%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 06:58:53 PM UTC 2026
% Result : Theorem 32.37s 5.95s
% Output : Refutation 32.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 156
% Syntax : Number of formulae : 312 ( 21 unt; 0 typ; 14 def)
% Number of atoms : 12528 (5790 equ; 0 cnn)
% Maximal formula atoms : 530 ( 40 avg)
% Number of connectives : 31141 (3249 ~;3043 |;2504 &;21100 @)
% ( 521 <=>; 475 =>; 0 <=; 0 <~>)
% Maximal formula depth : 194 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2321 (2321 >; 0 *; 0 +; 0 <<)
% Number of symbols : 764 ( 760 usr; 307 con; 0-4 aty)
% ( 249 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 6353 ( 374 ^;4548 !;1431 ?;6353 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(type_def_8,type,
d_term: $tType ).
thf(type_def_9,type,
d_subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_124,type,
d_term: $tType ).
thf(func_def_125,type,
d_subst: $tType ).
thf(func_def_126,type,
d2term: d_term > term ).
thf(func_def_127,type,
d2subst: d_subst > subst ).
thf(func_def_128,type,
d_one: d_term ).
thf(func_def_129,type,
d_id: d_subst ).
thf(func_def_142,type,
sP0: ( subst > term > subst > $o ) > $o ).
thf(func_def_143,type,
sP1: ( term > $o ) > $o ).
thf(func_def_147,type,
sP5: ( subst > term > subst > $o ) > $o ).
thf(func_def_148,type,
sP6: ( subst > term > subst > $o ) > $o ).
thf(func_def_149,type,
sP7: ( term > $o ) > $o ).
thf(func_def_150,type,
sP8: ( subst > term > subst > $o ) > $o ).
thf(func_def_151,type,
sP9: ( subst > term > subst > $o ) > $o ).
thf(func_def_156,type,
sP14: ( subst > term > subst > $o ) > $o ).
thf(func_def_157,type,
sP15: ( subst > term > subst > $o ) > $o ).
thf(func_def_158,type,
sP16: ( term > $o ) > $o ).
thf(func_def_162,type,
sP20: ( term > $o ) > $o ).
thf(func_def_163,type,
sP21: ( term > $o ) > $o ).
thf(func_def_167,type,
sP25: ( subst > term > subst > $o ) > $o ).
thf(func_def_170,type,
sP28: ( term > $o ) > $o ).
thf(func_def_174,type,
sP32: ( term > $o ) > $o ).
thf(func_def_176,type,
sP34: ( term > $o ) > $o ).
thf(func_def_177,type,
sP35: ( term > $o ) > $o ).
thf(func_def_180,type,
sP38: ( subst > term > subst > $o ) > $o ).
thf(func_def_182,type,
sP40: ( subst > term > subst > $o ) > $o ).
thf(func_def_184,type,
sP42: ( subst > term > subst > $o ) > $o ).
thf(func_def_185,type,
sP43: ( subst > term > subst > $o ) > $o ).
thf(func_def_187,type,
sP45: ( term > $o ) > $o ).
thf(func_def_190,type,
sP48: ( subst > term > subst > $o ) > $o ).
thf(func_def_192,type,
sP50: ( subst > term > subst > $o ) > $o ).
thf(func_def_195,type,
sP53: ( subst > term > subst > $o ) > $o ).
thf(func_def_196,type,
sP54: ( subst > term > subst > $o ) > $o ).
thf(func_def_201,type,
sK59: term > $o ).
thf(func_def_202,type,
sK60: subst > term > subst > $o ).
thf(func_def_203,type,
sK61: term ).
thf(func_def_204,type,
sK62: ( subst > term > term ) > term ).
thf(func_def_205,type,
sK63: ( subst > term > term ) > subst ).
thf(func_def_206,type,
sK64: ( subst > term > term ) > subst ).
thf(func_def_207,type,
sK65: ( subst > term > term ) > term ).
thf(func_def_208,type,
sK66: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_209,type,
sK67: term > ( term > $o ) > term ).
thf(func_def_210,type,
sK68: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_211,type,
sK69: term ).
thf(func_def_212,type,
sK70: subst > term > subst > $o ).
thf(func_def_213,type,
sK71: term > $o ).
thf(func_def_214,type,
sK72: ( subst > term > term ) > term ).
thf(func_def_215,type,
sK73: ( subst > term > term ) > subst ).
thf(func_def_216,type,
sK74: ( subst > term > term ) > subst ).
thf(func_def_217,type,
sK75: ( subst > term > term ) > term ).
thf(func_def_218,type,
sK76: term > subst > term > term ).
thf(func_def_219,type,
sK77: ( term > $o ) > term > term ).
thf(func_def_220,type,
sK78: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_221,type,
sK79: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_222,type,
sK80: term ).
thf(func_def_223,type,
sK81: term ).
thf(func_def_224,type,
sK82: ( subst > term > term ) > term ).
thf(func_def_225,type,
sK83: ( subst > term > term ) > subst ).
thf(func_def_226,type,
sK84: term ).
thf(func_def_227,type,
sK85: subst > term > subst > $o ).
thf(func_def_228,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK87: ( subst > term > subst > $o ) > term ).
thf(func_def_230,type,
sK88: ( subst > term > subst > $o ) > subst ).
thf(func_def_231,type,
sK89: ( subst > term > subst > $o ) > subst ).
thf(func_def_232,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK91: ( subst > term > subst > $o ) > subst ).
thf(func_def_234,type,
sK92: ( subst > term > subst > $o ) > subst ).
thf(func_def_235,type,
sK93: ( subst > term > subst > $o ) > term ).
thf(func_def_236,type,
sK94: ( subst > term > subst > $o ) > term > term ).
thf(func_def_237,type,
sK95: term ).
thf(func_def_238,type,
sK96: ( subst > term > subst > $o ) > term > term ).
thf(func_def_239,type,
sK97: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_240,type,
sK98: term ).
thf(func_def_241,type,
sK99: subst > term > subst > $o ).
thf(func_def_242,type,
sK100: ( subst > term > term ) > term ).
thf(func_def_243,type,
sK101: ( subst > term > term ) > term ).
thf(func_def_244,type,
sK102: ( subst > term > term ) > subst ).
thf(func_def_245,type,
sK103: ( subst > term > term ) > subst ).
thf(func_def_246,type,
sK104: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_247,type,
sK105: ( subst > term > term ) > subst ).
thf(func_def_248,type,
sK106: ( subst > term > term ) > term ).
thf(func_def_249,type,
sK107: ( subst > term > term ) > subst ).
thf(func_def_250,type,
sK108: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_251,type,
sK109: ( subst > term > subst > $o ) > term ).
thf(func_def_252,type,
sK110: ( subst > term > subst > $o ) > term ).
thf(func_def_253,type,
sK111: term ).
thf(func_def_254,type,
sK112: subst > term > subst > $o ).
thf(func_def_255,type,
sK113: ( subst > term > term ) > term ).
thf(func_def_256,type,
sK114: term > ( subst > term > term ) > subst ).
thf(func_def_257,type,
sK115: term > ( subst > term > term ) > term ).
thf(func_def_258,type,
sK116: term > ( subst > term > term ) > subst ).
thf(func_def_259,type,
sK117: term > ( subst > term > term ) > term ).
thf(func_def_260,type,
sK118: term > ( subst > term > term ) > subst ).
thf(func_def_261,type,
sK119: term > ( subst > term > term ) > subst ).
thf(func_def_262,type,
sK120: ( subst > term > subst > $o ) > term > term ).
thf(func_def_263,type,
sK121: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_264,type,
sK122: ( subst > term > subst > $o ) > term ).
thf(func_def_265,type,
sK123: term ).
thf(func_def_266,type,
sK124: subst > term > subst > $o ).
thf(func_def_267,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_269,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK128: ( subst > term > subst > $o ) > term ).
thf(func_def_271,type,
sK129: ( subst > term > subst > $o ) > term > term ).
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 ) > subst ).
thf(func_def_275,type,
sK133: ( subst > term > subst > $o ) > term ).
thf(func_def_276,type,
sK134: ( subst > term > term ) > term ).
thf(func_def_277,type,
sK135: ( subst > term > term ) > subst ).
thf(func_def_278,type,
sK136: ( subst > term > term ) > subst ).
thf(func_def_279,type,
sK137: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_280,type,
sK138: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_281,type,
sK139: subst > term > subst > $o ).
thf(func_def_282,type,
sK140: term ).
thf(func_def_283,type,
sK141: term > $o ).
thf(func_def_284,type,
sK142: term ).
thf(func_def_285,type,
sK143: ( subst > term > subst > $o ) > subst ).
thf(func_def_286,type,
sK144: ( subst > term > subst > $o ) > subst ).
thf(func_def_287,type,
sK145: ( subst > term > subst > $o ) > subst ).
thf(func_def_288,type,
sK146: ( subst > term > subst > $o ) > term ).
thf(func_def_289,type,
sK147: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK148: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK149: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK150: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK151: ( subst > term > subst > $o ) > term ).
thf(func_def_294,type,
sK152: ( term > $o ) > term > term ).
thf(func_def_295,type,
sK153: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_296,type,
sK154: ( subst > term > term ) > subst ).
thf(func_def_297,type,
sK155: ( subst > term > term ) > term ).
thf(func_def_298,type,
sK156: ( subst > term > term ) > subst ).
thf(func_def_299,type,
sK157: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_300,type,
sK158: subst > term > subst > $o ).
thf(func_def_301,type,
sK159: term ).
thf(func_def_302,type,
sK160: ( subst > term > term ) > subst ).
thf(func_def_303,type,
sK161: ( subst > term > term ) > subst ).
thf(func_def_304,type,
sK162: ( subst > term > term ) > term ).
thf(func_def_305,type,
sK163: ( subst > term > term ) > term ).
thf(func_def_306,type,
sK164: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_307,type,
sK165: term > ( subst > term > subst > $o ) > term ).
thf(func_def_308,type,
sK166: term ).
thf(func_def_309,type,
sK167: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_310,type,
sK168: ( subst > term > subst > $o ) > term > term ).
thf(func_def_311,type,
sK169: term ).
thf(func_def_312,type,
sK170: subst > term > subst > $o ).
thf(func_def_313,type,
sK171: ( subst > term > term ) > term ).
thf(func_def_314,type,
sK172: ( subst > term > term ) > subst ).
thf(func_def_315,type,
sK173: ( subst > term > term ) > subst ).
thf(func_def_316,type,
sK174: ( subst > term > term ) > term ).
thf(func_def_317,type,
sK175: ( term > $o ) > term ).
thf(func_def_318,type,
sK176: ( term > $o ) > term ).
thf(func_def_319,type,
sK177: term ).
thf(func_def_320,type,
sK178: subst > term > subst > $o ).
thf(func_def_321,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_322,type,
sK180: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK181: ( subst > term > subst > $o ) > subst ).
thf(func_def_324,type,
sK182: ( subst > term > subst > $o ) > term ).
thf(func_def_325,type,
sK183: ( subst > term > subst > $o ) > subst ).
thf(func_def_326,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_327,type,
sK185: ( subst > term > subst > $o ) > subst ).
thf(func_def_328,type,
sK186: ( subst > term > subst > $o ) > subst ).
thf(func_def_329,type,
sK187: ( subst > term > subst > $o ) > term ).
thf(func_def_330,type,
sK188: ( subst > term > subst > $o ) > term ).
thf(func_def_331,type,
sK189: ( subst > term > subst > $o ) > term ).
thf(func_def_332,type,
sK190: ( subst > term > term ) > subst ).
thf(func_def_333,type,
sK191: ( subst > term > term ) > term ).
thf(func_def_334,type,
sK192: ( subst > term > term ) > subst ).
thf(func_def_335,type,
sK193: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_336,type,
sK194: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_337,type,
sK195: subst > term > subst > $o ).
thf(func_def_338,type,
sK196: term ).
thf(func_def_339,type,
sK197: term ).
thf(func_def_340,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK199: ( subst > term > subst > $o ) > term ).
thf(func_def_342,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_343,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_344,type,
sK202: ( subst > term > subst > $o ) > term ).
thf(func_def_345,type,
sK203: ( subst > term > subst > $o ) > subst ).
thf(func_def_346,type,
sK204: ( subst > term > subst > $o ) > subst ).
thf(func_def_347,type,
sK205: ( subst > term > subst > $o ) > subst ).
thf(func_def_348,type,
sK206: ( subst > term > subst > $o ) > term ).
thf(func_def_349,type,
sK207: ( subst > term > subst > $o ) > term ).
thf(func_def_350,type,
sK208: term ).
thf(func_def_351,type,
sK209: subst > term > subst > $o ).
thf(func_def_352,type,
sK210: term ).
thf(func_def_353,type,
sK211: term > $o ).
thf(func_def_354,type,
sK212: ( subst > term > subst > $o ) > term ).
thf(func_def_355,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_356,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_357,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK216: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_360,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_361,type,
sK219: ( subst > term > subst > $o ) > term ).
thf(func_def_362,type,
sK220: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_363,type,
sK221: ( subst > term > subst > $o ) > term ).
thf(func_def_364,type,
sK222: ( subst > term > subst > $o ) > term ).
thf(func_def_365,type,
sK223: ( term > $o ) > term ).
thf(func_def_366,type,
sK224: ( term > $o ) > term ).
thf(func_def_367,type,
sK225: term > $o ).
thf(func_def_368,type,
sK226: term ).
thf(func_def_369,type,
sK227: subst ).
thf(func_def_370,type,
sK228: term ).
thf(func_def_371,type,
sK229: subst ).
thf(func_def_372,type,
sK230: term ).
thf(func_def_373,type,
sK231: subst ).
thf(func_def_374,type,
sK232: subst ).
thf(func_def_375,type,
sK233: term ).
thf(func_def_376,type,
sK234: term > $o ).
thf(func_def_377,type,
sK235: term > term ).
thf(func_def_378,type,
sK236: ( term > $o ) > subst > term ).
thf(func_def_379,type,
sK237: ( term > $o ) > term ).
thf(func_def_380,type,
sK238: ( term > $o ) > term ).
thf(func_def_381,type,
sK239: ( term > $o ) > term ).
thf(func_def_382,type,
sK240: ( term > $o ) > term ).
thf(func_def_383,type,
sK241: ( term > $o ) > term ).
thf(func_def_384,type,
sK242: term ).
thf(func_def_385,type,
sK243: subst ).
thf(func_def_386,type,
sK244: term > $o ).
thf(func_def_387,type,
sK245: term > term ).
thf(func_def_388,type,
sK246: ( term > $o ) > subst > term ).
thf(func_def_389,type,
sK247: ( term > $o ) > term ).
thf(func_def_390,type,
sK248: ( term > $o ) > term ).
thf(func_def_391,type,
sK249: ( term > $o ) > term ).
thf(func_def_392,type,
sK250: subst > term > subst > $o ).
thf(func_def_393,type,
sK251: term ).
thf(func_def_394,type,
sK252: ( subst > term > term ) > subst ).
thf(func_def_395,type,
sK253: ( subst > term > term ) > subst ).
thf(func_def_396,type,
sK254: ( subst > term > term ) > term ).
thf(func_def_397,type,
sK255: ( subst > term > term ) > term ).
thf(func_def_398,type,
sK256: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_399,type,
sK257: term > ( subst > term > subst > $o ) > term ).
thf(func_def_400,type,
sK258: subst > term > subst > $o ).
thf(func_def_401,type,
sK259: term ).
thf(func_def_402,type,
sK260: ( subst > term > term ) > term ).
thf(func_def_403,type,
sK261: ( subst > term > term ) > subst ).
thf(func_def_404,type,
sK262: ( subst > term > term ) > subst ).
thf(func_def_405,type,
sK263: ( subst > term > term ) > term ).
thf(func_def_406,type,
sK264: term > ( subst > term > subst > $o ) > term ).
thf(func_def_407,type,
sK265: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_408,type,
sK266: term > $o ).
thf(func_def_409,type,
sK267: term ).
thf(func_def_410,type,
sK268: term > term ).
thf(func_def_411,type,
sK269: ( term > $o ) > term ).
thf(func_def_412,type,
sK270: ( term > $o ) > term ).
thf(func_def_413,type,
sK271: ( term > $o ) > term ).
thf(func_def_414,type,
sK272: ( term > $o ) > term ).
thf(func_def_415,type,
sK273: subst > term > subst > $o ).
thf(func_def_416,type,
sK274: term ).
thf(func_def_417,type,
sK275: ( subst > term > term ) > subst ).
thf(func_def_418,type,
sK276: ( subst > term > term ) > subst ).
thf(func_def_419,type,
sK277: ( subst > term > term ) > term ).
thf(func_def_420,type,
sK278: ( subst > term > term ) > term ).
thf(func_def_421,type,
sK279: term > ( subst > term > subst > $o ) > term ).
thf(func_def_422,type,
sK280: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_423,type,
sK281: term ).
thf(func_def_424,type,
sK282: term > $o ).
thf(func_def_425,type,
sK283: subst > term > subst > $o ).
thf(func_def_426,type,
sK284: ( subst > term > subst > $o ) > subst ).
thf(func_def_427,type,
sK285: ( subst > term > subst > $o ) > subst ).
thf(func_def_428,type,
sK286: ( subst > term > subst > $o ) > subst ).
thf(func_def_429,type,
sK287: ( subst > term > subst > $o ) > term ).
thf(func_def_430,type,
sK288: ( term > $o ) > term > term ).
thf(func_def_431,type,
sK289: ( subst > term > subst > $o ) > term ).
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 > $o ) > term ).
thf(func_def_436,type,
sK294: ( subst > term > term ) > subst ).
thf(func_def_437,type,
sK295: ( subst > term > term ) > subst ).
thf(func_def_438,type,
sK296: ( subst > term > term ) > term ).
thf(func_def_439,type,
sK297: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_440,type,
sK298: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_441,type,
sK299: subst > term > term ).
thf(func_def_442,type,
sK300: subst ).
thf(func_def_443,type,
sK301: term ).
thf(func_def_444,type,
sK302: subst > term > term ).
thf(func_def_445,type,
sK303: term ).
thf(func_def_446,type,
sK304: term ).
thf(func_def_447,type,
sK305: term ).
thf(func_def_448,type,
sK306: subst ).
thf(func_def_449,type,
sK307: term ).
thf(func_def_450,type,
sK308: subst ).
thf(func_def_451,type,
sK309: ( subst > term > term ) > subst ).
thf(func_def_452,type,
sK310: ( subst > term > term ) > subst ).
thf(func_def_453,type,
sK311: ( subst > term > term ) > term ).
thf(func_def_454,type,
sK312: ( subst > term > term ) > subst ).
thf(func_def_455,type,
sK313: ( subst > term > term ) > term ).
thf(func_def_456,type,
sK314: ( subst > term > term ) > subst ).
thf(func_def_457,type,
sK315: ( term > $o ) > term ).
thf(func_def_458,type,
sK316: ( term > $o ) > subst > term ).
thf(func_def_459,type,
sK317: subst ).
thf(func_def_460,type,
sK318: term > $o ).
thf(func_def_461,type,
sK319: term ).
thf(func_def_462,type,
sK320: term > term ).
thf(func_def_463,type,
sK321: term ).
thf(func_def_464,type,
sK322: term > $o ).
thf(func_def_465,type,
sK323: term ).
thf(func_def_466,type,
sK324: term > term ).
thf(func_def_467,type,
sK325: ( term > $o ) > term ).
thf(func_def_468,type,
sK326: ( term > $o ) > term ).
thf(func_def_469,type,
sK327: ( term > $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: ( term > $o ) > term ).
thf(func_def_473,type,
sK331: ( term > $o ) > term ).
thf(func_def_474,type,
sK332: ( term > $o ) > term ).
thf(func_def_475,type,
sK333: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_476,type,
sK334: term > $o ).
thf(func_def_477,type,
sK335: term ).
thf(func_def_478,type,
sK336: term > term ).
thf(func_def_479,type,
sK337: subst > term > subst > $o ).
thf(func_def_480,type,
sK338: ( term > $o ) > term ).
thf(func_def_481,type,
sK339: term ).
thf(func_def_482,type,
sK340: ( term > $o ) > term > term ).
thf(func_def_483,type,
sK341: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_484,type,
sK342: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_485,type,
sK343: term ).
thf(func_def_486,type,
sK344: subst > term > subst > $o ).
thf(func_def_487,type,
sK345: term > $o ).
thf(func_def_488,type,
sK346: ( subst > term > term ) > term ).
thf(func_def_489,type,
sK347: ( subst > term > term ) > subst ).
thf(func_def_490,type,
sK348: ( subst > term > term ) > term ).
thf(func_def_491,type,
sK349: ( subst > term > term ) > subst ).
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 ) > term ).
thf(func_def_496,type,
sK354: ( subst > term > subst > $o ) > subst ).
thf(func_def_497,type,
sK355: ( subst > term > subst > $o ) > subst ).
thf(func_def_498,type,
sK356: ( subst > term > subst > $o ) > term ).
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: ( subst > term > subst > $o ) > subst ).
thf(func_def_503,type,
sK361: ( term > $o ) > term ).
thf(func_def_504,type,
sK362: ( term > $o ) > term ).
thf(func_def_505,type,
sK363: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_506,type,
sK364: ( subst > term > term ) > subst ).
thf(func_def_507,type,
sK365: ( subst > term > term ) > subst ).
thf(func_def_508,type,
sK366: ( subst > term > term ) > term ).
thf(func_def_509,type,
sK367: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_510,type,
sK368: ( subst > term > subst > $o ) > term ).
thf(func_def_511,type,
sK369: ( subst > term > subst > $o ) > term ).
thf(func_def_512,type,
sK370: ( term > $o ) > term ).
thf(func_def_513,type,
sK371: ( term > $o ) > term ).
thf(func_def_514,type,
sK372: term > $o ).
thf(func_def_515,type,
sK373: term ).
thf(func_def_516,type,
sK374: term > term ).
thf(func_def_517,type,
sK375: ( subst > term > subst > $o ) > subst ).
thf(func_def_518,type,
sK376: ( subst > term > subst > $o ) > subst ).
thf(func_def_519,type,
sK377: ( subst > term > subst > $o ) > term ).
thf(func_def_520,type,
sK378: ( subst > term > subst > $o ) > subst ).
thf(func_def_521,type,
sK379: ( subst > term > subst > $o ) > term ).
thf(func_def_522,type,
sK380: ( subst > term > subst > $o ) > subst ).
thf(func_def_523,type,
sK381: ( subst > term > subst > $o ) > subst ).
thf(func_def_524,type,
sK382: ( subst > term > subst > $o ) > subst ).
thf(func_def_525,type,
sK383: 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 ).
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 ) > subst ).
thf(func_def_533,type,
sK391: ( subst > term > subst > $o ) > 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 ) > term ).
thf(func_def_537,type,
sK395: ( subst > term > subst > $o ) > subst ).
thf(func_def_538,type,
sK396: ( subst > term > subst > $o ) > term ).
thf(func_def_539,type,
sK397: ( subst > term > subst > $o ) > subst ).
thf(func_def_540,type,
sK398: ( subst > term > subst > $o ) > term ).
thf(func_def_541,type,
sK399: ( subst > term > subst > $o ) > subst ).
thf(func_def_542,type,
sK400: ( subst > term > subst > $o ) > subst ).
thf(func_def_543,type,
sK401: term > ( subst > term > subst > $o ) > term ).
thf(func_def_544,type,
sK402: ( subst > term > subst > $o ) > subst ).
thf(func_def_545,type,
sK403: ( subst > term > subst > $o ) > subst ).
thf(func_def_546,type,
sK404: ( subst > term > subst > $o ) > term ).
thf(func_def_547,type,
sK405: ( subst > term > subst > $o ) > subst ).
thf(func_def_548,type,
sK406: subst > term > subst > $o ).
thf(func_def_549,type,
sK407: term ).
thf(func_def_550,type,
sK408: ( subst > term > subst > $o ) > term ).
thf(func_def_551,type,
sK409: ( subst > term > subst > $o ) > term ).
thf(func_def_552,type,
sK410: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_553,type,
sK411: ( subst > term > term ) > subst ).
thf(func_def_554,type,
sK412: ( subst > term > term ) > subst ).
thf(func_def_555,type,
sK413: ( subst > term > term ) > term ).
thf(func_def_556,type,
sK414: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_557,type,
sK415: ( term > $o ) > term ).
thf(func_def_558,type,
sK416: ( term > $o ) > term ).
thf(func_def_559,type,
sK417: ( subst > term > subst > $o ) > term ).
thf(func_def_560,type,
sK418: ( subst > term > subst > $o ) > term ).
thf(func_def_561,type,
sK419: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_562,type,
sK420: ( subst > term > term ) > subst ).
thf(func_def_563,type,
sK421: ( subst > term > term ) > subst ).
thf(func_def_564,type,
sK422: ( subst > term > term ) > term ).
thf(func_def_565,type,
sK423: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_566,type,
sK424: ( term > $o ) > term ).
thf(func_def_567,type,
sK425: ( term > $o ) > term ).
thf(func_def_568,type,
sK426: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_569,type,
sK427: term > $o ).
thf(func_def_570,type,
sK428: term ).
thf(func_def_571,type,
sK429: term > term ).
thf(func_def_572,type,
sK430: term ).
thf(func_def_573,type,
sK431: subst > term > subst > $o ).
thf(func_def_574,type,
sK432: ( term > $o ) > term ).
thf(func_def_575,type,
sK433: subst > term > subst > $o ).
thf(func_def_576,type,
sK434: term ).
thf(func_def_577,type,
sK435: ( subst > term > term ) > term ).
thf(func_def_578,type,
sK436: ( subst > term > term ) > subst ).
thf(func_def_579,type,
sK437: ( subst > term > term ) > term ).
thf(func_def_580,type,
sK438: ( subst > term > term ) > subst ).
thf(func_def_581,type,
sK439: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_582,type,
sK440: ( term > $o ) > term > term ).
thf(func_def_583,type,
sK441: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_584,type,
sK442: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_585,type,
sK443: term ).
thf(func_def_586,type,
sK444: term > $o ).
thf(func_def_587,type,
sK445: subst > term > subst > $o ).
thf(func_def_588,type,
sK446: ( subst > term > term ) > term ).
thf(func_def_589,type,
sK447: ( subst > term > term ) > subst ).
thf(func_def_590,type,
sK448: ( subst > term > term ) > subst ).
thf(func_def_591,type,
sK449: ( subst > term > term ) > term ).
thf(func_def_592,type,
sK450: ( term > $o ) > term ).
thf(func_def_593,type,
sK451: ( term > $o ) > term ).
thf(func_def_594,type,
sK452: ( subst > term > subst > $o ) > term ).
thf(func_def_595,type,
sK453: ( subst > term > subst > $o ) > term ).
thf(func_def_596,type,
sK454: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_597,type,
sK455: term ).
thf(func_def_598,type,
sK456: subst > term > subst > $o ).
thf(func_def_599,type,
sK457: ( subst > term > term ) > term ).
thf(func_def_600,type,
sK458: ( subst > term > term ) > term ).
thf(func_def_601,type,
sK459: ( subst > term > term ) > subst ).
thf(func_def_602,type,
sK460: ( subst > term > term ) > subst ).
thf(func_def_603,type,
sK461: term > $o ).
thf(func_def_604,type,
sK462: term ).
thf(func_def_605,type,
sK463: term > $o ).
thf(func_def_606,type,
sK464: subst ).
thf(func_def_607,type,
sK465: subst ).
thf(func_def_608,type,
sK466: term ).
thf(func_def_609,type,
sK467: subst > ( term > $o ) > term > ( term > $o ) > term ).
thf(func_def_610,type,
sK468: term ).
thf(func_def_611,type,
sK469: subst ).
thf(func_def_612,type,
sK470: term > $o ).
thf(func_def_613,type,
sK471: term > $o ).
thf(func_def_614,type,
sK472: term ).
thf(func_def_615,type,
sK473: term ).
thf(func_def_616,type,
sK474: subst ).
thf(func_def_617,type,
sK475: term ).
thf(func_def_618,type,
sK476: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_619,type,
sK477: subst > term > subst > $o ).
thf(func_def_620,type,
sK478: ( term > $o ) > term ).
thf(func_def_621,type,
sK479: term ).
thf(func_def_622,type,
sK480: term ).
thf(func_def_623,type,
sK481: term ).
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: subst > term > term ).
thf(func_def_630,type,
sK488: ( subst > term > term ) > term ).
thf(func_def_631,type,
sK489: ( subst > term > term ) > subst ).
thf(func_def_632,type,
sK490: ( subst > term > term ) > subst ).
thf(func_def_633,type,
sK491: term > d_term ).
thf(func_def_634,type,
sK492: term ).
thf(func_def_635,type,
sK493: subst ).
thf(func_def_636,type,
sK494: subst ).
thf(func_def_637,type,
sK495: term ).
thf(func_def_638,type,
sK496: subst ).
thf(func_def_639,type,
sK497: term > $o ).
thf(func_def_640,type,
sK498: term > $o ).
thf(func_def_641,type,
sK499: term ).
thf(func_def_642,type,
sK500: term ).
thf(func_def_643,type,
sK501: subst ).
thf(func_def_644,type,
sK502: term ).
thf(func_def_645,type,
sK503: term ).
thf(func_def_646,type,
sK504: term ).
thf(func_def_647,type,
sK505: term ).
thf(func_def_648,type,
sK506: term ).
thf(func_def_649,type,
sK507: term ).
thf(func_def_650,type,
sK508: term ).
thf(func_def_651,type,
sK509: term ).
thf(func_def_652,type,
sK510: term ).
thf(func_def_653,type,
sK511: subst ).
thf(func_def_654,type,
sK512: subst ).
thf(func_def_655,type,
sK513: term ).
thf(func_def_656,type,
sK514: term > $o ).
thf(func_def_657,type,
sK515: ( term > $o ) > term ).
thf(func_def_658,type,
sK516: ( term > $o ) > term ).
thf(func_def_659,type,
sK517: term > subst > ( term > $o ) > term > $o ).
thf(func_def_660,type,
sK518: term > $o ).
thf(func_def_661,type,
sK519: subst ).
thf(func_def_662,type,
sK520: term ).
thf(func_def_663,type,
sK521: ( term > $o ) > term ).
thf(func_def_664,type,
sK522: term ).
thf(func_def_665,type,
sK523: subst ).
thf(func_def_666,type,
sK524: term ).
thf(func_def_667,type,
sK525: term ).
thf(func_def_668,type,
sK526: term ).
thf(func_def_669,type,
sK527: term ).
thf(func_def_670,type,
sK528: subst > term > subst > $o ).
thf(func_def_671,type,
sK529: ( term > $o ) > term ).
thf(func_def_672,type,
sK530: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_673,type,
sK531: subst ).
thf(func_def_674,type,
sK532: subst ).
thf(func_def_675,type,
sK533: subst ).
thf(func_def_676,type,
sK534: subst ).
thf(func_def_677,type,
sK535: subst ).
thf(func_def_678,type,
sK536: term ).
thf(func_def_679,type,
sK537: ( subst > term > term ) > term ).
thf(func_def_680,type,
sK538: ( subst > term > term ) > subst ).
thf(func_def_681,type,
sK539: term > subst > term > 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 > subst > term > term ).
thf(func_def_690,type,
sK548: term ).
thf(func_def_691,type,
sK549: term > subst > term > term ).
thf(func_def_692,type,
sK550: term ).
thf(func_def_693,type,
sK551: ( subst > term > term ) > term ).
thf(func_def_694,type,
sK552: ( subst > term > term ) > subst ).
thf(func_def_695,type,
sK553: term ).
thf(func_def_696,type,
sK554: term ).
thf(func_def_697,type,
sK555: subst > d_subst ).
thf(func_def_698,type,
sK556: subst ).
thf(func_def_699,type,
sK557: term ).
thf(func_def_700,type,
sK558: term ).
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: subst ).
thf(func_def_708,type,
sK566: term ).
thf(func_def_709,type,
sK567: term > $o ).
thf(func_def_710,type,
sK568: ( term > $o ) > term ).
thf(func_def_711,type,
sK569: ( term > $o ) > term > subst > term > $o ).
thf(func_def_712,type,
sK570: term ).
thf(func_def_713,type,
sK571: term ).
thf(func_def_714,type,
sK572: term ).
thf(func_def_715,type,
sK573: term ).
thf(func_def_716,type,
sK574: subst ).
thf(func_def_717,type,
sK575: term ).
thf(func_def_718,type,
sK576: term > $o ).
thf(func_def_719,type,
sK577: term > $o ).
thf(func_def_720,type,
sK578: ( term > $o ) > ( term > $o ) > term > subst > term ).
thf(func_def_721,type,
sK579: term ).
thf(func_def_722,type,
sK580: term > subst > term > term ).
thf(func_def_723,type,
sK581: ( subst > term > term ) > subst ).
thf(func_def_724,type,
sK582: ( subst > term > term ) > subst ).
thf(func_def_725,type,
sK583: ( subst > term > term ) > term ).
thf(func_def_726,type,
sK584: ( subst > term > term ) > subst ).
thf(func_def_727,type,
sK585: ( subst > term > term ) > subst ).
thf(func_def_728,type,
sK586: ( subst > term > term ) > term ).
thf(func_def_729,type,
sK587: term ).
thf(func_def_730,type,
sK588: subst ).
thf(func_def_731,type,
sK589: subst > term > term ).
thf(func_def_732,type,
sK590: subst > term > term ).
thf(func_def_734,type,
sK592: subst > term > subst > $o ).
thf(func_def_735,type,
sK593: ( subst > term > term ) > subst ).
thf(func_def_736,type,
sK594: ( subst > term > term ) > subst ).
thf(func_def_737,type,
sK595: ( subst > term > term ) > term ).
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 ) > term ).
thf(func_def_743,type,
sK601: ( subst > term > subst > $o ) > subst ).
thf(func_def_744,type,
sK602: ( subst > term > subst > $o ) > subst ).
thf(func_def_745,type,
sK603: ( subst > term > subst > $o ) > subst ).
thf(func_def_746,type,
sK604: ( subst > term > subst > $o ) > subst ).
thf(func_def_747,type,
sK605: ( subst > term > subst > $o ) > subst ).
thf(func_def_748,type,
sK606: ( subst > term > subst > $o ) > term ).
thf(func_def_749,type,
sK607: ( subst > term > subst > $o ) > term ).
thf(func_def_750,type,
sK608: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_751,type,
sK609: ( subst > term > subst > $o ) > term ).
thf(func_def_752,type,
sK610: ( subst > term > subst > $o ) > term ).
thf(func_def_753,type,
sK611: ( subst > term > subst > $o ) > term ).
thf(func_def_754,type,
sK612: ( subst > term > subst > $o ) > term ).
thf(func_def_755,type,
sK613: ( subst > term > subst > $o ) > term ).
thf(func_def_756,type,
sK614: ( subst > term > subst > $o ) > term ).
thf(func_def_757,type,
sK615: ( subst > term > subst > $o ) > term ).
thf(func_def_758,type,
sK616: ( subst > term > subst > $o ) > term ).
thf(func_def_759,type,
sK617: ( subst > term > subst > $o ) > term ).
thf(func_def_760,type,
sK618: ( subst > term > subst > $o ) > term ).
thf(func_def_761,type,
sK619: ( subst > term > subst > $o ) > term ).
thf(func_def_763,type,
ph620:
!>[X0: $tType] : X0 ).
thf(f11475,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3360,f5265,f5283,f5297,f5980,f5999,f6166,f6645,f7595,f8060,f11383,f11385,f11397,f11468,f11474]) ).
thf(f11474,plain,
( ~ spl591_573
| ~ spl591_576
| ~ spl591_682 ),
inference(avatar_contradiction_clause,[status(thm)],[f11473]) ).
thf(f11473,plain,
( $false
| ~ spl591_573
| ~ spl591_576
| ~ spl591_682 ),
inference(trivial_inequality_removal,[status(thm)],[f11472]) ).
thf(f11472,plain,
( ( $true = $false )
| ~ spl591_573
| ~ spl591_576
| ~ spl591_682 ),
inference(forward_demodulation,[status(thm)],[f5275,f11456]) ).
thf(f11456,plain,
( ! [X0: term] :
( $false
= ( sK592 @ ( d2subst @ d_id ) @ X0 @ ( d2subst @ d_id ) ) )
| ~ spl591_573
| ~ spl591_682 ),
inference(superposition,[status(thm)],[f5260,f6182]) ).
thf(f6182,plain,
( ! [X149: term,X147: term] : ( X147 = X149 )
| ~ spl591_682 ),
inference(avatar_component_clause,[status(thm)],[f6181]) ).
thf(f6181,definition,
( spl591_682
<=> ! [X149: term,X147: term] : ( X147 = X149 ) ),
introduced(definition,[new_symbols(naming,[spl591_682])],[avatar_definition]) ).
thf(f5260,plain,
( ( ( sK592 @ ( d2subst @ d_id ) @ sK597 @ ( d2subst @ d_id ) )
= $false )
| ~ spl591_573 ),
inference(avatar_component_clause,[status(thm)],[f5258]) ).
thf(f5258,definition,
( spl591_573
<=> ( ( sK592 @ ( d2subst @ d_id ) @ sK597 @ ( d2subst @ d_id ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl591_573])],[avatar_definition]) ).
thf(f5275,plain,
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl591_576 ),
inference(avatar_component_clause,[status(thm)],[f5273]) ).
thf(f5273,definition,
( spl591_576
<=> ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_576])],[avatar_definition]) ).
thf(f11468,plain,
( ~ spl591_573
| ~ spl591_731 ),
inference(avatar_contradiction_clause,[status(thm)],[f11467]) ).
thf(f11467,plain,
( $false
| ~ spl591_573
| ~ spl591_731 ),
inference(trivial_inequality_removal,[status(thm)],[f11463]) ).
thf(f11463,plain,
( ( $true = $false )
| ~ spl591_573
| ~ spl591_731 ),
inference(superposition,[status(thm)],[f5260,f7085]) ).
thf(f7085,plain,
( ! [X2: subst,X1: term] :
( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true )
| ~ spl591_731 ),
inference(avatar_component_clause,[status(thm)],[f7084]) ).
thf(f7084,definition,
( spl591_731
<=> ! [X2: subst,X1: term] :
( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_731])],[avatar_definition]) ).
thf(f11397,plain,
( ~ spl591_577
| ~ spl591_682
| ~ spl591_732 ),
inference(avatar_contradiction_clause,[status(thm)],[f11396]) ).
thf(f11396,plain,
( $false
| ~ spl591_577
| ~ spl591_682
| ~ spl591_732 ),
inference(trivial_inequality_removal,[status(thm)],[f11395]) ).
thf(f11395,plain,
( ( $true = $false )
| ~ spl591_577
| ~ spl591_682
| ~ spl591_732 ),
inference(forward_demodulation,[status(thm)],[f11394,f7088]) ).
thf(f7088,plain,
( ! [X3: subst] :
( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X3 )
= $false )
| ~ spl591_732 ),
inference(avatar_component_clause,[status(thm)],[f7087]) ).
thf(f7087,definition,
( spl591_732
<=> ! [X3: subst] :
( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl591_732])],[avatar_definition]) ).
thf(f11394,plain,
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl591_577
| ~ spl591_682 ),
inference(forward_demodulation,[status(thm)],[f11387,f5725]) ).
thf(f5725,plain,
! [X77: term] :
( ( d2term @ d_one )
= X77 ),
inference(backward_demodulation,[status(thm)],[f1197,f1096]) ).
thf(f1096,plain,
! [X201: d_term] : ( d_one = X201 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP58 != $true ) )
& ( ( $true = sP57 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X0: d_subst] : ( d_id = X0 )
& ( ! [X1: term,X2: subst > term > subst > $o] :
( ( ! [X4: term] :
( ( $true
!= ( X2 @ id @ X4 @ id ) )
| ( $true
= ( X2 @ id @ ( sK454 @ X2 @ id @ X4 ) @ id ) ) )
& ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( sK454 @ X2 @ X7 @ X5 ) @ X6 )
= ( sK454 @ X2 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( X2 @ id @ ( lam @ ( sK454 @ X2 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( sP53 @ X2 ) )
| ( $true
= ( X2 @ id @ X1 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ! [X10: subst > term > term] :
( ( ( $true
= ( sK456 @ id @ ( sK457 @ X10 ) @ id ) )
& ( $true
!= ( sK456 @ id @ ( X10 @ id @ ( sK457 @ X10 ) ) @ id ) ) )
| ( ( X10 @ ( comp @ ( sK460 @ X10 ) @ ( sK459 @ X10 ) ) @ ( sub @ ( sK458 @ X10 ) @ ( sK459 @ X10 ) ) )
!= ( sub @ ( X10 @ ( sK460 @ X10 ) @ ( sK458 @ X10 ) ) @ ( sK459 @ X10 ) ) )
| ( $true
= ( sK456 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( sP53 @ sK456 ) )
& ( $true
!= ( sK456 @ id @ sK455 @ id ) ) ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X15: subst,X16: term] :
( ( sub @ one @ ( push @ X16 @ X15 ) )
= X16 )
& ! [X21: term] :
( ( sK463 @ X21 )
= ( sK461 @ ( sub @ X21 @ ( push @ sK462 @ sK464 ) ) ) )
& ( $true
!= ( sK463 @ one ) )
& ( $true
= ( sK461 @ sK462 ) ) ) )
& ( ( ( sub @ one @ ( push @ sK466 @ sK465 ) )
!= sK466 )
| ! [X24: term > $o,X25: term,X26: term > $o,X27: subst] :
( ( ( X24 @ ( sub @ ( sK467 @ X27 @ X26 @ X25 @ X24 ) @ ( push @ X25 @ X27 ) ) )
!= ( X26 @ ( sK467 @ X27 @ X26 @ X25 @ X24 ) ) )
| ( ( X26 @ one )
= $true )
| ( ( X24 @ X25 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X29: term,X30: subst,X31: term > $o,X32: term > $o,X33: term] :
( ( $true
!= ( X32 @ X33 ) )
| ( $true
= ( X31 @ ( sub @ X33 @ ( push @ X29 @ X30 ) ) ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK471 @ sK472 )
= $true )
& ( $true
!= ( sK470 @ ( sub @ sK472 @ ( push @ sK468 @ sK469 ) ) ) ) ) )
& ( ! [X39: term] :
( ( sub @ X39 @ id )
= X39 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ( sK473
!= ( sub @ sK473 @ id ) ) )
& ( ! [X41: subst,X42: term] :
( ( comp @ sh @ ( push @ X42 @ X41 ) )
= X41 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ( sK474
!= ( comp @ sh @ ( push @ sK475 @ sK474 ) ) ) )
& ( ! [X45: subst > term > subst > $o,X47: term] :
( ( sK476 @ X45 @ X47 )
= ( X45 @ id @ X47 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ! [X49: term > $o] :
( ( sK477 @ id @ ( sK478 @ X49 ) @ id )
!= ( X49 @ ( sK478 @ X49 ) ) ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP52 ) )
& ( ( $true = sP52 )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
| ( ( sK479 != sK480 )
& ( ( lam @ sK480 )
= ( lam @ sK479 ) ) ) )
& ( ! [X53: term,X54: term] :
( ( X53 = X54 )
| ( ( lam @ X54 )
!= ( lam @ X53 ) ) )
| ( laminj != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( ( ap @ ( sub @ sK482 @ id ) @ sK483 )
= ( ap @ ( sub @ sK484 @ id ) @ sK481 ) )
& ( sK483 != sK481 ) ) )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ ( sub @ X62 @ id ) @ X59 )
!= ( ap @ ( sub @ X60 @ id ) @ X61 ) )
| ( X59 = X61 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2subst @ d_id )
= id )
& ! [X63: d_term,X64: d_term] :
( ( X63 = X64 )
| ( ( d2term @ X64 )
!= ( d2term @ X63 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( $true = sP49 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP49 ) )
& ( ( hoaslamnotap = $true )
| ( ! [X68: term,X69: subst,X70: subst] :
( ( sub @ ( sK487 @ X70 @ X68 ) @ X69 )
= ( sK487 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) ) )
& ( ( ap @ ( sub @ sK486 @ id ) @ sK485 )
= ( lam @ ( sK487 @ sh @ one ) ) ) ) )
& ( ! [X71: term,X72: term,X73: subst > term > term] :
( ( ( sub @ ( X73 @ ( sK490 @ X73 ) @ ( sK488 @ X73 ) ) @ ( sK489 @ X73 ) )
!= ( X73 @ ( comp @ ( sK490 @ X73 ) @ ( sK489 @ X73 ) ) @ ( sub @ ( sK488 @ X73 ) @ ( sK489 @ X73 ) ) ) )
| ( ( lam @ ( X73 @ sh @ one ) )
!= ( ap @ ( sub @ X72 @ id ) @ X71 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ! [X77: term] :
( ( d2term @ ( sK491 @ X77 ) )
= X77 )
& ( ! [X79: subst,X80: term > $o,X81: term > $o,X82: term,X83: term] :
( ( ( X80 @ ( sub @ X83 @ ( push @ X82 @ X79 ) ) )
= $true )
| ( $true
!= ( X81 @ X83 ) ) )
| ( sK492
!= ( sub @ one @ ( push @ sK492 @ sK493 ) ) )
| ( sK494
!= ( comp @ sh @ ( push @ sK495 @ sK494 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ( $true
!= ( sK497 @ ( sub @ sK500 @ ( push @ sK499 @ sK496 ) ) ) )
& ( $true
= ( sK498 @ sK500 ) )
& ! [X93: term,X94: subst] :
( ( sub @ one @ ( push @ X93 @ X94 ) )
= X93 )
& ! [X95: subst,X96: term] :
( ( comp @ sh @ ( push @ X96 @ X95 ) )
= X95 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X97: subst] :
( ( comp @ id @ X97 )
= X97 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ( ( comp @ id @ sK501 )
!= sK501 ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X99: term,X100: term,X101: term,X102: term] :
( ( X99 = X100 )
| ( ( ap @ X100 @ X102 )
!= ( ap @ X99 @ X101 ) ) )
& ! [X103: term] :
( ( sub @ X103 @ id )
= X103 )
& ( ( ap @ ( sub @ sK502 @ id ) @ sK504 )
= ( ap @ ( sub @ sK505 @ id ) @ sK503 ) )
& ( sK502 != sK505 ) ) )
& ( ( ( sK507 != sK506 )
& ( ( ap @ sK507 @ sK509 )
= ( ap @ sK506 @ sK508 ) ) )
| ( ( sub @ sK510 @ id )
!= sK510 )
| ! [X113: term,X114: term,X115: term,X116: term] :
( ( ( ap @ ( sub @ X113 @ id ) @ X115 )
!= ( ap @ ( sub @ X116 @ id ) @ X114 ) )
| ( X113 = X116 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( ! [X117: subst] :
( ( comp @ id @ X117 )
= X117 )
& ! [X118: subst] :
( ( comp @ X118 @ id )
= X118 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ( ( comp @ id @ sK511 )
!= sK511 )
| ( sK512
!= ( comp @ sK512 @ id ) ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
| ( ( $true
!= ( sK514 @ sK513 ) )
& ( $true
!= ( sP45 @ sK514 ) )
& ! [X123: term] :
( ( ( var @ X123 )
!= $true )
| ( $true
= ( sK514 @ X123 ) ) )
& ! [X124: term] :
( ( $true
!= ( sK514 @ X124 ) )
| ( $true
= ( sK514 @ ( lam @ X124 ) ) ) ) ) )
& ( ! [X125: term,X126: term > $o] :
( ( $true
= ( X126 @ X125 ) )
| ( ( sP45 @ X126 )
= $true )
| ( ( $true
= ( var @ ( sK515 @ X126 ) ) )
& ( $true
!= ( X126 @ ( sK515 @ X126 ) ) ) )
| ( ( $true
= ( X126 @ ( sK516 @ X126 ) ) )
& ( $true
!= ( X126 @ ( lam @ ( sK516 @ X126 ) ) ) ) ) )
| ( induction != $true ) )
& ( ! [X129: term > $o,X130: subst,X131: term,X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X131 @ X130 ) ) )
= ( sK517 @ X131 @ X130 @ X129 @ X133 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ! [X137: term > $o] :
( ( sK518 @ ( sub @ ( sK521 @ X137 ) @ ( push @ sK520 @ sK519 ) ) )
!= ( X137 @ ( sK521 @ X137 ) ) ) )
& ( ( axvarcons = $true )
| ( sK522
!= ( sub @ one @ ( push @ sK522 @ sK523 ) ) ) )
& ( ! [X141: term,X142: subst] :
( ( sub @ one @ ( push @ X141 @ X142 ) )
= X141 )
| ( axvarcons != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
| ( ( ( ap @ sK526 @ sK525 )
= ( ap @ sK524 @ sK527 ) )
& ( sK526 != sK524 ) ) )
& ( ! [X147: term,X148: term,X149: term,X150: term] :
( ( ( ap @ X149 @ X148 )
!= ( ap @ X147 @ X150 ) )
| ( X147 = X149 ) )
| ( apinj1 != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X152: term > $o] :
( ( sK528 @ id @ ( sK529 @ X152 ) @ id )
!= ( X152 @ ( sK529 @ X152 ) ) ) )
& ( ! [X154: subst > term > subst > $o,X156: term] :
( ( X154 @ id @ X156 @ id )
= ( sK530 @ X154 @ X156 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( apnotvar = $true )
& ( ( $true = sP44 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP44 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
| ( ! [X157: subst] :
( ( comp @ X157 @ id )
= X157 )
& ( ( sK531
!= ( comp @ sK531 @ id ) )
| ( ( comp @ id @ sK532 )
!= sK532 ) )
& ! [X160: subst] :
( ( comp @ id @ X160 )
= X160 ) ) )
& ( ( ( comp @ sK533 @ id )
!= sK533 )
| ( ! [X162: subst] :
( ( comp @ X162 @ id )
= X162 )
& ! [X163: subst] :
( ( comp @ id @ X163 )
= X163 ) )
| ( sK534
!= ( comp @ id @ sK534 ) )
| ( substmonoid_lthm != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP41 ) )
& ( ( $true = sP41 )
| ( hoasinduction_lem2 != $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP39 ) )
& ( ( $true = sP39 )
| ( hoasinduction_lem2v2 != $true ) )
& ( pushprop_gthm = $true )
& ( ! [X165: subst] :
( ( push @ ( sub @ one @ X165 ) @ ( comp @ sh @ X165 ) )
= X165 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ( ( push @ ( sub @ one @ sK535 ) @ ( comp @ sh @ sK535 ) )
!= sK535 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X168: subst > term > term] :
( ( sub @ sK536 @ ( push @ ( sK537 @ X168 ) @ ( sK538 @ X168 ) ) )
!= ( X168 @ ( sK538 @ X168 ) @ ( sK537 @ X168 ) ) ) )
& ( ! [X171: term,X173: term,X174: subst] :
( ( sK539 @ X171 @ X174 @ X173 )
= ( sub @ X171 @ ( push @ X173 @ X174 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( termmset = $true )
| ( sK540
!= ( sub @ sK540 @ id ) ) )
& ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
| ( termmset != $true ) )
& ( ( shinj = $true )
| ( ( ( sub @ sK542 @ sh )
= ( sub @ sK541 @ sh ) )
& ( sK541 != sK542 ) ) )
& ( ! [X179: term,X180: term] :
( ( ( sub @ X180 @ sh )
!= ( sub @ X179 @ sh ) )
| ( X179 = X180 ) )
| ( shinj != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X181: term,X182: term,X183: term,X184: term] :
( ( X183 = X184 )
| ( ( ap @ X181 @ X184 )
!= ( ap @ X182 @ X183 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( sK545 != sK546 )
& ( ( ap @ sK543 @ sK546 )
= ( ap @ sK544 @ sK545 ) ) ) )
& ( ( $true = sP37 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP37 ) )
& ( ! [X189: term] :
( ( sK547 @ X189 @ sh @ one )
= ( sub @ X189 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X192: subst > term > term] :
( ( X192 @ sh @ one )
!= ( sub @ sK548 @ ( push @ one @ sh ) ) ) )
& ( ! [X193: term,X195: term,X196: subst] :
( ( sK549 @ X193 @ X196 @ X195 )
= ( sub @ X193 @ ( push @ X195 @ X196 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X198: subst > term > term] :
( ( sub @ sK550 @ ( push @ ( sK551 @ X198 ) @ ( sK552 @ X198 ) ) )
!= ( X198 @ ( sK552 @ X198 ) @ ( sK551 @ X198 ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( $true = sP33 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP33 ) )
& ( ( $true = sP31 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( $true != sP31 ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X201: d_term] : ( d_one = X201 )
& ( ( sP30 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP30 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP29 ) )
& ( ( $true = sP29 )
| ( induction2 != $true ) )
& ! [X202: d_subst,X203: d_subst] :
( ( ( d2subst @ X202 )
!= ( d2subst @ X203 ) )
| ( X202 = X203 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( sK553
!= ( sub @ sK553 @ id ) )
| ! [X205: term] :
( ( sub @ X205 @ id )
= X205 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X206: term] :
( ( sub @ X206 @ id )
= X206 )
& ( sK554
!= ( sub @ sK554 @ id ) ) ) )
& ( ( sP27 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP27 != $true ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP26 ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP24 ) )
& ( ( $true = sP24 )
| ( hoaslaminj_lthm != $true ) )
& ! [X208: subst] :
( ( d2subst @ ( sK555 @ X208 ) )
= X208 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
| ( ( comp @ sK556 @ id )
!= sK556 ) )
& ( ! [X211: subst] :
( ( comp @ X211 @ id )
= X211 )
| ( axidr != $true ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X212 @ id ) @ X214 )
!= ( ap @ ( sub @ X215 @ id ) @ X213 ) )
| ( X213 = X214 ) )
| ( ( sK557 != sK559 )
& ( ( ap @ sK558 @ sK559 )
= ( ap @ sK560 @ sK557 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ( ( ap @ ( sub @ sK561 @ id ) @ sK563 )
= ( ap @ ( sub @ sK564 @ id ) @ sK562 ) )
& ( sK563 != sK562 )
& ! [X224: term,X225: term,X226: term,X227: term] :
( ( X224 = X226 )
| ( ( ap @ X225 @ X226 )
!= ( ap @ X227 @ X224 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
| ! [X231: term > $o] :
( ( sK567 @ ( sub @ ( sK568 @ X231 ) @ ( push @ sK566 @ sK565 ) ) )
!= ( X231 @ ( sK568 @ X231 ) ) ) )
& ( ! [X233: subst,X234: term,X235: term > $o,X237: term] :
( ( sK569 @ X235 @ X234 @ X233 @ X237 )
= ( X235 @ ( sub @ X237 @ ( push @ X234 @ X233 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP23 ) )
& ( ( $true = sP23 )
| ( induction2_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X238: term,X239: term,X240: term,X241: term] :
( ( ( ap @ ( sub @ X238 @ id ) @ X239 )
!= ( ap @ ( sub @ X240 @ id ) @ X241 ) )
| ( X238 = X240 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( ( ap @ ( sub @ sK570 @ id ) @ sK571 )
= ( ap @ ( sub @ sK572 @ id ) @ sK573 ) )
& ( sK572 != sK570 ) ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP19 ) )
& ( ( $true = sP19 )
| ( hoasinduction_lthm_3 != $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( $true = sP13 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP13 ) )
& ( ( pushprop_lem1v2 = $true )
| ( ! [X250: term] :
( ( sK577 @ X250 )
= ( sK576 @ ( sub @ X250 @ ( push @ sK575 @ sK574 ) ) ) )
& ( $true
= ( sK576 @ sK575 ) )
& ( $true
!= ( sK577 @ one ) ) ) )
& ( ! [X251: subst,X252: term,X253: term > $o,X254: term > $o] :
( ( ( X253 @ ( sub @ ( sK578 @ X254 @ X253 @ X252 @ X251 ) @ ( push @ X252 @ X251 ) ) )
!= ( X254 @ ( sK578 @ X254 @ X253 @ X252 @ X251 ) ) )
| ( $true
!= ( X253 @ X252 ) )
| ( $true
= ( X254 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X257: subst > term > term] :
( ( X257 @ sh @ one )
!= ( sub @ sK579 @ ( push @ one @ sh ) ) ) )
& ( ! [X258: term] :
( ( sK580 @ X258 @ sh @ one )
= ( sub @ X258 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X260: term,X261: subst,X262: subst > term > term,X263: subst > term > term] :
( ( ( sub @ ( X262 @ ( sK581 @ X262 ) @ ( sK583 @ X262 ) ) @ ( sK582 @ X262 ) )
!= ( X262 @ ( comp @ ( sK581 @ X262 ) @ ( sK582 @ X262 ) ) @ ( sub @ ( sK583 @ X262 ) @ ( sK582 @ X262 ) ) ) )
| ( ( X262 @ X261 @ X260 )
= ( X263 @ X261 @ X260 ) )
| ( ( sub @ ( X263 @ ( sK584 @ X263 ) @ ( sK586 @ X263 ) ) @ ( sK585 @ X263 ) )
!= ( X263 @ ( comp @ ( sK584 @ X263 ) @ ( sK585 @ X263 ) ) @ ( sub @ ( sK586 @ X263 ) @ ( sK585 @ X263 ) ) ) )
| ( ( lam @ ( X263 @ sh @ one ) )
!= ( lam @ ( X262 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ( ! [X274: subst,X275: subst,X276: term] :
( ( sK589 @ ( comp @ X274 @ X275 ) @ ( sub @ X276 @ X275 ) )
= ( sub @ ( sK589 @ X274 @ X276 ) @ X275 ) )
& ( ( sK589 @ sK588 @ sK587 )
!= ( sK590 @ sK588 @ sK587 ) )
& ! [X277: subst,X278: subst,X279: term] :
( ( sK590 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) )
= ( sub @ ( sK590 @ X277 @ X279 ) @ X278 ) )
& ( ( lam @ ( sK589 @ sh @ one ) )
= ( lam @ ( sK590 @ sh @ one ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474]) ).
thf(f474,plain,
! [X2: subst > term > subst > $o] :
( ? [X3: subst > term > term] :
( ! [X4: term] :
( ( $true
!= ( X2 @ id @ X4 @ id ) )
| ( $true
= ( X2 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
& ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X3 @ X7 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( $true
!= ( X2 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
=> ( ! [X4: term] :
( ( $true
!= ( X2 @ id @ X4 @ id ) )
| ( $true
= ( X2 @ id @ ( sK454 @ X2 @ id @ X4 ) @ id ) ) )
& ! [X7: subst,X6: subst,X5: term] :
( ( sub @ ( sK454 @ X2 @ X7 @ X5 ) @ X6 )
= ( sK454 @ X2 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( ( X2 @ id @ ( lam @ ( sK454 @ X2 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f475,plain,
( ? [X8: term,X9: subst > term > subst > $o] :
( ! [X10: subst > term > term] :
( ? [X11: term] :
( ( $true
= ( X9 @ id @ X11 @ id ) )
& ( $true
!= ( X9 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
| ? [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
!= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) )
| ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( sP53 @ X9 ) )
& ( $true
!= ( X9 @ id @ X8 @ id ) ) )
=> ( ! [X10: subst > term > term] :
( ? [X11: term] :
( ( $true
= ( sK456 @ id @ X11 @ id ) )
& ( $true
!= ( sK456 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
| ? [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
!= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) )
| ( $true
= ( sK456 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( sP53 @ sK456 ) )
& ( $true
!= ( sK456 @ id @ sK455 @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f476,plain,
! [X10: subst > term > term] :
( ? [X11: term] :
( ( $true
= ( sK456 @ id @ X11 @ id ) )
& ( $true
!= ( sK456 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
=> ( ( $true
= ( sK456 @ id @ ( sK457 @ X10 ) @ id ) )
& ( $true
!= ( sK456 @ id @ ( X10 @ id @ ( sK457 @ X10 ) ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f477,plain,
! [X10: subst > term > term] :
( ? [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
!= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) )
=> ( ( X10 @ ( comp @ ( sK460 @ X10 ) @ ( sK459 @ X10 ) ) @ ( sub @ ( sK458 @ X10 ) @ ( sK459 @ X10 ) ) )
!= ( sub @ ( X10 @ ( sK460 @ X10 ) @ ( sK458 @ X10 ) ) @ ( sK459 @ X10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f478,plain,
( ? [X17: term > $o,X18: term,X19: term > $o,X20: subst] :
( ! [X21: term] :
( ( X17 @ ( sub @ X21 @ ( push @ X18 @ X20 ) ) )
= ( X19 @ X21 ) )
& ( ( X19 @ one )
!= $true )
& ( ( X17 @ X18 )
= $true ) )
=> ( ! [X21: term] :
( ( sK463 @ X21 )
= ( sK461 @ ( sub @ X21 @ ( push @ sK462 @ sK464 ) ) ) )
& ( $true
!= ( sK463 @ one ) )
& ( $true
= ( sK461 @ sK462 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f479,plain,
( ? [X22: subst,X23: term] :
( ( sub @ one @ ( push @ X23 @ X22 ) )
!= X23 )
=> ( ( sub @ one @ ( push @ sK466 @ sK465 ) )
!= sK466 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f480,plain,
! [X24: term > $o,X25: term,X26: term > $o,X27: subst] :
( ? [X28: term] :
( ( X24 @ ( sub @ X28 @ ( push @ X25 @ X27 ) ) )
!= ( X26 @ X28 ) )
=> ( ( X24 @ ( sub @ ( sK467 @ X27 @ X26 @ X25 @ X24 ) @ ( push @ X25 @ X27 ) ) )
!= ( X26 @ ( sK467 @ X27 @ X26 @ X25 @ X24 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f481,plain,
( ? [X34: term,X35: subst,X36: term > $o,X37: term > $o,X38: term] :
( ( $true
= ( X37 @ X38 ) )
& ( ( X36 @ ( sub @ X38 @ ( push @ X34 @ X35 ) ) )
!= $true ) )
=> ( ( ( sK471 @ sK472 )
= $true )
& ( $true
!= ( sK470 @ ( sub @ sK472 @ ( push @ sK468 @ sK469 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ? [X40: term] :
( ( sub @ X40 @ id )
!= X40 )
=> ( sK473
!= ( sub @ sK473 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f483,plain,
( ? [X43: subst,X44: term] :
( ( comp @ sh @ ( push @ X44 @ X43 ) )
!= X43 )
=> ( sK474
!= ( comp @ sh @ ( push @ sK475 @ sK474 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f484,plain,
! [X45: subst > term > subst > $o] :
( ? [X46: term > $o] :
! [X47: term] :
( ( X46 @ X47 )
= ( X45 @ id @ X47 @ id ) )
=> ! [X47: term] :
( ( sK476 @ X45 @ X47 )
= ( X45 @ id @ X47 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f485,plain,
( ? [X48: subst > term > subst > $o] :
! [X49: term > $o] :
? [X50: term] :
( ( X49 @ X50 )
!= ( X48 @ id @ X50 @ id ) )
=> ! [X49: term > $o] :
? [X50: term] :
( ( sK477 @ id @ X50 @ id )
!= ( X49 @ X50 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f486,plain,
! [X49: term > $o] :
( ? [X50: term] :
( ( sK477 @ id @ X50 @ id )
!= ( X49 @ X50 ) )
=> ( ( sK477 @ id @ ( sK478 @ X49 ) @ id )
!= ( X49 @ ( sK478 @ X49 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f487,plain,
( ? [X51: term,X52: term] :
( ( X51 != X52 )
& ( ( lam @ X52 )
= ( lam @ X51 ) ) )
=> ( ( sK479 != sK480 )
& ( ( lam @ sK480 )
= ( lam @ sK479 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f488,plain,
( ? [X55: term,X56: term,X57: term,X58: term] :
( ( ( ap @ ( sub @ X56 @ id ) @ X57 )
= ( ap @ ( sub @ X58 @ id ) @ X55 ) )
& ( X55 != X57 ) )
=> ( ( ( ap @ ( sub @ sK482 @ id ) @ sK483 )
= ( ap @ ( sub @ sK484 @ id ) @ sK481 ) )
& ( sK483 != sK481 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f489,plain,
( ? [X65: term,X66: term,X67: subst > term > term] :
( ! [X68: term,X69: subst,X70: subst] :
( ( X67 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) )
= ( sub @ ( X67 @ X70 @ X68 ) @ X69 ) )
& ( ( ap @ ( sub @ X66 @ id ) @ X65 )
= ( lam @ ( X67 @ sh @ one ) ) ) )
=> ( ! [X70: subst,X69: subst,X68: term] :
( ( sub @ ( sK487 @ X70 @ X68 ) @ X69 )
= ( sK487 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) ) )
& ( ( ap @ ( sub @ sK486 @ id ) @ sK485 )
= ( lam @ ( sK487 @ sh @ one ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f490,plain,
! [X73: subst > term > term] :
( ? [X74: term,X75: subst,X76: subst] :
( ( sub @ ( X73 @ X76 @ X74 ) @ X75 )
!= ( X73 @ ( comp @ X76 @ X75 ) @ ( sub @ X74 @ X75 ) ) )
=> ( ( sub @ ( X73 @ ( sK490 @ X73 ) @ ( sK488 @ X73 ) ) @ ( sK489 @ X73 ) )
!= ( X73 @ ( comp @ ( sK490 @ X73 ) @ ( sK489 @ X73 ) ) @ ( sub @ ( sK488 @ X73 ) @ ( sK489 @ X73 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f491,plain,
! [X77: term] :
( ? [X78: d_term] :
( ( d2term @ X78 )
= X77 )
=> ( ( d2term @ ( sK491 @ X77 ) )
= X77 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f492,plain,
( ? [X84: term,X85: subst] :
( ( sub @ one @ ( push @ X84 @ X85 ) )
!= X84 )
=> ( sK492
!= ( sub @ one @ ( push @ sK492 @ sK493 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f493,plain,
( ? [X86: subst,X87: term] :
( ( comp @ sh @ ( push @ X87 @ X86 ) )
!= X86 )
=> ( sK494
!= ( comp @ sh @ ( push @ sK495 @ sK494 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f494,plain,
( ? [X88: subst,X89: term > $o,X90: term > $o,X91: term,X92: term] :
( ( $true
!= ( X89 @ ( sub @ X92 @ ( push @ X91 @ X88 ) ) ) )
& ( ( X90 @ X92 )
= $true ) )
=> ( ( $true
!= ( sK497 @ ( sub @ sK500 @ ( push @ sK499 @ sK496 ) ) ) )
& ( $true
= ( sK498 @ sK500 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f495,plain,
( ? [X98: subst] :
( ( comp @ id @ X98 )
!= X98 )
=> ( ( comp @ id @ sK501 )
!= sK501 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f496,plain,
( ? [X104: term,X105: term,X106: term,X107: term] :
( ( ( ap @ ( sub @ X107 @ id ) @ X105 )
= ( ap @ ( sub @ X104 @ id ) @ X106 ) )
& ( X104 != X107 ) )
=> ( ( ( ap @ ( sub @ sK502 @ id ) @ sK504 )
= ( ap @ ( sub @ sK505 @ id ) @ sK503 ) )
& ( sK502 != sK505 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f497,plain,
( ? [X108: term,X109: term,X110: term,X111: term] :
( ( X108 != X109 )
& ( ( ap @ X109 @ X111 )
= ( ap @ X108 @ X110 ) ) )
=> ( ( sK507 != sK506 )
& ( ( ap @ sK507 @ sK509 )
= ( ap @ sK506 @ sK508 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f498,plain,
( ? [X112: term] :
( ( sub @ X112 @ id )
!= X112 )
=> ( ( sub @ sK510 @ id )
!= sK510 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f499,plain,
( ? [X119: subst] :
( ( comp @ id @ X119 )
!= X119 )
=> ( ( comp @ id @ sK511 )
!= sK511 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f500,plain,
( ? [X120: subst] :
( ( comp @ X120 @ id )
!= X120 )
=> ( sK512
!= ( comp @ sK512 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f501,plain,
( ? [X121: term,X122: term > $o] :
( ( $true
!= ( X122 @ X121 ) )
& ( ( sP45 @ X122 )
!= $true )
& ! [X123: term] :
( ( ( var @ X123 )
!= $true )
| ( ( X122 @ X123 )
= $true ) )
& ! [X124: term] :
( ( $true
!= ( X122 @ X124 ) )
| ( ( X122 @ ( lam @ X124 ) )
= $true ) ) )
=> ( ( $true
!= ( sK514 @ sK513 ) )
& ( $true
!= ( sP45 @ sK514 ) )
& ! [X123: term] :
( ( ( var @ X123 )
!= $true )
| ( $true
= ( sK514 @ X123 ) ) )
& ! [X124: term] :
( ( $true
!= ( sK514 @ X124 ) )
| ( $true
= ( sK514 @ ( lam @ X124 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f502,plain,
! [X126: term > $o] :
( ? [X127: term] :
( ( $true
= ( var @ X127 ) )
& ( ( X126 @ X127 )
!= $true ) )
=> ( ( $true
= ( var @ ( sK515 @ X126 ) ) )
& ( $true
!= ( X126 @ ( sK515 @ X126 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f503,plain,
! [X126: term > $o] :
( ? [X128: term] :
( ( $true
= ( X126 @ X128 ) )
& ( $true
!= ( X126 @ ( lam @ X128 ) ) ) )
=> ( ( $true
= ( X126 @ ( sK516 @ X126 ) ) )
& ( $true
!= ( X126 @ ( lam @ ( sK516 @ X126 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f504,plain,
! [X129: term > $o,X130: subst,X131: term] :
( ? [X132: term > $o] :
! [X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X131 @ X130 ) ) )
= ( X132 @ X133 ) )
=> ! [X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X131 @ X130 ) ) )
= ( sK517 @ X131 @ X130 @ X129 @ X133 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
( ? [X134: term > $o,X135: subst,X136: term] :
! [X137: term > $o] :
? [X138: term] :
( ( X134 @ ( sub @ X138 @ ( push @ X136 @ X135 ) ) )
!= ( X137 @ X138 ) )
=> ! [X137: term > $o] :
? [X138: term] :
( ( sK518 @ ( sub @ X138 @ ( push @ sK520 @ sK519 ) ) )
!= ( X137 @ X138 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f506,plain,
! [X137: term > $o] :
( ? [X138: term] :
( ( sK518 @ ( sub @ X138 @ ( push @ sK520 @ sK519 ) ) )
!= ( X137 @ X138 ) )
=> ( ( sK518 @ ( sub @ ( sK521 @ X137 ) @ ( push @ sK520 @ sK519 ) ) )
!= ( X137 @ ( sK521 @ X137 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f507,plain,
( ? [X139: term,X140: subst] :
( ( sub @ one @ ( push @ X139 @ X140 ) )
!= X139 )
=> ( sK522
!= ( sub @ one @ ( push @ sK522 @ sK523 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f508,plain,
( ? [X143: term,X144: term,X145: term,X146: term] :
( ( ( ap @ X143 @ X146 )
= ( ap @ X145 @ X144 ) )
& ( X143 != X145 ) )
=> ( ( ( ap @ sK526 @ sK525 )
= ( ap @ sK524 @ sK527 ) )
& ( sK526 != sK524 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
( ? [X151: subst > term > subst > $o] :
! [X152: term > $o] :
? [X153: term] :
( ( X152 @ X153 )
!= ( X151 @ id @ X153 @ id ) )
=> ! [X152: term > $o] :
? [X153: term] :
( ( X152 @ X153 )
!= ( sK528 @ id @ X153 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f510,plain,
! [X152: term > $o] :
( ? [X153: term] :
( ( X152 @ X153 )
!= ( sK528 @ id @ X153 @ id ) )
=> ( ( sK528 @ id @ ( sK529 @ X152 ) @ id )
!= ( X152 @ ( sK529 @ X152 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
! [X154: subst > term > subst > $o] :
( ? [X155: term > $o] :
! [X156: term] :
( ( X154 @ id @ X156 @ id )
= ( X155 @ X156 ) )
=> ! [X156: term] :
( ( X154 @ id @ X156 @ id )
= ( sK530 @ X154 @ X156 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
( ? [X158: subst] :
( ( comp @ X158 @ id )
!= X158 )
=> ( sK531
!= ( comp @ sK531 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f513,plain,
( ? [X159: subst] :
( ( comp @ id @ X159 )
!= X159 )
=> ( ( comp @ id @ sK532 )
!= sK532 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ? [X161: subst] :
( ( comp @ X161 @ id )
!= X161 )
=> ( ( comp @ sK533 @ id )
!= sK533 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f515,plain,
( ? [X164: subst] :
( ( comp @ id @ X164 )
!= X164 )
=> ( sK534
!= ( comp @ id @ sK534 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f516,plain,
( ? [X166: subst] :
( ( push @ ( sub @ one @ X166 ) @ ( comp @ sh @ X166 ) )
!= X166 )
=> ( ( push @ ( sub @ one @ sK535 ) @ ( comp @ sh @ sK535 ) )
!= sK535 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f517,plain,
( ? [X167: term] :
! [X168: subst > term > term] :
? [X169: term,X170: subst] :
( ( X168 @ X170 @ X169 )
!= ( sub @ X167 @ ( push @ X169 @ X170 ) ) )
=> ! [X168: subst > term > term] :
? [X170: subst,X169: term] :
( ( sub @ sK536 @ ( push @ X169 @ X170 ) )
!= ( X168 @ X170 @ X169 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f518,plain,
! [X168: subst > term > term] :
( ? [X170: subst,X169: term] :
( ( sub @ sK536 @ ( push @ X169 @ X170 ) )
!= ( X168 @ X170 @ X169 ) )
=> ( ( sub @ sK536 @ ( push @ ( sK537 @ X168 ) @ ( sK538 @ X168 ) ) )
!= ( X168 @ ( sK538 @ X168 ) @ ( sK537 @ X168 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f519,plain,
! [X171: term] :
( ? [X172: subst > term > term] :
! [X173: term,X174: subst] :
( ( X172 @ X174 @ X173 )
= ( sub @ X171 @ ( push @ X173 @ X174 ) ) )
=> ! [X174: subst,X173: term] :
( ( sK539 @ X171 @ X174 @ X173 )
= ( sub @ X171 @ ( push @ X173 @ X174 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f520,plain,
( ? [X175: term] :
( ( sub @ X175 @ id )
!= X175 )
=> ( sK540
!= ( sub @ sK540 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f521,plain,
( ? [X177: term,X178: term] :
( ( ( sub @ X177 @ sh )
= ( sub @ X178 @ sh ) )
& ( X177 != X178 ) )
=> ( ( ( sub @ sK542 @ sh )
= ( sub @ sK541 @ sh ) )
& ( sK541 != sK542 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f522,plain,
( ? [X185: term,X186: term,X187: term,X188: term] :
( ( X187 != X188 )
& ( ( ap @ X185 @ X188 )
= ( ap @ X186 @ X187 ) ) )
=> ( ( sK545 != sK546 )
& ( ( ap @ sK543 @ sK546 )
= ( ap @ sK544 @ sK545 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f523,plain,
! [X189: term] :
( ? [X190: subst > term > term] :
( ( X190 @ sh @ one )
= ( sub @ X189 @ ( push @ one @ sh ) ) )
=> ( ( sK547 @ X189 @ sh @ one )
= ( sub @ X189 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f524,plain,
( ? [X191: term] :
! [X192: subst > term > term] :
( ( sub @ X191 @ ( push @ one @ sh ) )
!= ( X192 @ sh @ one ) )
=> ! [X192: subst > term > term] :
( ( X192 @ sh @ one )
!= ( sub @ sK548 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f525,plain,
! [X193: term] :
( ? [X194: subst > term > term] :
! [X195: term,X196: subst] :
( ( X194 @ X196 @ X195 )
= ( sub @ X193 @ ( push @ X195 @ X196 ) ) )
=> ! [X196: subst,X195: term] :
( ( sK549 @ X193 @ X196 @ X195 )
= ( sub @ X193 @ ( push @ X195 @ X196 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f526,plain,
( ? [X197: term] :
! [X198: subst > term > term] :
? [X199: term,X200: subst] :
( ( X198 @ X200 @ X199 )
!= ( sub @ X197 @ ( push @ X199 @ X200 ) ) )
=> ! [X198: subst > term > term] :
? [X200: subst,X199: term] :
( ( X198 @ X200 @ X199 )
!= ( sub @ sK550 @ ( push @ X199 @ X200 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f527,plain,
! [X198: subst > term > term] :
( ? [X200: subst,X199: term] :
( ( X198 @ X200 @ X199 )
!= ( sub @ sK550 @ ( push @ X199 @ X200 ) ) )
=> ( ( sub @ sK550 @ ( push @ ( sK551 @ X198 ) @ ( sK552 @ X198 ) ) )
!= ( X198 @ ( sK552 @ X198 ) @ ( sK551 @ X198 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f528,plain,
( ? [X204: term] :
( ( sub @ X204 @ id )
!= X204 )
=> ( sK553
!= ( sub @ sK553 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f529,plain,
( ? [X207: term] :
( ( sub @ X207 @ id )
!= X207 )
=> ( sK554
!= ( sub @ sK554 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f530,plain,
! [X208: subst] :
( ? [X209: d_subst] :
( ( d2subst @ X209 )
= X208 )
=> ( ( d2subst @ ( sK555 @ X208 ) )
= X208 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f531,plain,
( ? [X210: subst] :
( ( comp @ X210 @ id )
!= X210 )
=> ( ( comp @ sK556 @ id )
!= sK556 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f532,plain,
( ? [X216: term,X217: term,X218: term,X219: term] :
( ( X216 != X218 )
& ( ( ap @ X217 @ X218 )
= ( ap @ X219 @ X216 ) ) )
=> ( ( sK557 != sK559 )
& ( ( ap @ sK558 @ sK559 )
= ( ap @ sK560 @ sK557 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f533,plain,
( ? [X220: term,X221: term,X222: term,X223: term] :
( ( ( ap @ ( sub @ X223 @ id ) @ X221 )
= ( ap @ ( sub @ X220 @ id ) @ X222 ) )
& ( X221 != X222 ) )
=> ( ( ( ap @ ( sub @ sK561 @ id ) @ sK563 )
= ( ap @ ( sub @ sK564 @ id ) @ sK562 ) )
& ( sK563 != sK562 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f534,plain,
( ? [X228: subst,X229: term,X230: term > $o] :
! [X231: term > $o] :
? [X232: term] :
( ( X231 @ X232 )
!= ( X230 @ ( sub @ X232 @ ( push @ X229 @ X228 ) ) ) )
=> ! [X231: term > $o] :
? [X232: term] :
( ( X231 @ X232 )
!= ( sK567 @ ( sub @ X232 @ ( push @ sK566 @ sK565 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f535,plain,
! [X231: term > $o] :
( ? [X232: term] :
( ( X231 @ X232 )
!= ( sK567 @ ( sub @ X232 @ ( push @ sK566 @ sK565 ) ) ) )
=> ( ( sK567 @ ( sub @ ( sK568 @ X231 ) @ ( push @ sK566 @ sK565 ) ) )
!= ( X231 @ ( sK568 @ X231 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f536,plain,
! [X233: subst,X234: term,X235: term > $o] :
( ? [X236: term > $o] :
! [X237: term] :
( ( X236 @ X237 )
= ( X235 @ ( sub @ X237 @ ( push @ X234 @ X233 ) ) ) )
=> ! [X237: term] :
( ( sK569 @ X235 @ X234 @ X233 @ X237 )
= ( X235 @ ( sub @ X237 @ ( push @ X234 @ X233 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f537,plain,
( ? [X242: term,X243: term,X244: term,X245: term] :
( ( ( ap @ ( sub @ X242 @ id ) @ X243 )
= ( ap @ ( sub @ X244 @ id ) @ X245 ) )
& ( X242 != X244 ) )
=> ( ( ( ap @ ( sub @ sK570 @ id ) @ sK571 )
= ( ap @ ( sub @ sK572 @ id ) @ sK573 ) )
& ( sK572 != sK570 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
( ? [X246: subst,X247: term,X248: term > $o,X249: term > $o] :
( ! [X250: term] :
( ( X248 @ ( sub @ X250 @ ( push @ X247 @ X246 ) ) )
= ( X249 @ X250 ) )
& ( $true
= ( X248 @ X247 ) )
& ( $true
!= ( X249 @ one ) ) )
=> ( ! [X250: term] :
( ( sK577 @ X250 )
= ( sK576 @ ( sub @ X250 @ ( push @ sK575 @ sK574 ) ) ) )
& ( $true
= ( sK576 @ sK575 ) )
& ( $true
!= ( sK577 @ one ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f539,plain,
! [X251: subst,X252: term,X253: term > $o,X254: term > $o] :
( ? [X255: term] :
( ( X254 @ X255 )
!= ( X253 @ ( sub @ X255 @ ( push @ X252 @ X251 ) ) ) )
=> ( ( X253 @ ( sub @ ( sK578 @ X254 @ X253 @ X252 @ X251 ) @ ( push @ X252 @ X251 ) ) )
!= ( X254 @ ( sK578 @ X254 @ X253 @ X252 @ X251 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f540,plain,
( ? [X256: term] :
! [X257: subst > term > term] :
( ( X257 @ sh @ one )
!= ( sub @ X256 @ ( push @ one @ sh ) ) )
=> ! [X257: subst > term > term] :
( ( X257 @ sh @ one )
!= ( sub @ sK579 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f541,plain,
! [X258: term] :
( ? [X259: subst > term > term] :
( ( X259 @ sh @ one )
= ( sub @ X258 @ ( push @ one @ sh ) ) )
=> ( ( sK580 @ X258 @ sh @ one )
= ( sub @ X258 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f542,plain,
! [X262: subst > term > term] :
( ? [X264: subst,X265: subst,X266: term] :
( ( sub @ ( X262 @ X264 @ X266 ) @ X265 )
!= ( X262 @ ( comp @ X264 @ X265 ) @ ( sub @ X266 @ X265 ) ) )
=> ( ( sub @ ( X262 @ ( sK581 @ X262 ) @ ( sK583 @ X262 ) ) @ ( sK582 @ X262 ) )
!= ( X262 @ ( comp @ ( sK581 @ X262 ) @ ( sK582 @ X262 ) ) @ ( sub @ ( sK583 @ X262 ) @ ( sK582 @ X262 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
! [X263: subst > term > term] :
( ? [X267: subst,X268: subst,X269: term] :
( ( X263 @ ( comp @ X267 @ X268 ) @ ( sub @ X269 @ X268 ) )
!= ( sub @ ( X263 @ X267 @ X269 ) @ X268 ) )
=> ( ( sub @ ( X263 @ ( sK584 @ X263 ) @ ( sK586 @ X263 ) ) @ ( sK585 @ X263 ) )
!= ( X263 @ ( comp @ ( sK584 @ X263 ) @ ( sK585 @ X263 ) ) @ ( sub @ ( sK586 @ X263 ) @ ( sK585 @ X263 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f544,plain,
( ? [X270: term,X271: subst,X272: subst > term > term,X273: subst > term > term] :
( ! [X274: subst,X275: subst,X276: term] :
( ( sub @ ( X272 @ X274 @ X276 ) @ X275 )
= ( X272 @ ( comp @ X274 @ X275 ) @ ( sub @ X276 @ X275 ) ) )
& ( ( X272 @ X271 @ X270 )
!= ( X273 @ X271 @ X270 ) )
& ! [X277: subst,X278: subst,X279: term] :
( ( X273 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) )
= ( sub @ ( X273 @ X277 @ X279 ) @ X278 ) )
& ( ( lam @ ( X273 @ sh @ one ) )
= ( lam @ ( X272 @ sh @ one ) ) ) )
=> ( ! [X276: term,X275: subst,X274: subst] :
( ( sK589 @ ( comp @ X274 @ X275 ) @ ( sub @ X276 @ X275 ) )
= ( sub @ ( sK589 @ X274 @ X276 ) @ X275 ) )
& ( ( sK589 @ sK588 @ sK587 )
!= ( sK590 @ sK588 @ sK587 ) )
& ! [X279: term,X278: subst,X277: subst] :
( ( sK590 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) )
= ( sub @ ( sK590 @ X277 @ X279 ) @ X278 ) )
& ( ( lam @ ( sK589 @ sh @ one ) )
= ( lam @ ( sK590 @ sh @ one ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f473,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP58 != $true ) )
& ( ( $true = sP57 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X0: d_subst] : ( d_id = X0 )
& ( ! [X1: term,X2: subst > term > subst > $o] :
( ? [X3: subst > term > term] :
( ! [X4: term] :
( ( $true
!= ( X2 @ id @ X4 @ id ) )
| ( $true
= ( X2 @ id @ ( X3 @ id @ X4 ) @ id ) ) )
& ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X3 @ X7 @ X5 ) @ X6 )
= ( X3 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
& ( $true
!= ( X2 @ id @ ( lam @ ( X3 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( sP53 @ X2 ) )
| ( $true
= ( X2 @ id @ X1 @ id ) ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X8: term,X9: subst > term > subst > $o] :
( ! [X10: subst > term > term] :
( ? [X11: term] :
( ( $true
= ( X9 @ id @ X11 @ id ) )
& ( $true
!= ( X9 @ id @ ( X10 @ id @ X11 ) @ id ) ) )
| ? [X12: term,X13: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X13 ) @ ( sub @ X12 @ X13 ) )
!= ( sub @ ( X10 @ X14 @ X12 ) @ X13 ) )
| ( ( X9 @ id @ ( lam @ ( X10 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( sP53 @ X9 ) )
& ( $true
!= ( X9 @ id @ X8 @ id ) ) ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X15: subst,X16: term] :
( ( sub @ one @ ( push @ X16 @ X15 ) )
= X16 )
& ? [X17: term > $o,X18: term,X19: term > $o,X20: subst] :
( ! [X21: term] :
( ( X17 @ ( sub @ X21 @ ( push @ X18 @ X20 ) ) )
= ( X19 @ X21 ) )
& ( ( X19 @ one )
!= $true )
& ( ( X17 @ X18 )
= $true ) ) ) )
& ( ? [X22: subst,X23: term] :
( ( sub @ one @ ( push @ X23 @ X22 ) )
!= X23 )
| ! [X24: term > $o,X25: term,X26: term > $o,X27: subst] :
( ? [X28: term] :
( ( X24 @ ( sub @ X28 @ ( push @ X25 @ X27 ) ) )
!= ( X26 @ X28 ) )
| ( ( X26 @ one )
= $true )
| ( ( X24 @ X25 )
!= $true ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X29: term,X30: subst,X31: term > $o,X32: term > $o,X33: term] :
( ( $true
!= ( X32 @ X33 ) )
| ( $true
= ( X31 @ ( sub @ X33 @ ( push @ X29 @ X30 ) ) ) ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X34: term,X35: subst,X36: term > $o,X37: term > $o,X38: term] :
( ( $true
= ( X37 @ X38 ) )
& ( ( X36 @ ( sub @ X38 @ ( push @ X34 @ X35 ) ) )
!= $true ) ) )
& ( ! [X39: term] :
( ( sub @ X39 @ id )
= X39 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X40: term] :
( ( sub @ X40 @ id )
!= X40 ) )
& ( ! [X41: subst,X42: term] :
( ( comp @ sh @ ( push @ X42 @ X41 ) )
= X41 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X43: subst,X44: term] :
( ( comp @ sh @ ( push @ X44 @ X43 ) )
!= X43 ) )
& ( ! [X45: subst > term > subst > $o] :
? [X46: term > $o] :
! [X47: term] :
( ( X46 @ X47 )
= ( X45 @ id @ X47 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X48: subst > term > subst > $o] :
! [X49: term > $o] :
? [X50: term] :
( ( X49 @ X50 )
!= ( X48 @ id @ X50 @ id ) ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP52 ) )
& ( ( $true = sP52 )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
| ? [X51: term,X52: term] :
( ( X51 != X52 )
& ( ( lam @ X52 )
= ( lam @ X51 ) ) ) )
& ( ! [X53: term,X54: term] :
( ( X53 = X54 )
| ( ( lam @ X54 )
!= ( lam @ X53 ) ) )
| ( laminj != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X55: term,X56: term,X57: term,X58: term] :
( ( ( ap @ ( sub @ X56 @ id ) @ X57 )
= ( ap @ ( sub @ X58 @ id ) @ X55 ) )
& ( X55 != X57 ) ) )
& ( ! [X59: term,X60: term,X61: term,X62: term] :
( ( ( ap @ ( sub @ X62 @ id ) @ X59 )
!= ( ap @ ( sub @ X60 @ id ) @ X61 ) )
| ( X59 = X61 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2subst @ d_id )
= id )
& ! [X63: d_term,X64: d_term] :
( ( X63 = X64 )
| ( ( d2term @ X64 )
!= ( d2term @ X63 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( $true = sP49 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP49 ) )
& ( ( hoaslamnotap = $true )
| ? [X65: term,X66: term,X67: subst > term > term] :
( ! [X68: term,X69: subst,X70: subst] :
( ( X67 @ ( comp @ X70 @ X69 ) @ ( sub @ X68 @ X69 ) )
= ( sub @ ( X67 @ X70 @ X68 ) @ X69 ) )
& ( ( ap @ ( sub @ X66 @ id ) @ X65 )
= ( lam @ ( X67 @ sh @ one ) ) ) ) )
& ( ! [X71: term,X72: term,X73: subst > term > term] :
( ? [X74: term,X75: subst,X76: subst] :
( ( sub @ ( X73 @ X76 @ X74 ) @ X75 )
!= ( X73 @ ( comp @ X76 @ X75 ) @ ( sub @ X74 @ X75 ) ) )
| ( ( lam @ ( X73 @ sh @ one ) )
!= ( ap @ ( sub @ X72 @ id ) @ X71 ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ! [X77: term] :
? [X78: d_term] :
( ( d2term @ X78 )
= X77 )
& ( ! [X79: subst,X80: term > $o,X81: term > $o,X82: term,X83: term] :
( ( ( X80 @ ( sub @ X83 @ ( push @ X82 @ X79 ) ) )
= $true )
| ( $true
!= ( X81 @ X83 ) ) )
| ? [X84: term,X85: subst] :
( ( sub @ one @ ( push @ X84 @ X85 ) )
!= X84 )
| ? [X86: subst,X87: term] :
( ( comp @ sh @ ( push @ X87 @ X86 ) )
!= X86 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X88: subst,X89: term > $o,X90: term > $o,X91: term,X92: term] :
( ( $true
!= ( X89 @ ( sub @ X92 @ ( push @ X91 @ X88 ) ) ) )
& ( ( X90 @ X92 )
= $true ) )
& ! [X93: term,X94: subst] :
( ( sub @ one @ ( push @ X93 @ X94 ) )
= X93 )
& ! [X95: subst,X96: term] :
( ( comp @ sh @ ( push @ X96 @ X95 ) )
= X95 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X97: subst] :
( ( comp @ id @ X97 )
= X97 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X98: subst] :
( ( comp @ id @ X98 )
!= X98 ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X99: term,X100: term,X101: term,X102: term] :
( ( X99 = X100 )
| ( ( ap @ X100 @ X102 )
!= ( ap @ X99 @ X101 ) ) )
& ! [X103: term] :
( ( sub @ X103 @ id )
= X103 )
& ? [X104: term,X105: term,X106: term,X107: term] :
( ( ( ap @ ( sub @ X107 @ id ) @ X105 )
= ( ap @ ( sub @ X104 @ id ) @ X106 ) )
& ( X104 != X107 ) ) ) )
& ( ? [X108: term,X109: term,X110: term,X111: term] :
( ( X108 != X109 )
& ( ( ap @ X109 @ X111 )
= ( ap @ X108 @ X110 ) ) )
| ? [X112: term] :
( ( sub @ X112 @ id )
!= X112 )
| ! [X113: term,X114: term,X115: term,X116: term] :
( ( ( ap @ ( sub @ X113 @ id ) @ X115 )
!= ( ap @ ( sub @ X116 @ id ) @ X114 ) )
| ( X113 = X116 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( ! [X117: subst] :
( ( comp @ id @ X117 )
= X117 )
& ! [X118: subst] :
( ( comp @ X118 @ id )
= X118 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X119: subst] :
( ( comp @ id @ X119 )
!= X119 )
| ? [X120: subst] :
( ( comp @ X120 @ id )
!= X120 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
| ? [X121: term,X122: term > $o] :
( ( $true
!= ( X122 @ X121 ) )
& ( ( sP45 @ X122 )
!= $true )
& ! [X123: term] :
( ( ( var @ X123 )
!= $true )
| ( ( X122 @ X123 )
= $true ) )
& ! [X124: term] :
( ( $true
!= ( X122 @ X124 ) )
| ( ( X122 @ ( lam @ X124 ) )
= $true ) ) ) )
& ( ! [X125: term,X126: term > $o] :
( ( $true
= ( X126 @ X125 ) )
| ( ( sP45 @ X126 )
= $true )
| ? [X127: term] :
( ( $true
= ( var @ X127 ) )
& ( ( X126 @ X127 )
!= $true ) )
| ? [X128: term] :
( ( $true
= ( X126 @ X128 ) )
& ( $true
!= ( X126 @ ( lam @ X128 ) ) ) ) )
| ( induction != $true ) )
& ( ! [X129: term > $o,X130: subst,X131: term] :
? [X132: term > $o] :
! [X133: term] :
( ( X129 @ ( sub @ X133 @ ( push @ X131 @ X130 ) ) )
= ( X132 @ X133 ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X134: term > $o,X135: subst,X136: term] :
! [X137: term > $o] :
? [X138: term] :
( ( X134 @ ( sub @ X138 @ ( push @ X136 @ X135 ) ) )
!= ( X137 @ X138 ) ) )
& ( ( axvarcons = $true )
| ? [X139: term,X140: subst] :
( ( sub @ one @ ( push @ X139 @ X140 ) )
!= X139 ) )
& ( ! [X141: term,X142: subst] :
( ( sub @ one @ ( push @ X141 @ X142 ) )
= X141 )
| ( axvarcons != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
| ? [X143: term,X144: term,X145: term,X146: term] :
( ( ( ap @ X143 @ X146 )
= ( ap @ X145 @ X144 ) )
& ( X143 != X145 ) ) )
& ( ! [X147: term,X148: term,X149: term,X150: term] :
( ( ( ap @ X149 @ X148 )
!= ( ap @ X147 @ X150 ) )
| ( X147 = X149 ) )
| ( apinj1 != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X151: subst > term > subst > $o] :
! [X152: term > $o] :
? [X153: term] :
( ( X152 @ X153 )
!= ( X151 @ id @ X153 @ id ) ) )
& ( ! [X154: subst > term > subst > $o] :
? [X155: term > $o] :
! [X156: term] :
( ( X154 @ id @ X156 @ id )
= ( X155 @ X156 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( apnotvar = $true )
& ( ( $true = sP44 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP44 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
| ( ! [X157: subst] :
( ( comp @ X157 @ id )
= X157 )
& ( ? [X158: subst] :
( ( comp @ X158 @ id )
!= X158 )
| ? [X159: subst] :
( ( comp @ id @ X159 )
!= X159 ) )
& ! [X160: subst] :
( ( comp @ id @ X160 )
= X160 ) ) )
& ( ? [X161: subst] :
( ( comp @ X161 @ id )
!= X161 )
| ( ! [X162: subst] :
( ( comp @ X162 @ id )
= X162 )
& ! [X163: subst] :
( ( comp @ id @ X163 )
= X163 ) )
| ? [X164: subst] :
( ( comp @ id @ X164 )
!= X164 )
| ( substmonoid_lthm != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP41 ) )
& ( ( $true = sP41 )
| ( hoasinduction_lem2 != $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP39 ) )
& ( ( $true = sP39 )
| ( hoasinduction_lem2v2 != $true ) )
& ( pushprop_gthm = $true )
& ( ! [X165: subst] :
( ( push @ ( sub @ one @ X165 ) @ ( comp @ sh @ X165 ) )
= X165 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X166: subst] :
( ( push @ ( sub @ one @ X166 ) @ ( comp @ sh @ X166 ) )
!= X166 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X167: term] :
! [X168: subst > term > term] :
? [X169: term,X170: subst] :
( ( X168 @ X170 @ X169 )
!= ( sub @ X167 @ ( push @ X169 @ X170 ) ) ) )
& ( ! [X171: term] :
? [X172: subst > term > term] :
! [X173: term,X174: subst] :
( ( X172 @ X174 @ X173 )
= ( sub @ X171 @ ( push @ X173 @ X174 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( termmset = $true )
| ? [X175: term] :
( ( sub @ X175 @ id )
!= X175 ) )
& ( ! [X176: term] :
( ( sub @ X176 @ id )
= X176 )
| ( termmset != $true ) )
& ( ( shinj = $true )
| ? [X177: term,X178: term] :
( ( ( sub @ X177 @ sh )
= ( sub @ X178 @ sh ) )
& ( X177 != X178 ) ) )
& ( ! [X179: term,X180: term] :
( ( ( sub @ X180 @ sh )
!= ( sub @ X179 @ sh ) )
| ( X179 = X180 ) )
| ( shinj != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X181: term,X182: term,X183: term,X184: term] :
( ( X183 = X184 )
| ( ( ap @ X181 @ X184 )
!= ( ap @ X182 @ X183 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X185: term,X186: term,X187: term,X188: term] :
( ( X187 != X188 )
& ( ( ap @ X185 @ X188 )
= ( ap @ X186 @ X187 ) ) ) )
& ( ( $true = sP37 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP37 ) )
& ( ! [X189: term] :
? [X190: subst > term > term] :
( ( X190 @ sh @ one )
= ( sub @ X189 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X191: term] :
! [X192: subst > term > term] :
( ( sub @ X191 @ ( push @ one @ sh ) )
!= ( X192 @ sh @ one ) ) )
& ( ! [X193: term] :
? [X194: subst > term > term] :
! [X195: term,X196: subst] :
( ( X194 @ X196 @ X195 )
= ( sub @ X193 @ ( push @ X195 @ X196 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X197: term] :
! [X198: subst > term > term] :
? [X199: term,X200: subst] :
( ( X198 @ X200 @ X199 )
!= ( sub @ X197 @ ( push @ X199 @ X200 ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( $true = sP33 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP33 ) )
& ( ( $true = sP31 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( $true != sP31 ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X201: d_term] : ( d_one = X201 )
& ( ( sP30 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP30 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP29 ) )
& ( ( $true = sP29 )
| ( induction2 != $true ) )
& ! [X202: d_subst,X203: d_subst] :
( ( ( d2subst @ X202 )
!= ( d2subst @ X203 ) )
| ( X202 = X203 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ? [X204: term] :
( ( sub @ X204 @ id )
!= X204 )
| ! [X205: term] :
( ( sub @ X205 @ id )
= X205 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X206: term] :
( ( sub @ X206 @ id )
= X206 )
& ? [X207: term] :
( ( sub @ X207 @ id )
!= X207 ) ) )
& ( ( sP27 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP27 != $true ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP26 ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP24 ) )
& ( ( $true = sP24 )
| ( hoaslaminj_lthm != $true ) )
& ! [X208: subst] :
? [X209: d_subst] :
( ( d2subst @ X209 )
= X208 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
| ? [X210: subst] :
( ( comp @ X210 @ id )
!= X210 ) )
& ( ! [X211: subst] :
( ( comp @ X211 @ id )
= X211 )
| ( axidr != $true ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X212 @ id ) @ X214 )
!= ( ap @ ( sub @ X215 @ id ) @ X213 ) )
| ( X213 = X214 ) )
| ? [X216: term,X217: term,X218: term,X219: term] :
( ( X216 != X218 )
& ( ( ap @ X217 @ X218 )
= ( ap @ X219 @ X216 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X220: term,X221: term,X222: term,X223: term] :
( ( ( ap @ ( sub @ X223 @ id ) @ X221 )
= ( ap @ ( sub @ X220 @ id ) @ X222 ) )
& ( X221 != X222 ) )
& ! [X224: term,X225: term,X226: term,X227: term] :
( ( X224 = X226 )
| ( ( ap @ X225 @ X226 )
!= ( ap @ X227 @ X224 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
| ? [X228: subst,X229: term,X230: term > $o] :
! [X231: term > $o] :
? [X232: term] :
( ( X231 @ X232 )
!= ( X230 @ ( sub @ X232 @ ( push @ X229 @ X228 ) ) ) ) )
& ( ! [X233: subst,X234: term,X235: term > $o] :
? [X236: term > $o] :
! [X237: term] :
( ( X236 @ X237 )
= ( X235 @ ( sub @ X237 @ ( push @ X234 @ X233 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP23 ) )
& ( ( $true = sP23 )
| ( induction2_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X238: term,X239: term,X240: term,X241: term] :
( ( ( ap @ ( sub @ X238 @ id ) @ X239 )
!= ( ap @ ( sub @ X240 @ id ) @ X241 ) )
| ( X238 = X240 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X242: term,X243: term,X244: term,X245: term] :
( ( ( ap @ ( sub @ X242 @ id ) @ X243 )
= ( ap @ ( sub @ X244 @ id ) @ X245 ) )
& ( X242 != X244 ) ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP19 ) )
& ( ( $true = sP19 )
| ( hoasinduction_lthm_3 != $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( $true = sP13 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP13 ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X246: subst,X247: term,X248: term > $o,X249: term > $o] :
( ! [X250: term] :
( ( X248 @ ( sub @ X250 @ ( push @ X247 @ X246 ) ) )
= ( X249 @ X250 ) )
& ( $true
= ( X248 @ X247 ) )
& ( $true
!= ( X249 @ one ) ) ) )
& ( ! [X251: subst,X252: term,X253: term > $o,X254: term > $o] :
( ? [X255: term] :
( ( X254 @ X255 )
!= ( X253 @ ( sub @ X255 @ ( push @ X252 @ X251 ) ) ) )
| ( $true
!= ( X253 @ X252 ) )
| ( $true
= ( X254 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X256: term] :
! [X257: subst > term > term] :
( ( X257 @ sh @ one )
!= ( sub @ X256 @ ( push @ one @ sh ) ) ) )
& ( ! [X258: term] :
? [X259: subst > term > term] :
( ( X259 @ sh @ one )
= ( sub @ X258 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X260: term,X261: subst,X262: subst > term > term,X263: subst > term > term] :
( ? [X264: subst,X265: subst,X266: term] :
( ( sub @ ( X262 @ X264 @ X266 ) @ X265 )
!= ( X262 @ ( comp @ X264 @ X265 ) @ ( sub @ X266 @ X265 ) ) )
| ( ( X262 @ X261 @ X260 )
= ( X263 @ X261 @ X260 ) )
| ? [X267: subst,X268: subst,X269: term] :
( ( X263 @ ( comp @ X267 @ X268 ) @ ( sub @ X269 @ X268 ) )
!= ( sub @ ( X263 @ X267 @ X269 ) @ X268 ) )
| ( ( lam @ ( X263 @ sh @ one ) )
!= ( lam @ ( X262 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X270: term,X271: subst,X272: subst > term > term,X273: subst > term > term] :
( ! [X274: subst,X275: subst,X276: term] :
( ( sub @ ( X272 @ X274 @ X276 ) @ X275 )
= ( X272 @ ( comp @ X274 @ X275 ) @ ( sub @ X276 @ X275 ) ) )
& ( ( X272 @ X271 @ X270 )
!= ( X273 @ X271 @ X270 ) )
& ! [X277: subst,X278: subst,X279: term] :
( ( X273 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) )
= ( sub @ ( X273 @ X277 @ X279 ) @ X278 ) )
& ( ( lam @ ( X273 @ sh @ one ) )
= ( lam @ ( X272 @ sh @ one ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true ) ),
inference(rectify,[status(thm)],[f472]) ).
thf(f472,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP58 != $true ) )
& ( ( $true = sP57 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X48: d_subst] : ( d_id = X48 )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ? [X469: subst > term > term] :
( ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) )
& ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
& ( $true
!= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( sP53 @ X468 ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X467: term,X468: subst > term > subst > $o] :
( ! [X469: subst > term > term] :
( ? [X473: term] :
( ( $true
= ( X468 @ id @ X473 @ id ) )
& ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
!= $true ) )
| ? [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
!= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
| ( $true
= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( sP53 @ X468 ) )
& ( ( X468 @ id @ X467 @ id )
!= $true ) ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
= X351 )
& ? [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ! [X356: term] :
( ( X354 @ X356 )
= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
& ( $true
!= ( X354 @ one ) )
& ( $true
= ( X352 @ X353 ) ) ) ) )
& ( ? [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
!= X351 )
| ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ? [X356: term] :
( ( X354 @ X356 )
!= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
= ( X155 @ X156 ) )
& ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
!= $true ) ) )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X167: term] :
( ( sub @ X167 @ id )
!= X167 ) )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
!= X281 ) )
& ( ! [X204: subst > term > subst > $o] :
? [X205: term > $o] :
! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X204: subst > term > subst > $o] :
! [X205: term > $o] :
? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ id @ X206 @ id ) ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP52 ) )
& ( ( $true = sP52 )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
| ? [X93: term,X94: term] :
( ( X93 != X94 )
& ( ( lam @ X93 )
= ( lam @ X94 ) ) ) )
& ( ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) )
| ( laminj != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
& ( X212 != X214 ) ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2subst @ d_id )
= id )
& ! [X168: d_term,X169: d_term] :
( ( X168 = X169 )
| ( ( d2term @ X169 )
!= ( d2term @ X168 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( $true = sP49 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP49 ) )
& ( ( hoaslamnotap = $true )
| ? [X249: term,X250: term,X251: subst > term > term] :
( ! [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
& ( ( ap @ ( sub @ X250 @ id ) @ X249 )
= ( lam @ ( X251 @ sh @ one ) ) ) ) )
& ( ! [X249: term,X250: term,X251: subst > term > term] :
( ? [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
!= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
| ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) )
| ? [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
!= X291 )
| ? [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
!= X293 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
!= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
& ( ( X297 @ X299 )
= $true ) )
& ! [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
= X291 )
& ! [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
= X293 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X290: subst] :
( ( comp @ id @ X290 )
!= X290 ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( X85 = X86 )
| ( ( ap @ X85 @ X87 )
!= ( ap @ X86 @ X88 ) ) )
& ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
& ? [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
& ( X89 != X92 ) ) ) )
& ( ? [X85: term,X86: term,X87: term,X88: term] :
( ( X85 != X86 )
& ( ( ap @ X85 @ X87 )
= ( ap @ X86 @ X88 ) ) )
| ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 )
| ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X357: subst] :
( ( comp @ id @ X357 )
!= X357 )
| ? [X358: subst] :
( ( comp @ X358 @ id )
!= X358 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
| ? [X54: term,X55: term > $o] :
( ( $true
!= ( X55 @ X54 ) )
& ( $true
!= ( sP45 @ X55 ) )
& ! [X56: term] :
( ( $true
!= ( var @ X56 ) )
| ( $true
= ( X55 @ X56 ) ) )
& ! [X57: term] :
( ( $true
!= ( X55 @ X57 ) )
| ( $true
= ( X55 @ ( lam @ X57 ) ) ) ) ) )
& ( ! [X54: term,X55: term > $o] :
( ( $true
= ( X55 @ X54 ) )
| ( $true
= ( sP45 @ X55 ) )
| ? [X56: term] :
( ( $true
= ( var @ X56 ) )
& ( $true
!= ( X55 @ X56 ) ) )
| ? [X57: term] :
( ( $true
= ( X55 @ X57 ) )
& ( $true
!= ( X55 @ ( lam @ X57 ) ) ) ) )
| ( induction != $true ) )
& ( ! [X49: term > $o,X50: subst,X51: term] :
? [X52: term > $o] :
! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X49: term > $o,X50: subst,X51: term] :
! [X52: term > $o] :
? [X53: term] :
( ( X52 @ X53 )
!= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) ) )
& ( ( axvarcons = $true )
| ? [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
!= X449 ) )
& ( ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 )
| ( axvarcons != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
| ? [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
= ( ap @ X46 @ X45 ) )
& ( X44 != X46 ) ) )
& ( ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) )
| ( apinj1 != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X216: subst > term > subst > $o] :
! [X217: term > $o] :
? [X218: term] :
( ( X216 @ id @ X218 @ id )
!= ( X217 @ X218 ) ) )
& ( ! [X216: subst > term > subst > $o] :
? [X217: term > $o] :
! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( apnotvar = $true )
& ( ( $true = sP44 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP44 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
| ( ! [X345: subst] :
( ( comp @ X345 @ id )
= X345 )
& ( ? [X347: subst] :
( ( comp @ X347 @ id )
!= X347 )
| ? [X346: subst] :
( ( comp @ id @ X346 )
!= X346 ) )
& ! [X344: subst] :
( ( comp @ id @ X344 )
= X344 ) ) )
& ( ? [X345: subst] :
( ( comp @ X345 @ id )
!= X345 )
| ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) )
| ? [X344: subst] :
( ( comp @ id @ X344 )
!= X344 )
| ( substmonoid_lthm != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP41 ) )
& ( ( $true = sP41 )
| ( hoasinduction_lem2 != $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP39 ) )
& ( ( $true = sP39 )
| ( hoasinduction_lem2v2 != $true ) )
& ( pushprop_gthm = $true )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
!= X498 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X445: term] :
! [X446: subst > term > term] :
? [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
!= ( X446 @ X448 @ X447 ) ) )
& ( ! [X445: term] :
? [X446: subst > term > term] :
! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( termmset = $true )
| ? [X305: term] :
( ( sub @ X305 @ id )
!= X305 ) )
& ( ! [X305: term] :
( ( sub @ X305 @ id )
= X305 )
| ( termmset != $true ) )
& ( ( shinj = $true )
| ? [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
= ( sub @ X186 @ sh ) )
& ( X186 != X187 ) ) )
& ( ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) )
| ( shinj != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X188: term,X189: term,X190: term,X191: term] :
( ( X190 != X191 )
& ( ( ap @ X189 @ X190 )
= ( ap @ X188 @ X191 ) ) ) )
& ( ( $true = sP37 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP37 ) )
& ( ! [X38: term] :
? [X39: subst > term > term] :
( ( X39 @ sh @ one )
= ( sub @ X38 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X38: term] :
! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) ) )
& ( ! [X40: term] :
? [X41: subst > term > term] :
! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X40: term] :
! [X41: subst > term > term] :
? [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
!= ( sub @ X40 @ ( push @ X42 @ X43 ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( $true = sP33 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP33 ) )
& ( ( $true = sP31 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( $true != sP31 ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( sP30 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP30 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP29 ) )
& ( ( $true = sP29 )
| ( induction2 != $true ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
!= ( d2subst @ X349 ) )
| ( X348 = X349 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ? [X157: term] :
( ( sub @ X157 @ id )
!= X157 )
| ! [X158: term] :
( ( sub @ X158 @ id )
= X158 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X157: term] :
( ( sub @ X157 @ id )
= X157 )
& ? [X158: term] :
( ( sub @ X158 @ id )
!= X158 ) ) )
& ( ( sP27 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP27 != $true ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP26 ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP24 ) )
& ( ( $true = sP24 )
| ( hoaslaminj_lthm != $true ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
| ? [X4: subst] :
( ( comp @ X4 @ id )
!= X4 ) )
& ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 )
| ( axidr != $true ) )
& ( ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) )
| ? [X306: term,X307: term,X308: term,X309: term] :
( ( X306 != X308 )
& ( ( ap @ X307 @ X308 )
= ( ap @ X309 @ X306 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
& ( X311 != X312 ) )
& ! [X306: term,X307: term,X308: term,X309: term] :
( ( X306 = X308 )
| ( ( ap @ X307 @ X308 )
!= ( ap @ X309 @ X306 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
| ? [X207: subst,X208: term,X209: term > $o] :
! [X210: term > $o] :
? [X211: term] :
( ( X210 @ X211 )
!= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) ) )
& ( ! [X207: subst,X208: term,X209: term > $o] :
? [X210: term > $o] :
! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP23 ) )
& ( ( $true = sP23 )
| ( induction2_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
& ( X484 != X486 ) ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP19 ) )
& ( ( $true = sP19 )
| ( hoasinduction_lthm_3 != $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( $true = sP13 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP13 ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ! [X304: term] :
( ( X303 @ X304 )
= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
& ( $true
= ( X302 @ X301 ) )
& ( $true
!= ( X303 @ one ) ) ) )
& ( ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ? [X304: term] :
( ( X303 @ X304 )
!= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X0: term] :
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& ( ! [X0: term] :
? [X1: subst > term > term] :
( ( X1 @ sh @ one )
= ( sub @ X0 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ? [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
!= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) )
| ? [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
!= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ! [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
& ( ( X491 @ X489 @ X488 )
!= ( X490 @ X489 @ X488 ) )
& ! [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
& ( ( lam @ ( X491 @ sh @ one ) )
= ( lam @ ( X490 @ sh @ one ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true ) ),
inference(flattening,[status(thm)],[f471]) ).
thf(f471,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ( sP58 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP58 != $true ) )
& ( ( $true = sP57 )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( $true != sP57 ) )
& ( ( $true = sP56 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
| ( $true != sP56 ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X48: d_subst] : ( d_id = X48 )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ? [X469: subst > term > term] :
( ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) )
& ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
& ( $true
!= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( sP53 @ X468 ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X467: term,X468: subst > term > subst > $o] :
( ! [X469: subst > term > term] :
( ? [X473: term] :
( ( $true
= ( X468 @ id @ X473 @ id ) )
& ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
!= $true ) )
| ? [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
!= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
| ( $true
= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
& ( $true
!= ( sP53 @ X468 ) )
& ( ( X468 @ id @ X467 @ id )
!= $true ) ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
= X351 )
& ? [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ! [X356: term] :
( ( X354 @ X356 )
= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
& ( $true
!= ( X354 @ one ) )
& ( $true
= ( X352 @ X353 ) ) ) ) )
& ( ? [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
!= X351 )
| ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ? [X356: term] :
( ( X354 @ X356 )
!= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( pushprop_lem1 = $true )
| ? [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
= ( X155 @ X156 ) )
& ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
!= $true ) ) )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
| ( axvarid != $true ) )
& ( ( axvarid = $true )
| ? [X167: term] :
( ( sub @ X167 @ id )
!= X167 ) )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
| ( axshiftcons != $true ) )
& ( ( axshiftcons = $true )
| ? [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
!= X281 ) )
& ( ! [X204: subst > term > subst > $o] :
? [X205: term > $o] :
! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) )
| ( hoasinduction_lem0 != $true ) )
& ( ( hoasinduction_lem0 = $true )
| ? [X204: subst > term > subst > $o] :
! [X205: term > $o] :
? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ id @ X206 @ id ) ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP52 ) )
& ( ( $true = sP52 )
| ( hoasinduction_lem3aaa != $true ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
| ? [X93: term,X94: term] :
( ( X93 != X94 )
& ( ( lam @ X93 )
= ( lam @ X94 ) ) ) )
& ( ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) )
| ( laminj != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
& ( X212 != X214 ) ) )
& ( ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( $true != sP51 ) )
& ( ( $true = sP51 )
| ( hoasinduction_lem3 != $true ) )
& ( ( d2subst @ d_id )
= id )
& ! [X168: d_term,X169: d_term] :
( ( X168 = X169 )
| ( ( d2term @ X169 )
!= ( d2term @ X168 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( $true = sP49 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( $true != sP49 ) )
& ( ( hoaslamnotap = $true )
| ? [X249: term,X250: term,X251: subst > term > term] :
( ! [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
& ( ( ap @ ( sub @ X250 @ id ) @ X249 )
= ( lam @ ( X251 @ sh @ one ) ) ) ) )
& ( ! [X249: term,X250: term,X251: subst > term > term] :
( ? [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
!= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
| ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( $true != sP47 ) )
& ( ( $true = sP47 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( hoasapinj1_gthm = $true )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) )
| ? [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
!= X291 )
| ? [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
!= X293 )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ? [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
!= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
& ( ( X297 @ X299 )
= $true ) )
& ! [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
= X291 )
& ! [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
= X293 ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X290: subst] :
( ( comp @ id @ X290 )
!= X290 ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( X85 = X86 )
| ( ( ap @ X85 @ X87 )
!= ( ap @ X86 @ X88 ) ) )
& ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
& ? [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
& ( X89 != X92 ) ) ) )
& ( ? [X85: term,X86: term,X87: term,X88: term] :
( ( X85 != X86 )
& ( ( ap @ X85 @ X87 )
= ( ap @ X86 @ X88 ) ) )
| ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 )
| ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) )
| ( hoasapinj1_lthm != $true ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X357: subst] :
( ( comp @ id @ X357 )
!= X357 )
| ? [X358: subst] :
( ( comp @ X358 @ id )
!= X358 ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
| ? [X54: term,X55: term > $o] :
( ( $true
!= ( X55 @ X54 ) )
& ( $true
!= ( sP45 @ X55 ) )
& ! [X56: term] :
( ( $true
!= ( var @ X56 ) )
| ( $true
= ( X55 @ X56 ) ) )
& ! [X57: term] :
( ( $true
!= ( X55 @ X57 ) )
| ( $true
= ( X55 @ ( lam @ X57 ) ) ) ) ) )
& ( ! [X54: term,X55: term > $o] :
( ( $true
= ( X55 @ X54 ) )
| ( $true
= ( sP45 @ X55 ) )
| ? [X56: term] :
( ( $true
= ( var @ X56 ) )
& ( $true
!= ( X55 @ X56 ) ) )
| ? [X57: term] :
( ( $true
= ( X55 @ X57 ) )
& ( $true
!= ( X55 @ ( lam @ X57 ) ) ) ) )
| ( induction != $true ) )
& ( ! [X49: term > $o,X50: subst,X51: term] :
? [X52: term > $o] :
! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X49: term > $o,X50: subst,X51: term] :
! [X52: term > $o] :
? [X53: term] :
( ( X52 @ X53 )
!= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) ) )
& ( ( axvarcons = $true )
| ? [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
!= X449 ) )
& ( ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 )
| ( axvarcons != $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
| ? [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
= ( ap @ X46 @ X45 ) )
& ( X44 != X46 ) ) )
& ( ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) )
| ( apinj1 != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X216: subst > term > subst > $o] :
! [X217: term > $o] :
? [X218: term] :
( ( X216 @ id @ X218 @ id )
!= ( X217 @ X218 ) ) )
& ( ! [X216: subst > term > subst > $o] :
? [X217: term > $o] :
! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( apnotvar = $true )
& ( ( $true = sP44 )
| ( hoasinduction != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP44 ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
| ( ! [X345: subst] :
( ( comp @ X345 @ id )
= X345 )
& ( ? [X347: subst] :
( ( comp @ X347 @ id )
!= X347 )
| ? [X346: subst] :
( ( comp @ id @ X346 )
!= X346 ) )
& ! [X344: subst] :
( ( comp @ id @ X344 )
= X344 ) ) )
& ( ? [X345: subst] :
( ( comp @ X345 @ id )
!= X345 )
| ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) )
| ? [X344: subst] :
( ( comp @ id @ X344 )
!= X344 )
| ( substmonoid_lthm != $true ) )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP41 ) )
& ( ( $true = sP41 )
| ( hoasinduction_lem2 != $true ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP39 ) )
& ( ( $true = sP39 )
| ( hoasinduction_lem2v2 != $true ) )
& ( pushprop_gthm = $true )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
| ( axscons != $true ) )
& ( ( axscons = $true )
| ? [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
!= X498 ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X445: term] :
! [X446: subst > term > term] :
? [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
!= ( X446 @ X448 @ X447 ) ) )
& ( ! [X445: term] :
? [X446: subst > term > term] :
! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( ( termmset = $true )
| ? [X305: term] :
( ( sub @ X305 @ id )
!= X305 ) )
& ( ! [X305: term] :
( ( sub @ X305 @ id )
= X305 )
| ( termmset != $true ) )
& ( ( shinj = $true )
| ? [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
= ( sub @ X186 @ sh ) )
& ( X186 != X187 ) ) )
& ( ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) )
| ( shinj != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X188: term,X189: term,X190: term,X191: term] :
( ( X190 != X191 )
& ( ( ap @ X189 @ X190 )
= ( ap @ X188 @ X191 ) ) ) )
& ( ( $true = sP37 )
| ( induction2lem_lthm != $true ) )
& ( ( induction2lem_lthm = $true )
| ( $true != sP37 ) )
& ( ! [X38: term] :
? [X39: subst > term > term] :
( ( X39 @ sh @ one )
= ( sub @ X38 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X38: term] :
! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) ) )
& ( ! [X40: term] :
? [X41: subst > term > term] :
! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X40: term] :
! [X41: subst > term > term] :
? [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
!= ( sub @ X40 @ ( push @ X42 @ X43 ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( $true = sP33 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP33 ) )
& ( ( $true = sP31 )
| ( hoasinduction_lem3aa != $true ) )
& ( ( hoasinduction_lem3aa = $true )
| ( $true != sP31 ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( sP30 = $true )
| ( hoasinduction_lem3a != $true ) )
& ( ( hoasinduction_lem3a = $true )
| ( sP30 != $true ) )
& ( ( induction2 = $true )
| ( $true != sP29 ) )
& ( ( $true = sP29 )
| ( induction2 != $true ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
!= ( d2subst @ X349 ) )
| ( X348 = X349 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ? [X157: term] :
( ( sub @ X157 @ id )
!= X157 )
| ! [X158: term] :
( ( sub @ X158 @ id )
= X158 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ! [X157: term] :
( ( sub @ X157 @ id )
= X157 )
& ? [X158: term] :
( ( sub @ X158 @ id )
!= X158 ) ) )
& ( ( sP27 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP27 != $true ) )
& ( ( $true = sP26 )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( $true != sP26 ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
| ( $true != sP24 ) )
& ( ( $true = sP24 )
| ( hoaslaminj_lthm != $true ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
| ? [X4: subst] :
( ( comp @ X4 @ id )
!= X4 ) )
& ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 )
| ( axidr != $true ) )
& ( ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) )
| ? [X306: term,X307: term,X308: term,X309: term] :
( ( X306 != X308 )
& ( ( ap @ X307 @ X308 )
= ( ap @ X309 @ X306 ) ) )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( ? [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
& ( X311 != X312 ) )
& ! [X306: term,X307: term,X308: term,X309: term] :
( ( X306 = X308 )
| ( ( ap @ X307 @ X308 )
!= ( ap @ X309 @ X306 ) ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
| ? [X207: subst,X208: term,X209: term > $o] :
! [X210: term > $o] :
? [X211: term] :
( ( X210 @ X211 )
!= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) ) )
& ( ! [X207: subst,X208: term,X209: term > $o] :
? [X210: term > $o] :
! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( $true != sP23 ) )
& ( ( $true = sP23 )
| ( induction2_lthm != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
| ( hoasapinj1 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
& ( X484 != X486 ) ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( $true != sP19 ) )
& ( ( $true = sP19 )
| ( hoasinduction_lthm_3 != $true ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( $true = sP13 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( $true != sP13 ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ! [X304: term] :
( ( X303 @ X304 )
= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
& ( $true
= ( X302 @ X301 ) )
& ( $true
!= ( X303 @ one ) ) ) )
& ( ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ? [X304: term] :
( ( X303 @ X304 )
!= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X0: term] :
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& ( ! [X0: term] :
? [X1: subst > term > term] :
( ( X1 @ sh @ one )
= ( sub @ X0 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( $true != sP4 ) )
& ( ( $true = sP4 )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ? [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
!= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) )
| ? [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
!= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ! [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
& ( ( X491 @ X489 @ X488 )
!= ( X490 @ X489 @ X488 ) )
& ! [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
& ( ( lam @ ( X491 @ sh @ one ) )
= ( lam @ ( X490 @ sh @ one ) ) ) ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ( sP58 = $true )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( $true = sP57 )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( $true = sP56 )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X48: d_subst] : ( d_id = X48 )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ? [X469: subst > term > term] :
( ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) )
& ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
& ( $true
!= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( sP53 @ X468 ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ? [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
!= X351 )
| ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ? [X356: term] :
( ( X354 @ X356 )
!= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
<=> ( axvarid = $true ) )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
<=> ( axshiftcons = $true ) )
& ( ! [X204: subst > term > subst > $o] :
? [X205: term > $o] :
! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ( $true = sP52 ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
<=> ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) ) )
& ( ( hoasapinj2 = $true )
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) ) )
& ( ( hoasinduction_lem3 = $true )
<=> ( $true = sP51 ) )
& ( ( d2subst @ d_id )
= id )
& ! [X168: d_term,X169: d_term] :
( ( X168 = X169 )
| ( ( d2term @ X169 )
!= ( d2term @ X168 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( $true = sP49 )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X249: term,X250: term,X251: subst > term > term] :
( ? [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
!= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
| ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( $true = sP47 ) )
& ( hoasapinj1_gthm = $true )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ( ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) )
| ? [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
!= X291 )
| ? [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
!= X293 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
<=> ( axidl = $true ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ? [X85: term,X86: term,X87: term,X88: term] :
( ( X85 != X86 )
& ( ( ap @ X85 @ X87 )
= ( ap @ X86 @ X88 ) ) )
| ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 )
| ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) ) ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
<=> ( substmonoid = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
<=> ! [X54: term,X55: term > $o] :
( ( $true
= ( X55 @ X54 ) )
| ( $true
= ( sP45 @ X55 ) )
| ? [X56: term] :
( ( $true
= ( var @ X56 ) )
& ( $true
!= ( X55 @ X56 ) ) )
| ? [X57: term] :
( ( $true
= ( X55 @ X57 ) )
& ( $true
!= ( X55 @ ( lam @ X57 ) ) ) ) ) )
& ( ! [X49: term > $o,X50: subst,X51: term] :
? [X52: term > $o] :
! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( ( axvarcons = $true )
<=> ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
<=> ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X216: subst > term > subst > $o] :
? [X217: term > $o] :
! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) ) )
& ( apnotvar = $true )
& ( ( $true = sP44 )
<=> ( hoasinduction = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ? [X345: subst] :
( ( comp @ X345 @ id )
!= X345 )
| ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) )
| ? [X344: subst] :
( ( comp @ id @ X344 )
!= X344 ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ( $true = sP41 ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ( $true = sP39 ) )
& ( pushprop_gthm = $true )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
<=> ( axscons = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X445: term] :
? [X446: subst > term > term] :
! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) ) )
& ( ( termmset = $true )
<=> ! [X305: term] :
( ( sub @ X305 @ id )
= X305 ) )
& ( ( shinj = $true )
<=> ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
<=> ( apinj2 = $true ) )
& ( ( $true = sP37 )
<=> ( induction2lem_lthm = $true ) )
& ( ! [X38: term] :
? [X39: subst > term > term] :
( ( X39 @ sh @ one )
= ( sub @ X38 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ! [X40: term] :
? [X41: subst > term > term] :
! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( $true = sP33 )
<=> ( induction2lem = $true ) )
& ( ( $true = sP31 )
<=> ( hoasinduction_lem3aa = $true ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( sP30 = $true )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( induction2 = $true )
<=> ( $true = sP29 ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
!= ( d2subst @ X349 ) )
| ( X348 = X349 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( ? [X157: term] :
( ( sub @ X157 @ id )
!= X157 )
| ! [X158: term] :
( ( sub @ X158 @ id )
= X158 ) )
<=> ( termmset_lthm = $true ) )
& ( ( sP27 = $true )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( $true = sP26 )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( $true = sP24 ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ( ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) )
| ? [X306: term,X307: term,X308: term,X309: term] :
( ( X306 != X308 )
& ( ( ap @ X307 @ X308 )
= ( ap @ X309 @ X306 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X207: subst,X208: term,X209: term > $o] :
? [X210: term > $o] :
! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) ) )
& ( ( induction2_lthm = $true )
<=> ( $true = sP23 ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
<=> ( hoasapinj1 = $true ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( $true = sP19 ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( $true = sP13 )
<=> ( hoasinduction_lthm = $true ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ? [X304: term] :
( ( X303 @ X304 )
!= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) ) ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X0: term] :
? [X1: subst > term > term] :
( ( X1 @ sh @ one )
= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( $true = sP4 ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ? [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
!= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) )
| ? [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
!= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( axassoc = $true )
& ( hoasapinj2_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,
! [X240: subst > term > subst > $o] :
( ( $true
= ( sP0 @ X240 ) )
<=> ? [X242: term,X243: term] :
( ( $true
= ( X240 @ id @ X243 @ id ) )
& ( ( X240 @ id @ X242 @ id )
= $true )
& ( $true
!= ( X240 @ id @ ( ap @ ( sub @ X242 @ id ) @ X243 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
! [X222: term > $o] :
( ( $true
= ( sP1 @ X222 ) )
<=> ! [X227: term,X228: term] :
( ( $true
= ( X222 @ ( ap @ X228 @ X227 ) ) )
| ( $true
!= ( X222 @ X227 ) )
| ( $true
!= ( X222 @ X228 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( $true = sP2 )
<=> ? [X230: term,X231: term > $o,X232: subst > term > subst > $o] :
( ! [X233: term] :
( ( ( X231 @ ( sub @ X230 @ ( push @ X233 @ id ) ) )
= $true )
| ( $true
!= ( X231 @ X233 ) ) )
& ! [X234: subst > term > term] :
( ( $true
= ( X232 @ id @ ( lam @ ( X234 @ sh @ one ) ) @ id ) )
| ? [X236: term,X237: subst,X238: subst] :
( ( X234 @ ( comp @ X237 @ X238 ) @ ( sub @ X236 @ X238 ) )
!= ( sub @ ( X234 @ X237 @ X236 ) @ X238 ) )
| ? [X235: term] :
( ( $true
!= ( X232 @ id @ ( X234 @ id @ X235 ) @ id ) )
& ( $true
= ( X232 @ id @ X235 @ id ) ) ) )
& ( $true
!= ( X231 @ ( lam @ X230 ) ) )
& ! [X239: term] :
( ( X232 @ id @ X239 @ id )
= ( X231 @ X239 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( $true = sP3 )
<=> ! [X240: subst > term > subst > $o,X241: term] :
( ( $true
= ( X240 @ id @ X241 @ id ) )
| ? [X244: subst > term > term] :
( ! [X245: term] :
( ( $true
!= ( X240 @ id @ X245 @ id ) )
| ( $true
= ( X240 @ id @ ( X244 @ id @ X245 ) @ id ) ) )
& ! [X246: subst,X247: term,X248: subst] :
( ( X244 @ ( comp @ X246 @ X248 ) @ ( sub @ X247 @ X248 ) )
= ( sub @ ( X244 @ X246 @ X247 ) @ X248 ) )
& ( $true
!= ( X240 @ id @ ( lam @ ( X244 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( sP0 @ X240 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
( ( $true = sP4 )
<=> ( ? [X222: term > $o,X223: term] :
( ( $true
!= ( X222 @ X223 ) )
& ! [X225: term] :
( ? [X226: term] :
( ( $true
!= ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) )
& ( $true
= ( X222 @ X226 ) ) )
| ( $true
= ( X222 @ ( lam @ X225 ) ) ) )
& ! [X224: term] :
( ( $true
!= ( var @ X224 ) )
| ( ( X222 @ X224 )
= $true ) )
& ( $true
= ( sP1 @ X222 ) ) )
| ? [X229: term] :
( ( sub @ X229 @ id )
!= X229 )
| ( $true = sP2 )
| ? [X219: subst > term > subst > $o] :
! [X220: term > $o] :
? [X221: term] :
( ( X219 @ id @ X221 @ id )
!= ( X220 @ X221 ) )
| ( $true = sP3 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X411: subst > term > subst > $o] :
( ( ( sP5 @ X411 )
= $true )
<=> ! [X421: subst > term > term] :
( ? [X423: subst,X424: subst,X425: term] :
( ( sub @ ( X421 @ X424 @ X425 ) @ X423 )
!= ( X421 @ ( comp @ X424 @ X423 ) @ ( sub @ X425 @ X423 ) ) )
| ? [X422: term] :
( ( $true
= ( X411 @ id @ X422 @ id ) )
& ( ( X411 @ id @ ( X421 @ id @ X422 ) @ id )
!= $true ) )
| ( ( X411 @ id @ ( lam @ ( X421 @ sh @ one ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
! [X400: subst > term > subst > $o] :
( ( ( sP6 @ X400 )
= $true )
<=> ! [X409: term,X410: term] :
( ( $true
!= ( X400 @ id @ X410 @ id ) )
| ( $true
!= ( X400 @ id @ X409 @ id ) )
| ( $true
= ( X400 @ id @ ( ap @ ( sub @ X409 @ id ) @ X410 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
! [X391: term > $o] :
( ( $true
= ( sP7 @ X391 ) )
<=> ! [X396: term,X397: term] :
( ( $true
= ( X391 @ ( ap @ X396 @ X397 ) ) )
| ( ( X391 @ X397 )
!= $true )
| ( ( X391 @ X396 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X428: subst > term > subst > $o] :
( ( $true
= ( sP8 @ X428 ) )
<=> ? [X440: subst > term > term] :
( ! [X441: term] :
( ( $true
!= ( X428 @ id @ X441 @ id ) )
| ( $true
= ( X428 @ id @ ( X440 @ id @ X441 ) @ id ) ) )
& ! [X442: subst,X443: subst,X444: term] :
( ( X440 @ ( comp @ X442 @ X443 ) @ ( sub @ X444 @ X443 ) )
= ( sub @ ( X440 @ X442 @ X444 ) @ X443 ) )
& ( ( X428 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
! [X428: subst > term > subst > $o] :
( ( $true
= ( sP9 @ X428 ) )
<=> ? [X438: term,X439: term] :
( ( $true
= ( X428 @ id @ X438 @ id ) )
& ( ( X428 @ id @ X439 @ id )
= $true )
& ( ( X428 @ id @ ( ap @ ( sub @ X438 @ id ) @ X439 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
( ( $true = sP10 )
<=> ? [X411: subst > term > subst > $o,X412: term] :
( ! [X413: subst,X414: term,X415: subst,X416: subst] :
( ( $true
!= ( X411 @ X415 @ X414 @ ( comp @ X416 @ X413 ) ) )
| ( $true
= ( X411 @ ( comp @ X415 @ X416 ) @ ( sub @ X414 @ X416 ) @ X413 ) ) )
& ( ( sP5 @ X411 )
= $true )
& ( $true
!= ( X411 @ id @ ( lam @ X412 ) @ id ) )
& ! [X426: term] :
( ( $true
!= ( X411 @ id @ X426 @ id ) )
| ( $true
= ( X411 @ id @ ( sub @ X412 @ ( push @ X426 @ id ) ) @ id ) ) )
& ! [X417: subst,X418: subst,X419: term,X420: subst] :
( ( $true
!= ( X411 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) @ X417 ) )
| ( $true
= ( X411 @ X418 @ X419 @ ( comp @ X420 @ X417 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( $true = sP11 )
<=> ! [X427: term,X428: subst > term > subst > $o] :
( ( $true
= ( sP9 @ X428 ) )
| ? [X434: subst,X435: subst,X436: subst,X437: term] :
( ( $true
!= ( X428 @ ( comp @ X436 @ X434 ) @ ( sub @ X437 @ X434 ) @ X435 ) )
& ( ( X428 @ X436 @ X437 @ ( comp @ X434 @ X435 ) )
= $true ) )
| ( $true
= ( X428 @ id @ X427 @ id ) )
| ? [X430: subst,X431: subst,X432: term,X433: subst] :
( ( $true
= ( X428 @ ( comp @ X430 @ X431 ) @ ( sub @ X432 @ X431 ) @ X433 ) )
& ( ( X428 @ X430 @ X432 @ ( comp @ X431 @ X433 ) )
!= $true ) )
| ? [X429: term] :
( ( $true
= ( var @ ( sub @ X429 @ id ) ) )
& ( $true
!= ( X428 @ id @ X429 @ id ) ) )
| ( $true
= ( sP8 @ X428 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
( ( $true = sP12 )
<=> ? [X398: term,X399: term,X400: subst > term > subst > $o] :
( ( $true
= ( X400 @ id @ X399 @ id ) )
& ! [X401: subst,X402: subst,X403: term,X404: subst] :
( ( $true
!= ( X400 @ ( comp @ X402 @ X401 ) @ ( sub @ X403 @ X401 ) @ X404 ) )
| ( $true
= ( X400 @ X402 @ X403 @ ( comp @ X401 @ X404 ) ) ) )
& ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X400 @ ( comp @ X407 @ X406 ) @ ( sub @ X405 @ X406 ) @ X408 ) )
| ( $true
!= ( X400 @ X407 @ X405 @ ( comp @ X406 @ X408 ) ) ) )
& ( ( sP6 @ X400 )
= $true )
& ( $true
!= ( X400 @ id @ ( ap @ X398 @ X399 ) @ id ) )
& ( $true
= ( X400 @ id @ X398 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( $true = sP13 )
<=> ( ( $true = sP11 )
| ? [X391: term > $o,X392: term] :
( ( $true
!= ( X391 @ X392 ) )
& ! [X394: term] :
( ( $true
= ( X391 @ ( lam @ X394 ) ) )
| ? [X395: term] :
( ( $true
= ( X391 @ X395 ) )
& ( $true
!= ( X391 @ ( sub @ X394 @ ( push @ X395 @ id ) ) ) ) ) )
& ( $true
= ( sP7 @ X391 ) )
& ! [X393: term] :
( ( $true
= ( X391 @ X393 ) )
| ( $true
!= ( var @ X393 ) ) ) )
| ( $true = sP12 )
| ( $true = sP10 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X522: subst > term > subst > $o] :
( ( $true
= ( sP14 @ X522 ) )
<=> ? [X538: term,X539: term] :
( ( ( X522 @ id @ X539 @ id )
= $true )
& ( $true
!= ( X522 @ id @ ( ap @ ( sub @ X538 @ id ) @ X539 ) @ id ) )
& ( $true
= ( X522 @ id @ X538 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
! [X522: subst > term > subst > $o] :
( ( $true
= ( sP15 @ X522 ) )
<=> ? [X529: subst > term > term] :
( ! [X533: term] :
( ( ( X522 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X522 @ id @ X533 @ id )
!= $true ) )
& ! [X530: subst,X531: subst,X532: term] :
( ( X529 @ ( comp @ X530 @ X531 ) @ ( sub @ X532 @ X531 ) )
= ( sub @ ( X529 @ X530 @ X532 ) @ X531 ) )
& ( ( X522 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
! [X504: term > $o] :
( ( ( sP16 @ X504 )
= $true )
<=> ! [X506: term,X507: term] :
( ( $true
= ( X504 @ ( ap @ X507 @ X506 ) ) )
| ( $true
!= ( X504 @ X507 ) )
| ( $true
!= ( X504 @ X506 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
( ( $true = sP17 )
<=> ! [X522: subst > term > subst > $o,X523: term] :
( ( $true
= ( sP15 @ X522 ) )
| ( $true
= ( X522 @ id @ X523 @ id ) )
| ? [X534: subst,X535: term,X536: subst,X537: subst] :
( ( $true
!= ( X522 @ ( comp @ X537 @ X536 ) @ ( sub @ X535 @ X536 ) @ X534 ) )
& ( $true
= ( X522 @ X537 @ X535 @ ( comp @ X536 @ X534 ) ) ) )
| ? [X524: term] :
( ( ( var @ ( sub @ X524 @ id ) )
= $true )
& ( $true
!= ( X522 @ id @ X524 @ id ) ) )
| ? [X525: subst,X526: term,X527: subst,X528: subst] :
( ( $true
= ( X522 @ ( comp @ X527 @ X525 ) @ ( sub @ X526 @ X525 ) @ X528 ) )
& ( $true
!= ( X522 @ X527 @ X526 @ ( comp @ X525 @ X528 ) ) ) )
| ( $true
= ( sP14 @ X522 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
( ( $true = sP18 )
<=> ? [X512: term,X513: subst > term > subst > $o,X514: term > $o] :
( ! [X520: term] :
( ( ( X514 @ ( sub @ X512 @ ( push @ X520 @ id ) ) )
= $true )
| ( $true
!= ( X514 @ X520 ) ) )
& ! [X515: subst > term > term] :
( ? [X519: term] :
( ( $true
!= ( X513 @ id @ ( X515 @ id @ X519 ) @ id ) )
& ( ( X513 @ id @ X519 @ id )
= $true ) )
| ? [X516: subst,X517: term,X518: subst] :
( ( sub @ ( X515 @ X516 @ X517 ) @ X518 )
!= ( X515 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) ) )
| ( ( X513 @ id @ ( lam @ ( X515 @ sh @ one ) ) @ id )
= $true ) )
& ! [X521: term] :
( ( X514 @ X521 )
= ( X513 @ id @ X521 @ id ) )
& ( $true
!= ( X514 @ ( lam @ X512 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
( ( $true = sP19 )
<=> ( ? [X504: term > $o,X505: term] :
( ( ( sP16 @ X504 )
= $true )
& ( $true
!= ( X504 @ X505 ) )
& ! [X509: term] :
( ( $true
= ( X504 @ ( lam @ X509 ) ) )
| ? [X510: term] :
( ( ( X504 @ ( sub @ X509 @ ( push @ X510 @ id ) ) )
!= $true )
& ( ( X504 @ X510 )
= $true ) ) )
& ! [X508: term] :
( ( $true
= ( X504 @ X508 ) )
| ( $true
!= ( var @ X508 ) ) ) )
| ( $true = sP18 )
| ? [X501: subst > term > subst > $o] :
! [X502: term > $o] :
? [X503: term] :
( ( X501 @ id @ X503 @ id )
!= ( X502 @ X503 ) )
| ( $true = sP17 )
| ? [X511: term] :
( ( sub @ X511 @ id )
!= X511 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
! [X453: term > $o] :
( ( $true
= ( sP20 @ X453 ) )
<=> ! [X455: term,X456: term] :
( ( $true
= ( X453 @ ( ap @ X455 @ X456 ) ) )
| ( $true
!= ( X453 @ X455 ) )
| ( $true
!= ( X453 @ X456 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
! [X460: term > $o] :
( ( ( sP21 @ X460 )
= $true )
<=> ? [X465: term,X466: term] :
( ( $true
= ( X460 @ X465 ) )
& ( $true
!= ( X460 @ ( ap @ X465 @ X466 ) ) )
& ( $true
= ( X460 @ X466 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
( ( $true = sP22 )
<=> ! [X460: term > $o,X461: term] :
( ( $true
= ( X460 @ X461 ) )
| ? [X462: term] :
( ( $true
= ( var @ X462 ) )
& ( ( X460 @ X462 )
!= $true ) )
| ? [X463: term] :
( ( $true
!= ( X460 @ ( lam @ X463 ) ) )
& ! [X464: term] :
( ( $true
!= ( X460 @ X464 ) )
| ( ( X460 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
= $true ) ) )
| ( ( sP21 @ X460 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
( ( $true = sP23 )
<=> ( ( $true = sP22 )
| ? [X452: subst,X453: term > $o,X454: term] :
( ( $true
= ( sP20 @ X453 ) )
& ( $true
!= ( X453 @ ( sub @ X454 @ X452 ) ) )
& ! [X458: term] :
( ? [X459: term] :
( ( ( X453 @ ( sub @ X458 @ ( push @ X459 @ id ) ) )
!= $true )
& ( $true
= ( X453 @ X459 ) ) )
| ( $true
= ( X453 @ ( lam @ X458 ) ) ) )
& ! [X457: term] :
( ( $true
= ( X453 @ ( sub @ X457 @ X452 ) ) )
| ( $true
!= ( var @ X457 ) ) ) )
| ? [X451: term] :
( ( sub @ X451 @ id )
!= X451 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
( ( $true = sP24 )
<=> ( ? [X174: term,X175: term] :
( ( ( lam @ X175 )
= ( lam @ X174 ) )
& ( X174 != X175 ) )
| ? [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
!= X170 )
| ? [X172: term,X173: subst] :
( ( comp @ sh @ ( push @ X172 @ X173 ) )
!= X173 )
| ! [X176: subst > term > term,X177: subst,X178: term,X179: subst > term > term] :
( ( ( X179 @ X177 @ X178 )
= ( X176 @ X177 @ X178 ) )
| ? [X183: subst,X184: subst,X185: term] :
( ( sub @ ( X176 @ X183 @ X185 ) @ X184 )
!= ( X176 @ ( comp @ X183 @ X184 ) @ ( sub @ X185 @ X184 ) ) )
| ? [X180: subst,X181: term,X182: subst] :
( ( sub @ ( X179 @ X182 @ X181 ) @ X180 )
!= ( X179 @ ( comp @ X182 @ X180 ) @ ( sub @ X181 @ X180 ) ) )
| ( ( lam @ ( X176 @ sh @ one ) )
!= ( lam @ ( X179 @ sh @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
! [X265: subst > term > subst > $o] :
( ( $true
= ( sP25 @ X265 ) )
<=> ? [X270: subst > term > term] :
( ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
& ( $true
!= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
& ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
( ( $true = sP26 )
<=> ! [X263: term,X264: term > $o,X265: subst > term > subst > $o] :
( ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( $true
= ( X265 @ ( comp @ X277 @ X276 ) @ ( sub @ X279 @ X276 ) @ X278 ) )
& ( $true
!= ( X265 @ X277 @ X279 @ ( comp @ X276 @ X278 ) ) ) )
| ( $true
= ( X264 @ ( lam @ X263 ) ) )
| ( $true
= ( sP25 @ X265 ) )
| ? [X275: term] :
( ( $true
!= ( X264 @ ( sub @ X263 @ ( push @ X275 @ id ) ) ) )
& ( ( X264 @ X275 )
= $true ) )
| ? [X266: term,X267: subst,X268: subst,X269: subst] :
( ( $true
!= ( X265 @ ( comp @ X269 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 ) )
& ( ( X265 @ X269 @ X266 @ ( comp @ X268 @ X267 ) )
= $true ) )
| ? [X280: term] :
( ( X265 @ id @ X280 @ id )
!= ( X264 @ X280 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
( ( sP27 = $true )
<=> ! [X255: subst > term > subst > $o,X256: term] :
( ? [X257: term] :
( ( $true
!= ( X255 @ id @ ( sub @ X256 @ ( push @ X257 @ id ) ) @ id ) )
& ( $true
= ( X255 @ id @ X257 @ id ) ) )
| ( ( X255 @ id @ ( lam @ ( sub @ X256 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X258: subst > term > term] :
( ( $true
!= ( X255 @ id @ ( lam @ ( X258 @ sh @ one ) ) @ id ) )
& ! [X259: subst,X260: subst,X261: term] :
( ( sub @ ( X258 @ X259 @ X261 ) @ X260 )
= ( X258 @ ( comp @ X259 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
& ! [X262: term] :
( ( $true
!= ( X255 @ id @ X262 @ id ) )
| ( ( X255 @ id @ ( X258 @ id @ X262 ) @ id )
= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
! [X283: term > $o] :
( ( $true
= ( sP28 @ X283 ) )
<=> ? [X288: term,X289: term] :
( ( $true
!= ( X283 @ ( ap @ X288 @ X289 ) ) )
& ( ( X283 @ X289 )
= $true )
& ( $true
= ( X283 @ X288 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
( ( $true = sP29 )
<=> ! [X283: term > $o,X284: term] :
( ? [X285: term] :
( ( $true
!= ( X283 @ ( lam @ X285 ) ) )
& ! [X286: term] :
( ( ( X283 @ ( sub @ X285 @ ( push @ X286 @ id ) ) )
= $true )
| ( $true
!= ( X283 @ X286 ) ) ) )
| ( $true
= ( X283 @ X284 ) )
| ? [X287: term] :
( ( $true
!= ( X283 @ X287 ) )
& ( $true
= ( var @ X287 ) ) )
| ( $true
= ( sP28 @ X283 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( sP30 = $true )
<=> ! [X476: subst > term > subst > $o,X477: term] :
( ( $true
= ( X476 @ id @ ( lam @ X477 ) @ id ) )
| ? [X483: term] :
( ( $true
!= ( X476 @ id @ ( sub @ X477 @ ( push @ X483 @ id ) ) @ id ) )
& ( $true
= ( X476 @ id @ X483 @ id ) ) )
| ? [X478: subst > term > term] :
( ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X482 @ X481 ) @ ( sub @ X480 @ X481 ) )
= ( sub @ ( X478 @ X482 @ X480 ) @ X481 ) )
& ! [X479: term] :
( ( $true
= ( X476 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X476 @ id @ X479 @ id ) ) )
& ( $true
!= ( X476 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
( ( $true = sP31 )
<=> ! [X159: subst > term > subst > $o,X160: term] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X164: subst,X165: subst,X166: term] :
( ( X162 @ ( comp @ X165 @ X164 ) @ ( sub @ X166 @ X164 ) )
= ( sub @ ( X162 @ X165 @ X166 ) @ X164 ) )
& ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) ) )
| ( ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X161: term] :
( ( $true
!= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) )
& ( $true
= ( X159 @ id @ X161 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
! [X78: term > $o] :
( ( $true
= ( sP32 @ X78 ) )
<=> ? [X82: term,X83: term] :
( ( $true
= ( X78 @ X83 ) )
& ( $true
= ( X78 @ X82 ) )
& ( ( X78 @ ( ap @ X83 @ X82 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
( ( $true = sP33 )
<=> ! [X76: term,X77: subst,X78: term > $o] :
( ? [X81: term] :
( ( $true
= ( var @ X81 ) )
& ( $true
!= ( X78 @ ( sub @ X81 @ X77 ) ) ) )
| ( $true
= ( X78 @ ( sub @ X76 @ X77 ) ) )
| ( $true
= ( sP32 @ X78 ) )
| ? [X79: term] :
( ! [X80: term] :
( ( ( X78 @ X80 )
!= $true )
| ( ( X78 @ ( sub @ X79 @ ( push @ X80 @ id ) ) )
= $true ) )
& ( ( X78 @ ( lam @ X79 ) )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
! [X327: term > $o] :
( ( $true
= ( sP34 @ X327 ) )
<=> ? [X328: term,X329: term] :
( ( $true
!= ( X327 @ ( ap @ X329 @ X328 ) ) )
& ( $true
= ( X327 @ X328 ) )
& ( $true
= ( X327 @ X329 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
! [X319: term > $o] :
( ( $true
= ( sP35 @ X319 ) )
<=> ! [X323: term,X324: term] :
( ( $true
!= ( X319 @ X324 ) )
| ( $true
= ( X319 @ ( ap @ X323 @ X324 ) ) )
| ( $true
!= ( X319 @ X323 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
( ( $true = sP36 )
<=> ! [X325: subst,X326: term,X327: term > $o] :
( ? [X330: term] :
( ( $true
= ( var @ X330 ) )
& ( $true
!= ( X327 @ ( sub @ X330 @ X325 ) ) ) )
| ( $true
= ( sP34 @ X327 ) )
| ( $true
= ( X327 @ ( sub @ X326 @ X325 ) ) )
| ? [X331: term] :
( ( ( X327 @ ( lam @ X331 ) )
!= $true )
& ! [X332: term] :
( ( $true
!= ( X327 @ X332 ) )
| ( $true
= ( X327 @ ( sub @ X331 @ ( push @ X332 @ id ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
( ( $true = sP37 )
<=> ( ? [X319: term > $o,X320: term] :
( ( $true
!= ( X319 @ X320 ) )
& ! [X322: term] :
( ( $true
= ( X319 @ X322 ) )
| ( $true
!= ( var @ X322 ) ) )
& ! [X321: term] :
( ( ( X319 @ ( lam @ X321 ) )
= $true )
| ( $true
!= ( X319 @ X321 ) ) )
& ( $true
= ( sP35 @ X319 ) ) )
| ? [X318: subst] :
( ( comp @ X318 @ id )
!= X318 )
| ? [X314: term,X315: subst] :
( ( sub @ one @ ( push @ X314 @ X315 ) )
!= X314 )
| ? [X316: term,X317: subst] :
( ( comp @ sh @ ( push @ X316 @ X317 ) )
!= X317 )
| ( $true = sP36 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
! [X24: subst > term > subst > $o] :
( ( $true
= ( sP38 @ X24 ) )
<=> ? [X31: term,X32: term] :
( ( $true
!= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
& ( $true
= ( X24 @ id @ X32 @ id ) )
& ( $true
= ( X24 @ id @ X31 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
( ( $true = sP39 )
<=> ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ? [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
!= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
& ( $true
= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ? [X27: subst,X28: subst,X29: subst,X30: term] :
( ( $true
= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) )
& ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
!= $true ) )
| ? [X37: term] :
( ( X26 @ X37 )
!= ( X24 @ id @ X37 @ id ) )
| ( ( X26 @ X23 )
!= $true )
| ( $true
!= ( X26 @ X25 ) )
| ( $true
= ( sP38 @ X24 ) )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X378: subst > term > subst > $o] :
( ( $true
= ( sP40 @ X378 ) )
<=> ? [X381: term,X382: term] :
( ( $true
= ( X378 @ id @ X382 @ id ) )
& ( ( X378 @ id @ X381 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( $true = sP41 )
<=> ! [X378: subst > term > subst > $o,X379: term,X380: term] :
( ? [X383: subst,X384: term,X385: subst,X386: subst] :
( ( $true
= ( X378 @ ( comp @ X386 @ X383 ) @ ( sub @ X384 @ X383 ) @ X385 ) )
& ( $true
!= ( X378 @ X386 @ X384 @ ( comp @ X383 @ X385 ) ) ) )
| ? [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
= ( X378 @ X390 @ X387 @ ( comp @ X389 @ X388 ) ) )
& ( $true
!= ( X378 @ ( comp @ X390 @ X389 ) @ ( sub @ X387 @ X389 ) @ X388 ) ) )
| ( $true
= ( sP40 @ X378 ) )
| ( $true
!= ( X378 @ id @ X380 @ id ) )
| ( $true
!= ( X378 @ id @ X379 @ id ) )
| ( $true
= ( X378 @ id @ ( ap @ X380 @ X379 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
! [X6: subst > term > subst > $o] :
( ( $true
= ( sP42 @ X6 ) )
<=> ? [X12: subst > term > term] :
( ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
& ! [X13: term] :
( ( ( X6 @ id @ X13 @ id )
!= $true )
| ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
& ( $true
!= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
! [X6: subst > term > subst > $o] :
( ( $true
= ( sP43 @ X6 ) )
<=> ? [X21: term,X22: term] :
( ( $true
= ( X6 @ id @ X22 @ id ) )
& ( $true
!= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) )
& ( $true
= ( X6 @ id @ X21 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
( ( $true = sP44 )
<=> ! [X5: term,X6: subst > term > subst > $o] :
( ? [X11: term] :
( ( $true
= ( var @ ( sub @ X11 @ id ) ) )
& ( $true
!= ( X6 @ id @ X11 @ id ) ) )
| ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
!= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
& ( $true
= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ( $true
= ( sP43 @ X6 ) )
| ? [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
& ( $true
= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ( $true
= ( sP42 @ X6 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
! [X55: term > $o] :
( ( $true
= ( sP45 @ X55 ) )
<=> ? [X58: term,X59: term] :
( ( $true
= ( X55 @ X58 ) )
& ( ( X55 @ ( ap @ X58 @ X59 ) )
!= $true )
& ( $true
= ( X55 @ X59 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
( ( sP46 = $true )
<=> ? [X121: term,X122: subst > term > subst > $o] :
( ! [X123: subst > term > term] :
( ? [X124: term] :
( ( $true
= ( X122 @ id @ X124 @ id ) )
& ( $true
!= ( X122 @ id @ ( X123 @ id @ X124 ) @ id ) ) )
| ? [X125: subst,X126: subst,X127: term] :
( ( sub @ ( X123 @ X125 @ X127 ) @ X126 )
!= ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id ) ) )
& ! [X128: term] :
( ( $true
!= ( X122 @ id @ X128 @ id ) )
| ( $true
= ( X122 @ id @ ( sub @ X121 @ ( push @ X128 @ id ) ) @ id ) ) )
& ( $true
!= ( X122 @ id @ ( lam @ ( sub @ X121 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
( ( $true = sP47 )
<=> ( ! [X129: subst > term > subst > $o,X130: term] :
( ( $true
= ( X129 @ id @ ( lam @ X130 ) @ id ) )
| ? [X131: subst > term > term] :
( ! [X133: subst,X134: subst,X135: term] :
( ( sub @ ( X131 @ X133 @ X135 ) @ X134 )
= ( X131 @ ( comp @ X133 @ X134 ) @ ( sub @ X135 @ X134 ) ) )
& ! [X132: term] :
( ( $true
= ( X129 @ id @ ( X131 @ id @ X132 ) @ id ) )
| ( $true
!= ( X129 @ id @ X132 @ id ) ) )
& ( $true
!= ( X129 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id ) ) )
| ? [X136: term] :
( ( $true
= ( X129 @ id @ X136 @ id ) )
& ( $true
!= ( X129 @ id @ ( sub @ X130 @ ( push @ X136 @ id ) ) @ id ) ) ) )
| ( sP46 = $true )
| ? [X120: term] :
( ( sub @ X120 @ id )
!= X120 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
! [X360: subst > term > subst > $o] :
( ( $true
= ( sP48 @ X360 ) )
<=> ? [X368: subst > term > term] :
( ! [X369: term] :
( ( $true
= ( X360 @ id @ ( X368 @ id @ X369 ) @ id ) )
| ( $true
!= ( X360 @ id @ X369 @ id ) ) )
& ! [X370: subst,X371: term,X372: subst] :
( ( sub @ ( X368 @ X370 @ X371 ) @ X372 )
= ( X368 @ ( comp @ X370 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ( $true
!= ( X360 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
( ( $true = sP49 )
<=> ( ? [X359: term] :
( ( sub @ X359 @ id )
!= X359 )
| ! [X360: subst > term > subst > $o,X361: term,X362: term > $o] :
( ? [X364: subst,X365: subst,X366: subst,X367: term] :
( ( $true
= ( X360 @ ( comp @ X366 @ X365 ) @ ( sub @ X367 @ X365 ) @ X364 ) )
& ( $true
!= ( X360 @ X366 @ X367 @ ( comp @ X365 @ X364 ) ) ) )
| ? [X363: term] :
( ( X362 @ X363 )
!= ( X360 @ id @ X363 @ id ) )
| ? [X373: subst,X374: subst,X375: subst,X376: term] :
( ( $true
= ( X360 @ X375 @ X376 @ ( comp @ X373 @ X374 ) ) )
& ( $true
!= ( X360 @ ( comp @ X375 @ X373 ) @ ( sub @ X376 @ X373 ) @ X374 ) ) )
| ? [X377: term] :
( ( $true
!= ( X362 @ ( sub @ X361 @ ( push @ X377 @ id ) ) ) )
& ( ( X362 @ X377 )
= $true ) )
| ( $true
= ( sP48 @ X360 ) )
| ( $true
= ( X362 @ ( lam @ X361 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
! [X61: subst > term > subst > $o] :
( ( $true
= ( sP50 @ X61 ) )
<=> ? [X63: subst > term > term] :
( ! [X65: term,X66: subst,X67: subst] :
( ( X63 @ ( comp @ X67 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( X63 @ X67 @ X65 ) @ X66 ) )
& ! [X64: term] :
( ( $true
!= ( X61 @ id @ X64 @ id ) )
| ( $true
= ( X61 @ id @ ( X63 @ id @ X64 ) @ id ) ) )
& ( $true
!= ( X61 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
( ( $true = sP51 )
<=> ! [X60: term,X61: subst > term > subst > $o] :
( ? [X68: subst,X69: subst,X70: subst,X71: term] :
( ( $true
= ( X61 @ X70 @ X71 @ ( comp @ X69 @ X68 ) ) )
& ( ( X61 @ ( comp @ X70 @ X69 ) @ ( sub @ X71 @ X69 ) @ X68 )
!= $true ) )
| ? [X62: term] :
( ( $true
!= ( X61 @ id @ ( sub @ X60 @ ( push @ X62 @ id ) ) @ id ) )
& ( ( X61 @ id @ X62 @ id )
= $true ) )
| ( $true
= ( sP50 @ X61 ) )
| ( $true
= ( X61 @ id @ ( lam @ X60 ) @ id ) )
| ? [X72: subst,X73: subst,X74: subst,X75: term] :
( ( $true
= ( X61 @ ( comp @ X73 @ X74 ) @ ( sub @ X75 @ X74 ) @ X72 ) )
& ( $true
!= ( X61 @ X73 @ X75 @ ( comp @ X74 @ X72 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
( ( $true = sP52 )
<=> ! [X192: term,X193: subst > term > subst > $o] :
( ? [X194: term] :
( ( $true
!= ( X193 @ id @ ( sub @ X192 @ ( push @ X194 @ id ) ) @ id ) )
& ( $true
= ( X193 @ id @ X194 @ id ) ) )
| ? [X195: subst > term > term,X196: term] :
( ! [X197: term] :
( ( $true
= ( X193 @ id @ ( X195 @ id @ X197 ) @ id ) )
| ( $true
!= ( X193 @ id @ X197 @ id ) ) )
& ! [X201: subst,X202: term,X203: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X202 @ X201 ) @ ( comp @ X203 @ X201 ) ) )
= ( X195 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
& ! [X198: term,X199: subst,X200: subst] :
( ( sub @ ( sub @ X196 @ ( push @ X198 @ X199 ) ) @ X200 )
= ( sub @ ( X195 @ X199 @ X198 ) @ X200 ) )
& ( ( X193 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X193 @ id @ ( lam @ ( sub @ X192 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
! [X468: subst > term > subst > $o] :
( ( $true
= ( sP53 @ X468 ) )
<=> ? [X474: term,X475: term] :
( ( $true
= ( X468 @ id @ X475 @ id ) )
& ( $true
!= ( X468 @ id @ ( ap @ ( sub @ X474 @ id ) @ X475 ) @ id ) )
& ( $true
= ( X468 @ id @ X474 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X105: subst > term > subst > $o] :
( ( $true
= ( sP54 @ X105 ) )
<=> ? [X106: subst > term > term] :
( ! [X107: term] :
( ( $true
= ( X105 @ id @ ( X106 @ id @ X107 ) @ id ) )
| ( $true
!= ( X105 @ id @ X107 @ id ) ) )
& ( $true
!= ( X105 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
& ! [X108: subst,X109: term,X110: subst] :
( ( X106 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X110 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
( ( $true = sP55 )
<=> ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( $true
!= ( X97 @ id @ X103 @ id ) )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( $true
= ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id ) )
| ? [X99: term,X100: subst,X101: subst] :
( ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) )
!= ( sub @ ( X98 @ X101 @ X99 ) @ X100 ) ) )
& ( $true
!= ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( $true = sP56 )
<=> ( ! [X104: term,X105: subst > term > subst > $o] :
( ( $true
= ( X105 @ id @ ( lam @ X104 ) @ id ) )
| ? [X111: subst,X112: term,X113: subst,X114: subst] :
( ( $true
= ( X105 @ X114 @ X112 @ ( comp @ X111 @ X113 ) ) )
& ( $true
!= ( X105 @ ( comp @ X114 @ X111 ) @ ( sub @ X112 @ X111 ) @ X113 ) ) )
| ( $true
= ( sP54 @ X105 ) )
| ? [X116: subst,X117: subst,X118: subst,X119: term] :
( ( $true
!= ( X105 @ X116 @ X119 @ ( comp @ X118 @ X117 ) ) )
& ( ( X105 @ ( comp @ X116 @ X118 ) @ ( sub @ X119 @ X118 ) @ X117 )
= $true ) )
| ? [X115: term] :
( ( $true
= ( X105 @ id @ X115 @ id ) )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X115 @ id ) ) @ id )
!= $true ) ) )
| ( $true = sP55 )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
( ( $true = sP57 )
<=> ( ! [X142: term,X143: subst > term > subst > $o,X144: term > $o] :
( ? [X151: term] :
( ( ( X144 @ X151 )
= $true )
& ( $true
!= ( X144 @ ( sub @ X142 @ ( push @ X151 @ id ) ) ) ) )
| ( $true
= ( X144 @ ( lam @ X142 ) ) )
| ? [X146: subst > term > term] :
( ! [X147: term,X148: subst,X149: subst] :
( ( X146 @ ( comp @ X149 @ X148 ) @ ( sub @ X147 @ X148 ) )
= ( sub @ ( X146 @ X149 @ X147 ) @ X148 ) )
& ! [X150: term] :
( ( $true
!= ( X143 @ id @ X150 @ id ) )
| ( ( X143 @ id @ ( X146 @ id @ X150 ) @ id )
= $true ) )
& ( ( X143 @ id @ ( lam @ ( X146 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X145: term] :
( ( X144 @ X145 )
!= ( X143 @ id @ X145 @ id ) ) )
| ? [X141: term] :
( ( sub @ X141 @ id )
!= X141 )
| ? [X137: term] :
! [X138: subst > term > term] :
? [X139: term,X140: subst] :
( ( X138 @ X140 @ X139 )
!= ( sub @ X137 @ ( push @ X139 @ X140 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
( ( sP58 = $true )
<=> ! [X333: term > $o,X334: subst > term > subst > $o,X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ? [X336: subst > term > term] :
( ! [X340: term] :
( ( $true
= ( X334 @ id @ ( X336 @ id @ X340 ) @ id ) )
| ( $true
!= ( X334 @ id @ X340 @ id ) ) )
& ( $true
!= ( X334 @ id @ ( lam @ ( X336 @ sh @ one ) ) @ id ) )
& ! [X337: subst,X338: subst,X339: term] :
( ( sub @ ( X336 @ X338 @ X339 ) @ X337 )
= ( X336 @ ( comp @ X338 @ X337 ) @ ( sub @ X339 @ X337 ) ) ) )
| ? [X341: term] :
( ( ( X333 @ X341 )
= $true )
& ( $true
!= ( X333 @ ( sub @ X335 @ ( push @ X341 @ id ) ) ) ) )
| ? [X342: term] :
( ( X334 @ id @ X342 @ id )
!= ( X333 @ X342 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( pushprop_lem2v2_lthm = $true )
& ( ! [X333: term > $o,X334: subst > term > subst > $o,X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ? [X336: subst > term > term] :
( ! [X340: term] :
( ( $true
= ( X334 @ id @ ( X336 @ id @ X340 ) @ id ) )
| ( $true
!= ( X334 @ id @ X340 @ id ) ) )
& ( $true
!= ( X334 @ id @ ( lam @ ( X336 @ sh @ one ) ) @ id ) )
& ! [X337: subst,X338: subst,X339: term] :
( ( sub @ ( X336 @ X338 @ X339 ) @ X337 )
= ( X336 @ ( comp @ X338 @ X337 ) @ ( sub @ X339 @ X337 ) ) ) )
| ? [X341: term] :
( ( ( X333 @ X341 )
= $true )
& ( $true
!= ( X333 @ ( sub @ X335 @ ( push @ X341 @ id ) ) ) ) )
| ? [X342: term] :
( ( X334 @ id @ X342 @ id )
!= ( X333 @ X342 ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( ! [X142: term,X143: subst > term > subst > $o,X144: term > $o] :
( ? [X151: term] :
( ( ( X144 @ X151 )
= $true )
& ( $true
!= ( X144 @ ( sub @ X142 @ ( push @ X151 @ id ) ) ) ) )
| ( $true
= ( X144 @ ( lam @ X142 ) ) )
| ? [X146: subst > term > term] :
( ! [X147: term,X148: subst,X149: subst] :
( ( X146 @ ( comp @ X149 @ X148 ) @ ( sub @ X147 @ X148 ) )
= ( sub @ ( X146 @ X149 @ X147 ) @ X148 ) )
& ! [X150: term] :
( ( $true
!= ( X143 @ id @ X150 @ id ) )
| ( ( X143 @ id @ ( X146 @ id @ X150 ) @ id )
= $true ) )
& ( ( X143 @ id @ ( lam @ ( X146 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X145: term] :
( ( X144 @ X145 )
!= ( X143 @ id @ X145 @ id ) ) )
| ? [X141: term] :
( ( sub @ X141 @ id )
!= X141 )
| ? [X137: term] :
! [X138: subst > term > term] :
? [X139: term,X140: subst] :
( ( X138 @ X140 @ X139 )
!= ( sub @ X137 @ ( push @ X139 @ X140 ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( ! [X104: term,X105: subst > term > subst > $o] :
( ( $true
= ( X105 @ id @ ( lam @ X104 ) @ id ) )
| ? [X111: subst,X112: term,X113: subst,X114: subst] :
( ( $true
= ( X105 @ X114 @ X112 @ ( comp @ X111 @ X113 ) ) )
& ( $true
!= ( X105 @ ( comp @ X114 @ X111 ) @ ( sub @ X112 @ X111 ) @ X113 ) ) )
| ? [X106: subst > term > term] :
( ! [X107: term] :
( ( $true
= ( X105 @ id @ ( X106 @ id @ X107 ) @ id ) )
| ( $true
!= ( X105 @ id @ X107 @ id ) ) )
& ( $true
!= ( X105 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
& ! [X108: subst,X109: term,X110: subst] :
( ( X106 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X110 ) ) )
| ? [X116: subst,X117: subst,X118: subst,X119: term] :
( ( $true
!= ( X105 @ X116 @ X119 @ ( comp @ X118 @ X117 ) ) )
& ( ( X105 @ ( comp @ X116 @ X118 ) @ ( sub @ X119 @ X118 ) @ X117 )
= $true ) )
| ? [X115: term] :
( ( $true
= ( X105 @ id @ X115 @ id ) )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X115 @ id ) ) @ id )
!= $true ) ) )
| ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( $true
!= ( X97 @ id @ X103 @ id ) )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( $true
= ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id ) )
| ? [X99: term,X100: subst,X101: subst] :
( ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) )
!= ( sub @ ( X98 @ X101 @ X99 ) @ X100 ) ) )
& ( $true
!= ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 ) )
<=> ( hoasinduction_lem3_lthm = $true ) )
& ( ulamvarsh = $true )
& ( hoasapnotvar_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X48: d_subst] : ( d_id = X48 )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ? [X469: subst > term > term] :
( ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) )
& ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
& ( $true
!= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
| ? [X474: term,X475: term] :
( ( $true
= ( X468 @ id @ X475 @ id ) )
& ( $true
!= ( X468 @ id @ ( ap @ ( sub @ X474 @ id ) @ X475 ) @ id ) )
& ( $true
= ( X468 @ id @ X474 @ id ) ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( termmset_gthm = $true )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ? [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
!= X351 )
| ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ? [X356: term] :
( ( X354 @ X356 )
!= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
<=> ( axvarid = $true ) )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
<=> ( axshiftcons = $true ) )
& ( ! [X204: subst > term > subst > $o] :
? [X205: term > $o] :
! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( lamnotap != $true )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X192: term,X193: subst > term > subst > $o] :
( ? [X194: term] :
( ( $true
!= ( X193 @ id @ ( sub @ X192 @ ( push @ X194 @ id ) ) @ id ) )
& ( $true
= ( X193 @ id @ X194 @ id ) ) )
| ? [X195: subst > term > term,X196: term] :
( ! [X197: term] :
( ( $true
= ( X193 @ id @ ( X195 @ id @ X197 ) @ id ) )
| ( $true
!= ( X193 @ id @ X197 @ id ) ) )
& ! [X201: subst,X202: term,X203: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X202 @ X201 ) @ ( comp @ X203 @ X201 ) ) )
= ( X195 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
& ! [X198: term,X199: subst,X200: subst] :
( ( sub @ ( sub @ X196 @ ( push @ X198 @ X199 ) ) @ X200 )
= ( sub @ ( X195 @ X199 @ X198 ) @ X200 ) )
& ( ( X193 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X193 @ id @ ( lam @ ( sub @ X192 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lthm = $true )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( laminj = $true )
<=> ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) ) )
& ( ( hoasapinj2 = $true )
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X60: term,X61: subst > term > subst > $o] :
( ? [X68: subst,X69: subst,X70: subst,X71: term] :
( ( $true
= ( X61 @ X70 @ X71 @ ( comp @ X69 @ X68 ) ) )
& ( ( X61 @ ( comp @ X70 @ X69 ) @ ( sub @ X71 @ X69 ) @ X68 )
!= $true ) )
| ? [X62: term] :
( ( $true
!= ( X61 @ id @ ( sub @ X60 @ ( push @ X62 @ id ) ) @ id ) )
& ( ( X61 @ id @ X62 @ id )
= $true ) )
| ? [X63: subst > term > term] :
( ! [X65: term,X66: subst,X67: subst] :
( ( X63 @ ( comp @ X67 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( X63 @ X67 @ X65 ) @ X66 ) )
& ! [X64: term] :
( ( $true
!= ( X61 @ id @ X64 @ id ) )
| ( $true
= ( X61 @ id @ ( X63 @ id @ X64 ) @ id ) ) )
& ( $true
!= ( X61 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X61 @ id @ ( lam @ X60 ) @ id ) )
| ? [X72: subst,X73: subst,X74: subst,X75: term] :
( ( $true
= ( X61 @ ( comp @ X73 @ X74 ) @ ( sub @ X75 @ X74 ) @ X72 ) )
& ( $true
!= ( X61 @ X73 @ X75 @ ( comp @ X74 @ X72 ) ) ) ) ) )
& ( ( d2subst @ d_id )
= id )
& ! [X168: d_term,X169: d_term] :
( ( X168 = X169 )
| ( ( d2term @ X169 )
!= ( d2term @ X168 ) ) )
& ( hoaslamnotap_lthm = $true )
& ( ( ? [X359: term] :
( ( sub @ X359 @ id )
!= X359 )
| ! [X360: subst > term > subst > $o,X361: term,X362: term > $o] :
( ? [X364: subst,X365: subst,X366: subst,X367: term] :
( ( $true
= ( X360 @ ( comp @ X366 @ X365 ) @ ( sub @ X367 @ X365 ) @ X364 ) )
& ( $true
!= ( X360 @ X366 @ X367 @ ( comp @ X365 @ X364 ) ) ) )
| ? [X363: term] :
( ( X362 @ X363 )
!= ( X360 @ id @ X363 @ id ) )
| ? [X373: subst,X374: subst,X375: subst,X376: term] :
( ( $true
= ( X360 @ X375 @ X376 @ ( comp @ X373 @ X374 ) ) )
& ( $true
!= ( X360 @ ( comp @ X375 @ X373 ) @ ( sub @ X376 @ X373 ) @ X374 ) ) )
| ? [X377: term] :
( ( $true
!= ( X362 @ ( sub @ X361 @ ( push @ X377 @ id ) ) ) )
& ( ( X362 @ X377 )
= $true ) )
| ? [X368: subst > term > term] :
( ! [X369: term] :
( ( $true
= ( X360 @ id @ ( X368 @ id @ X369 ) @ id ) )
| ( $true
!= ( X360 @ id @ X369 @ id ) ) )
& ! [X370: subst,X371: term,X372: subst] :
( ( sub @ ( X368 @ X370 @ X371 ) @ X372 )
= ( X368 @ ( comp @ X370 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ( $true
!= ( X360 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X362 @ ( lam @ X361 ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ( hoaslamnotap = $true )
<=> ! [X249: term,X250: term,X251: subst > term > term] :
( ? [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
!= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
| ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X129: subst > term > subst > $o,X130: term] :
( ( $true
= ( X129 @ id @ ( lam @ X130 ) @ id ) )
| ? [X131: subst > term > term] :
( ! [X133: subst,X134: subst,X135: term] :
( ( sub @ ( X131 @ X133 @ X135 ) @ X134 )
= ( X131 @ ( comp @ X133 @ X134 ) @ ( sub @ X135 @ X134 ) ) )
& ! [X132: term] :
( ( $true
= ( X129 @ id @ ( X131 @ id @ X132 ) @ id ) )
| ( $true
!= ( X129 @ id @ X132 @ id ) ) )
& ( $true
!= ( X129 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id ) ) )
| ? [X136: term] :
( ( $true
= ( X129 @ id @ X136 @ id ) )
& ( $true
!= ( X129 @ id @ ( sub @ X130 @ ( push @ X136 @ id ) ) @ id ) ) ) )
| ? [X121: term,X122: subst > term > subst > $o] :
( ! [X123: subst > term > term] :
( ? [X124: term] :
( ( $true
= ( X122 @ id @ X124 @ id ) )
& ( $true
!= ( X122 @ id @ ( X123 @ id @ X124 ) @ id ) ) )
| ? [X125: subst,X126: subst,X127: term] :
( ( sub @ ( X123 @ X125 @ X127 ) @ X126 )
!= ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id ) ) )
& ! [X128: term] :
( ( $true
!= ( X122 @ id @ X128 @ id ) )
| ( $true
= ( X122 @ id @ ( sub @ X121 @ ( push @ X128 @ id ) ) @ id ) ) )
& ( $true
!= ( X122 @ id @ ( lam @ ( sub @ X121 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X120: term] :
( ( sub @ X120 @ id )
!= X120 ) ) )
& ( hoasapinj1_gthm = $true )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ( ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) )
| ? [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
!= X291 )
| ? [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
!= X293 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
<=> ( axidl = $true ) )
& ( axabs = $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ? [X85: term,X86: term,X87: term,X88: term] :
( ( X85 != X86 )
& ( ( ap @ X85 @ X87 )
= ( ap @ X86 @ X88 ) ) )
| ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 )
| ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) ) ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
<=> ( substmonoid = $true ) )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( induction = $true )
<=> ! [X54: term,X55: term > $o] :
( ( $true
= ( X55 @ X54 ) )
| ? [X58: term,X59: term] :
( ( $true
= ( X55 @ X58 ) )
& ( ( X55 @ ( ap @ X58 @ X59 ) )
!= $true )
& ( $true
= ( X55 @ X59 ) ) )
| ? [X56: term] :
( ( $true
= ( var @ X56 ) )
& ( $true
!= ( X55 @ X56 ) ) )
| ? [X57: term] :
( ( $true
= ( X55 @ X57 ) )
& ( $true
!= ( X55 @ ( lam @ X57 ) ) ) ) ) )
& ( ! [X49: term > $o,X50: subst,X51: term] :
? [X52: term > $o] :
! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( ( axvarcons = $true )
<=> ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( axapp = $true )
& ( pushprop_lthm_orig = $true )
& ( ( apinj1 = $true )
<=> ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X216: subst > term > subst > $o] :
? [X217: term > $o] :
! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) ) )
& ( apnotvar = $true )
& ( ! [X5: term,X6: subst > term > subst > $o] :
( ? [X11: term] :
( ( $true
= ( var @ ( sub @ X11 @ id ) ) )
& ( $true
!= ( X6 @ id @ X11 @ id ) ) )
| ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
!= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
& ( $true
= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ? [X21: term,X22: term] :
( ( $true
= ( X6 @ id @ X22 @ id ) )
& ( $true
!= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) )
& ( $true
= ( X6 @ id @ X21 @ id ) ) )
| ? [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
& ( $true
= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ? [X12: subst > term > term] :
( ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
& ! [X13: term] :
( ( ( X6 @ id @ X13 @ id )
!= $true )
| ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
& ( $true
!= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( axclos = $true )
& ( hoasapnotvar_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( axvarshift = $true )
& ( hoasinduction_lem1 = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ? [X345: subst] :
( ( comp @ X345 @ id )
!= X345 )
| ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) )
| ? [X344: subst] :
( ( comp @ id @ X344 )
!= X344 ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X378: subst > term > subst > $o,X379: term,X380: term] :
( ? [X383: subst,X384: term,X385: subst,X386: subst] :
( ( $true
= ( X378 @ ( comp @ X386 @ X383 ) @ ( sub @ X384 @ X383 ) @ X385 ) )
& ( $true
!= ( X378 @ X386 @ X384 @ ( comp @ X383 @ X385 ) ) ) )
| ? [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
= ( X378 @ X390 @ X387 @ ( comp @ X389 @ X388 ) ) )
& ( $true
!= ( X378 @ ( comp @ X390 @ X389 ) @ ( sub @ X387 @ X389 ) @ X388 ) ) )
| ? [X381: term,X382: term] :
( ( $true
= ( X378 @ id @ X382 @ id ) )
& ( ( X378 @ id @ X381 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) ) )
| ( $true
!= ( X378 @ id @ X380 @ id ) )
| ( $true
!= ( X378 @ id @ X379 @ id ) )
| ( $true
= ( X378 @ id @ ( ap @ X380 @ X379 ) @ id ) ) ) )
& ( ulamvarind = $true )
& ( hoasinduction_lem3a_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 ) ) ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ? [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
!= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
& ( $true
= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ? [X27: subst,X28: subst,X29: subst,X30: term] :
( ( $true
= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) )
& ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
!= $true ) )
| ? [X37: term] :
( ( X26 @ X37 )
!= ( X24 @ id @ X37 @ id ) )
| ( ( X26 @ X23 )
!= $true )
| ( $true
!= ( X26 @ X25 ) )
| ? [X31: term,X32: term] :
( ( $true
!= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
& ( $true
= ( X24 @ id @ X32 @ id ) )
& ( $true
= ( X24 @ id @ X31 @ id ) ) )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true ) ) )
& ( pushprop_gthm = $true )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
<=> ( axscons = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X445: term] :
? [X446: subst > term > term] :
! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) ) )
& ( ( termmset = $true )
<=> ! [X305: term] :
( ( sub @ X305 @ id )
= X305 ) )
& ( ( shinj = $true )
<=> ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
<=> ( apinj2 = $true ) )
& ( ( ? [X319: term > $o,X320: term] :
( ( $true
!= ( X319 @ X320 ) )
& ! [X322: term] :
( ( $true
= ( X319 @ X322 ) )
| ( $true
!= ( var @ X322 ) ) )
& ! [X321: term] :
( ( ( X319 @ ( lam @ X321 ) )
= $true )
| ( $true
!= ( X319 @ X321 ) ) )
& ! [X323: term,X324: term] :
( ( $true
!= ( X319 @ X324 ) )
| ( $true
= ( X319 @ ( ap @ X323 @ X324 ) ) )
| ( $true
!= ( X319 @ X323 ) ) ) )
| ? [X318: subst] :
( ( comp @ X318 @ id )
!= X318 )
| ? [X314: term,X315: subst] :
( ( sub @ one @ ( push @ X314 @ X315 ) )
!= X314 )
| ? [X316: term,X317: subst] :
( ( comp @ sh @ ( push @ X316 @ X317 ) )
!= X317 )
| ! [X325: subst,X326: term,X327: term > $o] :
( ? [X330: term] :
( ( $true
= ( var @ X330 ) )
& ( $true
!= ( X327 @ ( sub @ X330 @ X325 ) ) ) )
| ? [X328: term,X329: term] :
( ( $true
!= ( X327 @ ( ap @ X329 @ X328 ) ) )
& ( $true
= ( X327 @ X328 ) )
& ( $true
= ( X327 @ X329 ) ) )
| ( $true
= ( X327 @ ( sub @ X326 @ X325 ) ) )
| ? [X331: term] :
( ( ( X327 @ ( lam @ X331 ) )
!= $true )
& ! [X332: term] :
( ( $true
!= ( X327 @ X332 ) )
| ( $true
= ( X327 @ ( sub @ X331 @ ( push @ X332 @ id ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( ! [X38: term] :
? [X39: subst > term > term] :
( ( X39 @ sh @ one )
= ( sub @ X38 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ! [X40: term] :
? [X41: subst > term > term] :
! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoasinduction_gthm = $true )
& ( ! [X76: term,X77: subst,X78: term > $o] :
( ? [X81: term] :
( ( $true
= ( var @ X81 ) )
& ( $true
!= ( X78 @ ( sub @ X81 @ X77 ) ) ) )
| ( $true
= ( X78 @ ( sub @ X76 @ X77 ) ) )
| ? [X82: term,X83: term] :
( ( $true
= ( X78 @ X83 ) )
& ( $true
= ( X78 @ X82 ) )
& ( ( X78 @ ( ap @ X83 @ X82 ) )
!= $true ) )
| ? [X79: term] :
( ! [X80: term] :
( ( ( X78 @ X80 )
!= $true )
| ( ( X78 @ ( sub @ X79 @ ( push @ X80 @ id ) ) )
= $true ) )
& ( ( X78 @ ( lam @ X79 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ! [X159: subst > term > subst > $o,X160: term] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X164: subst,X165: subst,X166: term] :
( ( X162 @ ( comp @ X165 @ X164 ) @ ( sub @ X166 @ X164 ) )
= ( sub @ ( X162 @ X165 @ X166 ) @ X164 ) )
& ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) ) )
| ( ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X161: term] :
( ( $true
!= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) )
& ( $true
= ( X159 @ id @ X161 @ id ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( axmap = $true )
& ( substmonoid_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslaminj_gthm = $true )
& ! [X343: d_term] : ( d_one = X343 )
& ( ! [X476: subst > term > subst > $o,X477: term] :
( ( $true
= ( X476 @ id @ ( lam @ X477 ) @ id ) )
| ? [X483: term] :
( ( $true
!= ( X476 @ id @ ( sub @ X477 @ ( push @ X483 @ id ) ) @ id ) )
& ( $true
= ( X476 @ id @ X483 @ id ) ) )
| ? [X478: subst > term > term] :
( ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X482 @ X481 ) @ ( sub @ X480 @ X481 ) )
= ( sub @ ( X478 @ X482 @ X480 ) @ X481 ) )
& ! [X479: term] :
( ( $true
= ( X476 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X476 @ id @ X479 @ id ) ) )
& ( $true
!= ( X476 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( induction2 = $true )
<=> ! [X283: term > $o,X284: term] :
( ? [X285: term] :
( ( $true
!= ( X283 @ ( lam @ X285 ) ) )
& ! [X286: term] :
( ( ( X283 @ ( sub @ X285 @ ( push @ X286 @ id ) ) )
= $true )
| ( $true
!= ( X283 @ X286 ) ) ) )
| ( $true
= ( X283 @ X284 ) )
| ? [X287: term] :
( ( $true
!= ( X283 @ X287 ) )
& ( $true
= ( var @ X287 ) ) )
| ? [X288: term,X289: term] :
( ( $true
!= ( X283 @ ( ap @ X288 @ X289 ) ) )
& ( ( X283 @ X289 )
= $true )
& ( $true
= ( X283 @ X288 ) ) ) ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
!= ( d2subst @ X349 ) )
| ( X348 = X349 ) )
& ( induction2_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( ? [X157: term] :
( ( sub @ X157 @ id )
!= X157 )
| ! [X158: term] :
( ( sub @ X158 @ id )
= X158 ) )
<=> ( termmset_lthm = $true ) )
& ( ! [X255: subst > term > subst > $o,X256: term] :
( ? [X257: term] :
( ( $true
!= ( X255 @ id @ ( sub @ X256 @ ( push @ X257 @ id ) ) @ id ) )
& ( $true
= ( X255 @ id @ X257 @ id ) ) )
| ( ( X255 @ id @ ( lam @ ( sub @ X256 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X258: subst > term > term] :
( ( $true
!= ( X255 @ id @ ( lam @ ( X258 @ sh @ one ) ) @ id ) )
& ! [X259: subst,X260: subst,X261: term] :
( ( sub @ ( X258 @ X259 @ X261 ) @ X260 )
= ( X258 @ ( comp @ X259 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
& ! [X262: term] :
( ( $true
!= ( X255 @ id @ X262 @ id ) )
| ( ( X255 @ id @ ( X258 @ id @ X262 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ! [X263: term,X264: term > $o,X265: subst > term > subst > $o] :
( ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( $true
= ( X265 @ ( comp @ X277 @ X276 ) @ ( sub @ X279 @ X276 ) @ X278 ) )
& ( $true
!= ( X265 @ X277 @ X279 @ ( comp @ X276 @ X278 ) ) ) )
| ( $true
= ( X264 @ ( lam @ X263 ) ) )
| ? [X270: subst > term > term] :
( ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
& ( $true
!= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
& ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) ) )
| ? [X275: term] :
( ( $true
!= ( X264 @ ( sub @ X263 @ ( push @ X275 @ id ) ) ) )
& ( ( X264 @ X275 )
= $true ) )
| ? [X266: term,X267: subst,X268: subst,X269: subst] :
( ( $true
!= ( X265 @ ( comp @ X269 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 ) )
& ( ( X265 @ X269 @ X266 @ ( comp @ X268 @ X267 ) )
= $true ) )
| ? [X280: term] :
( ( X265 @ id @ X280 @ id )
!= ( X264 @ X280 ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( pushprop = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ? [X174: term,X175: term] :
( ( ( lam @ X175 )
= ( lam @ X174 ) )
& ( X174 != X175 ) )
| ? [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
!= X170 )
| ? [X172: term,X173: subst] :
( ( comp @ sh @ ( push @ X172 @ X173 ) )
!= X173 )
| ! [X176: subst > term > term,X177: subst,X178: term,X179: subst > term > term] :
( ( ( X179 @ X177 @ X178 )
= ( X176 @ X177 @ X178 ) )
| ? [X183: subst,X184: subst,X185: term] :
( ( sub @ ( X176 @ X183 @ X185 ) @ X184 )
!= ( X176 @ ( comp @ X183 @ X184 ) @ ( sub @ X185 @ X184 ) ) )
| ? [X180: subst,X181: term,X182: subst] :
( ( sub @ ( X179 @ X182 @ X181 ) @ X180 )
!= ( X179 @ ( comp @ X182 @ X180 ) @ ( sub @ X181 @ X180 ) ) )
| ( ( lam @ ( X176 @ sh @ one ) )
!= ( lam @ ( X179 @ sh @ one ) ) ) ) ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ( ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) )
| ? [X306: term,X307: term,X308: term,X309: term] :
( ( X306 != X308 )
& ( ( ap @ X307 @ X308 )
= ( ap @ X309 @ X306 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X207: subst,X208: term,X209: term > $o] :
? [X210: term > $o] :
! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X460: term > $o,X461: term] :
( ( $true
= ( X460 @ X461 ) )
| ? [X462: term] :
( ( $true
= ( var @ X462 ) )
& ( ( X460 @ X462 )
!= $true ) )
| ? [X463: term] :
( ( $true
!= ( X460 @ ( lam @ X463 ) ) )
& ! [X464: term] :
( ( $true
!= ( X460 @ X464 ) )
| ( ( X460 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
= $true ) ) )
| ? [X465: term,X466: term] :
( ( $true
= ( X460 @ X465 ) )
& ( $true
!= ( X460 @ ( ap @ X465 @ X466 ) ) )
& ( $true
= ( X460 @ X466 ) ) ) )
| ? [X452: subst,X453: term > $o,X454: term] :
( ! [X455: term,X456: term] :
( ( $true
= ( X453 @ ( ap @ X455 @ X456 ) ) )
| ( $true
!= ( X453 @ X455 ) )
| ( $true
!= ( X453 @ X456 ) ) )
& ( $true
!= ( X453 @ ( sub @ X454 @ X452 ) ) )
& ! [X458: term] :
( ? [X459: term] :
( ( ( X453 @ ( sub @ X458 @ ( push @ X459 @ id ) ) )
!= $true )
& ( $true
= ( X453 @ X459 ) ) )
| ( $true
= ( X453 @ ( lam @ X458 ) ) ) )
& ! [X457: term] :
( ( $true
= ( X453 @ ( sub @ X457 @ X452 ) ) )
| ( $true
!= ( var @ X457 ) ) ) )
| ? [X451: term] :
( ( sub @ X451 @ id )
!= X451 ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
<=> ( hoasapinj1 = $true ) )
& ( hoasapnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ? [X504: term > $o,X505: term] :
( ! [X506: term,X507: term] :
( ( $true
= ( X504 @ ( ap @ X507 @ X506 ) ) )
| ( $true
!= ( X504 @ X507 ) )
| ( $true
!= ( X504 @ X506 ) ) )
& ( $true
!= ( X504 @ X505 ) )
& ! [X509: term] :
( ( $true
= ( X504 @ ( lam @ X509 ) ) )
| ? [X510: term] :
( ( ( X504 @ ( sub @ X509 @ ( push @ X510 @ id ) ) )
!= $true )
& ( ( X504 @ X510 )
= $true ) ) )
& ! [X508: term] :
( ( $true
= ( X504 @ X508 ) )
| ( $true
!= ( var @ X508 ) ) ) )
| ? [X512: term,X513: subst > term > subst > $o,X514: term > $o] :
( ! [X520: term] :
( ( ( X514 @ ( sub @ X512 @ ( push @ X520 @ id ) ) )
= $true )
| ( $true
!= ( X514 @ X520 ) ) )
& ! [X515: subst > term > term] :
( ? [X519: term] :
( ( $true
!= ( X513 @ id @ ( X515 @ id @ X519 ) @ id ) )
& ( ( X513 @ id @ X519 @ id )
= $true ) )
| ? [X516: subst,X517: term,X518: subst] :
( ( sub @ ( X515 @ X516 @ X517 ) @ X518 )
!= ( X515 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) ) )
| ( ( X513 @ id @ ( lam @ ( X515 @ sh @ one ) ) @ id )
= $true ) )
& ! [X521: term] :
( ( X514 @ X521 )
= ( X513 @ id @ X521 @ id ) )
& ( $true
!= ( X514 @ ( lam @ X512 ) ) ) )
| ? [X501: subst > term > subst > $o] :
! [X502: term > $o] :
? [X503: term] :
( ( X501 @ id @ X503 @ id )
!= ( X502 @ X503 ) )
| ! [X522: subst > term > subst > $o,X523: term] :
( ? [X529: subst > term > term] :
( ! [X533: term] :
( ( ( X522 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X522 @ id @ X533 @ id )
!= $true ) )
& ! [X530: subst,X531: subst,X532: term] :
( ( X529 @ ( comp @ X530 @ X531 ) @ ( sub @ X532 @ X531 ) )
= ( sub @ ( X529 @ X530 @ X532 ) @ X531 ) )
& ( ( X522 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X522 @ id @ X523 @ id ) )
| ? [X534: subst,X535: term,X536: subst,X537: subst] :
( ( $true
!= ( X522 @ ( comp @ X537 @ X536 ) @ ( sub @ X535 @ X536 ) @ X534 ) )
& ( $true
= ( X522 @ X537 @ X535 @ ( comp @ X536 @ X534 ) ) ) )
| ? [X524: term] :
( ( ( var @ ( sub @ X524 @ id ) )
= $true )
& ( $true
!= ( X522 @ id @ X524 @ id ) ) )
| ? [X525: subst,X526: term,X527: subst,X528: subst] :
( ( $true
= ( X522 @ ( comp @ X527 @ X525 ) @ ( sub @ X526 @ X525 ) @ X528 ) )
& ( $true
!= ( X522 @ X527 @ X526 @ ( comp @ X525 @ X528 ) ) ) )
| ? [X538: term,X539: term] :
( ( ( X522 @ id @ X539 @ id )
= $true )
& ( $true
!= ( X522 @ id @ ( ap @ ( sub @ X538 @ id ) @ X539 ) @ id ) )
& ( $true
= ( X522 @ id @ X538 @ id ) ) ) )
| ? [X511: term] :
( ( sub @ X511 @ id )
!= X511 ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ulamvar1 != $true )
& ( ( ! [X427: term,X428: subst > term > subst > $o] :
( ? [X438: term,X439: term] :
( ( $true
= ( X428 @ id @ X438 @ id ) )
& ( ( X428 @ id @ X439 @ id )
= $true )
& ( ( X428 @ id @ ( ap @ ( sub @ X438 @ id ) @ X439 ) @ id )
!= $true ) )
| ? [X434: subst,X435: subst,X436: subst,X437: term] :
( ( $true
!= ( X428 @ ( comp @ X436 @ X434 ) @ ( sub @ X437 @ X434 ) @ X435 ) )
& ( ( X428 @ X436 @ X437 @ ( comp @ X434 @ X435 ) )
= $true ) )
| ( $true
= ( X428 @ id @ X427 @ id ) )
| ? [X430: subst,X431: subst,X432: term,X433: subst] :
( ( $true
= ( X428 @ ( comp @ X430 @ X431 ) @ ( sub @ X432 @ X431 ) @ X433 ) )
& ( ( X428 @ X430 @ X432 @ ( comp @ X431 @ X433 ) )
!= $true ) )
| ? [X429: term] :
( ( $true
= ( var @ ( sub @ X429 @ id ) ) )
& ( $true
!= ( X428 @ id @ X429 @ id ) ) )
| ? [X440: subst > term > term] :
( ! [X441: term] :
( ( $true
!= ( X428 @ id @ X441 @ id ) )
| ( $true
= ( X428 @ id @ ( X440 @ id @ X441 ) @ id ) ) )
& ! [X442: subst,X443: subst,X444: term] :
( ( X440 @ ( comp @ X442 @ X443 ) @ ( sub @ X444 @ X443 ) )
= ( sub @ ( X440 @ X442 @ X444 ) @ X443 ) )
& ( ( X428 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X391: term > $o,X392: term] :
( ( $true
!= ( X391 @ X392 ) )
& ! [X394: term] :
( ( $true
= ( X391 @ ( lam @ X394 ) ) )
| ? [X395: term] :
( ( $true
= ( X391 @ X395 ) )
& ( $true
!= ( X391 @ ( sub @ X394 @ ( push @ X395 @ id ) ) ) ) ) )
& ! [X396: term,X397: term] :
( ( $true
= ( X391 @ ( ap @ X396 @ X397 ) ) )
| ( ( X391 @ X397 )
!= $true )
| ( ( X391 @ X396 )
!= $true ) )
& ! [X393: term] :
( ( $true
= ( X391 @ X393 ) )
| ( $true
!= ( var @ X393 ) ) ) )
| ? [X398: term,X399: term,X400: subst > term > subst > $o] :
( ( $true
= ( X400 @ id @ X399 @ id ) )
& ! [X401: subst,X402: subst,X403: term,X404: subst] :
( ( $true
!= ( X400 @ ( comp @ X402 @ X401 ) @ ( sub @ X403 @ X401 ) @ X404 ) )
| ( $true
= ( X400 @ X402 @ X403 @ ( comp @ X401 @ X404 ) ) ) )
& ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X400 @ ( comp @ X407 @ X406 ) @ ( sub @ X405 @ X406 ) @ X408 ) )
| ( $true
!= ( X400 @ X407 @ X405 @ ( comp @ X406 @ X408 ) ) ) )
& ! [X409: term,X410: term] :
( ( $true
!= ( X400 @ id @ X410 @ id ) )
| ( $true
!= ( X400 @ id @ X409 @ id ) )
| ( $true
= ( X400 @ id @ ( ap @ ( sub @ X409 @ id ) @ X410 ) @ id ) ) )
& ( $true
!= ( X400 @ id @ ( ap @ X398 @ X399 ) @ id ) )
& ( $true
= ( X400 @ id @ X398 @ id ) ) )
| ? [X411: subst > term > subst > $o,X412: term] :
( ! [X413: subst,X414: term,X415: subst,X416: subst] :
( ( $true
!= ( X411 @ X415 @ X414 @ ( comp @ X416 @ X413 ) ) )
| ( $true
= ( X411 @ ( comp @ X415 @ X416 ) @ ( sub @ X414 @ X416 ) @ X413 ) ) )
& ! [X421: subst > term > term] :
( ? [X423: subst,X424: subst,X425: term] :
( ( sub @ ( X421 @ X424 @ X425 ) @ X423 )
!= ( X421 @ ( comp @ X424 @ X423 ) @ ( sub @ X425 @ X423 ) ) )
| ? [X422: term] :
( ( $true
= ( X411 @ id @ X422 @ id ) )
& ( ( X411 @ id @ ( X421 @ id @ X422 ) @ id )
!= $true ) )
| ( ( X411 @ id @ ( lam @ ( X421 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( X411 @ id @ ( lam @ X412 ) @ id ) )
& ! [X426: term] :
( ( $true
!= ( X411 @ id @ X426 @ id ) )
| ( $true
= ( X411 @ id @ ( sub @ X412 @ ( push @ X426 @ id ) ) @ id ) ) )
& ! [X417: subst,X418: subst,X419: term,X420: subst] :
( ( $true
!= ( X411 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) @ X417 ) )
| ( $true
= ( X411 @ X418 @ X419 @ ( comp @ X420 @ X417 ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ? [X304: term] :
( ( X303 @ X304 )
!= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) ) ) )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X0: term] :
? [X1: subst > term > term] :
( ( X1 @ sh @ one )
= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ? [X222: term > $o,X223: term] :
( ( $true
!= ( X222 @ X223 ) )
& ! [X225: term] :
( ? [X226: term] :
( ( $true
!= ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) )
& ( $true
= ( X222 @ X226 ) ) )
| ( $true
= ( X222 @ ( lam @ X225 ) ) ) )
& ! [X224: term] :
( ( $true
!= ( var @ X224 ) )
| ( ( X222 @ X224 )
= $true ) )
& ! [X227: term,X228: term] :
( ( $true
= ( X222 @ ( ap @ X228 @ X227 ) ) )
| ( $true
!= ( X222 @ X227 ) )
| ( $true
!= ( X222 @ X228 ) ) ) )
| ? [X229: term] :
( ( sub @ X229 @ id )
!= X229 )
| ? [X230: term,X231: term > $o,X232: subst > term > subst > $o] :
( ! [X233: term] :
( ( ( X231 @ ( sub @ X230 @ ( push @ X233 @ id ) ) )
= $true )
| ( $true
!= ( X231 @ X233 ) ) )
& ! [X234: subst > term > term] :
( ( $true
= ( X232 @ id @ ( lam @ ( X234 @ sh @ one ) ) @ id ) )
| ? [X236: term,X237: subst,X238: subst] :
( ( X234 @ ( comp @ X237 @ X238 ) @ ( sub @ X236 @ X238 ) )
!= ( sub @ ( X234 @ X237 @ X236 ) @ X238 ) )
| ? [X235: term] :
( ( $true
!= ( X232 @ id @ ( X234 @ id @ X235 ) @ id ) )
& ( $true
= ( X232 @ id @ X235 @ id ) ) ) )
& ( $true
!= ( X231 @ ( lam @ X230 ) ) )
& ! [X239: term] :
( ( X232 @ id @ X239 @ id )
= ( X231 @ X239 ) ) )
| ? [X219: subst > term > subst > $o] :
! [X220: term > $o] :
? [X221: term] :
( ( X219 @ id @ X221 @ id )
!= ( X220 @ X221 ) )
| ! [X240: subst > term > subst > $o,X241: term] :
( ( $true
= ( X240 @ id @ X241 @ id ) )
| ? [X244: subst > term > term] :
( ! [X245: term] :
( ( $true
!= ( X240 @ id @ X245 @ id ) )
| ( $true
= ( X240 @ id @ ( X244 @ id @ X245 ) @ id ) ) )
& ! [X246: subst,X247: term,X248: subst] :
( ( X244 @ ( comp @ X246 @ X248 ) @ ( sub @ X247 @ X248 ) )
= ( sub @ ( X244 @ X246 @ X247 ) @ X248 ) )
& ( $true
!= ( X240 @ id @ ( lam @ ( X244 @ sh @ one ) ) @ id ) ) )
| ? [X242: term,X243: term] :
( ( $true
= ( X240 @ id @ X243 @ id ) )
& ( ( X240 @ id @ X242 @ id )
= $true )
& ( $true
!= ( X240 @ id @ ( ap @ ( sub @ X242 @ id ) @ X243 ) @ id ) ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( lamnotvar = $true )
& ( ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ? [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
!= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) )
| ? [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
!= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( axassoc = $true )
& ( hoasapinj2_gthm = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( pushprop_lem2v2_gthm = $true )
& ( induction2lem_gthm = $true )
& ( ( shinj = $true )
<=> ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) ) )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X104: term,X105: subst > term > subst > $o] :
( ( $true
= ( X105 @ id @ ( lam @ X104 ) @ id ) )
| ? [X111: subst,X112: term,X113: subst,X114: subst] :
( ( $true
= ( X105 @ X114 @ X112 @ ( comp @ X111 @ X113 ) ) )
& ( $true
!= ( X105 @ ( comp @ X114 @ X111 ) @ ( sub @ X112 @ X111 ) @ X113 ) ) )
| ? [X106: subst > term > term] :
( ! [X107: term] :
( ( $true
= ( X105 @ id @ ( X106 @ id @ X107 ) @ id ) )
| ( $true
!= ( X105 @ id @ X107 @ id ) ) )
& ( $true
!= ( X105 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
& ! [X108: subst,X109: term,X110: subst] :
( ( X106 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X110 ) ) )
| ? [X116: subst,X117: subst,X118: subst,X119: term] :
( ( $true
!= ( X105 @ X116 @ X119 @ ( comp @ X118 @ X117 ) ) )
& ( ( X105 @ ( comp @ X116 @ X118 ) @ ( sub @ X119 @ X118 ) @ X117 )
= $true ) )
| ? [X115: term] :
( ( $true
= ( X105 @ id @ X115 @ id ) )
& ( ( X105 @ id @ ( sub @ X104 @ ( push @ X115 @ id ) ) @ id )
!= $true ) ) )
| ? [X96: term,X97: subst > term > subst > $o] :
( ! [X103: term] :
( ( $true
!= ( X97 @ id @ X103 @ id ) )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) )
& ! [X98: subst > term > term] :
( ? [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
!= $true )
& ( $true
= ( X97 @ id @ X102 @ id ) ) )
| ( $true
= ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id ) )
| ? [X99: term,X100: subst,X101: subst] :
( ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) )
!= ( sub @ ( X98 @ X101 @ X99 ) @ X100 ) ) )
& ( $true
!= ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X95: term] :
( ( sub @ X95 @ id )
!= X95 ) ) )
& ( ( ! [X522: subst > term > subst > $o,X523: term] :
( ? [X529: subst > term > term] :
( ! [X533: term] :
( ( ( X522 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X522 @ id @ X533 @ id )
!= $true ) )
& ! [X530: subst,X531: subst,X532: term] :
( ( X529 @ ( comp @ X530 @ X531 ) @ ( sub @ X532 @ X531 ) )
= ( sub @ ( X529 @ X530 @ X532 ) @ X531 ) )
& ( ( X522 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X522 @ id @ X523 @ id ) )
| ? [X534: subst,X535: term,X536: subst,X537: subst] :
( ( $true
!= ( X522 @ ( comp @ X537 @ X536 ) @ ( sub @ X535 @ X536 ) @ X534 ) )
& ( $true
= ( X522 @ X537 @ X535 @ ( comp @ X536 @ X534 ) ) ) )
| ? [X524: term] :
( ( ( var @ ( sub @ X524 @ id ) )
= $true )
& ( $true
!= ( X522 @ id @ X524 @ id ) ) )
| ? [X525: subst,X526: term,X527: subst,X528: subst] :
( ( $true
= ( X522 @ ( comp @ X527 @ X525 ) @ ( sub @ X526 @ X525 ) @ X528 ) )
& ( $true
!= ( X522 @ X527 @ X526 @ ( comp @ X525 @ X528 ) ) ) )
| ? [X538: term,X539: term] :
( ( ( X522 @ id @ X539 @ id )
= $true )
& ( $true
!= ( X522 @ id @ ( ap @ ( sub @ X538 @ id ) @ X539 ) @ id ) )
& ( $true
= ( X522 @ id @ X538 @ id ) ) ) )
| ? [X512: term,X513: subst > term > subst > $o,X514: term > $o] :
( ! [X520: term] :
( ( ( X514 @ ( sub @ X512 @ ( push @ X520 @ id ) ) )
= $true )
| ( $true
!= ( X514 @ X520 ) ) )
& ! [X515: subst > term > term] :
( ? [X519: term] :
( ( $true
!= ( X513 @ id @ ( X515 @ id @ X519 ) @ id ) )
& ( ( X513 @ id @ X519 @ id )
= $true ) )
| ? [X516: subst,X517: term,X518: subst] :
( ( sub @ ( X515 @ X516 @ X517 ) @ X518 )
!= ( X515 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) ) )
| ( ( X513 @ id @ ( lam @ ( X515 @ sh @ one ) ) @ id )
= $true ) )
& ! [X521: term] :
( ( X514 @ X521 )
= ( X513 @ id @ X521 @ id ) )
& ( $true
!= ( X514 @ ( lam @ X512 ) ) ) )
| ? [X511: term] :
( ( sub @ X511 @ id )
!= X511 )
| ? [X504: term > $o,X505: term] :
( ! [X506: term,X507: term] :
( ( $true
= ( X504 @ ( ap @ X507 @ X506 ) ) )
| ( $true
!= ( X504 @ X507 ) )
| ( $true
!= ( X504 @ X506 ) ) )
& ( $true
!= ( X504 @ X505 ) )
& ! [X509: term] :
( ( $true
= ( X504 @ ( lam @ X509 ) ) )
| ? [X510: term] :
( ( ( X504 @ ( sub @ X509 @ ( push @ X510 @ id ) ) )
!= $true )
& ( ( X504 @ X510 )
= $true ) ) )
& ! [X508: term] :
( ( $true
= ( X504 @ X508 ) )
| ( $true
!= ( var @ X508 ) ) ) )
| ? [X501: subst > term > subst > $o] :
! [X502: term > $o] :
? [X503: term] :
( ( X501 @ id @ X503 @ id )
!= ( X502 @ X503 ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) )
| ? [X85: term,X86: term,X87: term,X88: term] :
( ( X85 != X86 )
& ( ( ap @ X85 @ X87 )
= ( ap @ X86 @ X88 ) ) )
| ? [X84: term] :
( ( sub @ X84 @ id )
!= X84 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ? [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
!= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) )
| ? [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
!= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset = $true )
<=> ! [X305: term] :
( ( sub @ X305 @ id )
= X305 ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X378: subst > term > subst > $o,X379: term,X380: term] :
( ? [X383: subst,X384: term,X385: subst,X386: subst] :
( ( $true
= ( X378 @ ( comp @ X386 @ X383 ) @ ( sub @ X384 @ X383 ) @ X385 ) )
& ( $true
!= ( X378 @ X386 @ X384 @ ( comp @ X383 @ X385 ) ) ) )
| ? [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
= ( X378 @ X390 @ X387 @ ( comp @ X389 @ X388 ) ) )
& ( $true
!= ( X378 @ ( comp @ X390 @ X389 ) @ ( sub @ X387 @ X389 ) @ X388 ) ) )
| ? [X381: term,X382: term] :
( ( $true
= ( X378 @ id @ X382 @ id ) )
& ( ( X378 @ id @ X381 @ id )
= $true )
& ( $true
!= ( X378 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) ) )
| ( $true
!= ( X378 @ id @ X380 @ id ) )
| ( $true
!= ( X378 @ id @ X379 @ id ) )
| ( $true
= ( X378 @ id @ ( ap @ X380 @ X379 ) @ id ) ) ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ? [X304: term] :
( ( X303 @ X304 )
!= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) ) ) )
& ( substmonoid_gthm = $true )
& ( axapp = $true )
& ( ( laminj = $true )
<=> ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ! [X38: term] :
? [X39: subst > term > term] :
( ( X39 @ sh @ one )
= ( sub @ X38 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ulamvarind = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X255: subst > term > subst > $o,X256: term] :
( ? [X257: term] :
( ( $true
!= ( X255 @ id @ ( sub @ X256 @ ( push @ X257 @ id ) ) @ id ) )
& ( $true
= ( X255 @ id @ X257 @ id ) ) )
| ( ( X255 @ id @ ( lam @ ( sub @ X256 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X258: subst > term > term] :
( ( $true
!= ( X255 @ id @ ( lam @ ( X258 @ sh @ one ) ) @ id ) )
& ! [X259: subst,X260: subst,X261: term] :
( ( sub @ ( X258 @ X259 @ X261 ) @ X260 )
= ( X258 @ ( comp @ X259 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
& ! [X262: term] :
( ( $true
!= ( X255 @ id @ X262 @ id ) )
| ( ( X255 @ id @ ( X258 @ id @ X262 ) @ id )
= $true ) ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
<=> ( axvarid = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoaslamnotvar = $true )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
<=> ( axshiftcons = $true ) )
& ( ( substmonoid_lthm = $true )
<=> ( ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) )
| ? [X345: subst] :
( ( comp @ X345 @ id )
!= X345 )
| ? [X344: subst] :
( ( comp @ id @ X344 )
!= X344 ) ) )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ( induction = $true )
<=> ! [X54: term,X55: term > $o] :
( ( $true
= ( X55 @ X54 ) )
| ? [X58: term,X59: term] :
( ( $true
= ( X55 @ X58 ) )
& ( ( X55 @ ( ap @ X58 @ X59 ) )
!= $true )
& ( $true
= ( X55 @ X59 ) ) )
| ? [X56: term] :
( ( $true
= ( var @ X56 ) )
& ( $true
!= ( X55 @ X56 ) ) )
| ? [X57: term] :
( ( $true
= ( X55 @ X57 ) )
& ( $true
!= ( X55 @ ( lam @ X57 ) ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X427: term,X428: subst > term > subst > $o] :
( ? [X438: term,X439: term] :
( ( $true
= ( X428 @ id @ X438 @ id ) )
& ( ( X428 @ id @ X439 @ id )
= $true )
& ( ( X428 @ id @ ( ap @ ( sub @ X438 @ id ) @ X439 ) @ id )
!= $true ) )
| ? [X434: subst,X435: subst,X436: subst,X437: term] :
( ( $true
!= ( X428 @ ( comp @ X436 @ X434 ) @ ( sub @ X437 @ X434 ) @ X435 ) )
& ( ( X428 @ X436 @ X437 @ ( comp @ X434 @ X435 ) )
= $true ) )
| ( $true
= ( X428 @ id @ X427 @ id ) )
| ? [X430: subst,X431: subst,X432: term,X433: subst] :
( ( $true
= ( X428 @ ( comp @ X430 @ X431 ) @ ( sub @ X432 @ X431 ) @ X433 ) )
& ( ( X428 @ X430 @ X432 @ ( comp @ X431 @ X433 ) )
!= $true ) )
| ? [X429: term] :
( ( $true
= ( var @ ( sub @ X429 @ id ) ) )
& ( $true
!= ( X428 @ id @ X429 @ id ) ) )
| ? [X440: subst > term > term] :
( ! [X441: term] :
( ( $true
!= ( X428 @ id @ X441 @ id ) )
| ( $true
= ( X428 @ id @ ( X440 @ id @ X441 ) @ id ) ) )
& ! [X442: subst,X443: subst,X444: term] :
( ( X440 @ ( comp @ X442 @ X443 ) @ ( sub @ X444 @ X443 ) )
= ( sub @ ( X440 @ X442 @ X444 ) @ X443 ) )
& ( ( X428 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
!= $true ) ) )
| ? [X411: subst > term > subst > $o,X412: term] :
( ! [X413: subst,X414: term,X415: subst,X416: subst] :
( ( $true
!= ( X411 @ X415 @ X414 @ ( comp @ X416 @ X413 ) ) )
| ( $true
= ( X411 @ ( comp @ X415 @ X416 ) @ ( sub @ X414 @ X416 ) @ X413 ) ) )
& ! [X421: subst > term > term] :
( ? [X423: subst,X424: subst,X425: term] :
( ( sub @ ( X421 @ X424 @ X425 ) @ X423 )
!= ( X421 @ ( comp @ X424 @ X423 ) @ ( sub @ X425 @ X423 ) ) )
| ? [X422: term] :
( ( $true
= ( X411 @ id @ X422 @ id ) )
& ( ( X411 @ id @ ( X421 @ id @ X422 ) @ id )
!= $true ) )
| ( ( X411 @ id @ ( lam @ ( X421 @ sh @ one ) ) @ id )
= $true ) )
& ( $true
!= ( X411 @ id @ ( lam @ X412 ) @ id ) )
& ! [X426: term] :
( ( $true
!= ( X411 @ id @ X426 @ id ) )
| ( $true
= ( X411 @ id @ ( sub @ X412 @ ( push @ X426 @ id ) ) @ id ) ) )
& ! [X417: subst,X418: subst,X419: term,X420: subst] :
( ( $true
!= ( X411 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) @ X417 ) )
| ( $true
= ( X411 @ X418 @ X419 @ ( comp @ X420 @ X417 ) ) ) ) )
| ? [X398: term,X399: term,X400: subst > term > subst > $o] :
( ( $true
= ( X400 @ id @ X399 @ id ) )
& ! [X401: subst,X402: subst,X403: term,X404: subst] :
( ( $true
!= ( X400 @ ( comp @ X402 @ X401 ) @ ( sub @ X403 @ X401 ) @ X404 ) )
| ( $true
= ( X400 @ X402 @ X403 @ ( comp @ X401 @ X404 ) ) ) )
& ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X400 @ ( comp @ X407 @ X406 ) @ ( sub @ X405 @ X406 ) @ X408 ) )
| ( $true
!= ( X400 @ X407 @ X405 @ ( comp @ X406 @ X408 ) ) ) )
& ! [X409: term,X410: term] :
( ( $true
!= ( X400 @ id @ X410 @ id ) )
| ( $true
!= ( X400 @ id @ X409 @ id ) )
| ( $true
= ( X400 @ id @ ( ap @ ( sub @ X409 @ id ) @ X410 ) @ id ) ) )
& ( $true
!= ( X400 @ id @ ( ap @ X398 @ X399 ) @ id ) )
& ( $true
= ( X400 @ id @ X398 @ id ) ) )
| ? [X391: term > $o,X392: term] :
( ( $true
!= ( X391 @ X392 ) )
& ! [X394: term] :
( ( $true
= ( X391 @ ( lam @ X394 ) ) )
| ? [X395: term] :
( ( $true
= ( X391 @ X395 ) )
& ( $true
!= ( X391 @ ( sub @ X394 @ ( push @ X395 @ id ) ) ) ) ) )
& ! [X396: term,X397: term] :
( ( $true
= ( X391 @ ( ap @ X396 @ X397 ) ) )
| ( ( X391 @ X397 )
!= $true )
| ( ( X391 @ X396 )
!= $true ) )
& ! [X393: term] :
( ( $true
= ( X391 @ X393 ) )
| ( $true
!= ( var @ X393 ) ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ! [X204: subst > term > subst > $o] :
? [X205: term > $o] :
! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ulamvarsh = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X216: subst > term > subst > $o] :
? [X217: term > $o] :
! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) ) )
& ( pushprop = $true )
& ( apnotvar = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X176: subst > term > term,X177: subst,X178: term,X179: subst > term > term] :
( ( ( X179 @ X177 @ X178 )
= ( X176 @ X177 @ X178 ) )
| ? [X183: subst,X184: subst,X185: term] :
( ( sub @ ( X176 @ X183 @ X185 ) @ X184 )
!= ( X176 @ ( comp @ X183 @ X184 ) @ ( sub @ X185 @ X184 ) ) )
| ? [X180: subst,X181: term,X182: subst] :
( ( sub @ ( X179 @ X182 @ X181 ) @ X180 )
!= ( X179 @ ( comp @ X182 @ X180 ) @ ( sub @ X181 @ X180 ) ) )
| ( ( lam @ ( X176 @ sh @ one ) )
!= ( lam @ ( X179 @ sh @ one ) ) ) )
| ? [X174: term,X175: term] :
( ( ( lam @ X175 )
= ( lam @ X174 ) )
& ( X174 != X175 ) )
| ? [X172: term,X173: subst] :
( ( comp @ sh @ ( push @ X172 @ X173 ) )
!= X173 )
| ? [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
!= X170 ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
<=> ( apinj2 = $true ) )
& ( ( ? [X157: term] :
( ( sub @ X157 @ id )
!= X157 )
| ! [X158: term] :
( ( sub @ X158 @ id )
= X158 ) )
<=> ( termmset_lthm = $true ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( pushprop_lthm_orig = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X60: term,X61: subst > term > subst > $o] :
( ? [X68: subst,X69: subst,X70: subst,X71: term] :
( ( $true
= ( X61 @ X70 @ X71 @ ( comp @ X69 @ X68 ) ) )
& ( ( X61 @ ( comp @ X70 @ X69 ) @ ( sub @ X71 @ X69 ) @ X68 )
!= $true ) )
| ? [X62: term] :
( ( $true
!= ( X61 @ id @ ( sub @ X60 @ ( push @ X62 @ id ) ) @ id ) )
& ( ( X61 @ id @ X62 @ id )
= $true ) )
| ? [X63: subst > term > term] :
( ! [X65: term,X66: subst,X67: subst] :
( ( X63 @ ( comp @ X67 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( X63 @ X67 @ X65 ) @ X66 ) )
& ! [X64: term] :
( ( $true
!= ( X61 @ id @ X64 @ id ) )
| ( $true
= ( X61 @ id @ ( X63 @ id @ X64 ) @ id ) ) )
& ( $true
!= ( X61 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X61 @ id @ ( lam @ X60 ) @ id ) )
| ? [X72: subst,X73: subst,X74: subst,X75: term] :
( ( $true
= ( X61 @ ( comp @ X73 @ X74 ) @ ( sub @ X75 @ X74 ) @ X72 ) )
& ( $true
!= ( X61 @ X73 @ X75 @ ( comp @ X74 @ X72 ) ) ) ) ) )
& ( ( ! [X129: subst > term > subst > $o,X130: term] :
( ( $true
= ( X129 @ id @ ( lam @ X130 ) @ id ) )
| ? [X131: subst > term > term] :
( ! [X133: subst,X134: subst,X135: term] :
( ( sub @ ( X131 @ X133 @ X135 ) @ X134 )
= ( X131 @ ( comp @ X133 @ X134 ) @ ( sub @ X135 @ X134 ) ) )
& ! [X132: term] :
( ( $true
= ( X129 @ id @ ( X131 @ id @ X132 ) @ id ) )
| ( $true
!= ( X129 @ id @ X132 @ id ) ) )
& ( $true
!= ( X129 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id ) ) )
| ? [X136: term] :
( ( $true
= ( X129 @ id @ X136 @ id ) )
& ( $true
!= ( X129 @ id @ ( sub @ X130 @ ( push @ X136 @ id ) ) @ id ) ) ) )
| ? [X121: term,X122: subst > term > subst > $o] :
( ! [X123: subst > term > term] :
( ? [X124: term] :
( ( $true
= ( X122 @ id @ X124 @ id ) )
& ( $true
!= ( X122 @ id @ ( X123 @ id @ X124 ) @ id ) ) )
| ? [X125: subst,X126: subst,X127: term] :
( ( sub @ ( X123 @ X125 @ X127 ) @ X126 )
!= ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id ) ) )
& ! [X128: term] :
( ( $true
!= ( X122 @ id @ X128 @ id ) )
| ( $true
= ( X122 @ id @ ( sub @ X121 @ ( push @ X128 @ id ) ) @ id ) ) )
& ( $true
!= ( X122 @ id @ ( lam @ ( sub @ X121 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ? [X120: term] :
( ( sub @ X120 @ id )
!= X120 ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ( hoasinduction_lem3b = $true )
<=> ! [X0: term] :
? [X1: subst > term > term] :
( ( X1 @ sh @ one )
= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ? [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
!= X351 )
| ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ? [X356: term] :
( ( X354 @ X356 )
!= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) ) ) ) )
& ( ( ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) )
| ? [X306: term,X307: term,X308: term,X309: term] :
( ( X306 != X308 )
& ( ( ap @ X307 @ X308 )
= ( ap @ X309 @ X306 ) ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ! [X5: term,X6: subst > term > subst > $o] :
( ? [X11: term] :
( ( $true
= ( var @ ( sub @ X11 @ id ) ) )
& ( $true
!= ( X6 @ id @ X11 @ id ) ) )
| ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
!= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
& ( $true
= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ? [X21: term,X22: term] :
( ( $true
= ( X6 @ id @ X22 @ id ) )
& ( $true
!= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) )
& ( $true
= ( X6 @ id @ X21 @ id ) ) )
| ? [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
& ( $true
= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ? [X12: subst > term > term] :
( ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
& ! [X13: term] :
( ( ( X6 @ id @ X13 @ id )
!= $true )
| ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
& ( $true
!= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( axvarcons = $true )
<=> ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X445: term] :
? [X446: subst > term > term] :
! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) ) )
& ( axabs = $true )
& ( lamnotap != $true )
& ( pushprop_lthm = $true )
& ( ( ! [X240: subst > term > subst > $o,X241: term] :
( ( $true
= ( X240 @ id @ X241 @ id ) )
| ? [X244: subst > term > term] :
( ! [X245: term] :
( ( $true
!= ( X240 @ id @ X245 @ id ) )
| ( $true
= ( X240 @ id @ ( X244 @ id @ X245 ) @ id ) ) )
& ! [X246: subst,X247: term,X248: subst] :
( ( X244 @ ( comp @ X246 @ X248 ) @ ( sub @ X247 @ X248 ) )
= ( sub @ ( X244 @ X246 @ X247 ) @ X248 ) )
& ( $true
!= ( X240 @ id @ ( lam @ ( X244 @ sh @ one ) ) @ id ) ) )
| ? [X242: term,X243: term] :
( ( $true
= ( X240 @ id @ X243 @ id ) )
& ( ( X240 @ id @ X242 @ id )
= $true )
& ( $true
!= ( X240 @ id @ ( ap @ ( sub @ X242 @ id ) @ X243 ) @ id ) ) ) )
| ? [X230: term,X231: term > $o,X232: subst > term > subst > $o] :
( ! [X233: term] :
( ( ( X231 @ ( sub @ X230 @ ( push @ X233 @ id ) ) )
= $true )
| ( $true
!= ( X231 @ X233 ) ) )
& ! [X234: subst > term > term] :
( ( $true
= ( X232 @ id @ ( lam @ ( X234 @ sh @ one ) ) @ id ) )
| ? [X236: term,X237: subst,X238: subst] :
( ( X234 @ ( comp @ X237 @ X238 ) @ ( sub @ X236 @ X238 ) )
!= ( sub @ ( X234 @ X237 @ X236 ) @ X238 ) )
| ? [X235: term] :
( ( $true
!= ( X232 @ id @ ( X234 @ id @ X235 ) @ id ) )
& ( $true
= ( X232 @ id @ X235 @ id ) ) ) )
& ( $true
!= ( X231 @ ( lam @ X230 ) ) )
& ! [X239: term] :
( ( X232 @ id @ X239 @ id )
= ( X231 @ X239 ) ) )
| ? [X229: term] :
( ( sub @ X229 @ id )
!= X229 )
| ? [X222: term > $o,X223: term] :
( ( $true
!= ( X222 @ X223 ) )
& ! [X225: term] :
( ? [X226: term] :
( ( $true
!= ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) )
& ( $true
= ( X222 @ X226 ) ) )
| ( $true
= ( X222 @ ( lam @ X225 ) ) ) )
& ! [X224: term] :
( ( $true
!= ( var @ X224 ) )
| ( ( X222 @ X224 )
= $true ) )
& ! [X227: term,X228: term] :
( ( $true
= ( X222 @ ( ap @ X228 @ X227 ) ) )
| ( $true
!= ( X222 @ X227 ) )
| ( $true
!= ( X222 @ X228 ) ) ) )
| ? [X219: subst > term > subst > $o] :
! [X220: term > $o] :
? [X221: term] :
( ( X219 @ id @ X221 @ id )
!= ( X220 @ X221 ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem3v2 = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( hoaslamnotap = $true )
<=> ! [X249: term,X250: term,X251: subst > term > term] :
( ? [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
!= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) )
| ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) ) ) )
& ( hoasapinj2_gthm = $true )
& ( ( ? [X359: term] :
( ( sub @ X359 @ id )
!= X359 )
| ! [X360: subst > term > subst > $o,X361: term,X362: term > $o] :
( ? [X364: subst,X365: subst,X366: subst,X367: term] :
( ( $true
= ( X360 @ ( comp @ X366 @ X365 ) @ ( sub @ X367 @ X365 ) @ X364 ) )
& ( $true
!= ( X360 @ X366 @ X367 @ ( comp @ X365 @ X364 ) ) ) )
| ? [X363: term] :
( ( X362 @ X363 )
!= ( X360 @ id @ X363 @ id ) )
| ? [X373: subst,X374: subst,X375: subst,X376: term] :
( ( $true
= ( X360 @ X375 @ X376 @ ( comp @ X373 @ X374 ) ) )
& ( $true
!= ( X360 @ ( comp @ X375 @ X373 ) @ ( sub @ X376 @ X373 ) @ X374 ) ) )
| ? [X377: term] :
( ( $true
!= ( X362 @ ( sub @ X361 @ ( push @ X377 @ id ) ) ) )
& ( ( X362 @ X377 )
= $true ) )
| ? [X368: subst > term > term] :
( ! [X369: term] :
( ( $true
= ( X360 @ id @ ( X368 @ id @ X369 ) @ id ) )
| ( $true
!= ( X360 @ id @ X369 @ id ) ) )
& ! [X370: subst,X371: term,X372: subst] :
( ( sub @ ( X368 @ X370 @ X371 ) @ X372 )
= ( X368 @ ( comp @ X370 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
& ( $true
!= ( X360 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X362 @ ( lam @ X361 ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
<=> ( axscons = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axmap = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
<=> ( substmonoid = $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ! [X333: term > $o,X334: subst > term > subst > $o,X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ? [X336: subst > term > term] :
( ! [X340: term] :
( ( $true
= ( X334 @ id @ ( X336 @ id @ X340 ) @ id ) )
| ( $true
!= ( X334 @ id @ X340 @ id ) ) )
& ( $true
!= ( X334 @ id @ ( lam @ ( X336 @ sh @ one ) ) @ id ) )
& ! [X337: subst,X338: subst,X339: term] :
( ( sub @ ( X336 @ X338 @ X339 ) @ X337 )
= ( X336 @ ( comp @ X338 @ X337 ) @ ( sub @ X339 @ X337 ) ) ) )
| ? [X341: term] :
( ( ( X333 @ X341 )
= $true )
& ( $true
!= ( X333 @ ( sub @ X335 @ ( push @ X341 @ id ) ) ) ) )
| ? [X342: term] :
( ( X334 @ id @ X342 @ id )
!= ( X333 @ X342 ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
<=> ( hoasapinj1 = $true ) )
& ( ! [X263: term,X264: term > $o,X265: subst > term > subst > $o] :
( ? [X276: subst,X277: subst,X278: subst,X279: term] :
( ( $true
= ( X265 @ ( comp @ X277 @ X276 ) @ ( sub @ X279 @ X276 ) @ X278 ) )
& ( $true
!= ( X265 @ X277 @ X279 @ ( comp @ X276 @ X278 ) ) ) )
| ( $true
= ( X264 @ ( lam @ X263 ) ) )
| ? [X270: subst > term > term] :
( ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
& ( $true
!= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
& ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) ) )
| ? [X275: term] :
( ( $true
!= ( X264 @ ( sub @ X263 @ ( push @ X275 @ id ) ) ) )
& ( ( X264 @ X275 )
= $true ) )
| ? [X266: term,X267: subst,X268: subst,X269: subst] :
( ( $true
!= ( X265 @ ( comp @ X269 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 ) )
& ( ( X265 @ X269 @ X266 @ ( comp @ X268 @ X267 ) )
= $true ) )
| ? [X280: term] :
( ( X265 @ id @ X280 @ id )
!= ( X264 @ X280 ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
!= ( d2subst @ X349 ) )
| ( X348 = X349 ) )
& ( axclos = $true )
& ( pushprop_lem0_gthm = $true )
& ( ! [X476: subst > term > subst > $o,X477: term] :
( ( $true
= ( X476 @ id @ ( lam @ X477 ) @ id ) )
| ? [X483: term] :
( ( $true
!= ( X476 @ id @ ( sub @ X477 @ ( push @ X483 @ id ) ) @ id ) )
& ( $true
= ( X476 @ id @ X483 @ id ) ) )
| ? [X478: subst > term > term] :
( ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X482 @ X481 ) @ ( sub @ X480 @ X481 ) )
= ( sub @ ( X478 @ X482 @ X480 ) @ X481 ) )
& ! [X479: term] :
( ( $true
= ( X476 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X476 @ id @ X479 @ id ) ) )
& ( $true
!= ( X476 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X142: term,X143: subst > term > subst > $o,X144: term > $o] :
( ? [X151: term] :
( ( ( X144 @ X151 )
= $true )
& ( $true
!= ( X144 @ ( sub @ X142 @ ( push @ X151 @ id ) ) ) ) )
| ( $true
= ( X144 @ ( lam @ X142 ) ) )
| ? [X146: subst > term > term] :
( ! [X147: term,X148: subst,X149: subst] :
( ( X146 @ ( comp @ X149 @ X148 ) @ ( sub @ X147 @ X148 ) )
= ( sub @ ( X146 @ X149 @ X147 ) @ X148 ) )
& ! [X150: term] :
( ( $true
!= ( X143 @ id @ X150 @ id ) )
| ( ( X143 @ id @ ( X146 @ id @ X150 ) @ id )
= $true ) )
& ( ( X143 @ id @ ( lam @ ( X146 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X145: term] :
( ( X144 @ X145 )
!= ( X143 @ id @ X145 @ id ) ) )
| ? [X141: term] :
( ( sub @ X141 @ id )
!= X141 )
| ? [X137: term] :
! [X138: subst > term > term] :
? [X139: term,X140: subst] :
( ( X138 @ X140 @ X139 )
!= ( sub @ X137 @ ( push @ X139 @ X140 ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X159: subst > term > subst > $o,X160: term] :
( ? [X162: subst > term > term] :
( ( $true
!= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
& ! [X164: subst,X165: subst,X166: term] :
( ( X162 @ ( comp @ X165 @ X164 ) @ ( sub @ X166 @ X164 ) )
= ( sub @ ( X162 @ X165 @ X166 ) @ X164 ) )
& ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) ) )
| ( ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X161: term] :
( ( $true
!= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) )
& ( $true
= ( X159 @ id @ X161 @ id ) ) ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ? [X469: subst > term > term] :
( ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) )
& ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
& ( $true
!= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) ) )
| ? [X474: term,X475: term] :
( ( $true
= ( X468 @ id @ X475 @ id ) )
& ( $true
!= ( X468 @ id @ ( ap @ ( sub @ X474 @ id ) @ X475 ) @ id ) )
& ( $true
= ( X468 @ id @ X474 @ id ) ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ( induction2 = $true )
<=> ! [X283: term > $o,X284: term] :
( ? [X285: term] :
( ( $true
!= ( X283 @ ( lam @ X285 ) ) )
& ! [X286: term] :
( ( ( X283 @ ( sub @ X285 @ ( push @ X286 @ id ) ) )
= $true )
| ( $true
!= ( X283 @ X286 ) ) ) )
| ( $true
= ( X283 @ X284 ) )
| ? [X287: term] :
( ( $true
!= ( X283 @ X287 ) )
& ( $true
= ( var @ X287 ) ) )
| ? [X288: term,X289: term] :
( ( $true
!= ( X283 @ ( ap @ X288 @ X289 ) ) )
& ( ( X283 @ X289 )
= $true )
& ( $true
= ( X283 @ X288 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( ! [X460: term > $o,X461: term] :
( ( $true
= ( X460 @ X461 ) )
| ? [X462: term] :
( ( $true
= ( var @ X462 ) )
& ( ( X460 @ X462 )
!= $true ) )
| ? [X463: term] :
( ( $true
!= ( X460 @ ( lam @ X463 ) ) )
& ! [X464: term] :
( ( $true
!= ( X460 @ X464 ) )
| ( ( X460 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
= $true ) ) )
| ? [X465: term,X466: term] :
( ( $true
= ( X460 @ X465 ) )
& ( $true
!= ( X460 @ ( ap @ X465 @ X466 ) ) )
& ( $true
= ( X460 @ X466 ) ) ) )
| ? [X452: subst,X453: term > $o,X454: term] :
( ! [X455: term,X456: term] :
( ( $true
= ( X453 @ ( ap @ X455 @ X456 ) ) )
| ( $true
!= ( X453 @ X455 ) )
| ( $true
!= ( X453 @ X456 ) ) )
& ( $true
!= ( X453 @ ( sub @ X454 @ X452 ) ) )
& ! [X458: term] :
( ? [X459: term] :
( ( ( X453 @ ( sub @ X458 @ ( push @ X459 @ id ) ) )
!= $true )
& ( $true
= ( X453 @ X459 ) ) )
| ( $true
= ( X453 @ ( lam @ X458 ) ) ) )
& ! [X457: term] :
( ( $true
= ( X453 @ ( sub @ X457 @ X452 ) ) )
| ( $true
!= ( var @ X457 ) ) ) )
| ? [X451: term] :
( ( sub @ X451 @ id )
!= X451 ) )
<=> ( induction2_lthm = $true ) )
& ! [X168: d_term,X169: d_term] :
( ( X168 = X169 )
| ( ( d2term @ X169 )
!= ( d2term @ X168 ) ) )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X192: term,X193: subst > term > subst > $o] :
( ? [X194: term] :
( ( $true
!= ( X193 @ id @ ( sub @ X192 @ ( push @ X194 @ id ) ) @ id ) )
& ( $true
= ( X193 @ id @ X194 @ id ) ) )
| ? [X195: subst > term > term,X196: term] :
( ! [X197: term] :
( ( $true
= ( X193 @ id @ ( X195 @ id @ X197 ) @ id ) )
| ( $true
!= ( X193 @ id @ X197 @ id ) ) )
& ! [X201: subst,X202: term,X203: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X202 @ X201 ) @ ( comp @ X203 @ X201 ) ) )
= ( X195 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
& ! [X198: term,X199: subst,X200: subst] :
( ( sub @ ( sub @ X196 @ ( push @ X198 @ X199 ) ) @ X200 )
= ( sub @ ( X195 @ X199 @ X198 ) @ X200 ) )
& ( ( X193 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
!= $true ) )
| ( $true
= ( X193 @ id @ ( lam @ ( sub @ X192 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) )
| ? [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
!= X293 )
| ? [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
!= X291 ) ) )
& ! [X48: d_subst] : ( d_id = X48 )
& ( hoasapinj1_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X325: subst,X326: term,X327: term > $o] :
( ? [X330: term] :
( ( $true
= ( var @ X330 ) )
& ( $true
!= ( X327 @ ( sub @ X330 @ X325 ) ) ) )
| ? [X328: term,X329: term] :
( ( $true
!= ( X327 @ ( ap @ X329 @ X328 ) ) )
& ( $true
= ( X327 @ X328 ) )
& ( $true
= ( X327 @ X329 ) ) )
| ( $true
= ( X327 @ ( sub @ X326 @ X325 ) ) )
| ? [X331: term] :
( ( ( X327 @ ( lam @ X331 ) )
!= $true )
& ! [X332: term] :
( ( $true
!= ( X327 @ X332 ) )
| ( $true
= ( X327 @ ( sub @ X331 @ ( push @ X332 @ id ) ) ) ) ) ) )
| ? [X319: term > $o,X320: term] :
( ( $true
!= ( X319 @ X320 ) )
& ! [X322: term] :
( ( $true
= ( X319 @ X322 ) )
| ( $true
!= ( var @ X322 ) ) )
& ! [X321: term] :
( ( ( X319 @ ( lam @ X321 ) )
= $true )
| ( $true
!= ( X319 @ X321 ) ) )
& ! [X323: term,X324: term] :
( ( $true
!= ( X319 @ X324 ) )
| ( $true
= ( X319 @ ( ap @ X323 @ X324 ) ) )
| ( $true
!= ( X319 @ X323 ) ) ) )
| ? [X318: subst] :
( ( comp @ X318 @ id )
!= X318 )
| ? [X316: term,X317: subst] :
( ( comp @ sh @ ( push @ X316 @ X317 ) )
!= X317 )
| ? [X314: term,X315: subst] :
( ( sub @ one @ ( push @ X314 @ X315 ) )
!= X314 ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem3v2_lthm = $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 ) ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ? [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
!= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
& ( $true
= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ? [X27: subst,X28: subst,X29: subst,X30: term] :
( ( $true
= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) )
& ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
!= $true ) )
| ? [X37: term] :
( ( X26 @ X37 )
!= ( X24 @ id @ X37 @ id ) )
| ( ( X26 @ X23 )
!= $true )
| ( $true
!= ( X26 @ X25 ) )
| ? [X31: term,X32: term] :
( ( $true
!= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
& ( $true
= ( X24 @ id @ X32 @ id ) )
& ( $true
= ( X24 @ id @ X31 @ id ) ) )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true ) ) )
& ( ! [X40: term] :
? [X41: subst > term > term] :
! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( axvarshift = $true )
& ( pushprop_gthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) ) )
& ( ! [X76: term,X77: subst,X78: term > $o] :
( ? [X81: term] :
( ( $true
= ( var @ X81 ) )
& ( $true
!= ( X78 @ ( sub @ X81 @ X77 ) ) ) )
| ( $true
= ( X78 @ ( sub @ X76 @ X77 ) ) )
| ? [X82: term,X83: term] :
( ( $true
= ( X78 @ X83 ) )
& ( $true
= ( X78 @ X82 ) )
& ( ( X78 @ ( ap @ X83 @ X82 ) )
!= $true ) )
| ? [X79: term] :
( ! [X80: term] :
( ( ( X78 @ X80 )
!= $true )
| ( ( X78 @ ( sub @ X79 @ ( push @ X80 @ id ) ) )
= $true ) )
& ( ( X78 @ ( lam @ X79 ) )
!= $true ) ) )
<=> ( induction2lem = $true ) )
& ( ( apinj1 = $true )
<=> ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X49: term > $o,X50: subst,X51: term] :
? [X52: term > $o] :
! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X207: subst,X208: term,X209: term > $o] :
? [X210: term > $o] :
! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) ) )
& ( induction2_gthm = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( pushprop_lem2v2_gthm = $true )
& ( induction2lem_gthm = $true )
& ( ( shinj = $true )
<=> ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) ) )
& ( hoasinduction_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X95: term] :
( ( sub @ X95 @ id )
= X95 )
=> ( ! [X96: term,X97: subst > term > subst > $o] :
( ( $true
= ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X98: subst > term > term] :
( ~ ! [X102: term] :
( ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
= $true )
| ( $true
!= ( X97 @ id @ X102 @ id ) ) )
| ( $true
= ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id ) )
| ~ ! [X99: term,X100: subst,X101: subst] :
( ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) )
= ( sub @ ( X98 @ X101 @ X99 ) @ X100 ) ) )
| ~ ! [X103: term] :
( ( $true
!= ( X97 @ id @ X103 @ id ) )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) ) )
=> ! [X104: term,X105: subst > term > subst > $o] :
( ( $true
= ( X105 @ id @ ( lam @ X104 ) @ id ) )
| ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( $true
!= ( X105 @ X114 @ X112 @ ( comp @ X111 @ X113 ) ) )
| ( $true
= ( X105 @ ( comp @ X114 @ X111 ) @ ( sub @ X112 @ X111 ) @ X113 ) ) )
| ~ ! [X106: subst > term > term] :
( ~ ! [X107: term] :
( ( $true
= ( X105 @ id @ ( X106 @ id @ X107 ) @ id ) )
| ( $true
!= ( X105 @ id @ X107 @ id ) ) )
| ( $true
= ( X105 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
| ~ ! [X108: subst,X109: term,X110: subst] :
( ( X106 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X110 ) ) )
| ~ ! [X115: term] :
( ( ( X105 @ id @ ( sub @ X104 @ ( push @ X115 @ id ) ) @ id )
= $true )
| ( $true
!= ( X105 @ id @ X115 @ id ) ) )
| ~ ! [X116: subst,X117: subst,X118: subst,X119: term] :
( ( ( X105 @ ( comp @ X116 @ X118 ) @ ( sub @ X119 @ X118 ) @ X117 )
!= $true )
| ( $true
= ( X105 @ X116 @ X119 @ ( comp @ X118 @ X117 ) ) ) ) ) ) ) )
& ( ( ! [X501: subst > term > subst > $o] :
~ ! [X502: term > $o] :
~ ! [X503: term] :
( ( X501 @ id @ X503 @ id )
= ( X502 @ X503 ) )
=> ( ! [X504: term > $o,X505: term] :
( ( $true
= ( X504 @ X505 ) )
| ~ ! [X508: term] :
( ( $true
= ( X504 @ X508 ) )
| ( $true
!= ( var @ X508 ) ) )
| ~ ! [X509: term] :
( ( $true
= ( X504 @ ( lam @ X509 ) ) )
| ~ ! [X510: term] :
( ( ( X504 @ X510 )
!= $true )
| ( ( X504 @ ( sub @ X509 @ ( push @ X510 @ id ) ) )
= $true ) ) )
| ~ ! [X506: term,X507: term] :
( ( $true
= ( X504 @ ( ap @ X507 @ X506 ) ) )
| ( $true
!= ( X504 @ X507 ) )
| ( $true
!= ( X504 @ X506 ) ) ) )
=> ( ! [X511: term] :
( ( sub @ X511 @ id )
= X511 )
=> ( ! [X512: term,X513: subst > term > subst > $o,X514: term > $o] :
( ~ ! [X520: term] :
( ( ( X514 @ ( sub @ X512 @ ( push @ X520 @ id ) ) )
= $true )
| ( $true
!= ( X514 @ X520 ) ) )
| ~ ! [X521: term] :
( ( X514 @ X521 )
= ( X513 @ id @ X521 @ id ) )
| ~ ! [X515: subst > term > term] :
( ~ ! [X516: subst,X517: term,X518: subst] :
( ( sub @ ( X515 @ X516 @ X517 ) @ X518 )
= ( X515 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) ) )
| ~ ! [X519: term] :
( ( ( X513 @ id @ X519 @ id )
!= $true )
| ( $true
= ( X513 @ id @ ( X515 @ id @ X519 ) @ id ) ) )
| ( ( X513 @ id @ ( lam @ ( X515 @ sh @ one ) ) @ id )
= $true ) )
| ( $true
= ( X514 @ ( lam @ X512 ) ) ) )
=> ! [X522: subst > term > subst > $o,X523: term] :
( ( $true
= ( X522 @ id @ X523 @ id ) )
| ~ ! [X538: term,X539: term] :
( ( ( X522 @ id @ X539 @ id )
!= $true )
| ( $true
!= ( X522 @ id @ X538 @ id ) )
| ( $true
= ( X522 @ id @ ( ap @ ( sub @ X538 @ id ) @ X539 ) @ id ) ) )
| ~ ! [X529: subst > term > term] :
( ( ( X522 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X533: term] :
( ( ( X522 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X522 @ id @ X533 @ id )
!= $true ) )
| ~ ! [X530: subst,X531: subst,X532: term] :
( ( X529 @ ( comp @ X530 @ X531 ) @ ( sub @ X532 @ X531 ) )
= ( sub @ ( X529 @ X530 @ X532 ) @ X531 ) ) )
| ~ ! [X525: subst,X526: term,X527: subst,X528: subst] :
( ( $true
= ( X522 @ X527 @ X526 @ ( comp @ X525 @ X528 ) ) )
| ( $true
!= ( X522 @ ( comp @ X527 @ X525 ) @ ( sub @ X526 @ X525 ) @ X528 ) ) )
| ~ ! [X524: term] :
( ( ( var @ ( sub @ X524 @ id ) )
!= $true )
| ( $true
= ( X522 @ id @ X524 @ id ) ) )
| ~ ! [X534: subst,X535: term,X536: subst,X537: subst] :
( ( $true
= ( X522 @ ( comp @ X537 @ X536 ) @ ( sub @ X535 @ X536 ) @ X534 ) )
| ( $true
!= ( X522 @ X537 @ X535 @ ( comp @ X536 @ X534 ) ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
=> ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( ( ap @ X85 @ X87 )
!= ( ap @ X86 @ X88 ) )
| ( X85 = X86 ) )
=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( hoaslaminj = $true )
<=> ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ~ ! [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ~ ! [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( termmset = $true )
<=> ! [X305: term] :
( ( sub @ X305 @ id )
= X305 ) )
& ( ! [X378: subst > term > subst > $o,X379: term,X380: term] :
( ~ ! [X381: term,X382: term] :
( ( ( X378 @ id @ X381 @ id )
!= $true )
| ( $true
= ( X378 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) )
| ( $true
!= ( X378 @ id @ X382 @ id ) ) )
| ~ ! [X383: subst,X384: term,X385: subst,X386: subst] :
( ( $true
!= ( X378 @ ( comp @ X386 @ X383 ) @ ( sub @ X384 @ X383 ) @ X385 ) )
| ( $true
= ( X378 @ X386 @ X384 @ ( comp @ X383 @ X385 ) ) ) )
| ~ ! [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
!= ( X378 @ X390 @ X387 @ ( comp @ X389 @ X388 ) ) )
| ( $true
= ( X378 @ ( comp @ X390 @ X389 ) @ ( sub @ X387 @ X389 ) @ X388 ) ) )
| ( $true
= ( X378 @ id @ ( ap @ X380 @ X379 ) @ id ) )
| ( $true
!= ( X378 @ id @ X380 @ id ) )
| ( $true
!= ( X378 @ id @ X379 @ id ) ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( hoasapnotvar = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ( $true
!= ( X302 @ X301 ) )
| ( $true
= ( X303 @ one ) )
| ~ ! [X304: term] :
( ( X303 @ X304 )
= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( substmonoid_gthm = $true )
& ( axapp = $true )
& ( ( laminj = $true )
<=> ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X38: term] :
~ ! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) ) )
& ( ulamvarind = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem2_lthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X255: subst > term > subst > $o,X256: term] :
( ~ ! [X258: subst > term > term] :
( ~ ! [X259: subst,X260: subst,X261: term] :
( ( sub @ ( X258 @ X259 @ X261 ) @ X260 )
= ( X258 @ ( comp @ X259 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
| ~ ! [X262: term] :
( ( $true
!= ( X255 @ id @ X262 @ id ) )
| ( ( X255 @ id @ ( X258 @ id @ X262 ) @ id )
= $true ) )
| ( $true
= ( X255 @ id @ ( lam @ ( X258 @ sh @ one ) ) @ id ) ) )
| ( ( X255 @ id @ ( lam @ ( sub @ X256 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X257: term] :
( ( $true
!= ( X255 @ id @ X257 @ id ) )
| ( $true
= ( X255 @ id @ ( sub @ X256 @ ( push @ X257 @ id ) ) @ id ) ) ) ) )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
<=> ( axvarid = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoaslamnotvar = $true )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
<=> ( axshiftcons = $true ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X344: subst] :
( ( comp @ id @ X344 )
= X344 )
=> ( ! [X345: subst] :
( ( comp @ X345 @ id )
= X345 )
=> ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) ) ) ) )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ! [X54: term,X55: term > $o] :
( ~ ! [X57: term] :
( ( $true
!= ( X55 @ X57 ) )
| ( $true
= ( X55 @ ( lam @ X57 ) ) ) )
| ~ ! [X56: term] :
( ( $true
!= ( var @ X56 ) )
| ( $true
= ( X55 @ X56 ) ) )
| ~ ! [X58: term,X59: term] :
( ( ( X55 @ ( ap @ X58 @ X59 ) )
= $true )
| ( $true
!= ( X55 @ X58 ) )
| ( $true
!= ( X55 @ X59 ) ) )
| ( $true
= ( X55 @ X54 ) ) )
<=> ( induction = $true ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X391: term > $o,X392: term] :
( ~ ! [X393: term] :
( ( $true
= ( X391 @ X393 ) )
| ( $true
!= ( var @ X393 ) ) )
| ( $true
= ( X391 @ X392 ) )
| ~ ! [X396: term,X397: term] :
( ( $true
= ( X391 @ ( ap @ X396 @ X397 ) ) )
| ( ( X391 @ X397 )
!= $true )
| ( ( X391 @ X396 )
!= $true ) )
| ~ ! [X394: term] :
( ~ ! [X395: term] :
( ( $true
!= ( X391 @ X395 ) )
| ( $true
= ( X391 @ ( sub @ X394 @ ( push @ X395 @ id ) ) ) ) )
| ( $true
= ( X391 @ ( lam @ X394 ) ) ) ) )
=> ( ! [X398: term,X399: term,X400: subst > term > subst > $o] :
( ( $true
= ( X400 @ id @ ( ap @ X398 @ X399 ) @ id ) )
| ( $true
!= ( X400 @ id @ X399 @ id ) )
| ~ ! [X409: term,X410: term] :
( ( $true
!= ( X400 @ id @ X410 @ id ) )
| ( $true
!= ( X400 @ id @ X409 @ id ) )
| ( $true
= ( X400 @ id @ ( ap @ ( sub @ X409 @ id ) @ X410 ) @ id ) ) )
| ( $true
!= ( X400 @ id @ X398 @ id ) )
| ~ ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X400 @ ( comp @ X407 @ X406 ) @ ( sub @ X405 @ X406 ) @ X408 ) )
| ( $true
!= ( X400 @ X407 @ X405 @ ( comp @ X406 @ X408 ) ) ) )
| ~ ! [X401: subst,X402: subst,X403: term,X404: subst] :
( ( $true
!= ( X400 @ ( comp @ X402 @ X401 ) @ ( sub @ X403 @ X401 ) @ X404 ) )
| ( $true
= ( X400 @ X402 @ X403 @ ( comp @ X401 @ X404 ) ) ) ) )
=> ( ! [X411: subst > term > subst > $o,X412: term] :
( ~ ! [X426: term] :
( ( $true
!= ( X411 @ id @ X426 @ id ) )
| ( $true
= ( X411 @ id @ ( sub @ X412 @ ( push @ X426 @ id ) ) @ id ) ) )
| ~ ! [X421: subst > term > term] :
( ( ( X411 @ id @ ( lam @ ( X421 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X422: term] :
( ( ( X411 @ id @ ( X421 @ id @ X422 ) @ id )
= $true )
| ( $true
!= ( X411 @ id @ X422 @ id ) ) )
| ~ ! [X423: subst,X424: subst,X425: term] :
( ( sub @ ( X421 @ X424 @ X425 ) @ X423 )
= ( X421 @ ( comp @ X424 @ X423 ) @ ( sub @ X425 @ X423 ) ) ) )
| ( $true
= ( X411 @ id @ ( lam @ X412 ) @ id ) )
| ~ ! [X417: subst,X418: subst,X419: term,X420: subst] :
( ( $true
!= ( X411 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) @ X417 ) )
| ( $true
= ( X411 @ X418 @ X419 @ ( comp @ X420 @ X417 ) ) ) )
| ~ ! [X413: subst,X414: term,X415: subst,X416: subst] :
( ( $true
!= ( X411 @ X415 @ X414 @ ( comp @ X416 @ X413 ) ) )
| ( $true
= ( X411 @ ( comp @ X415 @ X416 ) @ ( sub @ X414 @ X416 ) @ X413 ) ) ) )
=> ! [X427: term,X428: subst > term > subst > $o] :
( ~ ! [X434: subst,X435: subst,X436: subst,X437: term] :
( ( $true
= ( X428 @ ( comp @ X436 @ X434 ) @ ( sub @ X437 @ X434 ) @ X435 ) )
| ( ( X428 @ X436 @ X437 @ ( comp @ X434 @ X435 ) )
!= $true ) )
| ~ ! [X430: subst,X431: subst,X432: term,X433: subst] :
( ( $true
!= ( X428 @ ( comp @ X430 @ X431 ) @ ( sub @ X432 @ X431 ) @ X433 ) )
| ( ( X428 @ X430 @ X432 @ ( comp @ X431 @ X433 ) )
= $true ) )
| ~ ! [X429: term] :
( ( $true
!= ( var @ ( sub @ X429 @ id ) ) )
| ( $true
= ( X428 @ id @ X429 @ id ) ) )
| ~ ! [X440: subst > term > term] :
( ~ ! [X441: term] :
( ( $true
!= ( X428 @ id @ X441 @ id ) )
| ( $true
= ( X428 @ id @ ( X440 @ id @ X441 ) @ id ) ) )
| ( ( X428 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X442: subst,X443: subst,X444: term] :
( ( X440 @ ( comp @ X442 @ X443 ) @ ( sub @ X444 @ X443 ) )
= ( sub @ ( X440 @ X442 @ X444 ) @ X443 ) ) )
| ( $true
= ( X428 @ id @ X427 @ id ) )
| ~ ! [X438: term,X439: term] :
( ( $true
!= ( X428 @ id @ X438 @ id ) )
| ( ( X428 @ id @ ( ap @ ( sub @ X438 @ id ) @ X439 ) @ id )
= $true )
| ( ( X428 @ id @ X439 @ id )
!= $true ) ) ) ) ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X204: subst > term > subst > $o] :
~ ! [X205: term > $o] :
~ ! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) ) )
& ( ulamvarsh = $true )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X216: subst > term > subst > $o] :
~ ! [X217: term > $o] :
~ ! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) ) )
& ( pushprop = $true )
& ( apnotvar = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
= X170 )
=> ( ! [X172: term,X173: subst] :
( ( comp @ sh @ ( push @ X172 @ X173 ) )
= X173 )
=> ( ! [X174: term,X175: term] :
( ( X174 = X175 )
| ( ( lam @ X175 )
!= ( lam @ X174 ) ) )
=> ! [X176: subst > term > term,X177: subst,X178: term,X179: subst > term > term] :
( ~ ! [X183: subst,X184: subst,X185: term] :
( ( sub @ ( X176 @ X183 @ X185 ) @ X184 )
= ( X176 @ ( comp @ X183 @ X184 ) @ ( sub @ X185 @ X184 ) ) )
| ( ( X179 @ X177 @ X178 )
= ( X176 @ X177 @ X178 ) )
| ( ( lam @ ( X176 @ sh @ one ) )
!= ( lam @ ( X179 @ sh @ one ) ) )
| ~ ! [X180: subst,X181: term,X182: subst] :
( ( sub @ ( X179 @ X182 @ X181 ) @ X180 )
= ( X179 @ ( comp @ X182 @ X180 ) @ ( sub @ X181 @ X180 ) ) ) ) ) ) ) )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
<=> ( apinj2 = $true ) )
& ( ( termmset_lthm = $true )
<=> ( ! [X157: term] :
( ( sub @ X157 @ id )
= X157 )
=> ! [X158: term] :
( ( sub @ X158 @ id )
= X158 ) ) )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( pushprop_lthm_orig = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X60: term,X61: subst > term > subst > $o] :
( ~ ! [X62: term] :
( ( ( X61 @ id @ X62 @ id )
!= $true )
| ( $true
= ( X61 @ id @ ( sub @ X60 @ ( push @ X62 @ id ) ) @ id ) ) )
| ( $true
= ( X61 @ id @ ( lam @ X60 ) @ id ) )
| ~ ! [X72: subst,X73: subst,X74: subst,X75: term] :
( ( $true
= ( X61 @ X73 @ X75 @ ( comp @ X74 @ X72 ) ) )
| ( $true
!= ( X61 @ ( comp @ X73 @ X74 ) @ ( sub @ X75 @ X74 ) @ X72 ) ) )
| ~ ! [X68: subst,X69: subst,X70: subst,X71: term] :
( ( $true
!= ( X61 @ X70 @ X71 @ ( comp @ X69 @ X68 ) ) )
| ( ( X61 @ ( comp @ X70 @ X69 ) @ ( sub @ X71 @ X69 ) @ X68 )
= $true ) )
| ~ ! [X63: subst > term > term] :
( ~ ! [X64: term] :
( ( $true
!= ( X61 @ id @ X64 @ id ) )
| ( $true
= ( X61 @ id @ ( X63 @ id @ X64 ) @ id ) ) )
| ~ ! [X65: term,X66: subst,X67: subst] :
( ( X63 @ ( comp @ X67 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( X63 @ X67 @ X65 ) @ X66 ) )
| ( $true
= ( X61 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id ) ) ) ) )
& ( ( ! [X120: term] :
( ( sub @ X120 @ id )
= X120 )
=> ( ! [X121: term,X122: subst > term > subst > $o] :
( ~ ! [X128: term] :
( ( $true
!= ( X122 @ id @ X128 @ id ) )
| ( $true
= ( X122 @ id @ ( sub @ X121 @ ( push @ X128 @ id ) ) @ id ) ) )
| ~ ! [X123: subst > term > term] :
( ~ ! [X124: term] :
( ( $true
= ( X122 @ id @ ( X123 @ id @ X124 ) @ id ) )
| ( $true
!= ( X122 @ id @ X124 @ id ) ) )
| ~ ! [X125: subst,X126: subst,X127: term] :
( ( sub @ ( X123 @ X125 @ X127 ) @ X126 )
= ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( sub @ X121 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X129: subst > term > subst > $o,X130: term] :
( ~ ! [X136: term] :
( ( $true
!= ( X129 @ id @ X136 @ id ) )
| ( $true
= ( X129 @ id @ ( sub @ X130 @ ( push @ X136 @ id ) ) @ id ) ) )
| ~ ! [X131: subst > term > term] :
( ( $true
= ( X129 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id ) )
| ~ ! [X132: term] :
( ( $true
= ( X129 @ id @ ( X131 @ id @ X132 ) @ id ) )
| ( $true
!= ( X129 @ id @ X132 @ id ) ) )
| ~ ! [X133: subst,X134: subst,X135: term] :
( ( sub @ ( X131 @ X133 @ X135 ) @ X134 )
= ( X131 @ ( comp @ X133 @ X134 ) @ ( sub @ X135 @ X134 ) ) ) )
| ( $true
= ( X129 @ id @ ( lam @ X130 ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( ! [X0: term] :
~ ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
= X351 )
=> ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ~ ! [X356: term] :
( ( X354 @ X356 )
= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) )
| ( $true
!= ( X352 @ X353 ) )
| ( $true
= ( X354 @ one ) ) ) ) )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X306: term,X307: term,X308: term,X309: term] :
( ( X306 = X308 )
| ( ( ap @ X307 @ X308 )
!= ( ap @ X309 @ X306 ) ) )
=> ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) ) ) )
& ( ( hoasinduction = $true )
<=> ! [X5: term,X6: subst > term > subst > $o] :
( ~ ! [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
| ( $true
!= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ~ ! [X21: term,X22: term] :
( ( $true
!= ( X6 @ id @ X21 @ id ) )
| ( $true
!= ( X6 @ id @ X22 @ id ) )
| ( $true
= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) ) )
| ~ ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) )
| ( $true
= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) ) )
| ~ ! [X12: subst > term > term] :
( ~ ! [X13: term] :
( ( ( X6 @ id @ X13 @ id )
!= $true )
| ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
| ~ ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
| ( $true
= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) )
| ~ ! [X11: term] :
( ( $true
= ( X6 @ id @ X11 @ id ) )
| ( $true
!= ( var @ ( sub @ X11 @ id ) ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( ( axvarcons = $true )
<=> ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X445: term] :
~ ! [X446: subst > term > term] :
~ ! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) ) )
& ( axabs = $true )
& ( lamnotap != $true )
& ( pushprop_lthm = $true )
& ( ( ! [X219: subst > term > subst > $o] :
~ ! [X220: term > $o] :
~ ! [X221: term] :
( ( X219 @ id @ X221 @ id )
= ( X220 @ X221 ) )
=> ( ! [X222: term > $o,X223: term] :
( ~ ! [X225: term] :
( ~ ! [X226: term] :
( ( $true
!= ( X222 @ X226 ) )
| ( $true
= ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) ) )
| ( $true
= ( X222 @ ( lam @ X225 ) ) ) )
| ~ ! [X227: term,X228: term] :
( ( $true
= ( X222 @ ( ap @ X228 @ X227 ) ) )
| ( $true
!= ( X222 @ X227 ) )
| ( $true
!= ( X222 @ X228 ) ) )
| ( $true
= ( X222 @ X223 ) )
| ~ ! [X224: term] :
( ( $true
!= ( var @ X224 ) )
| ( ( X222 @ X224 )
= $true ) ) )
=> ( ! [X229: term] :
( ( sub @ X229 @ id )
= X229 )
=> ( ! [X230: term,X231: term > $o,X232: subst > term > subst > $o] :
( ~ ! [X234: subst > term > term] :
( ~ ! [X235: term] :
( ( $true
= ( X232 @ id @ ( X234 @ id @ X235 ) @ id ) )
| ( $true
!= ( X232 @ id @ X235 @ id ) ) )
| ~ ! [X236: term,X237: subst,X238: subst] :
( ( X234 @ ( comp @ X237 @ X238 ) @ ( sub @ X236 @ X238 ) )
= ( sub @ ( X234 @ X237 @ X236 ) @ X238 ) )
| ( $true
= ( X232 @ id @ ( lam @ ( X234 @ sh @ one ) ) @ id ) ) )
| ~ ! [X239: term] :
( ( X232 @ id @ X239 @ id )
= ( X231 @ X239 ) )
| ( $true
= ( X231 @ ( lam @ X230 ) ) )
| ~ ! [X233: term] :
( ( ( X231 @ ( sub @ X230 @ ( push @ X233 @ id ) ) )
= $true )
| ( $true
!= ( X231 @ X233 ) ) ) )
=> ! [X240: subst > term > subst > $o,X241: term] :
( ~ ! [X242: term,X243: term] :
( ( $true
!= ( X240 @ id @ X243 @ id ) )
| ( ( X240 @ id @ X242 @ id )
!= $true )
| ( $true
= ( X240 @ id @ ( ap @ ( sub @ X242 @ id ) @ X243 ) @ id ) ) )
| ~ ! [X244: subst > term > term] :
( ~ ! [X246: subst,X247: term,X248: subst] :
( ( X244 @ ( comp @ X246 @ X248 ) @ ( sub @ X247 @ X248 ) )
= ( sub @ ( X244 @ X246 @ X247 ) @ X248 ) )
| ~ ! [X245: term] :
( ( $true
!= ( X240 @ id @ X245 @ id ) )
| ( $true
= ( X240 @ id @ ( X244 @ id @ X245 ) @ id ) ) )
| ( $true
= ( X240 @ id @ ( lam @ ( X244 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X240 @ id @ X241 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem3v2 = $true )
& ( one
= ( d2term @ d_one ) )
& ( ! [X249: term,X250: term,X251: subst > term > term] :
( ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) )
| ~ ! [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasapinj2_gthm = $true )
& ( ( ! [X359: term] :
( ( sub @ X359 @ id )
= X359 )
=> ! [X360: subst > term > subst > $o,X361: term,X362: term > $o] :
( ~ ! [X377: term] :
( ( ( X362 @ X377 )
!= $true )
| ( $true
= ( X362 @ ( sub @ X361 @ ( push @ X377 @ id ) ) ) ) )
| ( $true
= ( X362 @ ( lam @ X361 ) ) )
| ~ ! [X363: term] :
( ( X362 @ X363 )
= ( X360 @ id @ X363 @ id ) )
| ~ ! [X364: subst,X365: subst,X366: subst,X367: term] :
( ( $true
= ( X360 @ X366 @ X367 @ ( comp @ X365 @ X364 ) ) )
| ( $true
!= ( X360 @ ( comp @ X366 @ X365 ) @ ( sub @ X367 @ X365 ) @ X364 ) ) )
| ~ ! [X373: subst,X374: subst,X375: subst,X376: term] :
( ( $true
= ( X360 @ ( comp @ X375 @ X373 ) @ ( sub @ X376 @ X373 ) @ X374 ) )
| ( $true
!= ( X360 @ X375 @ X376 @ ( comp @ X373 @ X374 ) ) ) )
| ~ ! [X368: subst > term > term] :
( ~ ! [X370: subst,X371: term,X372: subst] :
( ( sub @ ( X368 @ X370 @ X371 ) @ X372 )
= ( X368 @ ( comp @ X370 @ X372 ) @ ( sub @ X371 @ X372 ) ) )
| ~ ! [X369: term] :
( ( $true
= ( X360 @ id @ ( X368 @ id @ X369 ) @ id ) )
| ( $true
!= ( X360 @ id @ X369 @ id ) ) )
| ( $true
= ( X360 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
<=> ( axscons = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ulamvar1 != $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( axmap = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
<=> ( substmonoid = $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X333: term > $o,X334: subst > term > subst > $o,X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ~ ! [X342: term] :
( ( X334 @ id @ X342 @ id )
= ( X333 @ X342 ) )
| ~ ! [X336: subst > term > term] :
( ~ ! [X337: subst,X338: subst,X339: term] :
( ( sub @ ( X336 @ X338 @ X339 ) @ X337 )
= ( X336 @ ( comp @ X338 @ X337 ) @ ( sub @ X339 @ X337 ) ) )
| ( $true
= ( X334 @ id @ ( lam @ ( X336 @ sh @ one ) ) @ id ) )
| ~ ! [X340: term] :
( ( $true
= ( X334 @ id @ ( X336 @ id @ X340 ) @ id ) )
| ( $true
!= ( X334 @ id @ X340 @ id ) ) ) )
| ~ ! [X341: term] :
( ( ( X333 @ X341 )
!= $true )
| ( $true
= ( X333 @ ( sub @ X335 @ ( push @ X341 @ id ) ) ) ) ) ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
<=> ( hoasapinj1 = $true ) )
& ( ! [X263: term,X264: term > $o,X265: subst > term > subst > $o] :
( ~ ! [X280: term] :
( ( X265 @ id @ X280 @ id )
= ( X264 @ X280 ) )
| ~ ! [X270: subst > term > term] :
( ~ ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) )
| ~ ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
| ( $true
= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X264 @ ( lam @ X263 ) ) )
| ~ ! [X276: subst,X277: subst,X278: subst,X279: term] :
( ( $true
= ( X265 @ X277 @ X279 @ ( comp @ X276 @ X278 ) ) )
| ( $true
!= ( X265 @ ( comp @ X277 @ X276 ) @ ( sub @ X279 @ X276 ) @ X278 ) ) )
| ~ ! [X266: term,X267: subst,X268: subst,X269: subst] :
( ( $true
= ( X265 @ ( comp @ X269 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 ) )
| ( ( X265 @ X269 @ X266 @ ( comp @ X268 @ X267 ) )
!= $true ) )
| ~ ! [X275: term] :
( ( ( X264 @ X275 )
!= $true )
| ( $true
= ( X264 @ ( sub @ X263 @ ( push @ X275 @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
= ( d2subst @ X349 ) )
=> ( X348 = X349 ) )
& ( axclos = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X476: subst > term > subst > $o,X477: term] :
( ~ ! [X483: term] :
( ( $true
= ( X476 @ id @ ( sub @ X477 @ ( push @ X483 @ id ) ) @ id ) )
| ( $true
!= ( X476 @ id @ X483 @ id ) ) )
| ~ ! [X478: subst > term > term] :
( ~ ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X482 @ X481 ) @ ( sub @ X480 @ X481 ) )
= ( sub @ ( X478 @ X482 @ X480 ) @ X481 ) )
| ~ ! [X479: term] :
( ( $true
= ( X476 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ( $true
!= ( X476 @ id @ X479 @ id ) ) )
| ( $true
= ( X476 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X476 @ id @ ( lam @ X477 ) @ id ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X137: term] :
~ ! [X138: subst > term > term] :
~ ! [X139: term,X140: subst] :
( ( X138 @ X140 @ X139 )
= ( sub @ X137 @ ( push @ X139 @ X140 ) ) )
=> ( ! [X141: term] :
( ( sub @ X141 @ id )
= X141 )
=> ! [X142: term,X143: subst > term > subst > $o,X144: term > $o] :
( ( $true
= ( X144 @ ( lam @ X142 ) ) )
| ~ ! [X151: term] :
( ( ( X144 @ X151 )
!= $true )
| ( $true
= ( X144 @ ( sub @ X142 @ ( push @ X151 @ id ) ) ) ) )
| ~ ! [X146: subst > term > term] :
( ~ ! [X150: term] :
( ( $true
!= ( X143 @ id @ X150 @ id ) )
| ( ( X143 @ id @ ( X146 @ id @ X150 ) @ id )
= $true ) )
| ( ( X143 @ id @ ( lam @ ( X146 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X147: term,X148: subst,X149: subst] :
( ( X146 @ ( comp @ X149 @ X148 ) @ ( sub @ X147 @ X148 ) )
= ( sub @ ( X146 @ X149 @ X147 ) @ X148 ) ) )
| ~ ! [X145: term] :
( ( X144 @ X145 )
= ( X143 @ id @ X145 @ id ) ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X159: subst > term > subst > $o,X160: term] :
( ~ ! [X161: term] :
( ( $true
!= ( X159 @ id @ X161 @ id ) )
| ( $true
= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) ) )
| ~ ! [X162: subst > term > term] :
( ~ ! [X164: subst,X165: subst,X166: term] :
( ( X162 @ ( comp @ X165 @ X164 ) @ ( sub @ X166 @ X164 ) )
= ( sub @ ( X162 @ X165 @ X166 ) @ X164 ) )
| ( $true
= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
| ~ ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) ) )
| ( ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id )
= $true ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapnotvar_gthm = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X467: term,X468: subst > term > subst > $o] :
( ( ( X468 @ id @ X467 @ id )
= $true )
| ~ ! [X474: term,X475: term] :
( ( $true
!= ( X468 @ id @ X475 @ id ) )
| ( $true
!= ( X468 @ id @ X474 @ id ) )
| ( $true
= ( X468 @ id @ ( ap @ ( sub @ X474 @ id ) @ X475 ) @ id ) ) )
| ~ ! [X469: subst > term > term] :
( ( $true
= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) )
| ~ ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
| ~ ! [X473: term] :
( ( $true
!= ( X468 @ id @ X473 @ id ) )
| ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true ) ) ) ) )
& ( ( induction2 = $true )
<=> ! [X283: term > $o,X284: term] :
( ( $true
= ( X283 @ X284 ) )
| ~ ! [X285: term] :
( ~ ! [X286: term] :
( ( ( X283 @ ( sub @ X285 @ ( push @ X286 @ id ) ) )
= $true )
| ( $true
!= ( X283 @ X286 ) ) )
| ( $true
= ( X283 @ ( lam @ X285 ) ) ) )
| ~ ! [X287: term] :
( ( $true
= ( X283 @ X287 ) )
| ( $true
!= ( var @ X287 ) ) )
| ~ ! [X288: term,X289: term] :
( ( $true
= ( X283 @ ( ap @ X288 @ X289 ) ) )
| ( ( X283 @ X289 )
!= $true )
| ( $true
!= ( X283 @ X288 ) ) ) ) )
& ( lamnotvar = $true )
& ( ( ! [X451: term] :
( ( sub @ X451 @ id )
= X451 )
=> ( ! [X452: subst,X453: term > $o,X454: term] :
( ~ ! [X455: term,X456: term] :
( ( $true
= ( X453 @ ( ap @ X455 @ X456 ) ) )
| ( $true
!= ( X453 @ X455 ) )
| ( $true
!= ( X453 @ X456 ) ) )
| ~ ! [X457: term] :
( ( $true
= ( X453 @ ( sub @ X457 @ X452 ) ) )
| ( $true
!= ( var @ X457 ) ) )
| ( $true
= ( X453 @ ( sub @ X454 @ X452 ) ) )
| ~ ! [X458: term] :
( ( $true
= ( X453 @ ( lam @ X458 ) ) )
| ~ ! [X459: term] :
( ( $true
!= ( X453 @ X459 ) )
| ( ( X453 @ ( sub @ X458 @ ( push @ X459 @ id ) ) )
= $true ) ) ) )
=> ! [X460: term > $o,X461: term] :
( ~ ! [X465: term,X466: term] :
( ( $true
= ( X460 @ ( ap @ X465 @ X466 ) ) )
| ( $true
!= ( X460 @ X466 ) )
| ( $true
!= ( X460 @ X465 ) ) )
| ~ ! [X462: term] :
( ( ( X460 @ X462 )
= $true )
| ( $true
!= ( var @ X462 ) ) )
| ( $true
= ( X460 @ X461 ) )
| ~ ! [X463: term] :
( ( $true
= ( X460 @ ( lam @ X463 ) ) )
| ~ ! [X464: term] :
( ( $true
!= ( X460 @ X464 ) )
| ( ( X460 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
= $true ) ) ) ) ) )
<=> ( induction2_lthm = $true ) )
& ! [X168: d_term,X169: d_term] :
( ( ( d2term @ X169 )
= ( d2term @ X168 ) )
=> ( X168 = X169 ) )
& ( ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X192: term,X193: subst > term > subst > $o] :
( ( $true
= ( X193 @ id @ ( lam @ ( sub @ X192 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X195: subst > term > term,X196: term] :
( ( ( X193 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X201: subst,X202: term,X203: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X202 @ X201 ) @ ( comp @ X203 @ X201 ) ) )
= ( X195 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) )
| ~ ! [X198: term,X199: subst,X200: subst] :
( ( sub @ ( sub @ X196 @ ( push @ X198 @ X199 ) ) @ X200 )
= ( sub @ ( X195 @ X199 @ X198 ) @ X200 ) )
| ~ ! [X197: term] :
( ( $true
= ( X193 @ id @ ( X195 @ id @ X197 ) @ id ) )
| ( $true
!= ( X193 @ id @ X197 @ id ) ) ) )
| ~ ! [X194: term] :
( ( $true
= ( X193 @ id @ ( sub @ X192 @ ( push @ X194 @ id ) ) @ id ) )
| ( $true
!= ( X193 @ id @ X194 @ id ) ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
= X291 )
=> ( ! [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
= X293 )
=> ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) )
| ( ( X297 @ X299 )
!= $true ) ) ) ) )
& ! [X48: d_subst] : ( d_id = X48 )
& ( hoasapinj1_gthm = $true )
& ( ( induction2lem_lthm = $true )
<=> ( ! [X314: term,X315: subst] :
( ( sub @ one @ ( push @ X314 @ X315 ) )
= X314 )
=> ( ! [X316: term,X317: subst] :
( ( comp @ sh @ ( push @ X316 @ X317 ) )
= X317 )
=> ( ! [X318: subst] :
( ( comp @ X318 @ id )
= X318 )
=> ( ! [X319: term > $o,X320: term] :
( ~ ! [X321: term] :
( ( ( X319 @ ( lam @ X321 ) )
= $true )
| ( $true
!= ( X319 @ X321 ) ) )
| ~ ! [X323: term,X324: term] :
( ( $true
!= ( X319 @ X324 ) )
| ( $true
= ( X319 @ ( ap @ X323 @ X324 ) ) )
| ( $true
!= ( X319 @ X323 ) ) )
| ( $true
= ( X319 @ X320 ) )
| ~ ! [X322: term] :
( ( $true
= ( X319 @ X322 ) )
| ( $true
!= ( var @ X322 ) ) ) )
=> ! [X325: subst,X326: term,X327: term > $o] :
( ~ ! [X328: term,X329: term] :
( ( $true
!= ( X327 @ X329 ) )
| ( $true
!= ( X327 @ X328 ) )
| ( $true
= ( X327 @ ( ap @ X329 @ X328 ) ) ) )
| ~ ! [X331: term] :
( ~ ! [X332: term] :
( ( $true
!= ( X327 @ X332 ) )
| ( $true
= ( X327 @ ( sub @ X331 @ ( push @ X332 @ id ) ) ) ) )
| ( ( X327 @ ( lam @ X331 ) )
= $true ) )
| ~ ! [X330: term] :
( ( $true
!= ( var @ X330 ) )
| ( $true
= ( X327 @ ( sub @ X330 @ X325 ) ) ) )
| ( $true
= ( X327 @ ( sub @ X326 @ X325 ) ) ) ) ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem3v2_lthm = $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 ) ) ) ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ~ ! [X37: term] :
( ( X26 @ X37 )
= ( X24 @ id @ X37 @ id ) )
| ~ ! [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
| ( $true
!= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ~ ! [X27: subst,X28: subst,X29: subst,X30: term] :
( ( $true
!= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) )
| ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
= $true ) )
| ( $true
!= ( X26 @ X25 ) )
| ( ( X26 @ X23 )
!= $true )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true )
| ~ ! [X31: term,X32: term] :
( ( $true
!= ( X24 @ id @ X31 @ id ) )
| ( $true
!= ( X24 @ id @ X32 @ id ) )
| ( $true
= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) ) ) ) )
& ( ! [X40: term] :
~ ! [X41: subst > term > term] :
~ ! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( axvarshift = $true )
& ( pushprop_gthm = $true )
& ( ( hoasapinj2 = $true )
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) ) )
& ( ( induction2lem = $true )
<=> ! [X76: term,X77: subst,X78: term > $o] :
( ~ ! [X79: term] :
( ( ( X78 @ ( lam @ X79 ) )
= $true )
| ~ ! [X80: term] :
( ( ( X78 @ X80 )
!= $true )
| ( ( X78 @ ( sub @ X79 @ ( push @ X80 @ id ) ) )
= $true ) ) )
| ~ ! [X82: term,X83: term] :
( ( ( X78 @ ( ap @ X83 @ X82 ) )
= $true )
| ( $true
!= ( X78 @ X83 ) )
| ( $true
!= ( X78 @ X82 ) ) )
| ~ ! [X81: term] :
( ( $true
= ( X78 @ ( sub @ X81 @ X77 ) ) )
| ( $true
!= ( var @ X81 ) ) )
| ( $true
= ( X78 @ ( sub @ X76 @ X77 ) ) ) ) )
& ( ( apinj1 = $true )
<=> ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X49: term > $o,X50: subst,X51: term] :
~ ! [X52: term > $o] :
~ ! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X207: subst,X208: term,X209: term > $o] :
~ ! [X210: term > $o] :
~ ! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( induction2_gthm = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ! [X0: term] :
~ ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( axabs = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction = $true )
<=> ! [X5: term,X6: subst > term > subst > $o] :
( ~ ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) )
| ( $true
= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) ) )
| ~ ! [X11: term] :
( ( $true
= ( X6 @ id @ X11 @ id ) )
| ( $true
!= ( var @ ( sub @ X11 @ id ) ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ~ ! [X12: subst > term > term] :
( ~ ! [X13: term] :
( ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) )
| ( ( X6 @ id @ X13 @ id )
!= $true ) )
| ~ ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
| ( $true
= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) )
| ~ ! [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
| ( $true
!= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ~ ! [X21: term,X22: term] :
( ( $true
= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) )
| ( $true
!= ( X6 @ id @ X21 @ id ) )
| ( $true
!= ( X6 @ id @ X22 @ id ) ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ~ ! [X27: subst,X28: subst,X29: subst,X30: term] :
( ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
= $true )
| ( $true
!= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) ) )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
| ( $true
!= ( X24 @ id @ X32 @ id ) )
| ( $true
!= ( X24 @ id @ X31 @ id ) ) )
| ~ ! [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
| ( $true
!= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ~ ! [X37: term] :
( ( X26 @ X37 )
= ( X24 @ id @ X37 @ id ) )
| ( ( X26 @ X23 )
!= $true )
| ( $true
!= ( X26 @ X25 ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X38: term] :
~ ! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) ) )
& ( ! [X40: term] :
~ ! [X41: subst > term > term] :
~ ! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( apinj1 = $true )
<=> ! [X44: term,X45: term,X46: term,X47: term] :
( ( ( ap @ X44 @ X47 )
!= ( ap @ X46 @ X45 ) )
| ( X44 = X46 ) ) )
& ! [X48: d_subst] : ( d_id = X48 )
& ( ! [X49: term > $o,X50: subst,X51: term] :
~ ! [X52: term > $o] :
~ ! [X53: term] :
( ( X52 @ X53 )
= ( X49 @ ( sub @ X53 @ ( push @ X51 @ X50 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( induction = $true )
<=> ! [X54: term,X55: term > $o] :
( ~ ! [X56: term] :
( ( $true
!= ( var @ X56 ) )
| ( $true
= ( X55 @ X56 ) ) )
| ~ ! [X57: term] :
( ( $true
= ( X55 @ ( lam @ X57 ) ) )
| ( $true
!= ( X55 @ X57 ) ) )
| ~ ! [X58: term,X59: term] :
( ( ( X55 @ ( ap @ X58 @ X59 ) )
= $true )
| ( $true
!= ( X55 @ X59 ) )
| ( $true
!= ( X55 @ X58 ) ) )
| ( $true
= ( X55 @ X54 ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X60: term,X61: subst > term > subst > $o] :
( ( $true
= ( X61 @ id @ ( lam @ X60 ) @ id ) )
| ~ ! [X62: term] :
( ( ( X61 @ id @ X62 @ id )
!= $true )
| ( $true
= ( X61 @ id @ ( sub @ X60 @ ( push @ X62 @ id ) ) @ id ) ) )
| ~ ! [X63: subst > term > term] :
( ~ ! [X64: term] :
( ( $true
!= ( X61 @ id @ X64 @ id ) )
| ( $true
= ( X61 @ id @ ( X63 @ id @ X64 ) @ id ) ) )
| ( $true
= ( X61 @ id @ ( lam @ ( X63 @ sh @ one ) ) @ id ) )
| ~ ! [X65: term,X66: subst,X67: subst] :
( ( X63 @ ( comp @ X67 @ X66 ) @ ( sub @ X65 @ X66 ) )
= ( sub @ ( X63 @ X67 @ X65 ) @ X66 ) ) )
| ~ ! [X68: subst,X69: subst,X70: subst,X71: term] :
( ( $true
!= ( X61 @ X70 @ X71 @ ( comp @ X69 @ X68 ) ) )
| ( ( X61 @ ( comp @ X70 @ X69 ) @ ( sub @ X71 @ X69 ) @ X68 )
= $true ) )
| ~ ! [X72: subst,X73: subst,X74: subst,X75: term] :
( ( $true
!= ( X61 @ ( comp @ X73 @ X74 ) @ ( sub @ X75 @ X74 ) @ X72 ) )
| ( $true
= ( X61 @ X73 @ X75 @ ( comp @ X74 @ X72 ) ) ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ( induction2lem = $true )
<=> ! [X76: term,X77: subst,X78: term > $o] :
( ~ ! [X79: term] :
( ( ( X78 @ ( lam @ X79 ) )
= $true )
| ~ ! [X80: term] :
( ( ( X78 @ X80 )
!= $true )
| ( ( X78 @ ( sub @ X79 @ ( push @ X80 @ id ) ) )
= $true ) ) )
| ~ ! [X81: term] :
( ( $true
= ( X78 @ ( sub @ X81 @ X77 ) ) )
| ( $true
!= ( var @ X81 ) ) )
| ( $true
= ( X78 @ ( sub @ X76 @ X77 ) ) )
| ~ ! [X82: term,X83: term] :
( ( ( X78 @ ( ap @ X83 @ X82 ) )
= $true )
| ( $true
!= ( X78 @ X83 ) )
| ( $true
!= ( X78 @ X82 ) ) ) ) )
& ( ( ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
=> ( ! [X85: term,X86: term,X87: term,X88: term] :
( ( ( ap @ X85 @ X87 )
!= ( ap @ X86 @ X88 ) )
| ( X85 = X86 ) )
=> ! [X89: term,X90: term,X91: term,X92: term] :
( ( ( ap @ ( sub @ X92 @ id ) @ X90 )
!= ( ap @ ( sub @ X89 @ id ) @ X91 ) )
| ( X89 = X92 ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( laminj = $true )
<=> ! [X93: term,X94: term] :
( ( X93 = X94 )
| ( ( lam @ X93 )
!= ( lam @ X94 ) ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X95: term] :
( ( sub @ X95 @ id )
= X95 )
=> ( ! [X96: term,X97: subst > term > subst > $o] :
( ~ ! [X98: subst > term > term] :
( ~ ! [X99: term,X100: subst,X101: subst] :
( ( X98 @ ( comp @ X101 @ X100 ) @ ( sub @ X99 @ X100 ) )
= ( sub @ ( X98 @ X101 @ X99 ) @ X100 ) )
| ( $true
= ( X97 @ id @ ( lam @ ( X98 @ sh @ one ) ) @ id ) )
| ~ ! [X102: term] :
( ( $true
!= ( X97 @ id @ X102 @ id ) )
| ( ( X97 @ id @ ( X98 @ id @ X102 ) @ id )
= $true ) ) )
| ( $true
= ( X97 @ id @ ( lam @ ( sub @ X96 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X103: term] :
( ( $true
!= ( X97 @ id @ X103 @ id ) )
| ( ( X97 @ id @ ( sub @ X96 @ ( push @ X103 @ id ) ) @ id )
= $true ) ) )
=> ! [X104: term,X105: subst > term > subst > $o] :
( ( $true
= ( X105 @ id @ ( lam @ X104 ) @ id ) )
| ~ ! [X106: subst > term > term] :
( ~ ! [X107: term] :
( ( $true
!= ( X105 @ id @ X107 @ id ) )
| ( $true
= ( X105 @ id @ ( X106 @ id @ X107 ) @ id ) ) )
| ( $true
= ( X105 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
| ~ ! [X108: subst,X109: term,X110: subst] :
( ( X106 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X110 ) ) )
| ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( $true
!= ( X105 @ X114 @ X112 @ ( comp @ X111 @ X113 ) ) )
| ( $true
= ( X105 @ ( comp @ X114 @ X111 ) @ ( sub @ X112 @ X111 ) @ X113 ) ) )
| ~ ! [X115: term] :
( ( $true
!= ( X105 @ id @ X115 @ id ) )
| ( ( X105 @ id @ ( sub @ X104 @ ( push @ X115 @ id ) ) @ id )
= $true ) )
| ~ ! [X116: subst,X117: subst,X118: subst,X119: term] :
( ( ( X105 @ ( comp @ X116 @ X118 ) @ ( sub @ X119 @ X118 ) @ X117 )
!= $true )
| ( $true
= ( X105 @ X116 @ X119 @ ( comp @ X118 @ X117 ) ) ) ) ) ) ) )
& ( ( ! [X120: term] :
( ( sub @ X120 @ id )
= X120 )
=> ( ! [X121: term,X122: subst > term > subst > $o] :
( ~ ! [X123: subst > term > term] :
( ~ ! [X124: term] :
( ( $true
!= ( X122 @ id @ X124 @ id ) )
| ( $true
= ( X122 @ id @ ( X123 @ id @ X124 ) @ id ) ) )
| ~ ! [X125: subst,X126: subst,X127: term] :
( ( sub @ ( X123 @ X125 @ X127 ) @ X126 )
= ( X123 @ ( comp @ X125 @ X126 ) @ ( sub @ X127 @ X126 ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( X123 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X122 @ id @ ( lam @ ( sub @ X121 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X128: term] :
( ( $true
= ( X122 @ id @ ( sub @ X121 @ ( push @ X128 @ id ) ) @ id ) )
| ( $true
!= ( X122 @ id @ X128 @ id ) ) ) )
=> ! [X129: subst > term > subst > $o,X130: term] :
( ( $true
= ( X129 @ id @ ( lam @ X130 ) @ id ) )
| ~ ! [X131: subst > term > term] :
( ~ ! [X132: term] :
( ( $true
= ( X129 @ id @ ( X131 @ id @ X132 ) @ id ) )
| ( $true
!= ( X129 @ id @ X132 @ id ) ) )
| ( $true
= ( X129 @ id @ ( lam @ ( X131 @ sh @ one ) ) @ id ) )
| ~ ! [X133: subst,X134: subst,X135: term] :
( ( sub @ ( X131 @ X133 @ X135 ) @ X134 )
= ( X131 @ ( comp @ X133 @ X134 ) @ ( sub @ X135 @ X134 ) ) ) )
| ~ ! [X136: term] :
( ( $true
= ( X129 @ id @ ( sub @ X130 @ ( push @ X136 @ id ) ) @ id ) )
| ( $true
!= ( X129 @ id @ X136 @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( ! [X137: term] :
~ ! [X138: subst > term > term] :
~ ! [X139: term,X140: subst] :
( ( X138 @ X140 @ X139 )
= ( sub @ X137 @ ( push @ X139 @ X140 ) ) )
=> ( ! [X141: term] :
( ( sub @ X141 @ id )
= X141 )
=> ! [X142: term,X143: subst > term > subst > $o,X144: term > $o] :
( ~ ! [X145: term] :
( ( X144 @ X145 )
= ( X143 @ id @ X145 @ id ) )
| ( $true
= ( X144 @ ( lam @ X142 ) ) )
| ~ ! [X146: subst > term > term] :
( ~ ! [X147: term,X148: subst,X149: subst] :
( ( X146 @ ( comp @ X149 @ X148 ) @ ( sub @ X147 @ X148 ) )
= ( sub @ ( X146 @ X149 @ X147 ) @ X148 ) )
| ~ ! [X150: term] :
( ( ( X143 @ id @ ( X146 @ id @ X150 ) @ id )
= $true )
| ( $true
!= ( X143 @ id @ X150 @ id ) ) )
| ( ( X143 @ id @ ( lam @ ( X146 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X151: term] :
( ( ( X144 @ X151 )
!= $true )
| ( $true
= ( X144 @ ( sub @ X142 @ ( push @ X151 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X152: term,X153: subst,X154: term > $o,X155: term > $o,X156: term] :
( ( $true
!= ( X155 @ X156 ) )
| ( ( X154 @ ( sub @ X156 @ ( push @ X152 @ X153 ) ) )
= $true ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X157: term] :
( ( sub @ X157 @ id )
= X157 )
=> ! [X158: term] :
( ( sub @ X158 @ id )
= X158 ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X159: subst > term > subst > $o,X160: term] :
( ~ ! [X161: term] :
( ( $true
= ( X159 @ id @ ( sub @ X160 @ ( push @ X161 @ id ) ) @ id ) )
| ( $true
!= ( X159 @ id @ X161 @ id ) ) )
| ~ ! [X162: subst > term > term] :
( ( $true
= ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id ) )
| ~ ! [X163: term] :
( ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) )
| ( $true
!= ( X159 @ id @ X163 @ id ) ) )
| ~ ! [X164: subst,X165: subst,X166: term] :
( ( X162 @ ( comp @ X165 @ X164 ) @ ( sub @ X166 @ X164 ) )
= ( sub @ ( X162 @ X165 @ X166 ) @ X164 ) ) )
| ( ( X159 @ id @ ( lam @ ( sub @ X160 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X167: term] :
( ( sub @ X167 @ id )
= X167 )
<=> ( axvarid = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X168: d_term,X169: d_term] :
( ( ( d2term @ X169 )
= ( d2term @ X168 ) )
=> ( X168 = X169 ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( axapp = $true )
& ( lamnotap != $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
= X170 )
=> ( ! [X172: term,X173: subst] :
( ( comp @ sh @ ( push @ X172 @ X173 ) )
= X173 )
=> ( ! [X174: term,X175: term] :
( ( X174 = X175 )
| ( ( lam @ X175 )
!= ( lam @ X174 ) ) )
=> ! [X176: subst > term > term,X177: subst,X178: term,X179: subst > term > term] :
( ~ ! [X183: subst,X184: subst,X185: term] :
( ( sub @ ( X176 @ X183 @ X185 ) @ X184 )
= ( X176 @ ( comp @ X183 @ X184 ) @ ( sub @ X185 @ X184 ) ) )
| ( ( X179 @ X177 @ X178 )
= ( X176 @ X177 @ X178 ) )
| ( ( lam @ ( X176 @ sh @ one ) )
!= ( lam @ ( X179 @ sh @ one ) ) )
| ~ ! [X180: subst,X181: term,X182: subst] :
( ( sub @ ( X179 @ X182 @ X181 ) @ X180 )
= ( X179 @ ( comp @ X182 @ X180 ) @ ( sub @ X181 @ X180 ) ) ) ) ) ) ) )
& ( lamnotvar = $true )
& ( ( shinj = $true )
<=> ! [X186: term,X187: term] :
( ( ( sub @ X187 @ sh )
!= ( sub @ X186 @ sh ) )
| ( X186 = X187 ) ) )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ! [X188: term,X189: term,X190: term,X191: term] :
( ( X190 = X191 )
| ( ( ap @ X189 @ X190 )
!= ( ap @ X188 @ X191 ) ) )
<=> ( apinj2 = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X192: term,X193: subst > term > subst > $o] :
( ( $true
= ( X193 @ id @ ( lam @ ( sub @ X192 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X194: term] :
( ( $true
= ( X193 @ id @ ( sub @ X192 @ ( push @ X194 @ id ) ) @ id ) )
| ( $true
!= ( X193 @ id @ X194 @ id ) ) )
| ~ ! [X195: subst > term > term,X196: term] :
( ( ( X193 @ id @ ( lam @ ( X195 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X197: term] :
( ( $true
!= ( X193 @ id @ X197 @ id ) )
| ( $true
= ( X193 @ id @ ( X195 @ id @ X197 ) @ id ) ) )
| ~ ! [X198: term,X199: subst,X200: subst] :
( ( sub @ ( sub @ X196 @ ( push @ X198 @ X199 ) ) @ X200 )
= ( sub @ ( X195 @ X199 @ X198 ) @ X200 ) )
| ~ ! [X201: subst,X202: term,X203: subst] :
( ( sub @ X196 @ ( push @ ( sub @ X202 @ X201 ) @ ( comp @ X203 @ X201 ) ) )
= ( X195 @ ( comp @ X203 @ X201 ) @ ( sub @ X202 @ X201 ) ) ) ) ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X204: subst > term > subst > $o] :
~ ! [X205: term > $o] :
~ ! [X206: term] :
( ( X205 @ X206 )
= ( X204 @ id @ X206 @ id ) ) )
& ( hoasapinj2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X207: subst,X208: term,X209: term > $o] :
~ ! [X210: term > $o] :
~ ! [X211: term] :
( ( X210 @ X211 )
= ( X209 @ ( sub @ X211 @ ( push @ X208 @ X207 ) ) ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X212: term,X213: term,X214: term,X215: term] :
( ( ( ap @ ( sub @ X215 @ id ) @ X212 )
!= ( ap @ ( sub @ X213 @ id ) @ X214 ) )
| ( X212 = X214 ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X216: subst > term > subst > $o] :
~ ! [X217: term > $o] :
~ ! [X218: term] :
( ( X216 @ id @ X218 @ id )
= ( X217 @ X218 ) ) )
& ( hoasapnotvar = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X219: subst > term > subst > $o] :
~ ! [X220: term > $o] :
~ ! [X221: term] :
( ( X219 @ id @ X221 @ id )
= ( X220 @ X221 ) )
=> ( ! [X222: term > $o,X223: term] :
( ~ ! [X224: term] :
( ( ( X222 @ X224 )
= $true )
| ( $true
!= ( var @ X224 ) ) )
| ~ ! [X225: term] :
( ( $true
= ( X222 @ ( lam @ X225 ) ) )
| ~ ! [X226: term] :
( ( $true
!= ( X222 @ X226 ) )
| ( $true
= ( X222 @ ( sub @ X225 @ ( push @ X226 @ id ) ) ) ) ) )
| ( $true
= ( X222 @ X223 ) )
| ~ ! [X227: term,X228: term] :
( ( $true
!= ( X222 @ X227 ) )
| ( $true
!= ( X222 @ X228 ) )
| ( $true
= ( X222 @ ( ap @ X228 @ X227 ) ) ) ) )
=> ( ! [X229: term] :
( ( sub @ X229 @ id )
= X229 )
=> ( ! [X230: term,X231: term > $o,X232: subst > term > subst > $o] :
( ( $true
= ( X231 @ ( lam @ X230 ) ) )
| ~ ! [X233: term] :
( ( ( X231 @ ( sub @ X230 @ ( push @ X233 @ id ) ) )
= $true )
| ( $true
!= ( X231 @ X233 ) ) )
| ~ ! [X234: subst > term > term] :
( ( $true
= ( X232 @ id @ ( lam @ ( X234 @ sh @ one ) ) @ id ) )
| ~ ! [X235: term] :
( ( $true
!= ( X232 @ id @ X235 @ id ) )
| ( $true
= ( X232 @ id @ ( X234 @ id @ X235 ) @ id ) ) )
| ~ ! [X236: term,X237: subst,X238: subst] :
( ( X234 @ ( comp @ X237 @ X238 ) @ ( sub @ X236 @ X238 ) )
= ( sub @ ( X234 @ X237 @ X236 ) @ X238 ) ) )
| ~ ! [X239: term] :
( ( X232 @ id @ X239 @ id )
= ( X231 @ X239 ) ) )
=> ! [X240: subst > term > subst > $o,X241: term] :
( ( $true
= ( X240 @ id @ X241 @ id ) )
| ~ ! [X242: term,X243: term] :
( ( ( X240 @ id @ X242 @ id )
!= $true )
| ( $true
= ( X240 @ id @ ( ap @ ( sub @ X242 @ id ) @ X243 ) @ id ) )
| ( $true
!= ( X240 @ id @ X243 @ id ) ) )
| ~ ! [X244: subst > term > term] :
( ( $true
= ( X240 @ id @ ( lam @ ( X244 @ sh @ one ) ) @ id ) )
| ~ ! [X245: term] :
( ( $true
!= ( X240 @ id @ X245 @ id ) )
| ( $true
= ( X240 @ id @ ( X244 @ id @ X245 ) @ id ) ) )
| ~ ! [X246: subst,X247: term,X248: subst] :
( ( X244 @ ( comp @ X246 @ X248 ) @ ( sub @ X247 @ X248 ) )
= ( sub @ ( X244 @ X246 @ X247 ) @ X248 ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X249: term,X250: term,X251: subst > term > term] :
( ( ( ap @ ( sub @ X250 @ id ) @ X249 )
!= ( lam @ ( X251 @ sh @ one ) ) )
| ~ ! [X252: term,X253: subst,X254: subst] :
( ( sub @ ( X251 @ X254 @ X252 ) @ X253 )
= ( X251 @ ( comp @ X254 @ X253 ) @ ( sub @ X252 @ X253 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X255: subst > term > subst > $o,X256: term] :
( ~ ! [X257: term] :
( ( $true
= ( X255 @ id @ ( sub @ X256 @ ( push @ X257 @ id ) ) @ id ) )
| ( $true
!= ( X255 @ id @ X257 @ id ) ) )
| ( ( X255 @ id @ ( lam @ ( sub @ X256 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X258: subst > term > term] :
( ~ ! [X259: subst,X260: subst,X261: term] :
( ( sub @ ( X258 @ X259 @ X261 ) @ X260 )
= ( X258 @ ( comp @ X259 @ X260 ) @ ( sub @ X261 @ X260 ) ) )
| ~ ! [X262: term] :
( ( $true
!= ( X255 @ id @ X262 @ id ) )
| ( ( X255 @ id @ ( X258 @ id @ X262 ) @ id )
= $true ) )
| ( $true
= ( X255 @ id @ ( lam @ ( X258 @ sh @ one ) ) @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X263: term,X264: term > $o,X265: subst > term > subst > $o] :
( ~ ! [X266: term,X267: subst,X268: subst,X269: subst] :
( ( $true
= ( X265 @ ( comp @ X269 @ X268 ) @ ( sub @ X266 @ X268 ) @ X267 ) )
| ( ( X265 @ X269 @ X266 @ ( comp @ X268 @ X267 ) )
!= $true ) )
| ~ ! [X270: subst > term > term] :
( ( $true
= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
| ~ ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) )
| ~ ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) ) )
| ~ ! [X275: term] :
( ( ( X264 @ X275 )
!= $true )
| ( $true
= ( X264 @ ( sub @ X263 @ ( push @ X275 @ id ) ) ) ) )
| ( $true
= ( X264 @ ( lam @ X263 ) ) )
| ~ ! [X276: subst,X277: subst,X278: subst,X279: term] :
( ( $true
= ( X265 @ X277 @ X279 @ ( comp @ X276 @ X278 ) ) )
| ( $true
!= ( X265 @ ( comp @ X277 @ X276 ) @ ( sub @ X279 @ X276 ) @ X278 ) ) )
| ~ ! [X280: term] :
( ( X265 @ id @ X280 @ id )
= ( X264 @ X280 ) ) ) )
& ( ! [X281: subst,X282: term] :
( ( comp @ sh @ ( push @ X282 @ X281 ) )
= X281 )
<=> ( axshiftcons = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( termmset_gthm = $true )
& ( axmap = $true )
& ( ! [X283: term > $o,X284: term] :
( ~ ! [X285: term] :
( ~ ! [X286: term] :
( ( ( X283 @ ( sub @ X285 @ ( push @ X286 @ id ) ) )
= $true )
| ( $true
!= ( X283 @ X286 ) ) )
| ( $true
= ( X283 @ ( lam @ X285 ) ) ) )
| ~ ! [X287: term] :
( ( $true
!= ( var @ X287 ) )
| ( $true
= ( X283 @ X287 ) ) )
| ~ ! [X288: term,X289: term] :
( ( ( X283 @ X289 )
!= $true )
| ( $true
= ( X283 @ ( ap @ X288 @ X289 ) ) )
| ( $true
!= ( X283 @ X288 ) ) )
| ( $true
= ( X283 @ X284 ) ) )
<=> ( induction2 = $true ) )
& ( ! [X290: subst] :
( ( comp @ id @ X290 )
= X290 )
<=> ( axidl = $true ) )
& ( ( ! [X291: term,X292: subst] :
( ( sub @ one @ ( push @ X291 @ X292 ) )
= X291 )
=> ( ! [X293: subst,X294: term] :
( ( comp @ sh @ ( push @ X294 @ X293 ) )
= X293 )
=> ! [X295: subst,X296: term > $o,X297: term > $o,X298: term,X299: term] :
( ( ( X297 @ X299 )
!= $true )
| ( $true
= ( X296 @ ( sub @ X299 @ ( push @ X298 @ X295 ) ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X300: subst,X301: term,X302: term > $o,X303: term > $o] :
( ( $true
= ( X303 @ one ) )
| ~ ! [X304: term] :
( ( X303 @ X304 )
= ( X302 @ ( sub @ X304 @ ( push @ X301 @ X300 ) ) ) )
| ( $true
!= ( X302 @ X301 ) ) ) )
& ( ( termmset = $true )
<=> ! [X305: term] :
( ( sub @ X305 @ id )
= X305 ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X306: term,X307: term,X308: term,X309: term] :
( ( X306 = X308 )
| ( ( ap @ X307 @ X308 )
!= ( ap @ X309 @ X306 ) ) )
=> ! [X310: term,X311: term,X312: term,X313: term] :
( ( ( ap @ ( sub @ X310 @ id ) @ X312 )
!= ( ap @ ( sub @ X313 @ id ) @ X311 ) )
| ( X311 = X312 ) ) ) )
& ( axvarshift = $true )
& ( ulamvar1 != $true )
& ( ( ! [X314: term,X315: subst] :
( ( sub @ one @ ( push @ X314 @ X315 ) )
= X314 )
=> ( ! [X316: term,X317: subst] :
( ( comp @ sh @ ( push @ X316 @ X317 ) )
= X317 )
=> ( ! [X318: subst] :
( ( comp @ X318 @ id )
= X318 )
=> ( ! [X319: term > $o,X320: term] :
( ~ ! [X321: term] :
( ( ( X319 @ ( lam @ X321 ) )
= $true )
| ( $true
!= ( X319 @ X321 ) ) )
| ( $true
= ( X319 @ X320 ) )
| ~ ! [X322: term] :
( ( $true
= ( X319 @ X322 ) )
| ( $true
!= ( var @ X322 ) ) )
| ~ ! [X323: term,X324: term] :
( ( $true
!= ( X319 @ X324 ) )
| ( $true
= ( X319 @ ( ap @ X323 @ X324 ) ) )
| ( $true
!= ( X319 @ X323 ) ) ) )
=> ! [X325: subst,X326: term,X327: term > $o] :
( ~ ! [X328: term,X329: term] :
( ( $true
!= ( X327 @ X329 ) )
| ( $true
!= ( X327 @ X328 ) )
| ( $true
= ( X327 @ ( ap @ X329 @ X328 ) ) ) )
| ~ ! [X330: term] :
( ( $true
!= ( var @ X330 ) )
| ( $true
= ( X327 @ ( sub @ X330 @ X325 ) ) ) )
| ~ ! [X331: term] :
( ~ ! [X332: term] :
( ( $true
!= ( X327 @ X332 ) )
| ( $true
= ( X327 @ ( sub @ X331 @ ( push @ X332 @ id ) ) ) ) )
| ( ( X327 @ ( lam @ X331 ) )
= $true ) )
| ( $true
= ( X327 @ ( sub @ X326 @ X325 ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ! [X333: term > $o,X334: subst > term > subst > $o,X335: term] :
( ( $true
= ( X333 @ ( lam @ X335 ) ) )
| ~ ! [X336: subst > term > term] :
( ~ ! [X337: subst,X338: subst,X339: term] :
( ( sub @ ( X336 @ X338 @ X339 ) @ X337 )
= ( X336 @ ( comp @ X338 @ X337 ) @ ( sub @ X339 @ X337 ) ) )
| ( $true
= ( X334 @ id @ ( lam @ ( X336 @ sh @ one ) ) @ id ) )
| ~ ! [X340: term] :
( ( $true
!= ( X334 @ id @ X340 @ id ) )
| ( $true
= ( X334 @ id @ ( X336 @ id @ X340 ) @ id ) ) ) )
| ~ ! [X341: term] :
( ( ( X333 @ X341 )
!= $true )
| ( $true
= ( X333 @ ( sub @ X335 @ ( push @ X341 @ id ) ) ) ) )
| ~ ! [X342: term] :
( ( X334 @ id @ X342 @ id )
= ( X333 @ X342 ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( induction2_gthm = $true )
& ! [X343: d_term] : ( d_one = X343 )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X344: subst] :
( ( comp @ id @ X344 )
= X344 )
=> ( ! [X345: subst] :
( ( comp @ X345 @ id )
= X345 )
=> ( ! [X347: subst] :
( ( comp @ X347 @ id )
= X347 )
& ! [X346: subst] :
( ( comp @ id @ X346 )
= X346 ) ) ) ) )
& ( axassoc = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X348: d_subst,X349: d_subst] :
( ( ( d2subst @ X348 )
= ( d2subst @ X349 ) )
=> ( X348 = X349 ) )
& ( ( ! [X350: subst,X351: term] :
( ( sub @ one @ ( push @ X351 @ X350 ) )
= X351 )
=> ! [X352: term > $o,X353: term,X354: term > $o,X355: subst] :
( ( $true
= ( X354 @ one ) )
| ( $true
!= ( X352 @ X353 ) )
| ~ ! [X356: term] :
( ( X354 @ X356 )
= ( X352 @ ( sub @ X356 @ ( push @ X353 @ X355 ) ) ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarsh = $true )
& ( ( ! [X357: subst] :
( ( comp @ id @ X357 )
= X357 )
& ! [X358: subst] :
( ( comp @ X358 @ id )
= X358 ) )
<=> ( substmonoid = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X359: term] :
( ( sub @ X359 @ id )
= X359 )
=> ! [X360: subst > term > subst > $o,X361: term,X362: term > $o] :
( ~ ! [X363: term] :
( ( X362 @ X363 )
= ( X360 @ id @ X363 @ id ) )
| ~ ! [X364: subst,X365: subst,X366: subst,X367: term] :
( ( $true
!= ( X360 @ ( comp @ X366 @ X365 ) @ ( sub @ X367 @ X365 ) @ X364 ) )
| ( $true
= ( X360 @ X366 @ X367 @ ( comp @ X365 @ X364 ) ) ) )
| ~ ! [X368: subst > term > term] :
( ~ ! [X369: term] :
( ( $true
= ( X360 @ id @ ( X368 @ id @ X369 ) @ id ) )
| ( $true
!= ( X360 @ id @ X369 @ id ) ) )
| ( $true
= ( X360 @ id @ ( lam @ ( X368 @ sh @ one ) ) @ id ) )
| ~ ! [X370: subst,X371: term,X372: subst] :
( ( sub @ ( X368 @ X370 @ X371 ) @ X372 )
= ( X368 @ ( comp @ X370 @ X372 ) @ ( sub @ X371 @ X372 ) ) ) )
| ~ ! [X373: subst,X374: subst,X375: subst,X376: term] :
( ( $true
!= ( X360 @ X375 @ X376 @ ( comp @ X373 @ X374 ) ) )
| ( $true
= ( X360 @ ( comp @ X375 @ X373 ) @ ( sub @ X376 @ X373 ) @ X374 ) ) )
| ~ ! [X377: term] :
( ( $true
= ( X362 @ ( sub @ X361 @ ( push @ X377 @ id ) ) ) )
| ( ( X362 @ X377 )
!= $true ) )
| ( $true
= ( X362 @ ( lam @ X361 ) ) ) ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X378: subst > term > subst > $o,X379: term,X380: term] :
( ~ ! [X381: term,X382: term] :
( ( ( X378 @ id @ X381 @ id )
!= $true )
| ( $true
= ( X378 @ id @ ( ap @ ( sub @ X381 @ id ) @ X382 ) @ id ) )
| ( $true
!= ( X378 @ id @ X382 @ id ) ) )
| ( $true
!= ( X378 @ id @ X380 @ id ) )
| ( $true
= ( X378 @ id @ ( ap @ X380 @ X379 ) @ id ) )
| ~ ! [X383: subst,X384: term,X385: subst,X386: subst] :
( ( $true
= ( X378 @ X386 @ X384 @ ( comp @ X383 @ X385 ) ) )
| ( $true
!= ( X378 @ ( comp @ X386 @ X383 ) @ ( sub @ X384 @ X383 ) @ X385 ) ) )
| ( $true
!= ( X378 @ id @ X379 @ id ) )
| ~ ! [X387: term,X388: subst,X389: subst,X390: subst] :
( ( $true
= ( X378 @ ( comp @ X390 @ X389 ) @ ( sub @ X387 @ X389 ) @ X388 ) )
| ( $true
!= ( X378 @ X390 @ X387 @ ( comp @ X389 @ X388 ) ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X391: term > $o,X392: term] :
( ~ ! [X393: term] :
( ( $true
!= ( var @ X393 ) )
| ( $true
= ( X391 @ X393 ) ) )
| ( $true
= ( X391 @ X392 ) )
| ~ ! [X394: term] :
( ~ ! [X395: term] :
( ( $true
!= ( X391 @ X395 ) )
| ( $true
= ( X391 @ ( sub @ X394 @ ( push @ X395 @ id ) ) ) ) )
| ( $true
= ( X391 @ ( lam @ X394 ) ) ) )
| ~ ! [X396: term,X397: term] :
( ( $true
= ( X391 @ ( ap @ X396 @ X397 ) ) )
| ( ( X391 @ X396 )
!= $true )
| ( ( X391 @ X397 )
!= $true ) ) )
=> ( ! [X398: term,X399: term,X400: subst > term > subst > $o] :
( ~ ! [X401: subst,X402: subst,X403: term,X404: subst] :
( ( $true
!= ( X400 @ ( comp @ X402 @ X401 ) @ ( sub @ X403 @ X401 ) @ X404 ) )
| ( $true
= ( X400 @ X402 @ X403 @ ( comp @ X401 @ X404 ) ) ) )
| ( $true
= ( X400 @ id @ ( ap @ X398 @ X399 ) @ id ) )
| ( $true
!= ( X400 @ id @ X398 @ id ) )
| ~ ! [X405: term,X406: subst,X407: subst,X408: subst] :
( ( $true
= ( X400 @ ( comp @ X407 @ X406 ) @ ( sub @ X405 @ X406 ) @ X408 ) )
| ( $true
!= ( X400 @ X407 @ X405 @ ( comp @ X406 @ X408 ) ) ) )
| ( $true
!= ( X400 @ id @ X399 @ id ) )
| ~ ! [X409: term,X410: term] :
( ( $true
!= ( X400 @ id @ X409 @ id ) )
| ( $true
!= ( X400 @ id @ X410 @ id ) )
| ( $true
= ( X400 @ id @ ( ap @ ( sub @ X409 @ id ) @ X410 ) @ id ) ) ) )
=> ( ! [X411: subst > term > subst > $o,X412: term] :
( ( $true
= ( X411 @ id @ ( lam @ X412 ) @ id ) )
| ~ ! [X413: subst,X414: term,X415: subst,X416: subst] :
( ( $true
= ( X411 @ ( comp @ X415 @ X416 ) @ ( sub @ X414 @ X416 ) @ X413 ) )
| ( $true
!= ( X411 @ X415 @ X414 @ ( comp @ X416 @ X413 ) ) ) )
| ~ ! [X417: subst,X418: subst,X419: term,X420: subst] :
( ( $true
!= ( X411 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) @ X417 ) )
| ( $true
= ( X411 @ X418 @ X419 @ ( comp @ X420 @ X417 ) ) ) )
| ~ ! [X421: subst > term > term] :
( ~ ! [X422: term] :
( ( ( X411 @ id @ ( X421 @ id @ X422 ) @ id )
= $true )
| ( $true
!= ( X411 @ id @ X422 @ id ) ) )
| ( ( X411 @ id @ ( lam @ ( X421 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X423: subst,X424: subst,X425: term] :
( ( sub @ ( X421 @ X424 @ X425 ) @ X423 )
= ( X421 @ ( comp @ X424 @ X423 ) @ ( sub @ X425 @ X423 ) ) ) )
| ~ ! [X426: term] :
( ( $true
!= ( X411 @ id @ X426 @ id ) )
| ( $true
= ( X411 @ id @ ( sub @ X412 @ ( push @ X426 @ id ) ) @ id ) ) ) )
=> ! [X427: term,X428: subst > term > subst > $o] :
( ~ ! [X429: term] :
( ( $true
!= ( var @ ( sub @ X429 @ id ) ) )
| ( $true
= ( X428 @ id @ X429 @ id ) ) )
| ~ ! [X430: subst,X431: subst,X432: term,X433: subst] :
( ( ( X428 @ X430 @ X432 @ ( comp @ X431 @ X433 ) )
= $true )
| ( $true
!= ( X428 @ ( comp @ X430 @ X431 ) @ ( sub @ X432 @ X431 ) @ X433 ) ) )
| ~ ! [X434: subst,X435: subst,X436: subst,X437: term] :
( ( $true
= ( X428 @ ( comp @ X436 @ X434 ) @ ( sub @ X437 @ X434 ) @ X435 ) )
| ( ( X428 @ X436 @ X437 @ ( comp @ X434 @ X435 ) )
!= $true ) )
| ~ ! [X438: term,X439: term] :
( ( ( X428 @ id @ ( ap @ ( sub @ X438 @ id ) @ X439 ) @ id )
= $true )
| ( $true
!= ( X428 @ id @ X438 @ id ) )
| ( ( X428 @ id @ X439 @ id )
!= $true ) )
| ~ ! [X440: subst > term > term] :
( ( ( X428 @ id @ ( lam @ ( X440 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X441: term] :
( ( $true
= ( X428 @ id @ ( X440 @ id @ X441 ) @ id ) )
| ( $true
!= ( X428 @ id @ X441 @ id ) ) )
| ~ ! [X442: subst,X443: subst,X444: term] :
( ( X440 @ ( comp @ X442 @ X443 ) @ ( sub @ X444 @ X443 ) )
= ( sub @ ( X440 @ X442 @ X444 ) @ X443 ) ) )
| ( $true
= ( X428 @ id @ X427 @ id ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X445: term] :
~ ! [X446: subst > term > term] :
~ ! [X447: term,X448: subst] :
( ( sub @ X445 @ ( push @ X447 @ X448 ) )
= ( X446 @ X448 @ X447 ) ) )
& ( ( axvarcons = $true )
<=> ! [X449: term,X450: subst] :
( ( sub @ one @ ( push @ X449 @ X450 ) )
= X449 ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X451: term] :
( ( sub @ X451 @ id )
= X451 )
=> ( ! [X452: subst,X453: term > $o,X454: term] :
( ~ ! [X455: term,X456: term] :
( ( $true
= ( X453 @ ( ap @ X455 @ X456 ) ) )
| ( $true
!= ( X453 @ X455 ) )
| ( $true
!= ( X453 @ X456 ) ) )
| ~ ! [X457: term] :
( ( $true
!= ( var @ X457 ) )
| ( $true
= ( X453 @ ( sub @ X457 @ X452 ) ) ) )
| ~ ! [X458: term] :
( ( $true
= ( X453 @ ( lam @ X458 ) ) )
| ~ ! [X459: term] :
( ( ( X453 @ ( sub @ X458 @ ( push @ X459 @ id ) ) )
= $true )
| ( $true
!= ( X453 @ X459 ) ) ) )
| ( $true
= ( X453 @ ( sub @ X454 @ X452 ) ) ) )
=> ! [X460: term > $o,X461: term] :
( ( $true
= ( X460 @ X461 ) )
| ~ ! [X462: term] :
( ( $true
!= ( var @ X462 ) )
| ( ( X460 @ X462 )
= $true ) )
| ~ ! [X463: term] :
( ~ ! [X464: term] :
( ( ( X460 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
= $true )
| ( $true
!= ( X460 @ X464 ) ) )
| ( $true
= ( X460 @ ( lam @ X463 ) ) ) )
| ~ ! [X465: term,X466: term] :
( ( $true
= ( X460 @ ( ap @ X465 @ X466 ) ) )
| ( $true
!= ( X460 @ X466 ) )
| ( $true
!= ( X460 @ X465 ) ) ) ) ) ) )
& ( ! [X467: term,X468: subst > term > subst > $o] :
( ~ ! [X469: subst > term > term] :
( ~ ! [X470: term,X471: subst,X472: subst] :
( ( sub @ ( X469 @ X472 @ X470 ) @ X471 )
= ( X469 @ ( comp @ X472 @ X471 ) @ ( sub @ X470 @ X471 ) ) )
| ( $true
= ( X468 @ id @ ( lam @ ( X469 @ sh @ one ) ) @ id ) )
| ~ ! [X473: term] :
( ( ( X468 @ id @ ( X469 @ id @ X473 ) @ id )
= $true )
| ( $true
!= ( X468 @ id @ X473 @ id ) ) ) )
| ~ ! [X474: term,X475: term] :
( ( $true
!= ( X468 @ id @ X475 @ id ) )
| ( $true
= ( X468 @ id @ ( ap @ ( sub @ X474 @ id ) @ X475 ) @ id ) )
| ( $true
!= ( X468 @ id @ X474 @ id ) ) )
| ( ( X468 @ id @ X467 @ id )
= $true ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X476: subst > term > subst > $o,X477: term] :
( ( $true
= ( X476 @ id @ ( lam @ X477 ) @ id ) )
| ~ ! [X478: subst > term > term] :
( ( $true
= ( X476 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id ) )
| ~ ! [X479: term] :
( ( $true
!= ( X476 @ id @ X479 @ id ) )
| ( $true
= ( X476 @ id @ ( X478 @ id @ X479 ) @ id ) ) )
| ~ ! [X480: term,X481: subst,X482: subst] :
( ( X478 @ ( comp @ X482 @ X481 ) @ ( sub @ X480 @ X481 ) )
= ( sub @ ( X478 @ X482 @ X480 ) @ X481 ) ) )
| ~ ! [X483: term] :
( ( $true
= ( X476 @ id @ ( sub @ X477 @ ( push @ X483 @ id ) ) @ id ) )
| ( $true
!= ( X476 @ id @ X483 @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ! [X484: term,X485: term,X486: term,X487: term] :
( ( ( ap @ ( sub @ X486 @ id ) @ X487 )
!= ( ap @ ( sub @ X484 @ id ) @ X485 ) )
| ( X484 = X486 ) )
<=> ( hoasapinj1 = $true ) )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X488: term,X489: subst,X490: subst > term > term,X491: subst > term > term] :
( ~ ! [X492: subst,X493: subst,X494: term] :
( ( X491 @ ( comp @ X492 @ X493 ) @ ( sub @ X494 @ X493 ) )
= ( sub @ ( X491 @ X492 @ X494 ) @ X493 ) )
| ~ ! [X495: subst,X496: subst,X497: term] :
( ( sub @ ( X490 @ X495 @ X497 ) @ X496 )
= ( X490 @ ( comp @ X495 @ X496 ) @ ( sub @ X497 @ X496 ) ) )
| ( ( lam @ ( X491 @ sh @ one ) )
!= ( lam @ ( X490 @ sh @ one ) ) )
| ( ( X491 @ X489 @ X488 )
= ( X490 @ X489 @ X488 ) ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_gthm = $true )
& ( axclos = $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 ) ) ) ) )
& ( ! [X498: subst] :
( ( push @ ( sub @ one @ X498 ) @ ( comp @ sh @ X498 ) )
= X498 )
<=> ( axscons = $true ) )
& ( hoasapnotvar_lthm = $true )
& ! [X499: term] :
? [X500: d_term] :
( ( d2term @ X500 )
= X499 )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X501: subst > term > subst > $o] :
~ ! [X502: term > $o] :
~ ! [X503: term] :
( ( X501 @ id @ X503 @ id )
= ( X502 @ X503 ) )
=> ( ! [X504: term > $o,X505: term] :
( ~ ! [X506: term,X507: term] :
( ( $true
= ( X504 @ ( ap @ X507 @ X506 ) ) )
| ( $true
!= ( X504 @ X507 ) )
| ( $true
!= ( X504 @ X506 ) ) )
| ~ ! [X508: term] :
( ( $true
= ( X504 @ X508 ) )
| ( $true
!= ( var @ X508 ) ) )
| ( $true
= ( X504 @ X505 ) )
| ~ ! [X509: term] :
( ~ ! [X510: term] :
( ( ( X504 @ X510 )
!= $true )
| ( ( X504 @ ( sub @ X509 @ ( push @ X510 @ id ) ) )
= $true ) )
| ( $true
= ( X504 @ ( lam @ X509 ) ) ) ) )
=> ( ! [X511: term] :
( ( sub @ X511 @ id )
= X511 )
=> ( ! [X512: term,X513: subst > term > subst > $o,X514: term > $o] :
( ~ ! [X515: subst > term > term] :
( ~ ! [X516: subst,X517: term,X518: subst] :
( ( sub @ ( X515 @ X516 @ X517 ) @ X518 )
= ( X515 @ ( comp @ X516 @ X518 ) @ ( sub @ X517 @ X518 ) ) )
| ( ( X513 @ id @ ( lam @ ( X515 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X519: term] :
( ( ( X513 @ id @ X519 @ id )
!= $true )
| ( $true
= ( X513 @ id @ ( X515 @ id @ X519 ) @ id ) ) ) )
| ( $true
= ( X514 @ ( lam @ X512 ) ) )
| ~ ! [X520: term] :
( ( $true
!= ( X514 @ X520 ) )
| ( ( X514 @ ( sub @ X512 @ ( push @ X520 @ id ) ) )
= $true ) )
| ~ ! [X521: term] :
( ( X514 @ X521 )
= ( X513 @ id @ X521 @ id ) ) )
=> ! [X522: subst > term > subst > $o,X523: term] :
( ( $true
= ( X522 @ id @ X523 @ id ) )
| ~ ! [X524: term] :
( ( ( var @ ( sub @ X524 @ id ) )
!= $true )
| ( $true
= ( X522 @ id @ X524 @ id ) ) )
| ~ ! [X525: subst,X526: term,X527: subst,X528: subst] :
( ( $true
!= ( X522 @ ( comp @ X527 @ X525 ) @ ( sub @ X526 @ X525 ) @ X528 ) )
| ( $true
= ( X522 @ X527 @ X526 @ ( comp @ X525 @ X528 ) ) ) )
| ~ ! [X529: subst > term > term] :
( ( ( X522 @ id @ ( lam @ ( X529 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X530: subst,X531: subst,X532: term] :
( ( X529 @ ( comp @ X530 @ X531 ) @ ( sub @ X532 @ X531 ) )
= ( sub @ ( X529 @ X530 @ X532 ) @ X531 ) )
| ~ ! [X533: term] :
( ( ( X522 @ id @ ( X529 @ id @ X533 ) @ id )
= $true )
| ( ( X522 @ id @ X533 @ id )
!= $true ) ) )
| ~ ! [X534: subst,X535: term,X536: subst,X537: subst] :
( ( $true
= ( X522 @ ( comp @ X537 @ X536 ) @ ( sub @ X535 @ X536 ) @ X534 ) )
| ( $true
!= ( X522 @ X537 @ X535 @ ( comp @ X536 @ X534 ) ) ) )
| ~ ! [X538: term,X539: term] :
( ( $true
= ( X522 @ id @ ( ap @ ( sub @ X538 @ id ) @ X539 ) @ id ) )
| ( ( X522 @ id @ X539 @ id )
!= $true )
| ( $true
!= ( X522 @ id @ X538 @ id ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ! [X0: term] :
~ ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( axabs = $true )
& ( hoasinduction_lem3_gthm = $true )
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( ( axidr = $true )
<=> ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) )
& ( ( d2subst @ d_id )
= id )
& ( ( hoasinduction = $true )
<=> ! [X5: term,X6: subst > term > subst > $o] :
( ~ ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) )
| ( $true
= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) ) )
| ~ ! [X11: term] :
( ( $true
= ( X6 @ id @ X11 @ id ) )
| ( $true
!= ( var @ ( sub @ X11 @ id ) ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ~ ! [X12: subst > term > term] :
( ~ ! [X13: term] :
( ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) )
| ( ( X6 @ id @ X13 @ id )
!= $true ) )
| ~ ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
| ( $true
= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) )
| ~ ! [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
| ( $true
!= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ~ ! [X21: term,X22: term] :
( ( $true
= ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id ) )
| ( $true
!= ( X6 @ id @ X21 @ id ) )
| ( $true
!= ( X6 @ id @ X22 @ id ) ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ~ ! [X27: subst,X28: subst,X29: subst,X30: term] :
( ( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
= $true )
| ( $true
!= ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) ) )
| ( ( X26 @ ( ap @ X25 @ X23 ) )
= $true )
| ~ ! [X31: term,X32: term] :
( ( $true
= ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id ) )
| ( $true
!= ( X24 @ id @ X32 @ id ) )
| ( $true
!= ( X24 @ id @ X31 @ id ) ) )
| ~ ! [X33: term,X34: subst,X35: subst,X36: subst] :
( ( $true
= ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 ) )
| ( $true
!= ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) ) )
| ~ ! [X37: term] :
( ( X26 @ X37 )
= ( X24 @ id @ X37 @ id ) )
| ( ( X26 @ X23 )
!= $true )
| ( $true
!= ( X26 @ X25 ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( pushprop = $true )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X38: term] :
~ ! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) ) )
& ( ! [X40: term] :
~ ! [X41: subst > term > term] :
~ ! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( induction2lem_gthm = $true )
& ( pushprop_lthm = $true )
& ( ( apinj1 = $true )
<=> ! [X46: term,X47: term,X48: term,X49: term] :
( ( ( ap @ X46 @ X49 )
!= ( ap @ X48 @ X47 ) )
| ( X46 = X48 ) ) )
& ! [X50: d_subst] : ( d_id = X50 )
& ( ! [X51: term > $o,X52: subst,X53: term] :
~ ! [X54: term > $o] :
~ ! [X55: term] :
( ( X54 @ X55 )
= ( X51 @ ( sub @ X55 @ ( push @ X53 @ X52 ) ) ) )
<=> ( pushprop_lem0 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( hoaslamnotvar = $true )
& ( ( induction = $true )
<=> ! [X56: term,X57: term > $o] :
( ~ ! [X58: term] :
( ( $true
!= ( var @ X58 ) )
| ( $true
= ( X57 @ X58 ) ) )
| ~ ! [X59: term] :
( ( ( X57 @ ( lam @ X59 ) )
= $true )
| ( $true
!= ( X57 @ X59 ) ) )
| ~ ! [X60: term,X61: term] :
( ( $true
= ( X57 @ ( ap @ X60 @ X61 ) ) )
| ( $true
!= ( X57 @ X61 ) )
| ( $true
!= ( X57 @ X60 ) ) )
| ( ( X57 @ X56 )
= $true ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X62: term,X63: subst > term > subst > $o] :
( ( $true
= ( X63 @ id @ ( lam @ X62 ) @ id ) )
| ~ ! [X64: term] :
( ( ( X63 @ id @ X64 @ id )
!= $true )
| ( ( X63 @ id @ ( sub @ X62 @ ( push @ X64 @ id ) ) @ id )
= $true ) )
| ~ ! [X65: subst > term > term] :
( ~ ! [X66: term] :
( ( ( X63 @ id @ X66 @ id )
!= $true )
| ( $true
= ( X63 @ id @ ( X65 @ id @ X66 ) @ id ) ) )
| ( ( X63 @ id @ ( lam @ ( X65 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X67: term,X68: subst,X69: subst] :
( ( X65 @ ( comp @ X69 @ X68 ) @ ( sub @ X67 @ X68 ) )
= ( sub @ ( X65 @ X69 @ X67 ) @ X68 ) ) )
| ~ ! [X70: subst,X71: subst,X72: subst,X73: term] :
( ( $true
!= ( X63 @ X72 @ X73 @ ( comp @ X71 @ X70 ) ) )
| ( $true
= ( X63 @ ( comp @ X72 @ X71 ) @ ( sub @ X73 @ X71 ) @ X70 ) ) )
| ~ ! [X74: subst,X75: subst,X76: subst,X77: term] :
( ( ( X63 @ ( comp @ X75 @ X76 ) @ ( sub @ X77 @ X76 ) @ X74 )
!= $true )
| ( ( X63 @ X75 @ X77 @ ( comp @ X76 @ X74 ) )
= $true ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ( induction2lem = $true )
<=> ! [X81: term,X82: subst,X83: term > $o] :
( ~ ! [X84: term] :
( ( $true
= ( X83 @ ( lam @ X84 ) ) )
| ~ ! [X85: term] :
( ( ( X83 @ X85 )
!= $true )
| ( $true
= ( X83 @ ( sub @ X84 @ ( push @ X85 @ id ) ) ) ) ) )
| ~ ! [X86: term] :
( ( $true
= ( X83 @ ( sub @ X86 @ X82 ) ) )
| ( $true
!= ( var @ X86 ) ) )
| ( $true
= ( X83 @ ( sub @ X81 @ X82 ) ) )
| ~ ! [X87: term,X88: term] :
( ( $true
= ( X83 @ ( ap @ X88 @ X87 ) ) )
| ( ( X83 @ X88 )
!= $true )
| ( $true
!= ( X83 @ X87 ) ) ) ) )
& ( ( ! [X89: term] :
( ( sub @ X89 @ id )
= X89 )
=> ( ! [X90: term,X91: term,X92: term,X93: term] :
( ( X90 = X91 )
| ( ( ap @ X90 @ X92 )
!= ( ap @ X91 @ X93 ) ) )
=> ! [X94: term,X95: term,X96: term,X97: term] :
( ( X94 = X97 )
| ( ( ap @ ( sub @ X94 @ id ) @ X96 )
!= ( ap @ ( sub @ X97 @ id ) @ X95 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X98: term,X99: term] :
( ( ( lam @ X99 )
!= ( lam @ X98 ) )
| ( X98 = X99 ) )
<=> ( laminj = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
=> ( ! [X101: term,X102: subst > term > subst > $o] :
( ~ ! [X103: subst > term > term] :
( ~ ! [X104: term,X105: subst,X106: subst] :
( ( X103 @ ( comp @ X106 @ X105 ) @ ( sub @ X104 @ X105 ) )
= ( sub @ ( X103 @ X106 @ X104 ) @ X105 ) )
| ( $true
= ( X102 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) )
| ~ ! [X107: term] :
( ( $true
!= ( X102 @ id @ X107 @ id ) )
| ( $true
= ( X102 @ id @ ( X103 @ id @ X107 ) @ id ) ) ) )
| ( $true
= ( X102 @ id @ ( lam @ ( sub @ X101 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X108: term] :
( ( $true
!= ( X102 @ id @ X108 @ id ) )
| ( $true
= ( X102 @ id @ ( sub @ X101 @ ( push @ X108 @ id ) ) @ id ) ) ) )
=> ! [X109: term,X110: subst > term > subst > $o] :
( ( $true
= ( X110 @ id @ ( lam @ X109 ) @ id ) )
| ~ ! [X111: subst > term > term] :
( ~ ! [X112: term] :
( ( ( X110 @ id @ X112 @ id )
!= $true )
| ( $true
= ( X110 @ id @ ( X111 @ id @ X112 ) @ id ) ) )
| ( $true
= ( X110 @ id @ ( lam @ ( X111 @ sh @ one ) ) @ id ) )
| ~ ! [X113: subst,X114: term,X115: subst] :
( ( sub @ ( X111 @ X113 @ X114 ) @ X115 )
= ( X111 @ ( comp @ X113 @ X115 ) @ ( sub @ X114 @ X115 ) ) ) )
| ~ ! [X116: subst,X117: term,X118: subst,X119: subst] :
( ( $true
!= ( X110 @ X119 @ X117 @ ( comp @ X116 @ X118 ) ) )
| ( ( X110 @ ( comp @ X119 @ X116 ) @ ( sub @ X117 @ X116 ) @ X118 )
= $true ) )
| ~ ! [X120: term] :
( ( $true
!= ( X110 @ id @ X120 @ id ) )
| ( $true
= ( X110 @ id @ ( sub @ X109 @ ( push @ X120 @ id ) ) @ id ) ) )
| ~ ! [X121: subst,X122: subst,X123: subst,X124: term] :
( ( $true
!= ( X110 @ ( comp @ X121 @ X123 ) @ ( sub @ X124 @ X123 ) @ X122 ) )
| ( $true
= ( X110 @ X121 @ X124 @ ( comp @ X123 @ X122 ) ) ) ) ) ) ) )
& ( ( ! [X125: term] :
( ( sub @ X125 @ id )
= X125 )
=> ( ! [X126: term,X127: subst > term > subst > $o] :
( ~ ! [X128: subst > term > term] :
( ~ ! [X129: term] :
( ( ( X127 @ id @ X129 @ id )
!= $true )
| ( $true
= ( X127 @ id @ ( X128 @ id @ X129 ) @ id ) ) )
| ~ ! [X130: subst,X131: subst,X132: term] :
( ( sub @ ( X128 @ X130 @ X132 ) @ X131 )
= ( X128 @ ( comp @ X130 @ X131 ) @ ( sub @ X132 @ X131 ) ) )
| ( $true
= ( X127 @ id @ ( lam @ ( X128 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X127 @ id @ ( lam @ ( sub @ X126 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X133: term] :
( ( $true
= ( X127 @ id @ ( sub @ X126 @ ( push @ X133 @ id ) ) @ id ) )
| ( $true
!= ( X127 @ id @ X133 @ id ) ) ) )
=> ! [X134: subst > term > subst > $o,X135: term] :
( ( $true
= ( X134 @ id @ ( lam @ X135 ) @ id ) )
| ~ ! [X136: subst > term > term] :
( ~ ! [X137: term] :
( ( $true
= ( X134 @ id @ ( X136 @ id @ X137 ) @ id ) )
| ( ( X134 @ id @ X137 @ id )
!= $true ) )
| ( $true
= ( X134 @ id @ ( lam @ ( X136 @ sh @ one ) ) @ id ) )
| ~ ! [X138: subst,X139: subst,X140: term] :
( ( X136 @ ( comp @ X138 @ X139 ) @ ( sub @ X140 @ X139 ) )
= ( sub @ ( X136 @ X138 @ X140 ) @ X139 ) ) )
| ~ ! [X141: term] :
( ( ( X134 @ id @ ( sub @ X135 @ ( push @ X141 @ id ) ) @ id )
= $true )
| ( $true
!= ( X134 @ id @ X141 @ id ) ) ) ) ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( ( ! [X142: term] :
~ ! [X143: subst > term > term] :
~ ! [X144: term,X145: subst] :
( ( sub @ X142 @ ( push @ X144 @ X145 ) )
= ( X143 @ X145 @ X144 ) )
=> ( ! [X146: term] :
( ( sub @ X146 @ id )
= X146 )
=> ! [X147: term,X148: subst > term > subst > $o,X149: term > $o] :
( ~ ! [X150: term] :
( ( X148 @ id @ X150 @ id )
= ( X149 @ X150 ) )
| ( $true
= ( X149 @ ( lam @ X147 ) ) )
| ~ ! [X151: subst > term > term] :
( ~ ! [X152: term,X153: subst,X154: subst] :
( ( sub @ ( X151 @ X154 @ X152 ) @ X153 )
= ( X151 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) ) )
| ~ ! [X155: term] :
( ( ( X148 @ id @ ( X151 @ id @ X155 ) @ id )
= $true )
| ( $true
!= ( X148 @ id @ X155 @ id ) ) )
| ( $true
= ( X148 @ id @ ( lam @ ( X151 @ sh @ one ) ) @ id ) ) )
| ~ ! [X156: term] :
( ( ( X149 @ X156 )
!= $true )
| ( $true
= ( X149 @ ( sub @ X147 @ ( push @ X156 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( pushprop_lem1 = $true )
<=> ! [X157: term,X158: subst,X159: term > $o,X160: term > $o,X161: term] :
( ( $true
!= ( X160 @ X161 ) )
| ( ( X159 @ ( sub @ X161 @ ( push @ X157 @ X158 ) ) )
= $true ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X162: term] :
( ( sub @ X162 @ id )
= X162 )
=> ! [X163: term] :
( ( sub @ X163 @ id )
= X163 ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( ulamvarind = $true )
& ( ! [X164: subst > term > subst > $o,X165: term] :
( ~ ! [X166: term] :
( ( $true
= ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id ) )
| ( $true
!= ( X164 @ id @ X166 @ id ) ) )
| ~ ! [X167: subst > term > term] :
( ( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X168: term] :
( ( ( X164 @ id @ ( X167 @ id @ X168 ) @ id )
= $true )
| ( $true
!= ( X164 @ id @ X168 @ id ) ) )
| ~ ! [X169: subst,X170: subst,X171: term] :
( ( X167 @ ( comp @ X170 @ X169 ) @ ( sub @ X171 @ X169 ) )
= ( sub @ ( X167 @ X170 @ X171 ) @ X169 ) ) )
| ( ( X164 @ id @ ( lam @ ( sub @ X165 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
<=> ( hoasinduction_lem3aa = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
<=> ( axvarid = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X173: d_term,X174: d_term] :
( ( ( d2term @ X174 )
= ( d2term @ X173 ) )
=> ( X173 = X174 ) )
& ( hoasapnotvar_gthm = $true )
& ( apnotvar = $true )
& ( axapp = $true )
& ( lamnotap != $true )
& ( pushprop_lem1_gthm = $true )
& ( ( ! [X175: term,X176: subst] :
( ( sub @ one @ ( push @ X175 @ X176 ) )
= X175 )
=> ( ! [X177: term,X178: subst] :
( ( comp @ sh @ ( push @ X177 @ X178 ) )
= X178 )
=> ( ! [X179: term,X180: term] :
( ( X179 = X180 )
| ( ( lam @ X180 )
!= ( lam @ X179 ) ) )
=> ! [X181: subst > term > term,X182: subst,X183: term,X184: subst > term > term] :
( ~ ! [X185: subst,X186: term,X187: subst] :
( ( X184 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) )
= ( sub @ ( X184 @ X187 @ X186 ) @ X185 ) )
| ~ ! [X188: subst,X189: subst,X190: term] :
( ( sub @ ( X181 @ X188 @ X190 ) @ X189 )
= ( X181 @ ( comp @ X188 @ X189 ) @ ( sub @ X190 @ X189 ) ) )
| ( ( X181 @ X182 @ X183 )
= ( X184 @ X182 @ X183 ) )
| ( ( lam @ ( X184 @ sh @ one ) )
!= ( lam @ ( X181 @ sh @ one ) ) ) ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( lamnotvar = $true )
& ( ( shinj = $true )
<=> ! [X191: term,X192: term] :
( ( X191 = X192 )
| ( ( sub @ X192 @ sh )
!= ( sub @ X191 @ sh ) ) ) )
& ( hoasinduction_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( apinj2 = $true )
<=> ! [X193: term,X194: term,X195: term,X196: term] :
( ( ( ap @ X193 @ X196 )
!= ( ap @ X194 @ X195 ) )
| ( X195 = X196 ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X197: term,X198: subst > term > subst > $o] :
( ( $true
= ( X198 @ id @ ( lam @ ( sub @ X197 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X199: term] :
( ( $true
= ( X198 @ id @ ( sub @ X197 @ ( push @ X199 @ id ) ) @ id ) )
| ( ( X198 @ id @ X199 @ id )
!= $true ) )
| ~ ! [X200: subst > term > term,X201: term] :
( ( $true
= ( X198 @ id @ ( lam @ ( X200 @ sh @ one ) ) @ id ) )
| ~ ! [X202: term] :
( ( $true
!= ( X198 @ id @ X202 @ id ) )
| ( $true
= ( X198 @ id @ ( X200 @ id @ X202 ) @ id ) ) )
| ~ ! [X203: term,X204: subst,X205: subst] :
( ( sub @ ( sub @ X201 @ ( push @ X203 @ X204 ) ) @ X205 )
= ( sub @ ( X200 @ X204 @ X203 ) @ X205 ) )
| ~ ! [X206: subst,X207: term,X208: subst] :
( ( X200 @ ( comp @ X208 @ X206 ) @ ( sub @ X207 @ X206 ) )
= ( sub @ X201 @ ( push @ ( sub @ X207 @ X206 ) @ ( comp @ X208 @ X206 ) ) ) ) ) ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X209: subst > term > subst > $o] :
~ ! [X210: term > $o] :
~ ! [X211: term] :
( ( X209 @ id @ X211 @ id )
= ( X210 @ X211 ) ) )
& ( hoasapinj2_gthm = $true )
& ( pushprop_lem2v2 = $true )
& ( ! [X212: subst,X213: term,X214: term > $o] :
~ ! [X215: term > $o] :
~ ! [X216: term] :
( ( X214 @ ( sub @ X216 @ ( push @ X213 @ X212 ) ) )
= ( X215 @ X216 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( hoasapinj2 = $true )
<=> ! [X217: term,X218: term,X219: term,X220: term] :
( ( X217 = X219 )
| ( ( ap @ ( sub @ X220 @ id ) @ X217 )
!= ( ap @ ( sub @ X218 @ id ) @ X219 ) ) ) )
& ( ! [X221: subst > term > subst > $o] :
~ ! [X222: term > $o] :
~ ! [X223: term] :
( ( X221 @ id @ X223 @ id )
= ( X222 @ X223 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoasapnotvar = $true )
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X224: subst > term > subst > $o] :
~ ! [X225: term > $o] :
~ ! [X226: term] :
( ( X224 @ id @ X226 @ id )
= ( X225 @ X226 ) )
=> ( ! [X227: term > $o,X228: term] :
( ~ ! [X229: term] :
( ( ( X227 @ X229 )
= $true )
| ( ( var @ X229 )
!= $true ) )
| ~ ! [X230: term] :
( ( $true
= ( X227 @ ( lam @ X230 ) ) )
| ~ ! [X231: term] :
( ( ( X227 @ X231 )
!= $true )
| ( $true
= ( X227 @ ( sub @ X230 @ ( push @ X231 @ id ) ) ) ) ) )
| ( $true
= ( X227 @ X228 ) )
| ~ ! [X232: term,X233: term] :
( ( $true
!= ( X227 @ X232 ) )
| ( $true
!= ( X227 @ X233 ) )
| ( $true
= ( X227 @ ( ap @ X233 @ X232 ) ) ) ) )
=> ( ! [X234: term] :
( ( sub @ X234 @ id )
= X234 )
=> ( ! [X235: term,X236: term > $o,X237: subst > term > subst > $o] :
( ( $true
= ( X236 @ ( lam @ X235 ) ) )
| ~ ! [X238: term] :
( ( $true
= ( X236 @ ( sub @ X235 @ ( push @ X238 @ id ) ) ) )
| ( $true
!= ( X236 @ X238 ) ) )
| ~ ! [X239: subst > term > term] :
( ( $true
= ( X237 @ id @ ( lam @ ( X239 @ sh @ one ) ) @ id ) )
| ~ ! [X240: term] :
( ( ( X237 @ id @ X240 @ id )
!= $true )
| ( $true
= ( X237 @ id @ ( X239 @ id @ X240 ) @ id ) ) )
| ~ ! [X241: term,X242: subst,X243: subst] :
( ( sub @ ( X239 @ X242 @ X241 ) @ X243 )
= ( X239 @ ( comp @ X242 @ X243 ) @ ( sub @ X241 @ X243 ) ) ) )
| ~ ! [X244: term] :
( ( X237 @ id @ X244 @ id )
= ( X236 @ X244 ) ) )
=> ! [X245: subst > term > subst > $o,X246: term] :
( ( $true
= ( X245 @ id @ X246 @ id ) )
| ~ ! [X247: term,X248: term] :
( ( $true
!= ( X245 @ id @ X247 @ id ) )
| ( $true
= ( X245 @ id @ ( ap @ ( sub @ X247 @ id ) @ X248 ) @ id ) )
| ( ( X245 @ id @ X248 @ id )
!= $true ) )
| ~ ! [X249: subst > term > term] :
( ( $true
= ( X245 @ id @ ( lam @ ( X249 @ sh @ one ) ) @ id ) )
| ~ ! [X250: term] :
( ( $true
!= ( X245 @ id @ X250 @ id ) )
| ( $true
= ( X245 @ id @ ( X249 @ id @ X250 ) @ id ) ) )
| ~ ! [X251: subst,X252: term,X253: subst] :
( ( X249 @ ( comp @ X251 @ X253 ) @ ( sub @ X252 @ X253 ) )
= ( sub @ ( X249 @ X251 @ X252 ) @ X253 ) ) ) ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( ! [X254: term,X255: term,X256: subst > term > term] :
( ~ ! [X257: term,X258: subst,X259: subst] :
( ( X256 @ ( comp @ X259 @ X258 ) @ ( sub @ X257 @ X258 ) )
= ( sub @ ( X256 @ X259 @ X257 ) @ X258 ) )
| ( ( lam @ ( X256 @ sh @ one ) )
!= ( ap @ ( sub @ X255 @ id ) @ X254 ) ) )
<=> ( hoaslamnotap = $true ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoasinduction_lem3aa_lthm = $true )
<=> ! [X260: subst > term > subst > $o,X261: term] :
( ~ ! [X262: term] :
( ( $true
= ( X260 @ id @ ( sub @ X261 @ ( push @ X262 @ id ) ) @ id ) )
| ( $true
!= ( X260 @ id @ X262 @ id ) ) )
| ( $true
= ( X260 @ id @ ( lam @ ( sub @ X261 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X263: subst > term > term] :
( ~ ! [X264: subst,X265: subst,X266: term] :
( ( sub @ ( X263 @ X264 @ X266 ) @ X265 )
= ( X263 @ ( comp @ X264 @ X265 ) @ ( sub @ X266 @ X265 ) ) )
| ~ ! [X267: term] :
( ( $true
!= ( X260 @ id @ X267 @ id ) )
| ( ( X260 @ id @ ( X263 @ id @ X267 ) @ id )
= $true ) )
| ( ( X260 @ id @ ( lam @ ( X263 @ sh @ one ) ) @ id )
= $true ) ) ) )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X268: term,X269: term > $o,X270: subst > term > subst > $o] :
( ~ ! [X271: term,X272: subst,X273: subst,X274: subst] :
( ( $true
= ( X270 @ ( comp @ X274 @ X273 ) @ ( sub @ X271 @ X273 ) @ X272 ) )
| ( $true
!= ( X270 @ X274 @ X271 @ ( comp @ X273 @ X272 ) ) ) )
| ~ ! [X275: subst > term > term] :
( ( $true
= ( X270 @ id @ ( lam @ ( X275 @ sh @ one ) ) @ id ) )
| ~ ! [X276: term] :
( ( $true
= ( X270 @ id @ ( X275 @ id @ X276 ) @ id ) )
| ( ( X270 @ id @ X276 @ id )
!= $true ) )
| ~ ! [X277: subst,X278: subst,X279: term] :
( ( sub @ ( X275 @ X277 @ X279 ) @ X278 )
= ( X275 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) ) ) )
| ~ ! [X280: term] :
( ( $true
!= ( X269 @ X280 ) )
| ( ( X269 @ ( sub @ X268 @ ( push @ X280 @ id ) ) )
= $true ) )
| ( ( X269 @ ( lam @ X268 ) )
= $true )
| ~ ! [X281: subst,X282: subst,X283: subst,X284: term] :
( ( $true
= ( X270 @ X282 @ X284 @ ( comp @ X281 @ X283 ) ) )
| ( $true
!= ( X270 @ ( comp @ X282 @ X281 ) @ ( sub @ X284 @ X281 ) @ X283 ) ) )
| ~ ! [X285: term] :
( ( X269 @ X285 )
= ( X270 @ id @ X285 @ id ) ) ) )
& ( ! [X286: subst,X287: term] :
( ( comp @ sh @ ( push @ X287 @ X286 ) )
= X286 )
<=> ( axshiftcons = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ( termmset_gthm = $true )
& ( axmap = $true )
& ( ! [X288: term > $o,X289: term] :
( ~ ! [X290: term] :
( ~ ! [X291: term] :
( ( $true
= ( X288 @ ( sub @ X290 @ ( push @ X291 @ id ) ) ) )
| ( $true
!= ( X288 @ X291 ) ) )
| ( $true
= ( X288 @ ( lam @ X290 ) ) ) )
| ~ ! [X292: term] :
( ( ( var @ X292 )
!= $true )
| ( $true
= ( X288 @ X292 ) ) )
| ~ ! [X293: term,X294: term] :
( ( ( X288 @ X294 )
!= $true )
| ( ( X288 @ ( ap @ X293 @ X294 ) )
= $true )
| ( $true
!= ( X288 @ X293 ) ) )
| ( $true
= ( X288 @ X289 ) ) )
<=> ( induction2 = $true ) )
& ( ! [X295: subst] :
( ( comp @ id @ X295 )
= X295 )
<=> ( axidl = $true ) )
& ( ( ! [X296: term,X297: subst] :
( ( sub @ one @ ( push @ X296 @ X297 ) )
= X296 )
=> ( ! [X298: subst,X299: term] :
( ( comp @ sh @ ( push @ X299 @ X298 ) )
= X298 )
=> ! [X300: subst,X301: term > $o,X302: term > $o,X303: term,X304: term] :
( ( ( X302 @ X304 )
!= $true )
| ( $true
= ( X301 @ ( sub @ X304 @ ( push @ X303 @ X300 ) ) ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( pushprop_lem1v2 = $true )
<=> ! [X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( ( X308 @ one )
= $true )
| ~ ! [X309: term] :
( ( X308 @ X309 )
= ( X307 @ ( sub @ X309 @ ( push @ X306 @ X305 ) ) ) )
| ( $true
!= ( X307 @ X306 ) ) ) )
& ( ! [X310: term] :
( ( sub @ X310 @ id )
= X310 )
<=> ( termmset = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X311: term,X312: term,X313: term,X314: term] :
( ( ( ap @ X312 @ X313 )
!= ( ap @ X314 @ X311 ) )
| ( X311 = X313 ) )
=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X316 = X317 )
| ( ( ap @ ( sub @ X318 @ id ) @ X316 )
!= ( ap @ ( sub @ X315 @ id ) @ X317 ) ) ) ) )
& ( axvarshift = $true )
& ( ulamvar1 != $true )
& ( ( ! [X319: term,X320: subst] :
( ( sub @ one @ ( push @ X319 @ X320 ) )
= X319 )
=> ( ! [X321: term,X322: subst] :
( ( comp @ sh @ ( push @ X321 @ X322 ) )
= X322 )
=> ( ! [X323: subst] :
( ( comp @ X323 @ id )
= X323 )
=> ( ! [X324: term > $o,X325: term] :
( ~ ! [X326: term] :
( ( $true
= ( X324 @ ( lam @ X326 ) ) )
| ( $true
!= ( X324 @ X326 ) ) )
| ( $true
= ( X324 @ X325 ) )
| ~ ! [X327: term] :
( ( $true
= ( X324 @ X327 ) )
| ( $true
!= ( var @ X327 ) ) )
| ~ ! [X328: term,X329: term] :
( ( $true
!= ( X324 @ X329 ) )
| ( $true
= ( X324 @ ( ap @ X328 @ X329 ) ) )
| ( $true
!= ( X324 @ X328 ) ) ) )
=> ! [X330: subst,X331: term,X332: term > $o] :
( ~ ! [X333: term,X334: term] :
( ( $true
!= ( X332 @ X334 ) )
| ( ( X332 @ X333 )
!= $true )
| ( $true
= ( X332 @ ( ap @ X334 @ X333 ) ) ) )
| ~ ! [X335: term] :
( ( $true
!= ( var @ X335 ) )
| ( $true
= ( X332 @ ( sub @ X335 @ X330 ) ) ) )
| ~ ! [X336: term] :
( ~ ! [X337: term] :
( ( $true
!= ( X332 @ X337 ) )
| ( $true
= ( X332 @ ( sub @ X336 @ ( push @ X337 @ id ) ) ) ) )
| ( ( X332 @ ( lam @ X336 ) )
= $true ) )
| ( $true
= ( X332 @ ( sub @ X331 @ X330 ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( ! [X338: term > $o,X339: subst > term > subst > $o,X340: term] :
( ( $true
= ( X338 @ ( lam @ X340 ) ) )
| ~ ! [X341: subst > term > term] :
( ~ ! [X342: subst,X343: subst,X344: term] :
( ( sub @ ( X341 @ X343 @ X344 ) @ X342 )
= ( X341 @ ( comp @ X343 @ X342 ) @ ( sub @ X344 @ X342 ) ) )
| ( $true
= ( X339 @ id @ ( lam @ ( X341 @ sh @ one ) ) @ id ) )
| ~ ! [X345: term] :
( ( $true
!= ( X339 @ id @ X345 @ id ) )
| ( ( X339 @ id @ ( X341 @ id @ X345 ) @ id )
= $true ) ) )
| ~ ! [X346: term] :
( ( $true
!= ( X338 @ X346 ) )
| ( $true
= ( X338 @ ( sub @ X340 @ ( push @ X346 @ id ) ) ) ) )
| ~ ! [X347: term] :
( ( X338 @ X347 )
= ( X339 @ id @ X347 @ id ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( induction2_gthm = $true )
& ! [X348: d_term] : ( d_one = X348 )
& ( ( ! [X349: subst] :
( ( comp @ id @ X349 )
= X349 )
=> ( ! [X350: subst] :
( ( comp @ X350 @ id )
= X350 )
=> ( ! [X351: subst] :
( ( comp @ id @ X351 )
= X351 )
& ! [X352: subst] :
( ( comp @ X352 @ id )
= X352 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( axassoc = $true )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X353: d_subst,X354: d_subst] :
( ( ( d2subst @ X354 )
= ( d2subst @ X353 ) )
=> ( X353 = X354 ) )
& ( ( ! [X355: subst,X356: term] :
( ( sub @ one @ ( push @ X356 @ X355 ) )
= X356 )
=> ! [X357: term > $o,X358: term,X359: term > $o,X360: subst] :
( ( $true
= ( X359 @ one ) )
| ( $true
!= ( X357 @ X358 ) )
| ~ ! [X361: term] :
( ( X357 @ ( sub @ X361 @ ( push @ X358 @ X360 ) ) )
= ( X359 @ X361 ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ulamvarsh = $true )
& ( ( ! [X362: subst] :
( ( comp @ id @ X362 )
= X362 )
& ! [X363: subst] :
( ( comp @ X363 @ id )
= X363 ) )
<=> ( substmonoid = $true ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X364: term] :
( ( sub @ X364 @ id )
= X364 )
=> ! [X365: subst > term > subst > $o,X366: term,X367: term > $o] :
( ~ ! [X368: term] :
( ( X365 @ id @ X368 @ id )
= ( X367 @ X368 ) )
| ~ ! [X369: subst,X370: subst,X371: subst,X372: term] :
( ( $true
!= ( X365 @ ( comp @ X371 @ X370 ) @ ( sub @ X372 @ X370 ) @ X369 ) )
| ( $true
= ( X365 @ X371 @ X372 @ ( comp @ X370 @ X369 ) ) ) )
| ~ ! [X373: subst > term > term] :
( ~ ! [X374: term] :
( ( $true
= ( X365 @ id @ ( X373 @ id @ X374 ) @ id ) )
| ( $true
!= ( X365 @ id @ X374 @ id ) ) )
| ( $true
= ( X365 @ id @ ( lam @ ( X373 @ sh @ one ) ) @ id ) )
| ~ ! [X375: subst,X376: term,X377: subst] :
( ( sub @ ( X373 @ X375 @ X376 ) @ X377 )
= ( X373 @ ( comp @ X375 @ X377 ) @ ( sub @ X376 @ X377 ) ) ) )
| ~ ! [X378: subst,X379: subst,X380: subst,X381: term] :
( ( ( X365 @ X380 @ X381 @ ( comp @ X378 @ X379 ) )
!= $true )
| ( ( X365 @ ( comp @ X380 @ X378 ) @ ( sub @ X381 @ X378 ) @ X379 )
= $true ) )
| ~ ! [X382: term] :
( ( $true
= ( X367 @ ( sub @ X366 @ ( push @ X382 @ id ) ) ) )
| ( $true
!= ( X367 @ X382 ) ) )
| ( ( X367 @ ( lam @ X366 ) )
= $true ) ) ) )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X383: subst > term > subst > $o,X384: term,X385: term] :
( ~ ! [X386: term,X387: term] :
( ( ( X383 @ id @ X386 @ id )
!= $true )
| ( ( X383 @ id @ ( ap @ ( sub @ X386 @ id ) @ X387 ) @ id )
= $true )
| ( $true
!= ( X383 @ id @ X387 @ id ) ) )
| ( $true
!= ( X383 @ id @ X385 @ id ) )
| ( $true
= ( X383 @ id @ ( ap @ X385 @ X384 ) @ id ) )
| ~ ! [X388: subst,X389: term,X390: subst,X391: subst] :
( ( $true
= ( X383 @ X391 @ X389 @ ( comp @ X388 @ X390 ) ) )
| ( $true
!= ( X383 @ ( comp @ X391 @ X388 ) @ ( sub @ X389 @ X388 ) @ X390 ) ) )
| ( ( X383 @ id @ X384 @ id )
!= $true )
| ~ ! [X392: term,X393: subst,X394: subst,X395: subst] :
( ( $true
= ( X383 @ ( comp @ X395 @ X394 ) @ ( sub @ X392 @ X394 ) @ X393 ) )
| ( $true
!= ( X383 @ X395 @ X392 @ ( comp @ X394 @ X393 ) ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X396: term > $o,X397: term] :
( ~ ! [X398: term] :
( ( $true
!= ( var @ X398 ) )
| ( $true
= ( X396 @ X398 ) ) )
| ( $true
= ( X396 @ X397 ) )
| ~ ! [X399: term] :
( ~ ! [X400: term] :
( ( ( X396 @ X400 )
!= $true )
| ( $true
= ( X396 @ ( sub @ X399 @ ( push @ X400 @ id ) ) ) ) )
| ( $true
= ( X396 @ ( lam @ X399 ) ) ) )
| ~ ! [X401: term,X402: term] :
( ( $true
= ( X396 @ ( ap @ X401 @ X402 ) ) )
| ( $true
!= ( X396 @ X401 ) )
| ( $true
!= ( X396 @ X402 ) ) ) )
=> ( ! [X403: term,X404: term,X405: subst > term > subst > $o] :
( ~ ! [X406: subst,X407: subst,X408: term,X409: subst] :
( ( $true
!= ( X405 @ ( comp @ X407 @ X406 ) @ ( sub @ X408 @ X406 ) @ X409 ) )
| ( $true
= ( X405 @ X407 @ X408 @ ( comp @ X406 @ X409 ) ) ) )
| ( $true
= ( X405 @ id @ ( ap @ X403 @ X404 ) @ id ) )
| ( $true
!= ( X405 @ id @ X403 @ id ) )
| ~ ! [X410: term,X411: subst,X412: subst,X413: subst] :
( ( $true
= ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X410 @ X411 ) @ X413 ) )
| ( ( X405 @ X412 @ X410 @ ( comp @ X411 @ X413 ) )
!= $true ) )
| ( $true
!= ( X405 @ id @ X404 @ id ) )
| ~ ! [X414: term,X415: term] :
( ( $true
!= ( X405 @ id @ X414 @ id ) )
| ( ( X405 @ id @ X415 @ id )
!= $true )
| ( ( X405 @ id @ ( ap @ ( sub @ X414 @ id ) @ X415 ) @ id )
= $true ) ) )
=> ( ! [X416: subst > term > subst > $o,X417: term] :
( ( $true
= ( X416 @ id @ ( lam @ X417 ) @ id ) )
| ~ ! [X418: subst,X419: term,X420: subst,X421: subst] :
( ( $true
= ( X416 @ ( comp @ X420 @ X421 ) @ ( sub @ X419 @ X421 ) @ X418 ) )
| ( $true
!= ( X416 @ X420 @ X419 @ ( comp @ X421 @ X418 ) ) ) )
| ~ ! [X422: subst,X423: subst,X424: term,X425: subst] :
( ( ( X416 @ ( comp @ X423 @ X425 ) @ ( sub @ X424 @ X425 ) @ X422 )
!= $true )
| ( $true
= ( X416 @ X423 @ X424 @ ( comp @ X425 @ X422 ) ) ) )
| ~ ! [X426: subst > term > term] :
( ~ ! [X427: term] :
( ( ( X416 @ id @ ( X426 @ id @ X427 ) @ id )
= $true )
| ( ( X416 @ id @ X427 @ id )
!= $true ) )
| ( $true
= ( X416 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id ) )
| ~ ! [X428: subst,X429: subst,X430: term] :
( ( sub @ ( X426 @ X429 @ X430 ) @ X428 )
= ( X426 @ ( comp @ X429 @ X428 ) @ ( sub @ X430 @ X428 ) ) ) )
| ~ ! [X431: term] :
( ( ( X416 @ id @ X431 @ id )
!= $true )
| ( $true
= ( X416 @ id @ ( sub @ X417 @ ( push @ X431 @ id ) ) @ id ) ) ) )
=> ! [X432: term,X433: subst > term > subst > $o] :
( ~ ! [X434: term] :
( ( $true
!= ( var @ ( sub @ X434 @ id ) ) )
| ( $true
= ( X433 @ id @ X434 @ id ) ) )
| ~ ! [X435: subst,X436: subst,X437: term,X438: subst] :
( ( $true
= ( X433 @ X435 @ X437 @ ( comp @ X436 @ X438 ) ) )
| ( $true
!= ( X433 @ ( comp @ X435 @ X436 ) @ ( sub @ X437 @ X436 ) @ X438 ) ) )
| ~ ! [X439: subst,X440: subst,X441: subst,X442: term] :
( ( $true
= ( X433 @ ( comp @ X441 @ X439 ) @ ( sub @ X442 @ X439 ) @ X440 ) )
| ( $true
!= ( X433 @ X441 @ X442 @ ( comp @ X439 @ X440 ) ) ) )
| ~ ! [X443: term,X444: term] :
( ( $true
= ( X433 @ id @ ( ap @ ( sub @ X443 @ id ) @ X444 ) @ id ) )
| ( ( X433 @ id @ X443 @ id )
!= $true )
| ( $true
!= ( X433 @ id @ X444 @ id ) ) )
| ~ ! [X445: subst > term > term] :
( ( $true
= ( X433 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id ) )
| ~ ! [X446: term] :
( ( ( X433 @ id @ ( X445 @ id @ X446 ) @ id )
= $true )
| ( ( X433 @ id @ X446 @ id )
!= $true ) )
| ~ ! [X447: subst,X448: subst,X449: term] :
( ( X445 @ ( comp @ X447 @ X448 ) @ ( sub @ X449 @ X448 ) )
= ( sub @ ( X445 @ X447 @ X449 ) @ X448 ) ) )
| ( ( X433 @ id @ X432 @ id )
= $true ) ) ) ) ) )
& ( ! [X450: term] :
~ ! [X451: subst > term > term] :
~ ! [X452: term,X453: subst] :
( ( X451 @ X453 @ X452 )
= ( sub @ X450 @ ( push @ X452 @ X453 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( ! [X454: term,X455: subst] :
( ( sub @ one @ ( push @ X454 @ X455 ) )
= X454 )
<=> ( axvarcons = $true ) )
& ( ( induction2_lthm = $true )
<=> ( ! [X456: term] :
( ( sub @ X456 @ id )
= X456 )
=> ( ! [X457: subst,X458: term > $o,X459: term] :
( ~ ! [X460: term,X461: term] :
( ( $true
= ( X458 @ ( ap @ X460 @ X461 ) ) )
| ( ( X458 @ X460 )
!= $true )
| ( $true
!= ( X458 @ X461 ) ) )
| ~ ! [X462: term] :
( ( $true
!= ( var @ X462 ) )
| ( ( X458 @ ( sub @ X462 @ X457 ) )
= $true ) )
| ~ ! [X463: term] :
( ( $true
= ( X458 @ ( lam @ X463 ) ) )
| ~ ! [X464: term] :
( ( $true
= ( X458 @ ( sub @ X463 @ ( push @ X464 @ id ) ) ) )
| ( $true
!= ( X458 @ X464 ) ) ) )
| ( $true
= ( X458 @ ( sub @ X459 @ X457 ) ) ) )
=> ! [X465: term > $o,X466: term] :
( ( $true
= ( X465 @ X466 ) )
| ~ ! [X467: term] :
( ( $true
!= ( var @ X467 ) )
| ( $true
= ( X465 @ X467 ) ) )
| ~ ! [X468: term] :
( ~ ! [X469: term] :
( ( $true
= ( X465 @ ( sub @ X468 @ ( push @ X469 @ id ) ) ) )
| ( $true
!= ( X465 @ X469 ) ) )
| ( $true
= ( X465 @ ( lam @ X468 ) ) ) )
| ~ ! [X470: term,X471: term] :
( ( ( X465 @ ( ap @ X470 @ X471 ) )
= $true )
| ( $true
!= ( X465 @ X471 ) )
| ( $true
!= ( X465 @ X470 ) ) ) ) ) ) )
& ( ! [X472: term,X473: subst > term > subst > $o] :
( ~ ! [X474: subst > term > term] :
( ~ ! [X475: term,X476: subst,X477: subst] :
( ( sub @ ( X474 @ X477 @ X475 ) @ X476 )
= ( X474 @ ( comp @ X477 @ X476 ) @ ( sub @ X475 @ X476 ) ) )
| ( $true
= ( X473 @ id @ ( lam @ ( X474 @ sh @ one ) ) @ id ) )
| ~ ! [X478: term] :
( ( ( X473 @ id @ ( X474 @ id @ X478 ) @ id )
= $true )
| ( $true
!= ( X473 @ id @ X478 @ id ) ) ) )
| ~ ! [X479: term,X480: term] :
( ( ( X473 @ id @ X480 @ id )
!= $true )
| ( $true
= ( X473 @ id @ ( ap @ ( sub @ X479 @ id ) @ X480 ) @ id ) )
| ( ( X473 @ id @ X479 @ id )
!= $true ) )
| ( $true
= ( X473 @ id @ X472 @ id ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X481: subst > term > subst > $o,X482: term] :
( ( $true
= ( X481 @ id @ ( lam @ X482 ) @ id ) )
| ~ ! [X483: subst > term > term] :
( ( $true
= ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id ) )
| ~ ! [X484: term] :
( ( ( X481 @ id @ X484 @ id )
!= $true )
| ( $true
= ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) ) )
| ~ ! [X485: term,X486: subst,X487: subst] :
( ( sub @ ( X483 @ X487 @ X485 ) @ X486 )
= ( X483 @ ( comp @ X487 @ X486 ) @ ( sub @ X485 @ X486 ) ) ) )
| ~ ! [X488: term] :
( ( ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id )
= $true )
| ( $true
!= ( X481 @ id @ X488 @ id ) ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X489: term,X490: term,X491: term,X492: term] :
( ( X489 = X491 )
| ( ( ap @ ( sub @ X491 @ id ) @ X492 )
!= ( ap @ ( sub @ X489 @ id ) @ X490 ) ) ) )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X493: term,X494: subst,X495: subst > term > term,X496: subst > term > term] :
( ( ( lam @ ( X496 @ sh @ one ) )
!= ( lam @ ( X495 @ sh @ one ) ) )
| ( ( X496 @ X494 @ X493 )
= ( X495 @ X494 @ X493 ) )
| ~ ! [X497: subst,X498: subst,X499: term] :
( ( X496 @ ( comp @ X497 @ X498 ) @ ( sub @ X499 @ X498 ) )
= ( sub @ ( X496 @ X497 @ X499 ) @ X498 ) )
| ~ ! [X500: subst,X501: subst,X502: term] :
( ( sub @ ( X495 @ X500 @ X502 ) @ X501 )
= ( X495 @ ( comp @ X500 @ X501 ) @ ( sub @ X502 @ X501 ) ) ) )
<=> ( hoaslaminj = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_gthm = $true )
& ( axclos = $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 ) ) ) ) )
& ( ! [X508: subst] :
( ( push @ ( sub @ one @ X508 ) @ ( comp @ sh @ X508 ) )
= X508 )
<=> ( axscons = $true ) )
& ( hoasapnotvar_lthm = $true )
& ! [X509: term] :
? [X510: d_term] :
( ( d2term @ X510 )
= X509 )
& ( pushprop_lthm_orig = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X511: subst > term > subst > $o] :
~ ! [X512: term > $o] :
~ ! [X513: term] :
( ( X512 @ X513 )
= ( X511 @ id @ X513 @ id ) )
=> ( ! [X514: term > $o,X515: term] :
( ~ ! [X516: term,X517: term] :
( ( $true
= ( X514 @ ( ap @ X517 @ X516 ) ) )
| ( $true
!= ( X514 @ X517 ) )
| ( $true
!= ( X514 @ X516 ) ) )
| ~ ! [X518: term] :
( ( $true
= ( X514 @ X518 ) )
| ( $true
!= ( var @ X518 ) ) )
| ( $true
= ( X514 @ X515 ) )
| ~ ! [X519: term] :
( ~ ! [X520: term] :
( ( $true
!= ( X514 @ X520 ) )
| ( $true
= ( X514 @ ( sub @ X519 @ ( push @ X520 @ id ) ) ) ) )
| ( $true
= ( X514 @ ( lam @ X519 ) ) ) ) )
=> ( ! [X521: term] :
( ( sub @ X521 @ id )
= X521 )
=> ( ! [X522: term,X523: subst > term > subst > $o,X524: term > $o] :
( ~ ! [X525: subst > term > term] :
( ~ ! [X526: subst,X527: term,X528: subst] :
( ( sub @ ( X525 @ X526 @ X527 ) @ X528 )
= ( X525 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) ) )
| ( $true
= ( X523 @ id @ ( lam @ ( X525 @ sh @ one ) ) @ id ) )
| ~ ! [X529: term] :
( ( $true
!= ( X523 @ id @ X529 @ id ) )
| ( ( X523 @ id @ ( X525 @ id @ X529 ) @ id )
= $true ) ) )
| ( $true
= ( X524 @ ( lam @ X522 ) ) )
| ~ ! [X530: term] :
( ( $true
!= ( X524 @ X530 ) )
| ( ( X524 @ ( sub @ X522 @ ( push @ X530 @ id ) ) )
= $true ) )
| ~ ! [X531: term] :
( ( X523 @ id @ X531 @ id )
= ( X524 @ X531 ) ) )
=> ! [X532: subst > term > subst > $o,X533: term] :
( ( $true
= ( X532 @ id @ X533 @ id ) )
| ~ ! [X534: term] :
( ( ( var @ ( sub @ X534 @ id ) )
!= $true )
| ( $true
= ( X532 @ id @ X534 @ id ) ) )
| ~ ! [X535: subst,X536: term,X537: subst,X538: subst] :
( ( $true
!= ( X532 @ ( comp @ X537 @ X535 ) @ ( sub @ X536 @ X535 ) @ X538 ) )
| ( $true
= ( X532 @ X537 @ X536 @ ( comp @ X535 @ X538 ) ) ) )
| ~ ! [X539: subst > term > term] :
( ( $true
= ( X532 @ id @ ( lam @ ( X539 @ sh @ one ) ) @ id ) )
| ~ ! [X540: subst,X541: subst,X542: term] :
( ( X539 @ ( comp @ X540 @ X541 ) @ ( sub @ X542 @ X541 ) )
= ( sub @ ( X539 @ X540 @ X542 ) @ X541 ) )
| ~ ! [X543: term] :
( ( $true
= ( X532 @ id @ ( X539 @ id @ X543 ) @ id ) )
| ( $true
!= ( X532 @ id @ X543 @ id ) ) ) )
| ~ ! [X544: subst,X545: term,X546: subst,X547: subst] :
( ( ( X532 @ ( comp @ X547 @ X546 ) @ ( sub @ X545 @ X546 ) @ X544 )
= $true )
| ( $true
!= ( X532 @ X547 @ X545 @ ( comp @ X546 @ X544 ) ) ) )
| ~ ! [X548: term,X549: term] :
( ( ( X532 @ id @ ( ap @ ( sub @ X548 @ id ) @ X549 ) @ id )
= $true )
| ( $true
!= ( X532 @ id @ X549 @ id ) )
| ( $true
!= ( X532 @ id @ X548 @ id ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( hoasinduction_lem3b
<=> ! [X0: term] :
~ ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ X0 @ ( push @ one @ sh ) ) ) )
& axabs
& hoasinduction_lem3_gthm
& ! [X2: subst] :
? [X3: d_subst] :
( ( d2subst @ X3 )
= X2 )
& ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 )
<=> axidr )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction
<=> ! [X5: term,X6: subst > term > subst > $o] :
( ~ ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ~ ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 )
| ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ~ ! [X11: term] :
( ( X6 @ id @ X11 @ id )
| ~ ( var @ ( sub @ X11 @ id ) ) )
| ( X6 @ id @ X5 @ id )
| ~ ! [X12: subst > term > term] :
( ~ ! [X13: term] :
( ( X6 @ id @ ( X12 @ id @ X13 ) @ id )
| ~ ( X6 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
| ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) )
| ~ ! [X17: subst,X18: subst,X19: term,X20: subst] :
( ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 )
| ~ ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) )
| ~ ! [X21: term,X22: term] :
( ( X6 @ id @ ( ap @ ( sub @ X22 @ id ) @ X21 ) @ id )
| ~ ( X6 @ id @ X21 @ id )
| ~ ( X6 @ id @ X22 @ id ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X23: term,X24: subst > term > subst > $o,X25: term,X26: term > $o] :
( ~ ! [X27: subst,X28: subst,X29: subst,X30: term] :
( ( X24 @ X27 @ X30 @ ( comp @ X28 @ X29 ) )
| ~ ( X24 @ ( comp @ X27 @ X28 ) @ ( sub @ X30 @ X28 ) @ X29 ) )
| ( X26 @ ( ap @ X25 @ X23 ) )
| ~ ! [X31: term,X32: term] :
( ( X24 @ id @ ( ap @ ( sub @ X32 @ id ) @ X31 ) @ id )
| ~ ( X24 @ id @ X32 @ id )
| ~ ( X24 @ id @ X31 @ id ) )
| ~ ! [X33: term,X34: subst,X35: subst,X36: subst] :
( ( X24 @ ( comp @ X34 @ X35 ) @ ( sub @ X33 @ X35 ) @ X36 )
| ~ ( X24 @ X34 @ X33 @ ( comp @ X35 @ X36 ) ) )
| ~ ! [X37: term] :
( ( X26 @ X37 )
= ( X24 @ id @ X37 @ id ) )
| ~ ( X26 @ X23 )
| ~ ( X26 @ X25 ) )
<=> hoasinduction_lem2v2 )
& pushprop
& hoaslaminj_gthm
& hoasinduction_lem2_gthm
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& pushprop_lem2v2_lthm
& ( ! [X38: term] :
~ ! [X39: subst > term > term] :
( ( X39 @ sh @ one )
!= ( sub @ X38 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X40: term] :
~ ! [X41: subst > term > term] :
~ ! [X42: term,X43: subst] :
( ( X41 @ X43 @ X42 )
= ( sub @ X40 @ ( push @ X42 @ X43 ) ) ) )
& ( ( ^ [X44: subst,X45: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& induction2lem_gthm
& pushprop_lthm
& ( apinj1
<=> ! [X46: term,X47: term,X48: term,X49: term] :
( ( ( ap @ X46 @ X49 )
!= ( ap @ X48 @ X47 ) )
| ( X46 = X48 ) ) )
& ! [X50: d_subst] : ( d_id = X50 )
& ( ! [X51: term > $o,X52: subst,X53: term] :
~ ! [X54: term > $o] :
~ ! [X55: term] :
( ( X54 @ X55 )
= ( X51 @ ( sub @ X55 @ ( push @ X53 @ X52 ) ) ) )
<=> pushprop_lem0 )
& hoasinduction_lem2v2_gthm
& hoaslamnotvar
& ( induction
<=> ! [X56: term,X57: term > $o] :
( ~ ! [X58: term] :
( ~ ( var @ X58 )
| ( X57 @ X58 ) )
| ~ ! [X59: term] :
( ( X57 @ ( lam @ X59 ) )
| ~ ( X57 @ X59 ) )
| ~ ! [X60: term,X61: term] :
( ( X57 @ ( ap @ X60 @ X61 ) )
| ~ ( X57 @ X61 )
| ~ ( X57 @ X60 ) )
| ( X57 @ X56 ) ) )
& ~ ( var @ ( d2term @ d_one ) )
& ( hoasinduction_lem3
<=> ! [X62: term,X63: subst > term > subst > $o] :
( ( X63 @ id @ ( lam @ X62 ) @ id )
| ~ ! [X64: term] :
( ~ ( X63 @ id @ X64 @ id )
| ( X63 @ id @ ( sub @ X62 @ ( push @ X64 @ id ) ) @ id ) )
| ~ ! [X65: subst > term > term] :
( ~ ! [X66: term] :
( ~ ( X63 @ id @ X66 @ id )
| ( X63 @ id @ ( X65 @ id @ X66 ) @ id ) )
| ( X63 @ id @ ( lam @ ( X65 @ sh @ one ) ) @ id )
| ~ ! [X67: term,X68: subst,X69: subst] :
( ( X65 @ ( comp @ X69 @ X68 ) @ ( sub @ X67 @ X68 ) )
= ( sub @ ( X65 @ X69 @ X67 ) @ X68 ) ) )
| ~ ! [X70: subst,X71: subst,X72: subst,X73: term] :
( ~ ( X63 @ X72 @ X73 @ ( comp @ X71 @ X70 ) )
| ( X63 @ ( comp @ X72 @ X71 ) @ ( sub @ X73 @ X71 ) @ X70 ) )
| ~ ! [X74: subst,X75: subst,X76: subst,X77: term] :
( ~ ( X63 @ ( comp @ X75 @ X76 ) @ ( sub @ X77 @ X76 ) @ X74 )
| ( X63 @ X75 @ X77 @ ( comp @ X76 @ X74 ) ) ) ) )
& ( ( ^ [X78: subst > term > subst > $o,X79: term > $o] :
! [X80: term] :
( ( X79 @ X80 )
= ( X78 @ id @ X80 @ id ) ) )
= hoasinduction_p_and_p_prime )
& pushprop_lem1v2_gthm
& ( induction2lem
<=> ! [X81: term,X82: subst,X83: term > $o] :
( ~ ! [X84: term] :
( ( X83 @ ( lam @ X84 ) )
| ~ ! [X85: term] :
( ~ ( X83 @ X85 )
| ( X83 @ ( sub @ X84 @ ( push @ X85 @ id ) ) ) ) )
| ~ ! [X86: term] :
( ( X83 @ ( sub @ X86 @ X82 ) )
| ~ ( var @ X86 ) )
| ( X83 @ ( sub @ X81 @ X82 ) )
| ~ ! [X87: term,X88: term] :
( ( X83 @ ( ap @ X88 @ X87 ) )
| ~ ( X83 @ X88 )
| ~ ( X83 @ X87 ) ) ) )
& ( ( ! [X89: term] :
( ( sub @ X89 @ id )
= X89 )
=> ( ! [X90: term,X91: term,X92: term,X93: term] :
( ( X90 = X91 )
| ( ( ap @ X90 @ X92 )
!= ( ap @ X91 @ X93 ) ) )
=> ! [X94: term,X95: term,X96: term,X97: term] :
( ( X94 = X97 )
| ( ( ap @ ( sub @ X94 @ id ) @ X96 )
!= ( ap @ ( sub @ X97 @ id ) @ X95 ) ) ) ) )
<=> hoasapinj1_lthm )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X98: term,X99: term] :
( ( ( lam @ X99 )
!= ( lam @ X98 ) )
| ( X98 = X99 ) )
<=> laminj )
& ( hoasinduction_lem3_lthm
<=> ( ! [X100: term] :
( ( sub @ X100 @ id )
= X100 )
=> ( ! [X101: term,X102: subst > term > subst > $o] :
( ~ ! [X103: subst > term > term] :
( ~ ! [X104: term,X105: subst,X106: subst] :
( ( X103 @ ( comp @ X106 @ X105 ) @ ( sub @ X104 @ X105 ) )
= ( sub @ ( X103 @ X106 @ X104 ) @ X105 ) )
| ( X102 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id )
| ~ ! [X107: term] :
( ~ ( X102 @ id @ X107 @ id )
| ( X102 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
| ( X102 @ id @ ( lam @ ( sub @ X101 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X108: term] :
( ~ ( X102 @ id @ X108 @ id )
| ( X102 @ id @ ( sub @ X101 @ ( push @ X108 @ id ) ) @ id ) ) )
=> ! [X109: term,X110: subst > term > subst > $o] :
( ( X110 @ id @ ( lam @ X109 ) @ id )
| ~ ! [X111: subst > term > term] :
( ~ ! [X112: term] :
( ~ ( X110 @ id @ X112 @ id )
| ( X110 @ id @ ( X111 @ id @ X112 ) @ id ) )
| ( X110 @ id @ ( lam @ ( X111 @ sh @ one ) ) @ id )
| ~ ! [X113: subst,X114: term,X115: subst] :
( ( sub @ ( X111 @ X113 @ X114 ) @ X115 )
= ( X111 @ ( comp @ X113 @ X115 ) @ ( sub @ X114 @ X115 ) ) ) )
| ~ ! [X116: subst,X117: term,X118: subst,X119: subst] :
( ~ ( X110 @ X119 @ X117 @ ( comp @ X116 @ X118 ) )
| ( X110 @ ( comp @ X119 @ X116 ) @ ( sub @ X117 @ X116 ) @ X118 ) )
| ~ ! [X120: term] :
( ~ ( X110 @ id @ X120 @ id )
| ( X110 @ id @ ( sub @ X109 @ ( push @ X120 @ id ) ) @ id ) )
| ~ ! [X121: subst,X122: subst,X123: subst,X124: term] :
( ~ ( X110 @ ( comp @ X121 @ X123 ) @ ( sub @ X124 @ X123 ) @ X122 )
| ( X110 @ X121 @ X124 @ ( comp @ X123 @ X122 ) ) ) ) ) ) )
& ( ( ! [X125: term] :
( ( sub @ X125 @ id )
= X125 )
=> ( ! [X126: term,X127: subst > term > subst > $o] :
( ~ ! [X128: subst > term > term] :
( ~ ! [X129: term] :
( ~ ( X127 @ id @ X129 @ id )
| ( X127 @ id @ ( X128 @ id @ X129 ) @ id ) )
| ~ ! [X130: subst,X131: subst,X132: term] :
( ( sub @ ( X128 @ X130 @ X132 ) @ X131 )
= ( X128 @ ( comp @ X130 @ X131 ) @ ( sub @ X132 @ X131 ) ) )
| ( X127 @ id @ ( lam @ ( X128 @ sh @ one ) ) @ id ) )
| ( X127 @ id @ ( lam @ ( sub @ X126 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X133: term] :
( ( X127 @ id @ ( sub @ X126 @ ( push @ X133 @ id ) ) @ id )
| ~ ( X127 @ id @ X133 @ id ) ) )
=> ! [X134: subst > term > subst > $o,X135: term] :
( ( X134 @ id @ ( lam @ X135 ) @ id )
| ~ ! [X136: subst > term > term] :
( ~ ! [X137: term] :
( ( X134 @ id @ ( X136 @ id @ X137 ) @ id )
| ~ ( X134 @ id @ X137 @ id ) )
| ( X134 @ id @ ( lam @ ( X136 @ sh @ one ) ) @ id )
| ~ ! [X138: subst,X139: subst,X140: term] :
( ( X136 @ ( comp @ X138 @ X139 ) @ ( sub @ X140 @ X139 ) )
= ( sub @ ( X136 @ X138 @ X140 ) @ X139 ) ) )
| ~ ! [X141: term] :
( ( X134 @ id @ ( sub @ X135 @ ( push @ X141 @ id ) ) @ id )
| ~ ( X134 @ id @ X141 @ id ) ) ) ) )
<=> hoasinduction_lem3a_lthm )
& ( ( ! [X142: term] :
~ ! [X143: subst > term > term] :
~ ! [X144: term,X145: subst] :
( ( sub @ X142 @ ( push @ X144 @ X145 ) )
= ( X143 @ X145 @ X144 ) )
=> ( ! [X146: term] :
( ( sub @ X146 @ id )
= X146 )
=> ! [X147: term,X148: subst > term > subst > $o,X149: term > $o] :
( ~ ! [X150: term] :
( ( X148 @ id @ X150 @ id )
= ( X149 @ X150 ) )
| ( X149 @ ( lam @ X147 ) )
| ~ ! [X151: subst > term > term] :
( ~ ! [X152: term,X153: subst,X154: subst] :
( ( sub @ ( X151 @ X154 @ X152 ) @ X153 )
= ( X151 @ ( comp @ X154 @ X153 ) @ ( sub @ X152 @ X153 ) ) )
| ~ ! [X155: term] :
( ( X148 @ id @ ( X151 @ id @ X155 ) @ id )
| ~ ( X148 @ id @ X155 @ id ) )
| ( X148 @ id @ ( lam @ ( X151 @ sh @ one ) ) @ id ) )
| ~ ! [X156: term] :
( ~ ( X149 @ X156 )
| ( X149 @ ( sub @ X147 @ ( push @ X156 @ id ) ) ) ) ) ) )
<=> hoasinduction_lem3v2a_lthm )
& hoasapinj1_gthm
& ( pushprop_lem1
<=> ! [X157: term,X158: subst,X159: term > $o,X160: term > $o,X161: term] :
( ~ ( X160 @ X161 )
| ( X159 @ ( sub @ X161 @ ( push @ X157 @ X158 ) ) ) ) )
& hoasinduction_lem1_lthm
& ( termmset_lthm
<=> ( ! [X162: term] :
( ( sub @ X162 @ id )
= X162 )
=> ! [X163: term] :
( ( sub @ X163 @ id )
= X163 ) ) )
& hoasinduction_lem1
& pushprop_lem2v2_gthm
& ulamvarind
& ( ! [X164: subst > term > subst > $o,X165: term] :
( ~ ! [X166: term] :
( ( X164 @ id @ ( sub @ X165 @ ( push @ X166 @ id ) ) @ id )
| ~ ( X164 @ id @ X166 @ id ) )
| ~ ! [X167: subst > term > term] :
( ( X164 @ id @ ( lam @ ( X167 @ sh @ one ) ) @ id )
| ~ ! [X168: term] :
( ( X164 @ id @ ( X167 @ id @ X168 ) @ id )
| ~ ( X164 @ id @ X168 @ id ) )
| ~ ! [X169: subst,X170: subst,X171: term] :
( ( X167 @ ( comp @ X170 @ X169 ) @ ( sub @ X171 @ X169 ) )
= ( sub @ ( X167 @ X170 @ X171 ) @ X169 ) ) )
| ( X164 @ id @ ( lam @ ( sub @ X165 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa )
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ! [X172: term] :
( ( sub @ X172 @ id )
= X172 )
<=> axvarid )
& hoasinduction_lem3v2_gthm
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X173: d_term,X174: d_term] :
( ( ( d2term @ X174 )
= ( d2term @ X173 ) )
=> ( X173 = X174 ) )
& hoasapnotvar_gthm
& apnotvar
& axapp
& ~ lamnotap
& pushprop_lem1_gthm
& ( ( ! [X175: term,X176: subst] :
( ( sub @ one @ ( push @ X175 @ X176 ) )
= X175 )
=> ( ! [X177: term,X178: subst] :
( ( comp @ sh @ ( push @ X177 @ X178 ) )
= X178 )
=> ( ! [X179: term,X180: term] :
( ( X179 = X180 )
| ( ( lam @ X180 )
!= ( lam @ X179 ) ) )
=> ! [X181: subst > term > term,X182: subst,X183: term,X184: subst > term > term] :
( ~ ! [X185: subst,X186: term,X187: subst] :
( ( X184 @ ( comp @ X187 @ X185 ) @ ( sub @ X186 @ X185 ) )
= ( sub @ ( X184 @ X187 @ X186 ) @ X185 ) )
| ~ ! [X188: subst,X189: subst,X190: term] :
( ( sub @ ( X181 @ X188 @ X190 ) @ X189 )
= ( X181 @ ( comp @ X188 @ X189 ) @ ( sub @ X190 @ X189 ) ) )
| ( ( X181 @ X182 @ X183 )
= ( X184 @ X182 @ X183 ) )
| ( ( lam @ ( X184 @ sh @ one ) )
!= ( lam @ ( X181 @ sh @ one ) ) ) ) ) ) )
<=> hoaslaminj_lthm )
& lamnotvar
& ( shinj
<=> ! [X191: term,X192: term] :
( ( X191 = X192 )
| ( ( sub @ X192 @ sh )
!= ( sub @ X191 @ sh ) ) ) )
& hoasinduction_gthm
& hoasinduction_lem2_lthm
& ( apinj2
<=> ! [X193: term,X194: term,X195: term,X196: term] :
( ( ( ap @ X193 @ X196 )
!= ( ap @ X194 @ X195 ) )
| ( X195 = X196 ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X197: term,X198: subst > term > subst > $o] :
( ( X198 @ id @ ( lam @ ( sub @ X197 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X199: term] :
( ( X198 @ id @ ( sub @ X197 @ ( push @ X199 @ id ) ) @ id )
| ~ ( X198 @ id @ X199 @ id ) )
| ~ ! [X200: subst > term > term,X201: term] :
( ( X198 @ id @ ( lam @ ( X200 @ sh @ one ) ) @ id )
| ~ ! [X202: term] :
( ~ ( X198 @ id @ X202 @ id )
| ( X198 @ id @ ( X200 @ id @ X202 ) @ id ) )
| ~ ! [X203: term,X204: subst,X205: subst] :
( ( sub @ ( sub @ X201 @ ( push @ X203 @ X204 ) ) @ X205 )
= ( sub @ ( X200 @ X204 @ X203 ) @ X205 ) )
| ~ ! [X206: subst,X207: term,X208: subst] :
( ( X200 @ ( comp @ X208 @ X206 ) @ ( sub @ X207 @ X206 ) )
= ( sub @ X201 @ ( push @ ( sub @ X207 @ X206 ) @ ( comp @ X208 @ X206 ) ) ) ) ) ) )
& ( hoasinduction_lem0
<=> ! [X209: subst > term > subst > $o] :
~ ! [X210: term > $o] :
~ ! [X211: term] :
( ( X209 @ id @ X211 @ id )
= ( X210 @ X211 ) ) )
& hoasapinj2_gthm
& pushprop_lem2v2
& ( ! [X212: subst,X213: term,X214: term > $o] :
~ ! [X215: term > $o] :
~ ! [X216: term] :
( ( X214 @ ( sub @ X216 @ ( push @ X213 @ X212 ) ) )
= ( X215 @ X216 ) )
<=> pushprop_lem0_lthm )
& ( hoasapinj2
<=> ! [X217: term,X218: term,X219: term,X220: term] :
( ( X217 = X219 )
| ( ( ap @ ( sub @ X220 @ id ) @ X217 )
!= ( ap @ ( sub @ X218 @ id ) @ X219 ) ) ) )
& ( ! [X221: subst > term > subst > $o] :
~ ! [X222: term > $o] :
~ ! [X223: term] :
( ( X221 @ id @ X223 @ id )
= ( X222 @ X223 ) )
<=> hoasinduction_lem0_lthm )
& hoasapnotvar
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X224: subst > term > subst > $o] :
~ ! [X225: term > $o] :
~ ! [X226: term] :
( ( X224 @ id @ X226 @ id )
= ( X225 @ X226 ) )
=> ( ! [X227: term > $o,X228: term] :
( ~ ! [X229: term] :
( ( X227 @ X229 )
| ~ ( var @ X229 ) )
| ~ ! [X230: term] :
( ( X227 @ ( lam @ X230 ) )
| ~ ! [X231: term] :
( ~ ( X227 @ X231 )
| ( X227 @ ( sub @ X230 @ ( push @ X231 @ id ) ) ) ) )
| ( X227 @ X228 )
| ~ ! [X232: term,X233: term] :
( ~ ( X227 @ X232 )
| ~ ( X227 @ X233 )
| ( X227 @ ( ap @ X233 @ X232 ) ) ) )
=> ( ! [X234: term] :
( ( sub @ X234 @ id )
= X234 )
=> ( ! [X235: term,X236: term > $o,X237: subst > term > subst > $o] :
( ( X236 @ ( lam @ X235 ) )
| ~ ! [X238: term] :
( ( X236 @ ( sub @ X235 @ ( push @ X238 @ id ) ) )
| ~ ( X236 @ X238 ) )
| ~ ! [X239: subst > term > term] :
( ( X237 @ id @ ( lam @ ( X239 @ sh @ one ) ) @ id )
| ~ ! [X240: term] :
( ~ ( X237 @ id @ X240 @ id )
| ( X237 @ id @ ( X239 @ id @ X240 ) @ id ) )
| ~ ! [X241: term,X242: subst,X243: subst] :
( ( sub @ ( X239 @ X242 @ X241 ) @ X243 )
= ( X239 @ ( comp @ X242 @ X243 ) @ ( sub @ X241 @ X243 ) ) ) )
| ~ ! [X244: term] :
( ( X237 @ id @ X244 @ id )
= ( X236 @ X244 ) ) )
=> ! [X245: subst > term > subst > $o,X246: term] :
( ( X245 @ id @ X246 @ id )
| ~ ! [X247: term,X248: term] :
( ~ ( X245 @ id @ X247 @ id )
| ( X245 @ id @ ( ap @ ( sub @ X247 @ id ) @ X248 ) @ id )
| ~ ( X245 @ id @ X248 @ id ) )
| ~ ! [X249: subst > term > term] :
( ( X245 @ id @ ( lam @ ( X249 @ sh @ one ) ) @ id )
| ~ ! [X250: term] :
( ~ ( X245 @ id @ X250 @ id )
| ( X245 @ id @ ( X249 @ id @ X250 ) @ id ) )
| ~ ! [X251: subst,X252: term,X253: subst] :
( ( X249 @ ( comp @ X251 @ X253 ) @ ( sub @ X252 @ X253 ) )
= ( sub @ ( X249 @ X251 @ X252 ) @ X253 ) ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& substmonoid_gthm
& pushprop_lem3v2_lthm
& ( ! [X254: term,X255: term,X256: subst > term > term] :
( ~ ! [X257: term,X258: subst,X259: subst] :
( ( X256 @ ( comp @ X259 @ X258 ) @ ( sub @ X257 @ X258 ) )
= ( sub @ ( X256 @ X259 @ X257 ) @ X258 ) )
| ( ( lam @ ( X256 @ sh @ one ) )
!= ( ap @ ( sub @ X255 @ id ) @ X254 ) ) )
<=> hoaslamnotap )
& pushprop_lem0_gthm
& ( hoasinduction_lem3aa_lthm
<=> ! [X260: subst > term > subst > $o,X261: term] :
( ~ ! [X262: term] :
( ( X260 @ id @ ( sub @ X261 @ ( push @ X262 @ id ) ) @ id )
| ~ ( X260 @ id @ X262 @ id ) )
| ( X260 @ id @ ( lam @ ( sub @ X261 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X263: subst > term > term] :
( ~ ! [X264: subst,X265: subst,X266: term] :
( ( sub @ ( X263 @ X264 @ X266 ) @ X265 )
= ( X263 @ ( comp @ X264 @ X265 ) @ ( sub @ X266 @ X265 ) ) )
| ~ ! [X267: term] :
( ~ ( X260 @ id @ X267 @ id )
| ( X260 @ id @ ( X263 @ id @ X267 ) @ id ) )
| ( X260 @ id @ ( lam @ ( X263 @ sh @ one ) ) @ id ) ) ) )
& ( hoasinduction_lem3v2
<=> ! [X268: term,X269: term > $o,X270: subst > term > subst > $o] :
( ~ ! [X271: term,X272: subst,X273: subst,X274: subst] :
( ( X270 @ ( comp @ X274 @ X273 ) @ ( sub @ X271 @ X273 ) @ X272 )
| ~ ( X270 @ X274 @ X271 @ ( comp @ X273 @ X272 ) ) )
| ~ ! [X275: subst > term > term] :
( ( X270 @ id @ ( lam @ ( X275 @ sh @ one ) ) @ id )
| ~ ! [X276: term] :
( ( X270 @ id @ ( X275 @ id @ X276 ) @ id )
| ~ ( X270 @ id @ X276 @ id ) )
| ~ ! [X277: subst,X278: subst,X279: term] :
( ( sub @ ( X275 @ X277 @ X279 ) @ X278 )
= ( X275 @ ( comp @ X277 @ X278 ) @ ( sub @ X279 @ X278 ) ) ) )
| ~ ! [X280: term] :
( ~ ( X269 @ X280 )
| ( X269 @ ( sub @ X268 @ ( push @ X280 @ id ) ) ) )
| ( X269 @ ( lam @ X268 ) )
| ~ ! [X281: subst,X282: subst,X283: subst,X284: term] :
( ( X270 @ X282 @ X284 @ ( comp @ X281 @ X283 ) )
| ~ ( X270 @ ( comp @ X282 @ X281 ) @ ( sub @ X284 @ X281 ) @ X283 ) )
| ~ ! [X285: term] :
( ( X269 @ X285 )
= ( X270 @ id @ X285 @ id ) ) ) )
& ( ! [X286: subst,X287: term] :
( ( comp @ sh @ ( push @ X287 @ X286 ) )
= X286 )
<=> axshiftcons )
& hoasinduction_lem3b_gthm
& termmset_gthm
& axmap
& ( ! [X288: term > $o,X289: term] :
( ~ ! [X290: term] :
( ~ ! [X291: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X291 @ id ) ) )
| ~ ( X288 @ X291 ) )
| ( X288 @ ( lam @ X290 ) ) )
| ~ ! [X292: term] :
( ~ ( var @ X292 )
| ( X288 @ X292 ) )
| ~ ! [X293: term,X294: term] :
( ~ ( X288 @ X294 )
| ( X288 @ ( ap @ X293 @ X294 ) )
| ~ ( X288 @ X293 ) )
| ( X288 @ X289 ) )
<=> induction2 )
& ( ! [X295: subst] :
( ( comp @ id @ X295 )
= X295 )
<=> axidl )
& ( ( ! [X296: term,X297: subst] :
( ( sub @ one @ ( push @ X296 @ X297 ) )
= X296 )
=> ( ! [X298: subst,X299: term] :
( ( comp @ sh @ ( push @ X299 @ X298 ) )
= X298 )
=> ! [X300: subst,X301: term > $o,X302: term > $o,X303: term,X304: term] :
( ~ ( X302 @ X304 )
| ( X301 @ ( sub @ X304 @ ( push @ X303 @ X300 ) ) ) ) ) )
<=> pushprop_lem1_lthm )
& ( pushprop_lem1v2
<=> ! [X305: subst,X306: term,X307: term > $o,X308: term > $o] :
( ( X308 @ one )
| ~ ! [X309: term] :
( ( X308 @ X309 )
= ( X307 @ ( sub @ X309 @ ( push @ X306 @ X305 ) ) ) )
| ~ ( X307 @ X306 ) ) )
& ( ! [X310: term] :
( ( sub @ X310 @ id )
= X310 )
<=> termmset )
& hoaslamnotap_lthm
& hoasinduction_lem1v2
& ( hoasapinj2_lthm
<=> ( ! [X311: term,X312: term,X313: term,X314: term] :
( ( ( ap @ X312 @ X313 )
!= ( ap @ X314 @ X311 ) )
| ( X311 = X313 ) )
=> ! [X315: term,X316: term,X317: term,X318: term] :
( ( X316 = X317 )
| ( ( ap @ ( sub @ X318 @ id ) @ X316 )
!= ( ap @ ( sub @ X315 @ id ) @ X317 ) ) ) ) )
& axvarshift
& ~ ulamvar1
& ( ( ! [X319: term,X320: subst] :
( ( sub @ one @ ( push @ X319 @ X320 ) )
= X319 )
=> ( ! [X321: term,X322: subst] :
( ( comp @ sh @ ( push @ X321 @ X322 ) )
= X322 )
=> ( ! [X323: subst] :
( ( comp @ X323 @ id )
= X323 )
=> ( ! [X324: term > $o,X325: term] :
( ~ ! [X326: term] :
( ( X324 @ ( lam @ X326 ) )
| ~ ( X324 @ X326 ) )
| ( X324 @ X325 )
| ~ ! [X327: term] :
( ( X324 @ X327 )
| ~ ( var @ X327 ) )
| ~ ! [X328: term,X329: term] :
( ~ ( X324 @ X329 )
| ( X324 @ ( ap @ X328 @ X329 ) )
| ~ ( X324 @ X328 ) ) )
=> ! [X330: subst,X331: term,X332: term > $o] :
( ~ ! [X333: term,X334: term] :
( ~ ( X332 @ X334 )
| ~ ( X332 @ X333 )
| ( X332 @ ( ap @ X334 @ X333 ) ) )
| ~ ! [X335: term] :
( ~ ( var @ X335 )
| ( X332 @ ( sub @ X335 @ X330 ) ) )
| ~ ! [X336: term] :
( ~ ! [X337: term] :
( ~ ( X332 @ X337 )
| ( X332 @ ( sub @ X336 @ ( push @ X337 @ id ) ) ) )
| ( X332 @ ( lam @ X336 ) ) )
| ( X332 @ ( sub @ X331 @ X330 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoasinduction_lem1v2_gthm
& pushprop_lem3v2
& ( ! [X338: term > $o,X339: subst > term > subst > $o,X340: term] :
( ( X338 @ ( lam @ X340 ) )
| ~ ! [X341: subst > term > term] :
( ~ ! [X342: subst,X343: subst,X344: term] :
( ( sub @ ( X341 @ X343 @ X344 ) @ X342 )
= ( X341 @ ( comp @ X343 @ X342 ) @ ( sub @ X344 @ X342 ) ) )
| ( X339 @ id @ ( lam @ ( X341 @ sh @ one ) ) @ id )
| ~ ! [X345: term] :
( ~ ( X339 @ id @ X345 @ id )
| ( X339 @ id @ ( X341 @ id @ X345 ) @ id ) ) )
| ~ ! [X346: term] :
( ~ ( X338 @ X346 )
| ( X338 @ ( sub @ X340 @ ( push @ X346 @ id ) ) ) )
| ~ ! [X347: term] :
( ( X338 @ X347 )
= ( X339 @ id @ X347 @ id ) ) )
<=> hoasinduction_lem3v2a )
& induction2_gthm
& ! [X348: d_term] : ( d_one = X348 )
& ( ( ! [X349: subst] :
( ( comp @ id @ X349 )
= X349 )
=> ( ! [X350: subst] :
( ( comp @ X350 @ id )
= X350 )
=> ( ! [X351: subst] :
( ( comp @ id @ X351 )
= X351 )
& ! [X352: subst] :
( ( comp @ X352 @ id )
= X352 ) ) ) )
<=> substmonoid_lthm )
& axassoc
& hoasinduction_lem3a_gthm
& hoaslamnotap_gthm
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X353: d_subst,X354: d_subst] :
( ( ( d2subst @ X354 )
= ( d2subst @ X353 ) )
=> ( X353 = X354 ) )
& ( ( ! [X355: subst,X356: term] :
( ( sub @ one @ ( push @ X356 @ X355 ) )
= X356 )
=> ! [X357: term > $o,X358: term,X359: term > $o,X360: subst] :
( ( X359 @ one )
| ~ ( X357 @ X358 )
| ~ ! [X361: term] :
( ( X357 @ ( sub @ X361 @ ( push @ X358 @ X360 ) ) )
= ( X359 @ X361 ) ) ) )
<=> pushprop_lem1v2_lthm )
& hoaslamnotvar_gthm
& ulamvarsh
& ( ( ! [X362: subst] :
( ( comp @ id @ X362 )
= X362 )
& ! [X363: subst] :
( ( comp @ X363 @ id )
= X363 ) )
<=> substmonoid )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X364: term] :
( ( sub @ X364 @ id )
= X364 )
=> ! [X365: subst > term > subst > $o,X366: term,X367: term > $o] :
( ~ ! [X368: term] :
( ( X365 @ id @ X368 @ id )
= ( X367 @ X368 ) )
| ~ ! [X369: subst,X370: subst,X371: subst,X372: term] :
( ~ ( X365 @ ( comp @ X371 @ X370 ) @ ( sub @ X372 @ X370 ) @ X369 )
| ( X365 @ X371 @ X372 @ ( comp @ X370 @ X369 ) ) )
| ~ ! [X373: subst > term > term] :
( ~ ! [X374: term] :
( ( X365 @ id @ ( X373 @ id @ X374 ) @ id )
| ~ ( X365 @ id @ X374 @ id ) )
| ( X365 @ id @ ( lam @ ( X373 @ sh @ one ) ) @ id )
| ~ ! [X375: subst,X376: term,X377: subst] :
( ( sub @ ( X373 @ X375 @ X376 ) @ X377 )
= ( X373 @ ( comp @ X375 @ X377 ) @ ( sub @ X376 @ X377 ) ) ) )
| ~ ! [X378: subst,X379: subst,X380: subst,X381: term] :
( ~ ( X365 @ X380 @ X381 @ ( comp @ X378 @ X379 ) )
| ( X365 @ ( comp @ X380 @ X378 ) @ ( sub @ X381 @ X378 ) @ X379 ) )
| ~ ! [X382: term] :
( ( X367 @ ( sub @ X366 @ ( push @ X382 @ id ) ) )
| ~ ( X367 @ X382 ) )
| ( X367 @ ( lam @ X366 ) ) ) ) )
& ( hoasinduction_lem2
<=> ! [X383: subst > term > subst > $o,X384: term,X385: term] :
( ~ ! [X386: term,X387: term] :
( ~ ( X383 @ id @ X386 @ id )
| ( X383 @ id @ ( ap @ ( sub @ X386 @ id ) @ X387 ) @ id )
| ~ ( X383 @ id @ X387 @ id ) )
| ~ ( X383 @ id @ X385 @ id )
| ( X383 @ id @ ( ap @ X385 @ X384 ) @ id )
| ~ ! [X388: subst,X389: term,X390: subst,X391: subst] :
( ( X383 @ X391 @ X389 @ ( comp @ X388 @ X390 ) )
| ~ ( X383 @ ( comp @ X391 @ X388 ) @ ( sub @ X389 @ X388 ) @ X390 ) )
| ~ ( X383 @ id @ X384 @ id )
| ~ ! [X392: term,X393: subst,X394: subst,X395: subst] :
( ( X383 @ ( comp @ X395 @ X394 ) @ ( sub @ X392 @ X394 ) @ X393 )
| ~ ( X383 @ X395 @ X392 @ ( comp @ X394 @ X393 ) ) ) ) )
& ( hoasinduction_lthm
<=> ( ! [X396: term > $o,X397: term] :
( ~ ! [X398: term] :
( ~ ( var @ X398 )
| ( X396 @ X398 ) )
| ( X396 @ X397 )
| ~ ! [X399: term] :
( ~ ! [X400: term] :
( ~ ( X396 @ X400 )
| ( X396 @ ( sub @ X399 @ ( push @ X400 @ id ) ) ) )
| ( X396 @ ( lam @ X399 ) ) )
| ~ ! [X401: term,X402: term] :
( ( X396 @ ( ap @ X401 @ X402 ) )
| ~ ( X396 @ X401 )
| ~ ( X396 @ X402 ) ) )
=> ( ! [X403: term,X404: term,X405: subst > term > subst > $o] :
( ~ ! [X406: subst,X407: subst,X408: term,X409: subst] :
( ~ ( X405 @ ( comp @ X407 @ X406 ) @ ( sub @ X408 @ X406 ) @ X409 )
| ( X405 @ X407 @ X408 @ ( comp @ X406 @ X409 ) ) )
| ( X405 @ id @ ( ap @ X403 @ X404 ) @ id )
| ~ ( X405 @ id @ X403 @ id )
| ~ ! [X410: term,X411: subst,X412: subst,X413: subst] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X410 @ X411 ) @ X413 )
| ~ ( X405 @ X412 @ X410 @ ( comp @ X411 @ X413 ) ) )
| ~ ( X405 @ id @ X404 @ id )
| ~ ! [X414: term,X415: term] :
( ~ ( X405 @ id @ X414 @ id )
| ~ ( X405 @ id @ X415 @ id )
| ( X405 @ id @ ( ap @ ( sub @ X414 @ id ) @ X415 ) @ id ) ) )
=> ( ! [X416: subst > term > subst > $o,X417: term] :
( ( X416 @ id @ ( lam @ X417 ) @ id )
| ~ ! [X418: subst,X419: term,X420: subst,X421: subst] :
( ( X416 @ ( comp @ X420 @ X421 ) @ ( sub @ X419 @ X421 ) @ X418 )
| ~ ( X416 @ X420 @ X419 @ ( comp @ X421 @ X418 ) ) )
| ~ ! [X422: subst,X423: subst,X424: term,X425: subst] :
( ~ ( X416 @ ( comp @ X423 @ X425 ) @ ( sub @ X424 @ X425 ) @ X422 )
| ( X416 @ X423 @ X424 @ ( comp @ X425 @ X422 ) ) )
| ~ ! [X426: subst > term > term] :
( ~ ! [X427: term] :
( ( X416 @ id @ ( X426 @ id @ X427 ) @ id )
| ~ ( X416 @ id @ X427 @ id ) )
| ( X416 @ id @ ( lam @ ( X426 @ sh @ one ) ) @ id )
| ~ ! [X428: subst,X429: subst,X430: term] :
( ( sub @ ( X426 @ X429 @ X430 ) @ X428 )
= ( X426 @ ( comp @ X429 @ X428 ) @ ( sub @ X430 @ X428 ) ) ) )
| ~ ! [X431: term] :
( ~ ( X416 @ id @ X431 @ id )
| ( X416 @ id @ ( sub @ X417 @ ( push @ X431 @ id ) ) @ id ) ) )
=> ! [X432: term,X433: subst > term > subst > $o] :
( ~ ! [X434: term] :
( ~ ( var @ ( sub @ X434 @ id ) )
| ( X433 @ id @ X434 @ id ) )
| ~ ! [X435: subst,X436: subst,X437: term,X438: subst] :
( ( X433 @ X435 @ X437 @ ( comp @ X436 @ X438 ) )
| ~ ( X433 @ ( comp @ X435 @ X436 ) @ ( sub @ X437 @ X436 ) @ X438 ) )
| ~ ! [X439: subst,X440: subst,X441: subst,X442: term] :
( ( X433 @ ( comp @ X441 @ X439 ) @ ( sub @ X442 @ X439 ) @ X440 )
| ~ ( X433 @ X441 @ X442 @ ( comp @ X439 @ X440 ) ) )
| ~ ! [X443: term,X444: term] :
( ( X433 @ id @ ( ap @ ( sub @ X443 @ id ) @ X444 ) @ id )
| ~ ( X433 @ id @ X443 @ id )
| ~ ( X433 @ id @ X444 @ id ) )
| ~ ! [X445: subst > term > term] :
( ( X433 @ id @ ( lam @ ( X445 @ sh @ one ) ) @ id )
| ~ ! [X446: term] :
( ( X433 @ id @ ( X445 @ id @ X446 ) @ id )
| ~ ( X433 @ id @ X446 @ id ) )
| ~ ! [X447: subst,X448: subst,X449: term] :
( ( X445 @ ( comp @ X447 @ X448 ) @ ( sub @ X449 @ X448 ) )
= ( sub @ ( X445 @ X447 @ X449 ) @ X448 ) ) )
| ( X433 @ id @ X432 @ id ) ) ) ) ) )
& ( ! [X450: term] :
~ ! [X451: subst > term > term] :
~ ! [X452: term,X453: subst] :
( ( X451 @ X453 @ X452 )
= ( sub @ X450 @ ( push @ X452 @ X453 ) ) )
<=> hoasinduction_lem3v2_f )
& ( ! [X454: term,X455: subst] :
( ( sub @ one @ ( push @ X454 @ X455 ) )
= X454 )
<=> axvarcons )
& ( induction2_lthm
<=> ( ! [X456: term] :
( ( sub @ X456 @ id )
= X456 )
=> ( ! [X457: subst,X458: term > $o,X459: term] :
( ~ ! [X460: term,X461: term] :
( ( X458 @ ( ap @ X460 @ X461 ) )
| ~ ( X458 @ X460 )
| ~ ( X458 @ X461 ) )
| ~ ! [X462: term] :
( ~ ( var @ X462 )
| ( X458 @ ( sub @ X462 @ X457 ) ) )
| ~ ! [X463: term] :
( ( X458 @ ( lam @ X463 ) )
| ~ ! [X464: term] :
( ( X458 @ ( sub @ X463 @ ( push @ X464 @ id ) ) )
| ~ ( X458 @ X464 ) ) )
| ( X458 @ ( sub @ X459 @ X457 ) ) )
=> ! [X465: term > $o,X466: term] :
( ( X465 @ X466 )
| ~ ! [X467: term] :
( ~ ( var @ X467 )
| ( X465 @ X467 ) )
| ~ ! [X468: term] :
( ~ ! [X469: term] :
( ( X465 @ ( sub @ X468 @ ( push @ X469 @ id ) ) )
| ~ ( X465 @ X469 ) )
| ( X465 @ ( lam @ X468 ) ) )
| ~ ! [X470: term,X471: term] :
( ( X465 @ ( ap @ X470 @ X471 ) )
| ~ ( X465 @ X471 )
| ~ ( X465 @ X470 ) ) ) ) ) )
& ( ! [X472: term,X473: subst > term > subst > $o] :
( ~ ! [X474: subst > term > term] :
( ~ ! [X475: term,X476: subst,X477: subst] :
( ( sub @ ( X474 @ X477 @ X475 ) @ X476 )
= ( X474 @ ( comp @ X477 @ X476 ) @ ( sub @ X475 @ X476 ) ) )
| ( X473 @ id @ ( lam @ ( X474 @ sh @ one ) ) @ id )
| ~ ! [X478: term] :
( ( X473 @ id @ ( X474 @ id @ X478 ) @ id )
| ~ ( X473 @ id @ X478 @ id ) ) )
| ~ ! [X479: term,X480: term] :
( ~ ( X473 @ id @ X480 @ id )
| ( X473 @ id @ ( ap @ ( sub @ X479 @ id ) @ X480 ) @ id )
| ~ ( X473 @ id @ X479 @ id ) )
| ( X473 @ id @ X472 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ! [X481: subst > term > subst > $o,X482: term] :
( ( X481 @ id @ ( lam @ X482 ) @ id )
| ~ ! [X483: subst > term > term] :
( ( X481 @ id @ ( lam @ ( X483 @ sh @ one ) ) @ id )
| ~ ! [X484: term] :
( ~ ( X481 @ id @ X484 @ id )
| ( X481 @ id @ ( X483 @ id @ X484 ) @ id ) )
| ~ ! [X485: term,X486: subst,X487: subst] :
( ( sub @ ( X483 @ X487 @ X485 ) @ X486 )
= ( X483 @ ( comp @ X487 @ X486 ) @ ( sub @ X485 @ X486 ) ) ) )
| ~ ! [X488: term] :
( ( X481 @ id @ ( sub @ X482 @ ( push @ X488 @ id ) ) @ id )
| ~ ( X481 @ id @ X488 @ id ) ) )
<=> hoasinduction_lem3a )
& ( hoasapinj1
<=> ! [X489: term,X490: term,X491: term,X492: term] :
( ( X489 = X491 )
| ( ( ap @ ( sub @ X491 @ id ) @ X492 )
!= ( ap @ ( sub @ X489 @ id ) @ X490 ) ) ) )
& hoaslamnotvar_lthm
& ( ! [X493: term,X494: subst,X495: subst > term > term,X496: subst > term > term] :
( ( ( lam @ ( X496 @ sh @ one ) )
!= ( lam @ ( X495 @ sh @ one ) ) )
| ( ( X496 @ X494 @ X493 )
= ( X495 @ X494 @ X493 ) )
| ~ ! [X497: subst,X498: subst,X499: term] :
( ( X496 @ ( comp @ X497 @ X498 ) @ ( sub @ X499 @ X498 ) )
= ( sub @ ( X496 @ X497 @ X499 ) @ X498 ) )
| ~ ! [X500: subst,X501: subst,X502: term] :
( ( sub @ ( X495 @ X500 @ X502 ) @ X501 )
= ( X495 @ ( comp @ X500 @ X501 ) @ ( sub @ X502 @ X501 ) ) ) )
<=> hoaslaminj )
& hoasinduction_lem1_gthm
& pushprop_gthm
& axclos
& ( ( ^ [X503: term,X504: subst,X505: term > $o,X506: term > $o] :
! [X507: term] :
( ( X505 @ ( sub @ X507 @ ( push @ X503 @ X504 ) ) )
= ( X506 @ X507 ) ) )
= pushprop_p_and_p_prime )
& ( ! [X508: subst] :
( ( push @ ( sub @ one @ X508 ) @ ( comp @ sh @ X508 ) )
= X508 )
<=> axscons )
& hoasapnotvar_lthm
& ! [X509: term] :
? [X510: d_term] :
( ( d2term @ X510 )
= X509 )
& pushprop_lthm_orig
& ( hoasinduction_lthm_3
<=> ( ! [X511: subst > term > subst > $o] :
~ ! [X512: term > $o] :
~ ! [X513: term] :
( ( X512 @ X513 )
= ( X511 @ id @ X513 @ id ) )
=> ( ! [X514: term > $o,X515: term] :
( ~ ! [X516: term,X517: term] :
( ( X514 @ ( ap @ X517 @ X516 ) )
| ~ ( X514 @ X517 )
| ~ ( X514 @ X516 ) )
| ~ ! [X518: term] :
( ( X514 @ X518 )
| ~ ( var @ X518 ) )
| ( X514 @ X515 )
| ~ ! [X519: term] :
( ~ ! [X520: term] :
( ~ ( X514 @ X520 )
| ( X514 @ ( sub @ X519 @ ( push @ X520 @ id ) ) ) )
| ( X514 @ ( lam @ X519 ) ) ) )
=> ( ! [X521: term] :
( ( sub @ X521 @ id )
= X521 )
=> ( ! [X522: term,X523: subst > term > subst > $o,X524: term > $o] :
( ~ ! [X525: subst > term > term] :
( ~ ! [X526: subst,X527: term,X528: subst] :
( ( sub @ ( X525 @ X526 @ X527 ) @ X528 )
= ( X525 @ ( comp @ X526 @ X528 ) @ ( sub @ X527 @ X528 ) ) )
| ( X523 @ id @ ( lam @ ( X525 @ sh @ one ) ) @ id )
| ~ ! [X529: term] :
( ~ ( X523 @ id @ X529 @ id )
| ( X523 @ id @ ( X525 @ id @ X529 ) @ id ) ) )
| ( X524 @ ( lam @ X522 ) )
| ~ ! [X530: term] :
( ~ ( X524 @ X530 )
| ( X524 @ ( sub @ X522 @ ( push @ X530 @ id ) ) ) )
| ~ ! [X531: term] :
( ( X523 @ id @ X531 @ id )
= ( X524 @ X531 ) ) )
=> ! [X532: subst > term > subst > $o,X533: term] :
( ( X532 @ id @ X533 @ id )
| ~ ! [X534: term] :
( ~ ( var @ ( sub @ X534 @ id ) )
| ( X532 @ id @ X534 @ id ) )
| ~ ! [X535: subst,X536: term,X537: subst,X538: subst] :
( ~ ( X532 @ ( comp @ X537 @ X535 ) @ ( sub @ X536 @ X535 ) @ X538 )
| ( X532 @ X537 @ X536 @ ( comp @ X535 @ X538 ) ) )
| ~ ! [X539: subst > term > term] :
( ( X532 @ id @ ( lam @ ( X539 @ sh @ one ) ) @ id )
| ~ ! [X540: subst,X541: subst,X542: term] :
( ( X539 @ ( comp @ X540 @ X541 ) @ ( sub @ X542 @ X541 ) )
= ( sub @ ( X539 @ X540 @ X542 ) @ X541 ) )
| ~ ! [X543: term] :
( ( X532 @ id @ ( X539 @ id @ X543 ) @ id )
| ~ ( X532 @ id @ X543 @ id ) ) )
| ~ ! [X544: subst,X545: term,X546: subst,X547: subst] :
( ( X532 @ ( comp @ X547 @ X546 ) @ ( sub @ X545 @ X546 ) @ X544 )
| ~ ( X532 @ X547 @ X545 @ ( comp @ X546 @ X544 ) ) )
| ~ ! [X548: term,X549: term] :
( ( X532 @ id @ ( ap @ ( sub @ X548 @ id ) @ X549 ) @ id )
| ~ ( X532 @ id @ X549 @ id )
| ~ ( X532 @ id @ X548 @ id ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( hoasinduction_lem3b
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) ) )
& axabs
& hoasinduction_lem3_gthm
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
<=> axidr )
& ( ( d2subst @ d_id )
= id )
& ( hoasinduction
<=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ 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 ) )
| ~ ! [X14: subst,X26: subst,X13: term,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X45: term,X10: subst > term > subst > $o,X44: term,X11: term > $o] :
( ~ ! [X14: subst,X26: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X13: term,X14: subst,X26: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ( X11 @ X45 )
| ~ ( X11 @ X44 ) )
<=> hoasinduction_lem2v2 )
& pushprop
& hoaslaminj_gthm
& hoasinduction_lem2_gthm
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& pushprop_lem2v2_lthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& ( hoasinduction_lem3v2_f_lthm
<=> ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) ) )
& ( ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) )
= hoaslam )
& induction2lem_gthm
& pushprop_lthm
& ( apinj1
<=> ! [X13: term,X20: term,X15: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) ) )
& ! [X5: d_subst] : ( d_id = X5 )
& ( ! [X10: term > $o,X14: subst,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0 )
& hoasinduction_lem2v2_gthm
& hoaslamnotvar
& ( induction
<=> ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ( X10 @ X21 ) ) )
& ~ ( var @ ( d2term @ d_one ) )
& ( hoasinduction_lem3
<=> ! [X27: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) )
& ( ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
= hoasinduction_p_and_p_prime )
& pushprop_lem1v2_gthm
& ( induction2lem
<=> ! [X16: term,X17: subst,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X15: term,X13: term,X20: term,X19: term] :
( ( X13 = X15 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) )
=> ! [X13: term,X20: term,X19: term,X15: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) ) )
<=> hoasapinj1_lthm )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X13: term,X15: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
<=> laminj )
& ( hoasinduction_lem3_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X27: term,X10: subst > term > subst > $o] :
( ( 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 )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X26: subst,X13: term,X25: subst,X14: 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 ) )
| ~ ! [X14: subst,X25: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) ) ) )
& ( ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
=> ! [X10: subst > term > subst > $o,X43: term] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) ) )
<=> hoasinduction_lem3a_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,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) ) ) )
<=> hoasinduction_lem3v2a_lthm )
& hoasapinj1_gthm
& ( pushprop_lem1
<=> ! [X15: term,X14: subst,X26: term > $o,X10: term > $o,X13: term] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) )
& hoasinduction_lem1_lthm
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& hoasinduction_lem1
& pushprop_lem2v2_gthm
& ulamvarind
& ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id ) )
<=> hoasinduction_lem3aa )
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& hoasinduction_lem3v2_gthm
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& hoasapnotvar_gthm
& apnotvar
& axapp
& ~ lamnotap
& pushprop_lem1_gthm
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X15: term,X13: term] :
( ( X13 = X15 )
| ( ( lam @ X13 )
!= ( lam @ X15 ) ) )
=> ! [X31: subst > term > term,X32: subst,X33: term,X18: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) ) ) ) ) )
<=> hoaslaminj_lthm )
& lamnotvar
& ( shinj
<=> ! [X13: term,X15: term] :
( ( X13 = X15 )
| ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) ) ) )
& hoasinduction_gthm
& hoasinduction_lem2_lthm
& ( apinj2
<=> ! [X13: term,X15: term,X20: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) ) )
& ( hoasinduction_lem3aaa
<=> ! [X34: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term,X35: term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X37: term,X36: subst,X38: subst] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ~ ! [X41: subst,X40: term,X39: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) ) ) ) )
& ( hoasinduction_lem0
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& hoasapinj2_gthm
& pushprop_lem2v2
& ( ! [X14: subst,X13: term,X10: term > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
<=> pushprop_lem0_lthm )
& ( hoasapinj2
<=> ! [X20: term,X13: term,X19: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0_lthm )
& hoasapnotvar
& ( ( d2subst @ d_id )
= sh )
& ( ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) )
| ( X10 @ X22 )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X29: term,X11: term > $o,X10: subst > term > subst > $o] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
=> ! [X10: subst > term > subst > $o,X30: term] :
( ( X10 @ id @ X30 @ id )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) ) )
<=> hoasinduction_no_psi_cond_lthm )
& substmonoid_gthm
& pushprop_lem3v2_lthm
& ( ! [X47: term,X46: term,X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) ) )
<=> hoaslamnotap )
& pushprop_lem0_gthm
& ( hoasinduction_lem3aa_lthm
<=> ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) ) )
& ( hoasinduction_lem3v2
<=> ! [X48: term,X11: term > $o,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X25: subst,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [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 ) ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X26: subst,X14: subst,X25: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) ) )
& ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
<=> axshiftcons )
& hoasinduction_lem3b_gthm
& termmset_gthm
& axmap
& ( ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 ) )
<=> induction2 )
& ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
<=> axidl )
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X14: subst,X26: term > $o,X10: term > $o,X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) ) )
<=> pushprop_lem1_lthm )
& ( pushprop_lem1v2
<=> ! [X14: subst,X13: term,X10: term > $o,X11: term > $o] :
( ( X11 @ one )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ~ ( X10 @ X13 ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& hoaslamnotap_lthm
& hoasinduction_lem1v2
& ( hoasapinj2_lthm
<=> ( ! [X20: term,X13: term,X19: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
=> ! [X13: term,X20: term,X19: term,X15: term] :
( ( X19 = X20 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) ) )
& axvarshift
& ~ ulamvar1
& ( ( ! [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 ) )
| ( X10 @ X21 )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) ) )
=> ! [X17: subst,X16: term,X10: term > $o] :
( ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoasinduction_lem1v2_gthm
& pushprop_lem3v2
& ( ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ( X11 @ ( lam @ X29 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
<=> hoasinduction_lem3v2a )
& induction2_gthm
& ! [X1: d_term] : ( d_one = X1 )
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) ) ) )
<=> substmonoid_lthm )
& axassoc
& hoasinduction_lem3a_gthm
& hoaslamnotap_gthm
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ! [X6: d_subst,X7: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X10: term > $o,X13: term,X11: term > $o,X14: subst] :
( ( X11 @ one )
| ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) )
<=> pushprop_lem1v2_lthm )
& hoaslamnotvar_gthm
& ulamvarsh
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
<=> substmonoid )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X48: term,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X25: subst,X26: subst,X14: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) )
| ( X11 @ ( lam @ X48 ) ) ) ) )
& ( hoasinduction_lem2
<=> ! [X10: subst > term > subst > $o,X24: term,X23: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ~ ( X10 @ id @ X23 @ id )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X13: term,X25: subst,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) )
& ( hoasinduction_lthm
<=> ( ! [X10: term > $o,X22: term] :
( ~ ! [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 ) ) )
=> ( ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ( X10 @ id @ X24 @ id )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) ) )
=> ( ! [X10: subst > term > subst > $o,X27: term] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X14: subst,X26: subst,X13: term,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ 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 ) ) ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& ( induction2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X17: subst,X10: term > $o,X16: term] :
( ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X15: term] :
( ~ ( var @ X15 )
| ( X10 @ ( sub @ X15 @ X17 ) ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
=> ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) ) ) ) ) )
& ( ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ X30 @ id ) )
<=> hoasinduction_no_psi_cond )
& ( ! [X10: subst > term > subst > $o,X43: term] :
( ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_lem3a )
& ( hoasapinj1
<=> ! [X15: term,X20: term,X13: term,X19: term] :
( ( X13 = X15 )
| ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) ) ) )
& hoaslamnotvar_lthm
& ( ! [X33: term,X32: subst,X18: subst > term > term,X31: subst > term > term] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
<=> hoaslaminj )
& hoasinduction_lem1_gthm
& pushprop_gthm
& axclos
& ( ( ^ [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
= pushprop_p_and_p_prime )
& ( ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 )
<=> axscons )
& hoasapnotvar_lthm
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& pushprop_lthm_orig
& ( hoasinduction_lthm_3
<=> ( ! [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 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X29: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ( X10 @ id @ X28 @ id )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X25: subst,X13: term,X26: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDduru1qPi/DTF2THF_30868.p',alg444_1) ).
thf(f1197,plain,
! [X77: term] :
( ( d2term @ ( sK491 @ X77 ) )
= X77 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f11387,plain,
( ! [X1: subst > term > term] :
( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) )
| ~ spl591_577
| ~ spl591_682 ),
inference(subsumption_resolution,[status(thm)],[f5282,f6182]) ).
thf(f5282,plain,
( ! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK595 @ X1 ) @ ( d2subst @ d_id ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK595 @ X1 ) ) @ ( d2subst @ d_id ) ) ) )
| ~ spl591_577 ),
inference(avatar_component_clause,[status(thm)],[f5281]) ).
thf(f5281,definition,
( spl591_577
<=> ! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK595 @ X1 ) @ ( d2subst @ d_id ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK595 @ X1 ) ) @ ( d2subst @ d_id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_577])],[avatar_definition]) ).
thf(f11385,plain,
( spl591_732
| spl591_731
| ~ spl591_580 ),
inference(avatar_split_clause,[status(thm)],[f11384,f5295,f7084,f7087]) ).
thf(f5295,definition,
( spl591_580
<=> ! [X2: subst,X4: subst,X1: term,X3: subst] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X4 ) @ X3 )
= $false )
| ( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl591_580])],[avatar_definition]) ).
thf(f11384,plain,
( ! [X2: subst,X3: subst,X1: term] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X3 )
= $false )
| ( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true ) )
| ~ spl591_580 ),
inference(forward_demodulation,[status(thm)],[f5296,f5725]) ).
thf(f5296,plain,
( ! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X4 ) @ X3 )
= $false ) )
| ~ spl591_580 ),
inference(avatar_component_clause,[status(thm)],[f5295]) ).
thf(f11383,plain,
( spl591_661
| ~ spl591_680 ),
inference(avatar_contradiction_clause,[status(thm)],[f11382]) ).
thf(f11382,plain,
( $false
| spl591_661
| ~ spl591_680 ),
inference(subsumption_resolution,[status(thm)],[f11358,f5979]) ).
thf(f5979,plain,
( ( $true
!= ( sP42 @ sK178 ) )
| spl591_661 ),
inference(avatar_component_clause,[status(thm)],[f5977]) ).
thf(f5977,definition,
( spl591_661
<=> ( $true
= ( sP42 @ sK178 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_661])],[avatar_definition]) ).
thf(f11358,plain,
( ( $true
= ( sP42 @ sK178 ) )
| ~ spl591_680 ),
inference(trivial_inequality_removal,[status(thm)],[f11350]) ).
thf(f11350,plain,
( ( $true != $true )
| ( $true
= ( sP42 @ sK178 ) )
| ~ spl591_680 ),
inference(superposition,[status(thm)],[f6165,f5901]) ).
thf(f5901,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( sP42 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f5900,f5865]) ).
thf(f5865,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ X10 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f5814,f5838]) ).
thf(f5838,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sP25 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f5837]) ).
thf(f5837,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sP25 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f5836,f5725]) ).
thf(f5836,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( sP25 @ X0 ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f5835,f5725]) ).
thf(f5835,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( sP25 @ X0 ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f5834,f5725]) ).
thf(f5834,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( d2term @ d_one )
!= ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( sP25 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f5780,f5725]) ).
thf(f5780,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sP25 @ X0 ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f4252,f5725]) ).
thf(f4252,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK296 @ X1 ) ) @ ( d2subst @ d_id ) )
!= ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK296 @ X1 ) @ ( d2subst @ d_id ) ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( sP25 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f4251,f4214]) ).
thf(f4214,plain,
! [X208: subst] :
( ( d2subst @ d_id )
= X208 ),
inference(forward_demodulation,[status(thm)],[f1078,f1249]) ).
thf(f1249,plain,
! [X0: d_subst] : ( d_id = X0 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1078,plain,
! [X208: subst] :
( ( d2subst @ ( sK555 @ X208 ) )
= X208 ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f4251,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK296 @ X1 ) ) @ ( d2subst @ d_id ) )
!= ( X1 @ ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) @ ( sub @ ( sK296 @ X1 ) @ ( d2subst @ d_id ) ) ) )
| ( $true
= ( sP25 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4222,f4214]) ).
thf(f4222,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X1 @ ( comp @ ( d2subst @ d_id ) @ ( sK295 @ X1 ) ) @ ( sub @ ( sK296 @ X1 ) @ ( sK295 @ X1 ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK296 @ X1 ) ) @ ( sK295 @ X1 ) ) )
| ( $true
= ( sP25 @ X0 ) ) ),
inference(backward_demodulation,[status(thm)],[f1469,f4214]) ).
thf(f1469,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK294 @ X1 ) @ ( sK295 @ X1 ) ) @ ( sub @ ( sK296 @ X1 ) @ ( sK295 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK294 @ X1 ) @ ( sK296 @ X1 ) ) @ ( sK295 @ X1 ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sP25 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK297 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f834,f1208,f1098,f1089,f1208,f1208,f1208]) ).
thf(f1089,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1098,plain,
( ( d2subst @ d_id )
= sh ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1208,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f834,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( sP25 @ X0 ) )
| ( ( X1 @ ( comp @ ( sK294 @ X1 ) @ ( sK295 @ X1 ) ) @ ( sub @ ( sK296 @ X1 ) @ ( sK295 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK294 @ X1 ) @ ( sK296 @ X1 ) ) @ ( sK295 @ X1 ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( ( X0 @ id @ ( sK297 @ X1 @ X0 ) @ id )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f306,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP25 @ X0 ) )
| ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK294 @ X1 ) @ ( sK295 @ X1 ) ) @ ( sub @ ( sK296 @ X1 ) @ ( sK295 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK294 @ X1 ) @ ( sK296 @ X1 ) ) @ ( sK295 @ X1 ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK297 @ X1 @ X0 ) ) @ id ) )
& ( ( X0 @ id @ ( sK297 @ X1 @ X0 ) @ id )
= $true ) ) ) )
& ( ( ! [X7: subst,X8: subst,X9: term] :
( ( sK298 @ X0 @ ( comp @ X7 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( sK298 @ X0 @ X7 @ X9 ) @ X8 ) )
& ( ( X0 @ id @ ( lam @ ( sK298 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( sK298 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
| ( $true
!= ( sP25 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK294,sK295,sK296,sK297,sK298])],[f302,f305,f304,f303]) ).
thf(f303,plain,
! [X1: subst > term > term] :
( ? [X2: subst,X3: subst,X4: term] :
( ( sub @ ( X1 @ X2 @ X4 ) @ X3 )
!= ( X1 @ ( comp @ X2 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ ( comp @ ( sK294 @ X1 ) @ ( sK295 @ X1 ) ) @ ( sub @ ( sK296 @ X1 ) @ ( sK295 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK294 @ X1 ) @ ( sK296 @ X1 ) ) @ ( sK295 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f304,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X5: term] :
( ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
& ( $true
= ( X0 @ id @ X5 @ id ) ) )
=> ( ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK297 @ X1 @ X0 ) ) @ id ) )
& ( ( X0 @ id @ ( sK297 @ X1 @ X0 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f305,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ! [X7: subst,X8: subst,X9: term] :
( ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( X6 @ X7 @ X9 ) @ X8 ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
=> ( ! [X9: term,X8: subst,X7: subst] :
( ( sK298 @ X0 @ ( comp @ X7 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( sK298 @ X0 @ X7 @ X9 ) @ X8 ) )
& ( ( X0 @ id @ ( lam @ ( sK298 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( sK298 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f302,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP25 @ X0 ) )
| ! [X1: subst > term > term] :
( ? [X2: subst,X3: subst,X4: term] :
( ( sub @ ( X1 @ X2 @ X4 ) @ X3 )
!= ( X1 @ ( comp @ X2 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
| ? [X5: term] :
( ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
& ( $true
= ( X0 @ id @ X5 @ id ) ) ) ) )
& ( ? [X6: subst > term > term] :
( ! [X7: subst,X8: subst,X9: term] :
( ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X9 @ X8 ) )
= ( sub @ ( X6 @ X7 @ X9 ) @ X8 ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id ) )
& ! [X10: term] :
( ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) ) ) )
| ( $true
!= ( sP25 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f301]) ).
thf(f301,plain,
! [X265: subst > term > subst > $o] :
( ( ( $true
= ( sP25 @ X265 ) )
| ! [X270: subst > term > term] :
( ? [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
!= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
| ( $true
= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
| ? [X271: term] :
( ( $true
!= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
& ( $true
= ( X265 @ id @ X271 @ id ) ) ) ) )
& ( ? [X270: subst > term > term] :
( ! [X272: subst,X273: subst,X274: term] :
( ( X270 @ ( comp @ X272 @ X273 ) @ ( sub @ X274 @ X273 ) )
= ( sub @ ( X270 @ X272 @ X274 ) @ X273 ) )
& ( $true
!= ( X265 @ id @ ( lam @ ( X270 @ sh @ one ) ) @ id ) )
& ! [X271: term] :
( ( $true
= ( X265 @ id @ ( X270 @ id @ X271 ) @ id ) )
| ( $true
!= ( X265 @ id @ X271 @ id ) ) ) )
| ( $true
!= ( sP25 @ X265 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
thf(f5814,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
!= ( sP25 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ X10 @ ( d2subst @ d_id ) )
!= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1471,f5725]) ).
thf(f1471,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK298 @ X0 @ ( d2subst @ d_id ) @ X10 ) @ ( d2subst @ d_id ) ) )
| ( $true
!= ( sP25 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ X10 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f831,f1208,f1208,f1208,f1208,f1208]) ).
thf(f831,plain,
! [X10: term,X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ id @ ( sK298 @ X0 @ id @ X10 ) @ id ) )
| ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
!= ( sP25 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f5900,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP42 @ X0 )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f5899,f5725]) ).
thf(f5899,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP42 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f5898,f5725]) ).
thf(f5898,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP42 @ X0 )
= $true )
| ( ( d2term @ d_one )
!= ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f5777,f5725]) ).
thf(f5777,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) @ ( d2subst @ d_id ) ) )
| ( ( sP42 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(backward_demodulation,[status(thm)],[f5418,f5725]) ).
thf(f5418,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK191 @ X1 ) ) @ ( d2subst @ d_id ) )
!= ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK191 @ X1 ) @ ( d2subst @ d_id ) ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( sP42 @ X0 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f5417,f4214]) ).
thf(f5417,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) ) )
| ( ( sP42 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f5416,f4214]) ).
thf(f5416,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP42 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK192 @ X1 ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1388,f4214]) ).
thf(f1388,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP42 @ X0 )
= $true )
| ( ( sub @ ( X1 @ ( sK192 @ X1 ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) )
!= ( X1 @ ( comp @ ( sK192 @ X1 ) @ ( sK190 @ X1 ) ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( sK193 @ X1 @ X0 ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X1 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f702,f1208,f1208,f1208,f1098,f1089,f1208]) ).
thf(f702,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP42 @ X0 )
= $true )
| ( ( sub @ ( X1 @ ( sK192 @ X1 ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) )
!= ( X1 @ ( comp @ ( sK192 @ X1 ) @ ( sK190 @ X1 ) ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) ) )
| ( $true
= ( X0 @ id @ ( sK193 @ X1 @ X0 ) @ id ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
thf(f200,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP42 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK192 @ X1 ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) )
!= ( X1 @ ( comp @ ( sK192 @ X1 ) @ ( sK190 @ X1 ) ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) ) )
| ( ( $true
= ( X0 @ id @ ( sK193 @ X1 @ X0 ) @ id ) )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK193 @ X1 @ X0 ) ) @ id ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) )
& ( ( ! [X7: subst,X8: term,X9: subst] :
( ( sK194 @ X0 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) )
= ( sub @ ( sK194 @ X0 @ X9 @ X8 ) @ X7 ) )
& ! [X10: term] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
= ( X0 @ id @ ( sK194 @ X0 @ id @ X10 ) @ id ) ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( sK194 @ X0 @ sh @ one ) ) @ id ) ) )
| ( ( sP42 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191,sK192,sK193,sK194])],[f196,f199,f198,f197]) ).
thf(f197,plain,
! [X1: subst > term > term] :
( ? [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X4 @ X3 ) @ X2 )
!= ( X1 @ ( comp @ X4 @ X2 ) @ ( sub @ X3 @ X2 ) ) )
=> ( ( sub @ ( X1 @ ( sK192 @ X1 ) @ ( sK191 @ X1 ) ) @ ( sK190 @ X1 ) )
!= ( X1 @ ( comp @ ( sK192 @ X1 ) @ ( sK190 @ X1 ) ) @ ( sub @ ( sK191 @ X1 ) @ ( sK190 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f198,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X5: term] :
( ( $true
= ( X0 @ id @ X5 @ id ) )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) ) )
=> ( ( $true
= ( X0 @ id @ ( sK193 @ X1 @ X0 ) @ id ) )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ ( sK193 @ X1 @ X0 ) ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f199,plain,
! [X0: subst > term > subst > $o] :
( ? [X6: subst > term > term] :
( ! [X7: subst,X8: term,X9: subst] :
( ( X6 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) )
= ( sub @ ( X6 @ X9 @ X8 ) @ X7 ) )
& ! [X10: term] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id ) ) )
=> ( ! [X9: subst,X8: term,X7: subst] :
( ( sK194 @ X0 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) )
= ( sub @ ( sK194 @ X0 @ X9 @ X8 ) @ X7 ) )
& ! [X10: term] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
= ( X0 @ id @ ( sK194 @ X0 @ id @ X10 ) @ id ) ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( sK194 @ X0 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f196,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP42 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ? [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X4 @ X3 ) @ X2 )
!= ( X1 @ ( comp @ X4 @ X2 ) @ ( sub @ X3 @ X2 ) ) )
| ? [X5: term] :
( ( $true
= ( X0 @ id @ X5 @ id ) )
& ( $true
!= ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) )
& ( ? [X6: subst > term > term] :
( ! [X7: subst,X8: term,X9: subst] :
( ( X6 @ ( comp @ X9 @ X7 ) @ ( sub @ X8 @ X7 ) )
= ( sub @ ( X6 @ X9 @ X8 ) @ X7 ) )
& ! [X10: term] :
( ( $true
!= ( X0 @ id @ X10 @ id ) )
| ( $true
= ( X0 @ id @ ( X6 @ id @ X10 ) @ id ) ) )
& ( $true
!= ( X0 @ id @ ( lam @ ( X6 @ sh @ one ) ) @ id ) ) )
| ( ( sP42 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f195]) ).
thf(f195,plain,
! [X6: subst > term > subst > $o] :
( ( ( $true
= ( sP42 @ X6 ) )
| ! [X12: subst > term > term] :
( ? [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
!= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
| ? [X13: term] :
( ( ( X6 @ id @ X13 @ id )
= $true )
& ( $true
!= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
| ( $true
= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) ) )
& ( ? [X12: subst > term > term] :
( ! [X14: subst,X15: term,X16: subst] :
( ( sub @ ( X12 @ X16 @ X15 ) @ X14 )
= ( X12 @ ( comp @ X16 @ X14 ) @ ( sub @ X15 @ X14 ) ) )
& ! [X13: term] :
( ( ( X6 @ id @ X13 @ id )
!= $true )
| ( $true
= ( X6 @ id @ ( X12 @ id @ X13 ) @ id ) ) )
& ( $true
!= ( X6 @ id @ ( lam @ ( X12 @ sh @ one ) ) @ id ) ) )
| ( $true
!= ( sP42 @ X6 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
thf(f6165,plain,
( ! [X9: subst] :
( $true
!= ( sK178 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X9 ) )
| ~ spl591_680 ),
inference(avatar_component_clause,[status(thm)],[f6164]) ).
thf(f6164,definition,
( spl591_680
<=> ! [X9: subst] :
( $true
!= ( sK178 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X9 ) ) ),
introduced(definition,[new_symbols(naming,[spl591_680])],[avatar_definition]) ).
thf(f8060,plain,
spl591_682,
inference(avatar_split_clause,[status(thm)],[f8053,f6181]) ).
thf(f8053,plain,
! [X0: term,X1: term] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f5725,f5725]) ).
thf(f7595,plain,
( spl591_251
| ~ spl591_679 ),
inference(avatar_contradiction_clause,[status(thm)],[f7594]) ).
thf(f7594,plain,
( $false
| spl591_251
| ~ spl591_679 ),
inference(subsumption_resolution,[status(thm)],[f3359,f6162]) ).
thf(f6162,plain,
( ! [X10: term,X7: subst] :
( $true
= ( sK178 @ X7 @ X10 @ ( d2subst @ d_id ) ) )
| ~ spl591_679 ),
inference(avatar_component_clause,[status(thm)],[f6161]) ).
thf(f6161,definition,
( spl591_679
<=> ! [X7: subst,X10: term] :
( $true
= ( sK178 @ X7 @ X10 @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl591_679])],[avatar_definition]) ).
thf(f3359,plain,
( ( ( sK178 @ ( d2subst @ d_id ) @ sK177 @ ( d2subst @ d_id ) )
!= $true )
| spl591_251 ),
inference(avatar_component_clause,[status(thm)],[f3357]) ).
thf(f3357,definition,
( spl591_251
<=> ( ( sK178 @ ( d2subst @ d_id ) @ sK177 @ ( d2subst @ d_id ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl591_251])],[avatar_definition]) ).
thf(f6645,plain,
( ~ spl591_106
| ~ spl591_574 ),
inference(avatar_contradiction_clause,[status(thm)],[f6644]) ).
thf(f6644,plain,
( $false
| ~ spl591_106
| ~ spl591_574 ),
inference(trivial_inequality_removal,[status(thm)],[f6643]) ).
thf(f6643,plain,
( ( $true = $false )
| ~ spl591_106
| ~ spl591_574 ),
inference(forward_demodulation,[status(thm)],[f2728,f5264]) ).
thf(f5264,plain,
( ( hoasinduction = $false )
| ~ spl591_574 ),
inference(avatar_component_clause,[status(thm)],[f5262]) ).
thf(f5262,definition,
( spl591_574
<=> ( hoasinduction = $false ) ),
introduced(definition,[new_symbols(naming,[spl591_574])],[avatar_definition]) ).
thf(f2728,plain,
( ( hoasinduction = $true )
| ~ spl591_106 ),
inference(avatar_component_clause,[status(thm)],[f2727]) ).
thf(f2727,definition,
( spl591_106
<=> ( hoasinduction = $true ) ),
introduced(definition,[new_symbols(naming,[spl591_106])],[avatar_definition]) ).
thf(f6166,plain,
( spl591_679
| spl591_69
| spl591_680 ),
inference(avatar_split_clause,[status(thm)],[f6159,f6164,f2570,f6161]) ).
thf(f2570,definition,
( spl591_69
<=> ( $true = sP44 ) ),
introduced(definition,[new_symbols(naming,[spl591_69])],[avatar_definition]) ).
thf(f6159,plain,
! [X10: term,X9: subst,X7: subst] :
( ( $true = sP44 )
| ( $true
!= ( sK178 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X9 ) )
| ( $true
= ( sK178 @ X7 @ X10 @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f6158,f4214]) ).
thf(f6158,plain,
! [X10: term,X8: subst,X9: subst,X7: subst] :
( ( $true
= ( sK178 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( sK178 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X9 ) )
| ( $true = sP44 ) ),
inference(forward_demodulation,[status(thm)],[f6157,f5725]) ).
thf(f6157,plain,
! [X10: term,X8: subst,X9: subst,X7: subst] :
( ( $true
!= ( sK178 @ ( d2subst @ d_id ) @ ( sub @ X10 @ X8 ) @ X9 ) )
| ( $true
= ( sK178 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true = sP44 ) ),
inference(forward_demodulation,[status(thm)],[f690,f4214]) ).
thf(f690,plain,
! [X10: term,X8: subst,X9: subst,X7: subst] :
( ( $true
!= ( sK178 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) )
| ( $true
= ( sK178 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true = sP44 ) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
thf(f190,plain,
( ( ( $true = sP44 )
| ( ! [X2: term] :
( ( $true
!= ( var @ ( sub @ X2 @ id ) ) )
| ( ( sK178 @ id @ X2 @ id )
= $true ) )
& ! [X3: subst,X4: subst,X5: term,X6: subst] :
( ( $true
= ( sK178 @ ( comp @ X3 @ X4 ) @ ( sub @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( sK178 @ X3 @ X5 @ ( comp @ X4 @ X6 ) ) ) )
& ( $true
!= ( sP43 @ sK178 ) )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
= ( sK178 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( sK178 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
& ( $true
!= ( sK178 @ id @ sK177 @ id ) )
& ( $true
!= ( sP42 @ sK178 ) ) ) )
& ( ! [X11: term,X12: subst > term > subst > $o] :
( ( ( $true
= ( var @ ( sub @ ( sK179 @ X12 ) @ id ) ) )
& ( $true
!= ( X12 @ id @ ( sK179 @ X12 ) @ id ) ) )
| ( ( ( X12 @ ( comp @ ( sK180 @ X12 ) @ ( sK181 @ X12 ) ) @ ( sub @ ( sK182 @ X12 ) @ ( sK181 @ X12 ) ) @ ( sK183 @ X12 ) )
!= $true )
& ( ( X12 @ ( sK180 @ X12 ) @ ( sK182 @ X12 ) @ ( comp @ ( sK181 @ X12 ) @ ( sK183 @ X12 ) ) )
= $true ) )
| ( ( sP43 @ X12 )
= $true )
| ( ( $true
!= ( X12 @ ( sK184 @ X12 ) @ ( sK187 @ X12 ) @ ( comp @ ( sK185 @ X12 ) @ ( sK186 @ X12 ) ) ) )
& ( $true
= ( X12 @ ( comp @ ( sK184 @ X12 ) @ ( sK185 @ X12 ) ) @ ( sub @ ( sK187 @ X12 ) @ ( sK185 @ X12 ) ) @ ( sK186 @ X12 ) ) ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP42 @ X12 ) ) )
| ( $true != sP44 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177,sK178,sK179,sK180,sK181,sK182,sK183,sK184,sK185,sK186,sK187])],[f185,f189,f188,f187,f186]) ).
thf(f186,plain,
( ? [X0: term,X1: subst > term > subst > $o] :
( ! [X2: term] :
( ( $true
!= ( var @ ( sub @ X2 @ id ) ) )
| ( $true
= ( X1 @ id @ X2 @ id ) ) )
& ! [X3: subst,X4: subst,X5: term,X6: subst] :
( ( $true
= ( X1 @ ( comp @ X3 @ X4 ) @ ( sub @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( X1 @ X3 @ X5 @ ( comp @ X4 @ X6 ) ) ) )
& ( $true
!= ( sP43 @ X1 ) )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
= ( X1 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( X1 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) )
& ( $true
!= ( sP42 @ X1 ) ) )
=> ( ! [X2: term] :
( ( $true
!= ( var @ ( sub @ X2 @ id ) ) )
| ( ( sK178 @ id @ X2 @ id )
= $true ) )
& ! [X6: subst,X5: term,X4: subst,X3: subst] :
( ( $true
= ( sK178 @ ( comp @ X3 @ X4 ) @ ( sub @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( sK178 @ X3 @ X5 @ ( comp @ X4 @ X6 ) ) ) )
& ( $true
!= ( sP43 @ sK178 ) )
& ! [X10: term,X9: subst,X8: subst,X7: subst] :
( ( $true
= ( sK178 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( sK178 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
& ( $true
!= ( sK178 @ id @ sK177 @ id ) )
& ( $true
!= ( sP42 @ sK178 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f187,plain,
! [X12: subst > term > subst > $o] :
( ? [X13: term] :
( ( ( var @ ( sub @ X13 @ id ) )
= $true )
& ( $true
!= ( X12 @ id @ X13 @ id ) ) )
=> ( ( $true
= ( var @ ( sub @ ( sK179 @ X12 ) @ id ) ) )
& ( $true
!= ( X12 @ id @ ( sK179 @ X12 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f188,plain,
! [X12: subst > term > subst > $o] :
( ? [X14: subst,X15: subst,X16: term,X17: subst] :
( ( $true
!= ( X12 @ ( comp @ X14 @ X15 ) @ ( sub @ X16 @ X15 ) @ X17 ) )
& ( $true
= ( X12 @ X14 @ X16 @ ( comp @ X15 @ X17 ) ) ) )
=> ( ( ( X12 @ ( comp @ ( sK180 @ X12 ) @ ( sK181 @ X12 ) ) @ ( sub @ ( sK182 @ X12 ) @ ( sK181 @ X12 ) ) @ ( sK183 @ X12 ) )
!= $true )
& ( ( X12 @ ( sK180 @ X12 ) @ ( sK182 @ X12 ) @ ( comp @ ( sK181 @ X12 ) @ ( sK183 @ X12 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f189,plain,
! [X12: subst > term > subst > $o] :
( ? [X18: subst,X19: subst,X20: subst,X21: term] :
( ( $true
!= ( X12 @ X18 @ X21 @ ( comp @ X19 @ X20 ) ) )
& ( $true
= ( X12 @ ( comp @ X18 @ X19 ) @ ( sub @ X21 @ X19 ) @ X20 ) ) )
=> ( ( $true
!= ( X12 @ ( sK184 @ X12 ) @ ( sK187 @ X12 ) @ ( comp @ ( sK185 @ X12 ) @ ( sK186 @ X12 ) ) ) )
& ( $true
= ( X12 @ ( comp @ ( sK184 @ X12 ) @ ( sK185 @ X12 ) ) @ ( sub @ ( sK187 @ X12 ) @ ( sK185 @ X12 ) ) @ ( sK186 @ X12 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f185,plain,
( ( ( $true = sP44 )
| ? [X0: term,X1: subst > term > subst > $o] :
( ! [X2: term] :
( ( $true
!= ( var @ ( sub @ X2 @ id ) ) )
| ( $true
= ( X1 @ id @ X2 @ id ) ) )
& ! [X3: subst,X4: subst,X5: term,X6: subst] :
( ( $true
= ( X1 @ ( comp @ X3 @ X4 ) @ ( sub @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( X1 @ X3 @ X5 @ ( comp @ X4 @ X6 ) ) ) )
& ( $true
!= ( sP43 @ X1 ) )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
= ( X1 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( X1 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
& ( $true
!= ( X1 @ id @ X0 @ id ) )
& ( $true
!= ( sP42 @ X1 ) ) ) )
& ( ! [X11: term,X12: subst > term > subst > $o] :
( ? [X13: term] :
( ( ( var @ ( sub @ X13 @ id ) )
= $true )
& ( $true
!= ( X12 @ id @ X13 @ id ) ) )
| ? [X14: subst,X15: subst,X16: term,X17: subst] :
( ( $true
!= ( X12 @ ( comp @ X14 @ X15 ) @ ( sub @ X16 @ X15 ) @ X17 ) )
& ( $true
= ( X12 @ X14 @ X16 @ ( comp @ X15 @ X17 ) ) ) )
| ( ( sP43 @ X12 )
= $true )
| ? [X18: subst,X19: subst,X20: subst,X21: term] :
( ( $true
!= ( X12 @ X18 @ X21 @ ( comp @ X19 @ X20 ) ) )
& ( $true
= ( X12 @ ( comp @ X18 @ X19 ) @ ( sub @ X21 @ X19 ) @ X20 ) ) )
| ( $true
= ( X12 @ id @ X11 @ id ) )
| ( $true
= ( sP42 @ X12 ) ) )
| ( $true != sP44 ) ) ),
inference(rectify,[status(thm)],[f184]) ).
thf(f184,plain,
( ( ( $true = sP44 )
| ? [X5: term,X6: subst > term > subst > $o] :
( ! [X11: term] :
( ( $true
!= ( var @ ( sub @ X11 @ id ) ) )
| ( $true
= ( X6 @ id @ X11 @ id ) ) )
& ! [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
| ( $true
!= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
& ( $true
!= ( sP43 @ X6 ) )
& ! [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
| ( $true
!= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
& ( $true
!= ( X6 @ id @ X5 @ id ) )
& ( $true
!= ( sP42 @ X6 ) ) ) )
& ( ! [X5: term,X6: subst > term > subst > $o] :
( ? [X11: term] :
( ( $true
= ( var @ ( sub @ X11 @ id ) ) )
& ( $true
!= ( X6 @ id @ X11 @ id ) ) )
| ? [X17: subst,X18: subst,X19: term,X20: subst] :
( ( $true
!= ( X6 @ ( comp @ X17 @ X18 ) @ ( sub @ X19 @ X18 ) @ X20 ) )
& ( $true
= ( X6 @ X17 @ X19 @ ( comp @ X18 @ X20 ) ) ) )
| ( $true
= ( sP43 @ X6 ) )
| ? [X7: subst,X8: subst,X9: subst,X10: term] :
( ( $true
!= ( X6 @ X7 @ X10 @ ( comp @ X8 @ X9 ) ) )
& ( $true
= ( X6 @ ( comp @ X7 @ X8 ) @ ( sub @ X10 @ X8 ) @ X9 ) ) )
| ( $true
= ( X6 @ id @ X5 @ id ) )
| ( $true
= ( sP42 @ X6 ) ) )
| ( $true != sP44 ) ) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
thf(f5999,plain,
( ~ spl591_69
| spl591_106 ),
inference(avatar_split_clause,[status(thm)],[f1154,f2727,f2570]) ).
thf(f1154,plain,
( ( $true != sP44 )
| ( hoasinduction = $true ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f5980,plain,
( spl591_69
| ~ spl591_661 ),
inference(avatar_split_clause,[status(thm)],[f688,f5977,f2570]) ).
thf(f688,plain,
( ( $true
!= ( sP42 @ sK178 ) )
| ( $true = sP44 ) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
thf(f5297,plain,
( spl591_574
| spl591_580 ),
inference(avatar_split_clause,[status(thm)],[f5293,f5295,f5262]) ).
thf(f5293,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X4 ) @ X3 )
= $false )
| ( ( sK592 @ X2 @ X1 @ ( d2subst @ d_id ) )
= $true )
| ( hoasinduction = $false ) ),
inference(forward_demodulation,[status(thm)],[f5292,f4214]) ).
thf(f5292,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( ( sK592 @ X2 @ X1 @ ( comp @ X4 @ X3 ) )
= $true )
| ( hoasinduction = $false )
| ( ( sK592 @ ( d2subst @ d_id ) @ ( sub @ X1 @ X4 ) @ X3 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f1723,f4214]) ).
thf(f1723,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( ( sK592 @ ( comp @ X2 @ X4 ) @ ( sub @ X1 @ X4 ) @ X3 )
= $false )
| ( hoasinduction = $false )
| ( ( sK592 @ X2 @ X1 @ ( comp @ X4 @ X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1722]) ).
thf(f1722,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( $true
= ( ( sK592 @ ( comp @ X2 @ X4 ) @ ( sub @ X1 @ X4 ) @ X3 )
=> ( sK592 @ X2 @ X1 @ ( comp @ X4 @ X3 ) ) ) )
| ( hoasinduction = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1721]) ).
thf(f1721,plain,
! [X2: subst,X3: subst,X1: term,X4: subst] :
( ( hoasinduction = $false )
| ( $true
= ( ^ [Y0: subst] :
( ( sK592 @ ( comp @ X2 @ Y0 ) @ ( sub @ X1 @ Y0 ) @ X3 )
=> ( sK592 @ X2 @ X1 @ ( comp @ Y0 @ X3 ) ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f1720]) ).
thf(f1720,plain,
! [X2: subst,X3: subst,X1: term] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK592 @ ( comp @ X2 @ Y0 ) @ ( sub @ X1 @ Y0 ) @ X3 )
=> ( sK592 @ X2 @ X1 @ ( comp @ Y0 @ X3 ) ) ) ) )
| ( hoasinduction = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1719]) ).
thf(f1719,plain,
! [X2: subst,X3: subst,X1: term] :
( ( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK592 @ ( comp @ X2 @ Y1 ) @ ( sub @ X1 @ Y1 ) @ Y0 )
=> ( sK592 @ X2 @ X1 @ ( comp @ Y1 @ Y0 ) ) ) )
@ X3 ) )
| ( hoasinduction = $false ) ),
inference(pi_clausification,[status(thm)],[f1718]) ).
thf(f1718,plain,
! [X2: subst,X1: term] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK592 @ ( comp @ X2 @ Y1 ) @ ( sub @ X1 @ Y1 ) @ Y0 )
=> ( sK592 @ X2 @ X1 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
| ( hoasinduction = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1717]) ).
thf(f1717,plain,
! [X2: subst,X1: term] :
( ( hoasinduction = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK592 @ ( comp @ Y0 @ Y2 ) @ ( sub @ X1 @ Y2 ) @ Y1 )
=> ( sK592 @ Y0 @ X1 @ ( comp @ Y2 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1716]) ).
thf(f1716,plain,
! [X1: term] :
( ( hoasinduction = $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK592 @ ( comp @ Y0 @ Y2 ) @ ( sub @ X1 @ Y2 ) @ Y1 )
=> ( sK592 @ Y0 @ X1 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1715]) ).
thf(f1715,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK592 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( hoasinduction = $false ) ),
inference(pi_clausification,[status(thm)],[f1714]) ).
thf(f1714,plain,
( ( hoasinduction = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK592 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1702]) ).
thf(f1702,plain,
( ( hoasinduction = $false )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK592 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1701]) ).
thf(f1701,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ Y2 @ Y0 @ ( comp @ Y1 @ Y3 ) )
=> ( sK592 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK592 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK592 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1700]) ).
thf(f1700,plain,
( ( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) ) ) )
@ sK592 ) )
| ( hoasinduction = $false ) ),
inference(sigma_clausification,[status(thm)],[f1699]) ).
thf(f1699,plain,
( ( hoasinduction = $false )
| ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1697]) ).
thf(f1697,plain,
( hoasinduction
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1664]) ).
thf(f1664,plain,
( hoasinduction
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( d2subst @ d_id ) @ Y2 @ ( d2subst @ d_id ) )
=> ( Y0 @ ( d2subst @ d_id ) @ ( Y1 @ ( d2subst @ d_id ) @ Y2 ) @ ( d2subst @ d_id ) ) ) )
=> ( Y0 @ ( d2subst @ d_id )
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( d2term @ d_one )
@ ( d2subst @ d_id )
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1260,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1219,f1208,f1208,f1208,f1208]) ).
thf(f1219,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) ),
inference(cnf_transformation,[status(thm)],[f545]) ).
thf(f1260,plain,
( hoasinduction
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ 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] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( hoasinduction
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ 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] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( hoasinduction
!= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y3 @ Y1 @ ( comp @ Y2 @ Y4 ) )
=> ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y4 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ 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] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( hoasinduction
!= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: subst,X3: subst,X4: term] :
( ( X0 @ X2 @ X4 @ ( comp @ X3 @ X1 ) )
=> ( X0 @ ( comp @ X2 @ X3 ) @ ( sub @ X4 @ X3 ) @ X1 ) )
=> ( ! [X5: subst,X6: subst,X7: subst,X8: term] :
( ( X0 @ ( comp @ X7 @ X5 ) @ ( sub @ X8 @ X5 ) @ X6 )
=> ( X0 @ X7 @ X8 @ ( comp @ X5 @ X6 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ( ! [X10: term,X11: term] :
( ( X0 @ id @ X11 @ id )
=> ( ( X0 @ id @ X10 @ id )
=> ( X0 @ id @ ( hoasap @ id @ X11 @ id @ X10 ) @ id ) ) )
=> ( ! [X12: subst > term > term] :
( ! [X13: term,X14: subst,X15: subst] :
( ( sub @ ( X12 @ X15 @ X13 ) @ X14 )
= ( X12 @ ( comp @ X15 @ X14 ) @ ( sub @ X13 @ X14 ) ) )
=> ( ! [X16: term] :
( ( X0 @ id @ X16 @ id )
=> ( X0 @ id @ ( X12 @ id @ X16 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X17: subst,X18: term] : ( X12 @ X17 @ X18 ) )
@ id ) ) )
=> ! [X19: term] : ( X0 @ id @ X19 @ id ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( hoasinduction
!= ( ! [X10: subst > term > subst > $o] :
( ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
=> ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
=> ( ! [X13: term] :
( ( hoasvar @ id @ X13 @ id )
=> ( X10 @ id @ X13 @ id ) )
=> ( ! [X15: term,X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( hoasap @ id @ X13 @ id @ 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 @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ! [X13: term] : ( X10 @ id @ X13 @ id ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( hoasinduction
= ( ! [X10: subst > term > subst > $o] :
( ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
=> ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
=> ( ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
=> ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
=> ( ! [X13: term] :
( ( hoasvar @ id @ X13 @ id )
=> ( X10 @ id @ X13 @ id ) )
=> ( ! [X15: term,X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( hoasap @ id @ X13 @ id @ 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 @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ! [X13: term] : ( X10 @ id @ X13 @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDduru1qPi/DTF2THF_30868.p',hoasinduction) ).
thf(f5283,plain,
( spl591_576
| spl591_577
| spl591_574 ),
inference(avatar_split_clause,[status(thm)],[f5279,f5262,f5281,f5273]) ).
thf(f5279,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( d2subst @ d_id ) @ ( sub @ ( sK595 @ X1 ) @ ( d2subst @ d_id ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK595 @ X1 ) ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction = $false ) ),
inference(forward_demodulation,[status(thm)],[f5278,f4214]) ).
thf(f5278,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK595 @ X1 ) ) @ ( d2subst @ d_id ) )
!= ( X1 @ ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) @ ( sub @ ( sK595 @ X1 ) @ ( d2subst @ d_id ) ) ) )
| ( hoasinduction = $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f5277,f4214]) ).
thf(f5277,plain,
! [X1: subst > term > term] :
( ( hoasinduction = $false )
| ( ( X1 @ ( comp @ ( d2subst @ d_id ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) )
!= ( sub @ ( X1 @ ( d2subst @ d_id ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1753,f4214]) ).
thf(f1753,plain,
! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) ) )
| ( hoasinduction = $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1751]) ).
thf(f1751,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction = $false )
| ( ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) ) )
| ( $false
= ( ( sK592 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ ( sK596 @ X1 ) ) @ ( d2subst @ d_id ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1750]) ).
thf(f1750,plain,
! [X1: subst > term > term] :
( ( ( ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) )
@ ( sK596 @ X1 ) )
= $false )
| ( ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) ) )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction = $false ) ),
inference(sigma_clausification,[status(thm)],[f1749]) ).
thf(f1749,plain,
! [X1: subst > term > term] :
( ( hoasinduction = $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f1748]) ).
thf(f1748,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction = $false )
| ( $false
= ( ( sub @ ( X1 @ ( sK593 @ X1 ) @ ( sK595 @ X1 ) ) @ ( sK594 @ X1 ) )
= ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ ( sK595 @ X1 ) @ ( sK594 @ X1 ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1747]) ).
thf(f1747,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( $false
= ( ^ [Y0: term] :
( ( sub @ ( X1 @ ( sK593 @ X1 ) @ Y0 ) @ ( sK594 @ X1 ) )
= ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ Y0 @ ( sK594 @ X1 ) ) ) )
@ ( sK595 @ X1 ) ) )
| ( hoasinduction = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1746]) ).
thf(f1746,plain,
! [X1: subst > term > term] :
( ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ ( X1 @ ( sK593 @ X1 ) @ Y0 ) @ ( sK594 @ X1 ) )
= ( X1 @ ( comp @ ( sK593 @ X1 ) @ ( sK594 @ X1 ) ) @ ( sub @ Y0 @ ( sK594 @ X1 ) ) ) ) )
= $false )
| ( hoasinduction = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1745]) ).
thf(f1745,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( X1 @ ( sK593 @ X1 ) @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ ( sK593 @ X1 ) @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) )
@ ( sK594 @ X1 ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( hoasinduction = $false ) ),
inference(sigma_clausification,[status(thm)],[f1744]) ).
thf(f1744,plain,
! [X1: subst > term > term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( X1 @ ( sK593 @ X1 ) @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ ( sK593 @ X1 ) @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( hoasinduction = $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1743]) ).
thf(f1743,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( X1 @ Y0 @ Y2 ) @ Y1 )
= ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) )
@ ( sK593 @ X1 ) ) )
| ( hoasinduction = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1742]) ).
thf(f1742,plain,
! [X1: subst > term > term] :
( ( hoasinduction = $false )
| ( $true
= ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( X1 @ Y0 @ Y2 ) @ Y1 )
= ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1741]) ).
thf(f1741,plain,
! [X1: subst > term > term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
= $true )
| ( hoasinduction = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( X1 @ Y0 @ Y2 ) @ Y1 )
= ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1740]) ).
thf(f1740,plain,
! [X1: subst > term > term] :
( ( hoasinduction = $false )
| ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( X1 @ Y0 @ Y2 ) @ Y1 )
= ( X1 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( X1 @ ( d2subst @ d_id ) @ Y0 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1739]) ).
thf(f1739,plain,
! [X1: subst > term > term] :
( ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
@ X1 )
= $true )
| ( hoasinduction = $false ) ),
inference(pi_clausification,[status(thm)],[f1738]) ).
thf(f1738,plain,
( ( hoasinduction = $false )
| ( $true
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1729]) ).
thf(f1729,plain,
( ( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
= $false )
| ( hoasinduction = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1724]) ).
thf(f1724,plain,
( ( hoasinduction = $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1713]) ).
thf(f1713,plain,
( ( hoasinduction = $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( hoasvar @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
=> ( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( hoasap @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK592 @ ( d2subst @ d_id ) @ Y1 @ ( d2subst @ d_id ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( Y0 @ ( d2subst @ d_id ) @ Y1 ) @ ( d2subst @ d_id ) ) ) )
=> ( sK592 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1702]) ).
thf(f5265,plain,
( spl591_573
| spl591_574 ),
inference(avatar_split_clause,[status(thm)],[f1755,f5262,f5258]) ).
thf(f1755,plain,
( ( ( sK592 @ ( d2subst @ d_id ) @ sK597 @ ( d2subst @ d_id ) )
= $false )
| ( hoasinduction = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1754]) ).
thf(f1754,plain,
( ( ( ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) )
@ sK597 )
= $false )
| ( hoasinduction = $false ) ),
inference(sigma_clausification,[status(thm)],[f1737]) ).
thf(f1737,plain,
( ( ( !! @ term
@ ^ [Y0: term] : ( sK592 @ ( d2subst @ d_id ) @ Y0 @ ( d2subst @ d_id ) ) )
= $false )
| ( hoasinduction = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1729]) ).
thf(f3360,plain,
( ~ spl591_251
| spl591_69 ),
inference(avatar_split_clause,[status(thm)],[f1375,f2570,f3357]) ).
thf(f1375,plain,
( ( $true = sP44 )
| ( ( sK178 @ ( d2subst @ d_id ) @ sK177 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f689,f1208,f1208]) ).
thf(f689,plain,
( ( $true = sP44 )
| ( $true
!= ( sK178 @ id @ sK177 @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 09:12:25 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.19/0.47 % Domain : Software Verification
% 0.19/0.47 % Problem : Benchmark: ALG444^1, Active target: hoasinduction
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Kon26]
% 0.19/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : ? v9.3.0
% 0.19/0.47 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.19/0.47 % Number of atoms : 256 ( 129 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 248 ( 128 avg)
% 0.19/0.47 % Number of connectives : 2653 ( 333 ~; 306 |; 129 &;1778 @)
% 0.19/0.47 % ( 56 <=>; 51 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 151 ( 76 avg)
% 0.19/0.47 % Number of types : 5 ( 4 usr)
% 0.19/0.47 % Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.19/0.47 % Number of variables : 570 ( 10 ^; 558 !; 2 ?; 570 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(term_type,type,
% 0.19/0.47 term: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(subst_type,type,
% 0.19/0.47 subst: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(one_decl,type,
% 0.19/0.47 one: term ).
% 0.19/0.47
% 0.19/0.47 thf(ap_decl,type,
% 0.19/0.47 ap: term > term > term ).
% 0.19/0.47
% 0.19/0.47 thf(lam_decl,type,
% 0.19/0.47 lam: term > term ).
% 0.19/0.47
% 0.19/0.47 thf(sub_decl,type,
% 0.19/0.47 sub: term > subst > term ).
% 0.19/0.47
% 0.19/0.47 thf(id_decl,type,
% 0.19/0.47 id: subst ).
% 0.19/0.47
% 0.19/0.47 thf(sh_decl,type,
% 0.19/0.47 sh: subst ).
% 0.19/0.47
% 0.19/0.47 thf(push_decl,type,
% 0.19/0.47 push: term > subst > subst ).
% 0.19/0.47
% 0.19/0.47 thf(comp_decl,type,
% 0.19/0.47 comp: subst > subst > subst ).
% 0.19/0.47
% 0.19/0.47 thf(var_decl,type,
% 0.19/0.47 var: term > $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1v2_decl,type,
% 0.19/0.47 pushprop_lem1v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1_gthm_decl,type,
% 0.19/0.47 pushprop_lem1_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axmap_decl,type,
% 0.19/0.47 axmap: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem0_gthm_decl,type,
% 0.19/0.47 pushprop_lem0_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(shinj_decl,type,
% 0.19/0.47 shinj: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem1v2_decl,type,
% 0.19/0.47 hoasinduction_lem1v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem1v2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasap_decl,type,
% 0.19/0.47 hoasap: subst > term > subst > term > term ).
% 0.19/0.47
% 0.19/0.47 thf(induction2lem_decl,type,
% 0.19/0.47 induction2lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2_f_decl,type,
% 0.19/0.47 hoasinduction_lem3v2_f: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axvarshift_decl,type,
% 0.19/0.47 axvarshift: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj2_decl,type,
% 0.19/0.47 hoasapinj2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapnotvar_gthm_decl,type,
% 0.19/0.47 hoasapnotvar_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj1_decl,type,
% 0.19/0.47 hoasapinj1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ulamvar1_decl,type,
% 0.19/0.47 ulamvar1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction2lem_lthm_decl,type,
% 0.19/0.47 induction2lem_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem3v2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(apnotvar_decl,type,
% 0.19/0.47 apnotvar: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lthm_orig_decl,type,
% 0.19/0.47 pushprop_lthm_orig: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3v2_f_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lthm_decl,type,
% 0.19/0.47 hoasinduction_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.19/0.47 hoasinduction_no_psi_cond_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslaminj_decl,type,
% 0.19/0.47 hoaslaminj: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3aaa_decl,type,
% 0.19/0.47 hoasinduction_lem3aaa: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction2lem_gthm_decl,type,
% 0.19/0.47 induction2lem_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3aa_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3_decl,type,
% 0.19/0.47 hoasinduction_lem3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem2_decl,type,
% 0.19/0.47 hoasinduction_lem2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(termmset_lthm_decl,type,
% 0.19/0.47 termmset_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem1_decl,type,
% 0.19/0.47 hoasinduction_lem1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotap_lthm_decl,type,
% 0.19/0.47 hoaslamnotap_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1v2_lthm_decl,type,
% 0.19/0.47 pushprop_lem1v2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapnotvar_decl,type,
% 0.19/0.47 hoasapnotvar: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem0_decl,type,
% 0.19/0.47 hoasinduction_lem0: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_decl,type,
% 0.19/0.47 hoasinduction: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_gthm_decl,type,
% 0.19/0.47 hoasinduction_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axapp_decl,type,
% 0.19/0.47 axapp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotvar_lthm_decl,type,
% 0.19/0.47 hoaslamnotvar_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem3v2_lthm_decl,type,
% 0.19/0.47 pushprop_lem3v2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3b_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ulamvarind_decl,type,
% 0.19/0.47 ulamvarind: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction_decl,type,
% 0.19/0.47 induction: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3a_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(termmset_gthm_decl,type,
% 0.19/0.47 termmset_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3aa_decl,type,
% 0.19/0.47 hoasinduction_lem3aa: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1v2_gthm_decl,type,
% 0.19/0.47 pushprop_lem1v2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotap_gthm_decl,type,
% 0.19/0.47 hoaslamnotap_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotvar_gthm_decl,type,
% 0.19/0.47 hoaslamnotvar_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem3b_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem2v2_decl,type,
% 0.19/0.47 pushprop_lem2v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem3a_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axclos_decl,type,
% 0.19/0.47 axclos: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axassoc_decl,type,
% 0.19/0.47 axassoc: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem2v2_decl,type,
% 0.19/0.47 hoasinduction_lem2v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lthm_decl,type,
% 0.19/0.47 pushprop_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(apinj2_decl,type,
% 0.19/0.47 apinj2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(apinj1_decl,type,
% 0.19/0.47 apinj1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj2_lthm_decl,type,
% 0.19/0.47 hoasapinj2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2a_decl,type,
% 0.19/0.47 hoasinduction_lem3v2a: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj1_lthm_decl,type,
% 0.19/0.47 hoasapinj1_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslaminj_lthm_decl,type,
% 0.19/0.47 hoaslaminj_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axvarcons_decl,type,
% 0.19/0.47 axvarcons: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslam_decl,type,
% 0.19/0.47 hoaslam: subst > ( subst > term > term ) > term ).
% 0.19/0.47
% 0.19/0.47 thf(axscons_decl,type,
% 0.19/0.47 axscons: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem2v2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axidr_decl,type,
% 0.19/0.47 axidr: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1_decl,type,
% 0.19/0.47 pushprop_lem1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(laminj_decl,type,
% 0.19/0.47 laminj: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem0_decl,type,
% 0.19/0.47 pushprop_lem0: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_gthm_decl,type,
% 0.19/0.47 pushprop_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axabs_decl,type,
% 0.19/0.47 axabs: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3v2a_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem2_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj2_gthm_decl,type,
% 0.19/0.47 hoasapinj2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.19/0.47 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem1_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem1_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lamnotap_decl,type,
% 0.19/0.47 lamnotap: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapinj1_gthm_decl,type,
% 0.19/0.47 hoasapinj1_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotvar_decl,type,
% 0.19/0.47 hoaslamnotvar: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axidl_decl,type,
% 0.19/0.47 axidl: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslaminj_gthm_decl,type,
% 0.19/0.47 hoaslaminj_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction2_lthm_decl,type,
% 0.19/0.47 induction2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem0_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem0_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(substmonoid_lthm_decl,type,
% 0.19/0.47 substmonoid_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_decl,type,
% 0.19/0.47 pushprop: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem3_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem2_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3b_decl,type,
% 0.19/0.47 hoasinduction_lem3b: $o ).
% 0.19/0.47
% 0.19/0.47 thf(substmonoid_decl,type,
% 0.19/0.47 substmonoid: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lamnotvar_decl,type,
% 0.19/0.47 lamnotvar: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3a_decl,type,
% 0.19/0.47 hoasinduction_lem3a: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem1_gthm_decl,type,
% 0.19/0.47 hoasinduction_lem1_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_no_psi_cond_decl,type,
% 0.19/0.47 hoasinduction_no_psi_cond: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction2_gthm_decl,type,
% 0.19/0.47 induction2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem2v2_lthm_decl,type,
% 0.19/0.47 pushprop_lem2v2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasvar_decl,type,
% 0.19/0.47 hoasvar: subst > term > subst > $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoaslamnotap_decl,type,
% 0.19/0.47 hoaslamnotap: $o ).
% 0.19/0.47
% 0.19/0.47 thf(substmonoid_gthm_decl,type,
% 0.19/0.47 substmonoid_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ulamvarsh_decl,type,
% 0.19/0.47 ulamvarsh: $o ).
% 0.19/0.47
% 0.19/0.47 thf(induction2_decl,type,
% 0.19/0.47 induction2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem3v2_decl,type,
% 0.19/0.47 pushprop_lem3v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem2v2_gthm_decl,type,
% 0.19/0.47 pushprop_lem2v2_gthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem1_lthm_decl,type,
% 0.19/0.47 pushprop_lem1_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2_decl,type,
% 0.19/0.47 hoasinduction_lem3v2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(axshiftcons_decl,type,
% 0.19/0.47 axshiftcons: $o ).
% 0.19/0.47
% 0.19/0.47 thf(termmset_decl,type,
% 0.19/0.47 termmset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_lem0_lthm_decl,type,
% 0.19/0.47 pushprop_lem0_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasapnotvar_lthm_decl,type,
% 0.19/0.47 hoasapnotvar_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.19/0.47 hoasinduction_lem3v2_lthm: $o ).
% 0.19/0.47
% 0.19/0.47 thf(pushprop_p_and_p_prime_decl,type,
% 0.19/0.47 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(axvarid_decl,type,
% 0.19/0.47 axvarid: $o ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction_lthm_3_decl,type,
% 0.19/0.47 hoasinduction_lthm_3: $o ).
% 0.19/0.47
% 0.19/0.47 %----Types of the domains
% 0.19/0.47 thf(d_term_type,type,
% 0.19/0.47 d_term: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(d_subst_type,type,
% 0.19/0.47 d_subst: $tType ).
% 0.19/0.47
% 0.19/0.47 %----Types of the promotion functions
% 0.19/0.47 thf(d2term_decl,type,
% 0.19/0.47 d2term: d_term > term ).
% 0.19/0.47
% 0.19/0.47 thf(d2subst_decl,type,
% 0.19/0.47 d2subst: d_subst > subst ).
% 0.19/0.47
% 0.19/0.47 %----Types of the domain elements
% 0.19/0.47 thf(d_one_decl,type,
% 0.19/0.47 d_one: d_term ).
% 0.19/0.47
% 0.19/0.47 thf(d_id_decl,type,
% 0.19/0.47 d_id: d_subst ).
% 0.19/0.47
% 0.19/0.47 thf(alg444_1,axiom,
% 0.19/0.47 ( ! [T: term] :
% 0.19/0.47 ? [DT: d_term] :
% 0.19/0.47 ( T
% 0.19/0.47 = ( d2term @ DT ) )
% 0.19/0.47 & ! [DT: d_term] : ( DT = d_one )
% 0.19/0.47 & ! [DT1: d_term,DT2: d_term] :
% 0.19/0.47 ( ( ( d2term @ DT1 )
% 0.19/0.47 = ( d2term @ DT2 ) )
% 0.19/0.47 => ( DT1 = DT2 ) )
% 0.19/0.47 & ! [S: subst] :
% 0.19/0.47 ? [DS: d_subst] :
% 0.19/0.47 ( S
% 0.19/0.47 = ( d2subst @ DS ) )
% 0.19/0.47 & ! [DS: d_subst] : ( DS = d_id )
% 0.19/0.47 & ! [DS1: d_subst,DS2: d_subst] :
% 0.19/0.47 ( ( ( d2subst @ DS1 )
% 0.19/0.47 = ( d2subst @ DS2 ) )
% 0.19/0.47 => ( DS1 = DS2 ) )
% 0.19/0.47 & ( one
% 0.19/0.47 = ( d2term @ d_one ) )
% 0.19/0.47 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.19/0.47 = ( d2term @ d_one ) )
% 0.19/0.47 & ( ( lam @ ( d2term @ d_one ) )
% 0.19/0.47 = ( d2term @ d_one ) )
% 0.19/0.47 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.47 = ( d2term @ d_one ) )
% 0.19/0.47 & ( id
% 0.19/0.47 = ( d2subst @ d_id ) )
% 0.19/0.47 & ( sh
% 0.19/0.47 = ( d2subst @ d_id ) )
% 0.19/0.47 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.47 = ( d2subst @ d_id ) )
% 0.19/0.47 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.19/0.47 = ( d2subst @ d_id ) )
% 0.19/0.47 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.19/0.47 = ( d2term @ d_one ) )
% 0.19/0.47 & ( hoaslam
% 0.19/0.47 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.19/0.47 & ( hoasinduction_p_and_p_prime
% 0.19/0.47 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.19/0.47 ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) ) ) )
% 0.19/0.47 & ( pushprop_p_and_p_prime
% 0.19/0.47 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.19/0.47 ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.19/0.47 & ~ ( var @ ( d2term @ d_one ) )
% 0.19/0.47 & ( pushprop_lem1v2
% 0.19/0.47 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.19/0.47 | ( Q @ one ) ) )
% 0.19/0.47 & pushprop_lem1_gthm
% 0.19/0.47 & axmap
% 0.19/0.47 & pushprop_lem0_gthm
% 0.19/0.47 & ( shinj
% 0.19/0.47 <=> ! [A: term,B: term] :
% 0.19/0.47 ( ( ( sub @ A @ sh )
% 0.19/0.47 != ( sub @ B @ sh ) )
% 0.19/0.47 | ( A = B ) ) )
% 0.19/0.47 & hoasinduction_lem1v2
% 0.19/0.47 & hoasinduction_lem1v2_gthm
% 0.19/0.47 & ( induction2lem
% 0.19/0.47 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.47 ( ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( var @ B )
% 0.19/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.19/0.47 & ( hoasinduction_lem3v2_f
% 0.19/0.47 <=> ! [B: term] :
% 0.19/0.47 ~ ! [F: subst > term > term] :
% 0.19/0.47 ~ ! [A: term,M: subst] :
% 0.19/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.47 = ( F @ M @ A ) ) )
% 0.19/0.47 & axvarshift
% 0.19/0.47 & ( hoasapinj2
% 0.19/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.47 | ( C = D ) ) )
% 0.19/0.47 & hoasapnotvar_gthm
% 0.19/0.47 & ( hoasapinj1
% 0.19/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.47 | ( A = B ) ) )
% 0.19/0.47 & ~ ulamvar1
% 0.19/0.47 & ( induction2lem_lthm
% 0.19/0.47 <=> ( ! [A: term,M: subst] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.47 => ( ! [A: term,M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.47 => ( ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ M @ id ) )
% 0.19/0.47 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2140 ) )
% 0.19/0.47 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.47 ( ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( var @ B )
% 0.19/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.19/0.47 & hoasinduction_lem3v2_gthm
% 0.19/0.47 & apnotvar
% 0.19/0.47 & pushprop_lthm_orig
% 0.19/0.47 & ( hoasinduction_lem3v2_f_lthm
% 0.19/0.47 <=> ! [B: term] :
% 0.19/0.47 ~ ! [F: subst > term > term] :
% 0.19/0.47 ~ ! [A: term,M: subst] :
% 0.19/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.47 = ( F @ M @ A ) ) )
% 0.19/0.47 & ( hoasinduction_lthm
% 0.19/0.47 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2367 ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.19/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.47 | ( P @ id @ A @ id ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.19/0.47 & ( hoasinduction_no_psi_cond_lthm
% 0.19/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2367 ) )
% 0.19/0.47 => ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.19/0.47 ( ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.19/0.47 & ( hoaslaminj
% 0.19/0.47 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.19/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.19/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.19/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.19/0.47 & ( hoasinduction_lem3aaa
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.19/0.47 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.19/0.47 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.19/0.47 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.19/0.47 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.19/0.47 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.19/0.47 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.47 & induction2lem_gthm
% 0.19/0.47 & ( hoasinduction_lem3aa_lthm
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.47 & ( hoasinduction_lem3
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.19/0.47 & ( hoasinduction_lem2
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.19/0.47 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.19/0.47 & ( termmset_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) ) ) )
% 0.19/0.47 & hoasinduction_lem1
% 0.19/0.47 & hoaslamnotap_lthm
% 0.19/0.47 & ( pushprop_lem1v2_lthm
% 0.19/0.47 <=> ( ! [A: term,M: subst] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.47 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.19/0.47 | ( Q @ one ) ) ) )
% 0.19/0.47 & hoasapnotvar
% 0.19/0.47 & ( hoasinduction_lem0
% 0.19/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) ) )
% 0.19/0.47 & ( hoasinduction
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.47 | ( P @ id @ A @ id ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.19/0.47 & hoasinduction_gthm
% 0.19/0.47 & axapp
% 0.19/0.47 & hoaslamnotvar_lthm
% 0.19/0.47 & pushprop_lem3v2_lthm
% 0.19/0.47 & ( hoasinduction_lem3b_lthm
% 0.19/0.47 <=> ! [B: term] :
% 0.19/0.47 ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ( F @ sh @ one )
% 0.19/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.19/0.47 & ulamvarind
% 0.19/0.47 & ( induction
% 0.19/0.47 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2140 ) ) )
% 0.19/0.47 & ( hoasinduction_lem3a_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.19/0.47 & termmset_gthm
% 0.19/0.47 & ( hoasinduction_lem3aa
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.19/0.47 & pushprop_lem1v2_gthm
% 0.19/0.47 & hoaslamnotap_gthm
% 0.19/0.47 & hoaslamnotvar_gthm
% 0.19/0.47 & hoasinduction_lem3b_gthm
% 0.19/0.47 & pushprop_lem2v2
% 0.19/0.47 & hoasinduction_lem3a_gthm
% 0.19/0.47 & axclos
% 0.19/0.47 & axassoc
% 0.19/0.47 & ( hoasinduction_lem2v2
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ( Q @ Bound_variable_2820 )
% 0.19/0.47 | ~ ( Q @ Bound_variable_2822 )
% 0.19/0.47 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.19/0.47 & pushprop_lthm
% 0.19/0.47 & ( apinj2
% 0.19/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ A @ C )
% 0.19/0.47 != ( ap @ B @ D ) )
% 0.19/0.47 | ( C = D ) ) )
% 0.19/0.47 & ( apinj1
% 0.19/0.47 <=> ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ A @ C )
% 0.19/0.47 != ( ap @ B @ D ) )
% 0.19/0.47 | ( A = B ) ) )
% 0.19/0.47 & ( hoasapinj2_lthm
% 0.19/0.47 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ A @ C )
% 0.19/0.47 != ( ap @ B @ D ) )
% 0.19/0.47 | ( C = D ) )
% 0.19/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.47 | ( C = D ) ) ) )
% 0.19/0.47 & ( hoasinduction_lem3v2a
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.19/0.47 & ( hoasapinj1_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ A @ C )
% 0.19/0.47 != ( ap @ B @ D ) )
% 0.19/0.47 | ( A = B ) )
% 0.19/0.47 => ! [A: term,B: term,C: term,D: term] :
% 0.19/0.47 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.19/0.47 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.19/0.47 | ( A = B ) ) ) ) )
% 0.19/0.47 & ( hoaslaminj_lthm
% 0.19/0.47 <=> ( ! [A: term,M: subst] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.47 => ( ! [A: term,M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.47 => ( ! [A: term,B: term] :
% 0.19/0.47 ( ( ( lam @ A )
% 0.19/0.47 != ( lam @ B ) )
% 0.19/0.47 | ( A = B ) )
% 0.19/0.47 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.19/0.47 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.47 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.19/0.47 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.19/0.47 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.19/0.47 & ( axvarcons
% 0.19/0.47 <=> ! [A: term,M: subst] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.19/0.47 & ( axscons
% 0.19/0.47 <=> ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.19/0.47 & hoasinduction_lem2v2_gthm
% 0.19/0.47 & ( axidr
% 0.19/0.47 <=> ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ M @ id ) ) )
% 0.19/0.47 & ( pushprop_lem1
% 0.19/0.47 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.19/0.47 & ( laminj
% 0.19/0.47 <=> ! [A: term,B: term] :
% 0.19/0.47 ( ( ( lam @ A )
% 0.19/0.47 != ( lam @ B ) )
% 0.19/0.47 | ( A = B ) ) )
% 0.19/0.47 & ( hoasinduction_lem3_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.19/0.47 & ( pushprop_lem0
% 0.19/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.19/0.47 & pushprop_gthm
% 0.19/0.47 & axabs
% 0.19/0.47 & ( hoasinduction_lem3v2a_lthm
% 0.19/0.47 <=> ( ! [B: term] :
% 0.19/0.47 ~ ! [F: subst > term > term] :
% 0.19/0.47 ~ ! [A: term,M: subst] :
% 0.19/0.47 ( ( sub @ B @ ( push @ A @ M ) )
% 0.19/0.47 = ( F @ M @ A ) )
% 0.19/0.47 => ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.19/0.47 & hoasinduction_lem2_lthm
% 0.19/0.47 & hoasapinj2_gthm
% 0.19/0.47 & hoasinduction_lem1_lthm
% 0.19/0.47 & ~ lamnotap
% 0.19/0.47 & hoasapinj1_gthm
% 0.19/0.47 & hoaslamnotvar
% 0.19/0.47 & ( axidl
% 0.19/0.47 <=> ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ id @ M ) ) )
% 0.19/0.47 & hoaslaminj_gthm
% 0.19/0.47 & ( induction2_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.19/0.47 ( ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( var @ B )
% 0.19/0.47 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.19/0.47 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.19/0.47 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.19/0.47 & ( hoasinduction_lem0_lthm
% 0.19/0.47 <=> ! [P: subst > term > subst > $o] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) ) )
% 0.19/0.47 & ( substmonoid_lthm
% 0.19/0.47 <=> ( ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ id @ M ) )
% 0.19/0.47 => ( ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ M @ id ) )
% 0.19/0.47 => ( ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ id @ M ) )
% 0.19/0.47 & ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ M @ id ) ) ) ) ) )
% 0.19/0.47 & pushprop
% 0.19/0.47 & hoasinduction_lem3_gthm
% 0.19/0.47 & hoasinduction_lem2_gthm
% 0.19/0.47 & ( hoasinduction_lem3b
% 0.19/0.47 <=> ! [B: term] :
% 0.19/0.47 ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ( F @ sh @ one )
% 0.19/0.47 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.19/0.47 & ( substmonoid
% 0.19/0.47 <=> ( ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ id @ M ) )
% 0.19/0.47 & ! [M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ M @ id ) ) ) )
% 0.19/0.47 & lamnotvar
% 0.19/0.47 & ( hoasinduction_lem3a
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.19/0.47 & hoasinduction_lem1_gthm
% 0.19/0.47 & ( hoasinduction_no_psi_cond
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.19/0.47 ( ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.19/0.47 & induction2_gthm
% 0.19/0.47 & pushprop_lem2v2_lthm
% 0.19/0.47 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.19/0.47 & ( hoaslamnotap
% 0.19/0.47 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ( ( lam @ ( F @ sh @ one ) )
% 0.19/0.47 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.19/0.47 & substmonoid_gthm
% 0.19/0.47 & ulamvarsh
% 0.19/0.47 & ( induction2
% 0.19/0.47 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2367 ) ) )
% 0.19/0.47 & pushprop_lem3v2
% 0.19/0.47 & pushprop_lem2v2_gthm
% 0.19/0.47 & ( pushprop_lem1_lthm
% 0.19/0.47 <=> ( ! [A: term,M: subst] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.19/0.47 => ( ! [A: term,M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.19/0.47 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.19/0.47 & ( hoasinduction_lem3v2
% 0.19/0.47 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.19/0.47 & ( axshiftcons
% 0.19/0.47 <=> ! [A: term,M: subst] :
% 0.19/0.47 ( M
% 0.19/0.47 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.19/0.47 & ( termmset
% 0.19/0.47 <=> ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) ) )
% 0.19/0.47 & ( pushprop_lem0_lthm
% 0.19/0.47 <=> ! [P: term > $o,A: term,M: subst] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.19/0.47 & hoasapnotvar_lthm
% 0.19/0.47 & ( hoasinduction_lem3v2_lthm
% 0.19/0.47 <=> ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.19/0.47 & ( axvarid
% 0.19/0.47 <=> ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) ) )
% 0.19/0.47 & ( hoasinduction_lthm_3
% 0.19/0.47 <=> ( ! [P: subst > term > subst > $o] :
% 0.19/0.47 ~ ! [Q: term > $o] :
% 0.19/0.47 ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.19/0.47 ( ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ A )
% 0.19/0.47 | ( P @ A ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ A )
% 0.19/0.47 | ~ ( P @ B )
% 0.19/0.47 | ( P @ ( ap @ A @ B ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ! [B: term] :
% 0.19/0.47 ( ~ ( P @ B )
% 0.19/0.47 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( P @ ( lam @ A ) ) )
% 0.19/0.47 | ( P @ Bound_variable_2367 ) )
% 0.19/0.47 => ( ! [A: term] :
% 0.19/0.47 ( A
% 0.19/0.47 = ( sub @ A @ id ) )
% 0.19/0.47 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.19/0.47 ( ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ~ ! [X: term] :
% 0.19/0.47 ( ( Q @ X )
% 0.19/0.47 = ( P @ id @ X @ id ) )
% 0.19/0.47 | ~ ! [B: term] :
% 0.19/0.47 ( ~ ( Q @ B )
% 0.19/0.47 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.19/0.47 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.19/0.47 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( var @ ( sub @ A @ id ) )
% 0.19/0.47 | ( P @ id @ A @ id ) )
% 0.19/0.47 | ~ ! [A: term,B: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ~ ( P @ id @ B @ id )
% 0.19/0.47 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.19/0.47 | ~ ! [F: subst > term > term] :
% 0.19/0.47 ( ~ ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 | ~ ! [A: term] :
% 0.19/0.47 ( ~ ( P @ id @ A @ id )
% 0.19/0.47 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.19/0.47 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(hoasinduction,conjecture,
% 0.19/0.47 ( hoasinduction
% 0.19/0.47 = ( ! [P: subst > term > subst > $o] :
% 0.19/0.47 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.19/0.47 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.19/0.47 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.19/0.47 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.19/0.47 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.19/0.47 => ( ! [A: term] :
% 0.19/0.47 ( ( hoasvar @ id @ A @ id )
% 0.19/0.47 => ( P @ id @ A @ id ) )
% 0.19/0.47 => ( ! [A: term,B: term] :
% 0.19/0.47 ( ( P @ id @ A @ id )
% 0.19/0.47 => ( ( P @ id @ B @ id )
% 0.19/0.47 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.19/0.47 => ( ! [F: subst > term > term] :
% 0.19/0.47 ( ! [M: subst,A: term,N: subst] :
% 0.19/0.47 ( ( sub @ ( F @ M @ A ) @ N )
% 0.19/0.47 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.19/0.47 => ( ! [A: term] :
% 0.19/0.47 ( ( P @ id @ A @ id )
% 0.19/0.47 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.19/0.47 => ( P @ id
% 0.19/0.47 @ ( hoaslam @ id
% 0.19/0.47 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.19/0.47 @ id ) ) )
% 0.19/0.47 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 2.33/1.47 ---- Embedded in THF ---
% 2.33/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.33/1.47 %%% Generated on Tue May 05 09:12:26 EDT 2026
% 2.33/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.33/1.47 %%% Logic specification used:
% 2.33/1.47 %%% thf(spec, logic, $$dhol).
% 2.33/1.47
% 2.33/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CDduru1qPi/DTF2DTF30868.p
% See solution above
% 2.33/1.47 ------------------------
% 2.33/1.49 ---- Cleaned THF ---
% 2.33/1.50 thf(term_type,type,
% 2.33/1.50 term: $tType ).
% 2.33/1.50
% 2.33/1.50 thf(subst_type,type,
% 2.33/1.50 subst: $tType ).
% 2.33/1.50
% 2.33/1.50 thf(one_decl,type,
% 2.33/1.50 one: term ).
% 2.33/1.50
% 2.33/1.50 thf(ap_decl,type,
% 2.33/1.50 ap: term > term > term ).
% 2.33/1.50
% 2.33/1.50 thf(lam_decl,type,
% 2.33/1.50 lam: term > term ).
% 2.33/1.50
% 2.33/1.50 thf(sub_decl,type,
% 2.33/1.50 sub: term > subst > term ).
% 2.33/1.50
% 2.33/1.50 thf(id_decl,type,
% 2.33/1.50 id: subst ).
% 2.33/1.50
% 2.33/1.50 thf(sh_decl,type,
% 2.33/1.50 sh: subst ).
% 2.33/1.50
% 2.33/1.50 thf(push_decl,type,
% 2.33/1.50 push: term > subst > subst ).
% 2.33/1.50
% 2.33/1.50 thf(comp_decl,type,
% 2.33/1.50 comp: subst > subst > subst ).
% 2.33/1.50
% 2.33/1.50 thf(var_decl,type,
% 2.33/1.50 var: term > $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1v2_decl,type,
% 2.33/1.50 pushprop_lem1v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1_gthm_decl,type,
% 2.33/1.50 pushprop_lem1_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axmap_decl,type,
% 2.33/1.50 axmap: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem0_gthm_decl,type,
% 2.33/1.50 pushprop_lem0_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(shinj_decl,type,
% 2.33/1.50 shinj: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem1v2_decl,type,
% 2.33/1.50 hoasinduction_lem1v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem1v2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasap_decl,type,
% 2.33/1.50 hoasap: subst > term > subst > term > term ).
% 2.33/1.50
% 2.33/1.50 thf(induction2lem_decl,type,
% 2.33/1.50 induction2lem: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2_f_decl,type,
% 2.33/1.50 hoasinduction_lem3v2_f: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axvarshift_decl,type,
% 2.33/1.50 axvarshift: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj2_decl,type,
% 2.33/1.50 hoasapinj2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapnotvar_gthm_decl,type,
% 2.33/1.50 hoasapnotvar_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj1_decl,type,
% 2.33/1.50 hoasapinj1: $o ).
% 2.33/1.50
% 2.33/1.50 thf(ulamvar1_decl,type,
% 2.33/1.50 ulamvar1: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction2lem_lthm_decl,type,
% 2.33/1.50 induction2lem_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem3v2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(apnotvar_decl,type,
% 2.33/1.50 apnotvar: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lthm_orig_decl,type,
% 2.33/1.50 pushprop_lthm_orig: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3v2_f_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lthm_decl,type,
% 2.33/1.50 hoasinduction_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.33/1.50 hoasinduction_no_psi_cond_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslaminj_decl,type,
% 2.33/1.50 hoaslaminj: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3aaa_decl,type,
% 2.33/1.50 hoasinduction_lem3aaa: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction2lem_gthm_decl,type,
% 2.33/1.50 induction2lem_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3aa_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3_decl,type,
% 2.33/1.50 hoasinduction_lem3: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem2_decl,type,
% 2.33/1.50 hoasinduction_lem2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(termmset_lthm_decl,type,
% 2.33/1.50 termmset_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem1_decl,type,
% 2.33/1.50 hoasinduction_lem1: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotap_lthm_decl,type,
% 2.33/1.50 hoaslamnotap_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1v2_lthm_decl,type,
% 2.33/1.50 pushprop_lem1v2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapnotvar_decl,type,
% 2.33/1.50 hoasapnotvar: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem0_decl,type,
% 2.33/1.50 hoasinduction_lem0: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_decl,type,
% 2.33/1.50 hoasinduction: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_gthm_decl,type,
% 2.33/1.50 hoasinduction_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axapp_decl,type,
% 2.33/1.50 axapp: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotvar_lthm_decl,type,
% 2.33/1.50 hoaslamnotvar_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem3v2_lthm_decl,type,
% 2.33/1.50 pushprop_lem3v2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3b_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(ulamvarind_decl,type,
% 2.33/1.50 ulamvarind: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction_decl,type,
% 2.33/1.50 induction: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3a_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(termmset_gthm_decl,type,
% 2.33/1.50 termmset_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3aa_decl,type,
% 2.33/1.50 hoasinduction_lem3aa: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1v2_gthm_decl,type,
% 2.33/1.50 pushprop_lem1v2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotap_gthm_decl,type,
% 2.33/1.50 hoaslamnotap_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotvar_gthm_decl,type,
% 2.33/1.50 hoaslamnotvar_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem3b_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem2v2_decl,type,
% 2.33/1.50 pushprop_lem2v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem3a_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axclos_decl,type,
% 2.33/1.50 axclos: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axassoc_decl,type,
% 2.33/1.50 axassoc: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem2v2_decl,type,
% 2.33/1.50 hoasinduction_lem2v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lthm_decl,type,
% 2.33/1.50 pushprop_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(apinj2_decl,type,
% 2.33/1.50 apinj2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(apinj1_decl,type,
% 2.33/1.50 apinj1: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj2_lthm_decl,type,
% 2.33/1.50 hoasapinj2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2a_decl,type,
% 2.33/1.50 hoasinduction_lem3v2a: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj1_lthm_decl,type,
% 2.33/1.50 hoasapinj1_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslaminj_lthm_decl,type,
% 2.33/1.50 hoaslaminj_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axvarcons_decl,type,
% 2.33/1.50 axvarcons: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslam_decl,type,
% 2.33/1.50 hoaslam: subst > ( subst > term > term ) > term ).
% 2.33/1.50
% 2.33/1.50 thf(axscons_decl,type,
% 2.33/1.50 axscons: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem2v2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axidr_decl,type,
% 2.33/1.50 axidr: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1_decl,type,
% 2.33/1.50 pushprop_lem1: $o ).
% 2.33/1.50
% 2.33/1.50 thf(laminj_decl,type,
% 2.33/1.50 laminj: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem0_decl,type,
% 2.33/1.50 pushprop_lem0: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_gthm_decl,type,
% 2.33/1.50 pushprop_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axabs_decl,type,
% 2.33/1.50 axabs: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3v2a_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem2_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj2_gthm_decl,type,
% 2.33/1.50 hoasapinj2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.33/1.50 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem1_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem1_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(lamnotap_decl,type,
% 2.33/1.50 lamnotap: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapinj1_gthm_decl,type,
% 2.33/1.50 hoasapinj1_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotvar_decl,type,
% 2.33/1.50 hoaslamnotvar: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axidl_decl,type,
% 2.33/1.50 axidl: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslaminj_gthm_decl,type,
% 2.33/1.50 hoaslaminj_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction2_lthm_decl,type,
% 2.33/1.50 induction2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem0_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem0_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(substmonoid_lthm_decl,type,
% 2.33/1.50 substmonoid_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_decl,type,
% 2.33/1.50 pushprop: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem3_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem2_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3b_decl,type,
% 2.33/1.50 hoasinduction_lem3b: $o ).
% 2.33/1.50
% 2.33/1.50 thf(substmonoid_decl,type,
% 2.33/1.50 substmonoid: $o ).
% 2.33/1.50
% 2.33/1.50 thf(lamnotvar_decl,type,
% 2.33/1.50 lamnotvar: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3a_decl,type,
% 2.33/1.50 hoasinduction_lem3a: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem1_gthm_decl,type,
% 2.33/1.50 hoasinduction_lem1_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_no_psi_cond_decl,type,
% 2.33/1.50 hoasinduction_no_psi_cond: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction2_gthm_decl,type,
% 2.33/1.50 induction2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem2v2_lthm_decl,type,
% 2.33/1.50 pushprop_lem2v2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasvar_decl,type,
% 2.33/1.50 hoasvar: subst > term > subst > $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoaslamnotap_decl,type,
% 2.33/1.50 hoaslamnotap: $o ).
% 2.33/1.50
% 2.33/1.50 thf(substmonoid_gthm_decl,type,
% 2.33/1.50 substmonoid_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(ulamvarsh_decl,type,
% 2.33/1.50 ulamvarsh: $o ).
% 2.33/1.50
% 2.33/1.50 thf(induction2_decl,type,
% 2.33/1.50 induction2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem3v2_decl,type,
% 2.33/1.50 pushprop_lem3v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem2v2_gthm_decl,type,
% 2.33/1.50 pushprop_lem2v2_gthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem1_lthm_decl,type,
% 2.33/1.50 pushprop_lem1_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2_decl,type,
% 2.33/1.50 hoasinduction_lem3v2: $o ).
% 2.33/1.50
% 2.33/1.50 thf(axshiftcons_decl,type,
% 2.33/1.50 axshiftcons: $o ).
% 2.33/1.50
% 2.33/1.50 thf(termmset_decl,type,
% 2.33/1.50 termmset: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_lem0_lthm_decl,type,
% 2.33/1.50 pushprop_lem0_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasapnotvar_lthm_decl,type,
% 2.33/1.50 hoasapnotvar_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.33/1.50 hoasinduction_lem3v2_lthm: $o ).
% 2.33/1.50
% 2.33/1.50 thf(pushprop_p_and_p_prime_decl,type,
% 2.33/1.50 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.33/1.50
% 2.33/1.50 thf(axvarid_decl,type,
% 2.33/1.50 axvarid: $o ).
% 2.33/1.50
% 2.33/1.50 thf(hoasinduction_lthm_3_decl,type,
% 2.33/1.50 hoasinduction_lthm_3: $o ).
% 2.33/1.50
% 2.33/1.50 thf(d_term_type,type,
% 2.33/1.50 d_term: $tType ).
% 2.33/1.50
% 2.33/1.50 thf(d_subst_type,type,
% 2.33/1.50 d_subst: $tType ).
% 2.33/1.50
% 2.33/1.50 thf(d2term_decl,type,
% 2.33/1.50 d2term: d_term > term ).
% 2.33/1.50
% 2.33/1.50 thf(d2subst_decl,type,
% 2.33/1.50 d2subst: d_subst > subst ).
% 2.33/1.50
% 2.33/1.50 thf(d_one_decl,type,
% 2.33/1.50 d_one: d_term ).
% 2.33/1.50
% 2.33/1.50 thf(d_id_decl,type,
% 2.33/1.50 d_id: d_subst ).
% 2.33/1.50
% 2.33/1.50 thf(alg444_1,axiom,
% 2.33/1.50 ( ! [T: term] :
% 2.33/1.50 ? [DT: d_term] :
% 2.33/1.50 ( T
% 2.33/1.50 = ( d2term @ DT ) )
% 2.33/1.50 & ! [DT: d_term] : ( DT = d_one )
% 2.33/1.50 & ! [DT1: d_term,DT2: d_term] :
% 2.33/1.50 ( ( ( d2term @ DT1 )
% 2.33/1.50 = ( d2term @ DT2 ) )
% 2.33/1.50 => ( DT1 = DT2 ) )
% 2.33/1.50 & ! [S: subst] :
% 2.33/1.50 ? [DS: d_subst] :
% 2.33/1.50 ( S
% 2.33/1.50 = ( d2subst @ DS ) )
% 2.33/1.50 & ! [DS: d_subst] : ( DS = d_id )
% 2.33/1.50 & ! [DS1: d_subst,DS2: d_subst] :
% 2.33/1.50 ( ( ( d2subst @ DS1 )
% 2.33/1.50 = ( d2subst @ DS2 ) )
% 2.33/1.50 => ( DS1 = DS2 ) )
% 2.33/1.50 & ( one
% 2.33/1.50 = ( d2term @ d_one ) )
% 2.33/1.50 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.33/1.50 = ( d2term @ d_one ) )
% 2.33/1.50 & ( ( lam @ ( d2term @ d_one ) )
% 2.33/1.50 = ( d2term @ d_one ) )
% 2.33/1.50 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.33/1.50 = ( d2term @ d_one ) )
% 2.33/1.50 & ( id
% 2.33/1.50 = ( d2subst @ d_id ) )
% 2.33/1.50 & ( sh
% 2.33/1.50 = ( d2subst @ d_id ) )
% 2.33/1.50 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.33/1.50 = ( d2subst @ d_id ) )
% 2.33/1.50 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.33/1.50 = ( d2subst @ d_id ) )
% 2.33/1.50 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.33/1.50 = ( d2term @ d_one ) )
% 2.33/1.50 & ( hoaslam
% 2.33/1.50 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.33/1.50 & ( hoasinduction_p_and_p_prime
% 2.33/1.50 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.33/1.50 ! [X: term] :
% 2.33/1.50 ( ( Q @ X )
% 2.33/1.50 = ( P @ id @ X @ id ) ) ) )
% 2.33/1.50 & ( pushprop_p_and_p_prime
% 2.33/1.50 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.33/1.50 ! [X: term] :
% 2.33/1.50 ( ( Q @ X )
% 2.33/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.33/1.50 & ~ ( var @ ( d2term @ d_one ) )
% 2.33/1.50 & ( pushprop_lem1v2
% 2.33/1.50 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ! [X: term] :
% 2.33/1.50 ( ( Q @ X )
% 2.33/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.33/1.50 | ( Q @ one ) ) )
% 2.33/1.50 & pushprop_lem1_gthm
% 2.33/1.50 & axmap
% 2.33/1.50 & pushprop_lem0_gthm
% 2.33/1.50 & ( shinj
% 2.33/1.50 <=> ! [A: term,B: term] :
% 2.33/1.50 ( ( ( sub @ A @ sh )
% 2.33/1.50 != ( sub @ B @ sh ) )
% 2.33/1.50 | ( A = B ) ) )
% 2.33/1.50 & hoasinduction_lem1v2
% 2.33/1.50 & hoasinduction_lem1v2_gthm
% 2.33/1.50 & ( induction2lem
% 2.33/1.50 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.33/1.50 ( ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ( P @ B )
% 2.33/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ B )
% 2.33/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.33/1.50 | ( P @ ( lam @ A ) ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( var @ B )
% 2.33/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.33/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.33/1.50 & ( hoasinduction_lem3v2_f
% 2.33/1.50 <=> ! [B: term] :
% 2.33/1.50 ~ ! [F: subst > term > term] :
% 2.33/1.50 ~ ! [A: term,M: subst] :
% 2.33/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.33/1.50 = ( F @ M @ A ) ) )
% 2.33/1.50 & axvarshift
% 2.33/1.50 & ( hoasapinj2
% 2.33/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.33/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.33/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.33/1.50 | ( C = D ) ) )
% 2.33/1.50 & hoasapnotvar_gthm
% 2.33/1.50 & ( hoasapinj1
% 2.33/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.33/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.33/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.33/1.50 | ( A = B ) ) )
% 2.33/1.50 & ~ ulamvar1
% 2.33/1.50 & ( induction2lem_lthm
% 2.33/1.50 <=> ( ! [A: term,M: subst] :
% 2.33/1.50 ( A
% 2.33/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.33/1.50 => ( ! [A: term,M: subst] :
% 2.33/1.50 ( M
% 2.33/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.33/1.50 => ( ! [M: subst] :
% 2.33/1.50 ( M
% 2.33/1.50 = ( comp @ M @ id ) )
% 2.33/1.50 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.33/1.50 ( ~ ! [A: term] :
% 2.33/1.50 ( ~ ( var @ A )
% 2.33/1.50 | ( P @ A ) )
% 2.33/1.50 | ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ( P @ B )
% 2.33/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ( P @ ( lam @ A ) ) )
% 2.33/1.50 | ( P @ Bound_variable_2140 ) )
% 2.33/1.50 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.33/1.50 ( ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ( P @ B )
% 2.33/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ B )
% 2.33/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.33/1.50 | ( P @ ( lam @ A ) ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( var @ B )
% 2.33/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.33/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.33/1.50 & hoasinduction_lem3v2_gthm
% 2.33/1.50 & apnotvar
% 2.33/1.50 & pushprop_lthm_orig
% 2.33/1.50 & ( hoasinduction_lem3v2_f_lthm
% 2.33/1.50 <=> ! [B: term] :
% 2.33/1.50 ~ ! [F: subst > term > term] :
% 2.33/1.50 ~ ! [A: term,M: subst] :
% 2.33/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.33/1.50 = ( F @ M @ A ) ) )
% 2.33/1.50 & ( hoasinduction_lthm
% 2.33/1.50 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.33/1.50 ( ~ ! [A: term] :
% 2.33/1.50 ( ~ ( var @ A )
% 2.33/1.50 | ( P @ A ) )
% 2.33/1.50 | ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ( P @ B )
% 2.33/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ B )
% 2.33/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.33/1.50 | ( P @ ( lam @ A ) ) )
% 2.33/1.50 | ( P @ Bound_variable_2367 ) )
% 2.33/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.33/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.33/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.33/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.33/1.50 | ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.33/1.50 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.33/1.50 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.33/1.50 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.33/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.33/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.33/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.33/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.33/1.50 | ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.33/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.33/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.33/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.33/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.33/1.50 | ( P @ id @ A @ id ) )
% 2.33/1.50 | ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.33/1.50 | ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.33/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.33/1.50 & ( hoasinduction_no_psi_cond_lthm
% 2.33/1.50 <=> ( ! [P: subst > term > subst > $o] :
% 2.33/1.50 ~ ! [Q: term > $o] :
% 2.33/1.50 ~ ! [X: term] :
% 2.33/1.50 ( ( Q @ X )
% 2.33/1.50 = ( P @ id @ X @ id ) )
% 2.33/1.50 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.33/1.50 ( ~ ! [A: term] :
% 2.33/1.50 ( ~ ( var @ A )
% 2.33/1.50 | ( P @ A ) )
% 2.33/1.50 | ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ A )
% 2.33/1.50 | ~ ( P @ B )
% 2.33/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ B )
% 2.33/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.33/1.50 | ( P @ ( lam @ A ) ) )
% 2.33/1.50 | ( P @ Bound_variable_2367 ) )
% 2.33/1.50 => ( ! [A: term] :
% 2.33/1.50 ( A
% 2.33/1.50 = ( sub @ A @ id ) )
% 2.33/1.50 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.33/1.50 ( ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.33/1.50 | ~ ! [X: term] :
% 2.33/1.50 ( ( Q @ X )
% 2.33/1.50 = ( P @ id @ X @ id ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( Q @ B )
% 2.33/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.33/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.33/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.33/1.50 ( ~ ! [A: term,B: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.33/1.50 | ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.33/1.50 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.33/1.50 & ( hoaslaminj
% 2.33/1.50 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.33/1.50 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.33/1.50 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.33/1.50 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.33/1.50 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.33/1.50 & ( hoasinduction_lem3aaa
% 2.33/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.33/1.50 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.33/1.50 ( ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.33/1.50 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.33/1.50 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.33/1.50 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.33/1.50 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.33/1.50 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.33/1.50 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.33/1.50 & induction2lem_gthm
% 2.33/1.50 & ( hoasinduction_lem3aa_lthm
% 2.33/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.33/1.50 ( ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.33/1.50 | ~ ! [B: term] :
% 2.33/1.50 ( ~ ( P @ id @ B @ id )
% 2.33/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.33/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.33/1.50 & ( hoasinduction_lem3
% 2.33/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.33/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.33/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.33/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.33/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.33/1.50 | ~ ! [F: subst > term > term] :
% 2.33/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.33/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.33/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.33/1.50 | ~ ! [A: term] :
% 2.33/1.50 ( ~ ( P @ id @ A @ id )
% 2.33/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.33/1.50 | ( 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,conjecture,
% 2.53/1.50 ( hoasinduction
% 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 => ( ! [A: term] :
% 2.53/1.50 ( ( hoasvar @ id @ 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 @ ( hoasap @ id @ 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
% 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] : ( P @ id @ A @ id ) ) ) ) ) ) ) ) ).
% 2.53/1.50 ------------------------
% 2.53/1.52 % (31220)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_30868 for (2999ds/27Mi)
% 2.53/1.52 % (31218)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/183Mi)
% 2.53/1.52 % (31224)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/18Mi)
% 2.53/1.53 % (31224)Instruction limit reached!
% 2.53/1.53 % (31224)------------------------------
% 2.53/1.53 % (31224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (31224)Termination reason: Unknown
% 2.53/1.53 % (31224)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (31224)Memory used [KB]: 2046
% 2.53/1.53 % (31224)Time elapsed: 0.008 s
% 2.53/1.53 % (31224)Instructions burned: 20 (million)
% 2.53/1.53 % (31224)------------------------------
% 2.53/1.53 % (31224)------------------------------
% 2.53/1.53 % (31219)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_30868 for (2999ds/4Mi)
% 2.53/1.53 % (31221)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/2Mi)
% 2.53/1.53 % (31222)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_30868 for (2999ds/2Mi)
% 2.53/1.53 % (31223)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_30868 for (2999ds/275Mi)
% 2.53/1.53 % (31220)Instruction limit reached!
% 2.53/1.53 % (31220)------------------------------
% 2.53/1.53 % (31220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (31220)Termination reason: Unknown
% 2.53/1.53 % (31220)Termination phase: Property scanning
% 2.53/1.53
% 2.53/1.53 % (31220)Memory used [KB]: 2174
% 2.53/1.53 % (31220)Time elapsed: 0.010 s
% 2.53/1.53 % (31220)Instructions burned: 27 (million)
% 2.53/1.53 % (31220)------------------------------
% 2.53/1.53 % (31220)------------------------------
% 2.53/1.53 % (31221)Instruction limit reached!
% 2.53/1.53 % (31221)------------------------------
% 2.53/1.53 % (31221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (31221)Termination reason: Unknown
% 2.53/1.53 % (31221)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (31221)Memory used [KB]: 1279
% 2.53/1.53 % (31221)Time elapsed: 0.004 s
% 2.53/1.53 % (31221)Instructions burned: 3 (million)
% 2.53/1.53 % (31221)------------------------------
% 2.53/1.53 % (31221)------------------------------
% 2.53/1.53 % (31222)Instruction limit reached!
% 2.53/1.53 % (31222)------------------------------
% 2.53/1.53 % (31222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (31222)Termination reason: Unknown
% 2.53/1.53 % (31222)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (31222)Memory used [KB]: 1279
% 2.53/1.53 % (31222)Time elapsed: 0.004 s
% 2.53/1.53 % (31222)Instructions burned: 3 (million)
% 2.53/1.53 % (31222)------------------------------
% 2.53/1.53 % (31222)------------------------------
% 2.53/1.53 % (31219)Instruction limit reached!
% 2.53/1.53 % (31219)------------------------------
% 2.53/1.53 % (31219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (31219)Termination reason: Unknown
% 2.53/1.53 % (31219)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (31219)Memory used [KB]: 1279
% 2.53/1.53 % (31219)Time elapsed: 0.005 s
% 2.53/1.53 % (31219)Instructions burned: 5 (million)
% 2.53/1.53 % (31219)------------------------------
% 2.53/1.53 % (31219)------------------------------
% 2.53/1.54 % (31226)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_30868 for (2999ds/37Mi)
% 2.53/1.54 % (31225)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/3Mi)
% 2.53/1.54 % (31225)Instruction limit reached!
% 2.53/1.54 % (31225)------------------------------
% 2.53/1.54 % (31225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (31225)Termination reason: Unknown
% 2.53/1.54 % (31225)Termination phase: shuffling
% 2.53/1.54
% 2.53/1.54 % (31225)Memory used [KB]: 1279
% 2.53/1.54 % (31225)Time elapsed: 0.002 s
% 2.53/1.54 % (31225)Instructions burned: 4 (million)
% 2.53/1.54 % (31225)------------------------------
% 2.53/1.54 % (31225)------------------------------
% 2.53/1.55 % (31227)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_30868 for (2999ds/15Mi)
% 2.53/1.55 % (31228)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_30868 for (2999ds/3Mi)
% 2.53/1.55 % (31226)Instruction limit reached!
% 2.53/1.55 % (31226)------------------------------
% 2.53/1.55 % (31226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (31226)Termination reason: Unknown
% 2.53/1.55 % (31226)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.55 % (31226)Memory used [KB]: 1918
% 2.53/1.55 % (31226)Time elapsed: 0.011 s
% 2.53/1.55 % (31226)Instructions burned: 38 (million)
% 2.53/1.55 % (31226)------------------------------
% 2.53/1.55 % (31226)------------------------------
% 2.53/1.55 % (31229)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_30868 for (2999ds/1041Mi)
% 2.53/1.55 % (31228)Instruction limit reached!
% 2.53/1.55 % (31228)------------------------------
% 2.53/1.55 % (31228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (31228)Termination reason: Unknown
% 2.53/1.55 % (31228)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.55 % (31228)Memory used [KB]: 1279
% 2.53/1.55 % (31228)Time elapsed: 0.004 s
% 2.53/1.55 % (31228)Instructions burned: 4 (million)
% 2.53/1.55 % (31228)------------------------------
% 2.53/1.55 % (31228)------------------------------
% 2.53/1.55 % (31230)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/7Mi)
% 2.53/1.55 % (31230)Instruction limit reached!
% 2.53/1.55 % (31230)------------------------------
% 2.53/1.55 % (31230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (31230)Termination reason: Unknown
% 2.53/1.55 % (31230)Termination phase: shuffling
% 2.53/1.55
% 2.53/1.56 % (31230)Memory used [KB]: 1407
% 2.53/1.56 % (31230)Time elapsed: 0.004 s
% 2.53/1.56 % (31230)Instructions burned: 7 (million)
% 2.53/1.56 % (31230)------------------------------
% 2.53/1.56 % (31230)------------------------------
% 2.53/1.56 % (31223)Refutation not found, incomplete strategy
% 2.53/1.56 % (31223)------------------------------
% 2.53/1.56 % (31223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (31223)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.56
% 2.53/1.56
% 2.53/1.56 % (31223)Memory used [KB]: 6780
% 2.53/1.56 % (31223)Time elapsed: 0.028 s
% 2.53/1.56 % (31223)Instructions burned: 45 (million)
% 2.53/1.56 % (31223)------------------------------
% 2.53/1.56 % (31223)------------------------------
% 2.53/1.56 % (31227)Instruction limit reached!
% 2.53/1.56 % (31227)------------------------------
% 2.53/1.56 % (31227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (31227)Termination reason: Unknown
% 2.53/1.56 % (31227)Termination phase: shuffling
% 2.53/1.56
% 2.53/1.56 % (31227)Memory used [KB]: 1918
% 2.53/1.56 % (31227)Time elapsed: 0.011 s
% 2.53/1.56 % (31227)Instructions burned: 16 (million)
% 2.53/1.56 % (31227)------------------------------
% 2.53/1.56 % (31227)------------------------------
% 2.53/1.56 % (31231)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/16Mi)
% 2.53/1.57 % (31233)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_30868 for (2999ds/3Mi)
% 2.53/1.57 % (31231)Instruction limit reached!
% 2.53/1.57 % (31231)------------------------------
% 2.53/1.57 % (31231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (31231)Termination reason: Unknown
% 2.53/1.57 % (31231)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (31231)Memory used [KB]: 1791
% 2.53/1.57 % (31231)Time elapsed: 0.006 s
% 2.53/1.57 % (31231)Instructions burned: 16 (million)
% 2.53/1.57 % (31231)------------------------------
% 2.53/1.57 % (31231)------------------------------
% 2.53/1.57 % (31233)Instruction limit reached!
% 2.53/1.57 % (31233)------------------------------
% 2.53/1.57 % (31233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (31233)Termination reason: Unknown
% 2.53/1.57 % (31233)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (31233)Memory used [KB]: 1279
% 2.53/1.57 % (31233)Time elapsed: 0.002 s
% 2.53/1.57 % (31233)Instructions burned: 4 (million)
% 2.53/1.57 % (31233)------------------------------
% 2.53/1.57 % (31233)------------------------------
% 2.53/1.57 % (31232)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_30868 for (2999ds/3Mi)
% 2.53/1.57 % (31232)Instruction limit reached!
% 2.53/1.57 % (31232)------------------------------
% 2.53/1.57 % (31232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (31232)Termination reason: Unknown
% 2.53/1.57 % (31232)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (31232)Memory used [KB]: 1279
% 2.53/1.57 % (31232)Time elapsed: 0.004 s
% 2.53/1.57 % (31232)Instructions burned: 4 (million)
% 2.53/1.57 % (31232)------------------------------
% 2.53/1.57 % (31232)------------------------------
% 2.53/1.57 % (31218)Instruction limit reached!
% 2.53/1.57 % (31218)------------------------------
% 2.53/1.57 % (31218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (31218)Termination reason: Unknown
% 2.53/1.57 % (31218)Termination phase: Property scanning
% 2.53/1.57
% 2.53/1.57 % (31218)Memory used [KB]: 4349
% 2.53/1.57 % (31218)Time elapsed: 0.052 s
% 2.53/1.57 % (31218)Instructions burned: 186 (million)
% 2.53/1.57 % (31218)------------------------------
% 2.53/1.57 % (31218)------------------------------
% 2.53/1.58 % (31236)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/4Mi)
% 2.53/1.58 % (31234)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/7Mi)
% 2.53/1.58 % (31237)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/18Mi)
% 2.53/1.58 % (31236)Instruction limit reached!
% 2.53/1.58 % (31236)------------------------------
% 2.53/1.58 % (31236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (31236)Termination reason: Unknown
% 2.53/1.58 % (31236)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (31236)Memory used [KB]: 1407
% 2.53/1.58 % (31236)Time elapsed: 0.003 s
% 2.53/1.58 % (31236)Instructions burned: 7 (million)
% 2.53/1.58 % (31236)------------------------------
% 2.53/1.58 % (31236)------------------------------
% 2.53/1.58 % (31235)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/3Mi)
% 2.53/1.58 % (31235)Instruction limit reached!
% 2.53/1.58 % (31235)------------------------------
% 2.53/1.58 % (31235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (31235)Termination reason: Unknown
% 2.53/1.58 % (31235)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (31235)Memory used [KB]: 1279
% 2.53/1.58 % (31235)Time elapsed: 0.004 s
% 2.53/1.58 % (31235)Instructions burned: 4 (million)
% 2.53/1.58 % (31235)------------------------------
% 2.53/1.58 % (31235)------------------------------
% 2.53/1.58 % (31234)Instruction limit reached!
% 2.53/1.58 % (31234)------------------------------
% 2.53/1.58 % (31234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (31234)Termination reason: Unknown
% 2.53/1.58 % (31234)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (31234)Memory used [KB]: 1407
% 2.53/1.58 % (31234)Time elapsed: 0.006 s
% 2.53/1.58 % (31234)Instructions burned: 7 (million)
% 2.53/1.58 % (31234)------------------------------
% 2.53/1.58 % (31234)------------------------------
% 2.53/1.58 % (31237)Instruction limit reached!
% 2.53/1.58 % (31237)------------------------------
% 2.53/1.58 % (31237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (31237)Termination reason: Unknown
% 2.53/1.58 % (31237)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (31237)Memory used [KB]: 2046
% 2.53/1.58 % (31237)Time elapsed: 0.008 s
% 2.53/1.58 % (31237)Instructions burned: 19 (million)
% 2.53/1.58 % (31237)------------------------------
% 2.53/1.58 % (31237)------------------------------
% 2.53/1.58 % (31239)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/6Mi)
% 2.53/1.59 % (31239)Instruction limit reached!
% 2.53/1.59 % (31239)------------------------------
% 2.53/1.59 % (31239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (31239)Termination reason: Unknown
% 2.53/1.59 % (31239)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (31239)Memory used [KB]: 1407
% 2.53/1.59 % (31239)Time elapsed: 0.003 s
% 2.53/1.59 % (31239)Instructions burned: 7 (million)
% 2.53/1.59 % (31239)------------------------------
% 2.53/1.59 % (31239)------------------------------
% 2.53/1.59 % (31240)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_30868 for (2999ds/902Mi)
% 2.53/1.59 % (31238)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/710Mi)
% 2.53/1.59 % (31243)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_30868 for (2999ds/6Mi)
% 2.53/1.60 % (31243)Instruction limit reached!
% 2.53/1.60 % (31243)------------------------------
% 2.53/1.60 % (31243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.60 % (31243)Termination reason: Unknown
% 2.53/1.60 % (31243)Termination phase: shuffling
% 2.53/1.60
% 2.53/1.60 % (31243)Memory used [KB]: 1407
% 2.53/1.60 % (31243)Time elapsed: 0.004 s
% 2.53/1.60 % (31243)Instructions burned: 7 (million)
% 2.53/1.60 % (31243)------------------------------
% 2.53/1.60 % (31243)------------------------------
% 2.53/1.60 % (31244)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/377Mi)
% 2.53/1.60 % (31241)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_30868 for (2999ds/21Mi)
% 2.53/1.60 % (31242)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/5Mi)
% 2.53/1.60 % (31242)Instruction limit reached!
% 2.53/1.60 % (31242)------------------------------
% 2.53/1.60 % (31242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.60 % (31242)Termination reason: Unknown
% 2.53/1.60 % (31242)Termination phase: shuffling
% 2.53/1.60
% 2.53/1.60 % (31242)Memory used [KB]: 1279
% 2.53/1.60 % (31242)Time elapsed: 0.005 s
% 2.53/1.60 % (31242)Instructions burned: 5 (million)
% 2.53/1.60 % (31242)------------------------------
% 2.53/1.60 % (31242)------------------------------
% 2.53/1.61 % (31245)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_30868 for (2999ds/779Mi)
% 2.53/1.61 % (31241)Instruction limit reached!
% 2.53/1.61 % (31241)------------------------------
% 2.53/1.61 % (31241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (31241)Termination reason: Unknown
% 2.53/1.61 % (31241)Termination phase: shuffling
% 2.53/1.61
% 2.53/1.61 % (31241)Memory used [KB]: 2174
% 2.53/1.61 % (31241)Time elapsed: 0.015 s
% 2.53/1.61 % (31241)Instructions burned: 22 (million)
% 2.53/1.61 % (31241)------------------------------
% 2.53/1.61 % (31241)------------------------------
% 2.53/1.62 % (31246)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_30868 for (2999ds/19Mi)
% 2.53/1.63 % (31247)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30868 for (2999ds/879Mi)
% 2.53/1.63 % (31246)Instruction limit reached!
% 2.53/1.63 % (31246)------------------------------
% 2.53/1.63 % (31246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.63 % (31246)Termination reason: Unknown
% 2.53/1.63 % (31246)Termination phase: shuffling
% 2.53/1.63
% 2.53/1.63 % (31246)Memory used [KB]: 1663
% 2.53/1.63 % (31246)Time elapsed: 0.012 s
% 2.53/1.63 % (31246)Instructions burned: 20 (million)
% 2.53/1.63 % (31246)------------------------------
% 2.53/1.63 % (31246)------------------------------
% 2.53/1.65 % (31248)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30868 for (2998ds/17Mi)
% 2.53/1.65 % (31240)Refutation not found, incomplete strategy
% 2.53/1.65 % (31240)------------------------------
% 2.53/1.65 % (31240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.65 % (31240)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.65
% 2.53/1.65
% 2.53/1.65 % (31240)Memory used [KB]: 9466
% 2.53/1.65 % (31240)Time elapsed: 0.061 s
% 2.53/1.65 % (31240)Instructions burned: 212 (million)
% 2.53/1.65 % (31240)------------------------------
% 2.53/1.65 % (31240)------------------------------
% 2.53/1.65 % (31248)Instruction limit reached!
% 2.53/1.65 % (31248)------------------------------
% 2.53/1.65 % (31248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.65 % (31248)Termination reason: Unknown
% 2.53/1.65 % (31248)Termination phase: shuffling
% 2.53/1.65
% 2.53/1.65 % (31248)Memory used [KB]: 1918
% 2.53/1.65 % (31248)Time elapsed: 0.011 s
% 2.53/1.65 % (31248)Instructions burned: 17 (million)
% 2.53/1.65 % (31248)------------------------------
% 2.53/1.65 % (31248)------------------------------
% 2.53/1.66 % (31249)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30868 for (2998ds/3Mi)
% 2.53/1.66 % (31249)Instruction limit reached!
% 2.53/1.66 % (31249)------------------------------
% 2.53/1.66 % (31249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.66 % (31249)Termination reason: Unknown
% 2.53/1.66 % (31249)Termination phase: shuffling
% 2.53/1.66
% 2.53/1.66 % (31249)Memory used [KB]: 1279
% 2.53/1.66 % (31249)Time elapsed: 0.002 s
% 2.53/1.66 % (31249)Instructions burned: 3 (million)
% 2.53/1.66 % (31249)------------------------------
% 2.53/1.66 % (31249)------------------------------
% 2.53/1.67 % (31250)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30868 for (2998ds/30Mi)
% 2.53/1.67 % (31251)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30868 for (2998ds/127Mi)
% 2.53/1.68 % (31250)Instruction limit reached!
% 2.53/1.68 % (31250)------------------------------
% 2.53/1.68 % (31250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.68 % (31250)Termination reason: Unknown
% 2.53/1.68 % (31250)Termination phase: Property scanning
% 2.53/1.68
% 2.53/1.68 % (31250)Memory used [KB]: 2174
% 2.53/1.68 % (31250)Time elapsed: 0.011 s
% 2.53/1.68 % (31250)Instructions burned: 30 (million)
% 2.53/1.68 % (31250)------------------------------
% 2.53/1.68 % (31250)------------------------------
% 2.53/1.69 % (31252)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30868 for (2998ds/100Mi)
% 2.53/1.70 % (31244)Instruction limit reached!
% 2.53/1.70 % (31244)------------------------------
% 2.53/1.70 % (31244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.70 % (31244)Termination reason: Unknown
% 2.53/1.70 % (31244)Termination phase: Saturation
% 2.53/1.70
% 2.53/1.70 % (31244)Memory used [KB]: 10234
% 2.53/1.70 % (31244)Time elapsed: 0.108 s
% 2.53/1.70 % (31244)Instructions burned: 379 (million)
% 2.53/1.70 % (31244)------------------------------
% 2.53/1.70 % (31244)------------------------------
% 2.53/1.70 % (31251)Instruction limit reached!
% 2.53/1.70 % (31251)------------------------------
% 2.53/1.70 % (31251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.70 % (31251)Termination reason: Unknown
% 2.53/1.70 % (31251)Termination phase: Property scanning
% 2.53/1.70
% 2.53/1.70 % (31251)Memory used [KB]: 4221
% 2.53/1.70 % (31251)Time elapsed: 0.037 s
% 2.53/1.70 % (31251)Instructions burned: 128 (million)
% 2.53/1.70 % (31251)------------------------------
% 2.53/1.70 % (31251)------------------------------
% 2.53/1.71 % (31253)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_30868 for (2997ds/3Mi)
% 2.53/1.71 % (31254)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_30868 for (2997ds/20Mi)
% 2.53/1.71 % (31253)Instruction limit reached!
% 2.53/1.71 % (31253)------------------------------
% 2.53/1.71 % (31253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.71 % (31253)Termination reason: Unknown
% 2.53/1.71 % (31253)Termination phase: shuffling
% 2.53/1.71
% 2.53/1.71 % (31253)Memory used [KB]: 1151
% 2.53/1.71 % (31253)Time elapsed: 0.002 s
% 2.53/1.71 % (31253)Instructions burned: 3 (million)
% 2.53/1.71 % (31253)------------------------------
% 2.53/1.71 % (31253)------------------------------
% 2.53/1.72 % (31252)Instruction limit reached!
% 2.53/1.72 % (31252)------------------------------
% 2.53/1.72 % (31252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.72 % (31252)Termination reason: Unknown
% 2.53/1.72 % (31252)Termination phase: Saturation
% 2.53/1.72
% 2.53/1.72 % (31252)Memory used [KB]: 6524
% 2.53/1.72 % (31252)Time elapsed: 0.030 s
% 2.53/1.72 % (31252)Instructions burned: 103 (million)
% 2.53/1.72 % (31252)------------------------------
% 2.53/1.72 % (31252)------------------------------
% 2.53/1.72 % (31254)Instruction limit reached!
% 2.53/1.72 % (31254)------------------------------
% 2.53/1.72 % (31254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.72 % (31254)Termination reason: Unknown
% 2.53/1.72 % (31254)Termination phase: shuffling
% 2.53/1.72
% 2.53/1.72 % (31254)Memory used [KB]: 2174
% 2.53/1.72 % (31254)Time elapsed: 0.008 s
% 2.53/1.72 % (31254)Instructions burned: 22 (million)
% 2.53/1.72 % (31254)------------------------------
% 2.53/1.72 % (31254)------------------------------
% 2.53/1.72 % (31255)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_30868 for (2997ds/86Mi)
% 2.53/1.73 % (31256)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_30868 for (2997ds/107Mi)
% 2.53/1.73 % (31257)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_30868 for (2997ds/39Mi)
% 2.53/1.74 % (31257)Instruction limit reached!
% 2.53/1.74 % (31257)------------------------------
% 2.53/1.74 % (31257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.74 % (31257)Termination reason: Unknown
% 2.53/1.74 % (31257)Termination phase: Property scanning
% 2.53/1.74
% 2.53/1.74 % (31257)Memory used [KB]: 1918
% 2.53/1.74 % (31257)Time elapsed: 0.012 s
% 2.53/1.74 % (31257)Instructions burned: 39 (million)
% 2.53/1.74 % (31257)------------------------------
% 2.53/1.74 % (31257)------------------------------
% 2.53/1.75 % (31255)Instruction limit reached!
% 2.53/1.75 % (31255)------------------------------
% 2.53/1.75 % (31255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.75 % (31255)Termination reason: Unknown
% 2.53/1.75 % (31255)Termination phase: Preprocessing 3
% 2.53/1.75
% 2.53/1.75 % (31255)Memory used [KB]: 4093
% 2.53/1.75 % (31255)Time elapsed: 0.027 s
% 2.53/1.75 % (31255)Instructions burned: 88 (million)
% 2.53/1.75 % (31255)------------------------------
% 2.53/1.75 % (31255)------------------------------
% 2.53/1.75 % (31258)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_30868 for (2997ds/448Mi)
% 2.53/1.76 % (31259)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_30868 for (2997ds/46Mi)
% 2.53/1.76 % (31256)Instruction limit reached!
% 2.53/1.76 % (31256)------------------------------
% 2.53/1.76 % (31256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.76 % (31256)Termination reason: Unknown
% 2.53/1.76 % (31256)Termination phase: Property scanning
% 2.53/1.76
% 2.53/1.76 % (31256)Memory used [KB]: 4349
% 2.53/1.76 % (31256)Time elapsed: 0.035 s
% 2.53/1.76 % (31256)Instructions burned: 108 (million)
% 2.53/1.76 % (31256)------------------------------
% 2.53/1.76 % (31256)------------------------------
% 2.53/1.77 % (31260)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_30868 for (2997ds/98Mi)
% 2.53/1.77 % (31259)Instruction limit reached!
% 2.53/1.77 % (31259)------------------------------
% 2.53/1.77 % (31259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.77 % (31259)Termination reason: Unknown
% 2.53/1.77 % (31259)Termination phase: Preprocessing 1
% 2.53/1.77
% 2.53/1.77 % (31259)Memory used [KB]: 2430
% 2.53/1.77 % (31259)Time elapsed: 0.015 s
% 2.53/1.77 % (31259)Instructions burned: 48 (million)
% 2.53/1.77 % (31259)------------------------------
% 2.53/1.77 % (31259)------------------------------
% 2.53/1.78 % (31261)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_30868 for (2997ds/507Mi)
% 2.53/1.80 % (31260)Instruction limit reached!
% 2.53/1.80 % (31260)------------------------------
% 2.53/1.80 % (31260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.80 % (31260)Termination reason: Unknown
% 2.53/1.80 % (31260)Termination phase: Saturation
% 2.53/1.80
% 2.53/1.80 % (31260)Memory used [KB]: 2046
% 2.53/1.80 % (31260)Time elapsed: 0.029 s
% 2.53/1.80 % (31260)Instructions burned: 100 (million)
% 2.53/1.80 % (31260)------------------------------
% 2.53/1.80 % (31260)------------------------------
% 2.53/1.80 % (31245)Instruction limit reached!
% 2.53/1.80 % (31245)------------------------------
% 2.53/1.80 % (31245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.80 % (31245)Termination reason: Unknown
% 2.53/1.80 % (31245)Termination phase: Saturation
% 2.53/1.80
% 2.53/1.80 % (31245)Memory used [KB]: 7036
% 2.53/1.80 % (31245)Time elapsed: 0.195 s
% 2.53/1.80 % (31245)Instructions burned: 781 (million)
% 2.53/1.80 % (31245)------------------------------
% 2.53/1.80 % (31245)------------------------------
% 2.53/1.81 % (31262)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_30868 for (2997ds/149Mi)
% 2.53/1.81 % (31263)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30868 for (2996ds/39Mi)
% 2.53/1.82 % (31263)Instruction limit reached!
% 2.53/1.82 % (31263)------------------------------
% 2.53/1.82 % (31263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.82 % (31263)Termination reason: Unknown
% 2.53/1.82 % (31263)Termination phase: Preprocessing 1
% 2.53/1.82
% 2.53/1.82 % (31263)Memory used [KB]: 2302
% 2.53/1.82 % (31263)Time elapsed: 0.013 s
% 2.53/1.82 % (31263)Instructions burned: 41 (million)
% 2.53/1.82 % (31263)------------------------------
% 2.53/1.82 % (31263)------------------------------
% 2.53/1.83 % (31264)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_30868 for (2996ds/6Mi)
% 2.53/1.83 % (31264)Instruction limit reached!
% 2.53/1.83 % (31264)------------------------------
% 2.53/1.83 % (31264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (31264)Termination reason: Unknown
% 2.53/1.83 % (31264)Termination phase: shuffling
% 2.53/1.83
% 2.53/1.83 % (31264)Memory used [KB]: 1407
% 2.53/1.83 % (31264)Time elapsed: 0.003 s
% 2.53/1.83 % (31264)Instructions burned: 6 (million)
% 2.53/1.83 % (31264)------------------------------
% 2.53/1.83 % (31264)------------------------------
% 2.53/1.84 % (31229)Instruction limit reached!
% 2.53/1.84 % (31229)------------------------------
% 2.53/1.84 % (31229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.84 % (31229)Termination reason: Unknown
% 2.53/1.84 % (31229)Termination phase: Saturation
% 2.53/1.84
% 2.53/1.84 % (31229)Memory used [KB]: 7547
% 2.53/1.84 % (31229)Time elapsed: 0.288 s
% 2.53/1.84 % (31229)Instructions burned: 1043 (million)
% 2.53/1.84 % (31229)------------------------------
% 2.53/1.84 % (31229)------------------------------
% 2.53/1.84 % (31265)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_30868 for (2996ds/1087Mi)
% 2.53/1.85 % (31266)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30868 for (2996ds/47Mi)
% 2.53/1.85 % (31238)Instruction limit reached!
% 2.53/1.85 % (31238)------------------------------
% 2.53/1.85 % (31238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (31238)Termination reason: Unknown
% 2.53/1.85 % (31238)Termination phase: Saturation
% 2.53/1.85
% 2.53/1.85 % (31238)Memory used [KB]: 11897
% 2.53/1.85 % (31238)Time elapsed: 0.262 s
% 2.53/1.85 % (31238)Instructions burned: 712 (million)
% 2.53/1.85 % (31238)------------------------------
% 2.53/1.85 % (31238)------------------------------
% 2.53/1.85 % (31262)Instruction limit reached!
% 2.53/1.85 % (31262)------------------------------
% 2.53/1.85 % (31262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (31262)Termination reason: Unknown
% 2.53/1.85 % (31262)Termination phase: Property scanning
% 2.53/1.85
% 2.53/1.85 % (31262)Memory used [KB]: 7803
% 2.53/1.85 % (31262)Time elapsed: 0.047 s
% 2.53/1.85 % (31262)Instructions burned: 150 (million)
% 2.53/1.85 % (31262)------------------------------
% 2.53/1.85 % (31262)------------------------------
% 2.53/1.86 % (31261)Refutation not found, incomplete strategy
% 2.53/1.86 % (31261)------------------------------
% 2.53/1.86 % (31261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.86 % (31261)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.86
% 2.53/1.86
% 2.53/1.86 % (31261)Memory used [KB]: 9850
% 2.53/1.86 % (31261)Time elapsed: 0.079 s
% 2.53/1.86 % (31261)Instructions burned: 278 (million)
% 2.53/1.86 % (31261)------------------------------
% 2.53/1.86 % (31261)------------------------------
% 2.53/1.86 % (31267)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_30868 for (2996ds/44Mi)
% 2.53/1.86 % (31266)Instruction limit reached!
% 2.53/1.86 % (31266)------------------------------
% 2.53/1.86 % (31266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.86 % (31266)Termination reason: Unknown
% 2.53/1.86 % (31266)Termination phase: Preprocessing 3
% 2.53/1.86
% 2.53/1.86 % (31266)Memory used [KB]: 2430
% 2.53/1.86 % (31266)Time elapsed: 0.016 s
% 2.53/1.86 % (31266)Instructions burned: 48 (million)
% 2.53/1.86 % (31266)------------------------------
% 2.53/1.86 % (31266)------------------------------
% 2.53/1.86 % (31268)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_30868 for (2996ds/432Mi)
% 2.53/1.87 % (31269)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30868 for (2996ds/62Mi)
% 2.53/1.87 % (31270)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_30868 for (2996ds/31Mi)
% 2.53/1.87 % (31267)Instruction limit reached!
% 2.53/1.87 % (31267)------------------------------
% 2.53/1.87 % (31267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (31267)Termination reason: Unknown
% 2.53/1.87 % (31267)Termination phase: Property scanning
% 2.53/1.87
% 2.53/1.87 % (31267)Memory used [KB]: 1918
% 2.53/1.87 % (31267)Time elapsed: 0.014 s
% 2.53/1.87 % (31267)Instructions burned: 47 (million)
% 2.53/1.87 % (31267)------------------------------
% 2.53/1.87 % (31267)------------------------------
% 2.53/1.88 % (31258)Instruction limit reached!
% 2.53/1.88 % (31258)------------------------------
% 2.53/1.88 % (31258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.88 % (31258)Termination reason: Unknown
% 2.53/1.88 % (31258)Termination phase: Saturation
% 2.53/1.88
% 2.53/1.88 % (31258)Memory used [KB]: 7547
% 2.53/1.88 % (31258)Time elapsed: 0.127 s
% 2.53/1.88 % (31258)Instructions burned: 450 (million)
% 2.53/1.88 % (31258)------------------------------
% 2.53/1.88 % (31258)------------------------------
% 2.53/1.88 % (31270)Instruction limit reached!
% 2.53/1.88 % (31270)------------------------------
% 2.53/1.88 % (31270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.88 % (31270)Termination reason: Unknown
% 2.53/1.88 % (31270)Termination phase: Property scanning
% 2.53/1.88
% 2.53/1.88 % (31270)Memory used [KB]: 2174
% 2.53/1.88 % (31270)Time elapsed: 0.012 s
% 2.53/1.88 % (31270)Instructions burned: 31 (million)
% 2.53/1.88 % (31270)------------------------------
% 2.53/1.88 % (31270)------------------------------
% 2.53/1.88 % (31271)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30868 for (2996ds/96Mi)
% 2.53/1.89 % (31272)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_30868 for (2996ds/453Mi)
% 2.53/1.89 % (31269)Instruction limit reached!
% 2.53/1.89 % (31269)------------------------------
% 2.53/1.89 % (31269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (31269)Termination reason: Unknown
% 2.53/1.89 % (31269)Termination phase: Property scanning
% 2.53/1.89
% 2.53/1.89 % (31269)Memory used [KB]: 2046
% 2.53/1.89 % (31269)Time elapsed: 0.018 s
% 2.53/1.89 % (31269)Instructions burned: 64 (million)
% 2.53/1.89 % (31269)------------------------------
% 2.53/1.89 % (31269)------------------------------
% 2.53/1.89 % (31273)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_30868 for (2996ds/71Mi)
% 2.53/1.90 % (31274)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30868 for (2996ds/83Mi)
% 2.53/1.91 % (31271)Instruction limit reached!
% 2.53/1.91 % (31271)------------------------------
% 2.53/1.91 % (31271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.91 % (31271)Termination reason: Unknown
% 2.53/1.91 % (31271)Termination phase: Preprocessing 3
% 2.53/1.91
% 2.53/1.91 % (31271)Memory used [KB]: 4221
% 2.53/1.91 % (31271)Time elapsed: 0.032 s
% 2.53/1.91 % (31271)Instructions burned: 97 (million)
% 2.53/1.91 % (31271)------------------------------
% 2.53/1.91 % (31271)------------------------------
% 2.53/1.91 % (31247)Instruction limit reached!
% 2.53/1.91 % (31247)------------------------------
% 2.53/1.91 % (31247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.91 % (31247)Termination reason: Unknown
% 2.53/1.91 % (31247)Termination phase: Saturation
% 2.53/1.91
% 2.53/1.91 % (31247)Memory used [KB]: 11257
% 2.53/1.91 % (31247)Time elapsed: 0.289 s
% 2.53/1.91 % (31247)Instructions burned: 881 (million)
% 2.53/1.91 % (31247)------------------------------
% 2.53/1.91 % (31247)------------------------------
% 2.53/1.92 % (31273)Instruction limit reached!
% 2.53/1.92 % (31273)------------------------------
% 2.53/1.92 % (31273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (31273)Termination reason: Unknown
% 2.53/1.92 % (31273)Termination phase: Preprocessing 3
% 2.53/1.92
% 2.53/1.92 % (31273)Memory used [KB]: 3326
% 2.53/1.92 % (31273)Time elapsed: 0.024 s
% 2.53/1.92 % (31273)Instructions burned: 72 (million)
% 2.53/1.92 % (31273)------------------------------
% 2.53/1.92 % (31273)------------------------------
% 2.53/1.92 % (31274)Instruction limit reached!
% 2.53/1.92 % (31274)------------------------------
% 2.53/1.92 % (31274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (31274)Termination reason: Unknown
% 2.53/1.92 % (31274)Termination phase: Saturation
% 2.53/1.92
% 2.53/1.92 % (31274)Memory used [KB]: 6908
% 2.53/1.92 % (31274)Time elapsed: 0.025 s
% 2.53/1.92 % (31274)Instructions burned: 86 (million)
% 2.53/1.92 % (31274)------------------------------
% 2.53/1.92 % (31274)------------------------------
% 2.53/1.92 % (31275)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30868 for (2995ds/11Mi)
% 2.53/1.93 % (31276)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_30868 for (2995ds/41Mi)
% 2.53/1.93 % (31277)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30868 for (2995ds/6Mi)
% 2.53/1.93 % (31277)Instruction limit reached!
% 2.53/1.93 % (31277)------------------------------
% 2.53/1.93 % (31277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.93 % (31277)Termination reason: Unknown
% 2.53/1.93 % (31277)Termination phase: shuffling
% 2.53/1.93
% 2.53/1.93 % (31277)Memory used [KB]: 1407
% 2.53/1.93 % (31277)Time elapsed: 0.003 s
% 2.53/1.93 % (31277)Instructions burned: 7 (million)
% 2.53/1.93 % (31277)------------------------------
% 2.53/1.93 % (31277)------------------------------
% 2.53/1.93 % (31275)Instruction limit reached!
% 2.53/1.93 % (31275)------------------------------
% 2.53/1.93 % (31275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.93 % (31275)Termination reason: Unknown
% 2.53/1.93 % (31275)Termination phase: shuffling
% 2.53/1.93
% 2.53/1.93 % (31275)Memory used [KB]: 1535
% 2.53/1.93 % (31275)Time elapsed: 0.005 s
% 2.53/1.93 % (31275)Instructions burned: 14 (million)
% 2.53/1.93 % (31275)------------------------------
% 2.53/1.93 % (31275)------------------------------
% 2.53/1.93 % (31278)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30868 for (2995ds/150Mi)
% 2.53/1.94 % (31279)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30868 for (2995ds/343Mi)
% 2.53/1.94 % (31276)Instruction limit reached!
% 2.53/1.94 % (31276)------------------------------
% 2.53/1.94 % (31276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.94 % (31276)Termination reason: Unknown
% 2.53/1.94 % (31276)Termination phase: Property scanning
% 2.53/1.94
% 2.53/1.94 % (31276)Memory used [KB]: 1918
% 2.53/1.94 % (31276)Time elapsed: 0.013 s
% 2.53/1.94 % (31276)Instructions burned: 43 (million)
% 2.53/1.94 % (31276)------------------------------
% 2.53/1.94 % (31276)------------------------------
% 2.53/1.94 % (31280)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_30868 for (2995ds/109Mi)
% 2.53/1.95 % (31281)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_30868 for (2995ds/253Mi)
% 2.53/1.97 % (31278)Instruction limit reached!
% 2.53/1.97 % (31278)------------------------------
% 2.53/1.97 % (31278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.97 % (31278)Termination reason: Unknown
% 2.53/1.97 % (31278)Termination phase: Property scanning
% 2.53/1.97
% 2.53/1.97 % (31278)Memory used [KB]: 4349
% 2.53/1.97 % (31278)Time elapsed: 0.043 s
% 2.53/1.97 % (31278)Instructions burned: 151 (million)
% 2.53/1.97 % (31278)------------------------------
% 2.53/1.97 % (31278)------------------------------
% 2.53/1.97 % (31280)Instruction limit reached!
% 2.53/1.97 % (31280)------------------------------
% 2.53/1.97 % (31280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.97 % (31280)Termination reason: Unknown
% 2.53/1.97 % (31280)Termination phase: Property scanning
% 2.53/1.97
% 2.53/1.97 % (31280)Memory used [KB]: 4093
% 2.53/1.97 % (31280)Time elapsed: 0.036 s
% 2.53/1.97 % (31280)Instructions burned: 112 (million)
% 2.53/1.97 % (31280)------------------------------
% 2.53/1.97 % (31280)------------------------------
% 2.53/1.98 % (31282)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30868 for (2995ds/140Mi)
% 2.53/1.98 % (31268)Instruction limit reached!
% 2.53/1.98 % (31268)------------------------------
% 2.53/1.98 % (31268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.98 % (31268)Termination reason: Unknown
% 2.53/1.98 % (31268)Termination phase: Saturation
% 2.53/1.98
% 2.53/1.98 % (31268)Memory used [KB]: 2430
% 2.53/1.98 % (31268)Time elapsed: 0.122 s
% 2.53/1.98 % (31268)Instructions burned: 433 (million)
% 2.53/1.98 % (31268)------------------------------
% 2.53/1.98 % (31268)------------------------------
% 2.53/1.98 % (31283)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_30868 for (2995ds/614Mi)
% 2.53/1.99 % (31284)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_30868 for (2995ds/202Mi)
% 2.53/2.00 % (31272)Instruction limit reached!
% 2.53/2.00 % (31272)------------------------------
% 2.53/2.00 % (31272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/2.00 % (31272)Termination reason: Unknown
% 2.53/2.00 % (31272)Termination phase: Saturation
% 2.53/2.00
% 2.53/2.00 % (31272)Memory used [KB]: 6652
% 2.53/2.00 % (31272)Time elapsed: 0.114 s
% 2.53/2.00 % (31272)Instructions burned: 456 (million)
% 2.53/2.00 % (31272)------------------------------
% 2.53/2.00 % (31272)------------------------------
% 2.53/2.01 % (31285)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_30868 for (2995ds/339Mi)
% 5.97/2.02 % (31282)Instruction limit reached!
% 5.97/2.02 % (31282)------------------------------
% 5.97/2.02 % (31282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.02 % (31282)Termination reason: Unknown
% 5.97/2.02 % (31282)Termination phase: Property scanning
% 5.97/2.02
% 5.97/2.02 % (31282)Memory used [KB]: 4221
% 5.97/2.02 % (31282)Time elapsed: 0.040 s
% 5.97/2.02 % (31282)Instructions burned: 144 (million)
% 5.97/2.02 % (31282)------------------------------
% 5.97/2.02 % (31282)------------------------------
% 5.97/2.03 % (31281)Instruction limit reached!
% 5.97/2.03 % (31281)------------------------------
% 5.97/2.03 % (31281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.03 % (31281)Termination reason: Unknown
% 5.97/2.03 % (31281)Termination phase: Saturation
% 5.97/2.03
% 5.97/2.03 % (31281)Memory used [KB]: 7419
% 5.97/2.03 % (31281)Time elapsed: 0.083 s
% 5.97/2.03 % (31281)Instructions burned: 255 (million)
% 5.97/2.03 % (31281)------------------------------
% 5.97/2.03 % (31281)------------------------------
% 5.97/2.03 % (31286)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_30868 for (2994ds/283Mi)
% 5.97/2.04 % (31287)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30868 for (2994ds/134Mi)
% 5.97/2.05 % (31284)Instruction limit reached!
% 5.97/2.05 % (31284)------------------------------
% 5.97/2.05 % (31284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.05 % (31284)Termination reason: Unknown
% 5.97/2.05 % (31284)Termination phase: Saturation
% 5.97/2.05
% 5.97/2.05 % (31284)Memory used [KB]: 4477
% 5.97/2.05 % (31284)Time elapsed: 0.056 s
% 5.97/2.05 % (31284)Instructions burned: 202 (million)
% 5.97/2.05 % (31284)------------------------------
% 5.97/2.05 % (31284)------------------------------
% 5.97/2.06 % (31288)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30868 for (2994ds/298Mi)
% 5.97/2.07 % (31279)Instruction limit reached!
% 5.97/2.07 % (31279)------------------------------
% 5.97/2.07 % (31279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.07 % (31279)Termination reason: Unknown
% 5.97/2.07 % (31279)Termination phase: Saturation
% 5.97/2.07
% 5.97/2.07 % (31279)Memory used [KB]: 8059
% 5.97/2.07 % (31279)Time elapsed: 0.137 s
% 5.97/2.07 % (31279)Instructions burned: 343 (million)
% 5.97/2.07 % (31279)------------------------------
% 5.97/2.07 % (31279)------------------------------
% 5.97/2.08 % (31287)Instruction limit reached!
% 5.97/2.08 % (31287)------------------------------
% 5.97/2.08 % (31287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.08 % (31287)Termination reason: Unknown
% 5.97/2.08 % (31287)Termination phase: Property scanning
% 5.97/2.08
% 5.97/2.08 % (31287)Memory used [KB]: 4221
% 5.97/2.08 % (31287)Time elapsed: 0.038 s
% 5.97/2.08 % (31287)Instructions burned: 134 (million)
% 5.97/2.08 % (31287)------------------------------
% 5.97/2.08 % (31287)------------------------------
% 5.97/2.09 % (31290)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_30868 for (2994ds/258Mi)
% 5.97/2.09 % (31289)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30868 for (2994ds/192Mi)
% 5.97/2.10 % (31285)Instruction limit reached!
% 5.97/2.10 % (31285)------------------------------
% 5.97/2.10 % (31285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.10 % (31285)Termination reason: Unknown
% 5.97/2.10 % (31285)Termination phase: Saturation
% 5.97/2.10
% 5.97/2.10 % (31285)Memory used [KB]: 9594
% 5.97/2.10 % (31285)Time elapsed: 0.092 s
% 5.97/2.10 % (31285)Instructions burned: 342 (million)
% 5.97/2.10 % (31285)------------------------------
% 5.97/2.10 % (31285)------------------------------
% 5.97/2.10 % (31286)Instruction limit reached!
% 5.97/2.10 % (31286)------------------------------
% 5.97/2.10 % (31286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.10 % (31286)Termination reason: Unknown
% 5.97/2.10 % (31286)Termination phase: Saturation
% 5.97/2.10
% 5.97/2.10 % (31286)Memory used [KB]: 7036
% 5.97/2.10 % (31286)Time elapsed: 0.073 s
% 5.97/2.10 % (31286)Instructions burned: 284 (million)
% 5.97/2.10 % (31286)------------------------------
% 5.97/2.10 % (31286)------------------------------
% 5.97/2.11 % (31291)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_30868 for (2994ds/90Mi)
% 5.97/2.11 % (31292)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_30868 for (2994ds/231Mi)
% 6.55/2.13 % (31288)Instruction limit reached!
% 6.55/2.13 % (31288)------------------------------
% 6.55/2.13 % (31288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.13 % (31288)Termination reason: Unknown
% 6.55/2.13 % (31288)Termination phase: Saturation
% 6.55/2.13
% 6.55/2.13 % (31288)Memory used [KB]: 6652
% 6.55/2.13 % (31288)Time elapsed: 0.076 s
% 6.55/2.13 % (31288)Instructions burned: 298 (million)
% 6.55/2.13 % (31288)------------------------------
% 6.55/2.13 % (31288)------------------------------
% 6.55/2.13 % (31291)Instruction limit reached!
% 6.55/2.13 % (31291)------------------------------
% 6.55/2.13 % (31291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.13 % (31291)Termination reason: Unknown
% 6.55/2.13 % (31291)Termination phase: Preprocessing 3
% 6.55/2.13
% 6.55/2.13 % (31291)Memory used [KB]: 3965
% 6.55/2.13 % (31291)Time elapsed: 0.027 s
% 6.55/2.13 % (31291)Instructions burned: 90 (million)
% 6.55/2.13 % (31291)------------------------------
% 6.55/2.13 % (31291)------------------------------
% 6.55/2.14 % (31293)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_30868 for (2993ds/458Mi)
% 6.55/2.14 % (31294)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_30868 for (2993ds/31Mi)
% 6.55/2.15 % (31290)Instruction limit reached!
% 6.55/2.15 % (31290)------------------------------
% 6.55/2.15 % (31290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.15 % (31290)Termination reason: Unknown
% 6.55/2.15 % (31290)Termination phase: Property scanning
% 6.55/2.15
% 6.55/2.15 % (31290)Memory used [KB]: 7803
% 6.55/2.15 % (31290)Time elapsed: 0.069 s
% 6.55/2.15 % (31290)Instructions burned: 259 (million)
% 6.55/2.15 % (31290)------------------------------
% 6.55/2.15 % (31290)------------------------------
% 6.55/2.15 % (31294)Instruction limit reached!
% 6.55/2.15 % (31294)------------------------------
% 6.55/2.15 % (31294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.15 % (31294)Termination reason: Unknown
% 6.55/2.15 % (31294)Termination phase: Property scanning
% 6.55/2.15
% 6.55/2.15 % (31294)Memory used [KB]: 2174
% 6.55/2.15 % (31294)Time elapsed: 0.011 s
% 6.55/2.15 % (31294)Instructions burned: 33 (million)
% 6.55/2.15 % (31294)------------------------------
% 6.55/2.15 % (31294)------------------------------
% 6.55/2.16 % (31283)Instruction limit reached!
% 6.55/2.16 % (31283)------------------------------
% 6.55/2.16 % (31283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.16 % (31283)Termination reason: Unknown
% 6.55/2.16 % (31283)Termination phase: Saturation
% 6.55/2.16
% 6.55/2.16 % (31283)Memory used [KB]: 12920
% 6.55/2.16 % (31283)Time elapsed: 0.180 s
% 6.55/2.16 % (31283)Instructions burned: 615 (million)
% 6.55/2.16 % (31283)------------------------------
% 6.55/2.16 % (31283)------------------------------
% 6.55/2.16 % (31295)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_30868 for (2993ds/297Mi)
% 6.55/2.16 % (31296)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_30868 for (2993ds/987Mi)
% 6.55/2.17 % (31289)Instruction limit reached!
% 6.55/2.17 % (31289)------------------------------
% 6.55/2.17 % (31289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.17 % (31289)Termination reason: Unknown
% 6.55/2.17 % (31289)Termination phase: Property scanning
% 6.55/2.17
% 6.55/2.17 % (31289)Memory used [KB]: 4605
% 6.55/2.17 % (31289)Time elapsed: 0.076 s
% 6.55/2.17 % (31289)Instructions burned: 193 (million)
% 6.55/2.17 % (31289)------------------------------
% 6.55/2.17 % (31289)------------------------------
% 6.55/2.17 % (31292)Instruction limit reached!
% 6.55/2.17 % (31292)------------------------------
% 6.55/2.17 % (31292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.17 % (31292)Termination reason: Unknown
% 6.55/2.17 % (31292)Termination phase: Saturation
% 6.55/2.17
% 6.55/2.17 % (31292)Memory used [KB]: 7164
% 6.55/2.17 % (31292)Time elapsed: 0.059 s
% 6.55/2.17 % (31292)Instructions burned: 234 (million)
% 6.55/2.17 % (31292)------------------------------
% 6.55/2.17 % (31292)------------------------------
% 6.55/2.17 % (31297)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_30868 for (2993ds/182Mi)
% 6.55/2.18 % (31298)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_30868 for (2993ds/182Mi)
% 6.55/2.18 % (31299)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_30868 for (2993ds/154Mi)
% 6.55/2.18 % (31265)Instruction limit reached!
% 6.55/2.18 % (31265)------------------------------
% 6.55/2.18 % (31265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.18 % (31265)Termination reason: Unknown
% 6.55/2.18 % (31265)Termination phase: Saturation
% 6.55/2.18
% 6.55/2.18 % (31265)Memory used [KB]: 11513
% 6.55/2.18 % (31265)Time elapsed: 0.340 s
% 6.55/2.18 % (31265)Instructions burned: 1087 (million)
% 6.55/2.18 % (31265)------------------------------
% 6.55/2.18 % (31265)------------------------------
% 6.55/2.19 % (31300)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_30868 for (2993ds/79Mi)
% 7.07/2.21 % (31300)Instruction limit reached!
% 7.07/2.21 % (31300)------------------------------
% 7.07/2.21 % (31300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.21 % (31300)Termination reason: Unknown
% 7.07/2.21 % (31300)Termination phase: Preprocessing 3
% 7.07/2.21
% 7.07/2.21 % (31300)Memory used [KB]: 3837
% 7.07/2.21 % (31300)Time elapsed: 0.025 s
% 7.07/2.21 % (31300)Instructions burned: 81 (million)
% 7.07/2.21 % (31300)------------------------------
% 7.07/2.21 % (31300)------------------------------
% 7.07/2.22 % (31299)Instruction limit reached!
% 7.07/2.22 % (31299)------------------------------
% 7.07/2.22 % (31299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.22 % (31299)Termination reason: Unknown
% 7.07/2.22 % (31299)Termination phase: Saturation
% 7.07/2.22
% 7.07/2.22 % (31299)Memory used [KB]: 2558
% 7.07/2.22 % (31299)Time elapsed: 0.041 s
% 7.07/2.22 % (31299)Instructions burned: 156 (million)
% 7.07/2.22 % (31299)------------------------------
% 7.07/2.22 % (31299)------------------------------
% 7.07/2.22 % (31297)Instruction limit reached!
% 7.07/2.22 % (31297)------------------------------
% 7.07/2.22 % (31297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.22 % (31297)Termination reason: Unknown
% 7.07/2.22 % (31297)Termination phase: Property scanning
% 7.07/2.22
% 7.07/2.22 % (31297)Memory used [KB]: 7803
% 7.07/2.22 % (31297)Time elapsed: 0.052 s
% 7.07/2.22 % (31297)Instructions burned: 184 (million)
% 7.07/2.22 % (31297)------------------------------
% 7.07/2.22 % (31297)------------------------------
% 7.07/2.23 % (31301)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_30868 for (2992ds/216Mi)
% 7.07/2.23 % (31302)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30868 for (2992ds/114Mi)
% 7.07/2.23 % (31298)Instruction limit reached!
% 7.07/2.23 % (31298)------------------------------
% 7.07/2.23 % (31298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.23 % (31298)Termination reason: Unknown
% 7.07/2.23 % (31298)Termination phase: Saturation
% 7.07/2.23
% 7.07/2.23 % (31298)Memory used [KB]: 9083
% 7.07/2.23 % (31298)Time elapsed: 0.057 s
% 7.07/2.23 % (31298)Instructions burned: 183 (million)
% 7.07/2.23 % (31298)------------------------------
% 7.07/2.23 % (31298)------------------------------
% 7.07/2.23 % (31303)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_30868 for (2992ds/922Mi)
% 7.07/2.24 % (31304)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_30868 for (2992ds/182Mi)
% 7.07/2.25 % (31295)Instruction limit reached!
% 7.07/2.25 % (31295)------------------------------
% 7.07/2.25 % (31295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.25 % (31295)Termination reason: Unknown
% 7.07/2.25 % (31295)Termination phase: Saturation
% 7.07/2.25
% 7.07/2.25 % (31295)Memory used [KB]: 6908
% 7.07/2.25 % (31295)Time elapsed: 0.087 s
% 7.07/2.25 % (31295)Instructions burned: 297 (million)
% 7.07/2.25 % (31295)------------------------------
% 7.07/2.25 % (31295)------------------------------
% 7.07/2.26 % (31305)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_30868 for (2992ds/164Mi)
% 7.07/2.26 % (31302)Instruction limit reached!
% 7.07/2.26 % (31302)------------------------------
% 7.07/2.26 % (31302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.26 % (31302)Termination reason: Unknown
% 7.07/2.26 % (31302)Termination phase: Property scanning
% 7.07/2.26
% 7.07/2.26 % (31302)Memory used [KB]: 4221
% 7.07/2.26 % (31302)Time elapsed: 0.034 s
% 7.07/2.26 % (31302)Instructions burned: 118 (million)
% 7.07/2.26 % (31302)------------------------------
% 7.07/2.26 % (31302)------------------------------
% 7.07/2.27 % (31306)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_30868 for (2992ds/50Mi)
% 7.07/2.27 % (31293)Instruction limit reached!
% 7.07/2.27 % (31293)------------------------------
% 7.07/2.27 % (31293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.27 % (31293)Termination reason: Unknown
% 7.07/2.27 % (31293)Termination phase: Saturation
% 7.07/2.27
% 7.07/2.27 % (31293)Memory used [KB]: 10874
% 7.07/2.27 % (31293)Time elapsed: 0.131 s
% 7.07/2.27 % (31293)Instructions burned: 459 (million)
% 7.07/2.27 % (31293)------------------------------
% 7.07/2.27 % (31293)------------------------------
% 7.07/2.28 % (31307)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30868 for (2992ds/368Mi)
% 7.07/2.28 % (31306)Instruction limit reached!
% 7.07/2.28 % (31306)------------------------------
% 7.07/2.28 % (31306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.28 % (31306)Termination reason: Unknown
% 7.07/2.28 % (31306)Termination phase: Property scanning
% 7.07/2.28
% 7.07/2.28 % (31306)Memory used [KB]: 1918
% 7.07/2.28 % (31306)Time elapsed: 0.014 s
% 7.07/2.28 % (31306)Instructions burned: 50 (million)
% 7.07/2.28 % (31306)------------------------------
% 7.07/2.28 % (31306)------------------------------
% 7.07/2.29 % (31301)Instruction limit reached!
% 7.07/2.29 % (31301)------------------------------
% 7.07/2.29 % (31301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.29 % (31301)Termination reason: Unknown
% 7.07/2.29 % (31301)Termination phase: Saturation
% 7.07/2.29
% 7.07/2.29 % (31301)Memory used [KB]: 6780
% 7.07/2.29 % (31301)Time elapsed: 0.062 s
% 7.07/2.29 % (31301)Instructions burned: 216 (million)
% 7.07/2.29 % (31301)------------------------------
% 7.07/2.29 % (31301)------------------------------
% 7.07/2.29 % (31304)Instruction limit reached!
% 7.07/2.29 % (31304)------------------------------
% 7.07/2.29 % (31304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.29 % (31304)Termination reason: Unknown
% 7.07/2.29 % (31304)Termination phase: Saturation
% 7.07/2.29
% 7.07/2.29 % (31304)Memory used [KB]: 6652
% 7.07/2.29 % (31304)Time elapsed: 0.051 s
% 7.07/2.29 % (31304)Instructions burned: 183 (million)
% 7.07/2.29 % (31304)------------------------------
% 7.07/2.29 % (31304)------------------------------
% 7.07/2.29 % (31308)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_30868 for (2992ds/1021Mi)
% 7.07/2.30 % (31309)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_30868 for (2992ds/267Mi)
% 7.70/2.30 % (31310)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_30868 for (2992ds/204Mi)
% 7.70/2.30 % (31305)Instruction limit reached!
% 7.70/2.30 % (31305)------------------------------
% 7.70/2.30 % (31305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.30 % (31305)Termination reason: Unknown
% 7.70/2.30 % (31305)Termination phase: Saturation
% 7.70/2.30
% 7.70/2.30 % (31305)Memory used [KB]: 2302
% 7.70/2.30 % (31305)Time elapsed: 0.046 s
% 7.70/2.30 % (31305)Instructions burned: 166 (million)
% 7.70/2.30 % (31305)------------------------------
% 7.70/2.30 % (31305)------------------------------
% 7.70/2.31 % (31311)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_30868 for (2991ds/26Mi)
% 7.70/2.32 % (31311)Instruction limit reached!
% 7.70/2.32 % (31311)------------------------------
% 7.70/2.32 % (31311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.32 % (31311)Termination reason: Unknown
% 7.70/2.32 % (31311)Termination phase: shuffling
% 7.70/2.32
% 7.70/2.32 % (31311)Memory used [KB]: 1791
% 7.70/2.32 % (31311)Time elapsed: 0.009 s
% 7.70/2.32 % (31311)Instructions burned: 27 (million)
% 7.70/2.32 % (31311)------------------------------
% 7.70/2.32 % (31311)------------------------------
% 7.70/2.33 % (31312)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_30868 for (2991ds/53Mi)
% 7.70/2.34 % (31312)Instruction limit reached!
% 7.70/2.34 % (31312)------------------------------
% 7.70/2.34 % (31312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.34 % (31312)Termination reason: Unknown
% 7.70/2.34 % (31312)Termination phase: Property scanning
% 7.70/2.34
% 7.70/2.34 % (31312)Memory used [KB]: 1918
% 7.70/2.34 % (31312)Time elapsed: 0.015 s
% 7.70/2.34 % (31312)Instructions burned: 55 (million)
% 7.70/2.34 % (31312)------------------------------
% 7.70/2.34 % (31312)------------------------------
% 7.70/2.35 % (31313)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_30868 for (2991ds/4436Mi)
% 7.70/2.36 % (31310)Instruction limit reached!
% 7.70/2.36 % (31310)------------------------------
% 7.70/2.36 % (31310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.36 % (31310)Termination reason: Unknown
% 7.70/2.36 % (31310)Termination phase: Property scanning
% 7.70/2.36
% 7.70/2.36 % (31310)Memory used [KB]: 4477
% 7.70/2.36 % (31310)Time elapsed: 0.061 s
% 7.70/2.36 % (31310)Instructions burned: 206 (million)
% 7.70/2.36 % (31310)------------------------------
% 7.70/2.36 % (31310)------------------------------
% 7.70/2.36 % (31309)Instruction limit reached!
% 7.70/2.36 % (31309)------------------------------
% 7.70/2.36 % (31309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.36 % (31309)Termination reason: Unknown
% 7.70/2.36 % (31309)Termination phase: Saturation
% 7.70/2.36
% 7.70/2.36 % (31309)Memory used [KB]: 6780
% 7.70/2.36 % (31309)Time elapsed: 0.070 s
% 7.70/2.36 % (31309)Instructions burned: 270 (million)
% 7.70/2.36 % (31309)------------------------------
% 7.70/2.36 % (31309)------------------------------
% 7.70/2.37 % (31314)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_30868 for (2991ds/1539Mi)
% 7.70/2.37 % (31315)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_30868 for (2991ds/408Mi)
% 7.70/2.38 % (31307)Instruction limit reached!
% 7.70/2.38 % (31307)------------------------------
% 7.70/2.38 % (31307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.70/2.38 % (31307)Termination reason: Unknown
% 7.70/2.38 % (31307)Termination phase: Saturation
% 7.70/2.38
% 7.70/2.38 % (31307)Memory used [KB]: 10874
% 7.70/2.38 % (31307)Time elapsed: 0.103 s
% 7.70/2.38 % (31307)Instructions burned: 368 (million)
% 7.70/2.38 % (31307)------------------------------
% 7.70/2.38 % (31307)------------------------------
% 7.70/2.39 % (31316)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_30868 for (2991ds/5205Mi)
% 8.07/2.41 % (31296)Instruction limit reached!
% 8.07/2.41 % (31296)------------------------------
% 8.07/2.41 % (31296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.41 % (31296)Termination reason: Unknown
% 8.07/2.41 % (31296)Termination phase: Saturation
% 8.07/2.41
% 8.07/2.41 % (31296)Memory used [KB]: 7547
% 8.07/2.41 % (31296)Time elapsed: 0.245 s
% 8.07/2.41 % (31296)Instructions burned: 990 (million)
% 8.07/2.41 % (31296)------------------------------
% 8.07/2.41 % (31296)------------------------------
% 8.07/2.42 % (31317)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_30868 for (2990ds/1913Mi)
% 8.07/2.49 % (31315)Instruction limit reached!
% 8.07/2.49 % (31315)------------------------------
% 8.07/2.49 % (31315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.49 % (31315)Termination reason: Unknown
% 8.07/2.49 % (31315)Termination phase: Saturation
% 8.07/2.49
% 8.07/2.49 % (31315)Memory used [KB]: 11001
% 8.07/2.49 % (31315)Time elapsed: 0.122 s
% 8.07/2.49 % (31315)Instructions burned: 410 (million)
% 8.07/2.49 % (31315)------------------------------
% 8.07/2.49 % (31315)------------------------------
% 8.45/2.51 % (31318)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_30868 for (2990ds/4350Mi)
% 8.45/2.52 % (31303)Instruction limit reached!
% 8.45/2.52 % (31303)------------------------------
% 8.45/2.52 % (31303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.45/2.52 % (31303)Termination reason: Unknown
% 8.45/2.52 % (31303)Termination phase: Saturation
% 8.45/2.52
% 8.45/2.52 % (31303)Memory used [KB]: 12537
% 8.45/2.52 % (31303)Time elapsed: 0.286 s
% 8.45/2.52 % (31303)Instructions burned: 924 (million)
% 8.45/2.52 % (31303)------------------------------
% 8.45/2.52 % (31303)------------------------------
% 8.45/2.53 % (31319)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_30868 for (2989ds/68Mi)
% 8.45/2.55 % (31319)Instruction limit reached!
% 8.45/2.55 % (31319)------------------------------
% 8.45/2.55 % (31319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.45/2.55 % (31319)Termination reason: Unknown
% 8.45/2.55 % (31319)Termination phase: Preprocessing 3
% 8.45/2.55
% 8.45/2.55 % (31319)Memory used [KB]: 3070
% 8.45/2.55 % (31319)Time elapsed: 0.021 s
% 8.45/2.55 % (31319)Instructions burned: 69 (million)
% 8.45/2.55 % (31319)------------------------------
% 8.45/2.55 % (31319)------------------------------
% 8.45/2.56 % (31320)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_30868 for (2989ds/358Mi)
% 8.78/2.60 % (31308)Instruction limit reached!
% 8.78/2.60 % (31308)------------------------------
% 8.78/2.60 % (31308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.78/2.60 % (31308)Termination reason: Unknown
% 8.78/2.60 % (31308)Termination phase: Saturation
% 8.78/2.60
% 8.78/2.60 % (31308)Memory used [KB]: 12281
% 8.78/2.60 % (31308)Time elapsed: 0.305 s
% 8.78/2.60 % (31308)Instructions burned: 1021 (million)
% 8.78/2.60 % (31308)------------------------------
% 8.78/2.60 % (31308)------------------------------
% 8.78/2.61 % (31326)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_30868 for (2989ds/31Mi)
% 8.78/2.62 % (31326)Instruction limit reached!
% 8.78/2.62 % (31326)------------------------------
% 8.78/2.62 % (31326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.78/2.62 % (31326)Termination reason: Unknown
% 8.78/2.62 % (31326)Termination phase: Property scanning
% 8.78/2.62
% 8.78/2.62 % (31326)Memory used [KB]: 2174
% 8.78/2.62 % (31326)Time elapsed: 0.011 s
% 8.78/2.62 % (31326)Instructions burned: 32 (million)
% 8.78/2.62 % (31326)------------------------------
% 8.78/2.62 % (31326)------------------------------
% 8.78/2.63 % (31338)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30868 for (2988ds/279Mi)
% 8.78/2.66 % (31320)Instruction limit reached!
% 8.78/2.66 % (31320)------------------------------
% 8.78/2.66 % (31320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.78/2.66 % (31320)Termination reason: Unknown
% 8.78/2.66 % (31320)Termination phase: Saturation
% 8.78/2.66
% 8.78/2.66 % (31320)Memory used [KB]: 9594
% 8.78/2.66 % (31320)Time elapsed: 0.101 s
% 8.78/2.66 % (31320)Instructions burned: 358 (million)
% 8.78/2.66 % (31320)------------------------------
% 8.78/2.66 % (31320)------------------------------
% 8.78/2.67 % (31339)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30868 for (2988ds/258Mi)
% 9.22/2.70 % (31338)Instruction limit reached!
% 9.22/2.70 % (31338)------------------------------
% 9.22/2.70 % (31338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.70 % (31338)Termination reason: Unknown
% 9.22/2.70 % (31338)Termination phase: Saturation
% 9.22/2.70
% 9.22/2.70 % (31338)Memory used [KB]: 7675
% 9.22/2.70 % (31338)Time elapsed: 0.074 s
% 9.22/2.70 % (31338)Instructions burned: 280 (million)
% 9.22/2.70 % (31338)------------------------------
% 9.22/2.70 % (31338)------------------------------
% 9.22/2.71 % (31340)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_30868 for (2988ds/26Mi)
% 9.22/2.72 % (31340)Instruction limit reached!
% 9.22/2.72 % (31340)------------------------------
% 9.22/2.72 % (31340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.72 % (31340)Termination reason: Unknown
% 9.22/2.72 % (31340)Termination phase: shuffling
% 9.22/2.72
% 9.22/2.72 % (31340)Memory used [KB]: 1791
% 9.22/2.72 % (31340)Time elapsed: 0.008 s
% 9.22/2.72 % (31340)Instructions burned: 26 (million)
% 9.22/2.72 % (31340)------------------------------
% 9.22/2.72 % (31340)------------------------------
% 9.22/2.73 % (31341)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_30868 for (2987ds/995Mi)
% 9.22/2.74 % (31339)Instruction limit reached!
% 9.22/2.74 % (31339)------------------------------
% 9.22/2.74 % (31339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.22/2.74 % (31339)Termination reason: Unknown
% 9.22/2.74 % (31339)Termination phase: Saturation
% 9.22/2.74
% 9.22/2.74 % (31339)Memory used [KB]: 9466
% 9.22/2.74 % (31339)Time elapsed: 0.073 s
% 9.22/2.74 % (31339)Instructions burned: 258 (million)
% 9.22/2.74 % (31339)------------------------------
% 9.22/2.74 % (31339)------------------------------
% 9.22/2.75 % (31342)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_30868 for (2987ds/373Mi)
% 9.41/2.83 % (31314)Instruction limit reached!
% 9.41/2.83 % (31314)------------------------------
% 9.41/2.83 % (31314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.83 % (31314)Termination reason: Unknown
% 9.41/2.83 % (31314)Termination phase: Saturation
% 9.41/2.83
% 9.41/2.83 % (31314)Memory used [KB]: 13048
% 9.41/2.83 % (31314)Time elapsed: 0.456 s
% 9.41/2.83 % (31314)Instructions burned: 1539 (million)
% 9.41/2.83 % (31314)------------------------------
% 9.41/2.83 % (31314)------------------------------
% 9.41/2.84 % (31343)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_30868 for (2986ds/253Mi)
% 9.41/2.86 % (31342)Instruction limit reached!
% 9.41/2.86 % (31342)------------------------------
% 9.41/2.86 % (31342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.86 % (31342)Termination reason: Unknown
% 9.41/2.86 % (31342)Termination phase: Saturation
% 9.41/2.86
% 9.41/2.86 % (31342)Memory used [KB]: 10362
% 9.41/2.86 % (31342)Time elapsed: 0.133 s
% 9.41/2.86 % (31342)Instructions burned: 375 (million)
% 9.41/2.86 % (31342)------------------------------
% 9.41/2.86 % (31342)------------------------------
% 9.41/2.87 % (31344)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_30868 for (2986ds/832Mi)
% 9.99/2.90 % (31343)Instruction limit reached!
% 9.99/2.90 % (31343)------------------------------
% 9.99/2.90 % (31343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.99/2.90 % (31343)Termination reason: Unknown
% 9.99/2.90 % (31343)Termination phase: Saturation
% 9.99/2.90
% 9.99/2.90 % (31343)Memory used [KB]: 6780
% 9.99/2.90 % (31343)Time elapsed: 0.065 s
% 9.99/2.90 % (31343)Instructions burned: 255 (million)
% 9.99/2.90 % (31343)------------------------------
% 9.99/2.90 % (31343)------------------------------
% 9.99/2.91 % (31345)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_30868 for (2986ds/668Mi)
% 9.99/2.95 % (31344)Refutation not found, incomplete strategy
% 9.99/2.95 % (31344)------------------------------
% 9.99/2.95 % (31344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.99/2.95 % (31344)Termination reason: Refutation not found, incomplete strategy
% 9.99/2.95
% 9.99/2.95
% 9.99/2.95 % (31344)Memory used [KB]: 9850
% 9.99/2.95 % (31344)Time elapsed: 0.102 s
% 9.99/2.95 % (31344)Instructions burned: 276 (million)
% 9.99/2.95 % (31344)------------------------------
% 9.99/2.95 % (31344)------------------------------
% 9.99/2.96 % (31346)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_30868 for (2985ds/40Mi)
% 9.99/2.97 % (31346)Instruction limit reached!
% 9.99/2.97 % (31346)------------------------------
% 9.99/2.97 % (31346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.99/2.97 % (31346)Termination reason: Unknown
% 9.99/2.97 % (31346)Termination phase: Property scanning
% 9.99/2.97
% 9.99/2.97 % (31346)Memory used [KB]: 1918
% 9.99/2.97 % (31346)Time elapsed: 0.012 s
% 9.99/2.97 % (31346)Instructions burned: 42 (million)
% 9.99/2.97 % (31346)------------------------------
% 9.99/2.97 % (31346)------------------------------
% 9.99/2.98 % (31341)Instruction limit reached!
% 9.99/2.98 % (31341)------------------------------
% 9.99/2.98 % (31341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.99/2.98 % (31341)Termination reason: Unknown
% 9.99/2.98 % (31341)Termination phase: Saturation
% 9.99/2.98
% 9.99/2.98 % (31341)Memory used [KB]: 6652
% 9.99/2.98 % (31341)Time elapsed: 0.251 s
% 9.99/2.98 % (31341)Instructions burned: 998 (million)
% 9.99/2.98 % (31341)------------------------------
% 9.99/2.98 % (31341)------------------------------
% 9.99/2.98 % (31347)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_30868 for (2985ds/294Mi)
% 9.99/2.99 % (31348)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_30868 for (2985ds/187Mi)
% 9.99/3.00 % (31317)Instruction limit reached!
% 9.99/3.00 % (31317)------------------------------
% 9.99/3.00 % (31317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.99/3.00 % (31317)Termination reason: Unknown
% 9.99/3.00 % (31317)Termination phase: Saturation
% 9.99/3.00
% 9.99/3.00 % (31317)Memory used [KB]: 6396
% 9.99/3.00 % (31317)Time elapsed: 0.588 s
% 9.99/3.00 % (31317)Instructions burned: 1914 (million)
% 9.99/3.00 % (31317)------------------------------
% 9.99/3.00 % (31317)------------------------------
% 9.99/3.01 % (31349)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30868 for (2984ds/371Mi)
% 13.05/3.04 % (31348)Instruction limit reached!
% 13.05/3.04 % (31348)------------------------------
% 13.05/3.04 % (31348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.04 % (31348)Termination reason: Unknown
% 13.05/3.04 % (31348)Termination phase: Property scanning
% 13.05/3.04
% 13.05/3.04 % (31348)Memory used [KB]: 4605
% 13.05/3.04 % (31348)Time elapsed: 0.051 s
% 13.05/3.04 % (31348)Instructions burned: 190 (million)
% 13.05/3.04 % (31348)------------------------------
% 13.05/3.04 % (31348)------------------------------
% 13.05/3.05 % (31350)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30868 for (2984ds/1827Mi)
% 13.05/3.05 % (31349)Refutation not found, incomplete strategy
% 13.05/3.05 % (31349)------------------------------
% 13.05/3.05 % (31349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.05 % (31349)Termination reason: Refutation not found, incomplete strategy
% 13.05/3.05
% 13.05/3.05
% 13.05/3.05 % (31349)Memory used [KB]: 7291
% 13.05/3.05 % (31349)Time elapsed: 0.034 s
% 13.05/3.05 % (31349)Instructions burned: 116 (million)
% 13.05/3.05 % (31349)------------------------------
% 13.05/3.05 % (31349)------------------------------
% 13.05/3.05 % (31347)Instruction limit reached!
% 13.05/3.05 % (31347)------------------------------
% 13.05/3.05 % (31347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.05 % (31347)Termination reason: Unknown
% 13.05/3.05 % (31347)Termination phase: Saturation
% 13.05/3.05
% 13.05/3.05 % (31347)Memory used [KB]: 7803
% 13.05/3.05 % (31347)Time elapsed: 0.073 s
% 13.05/3.05 % (31347)Instructions burned: 295 (million)
% 13.05/3.05 % (31347)------------------------------
% 13.05/3.05 % (31347)------------------------------
% 13.05/3.06 % (31351)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_30868 for (2984ds/70Mi)
% 13.05/3.06 % (31352)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_30868 for (2984ds/316Mi)
% 13.05/3.07 % (31345)Instruction limit reached!
% 13.05/3.07 % (31345)------------------------------
% 13.05/3.07 % (31345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.07 % (31345)Termination reason: Unknown
% 13.05/3.07 % (31345)Termination phase: Saturation
% 13.05/3.07
% 13.05/3.07 % (31345)Memory used [KB]: 11129
% 13.05/3.07 % (31345)Time elapsed: 0.163 s
% 13.05/3.07 % (31345)Instructions burned: 669 (million)
% 13.05/3.07 % (31345)------------------------------
% 13.05/3.07 % (31345)------------------------------
% 13.05/3.08 % (31351)Instruction limit reached!
% 13.05/3.08 % (31351)------------------------------
% 13.05/3.08 % (31351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.08 % (31351)Termination reason: Unknown
% 13.05/3.08 % (31351)Termination phase: Property scanning
% 13.05/3.08
% 13.05/3.08 % (31351)Memory used [KB]: 2046
% 13.05/3.08 % (31351)Time elapsed: 0.019 s
% 13.05/3.08 % (31351)Instructions burned: 72 (million)
% 13.05/3.08 % (31351)------------------------------
% 13.05/3.08 % (31351)------------------------------
% 13.05/3.08 % (31353)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_30868 for (2984ds/932Mi)
% 13.05/3.09 % (31354)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_30868 for (2984ds/4714Mi)
% 13.54/3.14 % (31352)Instruction limit reached!
% 13.54/3.14 % (31352)------------------------------
% 13.54/3.14 % (31352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.54/3.14 % (31352)Termination reason: Unknown
% 13.54/3.14 % (31352)Termination phase: Saturation
% 13.54/3.14
% 13.54/3.14 % (31352)Memory used [KB]: 7164
% 13.54/3.14 % (31352)Time elapsed: 0.085 s
% 13.54/3.14 % (31352)Instructions burned: 317 (million)
% 13.54/3.14 % (31352)------------------------------
% 13.54/3.14 % (31352)------------------------------
% 13.54/3.15 % (31355)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_30868 for (2983ds/8250Mi)
% 14.15/3.32 % (31353)Instruction limit reached!
% 14.15/3.32 % (31353)------------------------------
% 14.15/3.32 % (31353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.32 % (31353)Termination reason: Unknown
% 14.15/3.32 % (31353)Termination phase: Saturation
% 14.15/3.32
% 14.15/3.32 % (31353)Memory used [KB]: 8187
% 14.15/3.32 % (31353)Time elapsed: 0.238 s
% 14.15/3.32 % (31353)Instructions burned: 934 (million)
% 14.15/3.32 % (31353)------------------------------
% 14.15/3.32 % (31353)------------------------------
% 14.15/3.33 % (31356)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_30868 for (2981ds/770Mi)
% 14.15/3.34 % (31356)Refutation not found, incomplete strategy
% 14.15/3.34 % (31356)------------------------------
% 14.15/3.34 % (31356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.34 % (31356)Termination reason: Refutation not found, incomplete strategy
% 14.15/3.34
% 14.15/3.34
% 14.15/3.34 % (31356)Memory used [KB]: 6780
% 14.15/3.34 % (31356)Time elapsed: 0.014 s
% 14.15/3.34 % (31356)Instructions burned: 43 (million)
% 14.15/3.34 % (31356)------------------------------
% 14.15/3.34 % (31356)------------------------------
% 14.15/3.35 % (31357)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30868 for (2981ds/794Mi)
% 15.02/3.59 % (31357)Instruction limit reached!
% 15.02/3.59 % (31357)------------------------------
% 15.02/3.59 % (31357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.59 % (31357)Termination reason: Unknown
% 15.02/3.59 % (31357)Termination phase: Saturation
% 15.02/3.59
% 15.02/3.59 % (31357)Memory used [KB]: 8187
% 15.02/3.59 % (31357)Time elapsed: 0.245 s
% 15.02/3.59 % (31357)Instructions burned: 795 (million)
% 15.02/3.59 % (31357)------------------------------
% 15.02/3.59 % (31357)------------------------------
% 15.59/3.61 % (31358)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30868 for (2979ds/464Mi)
% 15.59/3.61 % (31350)Instruction limit reached!
% 15.59/3.61 % (31350)------------------------------
% 15.59/3.61 % (31350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.59/3.61 % (31350)Termination reason: Unknown
% 15.59/3.61 % (31350)Termination phase: Saturation
% 15.59/3.61
% 15.59/3.61 % (31350)Memory used [KB]: 13688
% 15.59/3.61 % (31350)Time elapsed: 0.562 s
% 15.59/3.61 % (31350)Instructions burned: 1829 (million)
% 15.59/3.61 % (31350)------------------------------
% 15.59/3.61 % (31350)------------------------------
% 15.59/3.62 % (31359)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_30868 for (2978ds/1376Mi)
% 16.47/3.70 % (31313)Instruction limit reached!
% 16.47/3.70 % (31313)------------------------------
% 16.47/3.70 % (31313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.47/3.70 % (31313)Termination reason: Unknown
% 16.47/3.70 % (31313)Termination phase: Saturation
% 16.47/3.70
% 16.47/3.70 % (31313)Memory used [KB]: 15095
% 16.47/3.70 % (31313)Time elapsed: 1.346 s
% 16.47/3.70 % (31313)Instructions burned: 4437 (million)
% 16.47/3.70 % (31313)------------------------------
% 16.47/3.70 % (31313)------------------------------
% 16.47/3.70 % (31316)Instruction limit reached!
% 16.47/3.70 % (31316)------------------------------
% 16.47/3.70 % (31316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.47/3.70 % (31316)Termination reason: Unknown
% 16.47/3.70 % (31316)Termination phase: Saturation
% 16.47/3.70
% 16.47/3.70 % (31316)Memory used [KB]: 7931
% 16.47/3.70 % (31316)Time elapsed: 1.305 s
% 16.47/3.70 % (31316)Instructions burned: 5208 (million)
% 16.47/3.70 % (31316)------------------------------
% 16.47/3.70 % (31316)------------------------------
% 16.47/3.71 % (31360)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30868 for (2977ds/906Mi)
% 16.47/3.71 % (31361)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_30868 for (2977ds/434Mi)
% 16.47/3.72 % (31318)Instruction limit reached!
% 16.47/3.72 % (31318)------------------------------
% 16.47/3.72 % (31318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.47/3.72 % (31318)Termination reason: Unknown
% 16.47/3.72 % (31318)Termination phase: Saturation
% 16.47/3.72
% 16.47/3.72 % (31318)Memory used [KB]: 18805
% 16.47/3.72 % (31318)Time elapsed: 1.218 s
% 16.47/3.72 % (31318)Instructions burned: 4352 (million)
% 16.47/3.72 % (31318)------------------------------
% 16.47/3.72 % (31318)------------------------------
% 16.47/3.73 % (31358)Instruction limit reached!
% 16.47/3.73 % (31358)------------------------------
% 16.47/3.73 % (31358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.47/3.73 % (31358)Termination reason: Unknown
% 16.47/3.73 % (31358)Termination phase: Saturation
% 16.47/3.73
% 16.47/3.73 % (31358)Memory used [KB]: 11769
% 16.47/3.73 % (31358)Time elapsed: 0.127 s
% 16.47/3.73 % (31358)Instructions burned: 464 (million)
% 16.47/3.73 % (31358)------------------------------
% 16.47/3.73 % (31358)------------------------------
% 16.47/3.73 % (31362)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_30868 for (2977ds/865Mi)
% 16.47/3.74 % (31363)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_30868 for (2977ds/593Mi)
% 16.66/3.83 % (31361)Instruction limit reached!
% 16.66/3.83 % (31361)------------------------------
% 16.66/3.83 % (31361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.83 % (31361)Termination reason: Unknown
% 16.66/3.83 % (31361)Termination phase: Saturation
% 16.66/3.83
% 16.66/3.83 % (31361)Memory used [KB]: 7291
% 16.66/3.83 % (31361)Time elapsed: 0.121 s
% 16.66/3.83 % (31361)Instructions burned: 436 (million)
% 16.66/3.83 % (31361)------------------------------
% 16.66/3.83 % (31361)------------------------------
% 16.66/3.84 % (31364)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_30868 for (2976ds/443Mi)
% 16.66/3.89 % (31363)Instruction limit reached!
% 16.66/3.89 % (31363)------------------------------
% 16.66/3.89 % (31363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.89 % (31363)Termination reason: Unknown
% 16.66/3.89 % (31363)Termination phase: Saturation
% 16.66/3.89
% 16.66/3.89 % (31363)Memory used [KB]: 6908
% 16.66/3.89 % (31363)Time elapsed: 0.151 s
% 16.66/3.89 % (31363)Instructions burned: 593 (million)
% 16.66/3.89 % (31363)------------------------------
% 16.66/3.89 % (31363)------------------------------
% 16.96/3.90 % (31365)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_30868 for (2976ds/594Mi)
% 16.96/3.96 % (31364)Instruction limit reached!
% 16.96/3.96 % (31364)------------------------------
% 16.96/3.96 % (31364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.96 % (31364)Termination reason: Unknown
% 16.96/3.96 % (31364)Termination phase: Saturation
% 16.96/3.96
% 16.96/3.96 % (31364)Memory used [KB]: 11385
% 16.96/3.96 % (31364)Time elapsed: 0.127 s
% 16.96/3.96 % (31364)Instructions burned: 444 (million)
% 16.96/3.96 % (31364)------------------------------
% 16.96/3.96 % (31364)------------------------------
% 16.96/3.96 % (31359)Instruction limit reached!
% 16.96/3.96 % (31359)------------------------------
% 16.96/3.96 % (31359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.96 % (31359)Termination reason: Unknown
% 16.96/3.96 % (31359)Termination phase: Saturation
% 16.96/3.96
% 16.96/3.96 % (31359)Memory used [KB]: 8699
% 16.96/3.96 % (31359)Time elapsed: 0.349 s
% 16.96/3.96 % (31359)Instructions burned: 1377 (million)
% 16.96/3.96 % (31359)------------------------------
% 16.96/3.96 % (31359)------------------------------
% 16.96/3.98 % (31367)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_30868 for (2975ds/5411Mi)
% 16.96/3.98 % (31366)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_30868 for (2975ds/327Mi)
% 16.96/3.98 % (31362)Instruction limit reached!
% 16.96/3.98 % (31362)------------------------------
% 16.96/3.98 % (31362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.98 % (31362)Termination reason: Unknown
% 16.96/3.98 % (31362)Termination phase: Saturation
% 16.96/3.98
% 16.96/3.98 % (31362)Memory used [KB]: 7931
% 16.96/3.98 % (31362)Time elapsed: 0.246 s
% 16.96/3.98 % (31362)Instructions burned: 865 (million)
% 16.96/3.98 % (31362)------------------------------
% 16.96/3.98 % (31362)------------------------------
% 16.96/3.99 % (31368)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_30868 for (2975ds/1762Mi)
% 16.96/3.99 % (31367)Refutation not found, incomplete strategy
% 16.96/3.99 % (31367)------------------------------
% 16.96/3.99 % (31367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.99 % (31367)Termination reason: Refutation not found, incomplete strategy
% 16.96/3.99
% 16.96/3.99
% 16.96/3.99 % (31367)Memory used [KB]: 6780
% 16.96/3.99 % (31367)Time elapsed: 0.015 s
% 16.96/3.99 % (31367)Instructions burned: 44 (million)
% 16.96/3.99 % (31367)------------------------------
% 16.96/3.99 % (31367)------------------------------
% 16.96/3.99 % (31360)Instruction limit reached!
% 16.96/3.99 % (31360)------------------------------
% 16.96/3.99 % (31360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/3.99 % (31360)Termination reason: Unknown
% 16.96/3.99 % (31360)Termination phase: Saturation
% 16.96/3.99
% 16.96/3.99 % (31360)Memory used [KB]: 16630
% 16.96/3.99 % (31360)Time elapsed: 0.284 s
% 16.96/3.99 % (31360)Instructions burned: 907 (million)
% 16.96/3.99 % (31360)------------------------------
% 16.96/3.99 % (31360)------------------------------
% 16.96/4.00 % (31369)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_30868 for (2975ds/96Mi)
% 16.96/4.00 % (31370)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_30868 for (2975ds/503Mi)
% 16.96/4.02 % (31369)Instruction limit reached!
% 16.96/4.02 % (31369)------------------------------
% 16.96/4.02 % (31369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.96/4.02 % (31369)Termination reason: Unknown
% 16.96/4.02 % (31369)Termination phase: Saturation
% 16.96/4.02
% 16.96/4.02 % (31369)Memory used [KB]: 6524
% 16.96/4.02 % (31369)Time elapsed: 0.025 s
% 16.96/4.02 % (31369)Instructions burned: 97 (million)
% 16.96/4.02 % (31369)------------------------------
% 16.96/4.02 % (31369)------------------------------
% 20.06/4.03 % (31371)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_30868 for (2974ds/90Mi)
% 20.06/4.06 % (31371)Instruction limit reached!
% 20.06/4.06 % (31371)------------------------------
% 20.06/4.06 % (31371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.06 % (31371)Termination reason: Unknown
% 20.06/4.06 % (31371)Termination phase: Preprocessing 3
% 20.06/4.06
% 20.06/4.06 % (31371)Memory used [KB]: 4093
% 20.06/4.06 % (31371)Time elapsed: 0.028 s
% 20.06/4.06 % (31371)Instructions burned: 92 (million)
% 20.06/4.06 % (31371)------------------------------
% 20.06/4.06 % (31371)------------------------------
% 20.06/4.07 % (31372)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_30868 for (2974ds/593Mi)
% 20.06/4.07 % (31365)Instruction limit reached!
% 20.06/4.07 % (31365)------------------------------
% 20.06/4.07 % (31365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.07 % (31365)Termination reason: Unknown
% 20.06/4.07 % (31365)Termination phase: Saturation
% 20.06/4.07
% 20.06/4.07 % (31365)Memory used [KB]: 10618
% 20.06/4.07 % (31365)Time elapsed: 0.172 s
% 20.06/4.07 % (31365)Instructions burned: 594 (million)
% 20.06/4.07 % (31365)------------------------------
% 20.06/4.07 % (31365)------------------------------
% 20.06/4.07 % (31366)Instruction limit reached!
% 20.06/4.07 % (31366)------------------------------
% 20.06/4.07 % (31366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.07 % (31366)Termination reason: Unknown
% 20.06/4.07 % (31366)Termination phase: Saturation
% 20.06/4.07
% 20.06/4.07 % (31366)Memory used [KB]: 10618
% 20.06/4.07 % (31366)Time elapsed: 0.101 s
% 20.06/4.07 % (31366)Instructions burned: 327 (million)
% 20.06/4.07 % (31366)------------------------------
% 20.06/4.07 % (31366)------------------------------
% 20.06/4.08 % (31373)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_30868 for (2974ds/1512Mi)
% 20.06/4.08 % (31374)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_30868 for (2974ds/569Mi)
% 20.65/4.14 % (31370)Instruction limit reached!
% 20.65/4.14 % (31370)------------------------------
% 20.65/4.14 % (31370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.14 % (31370)Termination reason: Unknown
% 20.65/4.14 % (31370)Termination phase: Saturation
% 20.65/4.14
% 20.65/4.14 % (31370)Memory used [KB]: 8443
% 20.65/4.14 % (31370)Time elapsed: 0.142 s
% 20.65/4.14 % (31370)Instructions burned: 504 (million)
% 20.65/4.14 % (31370)------------------------------
% 20.65/4.14 % (31370)------------------------------
% 20.65/4.15 % (31375)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_30868 for (2973ds/501Mi)
% 20.65/4.16 % (31373)Refutation not found, incomplete strategy
% 20.65/4.16 % (31373)------------------------------
% 20.65/4.16 % (31373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.16 % (31373)Termination reason: Refutation not found, incomplete strategy
% 20.65/4.16
% 20.65/4.16
% 20.65/4.16 % (31373)Memory used [KB]: 9978
% 20.65/4.16 % (31373)Time elapsed: 0.079 s
% 20.65/4.16 % (31373)Instructions burned: 271 (million)
% 20.65/4.16 % (31373)------------------------------
% 20.65/4.16 % (31373)------------------------------
% 20.65/4.17 % (31376)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_30868 for (2973ds/562Mi)
% 20.98/4.23 % (31374)Instruction limit reached!
% 20.98/4.23 % (31374)------------------------------
% 20.98/4.23 % (31374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.23 % (31374)Termination reason: Unknown
% 20.98/4.23 % (31374)Termination phase: Saturation
% 20.98/4.23
% 20.98/4.23 % (31374)Memory used [KB]: 6652
% 20.98/4.23 % (31374)Time elapsed: 0.143 s
% 20.98/4.23 % (31374)Instructions burned: 572 (million)
% 20.98/4.23 % (31374)------------------------------
% 20.98/4.23 % (31374)------------------------------
% 20.98/4.24 % (31377)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30868 for (2972ds/406Mi)
% 20.98/4.24 % (31372)Instruction limit reached!
% 20.98/4.24 % (31372)------------------------------
% 20.98/4.24 % (31372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.24 % (31372)Termination reason: Unknown
% 20.98/4.24 % (31372)Termination phase: Saturation
% 20.98/4.24
% 20.98/4.24 % (31372)Memory used [KB]: 11385
% 20.98/4.24 % (31372)Time elapsed: 0.174 s
% 20.98/4.24 % (31372)Instructions burned: 593 (million)
% 20.98/4.24 % (31372)------------------------------
% 20.98/4.24 % (31372)------------------------------
% 20.98/4.25 % (31378)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_30868 for (2972ds/582Mi)
% 20.98/4.29 % (31375)Instruction limit reached!
% 20.98/4.29 % (31375)------------------------------
% 20.98/4.29 % (31375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.29 % (31375)Termination reason: Unknown
% 20.98/4.29 % (31375)Termination phase: Saturation
% 20.98/4.29
% 20.98/4.29 % (31375)Memory used [KB]: 11129
% 20.98/4.29 % (31375)Time elapsed: 0.142 s
% 20.98/4.29 % (31375)Instructions burned: 503 (million)
% 20.98/4.29 % (31375)------------------------------
% 20.98/4.29 % (31375)------------------------------
% 21.77/4.30 % (31379)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_30868 for (2972ds/456Mi)
% 21.77/4.31 % (31354)Instruction limit reached!
% 21.77/4.31 % (31354)------------------------------
% 21.77/4.31 % (31354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.77/4.31 % (31354)Termination reason: Unknown
% 21.77/4.31 % (31354)Termination phase: Saturation
% 21.77/4.31
% 21.77/4.31 % (31354)Memory used [KB]: 11641
% 21.77/4.31 % (31354)Time elapsed: 1.222 s
% 21.77/4.31 % (31354)Instructions burned: 4715 (million)
% 21.77/4.31 % (31354)------------------------------
% 21.77/4.31 % (31354)------------------------------
% 21.77/4.31 % (31376)Instruction limit reached!
% 21.77/4.31 % (31376)------------------------------
% 21.77/4.31 % (31376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.77/4.31 % (31376)Termination reason: Unknown
% 21.77/4.31 % (31376)Termination phase: Saturation
% 21.77/4.31
% 21.77/4.31 % (31376)Memory used [KB]: 6780
% 21.77/4.31 % (31376)Time elapsed: 0.139 s
% 21.77/4.31 % (31376)Instructions burned: 563 (million)
% 21.77/4.31 % (31376)------------------------------
% 21.77/4.31 % (31376)------------------------------
% 21.77/4.32 % (31380)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_30868 for (2971ds/393Mi)
% 21.77/4.32 % (31381)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_30868 for (2971ds/1335Mi)
% 21.77/4.36 % (31377)Instruction limit reached!
% 21.77/4.36 % (31377)------------------------------
% 21.77/4.36 % (31377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.77/4.36 % (31377)Termination reason: Unknown
% 21.77/4.36 % (31377)Termination phase: Saturation
% 21.77/4.36
% 21.77/4.36 % (31377)Memory used [KB]: 10234
% 21.77/4.36 % (31377)Time elapsed: 0.121 s
% 21.77/4.36 % (31377)Instructions burned: 406 (million)
% 21.77/4.36 % (31377)------------------------------
% 21.77/4.36 % (31377)------------------------------
% 21.77/4.37 % (31382)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_30868 for (2971ds/3373Mi)
% 22.28/4.42 % (31380)Instruction limit reached!
% 22.28/4.42 % (31380)------------------------------
% 22.28/4.42 % (31380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.42 % (31380)Termination reason: Unknown
% 22.28/4.42 % (31380)Termination phase: Saturation
% 22.28/4.42
% 22.28/4.42 % (31380)Memory used [KB]: 7036
% 22.28/4.42 % (31380)Time elapsed: 0.106 s
% 22.28/4.42 % (31380)Instructions burned: 396 (million)
% 22.28/4.42 % (31380)------------------------------
% 22.28/4.42 % (31380)------------------------------
% 22.28/4.43 % (31378)Instruction limit reached!
% 22.28/4.43 % (31378)------------------------------
% 22.28/4.43 % (31378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.43 % (31378)Termination reason: Unknown
% 22.28/4.43 % (31378)Termination phase: Saturation
% 22.28/4.43
% 22.28/4.43 % (31378)Memory used [KB]: 10106
% 22.28/4.43 % (31378)Time elapsed: 0.178 s
% 22.28/4.43 % (31378)Instructions burned: 583 (million)
% 22.28/4.43 % (31378)------------------------------
% 22.28/4.43 % (31378)------------------------------
% 22.28/4.43 % (31383)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/474Mi)
% 22.28/4.43 % (31368)Instruction limit reached!
% 22.28/4.43 % (31368)------------------------------
% 22.28/4.43 % (31368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.43 % (31368)Termination reason: Unknown
% 22.28/4.43 % (31368)Termination phase: Saturation
% 22.28/4.43
% 22.28/4.43 % (31368)Memory used [KB]: 15351
% 22.28/4.43 % (31368)Time elapsed: 0.448 s
% 22.28/4.43 % (31368)Instructions burned: 1762 (million)
% 22.28/4.43 % (31368)------------------------------
% 22.28/4.43 % (31368)------------------------------
% 22.28/4.44 % (31379)Instruction limit reached!
% 22.28/4.44 % (31379)------------------------------
% 22.28/4.44 % (31379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.44 % (31379)Termination reason: Unknown
% 22.28/4.44 % (31379)Termination phase: Saturation
% 22.28/4.44
% 22.28/4.44 % (31379)Memory used [KB]: 11385
% 22.28/4.44 % (31379)Time elapsed: 0.133 s
% 22.28/4.44 % (31379)Instructions burned: 459 (million)
% 22.28/4.44 % (31379)------------------------------
% 22.28/4.44 % (31379)------------------------------
% 22.28/4.44 % (31384)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/157Mi)
% 22.28/4.44 % (31385)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/590Mi)
% 22.28/4.45 % (31386)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/104Mi)
% 22.28/4.46 % (31381)Refutation not found, non-redundant clauses discarded% (31381)------------------------------
% 22.28/4.46 % (31381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.46 % (31381)Termination reason: Refutation not found, non-redundant clauses discarded
% 22.28/4.46
% 22.28/4.46 % (31381)Memory used [KB]: 7547
% 22.28/4.46 % (31381)Time elapsed: 0.145 s
% 22.28/4.46 % (31381)Instructions burned: 509 (million)
% 22.28/4.46 % (31381)------------------------------
% 22.28/4.46 % (31381)------------------------------
% 22.28/4.47 % (31387)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/414Mi)
% 22.28/4.48 % (31386)Instruction limit reached!
% 22.28/4.48 % (31386)------------------------------
% 22.28/4.48 % (31386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.48 % (31386)Termination reason: Unknown
% 22.28/4.48 % (31386)Termination phase: Property scanning
% 22.28/4.48
% 22.28/4.48 % (31386)Memory used [KB]: 4221
% 22.28/4.48 % (31386)Time elapsed: 0.032 s
% 22.28/4.48 % (31386)Instructions burned: 104 (million)
% 22.28/4.48 % (31386)------------------------------
% 22.28/4.48 % (31386)------------------------------
% 22.28/4.48 % (31384)Instruction limit reached!
% 22.28/4.48 % (31384)------------------------------
% 22.28/4.48 % (31384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.28/4.48 % (31384)Termination reason: Unknown
% 22.28/4.48 % (31384)Termination phase: Saturation
% 22.28/4.48
% 22.28/4.48 % (31384)Memory used [KB]: 6652
% 22.28/4.48 % (31384)Time elapsed: 0.042 s
% 22.28/4.48 % (31384)Instructions burned: 158 (million)
% 22.28/4.48 % (31384)------------------------------
% 22.28/4.48 % (31384)------------------------------
% 22.28/4.49 % (31388)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/715Mi)
% 22.28/4.49 % (31389)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_30868 for (2970ds/961Mi)
% 23.11/4.56 % (31383)Instruction limit reached!
% 23.11/4.56 % (31383)------------------------------
% 23.11/4.56 % (31383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.56 % (31383)Termination reason: Unknown
% 23.11/4.56 % (31383)Termination phase: Saturation
% 23.11/4.56
% 23.11/4.56 % (31383)Memory used [KB]: 7419
% 23.11/4.56 % (31383)Time elapsed: 0.126 s
% 23.11/4.56 % (31383)Instructions burned: 476 (million)
% 23.11/4.56 % (31383)------------------------------
% 23.11/4.56 % (31383)------------------------------
% 23.11/4.57 % (31390)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_30868 for (2969ds/1213Mi)
% 23.11/4.58 % (31387)Instruction limit reached!
% 23.11/4.58 % (31387)------------------------------
% 23.11/4.58 % (31387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.11/4.58 % (31387)Termination reason: Unknown
% 23.11/4.58 % (31387)Termination phase: Saturation
% 23.11/4.58
% 23.11/4.58 % (31387)Memory used [KB]: 6652
% 23.11/4.58 % (31387)Time elapsed: 0.106 s
% 23.11/4.58 % (31387)Instructions burned: 417 (million)
% 23.11/4.58 % (31387)------------------------------
% 23.11/4.58 % (31387)------------------------------
% 23.11/4.59 % (31391)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_30868 for (2969ds/1979Mi)
% 23.46/4.61 % (31385)Instruction limit reached!
% 23.46/4.61 % (31385)------------------------------
% 23.46/4.61 % (31385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.46/4.61 % (31385)Termination reason: Unknown
% 23.46/4.61 % (31385)Termination phase: Saturation
% 23.46/4.61
% 23.46/4.61 % (31385)Memory used [KB]: 9978
% 23.46/4.61 % (31385)Time elapsed: 0.164 s
% 23.46/4.61 % (31385)Instructions burned: 591 (million)
% 23.46/4.61 % (31385)------------------------------
% 23.46/4.61 % (31385)------------------------------
% 23.46/4.62 % (31392)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_30868 for (2968ds/481Mi)
% 23.46/4.69 % (31388)Instruction limit reached!
% 23.46/4.69 % (31388)------------------------------
% 23.46/4.69 % (31388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.46/4.69 % (31388)Termination reason: Unknown
% 23.46/4.69 % (31388)Termination phase: Saturation
% 23.46/4.69
% 23.46/4.69 % (31388)Memory used [KB]: 6396
% 23.46/4.70 % (31388)Time elapsed: 0.210 s
% 23.46/4.70 % (31388)Instructions burned: 717 (million)
% 23.46/4.70 % (31388)------------------------------
% 23.46/4.70 % (31388)------------------------------
% 23.96/4.71 % (31423)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_30868 for (2968ds/783Mi)
% 23.96/4.74 % (31392)Instruction limit reached!
% 23.96/4.74 % (31392)------------------------------
% 23.96/4.74 % (31392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.96/4.74 % (31392)Termination reason: Unknown
% 23.96/4.74 % (31392)Termination phase: Saturation
% 23.96/4.74
% 23.96/4.74 % (31392)Memory used [KB]: 7419
% 23.96/4.74 % (31392)Time elapsed: 0.120 s
% 23.96/4.74 % (31392)Instructions burned: 481 (million)
% 23.96/4.74 % (31392)------------------------------
% 23.96/4.74 % (31392)------------------------------
% 23.96/4.75 % (31424)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_30868 for (2967ds/432Mi)
% 23.96/4.77 % (31389)Instruction limit reached!
% 23.96/4.77 % (31389)------------------------------
% 23.96/4.77 % (31389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.96/4.77 % (31389)Termination reason: Unknown
% 23.96/4.77 % (31389)Termination phase: Saturation
% 23.96/4.77
% 23.96/4.77 % (31389)Memory used [KB]: 12920
% 23.96/4.77 % (31389)Time elapsed: 0.284 s
% 23.96/4.77 % (31389)Instructions burned: 963 (million)
% 23.96/4.77 % (31389)------------------------------
% 23.96/4.77 % (31389)------------------------------
% 23.96/4.78 % (31425)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_30868 for (2967ds/1670Mi)
% 24.48/4.87 % (31424)Instruction limit reached!
% 24.48/4.87 % (31424)------------------------------
% 24.48/4.87 % (31424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.48/4.87 % (31424)Termination reason: Unknown
% 24.48/4.87 % (31424)Termination phase: Saturation
% 24.48/4.87
% 24.48/4.87 % (31424)Memory used [KB]: 8187
% 24.48/4.87 % (31424)Time elapsed: 0.123 s
% 24.48/4.87 % (31424)Instructions burned: 433 (million)
% 24.48/4.87 % (31424)------------------------------
% 24.48/4.87 % (31424)------------------------------
% 24.48/4.88 % (31426)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_30868 for (2966ds/90Mi)
% 24.71/4.90 % (31426)Instruction limit reached!
% 24.71/4.90 % (31426)------------------------------
% 24.71/4.90 % (31426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.90 % (31426)Termination reason: Unknown
% 24.71/4.90 % (31426)Termination phase: Preprocessing 3
% 24.71/4.90
% 24.71/4.90 % (31426)Memory used [KB]: 3965
% 24.71/4.90 % (31426)Time elapsed: 0.027 s
% 24.71/4.90 % (31426)Instructions burned: 90 (million)
% 24.71/4.90 % (31426)------------------------------
% 24.71/4.90 % (31426)------------------------------
% 24.71/4.91 % (31427)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_30868 for (2966ds/346Mi)
% 24.71/4.93 % (31423)Instruction limit reached!
% 24.71/4.93 % (31423)------------------------------
% 24.71/4.93 % (31423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.93 % (31423)Termination reason: Unknown
% 24.71/4.93 % (31423)Termination phase: Saturation
% 24.71/4.93
% 24.71/4.93 % (31423)Memory used [KB]: 8827
% 24.71/4.93 % (31423)Time elapsed: 0.228 s
% 24.71/4.93 % (31423)Instructions burned: 784 (million)
% 24.71/4.93 % (31423)------------------------------
% 24.71/4.93 % (31423)------------------------------
% 24.71/4.93 % (31390)Instruction limit reached!
% 24.71/4.93 % (31390)------------------------------
% 24.71/4.93 % (31390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.93 % (31390)Termination reason: Unknown
% 24.71/4.93 % (31390)Termination phase: Saturation
% 24.71/4.93
% 24.71/4.93 % (31390)Memory used [KB]: 12153
% 24.71/4.93 % (31390)Time elapsed: 0.370 s
% 24.71/4.93 % (31390)Instructions burned: 1213 (million)
% 24.71/4.93 % (31390)------------------------------
% 24.71/4.93 % (31390)------------------------------
% 24.71/4.94 % (31428)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_30868 for (2965ds/401Mi)
% 24.71/4.94 % (31429)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_30868 for (2965ds/6454Mi)
% 24.71/5.00 % (31427)Instruction limit reached!
% 24.71/5.00 % (31427)------------------------------
% 24.71/5.00 % (31427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/5.00 % (31427)Termination reason: Unknown
% 24.71/5.00 % (31427)Termination phase: Saturation
% 24.71/5.00
% 24.71/5.00 % (31427)Memory used [KB]: 7419
% 24.71/5.00 % (31427)Time elapsed: 0.091 s
% 24.71/5.00 % (31427)Instructions burned: 348 (million)
% 24.71/5.00 % (31427)------------------------------
% 24.71/5.00 % (31427)------------------------------
% 24.71/5.01 % (31430)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_30868 for (2965ds/283Mi)
% 27.08/5.04 % (31428)Instruction limit reached!
% 27.08/5.04 % (31428)------------------------------
% 27.08/5.04 % (31428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.08/5.04 % (31428)Termination reason: Unknown
% 27.08/5.04 % (31428)Termination phase: Saturation
% 27.08/5.04
% 27.08/5.04 % (31428)Memory used [KB]: 6652
% 27.08/5.04 % (31428)Time elapsed: 0.099 s
% 27.08/5.04 % (31428)Instructions burned: 403 (million)
% 27.08/5.04 % (31428)------------------------------
% 27.08/5.04 % (31428)------------------------------
% 27.08/5.05 % (31431)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_30868 for (2964ds/865Mi)
% 27.08/5.09 % (31430)Instruction limit reached!
% 27.08/5.09 % (31430)------------------------------
% 27.08/5.09 % (31430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.08/5.09 % (31430)Termination reason: Unknown
% 27.08/5.09 % (31430)Termination phase: Saturation
% 27.08/5.09
% 27.08/5.09 % (31430)Memory used [KB]: 9210
% 27.08/5.09 % (31430)Time elapsed: 0.077 s
% 27.08/5.09 % (31430)Instructions burned: 285 (million)
% 27.08/5.09 % (31430)------------------------------
% 27.08/5.09 % (31430)------------------------------
% 27.08/5.10 % (31432)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_30868 for (2964ds/4528Mi)
% 27.08/5.11 % (31432)Refutation not found, incomplete strategy
% 27.08/5.11 % (31432)------------------------------
% 27.08/5.11 % (31432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.08/5.11 % (31432)Termination reason: Refutation not found, incomplete strategy
% 27.08/5.11
% 27.08/5.11
% 27.08/5.11 % (31432)Memory used [KB]: 2174
% 27.08/5.11 % (31432)Time elapsed: 0.013 s
% 27.08/5.11 % (31432)Instructions burned: 41 (million)
% 27.08/5.11 % (31432)------------------------------
% 27.08/5.11 % (31432)------------------------------
% 27.08/5.12 % (31433)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_30868 for (2964ds/1001Mi)
% 27.73/5.15 % (31431)Refutation not found, incomplete strategy
% 27.73/5.15 % (31431)------------------------------
% 27.73/5.15 % (31431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.73/5.15 % (31431)Termination reason: Refutation not found, incomplete strategy
% 27.73/5.15
% 27.73/5.15
% 27.73/5.15 % (31431)Memory used [KB]: 10746
% 27.73/5.15 % (31431)Time elapsed: 0.105 s
% 27.73/5.15 % (31431)Instructions burned: 358 (million)
% 27.73/5.15 % (31431)------------------------------
% 27.73/5.15 % (31431)------------------------------
% 27.73/5.16 % (31434)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_30868 for (2963ds/102Mi)
% 27.73/5.19 % (31434)Instruction limit reached!
% 27.73/5.19 % (31434)------------------------------
% 27.73/5.19 % (31434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.73/5.19 % (31434)Termination reason: Unknown
% 27.73/5.19 % (31434)Termination phase: Saturation
% 27.73/5.19
% 27.73/5.19 % (31434)Memory used [KB]: 6524
% 27.73/5.19 % (31434)Time elapsed: 0.028 s
% 27.73/5.19 % (31434)Instructions burned: 103 (million)
% 27.73/5.19 % (31434)------------------------------
% 27.73/5.19 % (31434)------------------------------
% 27.73/5.19 % (31391)Instruction limit reached!
% 27.73/5.19 % (31391)------------------------------
% 27.73/5.19 % (31391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.73/5.19 % (31391)Termination reason: Unknown
% 27.73/5.19 % (31391)Termination phase: Saturation
% 27.73/5.19
% 27.73/5.19 % (31391)Memory used [KB]: 12665
% 27.73/5.19 % (31391)Time elapsed: 0.609 s
% 27.73/5.19 % (31391)Instructions burned: 1979 (million)
% 27.73/5.19 % (31391)------------------------------
% 27.73/5.19 % (31391)------------------------------
% 27.73/5.19 % (31425)Instruction limit reached!
% 27.73/5.19 % (31425)------------------------------
% 27.73/5.19 % (31425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.73/5.19 % (31425)Termination reason: Unknown
% 27.73/5.19 % (31425)Termination phase: Saturation
% 27.73/5.19
% 27.73/5.19 % (31425)Memory used [KB]: 6652
% 27.73/5.19 % (31425)Time elapsed: 0.413 s
% 27.73/5.19 % (31425)Instructions burned: 1673 (million)
% 27.73/5.19 % (31425)------------------------------
% 27.73/5.19 % (31425)------------------------------
% 28.26/5.20 % (31435)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_30868 for (2963ds/952Mi)
% 28.26/5.20 % (31436)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_30868 for (2963ds/578Mi)
% 28.26/5.20 % (31437)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_30868 for (2963ds/643Mi)
% 28.57/5.35 % (31436)Instruction limit reached!
% 28.57/5.35 % (31436)------------------------------
% 28.57/5.35 % (31436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.57/5.35 % (31436)Termination reason: Unknown
% 28.57/5.35 % (31436)Termination phase: Saturation
% 28.57/5.35
% 28.57/5.35 % (31436)Memory used [KB]: 7675
% 28.57/5.35 % (31436)Time elapsed: 0.171 s
% 28.57/5.35 % (31436)Instructions burned: 580 (million)
% 28.57/5.35 % (31436)------------------------------
% 28.57/5.35 % (31436)------------------------------
% 28.57/5.36 % (31437)Instruction limit reached!
% 28.57/5.36 % (31437)------------------------------
% 28.57/5.36 % (31437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.57/5.36 % (31437)Termination reason: Unknown
% 28.57/5.36 % (31437)Termination phase: Saturation
% 28.57/5.36
% 28.57/5.36 % (31437)Memory used [KB]: 6652
% 28.57/5.36 % (31437)Time elapsed: 0.154 s
% 28.57/5.36 % (31437)Instructions burned: 646 (million)
% 28.57/5.36 % (31437)------------------------------
% 28.57/5.36 % (31437)------------------------------
% 28.57/5.36 % (31438)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_30868 for (2961ds/865Mi)
% 28.57/5.37 % (31439)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_30868 for (2961ds/1174Mi)
% 28.57/5.38 % (31382)Instruction limit reached!
% 28.57/5.38 % (31382)------------------------------
% 28.57/5.38 % (31382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.57/5.38 % (31382)Termination reason: Unknown
% 28.57/5.38 % (31382)Termination phase: Saturation
% 28.57/5.38
% 28.57/5.38 % (31382)Memory used [KB]: 15223
% 28.57/5.38 % (31382)Time elapsed: 1.019 s
% 28.57/5.38 % (31382)Instructions burned: 3376 (million)
% 28.57/5.38 % (31382)------------------------------
% 28.57/5.38 % (31382)------------------------------
% 28.57/5.39 % (31440)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_30868 for (2961ds/644Mi)
% 29.19/5.41 % (31433)Instruction limit reached!
% 29.19/5.41 % (31433)------------------------------
% 29.19/5.41 % (31433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/5.41 % (31433)Termination reason: Unknown
% 29.19/5.41 % (31433)Termination phase: Saturation
% 29.19/5.41
% 29.19/5.41 % (31433)Memory used [KB]: 15991
% 29.19/5.41 % (31433)Time elapsed: 0.314 s
% 29.19/5.41 % (31433)Instructions burned: 1003 (million)
% 29.19/5.41 % (31433)------------------------------
% 29.19/5.41 % (31433)------------------------------
% 29.19/5.42 % (31441)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_30868 for (2960ds/1201Mi)
% 29.19/5.48 % (31435)Instruction limit reached!
% 29.19/5.48 % (31435)------------------------------
% 29.19/5.48 % (31435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/5.48 % (31435)Termination reason: Unknown
% 29.19/5.48 % (31435)Termination phase: Saturation
% 29.19/5.48
% 29.19/5.48 % (31435)Memory used [KB]: 12153
% 29.19/5.48 % (31435)Time elapsed: 0.278 s
% 29.19/5.48 % (31435)Instructions burned: 952 (million)
% 29.19/5.48 % (31435)------------------------------
% 29.19/5.48 % (31435)------------------------------
% 29.19/5.49 % (31442)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_30868 for (2960ds/1046Mi)
% 29.19/5.49 % (31440)Refutation not found, incomplete strategy
% 29.19/5.49 % (31440)------------------------------
% 29.19/5.49 % (31440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/5.49 % (31440)Termination reason: Refutation not found, incomplete strategy
% 29.19/5.49
% 29.19/5.49
% 29.19/5.49 % (31440)Memory used [KB]: 11257
% 29.19/5.49 % (31440)Time elapsed: 0.097 s
% 29.19/5.49 % (31440)Instructions burned: 332 (million)
% 29.19/5.49 % (31440)------------------------------
% 29.19/5.49 % (31440)------------------------------
% 30.08/5.50 % (31443)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_30868 for (2960ds/222Mi)
% 30.08/5.56 % (31443)Instruction limit reached!
% 30.08/5.56 % (31443)------------------------------
% 30.08/5.56 % (31443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.08/5.56 % (31443)Termination reason: Unknown
% 30.08/5.56 % (31443)Termination phase: Saturation
% 30.08/5.56
% 30.08/5.56 % (31443)Memory used [KB]: 6908
% 30.08/5.56 % (31443)Time elapsed: 0.060 s
% 30.08/5.56 % (31443)Instructions burned: 223 (million)
% 30.08/5.56 % (31443)------------------------------
% 30.08/5.56 % (31443)------------------------------
% 30.08/5.57 % (31444)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_30868 for (2959ds/68Mi)
% 30.08/5.59 % (31444)Instruction limit reached!
% 30.08/5.59 % (31444)------------------------------
% 30.08/5.59 % (31444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.08/5.59 % (31444)Termination reason: Unknown
% 30.08/5.59 % (31444)Termination phase: Preprocessing 3
% 30.08/5.59
% 30.08/5.59 % (31444)Memory used [KB]: 3070
% 30.08/5.59 % (31444)Time elapsed: 0.021 s
% 30.08/5.59 % (31444)Instructions burned: 69 (million)
% 30.08/5.59 % (31444)------------------------------
% 30.08/5.59 % (31444)------------------------------
% 30.39/5.60 % (31445)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_30868 for (2959ds/454Mi)
% 30.39/5.62 % (31355)Instruction limit reached!
% 30.39/5.62 % (31355)------------------------------
% 30.39/5.62 % (31355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.39/5.62 % (31355)Termination reason: Unknown
% 30.39/5.62 % (31355)Termination phase: Saturation
% 30.39/5.62
% 30.39/5.62 % (31355)Memory used [KB]: 19957
% 30.39/5.62 % (31355)Time elapsed: 2.469 s
% 30.39/5.62 % (31355)Instructions burned: 8251 (million)
% 30.39/5.62 % (31355)------------------------------
% 30.39/5.62 % (31355)------------------------------
% 30.39/5.62 % (31438)Instruction limit reached!
% 30.39/5.62 % (31438)------------------------------
% 30.39/5.62 % (31438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.39/5.62 % (31438)Termination reason: Unknown
% 30.39/5.62 % (31438)Termination phase: Saturation
% 30.39/5.62
% 30.39/5.62 % (31438)Memory used [KB]: 11769
% 30.39/5.62 % (31438)Time elapsed: 0.261 s
% 30.39/5.62 % (31438)Instructions burned: 865 (million)
% 30.39/5.62 % (31438)------------------------------
% 30.39/5.62 % (31438)------------------------------
% 30.39/5.63 % (31446)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_30868 for (2958ds/360Mi)
% 30.39/5.63 % (31447)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_30868 for (2958ds/157Mi)
% 30.39/5.67 % (31447)Instruction limit reached!
% 30.39/5.67 % (31447)------------------------------
% 30.39/5.67 % (31447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.39/5.67 % (31447)Termination reason: Unknown
% 30.39/5.67 % (31447)Termination phase: Saturation
% 30.39/5.67
% 30.39/5.67 % (31447)Memory used [KB]: 6524
% 30.39/5.67 % (31447)Time elapsed: 0.041 s
% 30.39/5.67 % (31447)Instructions burned: 161 (million)
% 30.39/5.67 % (31447)------------------------------
% 30.39/5.67 % (31447)------------------------------
% 30.39/5.68 % (31448)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_30868 for (2958ds/5061Mi)
% 30.84/5.71 % (31445)Instruction limit reached!
% 30.84/5.71 % (31445)------------------------------
% 30.84/5.71 % (31445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.84/5.71 % (31445)Termination reason: Unknown
% 30.84/5.71 % (31445)Termination phase: Saturation
% 30.84/5.71
% 30.84/5.71 % (31445)Memory used [KB]: 11129
% 30.84/5.71 % (31445)Time elapsed: 0.113 s
% 30.84/5.71 % (31445)Instructions burned: 457 (million)
% 30.84/5.71 % (31445)------------------------------
% 30.84/5.71 % (31445)------------------------------
% 30.84/5.72 % (31439)Instruction limit reached!
% 30.84/5.72 % (31439)------------------------------
% 30.84/5.72 % (31439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.84/5.72 % (31439)Termination reason: Unknown
% 30.84/5.72 % (31439)Termination phase: Saturation
% 30.84/5.72
% 30.84/5.72 % (31439)Memory used [KB]: 13304
% 30.84/5.72 % (31439)Time elapsed: 0.372 s
% 30.84/5.72 % (31439)Instructions burned: 1175 (million)
% 30.84/5.72 % (31439)------------------------------
% 30.84/5.72 % (31439)------------------------------
% 30.84/5.72 % (31449)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_30868 for (2957ds/2401Mi)
% 30.84/5.72 % (31446)Instruction limit reached!
% 30.84/5.72 % (31446)------------------------------
% 30.84/5.72 % (31446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.84/5.72 % (31446)Termination reason: Unknown
% 30.84/5.72 % (31446)Termination phase: Saturation
% 30.84/5.72
% 30.84/5.72 % (31446)Memory used [KB]: 6908
% 30.84/5.72 % (31446)Time elapsed: 0.094 s
% 30.84/5.72 % (31446)Instructions burned: 361 (million)
% 30.84/5.72 % (31446)------------------------------
% 30.84/5.72 % (31446)------------------------------
% 30.84/5.73 % (31450)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_30868 for (2957ds/5798Mi)
% 30.84/5.73 % (31451)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_30868 for (2957ds/346Mi)
% 30.84/5.75 % (31442)Instruction limit reached!
% 30.84/5.75 % (31442)------------------------------
% 30.84/5.75 % (31442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.84/5.75 % (31442)Termination reason: Unknown
% 30.84/5.75 % (31442)Termination phase: Saturation
% 30.84/5.75
% 30.84/5.75 % (31442)Memory used [KB]: 6908
% 30.84/5.75 % (31442)Time elapsed: 0.261 s
% 30.84/5.75 % (31442)Instructions burned: 1047 (million)
% 30.84/5.75 % (31442)------------------------------
% 30.84/5.75 % (31442)------------------------------
% 30.84/5.76 % (31452)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_30868 for (2957ds/1321Mi)
% 30.84/5.79 % (31441)Instruction limit reached!
% 30.84/5.79 % (31441)------------------------------
% 30.84/5.79 % (31441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.84/5.79 % (31441)Termination reason: Unknown
% 30.84/5.79 % (31441)Termination phase: Saturation
% 30.84/5.79
% 30.84/5.79 % (31441)Memory used [KB]: 12025
% 30.84/5.79 % (31441)Time elapsed: 0.365 s
% 30.84/5.79 % (31441)Instructions burned: 1202 (million)
% 30.84/5.79 % (31441)------------------------------
% 30.84/5.79 % (31441)------------------------------
% 32.17/5.80 % (31453)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_30868 for (2957ds/1312Mi)
% 32.17/5.82 % (31451)Instruction limit reached!
% 32.17/5.82 % (31451)------------------------------
% 32.17/5.82 % (31451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.17/5.82 % (31451)Termination reason: Unknown
% 32.17/5.82 % (31451)Termination phase: Saturation
% 32.17/5.82
% 32.17/5.82 % (31451)Memory used [KB]: 7419
% 32.17/5.82 % (31451)Time elapsed: 0.087 s
% 32.17/5.82 % (31451)Instructions burned: 346 (million)
% 32.17/5.82 % (31451)------------------------------
% 32.17/5.82 % (31451)------------------------------
% 32.17/5.83 % (31454)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_30868 for (2956ds/672Mi)
% 32.37/5.90 % (31429)First to succeed.
% 32.37/5.95 % (31429)Refutation found. Thanks to Tanya!
% 32.37/5.95 % SZS status Theorem for DTF2THF_30868
% 32.37/5.95 % SZS output start Proof for DTF2THF_30868
% 32.37/5.95 thf(type_def_5, type, term: $tType).
% 32.37/5.95 thf(type_def_7, type, subst: $tType).
% 32.37/5.95 thf(type_def_8, type, d_term: $tType).
% 32.37/5.95 thf(type_def_9, type, d_subst: $tType).
% 32.37/5.95 thf(func_def_0, type, term: $tType).
% 32.37/5.95 thf(func_def_1, type, subst: $tType).
% 32.37/5.95 thf(func_def_2, type, one: term).
% 32.37/5.95 thf(func_def_3, type, ap: term > term > term).
% 32.37/5.95 thf(func_def_4, type, lam: term > term).
% 32.37/5.95 thf(func_def_5, type, sub: term > subst > term).
% 32.37/5.95 thf(func_def_6, type, id: subst).
% 32.37/5.95 thf(func_def_7, type, sh: subst).
% 32.37/5.95 thf(func_def_8, type, push: term > subst > subst).
% 32.37/5.95 thf(func_def_9, type, comp: subst > subst > subst).
% 32.37/5.95 thf(func_def_10, type, var: term > $o).
% 32.37/5.95 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 32.37/5.95 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 32.37/5.95 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 32.37/5.95 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 32.37/5.95 thf(func_def_124, type, d_term: $tType).
% 32.37/5.95 thf(func_def_125, type, d_subst: $tType).
% 32.37/5.95 thf(func_def_126, type, d2term: d_term > term).
% 32.37/5.95 thf(func_def_127, type, d2subst: d_subst > subst).
% 32.37/5.95 thf(func_def_128, type, d_one: d_term).
% 32.37/5.95 thf(func_def_129, type, d_id: d_subst).
% 32.37/5.95 thf(func_def_142, type, sP0: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_143, type, sP1: (term > $o) > $o).
% 32.37/5.95 thf(func_def_147, type, sP5: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_148, type, sP6: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_149, type, sP7: (term > $o) > $o).
% 32.37/5.95 thf(func_def_150, type, sP8: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_151, type, sP9: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_156, type, sP14: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_157, type, sP15: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_158, type, sP16: (term > $o) > $o).
% 32.37/5.95 thf(func_def_162, type, sP20: (term > $o) > $o).
% 32.37/5.95 thf(func_def_163, type, sP21: (term > $o) > $o).
% 32.37/5.95 thf(func_def_167, type, sP25: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_170, type, sP28: (term > $o) > $o).
% 32.37/5.95 thf(func_def_174, type, sP32: (term > $o) > $o).
% 32.37/5.95 thf(func_def_176, type, sP34: (term > $o) > $o).
% 32.37/5.95 thf(func_def_177, type, sP35: (term > $o) > $o).
% 32.37/5.95 thf(func_def_180, type, sP38: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_182, type, sP40: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_184, type, sP42: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_185, type, sP43: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_187, type, sP45: (term > $o) > $o).
% 32.37/5.95 thf(func_def_190, type, sP48: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_192, type, sP50: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_195, type, sP53: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_196, type, sP54: (subst > term > subst > $o) > $o).
% 32.37/5.95 thf(func_def_201, type, sK59: term > $o).
% 32.37/5.95 thf(func_def_202, type, sK60: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_203, type, sK61: term).
% 32.37/5.95 thf(func_def_204, type, sK62: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_205, type, sK63: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_206, type, sK64: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_207, type, sK65: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_208, type, sK66: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_209, type, sK67: term > (term > $o) > term).
% 32.37/5.95 thf(func_def_210, type, sK68: (subst > term > subst > $o) > (term > $o) > term).
% 32.37/5.95 thf(func_def_211, type, sK69: term).
% 32.37/5.95 thf(func_def_212, type, sK70: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_213, type, sK71: term > $o).
% 32.37/5.95 thf(func_def_214, type, sK72: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_215, type, sK73: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_216, type, sK74: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_217, type, sK75: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_218, type, sK76: term > subst > term > term).
% 32.37/5.95 thf(func_def_219, type, sK77: (term > $o) > term > term).
% 32.37/5.95 thf(func_def_220, type, sK78: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_221, type, sK79: (term > $o) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_222, type, sK80: term).
% 32.37/5.95 thf(func_def_223, type, sK81: term).
% 32.37/5.95 thf(func_def_224, type, sK82: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_225, type, sK83: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_226, type, sK84: term).
% 32.37/5.95 thf(func_def_227, type, sK85: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_228, type, sK86: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_229, type, sK87: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_230, type, sK88: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_231, type, sK89: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_232, type, sK90: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_233, type, sK91: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_234, type, sK92: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_235, type, sK93: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_236, type, sK94: (subst > term > subst > $o) > term > term).
% 32.37/5.95 thf(func_def_237, type, sK95: term).
% 32.37/5.95 thf(func_def_238, type, sK96: (subst > term > subst > $o) > term > term).
% 32.37/5.95 thf(func_def_239, type, sK97: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_240, type, sK98: term).
% 32.37/5.95 thf(func_def_241, type, sK99: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_242, type, sK100: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_243, type, sK101: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_244, type, sK102: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_245, type, sK103: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_246, type, sK104: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_247, type, sK105: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_248, type, sK106: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_249, type, sK107: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_250, type, sK108: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_251, type, sK109: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_252, type, sK110: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_253, type, sK111: term).
% 32.37/5.95 thf(func_def_254, type, sK112: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_255, type, sK113: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_256, type, sK114: term > (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_257, type, sK115: term > (subst > term > term) > term).
% 32.37/5.95 thf(func_def_258, type, sK116: term > (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_259, type, sK117: term > (subst > term > term) > term).
% 32.37/5.95 thf(func_def_260, type, sK118: term > (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_261, type, sK119: term > (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_262, type, sK120: (subst > term > subst > $o) > term > term).
% 32.37/5.95 thf(func_def_263, type, sK121: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_264, type, sK122: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_265, type, sK123: term).
% 32.37/5.95 thf(func_def_266, type, sK124: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_267, type, sK125: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_268, type, sK126: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_269, type, sK127: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_270, type, sK128: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_271, type, sK129: (subst > term > subst > $o) > term > term).
% 32.37/5.95 thf(func_def_272, type, sK130: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_273, type, sK131: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_274, type, sK132: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_275, type, sK133: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_276, type, sK134: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_277, type, sK135: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_278, type, sK136: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_279, type, sK137: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_280, type, sK138: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_281, type, sK139: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_282, type, sK140: term).
% 32.37/5.95 thf(func_def_283, type, sK141: term > $o).
% 32.37/5.95 thf(func_def_284, type, sK142: term).
% 32.37/5.95 thf(func_def_285, type, sK143: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_286, type, sK144: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_287, type, sK145: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_288, type, sK146: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_289, type, sK147: (term > $o) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_290, type, sK148: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_291, type, sK149: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_292, type, sK150: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_293, type, sK151: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_294, type, sK152: (term > $o) > term > term).
% 32.37/5.95 thf(func_def_295, type, sK153: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_296, type, sK154: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_297, type, sK155: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_298, type, sK156: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_299, type, sK157: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_300, type, sK158: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_301, type, sK159: term).
% 32.37/5.95 thf(func_def_302, type, sK160: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_303, type, sK161: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_304, type, sK162: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_305, type, sK163: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_306, type, sK164: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_307, type, sK165: term > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_308, type, sK166: term).
% 32.37/5.95 thf(func_def_309, type, sK167: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_310, type, sK168: (subst > term > subst > $o) > term > term).
% 32.37/5.95 thf(func_def_311, type, sK169: term).
% 32.37/5.95 thf(func_def_312, type, sK170: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_313, type, sK171: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_314, type, sK172: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_315, type, sK173: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_316, type, sK174: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_317, type, sK175: (term > $o) > term).
% 32.37/5.95 thf(func_def_318, type, sK176: (term > $o) > term).
% 32.37/5.95 thf(func_def_319, type, sK177: term).
% 32.37/5.95 thf(func_def_320, type, sK178: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_321, type, sK179: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_322, type, sK180: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_323, type, sK181: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_324, type, sK182: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_325, type, sK183: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_326, type, sK184: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_327, type, sK185: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_328, type, sK186: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_329, type, sK187: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_330, type, sK188: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_331, type, sK189: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_332, type, sK190: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_333, type, sK191: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_334, type, sK192: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_335, type, sK193: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_336, type, sK194: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_337, type, sK195: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_338, type, sK196: term).
% 32.37/5.95 thf(func_def_339, type, sK197: term).
% 32.37/5.95 thf(func_def_340, type, sK198: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_341, type, sK199: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_342, type, sK200: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_343, type, sK201: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_344, type, sK202: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_345, type, sK203: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_346, type, sK204: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_347, type, sK205: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_348, type, sK206: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_349, type, sK207: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_350, type, sK208: term).
% 32.37/5.95 thf(func_def_351, type, sK209: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_352, type, sK210: term).
% 32.37/5.95 thf(func_def_353, type, sK211: term > $o).
% 32.37/5.95 thf(func_def_354, type, sK212: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_355, type, sK213: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_356, type, sK214: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_357, type, sK215: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_358, type, sK216: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_359, type, sK217: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_360, type, sK218: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_361, type, sK219: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_362, type, sK220: (term > $o) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_363, type, sK221: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_364, type, sK222: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_365, type, sK223: (term > $o) > term).
% 32.37/5.95 thf(func_def_366, type, sK224: (term > $o) > term).
% 32.37/5.95 thf(func_def_367, type, sK225: term > $o).
% 32.37/5.95 thf(func_def_368, type, sK226: term).
% 32.37/5.95 thf(func_def_369, type, sK227: subst).
% 32.37/5.95 thf(func_def_370, type, sK228: term).
% 32.37/5.95 thf(func_def_371, type, sK229: subst).
% 32.37/5.95 thf(func_def_372, type, sK230: term).
% 32.37/5.95 thf(func_def_373, type, sK231: subst).
% 32.37/5.95 thf(func_def_374, type, sK232: subst).
% 32.37/5.95 thf(func_def_375, type, sK233: term).
% 32.37/5.95 thf(func_def_376, type, sK234: term > $o).
% 32.37/5.95 thf(func_def_377, type, sK235: term > term).
% 32.37/5.95 thf(func_def_378, type, sK236: (term > $o) > subst > term).
% 32.37/5.95 thf(func_def_379, type, sK237: (term > $o) > term).
% 32.37/5.95 thf(func_def_380, type, sK238: (term > $o) > term).
% 32.37/5.95 thf(func_def_381, type, sK239: (term > $o) > term).
% 32.37/5.95 thf(func_def_382, type, sK240: (term > $o) > term).
% 32.37/5.95 thf(func_def_383, type, sK241: (term > $o) > term).
% 32.37/5.95 thf(func_def_384, type, sK242: term).
% 32.37/5.95 thf(func_def_385, type, sK243: subst).
% 32.37/5.95 thf(func_def_386, type, sK244: term > $o).
% 32.37/5.95 thf(func_def_387, type, sK245: term > term).
% 32.37/5.95 thf(func_def_388, type, sK246: (term > $o) > subst > term).
% 32.37/5.95 thf(func_def_389, type, sK247: (term > $o) > term).
% 32.37/5.95 thf(func_def_390, type, sK248: (term > $o) > term).
% 32.37/5.95 thf(func_def_391, type, sK249: (term > $o) > term).
% 32.37/5.95 thf(func_def_392, type, sK250: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_393, type, sK251: term).
% 32.37/5.95 thf(func_def_394, type, sK252: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_395, type, sK253: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_396, type, sK254: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_397, type, sK255: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_398, type, sK256: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_399, type, sK257: term > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_400, type, sK258: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_401, type, sK259: term).
% 32.37/5.95 thf(func_def_402, type, sK260: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_403, type, sK261: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_404, type, sK262: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_405, type, sK263: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_406, type, sK264: term > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_407, type, sK265: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_408, type, sK266: term > $o).
% 32.37/5.95 thf(func_def_409, type, sK267: term).
% 32.37/5.95 thf(func_def_410, type, sK268: term > term).
% 32.37/5.95 thf(func_def_411, type, sK269: (term > $o) > term).
% 32.37/5.95 thf(func_def_412, type, sK270: (term > $o) > term).
% 32.37/5.95 thf(func_def_413, type, sK271: (term > $o) > term).
% 32.37/5.95 thf(func_def_414, type, sK272: (term > $o) > term).
% 32.37/5.95 thf(func_def_415, type, sK273: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_416, type, sK274: term).
% 32.37/5.95 thf(func_def_417, type, sK275: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_418, type, sK276: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_419, type, sK277: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_420, type, sK278: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_421, type, sK279: term > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_422, type, sK280: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_423, type, sK281: term).
% 32.37/5.95 thf(func_def_424, type, sK282: term > $o).
% 32.37/5.95 thf(func_def_425, type, sK283: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_426, type, sK284: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_427, type, sK285: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_428, type, sK286: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_429, type, sK287: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_430, type, sK288: (term > $o) > term > term).
% 32.37/5.95 thf(func_def_431, type, sK289: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_432, type, sK290: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_433, type, sK291: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_434, type, sK292: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_435, type, sK293: (subst > term > subst > $o) > (term > $o) > term).
% 32.37/5.95 thf(func_def_436, type, sK294: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_437, type, sK295: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_438, type, sK296: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_439, type, sK297: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_440, type, sK298: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_441, type, sK299: subst > term > term).
% 32.37/5.95 thf(func_def_442, type, sK300: subst).
% 32.37/5.95 thf(func_def_443, type, sK301: term).
% 32.37/5.95 thf(func_def_444, type, sK302: subst > term > term).
% 32.37/5.95 thf(func_def_445, type, sK303: term).
% 32.37/5.95 thf(func_def_446, type, sK304: term).
% 32.37/5.95 thf(func_def_447, type, sK305: term).
% 32.37/5.95 thf(func_def_448, type, sK306: subst).
% 32.37/5.95 thf(func_def_449, type, sK307: term).
% 32.37/5.95 thf(func_def_450, type, sK308: subst).
% 32.37/5.95 thf(func_def_451, type, sK309: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_452, type, sK310: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_453, type, sK311: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_454, type, sK312: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_455, type, sK313: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_456, type, sK314: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_457, type, sK315: (term > $o) > term).
% 32.37/5.95 thf(func_def_458, type, sK316: (term > $o) > subst > term).
% 32.37/5.95 thf(func_def_459, type, sK317: subst).
% 32.37/5.95 thf(func_def_460, type, sK318: term > $o).
% 32.37/5.95 thf(func_def_461, type, sK319: term).
% 32.37/5.95 thf(func_def_462, type, sK320: term > term).
% 32.37/5.95 thf(func_def_463, type, sK321: term).
% 32.37/5.95 thf(func_def_464, type, sK322: term > $o).
% 32.37/5.95 thf(func_def_465, type, sK323: term).
% 32.37/5.95 thf(func_def_466, type, sK324: term > term).
% 32.37/5.95 thf(func_def_467, type, sK325: (term > $o) > term).
% 32.37/5.95 thf(func_def_468, type, sK326: (term > $o) > term).
% 32.37/5.95 thf(func_def_469, type, sK327: (term > $o) > term).
% 32.37/5.95 thf(func_def_470, type, sK328: (term > $o) > term).
% 32.37/5.95 thf(func_def_471, type, sK329: (term > $o) > term).
% 32.37/5.95 thf(func_def_472, type, sK330: (term > $o) > term).
% 32.37/5.95 thf(func_def_473, type, sK331: (term > $o) > term).
% 32.37/5.95 thf(func_def_474, type, sK332: (term > $o) > term).
% 32.37/5.95 thf(func_def_475, type, sK333: (subst > term > subst > $o) > term > $o).
% 32.37/5.95 thf(func_def_476, type, sK334: term > $o).
% 32.37/5.95 thf(func_def_477, type, sK335: term).
% 32.37/5.95 thf(func_def_478, type, sK336: term > term).
% 32.37/5.95 thf(func_def_479, type, sK337: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_480, type, sK338: (term > $o) > term).
% 32.37/5.95 thf(func_def_481, type, sK339: term).
% 32.37/5.95 thf(func_def_482, type, sK340: (term > $o) > term > term).
% 32.37/5.95 thf(func_def_483, type, sK341: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_484, type, sK342: (term > $o) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_485, type, sK343: term).
% 32.37/5.95 thf(func_def_486, type, sK344: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_487, type, sK345: term > $o).
% 32.37/5.95 thf(func_def_488, type, sK346: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_489, type, sK347: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_490, type, sK348: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_491, type, sK349: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_492, type, sK350: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_493, type, sK351: term).
% 32.37/5.95 thf(func_def_494, type, sK352: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_495, type, sK353: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_496, type, sK354: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_497, type, sK355: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_498, type, sK356: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_499, type, sK357: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_500, type, sK358: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_501, type, sK359: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_502, type, sK360: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_503, type, sK361: (term > $o) > term).
% 32.37/5.95 thf(func_def_504, type, sK362: (term > $o) > term).
% 32.37/5.95 thf(func_def_505, type, sK363: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_506, type, sK364: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_507, type, sK365: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_508, type, sK366: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_509, type, sK367: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_510, type, sK368: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_511, type, sK369: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_512, type, sK370: (term > $o) > term).
% 32.37/5.95 thf(func_def_513, type, sK371: (term > $o) > term).
% 32.37/5.95 thf(func_def_514, type, sK372: term > $o).
% 32.37/5.95 thf(func_def_515, type, sK373: term).
% 32.37/5.95 thf(func_def_516, type, sK374: term > term).
% 32.37/5.95 thf(func_def_517, type, sK375: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_518, type, sK376: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_519, type, sK377: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_520, type, sK378: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_521, type, sK379: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_522, type, sK380: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_523, type, sK381: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_524, type, sK382: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_525, type, sK383: term).
% 32.37/5.95 thf(func_def_526, type, sK384: term).
% 32.37/5.95 thf(func_def_527, type, sK385: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_528, type, sK386: term).
% 32.37/5.95 thf(func_def_529, type, sK387: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_530, type, sK388: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_531, type, sK389: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_532, type, sK390: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_533, type, sK391: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_534, type, sK392: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_535, type, sK393: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_536, type, sK394: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_537, type, sK395: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_538, type, sK396: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_539, type, sK397: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_540, type, sK398: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_541, type, sK399: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_542, type, sK400: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_543, type, sK401: term > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_544, type, sK402: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_545, type, sK403: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_546, type, sK404: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_547, type, sK405: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_548, type, sK406: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_549, type, sK407: term).
% 32.37/5.95 thf(func_def_550, type, sK408: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_551, type, sK409: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_552, type, sK410: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_553, type, sK411: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_554, type, sK412: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_555, type, sK413: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_556, type, sK414: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_557, type, sK415: (term > $o) > term).
% 32.37/5.95 thf(func_def_558, type, sK416: (term > $o) > term).
% 32.37/5.95 thf(func_def_559, type, sK417: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_560, type, sK418: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_561, type, sK419: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_562, type, sK420: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_563, type, sK421: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_564, type, sK422: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_565, type, sK423: (subst > term > term) > (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_566, type, sK424: (term > $o) > term).
% 32.37/5.95 thf(func_def_567, type, sK425: (term > $o) > term).
% 32.37/5.95 thf(func_def_568, type, sK426: (subst > term > subst > $o) > term > $o).
% 32.37/5.95 thf(func_def_569, type, sK427: term > $o).
% 32.37/5.95 thf(func_def_570, type, sK428: term).
% 32.37/5.95 thf(func_def_571, type, sK429: term > term).
% 32.37/5.95 thf(func_def_572, type, sK430: term).
% 32.37/5.95 thf(func_def_573, type, sK431: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_574, type, sK432: (term > $o) > term).
% 32.37/5.95 thf(func_def_575, type, sK433: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_576, type, sK434: term).
% 32.37/5.95 thf(func_def_577, type, sK435: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_578, type, sK436: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_579, type, sK437: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_580, type, sK438: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_581, type, sK439: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_582, type, sK440: (term > $o) > term > term).
% 32.37/5.95 thf(func_def_583, type, sK441: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_584, type, sK442: (subst > term > subst > $o) > (term > $o) > term).
% 32.37/5.95 thf(func_def_585, type, sK443: term).
% 32.37/5.95 thf(func_def_586, type, sK444: term > $o).
% 32.37/5.95 thf(func_def_587, type, sK445: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_588, type, sK446: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_589, type, sK447: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_590, type, sK448: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_591, type, sK449: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_592, type, sK450: (term > $o) > term).
% 32.37/5.95 thf(func_def_593, type, sK451: (term > $o) > term).
% 32.37/5.95 thf(func_def_594, type, sK452: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_595, type, sK453: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_596, type, sK454: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_597, type, sK455: term).
% 32.37/5.95 thf(func_def_598, type, sK456: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_599, type, sK457: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_600, type, sK458: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_601, type, sK459: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_602, type, sK460: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_603, type, sK461: term > $o).
% 32.37/5.95 thf(func_def_604, type, sK462: term).
% 32.37/5.95 thf(func_def_605, type, sK463: term > $o).
% 32.37/5.95 thf(func_def_606, type, sK464: subst).
% 32.37/5.95 thf(func_def_607, type, sK465: subst).
% 32.37/5.95 thf(func_def_608, type, sK466: term).
% 32.37/5.95 thf(func_def_609, type, sK467: subst > (term > $o) > term > (term > $o) > term).
% 32.37/5.95 thf(func_def_610, type, sK468: term).
% 32.37/5.95 thf(func_def_611, type, sK469: subst).
% 32.37/5.95 thf(func_def_612, type, sK470: term > $o).
% 32.37/5.95 thf(func_def_613, type, sK471: term > $o).
% 32.37/5.95 thf(func_def_614, type, sK472: term).
% 32.37/5.95 thf(func_def_615, type, sK473: term).
% 32.37/5.95 thf(func_def_616, type, sK474: subst).
% 32.37/5.95 thf(func_def_617, type, sK475: term).
% 32.37/5.95 thf(func_def_618, type, sK476: (subst > term > subst > $o) > term > $o).
% 32.37/5.95 thf(func_def_619, type, sK477: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_620, type, sK478: (term > $o) > term).
% 32.37/5.95 thf(func_def_621, type, sK479: term).
% 32.37/5.95 thf(func_def_622, type, sK480: term).
% 32.37/5.95 thf(func_def_623, type, sK481: term).
% 32.37/5.95 thf(func_def_624, type, sK482: term).
% 32.37/5.95 thf(func_def_625, type, sK483: term).
% 32.37/5.95 thf(func_def_626, type, sK484: term).
% 32.37/5.95 thf(func_def_627, type, sK485: term).
% 32.37/5.95 thf(func_def_628, type, sK486: term).
% 32.37/5.95 thf(func_def_629, type, sK487: subst > term > term).
% 32.37/5.95 thf(func_def_630, type, sK488: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_631, type, sK489: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_632, type, sK490: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_633, type, sK491: term > d_term).
% 32.37/5.95 thf(func_def_634, type, sK492: term).
% 32.37/5.95 thf(func_def_635, type, sK493: subst).
% 32.37/5.95 thf(func_def_636, type, sK494: subst).
% 32.37/5.95 thf(func_def_637, type, sK495: term).
% 32.37/5.95 thf(func_def_638, type, sK496: subst).
% 32.37/5.95 thf(func_def_639, type, sK497: term > $o).
% 32.37/5.95 thf(func_def_640, type, sK498: term > $o).
% 32.37/5.95 thf(func_def_641, type, sK499: term).
% 32.37/5.95 thf(func_def_642, type, sK500: term).
% 32.37/5.95 thf(func_def_643, type, sK501: subst).
% 32.37/5.95 thf(func_def_644, type, sK502: term).
% 32.37/5.95 thf(func_def_645, type, sK503: term).
% 32.37/5.95 thf(func_def_646, type, sK504: term).
% 32.37/5.95 thf(func_def_647, type, sK505: term).
% 32.37/5.95 thf(func_def_648, type, sK506: term).
% 32.37/5.95 thf(func_def_649, type, sK507: term).
% 32.37/5.95 thf(func_def_650, type, sK508: term).
% 32.37/5.95 thf(func_def_651, type, sK509: term).
% 32.37/5.95 thf(func_def_652, type, sK510: term).
% 32.37/5.95 thf(func_def_653, type, sK511: subst).
% 32.37/5.95 thf(func_def_654, type, sK512: subst).
% 32.37/5.95 thf(func_def_655, type, sK513: term).
% 32.37/5.95 thf(func_def_656, type, sK514: term > $o).
% 32.37/5.95 thf(func_def_657, type, sK515: (term > $o) > term).
% 32.37/5.95 thf(func_def_658, type, sK516: (term > $o) > term).
% 32.37/5.95 thf(func_def_659, type, sK517: term > subst > (term > $o) > term > $o).
% 32.37/5.95 thf(func_def_660, type, sK518: term > $o).
% 32.37/5.95 thf(func_def_661, type, sK519: subst).
% 32.37/5.95 thf(func_def_662, type, sK520: term).
% 32.37/5.95 thf(func_def_663, type, sK521: (term > $o) > term).
% 32.37/5.95 thf(func_def_664, type, sK522: term).
% 32.37/5.95 thf(func_def_665, type, sK523: subst).
% 32.37/5.95 thf(func_def_666, type, sK524: term).
% 32.37/5.95 thf(func_def_667, type, sK525: term).
% 32.37/5.95 thf(func_def_668, type, sK526: term).
% 32.37/5.95 thf(func_def_669, type, sK527: term).
% 32.37/5.95 thf(func_def_670, type, sK528: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_671, type, sK529: (term > $o) > term).
% 32.37/5.95 thf(func_def_672, type, sK530: (subst > term > subst > $o) > term > $o).
% 32.37/5.95 thf(func_def_673, type, sK531: subst).
% 32.37/5.95 thf(func_def_674, type, sK532: subst).
% 32.37/5.95 thf(func_def_675, type, sK533: subst).
% 32.37/5.95 thf(func_def_676, type, sK534: subst).
% 32.37/5.95 thf(func_def_677, type, sK535: subst).
% 32.37/5.95 thf(func_def_678, type, sK536: term).
% 32.37/5.95 thf(func_def_679, type, sK537: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_680, type, sK538: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_681, type, sK539: term > subst > term > term).
% 32.37/5.95 thf(func_def_682, type, sK540: term).
% 32.37/5.95 thf(func_def_683, type, sK541: term).
% 32.37/5.95 thf(func_def_684, type, sK542: term).
% 32.37/5.95 thf(func_def_685, type, sK543: term).
% 32.37/5.95 thf(func_def_686, type, sK544: term).
% 32.37/5.95 thf(func_def_687, type, sK545: term).
% 32.37/5.95 thf(func_def_688, type, sK546: term).
% 32.37/5.95 thf(func_def_689, type, sK547: term > subst > term > term).
% 32.37/5.95 thf(func_def_690, type, sK548: term).
% 32.37/5.95 thf(func_def_691, type, sK549: term > subst > term > term).
% 32.37/5.95 thf(func_def_692, type, sK550: term).
% 32.37/5.95 thf(func_def_693, type, sK551: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_694, type, sK552: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_695, type, sK553: term).
% 32.37/5.95 thf(func_def_696, type, sK554: term).
% 32.37/5.95 thf(func_def_697, type, sK555: subst > d_subst).
% 32.37/5.95 thf(func_def_698, type, sK556: subst).
% 32.37/5.95 thf(func_def_699, type, sK557: term).
% 32.37/5.95 thf(func_def_700, type, sK558: term).
% 32.37/5.95 thf(func_def_701, type, sK559: term).
% 32.37/5.95 thf(func_def_702, type, sK560: term).
% 32.37/5.95 thf(func_def_703, type, sK561: term).
% 32.37/5.95 thf(func_def_704, type, sK562: term).
% 32.37/5.95 thf(func_def_705, type, sK563: term).
% 32.37/5.95 thf(func_def_706, type, sK564: term).
% 32.37/5.95 thf(func_def_707, type, sK565: subst).
% 32.37/5.95 thf(func_def_708, type, sK566: term).
% 32.37/5.95 thf(func_def_709, type, sK567: term > $o).
% 32.37/5.95 thf(func_def_710, type, sK568: (term > $o) > term).
% 32.37/5.95 thf(func_def_711, type, sK569: (term > $o) > term > subst > term > $o).
% 32.37/5.95 thf(func_def_712, type, sK570: term).
% 32.37/5.95 thf(func_def_713, type, sK571: term).
% 32.37/5.95 thf(func_def_714, type, sK572: term).
% 32.37/5.95 thf(func_def_715, type, sK573: term).
% 32.37/5.95 thf(func_def_716, type, sK574: subst).
% 32.37/5.95 thf(func_def_717, type, sK575: term).
% 32.37/5.95 thf(func_def_718, type, sK576: term > $o).
% 32.37/5.95 thf(func_def_719, type, sK577: term > $o).
% 32.37/5.95 thf(func_def_720, type, sK578: (term > $o) > (term > $o) > term > subst > term).
% 32.37/5.95 thf(func_def_721, type, sK579: term).
% 32.37/5.95 thf(func_def_722, type, sK580: term > subst > term > term).
% 32.37/5.95 thf(func_def_723, type, sK581: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_724, type, sK582: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_725, type, sK583: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_726, type, sK584: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_727, type, sK585: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_728, type, sK586: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_729, type, sK587: term).
% 32.37/5.95 thf(func_def_730, type, sK588: subst).
% 32.37/5.95 thf(func_def_731, type, sK589: subst > term > term).
% 32.37/5.95 thf(func_def_732, type, sK590: subst > term > term).
% 32.37/5.95 thf(func_def_734, type, sK592: subst > term > subst > $o).
% 32.37/5.95 thf(func_def_735, type, sK593: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_736, type, sK594: (subst > term > term) > subst).
% 32.37/5.95 thf(func_def_737, type, sK595: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_738, type, sK596: (subst > term > term) > term).
% 32.37/5.95 thf(func_def_739, type, sK597: term).
% 32.37/5.95 thf(func_def_740, type, sK598: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_741, type, sK599: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_742, type, sK600: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_743, type, sK601: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_744, type, sK602: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_745, type, sK603: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_746, type, sK604: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_747, type, sK605: (subst > term > subst > $o) > subst).
% 32.37/5.95 thf(func_def_748, type, sK606: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_749, type, sK607: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_750, type, sK608: (subst > term > subst > $o) > subst > term > term).
% 32.37/5.95 thf(func_def_751, type, sK609: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_752, type, sK610: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_753, type, sK611: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_754, type, sK612: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_755, type, sK613: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_756, type, sK614: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_757, type, sK615: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_758, type, sK616: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_759, type, sK617: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_760, type, sK618: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_761, type, sK619: (subst > term > subst > $o) > term).
% 32.37/5.95 thf(func_def_763, type, ph620: !>[X0: $tType]:(X0)).
% 32.37/5.95 thf(f11475,plain,(
% 32.37/5.95 $false),
% 32.37/5.95 inference(avatar_sat_refutation,[status(thm)],[f3360,f5265,f5283,f5297,f5980,f5999,f6166,f6645,f7595,f8060,f11383,f11385,f11397,f11468,f11474])).
% 32.37/5.95 thf(f11474,plain,(
% 32.37/5.95 ~spl591_573 | ~spl591_576 | ~spl591_682),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f11473])).
% 32.37/5.95 thf(f11473,plain,(
% 32.37/5.95 $false | (~spl591_573 | ~spl591_576 | ~spl591_682)),
% 32.37/5.95 inference(trivial_inequality_removal,[status(thm)],[f11472])).
% 32.37/5.95 thf(f11472,plain,(
% 32.37/5.95 ($true = $false) | (~spl591_573 | ~spl591_576 | ~spl591_682)),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5275,f11456])).
% 32.37/5.95 thf(f11456,plain,(
% 32.37/5.95 ( ! [X0 : term] : (($false = (sK592 @ (d2subst @ d_id) @ X0 @ (d2subst @ d_id)))) ) | (~spl591_573 | ~spl591_682)),
% 32.37/5.95 inference(superposition,[status(thm)],[f5260,f6182])).
% 32.37/5.95 thf(f6182,plain,(
% 32.37/5.95 ( ! [X149 : term,X147 : term] : ((X147 = X149)) ) | ~spl591_682),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f6181])).
% 32.37/5.95 thf(f6181,definition,(
% 32.37/5.95 spl591_682 <=> ! [X149 : term,X147 : term] : (X147 = X149)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_682])],[avatar_definition])).
% 32.37/5.95 thf(f5260,plain,(
% 32.37/5.95 ((sK592 @ (d2subst @ d_id) @ sK597 @ (d2subst @ d_id)) = $false) | ~spl591_573),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5258])).
% 32.37/5.95 thf(f5258,definition,(
% 32.37/5.95 spl591_573 <=> ((sK592 @ (d2subst @ d_id) @ sK597 @ (d2subst @ d_id)) = $false)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_573])],[avatar_definition])).
% 32.37/5.95 thf(f5275,plain,(
% 32.37/5.95 ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ~spl591_576),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5273])).
% 32.37/5.95 thf(f5273,definition,(
% 32.37/5.95 spl591_576 <=> ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_576])],[avatar_definition])).
% 32.37/5.95 thf(f11468,plain,(
% 32.37/5.95 ~spl591_573 | ~spl591_731),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f11467])).
% 32.37/5.95 thf(f11467,plain,(
% 32.37/5.95 $false | (~spl591_573 | ~spl591_731)),
% 32.37/5.95 inference(trivial_inequality_removal,[status(thm)],[f11463])).
% 32.37/5.95 thf(f11463,plain,(
% 32.37/5.95 ($true = $false) | (~spl591_573 | ~spl591_731)),
% 32.37/5.95 inference(superposition,[status(thm)],[f5260,f7085])).
% 32.37/5.95 thf(f7085,plain,(
% 32.37/5.95 ( ! [X2 : subst,X1 : term] : (((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true)) ) | ~spl591_731),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f7084])).
% 32.37/5.95 thf(f7084,definition,(
% 32.37/5.95 spl591_731 <=> ! [X2 : subst,X1 : term] : ((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_731])],[avatar_definition])).
% 32.37/5.95 thf(f11397,plain,(
% 32.37/5.95 ~spl591_577 | ~spl591_682 | ~spl591_732),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f11396])).
% 32.37/5.95 thf(f11396,plain,(
% 32.37/5.95 $false | (~spl591_577 | ~spl591_682 | ~spl591_732)),
% 32.37/5.95 inference(trivial_inequality_removal,[status(thm)],[f11395])).
% 32.37/5.95 thf(f11395,plain,(
% 32.37/5.95 ($true = $false) | (~spl591_577 | ~spl591_682 | ~spl591_732)),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f11394,f7088])).
% 32.37/5.95 thf(f7088,plain,(
% 32.37/5.95 ( ! [X3 : subst] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ X3) = $false)) ) | ~spl591_732),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f7087])).
% 32.37/5.95 thf(f7087,definition,(
% 32.37/5.95 spl591_732 <=> ! [X3 : subst] : ((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ X3) = $false)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_732])],[avatar_definition])).
% 32.37/5.95 thf(f11394,plain,(
% 32.37/5.95 ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (~spl591_577 | ~spl591_682)),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f11387,f5725])).
% 32.37/5.95 thf(f5725,plain,(
% 32.37/5.95 ( ! [X77 : term] : (((d2term @ d_one) = X77)) )),
% 32.37/5.95 inference(backward_demodulation,[status(thm)],[f1197,f1096])).
% 32.37/5.95 thf(f1096,plain,(
% 32.37/5.95 ( ! [X201 : d_term] : ((d_one = X201)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f545,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (($true = sP57) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP57)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X0 : d_subst] : (d_id = X0) & (! [X1 : term,X2 : subst > term > subst > $o] : ((! [X4 : term] : (($true != (X2 @ id @ X4 @ id)) | ($true = (X2 @ id @ (sK454 @ X2 @ id @ X4) @ id))) & ! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (sK454 @ X2 @ X7 @ X5) @ X6) = (sK454 @ X2 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ((X2 @ id @ (lam @ (sK454 @ X2 @ sh @ one)) @ id) != $true)) | ($true = (sP53 @ X2)) | ($true = (X2 @ id @ X1 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X10 : subst > term > term] : ((($true = (sK456 @ id @ (sK457 @ X10) @ id)) & ($true != (sK456 @ id @ (X10 @ id @ (sK457 @ X10)) @ id))) | ((X10 @ (comp @ (sK460 @ X10) @ (sK459 @ X10)) @ (sub @ (sK458 @ X10) @ (sK459 @ X10))) != (sub @ (X10 @ (sK460 @ X10) @ (sK458 @ X10)) @ (sK459 @ X10))) | ($true = (sK456 @ id @ (lam @ (X10 @ sh @ one)) @ id))) & ($true != (sP53 @ sK456)) & ($true != (sK456 @ id @ sK455 @ id)))) & (termmset_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X15 : subst,X16 : term] : ((sub @ one @ (push @ X16 @ X15)) = X16) & (! [X21 : term] : ((sK463 @ X21) = (sK461 @ (sub @ X21 @ (push @ sK462 @ sK464)))) & ($true != (sK463 @ one)) & ($true = (sK461 @ sK462))))) & (((sub @ one @ (push @ sK466 @ sK465)) != sK466) | ! [X24 : term > $o,X25 : term,X26 : term > $o,X27 : subst] : (((X24 @ (sub @ (sK467 @ X27 @ X26 @ X25 @ X24) @ (push @ X25 @ X27))) != (X26 @ (sK467 @ X27 @ X26 @ X25 @ X24))) | ((X26 @ one) = $true) | ((X24 @ X25) != $true)) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X29 : term,X30 : subst,X31 : term > $o,X32 : term > $o,X33 : term] : (($true != (X32 @ X33)) | ($true = (X31 @ (sub @ X33 @ (push @ X29 @ X30))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (((sK471 @ sK472) = $true) & ($true != (sK470 @ (sub @ sK472 @ (push @ sK468 @ sK469)))))) & (! [X39 : term] : ((sub @ X39 @ id) = X39) | (axvarid != $true)) & ((axvarid = $true) | (sK473 != (sub @ sK473 @ id))) & (! [X41 : subst,X42 : term] : ((comp @ sh @ (push @ X42 @ X41)) = X41) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK474 != (comp @ sh @ (push @ sK475 @ sK474)))) & (! [X45 : subst > term > subst > $o] : ! [X47 : term] : ((sK476 @ X45 @ X47) = (X45 @ id @ X47 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X49 : term > $o] : ((sK477 @ id @ (sK478 @ X49) @ id) != (X49 @ (sK478 @ X49)))) & (lamnotap != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((laminj = $true) | ((sK479 != sK480) & ((lam @ sK480) = (lam @ sK479)))) & (! [X53 : term,X54 : term] : ((X53 = X54) | ((lam @ X54) != (lam @ X53))) | (laminj != $true)) & ((hoasapinj2 = $true) | (((ap @ (sub @ sK482 @ id) @ sK483) = (ap @ (sub @ sK484 @ id) @ sK481)) & (sK483 != sK481))) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ (sub @ X62 @ id) @ X59) != (ap @ (sub @ X60 @ id) @ X61)) | (X59 = X61)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3 != $true)) & ((d2subst @ d_id) = id) & ! [X63 : d_term,X64 : d_term] : ((X63 = X64) | ((d2term @ X64) != (d2term @ X63))) & (hoaslamnotap_lthm = $true) & (($true = sP49) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP49)) & ((hoaslamnotap = $true) | (! [X68 : term,X69 : subst,X70 : subst] : ((sub @ (sK487 @ X70 @ X68) @ X69) = (sK487 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69))) & ((ap @ (sub @ sK486 @ id) @ sK485) = (lam @ (sK487 @ sh @ one))))) & (! [X71 : term,X72 : term,X73 : subst > term > term] : (((sub @ (X73 @ (sK490 @ X73) @ (sK488 @ X73)) @ (sK489 @ X73)) != (X73 @ (comp @ (sK490 @ X73) @ (sK489 @ X73)) @ (sub @ (sK488 @ X73) @ (sK489 @ X73)))) | ((lam @ (X73 @ sh @ one)) != (ap @ (sub @ X72 @ id) @ X71))) | (hoaslamnotap != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3a_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X77 : term] : ((d2term @ (sK491 @ X77)) = X77) & (! [X79 : subst,X80 : term > $o,X81 : term > $o,X82 : term,X83 : term] : (((X80 @ (sub @ X83 @ (push @ X82 @ X79))) = $true) | ($true != (X81 @ X83))) | (sK492 != (sub @ one @ (push @ sK492 @ sK493))) | (sK494 != (comp @ sh @ (push @ sK495 @ sK494))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | ((($true != (sK497 @ (sub @ sK500 @ (push @ sK499 @ sK496)))) & ($true = (sK498 @ sK500))) & ! [X93 : term,X94 : subst] : ((sub @ one @ (push @ X93 @ X94)) = X93) & ! [X95 : subst,X96 : term] : ((comp @ sh @ (push @ X96 @ X95)) = X95))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X97 : subst] : ((comp @ id @ X97) = X97) | (axidl != $true)) & ((axidl = $true) | ((comp @ id @ sK501) != sK501)) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X99 : term,X100 : term,X101 : term,X102 : term] : ((X99 = X100) | ((ap @ X100 @ X102) != (ap @ X99 @ X101))) & ! [X103 : term] : ((sub @ X103 @ id) = X103) & (((ap @ (sub @ sK502 @ id) @ sK504) = (ap @ (sub @ sK505 @ id) @ sK503)) & (sK502 != sK505)))) & (((sK507 != sK506) & ((ap @ sK507 @ sK509) = (ap @ sK506 @ sK508))) | ((sub @ sK510 @ id) != sK510) | ! [X113 : term,X114 : term,X115 : term,X116 : term] : (((ap @ (sub @ X113 @ id) @ X115) != (ap @ (sub @ X116 @ id) @ X114)) | (X113 = X116)) | (hoasapinj1_lthm != $true)) & ((! [X117 : subst] : ((comp @ id @ X117) = X117) & ! [X118 : subst] : ((comp @ X118 @ id) = X118)) | (substmonoid != $true)) & ((substmonoid = $true) | ((comp @ id @ sK511) != sK511) | (sK512 != (comp @ sK512 @ id))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) | (($true != (sK514 @ sK513)) & ($true != (sP45 @ sK514)) & ! [X123 : term] : (((var @ X123) != $true) | ($true = (sK514 @ X123))) & ! [X124 : term] : (($true != (sK514 @ X124)) | ($true = (sK514 @ (lam @ X124)))))) & (! [X125 : term,X126 : term > $o] : (($true = (X126 @ X125)) | ((sP45 @ X126) = $true) | (($true = (var @ (sK515 @ X126))) & ($true != (X126 @ (sK515 @ X126)))) | (($true = (X126 @ (sK516 @ X126))) & ($true != (X126 @ (lam @ (sK516 @ X126)))))) | (induction != $true)) & (! [X129 : term > $o,X130 : subst,X131 : term] : ! [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X131 @ X130))) = (sK517 @ X131 @ X130 @ X129 @ X133)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X137 : term > $o] : ((sK518 @ (sub @ (sK521 @ X137) @ (push @ sK520 @ sK519))) != (X137 @ (sK521 @ X137)))) & ((axvarcons = $true) | (sK522 != (sub @ one @ (push @ sK522 @ sK523)))) & (! [X141 : term,X142 : subst] : ((sub @ one @ (push @ X141 @ X142)) = X141) | (axvarcons != $true)) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) | (((ap @ sK526 @ sK525) = (ap @ sK524 @ sK527)) & (sK526 != sK524))) & (! [X147 : term,X148 : term,X149 : term,X150 : term] : (((ap @ X149 @ X148) != (ap @ X147 @ X150)) | (X147 = X149)) | (apinj1 != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X152 : term > $o] : ((sK528 @ id @ (sK529 @ X152) @ id) != (X152 @ (sK529 @ X152)))) & (! [X154 : subst > term > subst > $o] : ! [X156 : term] : ((X154 @ id @ X156 @ id) = (sK530 @ X154 @ X156)) | (hoasinduction_lem0_lthm != $true)) & (apnotvar = $true) & (($true = sP44) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP44)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X157 : subst] : ((comp @ X157 @ id) = X157) & ((sK531 != (comp @ sK531 @ id)) | ((comp @ id @ sK532) != sK532)) & ! [X160 : subst] : ((comp @ id @ X160) = X160))) & (((comp @ sK533 @ id) != sK533) | (! [X162 : subst] : ((comp @ X162 @ id) = X162) & ! [X163 : subst] : ((comp @ id @ X163) = X163)) | (sK534 != (comp @ id @ sK534)) | (substmonoid_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem2v2 != $true)) & (pushprop_gthm = $true) & (! [X165 : subst] : ((push @ (sub @ one @ X165) @ (comp @ sh @ X165)) = X165) | (axscons != $true)) & ((axscons = $true) | ((push @ (sub @ one @ sK535) @ (comp @ sh @ sK535)) != sK535)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3v2_f = $true) | ! [X168 : subst > term > term] : ((sub @ sK536 @ (push @ (sK537 @ X168) @ (sK538 @ X168))) != (X168 @ (sK538 @ X168) @ (sK537 @ X168)))) & (! [X171 : term] : ! [X173 : term,X174 : subst] : ((sK539 @ X171 @ X174 @ X173) = (sub @ X171 @ (push @ X173 @ X174))) | (hoasinduction_lem3v2_f != $true)) & ((termmset = $true) | (sK540 != (sub @ sK540 @ id))) & (! [X176 : term] : ((sub @ X176 @ id) = X176) | (termmset != $true)) & ((shinj = $true) | (((sub @ sK542 @ sh) = (sub @ sK541 @ sh)) & (sK541 != sK542))) & (! [X179 : term,X180 : term] : (((sub @ X180 @ sh) != (sub @ X179 @ sh)) | (X179 = X180)) | (shinj != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X183 = X184) | ((ap @ X181 @ X184) != (ap @ X182 @ X183))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK545 != sK546) & ((ap @ sK543 @ sK546) = (ap @ sK544 @ sK545)))) & (($true = sP37) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP37)) & (! [X189 : term] : ((sK547 @ X189 @ sh @ one) = (sub @ X189 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X192 : subst > term > term] : ((X192 @ sh @ one) != (sub @ sK548 @ (push @ one @ sh)))) & (! [X193 : term] : ! [X195 : term,X196 : subst] : ((sK549 @ X193 @ X196 @ X195) = (sub @ X193 @ (push @ X195 @ X196))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X198 : subst > term > term] : ((sub @ sK550 @ (push @ (sK551 @ X198) @ (sK552 @ X198))) != (X198 @ (sK552 @ X198) @ (sK551 @ X198)))) & (hoasinduction_gthm = $true) & (($true = sP33) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP31) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP31)) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X201 : d_term] : (d_one = X201) & ((sP30 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP30 != $true)) & ((induction2 = $true) | ($true != sP29)) & (($true = sP29) | (induction2 != $true)) & ! [X202 : d_subst,X203 : d_subst] : (((d2subst @ X202) != (d2subst @ X203)) | (X202 = X203)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & ((sK553 != (sub @ sK553 @ id)) | ! [X205 : term] : ((sub @ X205 @ id) = X205) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X206 : term] : ((sub @ X206 @ id) = X206) & (sK554 != (sub @ sK554 @ id)))) & ((sP27 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP27 != $true)) & (($true = sP26) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP26)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & ! [X208 : subst] : ((d2subst @ (sK555 @ X208)) = X208) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) | ((comp @ sK556 @ id) != sK556)) & (! [X211 : subst] : ((comp @ X211 @ id) = X211) | (axidr != $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X212 @ id) @ X214) != (ap @ (sub @ X215 @ id) @ X213)) | (X213 = X214)) | ((sK557 != sK559) & ((ap @ sK558 @ sK559) = (ap @ sK560 @ sK557))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ((((ap @ (sub @ sK561 @ id) @ sK563) = (ap @ (sub @ sK564 @ id) @ sK562)) & (sK563 != sK562)) & ! [X224 : term,X225 : term,X226 : term,X227 : term] : ((X224 = X226) | ((ap @ X225 @ X226) != (ap @ X227 @ X224))))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ! [X231 : term > $o] : ((sK567 @ (sub @ (sK568 @ X231) @ (push @ sK566 @ sK565))) != (X231 @ (sK568 @ X231)))) & (! [X233 : subst,X234 : term,X235 : term > $o] : ! [X237 : term] : ((sK569 @ X235 @ X234 @ X233 @ X237) = (X235 @ (sub @ X237 @ (push @ X234 @ X233)))) | (pushprop_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP23)) & (($true = sP23) | (induction2_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X238 : term,X239 : term,X240 : term,X241 : term] : (((ap @ (sub @ X238 @ id) @ X239) != (ap @ (sub @ X240 @ id) @ X241)) | (X238 = X240)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | (((ap @ (sub @ sK570 @ id) @ sK571) = (ap @ (sub @ sK572 @ id) @ sK573)) & (sK572 != sK570))) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (($true = sP13) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP13)) & ((pushprop_lem1v2 = $true) | (! [X250 : term] : ((sK577 @ X250) = (sK576 @ (sub @ X250 @ (push @ sK575 @ sK574)))) & ($true = (sK576 @ sK575)) & ($true != (sK577 @ one)))) & (! [X251 : subst,X252 : term,X253 : term > $o,X254 : term > $o] : (((X253 @ (sub @ (sK578 @ X254 @ X253 @ X252 @ X251) @ (push @ X252 @ X251))) != (X254 @ (sK578 @ X254 @ X253 @ X252 @ X251))) | ($true != (X253 @ X252)) | ($true = (X254 @ one))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3b = $true) | ! [X257 : subst > term > term] : ((X257 @ sh @ one) != (sub @ sK579 @ (push @ one @ sh)))) & (! [X258 : term] : ((sK580 @ X258 @ sh @ one) = (sub @ X258 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (! [X260 : term,X261 : subst,X262 : subst > term > term,X263 : subst > term > term] : (((sub @ (X262 @ (sK581 @ X262) @ (sK583 @ X262)) @ (sK582 @ X262)) != (X262 @ (comp @ (sK581 @ X262) @ (sK582 @ X262)) @ (sub @ (sK583 @ X262) @ (sK582 @ X262)))) | ((X262 @ X261 @ X260) = (X263 @ X261 @ X260)) | ((sub @ (X263 @ (sK584 @ X263) @ (sK586 @ X263)) @ (sK585 @ X263)) != (X263 @ (comp @ (sK584 @ X263) @ (sK585 @ X263)) @ (sub @ (sK586 @ X263) @ (sK585 @ X263)))) | ((lam @ (X263 @ sh @ one)) != (lam @ (X262 @ sh @ one)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X274 : subst,X275 : subst,X276 : term] : ((sK589 @ (comp @ X274 @ X275) @ (sub @ X276 @ X275)) = (sub @ (sK589 @ X274 @ X276) @ X275)) & ((sK589 @ sK588 @ sK587) != (sK590 @ sK588 @ sK587)) & ! [X277 : subst,X278 : subst,X279 : term] : ((sK590 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)) = (sub @ (sK590 @ X277 @ X279) @ X278)) & ((lam @ (sK589 @ sh @ one)) = (lam @ (sK590 @ sh @ one))))) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590])],[f473,f544,f543,f542,f541,f540,f539,f538,f537,f536,f535,f534,f533,f532,f531,f530,f529,f528,f527,f526,f525,f524,f523,f522,f521,f520,f519,f518,f517,f516,f515,f514,f513,f512,f511,f510,f509,f508,f507,f506,f505,f504,f503,f502,f501,f500,f499,f498,f497,f496,f495,f494,f493,f492,f491,f490,f489,f488,f487,f486,f485,f484,f483,f482,f481,f480,f479,f478,f477,f476,f475,f474])).
% 32.37/5.95 thf(f474,plain,(
% 32.37/5.95 ! [X2 : subst > term > subst > $o] : (? [X3 : subst > term > term] : (! [X4 : term] : (($true != (X2 @ id @ X4 @ id)) | ($true = (X2 @ id @ (X3 @ id @ X4) @ id))) & ! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X3 @ X7 @ X5) @ X6) = (X3 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ($true != (X2 @ id @ (lam @ (X3 @ sh @ one)) @ id))) => (! [X4 : term] : (($true != (X2 @ id @ X4 @ id)) | ($true = (X2 @ id @ (sK454 @ X2 @ id @ X4) @ id))) & ! [X7 : subst,X6 : subst,X5 : term] : ((sub @ (sK454 @ X2 @ X7 @ X5) @ X6) = (sK454 @ X2 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ((X2 @ id @ (lam @ (sK454 @ X2 @ sh @ one)) @ id) != $true)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f475,plain,(
% 32.37/5.95 ? [X8 : term,X9 : subst > term > subst > $o] : (! [X10 : subst > term > term] : (? [X11 : term] : (($true = (X9 @ id @ X11 @ id)) & ($true != (X9 @ id @ (X10 @ id @ X11) @ id))) | ? [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) != (sub @ (X10 @ X14 @ X12) @ X13)) | ((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true)) & ($true != (sP53 @ X9)) & ($true != (X9 @ id @ X8 @ id))) => (! [X10 : subst > term > term] : (? [X11 : term] : (($true = (sK456 @ id @ X11 @ id)) & ($true != (sK456 @ id @ (X10 @ id @ X11) @ id))) | ? [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) != (sub @ (X10 @ X14 @ X12) @ X13)) | ($true = (sK456 @ id @ (lam @ (X10 @ sh @ one)) @ id))) & ($true != (sP53 @ sK456)) & ($true != (sK456 @ id @ sK455 @ id)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f476,plain,(
% 32.37/5.95 ! [X10 : subst > term > term] : (? [X11 : term] : (($true = (sK456 @ id @ X11 @ id)) & ($true != (sK456 @ id @ (X10 @ id @ X11) @ id))) => (($true = (sK456 @ id @ (sK457 @ X10) @ id)) & ($true != (sK456 @ id @ (X10 @ id @ (sK457 @ X10)) @ id))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f477,plain,(
% 32.37/5.95 ! [X10 : subst > term > term] : (? [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) != (sub @ (X10 @ X14 @ X12) @ X13)) => ((X10 @ (comp @ (sK460 @ X10) @ (sK459 @ X10)) @ (sub @ (sK458 @ X10) @ (sK459 @ X10))) != (sub @ (X10 @ (sK460 @ X10) @ (sK458 @ X10)) @ (sK459 @ X10))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f478,plain,(
% 32.37/5.95 ? [X17 : term > $o,X18 : term,X19 : term > $o,X20 : subst] : (! [X21 : term] : ((X17 @ (sub @ X21 @ (push @ X18 @ X20))) = (X19 @ X21)) & ((X19 @ one) != $true) & ((X17 @ X18) = $true)) => (! [X21 : term] : ((sK463 @ X21) = (sK461 @ (sub @ X21 @ (push @ sK462 @ sK464)))) & ($true != (sK463 @ one)) & ($true = (sK461 @ sK462)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f479,plain,(
% 32.37/5.95 ? [X22 : subst,X23 : term] : ((sub @ one @ (push @ X23 @ X22)) != X23) => ((sub @ one @ (push @ sK466 @ sK465)) != sK466)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f480,plain,(
% 32.37/5.95 ! [X24 : term > $o,X25 : term,X26 : term > $o,X27 : subst] : (? [X28 : term] : ((X24 @ (sub @ X28 @ (push @ X25 @ X27))) != (X26 @ X28)) => ((X24 @ (sub @ (sK467 @ X27 @ X26 @ X25 @ X24) @ (push @ X25 @ X27))) != (X26 @ (sK467 @ X27 @ X26 @ X25 @ X24))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f481,plain,(
% 32.37/5.95 ? [X34 : term,X35 : subst,X36 : term > $o,X37 : term > $o,X38 : term] : (($true = (X37 @ X38)) & ((X36 @ (sub @ X38 @ (push @ X34 @ X35))) != $true)) => (((sK471 @ sK472) = $true) & ($true != (sK470 @ (sub @ sK472 @ (push @ sK468 @ sK469)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f482,plain,(
% 32.37/5.95 ? [X40 : term] : ((sub @ X40 @ id) != X40) => (sK473 != (sub @ sK473 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f483,plain,(
% 32.37/5.95 ? [X43 : subst,X44 : term] : ((comp @ sh @ (push @ X44 @ X43)) != X43) => (sK474 != (comp @ sh @ (push @ sK475 @ sK474)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f484,plain,(
% 32.37/5.95 ! [X45 : subst > term > subst > $o] : (? [X46 : term > $o] : ! [X47 : term] : ((X46 @ X47) = (X45 @ id @ X47 @ id)) => ! [X47 : term] : ((sK476 @ X45 @ X47) = (X45 @ id @ X47 @ id)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f485,plain,(
% 32.37/5.95 ? [X48 : subst > term > subst > $o] : ! [X49 : term > $o] : ? [X50 : term] : ((X49 @ X50) != (X48 @ id @ X50 @ id)) => ! [X49 : term > $o] : ? [X50 : term] : ((sK477 @ id @ X50 @ id) != (X49 @ X50))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f486,plain,(
% 32.37/5.95 ! [X49 : term > $o] : (? [X50 : term] : ((sK477 @ id @ X50 @ id) != (X49 @ X50)) => ((sK477 @ id @ (sK478 @ X49) @ id) != (X49 @ (sK478 @ X49))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f487,plain,(
% 32.37/5.95 ? [X51 : term,X52 : term] : ((X51 != X52) & ((lam @ X52) = (lam @ X51))) => ((sK479 != sK480) & ((lam @ sK480) = (lam @ sK479)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f488,plain,(
% 32.37/5.95 ? [X55 : term,X56 : term,X57 : term,X58 : term] : (((ap @ (sub @ X56 @ id) @ X57) = (ap @ (sub @ X58 @ id) @ X55)) & (X55 != X57)) => (((ap @ (sub @ sK482 @ id) @ sK483) = (ap @ (sub @ sK484 @ id) @ sK481)) & (sK483 != sK481))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f489,plain,(
% 32.37/5.95 ? [X65 : term,X66 : term,X67 : subst > term > term] : (! [X68 : term,X69 : subst,X70 : subst] : ((X67 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69)) = (sub @ (X67 @ X70 @ X68) @ X69)) & ((ap @ (sub @ X66 @ id) @ X65) = (lam @ (X67 @ sh @ one)))) => (! [X70 : subst,X69 : subst,X68 : term] : ((sub @ (sK487 @ X70 @ X68) @ X69) = (sK487 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69))) & ((ap @ (sub @ sK486 @ id) @ sK485) = (lam @ (sK487 @ sh @ one))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f490,plain,(
% 32.37/5.95 ! [X73 : subst > term > term] : (? [X74 : term,X75 : subst,X76 : subst] : ((sub @ (X73 @ X76 @ X74) @ X75) != (X73 @ (comp @ X76 @ X75) @ (sub @ X74 @ X75))) => ((sub @ (X73 @ (sK490 @ X73) @ (sK488 @ X73)) @ (sK489 @ X73)) != (X73 @ (comp @ (sK490 @ X73) @ (sK489 @ X73)) @ (sub @ (sK488 @ X73) @ (sK489 @ X73)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f491,plain,(
% 32.37/5.95 ! [X77 : term] : (? [X78 : d_term] : ((d2term @ X78) = X77) => ((d2term @ (sK491 @ X77)) = X77))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f492,plain,(
% 32.37/5.95 ? [X84 : term,X85 : subst] : ((sub @ one @ (push @ X84 @ X85)) != X84) => (sK492 != (sub @ one @ (push @ sK492 @ sK493)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f493,plain,(
% 32.37/5.95 ? [X86 : subst,X87 : term] : ((comp @ sh @ (push @ X87 @ X86)) != X86) => (sK494 != (comp @ sh @ (push @ sK495 @ sK494)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f494,plain,(
% 32.37/5.95 ? [X88 : subst,X89 : term > $o,X90 : term > $o,X91 : term,X92 : term] : (($true != (X89 @ (sub @ X92 @ (push @ X91 @ X88)))) & ((X90 @ X92) = $true)) => (($true != (sK497 @ (sub @ sK500 @ (push @ sK499 @ sK496)))) & ($true = (sK498 @ sK500)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f495,plain,(
% 32.37/5.95 ? [X98 : subst] : ((comp @ id @ X98) != X98) => ((comp @ id @ sK501) != sK501)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f496,plain,(
% 32.37/5.95 ? [X104 : term,X105 : term,X106 : term,X107 : term] : (((ap @ (sub @ X107 @ id) @ X105) = (ap @ (sub @ X104 @ id) @ X106)) & (X104 != X107)) => (((ap @ (sub @ sK502 @ id) @ sK504) = (ap @ (sub @ sK505 @ id) @ sK503)) & (sK502 != sK505))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f497,plain,(
% 32.37/5.95 ? [X108 : term,X109 : term,X110 : term,X111 : term] : ((X108 != X109) & ((ap @ X109 @ X111) = (ap @ X108 @ X110))) => ((sK507 != sK506) & ((ap @ sK507 @ sK509) = (ap @ sK506 @ sK508)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f498,plain,(
% 32.37/5.95 ? [X112 : term] : ((sub @ X112 @ id) != X112) => ((sub @ sK510 @ id) != sK510)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f499,plain,(
% 32.37/5.95 ? [X119 : subst] : ((comp @ id @ X119) != X119) => ((comp @ id @ sK511) != sK511)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f500,plain,(
% 32.37/5.95 ? [X120 : subst] : ((comp @ X120 @ id) != X120) => (sK512 != (comp @ sK512 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f501,plain,(
% 32.37/5.95 ? [X121 : term,X122 : term > $o] : (($true != (X122 @ X121)) & ((sP45 @ X122) != $true) & ! [X123 : term] : (((var @ X123) != $true) | ((X122 @ X123) = $true)) & ! [X124 : term] : (($true != (X122 @ X124)) | ((X122 @ (lam @ X124)) = $true))) => (($true != (sK514 @ sK513)) & ($true != (sP45 @ sK514)) & ! [X123 : term] : (((var @ X123) != $true) | ($true = (sK514 @ X123))) & ! [X124 : term] : (($true != (sK514 @ X124)) | ($true = (sK514 @ (lam @ X124)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f502,plain,(
% 32.37/5.95 ! [X126 : term > $o] : (? [X127 : term] : (($true = (var @ X127)) & ((X126 @ X127) != $true)) => (($true = (var @ (sK515 @ X126))) & ($true != (X126 @ (sK515 @ X126)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f503,plain,(
% 32.37/5.95 ! [X126 : term > $o] : (? [X128 : term] : (($true = (X126 @ X128)) & ($true != (X126 @ (lam @ X128)))) => (($true = (X126 @ (sK516 @ X126))) & ($true != (X126 @ (lam @ (sK516 @ X126))))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f504,plain,(
% 32.37/5.95 ! [X129 : term > $o,X130 : subst,X131 : term] : (? [X132 : term > $o] : ! [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X131 @ X130))) = (X132 @ X133)) => ! [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X131 @ X130))) = (sK517 @ X131 @ X130 @ X129 @ X133)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f505,plain,(
% 32.37/5.95 ? [X134 : term > $o,X135 : subst,X136 : term] : ! [X137 : term > $o] : ? [X138 : term] : ((X134 @ (sub @ X138 @ (push @ X136 @ X135))) != (X137 @ X138)) => ! [X137 : term > $o] : ? [X138 : term] : ((sK518 @ (sub @ X138 @ (push @ sK520 @ sK519))) != (X137 @ X138))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f506,plain,(
% 32.37/5.95 ! [X137 : term > $o] : (? [X138 : term] : ((sK518 @ (sub @ X138 @ (push @ sK520 @ sK519))) != (X137 @ X138)) => ((sK518 @ (sub @ (sK521 @ X137) @ (push @ sK520 @ sK519))) != (X137 @ (sK521 @ X137))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f507,plain,(
% 32.37/5.95 ? [X139 : term,X140 : subst] : ((sub @ one @ (push @ X139 @ X140)) != X139) => (sK522 != (sub @ one @ (push @ sK522 @ sK523)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f508,plain,(
% 32.37/5.95 ? [X143 : term,X144 : term,X145 : term,X146 : term] : (((ap @ X143 @ X146) = (ap @ X145 @ X144)) & (X143 != X145)) => (((ap @ sK526 @ sK525) = (ap @ sK524 @ sK527)) & (sK526 != sK524))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f509,plain,(
% 32.37/5.95 ? [X151 : subst > term > subst > $o] : ! [X152 : term > $o] : ? [X153 : term] : ((X152 @ X153) != (X151 @ id @ X153 @ id)) => ! [X152 : term > $o] : ? [X153 : term] : ((X152 @ X153) != (sK528 @ id @ X153 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f510,plain,(
% 32.37/5.95 ! [X152 : term > $o] : (? [X153 : term] : ((X152 @ X153) != (sK528 @ id @ X153 @ id)) => ((sK528 @ id @ (sK529 @ X152) @ id) != (X152 @ (sK529 @ X152))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f511,plain,(
% 32.37/5.95 ! [X154 : subst > term > subst > $o] : (? [X155 : term > $o] : ! [X156 : term] : ((X154 @ id @ X156 @ id) = (X155 @ X156)) => ! [X156 : term] : ((X154 @ id @ X156 @ id) = (sK530 @ X154 @ X156)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f512,plain,(
% 32.37/5.95 ? [X158 : subst] : ((comp @ X158 @ id) != X158) => (sK531 != (comp @ sK531 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f513,plain,(
% 32.37/5.95 ? [X159 : subst] : ((comp @ id @ X159) != X159) => ((comp @ id @ sK532) != sK532)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f514,plain,(
% 32.37/5.95 ? [X161 : subst] : ((comp @ X161 @ id) != X161) => ((comp @ sK533 @ id) != sK533)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f515,plain,(
% 32.37/5.95 ? [X164 : subst] : ((comp @ id @ X164) != X164) => (sK534 != (comp @ id @ sK534))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f516,plain,(
% 32.37/5.95 ? [X166 : subst] : ((push @ (sub @ one @ X166) @ (comp @ sh @ X166)) != X166) => ((push @ (sub @ one @ sK535) @ (comp @ sh @ sK535)) != sK535)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f517,plain,(
% 32.37/5.95 ? [X167 : term] : ! [X168 : subst > term > term] : ? [X169 : term,X170 : subst] : ((X168 @ X170 @ X169) != (sub @ X167 @ (push @ X169 @ X170))) => ! [X168 : subst > term > term] : ? [X170 : subst,X169 : term] : ((sub @ sK536 @ (push @ X169 @ X170)) != (X168 @ X170 @ X169))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f518,plain,(
% 32.37/5.95 ! [X168 : subst > term > term] : (? [X170 : subst,X169 : term] : ((sub @ sK536 @ (push @ X169 @ X170)) != (X168 @ X170 @ X169)) => ((sub @ sK536 @ (push @ (sK537 @ X168) @ (sK538 @ X168))) != (X168 @ (sK538 @ X168) @ (sK537 @ X168))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f519,plain,(
% 32.37/5.95 ! [X171 : term] : (? [X172 : subst > term > term] : ! [X173 : term,X174 : subst] : ((X172 @ X174 @ X173) = (sub @ X171 @ (push @ X173 @ X174))) => ! [X174 : subst,X173 : term] : ((sK539 @ X171 @ X174 @ X173) = (sub @ X171 @ (push @ X173 @ X174))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f520,plain,(
% 32.37/5.95 ? [X175 : term] : ((sub @ X175 @ id) != X175) => (sK540 != (sub @ sK540 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f521,plain,(
% 32.37/5.95 ? [X177 : term,X178 : term] : (((sub @ X177 @ sh) = (sub @ X178 @ sh)) & (X177 != X178)) => (((sub @ sK542 @ sh) = (sub @ sK541 @ sh)) & (sK541 != sK542))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f522,plain,(
% 32.37/5.95 ? [X185 : term,X186 : term,X187 : term,X188 : term] : ((X187 != X188) & ((ap @ X185 @ X188) = (ap @ X186 @ X187))) => ((sK545 != sK546) & ((ap @ sK543 @ sK546) = (ap @ sK544 @ sK545)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f523,plain,(
% 32.37/5.95 ! [X189 : term] : (? [X190 : subst > term > term] : ((X190 @ sh @ one) = (sub @ X189 @ (push @ one @ sh))) => ((sK547 @ X189 @ sh @ one) = (sub @ X189 @ (push @ one @ sh))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f524,plain,(
% 32.37/5.95 ? [X191 : term] : ! [X192 : subst > term > term] : ((sub @ X191 @ (push @ one @ sh)) != (X192 @ sh @ one)) => ! [X192 : subst > term > term] : ((X192 @ sh @ one) != (sub @ sK548 @ (push @ one @ sh)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f525,plain,(
% 32.37/5.95 ! [X193 : term] : (? [X194 : subst > term > term] : ! [X195 : term,X196 : subst] : ((X194 @ X196 @ X195) = (sub @ X193 @ (push @ X195 @ X196))) => ! [X196 : subst,X195 : term] : ((sK549 @ X193 @ X196 @ X195) = (sub @ X193 @ (push @ X195 @ X196))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f526,plain,(
% 32.37/5.95 ? [X197 : term] : ! [X198 : subst > term > term] : ? [X199 : term,X200 : subst] : ((X198 @ X200 @ X199) != (sub @ X197 @ (push @ X199 @ X200))) => ! [X198 : subst > term > term] : ? [X200 : subst,X199 : term] : ((X198 @ X200 @ X199) != (sub @ sK550 @ (push @ X199 @ X200)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f527,plain,(
% 32.37/5.95 ! [X198 : subst > term > term] : (? [X200 : subst,X199 : term] : ((X198 @ X200 @ X199) != (sub @ sK550 @ (push @ X199 @ X200))) => ((sub @ sK550 @ (push @ (sK551 @ X198) @ (sK552 @ X198))) != (X198 @ (sK552 @ X198) @ (sK551 @ X198))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f528,plain,(
% 32.37/5.95 ? [X204 : term] : ((sub @ X204 @ id) != X204) => (sK553 != (sub @ sK553 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f529,plain,(
% 32.37/5.95 ? [X207 : term] : ((sub @ X207 @ id) != X207) => (sK554 != (sub @ sK554 @ id))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f530,plain,(
% 32.37/5.95 ! [X208 : subst] : (? [X209 : d_subst] : ((d2subst @ X209) = X208) => ((d2subst @ (sK555 @ X208)) = X208))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f531,plain,(
% 32.37/5.95 ? [X210 : subst] : ((comp @ X210 @ id) != X210) => ((comp @ sK556 @ id) != sK556)),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f532,plain,(
% 32.37/5.95 ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 != X218) & ((ap @ X217 @ X218) = (ap @ X219 @ X216))) => ((sK557 != sK559) & ((ap @ sK558 @ sK559) = (ap @ sK560 @ sK557)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f533,plain,(
% 32.37/5.95 ? [X220 : term,X221 : term,X222 : term,X223 : term] : (((ap @ (sub @ X223 @ id) @ X221) = (ap @ (sub @ X220 @ id) @ X222)) & (X221 != X222)) => (((ap @ (sub @ sK561 @ id) @ sK563) = (ap @ (sub @ sK564 @ id) @ sK562)) & (sK563 != sK562))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f534,plain,(
% 32.37/5.95 ? [X228 : subst,X229 : term,X230 : term > $o] : ! [X231 : term > $o] : ? [X232 : term] : ((X231 @ X232) != (X230 @ (sub @ X232 @ (push @ X229 @ X228)))) => ! [X231 : term > $o] : ? [X232 : term] : ((X231 @ X232) != (sK567 @ (sub @ X232 @ (push @ sK566 @ sK565))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f535,plain,(
% 32.37/5.95 ! [X231 : term > $o] : (? [X232 : term] : ((X231 @ X232) != (sK567 @ (sub @ X232 @ (push @ sK566 @ sK565)))) => ((sK567 @ (sub @ (sK568 @ X231) @ (push @ sK566 @ sK565))) != (X231 @ (sK568 @ X231))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f536,plain,(
% 32.37/5.95 ! [X233 : subst,X234 : term,X235 : term > $o] : (? [X236 : term > $o] : ! [X237 : term] : ((X236 @ X237) = (X235 @ (sub @ X237 @ (push @ X234 @ X233)))) => ! [X237 : term] : ((sK569 @ X235 @ X234 @ X233 @ X237) = (X235 @ (sub @ X237 @ (push @ X234 @ X233)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f537,plain,(
% 32.37/5.95 ? [X242 : term,X243 : term,X244 : term,X245 : term] : (((ap @ (sub @ X242 @ id) @ X243) = (ap @ (sub @ X244 @ id) @ X245)) & (X242 != X244)) => (((ap @ (sub @ sK570 @ id) @ sK571) = (ap @ (sub @ sK572 @ id) @ sK573)) & (sK572 != sK570))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f538,plain,(
% 32.37/5.95 ? [X246 : subst,X247 : term,X248 : term > $o,X249 : term > $o] : (! [X250 : term] : ((X248 @ (sub @ X250 @ (push @ X247 @ X246))) = (X249 @ X250)) & ($true = (X248 @ X247)) & ($true != (X249 @ one))) => (! [X250 : term] : ((sK577 @ X250) = (sK576 @ (sub @ X250 @ (push @ sK575 @ sK574)))) & ($true = (sK576 @ sK575)) & ($true != (sK577 @ one)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f539,plain,(
% 32.37/5.95 ! [X251 : subst,X252 : term,X253 : term > $o,X254 : term > $o] : (? [X255 : term] : ((X254 @ X255) != (X253 @ (sub @ X255 @ (push @ X252 @ X251)))) => ((X253 @ (sub @ (sK578 @ X254 @ X253 @ X252 @ X251) @ (push @ X252 @ X251))) != (X254 @ (sK578 @ X254 @ X253 @ X252 @ X251))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f540,plain,(
% 32.37/5.95 ? [X256 : term] : ! [X257 : subst > term > term] : ((X257 @ sh @ one) != (sub @ X256 @ (push @ one @ sh))) => ! [X257 : subst > term > term] : ((X257 @ sh @ one) != (sub @ sK579 @ (push @ one @ sh)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f541,plain,(
% 32.37/5.95 ! [X258 : term] : (? [X259 : subst > term > term] : ((X259 @ sh @ one) = (sub @ X258 @ (push @ one @ sh))) => ((sK580 @ X258 @ sh @ one) = (sub @ X258 @ (push @ one @ sh))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f542,plain,(
% 32.37/5.95 ! [X262 : subst > term > term] : (? [X264 : subst,X265 : subst,X266 : term] : ((sub @ (X262 @ X264 @ X266) @ X265) != (X262 @ (comp @ X264 @ X265) @ (sub @ X266 @ X265))) => ((sub @ (X262 @ (sK581 @ X262) @ (sK583 @ X262)) @ (sK582 @ X262)) != (X262 @ (comp @ (sK581 @ X262) @ (sK582 @ X262)) @ (sub @ (sK583 @ X262) @ (sK582 @ X262)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f543,plain,(
% 32.37/5.95 ! [X263 : subst > term > term] : (? [X267 : subst,X268 : subst,X269 : term] : ((X263 @ (comp @ X267 @ X268) @ (sub @ X269 @ X268)) != (sub @ (X263 @ X267 @ X269) @ X268)) => ((sub @ (X263 @ (sK584 @ X263) @ (sK586 @ X263)) @ (sK585 @ X263)) != (X263 @ (comp @ (sK584 @ X263) @ (sK585 @ X263)) @ (sub @ (sK586 @ X263) @ (sK585 @ X263)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f544,plain,(
% 32.37/5.95 ? [X270 : term,X271 : subst,X272 : subst > term > term,X273 : subst > term > term] : (! [X274 : subst,X275 : subst,X276 : term] : ((sub @ (X272 @ X274 @ X276) @ X275) = (X272 @ (comp @ X274 @ X275) @ (sub @ X276 @ X275))) & ((X272 @ X271 @ X270) != (X273 @ X271 @ X270)) & ! [X277 : subst,X278 : subst,X279 : term] : ((X273 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)) = (sub @ (X273 @ X277 @ X279) @ X278)) & ((lam @ (X273 @ sh @ one)) = (lam @ (X272 @ sh @ one)))) => (! [X276 : term,X275 : subst,X274 : subst] : ((sK589 @ (comp @ X274 @ X275) @ (sub @ X276 @ X275)) = (sub @ (sK589 @ X274 @ X276) @ X275)) & ((sK589 @ sK588 @ sK587) != (sK590 @ sK588 @ sK587)) & ! [X279 : term,X278 : subst,X277 : subst] : ((sK590 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)) = (sub @ (sK590 @ X277 @ X279) @ X278)) & ((lam @ (sK589 @ sh @ one)) = (lam @ (sK590 @ sh @ one))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f473,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (($true = sP57) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP57)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X0 : d_subst] : (d_id = X0) & (! [X1 : term,X2 : subst > term > subst > $o] : (? [X3 : subst > term > term] : (! [X4 : term] : (($true != (X2 @ id @ X4 @ id)) | ($true = (X2 @ id @ (X3 @ id @ X4) @ id))) & ! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X3 @ X7 @ X5) @ X6) = (X3 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) & ($true != (X2 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = (sP53 @ X2)) | ($true = (X2 @ id @ X1 @ id))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X8 : term,X9 : subst > term > subst > $o] : (! [X10 : subst > term > term] : (? [X11 : term] : (($true = (X9 @ id @ X11 @ id)) & ($true != (X9 @ id @ (X10 @ id @ X11) @ id))) | ? [X12 : term,X13 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X13) @ (sub @ X12 @ X13)) != (sub @ (X10 @ X14 @ X12) @ X13)) | ((X9 @ id @ (lam @ (X10 @ sh @ one)) @ id) = $true)) & ($true != (sP53 @ X9)) & ($true != (X9 @ id @ X8 @ id)))) & (termmset_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X15 : subst,X16 : term] : ((sub @ one @ (push @ X16 @ X15)) = X16) & ? [X17 : term > $o,X18 : term,X19 : term > $o,X20 : subst] : (! [X21 : term] : ((X17 @ (sub @ X21 @ (push @ X18 @ X20))) = (X19 @ X21)) & ((X19 @ one) != $true) & ((X17 @ X18) = $true)))) & (? [X22 : subst,X23 : term] : ((sub @ one @ (push @ X23 @ X22)) != X23) | ! [X24 : term > $o,X25 : term,X26 : term > $o,X27 : subst] : (? [X28 : term] : ((X24 @ (sub @ X28 @ (push @ X25 @ X27))) != (X26 @ X28)) | ((X26 @ one) = $true) | ((X24 @ X25) != $true)) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X29 : term,X30 : subst,X31 : term > $o,X32 : term > $o,X33 : term] : (($true != (X32 @ X33)) | ($true = (X31 @ (sub @ X33 @ (push @ X29 @ X30))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X34 : term,X35 : subst,X36 : term > $o,X37 : term > $o,X38 : term] : (($true = (X37 @ X38)) & ((X36 @ (sub @ X38 @ (push @ X34 @ X35))) != $true))) & (! [X39 : term] : ((sub @ X39 @ id) = X39) | (axvarid != $true)) & ((axvarid = $true) | ? [X40 : term] : ((sub @ X40 @ id) != X40)) & (! [X41 : subst,X42 : term] : ((comp @ sh @ (push @ X42 @ X41)) = X41) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X43 : subst,X44 : term] : ((comp @ sh @ (push @ X44 @ X43)) != X43)) & (! [X45 : subst > term > subst > $o] : ? [X46 : term > $o] : ! [X47 : term] : ((X46 @ X47) = (X45 @ id @ X47 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X48 : subst > term > subst > $o] : ! [X49 : term > $o] : ? [X50 : term] : ((X49 @ X50) != (X48 @ id @ X50 @ id))) & (lamnotap != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((laminj = $true) | ? [X51 : term,X52 : term] : ((X51 != X52) & ((lam @ X52) = (lam @ X51)))) & (! [X53 : term,X54 : term] : ((X53 = X54) | ((lam @ X54) != (lam @ X53))) | (laminj != $true)) & ((hoasapinj2 = $true) | ? [X55 : term,X56 : term,X57 : term,X58 : term] : (((ap @ (sub @ X56 @ id) @ X57) = (ap @ (sub @ X58 @ id) @ X55)) & (X55 != X57))) & (! [X59 : term,X60 : term,X61 : term,X62 : term] : (((ap @ (sub @ X62 @ id) @ X59) != (ap @ (sub @ X60 @ id) @ X61)) | (X59 = X61)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3 != $true)) & ((d2subst @ d_id) = id) & ! [X63 : d_term,X64 : d_term] : ((X63 = X64) | ((d2term @ X64) != (d2term @ X63))) & (hoaslamnotap_lthm = $true) & (($true = sP49) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP49)) & ((hoaslamnotap = $true) | ? [X65 : term,X66 : term,X67 : subst > term > term] : (! [X68 : term,X69 : subst,X70 : subst] : ((X67 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69)) = (sub @ (X67 @ X70 @ X68) @ X69)) & ((ap @ (sub @ X66 @ id) @ X65) = (lam @ (X67 @ sh @ one))))) & (! [X71 : term,X72 : term,X73 : subst > term > term] : (? [X74 : term,X75 : subst,X76 : subst] : ((sub @ (X73 @ X76 @ X74) @ X75) != (X73 @ (comp @ X76 @ X75) @ (sub @ X74 @ X75))) | ((lam @ (X73 @ sh @ one)) != (ap @ (sub @ X72 @ id) @ X71))) | (hoaslamnotap != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3a_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X77 : term] : ? [X78 : d_term] : ((d2term @ X78) = X77) & (! [X79 : subst,X80 : term > $o,X81 : term > $o,X82 : term,X83 : term] : (((X80 @ (sub @ X83 @ (push @ X82 @ X79))) = $true) | ($true != (X81 @ X83))) | ? [X84 : term,X85 : subst] : ((sub @ one @ (push @ X84 @ X85)) != X84) | ? [X86 : subst,X87 : term] : ((comp @ sh @ (push @ X87 @ X86)) != X86) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X88 : subst,X89 : term > $o,X90 : term > $o,X91 : term,X92 : term] : (($true != (X89 @ (sub @ X92 @ (push @ X91 @ X88)))) & ((X90 @ X92) = $true)) & ! [X93 : term,X94 : subst] : ((sub @ one @ (push @ X93 @ X94)) = X93) & ! [X95 : subst,X96 : term] : ((comp @ sh @ (push @ X96 @ X95)) = X95))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X97 : subst] : ((comp @ id @ X97) = X97) | (axidl != $true)) & ((axidl = $true) | ? [X98 : subst] : ((comp @ id @ X98) != X98)) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X99 : term,X100 : term,X101 : term,X102 : term] : ((X99 = X100) | ((ap @ X100 @ X102) != (ap @ X99 @ X101))) & ! [X103 : term] : ((sub @ X103 @ id) = X103) & ? [X104 : term,X105 : term,X106 : term,X107 : term] : (((ap @ (sub @ X107 @ id) @ X105) = (ap @ (sub @ X104 @ id) @ X106)) & (X104 != X107)))) & (? [X108 : term,X109 : term,X110 : term,X111 : term] : ((X108 != X109) & ((ap @ X109 @ X111) = (ap @ X108 @ X110))) | ? [X112 : term] : ((sub @ X112 @ id) != X112) | ! [X113 : term,X114 : term,X115 : term,X116 : term] : (((ap @ (sub @ X113 @ id) @ X115) != (ap @ (sub @ X116 @ id) @ X114)) | (X113 = X116)) | (hoasapinj1_lthm != $true)) & ((! [X117 : subst] : ((comp @ id @ X117) = X117) & ! [X118 : subst] : ((comp @ X118 @ id) = X118)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X119 : subst] : ((comp @ id @ X119) != X119) | ? [X120 : subst] : ((comp @ X120 @ id) != X120)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) | ? [X121 : term,X122 : term > $o] : (($true != (X122 @ X121)) & ((sP45 @ X122) != $true) & ! [X123 : term] : (((var @ X123) != $true) | ((X122 @ X123) = $true)) & ! [X124 : term] : (($true != (X122 @ X124)) | ((X122 @ (lam @ X124)) = $true)))) & (! [X125 : term,X126 : term > $o] : (($true = (X126 @ X125)) | ((sP45 @ X126) = $true) | ? [X127 : term] : (($true = (var @ X127)) & ((X126 @ X127) != $true)) | ? [X128 : term] : (($true = (X126 @ X128)) & ($true != (X126 @ (lam @ X128))))) | (induction != $true)) & (! [X129 : term > $o,X130 : subst,X131 : term] : ? [X132 : term > $o] : ! [X133 : term] : ((X129 @ (sub @ X133 @ (push @ X131 @ X130))) = (X132 @ X133)) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X134 : term > $o,X135 : subst,X136 : term] : ! [X137 : term > $o] : ? [X138 : term] : ((X134 @ (sub @ X138 @ (push @ X136 @ X135))) != (X137 @ X138))) & ((axvarcons = $true) | ? [X139 : term,X140 : subst] : ((sub @ one @ (push @ X139 @ X140)) != X139)) & (! [X141 : term,X142 : subst] : ((sub @ one @ (push @ X141 @ X142)) = X141) | (axvarcons != $true)) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) | ? [X143 : term,X144 : term,X145 : term,X146 : term] : (((ap @ X143 @ X146) = (ap @ X145 @ X144)) & (X143 != X145))) & (! [X147 : term,X148 : term,X149 : term,X150 : term] : (((ap @ X149 @ X148) != (ap @ X147 @ X150)) | (X147 = X149)) | (apinj1 != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X151 : subst > term > subst > $o] : ! [X152 : term > $o] : ? [X153 : term] : ((X152 @ X153) != (X151 @ id @ X153 @ id))) & (! [X154 : subst > term > subst > $o] : ? [X155 : term > $o] : ! [X156 : term] : ((X154 @ id @ X156 @ id) = (X155 @ X156)) | (hoasinduction_lem0_lthm != $true)) & (apnotvar = $true) & (($true = sP44) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP44)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X157 : subst] : ((comp @ X157 @ id) = X157) & (? [X158 : subst] : ((comp @ X158 @ id) != X158) | ? [X159 : subst] : ((comp @ id @ X159) != X159)) & ! [X160 : subst] : ((comp @ id @ X160) = X160))) & (? [X161 : subst] : ((comp @ X161 @ id) != X161) | (! [X162 : subst] : ((comp @ X162 @ id) = X162) & ! [X163 : subst] : ((comp @ id @ X163) = X163)) | ? [X164 : subst] : ((comp @ id @ X164) != X164) | (substmonoid_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem2v2 != $true)) & (pushprop_gthm = $true) & (! [X165 : subst] : ((push @ (sub @ one @ X165) @ (comp @ sh @ X165)) = X165) | (axscons != $true)) & ((axscons = $true) | ? [X166 : subst] : ((push @ (sub @ one @ X166) @ (comp @ sh @ X166)) != X166)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3v2_f = $true) | ? [X167 : term] : ! [X168 : subst > term > term] : ? [X169 : term,X170 : subst] : ((X168 @ X170 @ X169) != (sub @ X167 @ (push @ X169 @ X170)))) & (! [X171 : term] : ? [X172 : subst > term > term] : ! [X173 : term,X174 : subst] : ((X172 @ X174 @ X173) = (sub @ X171 @ (push @ X173 @ X174))) | (hoasinduction_lem3v2_f != $true)) & ((termmset = $true) | ? [X175 : term] : ((sub @ X175 @ id) != X175)) & (! [X176 : term] : ((sub @ X176 @ id) = X176) | (termmset != $true)) & ((shinj = $true) | ? [X177 : term,X178 : term] : (((sub @ X177 @ sh) = (sub @ X178 @ sh)) & (X177 != X178))) & (! [X179 : term,X180 : term] : (((sub @ X180 @ sh) != (sub @ X179 @ sh)) | (X179 = X180)) | (shinj != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X181 : term,X182 : term,X183 : term,X184 : term] : ((X183 = X184) | ((ap @ X181 @ X184) != (ap @ X182 @ X183))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X185 : term,X186 : term,X187 : term,X188 : term] : ((X187 != X188) & ((ap @ X185 @ X188) = (ap @ X186 @ X187)))) & (($true = sP37) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP37)) & (! [X189 : term] : ? [X190 : subst > term > term] : ((X190 @ sh @ one) = (sub @ X189 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X191 : term] : ! [X192 : subst > term > term] : ((sub @ X191 @ (push @ one @ sh)) != (X192 @ sh @ one))) & (! [X193 : term] : ? [X194 : subst > term > term] : ! [X195 : term,X196 : subst] : ((X194 @ X196 @ X195) = (sub @ X193 @ (push @ X195 @ X196))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X197 : term] : ! [X198 : subst > term > term] : ? [X199 : term,X200 : subst] : ((X198 @ X200 @ X199) != (sub @ X197 @ (push @ X199 @ X200)))) & (hoasinduction_gthm = $true) & (($true = sP33) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP31) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP31)) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X201 : d_term] : (d_one = X201) & ((sP30 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP30 != $true)) & ((induction2 = $true) | ($true != sP29)) & (($true = sP29) | (induction2 != $true)) & ! [X202 : d_subst,X203 : d_subst] : (((d2subst @ X202) != (d2subst @ X203)) | (X202 = X203)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & (? [X204 : term] : ((sub @ X204 @ id) != X204) | ! [X205 : term] : ((sub @ X205 @ id) = X205) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X206 : term] : ((sub @ X206 @ id) = X206) & ? [X207 : term] : ((sub @ X207 @ id) != X207))) & ((sP27 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP27 != $true)) & (($true = sP26) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP26)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & ! [X208 : subst] : ? [X209 : d_subst] : ((d2subst @ X209) = X208) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) | ? [X210 : subst] : ((comp @ X210 @ id) != X210)) & (! [X211 : subst] : ((comp @ X211 @ id) = X211) | (axidr != $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X212 @ id) @ X214) != (ap @ (sub @ X215 @ id) @ X213)) | (X213 = X214)) | ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 != X218) & ((ap @ X217 @ X218) = (ap @ X219 @ X216))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X220 : term,X221 : term,X222 : term,X223 : term] : (((ap @ (sub @ X223 @ id) @ X221) = (ap @ (sub @ X220 @ id) @ X222)) & (X221 != X222)) & ! [X224 : term,X225 : term,X226 : term,X227 : term] : ((X224 = X226) | ((ap @ X225 @ X226) != (ap @ X227 @ X224))))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X228 : subst,X229 : term,X230 : term > $o] : ! [X231 : term > $o] : ? [X232 : term] : ((X231 @ X232) != (X230 @ (sub @ X232 @ (push @ X229 @ X228))))) & (! [X233 : subst,X234 : term,X235 : term > $o] : ? [X236 : term > $o] : ! [X237 : term] : ((X236 @ X237) = (X235 @ (sub @ X237 @ (push @ X234 @ X233)))) | (pushprop_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP23)) & (($true = sP23) | (induction2_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X238 : term,X239 : term,X240 : term,X241 : term] : (((ap @ (sub @ X238 @ id) @ X239) != (ap @ (sub @ X240 @ id) @ X241)) | (X238 = X240)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X242 : term,X243 : term,X244 : term,X245 : term] : (((ap @ (sub @ X242 @ id) @ X243) = (ap @ (sub @ X244 @ id) @ X245)) & (X242 != X244))) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (($true = sP13) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP13)) & ((pushprop_lem1v2 = $true) | ? [X246 : subst,X247 : term,X248 : term > $o,X249 : term > $o] : (! [X250 : term] : ((X248 @ (sub @ X250 @ (push @ X247 @ X246))) = (X249 @ X250)) & ($true = (X248 @ X247)) & ($true != (X249 @ one)))) & (! [X251 : subst,X252 : term,X253 : term > $o,X254 : term > $o] : (? [X255 : term] : ((X254 @ X255) != (X253 @ (sub @ X255 @ (push @ X252 @ X251)))) | ($true != (X253 @ X252)) | ($true = (X254 @ one))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3b = $true) | ? [X256 : term] : ! [X257 : subst > term > term] : ((X257 @ sh @ one) != (sub @ X256 @ (push @ one @ sh)))) & (! [X258 : term] : ? [X259 : subst > term > term] : ((X259 @ sh @ one) = (sub @ X258 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (! [X260 : term,X261 : subst,X262 : subst > term > term,X263 : subst > term > term] : (? [X264 : subst,X265 : subst,X266 : term] : ((sub @ (X262 @ X264 @ X266) @ X265) != (X262 @ (comp @ X264 @ X265) @ (sub @ X266 @ X265))) | ((X262 @ X261 @ X260) = (X263 @ X261 @ X260)) | ? [X267 : subst,X268 : subst,X269 : term] : ((X263 @ (comp @ X267 @ X268) @ (sub @ X269 @ X268)) != (sub @ (X263 @ X267 @ X269) @ X268)) | ((lam @ (X263 @ sh @ one)) != (lam @ (X262 @ sh @ one)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X270 : term,X271 : subst,X272 : subst > term > term,X273 : subst > term > term] : (! [X274 : subst,X275 : subst,X276 : term] : ((sub @ (X272 @ X274 @ X276) @ X275) = (X272 @ (comp @ X274 @ X275) @ (sub @ X276 @ X275))) & ((X272 @ X271 @ X270) != (X273 @ X271 @ X270)) & ! [X277 : subst,X278 : subst,X279 : term] : ((X273 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)) = (sub @ (X273 @ X277 @ X279) @ X278)) & ((lam @ (X273 @ sh @ one)) = (lam @ (X272 @ sh @ one))))) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(rectify,[status(thm)],[f472])).
% 32.37/5.95 thf(f472,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (($true = sP57) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP57)) & (($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56)) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X48 : d_subst] : (d_id = X48) & (! [X467 : term,X468 : subst > term > subst > $o] : (? [X469 : subst > term > term] : (! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true)) & ! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) & ($true != (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ($true = (sP53 @ X468)) | ((X468 @ id @ X467 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X467 : term,X468 : subst > term > subst > $o] : (! [X469 : subst > term > term] : (? [X473 : term] : (($true = (X468 @ id @ X473 @ id)) & ((X468 @ id @ (X469 @ id @ X473) @ id) != $true)) | ? [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) != (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) | ($true = (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) & ($true != (sP53 @ X468)) & ((X468 @ id @ X467 @ id) != $true))) & (termmset_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) = X351) & ? [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (! [X356 : term] : ((X354 @ X356) = (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) & ($true != (X354 @ one)) & ($true = (X352 @ X353))))) & (? [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) != X351) | ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (? [X356 : term] : ((X354 @ X356) != (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true = (X354 @ one)) | ($true != (X352 @ X353))) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true = (X155 @ X156)) & ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) != $true))) & (! [X167 : term] : ((sub @ X167 @ id) = X167) | (axvarid != $true)) & ((axvarid = $true) | ? [X167 : term] : ((sub @ X167 @ id) != X167)) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) != X281)) & (! [X204 : subst > term > subst > $o] : ? [X205 : term > $o] : ! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X204 : subst > term > subst > $o] : ! [X205 : term > $o] : ? [X206 : term] : ((X205 @ X206) != (X204 @ id @ X206 @ id))) & (lamnotap != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((laminj = $true) | ? [X93 : term,X94 : term] : ((X93 != X94) & ((lam @ X93) = (lam @ X94)))) & (! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94))) | (laminj != $true)) & ((hoasapinj2 = $true) | ? [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) = (ap @ (sub @ X213 @ id) @ X214)) & (X212 != X214))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3 != $true)) & ((d2subst @ d_id) = id) & ! [X168 : d_term,X169 : d_term] : ((X168 = X169) | ((d2term @ X169) != (d2term @ X168))) & (hoaslamnotap_lthm = $true) & (($true = sP49) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP49)) & ((hoaslamnotap = $true) | ? [X249 : term,X250 : term,X251 : subst > term > term] : (! [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) = (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) & ((ap @ (sub @ X250 @ id) @ X249) = (lam @ (X251 @ sh @ one))))) & (! [X249 : term,X250 : term,X251 : subst > term > term] : (? [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) != (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) | ((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one)))) | (hoaslamnotap != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3a_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & (! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true)) | ? [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) != X291) | ? [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) != X293) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true != (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) & ((X297 @ X299) = $true)) & ! [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) = X291) & ! [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) = X293))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X290 : subst] : ((comp @ id @ X290) = X290) | (axidl != $true)) & ((axidl = $true) | ? [X290 : subst] : ((comp @ id @ X290) != X290)) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 = X86) | ((ap @ X85 @ X87) != (ap @ X86 @ X88))) & ! [X84 : term] : ((sub @ X84 @ id) = X84) & ? [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) = (ap @ (sub @ X89 @ id) @ X91)) & (X89 != X92)))) & (? [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 != X86) & ((ap @ X85 @ X87) = (ap @ X86 @ X88))) | ? [X84 : term] : ((sub @ X84 @ id) != X84) | ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)) | (hoasapinj1_lthm != $true)) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X357 : subst] : ((comp @ id @ X357) != X357) | ? [X358 : subst] : ((comp @ X358 @ id) != X358)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) | ? [X54 : term,X55 : term > $o] : (($true != (X55 @ X54)) & ($true != (sP45 @ X55)) & ! [X56 : term] : (($true != (var @ X56)) | ($true = (X55 @ X56))) & ! [X57 : term] : (($true != (X55 @ X57)) | ($true = (X55 @ (lam @ X57)))))) & (! [X54 : term,X55 : term > $o] : (($true = (X55 @ X54)) | ($true = (sP45 @ X55)) | ? [X56 : term] : (($true = (var @ X56)) & ($true != (X55 @ X56))) | ? [X57 : term] : (($true = (X55 @ X57)) & ($true != (X55 @ (lam @ X57))))) | (induction != $true)) & (! [X49 : term > $o,X50 : subst,X51 : term] : ? [X52 : term > $o] : ! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X49 : term > $o,X50 : subst,X51 : term] : ! [X52 : term > $o] : ? [X53 : term] : ((X52 @ X53) != (X49 @ (sub @ X53 @ (push @ X51 @ X50))))) & ((axvarcons = $true) | ? [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) != X449)) & (! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449) | (axvarcons != $true)) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) | ? [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) = (ap @ X46 @ X45)) & (X44 != X46))) & (! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46)) | (apinj1 != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X216 : subst > term > subst > $o] : ! [X217 : term > $o] : ? [X218 : term] : ((X216 @ id @ X218 @ id) != (X217 @ X218))) & (! [X216 : subst > term > subst > $o] : ? [X217 : term > $o] : ! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218)) | (hoasinduction_lem0_lthm != $true)) & (apnotvar = $true) & (($true = sP44) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP44)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X345 : subst] : ((comp @ X345 @ id) = X345) & (? [X347 : subst] : ((comp @ X347 @ id) != X347) | ? [X346 : subst] : ((comp @ id @ X346) != X346)) & ! [X344 : subst] : ((comp @ id @ X344) = X344))) & (? [X345 : subst] : ((comp @ X345 @ id) != X345) | (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346)) | ? [X344 : subst] : ((comp @ id @ X344) != X344) | (substmonoid_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem2v2 != $true)) & (pushprop_gthm = $true) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) | (axscons != $true)) & ((axscons = $true) | ? [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) != X498)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3v2_f = $true) | ? [X445 : term] : ! [X446 : subst > term > term] : ? [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) != (X446 @ X448 @ X447))) & (! [X445 : term] : ? [X446 : subst > term > term] : ! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447)) | (hoasinduction_lem3v2_f != $true)) & ((termmset = $true) | ? [X305 : term] : ((sub @ X305 @ id) != X305)) & (! [X305 : term] : ((sub @ X305 @ id) = X305) | (termmset != $true)) & ((shinj = $true) | ? [X186 : term,X187 : term] : (((sub @ X187 @ sh) = (sub @ X186 @ sh)) & (X186 != X187))) & (! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187)) | (shinj != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 != X191) & ((ap @ X189 @ X190) = (ap @ X188 @ X191)))) & (($true = sP37) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP37)) & (! [X38 : term] : ? [X39 : subst > term > term] : ((X39 @ sh @ one) = (sub @ X38 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X38 : term] : ! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh)))) & (! [X40 : term] : ? [X41 : subst > term > term] : ! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X40 : term] : ! [X41 : subst > term > term] : ? [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) != (sub @ X40 @ (push @ X42 @ X43)))) & (hoasinduction_gthm = $true) & (($true = sP33) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP31) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP31)) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & ((sP30 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP30 != $true)) & ((induction2 = $true) | ($true != sP29)) & (($true = sP29) | (induction2 != $true)) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) != (d2subst @ X349)) | (X348 = X349)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & (? [X157 : term] : ((sub @ X157 @ id) != X157) | ! [X158 : term] : ((sub @ X158 @ id) = X158) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X157 : term] : ((sub @ X157 @ id) = X157) & ? [X158 : term] : ((sub @ X158 @ id) != X158))) & ((sP27 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP27 != $true)) & (($true = sP26) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP26)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) | ? [X4 : subst] : ((comp @ X4 @ id) != X4)) & (! [X4 : subst] : ((comp @ X4 @ id) = X4) | (axidr != $true)) & (! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)) | ? [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 != X308) & ((ap @ X307 @ X308) = (ap @ X309 @ X306))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) = (ap @ (sub @ X313 @ id) @ X311)) & (X311 != X312)) & ! [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 = X308) | ((ap @ X307 @ X308) != (ap @ X309 @ X306))))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X207 : subst,X208 : term,X209 : term > $o] : ! [X210 : term > $o] : ? [X211 : term] : ((X210 @ X211) != (X209 @ (sub @ X211 @ (push @ X208 @ X207))))) & (! [X207 : subst,X208 : term,X209 : term > $o] : ? [X210 : term > $o] : ! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207)))) | (pushprop_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP23)) & (($true = sP23) | (induction2_lthm != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) = (ap @ (sub @ X484 @ id) @ X485)) & (X484 != X486))) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (($true = sP13) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP13)) & ((pushprop_lem1v2 = $true) | ? [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (! [X304 : term] : ((X303 @ X304) = (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) & ($true = (X302 @ X301)) & ($true != (X303 @ one)))) & (! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (? [X304 : term] : ((X303 @ X304) != (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ($true != (X302 @ X301)) | ($true = (X303 @ one))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3b = $true) | ? [X0 : term] : ! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh)))) & (! [X0 : term] : ? [X1 : subst > term > term] : ((X1 @ sh @ one) = (sub @ X0 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (? [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) != (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)) | ? [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) != (sub @ (X491 @ X492 @ X494) @ X493)) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (! [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) = (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) & ((X491 @ X489 @ X488) != (X490 @ X489 @ X488)) & ! [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) = (sub @ (X491 @ X492 @ X494) @ X493)) & ((lam @ (X491 @ sh @ one)) = (lam @ (X490 @ sh @ one))))) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(flattening,[status(thm)],[f471])).
% 32.37/5.95 thf(f471,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & (((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true))) & ((($true = sP57) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP57))) & ((($true = sP56) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP56))) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X48 : d_subst] : (d_id = X48) & ((! [X467 : term,X468 : subst > term > subst > $o] : (? [X469 : subst > term > term] : (! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true)) & ! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) & ($true != (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ($true = (sP53 @ X468)) | ((X468 @ id @ X467 @ id) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X467 : term,X468 : subst > term > subst > $o] : (! [X469 : subst > term > term] : (? [X473 : term] : (($true = (X468 @ id @ X473 @ id)) & ((X468 @ id @ (X469 @ id @ X473) @ id) != $true)) | ? [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) != (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) | ($true = (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) & ($true != (sP53 @ X468)) & ((X468 @ id @ X467 @ id) != $true)))) & (termmset_gthm = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) = X351) & ? [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (! [X356 : term] : ((X354 @ X356) = (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) & ($true != (X354 @ one)) & ($true = (X352 @ X353))))) & ((? [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) != X351) | ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (? [X356 : term] : ((X354 @ X356) != (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true = (X354 @ one)) | ($true != (X352 @ X353)))) | (pushprop_lem1v2_lthm != $true))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true = (X155 @ X156)) & ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) != $true)))) & ((! [X167 : term] : ((sub @ X167 @ id) = X167) | (axvarid != $true)) & ((axvarid = $true) | ? [X167 : term] : ((sub @ X167 @ id) != X167))) & ((! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) != X281))) & ((! [X204 : subst > term > subst > $o] : ? [X205 : term > $o] : ! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id)) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X204 : subst > term > subst > $o] : ! [X205 : term > $o] : ? [X206 : term] : ((X205 @ X206) != (X204 @ id @ X206 @ id)))) & (lamnotap != $true) & (((hoasinduction_lem3aaa = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3aaa != $true))) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (((laminj = $true) | ? [X93 : term,X94 : term] : ((X93 != X94) & ((lam @ X93) = (lam @ X94)))) & (! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94))) | (laminj != $true))) & (((hoasapinj2 = $true) | ? [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) = (ap @ (sub @ X213 @ id) @ X214)) & (X212 != X214))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214)) | (hoasapinj2 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3 != $true))) & ((d2subst @ d_id) = id) & ! [X168 : d_term,X169 : d_term] : ((X168 = X169) | ((d2term @ X169) != (d2term @ X168))) & (hoaslamnotap_lthm = $true) & ((($true = sP49) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP49))) & (((hoaslamnotap = $true) | ? [X249 : term,X250 : term,X251 : subst > term > term] : (! [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) = (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) & ((ap @ (sub @ X250 @ id) @ X249) = (lam @ (X251 @ sh @ one))))) & (! [X249 : term,X250 : term,X251 : subst > term > term] : (? [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) != (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) | ((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one)))) | (hoaslamnotap != $true))) & (((hoasinduction_lem3a_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3a_lthm != $true))) & (hoasapinj1_gthm = $true) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & (((! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true)) | ? [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) != X291) | ? [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) != X293)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true != (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) & ((X297 @ X299) = $true)) & ! [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) = X291) & ! [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) = X293)))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X290 : subst] : ((comp @ id @ X290) = X290) | (axidl != $true)) & ((axidl = $true) | ? [X290 : subst] : ((comp @ id @ X290) != X290))) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & (((hoasapinj1_lthm = $true) | (! [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 = X86) | ((ap @ X85 @ X87) != (ap @ X86 @ X88))) & ! [X84 : term] : ((sub @ X84 @ id) = X84) & ? [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) = (ap @ (sub @ X89 @ id) @ X91)) & (X89 != X92)))) & ((? [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 != X86) & ((ap @ X85 @ X87) = (ap @ X86 @ X88))) | ? [X84 : term] : ((sub @ X84 @ id) != X84) | ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92))) | (hoasapinj1_lthm != $true))) & (((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X357 : subst] : ((comp @ id @ X357) != X357) | ? [X358 : subst] : ((comp @ X358 @ id) != X358)))) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (((induction = $true) | ? [X54 : term,X55 : term > $o] : (($true != (X55 @ X54)) & ($true != (sP45 @ X55)) & ! [X56 : term] : (($true != (var @ X56)) | ($true = (X55 @ X56))) & ! [X57 : term] : (($true != (X55 @ X57)) | ($true = (X55 @ (lam @ X57)))))) & (! [X54 : term,X55 : term > $o] : (($true = (X55 @ X54)) | ($true = (sP45 @ X55)) | ? [X56 : term] : (($true = (var @ X56)) & ($true != (X55 @ X56))) | ? [X57 : term] : (($true = (X55 @ X57)) & ($true != (X55 @ (lam @ X57))))) | (induction != $true))) & ((! [X49 : term > $o,X50 : subst,X51 : term] : ? [X52 : term > $o] : ! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X49 : term > $o,X50 : subst,X51 : term] : ! [X52 : term > $o] : ? [X53 : term] : ((X52 @ X53) != (X49 @ (sub @ X53 @ (push @ X51 @ X50)))))) & (((axvarcons = $true) | ? [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) != X449)) & (! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449) | (axvarcons != $true))) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & (((apinj1 = $true) | ? [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) = (ap @ X46 @ X45)) & (X44 != X46))) & (! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46)) | (apinj1 != $true))) & (((hoasinduction_lem0_lthm = $true) | ? [X216 : subst > term > subst > $o] : ! [X217 : term > $o] : ? [X218 : term] : ((X216 @ id @ X218 @ id) != (X217 @ X218))) & (! [X216 : subst > term > subst > $o] : ? [X217 : term > $o] : ! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218)) | (hoasinduction_lem0_lthm != $true))) & (apnotvar = $true) & ((($true = sP44) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP44))) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & (((substmonoid_lthm = $true) | (! [X345 : subst] : ((comp @ X345 @ id) = X345) & (? [X347 : subst] : ((comp @ X347 @ id) != X347) | ? [X346 : subst] : ((comp @ id @ X346) != X346)) & ! [X344 : subst] : ((comp @ id @ X344) = X344))) & ((? [X345 : subst] : ((comp @ X345 @ id) != X345) | (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346)) | ? [X344 : subst] : ((comp @ id @ X344) != X344)) | (substmonoid_lthm != $true))) & (((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true))) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem2v2 != $true))) & (pushprop_gthm = $true) & ((! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) | (axscons != $true)) & ((axscons = $true) | ? [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) != X498))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (((hoasinduction_lem3v2_f = $true) | ? [X445 : term] : ! [X446 : subst > term > term] : ? [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) != (X446 @ X448 @ X447))) & (! [X445 : term] : ? [X446 : subst > term > term] : ! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447)) | (hoasinduction_lem3v2_f != $true))) & (((termmset = $true) | ? [X305 : term] : ((sub @ X305 @ id) != X305)) & (! [X305 : term] : ((sub @ X305 @ id) = X305) | (termmset != $true))) & (((shinj = $true) | ? [X186 : term,X187 : term] : (((sub @ X187 @ sh) = (sub @ X186 @ sh)) & (X186 != X187))) & (! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187)) | (shinj != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 != X191) & ((ap @ X189 @ X190) = (ap @ X188 @ X191))))) & ((($true = sP37) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP37))) & ((! [X38 : term] : ? [X39 : subst > term > term] : ((X39 @ sh @ one) = (sub @ X38 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X38 : term] : ! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh))))) & ((! [X40 : term] : ? [X41 : subst > term > term] : ! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X40 : term] : ! [X41 : subst > term > term] : ? [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) != (sub @ X40 @ (push @ X42 @ X43))))) & (hoasinduction_gthm = $true) & ((($true = sP33) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP33))) & ((($true = sP31) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP31))) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & (((sP30 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP30 != $true))) & (((induction2 = $true) | ($true != sP29)) & (($true = sP29) | (induction2 != $true))) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) != (d2subst @ X349)) | (X348 = X349)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & (((? [X157 : term] : ((sub @ X157 @ id) != X157) | ! [X158 : term] : ((sub @ X158 @ id) = X158)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X157 : term] : ((sub @ X157 @ id) = X157) & ? [X158 : term] : ((sub @ X158 @ id) != X158)))) & (((sP27 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP27 != $true))) & ((($true = sP26) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP26))) & (pushprop = $true) & (((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true))) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (hoasinduction_lem2v2_gthm = $true) & (((axidr = $true) | ? [X4 : subst] : ((comp @ X4 @ id) != X4)) & (! [X4 : subst] : ((comp @ X4 @ id) = X4) | (axidr != $true))) & (((! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)) | ? [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 != X308) & ((ap @ X307 @ X308) = (ap @ X309 @ X306)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) = (ap @ (sub @ X313 @ id) @ X311)) & (X311 != X312)) & ! [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 = X308) | ((ap @ X307 @ X308) != (ap @ X309 @ X306)))))) & (hoaslamnotvar_lthm = $true) & (((pushprop_lem0_lthm = $true) | ? [X207 : subst,X208 : term,X209 : term > $o] : ! [X210 : term > $o] : ? [X211 : term] : ((X210 @ X211) != (X209 @ (sub @ X211 @ (push @ X208 @ X207))))) & (! [X207 : subst,X208 : term,X209 : term > $o] : ? [X210 : term > $o] : ! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207)))) | (pushprop_lem0_lthm != $true))) & (((induction2_lthm = $true) | ($true != sP23)) & (($true = sP23) | (induction2_lthm != $true))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) = (ap @ (sub @ X484 @ id) @ X485)) & (X484 != X486)))) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (((hoasinduction_lthm_3 = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lthm_3 != $true))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & ((($true = sP13) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP13))) & (((pushprop_lem1v2 = $true) | ? [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (! [X304 : term] : ((X303 @ X304) = (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) & ($true = (X302 @ X301)) & ($true != (X303 @ one)))) & (! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (? [X304 : term] : ((X303 @ X304) != (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ($true != (X302 @ X301)) | ($true = (X303 @ one))) | (pushprop_lem1v2 != $true))) & (((hoasinduction_lem3b = $true) | ? [X0 : term] : ! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh)))) & (! [X0 : term] : ? [X1 : subst > term > term] : ((X1 @ sh @ one) = (sub @ X0 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true))) & (hoasinduction_lem3v2_gthm = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction_no_psi_cond_lthm != $true))) & (induction2lem_gthm = $true) & (lamnotvar = $true) & ((! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (? [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) != (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)) | ? [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) != (sub @ (X491 @ X492 @ X494) @ X493)) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (! [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) = (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) & ((X491 @ X489 @ X488) != (X490 @ X489 @ X488)) & ! [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) = (sub @ (X491 @ X492 @ X494) @ X493)) & ((lam @ (X491 @ sh @ one)) = (lam @ (X490 @ sh @ one)))))) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(nnf_transformation,[status(thm)],[f73])).
% 32.37/5.95 thf(f73,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & ((sP58 = $true) <=> (hoasinduction_lem3v2a = $true)) & (($true = sP57) <=> (hoasinduction_lem3v2a_lthm = $true)) & (($true = sP56) <=> (hoasinduction_lem3_lthm = $true)) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X48 : d_subst] : (d_id = X48) & (! [X467 : term,X468 : subst > term > subst > $o] : (? [X469 : subst > term > term] : (! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true)) & ! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) & ($true != (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ($true = (sP53 @ X468)) | ((X468 @ id @ X467 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (termmset_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) != X351) | ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (? [X356 : term] : ((X354 @ X356) != (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true = (X354 @ one)) | ($true != (X352 @ X353))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) <=> (pushprop_lem1 = $true)) & (! [X167 : term] : ((sub @ X167 @ id) = X167) <=> (axvarid = $true)) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) <=> (axshiftcons = $true)) & (! [X204 : subst > term > subst > $o] : ? [X205 : term > $o] : ! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id)) <=> (hoasinduction_lem0 = $true)) & (lamnotap != $true) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP52)) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((laminj = $true) <=> ! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94)))) & ((hoasapinj2 = $true) <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214))) & ((hoasinduction_lem3 = $true) <=> ($true = sP51)) & ((d2subst @ d_id) = id) & ! [X168 : d_term,X169 : d_term] : ((X168 = X169) | ((d2term @ X169) != (d2term @ X168))) & (hoaslamnotap_lthm = $true) & (($true = sP49) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X249 : term,X250 : term,X251 : subst > term > term] : (? [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) != (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) | ((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one))))) & ((hoasinduction_lem3a_lthm = $true) <=> ($true = sP47)) & (hoasapinj1_gthm = $true) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & ((! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true)) | ? [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) != X291) | ? [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) != X293)) <=> (pushprop_lem1_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X290 : subst] : ((comp @ id @ X290) = X290) <=> (axidl = $true)) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 != X86) & ((ap @ X85 @ X87) = (ap @ X86 @ X88))) | ? [X84 : term] : ((sub @ X84 @ id) != X84) | ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)))) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) <=> (substmonoid = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) <=> ! [X54 : term,X55 : term > $o] : (($true = (X55 @ X54)) | ($true = (sP45 @ X55)) | ? [X56 : term] : (($true = (var @ X56)) & ($true != (X55 @ X56))) | ? [X57 : term] : (($true = (X55 @ X57)) & ($true != (X55 @ (lam @ X57)))))) & (! [X49 : term > $o,X50 : subst,X51 : term] : ? [X52 : term > $o] : ! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) <=> (pushprop_lem0 = $true)) & ((axvarcons = $true) <=> ! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449)) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) <=> ! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X216 : subst > term > subst > $o] : ? [X217 : term > $o] : ! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218))) & (apnotvar = $true) & (($true = sP44) <=> (hoasinduction = $true)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) <=> (? [X345 : subst] : ((comp @ X345 @ id) != X345) | (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346)) | ? [X344 : subst] : ((comp @ id @ X344) != X344))) & ((hoasinduction_lem2 = $true) <=> ($true = sP41)) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP39)) & (pushprop_gthm = $true) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) <=> (axscons = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X445 : term] : ? [X446 : subst > term > term] : ! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447))) & ((termmset = $true) <=> ! [X305 : term] : ((sub @ X305 @ id) = X305)) & ((shinj = $true) <=> ! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) <=> (apinj2 = $true)) & (($true = sP37) <=> (induction2lem_lthm = $true)) & (! [X38 : term] : ? [X39 : subst > term > term] : ((X39 @ sh @ one) = (sub @ X38 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X40 : term] : ? [X41 : subst > term > term] : ! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_gthm = $true) & (($true = sP33) <=> (induction2lem = $true)) & (($true = sP31) <=> (hoasinduction_lem3aa = $true)) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & ((sP30 = $true) <=> (hoasinduction_lem3a = $true)) & ((induction2 = $true) <=> ($true = sP29)) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) != (d2subst @ X349)) | (X348 = X349)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & ((? [X157 : term] : ((sub @ X157 @ id) != X157) | ! [X158 : term] : ((sub @ X158 @ id) = X158)) <=> (termmset_lthm = $true)) & ((sP27 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & (($true = sP26) <=> (hoasinduction_lem3v2 = $true)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) <=> ($true = sP24)) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & ((! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)) | ? [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 != X308) & ((ap @ X307 @ X308) = (ap @ X309 @ X306)))) <=> (hoasapinj2_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X207 : subst,X208 : term,X209 : term > $o] : ? [X210 : term > $o] : ! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207))))) & ((induction2_lthm = $true) <=> ($true = sP23)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) <=> (hoasapinj1 = $true)) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) <=> ($true = sP19)) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (($true = sP13) <=> (hoasinduction_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (? [X304 : term] : ((X303 @ X304) != (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ($true != (X302 @ X301)) | ($true = (X303 @ one)))) & ((hoasinduction_lem3b = $true) <=> ! [X0 : term] : ? [X1 : subst > term > term] : ((X1 @ sh @ one) = (sub @ X0 @ (push @ one @ sh)))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP4)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (? [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) != (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)) | ? [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) != (sub @ (X491 @ X492 @ X494) @ X493)) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one)))) <=> (hoaslaminj = $true)) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(definition_folding,[status(thm)],[f13,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 32.37/5.95 thf(f14,plain,(
% 32.37/5.95 ! [X240 : subst > term > subst > $o] : (($true = (sP0 @ X240)) <=> ? [X242 : term,X243 : term] : (($true = (X240 @ id @ X243 @ id)) & ((X240 @ id @ X242 @ id) = $true) & ($true != (X240 @ id @ (ap @ (sub @ X242 @ id) @ X243) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f15,plain,(
% 32.37/5.95 ! [X222 : term > $o] : (($true = (sP1 @ X222)) <=> ! [X227 : term,X228 : term] : (($true = (X222 @ (ap @ X228 @ X227))) | ($true != (X222 @ X227)) | ($true != (X222 @ X228))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f16,plain,(
% 32.37/5.95 ($true = sP2) <=> ? [X230 : term,X231 : term > $o,X232 : subst > term > subst > $o] : (! [X233 : term] : (((X231 @ (sub @ X230 @ (push @ X233 @ id))) = $true) | ($true != (X231 @ X233))) & ! [X234 : subst > term > term] : (($true = (X232 @ id @ (lam @ (X234 @ sh @ one)) @ id)) | ? [X236 : term,X237 : subst,X238 : subst] : ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)) != (sub @ (X234 @ X237 @ X236) @ X238)) | ? [X235 : term] : (($true != (X232 @ id @ (X234 @ id @ X235) @ id)) & ($true = (X232 @ id @ X235 @ id)))) & ($true != (X231 @ (lam @ X230))) & ! [X239 : term] : ((X232 @ id @ X239 @ id) = (X231 @ X239)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f17,plain,(
% 32.37/5.95 ($true = sP3) <=> ! [X240 : subst > term > subst > $o,X241 : term] : (($true = (X240 @ id @ X241 @ id)) | ? [X244 : subst > term > term] : (! [X245 : term] : (($true != (X240 @ id @ X245 @ id)) | ($true = (X240 @ id @ (X244 @ id @ X245) @ id))) & ! [X246 : subst,X247 : term,X248 : subst] : ((X244 @ (comp @ X246 @ X248) @ (sub @ X247 @ X248)) = (sub @ (X244 @ X246 @ X247) @ X248)) & ($true != (X240 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ($true = (sP0 @ X240)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f18,plain,(
% 32.37/5.95 ($true = sP4) <=> (? [X222 : term > $o,X223 : term] : (($true != (X222 @ X223)) & ! [X225 : term] : (? [X226 : term] : (($true != (X222 @ (sub @ X225 @ (push @ X226 @ id)))) & ($true = (X222 @ X226))) | ($true = (X222 @ (lam @ X225)))) & ! [X224 : term] : (($true != (var @ X224)) | ((X222 @ X224) = $true)) & ($true = (sP1 @ X222))) | ? [X229 : term] : ((sub @ X229 @ id) != X229) | ($true = sP2) | ? [X219 : subst > term > subst > $o] : ! [X220 : term > $o] : ? [X221 : term] : ((X219 @ id @ X221 @ id) != (X220 @ X221)) | ($true = sP3))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f19,plain,(
% 32.37/5.95 ! [X411 : subst > term > subst > $o] : (((sP5 @ X411) = $true) <=> ! [X421 : subst > term > term] : (? [X423 : subst,X424 : subst,X425 : term] : ((sub @ (X421 @ X424 @ X425) @ X423) != (X421 @ (comp @ X424 @ X423) @ (sub @ X425 @ X423))) | ? [X422 : term] : (($true = (X411 @ id @ X422 @ id)) & ((X411 @ id @ (X421 @ id @ X422) @ id) != $true)) | ((X411 @ id @ (lam @ (X421 @ sh @ one)) @ id) = $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f20,plain,(
% 32.37/5.95 ! [X400 : subst > term > subst > $o] : (((sP6 @ X400) = $true) <=> ! [X409 : term,X410 : term] : (($true != (X400 @ id @ X410 @ id)) | ($true != (X400 @ id @ X409 @ id)) | ($true = (X400 @ id @ (ap @ (sub @ X409 @ id) @ X410) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f21,plain,(
% 32.37/5.95 ! [X391 : term > $o] : (($true = (sP7 @ X391)) <=> ! [X396 : term,X397 : term] : (($true = (X391 @ (ap @ X396 @ X397))) | ((X391 @ X397) != $true) | ((X391 @ X396) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f22,plain,(
% 32.37/5.95 ! [X428 : subst > term > subst > $o] : (($true = (sP8 @ X428)) <=> ? [X440 : subst > term > term] : (! [X441 : term] : (($true != (X428 @ id @ X441 @ id)) | ($true = (X428 @ id @ (X440 @ id @ X441) @ id))) & ! [X442 : subst,X443 : subst,X444 : term] : ((X440 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443)) = (sub @ (X440 @ X442 @ X444) @ X443)) & ((X428 @ id @ (lam @ (X440 @ sh @ one)) @ id) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f23,plain,(
% 32.37/5.95 ! [X428 : subst > term > subst > $o] : (($true = (sP9 @ X428)) <=> ? [X438 : term,X439 : term] : (($true = (X428 @ id @ X438 @ id)) & ((X428 @ id @ X439 @ id) = $true) & ((X428 @ id @ (ap @ (sub @ X438 @ id) @ X439) @ id) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f24,plain,(
% 32.37/5.95 ($true = sP10) <=> ? [X411 : subst > term > subst > $o,X412 : term] : (! [X413 : subst,X414 : term,X415 : subst,X416 : subst] : (($true != (X411 @ X415 @ X414 @ (comp @ X416 @ X413))) | ($true = (X411 @ (comp @ X415 @ X416) @ (sub @ X414 @ X416) @ X413))) & ((sP5 @ X411) = $true) & ($true != (X411 @ id @ (lam @ X412) @ id)) & ! [X426 : term] : (($true != (X411 @ id @ X426 @ id)) | ($true = (X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))) & ! [X417 : subst,X418 : subst,X419 : term,X420 : subst] : (($true != (X411 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420) @ X417)) | ($true = (X411 @ X418 @ X419 @ (comp @ X420 @ X417)))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f25,plain,(
% 32.37/5.95 ($true = sP11) <=> ! [X427 : term,X428 : subst > term > subst > $o] : (($true = (sP9 @ X428)) | ? [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true != (X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)) & ((X428 @ X436 @ X437 @ (comp @ X434 @ X435)) = $true)) | ($true = (X428 @ id @ X427 @ id)) | ? [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (($true = (X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) & ((X428 @ X430 @ X432 @ (comp @ X431 @ X433)) != $true)) | ? [X429 : term] : (($true = (var @ (sub @ X429 @ id))) & ($true != (X428 @ id @ X429 @ id))) | ($true = (sP8 @ X428)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f26,plain,(
% 32.37/5.95 ($true = sP12) <=> ? [X398 : term,X399 : term,X400 : subst > term > subst > $o] : (($true = (X400 @ id @ X399 @ id)) & ! [X401 : subst,X402 : subst,X403 : term,X404 : subst] : (($true != (X400 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401) @ X404)) | ($true = (X400 @ X402 @ X403 @ (comp @ X401 @ X404)))) & ! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X400 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406) @ X408)) | ($true != (X400 @ X407 @ X405 @ (comp @ X406 @ X408)))) & ((sP6 @ X400) = $true) & ($true != (X400 @ id @ (ap @ X398 @ X399) @ id)) & ($true = (X400 @ id @ X398 @ id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f27,plain,(
% 32.37/5.95 ($true = sP13) <=> (($true = sP11) | ? [X391 : term > $o,X392 : term] : (($true != (X391 @ X392)) & ! [X394 : term] : (($true = (X391 @ (lam @ X394))) | ? [X395 : term] : (($true = (X391 @ X395)) & ($true != (X391 @ (sub @ X394 @ (push @ X395 @ id)))))) & ($true = (sP7 @ X391)) & ! [X393 : term] : (($true = (X391 @ X393)) | ($true != (var @ X393)))) | ($true = sP12) | ($true = sP10))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f28,plain,(
% 32.37/5.95 ! [X522 : subst > term > subst > $o] : (($true = (sP14 @ X522)) <=> ? [X538 : term,X539 : term] : (((X522 @ id @ X539 @ id) = $true) & ($true != (X522 @ id @ (ap @ (sub @ X538 @ id) @ X539) @ id)) & ($true = (X522 @ id @ X538 @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f29,plain,(
% 32.37/5.95 ! [X522 : subst > term > subst > $o] : (($true = (sP15 @ X522)) <=> ? [X529 : subst > term > term] : (! [X533 : term] : (((X522 @ id @ (X529 @ id @ X533) @ id) = $true) | ((X522 @ id @ X533 @ id) != $true)) & ! [X530 : subst,X531 : subst,X532 : term] : ((X529 @ (comp @ X530 @ X531) @ (sub @ X532 @ X531)) = (sub @ (X529 @ X530 @ X532) @ X531)) & ((X522 @ id @ (lam @ (X529 @ sh @ one)) @ id) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f30,plain,(
% 32.37/5.95 ! [X504 : term > $o] : (((sP16 @ X504) = $true) <=> ! [X506 : term,X507 : term] : (($true = (X504 @ (ap @ X507 @ X506))) | ($true != (X504 @ X507)) | ($true != (X504 @ X506))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f31,plain,(
% 32.37/5.95 ($true = sP17) <=> ! [X522 : subst > term > subst > $o,X523 : term] : (($true = (sP15 @ X522)) | ($true = (X522 @ id @ X523 @ id)) | ? [X534 : subst,X535 : term,X536 : subst,X537 : subst] : (($true != (X522 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) & ($true = (X522 @ X537 @ X535 @ (comp @ X536 @ X534)))) | ? [X524 : term] : (((var @ (sub @ X524 @ id)) = $true) & ($true != (X522 @ id @ X524 @ id))) | ? [X525 : subst,X526 : term,X527 : subst,X528 : subst] : (($true = (X522 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525) @ X528)) & ($true != (X522 @ X527 @ X526 @ (comp @ X525 @ X528)))) | ($true = (sP14 @ X522)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f32,plain,(
% 32.37/5.95 ($true = sP18) <=> ? [X512 : term,X513 : subst > term > subst > $o,X514 : term > $o] : (! [X520 : term] : (((X514 @ (sub @ X512 @ (push @ X520 @ id))) = $true) | ($true != (X514 @ X520))) & ! [X515 : subst > term > term] : (? [X519 : term] : (($true != (X513 @ id @ (X515 @ id @ X519) @ id)) & ((X513 @ id @ X519 @ id) = $true)) | ? [X516 : subst,X517 : term,X518 : subst] : ((sub @ (X515 @ X516 @ X517) @ X518) != (X515 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518))) | ((X513 @ id @ (lam @ (X515 @ sh @ one)) @ id) = $true)) & ! [X521 : term] : ((X514 @ X521) = (X513 @ id @ X521 @ id)) & ($true != (X514 @ (lam @ X512))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f33,plain,(
% 32.37/5.95 ($true = sP19) <=> (? [X504 : term > $o,X505 : term] : (((sP16 @ X504) = $true) & ($true != (X504 @ X505)) & ! [X509 : term] : (($true = (X504 @ (lam @ X509))) | ? [X510 : term] : (((X504 @ (sub @ X509 @ (push @ X510 @ id))) != $true) & ((X504 @ X510) = $true))) & ! [X508 : term] : (($true = (X504 @ X508)) | ($true != (var @ X508)))) | ($true = sP18) | ? [X501 : subst > term > subst > $o] : ! [X502 : term > $o] : ? [X503 : term] : ((X501 @ id @ X503 @ id) != (X502 @ X503)) | ($true = sP17) | ? [X511 : term] : ((sub @ X511 @ id) != X511))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f34,plain,(
% 32.37/5.95 ! [X453 : term > $o] : (($true = (sP20 @ X453)) <=> ! [X455 : term,X456 : term] : (($true = (X453 @ (ap @ X455 @ X456))) | ($true != (X453 @ X455)) | ($true != (X453 @ X456))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f35,plain,(
% 32.37/5.95 ! [X460 : term > $o] : (((sP21 @ X460) = $true) <=> ? [X465 : term,X466 : term] : (($true = (X460 @ X465)) & ($true != (X460 @ (ap @ X465 @ X466))) & ($true = (X460 @ X466))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f36,plain,(
% 32.37/5.95 ($true = sP22) <=> ! [X460 : term > $o,X461 : term] : (($true = (X460 @ X461)) | ? [X462 : term] : (($true = (var @ X462)) & ((X460 @ X462) != $true)) | ? [X463 : term] : (($true != (X460 @ (lam @ X463))) & ! [X464 : term] : (($true != (X460 @ X464)) | ((X460 @ (sub @ X463 @ (push @ X464 @ id))) = $true))) | ((sP21 @ X460) = $true))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f37,plain,(
% 32.37/5.95 ($true = sP23) <=> (($true = sP22) | ? [X452 : subst,X453 : term > $o,X454 : term] : (($true = (sP20 @ X453)) & ($true != (X453 @ (sub @ X454 @ X452))) & ! [X458 : term] : (? [X459 : term] : (((X453 @ (sub @ X458 @ (push @ X459 @ id))) != $true) & ($true = (X453 @ X459))) | ($true = (X453 @ (lam @ X458)))) & ! [X457 : term] : (($true = (X453 @ (sub @ X457 @ X452))) | ($true != (var @ X457)))) | ? [X451 : term] : ((sub @ X451 @ id) != X451))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f38,plain,(
% 32.37/5.95 ($true = sP24) <=> (? [X174 : term,X175 : term] : (((lam @ X175) = (lam @ X174)) & (X174 != X175)) | ? [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) != X170) | ? [X172 : term,X173 : subst] : ((comp @ sh @ (push @ X172 @ X173)) != X173) | ! [X176 : subst > term > term,X177 : subst,X178 : term,X179 : subst > term > term] : (((X179 @ X177 @ X178) = (X176 @ X177 @ X178)) | ? [X183 : subst,X184 : subst,X185 : term] : ((sub @ (X176 @ X183 @ X185) @ X184) != (X176 @ (comp @ X183 @ X184) @ (sub @ X185 @ X184))) | ? [X180 : subst,X181 : term,X182 : subst] : ((sub @ (X179 @ X182 @ X181) @ X180) != (X179 @ (comp @ X182 @ X180) @ (sub @ X181 @ X180))) | ((lam @ (X176 @ sh @ one)) != (lam @ (X179 @ sh @ one)))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f39,plain,(
% 32.37/5.95 ! [X265 : subst > term > subst > $o] : (($true = (sP25 @ X265)) <=> ? [X270 : subst > term > term] : (! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273)) & ($true != (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) & ! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ($true != (X265 @ id @ X271 @ id)))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f40,plain,(
% 32.37/5.95 ($true = sP26) <=> ! [X263 : term,X264 : term > $o,X265 : subst > term > subst > $o] : (? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (($true = (X265 @ (comp @ X277 @ X276) @ (sub @ X279 @ X276) @ X278)) & ($true != (X265 @ X277 @ X279 @ (comp @ X276 @ X278)))) | ($true = (X264 @ (lam @ X263))) | ($true = (sP25 @ X265)) | ? [X275 : term] : (($true != (X264 @ (sub @ X263 @ (push @ X275 @ id)))) & ((X264 @ X275) = $true)) | ? [X266 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != (X265 @ (comp @ X269 @ X268) @ (sub @ X266 @ X268) @ X267)) & ((X265 @ X269 @ X266 @ (comp @ X268 @ X267)) = $true)) | ? [X280 : term] : ((X265 @ id @ X280 @ id) != (X264 @ X280)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f41,plain,(
% 32.37/5.95 (sP27 = $true) <=> ! [X255 : subst > term > subst > $o,X256 : term] : (? [X257 : term] : (($true != (X255 @ id @ (sub @ X256 @ (push @ X257 @ id)) @ id)) & ($true = (X255 @ id @ X257 @ id))) | ((X255 @ id @ (lam @ (sub @ X256 @ (push @ one @ sh))) @ id) = $true) | ? [X258 : subst > term > term] : (($true != (X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) & ! [X259 : subst,X260 : subst,X261 : term] : ((sub @ (X258 @ X259 @ X261) @ X260) = (X258 @ (comp @ X259 @ X260) @ (sub @ X261 @ X260))) & ! [X262 : term] : (($true != (X255 @ id @ X262 @ id)) | ((X255 @ id @ (X258 @ id @ X262) @ id) = $true))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f42,plain,(
% 32.37/5.95 ! [X283 : term > $o] : (($true = (sP28 @ X283)) <=> ? [X288 : term,X289 : term] : (($true != (X283 @ (ap @ X288 @ X289))) & ((X283 @ X289) = $true) & ($true = (X283 @ X288))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f43,plain,(
% 32.37/5.95 ($true = sP29) <=> ! [X283 : term > $o,X284 : term] : (? [X285 : term] : (($true != (X283 @ (lam @ X285))) & ! [X286 : term] : (((X283 @ (sub @ X285 @ (push @ X286 @ id))) = $true) | ($true != (X283 @ X286)))) | ($true = (X283 @ X284)) | ? [X287 : term] : (($true != (X283 @ X287)) & ($true = (var @ X287))) | ($true = (sP28 @ X283)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f44,plain,(
% 32.37/5.95 (sP30 = $true) <=> ! [X476 : subst > term > subst > $o,X477 : term] : (($true = (X476 @ id @ (lam @ X477) @ id)) | ? [X483 : term] : (($true != (X476 @ id @ (sub @ X477 @ (push @ X483 @ id)) @ id)) & ($true = (X476 @ id @ X483 @ id))) | ? [X478 : subst > term > term] : (! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X482 @ X481) @ (sub @ X480 @ X481)) = (sub @ (X478 @ X482 @ X480) @ X481)) & ! [X479 : term] : (($true = (X476 @ id @ (X478 @ id @ X479) @ id)) | ($true != (X476 @ id @ X479 @ id))) & ($true != (X476 @ id @ (lam @ (X478 @ sh @ one)) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f45,plain,(
% 32.37/5.95 ($true = sP31) <=> ! [X159 : subst > term > subst > $o,X160 : term] : (? [X162 : subst > term > term] : (($true != (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X164 : subst,X165 : subst,X166 : term] : ((X162 @ (comp @ X165 @ X164) @ (sub @ X166 @ X164)) = (sub @ (X162 @ X165 @ X166) @ X164)) & ! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id)))) | ((X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id) = $true) | ? [X161 : term] : (($true != (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id)) & ($true = (X159 @ id @ X161 @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f46,plain,(
% 32.37/5.95 ! [X78 : term > $o] : (($true = (sP32 @ X78)) <=> ? [X82 : term,X83 : term] : (($true = (X78 @ X83)) & ($true = (X78 @ X82)) & ((X78 @ (ap @ X83 @ X82)) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f47,plain,(
% 32.37/5.95 ($true = sP33) <=> ! [X76 : term,X77 : subst,X78 : term > $o] : (? [X81 : term] : (($true = (var @ X81)) & ($true != (X78 @ (sub @ X81 @ X77)))) | ($true = (X78 @ (sub @ X76 @ X77))) | ($true = (sP32 @ X78)) | ? [X79 : term] : (! [X80 : term] : (((X78 @ X80) != $true) | ((X78 @ (sub @ X79 @ (push @ X80 @ id))) = $true)) & ((X78 @ (lam @ X79)) != $true)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f48,plain,(
% 32.37/5.95 ! [X327 : term > $o] : (($true = (sP34 @ X327)) <=> ? [X328 : term,X329 : term] : (($true != (X327 @ (ap @ X329 @ X328))) & ($true = (X327 @ X328)) & ($true = (X327 @ X329))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f49,plain,(
% 32.37/5.95 ! [X319 : term > $o] : (($true = (sP35 @ X319)) <=> ! [X323 : term,X324 : term] : (($true != (X319 @ X324)) | ($true = (X319 @ (ap @ X323 @ X324))) | ($true != (X319 @ X323))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f50,plain,(
% 32.37/5.95 ($true = sP36) <=> ! [X325 : subst,X326 : term,X327 : term > $o] : (? [X330 : term] : (($true = (var @ X330)) & ($true != (X327 @ (sub @ X330 @ X325)))) | ($true = (sP34 @ X327)) | ($true = (X327 @ (sub @ X326 @ X325))) | ? [X331 : term] : (((X327 @ (lam @ X331)) != $true) & ! [X332 : term] : (($true != (X327 @ X332)) | ($true = (X327 @ (sub @ X331 @ (push @ X332 @ id)))))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f51,plain,(
% 32.37/5.95 ($true = sP37) <=> (? [X319 : term > $o,X320 : term] : (($true != (X319 @ X320)) & ! [X322 : term] : (($true = (X319 @ X322)) | ($true != (var @ X322))) & ! [X321 : term] : (((X319 @ (lam @ X321)) = $true) | ($true != (X319 @ X321))) & ($true = (sP35 @ X319))) | ? [X318 : subst] : ((comp @ X318 @ id) != X318) | ? [X314 : term,X315 : subst] : ((sub @ one @ (push @ X314 @ X315)) != X314) | ? [X316 : term,X317 : subst] : ((comp @ sh @ (push @ X316 @ X317)) != X317) | ($true = sP36))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f52,plain,(
% 32.37/5.95 ! [X24 : subst > term > subst > $o] : (($true = (sP38 @ X24)) <=> ? [X31 : term,X32 : term] : (($true != (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) & ($true = (X24 @ id @ X32 @ id)) & ($true = (X24 @ id @ X31 @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f53,plain,(
% 32.37/5.95 ($true = sP39) <=> ! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (? [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true != (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) & ($true = (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ? [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (($true = (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29)) & ((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) != $true)) | ? [X37 : term] : ((X26 @ X37) != (X24 @ id @ X37 @ id)) | ((X26 @ X23) != $true) | ($true != (X26 @ X25)) | ($true = (sP38 @ X24)) | ((X26 @ (ap @ X25 @ X23)) = $true))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f54,plain,(
% 32.37/5.95 ! [X378 : subst > term > subst > $o] : (($true = (sP40 @ X378)) <=> ? [X381 : term,X382 : term] : (($true = (X378 @ id @ X382 @ id)) & ((X378 @ id @ X381 @ id) = $true) & ($true != (X378 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f55,plain,(
% 32.37/5.95 ($true = sP41) <=> ! [X378 : subst > term > subst > $o,X379 : term,X380 : term] : (? [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (($true = (X378 @ (comp @ X386 @ X383) @ (sub @ X384 @ X383) @ X385)) & ($true != (X378 @ X386 @ X384 @ (comp @ X383 @ X385)))) | ? [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (($true = (X378 @ X390 @ X387 @ (comp @ X389 @ X388))) & ($true != (X378 @ (comp @ X390 @ X389) @ (sub @ X387 @ X389) @ X388))) | ($true = (sP40 @ X378)) | ($true != (X378 @ id @ X380 @ id)) | ($true != (X378 @ id @ X379 @ id)) | ($true = (X378 @ id @ (ap @ X380 @ X379) @ id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f56,plain,(
% 32.37/5.95 ! [X6 : subst > term > subst > $o] : (($true = (sP42 @ X6)) <=> ? [X12 : subst > term > term] : (! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) & ! [X13 : term] : (((X6 @ id @ X13 @ id) != $true) | ($true = (X6 @ id @ (X12 @ id @ X13) @ id))) & ($true != (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f57,plain,(
% 32.37/5.95 ! [X6 : subst > term > subst > $o] : (($true = (sP43 @ X6)) <=> ? [X21 : term,X22 : term] : (($true = (X6 @ id @ X22 @ id)) & ($true != (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id)) & ($true = (X6 @ id @ X21 @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f58,plain,(
% 32.37/5.95 ($true = sP44) <=> ! [X5 : term,X6 : subst > term > subst > $o] : (? [X11 : term] : (($true = (var @ (sub @ X11 @ id))) & ($true != (X6 @ id @ X11 @ id))) | ? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true != (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) & ($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ($true = (sP43 @ X6)) | ? [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) & ($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) | ($true = (X6 @ id @ X5 @ id)) | ($true = (sP42 @ X6)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f59,plain,(
% 32.37/5.95 ! [X55 : term > $o] : (($true = (sP45 @ X55)) <=> ? [X58 : term,X59 : term] : (($true = (X55 @ X58)) & ((X55 @ (ap @ X58 @ X59)) != $true) & ($true = (X55 @ X59))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f60,plain,(
% 32.37/5.95 (sP46 = $true) <=> ? [X121 : term,X122 : subst > term > subst > $o] : (! [X123 : subst > term > term] : (? [X124 : term] : (($true = (X122 @ id @ X124 @ id)) & ($true != (X122 @ id @ (X123 @ id @ X124) @ id))) | ? [X125 : subst,X126 : subst,X127 : term] : ((sub @ (X123 @ X125 @ X127) @ X126) != (X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126))) | ($true = (X122 @ id @ (lam @ (X123 @ sh @ one)) @ id))) & ! [X128 : term] : (($true != (X122 @ id @ X128 @ id)) | ($true = (X122 @ id @ (sub @ X121 @ (push @ X128 @ id)) @ id))) & ($true != (X122 @ id @ (lam @ (sub @ X121 @ (push @ one @ sh))) @ id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f61,plain,(
% 32.37/5.95 ($true = sP47) <=> (! [X129 : subst > term > subst > $o,X130 : term] : (($true = (X129 @ id @ (lam @ X130) @ id)) | ? [X131 : subst > term > term] : (! [X133 : subst,X134 : subst,X135 : term] : ((sub @ (X131 @ X133 @ X135) @ X134) = (X131 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) & ! [X132 : term] : (($true = (X129 @ id @ (X131 @ id @ X132) @ id)) | ($true != (X129 @ id @ X132 @ id))) & ($true != (X129 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ? [X136 : term] : (($true = (X129 @ id @ X136 @ id)) & ($true != (X129 @ id @ (sub @ X130 @ (push @ X136 @ id)) @ id)))) | (sP46 = $true) | ? [X120 : term] : ((sub @ X120 @ id) != X120))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f62,plain,(
% 32.37/5.95 ! [X360 : subst > term > subst > $o] : (($true = (sP48 @ X360)) <=> ? [X368 : subst > term > term] : (! [X369 : term] : (($true = (X360 @ id @ (X368 @ id @ X369) @ id)) | ($true != (X360 @ id @ X369 @ id))) & ! [X370 : subst,X371 : term,X372 : subst] : ((sub @ (X368 @ X370 @ X371) @ X372) = (X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) & ($true != (X360 @ id @ (lam @ (X368 @ sh @ one)) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f63,plain,(
% 32.37/5.95 ($true = sP49) <=> (? [X359 : term] : ((sub @ X359 @ id) != X359) | ! [X360 : subst > term > subst > $o,X361 : term,X362 : term > $o] : (? [X364 : subst,X365 : subst,X366 : subst,X367 : term] : (($true = (X360 @ (comp @ X366 @ X365) @ (sub @ X367 @ X365) @ X364)) & ($true != (X360 @ X366 @ X367 @ (comp @ X365 @ X364)))) | ? [X363 : term] : ((X362 @ X363) != (X360 @ id @ X363 @ id)) | ? [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (($true = (X360 @ X375 @ X376 @ (comp @ X373 @ X374))) & ($true != (X360 @ (comp @ X375 @ X373) @ (sub @ X376 @ X373) @ X374))) | ? [X377 : term] : (($true != (X362 @ (sub @ X361 @ (push @ X377 @ id)))) & ((X362 @ X377) = $true)) | ($true = (sP48 @ X360)) | ($true = (X362 @ (lam @ X361)))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f64,plain,(
% 32.37/5.95 ! [X61 : subst > term > subst > $o] : (($true = (sP50 @ X61)) <=> ? [X63 : subst > term > term] : (! [X65 : term,X66 : subst,X67 : subst] : ((X63 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)) = (sub @ (X63 @ X67 @ X65) @ X66)) & ! [X64 : term] : (($true != (X61 @ id @ X64 @ id)) | ($true = (X61 @ id @ (X63 @ id @ X64) @ id))) & ($true != (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f65,plain,(
% 32.37/5.95 ($true = sP51) <=> ! [X60 : term,X61 : subst > term > subst > $o] : (? [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (($true = (X61 @ X70 @ X71 @ (comp @ X69 @ X68))) & ((X61 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X68) != $true)) | ? [X62 : term] : (($true != (X61 @ id @ (sub @ X60 @ (push @ X62 @ id)) @ id)) & ((X61 @ id @ X62 @ id) = $true)) | ($true = (sP50 @ X61)) | ($true = (X61 @ id @ (lam @ X60) @ id)) | ? [X72 : subst,X73 : subst,X74 : subst,X75 : term] : (($true = (X61 @ (comp @ X73 @ X74) @ (sub @ X75 @ X74) @ X72)) & ($true != (X61 @ X73 @ X75 @ (comp @ X74 @ X72)))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f66,plain,(
% 32.37/5.95 ($true = sP52) <=> ! [X192 : term,X193 : subst > term > subst > $o] : (? [X194 : term] : (($true != (X193 @ id @ (sub @ X192 @ (push @ X194 @ id)) @ id)) & ($true = (X193 @ id @ X194 @ id))) | ? [X195 : subst > term > term,X196 : term] : (! [X197 : term] : (($true = (X193 @ id @ (X195 @ id @ X197) @ id)) | ($true != (X193 @ id @ X197 @ id))) & ! [X201 : subst,X202 : term,X203 : subst] : ((sub @ X196 @ (push @ (sub @ X202 @ X201) @ (comp @ X203 @ X201))) = (X195 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) & ! [X198 : term,X199 : subst,X200 : subst] : ((sub @ (sub @ X196 @ (push @ X198 @ X199)) @ X200) = (sub @ (X195 @ X199 @ X198) @ X200)) & ((X193 @ id @ (lam @ (X195 @ sh @ one)) @ id) != $true)) | ($true = (X193 @ id @ (lam @ (sub @ X192 @ (push @ one @ sh))) @ id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f67,plain,(
% 32.37/5.95 ! [X468 : subst > term > subst > $o] : (($true = (sP53 @ X468)) <=> ? [X474 : term,X475 : term] : (($true = (X468 @ id @ X475 @ id)) & ($true != (X468 @ id @ (ap @ (sub @ X474 @ id) @ X475) @ id)) & ($true = (X468 @ id @ X474 @ id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f68,plain,(
% 32.37/5.95 ! [X105 : subst > term > subst > $o] : (($true = (sP54 @ X105)) <=> ? [X106 : subst > term > term] : (! [X107 : term] : (($true = (X105 @ id @ (X106 @ id @ X107) @ id)) | ($true != (X105 @ id @ X107 @ id))) & ($true != (X105 @ id @ (lam @ (X106 @ sh @ one)) @ id)) & ! [X108 : subst,X109 : term,X110 : subst] : ((X106 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110)) = (sub @ (X106 @ X108 @ X109) @ X110))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f69,plain,(
% 32.37/5.95 ($true = sP55) <=> ? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (($true != (X97 @ id @ X103 @ id)) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ($true = (X97 @ id @ (lam @ (X98 @ sh @ one)) @ id)) | ? [X99 : term,X100 : subst,X101 : subst] : ((X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)) != (sub @ (X98 @ X101 @ X99) @ X100))) & ($true != (X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f70,plain,(
% 32.37/5.95 ($true = sP56) <=> (! [X104 : term,X105 : subst > term > subst > $o] : (($true = (X105 @ id @ (lam @ X104) @ id)) | ? [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (($true = (X105 @ X114 @ X112 @ (comp @ X111 @ X113))) & ($true != (X105 @ (comp @ X114 @ X111) @ (sub @ X112 @ X111) @ X113))) | ($true = (sP54 @ X105)) | ? [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (($true != (X105 @ X116 @ X119 @ (comp @ X118 @ X117))) & ((X105 @ (comp @ X116 @ X118) @ (sub @ X119 @ X118) @ X117) = $true)) | ? [X115 : term] : (($true = (X105 @ id @ X115 @ id)) & ((X105 @ id @ (sub @ X104 @ (push @ X115 @ id)) @ id) != $true))) | ($true = sP55) | ? [X95 : term] : ((sub @ X95 @ id) != X95))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f71,plain,(
% 32.37/5.95 ($true = sP57) <=> (! [X142 : term,X143 : subst > term > subst > $o,X144 : term > $o] : (? [X151 : term] : (((X144 @ X151) = $true) & ($true != (X144 @ (sub @ X142 @ (push @ X151 @ id))))) | ($true = (X144 @ (lam @ X142))) | ? [X146 : subst > term > term] : (! [X147 : term,X148 : subst,X149 : subst] : ((X146 @ (comp @ X149 @ X148) @ (sub @ X147 @ X148)) = (sub @ (X146 @ X149 @ X147) @ X148)) & ! [X150 : term] : (($true != (X143 @ id @ X150 @ id)) | ((X143 @ id @ (X146 @ id @ X150) @ id) = $true)) & ((X143 @ id @ (lam @ (X146 @ sh @ one)) @ id) != $true)) | ? [X145 : term] : ((X144 @ X145) != (X143 @ id @ X145 @ id))) | ? [X141 : term] : ((sub @ X141 @ id) != X141) | ? [X137 : term] : ! [X138 : subst > term > term] : ? [X139 : term,X140 : subst] : ((X138 @ X140 @ X139) != (sub @ X137 @ (push @ X139 @ X140))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f72,plain,(
% 32.37/5.95 (sP58 = $true) <=> ! [X333 : term > $o,X334 : subst > term > subst > $o,X335 : term] : (($true = (X333 @ (lam @ X335))) | ? [X336 : subst > term > term] : (! [X340 : term] : (($true = (X334 @ id @ (X336 @ id @ X340) @ id)) | ($true != (X334 @ id @ X340 @ id))) & ($true != (X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)) & ! [X337 : subst,X338 : subst,X339 : term] : ((sub @ (X336 @ X338 @ X339) @ X337) = (X336 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337)))) | ? [X341 : term] : (((X333 @ X341) = $true) & ($true != (X333 @ (sub @ X335 @ (push @ X341 @ id))))) | ? [X342 : term] : ((X334 @ id @ X342 @ id) != (X333 @ X342)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 32.37/5.95 thf(f13,plain,(
% 32.37/5.95 (pushprop_lem2v2_lthm = $true) & (! [X333 : term > $o,X334 : subst > term > subst > $o,X335 : term] : (($true = (X333 @ (lam @ X335))) | ? [X336 : subst > term > term] : (! [X340 : term] : (($true = (X334 @ id @ (X336 @ id @ X340) @ id)) | ($true != (X334 @ id @ X340 @ id))) & ($true != (X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)) & ! [X337 : subst,X338 : subst,X339 : term] : ((sub @ (X336 @ X338 @ X339) @ X337) = (X336 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337)))) | ? [X341 : term] : (((X333 @ X341) = $true) & ($true != (X333 @ (sub @ X335 @ (push @ X341 @ id))))) | ? [X342 : term] : ((X334 @ id @ X342 @ id) != (X333 @ X342))) <=> (hoasinduction_lem3v2a = $true)) & ((! [X142 : term,X143 : subst > term > subst > $o,X144 : term > $o] : (? [X151 : term] : (((X144 @ X151) = $true) & ($true != (X144 @ (sub @ X142 @ (push @ X151 @ id))))) | ($true = (X144 @ (lam @ X142))) | ? [X146 : subst > term > term] : (! [X147 : term,X148 : subst,X149 : subst] : ((X146 @ (comp @ X149 @ X148) @ (sub @ X147 @ X148)) = (sub @ (X146 @ X149 @ X147) @ X148)) & ! [X150 : term] : (($true != (X143 @ id @ X150 @ id)) | ((X143 @ id @ (X146 @ id @ X150) @ id) = $true)) & ((X143 @ id @ (lam @ (X146 @ sh @ one)) @ id) != $true)) | ? [X145 : term] : ((X144 @ X145) != (X143 @ id @ X145 @ id))) | ? [X141 : term] : ((sub @ X141 @ id) != X141) | ? [X137 : term] : ! [X138 : subst > term > term] : ? [X139 : term,X140 : subst] : ((X138 @ X140 @ X139) != (sub @ X137 @ (push @ X139 @ X140)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X104 : term,X105 : subst > term > subst > $o] : (($true = (X105 @ id @ (lam @ X104) @ id)) | ? [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (($true = (X105 @ X114 @ X112 @ (comp @ X111 @ X113))) & ($true != (X105 @ (comp @ X114 @ X111) @ (sub @ X112 @ X111) @ X113))) | ? [X106 : subst > term > term] : (! [X107 : term] : (($true = (X105 @ id @ (X106 @ id @ X107) @ id)) | ($true != (X105 @ id @ X107 @ id))) & ($true != (X105 @ id @ (lam @ (X106 @ sh @ one)) @ id)) & ! [X108 : subst,X109 : term,X110 : subst] : ((X106 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110)) = (sub @ (X106 @ X108 @ X109) @ X110))) | ? [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (($true != (X105 @ X116 @ X119 @ (comp @ X118 @ X117))) & ((X105 @ (comp @ X116 @ X118) @ (sub @ X119 @ X118) @ X117) = $true)) | ? [X115 : term] : (($true = (X105 @ id @ X115 @ id)) & ((X105 @ id @ (sub @ X104 @ (push @ X115 @ id)) @ id) != $true))) | ? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (($true != (X97 @ id @ X103 @ id)) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ($true = (X97 @ id @ (lam @ (X98 @ sh @ one)) @ id)) | ? [X99 : term,X100 : subst,X101 : subst] : ((X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)) != (sub @ (X98 @ X101 @ X99) @ X100))) & ($true != (X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id))) | ? [X95 : term] : ((sub @ X95 @ id) != X95)) <=> (hoasinduction_lem3_lthm = $true)) & (ulamvarsh = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ! [X48 : d_subst] : (d_id = X48) & (! [X467 : term,X468 : subst > term > subst > $o] : (? [X469 : subst > term > term] : (! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true)) & ! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) & ($true != (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ? [X474 : term,X475 : term] : (($true = (X468 @ id @ X475 @ id)) & ($true != (X468 @ id @ (ap @ (sub @ X474 @ id) @ X475) @ id)) & ($true = (X468 @ id @ X474 @ id))) | ((X468 @ id @ X467 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (termmset_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) != X351) | ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (? [X356 : term] : ((X354 @ X356) != (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true = (X354 @ one)) | ($true != (X352 @ X353))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) <=> (pushprop_lem1 = $true)) & (! [X167 : term] : ((sub @ X167 @ id) = X167) <=> (axvarid = $true)) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) <=> (axshiftcons = $true)) & (! [X204 : subst > term > subst > $o] : ? [X205 : term > $o] : ! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id)) <=> (hoasinduction_lem0 = $true)) & (lamnotap != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X192 : term,X193 : subst > term > subst > $o] : (? [X194 : term] : (($true != (X193 @ id @ (sub @ X192 @ (push @ X194 @ id)) @ id)) & ($true = (X193 @ id @ X194 @ id))) | ? [X195 : subst > term > term,X196 : term] : (! [X197 : term] : (($true = (X193 @ id @ (X195 @ id @ X197) @ id)) | ($true != (X193 @ id @ X197 @ id))) & ! [X201 : subst,X202 : term,X203 : subst] : ((sub @ X196 @ (push @ (sub @ X202 @ X201) @ (comp @ X203 @ X201))) = (X195 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) & ! [X198 : term,X199 : subst,X200 : subst] : ((sub @ (sub @ X196 @ (push @ X198 @ X199)) @ X200) = (sub @ (X195 @ X199 @ X198) @ X200)) & ((X193 @ id @ (lam @ (X195 @ sh @ one)) @ id) != $true)) | ($true = (X193 @ id @ (lam @ (sub @ X192 @ (push @ one @ sh))) @ id)))) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((laminj = $true) <=> ! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94)))) & ((hoasapinj2 = $true) <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214))) & ((hoasinduction_lem3 = $true) <=> ! [X60 : term,X61 : subst > term > subst > $o] : (? [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (($true = (X61 @ X70 @ X71 @ (comp @ X69 @ X68))) & ((X61 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X68) != $true)) | ? [X62 : term] : (($true != (X61 @ id @ (sub @ X60 @ (push @ X62 @ id)) @ id)) & ((X61 @ id @ X62 @ id) = $true)) | ? [X63 : subst > term > term] : (! [X65 : term,X66 : subst,X67 : subst] : ((X63 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)) = (sub @ (X63 @ X67 @ X65) @ X66)) & ! [X64 : term] : (($true != (X61 @ id @ X64 @ id)) | ($true = (X61 @ id @ (X63 @ id @ X64) @ id))) & ($true != (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id))) | ($true = (X61 @ id @ (lam @ X60) @ id)) | ? [X72 : subst,X73 : subst,X74 : subst,X75 : term] : (($true = (X61 @ (comp @ X73 @ X74) @ (sub @ X75 @ X74) @ X72)) & ($true != (X61 @ X73 @ X75 @ (comp @ X74 @ X72)))))) & ((d2subst @ d_id) = id) & ! [X168 : d_term,X169 : d_term] : ((X168 = X169) | ((d2term @ X169) != (d2term @ X168))) & (hoaslamnotap_lthm = $true) & ((? [X359 : term] : ((sub @ X359 @ id) != X359) | ! [X360 : subst > term > subst > $o,X361 : term,X362 : term > $o] : (? [X364 : subst,X365 : subst,X366 : subst,X367 : term] : (($true = (X360 @ (comp @ X366 @ X365) @ (sub @ X367 @ X365) @ X364)) & ($true != (X360 @ X366 @ X367 @ (comp @ X365 @ X364)))) | ? [X363 : term] : ((X362 @ X363) != (X360 @ id @ X363 @ id)) | ? [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (($true = (X360 @ X375 @ X376 @ (comp @ X373 @ X374))) & ($true != (X360 @ (comp @ X375 @ X373) @ (sub @ X376 @ X373) @ X374))) | ? [X377 : term] : (($true != (X362 @ (sub @ X361 @ (push @ X377 @ id)))) & ((X362 @ X377) = $true)) | ? [X368 : subst > term > term] : (! [X369 : term] : (($true = (X360 @ id @ (X368 @ id @ X369) @ id)) | ($true != (X360 @ id @ X369 @ id))) & ! [X370 : subst,X371 : term,X372 : subst] : ((sub @ (X368 @ X370 @ X371) @ X372) = (X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) & ($true != (X360 @ id @ (lam @ (X368 @ sh @ one)) @ id))) | ($true = (X362 @ (lam @ X361))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X249 : term,X250 : term,X251 : subst > term > term] : (? [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) != (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) | ((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X129 : subst > term > subst > $o,X130 : term] : (($true = (X129 @ id @ (lam @ X130) @ id)) | ? [X131 : subst > term > term] : (! [X133 : subst,X134 : subst,X135 : term] : ((sub @ (X131 @ X133 @ X135) @ X134) = (X131 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) & ! [X132 : term] : (($true = (X129 @ id @ (X131 @ id @ X132) @ id)) | ($true != (X129 @ id @ X132 @ id))) & ($true != (X129 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ? [X136 : term] : (($true = (X129 @ id @ X136 @ id)) & ($true != (X129 @ id @ (sub @ X130 @ (push @ X136 @ id)) @ id)))) | ? [X121 : term,X122 : subst > term > subst > $o] : (! [X123 : subst > term > term] : (? [X124 : term] : (($true = (X122 @ id @ X124 @ id)) & ($true != (X122 @ id @ (X123 @ id @ X124) @ id))) | ? [X125 : subst,X126 : subst,X127 : term] : ((sub @ (X123 @ X125 @ X127) @ X126) != (X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126))) | ($true = (X122 @ id @ (lam @ (X123 @ sh @ one)) @ id))) & ! [X128 : term] : (($true != (X122 @ id @ X128 @ id)) | ($true = (X122 @ id @ (sub @ X121 @ (push @ X128 @ id)) @ id))) & ($true != (X122 @ id @ (lam @ (sub @ X121 @ (push @ one @ sh))) @ id))) | ? [X120 : term] : ((sub @ X120 @ id) != X120))) & (hoasapinj1_gthm = $true) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & ((! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true)) | ? [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) != X291) | ? [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) != X293)) <=> (pushprop_lem1_lthm = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X290 : subst] : ((comp @ id @ X290) = X290) <=> (axidl = $true)) & (axabs = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 != X86) & ((ap @ X85 @ X87) = (ap @ X86 @ X88))) | ? [X84 : term] : ((sub @ X84 @ id) != X84) | ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)))) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) <=> (substmonoid = $true)) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((induction = $true) <=> ! [X54 : term,X55 : term > $o] : (($true = (X55 @ X54)) | ? [X58 : term,X59 : term] : (($true = (X55 @ X58)) & ((X55 @ (ap @ X58 @ X59)) != $true) & ($true = (X55 @ X59))) | ? [X56 : term] : (($true = (var @ X56)) & ($true != (X55 @ X56))) | ? [X57 : term] : (($true = (X55 @ X57)) & ($true != (X55 @ (lam @ X57)))))) & (! [X49 : term > $o,X50 : subst,X51 : term] : ? [X52 : term > $o] : ! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) <=> (pushprop_lem0 = $true)) & ((axvarcons = $true) <=> ! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449)) & ((var @ (d2term @ d_one)) != $true) & (axapp = $true) & (pushprop_lthm_orig = $true) & ((apinj1 = $true) <=> ! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X216 : subst > term > subst > $o] : ? [X217 : term > $o] : ! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218))) & (apnotvar = $true) & (! [X5 : term,X6 : subst > term > subst > $o] : (? [X11 : term] : (($true = (var @ (sub @ X11 @ id))) & ($true != (X6 @ id @ X11 @ id))) | ? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true != (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) & ($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ? [X21 : term,X22 : term] : (($true = (X6 @ id @ X22 @ id)) & ($true != (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id)) & ($true = (X6 @ id @ X21 @ id))) | ? [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) & ($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) | ($true = (X6 @ id @ X5 @ id)) | ? [X12 : subst > term > term] : (! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) & ! [X13 : term] : (((X6 @ id @ X13 @ id) != $true) | ($true = (X6 @ id @ (X12 @ id @ X13) @ id))) & ($true != (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id)))) <=> (hoasinduction = $true)) & (hoasinduction_lem3b_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (axvarshift = $true) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) <=> (? [X345 : subst] : ((comp @ X345 @ id) != X345) | (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346)) | ? [X344 : subst] : ((comp @ id @ X344) != X344))) & ((hoasinduction_lem2 = $true) <=> ! [X378 : subst > term > subst > $o,X379 : term,X380 : term] : (? [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (($true = (X378 @ (comp @ X386 @ X383) @ (sub @ X384 @ X383) @ X385)) & ($true != (X378 @ X386 @ X384 @ (comp @ X383 @ X385)))) | ? [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (($true = (X378 @ X390 @ X387 @ (comp @ X389 @ X388))) & ($true != (X378 @ (comp @ X390 @ X389) @ (sub @ X387 @ X389) @ X388))) | ? [X381 : term,X382 : term] : (($true = (X378 @ id @ X382 @ id)) & ((X378 @ id @ X381 @ id) = $true) & ($true != (X378 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id))) | ($true != (X378 @ id @ X380 @ id)) | ($true != (X378 @ id @ X379 @ id)) | ($true = (X378 @ id @ (ap @ X380 @ X379) @ id)))) & (ulamvarind = $true) & (hoasinduction_lem3a_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)))))))))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (? [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true != (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) & ($true = (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ? [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (($true = (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29)) & ((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) != $true)) | ? [X37 : term] : ((X26 @ X37) != (X24 @ id @ X37 @ id)) | ((X26 @ X23) != $true) | ($true != (X26 @ X25)) | ? [X31 : term,X32 : term] : (($true != (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) & ($true = (X24 @ id @ X32 @ id)) & ($true = (X24 @ id @ X31 @ id))) | ((X26 @ (ap @ X25 @ X23)) = $true))) & (pushprop_gthm = $true) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) <=> (axscons = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X445 : term] : ? [X446 : subst > term > term] : ! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447))) & ((termmset = $true) <=> ! [X305 : term] : ((sub @ X305 @ id) = X305)) & ((shinj = $true) <=> ! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) <=> (apinj2 = $true)) & ((? [X319 : term > $o,X320 : term] : (($true != (X319 @ X320)) & ! [X322 : term] : (($true = (X319 @ X322)) | ($true != (var @ X322))) & ! [X321 : term] : (((X319 @ (lam @ X321)) = $true) | ($true != (X319 @ X321))) & ! [X323 : term,X324 : term] : (($true != (X319 @ X324)) | ($true = (X319 @ (ap @ X323 @ X324))) | ($true != (X319 @ X323)))) | ? [X318 : subst] : ((comp @ X318 @ id) != X318) | ? [X314 : term,X315 : subst] : ((sub @ one @ (push @ X314 @ X315)) != X314) | ? [X316 : term,X317 : subst] : ((comp @ sh @ (push @ X316 @ X317)) != X317) | ! [X325 : subst,X326 : term,X327 : term > $o] : (? [X330 : term] : (($true = (var @ X330)) & ($true != (X327 @ (sub @ X330 @ X325)))) | ? [X328 : term,X329 : term] : (($true != (X327 @ (ap @ X329 @ X328))) & ($true = (X327 @ X328)) & ($true = (X327 @ X329))) | ($true = (X327 @ (sub @ X326 @ X325))) | ? [X331 : term] : (((X327 @ (lam @ X331)) != $true) & ! [X332 : term] : (($true != (X327 @ X332)) | ($true = (X327 @ (sub @ X331 @ (push @ X332 @ id)))))))) <=> (induction2lem_lthm = $true)) & (! [X38 : term] : ? [X39 : subst > term > term] : ((X39 @ sh @ one) = (sub @ X38 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X40 : term] : ? [X41 : subst > term > term] : ! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_gthm = $true) & (! [X76 : term,X77 : subst,X78 : term > $o] : (? [X81 : term] : (($true = (var @ X81)) & ($true != (X78 @ (sub @ X81 @ X77)))) | ($true = (X78 @ (sub @ X76 @ X77))) | ? [X82 : term,X83 : term] : (($true = (X78 @ X83)) & ($true = (X78 @ X82)) & ((X78 @ (ap @ X83 @ X82)) != $true)) | ? [X79 : term] : (! [X80 : term] : (((X78 @ X80) != $true) | ((X78 @ (sub @ X79 @ (push @ X80 @ id))) = $true)) & ((X78 @ (lam @ X79)) != $true))) <=> (induction2lem = $true)) & (! [X159 : subst > term > subst > $o,X160 : term] : (? [X162 : subst > term > term] : (($true != (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X164 : subst,X165 : subst,X166 : term] : ((X162 @ (comp @ X165 @ X164) @ (sub @ X166 @ X164)) = (sub @ (X162 @ X165 @ X166) @ X164)) & ! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id)))) | ((X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id) = $true) | ? [X161 : term] : (($true != (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id)) & ($true = (X159 @ id @ X161 @ id)))) <=> (hoasinduction_lem3aa = $true)) & (axmap = $true) & (substmonoid_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((d2subst @ d_id) = sh) & (hoaslaminj_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & (! [X476 : subst > term > subst > $o,X477 : term] : (($true = (X476 @ id @ (lam @ X477) @ id)) | ? [X483 : term] : (($true != (X476 @ id @ (sub @ X477 @ (push @ X483 @ id)) @ id)) & ($true = (X476 @ id @ X483 @ id))) | ? [X478 : subst > term > term] : (! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X482 @ X481) @ (sub @ X480 @ X481)) = (sub @ (X478 @ X482 @ X480) @ X481)) & ! [X479 : term] : (($true = (X476 @ id @ (X478 @ id @ X479) @ id)) | ($true != (X476 @ id @ X479 @ id))) & ($true != (X476 @ id @ (lam @ (X478 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3a = $true)) & ((induction2 = $true) <=> ! [X283 : term > $o,X284 : term] : (? [X285 : term] : (($true != (X283 @ (lam @ X285))) & ! [X286 : term] : (((X283 @ (sub @ X285 @ (push @ X286 @ id))) = $true) | ($true != (X283 @ X286)))) | ($true = (X283 @ X284)) | ? [X287 : term] : (($true != (X283 @ X287)) & ($true = (var @ X287))) | ? [X288 : term,X289 : term] : (($true != (X283 @ (ap @ X288 @ X289))) & ((X283 @ X289) = $true) & ($true = (X283 @ X288))))) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) != (d2subst @ X349)) | (X348 = X349)) & (induction2_gthm = $true) & (one = (d2term @ d_one)) & ((? [X157 : term] : ((sub @ X157 @ id) != X157) | ! [X158 : term] : ((sub @ X158 @ id) = X158)) <=> (termmset_lthm = $true)) & (! [X255 : subst > term > subst > $o,X256 : term] : (? [X257 : term] : (($true != (X255 @ id @ (sub @ X256 @ (push @ X257 @ id)) @ id)) & ($true = (X255 @ id @ X257 @ id))) | ((X255 @ id @ (lam @ (sub @ X256 @ (push @ one @ sh))) @ id) = $true) | ? [X258 : subst > term > term] : (($true != (X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) & ! [X259 : subst,X260 : subst,X261 : term] : ((sub @ (X258 @ X259 @ X261) @ X260) = (X258 @ (comp @ X259 @ X260) @ (sub @ X261 @ X260))) & ! [X262 : term] : (($true != (X255 @ id @ X262 @ id)) | ((X255 @ id @ (X258 @ id @ X262) @ id) = $true)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X263 : term,X264 : term > $o,X265 : subst > term > subst > $o] : (? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (($true = (X265 @ (comp @ X277 @ X276) @ (sub @ X279 @ X276) @ X278)) & ($true != (X265 @ X277 @ X279 @ (comp @ X276 @ X278)))) | ($true = (X264 @ (lam @ X263))) | ? [X270 : subst > term > term] : (! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273)) & ($true != (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) & ! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ($true != (X265 @ id @ X271 @ id)))) | ? [X275 : term] : (($true != (X264 @ (sub @ X263 @ (push @ X275 @ id)))) & ((X264 @ X275) = $true)) | ? [X266 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != (X265 @ (comp @ X269 @ X268) @ (sub @ X266 @ X268) @ X267)) & ((X265 @ X269 @ X266 @ (comp @ X268 @ X267)) = $true)) | ? [X280 : term] : ((X265 @ id @ X280 @ id) != (X264 @ X280))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) <=> (? [X174 : term,X175 : term] : (((lam @ X175) = (lam @ X174)) & (X174 != X175)) | ? [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) != X170) | ? [X172 : term,X173 : subst] : ((comp @ sh @ (push @ X172 @ X173)) != X173) | ! [X176 : subst > term > term,X177 : subst,X178 : term,X179 : subst > term > term] : (((X179 @ X177 @ X178) = (X176 @ X177 @ X178)) | ? [X183 : subst,X184 : subst,X185 : term] : ((sub @ (X176 @ X183 @ X185) @ X184) != (X176 @ (comp @ X183 @ X184) @ (sub @ X185 @ X184))) | ? [X180 : subst,X181 : term,X182 : subst] : ((sub @ (X179 @ X182 @ X181) @ X180) != (X179 @ (comp @ X182 @ X180) @ (sub @ X181 @ X180))) | ((lam @ (X176 @ sh @ one)) != (lam @ (X179 @ sh @ one)))))) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & ((! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)) | ? [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 != X308) & ((ap @ X307 @ X308) = (ap @ X309 @ X306)))) <=> (hoasapinj2_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X207 : subst,X208 : term,X209 : term > $o] : ? [X210 : term > $o] : ! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207))))) & ((induction2_lthm = $true) <=> (! [X460 : term > $o,X461 : term] : (($true = (X460 @ X461)) | ? [X462 : term] : (($true = (var @ X462)) & ((X460 @ X462) != $true)) | ? [X463 : term] : (($true != (X460 @ (lam @ X463))) & ! [X464 : term] : (($true != (X460 @ X464)) | ((X460 @ (sub @ X463 @ (push @ X464 @ id))) = $true))) | ? [X465 : term,X466 : term] : (($true = (X460 @ X465)) & ($true != (X460 @ (ap @ X465 @ X466))) & ($true = (X460 @ X466)))) | ? [X452 : subst,X453 : term > $o,X454 : term] : (! [X455 : term,X456 : term] : (($true = (X453 @ (ap @ X455 @ X456))) | ($true != (X453 @ X455)) | ($true != (X453 @ X456))) & ($true != (X453 @ (sub @ X454 @ X452))) & ! [X458 : term] : (? [X459 : term] : (((X453 @ (sub @ X458 @ (push @ X459 @ id))) != $true) & ($true = (X453 @ X459))) | ($true = (X453 @ (lam @ X458)))) & ! [X457 : term] : (($true = (X453 @ (sub @ X457 @ X452))) | ($true != (var @ X457)))) | ? [X451 : term] : ((sub @ X451 @ id) != X451))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) <=> (hoasapinj1 = $true)) & (hoasapnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ((hoasinduction_lthm_3 = $true) <=> (? [X504 : term > $o,X505 : term] : (! [X506 : term,X507 : term] : (($true = (X504 @ (ap @ X507 @ X506))) | ($true != (X504 @ X507)) | ($true != (X504 @ X506))) & ($true != (X504 @ X505)) & ! [X509 : term] : (($true = (X504 @ (lam @ X509))) | ? [X510 : term] : (((X504 @ (sub @ X509 @ (push @ X510 @ id))) != $true) & ((X504 @ X510) = $true))) & ! [X508 : term] : (($true = (X504 @ X508)) | ($true != (var @ X508)))) | ? [X512 : term,X513 : subst > term > subst > $o,X514 : term > $o] : (! [X520 : term] : (((X514 @ (sub @ X512 @ (push @ X520 @ id))) = $true) | ($true != (X514 @ X520))) & ! [X515 : subst > term > term] : (? [X519 : term] : (($true != (X513 @ id @ (X515 @ id @ X519) @ id)) & ((X513 @ id @ X519 @ id) = $true)) | ? [X516 : subst,X517 : term,X518 : subst] : ((sub @ (X515 @ X516 @ X517) @ X518) != (X515 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518))) | ((X513 @ id @ (lam @ (X515 @ sh @ one)) @ id) = $true)) & ! [X521 : term] : ((X514 @ X521) = (X513 @ id @ X521 @ id)) & ($true != (X514 @ (lam @ X512)))) | ? [X501 : subst > term > subst > $o] : ! [X502 : term > $o] : ? [X503 : term] : ((X501 @ id @ X503 @ id) != (X502 @ X503)) | ! [X522 : subst > term > subst > $o,X523 : term] : (? [X529 : subst > term > term] : (! [X533 : term] : (((X522 @ id @ (X529 @ id @ X533) @ id) = $true) | ((X522 @ id @ X533 @ id) != $true)) & ! [X530 : subst,X531 : subst,X532 : term] : ((X529 @ (comp @ X530 @ X531) @ (sub @ X532 @ X531)) = (sub @ (X529 @ X530 @ X532) @ X531)) & ((X522 @ id @ (lam @ (X529 @ sh @ one)) @ id) != $true)) | ($true = (X522 @ id @ X523 @ id)) | ? [X534 : subst,X535 : term,X536 : subst,X537 : subst] : (($true != (X522 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) & ($true = (X522 @ X537 @ X535 @ (comp @ X536 @ X534)))) | ? [X524 : term] : (((var @ (sub @ X524 @ id)) = $true) & ($true != (X522 @ id @ X524 @ id))) | ? [X525 : subst,X526 : term,X527 : subst,X528 : subst] : (($true = (X522 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525) @ X528)) & ($true != (X522 @ X527 @ X526 @ (comp @ X525 @ X528)))) | ? [X538 : term,X539 : term] : (((X522 @ id @ X539 @ id) = $true) & ($true != (X522 @ id @ (ap @ (sub @ X538 @ id) @ X539) @ id)) & ($true = (X522 @ id @ X538 @ id)))) | ? [X511 : term] : ((sub @ X511 @ id) != X511))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & ((! [X427 : term,X428 : subst > term > subst > $o] : (? [X438 : term,X439 : term] : (($true = (X428 @ id @ X438 @ id)) & ((X428 @ id @ X439 @ id) = $true) & ((X428 @ id @ (ap @ (sub @ X438 @ id) @ X439) @ id) != $true)) | ? [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true != (X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)) & ((X428 @ X436 @ X437 @ (comp @ X434 @ X435)) = $true)) | ($true = (X428 @ id @ X427 @ id)) | ? [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (($true = (X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) & ((X428 @ X430 @ X432 @ (comp @ X431 @ X433)) != $true)) | ? [X429 : term] : (($true = (var @ (sub @ X429 @ id))) & ($true != (X428 @ id @ X429 @ id))) | ? [X440 : subst > term > term] : (! [X441 : term] : (($true != (X428 @ id @ X441 @ id)) | ($true = (X428 @ id @ (X440 @ id @ X441) @ id))) & ! [X442 : subst,X443 : subst,X444 : term] : ((X440 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443)) = (sub @ (X440 @ X442 @ X444) @ X443)) & ((X428 @ id @ (lam @ (X440 @ sh @ one)) @ id) != $true))) | ? [X391 : term > $o,X392 : term] : (($true != (X391 @ X392)) & ! [X394 : term] : (($true = (X391 @ (lam @ X394))) | ? [X395 : term] : (($true = (X391 @ X395)) & ($true != (X391 @ (sub @ X394 @ (push @ X395 @ id)))))) & ! [X396 : term,X397 : term] : (($true = (X391 @ (ap @ X396 @ X397))) | ((X391 @ X397) != $true) | ((X391 @ X396) != $true)) & ! [X393 : term] : (($true = (X391 @ X393)) | ($true != (var @ X393)))) | ? [X398 : term,X399 : term,X400 : subst > term > subst > $o] : (($true = (X400 @ id @ X399 @ id)) & ! [X401 : subst,X402 : subst,X403 : term,X404 : subst] : (($true != (X400 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401) @ X404)) | ($true = (X400 @ X402 @ X403 @ (comp @ X401 @ X404)))) & ! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X400 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406) @ X408)) | ($true != (X400 @ X407 @ X405 @ (comp @ X406 @ X408)))) & ! [X409 : term,X410 : term] : (($true != (X400 @ id @ X410 @ id)) | ($true != (X400 @ id @ X409 @ id)) | ($true = (X400 @ id @ (ap @ (sub @ X409 @ id) @ X410) @ id))) & ($true != (X400 @ id @ (ap @ X398 @ X399) @ id)) & ($true = (X400 @ id @ X398 @ id))) | ? [X411 : subst > term > subst > $o,X412 : term] : (! [X413 : subst,X414 : term,X415 : subst,X416 : subst] : (($true != (X411 @ X415 @ X414 @ (comp @ X416 @ X413))) | ($true = (X411 @ (comp @ X415 @ X416) @ (sub @ X414 @ X416) @ X413))) & ! [X421 : subst > term > term] : (? [X423 : subst,X424 : subst,X425 : term] : ((sub @ (X421 @ X424 @ X425) @ X423) != (X421 @ (comp @ X424 @ X423) @ (sub @ X425 @ X423))) | ? [X422 : term] : (($true = (X411 @ id @ X422 @ id)) & ((X411 @ id @ (X421 @ id @ X422) @ id) != $true)) | ((X411 @ id @ (lam @ (X421 @ sh @ one)) @ id) = $true)) & ($true != (X411 @ id @ (lam @ X412) @ id)) & ! [X426 : term] : (($true != (X411 @ id @ X426 @ id)) | ($true = (X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))) & ! [X417 : subst,X418 : subst,X419 : term,X420 : subst] : (($true != (X411 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420) @ X417)) | ($true = (X411 @ X418 @ X419 @ (comp @ X420 @ X417)))))) <=> (hoasinduction_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (? [X304 : term] : ((X303 @ X304) != (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ($true != (X302 @ X301)) | ($true = (X303 @ one)))) & ((hoasinduction_lem3b = $true) <=> ! [X0 : term] : ? [X1 : subst > term > term] : ((X1 @ sh @ one) = (sub @ X0 @ (push @ one @ sh)))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X222 : term > $o,X223 : term] : (($true != (X222 @ X223)) & ! [X225 : term] : (? [X226 : term] : (($true != (X222 @ (sub @ X225 @ (push @ X226 @ id)))) & ($true = (X222 @ X226))) | ($true = (X222 @ (lam @ X225)))) & ! [X224 : term] : (($true != (var @ X224)) | ((X222 @ X224) = $true)) & ! [X227 : term,X228 : term] : (($true = (X222 @ (ap @ X228 @ X227))) | ($true != (X222 @ X227)) | ($true != (X222 @ X228)))) | ? [X229 : term] : ((sub @ X229 @ id) != X229) | ? [X230 : term,X231 : term > $o,X232 : subst > term > subst > $o] : (! [X233 : term] : (((X231 @ (sub @ X230 @ (push @ X233 @ id))) = $true) | ($true != (X231 @ X233))) & ! [X234 : subst > term > term] : (($true = (X232 @ id @ (lam @ (X234 @ sh @ one)) @ id)) | ? [X236 : term,X237 : subst,X238 : subst] : ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)) != (sub @ (X234 @ X237 @ X236) @ X238)) | ? [X235 : term] : (($true != (X232 @ id @ (X234 @ id @ X235) @ id)) & ($true = (X232 @ id @ X235 @ id)))) & ($true != (X231 @ (lam @ X230))) & ! [X239 : term] : ((X232 @ id @ X239 @ id) = (X231 @ X239))) | ? [X219 : subst > term > subst > $o] : ! [X220 : term > $o] : ? [X221 : term] : ((X219 @ id @ X221 @ id) != (X220 @ X221)) | ! [X240 : subst > term > subst > $o,X241 : term] : (($true = (X240 @ id @ X241 @ id)) | ? [X244 : subst > term > term] : (! [X245 : term] : (($true != (X240 @ id @ X245 @ id)) | ($true = (X240 @ id @ (X244 @ id @ X245) @ id))) & ! [X246 : subst,X247 : term,X248 : subst] : ((X244 @ (comp @ X246 @ X248) @ (sub @ X247 @ X248)) = (sub @ (X244 @ X246 @ X247) @ X248)) & ($true != (X240 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ? [X242 : term,X243 : term] : (($true = (X240 @ id @ X243 @ id)) & ((X240 @ id @ X242 @ id) = $true) & ($true != (X240 @ id @ (ap @ (sub @ X242 @ id) @ X243) @ id)))))) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (? [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) != (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)) | ? [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) != (sub @ (X491 @ X492 @ X494) @ X493)) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one)))) <=> (hoaslaminj = $true)) & (axassoc = $true) & (hoasapinj2_gthm = $true)),
% 32.37/5.95 inference(flattening,[status(thm)],[f12])).
% 32.37/5.95 thf(f12,plain,(
% 32.37/5.95 (pushprop_lem2v2_gthm = $true) & (induction2lem_gthm = $true) & ((shinj = $true) <=> ! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X290 : subst] : ((comp @ id @ X290) = X290) <=> (axidl = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X104 : term,X105 : subst > term > subst > $o] : (($true = (X105 @ id @ (lam @ X104) @ id)) | ? [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (($true = (X105 @ X114 @ X112 @ (comp @ X111 @ X113))) & ($true != (X105 @ (comp @ X114 @ X111) @ (sub @ X112 @ X111) @ X113))) | ? [X106 : subst > term > term] : (! [X107 : term] : (($true = (X105 @ id @ (X106 @ id @ X107) @ id)) | ($true != (X105 @ id @ X107 @ id))) & ($true != (X105 @ id @ (lam @ (X106 @ sh @ one)) @ id)) & ! [X108 : subst,X109 : term,X110 : subst] : ((X106 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110)) = (sub @ (X106 @ X108 @ X109) @ X110))) | ? [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (($true != (X105 @ X116 @ X119 @ (comp @ X118 @ X117))) & ((X105 @ (comp @ X116 @ X118) @ (sub @ X119 @ X118) @ X117) = $true)) | ? [X115 : term] : (($true = (X105 @ id @ X115 @ id)) & ((X105 @ id @ (sub @ X104 @ (push @ X115 @ id)) @ id) != $true))) | ? [X96 : term,X97 : subst > term > subst > $o] : (! [X103 : term] : (($true != (X97 @ id @ X103 @ id)) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true)) & ! [X98 : subst > term > term] : (? [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) != $true) & ($true = (X97 @ id @ X102 @ id))) | ($true = (X97 @ id @ (lam @ (X98 @ sh @ one)) @ id)) | ? [X99 : term,X100 : subst,X101 : subst] : ((X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)) != (sub @ (X98 @ X101 @ X99) @ X100))) & ($true != (X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id)))) | ? [X95 : term] : ((sub @ X95 @ id) != X95))) & (((((! [X522 : subst > term > subst > $o,X523 : term] : (? [X529 : subst > term > term] : (! [X533 : term] : (((X522 @ id @ (X529 @ id @ X533) @ id) = $true) | ((X522 @ id @ X533 @ id) != $true)) & ! [X530 : subst,X531 : subst,X532 : term] : ((X529 @ (comp @ X530 @ X531) @ (sub @ X532 @ X531)) = (sub @ (X529 @ X530 @ X532) @ X531)) & ((X522 @ id @ (lam @ (X529 @ sh @ one)) @ id) != $true)) | ($true = (X522 @ id @ X523 @ id)) | ? [X534 : subst,X535 : term,X536 : subst,X537 : subst] : (($true != (X522 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) & ($true = (X522 @ X537 @ X535 @ (comp @ X536 @ X534)))) | ? [X524 : term] : (((var @ (sub @ X524 @ id)) = $true) & ($true != (X522 @ id @ X524 @ id))) | ? [X525 : subst,X526 : term,X527 : subst,X528 : subst] : (($true = (X522 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525) @ X528)) & ($true != (X522 @ X527 @ X526 @ (comp @ X525 @ X528)))) | ? [X538 : term,X539 : term] : (((X522 @ id @ X539 @ id) = $true) & ($true != (X522 @ id @ (ap @ (sub @ X538 @ id) @ X539) @ id)) & ($true = (X522 @ id @ X538 @ id)))) | ? [X512 : term,X513 : subst > term > subst > $o,X514 : term > $o] : (! [X520 : term] : (((X514 @ (sub @ X512 @ (push @ X520 @ id))) = $true) | ($true != (X514 @ X520))) & ! [X515 : subst > term > term] : (? [X519 : term] : (($true != (X513 @ id @ (X515 @ id @ X519) @ id)) & ((X513 @ id @ X519 @ id) = $true)) | ? [X516 : subst,X517 : term,X518 : subst] : ((sub @ (X515 @ X516 @ X517) @ X518) != (X515 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518))) | ((X513 @ id @ (lam @ (X515 @ sh @ one)) @ id) = $true)) & ! [X521 : term] : ((X514 @ X521) = (X513 @ id @ X521 @ id)) & ($true != (X514 @ (lam @ X512))))) | ? [X511 : term] : ((sub @ X511 @ id) != X511)) | ? [X504 : term > $o,X505 : term] : (! [X506 : term,X507 : term] : (($true = (X504 @ (ap @ X507 @ X506))) | ($true != (X504 @ X507)) | ($true != (X504 @ X506))) & ($true != (X504 @ X505)) & ! [X509 : term] : (($true = (X504 @ (lam @ X509))) | ? [X510 : term] : (((X504 @ (sub @ X509 @ (push @ X510 @ id))) != $true) & ((X504 @ X510) = $true))) & ! [X508 : term] : (($true = (X504 @ X508)) | ($true != (var @ X508))))) | ? [X501 : subst > term > subst > $o] : ! [X502 : term > $o] : ? [X503 : term] : ((X501 @ id @ X503 @ id) != (X502 @ X503))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (((! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)) | ? [X85 : term,X86 : term,X87 : term,X88 : term] : ((X85 != X86) & ((ap @ X85 @ X87) = (ap @ X86 @ X88)))) | ? [X84 : term] : ((sub @ X84 @ id) != X84)) <=> (hoasapinj1_lthm = $true)) & (! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (? [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) != (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)) | ? [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) != (sub @ (X491 @ X492 @ X494) @ X493)) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one)))) <=> (hoaslaminj = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset = $true) <=> ! [X305 : term] : ((sub @ X305 @ id) = X305)) & ((hoasinduction_lem2 = $true) <=> ! [X378 : subst > term > subst > $o,X379 : term,X380 : term] : (? [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (($true = (X378 @ (comp @ X386 @ X383) @ (sub @ X384 @ X383) @ X385)) & ($true != (X378 @ X386 @ X384 @ (comp @ X383 @ X385)))) | ? [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (($true = (X378 @ X390 @ X387 @ (comp @ X389 @ X388))) & ($true != (X378 @ (comp @ X390 @ X389) @ (sub @ X387 @ X389) @ X388))) | ? [X381 : term,X382 : term] : (($true = (X378 @ id @ X382 @ id)) & ((X378 @ id @ X381 @ id) = $true) & ($true != (X378 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id))) | ($true != (X378 @ id @ X380 @ id)) | ($true != (X378 @ id @ X379 @ id)) | ($true = (X378 @ id @ (ap @ X380 @ X379) @ id)))) & (hoasapnotvar = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (? [X304 : term] : ((X303 @ X304) != (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ($true != (X302 @ X301)) | ($true = (X303 @ one)))) & (substmonoid_gthm = $true) & (axapp = $true) & ((laminj = $true) <=> ! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((d2subst @ d_id) = id) & (! [X38 : term] : ? [X39 : subst > term > term] : ((X39 @ sh @ one) = (sub @ X38 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (ulamvarind = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X255 : subst > term > subst > $o,X256 : term] : (? [X257 : term] : (($true != (X255 @ id @ (sub @ X256 @ (push @ X257 @ id)) @ id)) & ($true = (X255 @ id @ X257 @ id))) | ((X255 @ id @ (lam @ (sub @ X256 @ (push @ one @ sh))) @ id) = $true) | ? [X258 : subst > term > term] : (($true != (X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) & ! [X259 : subst,X260 : subst,X261 : term] : ((sub @ (X258 @ X259 @ X261) @ X260) = (X258 @ (comp @ X259 @ X260) @ (sub @ X261 @ X260))) & ! [X262 : term] : (($true != (X255 @ id @ X262 @ id)) | ((X255 @ id @ (X258 @ id @ X262) @ id) = $true)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X167 : term] : ((sub @ X167 @ id) = X167) <=> (axvarid = $true)) & ((var @ (d2term @ d_one)) != $true) & (hoaslamnotvar = $true) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) <=> (axshiftcons = $true)) & ((substmonoid_lthm = $true) <=> (((! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346)) | ? [X345 : subst] : ((comp @ X345 @ id) != X345)) | ? [X344 : subst] : ((comp @ id @ X344) != X344))) & ! [X343 : d_term] : (d_one = X343) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & ((induction = $true) <=> ! [X54 : term,X55 : term > $o] : (($true = (X55 @ X54)) | ? [X58 : term,X59 : term] : (($true = (X55 @ X58)) & ((X55 @ (ap @ X58 @ X59)) != $true) & ($true = (X55 @ X59))) | ? [X56 : term] : (($true = (var @ X56)) & ($true != (X55 @ X56))) | ? [X57 : term] : (($true = (X55 @ X57)) & ($true != (X55 @ (lam @ X57)))))) & ((hoasinduction_lthm = $true) <=> (((! [X427 : term,X428 : subst > term > subst > $o] : (? [X438 : term,X439 : term] : (($true = (X428 @ id @ X438 @ id)) & ((X428 @ id @ X439 @ id) = $true) & ((X428 @ id @ (ap @ (sub @ X438 @ id) @ X439) @ id) != $true)) | ? [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true != (X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)) & ((X428 @ X436 @ X437 @ (comp @ X434 @ X435)) = $true)) | ($true = (X428 @ id @ X427 @ id)) | ? [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (($true = (X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) & ((X428 @ X430 @ X432 @ (comp @ X431 @ X433)) != $true)) | ? [X429 : term] : (($true = (var @ (sub @ X429 @ id))) & ($true != (X428 @ id @ X429 @ id))) | ? [X440 : subst > term > term] : (! [X441 : term] : (($true != (X428 @ id @ X441 @ id)) | ($true = (X428 @ id @ (X440 @ id @ X441) @ id))) & ! [X442 : subst,X443 : subst,X444 : term] : ((X440 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443)) = (sub @ (X440 @ X442 @ X444) @ X443)) & ((X428 @ id @ (lam @ (X440 @ sh @ one)) @ id) != $true))) | ? [X411 : subst > term > subst > $o,X412 : term] : (! [X413 : subst,X414 : term,X415 : subst,X416 : subst] : (($true != (X411 @ X415 @ X414 @ (comp @ X416 @ X413))) | ($true = (X411 @ (comp @ X415 @ X416) @ (sub @ X414 @ X416) @ X413))) & ! [X421 : subst > term > term] : (? [X423 : subst,X424 : subst,X425 : term] : ((sub @ (X421 @ X424 @ X425) @ X423) != (X421 @ (comp @ X424 @ X423) @ (sub @ X425 @ X423))) | ? [X422 : term] : (($true = (X411 @ id @ X422 @ id)) & ((X411 @ id @ (X421 @ id @ X422) @ id) != $true)) | ((X411 @ id @ (lam @ (X421 @ sh @ one)) @ id) = $true)) & ($true != (X411 @ id @ (lam @ X412) @ id)) & ! [X426 : term] : (($true != (X411 @ id @ X426 @ id)) | ($true = (X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))) & ! [X417 : subst,X418 : subst,X419 : term,X420 : subst] : (($true != (X411 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420) @ X417)) | ($true = (X411 @ X418 @ X419 @ (comp @ X420 @ X417)))))) | ? [X398 : term,X399 : term,X400 : subst > term > subst > $o] : (($true = (X400 @ id @ X399 @ id)) & ! [X401 : subst,X402 : subst,X403 : term,X404 : subst] : (($true != (X400 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401) @ X404)) | ($true = (X400 @ X402 @ X403 @ (comp @ X401 @ X404)))) & ! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X400 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406) @ X408)) | ($true != (X400 @ X407 @ X405 @ (comp @ X406 @ X408)))) & ! [X409 : term,X410 : term] : (($true != (X400 @ id @ X410 @ id)) | ($true != (X400 @ id @ X409 @ id)) | ($true = (X400 @ id @ (ap @ (sub @ X409 @ id) @ X410) @ id))) & ($true != (X400 @ id @ (ap @ X398 @ X399) @ id)) & ($true = (X400 @ id @ X398 @ id)))) | ? [X391 : term > $o,X392 : term] : (($true != (X391 @ X392)) & ! [X394 : term] : (($true = (X391 @ (lam @ X394))) | ? [X395 : term] : (($true = (X391 @ X395)) & ($true != (X391 @ (sub @ X394 @ (push @ X395 @ id)))))) & ! [X396 : term,X397 : term] : (($true = (X391 @ (ap @ X396 @ X397))) | ((X391 @ X397) != $true) | ((X391 @ X396) != $true)) & ! [X393 : term] : (($true = (X391 @ X393)) | ($true != (var @ X393)))))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X204 : subst > term > subst > $o] : ? [X205 : term > $o] : ! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id)) <=> (hoasinduction_lem0 = $true)) & (ulamvarsh = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X216 : subst > term > subst > $o] : ? [X217 : term > $o] : ! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218))) & (pushprop = $true) & (apnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X176 : subst > term > term,X177 : subst,X178 : term,X179 : subst > term > term] : (((X179 @ X177 @ X178) = (X176 @ X177 @ X178)) | ? [X183 : subst,X184 : subst,X185 : term] : ((sub @ (X176 @ X183 @ X185) @ X184) != (X176 @ (comp @ X183 @ X184) @ (sub @ X185 @ X184))) | ? [X180 : subst,X181 : term,X182 : subst] : ((sub @ (X179 @ X182 @ X181) @ X180) != (X179 @ (comp @ X182 @ X180) @ (sub @ X181 @ X180))) | ((lam @ (X176 @ sh @ one)) != (lam @ (X179 @ sh @ one)))) | ? [X174 : term,X175 : term] : (((lam @ X175) = (lam @ X174)) & (X174 != X175))) | ? [X172 : term,X173 : subst] : ((comp @ sh @ (push @ X172 @ X173)) != X173)) | ? [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) != X170))) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) <=> (apinj2 = $true)) & ((? [X157 : term] : ((sub @ X157 @ id) != X157) | ! [X158 : term] : ((sub @ X158 @ id) = X158)) <=> (termmset_lthm = $true)) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (pushprop_lthm_orig = $true) & ((d2subst @ d_id) = sh) & ((hoasinduction_lem3 = $true) <=> ! [X60 : term,X61 : subst > term > subst > $o] : (? [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (($true = (X61 @ X70 @ X71 @ (comp @ X69 @ X68))) & ((X61 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X68) != $true)) | ? [X62 : term] : (($true != (X61 @ id @ (sub @ X60 @ (push @ X62 @ id)) @ id)) & ((X61 @ id @ X62 @ id) = $true)) | ? [X63 : subst > term > term] : (! [X65 : term,X66 : subst,X67 : subst] : ((X63 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)) = (sub @ (X63 @ X67 @ X65) @ X66)) & ! [X64 : term] : (($true != (X61 @ id @ X64 @ id)) | ($true = (X61 @ id @ (X63 @ id @ X64) @ id))) & ($true != (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id))) | ($true = (X61 @ id @ (lam @ X60) @ id)) | ? [X72 : subst,X73 : subst,X74 : subst,X75 : term] : (($true = (X61 @ (comp @ X73 @ X74) @ (sub @ X75 @ X74) @ X72)) & ($true != (X61 @ X73 @ X75 @ (comp @ X74 @ X72)))))) & (((! [X129 : subst > term > subst > $o,X130 : term] : (($true = (X129 @ id @ (lam @ X130) @ id)) | ? [X131 : subst > term > term] : (! [X133 : subst,X134 : subst,X135 : term] : ((sub @ (X131 @ X133 @ X135) @ X134) = (X131 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) & ! [X132 : term] : (($true = (X129 @ id @ (X131 @ id @ X132) @ id)) | ($true != (X129 @ id @ X132 @ id))) & ($true != (X129 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ? [X136 : term] : (($true = (X129 @ id @ X136 @ id)) & ($true != (X129 @ id @ (sub @ X130 @ (push @ X136 @ id)) @ id)))) | ? [X121 : term,X122 : subst > term > subst > $o] : (! [X123 : subst > term > term] : (? [X124 : term] : (($true = (X122 @ id @ X124 @ id)) & ($true != (X122 @ id @ (X123 @ id @ X124) @ id))) | ? [X125 : subst,X126 : subst,X127 : term] : ((sub @ (X123 @ X125 @ X127) @ X126) != (X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126))) | ($true = (X122 @ id @ (lam @ (X123 @ sh @ one)) @ id))) & ! [X128 : term] : (($true != (X122 @ id @ X128 @ id)) | ($true = (X122 @ id @ (sub @ X121 @ (push @ X128 @ id)) @ id))) & ($true != (X122 @ id @ (lam @ (sub @ X121 @ (push @ one @ sh))) @ id)))) | ? [X120 : term] : ((sub @ X120 @ id) != X120)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X0 : term] : ? [X1 : subst > term > term] : ((X1 @ sh @ one) = (sub @ X0 @ (push @ one @ sh)))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) != X351) | ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (? [X356 : term] : ((X354 @ X356) != (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true = (X354 @ one)) | ($true != (X352 @ X353))))) & ((! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)) | ? [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 != X308) & ((ap @ X307 @ X308) = (ap @ X309 @ X306)))) <=> (hoasapinj2_lthm = $true)) & (! [X5 : term,X6 : subst > term > subst > $o] : (? [X11 : term] : (($true = (var @ (sub @ X11 @ id))) & ($true != (X6 @ id @ X11 @ id))) | ? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true != (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) & ($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ? [X21 : term,X22 : term] : (($true = (X6 @ id @ X22 @ id)) & ($true != (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id)) & ($true = (X6 @ id @ X21 @ id))) | ? [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) & ($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) | ($true = (X6 @ id @ X5 @ id)) | ? [X12 : subst > term > term] : (! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) & ! [X13 : term] : (((X6 @ id @ X13 @ id) != $true) | ($true = (X6 @ id @ (X12 @ id @ X13) @ id))) & ($true != (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id)))) <=> (hoasinduction = $true)) & (hoasapnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) <=> ! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449)) & (termmset_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X445 : term] : ? [X446 : subst > term > term] : ! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447))) & (axabs = $true) & (lamnotap != $true) & (pushprop_lthm = $true) & (((((! [X240 : subst > term > subst > $o,X241 : term] : (($true = (X240 @ id @ X241 @ id)) | ? [X244 : subst > term > term] : (! [X245 : term] : (($true != (X240 @ id @ X245 @ id)) | ($true = (X240 @ id @ (X244 @ id @ X245) @ id))) & ! [X246 : subst,X247 : term,X248 : subst] : ((X244 @ (comp @ X246 @ X248) @ (sub @ X247 @ X248)) = (sub @ (X244 @ X246 @ X247) @ X248)) & ($true != (X240 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ? [X242 : term,X243 : term] : (($true = (X240 @ id @ X243 @ id)) & ((X240 @ id @ X242 @ id) = $true) & ($true != (X240 @ id @ (ap @ (sub @ X242 @ id) @ X243) @ id)))) | ? [X230 : term,X231 : term > $o,X232 : subst > term > subst > $o] : (! [X233 : term] : (((X231 @ (sub @ X230 @ (push @ X233 @ id))) = $true) | ($true != (X231 @ X233))) & ! [X234 : subst > term > term] : (($true = (X232 @ id @ (lam @ (X234 @ sh @ one)) @ id)) | ? [X236 : term,X237 : subst,X238 : subst] : ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)) != (sub @ (X234 @ X237 @ X236) @ X238)) | ? [X235 : term] : (($true != (X232 @ id @ (X234 @ id @ X235) @ id)) & ($true = (X232 @ id @ X235 @ id)))) & ($true != (X231 @ (lam @ X230))) & ! [X239 : term] : ((X232 @ id @ X239 @ id) = (X231 @ X239)))) | ? [X229 : term] : ((sub @ X229 @ id) != X229)) | ? [X222 : term > $o,X223 : term] : (($true != (X222 @ X223)) & ! [X225 : term] : (? [X226 : term] : (($true != (X222 @ (sub @ X225 @ (push @ X226 @ id)))) & ($true = (X222 @ X226))) | ($true = (X222 @ (lam @ X225)))) & ! [X224 : term] : (($true != (var @ X224)) | ((X222 @ X224) = $true)) & ! [X227 : term,X228 : term] : (($true = (X222 @ (ap @ X228 @ X227))) | ($true != (X222 @ X227)) | ($true != (X222 @ X228))))) | ? [X219 : subst > term > subst > $o] : ! [X220 : term > $o] : ? [X221 : term] : ((X219 @ id @ X221 @ id) != (X220 @ X221))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2 = $true) & (one = (d2term @ d_one)) & ((hoaslamnotap = $true) <=> ! [X249 : term,X250 : term,X251 : subst > term > term] : (? [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) != (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253))) | ((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one))))) & (hoasapinj2_gthm = $true) & ((? [X359 : term] : ((sub @ X359 @ id) != X359) | ! [X360 : subst > term > subst > $o,X361 : term,X362 : term > $o] : (? [X364 : subst,X365 : subst,X366 : subst,X367 : term] : (($true = (X360 @ (comp @ X366 @ X365) @ (sub @ X367 @ X365) @ X364)) & ($true != (X360 @ X366 @ X367 @ (comp @ X365 @ X364)))) | ? [X363 : term] : ((X362 @ X363) != (X360 @ id @ X363 @ id)) | ? [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (($true = (X360 @ X375 @ X376 @ (comp @ X373 @ X374))) & ($true != (X360 @ (comp @ X375 @ X373) @ (sub @ X376 @ X373) @ X374))) | ? [X377 : term] : (($true != (X362 @ (sub @ X361 @ (push @ X377 @ id)))) & ((X362 @ X377) = $true)) | ? [X368 : subst > term > term] : (! [X369 : term] : (($true = (X360 @ id @ (X368 @ id @ X369) @ id)) | ($true != (X360 @ id @ X369 @ id))) & ! [X370 : subst,X371 : term,X372 : subst] : ((sub @ (X368 @ X370 @ X371) @ X372) = (X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) & ($true != (X360 @ id @ (lam @ (X368 @ sh @ one)) @ id))) | ($true = (X362 @ (lam @ X361))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) <=> (axscons = $true)) & (hoasinduction_lem2v2_gthm = $true) & (ulamvar1 != $true) & (hoasinduction_lem3v2_gthm = $true) & (axmap = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) <=> (substmonoid = $true)) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (! [X333 : term > $o,X334 : subst > term > subst > $o,X335 : term] : (($true = (X333 @ (lam @ X335))) | ? [X336 : subst > term > term] : (! [X340 : term] : (($true = (X334 @ id @ (X336 @ id @ X340) @ id)) | ($true != (X334 @ id @ X340 @ id))) & ($true != (X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)) & ! [X337 : subst,X338 : subst,X339 : term] : ((sub @ (X336 @ X338 @ X339) @ X337) = (X336 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337)))) | ? [X341 : term] : (((X333 @ X341) = $true) & ($true != (X333 @ (sub @ X335 @ (push @ X341 @ id))))) | ? [X342 : term] : ((X334 @ id @ X342 @ id) != (X333 @ X342))) <=> (hoasinduction_lem3v2a = $true)) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) <=> (hoasapinj1 = $true)) & (! [X263 : term,X264 : term > $o,X265 : subst > term > subst > $o] : (? [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (($true = (X265 @ (comp @ X277 @ X276) @ (sub @ X279 @ X276) @ X278)) & ($true != (X265 @ X277 @ X279 @ (comp @ X276 @ X278)))) | ($true = (X264 @ (lam @ X263))) | ? [X270 : subst > term > term] : (! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273)) & ($true != (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) & ! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ($true != (X265 @ id @ X271 @ id)))) | ? [X275 : term] : (($true != (X264 @ (sub @ X263 @ (push @ X275 @ id)))) & ((X264 @ X275) = $true)) | ? [X266 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != (X265 @ (comp @ X269 @ X268) @ (sub @ X266 @ X268) @ X267)) & ((X265 @ X269 @ X266 @ (comp @ X268 @ X267)) = $true)) | ? [X280 : term] : ((X265 @ id @ X280 @ id) != (X264 @ X280))) <=> (hoasinduction_lem3v2 = $true)) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) != (d2subst @ X349)) | (X348 = X349)) & (axclos = $true) & (pushprop_lem0_gthm = $true) & (! [X476 : subst > term > subst > $o,X477 : term] : (($true = (X476 @ id @ (lam @ X477) @ id)) | ? [X483 : term] : (($true != (X476 @ id @ (sub @ X477 @ (push @ X483 @ id)) @ id)) & ($true = (X476 @ id @ X483 @ id))) | ? [X478 : subst > term > term] : (! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X482 @ X481) @ (sub @ X480 @ X481)) = (sub @ (X478 @ X482 @ X480) @ X481)) & ! [X479 : term] : (($true = (X476 @ id @ (X478 @ id @ X479) @ id)) | ($true != (X476 @ id @ X479 @ id))) & ($true != (X476 @ id @ (lam @ (X478 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X142 : term,X143 : subst > term > subst > $o,X144 : term > $o] : (? [X151 : term] : (((X144 @ X151) = $true) & ($true != (X144 @ (sub @ X142 @ (push @ X151 @ id))))) | ($true = (X144 @ (lam @ X142))) | ? [X146 : subst > term > term] : (! [X147 : term,X148 : subst,X149 : subst] : ((X146 @ (comp @ X149 @ X148) @ (sub @ X147 @ X148)) = (sub @ (X146 @ X149 @ X147) @ X148)) & ! [X150 : term] : (($true != (X143 @ id @ X150 @ id)) | ((X143 @ id @ (X146 @ id @ X150) @ id) = $true)) & ((X143 @ id @ (lam @ (X146 @ sh @ one)) @ id) != $true)) | ? [X145 : term] : ((X144 @ X145) != (X143 @ id @ X145 @ id))) | ? [X141 : term] : ((sub @ X141 @ id) != X141)) | ? [X137 : term] : ! [X138 : subst > term > term] : ? [X139 : term,X140 : subst] : ((X138 @ X140 @ X139) != (sub @ X137 @ (push @ X139 @ X140))))) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X159 : subst > term > subst > $o,X160 : term] : (? [X162 : subst > term > term] : (($true != (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) & ! [X164 : subst,X165 : subst,X166 : term] : ((X162 @ (comp @ X165 @ X164) @ (sub @ X166 @ X164)) = (sub @ (X162 @ X165 @ X166) @ X164)) & ! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id)))) | ((X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id) = $true) | ? [X161 : term] : (($true != (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id)) & ($true = (X159 @ id @ X161 @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapnotvar_gthm = $true) & (! [X467 : term,X468 : subst > term > subst > $o] : (? [X469 : subst > term > term] : (! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true)) & ! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) & ($true != (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ? [X474 : term,X475 : term] : (($true = (X468 @ id @ X475 @ id)) & ($true != (X468 @ id @ (ap @ (sub @ X474 @ id) @ X475) @ id)) & ($true = (X468 @ id @ X474 @ id))) | ((X468 @ id @ X467 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((induction2 = $true) <=> ! [X283 : term > $o,X284 : term] : (? [X285 : term] : (($true != (X283 @ (lam @ X285))) & ! [X286 : term] : (((X283 @ (sub @ X285 @ (push @ X286 @ id))) = $true) | ($true != (X283 @ X286)))) | ($true = (X283 @ X284)) | ? [X287 : term] : (($true != (X283 @ X287)) & ($true = (var @ X287))) | ? [X288 : term,X289 : term] : (($true != (X283 @ (ap @ X288 @ X289))) & ((X283 @ X289) = $true) & ($true = (X283 @ X288))))) & (lamnotvar = $true) & (((! [X460 : term > $o,X461 : term] : (($true = (X460 @ X461)) | ? [X462 : term] : (($true = (var @ X462)) & ((X460 @ X462) != $true)) | ? [X463 : term] : (($true != (X460 @ (lam @ X463))) & ! [X464 : term] : (($true != (X460 @ X464)) | ((X460 @ (sub @ X463 @ (push @ X464 @ id))) = $true))) | ? [X465 : term,X466 : term] : (($true = (X460 @ X465)) & ($true != (X460 @ (ap @ X465 @ X466))) & ($true = (X460 @ X466)))) | ? [X452 : subst,X453 : term > $o,X454 : term] : (! [X455 : term,X456 : term] : (($true = (X453 @ (ap @ X455 @ X456))) | ($true != (X453 @ X455)) | ($true != (X453 @ X456))) & ($true != (X453 @ (sub @ X454 @ X452))) & ! [X458 : term] : (? [X459 : term] : (((X453 @ (sub @ X458 @ (push @ X459 @ id))) != $true) & ($true = (X453 @ X459))) | ($true = (X453 @ (lam @ X458)))) & ! [X457 : term] : (($true = (X453 @ (sub @ X457 @ X452))) | ($true != (var @ X457))))) | ? [X451 : term] : ((sub @ X451 @ id) != X451)) <=> (induction2_lthm = $true)) & ! [X168 : d_term,X169 : d_term] : ((X168 = X169) | ((d2term @ X169) != (d2term @ X168))) & (! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3aaa = $true) <=> ! [X192 : term,X193 : subst > term > subst > $o] : (? [X194 : term] : (($true != (X193 @ id @ (sub @ X192 @ (push @ X194 @ id)) @ id)) & ($true = (X193 @ id @ X194 @ id))) | ? [X195 : subst > term > term,X196 : term] : (! [X197 : term] : (($true = (X193 @ id @ (X195 @ id @ X197) @ id)) | ($true != (X193 @ id @ X197 @ id))) & ! [X201 : subst,X202 : term,X203 : subst] : ((sub @ X196 @ (push @ (sub @ X202 @ X201) @ (comp @ X203 @ X201))) = (X195 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) & ! [X198 : term,X199 : subst,X200 : subst] : ((sub @ (sub @ X196 @ (push @ X198 @ X199)) @ X200) = (sub @ (X195 @ X199 @ X198) @ X200)) & ((X193 @ id @ (lam @ (X195 @ sh @ one)) @ id) != $true)) | ($true = (X193 @ id @ (lam @ (sub @ X192 @ (push @ one @ sh))) @ id)))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true)) | ? [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) != X293)) | ? [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) != X291))) & ! [X48 : d_subst] : (d_id = X48) & (hoasapinj1_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X325 : subst,X326 : term,X327 : term > $o] : (? [X330 : term] : (($true = (var @ X330)) & ($true != (X327 @ (sub @ X330 @ X325)))) | ? [X328 : term,X329 : term] : (($true != (X327 @ (ap @ X329 @ X328))) & ($true = (X327 @ X328)) & ($true = (X327 @ X329))) | ($true = (X327 @ (sub @ X326 @ X325))) | ? [X331 : term] : (((X327 @ (lam @ X331)) != $true) & ! [X332 : term] : (($true != (X327 @ X332)) | ($true = (X327 @ (sub @ X331 @ (push @ X332 @ id))))))) | ? [X319 : term > $o,X320 : term] : (($true != (X319 @ X320)) & ! [X322 : term] : (($true = (X319 @ X322)) | ($true != (var @ X322))) & ! [X321 : term] : (((X319 @ (lam @ X321)) = $true) | ($true != (X319 @ X321))) & ! [X323 : term,X324 : term] : (($true != (X319 @ X324)) | ($true = (X319 @ (ap @ X323 @ X324))) | ($true != (X319 @ X323))))) | ? [X318 : subst] : ((comp @ X318 @ id) != X318)) | ? [X316 : term,X317 : subst] : ((comp @ sh @ (push @ X316 @ X317)) != X317)) | ? [X314 : term,X315 : subst] : ((sub @ one @ (push @ X314 @ X315)) != X314))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem3v2_lthm = $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)))))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (? [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true != (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) & ($true = (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ? [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (($true = (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29)) & ((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) != $true)) | ? [X37 : term] : ((X26 @ X37) != (X24 @ id @ X37 @ id)) | ((X26 @ X23) != $true) | ($true != (X26 @ X25)) | ? [X31 : term,X32 : term] : (($true != (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) & ($true = (X24 @ id @ X32 @ id)) & ($true = (X24 @ id @ X31 @ id))) | ((X26 @ (ap @ X25 @ X23)) = $true))) & (! [X40 : term] : ? [X41 : subst > term > term] : ! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axvarshift = $true) & (pushprop_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214))) & (! [X76 : term,X77 : subst,X78 : term > $o] : (? [X81 : term] : (($true = (var @ X81)) & ($true != (X78 @ (sub @ X81 @ X77)))) | ($true = (X78 @ (sub @ X76 @ X77))) | ? [X82 : term,X83 : term] : (($true = (X78 @ X83)) & ($true = (X78 @ X82)) & ((X78 @ (ap @ X83 @ X82)) != $true)) | ? [X79 : term] : (! [X80 : term] : (((X78 @ X80) != $true) | ((X78 @ (sub @ X79 @ (push @ X80 @ id))) = $true)) & ((X78 @ (lam @ X79)) != $true))) <=> (induction2lem = $true)) & ((apinj1 = $true) <=> ! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46))) & (hoaslaminj_gthm = $true) & (! [X49 : term > $o,X50 : subst,X51 : term] : ? [X52 : term > $o] : ! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) <=> (pushprop_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X207 : subst,X208 : term,X209 : term > $o] : ? [X210 : term > $o] : ! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207))))) & (induction2_gthm = $true)),
% 32.37/5.95 inference(ennf_transformation,[status(thm)],[f11])).
% 32.37/5.95 thf(f11,plain,(
% 32.37/5.95 (pushprop_lem2v2_gthm = $true) & (induction2lem_gthm = $true) & ((shinj = $true) <=> ! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X290 : subst] : ((comp @ id @ X290) = X290) <=> (axidl = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X95 : term] : ((sub @ X95 @ id) = X95) => (! [X96 : term,X97 : subst > term > subst > $o] : (($true = (X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id)) | ~! [X98 : subst > term > term] : (~! [X102 : term] : (((X97 @ id @ (X98 @ id @ X102) @ id) = $true) | ($true != (X97 @ id @ X102 @ id))) | ($true = (X97 @ id @ (lam @ (X98 @ sh @ one)) @ id)) | ~! [X99 : term,X100 : subst,X101 : subst] : ((X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)) = (sub @ (X98 @ X101 @ X99) @ X100))) | ~! [X103 : term] : (($true != (X97 @ id @ X103 @ id)) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true))) => ! [X104 : term,X105 : subst > term > subst > $o] : (($true = (X105 @ id @ (lam @ X104) @ id)) | ~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (($true != (X105 @ X114 @ X112 @ (comp @ X111 @ X113))) | ($true = (X105 @ (comp @ X114 @ X111) @ (sub @ X112 @ X111) @ X113))) | ~! [X106 : subst > term > term] : (~! [X107 : term] : (($true = (X105 @ id @ (X106 @ id @ X107) @ id)) | ($true != (X105 @ id @ X107 @ id))) | ($true = (X105 @ id @ (lam @ (X106 @ sh @ one)) @ id)) | ~! [X108 : subst,X109 : term,X110 : subst] : ((X106 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110)) = (sub @ (X106 @ X108 @ X109) @ X110))) | ~! [X115 : term] : (((X105 @ id @ (sub @ X104 @ (push @ X115 @ id)) @ id) = $true) | ($true != (X105 @ id @ X115 @ id))) | ~! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (((X105 @ (comp @ X116 @ X118) @ (sub @ X119 @ X118) @ X117) != $true) | ($true = (X105 @ X116 @ X119 @ (comp @ X118 @ X117)))))))) & ((! [X501 : subst > term > subst > $o] : ~! [X502 : term > $o] : ~! [X503 : term] : ((X501 @ id @ X503 @ id) = (X502 @ X503)) => (! [X504 : term > $o,X505 : term] : (($true = (X504 @ X505)) | ~! [X508 : term] : (($true = (X504 @ X508)) | ($true != (var @ X508))) | ~! [X509 : term] : (($true = (X504 @ (lam @ X509))) | ~! [X510 : term] : (((X504 @ X510) != $true) | ((X504 @ (sub @ X509 @ (push @ X510 @ id))) = $true))) | ~! [X506 : term,X507 : term] : (($true = (X504 @ (ap @ X507 @ X506))) | ($true != (X504 @ X507)) | ($true != (X504 @ X506)))) => (! [X511 : term] : ((sub @ X511 @ id) = X511) => (! [X512 : term,X513 : subst > term > subst > $o,X514 : term > $o] : (~! [X520 : term] : (((X514 @ (sub @ X512 @ (push @ X520 @ id))) = $true) | ($true != (X514 @ X520))) | ~! [X521 : term] : ((X514 @ X521) = (X513 @ id @ X521 @ id)) | ~! [X515 : subst > term > term] : (~! [X516 : subst,X517 : term,X518 : subst] : ((sub @ (X515 @ X516 @ X517) @ X518) = (X515 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518))) | ~! [X519 : term] : (((X513 @ id @ X519 @ id) != $true) | ($true = (X513 @ id @ (X515 @ id @ X519) @ id))) | ((X513 @ id @ (lam @ (X515 @ sh @ one)) @ id) = $true)) | ($true = (X514 @ (lam @ X512)))) => ! [X522 : subst > term > subst > $o,X523 : term] : (($true = (X522 @ id @ X523 @ id)) | ~! [X538 : term,X539 : term] : (((X522 @ id @ X539 @ id) != $true) | ($true != (X522 @ id @ X538 @ id)) | ($true = (X522 @ id @ (ap @ (sub @ X538 @ id) @ X539) @ id))) | ~! [X529 : subst > term > term] : (((X522 @ id @ (lam @ (X529 @ sh @ one)) @ id) = $true) | ~! [X533 : term] : (((X522 @ id @ (X529 @ id @ X533) @ id) = $true) | ((X522 @ id @ X533 @ id) != $true)) | ~! [X530 : subst,X531 : subst,X532 : term] : ((X529 @ (comp @ X530 @ X531) @ (sub @ X532 @ X531)) = (sub @ (X529 @ X530 @ X532) @ X531))) | ~! [X525 : subst,X526 : term,X527 : subst,X528 : subst] : (($true = (X522 @ X527 @ X526 @ (comp @ X525 @ X528))) | ($true != (X522 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525) @ X528))) | ~! [X524 : term] : (((var @ (sub @ X524 @ id)) != $true) | ($true = (X522 @ id @ X524 @ id))) | ~! [X534 : subst,X535 : term,X536 : subst,X537 : subst] : (($true = (X522 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) | ($true != (X522 @ X537 @ X535 @ (comp @ X536 @ X534))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((! [X84 : term] : ((sub @ X84 @ id) = X84) => (! [X85 : term,X86 : term,X87 : term,X88 : term] : (((ap @ X85 @ X87) != (ap @ X86 @ X88)) | (X85 = X86)) => ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)))) <=> (hoasapinj1_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (~! [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) = (sub @ (X491 @ X492 @ X494) @ X493)) | ~! [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) = (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((termmset = $true) <=> ! [X305 : term] : ((sub @ X305 @ id) = X305)) & (! [X378 : subst > term > subst > $o,X379 : term,X380 : term] : (~! [X381 : term,X382 : term] : (((X378 @ id @ X381 @ id) != $true) | ($true = (X378 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id)) | ($true != (X378 @ id @ X382 @ id))) | ~! [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (($true != (X378 @ (comp @ X386 @ X383) @ (sub @ X384 @ X383) @ X385)) | ($true = (X378 @ X386 @ X384 @ (comp @ X383 @ X385)))) | ~! [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (($true != (X378 @ X390 @ X387 @ (comp @ X389 @ X388))) | ($true = (X378 @ (comp @ X390 @ X389) @ (sub @ X387 @ X389) @ X388))) | ($true = (X378 @ id @ (ap @ X380 @ X379) @ id)) | ($true != (X378 @ id @ X380 @ id)) | ($true != (X378 @ id @ X379 @ id))) <=> (hoasinduction_lem2 = $true)) & (hoasapnotvar = $true) & (hoasinduction_lem1v2 = $true) & (! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (($true != (X302 @ X301)) | ($true = (X303 @ one)) | ~! [X304 : term] : ((X303 @ X304) = (X302 @ (sub @ X304 @ (push @ X301 @ X300))))) <=> (pushprop_lem1v2 = $true)) & (substmonoid_gthm = $true) & (axapp = $true) & ((laminj = $true) <=> ! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94)))) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((d2subst @ d_id) = id) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X38 : term] : ~! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh)))) & (ulamvarind = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X255 : subst > term > subst > $o,X256 : term] : (~! [X258 : subst > term > term] : (~! [X259 : subst,X260 : subst,X261 : term] : ((sub @ (X258 @ X259 @ X261) @ X260) = (X258 @ (comp @ X259 @ X260) @ (sub @ X261 @ X260))) | ~! [X262 : term] : (($true != (X255 @ id @ X262 @ id)) | ((X255 @ id @ (X258 @ id @ X262) @ id) = $true)) | ($true = (X255 @ id @ (lam @ (X258 @ sh @ one)) @ id))) | ((X255 @ id @ (lam @ (sub @ X256 @ (push @ one @ sh))) @ id) = $true) | ~! [X257 : term] : (($true != (X255 @ id @ X257 @ id)) | ($true = (X255 @ id @ (sub @ X256 @ (push @ X257 @ id)) @ id))))) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (! [X167 : term] : ((sub @ X167 @ id) = X167) <=> (axvarid = $true)) & ((var @ (d2term @ d_one)) != $true) & (hoaslamnotvar = $true) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) <=> (axshiftcons = $true)) & ((substmonoid_lthm = $true) <=> (! [X344 : subst] : ((comp @ id @ X344) = X344) => (! [X345 : subst] : ((comp @ X345 @ id) = X345) => (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346))))) & ! [X343 : d_term] : (d_one = X343) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & (! [X54 : term,X55 : term > $o] : (~! [X57 : term] : (($true != (X55 @ X57)) | ($true = (X55 @ (lam @ X57)))) | ~! [X56 : term] : (($true != (var @ X56)) | ($true = (X55 @ X56))) | ~! [X58 : term,X59 : term] : (((X55 @ (ap @ X58 @ X59)) = $true) | ($true != (X55 @ X58)) | ($true != (X55 @ X59))) | ($true = (X55 @ X54))) <=> (induction = $true)) & ((hoasinduction_lthm = $true) <=> (! [X391 : term > $o,X392 : term] : (~! [X393 : term] : (($true = (X391 @ X393)) | ($true != (var @ X393))) | ($true = (X391 @ X392)) | ~! [X396 : term,X397 : term] : (($true = (X391 @ (ap @ X396 @ X397))) | ((X391 @ X397) != $true) | ((X391 @ X396) != $true)) | ~! [X394 : term] : (~! [X395 : term] : (($true != (X391 @ X395)) | ($true = (X391 @ (sub @ X394 @ (push @ X395 @ id))))) | ($true = (X391 @ (lam @ X394))))) => (! [X398 : term,X399 : term,X400 : subst > term > subst > $o] : (($true = (X400 @ id @ (ap @ X398 @ X399) @ id)) | ($true != (X400 @ id @ X399 @ id)) | ~! [X409 : term,X410 : term] : (($true != (X400 @ id @ X410 @ id)) | ($true != (X400 @ id @ X409 @ id)) | ($true = (X400 @ id @ (ap @ (sub @ X409 @ id) @ X410) @ id))) | ($true != (X400 @ id @ X398 @ id)) | ~! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X400 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406) @ X408)) | ($true != (X400 @ X407 @ X405 @ (comp @ X406 @ X408)))) | ~! [X401 : subst,X402 : subst,X403 : term,X404 : subst] : (($true != (X400 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401) @ X404)) | ($true = (X400 @ X402 @ X403 @ (comp @ X401 @ X404))))) => (! [X411 : subst > term > subst > $o,X412 : term] : (~! [X426 : term] : (($true != (X411 @ id @ X426 @ id)) | ($true = (X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))) | ~! [X421 : subst > term > term] : (((X411 @ id @ (lam @ (X421 @ sh @ one)) @ id) = $true) | ~! [X422 : term] : (((X411 @ id @ (X421 @ id @ X422) @ id) = $true) | ($true != (X411 @ id @ X422 @ id))) | ~! [X423 : subst,X424 : subst,X425 : term] : ((sub @ (X421 @ X424 @ X425) @ X423) = (X421 @ (comp @ X424 @ X423) @ (sub @ X425 @ X423)))) | ($true = (X411 @ id @ (lam @ X412) @ id)) | ~! [X417 : subst,X418 : subst,X419 : term,X420 : subst] : (($true != (X411 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420) @ X417)) | ($true = (X411 @ X418 @ X419 @ (comp @ X420 @ X417)))) | ~! [X413 : subst,X414 : term,X415 : subst,X416 : subst] : (($true != (X411 @ X415 @ X414 @ (comp @ X416 @ X413))) | ($true = (X411 @ (comp @ X415 @ X416) @ (sub @ X414 @ X416) @ X413)))) => ! [X427 : term,X428 : subst > term > subst > $o] : (~! [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true = (X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)) | ((X428 @ X436 @ X437 @ (comp @ X434 @ X435)) != $true)) | ~! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (($true != (X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) | ((X428 @ X430 @ X432 @ (comp @ X431 @ X433)) = $true)) | ~! [X429 : term] : (($true != (var @ (sub @ X429 @ id))) | ($true = (X428 @ id @ X429 @ id))) | ~! [X440 : subst > term > term] : (~! [X441 : term] : (($true != (X428 @ id @ X441 @ id)) | ($true = (X428 @ id @ (X440 @ id @ X441) @ id))) | ((X428 @ id @ (lam @ (X440 @ sh @ one)) @ id) = $true) | ~! [X442 : subst,X443 : subst,X444 : term] : ((X440 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443)) = (sub @ (X440 @ X442 @ X444) @ X443))) | ($true = (X428 @ id @ X427 @ id)) | ~! [X438 : term,X439 : term] : (($true != (X428 @ id @ X438 @ id)) | ((X428 @ id @ (ap @ (sub @ X438 @ id) @ X439) @ id) = $true) | ((X428 @ id @ X439 @ id) != $true))))))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X204 : subst > term > subst > $o] : ~! [X205 : term > $o] : ~! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id))) & (ulamvarsh = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X216 : subst > term > subst > $o] : ~! [X217 : term > $o] : ~! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218))) & (pushprop = $true) & (apnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) = X170) => (! [X172 : term,X173 : subst] : ((comp @ sh @ (push @ X172 @ X173)) = X173) => (! [X174 : term,X175 : term] : ((X174 = X175) | ((lam @ X175) != (lam @ X174))) => ! [X176 : subst > term > term,X177 : subst,X178 : term,X179 : subst > term > term] : (~! [X183 : subst,X184 : subst,X185 : term] : ((sub @ (X176 @ X183 @ X185) @ X184) = (X176 @ (comp @ X183 @ X184) @ (sub @ X185 @ X184))) | ((X179 @ X177 @ X178) = (X176 @ X177 @ X178)) | ((lam @ (X176 @ sh @ one)) != (lam @ (X179 @ sh @ one))) | ~! [X180 : subst,X181 : term,X182 : subst] : ((sub @ (X179 @ X182 @ X181) @ X180) = (X179 @ (comp @ X182 @ X180) @ (sub @ X181 @ X180)))))))) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) <=> (apinj2 = $true)) & ((termmset_lthm = $true) <=> (! [X157 : term] : ((sub @ X157 @ id) = X157) => ! [X158 : term] : ((sub @ X158 @ id) = X158))) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (pushprop_lthm_orig = $true) & ((d2subst @ d_id) = sh) & ((hoasinduction_lem3 = $true) <=> ! [X60 : term,X61 : subst > term > subst > $o] : (~! [X62 : term] : (((X61 @ id @ X62 @ id) != $true) | ($true = (X61 @ id @ (sub @ X60 @ (push @ X62 @ id)) @ id))) | ($true = (X61 @ id @ (lam @ X60) @ id)) | ~! [X72 : subst,X73 : subst,X74 : subst,X75 : term] : (($true = (X61 @ X73 @ X75 @ (comp @ X74 @ X72))) | ($true != (X61 @ (comp @ X73 @ X74) @ (sub @ X75 @ X74) @ X72))) | ~! [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (($true != (X61 @ X70 @ X71 @ (comp @ X69 @ X68))) | ((X61 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X68) = $true)) | ~! [X63 : subst > term > term] : (~! [X64 : term] : (($true != (X61 @ id @ X64 @ id)) | ($true = (X61 @ id @ (X63 @ id @ X64) @ id))) | ~! [X65 : term,X66 : subst,X67 : subst] : ((X63 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)) = (sub @ (X63 @ X67 @ X65) @ X66)) | ($true = (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id))))) & ((! [X120 : term] : ((sub @ X120 @ id) = X120) => (! [X121 : term,X122 : subst > term > subst > $o] : (~! [X128 : term] : (($true != (X122 @ id @ X128 @ id)) | ($true = (X122 @ id @ (sub @ X121 @ (push @ X128 @ id)) @ id))) | ~! [X123 : subst > term > term] : (~! [X124 : term] : (($true = (X122 @ id @ (X123 @ id @ X124) @ id)) | ($true != (X122 @ id @ X124 @ id))) | ~! [X125 : subst,X126 : subst,X127 : term] : ((sub @ (X123 @ X125 @ X127) @ X126) = (X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126))) | ($true = (X122 @ id @ (lam @ (X123 @ sh @ one)) @ id))) | ($true = (X122 @ id @ (lam @ (sub @ X121 @ (push @ one @ sh))) @ id))) => ! [X129 : subst > term > subst > $o,X130 : term] : (~! [X136 : term] : (($true != (X129 @ id @ X136 @ id)) | ($true = (X129 @ id @ (sub @ X130 @ (push @ X136 @ id)) @ id))) | ~! [X131 : subst > term > term] : (($true = (X129 @ id @ (lam @ (X131 @ sh @ one)) @ id)) | ~! [X132 : term] : (($true = (X129 @ id @ (X131 @ id @ X132) @ id)) | ($true != (X129 @ id @ X132 @ id))) | ~! [X133 : subst,X134 : subst,X135 : term] : ((sub @ (X131 @ X133 @ X135) @ X134) = (X131 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134)))) | ($true = (X129 @ id @ (lam @ X130) @ id))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotap_lthm = $true) & (! [X0 : term] : ~! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) = X351) => ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (~! [X356 : term] : ((X354 @ X356) = (X352 @ (sub @ X356 @ (push @ X353 @ X355)))) | ($true != (X352 @ X353)) | ($true = (X354 @ one))))) & ((hoasapinj2_lthm = $true) <=> (! [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 = X308) | ((ap @ X307 @ X308) != (ap @ X309 @ X306))) => ! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)))) & ((hoasinduction = $true) <=> ! [X5 : term,X6 : subst > term > subst > $o] : (~! [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) | ($true != (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ~! [X21 : term,X22 : term] : (($true != (X6 @ id @ X21 @ id)) | ($true != (X6 @ id @ X22 @ id)) | ($true = (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id))) | ~! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9)) | ($true = (X6 @ X7 @ X10 @ (comp @ X8 @ X9)))) | ~! [X12 : subst > term > term] : (~! [X13 : term] : (((X6 @ id @ X13 @ id) != $true) | ($true = (X6 @ id @ (X12 @ id @ X13) @ id))) | ~! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) | ($true = (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id))) | ~! [X11 : term] : (($true = (X6 @ id @ X11 @ id)) | ($true != (var @ (sub @ X11 @ id)))) | ($true = (X6 @ id @ X5 @ id)))) & (hoasapnotvar_lthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) <=> ! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449)) & (termmset_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X445 : term] : ~! [X446 : subst > term > term] : ~! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447))) & (axabs = $true) & (lamnotap != $true) & (pushprop_lthm = $true) & ((! [X219 : subst > term > subst > $o] : ~! [X220 : term > $o] : ~! [X221 : term] : ((X219 @ id @ X221 @ id) = (X220 @ X221)) => (! [X222 : term > $o,X223 : term] : (~! [X225 : term] : (~! [X226 : term] : (($true != (X222 @ X226)) | ($true = (X222 @ (sub @ X225 @ (push @ X226 @ id))))) | ($true = (X222 @ (lam @ X225)))) | ~! [X227 : term,X228 : term] : (($true = (X222 @ (ap @ X228 @ X227))) | ($true != (X222 @ X227)) | ($true != (X222 @ X228))) | ($true = (X222 @ X223)) | ~! [X224 : term] : (($true != (var @ X224)) | ((X222 @ X224) = $true))) => (! [X229 : term] : ((sub @ X229 @ id) = X229) => (! [X230 : term,X231 : term > $o,X232 : subst > term > subst > $o] : (~! [X234 : subst > term > term] : (~! [X235 : term] : (($true = (X232 @ id @ (X234 @ id @ X235) @ id)) | ($true != (X232 @ id @ X235 @ id))) | ~! [X236 : term,X237 : subst,X238 : subst] : ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)) = (sub @ (X234 @ X237 @ X236) @ X238)) | ($true = (X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~! [X239 : term] : ((X232 @ id @ X239 @ id) = (X231 @ X239)) | ($true = (X231 @ (lam @ X230))) | ~! [X233 : term] : (((X231 @ (sub @ X230 @ (push @ X233 @ id))) = $true) | ($true != (X231 @ X233)))) => ! [X240 : subst > term > subst > $o,X241 : term] : (~! [X242 : term,X243 : term] : (($true != (X240 @ id @ X243 @ id)) | ((X240 @ id @ X242 @ id) != $true) | ($true = (X240 @ id @ (ap @ (sub @ X242 @ id) @ X243) @ id))) | ~! [X244 : subst > term > term] : (~! [X246 : subst,X247 : term,X248 : subst] : ((X244 @ (comp @ X246 @ X248) @ (sub @ X247 @ X248)) = (sub @ (X244 @ X246 @ X247) @ X248)) | ~! [X245 : term] : (($true != (X240 @ id @ X245 @ id)) | ($true = (X240 @ id @ (X244 @ id @ X245) @ id))) | ($true = (X240 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ($true = (X240 @ id @ X241 @ id))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2 = $true) & (one = (d2term @ d_one)) & (! [X249 : term,X250 : term,X251 : subst > term > term] : (((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one))) | ~! [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) = (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253)))) <=> (hoaslamnotap = $true)) & (hoasapinj2_gthm = $true) & ((! [X359 : term] : ((sub @ X359 @ id) = X359) => ! [X360 : subst > term > subst > $o,X361 : term,X362 : term > $o] : (~! [X377 : term] : (((X362 @ X377) != $true) | ($true = (X362 @ (sub @ X361 @ (push @ X377 @ id))))) | ($true = (X362 @ (lam @ X361))) | ~! [X363 : term] : ((X362 @ X363) = (X360 @ id @ X363 @ id)) | ~! [X364 : subst,X365 : subst,X366 : subst,X367 : term] : (($true = (X360 @ X366 @ X367 @ (comp @ X365 @ X364))) | ($true != (X360 @ (comp @ X366 @ X365) @ (sub @ X367 @ X365) @ X364))) | ~! [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (($true = (X360 @ (comp @ X375 @ X373) @ (sub @ X376 @ X373) @ X374)) | ($true != (X360 @ X375 @ X376 @ (comp @ X373 @ X374)))) | ~! [X368 : subst > term > term] : (~! [X370 : subst,X371 : term,X372 : subst] : ((sub @ (X368 @ X370 @ X371) @ X372) = (X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) | ~! [X369 : term] : (($true = (X360 @ id @ (X368 @ id @ X369) @ id)) | ($true != (X360 @ id @ X369 @ id))) | ($true = (X360 @ id @ (lam @ (X368 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) <=> (axscons = $true)) & (hoasinduction_lem2v2_gthm = $true) & (ulamvar1 != $true) & (hoasinduction_lem3v2_gthm = $true) & (axmap = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) <=> (substmonoid = $true)) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X333 : term > $o,X334 : subst > term > subst > $o,X335 : term] : (($true = (X333 @ (lam @ X335))) | ~! [X342 : term] : ((X334 @ id @ X342 @ id) = (X333 @ X342)) | ~! [X336 : subst > term > term] : (~! [X337 : subst,X338 : subst,X339 : term] : ((sub @ (X336 @ X338 @ X339) @ X337) = (X336 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337))) | ($true = (X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)) | ~! [X340 : term] : (($true = (X334 @ id @ (X336 @ id @ X340) @ id)) | ($true != (X334 @ id @ X340 @ id)))) | ~! [X341 : term] : (((X333 @ X341) != $true) | ($true = (X333 @ (sub @ X335 @ (push @ X341 @ id))))))) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) <=> (hoasapinj1 = $true)) & (! [X263 : term,X264 : term > $o,X265 : subst > term > subst > $o] : (~! [X280 : term] : ((X265 @ id @ X280 @ id) = (X264 @ X280)) | ~! [X270 : subst > term > term] : (~! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ($true != (X265 @ id @ X271 @ id))) | ~! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273)) | ($true = (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id))) | ($true = (X264 @ (lam @ X263))) | ~! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (($true = (X265 @ X277 @ X279 @ (comp @ X276 @ X278))) | ($true != (X265 @ (comp @ X277 @ X276) @ (sub @ X279 @ X276) @ X278))) | ~! [X266 : term,X267 : subst,X268 : subst,X269 : subst] : (($true = (X265 @ (comp @ X269 @ X268) @ (sub @ X266 @ X268) @ X267)) | ((X265 @ X269 @ X266 @ (comp @ X268 @ X267)) != $true)) | ~! [X275 : term] : (((X264 @ X275) != $true) | ($true = (X264 @ (sub @ X263 @ (push @ X275 @ id)))))) <=> (hoasinduction_lem3v2 = $true)) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) = (d2subst @ X349)) => (X348 = X349)) & (axclos = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X476 : subst > term > subst > $o,X477 : term] : (~! [X483 : term] : (($true = (X476 @ id @ (sub @ X477 @ (push @ X483 @ id)) @ id)) | ($true != (X476 @ id @ X483 @ id))) | ~! [X478 : subst > term > term] : (~! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X482 @ X481) @ (sub @ X480 @ X481)) = (sub @ (X478 @ X482 @ X480) @ X481)) | ~! [X479 : term] : (($true = (X476 @ id @ (X478 @ id @ X479) @ id)) | ($true != (X476 @ id @ X479 @ id))) | ($true = (X476 @ id @ (lam @ (X478 @ sh @ one)) @ id))) | ($true = (X476 @ id @ (lam @ X477) @ id)))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X137 : term] : ~! [X138 : subst > term > term] : ~! [X139 : term,X140 : subst] : ((X138 @ X140 @ X139) = (sub @ X137 @ (push @ X139 @ X140))) => (! [X141 : term] : ((sub @ X141 @ id) = X141) => ! [X142 : term,X143 : subst > term > subst > $o,X144 : term > $o] : (($true = (X144 @ (lam @ X142))) | ~! [X151 : term] : (((X144 @ X151) != $true) | ($true = (X144 @ (sub @ X142 @ (push @ X151 @ id))))) | ~! [X146 : subst > term > term] : (~! [X150 : term] : (($true != (X143 @ id @ X150 @ id)) | ((X143 @ id @ (X146 @ id @ X150) @ id) = $true)) | ((X143 @ id @ (lam @ (X146 @ sh @ one)) @ id) = $true) | ~! [X147 : term,X148 : subst,X149 : subst] : ((X146 @ (comp @ X149 @ X148) @ (sub @ X147 @ X148)) = (sub @ (X146 @ X149 @ X147) @ X148))) | ~! [X145 : term] : ((X144 @ X145) = (X143 @ id @ X145 @ id)))))) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X159 : subst > term > subst > $o,X160 : term] : (~! [X161 : term] : (($true != (X159 @ id @ X161 @ id)) | ($true = (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id))) | ~! [X162 : subst > term > term] : (~! [X164 : subst,X165 : subst,X166 : term] : ((X162 @ (comp @ X165 @ X164) @ (sub @ X166 @ X164)) = (sub @ (X162 @ X165 @ X166) @ X164)) | ($true = (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) | ~! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id)))) | ((X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id) = $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X467 : term,X468 : subst > term > subst > $o] : (((X468 @ id @ X467 @ id) = $true) | ~! [X474 : term,X475 : term] : (($true != (X468 @ id @ X475 @ id)) | ($true != (X468 @ id @ X474 @ id)) | ($true = (X468 @ id @ (ap @ (sub @ X474 @ id) @ X475) @ id))) | ~! [X469 : subst > term > term] : (($true = (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id)) | ~! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) | ~! [X473 : term] : (($true != (X468 @ id @ X473 @ id)) | ((X468 @ id @ (X469 @ id @ X473) @ id) = $true))))) & ((induction2 = $true) <=> ! [X283 : term > $o,X284 : term] : (($true = (X283 @ X284)) | ~! [X285 : term] : (~! [X286 : term] : (((X283 @ (sub @ X285 @ (push @ X286 @ id))) = $true) | ($true != (X283 @ X286))) | ($true = (X283 @ (lam @ X285)))) | ~! [X287 : term] : (($true = (X283 @ X287)) | ($true != (var @ X287))) | ~! [X288 : term,X289 : term] : (($true = (X283 @ (ap @ X288 @ X289))) | ((X283 @ X289) != $true) | ($true != (X283 @ X288))))) & (lamnotvar = $true) & ((! [X451 : term] : ((sub @ X451 @ id) = X451) => (! [X452 : subst,X453 : term > $o,X454 : term] : (~! [X455 : term,X456 : term] : (($true = (X453 @ (ap @ X455 @ X456))) | ($true != (X453 @ X455)) | ($true != (X453 @ X456))) | ~! [X457 : term] : (($true = (X453 @ (sub @ X457 @ X452))) | ($true != (var @ X457))) | ($true = (X453 @ (sub @ X454 @ X452))) | ~! [X458 : term] : (($true = (X453 @ (lam @ X458))) | ~! [X459 : term] : (($true != (X453 @ X459)) | ((X453 @ (sub @ X458 @ (push @ X459 @ id))) = $true)))) => ! [X460 : term > $o,X461 : term] : (~! [X465 : term,X466 : term] : (($true = (X460 @ (ap @ X465 @ X466))) | ($true != (X460 @ X466)) | ($true != (X460 @ X465))) | ~! [X462 : term] : (((X460 @ X462) = $true) | ($true != (var @ X462))) | ($true = (X460 @ X461)) | ~! [X463 : term] : (($true = (X460 @ (lam @ X463))) | ~! [X464 : term] : (($true != (X460 @ X464)) | ((X460 @ (sub @ X463 @ (push @ X464 @ id))) = $true)))))) <=> (induction2_lthm = $true)) & ! [X168 : d_term,X169 : d_term] : (((d2term @ X169) = (d2term @ X168)) => (X168 = X169)) & (! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (($true != (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3a_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3aaa = $true) <=> ! [X192 : term,X193 : subst > term > subst > $o] : (($true = (X193 @ id @ (lam @ (sub @ X192 @ (push @ one @ sh))) @ id)) | ~! [X195 : subst > term > term,X196 : term] : (((X193 @ id @ (lam @ (X195 @ sh @ one)) @ id) = $true) | ~! [X201 : subst,X202 : term,X203 : subst] : ((sub @ X196 @ (push @ (sub @ X202 @ X201) @ (comp @ X203 @ X201))) = (X195 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201))) | ~! [X198 : term,X199 : subst,X200 : subst] : ((sub @ (sub @ X196 @ (push @ X198 @ X199)) @ X200) = (sub @ (X195 @ X199 @ X198) @ X200)) | ~! [X197 : term] : (($true = (X193 @ id @ (X195 @ id @ X197) @ id)) | ($true != (X193 @ id @ X197 @ id)))) | ~! [X194 : term] : (($true = (X193 @ id @ (sub @ X192 @ (push @ X194 @ id)) @ id)) | ($true != (X193 @ id @ X194 @ id))))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) = X291) => (! [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) = X293) => ! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295)))) | ((X297 @ X299) != $true))))) & ! [X48 : d_subst] : (d_id = X48) & (hoasapinj1_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X314 : term,X315 : subst] : ((sub @ one @ (push @ X314 @ X315)) = X314) => (! [X316 : term,X317 : subst] : ((comp @ sh @ (push @ X316 @ X317)) = X317) => (! [X318 : subst] : ((comp @ X318 @ id) = X318) => (! [X319 : term > $o,X320 : term] : (~! [X321 : term] : (((X319 @ (lam @ X321)) = $true) | ($true != (X319 @ X321))) | ~! [X323 : term,X324 : term] : (($true != (X319 @ X324)) | ($true = (X319 @ (ap @ X323 @ X324))) | ($true != (X319 @ X323))) | ($true = (X319 @ X320)) | ~! [X322 : term] : (($true = (X319 @ X322)) | ($true != (var @ X322)))) => ! [X325 : subst,X326 : term,X327 : term > $o] : (~! [X328 : term,X329 : term] : (($true != (X327 @ X329)) | ($true != (X327 @ X328)) | ($true = (X327 @ (ap @ X329 @ X328)))) | ~! [X331 : term] : (~! [X332 : term] : (($true != (X327 @ X332)) | ($true = (X327 @ (sub @ X331 @ (push @ X332 @ id))))) | ((X327 @ (lam @ X331)) = $true)) | ~! [X330 : term] : (($true != (var @ X330)) | ($true = (X327 @ (sub @ X330 @ X325)))) | ($true = (X327 @ (sub @ X326 @ X325))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem3v2_lthm = $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)))))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (~! [X37 : term] : ((X26 @ X37) = (X24 @ id @ X37 @ id)) | ~! [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true = (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) | ($true != (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ~! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (($true != (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29)) | ((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) = $true)) | ($true != (X26 @ X25)) | ((X26 @ X23) != $true) | ((X26 @ (ap @ X25 @ X23)) = $true) | ~! [X31 : term,X32 : term] : (($true != (X24 @ id @ X31 @ id)) | ($true != (X24 @ id @ X32 @ id)) | ($true = (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id))))) & (! [X40 : term] : ~! [X41 : subst > term > term] : ~! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axvarshift = $true) & (pushprop_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214))) & ((induction2lem = $true) <=> ! [X76 : term,X77 : subst,X78 : term > $o] : (~! [X79 : term] : (((X78 @ (lam @ X79)) = $true) | ~! [X80 : term] : (((X78 @ X80) != $true) | ((X78 @ (sub @ X79 @ (push @ X80 @ id))) = $true))) | ~! [X82 : term,X83 : term] : (((X78 @ (ap @ X83 @ X82)) = $true) | ($true != (X78 @ X83)) | ($true != (X78 @ X82))) | ~! [X81 : term] : (($true = (X78 @ (sub @ X81 @ X77))) | ($true != (var @ X81))) | ($true = (X78 @ (sub @ X76 @ X77))))) & ((apinj1 = $true) <=> ! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46))) & (hoaslaminj_gthm = $true) & (! [X49 : term > $o,X50 : subst,X51 : term] : ~! [X52 : term > $o] : ~! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) <=> (pushprop_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & (! [X207 : subst,X208 : term,X209 : term > $o] : ~! [X210 : term > $o] : ~! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207)))) <=> (pushprop_lem0_lthm = $true)) & (induction2_gthm = $true)),
% 32.37/5.95 inference(flattening,[status(thm)],[f10])).
% 32.37/5.95 thf(f10,plain,(
% 32.37/5.95 (! [X0 : term] : ~! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & (axabs = $true) & (hoasinduction_lem3_gthm = $true) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & ((d2subst @ d_id) = id) & ((hoasinduction = $true) <=> ! [X5 : term,X6 : subst > term > subst > $o] : (~! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (~($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9)) | ($true = (X6 @ X7 @ X10 @ (comp @ X8 @ X9)))) | ~! [X11 : term] : (($true = (X6 @ id @ X11 @ id)) | ~($true = (var @ (sub @ X11 @ id)))) | ($true = (X6 @ id @ X5 @ id)) | ~! [X12 : subst > term > term] : (~! [X13 : term] : (($true = (X6 @ id @ (X12 @ id @ X13) @ id)) | ~((X6 @ id @ X13 @ id) = $true)) | ~! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) | ($true = (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id))) | ~! [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) | ~($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ~! [X21 : term,X22 : term] : (($true = (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id)) | ~($true = (X6 @ id @ X21 @ id)) | ~($true = (X6 @ id @ X22 @ id))))) & (one = (d2term @ d_one)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (~! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) = $true) | ~($true = (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29))) | ((X26 @ (ap @ X25 @ X23)) = $true) | ~! [X31 : term,X32 : term] : (($true = (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) | ~($true = (X24 @ id @ X32 @ id)) | ~($true = (X24 @ id @ X31 @ id))) | ~! [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true = (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) | ~($true = (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ~! [X37 : term] : ((X26 @ X37) = (X24 @ id @ X37 @ id)) | ~((X26 @ X23) = $true) | ~($true = (X26 @ X25))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X38 : term] : ~! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh)))) & (! [X40 : term] : ~! [X41 : subst > term > term] : ~! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X44 : term,X45 : term,X46 : term,X47 : term] : (((ap @ X44 @ X47) != (ap @ X46 @ X45)) | (X44 = X46))) & ! [X48 : d_subst] : (d_id = X48) & (! [X49 : term > $o,X50 : subst,X51 : term] : ~! [X52 : term > $o] : ~! [X53 : term] : ((X52 @ X53) = (X49 @ (sub @ X53 @ (push @ X51 @ X50)))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoaslamnotvar = $true) & ((induction = $true) <=> ! [X54 : term,X55 : term > $o] : (~! [X56 : term] : (~($true = (var @ X56)) | ($true = (X55 @ X56))) | ~! [X57 : term] : (($true = (X55 @ (lam @ X57))) | ~($true = (X55 @ X57))) | ~! [X58 : term,X59 : term] : (((X55 @ (ap @ X58 @ X59)) = $true) | ~($true = (X55 @ X59)) | ~($true = (X55 @ X58))) | ($true = (X55 @ X54)))) & ~((var @ (d2term @ d_one)) = $true) & ((hoasinduction_lem3 = $true) <=> ! [X60 : term,X61 : subst > term > subst > $o] : (($true = (X61 @ id @ (lam @ X60) @ id)) | ~! [X62 : term] : (~((X61 @ id @ X62 @ id) = $true) | ($true = (X61 @ id @ (sub @ X60 @ (push @ X62 @ id)) @ id))) | ~! [X63 : subst > term > term] : (~! [X64 : term] : (~($true = (X61 @ id @ X64 @ id)) | ($true = (X61 @ id @ (X63 @ id @ X64) @ id))) | ($true = (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) | ~! [X65 : term,X66 : subst,X67 : subst] : ((X63 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)) = (sub @ (X63 @ X67 @ X65) @ X66))) | ~! [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (~($true = (X61 @ X70 @ X71 @ (comp @ X69 @ X68))) | ((X61 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X68) = $true)) | ~! [X72 : subst,X73 : subst,X74 : subst,X75 : term] : (~($true = (X61 @ (comp @ X73 @ X74) @ (sub @ X75 @ X74) @ X72)) | ($true = (X61 @ X73 @ X75 @ (comp @ X74 @ X72)))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem1v2_gthm = $true) & ((induction2lem = $true) <=> ! [X76 : term,X77 : subst,X78 : term > $o] : (~! [X79 : term] : (((X78 @ (lam @ X79)) = $true) | ~! [X80 : term] : (~((X78 @ X80) = $true) | ((X78 @ (sub @ X79 @ (push @ X80 @ id))) = $true))) | ~! [X81 : term] : (($true = (X78 @ (sub @ X81 @ X77))) | ~($true = (var @ X81))) | ($true = (X78 @ (sub @ X76 @ X77))) | ~! [X82 : term,X83 : term] : (((X78 @ (ap @ X83 @ X82)) = $true) | ~($true = (X78 @ X83)) | ~($true = (X78 @ X82))))) & ((! [X84 : term] : ((sub @ X84 @ id) = X84) => (! [X85 : term,X86 : term,X87 : term,X88 : term] : (((ap @ X85 @ X87) != (ap @ X86 @ X88)) | (X85 = X86)) => ! [X89 : term,X90 : term,X91 : term,X92 : term] : (((ap @ (sub @ X92 @ id) @ X90) != (ap @ (sub @ X89 @ id) @ X91)) | (X89 = X92)))) <=> (hoasapinj1_lthm = $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((laminj = $true) <=> ! [X93 : term,X94 : term] : ((X93 = X94) | ((lam @ X93) != (lam @ X94)))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X95 : term] : ((sub @ X95 @ id) = X95) => (! [X96 : term,X97 : subst > term > subst > $o] : (~! [X98 : subst > term > term] : (~! [X99 : term,X100 : subst,X101 : subst] : ((X98 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)) = (sub @ (X98 @ X101 @ X99) @ X100)) | ($true = (X97 @ id @ (lam @ (X98 @ sh @ one)) @ id)) | ~! [X102 : term] : (~($true = (X97 @ id @ X102 @ id)) | ((X97 @ id @ (X98 @ id @ X102) @ id) = $true))) | ($true = (X97 @ id @ (lam @ (sub @ X96 @ (push @ one @ sh))) @ id)) | ~! [X103 : term] : (~($true = (X97 @ id @ X103 @ id)) | ((X97 @ id @ (sub @ X96 @ (push @ X103 @ id)) @ id) = $true))) => ! [X104 : term,X105 : subst > term > subst > $o] : (($true = (X105 @ id @ (lam @ X104) @ id)) | ~! [X106 : subst > term > term] : (~! [X107 : term] : (~($true = (X105 @ id @ X107 @ id)) | ($true = (X105 @ id @ (X106 @ id @ X107) @ id))) | ($true = (X105 @ id @ (lam @ (X106 @ sh @ one)) @ id)) | ~! [X108 : subst,X109 : term,X110 : subst] : ((X106 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110)) = (sub @ (X106 @ X108 @ X109) @ X110))) | ~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (~($true = (X105 @ X114 @ X112 @ (comp @ X111 @ X113))) | ($true = (X105 @ (comp @ X114 @ X111) @ (sub @ X112 @ X111) @ X113))) | ~! [X115 : term] : (~($true = (X105 @ id @ X115 @ id)) | ((X105 @ id @ (sub @ X104 @ (push @ X115 @ id)) @ id) = $true)) | ~! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (~((X105 @ (comp @ X116 @ X118) @ (sub @ X119 @ X118) @ X117) = $true) | ($true = (X105 @ X116 @ X119 @ (comp @ X118 @ X117)))))))) & ((! [X120 : term] : ((sub @ X120 @ id) = X120) => (! [X121 : term,X122 : subst > term > subst > $o] : (~! [X123 : subst > term > term] : (~! [X124 : term] : (~($true = (X122 @ id @ X124 @ id)) | ($true = (X122 @ id @ (X123 @ id @ X124) @ id))) | ~! [X125 : subst,X126 : subst,X127 : term] : ((sub @ (X123 @ X125 @ X127) @ X126) = (X123 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126))) | ($true = (X122 @ id @ (lam @ (X123 @ sh @ one)) @ id))) | ($true = (X122 @ id @ (lam @ (sub @ X121 @ (push @ one @ sh))) @ id)) | ~! [X128 : term] : (($true = (X122 @ id @ (sub @ X121 @ (push @ X128 @ id)) @ id)) | ~($true = (X122 @ id @ X128 @ id)))) => ! [X129 : subst > term > subst > $o,X130 : term] : (($true = (X129 @ id @ (lam @ X130) @ id)) | ~! [X131 : subst > term > term] : (~! [X132 : term] : (($true = (X129 @ id @ (X131 @ id @ X132) @ id)) | ~($true = (X129 @ id @ X132 @ id))) | ($true = (X129 @ id @ (lam @ (X131 @ sh @ one)) @ id)) | ~! [X133 : subst,X134 : subst,X135 : term] : ((sub @ (X131 @ X133 @ X135) @ X134) = (X131 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134)))) | ~! [X136 : term] : (($true = (X129 @ id @ (sub @ X130 @ (push @ X136 @ id)) @ id)) | ~($true = (X129 @ id @ X136 @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((! [X137 : term] : ~! [X138 : subst > term > term] : ~! [X139 : term,X140 : subst] : ((X138 @ X140 @ X139) = (sub @ X137 @ (push @ X139 @ X140))) => (! [X141 : term] : ((sub @ X141 @ id) = X141) => ! [X142 : term,X143 : subst > term > subst > $o,X144 : term > $o] : (~! [X145 : term] : ((X144 @ X145) = (X143 @ id @ X145 @ id)) | ($true = (X144 @ (lam @ X142))) | ~! [X146 : subst > term > term] : (~! [X147 : term,X148 : subst,X149 : subst] : ((X146 @ (comp @ X149 @ X148) @ (sub @ X147 @ X148)) = (sub @ (X146 @ X149 @ X147) @ X148)) | ~! [X150 : term] : (((X143 @ id @ (X146 @ id @ X150) @ id) = $true) | ~($true = (X143 @ id @ X150 @ id))) | ((X143 @ id @ (lam @ (X146 @ sh @ one)) @ id) = $true)) | ~! [X151 : term] : (~((X144 @ X151) = $true) | ($true = (X144 @ (sub @ X142 @ (push @ X151 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasapinj1_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X152 : term,X153 : subst,X154 : term > $o,X155 : term > $o,X156 : term] : (~($true = (X155 @ X156)) | ((X154 @ (sub @ X156 @ (push @ X152 @ X153))) = $true))) & (hoasinduction_lem1_lthm = $true) & ((termmset_lthm = $true) <=> (! [X157 : term] : ((sub @ X157 @ id) = X157) => ! [X158 : term] : ((sub @ X158 @ id) = X158))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & (ulamvarind = $true) & (! [X159 : subst > term > subst > $o,X160 : term] : (~! [X161 : term] : (($true = (X159 @ id @ (sub @ X160 @ (push @ X161 @ id)) @ id)) | ~($true = (X159 @ id @ X161 @ id))) | ~! [X162 : subst > term > term] : (($true = (X159 @ id @ (lam @ (X162 @ sh @ one)) @ id)) | ~! [X163 : term] : (($true = (X159 @ id @ (X162 @ id @ X163) @ id)) | ~($true = (X159 @ id @ X163 @ id))) | ~! [X164 : subst,X165 : subst,X166 : term] : ((X162 @ (comp @ X165 @ X164) @ (sub @ X166 @ X164)) = (sub @ (X162 @ X165 @ X166) @ X164))) | ((X159 @ id @ (lam @ (sub @ X160 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa = $true)) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (! [X167 : term] : ((sub @ X167 @ id) = X167) <=> (axvarid = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X168 : d_term,X169 : d_term] : (((d2term @ X169) = (d2term @ X168)) => (X168 = X169)) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (axapp = $true) & ~(lamnotap = $true) & (pushprop_lem1_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) = X170) => (! [X172 : term,X173 : subst] : ((comp @ sh @ (push @ X172 @ X173)) = X173) => (! [X174 : term,X175 : term] : ((X174 = X175) | ((lam @ X175) != (lam @ X174))) => ! [X176 : subst > term > term,X177 : subst,X178 : term,X179 : subst > term > term] : (~! [X183 : subst,X184 : subst,X185 : term] : ((sub @ (X176 @ X183 @ X185) @ X184) = (X176 @ (comp @ X183 @ X184) @ (sub @ X185 @ X184))) | ((X179 @ X177 @ X178) = (X176 @ X177 @ X178)) | ((lam @ (X176 @ sh @ one)) != (lam @ (X179 @ sh @ one))) | ~! [X180 : subst,X181 : term,X182 : subst] : ((sub @ (X179 @ X182 @ X181) @ X180) = (X179 @ (comp @ X182 @ X180) @ (sub @ X181 @ X180)))))))) & (lamnotvar = $true) & ((shinj = $true) <=> ! [X186 : term,X187 : term] : (((sub @ X187 @ sh) != (sub @ X186 @ sh)) | (X186 = X187))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (! [X188 : term,X189 : term,X190 : term,X191 : term] : ((X190 = X191) | ((ap @ X189 @ X190) != (ap @ X188 @ X191))) <=> (apinj2 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X192 : term,X193 : subst > term > subst > $o] : (($true = (X193 @ id @ (lam @ (sub @ X192 @ (push @ one @ sh))) @ id)) | ~! [X194 : term] : (($true = (X193 @ id @ (sub @ X192 @ (push @ X194 @ id)) @ id)) | ~($true = (X193 @ id @ X194 @ id))) | ~! [X195 : subst > term > term,X196 : term] : (((X193 @ id @ (lam @ (X195 @ sh @ one)) @ id) = $true) | ~! [X197 : term] : (~($true = (X193 @ id @ X197 @ id)) | ($true = (X193 @ id @ (X195 @ id @ X197) @ id))) | ~! [X198 : term,X199 : subst,X200 : subst] : ((sub @ (sub @ X196 @ (push @ X198 @ X199)) @ X200) = (sub @ (X195 @ X199 @ X198) @ X200)) | ~! [X201 : subst,X202 : term,X203 : subst] : ((sub @ X196 @ (push @ (sub @ X202 @ X201) @ (comp @ X203 @ X201))) = (X195 @ (comp @ X203 @ X201) @ (sub @ X202 @ X201)))))) & ((hoasinduction_lem0 = $true) <=> ! [X204 : subst > term > subst > $o] : ~! [X205 : term > $o] : ~! [X206 : term] : ((X205 @ X206) = (X204 @ id @ X206 @ id))) & (hoasapinj2_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X207 : subst,X208 : term,X209 : term > $o] : ~! [X210 : term > $o] : ~! [X211 : term] : ((X210 @ X211) = (X209 @ (sub @ X211 @ (push @ X208 @ X207)))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X212 : term,X213 : term,X214 : term,X215 : term] : (((ap @ (sub @ X215 @ id) @ X212) != (ap @ (sub @ X213 @ id) @ X214)) | (X212 = X214))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X216 : subst > term > subst > $o] : ~! [X217 : term > $o] : ~! [X218 : term] : ((X216 @ id @ X218 @ id) = (X217 @ X218))) & (hoasapnotvar = $true) & ((d2subst @ d_id) = sh) & ((! [X219 : subst > term > subst > $o] : ~! [X220 : term > $o] : ~! [X221 : term] : ((X219 @ id @ X221 @ id) = (X220 @ X221)) => (! [X222 : term > $o,X223 : term] : (~! [X224 : term] : (((X222 @ X224) = $true) | ~($true = (var @ X224))) | ~! [X225 : term] : (($true = (X222 @ (lam @ X225))) | ~! [X226 : term] : (~($true = (X222 @ X226)) | ($true = (X222 @ (sub @ X225 @ (push @ X226 @ id)))))) | ($true = (X222 @ X223)) | ~! [X227 : term,X228 : term] : (~($true = (X222 @ X227)) | ~($true = (X222 @ X228)) | ($true = (X222 @ (ap @ X228 @ X227))))) => (! [X229 : term] : ((sub @ X229 @ id) = X229) => (! [X230 : term,X231 : term > $o,X232 : subst > term > subst > $o] : (($true = (X231 @ (lam @ X230))) | ~! [X233 : term] : (((X231 @ (sub @ X230 @ (push @ X233 @ id))) = $true) | ~($true = (X231 @ X233))) | ~! [X234 : subst > term > term] : (($true = (X232 @ id @ (lam @ (X234 @ sh @ one)) @ id)) | ~! [X235 : term] : (~($true = (X232 @ id @ X235 @ id)) | ($true = (X232 @ id @ (X234 @ id @ X235) @ id))) | ~! [X236 : term,X237 : subst,X238 : subst] : ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)) = (sub @ (X234 @ X237 @ X236) @ X238))) | ~! [X239 : term] : ((X232 @ id @ X239 @ id) = (X231 @ X239))) => ! [X240 : subst > term > subst > $o,X241 : term] : (($true = (X240 @ id @ X241 @ id)) | ~! [X242 : term,X243 : term] : (~((X240 @ id @ X242 @ id) = $true) | ($true = (X240 @ id @ (ap @ (sub @ X242 @ id) @ X243) @ id)) | ~($true = (X240 @ id @ X243 @ id))) | ~! [X244 : subst > term > term] : (($true = (X240 @ id @ (lam @ (X244 @ sh @ one)) @ id)) | ~! [X245 : term] : (~($true = (X240 @ id @ X245 @ id)) | ($true = (X240 @ id @ (X244 @ id @ X245) @ id))) | ~! [X246 : subst,X247 : term,X248 : subst] : ((X244 @ (comp @ X246 @ X248) @ (sub @ X247 @ X248)) = (sub @ (X244 @ X246 @ X247) @ X248)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (substmonoid_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X249 : term,X250 : term,X251 : subst > term > term] : (((ap @ (sub @ X250 @ id) @ X249) != (lam @ (X251 @ sh @ one))) | ~! [X252 : term,X253 : subst,X254 : subst] : ((sub @ (X251 @ X254 @ X252) @ X253) = (X251 @ (comp @ X254 @ X253) @ (sub @ X252 @ X253)))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X255 : subst > term > subst > $o,X256 : term] : (~! [X257 : term] : (($true = (X255 @ id @ (sub @ X256 @ (push @ X257 @ id)) @ id)) | ~($true = (X255 @ id @ X257 @ id))) | ((X255 @ id @ (lam @ (sub @ X256 @ (push @ one @ sh))) @ id) = $true) | ~! [X258 : subst > term > term] : (~! [X259 : subst,X260 : subst,X261 : term] : ((sub @ (X258 @ X259 @ X261) @ X260) = (X258 @ (comp @ X259 @ X260) @ (sub @ X261 @ X260))) | ~! [X262 : term] : (~($true = (X255 @ id @ X262 @ id)) | ((X255 @ id @ (X258 @ id @ X262) @ id) = $true)) | ($true = (X255 @ id @ (lam @ (X258 @ sh @ one)) @ id))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X263 : term,X264 : term > $o,X265 : subst > term > subst > $o] : (~! [X266 : term,X267 : subst,X268 : subst,X269 : subst] : (($true = (X265 @ (comp @ X269 @ X268) @ (sub @ X266 @ X268) @ X267)) | ~((X265 @ X269 @ X266 @ (comp @ X268 @ X267)) = $true)) | ~! [X270 : subst > term > term] : (($true = (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) | ~! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ~($true = (X265 @ id @ X271 @ id))) | ~! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273))) | ~! [X275 : term] : (~((X264 @ X275) = $true) | ($true = (X264 @ (sub @ X263 @ (push @ X275 @ id))))) | ($true = (X264 @ (lam @ X263))) | ~! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (($true = (X265 @ X277 @ X279 @ (comp @ X276 @ X278))) | ~($true = (X265 @ (comp @ X277 @ X276) @ (sub @ X279 @ X276) @ X278))) | ~! [X280 : term] : ((X265 @ id @ X280 @ id) = (X264 @ X280)))) & (! [X281 : subst,X282 : term] : ((comp @ sh @ (push @ X282 @ X281)) = X281) <=> (axshiftcons = $true)) & (hoasinduction_lem3b_gthm = $true) & (termmset_gthm = $true) & (axmap = $true) & (! [X283 : term > $o,X284 : term] : (~! [X285 : term] : (~! [X286 : term] : (((X283 @ (sub @ X285 @ (push @ X286 @ id))) = $true) | ~($true = (X283 @ X286))) | ($true = (X283 @ (lam @ X285)))) | ~! [X287 : term] : (~($true = (var @ X287)) | ($true = (X283 @ X287))) | ~! [X288 : term,X289 : term] : (~((X283 @ X289) = $true) | ($true = (X283 @ (ap @ X288 @ X289))) | ~($true = (X283 @ X288))) | ($true = (X283 @ X284))) <=> (induction2 = $true)) & (! [X290 : subst] : ((comp @ id @ X290) = X290) <=> (axidl = $true)) & ((! [X291 : term,X292 : subst] : ((sub @ one @ (push @ X291 @ X292)) = X291) => (! [X293 : subst,X294 : term] : ((comp @ sh @ (push @ X294 @ X293)) = X293) => ! [X295 : subst,X296 : term > $o,X297 : term > $o,X298 : term,X299 : term] : (~((X297 @ X299) = $true) | ($true = (X296 @ (sub @ X299 @ (push @ X298 @ X295))))))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X300 : subst,X301 : term,X302 : term > $o,X303 : term > $o] : (($true = (X303 @ one)) | ~! [X304 : term] : ((X303 @ X304) = (X302 @ (sub @ X304 @ (push @ X301 @ X300)))) | ~($true = (X302 @ X301)))) & ((termmset = $true) <=> ! [X305 : term] : ((sub @ X305 @ id) = X305)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X306 : term,X307 : term,X308 : term,X309 : term] : ((X306 = X308) | ((ap @ X307 @ X308) != (ap @ X309 @ X306))) => ! [X310 : term,X311 : term,X312 : term,X313 : term] : (((ap @ (sub @ X310 @ id) @ X312) != (ap @ (sub @ X313 @ id) @ X311)) | (X311 = X312)))) & (axvarshift = $true) & ~(ulamvar1 = $true) & ((! [X314 : term,X315 : subst] : ((sub @ one @ (push @ X314 @ X315)) = X314) => (! [X316 : term,X317 : subst] : ((comp @ sh @ (push @ X316 @ X317)) = X317) => (! [X318 : subst] : ((comp @ X318 @ id) = X318) => (! [X319 : term > $o,X320 : term] : (~! [X321 : term] : (((X319 @ (lam @ X321)) = $true) | ~($true = (X319 @ X321))) | ($true = (X319 @ X320)) | ~! [X322 : term] : (($true = (X319 @ X322)) | ~($true = (var @ X322))) | ~! [X323 : term,X324 : term] : (~($true = (X319 @ X324)) | ($true = (X319 @ (ap @ X323 @ X324))) | ~($true = (X319 @ X323)))) => ! [X325 : subst,X326 : term,X327 : term > $o] : (~! [X328 : term,X329 : term] : (~($true = (X327 @ X329)) | ~($true = (X327 @ X328)) | ($true = (X327 @ (ap @ X329 @ X328)))) | ~! [X330 : term] : (~($true = (var @ X330)) | ($true = (X327 @ (sub @ X330 @ X325)))) | ~! [X331 : term] : (~! [X332 : term] : (~($true = (X327 @ X332)) | ($true = (X327 @ (sub @ X331 @ (push @ X332 @ id))))) | ((X327 @ (lam @ X331)) = $true)) | ($true = (X327 @ (sub @ X326 @ X325)))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2 = $true) & (! [X333 : term > $o,X334 : subst > term > subst > $o,X335 : term] : (($true = (X333 @ (lam @ X335))) | ~! [X336 : subst > term > term] : (~! [X337 : subst,X338 : subst,X339 : term] : ((sub @ (X336 @ X338 @ X339) @ X337) = (X336 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337))) | ($true = (X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)) | ~! [X340 : term] : (~($true = (X334 @ id @ X340 @ id)) | ($true = (X334 @ id @ (X336 @ id @ X340) @ id)))) | ~! [X341 : term] : (~((X333 @ X341) = $true) | ($true = (X333 @ (sub @ X335 @ (push @ X341 @ id))))) | ~! [X342 : term] : ((X334 @ id @ X342 @ id) = (X333 @ X342))) <=> (hoasinduction_lem3v2a = $true)) & (induction2_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & ((substmonoid_lthm = $true) <=> (! [X344 : subst] : ((comp @ id @ X344) = X344) => (! [X345 : subst] : ((comp @ X345 @ id) = X345) => (! [X347 : subst] : ((comp @ X347 @ id) = X347) & ! [X346 : subst] : ((comp @ id @ X346) = X346))))) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X348 : d_subst,X349 : d_subst] : (((d2subst @ X348) = (d2subst @ X349)) => (X348 = X349)) & ((! [X350 : subst,X351 : term] : ((sub @ one @ (push @ X351 @ X350)) = X351) => ! [X352 : term > $o,X353 : term,X354 : term > $o,X355 : subst] : (($true = (X354 @ one)) | ~($true = (X352 @ X353)) | ~! [X356 : term] : ((X354 @ X356) = (X352 @ (sub @ X356 @ (push @ X353 @ X355)))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & ((! [X357 : subst] : ((comp @ id @ X357) = X357) & ! [X358 : subst] : ((comp @ X358 @ id) = X358)) <=> (substmonoid = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X359 : term] : ((sub @ X359 @ id) = X359) => ! [X360 : subst > term > subst > $o,X361 : term,X362 : term > $o] : (~! [X363 : term] : ((X362 @ X363) = (X360 @ id @ X363 @ id)) | ~! [X364 : subst,X365 : subst,X366 : subst,X367 : term] : (~($true = (X360 @ (comp @ X366 @ X365) @ (sub @ X367 @ X365) @ X364)) | ($true = (X360 @ X366 @ X367 @ (comp @ X365 @ X364)))) | ~! [X368 : subst > term > term] : (~! [X369 : term] : (($true = (X360 @ id @ (X368 @ id @ X369) @ id)) | ~($true = (X360 @ id @ X369 @ id))) | ($true = (X360 @ id @ (lam @ (X368 @ sh @ one)) @ id)) | ~! [X370 : subst,X371 : term,X372 : subst] : ((sub @ (X368 @ X370 @ X371) @ X372) = (X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372)))) | ~! [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (~($true = (X360 @ X375 @ X376 @ (comp @ X373 @ X374))) | ($true = (X360 @ (comp @ X375 @ X373) @ (sub @ X376 @ X373) @ X374))) | ~! [X377 : term] : (($true = (X362 @ (sub @ X361 @ (push @ X377 @ id)))) | ~((X362 @ X377) = $true)) | ($true = (X362 @ (lam @ X361)))))) & ((hoasinduction_lem2 = $true) <=> ! [X378 : subst > term > subst > $o,X379 : term,X380 : term] : (~! [X381 : term,X382 : term] : (~((X378 @ id @ X381 @ id) = $true) | ($true = (X378 @ id @ (ap @ (sub @ X381 @ id) @ X382) @ id)) | ~($true = (X378 @ id @ X382 @ id))) | ~($true = (X378 @ id @ X380 @ id)) | ($true = (X378 @ id @ (ap @ X380 @ X379) @ id)) | ~! [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (($true = (X378 @ X386 @ X384 @ (comp @ X383 @ X385))) | ~($true = (X378 @ (comp @ X386 @ X383) @ (sub @ X384 @ X383) @ X385))) | ~($true = (X378 @ id @ X379 @ id)) | ~! [X387 : term,X388 : subst,X389 : subst,X390 : subst] : (($true = (X378 @ (comp @ X390 @ X389) @ (sub @ X387 @ X389) @ X388)) | ~($true = (X378 @ X390 @ X387 @ (comp @ X389 @ X388)))))) & ((hoasinduction_lthm = $true) <=> (! [X391 : term > $o,X392 : term] : (~! [X393 : term] : (~($true = (var @ X393)) | ($true = (X391 @ X393))) | ($true = (X391 @ X392)) | ~! [X394 : term] : (~! [X395 : term] : (~($true = (X391 @ X395)) | ($true = (X391 @ (sub @ X394 @ (push @ X395 @ id))))) | ($true = (X391 @ (lam @ X394)))) | ~! [X396 : term,X397 : term] : (($true = (X391 @ (ap @ X396 @ X397))) | ~((X391 @ X396) = $true) | ~((X391 @ X397) = $true))) => (! [X398 : term,X399 : term,X400 : subst > term > subst > $o] : (~! [X401 : subst,X402 : subst,X403 : term,X404 : subst] : (~($true = (X400 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401) @ X404)) | ($true = (X400 @ X402 @ X403 @ (comp @ X401 @ X404)))) | ($true = (X400 @ id @ (ap @ X398 @ X399) @ id)) | ~($true = (X400 @ id @ X398 @ id)) | ~! [X405 : term,X406 : subst,X407 : subst,X408 : subst] : (($true = (X400 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406) @ X408)) | ~($true = (X400 @ X407 @ X405 @ (comp @ X406 @ X408)))) | ~($true = (X400 @ id @ X399 @ id)) | ~! [X409 : term,X410 : term] : (~($true = (X400 @ id @ X409 @ id)) | ~($true = (X400 @ id @ X410 @ id)) | ($true = (X400 @ id @ (ap @ (sub @ X409 @ id) @ X410) @ id)))) => (! [X411 : subst > term > subst > $o,X412 : term] : (($true = (X411 @ id @ (lam @ X412) @ id)) | ~! [X413 : subst,X414 : term,X415 : subst,X416 : subst] : (($true = (X411 @ (comp @ X415 @ X416) @ (sub @ X414 @ X416) @ X413)) | ~($true = (X411 @ X415 @ X414 @ (comp @ X416 @ X413)))) | ~! [X417 : subst,X418 : subst,X419 : term,X420 : subst] : (~($true = (X411 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420) @ X417)) | ($true = (X411 @ X418 @ X419 @ (comp @ X420 @ X417)))) | ~! [X421 : subst > term > term] : (~! [X422 : term] : (((X411 @ id @ (X421 @ id @ X422) @ id) = $true) | ~($true = (X411 @ id @ X422 @ id))) | ((X411 @ id @ (lam @ (X421 @ sh @ one)) @ id) = $true) | ~! [X423 : subst,X424 : subst,X425 : term] : ((sub @ (X421 @ X424 @ X425) @ X423) = (X421 @ (comp @ X424 @ X423) @ (sub @ X425 @ X423)))) | ~! [X426 : term] : (~($true = (X411 @ id @ X426 @ id)) | ($true = (X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id)))) => ! [X427 : term,X428 : subst > term > subst > $o] : (~! [X429 : term] : (~($true = (var @ (sub @ X429 @ id))) | ($true = (X428 @ id @ X429 @ id))) | ~! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (((X428 @ X430 @ X432 @ (comp @ X431 @ X433)) = $true) | ~($true = (X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433))) | ~! [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true = (X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)) | ~((X428 @ X436 @ X437 @ (comp @ X434 @ X435)) = $true)) | ~! [X438 : term,X439 : term] : (((X428 @ id @ (ap @ (sub @ X438 @ id) @ X439) @ id) = $true) | ~($true = (X428 @ id @ X438 @ id)) | ~((X428 @ id @ X439 @ id) = $true)) | ~! [X440 : subst > term > term] : (((X428 @ id @ (lam @ (X440 @ sh @ one)) @ id) = $true) | ~! [X441 : term] : (($true = (X428 @ id @ (X440 @ id @ X441) @ id)) | ~($true = (X428 @ id @ X441 @ id))) | ~! [X442 : subst,X443 : subst,X444 : term] : ((X440 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443)) = (sub @ (X440 @ X442 @ X444) @ X443))) | ($true = (X428 @ id @ X427 @ id))))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X445 : term] : ~! [X446 : subst > term > term] : ~! [X447 : term,X448 : subst] : ((sub @ X445 @ (push @ X447 @ X448)) = (X446 @ X448 @ X447))) & ((axvarcons = $true) <=> ! [X449 : term,X450 : subst] : ((sub @ one @ (push @ X449 @ X450)) = X449)) & ((induction2_lthm = $true) <=> (! [X451 : term] : ((sub @ X451 @ id) = X451) => (! [X452 : subst,X453 : term > $o,X454 : term] : (~! [X455 : term,X456 : term] : (($true = (X453 @ (ap @ X455 @ X456))) | ~($true = (X453 @ X455)) | ~($true = (X453 @ X456))) | ~! [X457 : term] : (~($true = (var @ X457)) | ($true = (X453 @ (sub @ X457 @ X452)))) | ~! [X458 : term] : (($true = (X453 @ (lam @ X458))) | ~! [X459 : term] : (((X453 @ (sub @ X458 @ (push @ X459 @ id))) = $true) | ~($true = (X453 @ X459)))) | ($true = (X453 @ (sub @ X454 @ X452)))) => ! [X460 : term > $o,X461 : term] : (($true = (X460 @ X461)) | ~! [X462 : term] : (~($true = (var @ X462)) | ((X460 @ X462) = $true)) | ~! [X463 : term] : (~! [X464 : term] : (((X460 @ (sub @ X463 @ (push @ X464 @ id))) = $true) | ~($true = (X460 @ X464))) | ($true = (X460 @ (lam @ X463)))) | ~! [X465 : term,X466 : term] : (($true = (X460 @ (ap @ X465 @ X466))) | ~($true = (X460 @ X466)) | ~($true = (X460 @ X465))))))) & (! [X467 : term,X468 : subst > term > subst > $o] : (~! [X469 : subst > term > term] : (~! [X470 : term,X471 : subst,X472 : subst] : ((sub @ (X469 @ X472 @ X470) @ X471) = (X469 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) | ($true = (X468 @ id @ (lam @ (X469 @ sh @ one)) @ id)) | ~! [X473 : term] : (((X468 @ id @ (X469 @ id @ X473) @ id) = $true) | ~($true = (X468 @ id @ X473 @ id)))) | ~! [X474 : term,X475 : term] : (~($true = (X468 @ id @ X475 @ id)) | ($true = (X468 @ id @ (ap @ (sub @ X474 @ id) @ X475) @ id)) | ~($true = (X468 @ id @ X474 @ id))) | ((X468 @ id @ X467 @ id) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (! [X476 : subst > term > subst > $o,X477 : term] : (($true = (X476 @ id @ (lam @ X477) @ id)) | ~! [X478 : subst > term > term] : (($true = (X476 @ id @ (lam @ (X478 @ sh @ one)) @ id)) | ~! [X479 : term] : (~($true = (X476 @ id @ X479 @ id)) | ($true = (X476 @ id @ (X478 @ id @ X479) @ id))) | ~! [X480 : term,X481 : subst,X482 : subst] : ((X478 @ (comp @ X482 @ X481) @ (sub @ X480 @ X481)) = (sub @ (X478 @ X482 @ X480) @ X481))) | ~! [X483 : term] : (($true = (X476 @ id @ (sub @ X477 @ (push @ X483 @ id)) @ id)) | ~($true = (X476 @ id @ X483 @ id)))) <=> (hoasinduction_lem3a = $true)) & (! [X484 : term,X485 : term,X486 : term,X487 : term] : (((ap @ (sub @ X486 @ id) @ X487) != (ap @ (sub @ X484 @ id) @ X485)) | (X484 = X486)) <=> (hoasapinj1 = $true)) & (hoaslamnotvar_lthm = $true) & ((hoaslaminj = $true) <=> ! [X488 : term,X489 : subst,X490 : subst > term > term,X491 : subst > term > term] : (~! [X492 : subst,X493 : subst,X494 : term] : ((X491 @ (comp @ X492 @ X493) @ (sub @ X494 @ X493)) = (sub @ (X491 @ X492 @ X494) @ X493)) | ~! [X495 : subst,X496 : subst,X497 : term] : ((sub @ (X490 @ X495 @ X497) @ X496) = (X490 @ (comp @ X495 @ X496) @ (sub @ X497 @ X496))) | ((lam @ (X491 @ sh @ one)) != (lam @ (X490 @ sh @ one))) | ((X491 @ X489 @ X488) = (X490 @ X489 @ X488)))) & (hoasinduction_lem1_gthm = $true) & (pushprop_gthm = $true) & (axclos = $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)))))))))))) & (! [X498 : subst] : ((push @ (sub @ one @ X498) @ (comp @ sh @ X498)) = X498) <=> (axscons = $true)) & (hoasapnotvar_lthm = $true) & ! [X499 : term] : ? [X500 : d_term] : ((d2term @ X500) = X499) & (pushprop_lthm_orig = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X501 : subst > term > subst > $o] : ~! [X502 : term > $o] : ~! [X503 : term] : ((X501 @ id @ X503 @ id) = (X502 @ X503)) => (! [X504 : term > $o,X505 : term] : (~! [X506 : term,X507 : term] : (($true = (X504 @ (ap @ X507 @ X506))) | ~($true = (X504 @ X507)) | ~($true = (X504 @ X506))) | ~! [X508 : term] : (($true = (X504 @ X508)) | ~($true = (var @ X508))) | ($true = (X504 @ X505)) | ~! [X509 : term] : (~! [X510 : term] : (~((X504 @ X510) = $true) | ((X504 @ (sub @ X509 @ (push @ X510 @ id))) = $true)) | ($true = (X504 @ (lam @ X509))))) => (! [X511 : term] : ((sub @ X511 @ id) = X511) => (! [X512 : term,X513 : subst > term > subst > $o,X514 : term > $o] : (~! [X515 : subst > term > term] : (~! [X516 : subst,X517 : term,X518 : subst] : ((sub @ (X515 @ X516 @ X517) @ X518) = (X515 @ (comp @ X516 @ X518) @ (sub @ X517 @ X518))) | ((X513 @ id @ (lam @ (X515 @ sh @ one)) @ id) = $true) | ~! [X519 : term] : (~((X513 @ id @ X519 @ id) = $true) | ($true = (X513 @ id @ (X515 @ id @ X519) @ id)))) | ($true = (X514 @ (lam @ X512))) | ~! [X520 : term] : (~($true = (X514 @ X520)) | ((X514 @ (sub @ X512 @ (push @ X520 @ id))) = $true)) | ~! [X521 : term] : ((X514 @ X521) = (X513 @ id @ X521 @ id))) => ! [X522 : subst > term > subst > $o,X523 : term] : (($true = (X522 @ id @ X523 @ id)) | ~! [X524 : term] : (~((var @ (sub @ X524 @ id)) = $true) | ($true = (X522 @ id @ X524 @ id))) | ~! [X525 : subst,X526 : term,X527 : subst,X528 : subst] : (~($true = (X522 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525) @ X528)) | ($true = (X522 @ X527 @ X526 @ (comp @ X525 @ X528)))) | ~! [X529 : subst > term > term] : (((X522 @ id @ (lam @ (X529 @ sh @ one)) @ id) = $true) | ~! [X530 : subst,X531 : subst,X532 : term] : ((X529 @ (comp @ X530 @ X531) @ (sub @ X532 @ X531)) = (sub @ (X529 @ X530 @ X532) @ X531)) | ~! [X533 : term] : (((X522 @ id @ (X529 @ id @ X533) @ id) = $true) | ~((X522 @ id @ X533 @ id) = $true))) | ~! [X534 : subst,X535 : term,X536 : subst,X537 : subst] : (($true = (X522 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) | ~($true = (X522 @ X537 @ X535 @ (comp @ X536 @ X534)))) | ~! [X538 : term,X539 : term] : (($true = (X522 @ id @ (ap @ (sub @ X538 @ id) @ X539) @ id)) | ~((X522 @ id @ X539 @ id) = $true) | ~($true = (X522 @ id @ X538 @ id)))))))))),
% 32.37/5.95 inference(rectify,[status(thm)],[f6])).
% 32.37/5.95 thf(f6,plain,(
% 32.37/5.95 (! [X0 : term] : ~! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & (axabs = $true) & (hoasinduction_lem3_gthm = $true) & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & ((axidr = $true) <=> ! [X4 : subst] : ((comp @ X4 @ id) = X4)) & ((d2subst @ d_id) = id) & ((hoasinduction = $true) <=> ! [X5 : term,X6 : subst > term > subst > $o] : (~! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (~($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9)) | ($true = (X6 @ X7 @ X10 @ (comp @ X8 @ X9)))) | ~! [X11 : term] : (($true = (X6 @ id @ X11 @ id)) | ~($true = (var @ (sub @ X11 @ id)))) | ($true = (X6 @ id @ X5 @ id)) | ~! [X12 : subst > term > term] : (~! [X13 : term] : (($true = (X6 @ id @ (X12 @ id @ X13) @ id)) | ~((X6 @ id @ X13 @ id) = $true)) | ~! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) | ($true = (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id))) | ~! [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) | ~($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ~! [X21 : term,X22 : term] : (($true = (X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id)) | ~($true = (X6 @ id @ X21 @ id)) | ~($true = (X6 @ id @ X22 @ id))))) & (one = (d2term @ d_one)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (~! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : (((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) = $true) | ~($true = (X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29))) | ((X26 @ (ap @ X25 @ X23)) = $true) | ~! [X31 : term,X32 : term] : (($true = (X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id)) | ~($true = (X24 @ id @ X32 @ id)) | ~($true = (X24 @ id @ X31 @ id))) | ~! [X33 : term,X34 : subst,X35 : subst,X36 : subst] : (($true = (X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36)) | ~($true = (X24 @ X34 @ X33 @ (comp @ X35 @ X36)))) | ~! [X37 : term] : ((X26 @ X37) = (X24 @ id @ X37 @ id)) | ~((X26 @ X23) = $true) | ~($true = (X26 @ X25))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X38 : term] : ~! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh)))) & (! [X40 : term] : ~! [X41 : subst > term > term] : ~! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2lem_gthm = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X46 : term,X47 : term,X48 : term,X49 : term] : (((ap @ X46 @ X49) != (ap @ X48 @ X47)) | (X46 = X48))) & ! [X50 : d_subst] : (d_id = X50) & (! [X51 : term > $o,X52 : subst,X53 : term] : ~! [X54 : term > $o] : ~! [X55 : term] : ((X54 @ X55) = (X51 @ (sub @ X55 @ (push @ X53 @ X52)))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoaslamnotvar = $true) & ((induction = $true) <=> ! [X56 : term,X57 : term > $o] : (~! [X58 : term] : (~($true = (var @ X58)) | ($true = (X57 @ X58))) | ~! [X59 : term] : (((X57 @ (lam @ X59)) = $true) | ~($true = (X57 @ X59))) | ~! [X60 : term,X61 : term] : (($true = (X57 @ (ap @ X60 @ X61))) | ~($true = (X57 @ X61)) | ~($true = (X57 @ X60))) | ((X57 @ X56) = $true))) & ~((var @ (d2term @ d_one)) = $true) & ((hoasinduction_lem3 = $true) <=> ! [X62 : term,X63 : subst > term > subst > $o] : (($true = (X63 @ id @ (lam @ X62) @ id)) | ~! [X64 : term] : (~((X63 @ id @ X64 @ id) = $true) | ((X63 @ id @ (sub @ X62 @ (push @ X64 @ id)) @ id) = $true)) | ~! [X65 : subst > term > term] : (~! [X66 : term] : (~((X63 @ id @ X66 @ id) = $true) | ($true = (X63 @ id @ (X65 @ id @ X66) @ id))) | ((X63 @ id @ (lam @ (X65 @ sh @ one)) @ id) = $true) | ~! [X67 : term,X68 : subst,X69 : subst] : ((X65 @ (comp @ X69 @ X68) @ (sub @ X67 @ X68)) = (sub @ (X65 @ X69 @ X67) @ X68))) | ~! [X70 : subst,X71 : subst,X72 : subst,X73 : term] : (~($true = (X63 @ X72 @ X73 @ (comp @ X71 @ X70))) | ($true = (X63 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X70))) | ~! [X74 : subst,X75 : subst,X76 : subst,X77 : term] : (~((X63 @ (comp @ X75 @ X76) @ (sub @ X77 @ X76) @ X74) = $true) | ((X63 @ X75 @ X77 @ (comp @ X76 @ X74)) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem1v2_gthm = $true) & ((induction2lem = $true) <=> ! [X81 : term,X82 : subst,X83 : term > $o] : (~! [X84 : term] : (($true = (X83 @ (lam @ X84))) | ~! [X85 : term] : (~((X83 @ X85) = $true) | ($true = (X83 @ (sub @ X84 @ (push @ X85 @ id)))))) | ~! [X86 : term] : (($true = (X83 @ (sub @ X86 @ X82))) | ~($true = (var @ X86))) | ($true = (X83 @ (sub @ X81 @ X82))) | ~! [X87 : term,X88 : term] : (($true = (X83 @ (ap @ X88 @ X87))) | ~((X83 @ X88) = $true) | ~($true = (X83 @ X87))))) & ((! [X89 : term] : ((sub @ X89 @ id) = X89) => (! [X90 : term,X91 : term,X92 : term,X93 : term] : ((X90 = X91) | ((ap @ X90 @ X92) != (ap @ X91 @ X93))) => ! [X94 : term,X95 : term,X96 : term,X97 : term] : ((X94 = X97) | ((ap @ (sub @ X94 @ id) @ X96) != (ap @ (sub @ X97 @ id) @ X95))))) <=> (hoasapinj1_lthm = $true)) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X98 : term,X99 : term] : (((lam @ X99) != (lam @ X98)) | (X98 = X99)) <=> (laminj = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X100 : term] : ((sub @ X100 @ id) = X100) => (! [X101 : term,X102 : subst > term > subst > $o] : (~! [X103 : subst > term > term] : (~! [X104 : term,X105 : subst,X106 : subst] : ((X103 @ (comp @ X106 @ X105) @ (sub @ X104 @ X105)) = (sub @ (X103 @ X106 @ X104) @ X105)) | ($true = (X102 @ id @ (lam @ (X103 @ sh @ one)) @ id)) | ~! [X107 : term] : (~($true = (X102 @ id @ X107 @ id)) | ($true = (X102 @ id @ (X103 @ id @ X107) @ id)))) | ($true = (X102 @ id @ (lam @ (sub @ X101 @ (push @ one @ sh))) @ id)) | ~! [X108 : term] : (~($true = (X102 @ id @ X108 @ id)) | ($true = (X102 @ id @ (sub @ X101 @ (push @ X108 @ id)) @ id)))) => ! [X109 : term,X110 : subst > term > subst > $o] : (($true = (X110 @ id @ (lam @ X109) @ id)) | ~! [X111 : subst > term > term] : (~! [X112 : term] : (~((X110 @ id @ X112 @ id) = $true) | ($true = (X110 @ id @ (X111 @ id @ X112) @ id))) | ($true = (X110 @ id @ (lam @ (X111 @ sh @ one)) @ id)) | ~! [X113 : subst,X114 : term,X115 : subst] : ((sub @ (X111 @ X113 @ X114) @ X115) = (X111 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115)))) | ~! [X116 : subst,X117 : term,X118 : subst,X119 : subst] : (~($true = (X110 @ X119 @ X117 @ (comp @ X116 @ X118))) | ((X110 @ (comp @ X119 @ X116) @ (sub @ X117 @ X116) @ X118) = $true)) | ~! [X120 : term] : (~($true = (X110 @ id @ X120 @ id)) | ($true = (X110 @ id @ (sub @ X109 @ (push @ X120 @ id)) @ id))) | ~! [X121 : subst,X122 : subst,X123 : subst,X124 : term] : (~($true = (X110 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) | ($true = (X110 @ X121 @ X124 @ (comp @ X123 @ X122)))))))) & ((! [X125 : term] : ((sub @ X125 @ id) = X125) => (! [X126 : term,X127 : subst > term > subst > $o] : (~! [X128 : subst > term > term] : (~! [X129 : term] : (~((X127 @ id @ X129 @ id) = $true) | ($true = (X127 @ id @ (X128 @ id @ X129) @ id))) | ~! [X130 : subst,X131 : subst,X132 : term] : ((sub @ (X128 @ X130 @ X132) @ X131) = (X128 @ (comp @ X130 @ X131) @ (sub @ X132 @ X131))) | ($true = (X127 @ id @ (lam @ (X128 @ sh @ one)) @ id))) | ($true = (X127 @ id @ (lam @ (sub @ X126 @ (push @ one @ sh))) @ id)) | ~! [X133 : term] : (($true = (X127 @ id @ (sub @ X126 @ (push @ X133 @ id)) @ id)) | ~($true = (X127 @ id @ X133 @ id)))) => ! [X134 : subst > term > subst > $o,X135 : term] : (($true = (X134 @ id @ (lam @ X135) @ id)) | ~! [X136 : subst > term > term] : (~! [X137 : term] : (($true = (X134 @ id @ (X136 @ id @ X137) @ id)) | ~((X134 @ id @ X137 @ id) = $true)) | ($true = (X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) | ~! [X138 : subst,X139 : subst,X140 : term] : ((X136 @ (comp @ X138 @ X139) @ (sub @ X140 @ X139)) = (sub @ (X136 @ X138 @ X140) @ X139))) | ~! [X141 : term] : (((X134 @ id @ (sub @ X135 @ (push @ X141 @ id)) @ id) = $true) | ~($true = (X134 @ id @ X141 @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((! [X142 : term] : ~! [X143 : subst > term > term] : ~! [X144 : term,X145 : subst] : ((sub @ X142 @ (push @ X144 @ X145)) = (X143 @ X145 @ X144)) => (! [X146 : term] : ((sub @ X146 @ id) = X146) => ! [X147 : term,X148 : subst > term > subst > $o,X149 : term > $o] : (~! [X150 : term] : ((X148 @ id @ X150 @ id) = (X149 @ X150)) | ($true = (X149 @ (lam @ X147))) | ~! [X151 : subst > term > term] : (~! [X152 : term,X153 : subst,X154 : subst] : ((sub @ (X151 @ X154 @ X152) @ X153) = (X151 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153))) | ~! [X155 : term] : (((X148 @ id @ (X151 @ id @ X155) @ id) = $true) | ~($true = (X148 @ id @ X155 @ id))) | ($true = (X148 @ id @ (lam @ (X151 @ sh @ one)) @ id))) | ~! [X156 : term] : (~((X149 @ X156) = $true) | ($true = (X149 @ (sub @ X147 @ (push @ X156 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasapinj1_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X157 : term,X158 : subst,X159 : term > $o,X160 : term > $o,X161 : term] : (~($true = (X160 @ X161)) | ((X159 @ (sub @ X161 @ (push @ X157 @ X158))) = $true))) & (hoasinduction_lem1_lthm = $true) & ((termmset_lthm = $true) <=> (! [X162 : term] : ((sub @ X162 @ id) = X162) => ! [X163 : term] : ((sub @ X163 @ id) = X163))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & (ulamvarind = $true) & (! [X164 : subst > term > subst > $o,X165 : term] : (~! [X166 : term] : (($true = (X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) | ~($true = (X164 @ id @ X166 @ id))) | ~! [X167 : subst > term > term] : (((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) = $true) | ~! [X168 : term] : (((X164 @ id @ (X167 @ id @ X168) @ id) = $true) | ~($true = (X164 @ id @ X168 @ id))) | ~! [X169 : subst,X170 : subst,X171 : term] : ((X167 @ (comp @ X170 @ X169) @ (sub @ X171 @ X169)) = (sub @ (X167 @ X170 @ X171) @ X169))) | ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id) = $true)) <=> (hoasinduction_lem3aa = $true)) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & (! [X172 : term] : ((sub @ X172 @ id) = X172) <=> (axvarid = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X173 : d_term,X174 : d_term] : (((d2term @ X174) = (d2term @ X173)) => (X173 = X174)) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (axapp = $true) & ~(lamnotap = $true) & (pushprop_lem1_gthm = $true) & ((! [X175 : term,X176 : subst] : ((sub @ one @ (push @ X175 @ X176)) = X175) => (! [X177 : term,X178 : subst] : ((comp @ sh @ (push @ X177 @ X178)) = X178) => (! [X179 : term,X180 : term] : ((X179 = X180) | ((lam @ X180) != (lam @ X179))) => ! [X181 : subst > term > term,X182 : subst,X183 : term,X184 : subst > term > term] : (~! [X185 : subst,X186 : term,X187 : subst] : ((X184 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185)) = (sub @ (X184 @ X187 @ X186) @ X185)) | ~! [X188 : subst,X189 : subst,X190 : term] : ((sub @ (X181 @ X188 @ X190) @ X189) = (X181 @ (comp @ X188 @ X189) @ (sub @ X190 @ X189))) | ((X181 @ X182 @ X183) = (X184 @ X182 @ X183)) | ((lam @ (X184 @ sh @ one)) != (lam @ (X181 @ sh @ one))))))) <=> (hoaslaminj_lthm = $true)) & (lamnotvar = $true) & ((shinj = $true) <=> ! [X191 : term,X192 : term] : ((X191 = X192) | ((sub @ X192 @ sh) != (sub @ X191 @ sh)))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((apinj2 = $true) <=> ! [X193 : term,X194 : term,X195 : term,X196 : term] : (((ap @ X193 @ X196) != (ap @ X194 @ X195)) | (X195 = X196))) & ((hoasinduction_lem3aaa = $true) <=> ! [X197 : term,X198 : subst > term > subst > $o] : (($true = (X198 @ id @ (lam @ (sub @ X197 @ (push @ one @ sh))) @ id)) | ~! [X199 : term] : (($true = (X198 @ id @ (sub @ X197 @ (push @ X199 @ id)) @ id)) | ~((X198 @ id @ X199 @ id) = $true)) | ~! [X200 : subst > term > term,X201 : term] : (($true = (X198 @ id @ (lam @ (X200 @ sh @ one)) @ id)) | ~! [X202 : term] : (~($true = (X198 @ id @ X202 @ id)) | ($true = (X198 @ id @ (X200 @ id @ X202) @ id))) | ~! [X203 : term,X204 : subst,X205 : subst] : ((sub @ (sub @ X201 @ (push @ X203 @ X204)) @ X205) = (sub @ (X200 @ X204 @ X203) @ X205)) | ~! [X206 : subst,X207 : term,X208 : subst] : ((X200 @ (comp @ X208 @ X206) @ (sub @ X207 @ X206)) = (sub @ X201 @ (push @ (sub @ X207 @ X206) @ (comp @ X208 @ X206))))))) & ((hoasinduction_lem0 = $true) <=> ! [X209 : subst > term > subst > $o] : ~! [X210 : term > $o] : ~! [X211 : term] : ((X209 @ id @ X211 @ id) = (X210 @ X211))) & (hoasapinj2_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X212 : subst,X213 : term,X214 : term > $o] : ~! [X215 : term > $o] : ~! [X216 : term] : ((X214 @ (sub @ X216 @ (push @ X213 @ X212))) = (X215 @ X216)) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X217 : term,X218 : term,X219 : term,X220 : term] : ((X217 = X219) | ((ap @ (sub @ X220 @ id) @ X217) != (ap @ (sub @ X218 @ id) @ X219)))) & (! [X221 : subst > term > subst > $o] : ~! [X222 : term > $o] : ~! [X223 : term] : ((X221 @ id @ X223 @ id) = (X222 @ X223)) <=> (hoasinduction_lem0_lthm = $true)) & (hoasapnotvar = $true) & ((d2subst @ d_id) = sh) & ((! [X224 : subst > term > subst > $o] : ~! [X225 : term > $o] : ~! [X226 : term] : ((X224 @ id @ X226 @ id) = (X225 @ X226)) => (! [X227 : term > $o,X228 : term] : (~! [X229 : term] : (((X227 @ X229) = $true) | ~((var @ X229) = $true)) | ~! [X230 : term] : (($true = (X227 @ (lam @ X230))) | ~! [X231 : term] : (~((X227 @ X231) = $true) | ($true = (X227 @ (sub @ X230 @ (push @ X231 @ id)))))) | ($true = (X227 @ X228)) | ~! [X232 : term,X233 : term] : (~($true = (X227 @ X232)) | ~($true = (X227 @ X233)) | ($true = (X227 @ (ap @ X233 @ X232))))) => (! [X234 : term] : ((sub @ X234 @ id) = X234) => (! [X235 : term,X236 : term > $o,X237 : subst > term > subst > $o] : (($true = (X236 @ (lam @ X235))) | ~! [X238 : term] : (($true = (X236 @ (sub @ X235 @ (push @ X238 @ id)))) | ~($true = (X236 @ X238))) | ~! [X239 : subst > term > term] : (($true = (X237 @ id @ (lam @ (X239 @ sh @ one)) @ id)) | ~! [X240 : term] : (~((X237 @ id @ X240 @ id) = $true) | ($true = (X237 @ id @ (X239 @ id @ X240) @ id))) | ~! [X241 : term,X242 : subst,X243 : subst] : ((sub @ (X239 @ X242 @ X241) @ X243) = (X239 @ (comp @ X242 @ X243) @ (sub @ X241 @ X243)))) | ~! [X244 : term] : ((X237 @ id @ X244 @ id) = (X236 @ X244))) => ! [X245 : subst > term > subst > $o,X246 : term] : (($true = (X245 @ id @ X246 @ id)) | ~! [X247 : term,X248 : term] : (~($true = (X245 @ id @ X247 @ id)) | ($true = (X245 @ id @ (ap @ (sub @ X247 @ id) @ X248) @ id)) | ~((X245 @ id @ X248 @ id) = $true)) | ~! [X249 : subst > term > term] : (($true = (X245 @ id @ (lam @ (X249 @ sh @ one)) @ id)) | ~! [X250 : term] : (~($true = (X245 @ id @ X250 @ id)) | ($true = (X245 @ id @ (X249 @ id @ X250) @ id))) | ~! [X251 : subst,X252 : term,X253 : subst] : ((X249 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253)) = (sub @ (X249 @ X251 @ X252) @ X253)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (substmonoid_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X254 : term,X255 : term,X256 : subst > term > term] : (~! [X257 : term,X258 : subst,X259 : subst] : ((X256 @ (comp @ X259 @ X258) @ (sub @ X257 @ X258)) = (sub @ (X256 @ X259 @ X257) @ X258)) | ((lam @ (X256 @ sh @ one)) != (ap @ (sub @ X255 @ id) @ X254))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X260 : subst > term > subst > $o,X261 : term] : (~! [X262 : term] : (($true = (X260 @ id @ (sub @ X261 @ (push @ X262 @ id)) @ id)) | ~($true = (X260 @ id @ X262 @ id))) | ($true = (X260 @ id @ (lam @ (sub @ X261 @ (push @ one @ sh))) @ id)) | ~! [X263 : subst > term > term] : (~! [X264 : subst,X265 : subst,X266 : term] : ((sub @ (X263 @ X264 @ X266) @ X265) = (X263 @ (comp @ X264 @ X265) @ (sub @ X266 @ X265))) | ~! [X267 : term] : (~($true = (X260 @ id @ X267 @ id)) | ((X260 @ id @ (X263 @ id @ X267) @ id) = $true)) | ((X260 @ id @ (lam @ (X263 @ sh @ one)) @ id) = $true)))) & ((hoasinduction_lem3v2 = $true) <=> ! [X268 : term,X269 : term > $o,X270 : subst > term > subst > $o] : (~! [X271 : term,X272 : subst,X273 : subst,X274 : subst] : (($true = (X270 @ (comp @ X274 @ X273) @ (sub @ X271 @ X273) @ X272)) | ~($true = (X270 @ X274 @ X271 @ (comp @ X273 @ X272)))) | ~! [X275 : subst > term > term] : (($true = (X270 @ id @ (lam @ (X275 @ sh @ one)) @ id)) | ~! [X276 : term] : (($true = (X270 @ id @ (X275 @ id @ X276) @ id)) | ~((X270 @ id @ X276 @ id) = $true)) | ~! [X277 : subst,X278 : subst,X279 : term] : ((sub @ (X275 @ X277 @ X279) @ X278) = (X275 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)))) | ~! [X280 : term] : (~($true = (X269 @ X280)) | ((X269 @ (sub @ X268 @ (push @ X280 @ id))) = $true)) | ((X269 @ (lam @ X268)) = $true) | ~! [X281 : subst,X282 : subst,X283 : subst,X284 : term] : (($true = (X270 @ X282 @ X284 @ (comp @ X281 @ X283))) | ~($true = (X270 @ (comp @ X282 @ X281) @ (sub @ X284 @ X281) @ X283))) | ~! [X285 : term] : ((X269 @ X285) = (X270 @ id @ X285 @ id)))) & (! [X286 : subst,X287 : term] : ((comp @ sh @ (push @ X287 @ X286)) = X286) <=> (axshiftcons = $true)) & (hoasinduction_lem3b_gthm = $true) & (termmset_gthm = $true) & (axmap = $true) & (! [X288 : term > $o,X289 : term] : (~! [X290 : term] : (~! [X291 : term] : (($true = (X288 @ (sub @ X290 @ (push @ X291 @ id)))) | ~($true = (X288 @ X291))) | ($true = (X288 @ (lam @ X290)))) | ~! [X292 : term] : (~((var @ X292) = $true) | ($true = (X288 @ X292))) | ~! [X293 : term,X294 : term] : (~((X288 @ X294) = $true) | ((X288 @ (ap @ X293 @ X294)) = $true) | ~($true = (X288 @ X293))) | ($true = (X288 @ X289))) <=> (induction2 = $true)) & (! [X295 : subst] : ((comp @ id @ X295) = X295) <=> (axidl = $true)) & ((! [X296 : term,X297 : subst] : ((sub @ one @ (push @ X296 @ X297)) = X296) => (! [X298 : subst,X299 : term] : ((comp @ sh @ (push @ X299 @ X298)) = X298) => ! [X300 : subst,X301 : term > $o,X302 : term > $o,X303 : term,X304 : term] : (~((X302 @ X304) = $true) | ($true = (X301 @ (sub @ X304 @ (push @ X303 @ X300))))))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : (((X308 @ one) = $true) | ~! [X309 : term] : ((X308 @ X309) = (X307 @ (sub @ X309 @ (push @ X306 @ X305)))) | ~($true = (X307 @ X306)))) & (! [X310 : term] : ((sub @ X310 @ id) = X310) <=> (termmset = $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X311 : term,X312 : term,X313 : term,X314 : term] : (((ap @ X312 @ X313) != (ap @ X314 @ X311)) | (X311 = X313)) => ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X316 = X317) | ((ap @ (sub @ X318 @ id) @ X316) != (ap @ (sub @ X315 @ id) @ X317))))) & (axvarshift = $true) & ~(ulamvar1 = $true) & ((! [X319 : term,X320 : subst] : ((sub @ one @ (push @ X319 @ X320)) = X319) => (! [X321 : term,X322 : subst] : ((comp @ sh @ (push @ X321 @ X322)) = X322) => (! [X323 : subst] : ((comp @ X323 @ id) = X323) => (! [X324 : term > $o,X325 : term] : (~! [X326 : term] : (($true = (X324 @ (lam @ X326))) | ~($true = (X324 @ X326))) | ($true = (X324 @ X325)) | ~! [X327 : term] : (($true = (X324 @ X327)) | ~($true = (var @ X327))) | ~! [X328 : term,X329 : term] : (~($true = (X324 @ X329)) | ($true = (X324 @ (ap @ X328 @ X329))) | ~($true = (X324 @ X328)))) => ! [X330 : subst,X331 : term,X332 : term > $o] : (~! [X333 : term,X334 : term] : (~($true = (X332 @ X334)) | ~((X332 @ X333) = $true) | ($true = (X332 @ (ap @ X334 @ X333)))) | ~! [X335 : term] : (~($true = (var @ X335)) | ($true = (X332 @ (sub @ X335 @ X330)))) | ~! [X336 : term] : (~! [X337 : term] : (~($true = (X332 @ X337)) | ($true = (X332 @ (sub @ X336 @ (push @ X337 @ id))))) | ((X332 @ (lam @ X336)) = $true)) | ($true = (X332 @ (sub @ X331 @ X330)))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2 = $true) & (! [X338 : term > $o,X339 : subst > term > subst > $o,X340 : term] : (($true = (X338 @ (lam @ X340))) | ~! [X341 : subst > term > term] : (~! [X342 : subst,X343 : subst,X344 : term] : ((sub @ (X341 @ X343 @ X344) @ X342) = (X341 @ (comp @ X343 @ X342) @ (sub @ X344 @ X342))) | ($true = (X339 @ id @ (lam @ (X341 @ sh @ one)) @ id)) | ~! [X345 : term] : (~($true = (X339 @ id @ X345 @ id)) | ((X339 @ id @ (X341 @ id @ X345) @ id) = $true))) | ~! [X346 : term] : (~($true = (X338 @ X346)) | ($true = (X338 @ (sub @ X340 @ (push @ X346 @ id))))) | ~! [X347 : term] : ((X338 @ X347) = (X339 @ id @ X347 @ id))) <=> (hoasinduction_lem3v2a = $true)) & (induction2_gthm = $true) & ! [X348 : d_term] : (d_one = X348) & ((! [X349 : subst] : ((comp @ id @ X349) = X349) => (! [X350 : subst] : ((comp @ X350 @ id) = X350) => (! [X351 : subst] : ((comp @ id @ X351) = X351) & ! [X352 : subst] : ((comp @ X352 @ id) = X352)))) <=> (substmonoid_lthm = $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotap_gthm = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X353 : d_subst,X354 : d_subst] : (((d2subst @ X354) = (d2subst @ X353)) => (X353 = X354)) & ((! [X355 : subst,X356 : term] : ((sub @ one @ (push @ X356 @ X355)) = X356) => ! [X357 : term > $o,X358 : term,X359 : term > $o,X360 : subst] : (($true = (X359 @ one)) | ~($true = (X357 @ X358)) | ~! [X361 : term] : ((X357 @ (sub @ X361 @ (push @ X358 @ X360))) = (X359 @ X361)))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & ((! [X362 : subst] : ((comp @ id @ X362) = X362) & ! [X363 : subst] : ((comp @ X363 @ id) = X363)) <=> (substmonoid = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X364 : term] : ((sub @ X364 @ id) = X364) => ! [X365 : subst > term > subst > $o,X366 : term,X367 : term > $o] : (~! [X368 : term] : ((X365 @ id @ X368 @ id) = (X367 @ X368)) | ~! [X369 : subst,X370 : subst,X371 : subst,X372 : term] : (~($true = (X365 @ (comp @ X371 @ X370) @ (sub @ X372 @ X370) @ X369)) | ($true = (X365 @ X371 @ X372 @ (comp @ X370 @ X369)))) | ~! [X373 : subst > term > term] : (~! [X374 : term] : (($true = (X365 @ id @ (X373 @ id @ X374) @ id)) | ~($true = (X365 @ id @ X374 @ id))) | ($true = (X365 @ id @ (lam @ (X373 @ sh @ one)) @ id)) | ~! [X375 : subst,X376 : term,X377 : subst] : ((sub @ (X373 @ X375 @ X376) @ X377) = (X373 @ (comp @ X375 @ X377) @ (sub @ X376 @ X377)))) | ~! [X378 : subst,X379 : subst,X380 : subst,X381 : term] : (~((X365 @ X380 @ X381 @ (comp @ X378 @ X379)) = $true) | ((X365 @ (comp @ X380 @ X378) @ (sub @ X381 @ X378) @ X379) = $true)) | ~! [X382 : term] : (($true = (X367 @ (sub @ X366 @ (push @ X382 @ id)))) | ~($true = (X367 @ X382))) | ((X367 @ (lam @ X366)) = $true)))) & ((hoasinduction_lem2 = $true) <=> ! [X383 : subst > term > subst > $o,X384 : term,X385 : term] : (~! [X386 : term,X387 : term] : (~((X383 @ id @ X386 @ id) = $true) | ((X383 @ id @ (ap @ (sub @ X386 @ id) @ X387) @ id) = $true) | ~($true = (X383 @ id @ X387 @ id))) | ~($true = (X383 @ id @ X385 @ id)) | ($true = (X383 @ id @ (ap @ X385 @ X384) @ id)) | ~! [X388 : subst,X389 : term,X390 : subst,X391 : subst] : (($true = (X383 @ X391 @ X389 @ (comp @ X388 @ X390))) | ~($true = (X383 @ (comp @ X391 @ X388) @ (sub @ X389 @ X388) @ X390))) | ~((X383 @ id @ X384 @ id) = $true) | ~! [X392 : term,X393 : subst,X394 : subst,X395 : subst] : (($true = (X383 @ (comp @ X395 @ X394) @ (sub @ X392 @ X394) @ X393)) | ~($true = (X383 @ X395 @ X392 @ (comp @ X394 @ X393)))))) & ((hoasinduction_lthm = $true) <=> (! [X396 : term > $o,X397 : term] : (~! [X398 : term] : (~($true = (var @ X398)) | ($true = (X396 @ X398))) | ($true = (X396 @ X397)) | ~! [X399 : term] : (~! [X400 : term] : (~((X396 @ X400) = $true) | ($true = (X396 @ (sub @ X399 @ (push @ X400 @ id))))) | ($true = (X396 @ (lam @ X399)))) | ~! [X401 : term,X402 : term] : (($true = (X396 @ (ap @ X401 @ X402))) | ~($true = (X396 @ X401)) | ~($true = (X396 @ X402)))) => (! [X403 : term,X404 : term,X405 : subst > term > subst > $o] : (~! [X406 : subst,X407 : subst,X408 : term,X409 : subst] : (~($true = (X405 @ (comp @ X407 @ X406) @ (sub @ X408 @ X406) @ X409)) | ($true = (X405 @ X407 @ X408 @ (comp @ X406 @ X409)))) | ($true = (X405 @ id @ (ap @ X403 @ X404) @ id)) | ~($true = (X405 @ id @ X403 @ id)) | ~! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : (($true = (X405 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411) @ X413)) | ~((X405 @ X412 @ X410 @ (comp @ X411 @ X413)) = $true)) | ~($true = (X405 @ id @ X404 @ id)) | ~! [X414 : term,X415 : term] : (~($true = (X405 @ id @ X414 @ id)) | ~((X405 @ id @ X415 @ id) = $true) | ((X405 @ id @ (ap @ (sub @ X414 @ id) @ X415) @ id) = $true))) => (! [X416 : subst > term > subst > $o,X417 : term] : (($true = (X416 @ id @ (lam @ X417) @ id)) | ~! [X418 : subst,X419 : term,X420 : subst,X421 : subst] : (($true = (X416 @ (comp @ X420 @ X421) @ (sub @ X419 @ X421) @ X418)) | ~($true = (X416 @ X420 @ X419 @ (comp @ X421 @ X418)))) | ~! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : (~((X416 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425) @ X422) = $true) | ($true = (X416 @ X423 @ X424 @ (comp @ X425 @ X422)))) | ~! [X426 : subst > term > term] : (~! [X427 : term] : (((X416 @ id @ (X426 @ id @ X427) @ id) = $true) | ~((X416 @ id @ X427 @ id) = $true)) | ($true = (X416 @ id @ (lam @ (X426 @ sh @ one)) @ id)) | ~! [X428 : subst,X429 : subst,X430 : term] : ((sub @ (X426 @ X429 @ X430) @ X428) = (X426 @ (comp @ X429 @ X428) @ (sub @ X430 @ X428)))) | ~! [X431 : term] : (~((X416 @ id @ X431 @ id) = $true) | ($true = (X416 @ id @ (sub @ X417 @ (push @ X431 @ id)) @ id)))) => ! [X432 : term,X433 : subst > term > subst > $o] : (~! [X434 : term] : (~($true = (var @ (sub @ X434 @ id))) | ($true = (X433 @ id @ X434 @ id))) | ~! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : (($true = (X433 @ X435 @ X437 @ (comp @ X436 @ X438))) | ~($true = (X433 @ (comp @ X435 @ X436) @ (sub @ X437 @ X436) @ X438))) | ~! [X439 : subst,X440 : subst,X441 : subst,X442 : term] : (($true = (X433 @ (comp @ X441 @ X439) @ (sub @ X442 @ X439) @ X440)) | ~($true = (X433 @ X441 @ X442 @ (comp @ X439 @ X440)))) | ~! [X443 : term,X444 : term] : (($true = (X433 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id)) | ~((X433 @ id @ X443 @ id) = $true) | ~($true = (X433 @ id @ X444 @ id))) | ~! [X445 : subst > term > term] : (($true = (X433 @ id @ (lam @ (X445 @ sh @ one)) @ id)) | ~! [X446 : term] : (((X433 @ id @ (X445 @ id @ X446) @ id) = $true) | ~((X433 @ id @ X446 @ id) = $true)) | ~! [X447 : subst,X448 : subst,X449 : term] : ((X445 @ (comp @ X447 @ X448) @ (sub @ X449 @ X448)) = (sub @ (X445 @ X447 @ X449) @ X448))) | ((X433 @ id @ X432 @ id) = $true)))))) & (! [X450 : term] : ~! [X451 : subst > term > term] : ~! [X452 : term,X453 : subst] : ((X451 @ X453 @ X452) = (sub @ X450 @ (push @ X452 @ X453))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X454 : term,X455 : subst] : ((sub @ one @ (push @ X454 @ X455)) = X454) <=> (axvarcons = $true)) & ((induction2_lthm = $true) <=> (! [X456 : term] : ((sub @ X456 @ id) = X456) => (! [X457 : subst,X458 : term > $o,X459 : term] : (~! [X460 : term,X461 : term] : (($true = (X458 @ (ap @ X460 @ X461))) | ~((X458 @ X460) = $true) | ~($true = (X458 @ X461))) | ~! [X462 : term] : (~($true = (var @ X462)) | ((X458 @ (sub @ X462 @ X457)) = $true)) | ~! [X463 : term] : (($true = (X458 @ (lam @ X463))) | ~! [X464 : term] : (($true = (X458 @ (sub @ X463 @ (push @ X464 @ id)))) | ~($true = (X458 @ X464)))) | ($true = (X458 @ (sub @ X459 @ X457)))) => ! [X465 : term > $o,X466 : term] : (($true = (X465 @ X466)) | ~! [X467 : term] : (~($true = (var @ X467)) | ($true = (X465 @ X467))) | ~! [X468 : term] : (~! [X469 : term] : (($true = (X465 @ (sub @ X468 @ (push @ X469 @ id)))) | ~($true = (X465 @ X469))) | ($true = (X465 @ (lam @ X468)))) | ~! [X470 : term,X471 : term] : (((X465 @ (ap @ X470 @ X471)) = $true) | ~($true = (X465 @ X471)) | ~($true = (X465 @ X470))))))) & (! [X472 : term,X473 : subst > term > subst > $o] : (~! [X474 : subst > term > term] : (~! [X475 : term,X476 : subst,X477 : subst] : ((sub @ (X474 @ X477 @ X475) @ X476) = (X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) | ($true = (X473 @ id @ (lam @ (X474 @ sh @ one)) @ id)) | ~! [X478 : term] : (((X473 @ id @ (X474 @ id @ X478) @ id) = $true) | ~($true = (X473 @ id @ X478 @ id)))) | ~! [X479 : term,X480 : term] : (~((X473 @ id @ X480 @ id) = $true) | ($true = (X473 @ id @ (ap @ (sub @ X479 @ id) @ X480) @ id)) | ~((X473 @ id @ X479 @ id) = $true)) | ($true = (X473 @ id @ X472 @ id))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X481 : subst > term > subst > $o,X482 : term] : (($true = (X481 @ id @ (lam @ X482) @ id)) | ~! [X483 : subst > term > term] : (($true = (X481 @ id @ (lam @ (X483 @ sh @ one)) @ id)) | ~! [X484 : term] : (~((X481 @ id @ X484 @ id) = $true) | ($true = (X481 @ id @ (X483 @ id @ X484) @ id))) | ~! [X485 : term,X486 : subst,X487 : subst] : ((sub @ (X483 @ X487 @ X485) @ X486) = (X483 @ (comp @ X487 @ X486) @ (sub @ X485 @ X486)))) | ~! [X488 : term] : (((X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id) = $true) | ~($true = (X481 @ id @ X488 @ id)))) <=> (hoasinduction_lem3a = $true)) & ((hoasapinj1 = $true) <=> ! [X489 : term,X490 : term,X491 : term,X492 : term] : ((X489 = X491) | ((ap @ (sub @ X491 @ id) @ X492) != (ap @ (sub @ X489 @ id) @ X490)))) & (hoaslamnotvar_lthm = $true) & (! [X493 : term,X494 : subst,X495 : subst > term > term,X496 : subst > term > term] : (((lam @ (X496 @ sh @ one)) != (lam @ (X495 @ sh @ one))) | ((X496 @ X494 @ X493) = (X495 @ X494 @ X493)) | ~! [X497 : subst,X498 : subst,X499 : term] : ((X496 @ (comp @ X497 @ X498) @ (sub @ X499 @ X498)) = (sub @ (X496 @ X497 @ X499) @ X498)) | ~! [X500 : subst,X501 : subst,X502 : term] : ((sub @ (X495 @ X500 @ X502) @ X501) = (X495 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_gthm = $true) & (axclos = $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)))))))))))) & (! [X508 : subst] : ((push @ (sub @ one @ X508) @ (comp @ sh @ X508)) = X508) <=> (axscons = $true)) & (hoasapnotvar_lthm = $true) & ! [X509 : term] : ? [X510 : d_term] : ((d2term @ X510) = X509) & (pushprop_lthm_orig = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X511 : subst > term > subst > $o] : ~! [X512 : term > $o] : ~! [X513 : term] : ((X512 @ X513) = (X511 @ id @ X513 @ id)) => (! [X514 : term > $o,X515 : term] : (~! [X516 : term,X517 : term] : (($true = (X514 @ (ap @ X517 @ X516))) | ~($true = (X514 @ X517)) | ~($true = (X514 @ X516))) | ~! [X518 : term] : (($true = (X514 @ X518)) | ~($true = (var @ X518))) | ($true = (X514 @ X515)) | ~! [X519 : term] : (~! [X520 : term] : (~($true = (X514 @ X520)) | ($true = (X514 @ (sub @ X519 @ (push @ X520 @ id))))) | ($true = (X514 @ (lam @ X519))))) => (! [X521 : term] : ((sub @ X521 @ id) = X521) => (! [X522 : term,X523 : subst > term > subst > $o,X524 : term > $o] : (~! [X525 : subst > term > term] : (~! [X526 : subst,X527 : term,X528 : subst] : ((sub @ (X525 @ X526 @ X527) @ X528) = (X525 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528))) | ($true = (X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) | ~! [X529 : term] : (~($true = (X523 @ id @ X529 @ id)) | ((X523 @ id @ (X525 @ id @ X529) @ id) = $true))) | ($true = (X524 @ (lam @ X522))) | ~! [X530 : term] : (~($true = (X524 @ X530)) | ((X524 @ (sub @ X522 @ (push @ X530 @ id))) = $true)) | ~! [X531 : term] : ((X523 @ id @ X531 @ id) = (X524 @ X531))) => ! [X532 : subst > term > subst > $o,X533 : term] : (($true = (X532 @ id @ X533 @ id)) | ~! [X534 : term] : (~((var @ (sub @ X534 @ id)) = $true) | ($true = (X532 @ id @ X534 @ id))) | ~! [X535 : subst,X536 : term,X537 : subst,X538 : subst] : (~($true = (X532 @ (comp @ X537 @ X535) @ (sub @ X536 @ X535) @ X538)) | ($true = (X532 @ X537 @ X536 @ (comp @ X535 @ X538)))) | ~! [X539 : subst > term > term] : (($true = (X532 @ id @ (lam @ (X539 @ sh @ one)) @ id)) | ~! [X540 : subst,X541 : subst,X542 : term] : ((X539 @ (comp @ X540 @ X541) @ (sub @ X542 @ X541)) = (sub @ (X539 @ X540 @ X542) @ X541)) | ~! [X543 : term] : (($true = (X532 @ id @ (X539 @ id @ X543) @ id)) | ~($true = (X532 @ id @ X543 @ id)))) | ~! [X544 : subst,X545 : term,X546 : subst,X547 : subst] : (((X532 @ (comp @ X547 @ X546) @ (sub @ X545 @ X546) @ X544) = $true) | ~($true = (X532 @ X547 @ X545 @ (comp @ X546 @ X544)))) | ~! [X548 : term,X549 : term] : (((X532 @ id @ (ap @ (sub @ X548 @ id) @ X549) @ id) = $true) | ~($true = (X532 @ id @ X549 @ id)) | ~($true = (X532 @ id @ X548 @ id)))))))))),
% 32.37/5.95 inference(fool_elimination,[status(thm)],[f5])).
% 32.37/5.95 thf(f5,plain,(
% 32.37/5.95 (hoasinduction_lem3b <=> ! [X0 : term] : ~! [X1 : subst > term > term] : ((X1 @ sh @ one) != (sub @ X0 @ (push @ one @ sh)))) & axabs & hoasinduction_lem3_gthm & ! [X2 : subst] : ? [X3 : d_subst] : ((d2subst @ X3) = X2) & (! [X4 : subst] : ((comp @ X4 @ id) = X4) <=> axidr) & ((d2subst @ d_id) = id) & (hoasinduction <=> ! [X5 : term,X6 : subst > term > subst > $o] : (~! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (~(X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9) | (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) | ~! [X11 : term] : ((X6 @ id @ X11 @ id) | ~(var @ (sub @ X11 @ id))) | (X6 @ id @ X5 @ id) | ~! [X12 : subst > term > term] : (~! [X13 : term] : ((X6 @ id @ (X12 @ id @ X13) @ id) | ~(X6 @ id @ X13 @ id)) | ~! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) | (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id)) | ~! [X17 : subst,X18 : subst,X19 : term,X20 : subst] : ((X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20) | ~(X6 @ X17 @ X19 @ (comp @ X18 @ X20))) | ~! [X21 : term,X22 : term] : ((X6 @ id @ (ap @ (sub @ X22 @ id) @ X21) @ id) | ~(X6 @ id @ X21 @ id) | ~(X6 @ id @ X22 @ id)))) & (one = (d2term @ d_one)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X23 : term,X24 : subst > term > subst > $o,X25 : term,X26 : term > $o] : (~! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : ((X24 @ X27 @ X30 @ (comp @ X28 @ X29)) | ~(X24 @ (comp @ X27 @ X28) @ (sub @ X30 @ X28) @ X29)) | (X26 @ (ap @ X25 @ X23)) | ~! [X31 : term,X32 : term] : ((X24 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id) | ~(X24 @ id @ X32 @ id) | ~(X24 @ id @ X31 @ id)) | ~! [X33 : term,X34 : subst,X35 : subst,X36 : subst] : ((X24 @ (comp @ X34 @ X35) @ (sub @ X33 @ X35) @ X36) | ~(X24 @ X34 @ X33 @ (comp @ X35 @ X36))) | ~! [X37 : term] : ((X26 @ X37) = (X24 @ id @ X37 @ id)) | ~(X26 @ X23) | ~(X26 @ X25)) <=> hoasinduction_lem2v2) & pushprop & hoaslaminj_gthm & hoasinduction_lem2_gthm & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & pushprop_lem2v2_lthm & (! [X38 : term] : ~! [X39 : subst > term > term] : ((X39 @ sh @ one) != (sub @ X38 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X40 : term] : ~! [X41 : subst > term > term] : ~! [X42 : term,X43 : subst] : ((X41 @ X43 @ X42) = (sub @ X40 @ (push @ X42 @ X43)))) & ((^[X44 : subst, X45 : subst > term > term] : (d2term @ d_one)) = hoaslam) & induction2lem_gthm & pushprop_lthm & (apinj1 <=> ! [X46 : term,X47 : term,X48 : term,X49 : term] : (((ap @ X46 @ X49) != (ap @ X48 @ X47)) | (X46 = X48))) & ! [X50 : d_subst] : (d_id = X50) & (! [X51 : term > $o,X52 : subst,X53 : term] : ~! [X54 : term > $o] : ~! [X55 : term] : ((X54 @ X55) = (X51 @ (sub @ X55 @ (push @ X53 @ X52)))) <=> pushprop_lem0) & hoasinduction_lem2v2_gthm & hoaslamnotvar & (induction <=> ! [X56 : term,X57 : term > $o] : (~! [X58 : term] : (~(var @ X58) | (X57 @ X58)) | ~! [X59 : term] : ((X57 @ (lam @ X59)) | ~(X57 @ X59)) | ~! [X60 : term,X61 : term] : ((X57 @ (ap @ X60 @ X61)) | ~(X57 @ X61) | ~(X57 @ X60)) | (X57 @ X56))) & ~(var @ (d2term @ d_one)) & (hoasinduction_lem3 <=> ! [X62 : term,X63 : subst > term > subst > $o] : ((X63 @ id @ (lam @ X62) @ id) | ~! [X64 : term] : (~(X63 @ id @ X64 @ id) | (X63 @ id @ (sub @ X62 @ (push @ X64 @ id)) @ id)) | ~! [X65 : subst > term > term] : (~! [X66 : term] : (~(X63 @ id @ X66 @ id) | (X63 @ id @ (X65 @ id @ X66) @ id)) | (X63 @ id @ (lam @ (X65 @ sh @ one)) @ id) | ~! [X67 : term,X68 : subst,X69 : subst] : ((X65 @ (comp @ X69 @ X68) @ (sub @ X67 @ X68)) = (sub @ (X65 @ X69 @ X67) @ X68))) | ~! [X70 : subst,X71 : subst,X72 : subst,X73 : term] : (~(X63 @ X72 @ X73 @ (comp @ X71 @ X70)) | (X63 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X70)) | ~! [X74 : subst,X75 : subst,X76 : subst,X77 : term] : (~(X63 @ (comp @ X75 @ X76) @ (sub @ X77 @ X76) @ X74) | (X63 @ X75 @ X77 @ (comp @ X76 @ X74))))) & ((^[X78 : subst > term > subst > $o, X79 : term > $o] : (! [X80 : term] : ((X79 @ X80) = (X78 @ id @ X80 @ id)))) = hoasinduction_p_and_p_prime) & pushprop_lem1v2_gthm & (induction2lem <=> ! [X81 : term,X82 : subst,X83 : term > $o] : (~! [X84 : term] : ((X83 @ (lam @ X84)) | ~! [X85 : term] : (~(X83 @ X85) | (X83 @ (sub @ X84 @ (push @ X85 @ id))))) | ~! [X86 : term] : ((X83 @ (sub @ X86 @ X82)) | ~(var @ X86)) | (X83 @ (sub @ X81 @ X82)) | ~! [X87 : term,X88 : term] : ((X83 @ (ap @ X88 @ X87)) | ~(X83 @ X88) | ~(X83 @ X87)))) & ((! [X89 : term] : ((sub @ X89 @ id) = X89) => (! [X90 : term,X91 : term,X92 : term,X93 : term] : ((X90 = X91) | ((ap @ X90 @ X92) != (ap @ X91 @ X93))) => ! [X94 : term,X95 : term,X96 : term,X97 : term] : ((X94 = X97) | ((ap @ (sub @ X94 @ id) @ X96) != (ap @ (sub @ X97 @ id) @ X95))))) <=> hoasapinj1_lthm) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X98 : term,X99 : term] : (((lam @ X99) != (lam @ X98)) | (X98 = X99)) <=> laminj) & (hoasinduction_lem3_lthm <=> (! [X100 : term] : ((sub @ X100 @ id) = X100) => (! [X101 : term,X102 : subst > term > subst > $o] : (~! [X103 : subst > term > term] : (~! [X104 : term,X105 : subst,X106 : subst] : ((X103 @ (comp @ X106 @ X105) @ (sub @ X104 @ X105)) = (sub @ (X103 @ X106 @ X104) @ X105)) | (X102 @ id @ (lam @ (X103 @ sh @ one)) @ id) | ~! [X107 : term] : (~(X102 @ id @ X107 @ id) | (X102 @ id @ (X103 @ id @ X107) @ id))) | (X102 @ id @ (lam @ (sub @ X101 @ (push @ one @ sh))) @ id) | ~! [X108 : term] : (~(X102 @ id @ X108 @ id) | (X102 @ id @ (sub @ X101 @ (push @ X108 @ id)) @ id))) => ! [X109 : term,X110 : subst > term > subst > $o] : ((X110 @ id @ (lam @ X109) @ id) | ~! [X111 : subst > term > term] : (~! [X112 : term] : (~(X110 @ id @ X112 @ id) | (X110 @ id @ (X111 @ id @ X112) @ id)) | (X110 @ id @ (lam @ (X111 @ sh @ one)) @ id) | ~! [X113 : subst,X114 : term,X115 : subst] : ((sub @ (X111 @ X113 @ X114) @ X115) = (X111 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115)))) | ~! [X116 : subst,X117 : term,X118 : subst,X119 : subst] : (~(X110 @ X119 @ X117 @ (comp @ X116 @ X118)) | (X110 @ (comp @ X119 @ X116) @ (sub @ X117 @ X116) @ X118)) | ~! [X120 : term] : (~(X110 @ id @ X120 @ id) | (X110 @ id @ (sub @ X109 @ (push @ X120 @ id)) @ id)) | ~! [X121 : subst,X122 : subst,X123 : subst,X124 : term] : (~(X110 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122) | (X110 @ X121 @ X124 @ (comp @ X123 @ X122))))))) & ((! [X125 : term] : ((sub @ X125 @ id) = X125) => (! [X126 : term,X127 : subst > term > subst > $o] : (~! [X128 : subst > term > term] : (~! [X129 : term] : (~(X127 @ id @ X129 @ id) | (X127 @ id @ (X128 @ id @ X129) @ id)) | ~! [X130 : subst,X131 : subst,X132 : term] : ((sub @ (X128 @ X130 @ X132) @ X131) = (X128 @ (comp @ X130 @ X131) @ (sub @ X132 @ X131))) | (X127 @ id @ (lam @ (X128 @ sh @ one)) @ id)) | (X127 @ id @ (lam @ (sub @ X126 @ (push @ one @ sh))) @ id) | ~! [X133 : term] : ((X127 @ id @ (sub @ X126 @ (push @ X133 @ id)) @ id) | ~(X127 @ id @ X133 @ id))) => ! [X134 : subst > term > subst > $o,X135 : term] : ((X134 @ id @ (lam @ X135) @ id) | ~! [X136 : subst > term > term] : (~! [X137 : term] : ((X134 @ id @ (X136 @ id @ X137) @ id) | ~(X134 @ id @ X137 @ id)) | (X134 @ id @ (lam @ (X136 @ sh @ one)) @ id) | ~! [X138 : subst,X139 : subst,X140 : term] : ((X136 @ (comp @ X138 @ X139) @ (sub @ X140 @ X139)) = (sub @ (X136 @ X138 @ X140) @ X139))) | ~! [X141 : term] : ((X134 @ id @ (sub @ X135 @ (push @ X141 @ id)) @ id) | ~(X134 @ id @ X141 @ id))))) <=> hoasinduction_lem3a_lthm) & ((! [X142 : term] : ~! [X143 : subst > term > term] : ~! [X144 : term,X145 : subst] : ((sub @ X142 @ (push @ X144 @ X145)) = (X143 @ X145 @ X144)) => (! [X146 : term] : ((sub @ X146 @ id) = X146) => ! [X147 : term,X148 : subst > term > subst > $o,X149 : term > $o] : (~! [X150 : term] : ((X148 @ id @ X150 @ id) = (X149 @ X150)) | (X149 @ (lam @ X147)) | ~! [X151 : subst > term > term] : (~! [X152 : term,X153 : subst,X154 : subst] : ((sub @ (X151 @ X154 @ X152) @ X153) = (X151 @ (comp @ X154 @ X153) @ (sub @ X152 @ X153))) | ~! [X155 : term] : ((X148 @ id @ (X151 @ id @ X155) @ id) | ~(X148 @ id @ X155 @ id)) | (X148 @ id @ (lam @ (X151 @ sh @ one)) @ id)) | ~! [X156 : term] : (~(X149 @ X156) | (X149 @ (sub @ X147 @ (push @ X156 @ id))))))) <=> hoasinduction_lem3v2a_lthm) & hoasapinj1_gthm & (pushprop_lem1 <=> ! [X157 : term,X158 : subst,X159 : term > $o,X160 : term > $o,X161 : term] : (~(X160 @ X161) | (X159 @ (sub @ X161 @ (push @ X157 @ X158))))) & hoasinduction_lem1_lthm & (termmset_lthm <=> (! [X162 : term] : ((sub @ X162 @ id) = X162) => ! [X163 : term] : ((sub @ X163 @ id) = X163))) & hoasinduction_lem1 & pushprop_lem2v2_gthm & ulamvarind & (! [X164 : subst > term > subst > $o,X165 : term] : (~! [X166 : term] : ((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id) | ~(X164 @ id @ X166 @ id)) | ~! [X167 : subst > term > term] : ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id) | ~! [X168 : term] : ((X164 @ id @ (X167 @ id @ X168) @ id) | ~(X164 @ id @ X168 @ id)) | ~! [X169 : subst,X170 : subst,X171 : term] : ((X167 @ (comp @ X170 @ X169) @ (sub @ X171 @ X169)) = (sub @ (X167 @ X170 @ X171) @ X169))) | (X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X172 : term] : ((sub @ X172 @ id) = X172) <=> axvarid) & hoasinduction_lem3v2_gthm & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X173 : d_term,X174 : d_term] : (((d2term @ X174) = (d2term @ X173)) => (X173 = X174)) & hoasapnotvar_gthm & apnotvar & axapp & ~lamnotap & pushprop_lem1_gthm & ((! [X175 : term,X176 : subst] : ((sub @ one @ (push @ X175 @ X176)) = X175) => (! [X177 : term,X178 : subst] : ((comp @ sh @ (push @ X177 @ X178)) = X178) => (! [X179 : term,X180 : term] : ((X179 = X180) | ((lam @ X180) != (lam @ X179))) => ! [X181 : subst > term > term,X182 : subst,X183 : term,X184 : subst > term > term] : (~! [X185 : subst,X186 : term,X187 : subst] : ((X184 @ (comp @ X187 @ X185) @ (sub @ X186 @ X185)) = (sub @ (X184 @ X187 @ X186) @ X185)) | ~! [X188 : subst,X189 : subst,X190 : term] : ((sub @ (X181 @ X188 @ X190) @ X189) = (X181 @ (comp @ X188 @ X189) @ (sub @ X190 @ X189))) | ((X181 @ X182 @ X183) = (X184 @ X182 @ X183)) | ((lam @ (X184 @ sh @ one)) != (lam @ (X181 @ sh @ one))))))) <=> hoaslaminj_lthm) & lamnotvar & (shinj <=> ! [X191 : term,X192 : term] : ((X191 = X192) | ((sub @ X192 @ sh) != (sub @ X191 @ sh)))) & hoasinduction_gthm & hoasinduction_lem2_lthm & (apinj2 <=> ! [X193 : term,X194 : term,X195 : term,X196 : term] : (((ap @ X193 @ X196) != (ap @ X194 @ X195)) | (X195 = X196))) & (hoasinduction_lem3aaa <=> ! [X197 : term,X198 : subst > term > subst > $o] : ((X198 @ id @ (lam @ (sub @ X197 @ (push @ one @ sh))) @ id) | ~! [X199 : term] : ((X198 @ id @ (sub @ X197 @ (push @ X199 @ id)) @ id) | ~(X198 @ id @ X199 @ id)) | ~! [X200 : subst > term > term,X201 : term] : ((X198 @ id @ (lam @ (X200 @ sh @ one)) @ id) | ~! [X202 : term] : (~(X198 @ id @ X202 @ id) | (X198 @ id @ (X200 @ id @ X202) @ id)) | ~! [X203 : term,X204 : subst,X205 : subst] : ((sub @ (sub @ X201 @ (push @ X203 @ X204)) @ X205) = (sub @ (X200 @ X204 @ X203) @ X205)) | ~! [X206 : subst,X207 : term,X208 : subst] : ((X200 @ (comp @ X208 @ X206) @ (sub @ X207 @ X206)) = (sub @ X201 @ (push @ (sub @ X207 @ X206) @ (comp @ X208 @ X206))))))) & (hoasinduction_lem0 <=> ! [X209 : subst > term > subst > $o] : ~! [X210 : term > $o] : ~! [X211 : term] : ((X209 @ id @ X211 @ id) = (X210 @ X211))) & hoasapinj2_gthm & pushprop_lem2v2 & (! [X212 : subst,X213 : term,X214 : term > $o] : ~! [X215 : term > $o] : ~! [X216 : term] : ((X214 @ (sub @ X216 @ (push @ X213 @ X212))) = (X215 @ X216)) <=> pushprop_lem0_lthm) & (hoasapinj2 <=> ! [X217 : term,X218 : term,X219 : term,X220 : term] : ((X217 = X219) | ((ap @ (sub @ X220 @ id) @ X217) != (ap @ (sub @ X218 @ id) @ X219)))) & (! [X221 : subst > term > subst > $o] : ~! [X222 : term > $o] : ~! [X223 : term] : ((X221 @ id @ X223 @ id) = (X222 @ X223)) <=> hoasinduction_lem0_lthm) & hoasapnotvar & ((d2subst @ d_id) = sh) & ((! [X224 : subst > term > subst > $o] : ~! [X225 : term > $o] : ~! [X226 : term] : ((X224 @ id @ X226 @ id) = (X225 @ X226)) => (! [X227 : term > $o,X228 : term] : (~! [X229 : term] : ((X227 @ X229) | ~(var @ X229)) | ~! [X230 : term] : ((X227 @ (lam @ X230)) | ~! [X231 : term] : (~(X227 @ X231) | (X227 @ (sub @ X230 @ (push @ X231 @ id))))) | (X227 @ X228) | ~! [X232 : term,X233 : term] : (~(X227 @ X232) | ~(X227 @ X233) | (X227 @ (ap @ X233 @ X232)))) => (! [X234 : term] : ((sub @ X234 @ id) = X234) => (! [X235 : term,X236 : term > $o,X237 : subst > term > subst > $o] : ((X236 @ (lam @ X235)) | ~! [X238 : term] : ((X236 @ (sub @ X235 @ (push @ X238 @ id))) | ~(X236 @ X238)) | ~! [X239 : subst > term > term] : ((X237 @ id @ (lam @ (X239 @ sh @ one)) @ id) | ~! [X240 : term] : (~(X237 @ id @ X240 @ id) | (X237 @ id @ (X239 @ id @ X240) @ id)) | ~! [X241 : term,X242 : subst,X243 : subst] : ((sub @ (X239 @ X242 @ X241) @ X243) = (X239 @ (comp @ X242 @ X243) @ (sub @ X241 @ X243)))) | ~! [X244 : term] : ((X237 @ id @ X244 @ id) = (X236 @ X244))) => ! [X245 : subst > term > subst > $o,X246 : term] : ((X245 @ id @ X246 @ id) | ~! [X247 : term,X248 : term] : (~(X245 @ id @ X247 @ id) | (X245 @ id @ (ap @ (sub @ X247 @ id) @ X248) @ id) | ~(X245 @ id @ X248 @ id)) | ~! [X249 : subst > term > term] : ((X245 @ id @ (lam @ (X249 @ sh @ one)) @ id) | ~! [X250 : term] : (~(X245 @ id @ X250 @ id) | (X245 @ id @ (X249 @ id @ X250) @ id)) | ~! [X251 : subst,X252 : term,X253 : subst] : ((X249 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253)) = (sub @ (X249 @ X251 @ X252) @ X253)))))))) <=> hoasinduction_no_psi_cond_lthm) & substmonoid_gthm & pushprop_lem3v2_lthm & (! [X254 : term,X255 : term,X256 : subst > term > term] : (~! [X257 : term,X258 : subst,X259 : subst] : ((X256 @ (comp @ X259 @ X258) @ (sub @ X257 @ X258)) = (sub @ (X256 @ X259 @ X257) @ X258)) | ((lam @ (X256 @ sh @ one)) != (ap @ (sub @ X255 @ id) @ X254))) <=> hoaslamnotap) & pushprop_lem0_gthm & (hoasinduction_lem3aa_lthm <=> ! [X260 : subst > term > subst > $o,X261 : term] : (~! [X262 : term] : ((X260 @ id @ (sub @ X261 @ (push @ X262 @ id)) @ id) | ~(X260 @ id @ X262 @ id)) | (X260 @ id @ (lam @ (sub @ X261 @ (push @ one @ sh))) @ id) | ~! [X263 : subst > term > term] : (~! [X264 : subst,X265 : subst,X266 : term] : ((sub @ (X263 @ X264 @ X266) @ X265) = (X263 @ (comp @ X264 @ X265) @ (sub @ X266 @ X265))) | ~! [X267 : term] : (~(X260 @ id @ X267 @ id) | (X260 @ id @ (X263 @ id @ X267) @ id)) | (X260 @ id @ (lam @ (X263 @ sh @ one)) @ id)))) & (hoasinduction_lem3v2 <=> ! [X268 : term,X269 : term > $o,X270 : subst > term > subst > $o] : (~! [X271 : term,X272 : subst,X273 : subst,X274 : subst] : ((X270 @ (comp @ X274 @ X273) @ (sub @ X271 @ X273) @ X272) | ~(X270 @ X274 @ X271 @ (comp @ X273 @ X272))) | ~! [X275 : subst > term > term] : ((X270 @ id @ (lam @ (X275 @ sh @ one)) @ id) | ~! [X276 : term] : ((X270 @ id @ (X275 @ id @ X276) @ id) | ~(X270 @ id @ X276 @ id)) | ~! [X277 : subst,X278 : subst,X279 : term] : ((sub @ (X275 @ X277 @ X279) @ X278) = (X275 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)))) | ~! [X280 : term] : (~(X269 @ X280) | (X269 @ (sub @ X268 @ (push @ X280 @ id)))) | (X269 @ (lam @ X268)) | ~! [X281 : subst,X282 : subst,X283 : subst,X284 : term] : ((X270 @ X282 @ X284 @ (comp @ X281 @ X283)) | ~(X270 @ (comp @ X282 @ X281) @ (sub @ X284 @ X281) @ X283)) | ~! [X285 : term] : ((X269 @ X285) = (X270 @ id @ X285 @ id)))) & (! [X286 : subst,X287 : term] : ((comp @ sh @ (push @ X287 @ X286)) = X286) <=> axshiftcons) & hoasinduction_lem3b_gthm & termmset_gthm & axmap & (! [X288 : term > $o,X289 : term] : (~! [X290 : term] : (~! [X291 : term] : ((X288 @ (sub @ X290 @ (push @ X291 @ id))) | ~(X288 @ X291)) | (X288 @ (lam @ X290))) | ~! [X292 : term] : (~(var @ X292) | (X288 @ X292)) | ~! [X293 : term,X294 : term] : (~(X288 @ X294) | (X288 @ (ap @ X293 @ X294)) | ~(X288 @ X293)) | (X288 @ X289)) <=> induction2) & (! [X295 : subst] : ((comp @ id @ X295) = X295) <=> axidl) & ((! [X296 : term,X297 : subst] : ((sub @ one @ (push @ X296 @ X297)) = X296) => (! [X298 : subst,X299 : term] : ((comp @ sh @ (push @ X299 @ X298)) = X298) => ! [X300 : subst,X301 : term > $o,X302 : term > $o,X303 : term,X304 : term] : (~(X302 @ X304) | (X301 @ (sub @ X304 @ (push @ X303 @ X300)))))) <=> pushprop_lem1_lthm) & (pushprop_lem1v2 <=> ! [X305 : subst,X306 : term,X307 : term > $o,X308 : term > $o] : ((X308 @ one) | ~! [X309 : term] : ((X308 @ X309) = (X307 @ (sub @ X309 @ (push @ X306 @ X305)))) | ~(X307 @ X306))) & (! [X310 : term] : ((sub @ X310 @ id) = X310) <=> termmset) & hoaslamnotap_lthm & hoasinduction_lem1v2 & (hoasapinj2_lthm <=> (! [X311 : term,X312 : term,X313 : term,X314 : term] : (((ap @ X312 @ X313) != (ap @ X314 @ X311)) | (X311 = X313)) => ! [X315 : term,X316 : term,X317 : term,X318 : term] : ((X316 = X317) | ((ap @ (sub @ X318 @ id) @ X316) != (ap @ (sub @ X315 @ id) @ X317))))) & axvarshift & ~ulamvar1 & ((! [X319 : term,X320 : subst] : ((sub @ one @ (push @ X319 @ X320)) = X319) => (! [X321 : term,X322 : subst] : ((comp @ sh @ (push @ X321 @ X322)) = X322) => (! [X323 : subst] : ((comp @ X323 @ id) = X323) => (! [X324 : term > $o,X325 : term] : (~! [X326 : term] : ((X324 @ (lam @ X326)) | ~(X324 @ X326)) | (X324 @ X325) | ~! [X327 : term] : ((X324 @ X327) | ~(var @ X327)) | ~! [X328 : term,X329 : term] : (~(X324 @ X329) | (X324 @ (ap @ X328 @ X329)) | ~(X324 @ X328))) => ! [X330 : subst,X331 : term,X332 : term > $o] : (~! [X333 : term,X334 : term] : (~(X332 @ X334) | ~(X332 @ X333) | (X332 @ (ap @ X334 @ X333))) | ~! [X335 : term] : (~(var @ X335) | (X332 @ (sub @ X335 @ X330))) | ~! [X336 : term] : (~! [X337 : term] : (~(X332 @ X337) | (X332 @ (sub @ X336 @ (push @ X337 @ id)))) | (X332 @ (lam @ X336))) | (X332 @ (sub @ X331 @ X330))))))) <=> induction2lem_lthm) & hoasinduction_lem1v2_gthm & pushprop_lem3v2 & (! [X338 : term > $o,X339 : subst > term > subst > $o,X340 : term] : ((X338 @ (lam @ X340)) | ~! [X341 : subst > term > term] : (~! [X342 : subst,X343 : subst,X344 : term] : ((sub @ (X341 @ X343 @ X344) @ X342) = (X341 @ (comp @ X343 @ X342) @ (sub @ X344 @ X342))) | (X339 @ id @ (lam @ (X341 @ sh @ one)) @ id) | ~! [X345 : term] : (~(X339 @ id @ X345 @ id) | (X339 @ id @ (X341 @ id @ X345) @ id))) | ~! [X346 : term] : (~(X338 @ X346) | (X338 @ (sub @ X340 @ (push @ X346 @ id)))) | ~! [X347 : term] : ((X338 @ X347) = (X339 @ id @ X347 @ id))) <=> hoasinduction_lem3v2a) & induction2_gthm & ! [X348 : d_term] : (d_one = X348) & ((! [X349 : subst] : ((comp @ id @ X349) = X349) => (! [X350 : subst] : ((comp @ X350 @ id) = X350) => (! [X351 : subst] : ((comp @ id @ X351) = X351) & ! [X352 : subst] : ((comp @ X352 @ id) = X352)))) <=> substmonoid_lthm) & axassoc & hoasinduction_lem3a_gthm & hoaslamnotap_gthm & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X353 : d_subst,X354 : d_subst] : (((d2subst @ X354) = (d2subst @ X353)) => (X353 = X354)) & ((! [X355 : subst,X356 : term] : ((sub @ one @ (push @ X356 @ X355)) = X356) => ! [X357 : term > $o,X358 : term,X359 : term > $o,X360 : subst] : ((X359 @ one) | ~(X357 @ X358) | ~! [X361 : term] : ((X357 @ (sub @ X361 @ (push @ X358 @ X360))) = (X359 @ X361)))) <=> pushprop_lem1v2_lthm) & hoaslamnotvar_gthm & ulamvarsh & ((! [X362 : subst] : ((comp @ id @ X362) = X362) & ! [X363 : subst] : ((comp @ X363 @ id) = X363)) <=> substmonoid) & (hoasinduction_lem3v2_lthm <=> (! [X364 : term] : ((sub @ X364 @ id) = X364) => ! [X365 : subst > term > subst > $o,X366 : term,X367 : term > $o] : (~! [X368 : term] : ((X365 @ id @ X368 @ id) = (X367 @ X368)) | ~! [X369 : subst,X370 : subst,X371 : subst,X372 : term] : (~(X365 @ (comp @ X371 @ X370) @ (sub @ X372 @ X370) @ X369) | (X365 @ X371 @ X372 @ (comp @ X370 @ X369))) | ~! [X373 : subst > term > term] : (~! [X374 : term] : ((X365 @ id @ (X373 @ id @ X374) @ id) | ~(X365 @ id @ X374 @ id)) | (X365 @ id @ (lam @ (X373 @ sh @ one)) @ id) | ~! [X375 : subst,X376 : term,X377 : subst] : ((sub @ (X373 @ X375 @ X376) @ X377) = (X373 @ (comp @ X375 @ X377) @ (sub @ X376 @ X377)))) | ~! [X378 : subst,X379 : subst,X380 : subst,X381 : term] : (~(X365 @ X380 @ X381 @ (comp @ X378 @ X379)) | (X365 @ (comp @ X380 @ X378) @ (sub @ X381 @ X378) @ X379)) | ~! [X382 : term] : ((X367 @ (sub @ X366 @ (push @ X382 @ id))) | ~(X367 @ X382)) | (X367 @ (lam @ X366))))) & (hoasinduction_lem2 <=> ! [X383 : subst > term > subst > $o,X384 : term,X385 : term] : (~! [X386 : term,X387 : term] : (~(X383 @ id @ X386 @ id) | (X383 @ id @ (ap @ (sub @ X386 @ id) @ X387) @ id) | ~(X383 @ id @ X387 @ id)) | ~(X383 @ id @ X385 @ id) | (X383 @ id @ (ap @ X385 @ X384) @ id) | ~! [X388 : subst,X389 : term,X390 : subst,X391 : subst] : ((X383 @ X391 @ X389 @ (comp @ X388 @ X390)) | ~(X383 @ (comp @ X391 @ X388) @ (sub @ X389 @ X388) @ X390)) | ~(X383 @ id @ X384 @ id) | ~! [X392 : term,X393 : subst,X394 : subst,X395 : subst] : ((X383 @ (comp @ X395 @ X394) @ (sub @ X392 @ X394) @ X393) | ~(X383 @ X395 @ X392 @ (comp @ X394 @ X393))))) & (hoasinduction_lthm <=> (! [X396 : term > $o,X397 : term] : (~! [X398 : term] : (~(var @ X398) | (X396 @ X398)) | (X396 @ X397) | ~! [X399 : term] : (~! [X400 : term] : (~(X396 @ X400) | (X396 @ (sub @ X399 @ (push @ X400 @ id)))) | (X396 @ (lam @ X399))) | ~! [X401 : term,X402 : term] : ((X396 @ (ap @ X401 @ X402)) | ~(X396 @ X401) | ~(X396 @ X402))) => (! [X403 : term,X404 : term,X405 : subst > term > subst > $o] : (~! [X406 : subst,X407 : subst,X408 : term,X409 : subst] : (~(X405 @ (comp @ X407 @ X406) @ (sub @ X408 @ X406) @ X409) | (X405 @ X407 @ X408 @ (comp @ X406 @ X409))) | (X405 @ id @ (ap @ X403 @ X404) @ id) | ~(X405 @ id @ X403 @ id) | ~! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411) @ X413) | ~(X405 @ X412 @ X410 @ (comp @ X411 @ X413))) | ~(X405 @ id @ X404 @ id) | ~! [X414 : term,X415 : term] : (~(X405 @ id @ X414 @ id) | ~(X405 @ id @ X415 @ id) | (X405 @ id @ (ap @ (sub @ X414 @ id) @ X415) @ id))) => (! [X416 : subst > term > subst > $o,X417 : term] : ((X416 @ id @ (lam @ X417) @ id) | ~! [X418 : subst,X419 : term,X420 : subst,X421 : subst] : ((X416 @ (comp @ X420 @ X421) @ (sub @ X419 @ X421) @ X418) | ~(X416 @ X420 @ X419 @ (comp @ X421 @ X418))) | ~! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : (~(X416 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425) @ X422) | (X416 @ X423 @ X424 @ (comp @ X425 @ X422))) | ~! [X426 : subst > term > term] : (~! [X427 : term] : ((X416 @ id @ (X426 @ id @ X427) @ id) | ~(X416 @ id @ X427 @ id)) | (X416 @ id @ (lam @ (X426 @ sh @ one)) @ id) | ~! [X428 : subst,X429 : subst,X430 : term] : ((sub @ (X426 @ X429 @ X430) @ X428) = (X426 @ (comp @ X429 @ X428) @ (sub @ X430 @ X428)))) | ~! [X431 : term] : (~(X416 @ id @ X431 @ id) | (X416 @ id @ (sub @ X417 @ (push @ X431 @ id)) @ id))) => ! [X432 : term,X433 : subst > term > subst > $o] : (~! [X434 : term] : (~(var @ (sub @ X434 @ id)) | (X433 @ id @ X434 @ id)) | ~! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : ((X433 @ X435 @ X437 @ (comp @ X436 @ X438)) | ~(X433 @ (comp @ X435 @ X436) @ (sub @ X437 @ X436) @ X438)) | ~! [X439 : subst,X440 : subst,X441 : subst,X442 : term] : ((X433 @ (comp @ X441 @ X439) @ (sub @ X442 @ X439) @ X440) | ~(X433 @ X441 @ X442 @ (comp @ X439 @ X440))) | ~! [X443 : term,X444 : term] : ((X433 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id) | ~(X433 @ id @ X443 @ id) | ~(X433 @ id @ X444 @ id)) | ~! [X445 : subst > term > term] : ((X433 @ id @ (lam @ (X445 @ sh @ one)) @ id) | ~! [X446 : term] : ((X433 @ id @ (X445 @ id @ X446) @ id) | ~(X433 @ id @ X446 @ id)) | ~! [X447 : subst,X448 : subst,X449 : term] : ((X445 @ (comp @ X447 @ X448) @ (sub @ X449 @ X448)) = (sub @ (X445 @ X447 @ X449) @ X448))) | (X433 @ id @ X432 @ id)))))) & (! [X450 : term] : ~! [X451 : subst > term > term] : ~! [X452 : term,X453 : subst] : ((X451 @ X453 @ X452) = (sub @ X450 @ (push @ X452 @ X453))) <=> hoasinduction_lem3v2_f) & (! [X454 : term,X455 : subst] : ((sub @ one @ (push @ X454 @ X455)) = X454) <=> axvarcons) & (induction2_lthm <=> (! [X456 : term] : ((sub @ X456 @ id) = X456) => (! [X457 : subst,X458 : term > $o,X459 : term] : (~! [X460 : term,X461 : term] : ((X458 @ (ap @ X460 @ X461)) | ~(X458 @ X460) | ~(X458 @ X461)) | ~! [X462 : term] : (~(var @ X462) | (X458 @ (sub @ X462 @ X457))) | ~! [X463 : term] : ((X458 @ (lam @ X463)) | ~! [X464 : term] : ((X458 @ (sub @ X463 @ (push @ X464 @ id))) | ~(X458 @ X464))) | (X458 @ (sub @ X459 @ X457))) => ! [X465 : term > $o,X466 : term] : ((X465 @ X466) | ~! [X467 : term] : (~(var @ X467) | (X465 @ X467)) | ~! [X468 : term] : (~! [X469 : term] : ((X465 @ (sub @ X468 @ (push @ X469 @ id))) | ~(X465 @ X469)) | (X465 @ (lam @ X468))) | ~! [X470 : term,X471 : term] : ((X465 @ (ap @ X470 @ X471)) | ~(X465 @ X471) | ~(X465 @ X470)))))) & (! [X472 : term,X473 : subst > term > subst > $o] : (~! [X474 : subst > term > term] : (~! [X475 : term,X476 : subst,X477 : subst] : ((sub @ (X474 @ X477 @ X475) @ X476) = (X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) | (X473 @ id @ (lam @ (X474 @ sh @ one)) @ id) | ~! [X478 : term] : ((X473 @ id @ (X474 @ id @ X478) @ id) | ~(X473 @ id @ X478 @ id))) | ~! [X479 : term,X480 : term] : (~(X473 @ id @ X480 @ id) | (X473 @ id @ (ap @ (sub @ X479 @ id) @ X480) @ id) | ~(X473 @ id @ X479 @ id)) | (X473 @ id @ X472 @ id)) <=> hoasinduction_no_psi_cond) & (! [X481 : subst > term > subst > $o,X482 : term] : ((X481 @ id @ (lam @ X482) @ id) | ~! [X483 : subst > term > term] : ((X481 @ id @ (lam @ (X483 @ sh @ one)) @ id) | ~! [X484 : term] : (~(X481 @ id @ X484 @ id) | (X481 @ id @ (X483 @ id @ X484) @ id)) | ~! [X485 : term,X486 : subst,X487 : subst] : ((sub @ (X483 @ X487 @ X485) @ X486) = (X483 @ (comp @ X487 @ X486) @ (sub @ X485 @ X486)))) | ~! [X488 : term] : ((X481 @ id @ (sub @ X482 @ (push @ X488 @ id)) @ id) | ~(X481 @ id @ X488 @ id))) <=> hoasinduction_lem3a) & (hoasapinj1 <=> ! [X489 : term,X490 : term,X491 : term,X492 : term] : ((X489 = X491) | ((ap @ (sub @ X491 @ id) @ X492) != (ap @ (sub @ X489 @ id) @ X490)))) & hoaslamnotvar_lthm & (! [X493 : term,X494 : subst,X495 : subst > term > term,X496 : subst > term > term] : (((lam @ (X496 @ sh @ one)) != (lam @ (X495 @ sh @ one))) | ((X496 @ X494 @ X493) = (X495 @ X494 @ X493)) | ~! [X497 : subst,X498 : subst,X499 : term] : ((X496 @ (comp @ X497 @ X498) @ (sub @ X499 @ X498)) = (sub @ (X496 @ X497 @ X499) @ X498)) | ~! [X500 : subst,X501 : subst,X502 : term] : ((sub @ (X495 @ X500 @ X502) @ X501) = (X495 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501)))) <=> hoaslaminj) & hoasinduction_lem1_gthm & pushprop_gthm & axclos & ((^[X503 : term, X504 : subst, X505 : term > $o, X506 : term > $o] : (! [X507 : term] : ((X505 @ (sub @ X507 @ (push @ X503 @ X504))) = (X506 @ X507)))) = pushprop_p_and_p_prime) & (! [X508 : subst] : ((push @ (sub @ one @ X508) @ (comp @ sh @ X508)) = X508) <=> axscons) & hoasapnotvar_lthm & ! [X509 : term] : ? [X510 : d_term] : ((d2term @ X510) = X509) & pushprop_lthm_orig & (hoasinduction_lthm_3 <=> (! [X511 : subst > term > subst > $o] : ~! [X512 : term > $o] : ~! [X513 : term] : ((X512 @ X513) = (X511 @ id @ X513 @ id)) => (! [X514 : term > $o,X515 : term] : (~! [X516 : term,X517 : term] : ((X514 @ (ap @ X517 @ X516)) | ~(X514 @ X517) | ~(X514 @ X516)) | ~! [X518 : term] : ((X514 @ X518) | ~(var @ X518)) | (X514 @ X515) | ~! [X519 : term] : (~! [X520 : term] : (~(X514 @ X520) | (X514 @ (sub @ X519 @ (push @ X520 @ id)))) | (X514 @ (lam @ X519)))) => (! [X521 : term] : ((sub @ X521 @ id) = X521) => (! [X522 : term,X523 : subst > term > subst > $o,X524 : term > $o] : (~! [X525 : subst > term > term] : (~! [X526 : subst,X527 : term,X528 : subst] : ((sub @ (X525 @ X526 @ X527) @ X528) = (X525 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528))) | (X523 @ id @ (lam @ (X525 @ sh @ one)) @ id) | ~! [X529 : term] : (~(X523 @ id @ X529 @ id) | (X523 @ id @ (X525 @ id @ X529) @ id))) | (X524 @ (lam @ X522)) | ~! [X530 : term] : (~(X524 @ X530) | (X524 @ (sub @ X522 @ (push @ X530 @ id)))) | ~! [X531 : term] : ((X523 @ id @ X531 @ id) = (X524 @ X531))) => ! [X532 : subst > term > subst > $o,X533 : term] : ((X532 @ id @ X533 @ id) | ~! [X534 : term] : (~(var @ (sub @ X534 @ id)) | (X532 @ id @ X534 @ id)) | ~! [X535 : subst,X536 : term,X537 : subst,X538 : subst] : (~(X532 @ (comp @ X537 @ X535) @ (sub @ X536 @ X535) @ X538) | (X532 @ X537 @ X536 @ (comp @ X535 @ X538))) | ~! [X539 : subst > term > term] : ((X532 @ id @ (lam @ (X539 @ sh @ one)) @ id) | ~! [X540 : subst,X541 : subst,X542 : term] : ((X539 @ (comp @ X540 @ X541) @ (sub @ X542 @ X541)) = (sub @ (X539 @ X540 @ X542) @ X541)) | ~! [X543 : term] : ((X532 @ id @ (X539 @ id @ X543) @ id) | ~(X532 @ id @ X543 @ id))) | ~! [X544 : subst,X545 : term,X546 : subst,X547 : subst] : ((X532 @ (comp @ X547 @ X546) @ (sub @ X545 @ X546) @ X544) | ~(X532 @ X547 @ X545 @ (comp @ X546 @ X544))) | ~! [X548 : term,X549 : term] : ((X532 @ id @ (ap @ (sub @ X548 @ id) @ X549) @ id) | ~(X532 @ id @ X549 @ id) | ~(X532 @ id @ X548 @ id))))))))),
% 32.37/5.95 inference(rectify,[status(thm)],[f1])).
% 32.37/5.95 thf(f1,axiom,(
% 32.37/5.95 (hoasinduction_lem3b <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh)))) & axabs & hoasinduction_lem3_gthm & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & (! [X14 : subst] : ((comp @ X14 @ id) = X14) <=> axidr) & ((d2subst @ d_id) = id) & (hoasinduction <=> ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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)) | ~! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & (one = (d2term @ d_one)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X45 : term,X10 : subst > term > subst > $o,X44 : term,X11 : term > $o] : (~! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (ap @ X44 @ X45)) | ~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~(X11 @ X45) | ~(X11 @ X44)) <=> hoasinduction_lem2v2) & pushprop & hoaslaminj_gthm & hoasinduction_lem2_gthm & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & pushprop_lem2v2_lthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13))) & ((^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one)) = hoaslam) & induction2lem_gthm & pushprop_lthm & (apinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15))) & ! [X5 : d_subst] : (d_id = X5) & (! [X10 : term > $o,X14 : subst,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0) & hoasinduction_lem2v2_gthm & hoaslamnotvar & (induction <=> ! [X21 : term,X10 : term > $o] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X21))) & ~(var @ (d2term @ d_one)) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ X27) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & ((^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) = hoasinduction_p_and_p_prime) & pushprop_lem1v2_gthm & (induction2lem <=> ! [X16 : term,X17 : subst,X10 : term > $o] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X15 : term,X13 : term,X20 : term,X19 : term] : ((X13 = X15) | ((ap @ X13 @ X19) != (ap @ X15 @ X20))) => ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj1_lthm) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X13 : term,X15 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) <=> laminj) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X27 : term,X10 : subst > term > subst > $o] : ((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) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : 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)) | ~! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & ((! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X42 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X10 : subst > term > subst > $o,X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))))) <=> hoasinduction_lem3a_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,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))))) <=> hoasinduction_lem3v2a_lthm) & hoasapinj1_gthm & (pushprop_lem1 <=> ! [X15 : term,X14 : subst,X26 : term > $o,X10 : term > $o,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & hoasinduction_lem1_lthm & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & hoasinduction_lem1 & pushprop_lem2v2_gthm & ulamvarind & (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & hoasinduction_lem3v2_gthm & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & hoasapnotvar_gthm & apnotvar & axapp & ~lamnotap & pushprop_lem1_gthm & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X15 : term,X13 : term] : ((X13 = X15) | ((lam @ X13) != (lam @ X15))) => ! [X31 : subst > term > term,X32 : subst,X33 : term,X18 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))))))) <=> hoaslaminj_lthm) & lamnotvar & (shinj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | ((sub @ X13 @ sh) != (sub @ X15 @ sh)))) & hoasinduction_gthm & hoasinduction_lem2_lthm & (apinj2 <=> ! [X13 : term,X15 : term,X20 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term,X35 : term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X37 : term,X36 : subst,X38 : subst] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | ~! [X41 : subst,X40 : term,X39 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))))) & (hoasinduction_lem0 <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & hoasapinj2_gthm & pushprop_lem2v2 & (! [X14 : subst,X13 : term,X10 : term > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) <=> pushprop_lem0_lthm) & (hoasapinj2 <=> ! [X20 : term,X13 : term,X19 : term,X15 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0_lthm) & hoasapnotvar & ((d2subst @ d_id) = sh) & ((! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X29 : term,X11 : term > $o,X10 : subst > term > subst > $o] : ((X11 @ (lam @ X29)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) => ! [X10 : subst > term > subst > $o,X30 : term] : ((X10 @ id @ X30 @ id) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) <=> hoasinduction_no_psi_cond_lthm) & substmonoid_gthm & pushprop_lem3v2_lthm & (! [X47 : term,X46 : term,X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47))) <=> hoaslamnotap) & pushprop_lem0_gthm & (hoasinduction_lem3aa_lthm <=> ! [X10 : subst > term > subst > $o,X42 : term] : (~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))) & (hoasinduction_lem3v2 <=> ! [X48 : term,X11 : term > $o,X10 : subst > term > subst > $o] : (~! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [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)))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) & (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) <=> axshiftcons) & hoasinduction_lem3b_gthm & termmset_gthm & axmap & (! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22)) <=> induction2) & (! [X14 : subst] : ((comp @ id @ X14) = X14) <=> axidl) & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X14 : subst,X26 : term > $o,X10 : term > $o,X15 : term,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & (pushprop_lem1v2 <=> ! [X14 : subst,X13 : term,X10 : term > $o,X11 : term > $o] : ((X11 @ one) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | ~(X10 @ X13))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & hoaslamnotap_lthm & hoasinduction_lem1v2 & (hoasapinj2_lthm <=> (! [X20 : term,X13 : term,X19 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) => ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X19 = X20) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20))))) & axvarshift & ~ulamvar1 & ((! [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)) | (X10 @ X21) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => ! [X17 : subst,X16 : term,X10 : term > $o] : (~! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17))))))) <=> induction2lem_lthm) & hoasinduction_lem1v2_gthm & pushprop_lem3v2 & (! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : ((X11 @ (lam @ X29)) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) <=> hoasinduction_lem3v2a) & induction2_gthm & ! [X1 : d_term] : (d_one = X1) & ((! [X14 : subst] : ((comp @ id @ X14) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14)))) <=> substmonoid_lthm) & axassoc & hoasinduction_lem3a_gthm & hoaslamnotap_gthm & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & ! [X6 : d_subst,X7 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & ((! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X10 : term > $o,X13 : term,X11 : term > $o,X14 : subst] : ((X11 @ one) | ~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2_lthm) & hoaslamnotvar_gthm & ulamvarsh & ((! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14)) <=> substmonoid) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X48 : term,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X48))))) & (hoasinduction_lem2 <=> ! [X10 : subst > term > subst > $o,X24 : term,X23 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id) | ~! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lthm <=> (! [X10 : term > $o,X22 : term] : (~! [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))) => (! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : (~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) => (! [X10 : subst > term > subst > $o,X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ 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)))) | (X10 @ id @ X28 @ id)))))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & (induction2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X17 : subst,X10 : term > $o,X16 : term] : (~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17))) => ! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))))) & (! [X30 : term,X10 : subst > term > subst > $o] : (~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & (! [X10 : subst > term > subst > $o,X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3a) & (hoasapinj1 <=> ! [X15 : term,X20 : term,X13 : term,X19 : term] : ((X13 = X15) | ((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)))) & hoaslamnotvar_lthm & (! [X33 : term,X32 : subst,X18 : subst > term > term,X31 : subst > term > term] : (((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) <=> hoaslaminj) & hoasinduction_lem1_gthm & pushprop_gthm & axclos & ((^[X13 : term, X14 : subst, X10 : term > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) = pushprop_p_and_p_prime) & (! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14) <=> axscons) & hoasapnotvar_lthm & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & pushprop_lthm_orig & (hoasinduction_lthm_3 <=> (! [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 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X29 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X18 : subst > term > term] : (~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) => ! [X10 : subst > term > subst > $o,X28 : term] : ((X10 @ id @ X28 @ id) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id))))))))),
% 32.37/5.95 file('/export/starexec/sandbox2/tmp/tmp.CDduru1qPi/DTF2THF_30868.p',alg444_1)).
% 32.37/5.95 thf(f1197,plain,(
% 32.37/5.95 ( ! [X77 : term] : (((d2term @ (sK491 @ X77)) = X77)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f11387,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)))) ) | (~spl591_577 | ~spl591_682)),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f5282,f6182])).
% 32.37/5.95 thf(f5282,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1) @ (d2subst @ d_id))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1)) @ (d2subst @ d_id)))) ) | ~spl591_577),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5281])).
% 32.37/5.95 thf(f5281,definition,(
% 32.37/5.95 spl591_577 <=> ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1) @ (d2subst @ d_id))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1)) @ (d2subst @ d_id))))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_577])],[avatar_definition])).
% 32.37/5.95 thf(f11385,plain,(
% 32.37/5.95 spl591_732 | spl591_731 | ~spl591_580),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f11384,f5295,f7084,f7087])).
% 32.37/5.95 thf(f5295,definition,(
% 32.37/5.95 spl591_580 <=> ! [X2 : subst,X4 : subst,X1 : term,X3 : subst] : (((sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X4) @ X3) = $false) | ((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_580])],[avatar_definition])).
% 32.37/5.95 thf(f11384,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term] : (((sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ X3) = $false) | ((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true)) ) | ~spl591_580),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5296,f5725])).
% 32.37/5.95 thf(f5296,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true) | ((sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X4) @ X3) = $false)) ) | ~spl591_580),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5295])).
% 32.37/5.95 thf(f11383,plain,(
% 32.37/5.95 spl591_661 | ~spl591_680),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f11382])).
% 32.37/5.95 thf(f11382,plain,(
% 32.37/5.95 $false | (spl591_661 | ~spl591_680)),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f11358,f5979])).
% 32.37/5.95 thf(f5979,plain,(
% 32.37/5.95 ($true != (sP42 @ sK178)) | spl591_661),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5977])).
% 32.37/5.95 thf(f5977,definition,(
% 32.37/5.95 spl591_661 <=> ($true = (sP42 @ sK178))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_661])],[avatar_definition])).
% 32.37/5.95 thf(f11358,plain,(
% 32.37/5.95 ($true = (sP42 @ sK178)) | ~spl591_680),
% 32.37/5.95 inference(trivial_inequality_removal,[status(thm)],[f11350])).
% 32.37/5.95 thf(f11350,plain,(
% 32.37/5.95 ($true != $true) | ($true = (sP42 @ sK178)) | ~spl591_680),
% 32.37/5.95 inference(superposition,[status(thm)],[f6165,f5901])).
% 32.37/5.95 thf(f5901,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((sP42 @ X0) = $true)) )),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f5900,f5865])).
% 32.37/5.95 thf(f5865,plain,(
% 32.37/5.95 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ X10 @ (d2subst @ d_id)) != $true)) )),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f5814,f5838])).
% 32.37/5.95 thf(f5838,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (sP25 @ X0))) )),
% 32.37/5.95 inference(duplicate_literal_removal,[status(thm)],[f5837])).
% 32.37/5.95 thf(f5837,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (sP25 @ X0))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5836,f5725])).
% 32.37/5.95 thf(f5836,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (sP25 @ X0)) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5835,f5725])).
% 32.37/5.95 thf(f5835,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (sP25 @ X0)) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true)) )),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f5834,f5725])).
% 32.37/5.95 thf(f5834,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((d2term @ d_one) != (X1 @ (d2subst @ d_id) @ (sub @ (d2term @ d_one) @ (d2subst @ d_id)))) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (sP25 @ X0))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5780,f5725])).
% 32.37/5.95 thf(f5780,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X1 @ (d2subst @ d_id) @ (sub @ (d2term @ d_one) @ (d2subst @ d_id))) != (sub @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one)) @ (d2subst @ d_id))) | ($true = (sP25 @ X0)) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true)) )),
% 32.37/5.95 inference(backward_demodulation,[status(thm)],[f4252,f5725])).
% 32.37/5.95 thf(f4252,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((sub @ (X1 @ (d2subst @ d_id) @ (sK296 @ X1)) @ (d2subst @ d_id)) != (X1 @ (d2subst @ d_id) @ (sub @ (sK296 @ X1) @ (d2subst @ d_id)))) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (sP25 @ X0))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f4251,f4214])).
% 32.37/5.95 thf(f4214,plain,(
% 32.37/5.95 ( ! [X208 : subst] : (((d2subst @ d_id) = X208)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f1078,f1249])).
% 32.37/5.95 thf(f1249,plain,(
% 32.37/5.95 ( ! [X0 : d_subst] : ((d_id = X0)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f1078,plain,(
% 32.37/5.95 ( ! [X208 : subst] : (((d2subst @ (sK555 @ X208)) = X208)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f4251,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sub @ (X1 @ (d2subst @ d_id) @ (sK296 @ X1)) @ (d2subst @ d_id)) != (X1 @ (comp @ (d2subst @ d_id) @ (d2subst @ d_id)) @ (sub @ (sK296 @ X1) @ (d2subst @ d_id)))) | ($true = (sP25 @ X0)) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f4222,f4214])).
% 32.37/5.95 thf(f4222,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ((X1 @ (comp @ (d2subst @ d_id) @ (sK295 @ X1)) @ (sub @ (sK296 @ X1) @ (sK295 @ X1))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK296 @ X1)) @ (sK295 @ X1))) | ($true = (sP25 @ X0))) )),
% 32.37/5.95 inference(backward_demodulation,[status(thm)],[f1469,f4214])).
% 32.37/5.95 thf(f1469,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X1 @ (comp @ (sK294 @ X1) @ (sK295 @ X1)) @ (sub @ (sK296 @ X1) @ (sK295 @ X1))) != (sub @ (X1 @ (sK294 @ X1) @ (sK296 @ X1)) @ (sK295 @ X1))) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ($true = (sP25 @ X0)) | ((X0 @ (d2subst @ d_id) @ (sK297 @ X1 @ X0) @ (d2subst @ d_id)) = $true)) )),
% 32.37/5.95 inference(definition_unfolding,[status(thm)],[f834,f1208,f1098,f1089,f1208,f1208,f1208])).
% 32.37/5.95 thf(f1089,plain,(
% 32.37/5.95 (one = (d2term @ d_one))),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f1098,plain,(
% 32.37/5.95 ((d2subst @ d_id) = sh)),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f1208,plain,(
% 32.37/5.95 ((d2subst @ d_id) = id)),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f834,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (sP25 @ X0)) | ((X1 @ (comp @ (sK294 @ X1) @ (sK295 @ X1)) @ (sub @ (sK296 @ X1) @ (sK295 @ X1))) != (sub @ (X1 @ (sK294 @ X1) @ (sK296 @ X1)) @ (sK295 @ X1))) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ((X0 @ id @ (sK297 @ X1 @ X0) @ id) = $true)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f306])).
% 32.37/5.95 thf(f306,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : ((($true = (sP25 @ X0)) | ! [X1 : subst > term > term] : (((X1 @ (comp @ (sK294 @ X1) @ (sK295 @ X1)) @ (sub @ (sK296 @ X1) @ (sK295 @ X1))) != (sub @ (X1 @ (sK294 @ X1) @ (sK296 @ X1)) @ (sK295 @ X1))) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | (($true != (X0 @ id @ (X1 @ id @ (sK297 @ X1 @ X0)) @ id)) & ((X0 @ id @ (sK297 @ X1 @ X0) @ id) = $true)))) & ((! [X7 : subst,X8 : subst,X9 : term] : ((sK298 @ X0 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8)) = (sub @ (sK298 @ X0 @ X7 @ X9) @ X8)) & ((X0 @ id @ (lam @ (sK298 @ X0 @ sh @ one)) @ id) != $true) & ! [X10 : term] : (($true = (X0 @ id @ (sK298 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) | ($true != (sP25 @ X0))))),
% 32.37/5.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK294,sK295,sK296,sK297,sK298])],[f302,f305,f304,f303])).
% 32.37/5.95 thf(f303,plain,(
% 32.37/5.95 ! [X1 : subst > term > term] : (? [X2 : subst,X3 : subst,X4 : term] : ((sub @ (X1 @ X2 @ X4) @ X3) != (X1 @ (comp @ X2 @ X3) @ (sub @ X4 @ X3))) => ((X1 @ (comp @ (sK294 @ X1) @ (sK295 @ X1)) @ (sub @ (sK296 @ X1) @ (sK295 @ X1))) != (sub @ (X1 @ (sK294 @ X1) @ (sK296 @ X1)) @ (sK295 @ X1))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f304,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X5 : term] : (($true != (X0 @ id @ (X1 @ id @ X5) @ id)) & ($true = (X0 @ id @ X5 @ id))) => (($true != (X0 @ id @ (X1 @ id @ (sK297 @ X1 @ X0)) @ id)) & ((X0 @ id @ (sK297 @ X1 @ X0) @ id) = $true)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f305,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (! [X7 : subst,X8 : subst,X9 : term] : ((X6 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8)) = (sub @ (X6 @ X7 @ X9) @ X8)) & ($true != (X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) & ! [X10 : term] : (($true = (X0 @ id @ (X6 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) => (! [X9 : term,X8 : subst,X7 : subst] : ((sK298 @ X0 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8)) = (sub @ (sK298 @ X0 @ X7 @ X9) @ X8)) & ((X0 @ id @ (lam @ (sK298 @ X0 @ sh @ one)) @ id) != $true) & ! [X10 : term] : (($true = (X0 @ id @ (sK298 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f302,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : ((($true = (sP25 @ X0)) | ! [X1 : subst > term > term] : (? [X2 : subst,X3 : subst,X4 : term] : ((sub @ (X1 @ X2 @ X4) @ X3) != (X1 @ (comp @ X2 @ X3) @ (sub @ X4 @ X3))) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) | ? [X5 : term] : (($true != (X0 @ id @ (X1 @ id @ X5) @ id)) & ($true = (X0 @ id @ X5 @ id))))) & (? [X6 : subst > term > term] : (! [X7 : subst,X8 : subst,X9 : term] : ((X6 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8)) = (sub @ (X6 @ X7 @ X9) @ X8)) & ($true != (X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) & ! [X10 : term] : (($true = (X0 @ id @ (X6 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)))) | ($true != (sP25 @ X0))))),
% 32.37/5.95 inference(rectify,[status(thm)],[f301])).
% 32.37/5.95 thf(f301,plain,(
% 32.37/5.95 ! [X265 : subst > term > subst > $o] : ((($true = (sP25 @ X265)) | ! [X270 : subst > term > term] : (? [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) != (sub @ (X270 @ X272 @ X274) @ X273)) | ($true = (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) | ? [X271 : term] : (($true != (X265 @ id @ (X270 @ id @ X271) @ id)) & ($true = (X265 @ id @ X271 @ id))))) & (? [X270 : subst > term > term] : (! [X272 : subst,X273 : subst,X274 : term] : ((X270 @ (comp @ X272 @ X273) @ (sub @ X274 @ X273)) = (sub @ (X270 @ X272 @ X274) @ X273)) & ($true != (X265 @ id @ (lam @ (X270 @ sh @ one)) @ id)) & ! [X271 : term] : (($true = (X265 @ id @ (X270 @ id @ X271) @ id)) | ($true != (X265 @ id @ X271 @ id)))) | ($true != (sP25 @ X265))))),
% 32.37/5.95 inference(nnf_transformation,[status(thm)],[f39])).
% 32.37/5.95 thf(f5814,plain,(
% 32.37/5.95 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true != (sP25 @ X0)) | ((X0 @ (d2subst @ d_id) @ X10 @ (d2subst @ d_id)) != $true) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(backward_demodulation,[status(thm)],[f1471,f5725])).
% 32.37/5.95 thf(f1471,plain,(
% 32.37/5.95 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (sK298 @ X0 @ (d2subst @ d_id) @ X10) @ (d2subst @ d_id))) | ($true != (sP25 @ X0)) | ((X0 @ (d2subst @ d_id) @ X10 @ (d2subst @ d_id)) != $true)) )),
% 32.37/5.95 inference(definition_unfolding,[status(thm)],[f831,f1208,f1208,f1208,f1208,f1208])).
% 32.37/5.95 thf(f831,plain,(
% 32.37/5.95 ( ! [X10 : term,X0 : subst > term > subst > $o] : (($true = (X0 @ id @ (sK298 @ X0 @ id @ X10) @ id)) | ($true != (X0 @ id @ X10 @ id)) | ($true != (sP25 @ X0))) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f306])).
% 32.37/5.95 thf(f5900,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP42 @ X0) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5899,f5725])).
% 32.37/5.95 thf(f5899,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP42 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f5898,f5725])).
% 32.37/5.95 thf(f5898,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ((sP42 @ X0) = $true) | ((d2term @ d_one) != (X1 @ (d2subst @ d_id) @ (sub @ (d2term @ d_one) @ (d2subst @ d_id)))) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5777,f5725])).
% 32.37/5.95 thf(f5777,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X1 @ (d2subst @ d_id) @ (sub @ (d2term @ d_one) @ (d2subst @ d_id))) != (sub @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one)) @ (d2subst @ d_id))) | ((sP42 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(backward_demodulation,[status(thm)],[f5418,f5725])).
% 32.37/5.95 thf(f5418,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sub @ (X1 @ (d2subst @ d_id) @ (sK191 @ X1)) @ (d2subst @ d_id)) != (X1 @ (d2subst @ d_id) @ (sub @ (sK191 @ X1) @ (d2subst @ d_id)))) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((sP42 @ X0) = $true)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5417,f4214])).
% 32.37/5.95 thf(f5417,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (sub @ (sK191 @ X1) @ (sK190 @ X1))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK191 @ X1)) @ (sK190 @ X1))) | ((sP42 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5416,f4214])).
% 32.37/5.95 thf(f5416,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP42 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (sub @ (sK191 @ X1) @ (sK190 @ X1))) != (sub @ (X1 @ (sK192 @ X1) @ (sK191 @ X1)) @ (sK190 @ X1)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f1388,f4214])).
% 32.37/5.95 thf(f1388,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP42 @ X0) = $true) | ((sub @ (X1 @ (sK192 @ X1) @ (sK191 @ X1)) @ (sK190 @ X1)) != (X1 @ (comp @ (sK192 @ X1) @ (sK190 @ X1)) @ (sub @ (sK191 @ X1) @ (sK190 @ X1)))) | ((X0 @ (d2subst @ d_id) @ (sK193 @ X1 @ X0) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (lam @ (X1 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(definition_unfolding,[status(thm)],[f702,f1208,f1208,f1208,f1098,f1089,f1208])).
% 32.37/5.95 thf(f702,plain,(
% 32.37/5.95 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP42 @ X0) = $true) | ((sub @ (X1 @ (sK192 @ X1) @ (sK191 @ X1)) @ (sK190 @ X1)) != (X1 @ (comp @ (sK192 @ X1) @ (sK190 @ X1)) @ (sub @ (sK191 @ X1) @ (sK190 @ X1)))) | ($true = (X0 @ id @ (sK193 @ X1 @ X0) @ id)) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id))) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f200])).
% 32.37/5.95 thf(f200,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : ((((sP42 @ X0) = $true) | ! [X1 : subst > term > term] : (((sub @ (X1 @ (sK192 @ X1) @ (sK191 @ X1)) @ (sK190 @ X1)) != (X1 @ (comp @ (sK192 @ X1) @ (sK190 @ X1)) @ (sub @ (sK191 @ X1) @ (sK190 @ X1)))) | (($true = (X0 @ id @ (sK193 @ X1 @ X0) @ id)) & ($true != (X0 @ id @ (X1 @ id @ (sK193 @ X1 @ X0)) @ id))) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)))) & ((! [X7 : subst,X8 : term,X9 : subst] : ((sK194 @ X0 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)) = (sub @ (sK194 @ X0 @ X9 @ X8) @ X7)) & ! [X10 : term] : (($true != (X0 @ id @ X10 @ id)) | ($true = (X0 @ id @ (sK194 @ X0 @ id @ X10) @ id))) & ($true != (X0 @ id @ (lam @ (sK194 @ X0 @ sh @ one)) @ id))) | ((sP42 @ X0) != $true)))),
% 32.37/5.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191,sK192,sK193,sK194])],[f196,f199,f198,f197])).
% 32.37/5.95 thf(f197,plain,(
% 32.37/5.95 ! [X1 : subst > term > term] : (? [X2 : subst,X3 : term,X4 : subst] : ((sub @ (X1 @ X4 @ X3) @ X2) != (X1 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) => ((sub @ (X1 @ (sK192 @ X1) @ (sK191 @ X1)) @ (sK190 @ X1)) != (X1 @ (comp @ (sK192 @ X1) @ (sK190 @ X1)) @ (sub @ (sK191 @ X1) @ (sK190 @ X1)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f198,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X5 : term] : (($true = (X0 @ id @ X5 @ id)) & ($true != (X0 @ id @ (X1 @ id @ X5) @ id))) => (($true = (X0 @ id @ (sK193 @ X1 @ X0) @ id)) & ($true != (X0 @ id @ (X1 @ id @ (sK193 @ X1 @ X0)) @ id))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f199,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : (? [X6 : subst > term > term] : (! [X7 : subst,X8 : term,X9 : subst] : ((X6 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)) = (sub @ (X6 @ X9 @ X8) @ X7)) & ! [X10 : term] : (($true != (X0 @ id @ X10 @ id)) | ($true = (X0 @ id @ (X6 @ id @ X10) @ id))) & ($true != (X0 @ id @ (lam @ (X6 @ sh @ one)) @ id))) => (! [X9 : subst,X8 : term,X7 : subst] : ((sK194 @ X0 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)) = (sub @ (sK194 @ X0 @ X9 @ X8) @ X7)) & ! [X10 : term] : (($true != (X0 @ id @ X10 @ id)) | ($true = (X0 @ id @ (sK194 @ X0 @ id @ X10) @ id))) & ($true != (X0 @ id @ (lam @ (sK194 @ X0 @ sh @ one)) @ id))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f196,plain,(
% 32.37/5.95 ! [X0 : subst > term > subst > $o] : ((((sP42 @ X0) = $true) | ! [X1 : subst > term > term] : (? [X2 : subst,X3 : term,X4 : subst] : ((sub @ (X1 @ X4 @ X3) @ X2) != (X1 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) | ? [X5 : term] : (($true = (X0 @ id @ X5 @ id)) & ($true != (X0 @ id @ (X1 @ id @ X5) @ id))) | ($true = (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)))) & (? [X6 : subst > term > term] : (! [X7 : subst,X8 : term,X9 : subst] : ((X6 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)) = (sub @ (X6 @ X9 @ X8) @ X7)) & ! [X10 : term] : (($true != (X0 @ id @ X10 @ id)) | ($true = (X0 @ id @ (X6 @ id @ X10) @ id))) & ($true != (X0 @ id @ (lam @ (X6 @ sh @ one)) @ id))) | ((sP42 @ X0) != $true)))),
% 32.37/5.95 inference(rectify,[status(thm)],[f195])).
% 32.37/5.95 thf(f195,plain,(
% 32.37/5.95 ! [X6 : subst > term > subst > $o] : ((($true = (sP42 @ X6)) | ! [X12 : subst > term > term] : (? [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) != (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) | ? [X13 : term] : (((X6 @ id @ X13 @ id) = $true) & ($true != (X6 @ id @ (X12 @ id @ X13) @ id))) | ($true = (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id)))) & (? [X12 : subst > term > term] : (! [X14 : subst,X15 : term,X16 : subst] : ((sub @ (X12 @ X16 @ X15) @ X14) = (X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) & ! [X13 : term] : (((X6 @ id @ X13 @ id) != $true) | ($true = (X6 @ id @ (X12 @ id @ X13) @ id))) & ($true != (X6 @ id @ (lam @ (X12 @ sh @ one)) @ id))) | ($true != (sP42 @ X6))))),
% 32.37/5.95 inference(nnf_transformation,[status(thm)],[f56])).
% 32.37/5.95 thf(f6165,plain,(
% 32.37/5.95 ( ! [X9 : subst] : (($true != (sK178 @ (d2subst @ d_id) @ (d2term @ d_one) @ X9))) ) | ~spl591_680),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f6164])).
% 32.37/5.95 thf(f6164,definition,(
% 32.37/5.95 spl591_680 <=> ! [X9 : subst] : ($true != (sK178 @ (d2subst @ d_id) @ (d2term @ d_one) @ X9))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_680])],[avatar_definition])).
% 32.37/5.95 thf(f8060,plain,(
% 32.37/5.95 spl591_682),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f8053,f6181])).
% 32.37/5.95 thf(f8053,plain,(
% 32.37/5.95 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 32.37/5.95 inference(superposition,[status(thm)],[f5725,f5725])).
% 32.37/5.95 thf(f7595,plain,(
% 32.37/5.95 spl591_251 | ~spl591_679),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f7594])).
% 32.37/5.95 thf(f7594,plain,(
% 32.37/5.95 $false | (spl591_251 | ~spl591_679)),
% 32.37/5.95 inference(subsumption_resolution,[status(thm)],[f3359,f6162])).
% 32.37/5.95 thf(f6162,plain,(
% 32.37/5.95 ( ! [X10 : term,X7 : subst] : (($true = (sK178 @ X7 @ X10 @ (d2subst @ d_id)))) ) | ~spl591_679),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f6161])).
% 32.37/5.95 thf(f6161,definition,(
% 32.37/5.95 spl591_679 <=> ! [X7 : subst,X10 : term] : ($true = (sK178 @ X7 @ X10 @ (d2subst @ d_id)))),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_679])],[avatar_definition])).
% 32.37/5.95 thf(f3359,plain,(
% 32.37/5.95 ((sK178 @ (d2subst @ d_id) @ sK177 @ (d2subst @ d_id)) != $true) | spl591_251),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f3357])).
% 32.37/5.95 thf(f3357,definition,(
% 32.37/5.95 spl591_251 <=> ((sK178 @ (d2subst @ d_id) @ sK177 @ (d2subst @ d_id)) = $true)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_251])],[avatar_definition])).
% 32.37/5.95 thf(f6645,plain,(
% 32.37/5.95 ~spl591_106 | ~spl591_574),
% 32.37/5.95 inference(avatar_contradiction_clause,[status(thm)],[f6644])).
% 32.37/5.95 thf(f6644,plain,(
% 32.37/5.95 $false | (~spl591_106 | ~spl591_574)),
% 32.37/5.95 inference(trivial_inequality_removal,[status(thm)],[f6643])).
% 32.37/5.95 thf(f6643,plain,(
% 32.37/5.95 ($true = $false) | (~spl591_106 | ~spl591_574)),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f2728,f5264])).
% 32.37/5.95 thf(f5264,plain,(
% 32.37/5.95 (hoasinduction = $false) | ~spl591_574),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f5262])).
% 32.37/5.95 thf(f5262,definition,(
% 32.37/5.95 spl591_574 <=> (hoasinduction = $false)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_574])],[avatar_definition])).
% 32.37/5.95 thf(f2728,plain,(
% 32.37/5.95 (hoasinduction = $true) | ~spl591_106),
% 32.37/5.95 inference(avatar_component_clause,[status(thm)],[f2727])).
% 32.37/5.95 thf(f2727,definition,(
% 32.37/5.95 spl591_106 <=> (hoasinduction = $true)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_106])],[avatar_definition])).
% 32.37/5.95 thf(f6166,plain,(
% 32.37/5.95 spl591_679 | spl591_69 | spl591_680),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f6159,f6164,f2570,f6161])).
% 32.37/5.95 thf(f2570,definition,(
% 32.37/5.95 spl591_69 <=> ($true = sP44)),
% 32.37/5.95 introduced(definition,[new_symbols(naming,[spl591_69])],[avatar_definition])).
% 32.37/5.95 thf(f6159,plain,(
% 32.37/5.95 ( ! [X10 : term,X9 : subst,X7 : subst] : (($true = sP44) | ($true != (sK178 @ (d2subst @ d_id) @ (d2term @ d_one) @ X9)) | ($true = (sK178 @ X7 @ X10 @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f6158,f4214])).
% 32.37/5.95 thf(f6158,plain,(
% 32.37/5.95 ( ! [X10 : term,X8 : subst,X9 : subst,X7 : subst] : (($true = (sK178 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (sK178 @ (d2subst @ d_id) @ (d2term @ d_one) @ X9)) | ($true = sP44)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f6157,f5725])).
% 32.37/5.95 thf(f6157,plain,(
% 32.37/5.95 ( ! [X10 : term,X8 : subst,X9 : subst,X7 : subst] : (($true != (sK178 @ (d2subst @ d_id) @ (sub @ X10 @ X8) @ X9)) | ($true = (sK178 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true = sP44)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f690,f4214])).
% 32.37/5.95 thf(f690,plain,(
% 32.37/5.95 ( ! [X10 : term,X8 : subst,X9 : subst,X7 : subst] : (($true != (sK178 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9)) | ($true = (sK178 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true = sP44)) )),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f190])).
% 32.37/5.95 thf(f190,plain,(
% 32.37/5.95 (($true = sP44) | (! [X2 : term] : (($true != (var @ (sub @ X2 @ id))) | ((sK178 @ id @ X2 @ id) = $true)) & ! [X3 : subst,X4 : subst,X5 : term,X6 : subst] : (($true = (sK178 @ (comp @ X3 @ X4) @ (sub @ X5 @ X4) @ X6)) | ($true != (sK178 @ X3 @ X5 @ (comp @ X4 @ X6)))) & ($true != (sP43 @ sK178)) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true = (sK178 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (sK178 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) & ($true != (sK178 @ id @ sK177 @ id)) & ($true != (sP42 @ sK178)))) & (! [X11 : term,X12 : subst > term > subst > $o] : ((($true = (var @ (sub @ (sK179 @ X12) @ id))) & ($true != (X12 @ id @ (sK179 @ X12) @ id))) | (((X12 @ (comp @ (sK180 @ X12) @ (sK181 @ X12)) @ (sub @ (sK182 @ X12) @ (sK181 @ X12)) @ (sK183 @ X12)) != $true) & ((X12 @ (sK180 @ X12) @ (sK182 @ X12) @ (comp @ (sK181 @ X12) @ (sK183 @ X12))) = $true)) | ((sP43 @ X12) = $true) | (($true != (X12 @ (sK184 @ X12) @ (sK187 @ X12) @ (comp @ (sK185 @ X12) @ (sK186 @ X12)))) & ($true = (X12 @ (comp @ (sK184 @ X12) @ (sK185 @ X12)) @ (sub @ (sK187 @ X12) @ (sK185 @ X12)) @ (sK186 @ X12)))) | ($true = (X12 @ id @ X11 @ id)) | ($true = (sP42 @ X12))) | ($true != sP44))),
% 32.37/5.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK177,sK178,sK179,sK180,sK181,sK182,sK183,sK184,sK185,sK186,sK187])],[f185,f189,f188,f187,f186])).
% 32.37/5.95 thf(f186,plain,(
% 32.37/5.95 ? [X0 : term,X1 : subst > term > subst > $o] : (! [X2 : term] : (($true != (var @ (sub @ X2 @ id))) | ($true = (X1 @ id @ X2 @ id))) & ! [X3 : subst,X4 : subst,X5 : term,X6 : subst] : (($true = (X1 @ (comp @ X3 @ X4) @ (sub @ X5 @ X4) @ X6)) | ($true != (X1 @ X3 @ X5 @ (comp @ X4 @ X6)))) & ($true != (sP43 @ X1)) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true = (X1 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (X1 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) & ($true != (X1 @ id @ X0 @ id)) & ($true != (sP42 @ X1))) => (! [X2 : term] : (($true != (var @ (sub @ X2 @ id))) | ((sK178 @ id @ X2 @ id) = $true)) & ! [X6 : subst,X5 : term,X4 : subst,X3 : subst] : (($true = (sK178 @ (comp @ X3 @ X4) @ (sub @ X5 @ X4) @ X6)) | ($true != (sK178 @ X3 @ X5 @ (comp @ X4 @ X6)))) & ($true != (sP43 @ sK178)) & ! [X10 : term,X9 : subst,X8 : subst,X7 : subst] : (($true = (sK178 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (sK178 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) & ($true != (sK178 @ id @ sK177 @ id)) & ($true != (sP42 @ sK178)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f187,plain,(
% 32.37/5.95 ! [X12 : subst > term > subst > $o] : (? [X13 : term] : (((var @ (sub @ X13 @ id)) = $true) & ($true != (X12 @ id @ X13 @ id))) => (($true = (var @ (sub @ (sK179 @ X12) @ id))) & ($true != (X12 @ id @ (sK179 @ X12) @ id))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f188,plain,(
% 32.37/5.95 ! [X12 : subst > term > subst > $o] : (? [X14 : subst,X15 : subst,X16 : term,X17 : subst] : (($true != (X12 @ (comp @ X14 @ X15) @ (sub @ X16 @ X15) @ X17)) & ($true = (X12 @ X14 @ X16 @ (comp @ X15 @ X17)))) => (((X12 @ (comp @ (sK180 @ X12) @ (sK181 @ X12)) @ (sub @ (sK182 @ X12) @ (sK181 @ X12)) @ (sK183 @ X12)) != $true) & ((X12 @ (sK180 @ X12) @ (sK182 @ X12) @ (comp @ (sK181 @ X12) @ (sK183 @ X12))) = $true)))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f189,plain,(
% 32.37/5.95 ! [X12 : subst > term > subst > $o] : (? [X18 : subst,X19 : subst,X20 : subst,X21 : term] : (($true != (X12 @ X18 @ X21 @ (comp @ X19 @ X20))) & ($true = (X12 @ (comp @ X18 @ X19) @ (sub @ X21 @ X19) @ X20))) => (($true != (X12 @ (sK184 @ X12) @ (sK187 @ X12) @ (comp @ (sK185 @ X12) @ (sK186 @ X12)))) & ($true = (X12 @ (comp @ (sK184 @ X12) @ (sK185 @ X12)) @ (sub @ (sK187 @ X12) @ (sK185 @ X12)) @ (sK186 @ X12)))))),
% 32.37/5.95 introduced(definition,[],[choice_axiom])).
% 32.37/5.95 thf(f185,plain,(
% 32.37/5.95 (($true = sP44) | ? [X0 : term,X1 : subst > term > subst > $o] : (! [X2 : term] : (($true != (var @ (sub @ X2 @ id))) | ($true = (X1 @ id @ X2 @ id))) & ! [X3 : subst,X4 : subst,X5 : term,X6 : subst] : (($true = (X1 @ (comp @ X3 @ X4) @ (sub @ X5 @ X4) @ X6)) | ($true != (X1 @ X3 @ X5 @ (comp @ X4 @ X6)))) & ($true != (sP43 @ X1)) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true = (X1 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (X1 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) & ($true != (X1 @ id @ X0 @ id)) & ($true != (sP42 @ X1)))) & (! [X11 : term,X12 : subst > term > subst > $o] : (? [X13 : term] : (((var @ (sub @ X13 @ id)) = $true) & ($true != (X12 @ id @ X13 @ id))) | ? [X14 : subst,X15 : subst,X16 : term,X17 : subst] : (($true != (X12 @ (comp @ X14 @ X15) @ (sub @ X16 @ X15) @ X17)) & ($true = (X12 @ X14 @ X16 @ (comp @ X15 @ X17)))) | ((sP43 @ X12) = $true) | ? [X18 : subst,X19 : subst,X20 : subst,X21 : term] : (($true != (X12 @ X18 @ X21 @ (comp @ X19 @ X20))) & ($true = (X12 @ (comp @ X18 @ X19) @ (sub @ X21 @ X19) @ X20))) | ($true = (X12 @ id @ X11 @ id)) | ($true = (sP42 @ X12))) | ($true != sP44))),
% 32.37/5.95 inference(rectify,[status(thm)],[f184])).
% 32.37/5.95 thf(f184,plain,(
% 32.37/5.95 (($true = sP44) | ? [X5 : term,X6 : subst > term > subst > $o] : (! [X11 : term] : (($true != (var @ (sub @ X11 @ id))) | ($true = (X6 @ id @ X11 @ id))) & ! [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true = (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) | ($true != (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) & ($true != (sP43 @ X6)) & ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true = (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) | ($true != (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) & ($true != (X6 @ id @ X5 @ id)) & ($true != (sP42 @ X6)))) & (! [X5 : term,X6 : subst > term > subst > $o] : (? [X11 : term] : (($true = (var @ (sub @ X11 @ id))) & ($true != (X6 @ id @ X11 @ id))) | ? [X17 : subst,X18 : subst,X19 : term,X20 : subst] : (($true != (X6 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X20)) & ($true = (X6 @ X17 @ X19 @ (comp @ X18 @ X20)))) | ($true = (sP43 @ X6)) | ? [X7 : subst,X8 : subst,X9 : subst,X10 : term] : (($true != (X6 @ X7 @ X10 @ (comp @ X8 @ X9))) & ($true = (X6 @ (comp @ X7 @ X8) @ (sub @ X10 @ X8) @ X9))) | ($true = (X6 @ id @ X5 @ id)) | ($true = (sP42 @ X6))) | ($true != sP44))),
% 32.37/5.95 inference(nnf_transformation,[status(thm)],[f58])).
% 32.37/5.95 thf(f5999,plain,(
% 32.37/5.95 ~spl591_69 | spl591_106),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f1154,f2727,f2570])).
% 32.37/5.95 thf(f1154,plain,(
% 32.37/5.95 ($true != sP44) | (hoasinduction = $true)),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f5980,plain,(
% 32.37/5.95 spl591_69 | ~spl591_661),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f688,f5977,f2570])).
% 32.37/5.95 thf(f688,plain,(
% 32.37/5.95 ($true != (sP42 @ sK178)) | ($true = sP44)),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f190])).
% 32.37/5.95 thf(f5297,plain,(
% 32.37/5.95 spl591_574 | spl591_580),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f5293,f5295,f5262])).
% 32.37/5.95 thf(f5293,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (((sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X4) @ X3) = $false) | ((sK592 @ X2 @ X1 @ (d2subst @ d_id)) = $true) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5292,f4214])).
% 32.37/5.95 thf(f5292,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (((sK592 @ X2 @ X1 @ (comp @ X4 @ X3)) = $true) | (hoasinduction = $false) | ((sK592 @ (d2subst @ d_id) @ (sub @ X1 @ X4) @ X3) = $false)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f1723,f4214])).
% 32.37/5.95 thf(f1723,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (((sK592 @ (comp @ X2 @ X4) @ (sub @ X1 @ X4) @ X3) = $false) | (hoasinduction = $false) | ((sK592 @ X2 @ X1 @ (comp @ X4 @ X3)) = $true)) )),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1722])).
% 32.37/5.95 thf(f1722,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : (($true = ((sK592 @ (comp @ X2 @ X4) @ (sub @ X1 @ X4) @ X3) => (sK592 @ X2 @ X1 @ (comp @ X4 @ X3)))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1721])).
% 32.37/5.95 thf(f1721,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term,X4 : subst] : ((hoasinduction = $false) | ($true = ((^[Y0 : subst]: ((sK592 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0) @ X3) => (sK592 @ X2 @ X1 @ (comp @ Y0 @ X3)))) @ X4))) )),
% 32.37/5.95 inference(pi_clausification,[status(thm)],[f1720])).
% 32.37/5.95 thf(f1720,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: ((sK592 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0) @ X3) => (sK592 @ X2 @ X1 @ (comp @ Y0 @ X3)))))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1719])).
% 32.37/5.95 thf(f1719,plain,(
% 32.37/5.95 ( ! [X2 : subst,X3 : subst,X1 : term] : (($true = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sK592 @ (comp @ X2 @ Y1) @ (sub @ X1 @ Y1) @ Y0) => (sK592 @ X2 @ X1 @ (comp @ Y1 @ Y0)))))) @ X3)) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(pi_clausification,[status(thm)],[f1718])).
% 32.37/5.95 thf(f1718,plain,(
% 32.37/5.95 ( ! [X2 : subst,X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sK592 @ (comp @ X2 @ Y1) @ (sub @ X1 @ Y1) @ Y0) => (sK592 @ X2 @ X1 @ (comp @ Y1 @ Y0)))))))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1717])).
% 32.37/5.95 thf(f1717,plain,(
% 32.37/5.95 ( ! [X2 : subst,X1 : term] : ((hoasinduction = $false) | ($true = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sK592 @ (comp @ Y0 @ Y2) @ (sub @ X1 @ Y2) @ Y1) => (sK592 @ Y0 @ X1 @ (comp @ Y2 @ Y1)))))))) @ X2))) )),
% 32.37/5.95 inference(pi_clausification,[status(thm)],[f1716])).
% 32.37/5.95 thf(f1716,plain,(
% 32.37/5.95 ( ! [X1 : term] : ((hoasinduction = $false) | ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sK592 @ (comp @ Y0 @ Y2) @ (sub @ X1 @ Y2) @ Y1) => (sK592 @ Y0 @ X1 @ (comp @ Y2 @ Y1))))))))))) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1715])).
% 32.37/5.95 thf(f1715,plain,(
% 32.37/5.95 ( ! [X1 : term] : ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y1 @ Y3) @ (sub @ Y0 @ Y3) @ Y2) => (sK592 @ Y1 @ Y0 @ (comp @ Y3 @ Y2)))))))))) @ X1) = $true) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(pi_clausification,[status(thm)],[f1714])).
% 32.37/5.95 thf(f1714,plain,(
% 32.37/5.95 (hoasinduction = $false) | ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y1 @ Y3) @ (sub @ Y0 @ Y3) @ Y2) => (sK592 @ Y1 @ Y0 @ (comp @ Y3 @ Y2))))))))))) = $true)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1702])).
% 32.37/5.95 thf(f1702,plain,(
% 32.37/5.95 (hoasinduction = $false) | ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y1 @ Y3) @ (sub @ Y0 @ Y3) @ Y2) => (sK592 @ Y1 @ Y0 @ (comp @ Y3 @ Y2))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))))))))),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1701])).
% 32.37/5.95 thf(f1701,plain,(
% 32.37/5.95 (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ Y2 @ Y0 @ (comp @ Y1 @ Y3)) => (sK592 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1) @ Y3)))))))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y1 @ Y3) @ (sub @ Y0 @ Y3) @ Y2) => (sK592 @ Y1 @ Y0 @ (comp @ Y3 @ Y2))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))))))) = $false) | (hoasinduction = $false)),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1700])).
% 32.37/5.95 thf(f1700,plain,(
% 32.37/5.95 ($false = ((^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)))))))))) @ sK592)) | (hoasinduction = $false)),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1699])).
% 32.37/5.95 thf(f1699,plain,(
% 32.37/5.95 (hoasinduction = $false) | ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))))))))) = $false)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1697])).
% 32.37/5.95 thf(f1697,plain,(
% 32.37/5.95 (hoasinduction != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))))))))))),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1664])).
% 32.37/5.95 thf(f1664,plain,(
% 32.37/5.95 (hoasinduction != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ (d2subst @ d_id) @ Y2 @ (d2subst @ d_id)) => (Y0 @ (d2subst @ d_id) @ (Y1 @ (d2subst @ d_id) @ Y2) @ (d2subst @ d_id))))) => (Y0 @ (d2subst @ d_id) @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ (d2subst @ d_id) @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id))))))))))))),
% 32.37/5.95 inference(definition_unfolding,[status(thm)],[f1260,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1208,f1219,f1208,f1208,f1208,f1208])).
% 32.37/5.95 thf(f1219,plain,(
% 32.37/5.95 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f545])).
% 32.37/5.95 thf(f1260,plain,(
% 32.37/5.95 (hoasinduction != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y1 @ id) => ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (hoasap @ id @ Y1 @ id @ Y2) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ 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]: (Y0 @ id @ Y1 @ id)))))))))))),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f9])).
% 32.37/5.95 thf(f9,plain,(
% 32.37/5.95 (hoasinduction != (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y1 @ id) => ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (hoasap @ id @ Y1 @ id @ Y2) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ 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]: (Y0 @ id @ Y1 @ id)))))))))))),
% 32.37/5.95 inference(flattening,[status(thm)],[f8])).
% 32.37/5.95 thf(f8,plain,(
% 32.37/5.95 ~(hoasinduction = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y3 @ Y1 @ (comp @ Y2 @ Y4)) => (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y4) @ (sub @ Y1 @ Y4) @ Y3) => (Y0 @ Y2 @ Y1 @ (comp @ Y4 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y1 @ id) => ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (hoasap @ id @ Y1 @ id @ Y2) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ 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]: (Y0 @ id @ Y1 @ id)))))))))))),
% 32.37/5.95 inference(fool_elimination,[status(thm)],[f7])).
% 32.37/5.95 thf(f7,plain,(
% 32.37/5.95 ~(hoasinduction = ! [X0 : subst > term > subst > $o] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X2 @ X4 @ (comp @ X3 @ X1)) => (X0 @ (comp @ X2 @ X3) @ (sub @ X4 @ X3) @ X1)) => (! [X5 : subst,X6 : subst,X7 : subst,X8 : term] : ((X0 @ (comp @ X7 @ X5) @ (sub @ X8 @ X5) @ X6) => (X0 @ X7 @ X8 @ (comp @ X5 @ X6))) => (! [X9 : term] : ((hoasvar @ id @ X9 @ id) => (X0 @ id @ X9 @ id)) => (! [X10 : term,X11 : term] : ((X0 @ id @ X11 @ id) => ((X0 @ id @ X10 @ id) => (X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id))) => (! [X12 : subst > term > term] : (! [X13 : term,X14 : subst,X15 : subst] : ((sub @ (X12 @ X15 @ X13) @ X14) = (X12 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14))) => (! [X16 : term] : ((X0 @ id @ X16 @ id) => (X0 @ id @ (X12 @ id @ X16) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X17 : subst, X18 : term] : (X12 @ X17 @ X18))) @ id))) => ! [X19 : term] : (X0 @ id @ X19 @ id)))))))),
% 32.37/5.95 inference(rectify,[status(thm)],[f3])).
% 32.37/5.95 thf(f3,negated_conjecture,(
% 32.37/5.95 ~(hoasinduction = ! [X10 : subst > term > subst > $o] : (! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) => (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) => (! [X13 : term] : ((hoasvar @ id @ X13 @ id) => (X10 @ id @ X13 @ id)) => (! [X15 : term,X13 : term] : ((X10 @ id @ X13 @ id) => ((X10 @ id @ X15 @ id) => (X10 @ id @ (hoasap @ id @ X13 @ id @ 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 @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ! [X13 : term] : (X10 @ id @ X13 @ id)))))))),
% 32.37/5.95 inference(negated_conjecture,[status(cth)],[f2])).
% 32.37/5.95 thf(f2,conjecture,(
% 32.37/5.95 (hoasinduction = ! [X10 : subst > term > subst > $o] : (! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) => (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) => (! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) => (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) => (! [X13 : term] : ((hoasvar @ id @ X13 @ id) => (X10 @ id @ X13 @ id)) => (! [X15 : term,X13 : term] : ((X10 @ id @ X13 @ id) => ((X10 @ id @ X15 @ id) => (X10 @ id @ (hoasap @ id @ X13 @ id @ X15) @ id))) => (! [X18 : subst > term > term] : (! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ! [X13 : term] : (X10 @ id @ X13 @ id)))))))),
% 32.37/5.95 file('/export/starexec/sandbox2/tmp/tmp.CDduru1qPi/DTF2THF_30868.p',hoasinduction)).
% 32.37/5.95 thf(f5283,plain,(
% 32.37/5.95 spl591_576 | spl591_577 | spl591_574),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f5279,f5262,f5281,f5273])).
% 32.37/5.95 thf(f5279,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id))) | ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1) @ (d2subst @ d_id))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1)) @ (d2subst @ d_id))) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5278,f4214])).
% 32.37/5.95 thf(f5278,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id))) | ((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1)) @ (d2subst @ d_id)) != (X1 @ (comp @ (d2subst @ d_id) @ (d2subst @ d_id)) @ (sub @ (sK595 @ X1) @ (d2subst @ d_id)))) | (hoasinduction = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f5277,f4214])).
% 32.37/5.95 thf(f5277,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((hoasinduction = $false) | ((X1 @ (comp @ (d2subst @ d_id) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) != (sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1)) @ (sK594 @ X1))) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(forward_demodulation,[status(thm)],[f1753,f4214])).
% 32.37/5.95 thf(f1753,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (((X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) != (sub @ (X1 @ (sK593 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1))) | (hoasinduction = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($true = (sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1751])).
% 32.37/5.95 thf(f1751,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction = $false) | ((X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) != (sub @ (X1 @ (sK593 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1))) | ($false = ((sK592 @ (d2subst @ d_id) @ (sK596 @ X1) @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ (sK596 @ X1)) @ (d2subst @ d_id))))) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1750])).
% 32.37/5.95 thf(f1750,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((((^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id)))) @ (sK596 @ X1)) = $false) | ((X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) != (sub @ (X1 @ (sK593 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1))) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1749])).
% 32.37/5.95 thf(f1749,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((hoasinduction = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) != (sub @ (X1 @ (sK593 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1))) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 32.37/5.95 inference(equality_proxy_clausification,[status(thm)],[f1748])).
% 32.37/5.95 thf(f1748,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction = $false) | ($false = ((sub @ (X1 @ (sK593 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1)) = (X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))))) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1747])).
% 32.37/5.95 thf(f1747,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ($false = ((^[Y0 : term]: ((sub @ (X1 @ (sK593 @ X1) @ Y0) @ (sK594 @ X1)) = (X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ Y0 @ (sK594 @ X1))))) @ (sK595 @ X1))) | (hoasinduction = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1746])).
% 32.37/5.95 thf(f1746,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((!! @ term @ (^[Y0 : term]: ((sub @ (X1 @ (sK593 @ X1) @ Y0) @ (sK594 @ X1)) = (X1 @ (comp @ (sK593 @ X1) @ (sK594 @ X1)) @ (sub @ Y0 @ (sK594 @ X1)))))) = $false) | (hoasinduction = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1745])).
% 32.37/5.95 thf(f1745,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ (X1 @ (sK593 @ X1) @ Y1) @ Y0) = (X1 @ (comp @ (sK593 @ X1) @ Y0) @ (sub @ Y1 @ Y0)))))) @ (sK594 @ X1))) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1744])).
% 32.37/5.95 thf(f1744,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ (X1 @ (sK593 @ X1) @ Y1) @ Y0) = (X1 @ (comp @ (sK593 @ X1) @ Y0) @ (sub @ Y1 @ Y0))))))) = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | (hoasinduction = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1743])).
% 32.37/5.95 thf(f1743,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : (($false = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)))))))) @ (sK593 @ X1))) | (hoasinduction = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) )),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1742])).
% 32.37/5.95 thf(f1742,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((hoasinduction = $false) | ($true = (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))))))))) = $false) | ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) = $false)) )),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1741])).
% 32.37/5.95 thf(f1741,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) | (hoasinduction = $false) | ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))))))))) = $false)) )),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1740])).
% 32.37/5.95 thf(f1740,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((hoasinduction = $false) | ($true = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (X1 @ (d2subst @ d_id) @ Y0) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) )),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1739])).
% 32.37/5.95 thf(f1739,plain,(
% 32.37/5.95 ( ! [X1 : subst > term > term] : ((((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))) @ X1) = $true) | (hoasinduction = $false)) )),
% 32.37/5.95 inference(pi_clausification,[status(thm)],[f1738])).
% 32.37/5.95 thf(f1738,plain,(
% 32.37/5.95 (hoasinduction = $false) | ($true = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))))),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1729])).
% 32.37/5.95 thf(f1729,plain,(
% 32.37/5.95 (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) = $false) | (hoasinduction = $false)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1724])).
% 32.37/5.95 thf(f1724,plain,(
% 32.37/5.95 (hoasinduction = $false) | (((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))))) = $false)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1713])).
% 32.37/5.95 thf(f1713,plain,(
% 32.37/5.95 (hoasinduction = $false) | (((!! @ term @ (^[Y0 : term]: ((hoasvar @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)) => ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (hoasap @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id)))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ (d2subst @ d_id) @ Y1 @ (d2subst @ d_id)) => (sK592 @ (d2subst @ d_id) @ (Y0 @ (d2subst @ d_id) @ Y1) @ (d2subst @ d_id))))) => (sK592 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))))) => (!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))))))) = $false)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1702])).
% 32.37/5.95 thf(f5265,plain,(
% 32.37/5.95 spl591_573 | spl591_574),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f1755,f5262,f5258])).
% 32.37/5.95 thf(f1755,plain,(
% 32.37/5.95 ((sK592 @ (d2subst @ d_id) @ sK597 @ (d2subst @ d_id)) = $false) | (hoasinduction = $false)),
% 32.37/5.95 inference(beta_eta_normalization,[status(thm)],[f1754])).
% 32.37/5.95 thf(f1754,plain,(
% 32.37/5.95 (((^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id))) @ sK597) = $false) | (hoasinduction = $false)),
% 32.37/5.95 inference(sigma_clausification,[status(thm)],[f1737])).
% 32.37/5.95 thf(f1737,plain,(
% 32.37/5.95 ((!! @ term @ (^[Y0 : term]: (sK592 @ (d2subst @ d_id) @ Y0 @ (d2subst @ d_id)))) = $false) | (hoasinduction = $false)),
% 32.37/5.95 inference(binary_proxy_clausification,[status(thm)],[f1729])).
% 32.37/5.95 thf(f3360,plain,(
% 32.37/5.95 ~spl591_251 | spl591_69),
% 32.37/5.95 inference(avatar_split_clause,[status(thm)],[f1375,f2570,f3357])).
% 32.37/5.95 thf(f1375,plain,(
% 32.37/5.95 ($true = sP44) | ((sK178 @ (d2subst @ d_id) @ sK177 @ (d2subst @ d_id)) != $true)),
% 32.37/5.95 inference(definition_unfolding,[status(thm)],[f689,f1208,f1208])).
% 32.37/5.95 thf(f689,plain,(
% 32.37/5.95 ($true = sP44) | ($true != (sK178 @ id @ sK177 @ id))),
% 32.37/5.95 inference(cnf_transformation,[status(thm)],[f190])).
% 32.37/5.95 % SZS output end Proof for DTF2THF_30868
% 32.37/5.95 % (31429)------------------------------
% 32.37/5.95 % (31429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.37/5.95 % (31429)Termination reason: Refutation
% 32.37/5.95
% 32.37/5.95 % (31429)Memory used [KB]: 15991
% 32.37/5.95 % (31429)Time elapsed: 1.0000 s
% 32.37/5.95 % (31429)Instructions burned: 3093 (million)
% 32.37/5.95 % (31429)------------------------------
% 32.37/5.95 % (31429)------------------------------
% 32.37/5.95 % (31217)Success in time 4.446 s
%------------------------------------------------------------------------------