ((X366 @ id @ X367 @ id) = (X365 @ X367)) | ~! [X368 : term] : (($true = (X365 @ (sub @ X364 @ (push @ X368 @ id)))) | ~($true = (X365 @ X368))) | ~! [X369 : subst > term > term] : (~! [X370 : term] : (~($true = (X366 @ id @ X370 @ id)) | ((X366 @ id @ (X369 @ id @ X370) @ id) = $true)) | ($true = (X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) | ~! [X371 : term,X372 : subst,X373 : subst] : ((sub @ (X369 @ X373 @ X371) @ X372) = (X369 @ (comp @ X373 @ X372) @ (sub @ X371 @ X372)))) | ($true = (X365 @ (lam @ X364))))))) & ((pushprop_lem0 = $true) <=> ! [X374 : subst,X375 : term > $o,X376 : term] : ~! [X377 : term > $o] : ~! [X378 : term] : ((X375 @ (sub @ X378 @ (push @ X376 @ X374))) = (X377 @ X378))) & (hoasinduction_gthm = $true) & ((shinj = $true) <=> ! [X379 : term,X380 : term] : ((X379 = X380) | ((sub @ X379 @ sh) != (sub @ X380 @ sh)))) & ((induction2lem = $true) <=> ! [X381 : term > $o,X382 : subst,X383 : term] : (($true = (X381 @ (sub @ X383 @ X382))) | ~! [X384 : term] : (~! [X385 : term] : (~($true = (X381 @ X385)) | ($true = (X381 @ (sub @ X384 @ (push @ X385 @ id))))) | ($true = (X381 @ (lam @ X384)))) | ~! [X386 : term] : (($true = (X381 @ (sub @ X386 @ X382))) | ~($true = (var @ X386))) | ~! [X387 : term,X388 : term] : (($true = (X381 @ (ap @ X388 @ X387))) | ~($true = (X381 @ X388)) | ~($true = (X381 @ X387))))) & (ulamvarsh = $true) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : (((ap @ X390 @ X389) != (ap @ X392 @ X391)) | (X389 = X391)) <=> (apinj2 = $true)) & ((! [X393 : term] : ((sub @ X393 @ id) = X393) => (! [X394 : subst,X395 : term,X396 : term > $o] : (~! [X397 : term] : (($true = (X396 @ (sub @ X397 @ X394))) | ~($true = (var @ X397))) | ~! [X398 : term,X399 : term] : (($true = (X396 @ (ap @ X398 @ X399))) | ~($true = (X396 @ X399)) | ~($true = (X396 @ X398))) | ~! [X400 : term] : (~! [X401 : term] : (~($true = (X396 @ X401)) | ((X396 @ (sub @ X400 @ (push @ X401 @ id))) = $true)) | ($true = (X396 @ (lam @ X400)))) | ($true = (X396 @ (sub @ X395 @ X394)))) => ! [X402 : term,X403 : term > $o] : (~! [X404 : term] : (~((var @ X404) = $true) | ($true = (X403 @ X404))) | ($true = (X403 @ X402)) | ~! [X405 : term] : (~! [X406 : term] : (~($true = (X403 @ X406)) | ($true = (X403 @ (sub @ X405 @ (push @ X406 @ id))))) | ($true = (X403 @ (lam @ X405)))) | ~! [X407 : term,X408 : term] : (($true = (X403 @ (ap @ X407 @ X408))) | ~($true = (X403 @ X407)) | ~((X403 @ X408) = $true))))) <=> (induction2_lthm = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X409 : term,X410 : term,X411 : term,X412 : term] : (((ap @ X412 @ X409) != (ap @ X411 @ X410)) | (X409 = X410)) => ! [X413 : term,X414 : term,X415 : term,X416 : term] : (((ap @ (sub @ X414 @ id) @ X413) != (ap @ (sub @ X416 @ id) @ X415)) | (X413 = X415)))) & (pushprop_lem1v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axassoc = $true) & ((laminj = $true) <=> ! [X417 : term,X418 : term] : ((X417 = X418) | ((lam @ X418) != (lam @ X417)))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X419 : term,X420 : term,X421 : term > $o,X422 : subst > term > subst > $o] : (~! [X423 : subst,X424 : term,X425 : subst,X426 : subst] : (($true = (X422 @ X425 @ X424 @ (comp @ X426 @ X423))) | ~($true = (X422 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426) @ X423))) | ~! [X427 : term] : ((X422 @ id @ X427 @ id) = (X421 @ X427)) | ~! [X428 : subst,X429 : term,X430 : subst,X431 : subst] : (($true = (X422 @ (comp @ X431 @ X430) @ (sub @ X429 @ X430) @ X428)) | ~((X422 @ X431 @ X429 @ (comp @ X430 @ X428)) = $true)) | ~($true = (X421 @ X420)) | ~($true = (X421 @ X419)) | ($true = (X421 @ (ap @ X420 @ X419))) | ~! [X432 : term,X433 : term] : (($true = (X422 @ id @ (ap @ (sub @ X433 @ id) @ X432) @ id)) | ~($true = (X422 @ id @ X433 @ id)) | ~((X422 @ id @ X432 @ id) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X434 : term] : ~! [X435 : subst > term > term] : ~! [X436 : term,X437 : subst] : ((X435 @ X437 @ X436) = (sub @ X434 @ (push @ X436 @ X437))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X438 : subst,X439 : term > $o,X440 : term,X441 : term,X442 : term > $o] : (~($true = (X439 @ X441)) | ($true = (X442 @ (sub @ X441 @ (push @ X440 @ X438)))))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (! [X443 : subst > term > term,X444 : subst > term > term,X445 : term,X446 : subst] : (~! [X450 : subst,X451 : term,X452 : subst] : ((sub @ (X443 @ X452 @ X451) @ X450) = (X443 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) | ((lam @ (X444 @ sh @ one)) != (lam @ (X443 @ sh @ one))) | ((X444 @ X446 @ X445) = (X443 @ X446 @ X445)) | ~! [X447 : subst,X448 : term,X449 : subst] : ((sub @ (X444 @ X447 @ X448) @ X449) = (X444 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) <=> (hoaslaminj = $true)) & ! [X453 : d_term] : (d_one = X453) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop = $true) & (! [X454 : term] : ~! [X455 : subst > term > term] : ((X455 @ sh @ one) != (sub @ X454 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_lthm = $true) & (axvarshift = $true) & (pushprop_gthm = $true) & ((! [X456 : subst] : ((comp @ id @ X456) = X456) => (! [X457 : subst] : ((comp @ X457 @ id) = X457) => (! [X459 : subst] : ((comp @ id @ X459) = X459) & ! [X458 : subst] : ((comp @ X458 @ id) = X458)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X460 : term > $o,X461 : subst > term > subst > $o,X462 : term] : (($true = (X460 @ (lam @ X462))) | ~! [X463 : term] : ((X461 @ id @ X463 @ id) = (X460 @ X463)) | ~! [X464 : term] : (($true = (X460 @ (sub @ X462 @ (push @ X464 @ id)))) | ~($true = (X460 @ X464))) | ~! [X465 : subst > term > term] : (($true = (X461 @ id @ (lam @ (X465 @ sh @ one)) @ id)) | ~! [X466 : term,X467 : subst,X468 : subst] : ((sub @ (X465 @ X467 @ X466) @ X468) = (X465 @ (comp @ X467 @ X468) @ (sub @ X466 @ X468))) | ~! [X469 : term] : (~($true = (X461 @ id @ X469 @ id)) | ($true = (X461 @ id @ (X465 @ id @ X469) @ id)))))) & ((axvarcons = $true) <=> ! [X470 : term,X471 : subst] : ((sub @ one @ (push @ X470 @ X471)) = X470)) & (axabs = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X472 : subst,X473 : term] : ((sub @ one @ (push @ X473 @ X472)) = X473) => (! [X474 : subst,X475 : term] : ((comp @ sh @ (push @ X475 @ X474)) = X474) => ! [X476 : term > $o,X477 : term > $o,X478 : term,X479 : subst,X480 : term] : (((X477 @ (sub @ X480 @ (push @ X478 @ X479))) = $true) | ~($true = (X476 @ X480)))))) & (induction2lem_gthm = $true) & (pushprop_lem1_gthm = $true) & ((! [X481 : term] : ((sub @ X481 @ id) = X481) => (! [X482 : subst > term > subst > $o,X483 : term] : (~! [X484 : subst > term > term] : (~! [X485 : subst,X486 : term,X487 : subst] : ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)) = (sub @ (X484 @ X485 @ X486) @ X487)) | ($true = (X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) | ~! [X488 : term] : (($true = (X482 @ id @ (X484 @ id @ X488) @ id)) | ~($true = (X482 @ id @ X488 @ id)))) | ((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id) = $true) | ~! [X489 : term] : (~($true = (X482 @ id @ X489 @ id)) | ($true = (X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)))) => ! [X490 : term,X491 : subst > term > subst > $o] : (~! [X492 : subst > term > term] : (~! [X493 : term] : (~($true = (X491 @ id @ X493 @ id)) | ((X491 @ id @ (X492 @ id @ X493) @ id) = $true)) | ~! [X494 : subst,X495 : term,X496 : subst] : ((sub @ (X492 @ X494 @ X495) @ X496) = (X492 @ (comp @ X494 @ X496) @ (sub @ X495 @ X496))) | ($true = (X491 @ id @ (lam @ (X492 @ sh @ one)) @ id))) | ~! [X497 : term] : (($true = (X491 @ id @ (sub @ X490 @ (push @ X497 @ id)) @ id)) | ~($true = (X491 @ id @ X497 @ id))) | ~! [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (~($true = (X491 @ X499 @ X501 @ (comp @ X500 @ X498))) | ($true = (X491 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500) @ X498))) | ($true = (X491 @ id @ (lam @ X490) @ id)) | ~! [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (~($true = (X491 @ (comp @ X503 @ X502) @ (sub @ X505 @ X502) @ X504)) | ($true = (X491 @ X503 @ X505 @ (comp @ X502 @ X504))))))) <=> (hoasinduction_lem3_lthm = $true)) & ((! [X506 : subst > term > subst > $o] : ~! [X507 : term > $o] : ~! [X508 : term] : ((X506 @ id @ X508 @ id) = (X507 @ X508)) => (! [X509 : term > $o,X510 : term] : (~! [X511 : term,X512 : term] : (~((X509 @ X511) = $true) | ($true = (X509 @ (ap @ X512 @ X511))) | ~($true = (X509 @ X512))) | ($true = (X509 @ X510)) | ~! [X513 : term] : (~! [X514 : term] : (~($true = (X509 @ X514)) | ($true = (X509 @ (sub @ X513 @ (push @ X514 @ id))))) | ($true = (X509 @ (lam @ X513)))) | ~! [X515 : term] : (~($true = (var @ X515)) | ($true = (X509 @ X515)))) => (! [X516 : term] : ((sub @ X516 @ id) = X516) => (! [X517 : term > $o,X518 : subst > term > subst > $o,X519 : term] : (~! [X520 : term] : ((X517 @ X520) = (X518 @ id @ X520 @ id)) | ($true = (X517 @ (lam @ X519))) | ~! [X521 : term] : (((X517 @ (sub @ X519 @ (push @ X521 @ id))) = $true) | ~($true = (X517 @ X521))) | ~! [X522 : subst > term > term] : (~! [X523 : term] : (~((X518 @ id @ X523 @ id) = $true) | ($true = (X518 @ id @ (X522 @ id @ X523) @ id))) | ~! [X524 : term,X525 : subst,X526 : subst] : ((X522 @ (comp @ X525 @ X526) @ (sub @ X524 @ X526)) = (sub @ (X522 @ X525 @ X524) @ X526)) | ($true = (X518 @ id @ (lam @ (X522 @ sh @ one)) @ id)))) => ! [X527 : term,X528 : subst > term > subst > $o] : (~! [X529 : term,X530 : term] : (~($true = (X528 @ id @ X529 @ id)) | ~($true = (X528 @ id @ X530 @ id)) | ($true = (X528 @ id @ (ap @ (sub @ X529 @ id) @ X530) @ id))) | ~! [X531 : subst > term > term] : (~! [X532 : term] : (($true = (X528 @ id @ (X531 @ id @ X532) @ id)) | ~($true = (X528 @ id @ X532 @ id))) | ($true = (X528 @ id @ (lam @ (X531 @ sh @ one)) @ id)) | ~! [X533 : term,X534 : subst,X535 : subst] : ((sub @ (X531 @ X534 @ X533) @ X535) = (X531 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | ($true = (X528 @ id @ X527 @ id))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (axclos = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X536 : term] : ~! [X537 : subst > term > term] : ~! [X538 : term,X539 : subst] : ((sub @ X536 @ (push @ X538 @ X539)) = (X537 @ X539 @ X538))) & ~(lamnotap = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)),
% 15.37/3.55 inference(rectify,[status(thm)],[f6])).
% 15.37/3.55 thf(f6,plain,(
% 15.37/3.55 ((pushprop_lem1v2_lthm = $true) <=> (! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1) => ! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : (($true = (X5 @ one)) | ~((X2 @ X4) = $true) | ~! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvarind = $true) & ! [X7 : d_term,X8 : d_term] : (((d2term @ X7) = (d2term @ X8)) => (X7 = X8)) & ((! [X9 : term] : ((sub @ X9 @ id) = X9) => (! [X10 : subst > term > subst > $o,X11 : term] : (~! [X12 : subst > term > term] : (~! [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) = (sub @ (X12 @ X13 @ X14) @ X15)) | ($true = (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) | ~! [X16 : term] : (($true = (X10 @ id @ (X12 @ id @ X16) @ id)) | ~((X10 @ id @ X16 @ id) = $true))) | ((X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) = $true) | ~! [X17 : term] : (~($true = (X10 @ id @ X17 @ id)) | ($true = (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)))) => ! [X18 : subst > term > subst > $o,X19 : term] : (~! [X20 : term] : (((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) = $true) | ~($true = (X18 @ id @ X20 @ id))) | ~! [X21 : subst > term > term] : (~! [X22 : term] : (($true = (X18 @ id @ (X21 @ id @ X22) @ id)) | ~($true = (X18 @ id @ X22 @ id))) | ~! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25)) | ($true = (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id))) | ($true = (X18 @ id @ (lam @ X19) @ id))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> (termmset = $true)) & ! [X27 : d_subst] : (d_id = X27) & ~((var @ (d2term @ d_one)) = $true) & ((induction = $true) <=> ! [X28 : term > $o,X29 : term] : (($true = (X28 @ X29)) | ~! [X30 : term] : (((X28 @ X30) = $true) | ~($true = (var @ X30))) | ~! [X31 : term,X32 : term] : (($true = (X28 @ (ap @ X32 @ X31))) | ~((X28 @ X32) = $true) | ~($true = (X28 @ X31))) | ~! [X33 : term] : (((X28 @ (lam @ X33)) = $true) | ~((X28 @ X33) = $true)))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X34 : subst > term > subst > $o] : ~! [X35 : term > $o] : ~! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36))) & ((! [X37 : term] : ((sub @ X37 @ id) = X37) => (! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)) => ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X43) | ((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44))))) <=> (hoasapinj1_lthm = $true)) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (~! [X49 : term,X50 : term] : (~((X46 @ id @ X50 @ id) = $true) | ~((X46 @ id @ X49 @ id) = $true) | ($true = (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id))) | ~! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (~($true = (X46 @ X52 @ X54 @ (comp @ X51 @ X53))) | ($true = (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53))) | ~! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (~($true = (X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57)) | ($true = (X46 @ X58 @ X55 @ (comp @ X56 @ X57)))) | ~($true = (X46 @ id @ X48 @ id)) | ($true = (X46 @ id @ (ap @ X48 @ X47) @ id)) | ~($true = (X46 @ id @ X47 @ id))) <=> (hoasinduction_lem2 = $true)) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ X59 @ X62) != (ap @ X60 @ X61)) | (X59 = X60)) <=> (apinj1 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X63 : subst > term > subst > $o] : ~! [X64 : term > $o] : ~! [X65 : term] : ((X64 @ X65) = (X63 @ id @ X65 @ id)) => (! [X66 : term,X67 : term > $o] : (($true = (X67 @ X66)) | ~! [X68 : term] : (~($true = (var @ X68)) | ($true = (X67 @ X68))) | ~! [X69 : term,X70 : term] : (~($true = (X67 @ X69)) | ((X67 @ (ap @ X70 @ X69)) = $true) | ~((X67 @ X70) = $true)) | ~! [X71 : term] : (((X67 @ (lam @ X71)) = $true) | ~! [X72 : term] : (($true = (X67 @ (sub @ X71 @ (push @ X72 @ id)))) | ~((X67 @ X72) = $true)))) => (! [X73 : term] : ((sub @ X73 @ id) = X73) => (! [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : (($true = (X74 @ (lam @ X76))) | ~! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) | ~! [X78 : subst > term > term] : (~! [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X78 @ X81 @ X79) @ X80)) | ((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) = $true) | ~! [X82 : term] : (($true = (X75 @ id @ (X78 @ id @ X82) @ id)) | ~($true = (X75 @ id @ X82 @ id)))) | ~! [X83 : term] : (~($true = (X74 @ X83)) | ($true = (X74 @ (sub @ X76 @ (push @ X83 @ id)))))) => ! [X84 : term,X85 : subst > term > subst > $o] : (~! [X86 : term,X87 : term] : (~($true = (X85 @ id @ X87 @ id)) | ~($true = (X85 @ id @ X86 @ id)) | ((X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) = $true)) | ~! [X88 : term] : (~($true = (var @ (sub @ X88 @ id))) | ($true = (X85 @ id @ X88 @ id))) | ~! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (~((X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) = $true) | ($true = (X85 @ X90 @ X91 @ (comp @ X92 @ X89)))) | ~! [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (~($true = (X85 @ X96 @ X94 @ (comp @ X93 @ X95))) | ($true = (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95))) | ~! [X97 : subst > term > term] : (($true = (X85 @ id @ (lam @ (X97 @ sh @ one)) @ id)) | ~! [X98 : term] : (~((X85 @ id @ X98 @ id) = $true) | ($true = (X85 @ id @ (X97 @ id @ X98) @ id))) | ~! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100))) | ($true = (X85 @ id @ X84 @ id)))))))) & (hoaslamnotvar_lthm = $true) & (! [X102 : subst > term > subst > $o] : ~! [X103 : term > $o] : ~! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) <=> (hoasinduction_lem0 = $true)) & ((induction2 = $true) <=> ! [X105 : term > $o,X106 : term] : (~! [X107 : term] : (~($true = (var @ X107)) | ((X105 @ X107) = $true)) | ~! [X108 : term,X109 : term] : (($true = (X105 @ (ap @ X109 @ X108))) | ~($true = (X105 @ X108)) | ~($true = (X105 @ X109))) | ($true = (X105 @ X106)) | ~! [X110 : term] : (~! [X111 : term] : (($true = (X105 @ (sub @ X110 @ (push @ X111 @ id)))) | ~($true = (X105 @ X111))) | ((X105 @ (lam @ X110)) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X115 : term > $o,X116 : term,X117 : subst] : ~! [X118 : term > $o] : ~! [X119 : term] : ((X118 @ X119) = (X115 @ (sub @ X119 @ (push @ X116 @ X117))))) & ((hoasinduction_lem3aa = $true) <=> ! [X120 : term,X121 : subst > term > subst > $o] : (($true = (X121 @ id @ (lam @ (sub @ X120 @ (push @ one @ sh))) @ id)) | ~! [X122 : term] : (~($true = (X121 @ id @ X122 @ id)) | ((X121 @ id @ (sub @ X120 @ (push @ X122 @ id)) @ id) = $true)) | ~! [X123 : subst > term > term] : (((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) = $true) | ~! [X124 : term] : (($true = (X121 @ id @ (X123 @ id @ X124) @ id)) | ~($true = (X121 @ id @ X124 @ id))) | ~! [X125 : subst,X126 : subst,X127 : term] : ((X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X123 @ X125 @ X127) @ X126))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X128 : subst > term > subst > $o,X129 : term] : (($true = (X128 @ id @ X129 @ id)) | ~! [X130 : subst > term > term] : (~! [X131 : term] : (~($true = (X128 @ id @ X131 @ id)) | ($true = (X128 @ id @ (X130 @ id @ X131) @ id))) | ~! [X132 : subst,X133 : subst,X134 : term] : ((sub @ (X130 @ X132 @ X134) @ X133) = (X130 @ (comp @ X132 @ X133) @ (sub @ X134 @ X133))) | ($true = (X128 @ id @ (lam @ (X130 @ sh @ one)) @ id))) | ~! [X135 : term,X136 : term] : (((X128 @ id @ (ap @ (sub @ X136 @ id) @ X135) @ id) = $true) | ~($true = (X128 @ id @ X135 @ id)) | ~($true = (X128 @ id @ X136 @ id))))) & (! [X137 : term,X138 : subst > term > subst > $o] : (($true = (X138 @ id @ X137 @ id)) | ~! [X139 : subst,X140 : term,X141 : subst,X142 : subst] : (($true = (X138 @ (comp @ X139 @ X141) @ (sub @ X140 @ X141) @ X142)) | ~($true = (X138 @ X139 @ X140 @ (comp @ X141 @ X142)))) | ~! [X143 : subst > term > term] : (~! [X144 : term,X145 : subst,X146 : subst] : ((X143 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145)) = (sub @ (X143 @ X146 @ X144) @ X145)) | ~! [X147 : term] : (~($true = (X138 @ id @ X147 @ id)) | ($true = (X138 @ id @ (X143 @ id @ X147) @ id))) | ($true = (X138 @ id @ (lam @ (X143 @ sh @ one)) @ id))) | ~! [X148 : term] : (($true = (X138 @ id @ X148 @ id)) | ~((var @ (sub @ X148 @ id)) = $true)) | ~! [X149 : term,X150 : term] : (~($true = (X138 @ id @ X149 @ id)) | ~($true = (X138 @ id @ X150 @ id)) | ($true = (X138 @ id @ (ap @ (sub @ X150 @ id) @ X149) @ id))) | ~! [X151 : subst,X152 : subst,X153 : subst,X154 : term] : (((X138 @ X151 @ X154 @ (comp @ X152 @ X153)) = $true) | ~($true = (X138 @ (comp @ X151 @ X152) @ (sub @ X154 @ X152) @ X153)))) <=> (hoasinduction = $true)) & (! [X155 : term > $o,X156 : term > $o,X157 : subst,X158 : term] : (($true = (X156 @ one)) | ~! [X159 : term] : ((X156 @ X159) = (X155 @ (sub @ X159 @ (push @ X158 @ X157)))) | ~($true = (X155 @ X158))) <=> (pushprop_lem1v2 = $true)) & (hoasapnotvar_gthm = $true) & ((axscons = $true) <=> ! [X160 : subst] : ((push @ (sub @ one @ X160) @ (comp @ sh @ X160)) = X160)) & ((d2subst @ d_id) = sh) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $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)))))))))))) & (induction2_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X166 : term] : ? [X167 : d_term] : ((d2term @ X167) = X166) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X168 : term,X169 : subst > term > subst > $o] : (~! [X170 : subst > term > term] : (~! [X171 : subst,X172 : term,X173 : subst] : ((X170 @ (comp @ X173 @ X171) @ (sub @ X172 @ X171)) = (sub @ (X170 @ X173 @ X172) @ X171)) | ($true = (X169 @ id @ (lam @ (X170 @ sh @ one)) @ id)) | ~! [X174 : term] : (((X169 @ id @ (X170 @ id @ X174) @ id) = $true) | ~($true = (X169 @ id @ X174 @ id)))) | ($true = (X169 @ id @ (lam @ (sub @ X168 @ (push @ one @ sh))) @ id)) | ~! [X175 : term] : (($true = (X169 @ id @ (sub @ X168 @ (push @ X175 @ id)) @ id)) | ~($true = (X169 @ id @ X175 @ id))))) & ((! [X176 : term,X177 : subst] : ((sub @ one @ (push @ X176 @ X177)) = X176) => (! [X178 : term,X179 : subst] : ((comp @ sh @ (push @ X178 @ X179)) = X179) => (! [X180 : term,X181 : term] : ((X180 = X181) | ((lam @ X181) != (lam @ X180))) => ! [X182 : subst > term > term,X183 : term,X184 : subst,X185 : subst > term > term] : (~! [X186 : subst,X187 : subst,X188 : term] : ((sub @ (X182 @ X186 @ X188) @ X187) = (X182 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187))) | ~! [X189 : subst,X190 : subst,X191 : term] : ((sub @ (X185 @ X190 @ X191) @ X189) = (X185 @ (comp @ X190 @ X189) @ (sub @ X191 @ X189))) | ((lam @ (X185 @ sh @ one)) != (lam @ (X182 @ sh @ one))) | ((X182 @ X184 @ X183) = (X185 @ X184 @ X183)))))) <=> (hoaslaminj_lthm = $true)) & (axapp = $true) & (hoasinduction_lem2v2_gthm = $true) & (one = (d2term @ d_one)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X192 : subst > term > subst > $o,X193 : term] : (($true = (X192 @ id @ (lam @ (sub @ X193 @ (push @ one @ sh))) @ id)) | ~! [X194 : term] : (~((X192 @ id @ X194 @ id) = $true) | ($true = (X192 @ id @ (sub @ X193 @ (push @ X194 @ id)) @ id))) | ~! [X195 : subst > term > term,X196 : term] : (~! [X197 : subst,X198 : term,X199 : subst] : ((sub @ X196 @ (push @ (sub @ X198 @ X197) @ (comp @ X199 @ X197))) = (X195 @ (comp @ X199 @ X197) @ (sub @ X198 @ X197))) | ($true = (X192 @ id @ (lam @ (X195 @ sh @ one)) @ id)) | ~! [X200 : subst,X201 : term,X202 : subst] : ((sub @ (X195 @ X202 @ X201) @ X200) = (sub @ (sub @ X196 @ (push @ X201 @ X202)) @ X200)) | ~! [X203 : term] : (~($true = (X192 @ id @ X203 @ id)) | ($true = (X192 @ id @ (X195 @ id @ X203) @ id)))))) & (axmap = $true) & ((axidr = $true) <=> ! [X204 : subst] : ((comp @ X204 @ id) = X204)) & ((axidl = $true) <=> ! [X205 : subst] : ((comp @ id @ X205) = X205)) & (termmset_gthm = $true) & (! [X206 : subst > term > subst > $o,X207 : term] : (~! [X208 : subst,X209 : subst,X210 : term,X211 : subst] : (~($true = (X206 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209) @ X208)) | ((X206 @ X211 @ X210 @ (comp @ X209 @ X208)) = $true)) | ($true = (X206 @ id @ (lam @ X207) @ id)) | ~! [X212 : subst > term > term] : (~! [X213 : term] : (($true = (X206 @ id @ (X212 @ id @ X213) @ id)) | ~($true = (X206 @ id @ X213 @ id))) | ((X206 @ id @ (lam @ (X212 @ sh @ one)) @ id) = $true) | ~! [X214 : subst,X215 : term,X216 : subst] : ((sub @ (X212 @ X214 @ X215) @ X216) = (X212 @ (comp @ X214 @ X216) @ (sub @ X215 @ X216)))) | ~! [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (~($true = (X206 @ X218 @ X219 @ (comp @ X217 @ X220))) | ($true = (X206 @ (comp @ X218 @ X217) @ (sub @ X219 @ X217) @ X220))) | ~! [X221 : term] : (~($true = (X206 @ id @ X221 @ id)) | ($true = (X206 @ id @ (sub @ X207 @ (push @ X221 @ id)) @ id)))) <=> (hoasinduction_lem3 = $true)) & (hoasapinj2_gthm = $true) & (lamnotvar = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (! [X222 : term,X223 : term > $o,X224 : subst > term > subst > $o] : (~! [X225 : subst > term > term] : (($true = (X224 @ id @ (lam @ (X225 @ sh @ one)) @ id)) | ~! [X226 : term,X227 : subst,X228 : subst] : ((sub @ (X225 @ X228 @ X226) @ X227) = (X225 @ (comp @ X228 @ X227) @ (sub @ X226 @ X227))) | ~! [X229 : term] : (~((X224 @ id @ X229 @ id) = $true) | ($true = (X224 @ id @ (X225 @ id @ X229) @ id)))) | ~! [X230 : term] : (~($true = (X223 @ X230)) | ($true = (X223 @ (sub @ X222 @ (push @ X230 @ id))))) | ~! [X231 : subst,X232 : subst,X233 : term,X234 : subst] : (((X224 @ (comp @ X232 @ X231) @ (sub @ X233 @ X231) @ X234) = $true) | ~((X224 @ X232 @ X233 @ (comp @ X231 @ X234)) = $true)) | ~! [X235 : term,X236 : subst,X237 : subst,X238 : subst] : (($true = (X224 @ X236 @ X235 @ (comp @ X238 @ X237))) | ~($true = (X224 @ (comp @ X236 @ X238) @ (sub @ X235 @ X238) @ X237))) | ((X223 @ (lam @ X222)) = $true) | ~! [X239 : term] : ((X223 @ X239) = (X224 @ id @ X239 @ id))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X240 : term] : ((sub @ X240 @ id) = X240) => ! [X241 : term,X242 : term > $o,X243 : subst > term > subst > $o] : (~! [X244 : subst,X245 : subst,X246 : subst,X247 : term] : (($true = (X243 @ X246 @ X247 @ (comp @ X245 @ X244))) | ~($true = (X243 @ (comp @ X246 @ X245) @ (sub @ X247 @ X245) @ X244))) | ~! [X248 : term] : (~($true = (X242 @ X248)) | ($true = (X242 @ (sub @ X241 @ (push @ X248 @ id))))) | ~! [X249 : subst > term > term] : (~! [X250 : term,X251 : subst,X252 : subst] : ((X249 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)) = (sub @ (X249 @ X252 @ X250) @ X251)) | ~! [X253 : term] : (((X243 @ id @ (X249 @ id @ X253) @ id) = $true) | ~($true = (X243 @ id @ X253 @ id))) | ($true = (X243 @ id @ (lam @ (X249 @ sh @ one)) @ id))) | ~! [X254 : term] : ((X242 @ X254) = (X243 @ id @ X254 @ id)) | ~! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (~($true = (X243 @ X255 @ X256 @ (comp @ X257 @ X258))) | ($true = (X243 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257) @ X258))) | ($true = (X242 @ (lam @ X241))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X259 : term] : ((sub @ X259 @ id) = X259) => ! [X260 : term] : ((sub @ X260 @ id) = X260))) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X261 : term] : ~! [X262 : subst > term > term] : ((X262 @ sh @ one) != (sub @ X261 @ (push @ one @ sh)))) & (apnotvar = $true) & ((! [X263 : term,X264 : subst] : ((sub @ one @ (push @ X263 @ X264)) = X263) => (! [X265 : term,X266 : subst] : ((comp @ sh @ (push @ X265 @ X266)) = X266) => (! [X267 : subst] : ((comp @ X267 @ id) = X267) => (! [X268 : term > $o,X269 : term] : (~! [X270 : term] : (($true = (X268 @ (lam @ X270))) | ~($true = (X268 @ X270))) | ~! [X271 : term,X272 : term] : (~($true = (X268 @ X271)) | ~($true = (X268 @ X272)) | ($true = (X268 @ (ap @ X272 @ X271)))) | ~! [X273 : term] : (~($true = (var @ X273)) | ($true = (X268 @ X273))) | ($true = (X268 @ X269))) => ! [X274 : term,X275 : subst,X276 : term > $o] : (~! [X277 : term,X278 : term] : (($true = (X276 @ (ap @ X278 @ X277))) | ~($true = (X276 @ X277)) | ~($true = (X276 @ X278))) | ~! [X279 : term] : (~! [X280 : term] : (~($true = (X276 @ X280)) | ($true = (X276 @ (sub @ X279 @ (push @ X280 @ id))))) | ($true = (X276 @ (lam @ X279)))) | ($true = (X276 @ (sub @ X274 @ X275))) | ~! [X281 : term] : (($true = (X276 @ (sub @ X281 @ X275))) | ~($true = (var @ X281)))))))) <=> (induction2lem_lthm = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & ~(ulamvar1 = $true) & (! [X282 : term,X283 : subst] : ((comp @ sh @ (push @ X282 @ X283)) = X283) <=> (axshiftcons = $true)) & (! [X284 : subst > term > subst > $o,X285 : term] : (~! [X286 : term] : (~($true = (X284 @ id @ X286 @ id)) | ((X284 @ id @ (sub @ X285 @ (push @ X286 @ id)) @ id) = $true)) | ((X284 @ id @ (lam @ X285) @ id) = $true) | ~! [X287 : subst > term > term] : (~! [X288 : term] : (~($true = (X284 @ id @ X288 @ id)) | ($true = (X284 @ id @ (X287 @ id @ X288) @ id))) | ~! [X289 : subst,X290 : term,X291 : subst] : ((X287 @ (comp @ X291 @ X289) @ (sub @ X290 @ X289)) = (sub @ (X287 @ X291 @ X290) @ X289)) | ($true = (X284 @ id @ (lam @ (X287 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3a = $true)) & ! [X292 : subst] : ? [X293 : d_subst] : ((d2subst @ X293) = X292) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X294 : term,X295 : term,X296 : term,X297 : term] : ((X296 = X297) | ((ap @ (sub @ X295 @ id) @ X296) != (ap @ (sub @ X294 @ id) @ X297))) <=> (hoasapinj2 = $true)) & ! [X298 : d_subst,X299 : d_subst] : (((d2subst @ X298) = (d2subst @ X299)) => (X298 = X299)) & ((! [X300 : term > $o,X301 : term] : (~! [X302 : term] : (($true = (X300 @ (lam @ X302))) | ~! [X303 : term] : (((X300 @ (sub @ X302 @ (push @ X303 @ id))) = $true) | ~($true = (X300 @ X303)))) | ~! [X304 : term] : (($true = (X300 @ X304)) | ~($true = (var @ X304))) | ((X300 @ X301) = $true) | ~! [X305 : term,X306 : term] : (~($true = (X300 @ X306)) | ($true = (X300 @ (ap @ X306 @ X305))) | ~($true = (X300 @ X305)))) => (! [X307 : subst > term > subst > $o,X308 : term,X309 : term] : (((X307 @ id @ (ap @ X308 @ X309) @ id) = $true) | ~! [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (~($true = (X307 @ (comp @ X313 @ X310) @ (sub @ X311 @ X310) @ X312)) | ($true = (X307 @ X313 @ X311 @ (comp @ X310 @ X312)))) | ~! [X314 : term,X315 : term] : (~($true = (X307 @ id @ X314 @ id)) | ($true = (X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) | ~($true = (X307 @ id @ X315 @ id))) | ~($true = (X307 @ id @ X309 @ id)) | ~($true = (X307 @ id @ X308 @ id)) | ~! [X316 : term,X317 : subst,X318 : subst,X319 : subst] : (($true = (X307 @ (comp @ X319 @ X317) @ (sub @ X316 @ X317) @ X318)) | ~($true = (X307 @ X319 @ X316 @ (comp @ X317 @ X318))))) => (! [X320 : subst > term > subst > $o,X321 : term] : (~! [X322 : term] : (($true = (X320 @ id @ (sub @ X321 @ (push @ X322 @ id)) @ id)) | ~($true = (X320 @ id @ X322 @ id))) | ((X320 @ id @ (lam @ X321) @ id) = $true) | ~! [X323 : subst > term > term] : (~! [X324 : term] : (~($true = (X320 @ id @ X324 @ id)) | ($true = (X320 @ id @ (X323 @ id @ X324) @ id))) | ($true = (X320 @ id @ (lam @ (X323 @ sh @ one)) @ id)) | ~! [X325 : subst,X326 : subst,X327 : term] : ((X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325)) = (sub @ (X323 @ X326 @ X327) @ X325))) | ~! [X328 : subst,X329 : term,X330 : subst,X331 : subst] : (~($true = (X320 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328)) | ($true = (X320 @ X330 @ X329 @ (comp @ X331 @ X328)))) | ~! [X332 : subst,X333 : subst,X334 : term,X335 : subst] : (($true = (X320 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X335)) | ~($true = (X320 @ X333 @ X334 @ (comp @ X332 @ X335))))) => ! [X336 : term,X337 : subst > term > subst > $o] : (~! [X338 : term,X339 : term] : (($true = (X337 @ id @ (ap @ (sub @ X338 @ id) @ X339) @ id)) | ~($true = (X337 @ id @ X338 @ id)) | ~($true = (X337 @ id @ X339 @ id))) | ($true = (X337 @ id @ X336 @ id)) | ~! [X340 : term,X341 : subst,X342 : subst,X343 : subst] : (~($true = (X337 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) | ((X337 @ X342 @ X340 @ (comp @ X341 @ X343)) = $true)) | ~! [X344 : term] : (($true = (X337 @ id @ X344 @ id)) | ~($true = (var @ (sub @ X344 @ id)))) | ~! [X345 : subst > term > term] : (((X337 @ id @ (lam @ (X345 @ sh @ one)) @ id) = $true) | ~! [X346 : term] : (~($true = (X337 @ id @ X346 @ id)) | ($true = (X337 @ id @ (X345 @ id @ X346) @ id))) | ~! [X347 : subst,X348 : term,X349 : subst] : ((sub @ (X345 @ X347 @ X348) @ X349) = (X345 @ (comp @ X347 @ X349) @ (sub @ X348 @ X349)))) | ~! [X350 : subst,X351 : subst,X352 : subst,X353 : term] : (~($true = (X337 @ X350 @ X353 @ (comp @ X351 @ X352))) | ($true = (X337 @ (comp @ X350 @ X351) @ (sub @ X353 @ X351) @ X352))))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X354 : term,X355 : term,X356 : subst > term > term] : (~! [X357 : subst,X358 : term,X359 : subst] : ((X356 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359)) = (sub @ (X356 @ X357 @ X358) @ X359)) | ((lam @ (X356 @ sh @ one)) != (ap @ (sub @ X355 @ id) @ X354))) <=> (hoaslamnotap = $true)) & ((axvarid = $true) <=> ! [X360 : term] : ((sub @ X360 @ id) = X360)) & (! [X361 : term,X362 : term,X363 : term,X364 : term] : (((ap @ (sub @ X364 @ id) @ X363) != (ap @ (sub @ X362 @ id) @ X361)) | (X362 = X364)) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3a_gthm = $true) & ((! [X365 : subst] : ((comp @ id @ X365) = X365) & ! [X366 : subst] : ((comp @ X366 @ id) = X366)) <=> (substmonoid = $true)) & ((d2subst @ d_id) = id) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X367 : term] : ~! [X368 : subst > term > term] : ~! [X369 : term,X370 : subst] : ((sub @ X367 @ (push @ X369 @ X370)) = (X368 @ X370 @ X369)) => (! [X371 : term] : ((sub @ X371 @ id) = X371) => ! [X372 : term,X373 : term > $o,X374 : subst > term > subst > $o] : (~! [X375 : term] : ((X373 @ X375) = (X374 @ id @ X375 @ id)) | ~! [X376 : term] : (((X373 @ (sub @ X372 @ (push @ X376 @ id))) = $true) | ~($true = (X373 @ X376))) | ~! [X377 : subst > term > term] : (~! [X378 : term] : (~($true = (X374 @ id @ X378 @ id)) | ($true = (X374 @ id @ (X377 @ id @ X378) @ id))) | ($true = (X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) | ~! [X379 : term,X380 : subst,X381 : subst] : ((sub @ (X377 @ X381 @ X379) @ X380) = (X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) | ($true = (X373 @ (lam @ X372))))))) & ((pushprop_lem0 = $true) <=> ! [X382 : subst,X383 : term > $o,X384 : term] : ~! [X385 : term > $o] : ~! [X386 : term] : ((X383 @ (sub @ X386 @ (push @ X384 @ X382))) = (X385 @ X386))) & (hoasinduction_gthm = $true) & (! [X387 : term,X388 : term] : (((sub @ X387 @ sh) != (sub @ X388 @ sh)) | (X387 = X388)) <=> (shinj = $true)) & ((induction2lem = $true) <=> ! [X389 : term > $o,X390 : subst,X391 : term] : (($true = (X389 @ (sub @ X391 @ X390))) | ~! [X392 : term] : (~! [X393 : term] : (~($true = (X389 @ X393)) | ($true = (X389 @ (sub @ X392 @ (push @ X393 @ id))))) | ((X389 @ (lam @ X392)) = $true)) | ~! [X394 : term] : (($true = (X389 @ (sub @ X394 @ X390))) | ~($true = (var @ X394))) | ~! [X395 : term,X396 : term] : (($true = (X389 @ (ap @ X396 @ X395))) | ~($true = (X389 @ X396)) | ~($true = (X389 @ X395))))) & (ulamvarsh = $true) & (! [X397 : term,X398 : term,X399 : term,X400 : term] : (((ap @ X400 @ X399) != (ap @ X398 @ X397)) | (X397 = X399)) <=> (apinj2 = $true)) & ((! [X401 : term] : ((sub @ X401 @ id) = X401) => (! [X402 : subst,X403 : term,X404 : term > $o] : (~! [X405 : term] : (($true = (X404 @ (sub @ X405 @ X402))) | ~($true = (var @ X405))) | ~! [X406 : term,X407 : term] : (($true = (X404 @ (ap @ X406 @ X407))) | ~($true = (X404 @ X407)) | ~($true = (X404 @ X406))) | ~! [X408 : term] : (~! [X409 : term] : (~($true = (X404 @ X409)) | ($true = (X404 @ (sub @ X408 @ (push @ X409 @ id))))) | ($true = (X404 @ (lam @ X408)))) | ((X404 @ (sub @ X403 @ X402)) = $true)) => ! [X410 : term,X411 : term > $o] : (~! [X412 : term] : (~($true = (var @ X412)) | ($true = (X411 @ X412))) | ($true = (X411 @ X410)) | ~! [X413 : term] : (~! [X414 : term] : (~((X411 @ X414) = $true) | ((X411 @ (sub @ X413 @ (push @ X414 @ id))) = $true)) | ($true = (X411 @ (lam @ X413)))) | ~! [X415 : term,X416 : term] : (($true = (X411 @ (ap @ X415 @ X416))) | ~((X411 @ X415) = $true) | ~($true = (X411 @ X416)))))) <=> (induction2_lthm = $true)) & ((! [X417 : term,X418 : term,X419 : term,X420 : term] : (((ap @ X419 @ X418) != (ap @ X420 @ X417)) | (X417 = X418)) => ! [X421 : term,X422 : term,X423 : term,X424 : term] : (((ap @ (sub @ X422 @ id) @ X421) != (ap @ (sub @ X424 @ id) @ X423)) | (X421 = X423))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axassoc = $true) & ((laminj = $true) <=> ! [X427 : term,X428 : term] : (((lam @ X428) != (lam @ X427)) | (X427 = X428))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X429 : term,X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (~! [X433 : subst,X434 : term,X435 : subst,X436 : subst] : (($true = (X432 @ X435 @ X434 @ (comp @ X436 @ X433))) | ~($true = (X432 @ (comp @ X435 @ X436) @ (sub @ X434 @ X436) @ X433))) | ~! [X437 : term] : ((X431 @ X437) = (X432 @ id @ X437 @ id)) | ~! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : (($true = (X432 @ (comp @ X441 @ X440) @ (sub @ X439 @ X440) @ X438)) | ~($true = (X432 @ X441 @ X439 @ (comp @ X440 @ X438)))) | ~($true = (X431 @ X430)) | ~($true = (X431 @ X429)) | ($true = (X431 @ (ap @ X430 @ X429))) | ~! [X442 : term,X443 : term] : (($true = (X432 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id)) | ~((X432 @ id @ X443 @ id) = $true) | ~($true = (X432 @ id @ X442 @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X444 : term] : ~! [X445 : subst > term > term] : ~! [X446 : term,X447 : subst] : ((sub @ X444 @ (push @ X446 @ X447)) = (X445 @ X447 @ X446))) & (hoasinduction_lem1_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X448 : subst,X449 : term > $o,X450 : term,X451 : term,X452 : term > $o] : (~((X449 @ X451) = $true) | ((X452 @ (sub @ X451 @ (push @ X450 @ X448))) = $true))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (! [X453 : subst > term > term,X454 : subst > term > term,X455 : term,X456 : subst] : (~! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (X454 @ X457 @ X458) @ X459) = (X454 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459))) | ((X453 @ X456 @ X455) = (X454 @ X456 @ X455)) | ~! [X460 : subst,X461 : term,X462 : subst] : ((sub @ (X453 @ X462 @ X461) @ X460) = (X453 @ (comp @ X462 @ X460) @ (sub @ X461 @ X460))) | ((lam @ (X454 @ sh @ one)) != (lam @ (X453 @ sh @ one)))) <=> (hoaslaminj = $true)) & ! [X463 : d_term] : (d_one = X463) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop = $true) & (! [X464 : term] : ~! [X465 : subst > term > term] : ((X465 @ sh @ one) != (sub @ X464 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (pushprop_lem2v2_lthm = $true) & (axvarshift = $true) & (pushprop_gthm = $true) & ((! [X466 : subst] : ((comp @ id @ X466) = X466) => (! [X467 : subst] : ((comp @ X467 @ id) = X467) => (! [X468 : subst] : ((comp @ X468 @ id) = X468) & ! [X469 : subst] : ((comp @ id @ X469) = X469)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X470 : term > $o,X471 : subst > term > subst > $o,X472 : term] : (($true = (X470 @ (lam @ X472))) | ~! [X473 : term] : ((X471 @ id @ X473 @ id) = (X470 @ X473)) | ~! [X474 : term] : (($true = (X470 @ (sub @ X472 @ (push @ X474 @ id)))) | ~($true = (X470 @ X474))) | ~! [X475 : subst > term > term] : (($true = (X471 @ id @ (lam @ (X475 @ sh @ one)) @ id)) | ~! [X476 : term,X477 : subst,X478 : subst] : ((sub @ (X475 @ X477 @ X476) @ X478) = (X475 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) | ~! [X479 : term] : (~($true = (X471 @ id @ X479 @ id)) | ($true = (X471 @ id @ (X475 @ id @ X479) @ id)))))) & (! [X480 : term,X481 : subst] : ((sub @ one @ (push @ X480 @ X481)) = X480) <=> (axvarcons = $true)) & (axabs = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X482 : subst,X483 : term] : ((sub @ one @ (push @ X483 @ X482)) = X483) => (! [X484 : subst,X485 : term] : ((comp @ sh @ (push @ X485 @ X484)) = X484) => ! [X486 : term > $o,X487 : term > $o,X488 : term,X489 : subst,X490 : term] : (($true = (X487 @ (sub @ X490 @ (push @ X488 @ X489)))) | ~($true = (X486 @ X490)))))) & (induction2lem_gthm = $true) & (pushprop_lem1_gthm = $true) & ((! [X491 : term] : ((sub @ X491 @ id) = X491) => (! [X492 : subst > term > subst > $o,X493 : term] : (~! [X494 : subst > term > term] : (~! [X495 : subst,X496 : term,X497 : subst] : ((X494 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497)) = (sub @ (X494 @ X495 @ X496) @ X497)) | ($true = (X492 @ id @ (lam @ (X494 @ sh @ one)) @ id)) | ~! [X498 : term] : (($true = (X492 @ id @ (X494 @ id @ X498) @ id)) | ~($true = (X492 @ id @ X498 @ id)))) | ($true = (X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id)) | ~! [X499 : term] : (~($true = (X492 @ id @ X499 @ id)) | ($true = (X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))) => ! [X500 : term,X501 : subst > term > subst > $o] : (~! [X502 : subst > term > term] : (~! [X503 : term] : (~($true = (X501 @ id @ X503 @ id)) | ($true = (X501 @ id @ (X502 @ id @ X503) @ id))) | ~! [X504 : subst,X505 : term,X506 : subst] : ((sub @ (X502 @ X504 @ X505) @ X506) = (X502 @ (comp @ X504 @ X506) @ (sub @ X505 @ X506))) | ((X501 @ id @ (lam @ (X502 @ sh @ one)) @ id) = $true)) | ~! [X507 : term] : (($true = (X501 @ id @ (sub @ X500 @ (push @ X507 @ id)) @ id)) | ~($true = (X501 @ id @ X507 @ id))) | ~! [X508 : subst,X509 : subst,X510 : subst,X511 : term] : (~($true = (X501 @ X509 @ X511 @ (comp @ X510 @ X508))) | ($true = (X501 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510) @ X508))) | ($true = (X501 @ id @ (lam @ X500) @ id)) | ~! [X512 : subst,X513 : subst,X514 : subst,X515 : term] : (~((X501 @ (comp @ X513 @ X512) @ (sub @ X515 @ X512) @ X514) = $true) | ($true = (X501 @ X513 @ X515 @ (comp @ X512 @ X514))))))) <=> (hoasinduction_lem3_lthm = $true)) & ((! [X516 : subst > term > subst > $o] : ~! [X517 : term > $o] : ~! [X518 : term] : ((X517 @ X518) = (X516 @ id @ X518 @ id)) => (! [X519 : term > $o,X520 : term] : (~! [X521 : term,X522 : term] : (~($true = (X519 @ X521)) | ($true = (X519 @ (ap @ X522 @ X521))) | ~((X519 @ X522) = $true)) | ($true = (X519 @ X520)) | ~! [X523 : term] : (~! [X524 : term] : (~($true = (X519 @ X524)) | ($true = (X519 @ (sub @ X523 @ (push @ X524 @ id))))) | ($true = (X519 @ (lam @ X523)))) | ~! [X525 : term] : (~((var @ X525) = $true) | ($true = (X519 @ X525)))) => (! [X526 : term] : ((sub @ X526 @ id) = X526) => (! [X527 : term > $o,X528 : subst > term > subst > $o,X529 : term] : (~! [X530 : term] : ((X527 @ X530) = (X528 @ id @ X530 @ id)) | ($true = (X527 @ (lam @ X529))) | ~! [X531 : term] : (($true = (X527 @ (sub @ X529 @ (push @ X531 @ id)))) | ~($true = (X527 @ X531))) | ~! [X532 : subst > term > term] : (~! [X533 : term] : (~($true = (X528 @ id @ X533 @ id)) | ($true = (X528 @ id @ (X532 @ id @ X533) @ id))) | ~! [X534 : term,X535 : subst,X536 : subst] : ((X532 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536)) = (sub @ (X532 @ X535 @ X534) @ X536)) | ($true = (X528 @ id @ (lam @ (X532 @ sh @ one)) @ id)))) => ! [X537 : term,X538 : subst > term > subst > $o] : (~! [X539 : term,X540 : term] : (~($true = (X538 @ id @ X539 @ id)) | ~($true = (X538 @ id @ X540 @ id)) | ($true = (X538 @ id @ (ap @ (sub @ X539 @ id) @ X540) @ id))) | ~! [X541 : subst > term > term] : (~! [X542 : term] : (($true = (X538 @ id @ (X541 @ id @ X542) @ id)) | ~($true = (X538 @ id @ X542 @ id))) | ($true = (X538 @ id @ (lam @ (X541 @ sh @ one)) @ id)) | ~! [X543 : term,X544 : subst,X545 : subst] : ((X541 @ (comp @ X544 @ X545) @ (sub @ X543 @ X545)) = (sub @ (X541 @ X544 @ X543) @ X545))) | ($true = (X538 @ id @ X537 @ id))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (axclos = $true) & (! [X546 : term] : ~! [X547 : subst > term > term] : ~! [X548 : term,X549 : subst] : ((sub @ X546 @ (push @ X548 @ X549)) = (X547 @ X549 @ X548)) <=> (hoasinduction_lem3v2_f = $true)) & ~(lamnotap = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true)),
% 15.37/3.55 inference(fool_elimination,[status(thm)],[f5])).
% 15.37/3.55 thf(f5,plain,(
% 15.37/3.55 (pushprop_lem1v2_lthm <=> (! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1) => ! [X2 : term > $o,X3 : subst,X4 : term,X5 : term > $o] : ((X5 @ one) | ~(X2 @ X4) | ~! [X6 : term] : ((X2 @ (sub @ X6 @ (push @ X4 @ X3))) = (X5 @ X6))))) & hoasinduction_lem1v2 & hoasinduction_lem1_lthm & ulamvarind & ! [X7 : d_term,X8 : d_term] : (((d2term @ X7) = (d2term @ X8)) => (X7 = X8)) & ((! [X9 : term] : ((sub @ X9 @ id) = X9) => (! [X10 : subst > term > subst > $o,X11 : term] : (~! [X12 : subst > term > term] : (~! [X13 : subst,X14 : term,X15 : subst] : ((X12 @ (comp @ X13 @ X15) @ (sub @ X14 @ X15)) = (sub @ (X12 @ X13 @ X14) @ X15)) | (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id) | ~! [X16 : term] : ((X10 @ id @ (X12 @ id @ X16) @ id) | ~(X10 @ id @ X16 @ id))) | (X10 @ id @ (lam @ (sub @ X11 @ (push @ one @ sh))) @ id) | ~! [X17 : term] : (~(X10 @ id @ X17 @ id) | (X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id))) => ! [X18 : subst > term > subst > $o,X19 : term] : (~! [X20 : term] : ((X18 @ id @ (sub @ X19 @ (push @ X20 @ id)) @ id) | ~(X18 @ id @ X20 @ id)) | ~! [X21 : subst > term > term] : (~! [X22 : term] : ((X18 @ id @ (X21 @ id @ X22) @ id) | ~(X18 @ id @ X22 @ id)) | ~! [X23 : term,X24 : subst,X25 : subst] : ((X21 @ (comp @ X24 @ X25) @ (sub @ X23 @ X25)) = (sub @ (X21 @ X24 @ X23) @ X25)) | (X18 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | (X18 @ id @ (lam @ X19) @ id)))) <=> hoasinduction_lem3a_lthm) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X26 : term] : ((sub @ X26 @ id) = X26) <=> termmset) & ! [X27 : d_subst] : (d_id = X27) & ~(var @ (d2term @ d_one)) & (induction <=> ! [X28 : term > $o,X29 : term] : ((X28 @ X29) | ~! [X30 : term] : ((X28 @ X30) | ~(var @ X30)) | ~! [X31 : term,X32 : term] : ((X28 @ (ap @ X32 @ X31)) | ~(X28 @ X32) | ~(X28 @ X31)) | ~! [X33 : term] : ((X28 @ (lam @ X33)) | ~(X28 @ X33)))) & pushprop_lthm_orig & (hoasinduction_lem0_lthm <=> ! [X34 : subst > term > subst > $o] : ~! [X35 : term > $o] : ~! [X36 : term] : ((X34 @ id @ X36 @ id) = (X35 @ X36))) & ((! [X37 : term] : ((sub @ X37 @ id) = X37) => (! [X38 : term,X39 : term,X40 : term,X41 : term] : (((ap @ X38 @ X41) != (ap @ X40 @ X39)) | (X38 = X40)) => ! [X42 : term,X43 : term,X44 : term,X45 : term] : (((ap @ (sub @ X42 @ id) @ X45) != (ap @ (sub @ X43 @ id) @ X44)) | (X42 = X43)))) <=> hoasapinj1_lthm) & (! [X46 : subst > term > subst > $o,X47 : term,X48 : term] : (~! [X49 : term,X50 : term] : (~(X46 @ id @ X50 @ id) | ~(X46 @ id @ X49 @ id) | (X46 @ id @ (ap @ (sub @ X50 @ id) @ X49) @ id)) | ~! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (~(X46 @ X52 @ X54 @ (comp @ X51 @ X53)) | (X46 @ (comp @ X52 @ X51) @ (sub @ X54 @ X51) @ X53)) | ~! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (~(X46 @ (comp @ X58 @ X56) @ (sub @ X55 @ X56) @ X57) | (X46 @ X58 @ X55 @ (comp @ X56 @ X57))) | ~(X46 @ id @ X48 @ id) | (X46 @ id @ (ap @ X48 @ X47) @ id) | ~(X46 @ id @ X47 @ id)) <=> hoasinduction_lem2) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : ((X59 = X60) | ((ap @ X59 @ X62) != (ap @ X60 @ X61))) <=> apinj1) & (hoasinduction_lthm_3 <=> (! [X63 : subst > term > subst > $o] : ~! [X64 : term > $o] : ~! [X65 : term] : ((X64 @ X65) = (X63 @ id @ X65 @ id)) => (! [X66 : term,X67 : term > $o] : ((X67 @ X66) | ~! [X68 : term] : (~(var @ X68) | (X67 @ X68)) | ~! [X69 : term,X70 : term] : (~(X67 @ X69) | (X67 @ (ap @ X70 @ X69)) | ~(X67 @ X70)) | ~! [X71 : term] : ((X67 @ (lam @ X71)) | ~! [X72 : term] : ((X67 @ (sub @ X71 @ (push @ X72 @ id))) | ~(X67 @ X72)))) => (! [X73 : term] : ((sub @ X73 @ id) = X73) => (! [X74 : term > $o,X75 : subst > term > subst > $o,X76 : term] : ((X74 @ (lam @ X76)) | ~! [X77 : term] : ((X74 @ X77) = (X75 @ id @ X77 @ id)) | ~! [X78 : subst > term > term] : (~! [X79 : term,X80 : subst,X81 : subst] : ((X78 @ (comp @ X81 @ X80) @ (sub @ X79 @ X80)) = (sub @ (X78 @ X81 @ X79) @ X80)) | (X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) | ~! [X82 : term] : ((X75 @ id @ (X78 @ id @ X82) @ id) | ~(X75 @ id @ X82 @ id))) | ~! [X83 : term] : (~(X74 @ X83) | (X74 @ (sub @ X76 @ (push @ X83 @ id))))) => ! [X84 : term,X85 : subst > term > subst > $o] : (~! [X86 : term,X87 : term] : (~(X85 @ id @ X87 @ id) | ~(X85 @ id @ X86 @ id) | (X85 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id)) | ~! [X88 : term] : (~(var @ (sub @ X88 @ id)) | (X85 @ id @ X88 @ id)) | ~! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : (~(X85 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89) | (X85 @ X90 @ X91 @ (comp @ X92 @ X89))) | ~! [X93 : subst,X94 : term,X95 : subst,X96 : subst] : (~(X85 @ X96 @ X94 @ (comp @ X93 @ X95)) | (X85 @ (comp @ X96 @ X93) @ (sub @ X94 @ X93) @ X95)) | ~! [X97 : subst > term > term] : ((X85 @ id @ (lam @ (X97 @ sh @ one)) @ id) | ~! [X98 : term] : (~(X85 @ id @ X98 @ id) | (X85 @ id @ (X97 @ id @ X98) @ id)) | ~! [X99 : subst,X100 : subst,X101 : term] : ((X97 @ (comp @ X99 @ X100) @ (sub @ X101 @ X100)) = (sub @ (X97 @ X99 @ X101) @ X100))) | (X85 @ id @ X84 @ id))))))) & hoaslamnotvar_lthm & (! [X102 : subst > term > subst > $o] : ~! [X103 : term > $o] : ~! [X104 : term] : ((X102 @ id @ X104 @ id) = (X103 @ X104)) <=> hoasinduction_lem0) & (induction2 <=> ! [X105 : term > $o,X106 : term] : (~! [X107 : term] : (~(var @ X107) | (X105 @ X107)) | ~! [X108 : term,X109 : term] : ((X105 @ (ap @ X109 @ X108)) | ~(X105 @ X108) | ~(X105 @ X109)) | (X105 @ X106) | ~! [X110 : term] : (~! [X111 : term] : ((X105 @ (sub @ X110 @ (push @ X111 @ id))) | ~(X105 @ X111)) | (X105 @ (lam @ X110))))) & (hoasinduction_p_and_p_prime = (^[X112 : subst > term > subst > $o, X113 : term > $o] : (! [X114 : term] : ((X112 @ id @ X114 @ id) = (X113 @ X114))))) & (pushprop_lem0_lthm <=> ! [X115 : term > $o,X116 : term,X117 : subst] : ~! [X118 : term > $o] : ~! [X119 : term] : ((X118 @ X119) = (X115 @ (sub @ X119 @ (push @ X116 @ X117))))) & (hoasinduction_lem3aa <=> ! [X120 : term,X121 : subst > term > subst > $o] : ((X121 @ id @ (lam @ (sub @ X120 @ (push @ one @ sh))) @ id) | ~! [X122 : term] : (~(X121 @ id @ X122 @ id) | (X121 @ id @ (sub @ X120 @ (push @ X122 @ id)) @ id)) | ~! [X123 : subst > term > term] : ((X121 @ id @ (lam @ (X123 @ sh @ one)) @ id) | ~! [X124 : term] : ((X121 @ id @ (X123 @ id @ X124) @ id) | ~(X121 @ id @ X124 @ id)) | ~! [X125 : subst,X126 : subst,X127 : term] : ((X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126)) = (sub @ (X123 @ X125 @ X127) @ X126))))) & (hoasinduction_no_psi_cond <=> ! [X128 : subst > term > subst > $o,X129 : term] : ((X128 @ id @ X129 @ id) | ~! [X130 : subst > term > term] : (~! [X131 : term] : (~(X128 @ id @ X131 @ id) | (X128 @ id @ (X130 @ id @ X131) @ id)) | ~! [X132 : subst,X133 : subst,X134 : term] : ((sub @ (X130 @ X132 @ X134) @ X133) = (X130 @ (comp @ X132 @ X133) @ (sub @ X134 @ X133))) | (X128 @ id @ (lam @ (X130 @ sh @ one)) @ id)) | ~! [X135 : term,X136 : term] : ((X128 @ id @ (ap @ (sub @ X136 @ id) @ X135) @ id) | ~(X128 @ id @ X135 @ id) | ~(X128 @ id @ X136 @ id)))) & (! [X137 : term,X138 : subst > term > subst > $o] : ((X138 @ id @ X137 @ id) | ~! [X139 : subst,X140 : term,X141 : subst,X142 : subst] : ((X138 @ (comp @ X139 @ X141) @ (sub @ X140 @ X141) @ X142) | ~(X138 @ X139 @ X140 @ (comp @ X141 @ X142))) | ~! [X143 : subst > term > term] : (~! [X144 : term,X145 : subst,X146 : subst] : ((X143 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145)) = (sub @ (X143 @ X146 @ X144) @ X145)) | ~! [X147 : term] : (~(X138 @ id @ X147 @ id) | (X138 @ id @ (X143 @ id @ X147) @ id)) | (X138 @ id @ (lam @ (X143 @ sh @ one)) @ id)) | ~! [X148 : term] : ((X138 @ id @ X148 @ id) | ~(var @ (sub @ X148 @ id))) | ~! [X149 : term,X150 : term] : (~(X138 @ id @ X149 @ id) | ~(X138 @ id @ X150 @ id) | (X138 @ id @ (ap @ (sub @ X150 @ id) @ X149) @ id)) | ~! [X151 : subst,X152 : subst,X153 : subst,X154 : term] : ((X138 @ X151 @ X154 @ (comp @ X152 @ X153)) | ~(X138 @ (comp @ X151 @ X152) @ (sub @ X154 @ X152) @ X153))) <=> hoasinduction) & (! [X155 : term > $o,X156 : term > $o,X157 : subst,X158 : term] : ((X156 @ one) | ~! [X159 : term] : ((X156 @ X159) = (X155 @ (sub @ X159 @ (push @ X158 @ X157)))) | ~(X155 @ X158)) <=> pushprop_lem1v2) & hoasapnotvar_gthm & (axscons <=> ! [X160 : subst] : ((push @ (sub @ one @ X160) @ (comp @ sh @ X160)) = X160)) & ((d2subst @ d_id) = sh) & substmonoid_gthm & hoasapnotvar & hoasapinj1_gthm & pushprop_lem2v2_gthm & (pushprop_p_and_p_prime = (^[X161 : term, X162 : subst, X163 : term > $o, X164 : term > $o] : (! [X165 : term] : ((X163 @ (sub @ X165 @ (push @ X161 @ X162))) = (X164 @ X165))))) & induction2_gthm & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X166 : term] : ? [X167 : d_term] : ((d2term @ X167) = X166) & (hoasinduction_lem3aa_lthm <=> ! [X168 : term,X169 : subst > term > subst > $o] : (~! [X170 : subst > term > term] : (~! [X171 : subst,X172 : term,X173 : subst] : ((X170 @ (comp @ X173 @ X171) @ (sub @ X172 @ X171)) = (sub @ (X170 @ X173 @ X172) @ X171)) | (X169 @ id @ (lam @ (X170 @ sh @ one)) @ id) | ~! [X174 : term] : ((X169 @ id @ (X170 @ id @ X174) @ id) | ~(X169 @ id @ X174 @ id))) | (X169 @ id @ (lam @ (sub @ X168 @ (push @ one @ sh))) @ id) | ~! [X175 : term] : ((X169 @ id @ (sub @ X168 @ (push @ X175 @ id)) @ id) | ~(X169 @ id @ X175 @ id)))) & ((! [X176 : term,X177 : subst] : ((sub @ one @ (push @ X176 @ X177)) = X176) => (! [X178 : term,X179 : subst] : ((comp @ sh @ (push @ X178 @ X179)) = X179) => (! [X180 : term,X181 : term] : ((X180 = X181) | ((lam @ X181) != (lam @ X180))) => ! [X182 : subst > term > term,X183 : term,X184 : subst,X185 : subst > term > term] : (~! [X186 : subst,X187 : subst,X188 : term] : ((sub @ (X182 @ X186 @ X188) @ X187) = (X182 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187))) | ~! [X189 : subst,X190 : subst,X191 : term] : ((sub @ (X185 @ X190 @ X191) @ X189) = (X185 @ (comp @ X190 @ X189) @ (sub @ X191 @ X189))) | ((lam @ (X185 @ sh @ one)) != (lam @ (X182 @ sh @ one))) | ((X182 @ X184 @ X183) = (X185 @ X184 @ X183)))))) <=> hoaslaminj_lthm) & axapp & hoasinduction_lem2v2_gthm & (one = (d2term @ d_one)) & pushprop_lem3v2 & (hoasinduction_lem3aaa <=> ! [X192 : subst > term > subst > $o,X193 : term] : ((X192 @ id @ (lam @ (sub @ X193 @ (push @ one @ sh))) @ id) | ~! [X194 : term] : (~(X192 @ id @ X194 @ id) | (X192 @ id @ (sub @ X193 @ (push @ X194 @ id)) @ id)) | ~! [X195 : subst > term > term,X196 : term] : (~! [X197 : subst,X198 : term,X199 : subst] : ((sub @ X196 @ (push @ (sub @ X198 @ X197) @ (comp @ X199 @ X197))) = (X195 @ (comp @ X199 @ X197) @ (sub @ X198 @ X197))) | (X192 @ id @ (lam @ (X195 @ sh @ one)) @ id) | ~! [X200 : subst,X201 : term,X202 : subst] : ((sub @ (X195 @ X202 @ X201) @ X200) = (sub @ (sub @ X196 @ (push @ X201 @ X202)) @ X200)) | ~! [X203 : term] : (~(X192 @ id @ X203 @ id) | (X192 @ id @ (X195 @ id @ X203) @ id))))) & axmap & (axidr <=> ! [X204 : subst] : ((comp @ X204 @ id) = X204)) & (axidl <=> ! [X205 : subst] : ((comp @ id @ X205) = X205)) & termmset_gthm & (! [X206 : subst > term > subst > $o,X207 : term] : (~! [X208 : subst,X209 : subst,X210 : term,X211 : subst] : (~(X206 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209) @ X208) | (X206 @ X211 @ X210 @ (comp @ X209 @ X208))) | (X206 @ id @ (lam @ X207) @ id) | ~! [X212 : subst > term > term] : (~! [X213 : term] : ((X206 @ id @ (X212 @ id @ X213) @ id) | ~(X206 @ id @ X213 @ id)) | (X206 @ id @ (lam @ (X212 @ sh @ one)) @ id) | ~! [X214 : subst,X215 : term,X216 : subst] : ((sub @ (X212 @ X214 @ X215) @ X216) = (X212 @ (comp @ X214 @ X216) @ (sub @ X215 @ X216)))) | ~! [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (~(X206 @ X218 @ X219 @ (comp @ X217 @ X220)) | (X206 @ (comp @ X218 @ X217) @ (sub @ X219 @ X217) @ X220)) | ~! [X221 : term] : (~(X206 @ id @ X221 @ id) | (X206 @ id @ (sub @ X207 @ (push @ X221 @ id)) @ id))) <=> hoasinduction_lem3) & hoasapinj2_gthm & lamnotvar & hoaslamnotvar & hoasinduction_lem3_gthm & (! [X222 : term,X223 : term > $o,X224 : subst > term > subst > $o] : (~! [X225 : subst > term > term] : ((X224 @ id @ (lam @ (X225 @ sh @ one)) @ id) | ~! [X226 : term,X227 : subst,X228 : subst] : ((sub @ (X225 @ X228 @ X226) @ X227) = (X225 @ (comp @ X228 @ X227) @ (sub @ X226 @ X227))) | ~! [X229 : term] : (~(X224 @ id @ X229 @ id) | (X224 @ id @ (X225 @ id @ X229) @ id))) | ~! [X230 : term] : (~(X223 @ X230) | (X223 @ (sub @ X222 @ (push @ X230 @ id)))) | ~! [X231 : subst,X232 : subst,X233 : term,X234 : subst] : ((X224 @ (comp @ X232 @ X231) @ (sub @ X233 @ X231) @ X234) | ~(X224 @ X232 @ X233 @ (comp @ X231 @ X234))) | ~! [X235 : term,X236 : subst,X237 : subst,X238 : subst] : ((X224 @ X236 @ X235 @ (comp @ X238 @ X237)) | ~(X224 @ (comp @ X236 @ X238) @ (sub @ X235 @ X238) @ X237)) | (X223 @ (lam @ X222)) | ~! [X239 : term] : ((X223 @ X239) = (X224 @ id @ X239 @ id))) <=> hoasinduction_lem3v2) & ((! [X240 : term] : ((sub @ X240 @ id) = X240) => ! [X241 : term,X242 : term > $o,X243 : subst > term > subst > $o] : (~! [X244 : subst,X245 : subst,X246 : subst,X247 : term] : ((X243 @ X246 @ X247 @ (comp @ X245 @ X244)) | ~(X243 @ (comp @ X246 @ X245) @ (sub @ X247 @ X245) @ X244)) | ~! [X248 : term] : (~(X242 @ X248) | (X242 @ (sub @ X241 @ (push @ X248 @ id)))) | ~! [X249 : subst > term > term] : (~! [X250 : term,X251 : subst,X252 : subst] : ((X249 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)) = (sub @ (X249 @ X252 @ X250) @ X251)) | ~! [X253 : term] : ((X243 @ id @ (X249 @ id @ X253) @ id) | ~(X243 @ id @ X253 @ id)) | (X243 @ id @ (lam @ (X249 @ sh @ one)) @ id)) | ~! [X254 : term] : ((X242 @ X254) = (X243 @ id @ X254 @ id)) | ~! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (~(X243 @ X255 @ X256 @ (comp @ X257 @ X258)) | (X243 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257) @ X258)) | (X242 @ (lam @ X241)))) <=> hoasinduction_lem3v2_lthm) & (termmset_lthm <=> (! [X259 : term] : ((sub @ X259 @ id) = X259) => ! [X260 : term] : ((sub @ X260 @ id) = X260))) & hoaslaminj_gthm & (hoasinduction_lem3b <=> ! [X261 : term] : ~! [X262 : subst > term > term] : ((X262 @ sh @ one) != (sub @ X261 @ (push @ one @ sh)))) & apnotvar & ((! [X263 : term,X264 : subst] : ((sub @ one @ (push @ X263 @ X264)) = X263) => (! [X265 : term,X266 : subst] : ((comp @ sh @ (push @ X265 @ X266)) = X266) => (! [X267 : subst] : ((comp @ X267 @ id) = X267) => (! [X268 : term > $o,X269 : term] : (~! [X270 : term] : ((X268 @ (lam @ X270)) | ~(X268 @ X270)) | ~! [X271 : term,X272 : term] : (~(X268 @ X271) | ~(X268 @ X272) | (X268 @ (ap @ X272 @ X271))) | ~! [X273 : term] : (~(var @ X273) | (X268 @ X273)) | (X268 @ X269)) => ! [X274 : term,X275 : subst,X276 : term > $o] : (~! [X277 : term,X278 : term] : ((X276 @ (ap @ X278 @ X277)) | ~(X276 @ X277) | ~(X276 @ X278)) | ~! [X279 : term] : (~! [X280 : term] : (~(X276 @ X280) | (X276 @ (sub @ X279 @ (push @ X280 @ id)))) | (X276 @ (lam @ X279))) | (X276 @ (sub @ X274 @ X275)) | ~! [X281 : term] : ((X276 @ (sub @ X281 @ X275)) | ~(var @ X281))))))) <=> induction2lem_lthm) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop_lem3v2_lthm & hoasinduction_lem2_lthm & ~ulamvar1 & (! [X282 : term,X283 : subst] : ((comp @ sh @ (push @ X282 @ X283)) = X283) <=> axshiftcons) & (! [X284 : subst > term > subst > $o,X285 : term] : (~! [X286 : term] : (~(X284 @ id @ X286 @ id) | (X284 @ id @ (sub @ X285 @ (push @ X286 @ id)) @ id)) | (X284 @ id @ (lam @ X285) @ id) | ~! [X287 : subst > term > term] : (~! [X288 : term] : (~(X284 @ id @ X288 @ id) | (X284 @ id @ (X287 @ id @ X288) @ id)) | ~! [X289 : subst,X290 : term,X291 : subst] : ((X287 @ (comp @ X291 @ X289) @ (sub @ X290 @ X289)) = (sub @ (X287 @ X291 @ X290) @ X289)) | (X284 @ id @ (lam @ (X287 @ sh @ one)) @ id))) <=> hoasinduction_lem3a) & ! [X292 : subst] : ? [X293 : d_subst] : ((d2subst @ X293) = X292) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X294 : term,X295 : term,X296 : term,X297 : term] : ((X296 = X297) | ((ap @ (sub @ X295 @ id) @ X296) != (ap @ (sub @ X294 @ id) @ X297))) <=> hoasapinj2) & ! [X298 : d_subst,X299 : d_subst] : (((d2subst @ X298) = (d2subst @ X299)) => (X298 = X299)) & ((! [X300 : term > $o,X301 : term] : (~! [X302 : term] : ((X300 @ (lam @ X302)) | ~! [X303 : term] : ((X300 @ (sub @ X302 @ (push @ X303 @ id))) | ~(X300 @ X303))) | ~! [X304 : term] : ((X300 @ X304) | ~(var @ X304)) | (X300 @ X301) | ~! [X305 : term,X306 : term] : (~(X300 @ X306) | (X300 @ (ap @ X306 @ X305)) | ~(X300 @ X305))) => (! [X307 : subst > term > subst > $o,X308 : term,X309 : term] : ((X307 @ id @ (ap @ X308 @ X309) @ id) | ~! [X310 : subst,X311 : term,X312 : subst,X313 : subst] : (~(X307 @ (comp @ X313 @ X310) @ (sub @ X311 @ X310) @ X312) | (X307 @ X313 @ X311 @ (comp @ X310 @ X312))) | ~! [X314 : term,X315 : term] : (~(X307 @ id @ X314 @ id) | (X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id) | ~(X307 @ id @ X315 @ id)) | ~(X307 @ id @ X309 @ id) | ~(X307 @ id @ X308 @ id) | ~! [X316 : term,X317 : subst,X318 : subst,X319 : subst] : ((X307 @ (comp @ X319 @ X317) @ (sub @ X316 @ X317) @ X318) | ~(X307 @ X319 @ X316 @ (comp @ X317 @ X318)))) => (! [X320 : subst > term > subst > $o,X321 : term] : (~! [X322 : term] : ((X320 @ id @ (sub @ X321 @ (push @ X322 @ id)) @ id) | ~(X320 @ id @ X322 @ id)) | (X320 @ id @ (lam @ X321) @ id) | ~! [X323 : subst > term > term] : (~! [X324 : term] : (~(X320 @ id @ X324 @ id) | (X320 @ id @ (X323 @ id @ X324) @ id)) | (X320 @ id @ (lam @ (X323 @ sh @ one)) @ id) | ~! [X325 : subst,X326 : subst,X327 : term] : ((X323 @ (comp @ X326 @ X325) @ (sub @ X327 @ X325)) = (sub @ (X323 @ X326 @ X327) @ X325))) | ~! [X328 : subst,X329 : term,X330 : subst,X331 : subst] : (~(X320 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328) | (X320 @ X330 @ X329 @ (comp @ X331 @ X328))) | ~! [X332 : subst,X333 : subst,X334 : term,X335 : subst] : ((X320 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X335) | ~(X320 @ X333 @ X334 @ (comp @ X332 @ X335)))) => ! [X336 : term,X337 : subst > term > subst > $o] : (~! [X338 : term,X339 : term] : ((X337 @ id @ (ap @ (sub @ X338 @ id) @ X339) @ id) | ~(X337 @ id @ X338 @ id) | ~(X337 @ id @ X339 @ id)) | (X337 @ id @ X336 @ id) | ~! [X340 : term,X341 : subst,X342 : subst,X343 : subst] : (~(X337 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343) | (X337 @ X342 @ X340 @ (comp @ X341 @ X343))) | ~! [X344 : term] : ((X337 @ id @ X344 @ id) | ~(var @ (sub @ X344 @ id))) | ~! [X345 : subst > term > term] : ((X337 @ id @ (lam @ (X345 @ sh @ one)) @ id) | ~! [X346 : term] : (~(X337 @ id @ X346 @ id) | (X337 @ id @ (X345 @ id @ X346) @ id)) | ~! [X347 : subst,X348 : term,X349 : subst] : ((sub @ (X345 @ X347 @ X348) @ X349) = (X345 @ (comp @ X347 @ X349) @ (sub @ X348 @ X349)))) | ~! [X350 : subst,X351 : subst,X352 : subst,X353 : term] : (~(X337 @ X350 @ X353 @ (comp @ X351 @ X352)) | (X337 @ (comp @ X350 @ X351) @ (sub @ X353 @ X351) @ X352)))))) <=> hoasinduction_lthm) & hoaslamnotap_gthm & (! [X354 : term,X355 : term,X356 : subst > term > term] : (~! [X357 : subst,X358 : term,X359 : subst] : ((X356 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359)) = (sub @ (X356 @ X357 @ X358) @ X359)) | ((lam @ (X356 @ sh @ one)) != (ap @ (sub @ X355 @ id) @ X354))) <=> hoaslamnotap) & (axvarid <=> ! [X360 : term] : ((sub @ X360 @ id) = X360)) & (! [X361 : term,X362 : term,X363 : term,X364 : term] : (((ap @ (sub @ X364 @ id) @ X363) != (ap @ (sub @ X362 @ id) @ X361)) | (X362 = X364)) <=> hoasapinj1) & hoasinduction_lem3a_gthm & ((! [X365 : subst] : ((comp @ id @ X365) = X365) & ! [X366 : subst] : ((comp @ X366 @ id) = X366)) <=> substmonoid) & ((d2subst @ d_id) = id) & hoasinduction_lem2_gthm & hoasinduction_lem1 & pushprop_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X367 : term] : ~! [X368 : subst > term > term] : ~! [X369 : term,X370 : subst] : ((sub @ X367 @ (push @ X369 @ X370)) = (X368 @ X370 @ X369)) => (! [X371 : term] : ((sub @ X371 @ id) = X371) => ! [X372 : term,X373 : term > $o,X374 : subst > term > subst > $o] : (~! [X375 : term] : ((X373 @ X375) = (X374 @ id @ X375 @ id)) | ~! [X376 : term] : ((X373 @ (sub @ X372 @ (push @ X376 @ id))) | ~(X373 @ X376)) | ~! [X377 : subst > term > term] : (~! [X378 : term] : (~(X374 @ id @ X378 @ id) | (X374 @ id @ (X377 @ id @ X378) @ id)) | (X374 @ id @ (lam @ (X377 @ sh @ one)) @ id) | ~! [X379 : term,X380 : subst,X381 : subst] : ((sub @ (X377 @ X381 @ X379) @ X380) = (X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) | (X373 @ (lam @ X372)))))) & (pushprop_lem0 <=> ! [X382 : subst,X383 : term > $o,X384 : term] : ~! [X385 : term > $o] : ~! [X386 : term] : ((X383 @ (sub @ X386 @ (push @ X384 @ X382))) = (X385 @ X386))) & hoasinduction_gthm & (! [X387 : term,X388 : term] : (((sub @ X387 @ sh) != (sub @ X388 @ sh)) | (X387 = X388)) <=> shinj) & (induction2lem <=> ! [X389 : term > $o,X390 : subst,X391 : term] : ((X389 @ (sub @ X391 @ X390)) | ~! [X392 : term] : (~! [X393 : term] : (~(X389 @ X393) | (X389 @ (sub @ X392 @ (push @ X393 @ id)))) | (X389 @ (lam @ X392))) | ~! [X394 : term] : ((X389 @ (sub @ X394 @ X390)) | ~(var @ X394)) | ~! [X395 : term,X396 : term] : ((X389 @ (ap @ X396 @ X395)) | ~(X389 @ X396) | ~(X389 @ X395)))) & ulamvarsh & (! [X397 : term,X398 : term,X399 : term,X400 : term] : (((ap @ X400 @ X399) != (ap @ X398 @ X397)) | (X397 = X399)) <=> apinj2) & ((! [X401 : term] : ((sub @ X401 @ id) = X401) => (! [X402 : subst,X403 : term,X404 : term > $o] : (~! [X405 : term] : ((X404 @ (sub @ X405 @ X402)) | ~(var @ X405)) | ~! [X406 : term,X407 : term] : ((X404 @ (ap @ X406 @ X407)) | ~(X404 @ X407) | ~(X404 @ X406)) | ~! [X408 : term] : (~! [X409 : term] : (~(X404 @ X409) | (X404 @ (sub @ X408 @ (push @ X409 @ id)))) | (X404 @ (lam @ X408))) | (X404 @ (sub @ X403 @ X402))) => ! [X410 : term,X411 : term > $o] : (~! [X412 : term] : (~(var @ X412) | (X411 @ X412)) | (X411 @ X410) | ~! [X413 : term] : (~! [X414 : term] : (~(X411 @ X414) | (X411 @ (sub @ X413 @ (push @ X414 @ id)))) | (X411 @ (lam @ X413))) | ~! [X415 : term,X416 : term] : ((X411 @ (ap @ X415 @ X416)) | ~(X411 @ X415) | ~(X411 @ X416))))) <=> induction2_lthm) & ((! [X417 : term,X418 : term,X419 : term,X420 : term] : (((ap @ X419 @ X418) != (ap @ X420 @ X417)) | (X417 = X418)) => ! [X421 : term,X422 : term,X423 : term,X424 : term] : (((ap @ (sub @ X422 @ id) @ X421) != (ap @ (sub @ X424 @ id) @ X423)) | (X421 = X423))) <=> hoasapinj2_lthm) & pushprop_lem1v2_gthm & ((^[X425 : subst, X426 : subst > term > term] : (d2term @ d_one)) = hoaslam) & axassoc & (laminj <=> ! [X427 : term,X428 : term] : (((lam @ X428) != (lam @ X427)) | (X427 = X428))) & pushprop_lem0_gthm & hoasinduction_lem3b_gthm & (! [X429 : term,X430 : term,X431 : term > $o,X432 : subst > term > subst > $o] : (~! [X433 : subst,X434 : term,X435 : subst,X436 : subst] : ((X432 @ X435 @ X434 @ (comp @ X436 @ X433)) | ~(X432 @ (comp @ X435 @ X436) @ (sub @ X434 @ X436) @ X433)) | ~! [X437 : term] : ((X431 @ X437) = (X432 @ id @ X437 @ id)) | ~! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((X432 @ (comp @ X441 @ X440) @ (sub @ X439 @ X440) @ X438) | ~(X432 @ X441 @ X439 @ (comp @ X440 @ X438))) | ~(X431 @ X430) | ~(X431 @ X429) | (X431 @ (ap @ X430 @ X429)) | ~! [X442 : term,X443 : term] : ((X432 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id) | ~(X432 @ id @ X443 @ id) | ~(X432 @ id @ X442 @ id))) <=> hoasinduction_lem2v2) & hoasinduction_lem1v2_gthm & hoaslamnotvar_gthm & (hoasinduction_lem3v2_f_lthm <=> ! [X444 : term] : ~! [X445 : subst > term > term] : ~! [X446 : term,X447 : subst] : ((sub @ X444 @ (push @ X446 @ X447)) = (X445 @ X447 @ X446))) & hoasinduction_lem1_gthm & (pushprop_lem1 <=> ! [X448 : subst,X449 : term > $o,X450 : term,X451 : term,X452 : term > $o] : (~(X449 @ X451) | (X452 @ (sub @ X451 @ (push @ X450 @ X448))))) & hoaslamnotap_lthm & hoasapnotvar_lthm & (! [X453 : subst > term > term,X454 : subst > term > term,X455 : term,X456 : subst] : (~! [X457 : subst,X458 : term,X459 : subst] : ((sub @ (X454 @ X457 @ X458) @ X459) = (X454 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459))) | ((X453 @ X456 @ X455) = (X454 @ X456 @ X455)) | ~! [X460 : subst,X461 : term,X462 : subst] : ((sub @ (X453 @ X462 @ X461) @ X460) = (X453 @ (comp @ X462 @ X460) @ (sub @ X461 @ X460))) | ((lam @ (X454 @ sh @ one)) != (lam @ (X453 @ sh @ one)))) <=> hoaslaminj) & ! [X463 : d_term] : (d_one = X463) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & pushprop & (! [X464 : term] : ~! [X465 : subst > term > term] : ((X465 @ sh @ one) != (sub @ X464 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & pushprop_lem2v2 & hoasinduction_lem3v2_gthm & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop_lem2v2_lthm & axvarshift & pushprop_gthm & ((! [X466 : subst] : ((comp @ id @ X466) = X466) => (! [X467 : subst] : ((comp @ X467 @ id) = X467) => (! [X468 : subst] : ((comp @ X468 @ id) = X468) & ! [X469 : subst] : ((comp @ id @ X469) = X469)))) <=> substmonoid_lthm) & (hoasinduction_lem3v2a <=> ! [X470 : term > $o,X471 : subst > term > subst > $o,X472 : term] : ((X470 @ (lam @ X472)) | ~! [X473 : term] : ((X471 @ id @ X473 @ id) = (X470 @ X473)) | ~! [X474 : term] : ((X470 @ (sub @ X472 @ (push @ X474 @ id))) | ~(X470 @ X474)) | ~! [X475 : subst > term > term] : ((X471 @ id @ (lam @ (X475 @ sh @ one)) @ id) | ~! [X476 : term,X477 : subst,X478 : subst] : ((sub @ (X475 @ X477 @ X476) @ X478) = (X475 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) | ~! [X479 : term] : (~(X471 @ id @ X479 @ id) | (X471 @ id @ (X475 @ id @ X479) @ id))))) & (! [X480 : term,X481 : subst] : ((sub @ one @ (push @ X480 @ X481)) = X480) <=> axvarcons) & axabs & (pushprop_lem1_lthm <=> (! [X482 : subst,X483 : term] : ((sub @ one @ (push @ X483 @ X482)) = X483) => (! [X484 : subst,X485 : term] : ((comp @ sh @ (push @ X485 @ X484)) = X484) => ! [X486 : term > $o,X487 : term > $o,X488 : term,X489 : subst,X490 : term] : ((X487 @ (sub @ X490 @ (push @ X488 @ X489))) | ~(X486 @ X490))))) & induction2lem_gthm & pushprop_lem1_gthm & ((! [X491 : term] : ((sub @ X491 @ id) = X491) => (! [X492 : subst > term > subst > $o,X493 : term] : (~! [X494 : subst > term > term] : (~! [X495 : subst,X496 : term,X497 : subst] : ((X494 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497)) = (sub @ (X494 @ X495 @ X496) @ X497)) | (X492 @ id @ (lam @ (X494 @ sh @ one)) @ id) | ~! [X498 : term] : ((X492 @ id @ (X494 @ id @ X498) @ id) | ~(X492 @ id @ X498 @ id))) | (X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id) | ~! [X499 : term] : (~(X492 @ id @ X499 @ id) | (X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id))) => ! [X500 : term,X501 : subst > term > subst > $o] : (~! [X502 : subst > term > term] : (~! [X503 : term] : (~(X501 @ id @ X503 @ id) | (X501 @ id @ (X502 @ id @ X503) @ id)) | ~! [X504 : subst,X505 : term,X506 : subst] : ((sub @ (X502 @ X504 @ X505) @ X506) = (X502 @ (comp @ X504 @ X506) @ (sub @ X505 @ X506))) | (X501 @ id @ (lam @ (X502 @ sh @ one)) @ id)) | ~! [X507 : term] : ((X501 @ id @ (sub @ X500 @ (push @ X507 @ id)) @ id) | ~(X501 @ id @ X507 @ id)) | ~! [X508 : subst,X509 : subst,X510 : subst,X511 : term] : (~(X501 @ X509 @ X511 @ (comp @ X510 @ X508)) | (X501 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510) @ X508)) | (X501 @ id @ (lam @ X500) @ id) | ~! [X512 : subst,X513 : subst,X514 : subst,X515 : term] : (~(X501 @ (comp @ X513 @ X512) @ (sub @ X515 @ X512) @ X514) | (X501 @ X513 @ X515 @ (comp @ X512 @ X514)))))) <=> hoasinduction_lem3_lthm) & ((! [X516 : subst > term > subst > $o] : ~! [X517 : term > $o] : ~! [X518 : term] : ((X517 @ X518) = (X516 @ id @ X518 @ id)) => (! [X519 : term > $o,X520 : term] : (~! [X521 : term,X522 : term] : (~(X519 @ X521) | (X519 @ (ap @ X522 @ X521)) | ~(X519 @ X522)) | (X519 @ X520) | ~! [X523 : term] : (~! [X524 : term] : (~(X519 @ X524) | (X519 @ (sub @ X523 @ (push @ X524 @ id)))) | (X519 @ (lam @ X523))) | ~! [X525 : term] : (~(var @ X525) | (X519 @ X525))) => (! [X526 : term] : ((sub @ X526 @ id) = X526) => (! [X527 : term > $o,X528 : subst > term > subst > $o,X529 : term] : (~! [X530 : term] : ((X527 @ X530) = (X528 @ id @ X530 @ id)) | (X527 @ (lam @ X529)) | ~! [X531 : term] : ((X527 @ (sub @ X529 @ (push @ X531 @ id))) | ~(X527 @ X531)) | ~! [X532 : subst > term > term] : (~! [X533 : term] : (~(X528 @ id @ X533 @ id) | (X528 @ id @ (X532 @ id @ X533) @ id)) | ~! [X534 : term,X535 : subst,X536 : subst] : ((X532 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536)) = (sub @ (X532 @ X535 @ X534) @ X536)) | (X528 @ id @ (lam @ (X532 @ sh @ one)) @ id))) => ! [X537 : term,X538 : subst > term > subst > $o] : (~! [X539 : term,X540 : term] : (~(X538 @ id @ X539 @ id) | ~(X538 @ id @ X540 @ id) | (X538 @ id @ (ap @ (sub @ X539 @ id) @ X540) @ id)) | ~! [X541 : subst > term > term] : (~! [X542 : term] : ((X538 @ id @ (X541 @ id @ X542) @ id) | ~(X538 @ id @ X542 @ id)) | (X538 @ id @ (lam @ (X541 @ sh @ one)) @ id) | ~! [X543 : term,X544 : subst,X545 : subst] : ((X541 @ (comp @ X544 @ X545) @ (sub @ X543 @ X545)) = (sub @ (X541 @ X544 @ X543) @ X545))) | (X538 @ id @ X537 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & axclos & (! [X546 : term] : ~! [X547 : subst > term > term] : ~! [X548 : term,X549 : subst] : ((sub @ X546 @ (push @ X548 @ X549)) = (X547 @ X549 @ X548)) <=> hoasinduction_lem3v2_f) & ~lamnotap & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))),
% 15.37/3.55 inference(rectify,[status(thm)],[f1])).
% 15.37/3.55 thf(f1,axiom,(
% 15.37/3.55 (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X10 : term > $o,X14 : subst,X13 : term,X11 : term > $o] : ((X11 @ one) | ~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & hoasinduction_lem1v2 & hoasinduction_lem1_lthm & ulamvarind & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [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 @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : subst > term > subst > $o,X43 : term] : (~! [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)) | ~! [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)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & ! [X5 : d_subst] : (d_id = X5) & ~(var @ (d2term @ d_one)) & (induction <=> ! [X10 : term > $o,X21 : term] : ((X10 @ X21) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)))) & pushprop_lthm_orig & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X13 : term,X20 : term,X15 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) => ! [X15 : term,X13 : term,X19 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)))) <=> hoasapinj1_lthm) & (! [X10 : subst > term > subst > $o,X24 : term,X23 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id)) <=> hoasinduction_lem2) & (! [X15 : term,X13 : term,X19 : term,X20 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) <=> apinj1) & (hoasinduction_lthm_3 <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : ((X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ X28 @ id))))))) & hoaslamnotvar_lthm & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0) & (induction2 <=> ! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))) & (hoasinduction_p_and_p_prime = (^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))))) & (pushprop_lem0_lthm <=> ! [X10 : term > $o,X13 : term,X14 : subst] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (hoasinduction_no_psi_cond <=> ! [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)) | ~! [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)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & (! [X28 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ X28 @ id) | ~! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction) & (! [X10 : term > $o,X11 : term > $o,X14 : subst,X13 : term] : ((X11 @ one) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | ~(X10 @ X13)) <=> pushprop_lem1v2) & hoasapnotvar_gthm & (axscons <=> ! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14)) & ((d2subst @ d_id) = sh) & substmonoid_gthm & hoasapnotvar & hoasapinj1_gthm & pushprop_lem2v2_gthm & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : term > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & induction2_gthm & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & (hoasinduction_lem3aa_lthm <=> ! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X13 : term,X15 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15))) => ! [X31 : subst > term > term,X33 : term,X32 : subst,X18 : subst > term > term] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)))))) <=> hoaslaminj_lthm) & axapp & hoasinduction_lem2v2_gthm & (one = (d2term @ d_one)) & pushprop_lem3v2 & (hoasinduction_lem3aaa <=> ! [X10 : subst > term > subst > $o,X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term,X35 : term] : (~! [X41 : subst,X40 : term,X39 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X38 : subst,X37 : term,X36 : subst] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & axmap & (axidr <=> ! [X14 : subst] : ((comp @ X14 @ id) = X14)) & (axidl <=> ! [X14 : subst] : ((comp @ id @ X14) = X14)) & termmset_gthm & (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ 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,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3) & hoasapinj2_gthm & lamnotvar & hoaslamnotvar & hoasinduction_lem3_gthm & (! [X48 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) <=> hoasinduction_lem3v2) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X48 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)))) <=> hoasinduction_lem3v2_lthm) & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & hoaslaminj_gthm & (hoasinduction_lem3b <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & apnotvar & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X10 : term > $o,X21 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X21)) => ! [X16 : term,X17 : subst,X10 : term > $o] : (~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))))))) <=> induction2lem_lthm) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop_lem3v2_lthm & hoasinduction_lem2_lthm & ~ulamvar1 & (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) <=> axshiftcons) & (! [X10 : subst > term > subst > $o,X43 : term] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3a) & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))) <=> hoasapinj2) & ! [X7 : d_subst,X6 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & ((! [X10 : term > $o,X22 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) => (! [X10 : subst > term > subst > $o,X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X26 : subst,X13 : term,X25 : 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)) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : subst > term > subst > $o,X27 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [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)))) | ~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) <=> hoasinduction_lthm) & hoaslamnotap_gthm & (! [X47 : term,X46 : term,X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47))) <=> hoaslamnotap) & (axvarid <=> ! [X13 : term] : ((sub @ X13 @ id) = X13)) & (! [X19 : term,X13 : term,X20 : term,X15 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15)) <=> hoasapinj1) & hoasinduction_lem3a_gthm & ((! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14)) <=> substmonoid) & ((d2subst @ d_id) = id) & hoasinduction_lem2_gthm & hoasinduction_lem1 & pushprop_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X29 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X11 @ (lam @ X29)))))) & (pushprop_lem0 <=> ! [X14 : subst,X10 : term > $o,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & hoasinduction_gthm & (! [X13 : term,X15 : term] : (((sub @ X13 @ sh) != (sub @ X15 @ sh)) | (X13 = X15)) <=> shinj) & (induction2lem <=> ! [X10 : term > $o,X17 : subst,X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)))) & ulamvarsh & (! [X19 : term,X13 : term,X20 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) <=> apinj2) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X17 : subst,X16 : term,X10 : term > $o] : (~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (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))))) <=> induction2_lthm) & ((! [X20 : term,X19 : term,X13 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) => ! [X20 : term,X15 : term,X19 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) <=> hoasapinj2_lthm) & pushprop_lem1v2_gthm & ((^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one)) = hoaslam) & axassoc & (laminj <=> ! [X15 : term,X13 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15))) & pushprop_lem0_gthm & hoasinduction_lem3b_gthm & (! [X45 : term,X44 : term,X11 : term > $o,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)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X44) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem2v2) & hoasinduction_lem1v2_gthm & hoaslamnotvar_gthm & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13))) & hoasinduction_lem1_gthm & (pushprop_lem1 <=> ! [X14 : subst,X10 : term > $o,X15 : term,X13 : term,X26 : term > $o] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & hoaslamnotap_lthm & hoasapnotvar_lthm & (! [X18 : subst > term > term,X31 : subst > term > term,X33 : term,X32 : subst] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one)))) <=> hoaslaminj) & ! [X1 : d_term] : (d_one = X1) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & pushprop & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & pushprop_lem2v2 & hoasinduction_lem3v2_gthm & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & pushprop_lem2v2_lthm & axvarshift & pushprop_gthm & ((! [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) & (hoasinduction_lem3v2a <=> ! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & axabs & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X10 : term > $o,X26 : term > $o,X15 : term,X14 : subst,X13 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & induction2lem_gthm & pushprop_lem1_gthm & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [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 @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X27 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) <=> hoasinduction_lem3_lthm) & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X30 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ X30 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & axclos & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & ~lamnotap & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))),
% 15.37/3.55 file('/export/starexec/sandbox/tmp/tmp.OZKaewZbi7/DTF2THF_21668.p',alg444_1)).
% 15.37/3.55 thf(f1258,plain,(
% 15.37/3.55 ( ! [X0 : term] : (((d2term @ (sK457 @ X0)) = X0)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f8657,plain,(
% 15.37/3.55 ($false != (sK592 @ id @ one @ id)) | spl591_705),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f8656])).
% 15.37/3.55 thf(f8656,definition,(
% 15.37/3.55 spl591_705 <=> ($false = (sK592 @ id @ one @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_705])],[avatar_definition])).
% 15.37/3.55 thf(f2515,plain,(
% 15.37/3.55 ($false = (sK592 @ id @ (lam @ sK597) @ id)) | ~spl591_214),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2513])).
% 15.37/3.55 thf(f2513,definition,(
% 15.37/3.55 spl591_214 <=> ($false = (sK592 @ id @ (lam @ sK597) @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_214])],[avatar_definition])).
% 15.37/3.55 thf(f10345,plain,(
% 15.37/3.55 ~spl591_702 | ~spl591_705),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f10344])).
% 15.37/3.55 thf(f10344,plain,(
% 15.37/3.55 $false | (~spl591_702 | ~spl591_705)),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f10279,f9527])).
% 15.37/3.55 thf(f9527,plain,(
% 15.37/3.55 ($true != (sP12 @ sK592)) | ~spl591_702),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f9514])).
% 15.37/3.55 thf(f9514,plain,(
% 15.37/3.55 ($true != $true) | ($true != (sP12 @ sK592)) | ~spl591_702),
% 15.37/3.55 inference(superposition,[status(thm)],[f6120,f8641])).
% 15.37/3.55 thf(f8641,plain,(
% 15.37/3.55 ( ! [X4 : subst] : (($true = (sK592 @ id @ one @ X4))) ) | ~spl591_702),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f8640])).
% 15.37/3.55 thf(f8640,definition,(
% 15.37/3.55 spl591_702 <=> ! [X4 : subst] : ($true = (sK592 @ id @ one @ X4))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_702])],[avatar_definition])).
% 15.37/3.55 thf(f6120,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true != (X0 @ id @ one @ id)) | ($true != (sP12 @ X0))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6119,f1061])).
% 15.37/3.55 thf(f1061,plain,(
% 15.37/3.55 (one = (d2term @ d_one))),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f6119,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true != (sP12 @ X0)) | ($true != (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f923,f4480])).
% 15.37/3.55 thf(f923,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true != (sP12 @ X0)) | ($true != (X0 @ id @ (lam @ (sK365 @ X0 @ sh @ one)) @ id))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f386])).
% 15.37/3.55 thf(f386,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP12 @ X0)) | ! [X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | (($true != (X0 @ id @ (X1 @ id @ (sK361 @ X1 @ X0)) @ id)) & ($true = (X0 @ id @ (sK361 @ X1 @ X0) @ id))) | ((sub @ (X1 @ (sK362 @ X1) @ (sK363 @ X1)) @ (sK364 @ X1)) != (X1 @ (comp @ (sK362 @ X1) @ (sK364 @ X1)) @ (sub @ (sK363 @ X1) @ (sK364 @ X1)))))) & ((($true != (X0 @ id @ (lam @ (sK365 @ X0 @ sh @ one)) @ id)) & ! [X7 : term] : (((X0 @ id @ (sK365 @ X0 @ id @ X7) @ id) = $true) | ($true != (X0 @ id @ X7 @ id))) & ! [X8 : subst,X9 : term,X10 : subst] : ((sK365 @ X0 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)) = (sub @ (sK365 @ X0 @ X8 @ X9) @ X10))) | ($true != (sP12 @ X0))))),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK361,sK362,sK363,sK364,sK365])],[f382,f385,f384,f383])).
% 15.37/3.55 thf(f383,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) != $true) & ($true = (X0 @ id @ X2 @ id))) => (($true != (X0 @ id @ (X1 @ id @ (sK361 @ X1 @ X0)) @ id)) & ($true = (X0 @ id @ (sK361 @ X1 @ X0) @ id))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f384,plain,(
% 15.37/3.55 ! [X1 : subst > term > term] : (? [X3 : subst,X4 : term,X5 : subst] : ((sub @ (X1 @ X3 @ X4) @ X5) != (X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5))) => ((sub @ (X1 @ (sK362 @ X1) @ (sK363 @ X1)) @ (sK364 @ X1)) != (X1 @ (comp @ (sK362 @ X1) @ (sK364 @ X1)) @ (sub @ (sK363 @ X1) @ (sK364 @ X1)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f385,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X7 : term] : (($true = (X0 @ id @ (X6 @ id @ X7) @ id)) | ($true != (X0 @ id @ X7 @ id))) & ! [X8 : subst,X9 : term,X10 : subst] : ((sub @ (X6 @ X8 @ X9) @ X10) = (X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) => (($true != (X0 @ id @ (lam @ (sK365 @ X0 @ sh @ one)) @ id)) & ! [X7 : term] : (((X0 @ id @ (sK365 @ X0 @ id @ X7) @ id) = $true) | ($true != (X0 @ id @ X7 @ id))) & ! [X10 : subst,X9 : term,X8 : subst] : ((sK365 @ X0 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)) = (sub @ (sK365 @ X0 @ X8 @ X9) @ X10))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f382,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP12 @ X0)) | ! [X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ? [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) != $true) & ($true = (X0 @ id @ X2 @ id))) | ? [X3 : subst,X4 : term,X5 : subst] : ((sub @ (X1 @ X3 @ X4) @ X5) != (X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5))))) & (? [X6 : subst > term > term] : (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X7 : term] : (($true = (X0 @ id @ (X6 @ id @ X7) @ id)) | ($true != (X0 @ id @ X7 @ id))) & ! [X8 : subst,X9 : term,X10 : subst] : ((sub @ (X6 @ X8 @ X9) @ X10) = (X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) | ($true != (sP12 @ X0))))),
% 15.37/3.55 inference(rectify,[status(thm)],[f381])).
% 15.37/3.55 thf(f381,plain,(
% 15.37/3.55 ! [X198 : subst > term > subst > $o] : ((($true = (sP12 @ X198)) | ! [X204 : subst > term > term] : (((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) = $true) | ? [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) != $true) & ($true = (X198 @ id @ X205 @ id))) | ? [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) != (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208))))) & (? [X204 : subst > term > term] : (((X198 @ id @ (lam @ (X204 @ sh @ one)) @ id) != $true) & ! [X205 : term] : (((X198 @ id @ (X204 @ id @ X205) @ id) = $true) | ($true != (X198 @ id @ X205 @ id))) & ! [X206 : subst,X207 : term,X208 : subst] : ((sub @ (X204 @ X206 @ X207) @ X208) = (X204 @ (comp @ X206 @ X208) @ (sub @ X207 @ X208)))) | ($true != (sP12 @ X198))))),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f26])).
% 15.37/3.55 thf(f10279,plain,(
% 15.37/3.55 ($true = (sP12 @ sK592)) | ~spl591_705),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f10270])).
% 15.37/3.55 thf(f10270,plain,(
% 15.37/3.55 ($true = (sP12 @ sK592)) | ($true = $false) | ~spl591_705),
% 15.37/3.55 inference(superposition,[status(thm)],[f8524,f8658])).
% 15.37/3.55 thf(f8658,plain,(
% 15.37/3.55 ($false = (sK592 @ id @ one @ id)) | ~spl591_705),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f8656])).
% 15.37/3.55 thf(f8524,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ one @ id)) | ($true = (sP12 @ X0))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8523,f1061])).
% 15.37/3.55 thf(f8523,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (d2term @ d_one) @ id)) | ($true = (sP12 @ X0))) )),
% 15.37/3.55 inference(duplicate_literal_removal,[status(thm)],[f8522])).
% 15.37/3.55 thf(f8522,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (sP12 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8521,f4480])).
% 15.37/3.55 thf(f8521,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ($true = (sP12 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8520,f4480])).
% 15.37/3.55 thf(f8520,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (sP12 @ X0)) | ($true = (X0 @ id @ (sK361 @ X1 @ X0) @ id)) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id))) )),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f924,f4484])).
% 15.37/3.55 thf(f924,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ id @ (sK361 @ X1 @ X0) @ id)) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ($true = (sP12 @ X0)) | ((sub @ (X1 @ (sK362 @ X1) @ (sK363 @ X1)) @ (sK364 @ X1)) != (X1 @ (comp @ (sK362 @ X1) @ (sK364 @ X1)) @ (sub @ (sK363 @ X1) @ (sK364 @ X1))))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f386])).
% 15.37/3.55 thf(f9872,plain,(
% 15.37/3.55 spl591_104 | ~spl591_716),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f9869,f9467,f2050])).
% 15.37/3.55 thf(f2050,definition,(
% 15.37/3.55 spl591_104 <=> ($true = (sP17 @ sK305))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_104])],[avatar_definition])).
% 15.37/3.55 thf(f9467,definition,(
% 15.37/3.55 spl591_716 <=> ! [X5 : subst] : ($true != (sK305 @ id @ one @ X5))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_716])],[avatar_definition])).
% 15.37/3.55 thf(f9869,plain,(
% 15.37/3.55 ($true = (sP17 @ sK305)) | ~spl591_716),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f9861])).
% 15.37/3.55 thf(f9861,plain,(
% 15.37/3.55 ($true = (sP17 @ sK305)) | ($true != $true) | ~spl591_716),
% 15.37/3.55 inference(superposition,[status(thm)],[f9468,f8440])).
% 15.37/3.55 thf(f8440,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ one @ id)) | ($true = (sP17 @ X0))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8439,f1061])).
% 15.37/3.55 thf(f8439,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (sP17 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(duplicate_literal_removal,[status(thm)],[f8438])).
% 15.37/3.55 thf(f8438,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (d2term @ d_one) @ id)) | ($true = (X0 @ id @ (d2term @ d_one) @ id)) | ($true = (sP17 @ X0))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8437,f4480])).
% 15.37/3.55 thf(f8437,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ id @ (sK333 @ X1 @ X0) @ id)) | ($true = (sP17 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8436,f4480])).
% 15.37/3.55 thf(f8436,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ($true = (X0 @ id @ (sK333 @ X1 @ X0) @ id)) | ($true = (sP17 @ X0))) )),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f887,f4484])).
% 15.37/3.55 thf(f887,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sub @ (X1 @ (sK330 @ X1) @ (sK331 @ X1)) @ (sK332 @ X1)) != (X1 @ (comp @ (sK330 @ X1) @ (sK332 @ X1)) @ (sub @ (sK331 @ X1) @ (sK332 @ X1)))) | ($true = (X0 @ id @ (sK333 @ X1 @ X0) @ id)) | ($true = (sP17 @ X0)) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f355])).
% 15.37/3.55 thf(f355,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP17 @ X0)) | ! [X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ((sub @ (X1 @ (sK330 @ X1) @ (sK331 @ X1)) @ (sK332 @ X1)) != (X1 @ (comp @ (sK330 @ X1) @ (sK332 @ X1)) @ (sub @ (sK331 @ X1) @ (sK332 @ X1)))) | (($true != (X0 @ id @ (X1 @ id @ (sK333 @ X1 @ X0)) @ id)) & ($true = (X0 @ id @ (sK333 @ X1 @ X0) @ id))))) & ((($true != (X0 @ id @ (lam @ (sK334 @ X0 @ sh @ one)) @ id)) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (sK334 @ X0 @ X7 @ X8) @ X9) = (sK334 @ X0 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))) & ! [X10 : term] : (($true = (X0 @ id @ (sK334 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) | ($true != (sP17 @ X0))))),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK330,sK331,sK332,sK333,sK334])],[f351,f354,f353,f352])).
% 15.37/3.55 thf(f352,plain,(
% 15.37/3.55 ! [X1 : subst > term > term] : (? [X2 : subst,X3 : term,X4 : subst] : ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)) != (sub @ (X1 @ X2 @ X3) @ X4)) => ((sub @ (X1 @ (sK330 @ X1) @ (sK331 @ X1)) @ (sK332 @ X1)) != (X1 @ (comp @ (sK330 @ X1) @ (sK332 @ X1)) @ (sub @ (sK331 @ X1) @ (sK332 @ X1)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f353,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X5 : term] : (($true != (X0 @ id @ (X1 @ id @ X5) @ id)) & ((X0 @ id @ X5 @ id) = $true)) => (($true != (X0 @ id @ (X1 @ id @ (sK333 @ X1 @ X0)) @ id)) & ($true = (X0 @ id @ (sK333 @ X1 @ X0) @ id))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f354,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (X6 @ X7 @ X8) @ X9) = (X6 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))) & ! [X10 : term] : (($true = (X0 @ id @ (X6 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) => (($true != (X0 @ id @ (lam @ (sK334 @ X0 @ sh @ one)) @ id)) & ! [X9 : subst,X8 : term,X7 : subst] : ((sub @ (sK334 @ X0 @ X7 @ X8) @ X9) = (sK334 @ X0 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))) & ! [X10 : term] : (($true = (X0 @ id @ (sK334 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f351,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP17 @ X0)) | ! [X1 : subst > term > term] : (($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ? [X2 : subst,X3 : term,X4 : subst] : ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)) != (sub @ (X1 @ X2 @ X3) @ X4)) | ? [X5 : term] : (($true != (X0 @ id @ (X1 @ id @ X5) @ id)) & ((X0 @ id @ X5 @ id) = $true)))) & (? [X6 : subst > term > term] : (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id) != $true) & ! [X7 : subst,X8 : term,X9 : subst] : ((sub @ (X6 @ X7 @ X8) @ X9) = (X6 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))) & ! [X10 : term] : (($true = (X0 @ id @ (X6 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) | ($true != (sP17 @ X0))))),
% 15.37/3.55 inference(rectify,[status(thm)],[f350])).
% 15.37/3.55 thf(f350,plain,(
% 15.37/3.55 ! [X329 : subst > term > subst > $o] : ((($true = (sP17 @ X329)) | ! [X337 : subst > term > term] : (($true = (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) | ? [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) != (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341))) | ? [X338 : term] : (($true != (X329 @ id @ (X337 @ id @ X338) @ id)) & ((X329 @ id @ X338 @ id) = $true)))) & (? [X337 : subst > term > term] : (($true != (X329 @ id @ (lam @ (X337 @ sh @ one)) @ id)) & ! [X339 : subst,X340 : term,X341 : subst] : ((sub @ (X337 @ X339 @ X340) @ X341) = (X337 @ (comp @ X339 @ X341) @ (sub @ X340 @ X341))) & ! [X338 : term] : (($true = (X329 @ id @ (X337 @ id @ X338) @ id)) | ((X329 @ id @ X338 @ id) != $true))) | ($true != (sP17 @ X329))))),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f31])).
% 15.37/3.55 thf(f9468,plain,(
% 15.37/3.55 ( ! [X5 : subst] : (($true != (sK305 @ id @ one @ X5))) ) | ~spl591_716),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f9467])).
% 15.37/3.55 thf(f9825,plain,(
% 15.37/3.55 spl591_362 | ~spl591_717),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f9824])).
% 15.37/3.55 thf(f9824,plain,(
% 15.37/3.55 $false | (spl591_362 | ~spl591_717)),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f9807])).
% 15.37/3.55 thf(f9807,plain,(
% 15.37/3.55 ($true != $true) | (spl591_362 | ~spl591_717)),
% 15.37/3.55 inference(superposition,[status(thm)],[f3158,f9471])).
% 15.37/3.55 thf(f9471,plain,(
% 15.37/3.55 ( ! [X2 : term,X4 : subst] : (($true = (sK305 @ X4 @ X2 @ id))) ) | ~spl591_717),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f9470])).
% 15.37/3.55 thf(f9470,definition,(
% 15.37/3.55 spl591_717 <=> ! [X2 : term,X4 : subst] : ($true = (sK305 @ X4 @ X2 @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_717])],[avatar_definition])).
% 15.37/3.55 thf(f3158,plain,(
% 15.37/3.55 ($true != (sK305 @ id @ sK304 @ id)) | spl591_362),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f3156])).
% 15.37/3.55 thf(f3156,definition,(
% 15.37/3.55 spl591_362 <=> ($true = (sK305 @ id @ sK304 @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_362])],[avatar_definition])).
% 15.37/3.55 thf(f9472,plain,(
% 15.37/3.55 spl591_716 | spl591_717 | ~spl591_151),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f9465,f2250,f9470,f9467])).
% 15.37/3.55 thf(f2250,definition,(
% 15.37/3.55 spl591_151 <=> ! [X3 : subst,X4 : subst,X5 : subst,X2 : term] : (((sK305 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5) != $true) | ($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_151])],[avatar_definition])).
% 15.37/3.55 thf(f9465,plain,(
% 15.37/3.55 ( ! [X2 : term,X4 : subst,X5 : subst] : (($true = (sK305 @ X4 @ X2 @ id)) | ($true != (sK305 @ id @ one @ X5))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f9464,f1061])).
% 15.37/3.55 thf(f9464,plain,(
% 15.37/3.55 ( ! [X2 : term,X4 : subst,X5 : subst] : (($true = (sK305 @ X4 @ X2 @ id)) | ($true != (sK305 @ id @ (d2term @ d_one) @ X5))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f9463,f4480])).
% 15.37/3.55 thf(f9463,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true != (sK305 @ id @ (sub @ X2 @ X3) @ X5)) | ($true = (sK305 @ X4 @ X2 @ id))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f9462,f1226])).
% 15.37/3.55 thf(f1226,plain,(
% 15.37/3.55 ((d2subst @ d_id) = id)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f9462,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true = (sK305 @ X4 @ X2 @ id)) | ($true != (sK305 @ (d2subst @ d_id) @ (sub @ X2 @ X3) @ X5))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f9461,f1226])).
% 15.37/3.55 thf(f9461,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true = (sK305 @ X4 @ X2 @ (d2subst @ d_id))) | ($true != (sK305 @ (d2subst @ d_id) @ (sub @ X2 @ X3) @ X5))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f9460,f4466])).
% 15.37/3.55 thf(f4466,plain,(
% 15.37/3.55 ( ! [X201 : subst] : (((d2subst @ d_id) = X201)) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f1086,f1039])).
% 15.37/3.55 thf(f1039,plain,(
% 15.37/3.55 ( ! [X263 : d_subst] : ((d_id = X263)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f1086,plain,(
% 15.37/3.55 ( ! [X201 : subst] : (((d2subst @ (sK555 @ X201)) = X201)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f9460,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5))) | ($true != (sK305 @ (d2subst @ d_id) @ (sub @ X2 @ X3) @ X5))) ) | ~spl591_151),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f2251,f4466])).
% 15.37/3.55 thf(f2251,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (((sK305 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5) != $true) | ($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5)))) ) | ~spl591_151),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2250])).
% 15.37/3.55 thf(f9350,plain,(
% 15.37/3.55 ~spl591_703 | ~spl591_704),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f9349])).
% 15.37/3.55 thf(f9349,plain,(
% 15.37/3.55 $false | (~spl591_703 | ~spl591_704)),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f9348])).
% 15.37/3.55 thf(f9348,plain,(
% 15.37/3.55 ($true = $false) | (~spl591_703 | ~spl591_704)),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8654,f8644])).
% 15.37/3.55 thf(f8644,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term] : (((sK592 @ X2 @ X1 @ id) = $false)) ) | ~spl591_703),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f8643])).
% 15.37/3.55 thf(f8643,definition,(
% 15.37/3.55 spl591_703 <=> ! [X2 : subst,X1 : term] : ((sK592 @ X2 @ X1 @ id) = $false)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_703])],[avatar_definition])).
% 15.37/3.55 thf(f8654,plain,(
% 15.37/3.55 ($true = (sK592 @ id @ one @ id)) | ~spl591_704),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f8652])).
% 15.37/3.55 thf(f8652,definition,(
% 15.37/3.55 spl591_704 <=> ($true = (sK592 @ id @ one @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_704])],[avatar_definition])).
% 15.37/3.55 thf(f8677,plain,(
% 15.37/3.55 spl591_704 | ~spl591_218 | ~spl591_513),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f8676,f3817,f2530,f8652])).
% 15.37/3.55 thf(f2530,definition,(
% 15.37/3.55 spl591_218 <=> ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($true = (sK592 @ id @ (sK596 @ X1) @ id)) | ((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1)))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_218])],[avatar_definition])).
% 15.37/3.55 thf(f3817,definition,(
% 15.37/3.55 spl591_513 <=> ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ($true = (X12 @ id @ X11 @ id)) | ($true = (var @ (sub @ (sK314 @ X12) @ id))) | ((sP17 @ X12) = $true) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (sP16 @ X12)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_513])],[avatar_definition])).
% 15.37/3.55 thf(f8676,plain,(
% 15.37/3.55 ($true = (sK592 @ id @ one @ id)) | (~spl591_218 | ~spl591_513)),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f8675,f7255])).
% 15.37/3.55 thf(f7255,plain,(
% 15.37/3.55 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true != (X0 @ id @ X10 @ id)) | ($true = (X0 @ id @ one @ id))) ) | ~spl591_513),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f7254,f6699])).
% 15.37/3.55 thf(f6699,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (((X12 @ id @ one @ id) = $true) | ((sP17 @ X12) = $true) | ($true = (X12 @ id @ X11 @ id))) ) | ~spl591_513),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f4864,f5799])).
% 15.37/3.55 thf(f5799,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true != (sP16 @ X0)) | ($true = (X0 @ id @ one @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f5798,f1061])).
% 15.37/3.55 thf(f5798,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true != (sP16 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f889,f4480])).
% 15.37/3.55 thf(f889,plain,(
% 15.37/3.55 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (sK336 @ X0) @ id)) | ($true != (sP16 @ X0))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f359])).
% 15.37/3.55 thf(f359,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP16 @ X0)) | ! [X1 : term,X2 : term] : (($true != (X0 @ id @ X1 @ id)) | ($true = (X0 @ id @ (ap @ (sub @ X1 @ id) @ X2) @ id)) | ($true != (X0 @ id @ X2 @ id)))) & ((((X0 @ id @ (sK335 @ X0) @ id) = $true) & ($true != (X0 @ id @ (ap @ (sub @ (sK335 @ X0) @ id) @ (sK336 @ X0)) @ id)) & ($true = (X0 @ id @ (sK336 @ X0) @ id))) | ($true != (sP16 @ X0))))),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK335,sK336])],[f357,f358])).
% 15.37/3.55 thf(f358,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : (? [X3 : term,X4 : term] : (($true = (X0 @ id @ X3 @ id)) & ($true != (X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) & ($true = (X0 @ id @ X4 @ id))) => (((X0 @ id @ (sK335 @ X0) @ id) = $true) & ($true != (X0 @ id @ (ap @ (sub @ (sK335 @ X0) @ id) @ (sK336 @ X0)) @ id)) & ($true = (X0 @ id @ (sK336 @ X0) @ id))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f357,plain,(
% 15.37/3.55 ! [X0 : subst > term > subst > $o] : ((($true = (sP16 @ X0)) | ! [X1 : term,X2 : term] : (($true != (X0 @ id @ X1 @ id)) | ($true = (X0 @ id @ (ap @ (sub @ X1 @ id) @ X2) @ id)) | ($true != (X0 @ id @ X2 @ id)))) & (? [X3 : term,X4 : term] : (($true = (X0 @ id @ X3 @ id)) & ($true != (X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) & ($true = (X0 @ id @ X4 @ id))) | ($true != (sP16 @ X0))))),
% 15.37/3.55 inference(rectify,[status(thm)],[f356])).
% 15.37/3.55 thf(f356,plain,(
% 15.37/3.55 ! [X329 : subst > term > subst > $o] : ((($true = (sP16 @ X329)) | ! [X330 : term,X331 : term] : (((X329 @ id @ X330 @ id) != $true) | ($true = (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) | ((X329 @ id @ X331 @ id) != $true))) & (? [X330 : term,X331 : term] : (((X329 @ id @ X330 @ id) = $true) & ($true != (X329 @ id @ (ap @ (sub @ X330 @ id) @ X331) @ id)) & ((X329 @ id @ X331 @ id) = $true)) | ($true != (sP16 @ X329))))),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f30])).
% 15.37/3.55 thf(f4864,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ X11 @ id)) | ((X12 @ id @ one @ id) = $true) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(duplicate_literal_removal,[status(thm)],[f4863])).
% 15.37/3.55 thf(f4863,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ X11 @ id)) | ((X12 @ id @ one @ id) = $true) | ((X12 @ id @ one @ id) = $true) | ($true = (sP16 @ X12)) | ((sP17 @ X12) = $true)) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4862,f1226])).
% 15.37/3.55 thf(f4862,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (sP16 @ X12)) | ($true = (X12 @ id @ X11 @ id)) | ($true = (X12 @ id @ one @ (d2subst @ d_id))) | ((sP17 @ X12) = $true) | ((X12 @ id @ one @ id) = $true)) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4861,f4466])).
% 15.37/3.55 thf(f4861,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ one @ (sK309 @ X12))) | ((sP17 @ X12) = $true) | ($true = (X12 @ id @ X11 @ id)) | ($true = (sP16 @ X12)) | ((X12 @ id @ one @ id) = $true)) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4860,f1061])).
% 15.37/3.55 thf(f4860,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ (d2term @ d_one) @ (sK309 @ X12))) | ((X12 @ id @ one @ id) = $true) | ($true = (X12 @ id @ X11 @ id)) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4859,f1226])).
% 15.37/3.55 thf(f4859,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ one @ (d2subst @ d_id))) | ((sP17 @ X12) = $true) | ($true = (X12 @ id @ X11 @ id)) | ($true = (X12 @ id @ (d2term @ d_one) @ (sK309 @ X12))) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4858,f4480])).
% 15.37/3.55 thf(f4858,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12))) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12)) | ($true = (X12 @ id @ X11 @ id)) | ($true = (X12 @ id @ one @ (d2subst @ d_id)))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4857,f1226])).
% 15.37/3.55 thf(f4857,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (((sP17 @ X12) = $true) | ($true = (X12 @ (d2subst @ d_id) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12))) | ($true = (X12 @ id @ one @ (d2subst @ d_id))) | ($true = (X12 @ id @ X11 @ id)) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4856,f4466])).
% 15.37/3.55 thf(f4856,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (((sP17 @ X12) = $true) | ($true = (sP16 @ X12)) | ($true = (X12 @ id @ X11 @ id)) | ($true = (X12 @ id @ one @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ($true = (X12 @ (d2subst @ d_id) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4855,f4466])).
% 15.37/3.55 thf(f4855,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (X12 @ id @ X11 @ id)) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12)) | ($true = (X12 @ id @ one @ (comp @ (sK311 @ X12) @ (sK312 @ X12))))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4854,f1061])).
% 15.37/3.55 thf(f4854,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (sP16 @ X12)) | ($true = (X12 @ id @ (d2term @ d_one) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (X12 @ id @ X11 @ id)) | ((sP17 @ X12) = $true)) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4853,f4480])).
% 15.37/3.55 thf(f4853,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ((sP17 @ X12) = $true) | ($true = (X12 @ id @ X11 @ id)) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4852,f1226])).
% 15.37/3.55 thf(f4852,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ (d2subst @ d_id) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ((sP17 @ X12) = $true) | ($true = (X12 @ id @ X11 @ id)) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f4851,f4466])).
% 15.37/3.55 thf(f4851,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (((sP17 @ X12) = $true) | ($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (X12 @ id @ X11 @ id)) | ($true = (sP16 @ X12))) ) | ~spl591_513),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f3818,f4487])).
% 15.37/3.55 thf(f4487,plain,(
% 15.37/3.55 ( ! [X0 : term] : (($true != (var @ X0))) )),
% 15.37/3.55 inference(superposition,[status(thm)],[f4473,f4484])).
% 15.37/3.55 thf(f4473,plain,(
% 15.37/3.55 ($true != (var @ one))),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f1142,f1061])).
% 15.37/3.55 thf(f1142,plain,(
% 15.37/3.55 ((var @ (d2term @ d_one)) != $true)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f3818,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ id @ X11 @ id)) | ($true = (sP16 @ X12)) | ($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ((sP17 @ X12) = $true) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ($true = (var @ (sub @ (sK314 @ X12) @ id)))) ) | ~spl591_513),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f3817])).
% 15.37/3.55 thf(f7254,plain,(
% 15.37/3.55 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true != (X0 @ id @ X10 @ id)) | ($true != (sP17 @ X0)) | ($true = (X0 @ id @ one @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f7253,f1061])).
% 15.37/3.55 thf(f7253,plain,(
% 15.37/3.55 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true != (X0 @ id @ X10 @ id)) | ($true != (sP17 @ X0)) | ($true = (X0 @ id @ (d2term @ d_one) @ id))) )),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f884,f4480])).
% 15.37/3.55 thf(f884,plain,(
% 15.37/3.55 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (sK334 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)) | ($true != (sP17 @ X0))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f355])).
% 15.37/3.55 thf(f8675,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($true = (sK592 @ id @ one @ id)) | ($true = (sK592 @ id @ (sK596 @ X1) @ id))) ) | ~spl591_218),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8674,f1061])).
% 15.37/3.55 thf(f8674,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($true = (sK592 @ id @ (d2term @ d_one) @ id)) | ($true = (sK592 @ id @ (sK596 @ X1) @ id))) ) | ~spl591_218),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8673,f4480])).
% 15.37/3.55 thf(f8673,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($true = (sK592 @ id @ (sK596 @ X1) @ id))) ) | ~spl591_218),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f2531,f4484])).
% 15.37/3.55 thf(f2531,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1)))) | ($true = (sK592 @ id @ (sK596 @ X1) @ id))) ) | ~spl591_218),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2530])).
% 15.37/3.55 thf(f8645,plain,(
% 15.37/3.55 spl591_702 | spl591_703 | ~spl591_220),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f8638,f2538,f8643,f8640])).
% 15.37/3.55 thf(f2538,definition,(
% 15.37/3.55 spl591_220 <=> ! [X4 : subst,X3 : subst,X2 : subst,X1 : term] : (($false = (sK592 @ X2 @ X1 @ (comp @ X3 @ X4))) | ($true = (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ X4)))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_220])],[avatar_definition])).
% 15.37/3.55 thf(f8638,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term,X4 : subst] : (((sK592 @ X2 @ X1 @ id) = $false) | ($true = (sK592 @ id @ one @ X4))) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8637,f1061])).
% 15.37/3.55 thf(f8637,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term,X4 : subst] : (((sK592 @ X2 @ X1 @ id) = $false) | ((sK592 @ id @ (d2term @ d_one) @ X4) = $true)) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8636,f1226])).
% 15.37/3.55 thf(f8636,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term,X4 : subst] : (($false = (sK592 @ X2 @ X1 @ (d2subst @ d_id))) | ((sK592 @ id @ (d2term @ d_one) @ X4) = $true)) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8635,f4480])).
% 15.37/3.55 thf(f8635,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($true = (sK592 @ id @ (sub @ X1 @ X3) @ X4)) | ($false = (sK592 @ X2 @ X1 @ (d2subst @ d_id)))) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8634,f1226])).
% 15.37/3.55 thf(f8634,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($true = (sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X3) @ X4)) | ($false = (sK592 @ X2 @ X1 @ (d2subst @ d_id)))) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f8633,f4466])).
% 15.37/3.55 thf(f8633,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($false = (sK592 @ X2 @ X1 @ (comp @ X3 @ X4))) | ($true = (sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X3) @ X4))) ) | ~spl591_220),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f2539,f4466])).
% 15.37/3.55 thf(f2539,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($true = (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ X4)) | ($false = (sK592 @ X2 @ X1 @ (comp @ X3 @ X4)))) ) | ~spl591_220),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2538])).
% 15.37/3.55 thf(f8623,plain,(
% 15.37/3.55 ~spl591_189 | ~spl591_215),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f8622])).
% 15.37/3.55 thf(f8622,plain,(
% 15.37/3.55 $false | (~spl591_189 | ~spl591_215)),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f8621])).
% 15.37/3.55 thf(f8621,plain,(
% 15.37/3.55 ($true = $false) | (~spl591_189 | ~spl591_215)),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f2415,f2519])).
% 15.37/3.55 thf(f2519,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ~spl591_215),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2517])).
% 15.37/3.55 thf(f2517,definition,(
% 15.37/3.55 spl591_215 <=> (hoasinduction_lem3 = $false)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_215])],[avatar_definition])).
% 15.37/3.55 thf(f2415,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $true) | ~spl591_189),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2413])).
% 15.37/3.55 thf(f2413,definition,(
% 15.37/3.55 spl591_189 <=> (hoasinduction_lem3 = $true)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_189])],[avatar_definition])).
% 15.37/3.55 thf(f8591,plain,(
% 15.37/3.55 spl591_118 | ~spl591_681),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f8590])).
% 15.37/3.55 thf(f8590,plain,(
% 15.37/3.55 $false | (spl591_118 | ~spl591_681)),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f8564,f2112])).
% 15.37/3.55 thf(f2112,plain,(
% 15.37/3.55 ($true != (sP12 @ sK350)) | spl591_118),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2110])).
% 15.37/3.55 thf(f2110,definition,(
% 15.37/3.55 spl591_118 <=> ($true = (sP12 @ sK350))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_118])],[avatar_definition])).
% 15.37/3.55 thf(f8564,plain,(
% 15.37/3.55 ($true = (sP12 @ sK350)) | ~spl591_681),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f8556])).
% 15.37/3.55 thf(f8556,plain,(
% 15.37/3.55 ($true = (sP12 @ sK350)) | ($true != $true) | ~spl591_681),
% 15.37/3.55 inference(superposition,[status(thm)],[f6948,f8524])).
% 15.37/3.55 thf(f6948,plain,(
% 15.37/3.55 ( ! [X8 : term,X7 : subst] : (($true != (sK350 @ X7 @ X8 @ id))) ) | ~spl591_681),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f6947])).
% 15.37/3.55 thf(f6947,definition,(
% 15.37/3.55 spl591_681 <=> ! [X8 : term,X7 : subst] : ($true != (sK350 @ X7 @ X8 @ id))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_681])],[avatar_definition])).
% 15.37/3.55 thf(f7010,plain,(
% 15.37/3.55 ~spl591_241 | spl591_507 | ~spl591_680),
% 15.37/3.55 inference(avatar_contradiction_clause,[status(thm)],[f7009])).
% 15.37/3.55 thf(f7009,plain,(
% 15.37/3.55 $false | (~spl591_241 | spl591_507 | ~spl591_680)),
% 15.37/3.55 inference(trivial_inequality_removal,[status(thm)],[f6997])).
% 15.37/3.55 thf(f6997,plain,(
% 15.37/3.55 ($true != $true) | (~spl591_241 | spl591_507 | ~spl591_680)),
% 15.37/3.55 inference(superposition,[status(thm)],[f3791,f6994])).
% 15.37/3.55 thf(f6994,plain,(
% 15.37/3.55 ( ! [X4 : term,X5 : subst] : (($true = (sK350 @ X5 @ X4 @ id))) ) | (~spl591_241 | ~spl591_680)),
% 15.37/3.55 inference(subsumption_resolution,[status(thm)],[f6993,f6945])).
% 15.37/3.55 thf(f6945,plain,(
% 15.37/3.55 ( ! [X9 : subst] : (($true = (sK350 @ id @ one @ X9))) ) | ~spl591_680),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f6944])).
% 15.37/3.55 thf(f6944,definition,(
% 15.37/3.55 spl591_680 <=> ! [X9 : subst] : ($true = (sK350 @ id @ one @ X9))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_680])],[avatar_definition])).
% 15.37/3.55 thf(f6993,plain,(
% 15.37/3.55 ( ! [X2 : subst,X4 : term,X5 : subst] : (($true = (sK350 @ X5 @ X4 @ id)) | ((sK350 @ id @ one @ X2) != $true)) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6992,f1061])).
% 15.37/3.55 thf(f6992,plain,(
% 15.37/3.55 ( ! [X2 : subst,X4 : term,X5 : subst] : (($true != (sK350 @ id @ (d2term @ d_one) @ X2)) | ($true = (sK350 @ X5 @ X4 @ id))) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6991,f1226])).
% 15.37/3.55 thf(f6991,plain,(
% 15.37/3.55 ( ! [X2 : subst,X4 : term,X5 : subst] : (((sK350 @ X5 @ X4 @ (d2subst @ d_id)) = $true) | ($true != (sK350 @ id @ (d2term @ d_one) @ X2))) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6990,f4480])).
% 15.37/3.55 thf(f6990,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true != (sK350 @ id @ (sub @ X4 @ X3) @ X2)) | ((sK350 @ X5 @ X4 @ (d2subst @ d_id)) = $true)) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6989,f1226])).
% 15.37/3.55 thf(f6989,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (((sK350 @ (d2subst @ d_id) @ (sub @ X4 @ X3) @ X2) != $true) | ((sK350 @ X5 @ X4 @ (d2subst @ d_id)) = $true)) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6988,f4466])).
% 15.37/3.55 thf(f6988,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true) | ((sK350 @ X5 @ X4 @ (d2subst @ d_id)) = $true)) ) | ~spl591_241),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f2627,f4466])).
% 15.37/3.55 thf(f2627,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true = (sK350 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true)) ) | ~spl591_241),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2626])).
% 15.37/3.55 thf(f2626,definition,(
% 15.37/3.55 spl591_241 <=> ! [X3 : subst,X4 : term,X5 : subst,X2 : subst] : (($true = (sK350 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_241])],[avatar_definition])).
% 15.37/3.55 thf(f3791,plain,(
% 15.37/3.55 ((sK350 @ id @ (lam @ sK351) @ id) != $true) | spl591_507),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f3789])).
% 15.37/3.55 thf(f3789,definition,(
% 15.37/3.55 spl591_507 <=> ((sK350 @ id @ (lam @ sK351) @ id) = $true)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_507])],[avatar_definition])).
% 15.37/3.55 thf(f6949,plain,(
% 15.37/3.55 spl591_680 | spl591_681 | ~spl591_164),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f6942,f2306,f6947,f6944])).
% 15.37/3.55 thf(f2306,definition,(
% 15.37/3.55 spl591_164 <=> ! [X9 : subst,X7 : subst,X6 : subst,X8 : term] : (($true = (sK350 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9)) | ($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9))))),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_164])],[avatar_definition])).
% 15.37/3.55 thf(f6942,plain,(
% 15.37/3.55 ( ! [X8 : term,X9 : subst,X7 : subst] : (($true != (sK350 @ X7 @ X8 @ id)) | ($true = (sK350 @ id @ one @ X9))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6941,f1226])).
% 15.37/3.55 thf(f6941,plain,(
% 15.37/3.55 ( ! [X8 : term,X9 : subst,X7 : subst] : (($true != (sK350 @ X7 @ X8 @ (d2subst @ d_id))) | ($true = (sK350 @ id @ one @ X9))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6940,f1061])).
% 15.37/3.55 thf(f6940,plain,(
% 15.37/3.55 ( ! [X8 : term,X9 : subst,X7 : subst] : (((sK350 @ id @ (d2term @ d_one) @ X9) = $true) | ($true != (sK350 @ X7 @ X8 @ (d2subst @ d_id)))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6939,f4480])).
% 15.37/3.55 thf(f6939,plain,(
% 15.37/3.55 ( ! [X8 : term,X6 : subst,X9 : subst,X7 : subst] : (($true = (sK350 @ id @ (sub @ X8 @ X6) @ X9)) | ($true != (sK350 @ X7 @ X8 @ (d2subst @ d_id)))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6938,f4466])).
% 15.37/3.55 thf(f6938,plain,(
% 15.37/3.55 ( ! [X8 : term,X6 : subst,X9 : subst,X7 : subst] : (($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9))) | ($true = (sK350 @ id @ (sub @ X8 @ X6) @ X9))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f6937,f1226])).
% 15.37/3.55 thf(f6937,plain,(
% 15.37/3.55 ( ! [X8 : term,X6 : subst,X9 : subst,X7 : subst] : (($true = (sK350 @ (d2subst @ d_id) @ (sub @ X8 @ X6) @ X9)) | ($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9)))) ) | ~spl591_164),
% 15.37/3.55 inference(forward_demodulation,[status(thm)],[f2307,f4466])).
% 15.37/3.55 thf(f2307,plain,(
% 15.37/3.55 ( ! [X8 : term,X6 : subst,X9 : subst,X7 : subst] : (($true = (sK350 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9)) | ($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9)))) ) | ~spl591_164),
% 15.37/3.55 inference(avatar_component_clause,[status(thm)],[f2306])).
% 15.37/3.55 thf(f3880,plain,(
% 15.37/3.55 spl591_189 | ~spl591_5),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f1113,f1641,f2413])).
% 15.37/3.55 thf(f1641,definition,(
% 15.37/3.55 spl591_5 <=> ($true = sP13)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_5])],[avatar_definition])).
% 15.37/3.55 thf(f1113,plain,(
% 15.37/3.55 ($true != sP13) | (hoasinduction_lem3 = $true)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f545])).
% 15.37/3.55 thf(f3819,plain,(
% 15.37/3.55 spl591_513 | ~spl591_28),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f855,f1734,f3817])).
% 15.37/3.55 thf(f1734,definition,(
% 15.37/3.55 spl591_28 <=> ($true = sP21)),
% 15.37/3.55 introduced(definition,[new_symbols(naming,[spl591_28])],[avatar_definition])).
% 15.37/3.55 thf(f855,plain,(
% 15.37/3.55 ( ! [X11 : term,X12 : subst > term > subst > $o] : (($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) | ($true = (sP16 @ X12)) | ((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) | ((sP17 @ X12) = $true) | ($true = (var @ (sub @ (sK314 @ X12) @ id))) | ($true = (X12 @ id @ X11 @ id)) | ($true != sP21)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f334])).
% 15.37/3.55 thf(f334,plain,(
% 15.37/3.55 (($true = sP21) | (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (((sK305 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5) != $true) | ($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5)))) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : (($true != (sK305 @ X6 @ X9 @ (comp @ X7 @ X8))) | ((sK305 @ (comp @ X6 @ X7) @ (sub @ X9 @ X7) @ X8) = $true)) & ! [X10 : term] : (($true = (sK305 @ id @ X10 @ id)) | ($true != (var @ (sub @ X10 @ id)))) & ($true != (sP17 @ sK305)) & ($true != (sP16 @ sK305)) & ($true != (sK305 @ id @ sK304 @ id)))) & (! [X11 : term,X12 : subst > term > subst > $o] : ((((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) & ($true != (X12 @ (sK308 @ X12) @ (sK306 @ X12) @ (comp @ (sK307 @ X12) @ (sK309 @ X12))))) | (($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) & ((X12 @ (comp @ (sK310 @ X12) @ (sK311 @ X12)) @ (sub @ (sK313 @ X12) @ (sK311 @ X12)) @ (sK312 @ X12)) != $true)) | (($true != (X12 @ id @ (sK314 @ X12) @ id)) & ($true = (var @ (sub @ (sK314 @ X12) @ id)))) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12)) | ($true = (X12 @ id @ X11 @ id))) | ($true != sP21))),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK304,sK305,sK306,sK307,sK308,sK309,sK310,sK311,sK312,sK313,sK314])],[f329,f333,f332,f331,f330])).
% 15.37/3.55 thf(f330,plain,(
% 15.37/3.55 ? [X0 : term,X1 : subst > term > subst > $o] : (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true != (X1 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5)) | ((X1 @ X4 @ X2 @ (comp @ X3 @ X5)) = $true)) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : (($true != (X1 @ X6 @ X9 @ (comp @ X7 @ X8))) | ((X1 @ (comp @ X6 @ X7) @ (sub @ X9 @ X7) @ X8) = $true)) & ! [X10 : term] : (($true = (X1 @ id @ X10 @ id)) | ($true != (var @ (sub @ X10 @ id)))) & ($true != (sP17 @ X1)) & ($true != (sP16 @ X1)) & ($true != (X1 @ id @ X0 @ id))) => (! [X5 : subst,X4 : subst,X3 : subst,X2 : term] : (((sK305 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5) != $true) | ($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5)))) & ! [X9 : term,X8 : subst,X7 : subst,X6 : subst] : (($true != (sK305 @ X6 @ X9 @ (comp @ X7 @ X8))) | ((sK305 @ (comp @ X6 @ X7) @ (sub @ X9 @ X7) @ X8) = $true)) & ! [X10 : term] : (($true = (sK305 @ id @ X10 @ id)) | ($true != (var @ (sub @ X10 @ id)))) & ($true != (sP17 @ sK305)) & ($true != (sP16 @ sK305)) & ($true != (sK305 @ id @ sK304 @ id)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f331,plain,(
% 15.37/3.55 ! [X12 : subst > term > subst > $o] : (? [X13 : term,X14 : subst,X15 : subst,X16 : subst] : (($true = (X12 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14) @ X16)) & ($true != (X12 @ X15 @ X13 @ (comp @ X14 @ X16)))) => (((X12 @ (comp @ (sK308 @ X12) @ (sK307 @ X12)) @ (sub @ (sK306 @ X12) @ (sK307 @ X12)) @ (sK309 @ X12)) = $true) & ($true != (X12 @ (sK308 @ X12) @ (sK306 @ X12) @ (comp @ (sK307 @ X12) @ (sK309 @ X12))))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f332,plain,(
% 15.37/3.55 ! [X12 : subst > term > subst > $o] : (? [X17 : subst,X18 : subst,X19 : subst,X20 : term] : (($true = (X12 @ X17 @ X20 @ (comp @ X18 @ X19))) & ($true != (X12 @ (comp @ X17 @ X18) @ (sub @ X20 @ X18) @ X19))) => (($true = (X12 @ (sK310 @ X12) @ (sK313 @ X12) @ (comp @ (sK311 @ X12) @ (sK312 @ X12)))) & ((X12 @ (comp @ (sK310 @ X12) @ (sK311 @ X12)) @ (sub @ (sK313 @ X12) @ (sK311 @ X12)) @ (sK312 @ X12)) != $true)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f333,plain,(
% 15.37/3.55 ! [X12 : subst > term > subst > $o] : (? [X21 : term] : (((X12 @ id @ X21 @ id) != $true) & ((var @ (sub @ X21 @ id)) = $true)) => (($true != (X12 @ id @ (sK314 @ X12) @ id)) & ($true = (var @ (sub @ (sK314 @ X12) @ id)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f329,plain,(
% 15.37/3.55 (($true = sP21) | ? [X0 : term,X1 : subst > term > subst > $o] : (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true != (X1 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5)) | ((X1 @ X4 @ X2 @ (comp @ X3 @ X5)) = $true)) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : (($true != (X1 @ X6 @ X9 @ (comp @ X7 @ X8))) | ((X1 @ (comp @ X6 @ X7) @ (sub @ X9 @ X7) @ X8) = $true)) & ! [X10 : term] : (($true = (X1 @ id @ X10 @ id)) | ($true != (var @ (sub @ X10 @ id)))) & ($true != (sP17 @ X1)) & ($true != (sP16 @ X1)) & ($true != (X1 @ id @ X0 @ id)))) & (! [X11 : term,X12 : subst > term > subst > $o] : (? [X13 : term,X14 : subst,X15 : subst,X16 : subst] : (($true = (X12 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14) @ X16)) & ($true != (X12 @ X15 @ X13 @ (comp @ X14 @ X16)))) | ? [X17 : subst,X18 : subst,X19 : subst,X20 : term] : (($true = (X12 @ X17 @ X20 @ (comp @ X18 @ X19))) & ($true != (X12 @ (comp @ X17 @ X18) @ (sub @ X20 @ X18) @ X19))) | ? [X21 : term] : (((X12 @ id @ X21 @ id) != $true) & ((var @ (sub @ X21 @ id)) = $true)) | ((sP17 @ X12) = $true) | ($true = (sP16 @ X12)) | ($true = (X12 @ id @ X11 @ id))) | ($true != sP21))),
% 15.37/3.55 inference(rectify,[status(thm)],[f328])).
% 15.37/3.55 thf(f328,plain,(
% 15.37/3.55 (($true = sP21) | ? [X328 : term,X329 : subst > term > subst > $o] : (! [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true != (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) | ($true = (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) & ! [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true != (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) | ($true = (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) & ! [X336 : term] : (($true = (X329 @ id @ X336 @ id)) | ((var @ (sub @ X336 @ id)) != $true)) & ($true != (sP17 @ X329)) & ($true != (sP16 @ X329)) & ($true != (X329 @ id @ X328 @ id)))) & (! [X328 : term,X329 : subst > term > subst > $o] : (? [X332 : term,X333 : subst,X334 : subst,X335 : subst] : (($true = (X329 @ (comp @ X334 @ X333) @ (sub @ X332 @ X333) @ X335)) & ($true != (X329 @ X334 @ X332 @ (comp @ X333 @ X335)))) | ? [X342 : subst,X343 : subst,X344 : subst,X345 : term] : (($true = (X329 @ X342 @ X345 @ (comp @ X343 @ X344))) & ($true != (X329 @ (comp @ X342 @ X343) @ (sub @ X345 @ X343) @ X344))) | ? [X336 : term] : (($true != (X329 @ id @ X336 @ id)) & ((var @ (sub @ X336 @ id)) = $true)) | ($true = (sP17 @ X329)) | ($true = (sP16 @ X329)) | ($true = (X329 @ id @ X328 @ id))) | ($true != sP21))),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f35])).
% 15.37/3.55 thf(f3792,plain,(
% 15.37/3.55 spl591_5 | ~spl591_507),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f920,f3789,f1641])).
% 15.37/3.55 thf(f920,plain,(
% 15.37/3.55 ($true = sP13) | ((sK350 @ id @ (lam @ sK351) @ id) != $true)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f380])).
% 15.37/3.55 thf(f380,plain,(
% 15.37/3.55 (($true = sP13) | (((sK350 @ id @ (lam @ sK351) @ id) != $true) & ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true = (sK350 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true)) & ! [X6 : subst,X7 : subst,X8 : term,X9 : subst] : (($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9))) | ($true = (sK350 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9))) & ! [X10 : term] : (($true = (sK350 @ id @ (sub @ sK351 @ (push @ X10 @ id)) @ id)) | ($true != (sK350 @ id @ X10 @ id))) & ($true != (sP12 @ sK350)))) & (! [X11 : subst > term > subst > $o,X12 : term] : (($true = (X11 @ id @ (lam @ X12) @ id)) | (((X11 @ (sK355 @ X11) @ (sK354 @ X11) @ (comp @ (sK353 @ X11) @ (sK352 @ X11))) != $true) & ($true = (X11 @ (comp @ (sK355 @ X11) @ (sK353 @ X11)) @ (sub @ (sK354 @ X11) @ (sK353 @ X11)) @ (sK352 @ X11)))) | (($true = (X11 @ (sK357 @ X11) @ (sK358 @ X11) @ (comp @ (sK356 @ X11) @ (sK359 @ X11)))) & ($true != (X11 @ (comp @ (sK357 @ X11) @ (sK356 @ X11)) @ (sub @ (sK358 @ X11) @ (sK356 @ X11)) @ (sK359 @ X11)))) | (($true != (X11 @ id @ (sub @ X12 @ (push @ (sK360 @ X12 @ X11) @ id)) @ id)) & ($true = (X11 @ id @ (sK360 @ X12 @ X11) @ id))) | ((sP12 @ X11) = $true)) | ($true != sP13))),
% 15.37/3.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK350,sK351,sK352,sK353,sK354,sK355,sK356,sK357,sK358,sK359,sK360])],[f375,f379,f378,f377,f376])).
% 15.37/3.55 thf(f376,plain,(
% 15.37/3.55 ? [X0 : subst > term > subst > $o,X1 : term] : (($true != (X0 @ id @ (lam @ X1) @ id)) & ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true = (X0 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((X0 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true)) & ! [X6 : subst,X7 : subst,X8 : term,X9 : subst] : (($true != (X0 @ X7 @ X8 @ (comp @ X6 @ X9))) | ($true = (X0 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9))) & ! [X10 : term] : (((X0 @ id @ (sub @ X1 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ($true != (sP12 @ X0))) => (((sK350 @ id @ (lam @ sK351) @ id) != $true) & ! [X5 : subst,X4 : term,X3 : subst,X2 : subst] : (($true = (sK350 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true)) & ! [X9 : subst,X8 : term,X7 : subst,X6 : subst] : (($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9))) | ($true = (sK350 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9))) & ! [X10 : term] : (($true = (sK350 @ id @ (sub @ sK351 @ (push @ X10 @ id)) @ id)) | ($true != (sK350 @ id @ X10 @ id))) & ($true != (sP12 @ sK350)))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f377,plain,(
% 15.37/3.55 ! [X11 : subst > term > subst > $o] : (? [X13 : subst,X14 : subst,X15 : term,X16 : subst] : (($true != (X11 @ X16 @ X15 @ (comp @ X14 @ X13))) & ((X11 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14) @ X13) = $true)) => (((X11 @ (sK355 @ X11) @ (sK354 @ X11) @ (comp @ (sK353 @ X11) @ (sK352 @ X11))) != $true) & ($true = (X11 @ (comp @ (sK355 @ X11) @ (sK353 @ X11)) @ (sub @ (sK354 @ X11) @ (sK353 @ X11)) @ (sK352 @ X11)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f378,plain,(
% 15.37/3.55 ! [X11 : subst > term > subst > $o] : (? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X11 @ X18 @ X19 @ (comp @ X17 @ X20))) & ($true != (X11 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17) @ X20))) => (($true = (X11 @ (sK357 @ X11) @ (sK358 @ X11) @ (comp @ (sK356 @ X11) @ (sK359 @ X11)))) & ($true != (X11 @ (comp @ (sK357 @ X11) @ (sK356 @ X11)) @ (sub @ (sK358 @ X11) @ (sK356 @ X11)) @ (sK359 @ X11)))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f379,plain,(
% 15.37/3.55 ! [X11 : subst > term > subst > $o,X12 : term] : (? [X21 : term] : (($true != (X11 @ id @ (sub @ X12 @ (push @ X21 @ id)) @ id)) & ($true = (X11 @ id @ X21 @ id))) => (($true != (X11 @ id @ (sub @ X12 @ (push @ (sK360 @ X12 @ X11) @ id)) @ id)) & ($true = (X11 @ id @ (sK360 @ X12 @ X11) @ id))))),
% 15.37/3.55 introduced(definition,[],[choice_axiom])).
% 15.37/3.55 thf(f375,plain,(
% 15.37/3.55 (($true = sP13) | ? [X0 : subst > term > subst > $o,X1 : term] : (($true != (X0 @ id @ (lam @ X1) @ id)) & ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true = (X0 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((X0 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true)) & ! [X6 : subst,X7 : subst,X8 : term,X9 : subst] : (($true != (X0 @ X7 @ X8 @ (comp @ X6 @ X9))) | ($true = (X0 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9))) & ! [X10 : term] : (((X0 @ id @ (sub @ X1 @ (push @ X10 @ id)) @ id) = $true) | ($true != (X0 @ id @ X10 @ id))) & ($true != (sP12 @ X0)))) & (! [X11 : subst > term > subst > $o,X12 : term] : (($true = (X11 @ id @ (lam @ X12) @ id)) | ? [X13 : subst,X14 : subst,X15 : term,X16 : subst] : (($true != (X11 @ X16 @ X15 @ (comp @ X14 @ X13))) & ((X11 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14) @ X13) = $true)) | ? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X11 @ X18 @ X19 @ (comp @ X17 @ X20))) & ($true != (X11 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17) @ X20))) | ? [X21 : term] : (($true != (X11 @ id @ (sub @ X12 @ (push @ X21 @ id)) @ id)) & ($true = (X11 @ id @ X21 @ id))) | ((sP12 @ X11) = $true)) | ($true != sP13))),
% 15.37/3.55 inference(rectify,[status(thm)],[f374])).
% 15.37/3.55 thf(f374,plain,(
% 15.37/3.55 (($true = sP13) | ? [X198 : subst > term > subst > $o,X199 : term] : (($true != (X198 @ id @ (lam @ X199) @ id)) & ! [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true = (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) | ($true != (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) & ! [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true != (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) | ($true = (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) & ! [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) = $true) | ($true != (X198 @ id @ X213 @ id))) & ($true != (sP12 @ X198)))) & (! [X198 : subst > term > subst > $o,X199 : term] : (($true = (X198 @ id @ (lam @ X199) @ id)) | ? [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (($true != (X198 @ X203 @ X202 @ (comp @ X201 @ X200))) & ($true = (X198 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201) @ X200))) | ? [X209 : subst,X210 : subst,X211 : term,X212 : subst] : (($true = (X198 @ X210 @ X211 @ (comp @ X209 @ X212))) & ($true != (X198 @ (comp @ X210 @ X209) @ (sub @ X211 @ X209) @ X212))) | ? [X213 : term] : (((X198 @ id @ (sub @ X199 @ (push @ X213 @ id)) @ id) != $true) & ($true = (X198 @ id @ X213 @ id))) | ($true = (sP12 @ X198))) | ($true != sP13))),
% 15.37/3.55 inference(nnf_transformation,[status(thm)],[f27])).
% 15.37/3.55 thf(f3159,plain,(
% 15.37/3.55 spl591_28 | ~spl591_362),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f857,f3156,f1734])).
% 15.37/3.55 thf(f857,plain,(
% 15.37/3.55 ($true = sP21) | ($true != (sK305 @ id @ sK304 @ id))),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f334])).
% 15.37/3.55 thf(f2628,plain,(
% 15.37/3.55 spl591_241 | spl591_5),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f919,f1641,f2626])).
% 15.37/3.55 thf(f919,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true = (sK350 @ X5 @ X4 @ (comp @ X3 @ X2))) | ((sK350 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3) @ X2) != $true) | ($true = sP13)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f380])).
% 15.37/3.55 thf(f2540,plain,(
% 15.37/3.55 spl591_220 | spl591_215),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f1396,f2517,f2538])).
% 15.37/3.55 thf(f1396,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : ((hoasinduction_lem3 = $false) | ($false = (sK592 @ X2 @ X1 @ (comp @ X3 @ X4))) | ($true = (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ X4))) )),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1395])).
% 15.37/3.55 thf(f1395,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : ((hoasinduction_lem3 = $false) | ($true = ((sK592 @ X2 @ X1 @ (comp @ X3 @ X4)) => (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ X4)))) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1394])).
% 15.37/3.55 thf(f1394,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($true = ((^[Y0 : subst]: ((sK592 @ X2 @ X1 @ (comp @ X3 @ Y0)) => (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ Y0))) @ X4)) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(pi_clausification,[status(thm)],[f1393])).
% 15.37/3.55 thf(f1393,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term] : ((hoasinduction_lem3 = $false) | ($true = (!! @ subst @ (^[Y0 : subst]: ((sK592 @ X2 @ X1 @ (comp @ X3 @ Y0)) => (sK592 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3) @ Y0)))))) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1392])).
% 15.37/3.55 thf(f1392,plain,(
% 15.37/3.55 ( ! [X2 : subst,X3 : subst,X1 : term] : ((hoasinduction_lem3 = $false) | (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sK592 @ X2 @ X1 @ (comp @ Y0 @ Y1)) => (sK592 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0) @ Y1))))) @ X3) = $true)) )),
% 15.37/3.55 inference(pi_clausification,[status(thm)],[f1391])).
% 15.37/3.55 thf(f1391,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sK592 @ X2 @ X1 @ (comp @ Y0 @ Y1)) => (sK592 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0) @ Y1))))))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1390])).
% 15.37/3.55 thf(f1390,plain,(
% 15.37/3.55 ( ! [X2 : subst,X1 : term] : ((hoasinduction_lem3 = $false) | ($true = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sK592 @ Y0 @ X1 @ (comp @ Y1 @ Y2)) => (sK592 @ (comp @ Y0 @ Y1) @ (sub @ X1 @ Y1) @ Y2))))))) @ X2))) )),
% 15.37/3.55 inference(pi_clausification,[status(thm)],[f1389])).
% 15.37/3.55 thf(f1389,plain,(
% 15.37/3.55 ( ! [X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sK592 @ Y0 @ X1 @ (comp @ Y1 @ Y2)) => (sK592 @ (comp @ Y0 @ Y1) @ (sub @ X1 @ Y1) @ Y2))))))))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1388])).
% 15.37/3.55 thf(f1388,plain,(
% 15.37/3.55 ( ! [X1 : term] : ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ Y1 @ Y0 @ (comp @ Y2 @ Y3)) => (sK592 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3))))))))) @ X1) = $true) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(pi_clausification,[status(thm)],[f1387])).
% 15.37/3.55 thf(f1387,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ Y1 @ Y0 @ (comp @ Y2 @ Y3)) => (sK592 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3)))))))))))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1385])).
% 15.37/3.55 thf(f1385,plain,(
% 15.37/3.55 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ Y1 @ Y0 @ (comp @ Y2 @ Y3)) => (sK592 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3)))))))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sK592 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1) @ Y0) => (sK592 @ Y2 @ Y3 @ (comp @ Y1 @ Y0))))))))))) => ((!! @ (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]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (hoaslam @ id @ Y0) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK592 @ id @ (lam @ Y0) @ id)))))))) | (hoasinduction_lem3 = $false)),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1384])).
% 15.37/3.55 thf(f1384,plain,(
% 15.37/3.55 ($false = ((^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ Y1) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))) @ sK592)) | (hoasinduction_lem3 = $false)),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1383])).
% 15.37/3.55 thf(f1383,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ Y1) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))) = $false)),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1381])).
% 15.37/3.55 thf(f1381,plain,(
% 15.37/3.55 (hoasinduction_lem3 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ Y1) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1260])).
% 15.37/3.55 thf(f1260,plain,(
% 15.37/3.55 (hoasinduction_lem3 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f11])).
% 15.37/3.55 thf(f11,plain,(
% 15.37/3.55 (hoasinduction_lem3 != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))),
% 15.37/3.55 inference(flattening,[status(thm)],[f8])).
% 15.37/3.55 thf(f8,plain,(
% 15.37/3.55 ~(hoasinduction_lem3 = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2) @ Y1) => (Y0 @ Y3 @ Y4 @ (comp @ Y2 @ Y1))))))))))) => ((!! @ (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 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))),
% 15.37/3.55 inference(fool_elimination,[status(thm)],[f7])).
% 15.37/3.55 thf(f7,plain,(
% 15.37/3.55 ~(! [X0 : subst > term > subst > $o] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X3 @ X4 @ (comp @ X2 @ X1)) => (X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) => (! [X5 : term,X6 : subst,X7 : subst,X8 : subst] : ((X0 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7) @ X8) => (X0 @ X6 @ X5 @ (comp @ X7 @ X8))) => (! [X9 : subst > term > term] : (! [X10 : subst,X11 : subst,X12 : term] : ((X9 @ (comp @ X11 @ X10) @ (sub @ X12 @ X10)) = (sub @ (X9 @ X11 @ X12) @ X10)) => (! [X13 : term] : ((X0 @ id @ X13 @ id) => (X0 @ id @ (X9 @ id @ X13) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X14 : subst, X15 : term] : (X9 @ X14 @ X15))) @ id))) => ! [X16 : term] : (! [X17 : term] : ((X0 @ id @ X17 @ id) => (X0 @ id @ (sub @ X16 @ (push @ X17 @ id)) @ id)) => (X0 @ id @ (lam @ X16) @ id))))) = hoasinduction_lem3)),
% 15.37/3.55 inference(rectify,[status(thm)],[f3])).
% 15.37/3.55 thf(f3,negated_conjecture,(
% 15.37/3.55 ~(! [X10 : subst > term > subst > $o] : (! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X13 : term,X14 : subst,X26 : subst,X25 : 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))) => ! [X13 : term] : (! [X15 : term] : ((X10 @ id @ X15 @ id) => (X10 @ id @ (sub @ X13 @ (push @ X15 @ id)) @ id)) => (X10 @ id @ (lam @ X13) @ id))))) = hoasinduction_lem3)),
% 15.37/3.55 inference(negated_conjecture,[status(cth)],[f2])).
% 15.37/3.55 thf(f2,conjecture,(
% 15.37/3.55 (! [X10 : subst > term > subst > $o] : (! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X13 : term,X14 : subst,X26 : subst,X25 : 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))) => ! [X13 : term] : (! [X15 : term] : ((X10 @ id @ X15 @ id) => (X10 @ id @ (sub @ X13 @ (push @ X15 @ id)) @ id)) => (X10 @ id @ (lam @ X13) @ id))))) = hoasinduction_lem3)),
% 15.37/3.55 file('/export/starexec/sandbox/tmp/tmp.OZKaewZbi7/DTF2THF_21668.p',hoasinduction_lem3)).
% 15.37/3.55 thf(f2532,plain,(
% 15.37/3.55 spl591_218 | spl591_215),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f1424,f2517,f2530])).
% 15.37/3.55 thf(f1424,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | (hoasinduction_lem3 = $false) | ((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1)))) | ($true = (sK592 @ id @ (sK596 @ X1) @ id))) )),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1422])).
% 15.37/3.55 thf(f1422,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | (((sK592 @ id @ (sK596 @ X1) @ id) => (sK592 @ id @ (X1 @ id @ (sK596 @ X1)) @ id)) = $false) | (hoasinduction_lem3 = $false) | ((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1))))) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1421])).
% 15.37/3.55 thf(f1421,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1)))) | ($false = ((^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))) @ (sK596 @ X1))) | (hoasinduction_lem3 = $false) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true)) )),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1420])).
% 15.37/3.55 thf(f1420,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))))) | ((sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)) != (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1)))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(equality_proxy_clausification,[status(thm)],[f1419])).
% 15.37/3.55 thf(f1419,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($false = ((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK593 @ X1) @ (sK595 @ X1))) = (sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ (sK595 @ X1)))) | (hoasinduction_lem3 = $false) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))))) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1418])).
% 15.37/3.55 thf(f1418,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3 = $false) | ($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))))) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | (((^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK593 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ Y0))) @ (sK595 @ X1)) = $false)) )),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1417])).
% 15.37/3.55 thf(f1417,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($false = (!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK593 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK593 @ X1)) @ Y0))))) | (hoasinduction_lem3 = $false) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))))) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1416])).
% 15.37/3.55 thf(f1416,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))))) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | (hoasinduction_lem3 = $false) | ($false = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK593 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK593 @ X1)) @ Y1))))) @ (sK594 @ X1)))) )),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1415])).
% 15.37/3.55 thf(f1415,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK593 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK593 @ X1)) @ Y1)))))) = $false) | ((sK592 @ id @ (hoaslam @ id @ X1) @ id) = $true) | ($false = (!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1414])).
% 15.37/3.55 thf(f1414,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3 = $false) | ($true = ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (hoaslam @ id @ X1) @ id))) | ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK593 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK593 @ X1)) @ Y1)))))) = $false)) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1413])).
% 15.37/3.55 thf(f1413,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))) @ (sK593 @ X1))) | ($true = ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (hoaslam @ id @ X1) @ id))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1412])).
% 15.37/3.55 thf(f1412,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) | ($true = ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (hoaslam @ id @ X1) @ id))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1411])).
% 15.37/3.55 thf(f1411,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : (($true = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (hoaslam @ id @ X1) @ id)))) | (hoasinduction_lem3 = $false)) )),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1410])).
% 15.37/3.55 thf(f1410,plain,(
% 15.37/3.55 ( ! [X1 : subst > term > term] : ((hoasinduction_lem3 = $false) | ($true = ((^[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]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (hoaslam @ id @ Y0) @ id)))) @ X1))) )),
% 15.37/3.55 inference(pi_clausification,[status(thm)],[f1409])).
% 15.37/3.55 thf(f1409,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($true = (!! @ (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]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (hoaslam @ id @ Y0) @ id))))))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1397])).
% 15.37/3.55 thf(f1397,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($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]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (hoaslam @ id @ Y0) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK592 @ id @ (lam @ Y0) @ id))))))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1386])).
% 15.37/3.55 thf(f1386,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sK592 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1) @ Y0) => (sK592 @ Y2 @ Y3 @ (comp @ Y1 @ Y0))))))))))) => ((!! @ (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]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (hoaslam @ id @ Y0) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK592 @ id @ (lam @ Y0) @ id)))))))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1385])).
% 15.37/3.55 thf(f2520,plain,(
% 15.37/3.55 spl591_214 | spl591_215),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f1427,f2517,f2513])).
% 15.37/3.55 thf(f1427,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($false = (sK592 @ id @ (lam @ sK597) @ id))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1426])).
% 15.37/3.55 thf(f1426,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (sub @ sK597 @ (push @ Y0 @ id)) @ id)))) => (sK592 @ id @ (lam @ sK597) @ id)))),
% 15.37/3.55 inference(beta_eta_normalization,[status(thm)],[f1425])).
% 15.37/3.55 thf(f1425,plain,(
% 15.37/3.55 ($false = ((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK592 @ id @ (lam @ Y0) @ id))) @ sK597)) | (hoasinduction_lem3 = $false)),
% 15.37/3.55 inference(sigma_clausification,[status(thm)],[f1408])).
% 15.37/3.55 thf(f1408,plain,(
% 15.37/3.55 (hoasinduction_lem3 = $false) | ($false = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK592 @ id @ (lam @ Y0) @ id)))))),
% 15.37/3.55 inference(binary_proxy_clausification,[status(thm)],[f1397])).
% 15.37/3.55 thf(f2308,plain,(
% 15.37/3.55 spl591_5 | spl591_164),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f918,f2306,f1641])).
% 15.37/3.55 thf(f918,plain,(
% 15.37/3.55 ( ! [X8 : term,X6 : subst,X9 : subst,X7 : subst] : (($true = sP13) | ($true = (sK350 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X9)) | ($true != (sK350 @ X7 @ X8 @ (comp @ X6 @ X9)))) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f380])).
% 15.37/3.55 thf(f2252,plain,(
% 15.37/3.55 spl591_28 | spl591_151),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f862,f2250,f1734])).
% 15.37/3.55 thf(f862,plain,(
% 15.37/3.55 ( ! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (((sK305 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5) != $true) | ($true = (sK305 @ X4 @ X2 @ (comp @ X3 @ X5))) | ($true = sP21)) )),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f334])).
% 15.37/3.55 thf(f2113,plain,(
% 15.37/3.55 ~spl591_118 | spl591_5),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f916,f1641,f2110])).
% 15.37/3.55 thf(f916,plain,(
% 15.37/3.55 ($true != (sP12 @ sK350)) | ($true = sP13)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f380])).
% 15.37/3.55 thf(f2053,plain,(
% 15.37/3.55 spl591_28 | ~spl591_104),
% 15.37/3.55 inference(avatar_split_clause,[status(thm)],[f859,f2050,f1734])).
% 15.37/3.55 thf(f859,plain,(
% 15.37/3.55 ($true != (sP17 @ sK305)) | ($true = sP21)),
% 15.37/3.55 inference(cnf_transformation,[status(thm)],[f334])).
% 15.37/3.55 % SZS output end Proof for DTF2THF_21668
% 15.37/3.55 % (21886)------------------------------
% 15.37/3.55 % (21886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.55 % (21886)Termination reason: Refutation
% 15.37/3.55
% 15.37/3.55 % (21886)Memory used [KB]: 15095
% 15.37/3.55 % (21886)Time elapsed: 0.545 s
% 15.37/3.55 % (21886)Instructions burned: 1662 (million)
% 15.37/3.55 % (21886)------------------------------
% 15.37/3.55 % (21886)------------------------------
% 15.37/3.55 % (21767)Success in time 2.043 s
%------------------------------------------------------------------------------